SFPE Handbook of Fire Protection Engineering 5th Edition
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Morgan J. Hurley Editor-in-Chief
SFPE Handbook of Fire Protection Engineering Fifth Edition
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SFPE Handbook of Fire Protection Engineering
Morgan J. Hurley Editor-in-Chief
SFPE Handbook of Fire Protection Engineering Fifth Edition
Editor-in-Chief Morgan J. Hurley, P.E., FSFPE Aon Fire Protection Engineering Greenbelt, MD, USA
Editors Daniel Gottuk, Ph.D., P.E. Hughes Associates John R. Hall Jr., Ph.D. National Fire Protection Association Kazunori Harada, Dr. Eng. Kyoto University Erica Kuligowski, Ph.D. National Institute of Standards and Technology Milosh Puchovsky, P.E., FSFPE Worcester Polytechnic Institute Jose´ Torero, Ph.D. The University of Queensland John M. Watts Jr., Ph.D., FSFPE The Fire Safety Institute Christopher Wieczorek, Ph.D. FM Global
ISBN 978-1-4939-2564-3 ISBN 978-1-4939-2565-0 (eBook) DOI 10.1007/978-1-4939-2565-0 Library of Congress Control Number: 2015953225 Springer New York Heidelberg Dordrecht London # Society of Fire Protection Engineers 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer Science+Business Media LLC New York is part of Springer Science+Business Media (www.springer.com)
This edition of the SFPE Handbook of Fire Protection Engineering is dedicated to Philip DiNenno, who was the editor in chief for the first four editions of this handbook. In the mid-1980s, Phil DiNenno, Jack Watts, Doug Walton, Craig Beyler, and Dick Custer had an idea to create a collection of calculation methods for fire protection engineering. From this idea emerged the SFPE Handbook of Fire Protection Engineering, which was first published in 1988. No other single event had as significant an impact on establishing the profession of fire protection engineering as the publication of this handbook. As Vyto Babrauskas said: “The field [of fire protection engineering] has made very gratifying progress in these last four decades. . .. The most remarkable positive achievement I think has been the SFPE Handbook, published first in 1988. . . . [W]ith the publication of the first edition of the SFPE Handbook in 1988, all of a sudden we could properly describe this as a science-based profession.” [Babrauskas, V. “Some Neglected Areas in Fire Safety Engineering,” Fire Science and Technology Vol. 32 No. 1 (2013) pp. 35–48.] When they began creating the first edition, Phil and his colleagues had no model other than handbooks used in other professions. Phil contributed the leadership, vision, and motivation necessary to develop the handbook, and he did so using entirely volunteer resources. This would be an incredible accomplishment for anyone. Phil did it before he turned 35.
Foreword
This edition marks a passing of the torch for the SFPE Handbook of Fire Protection Engineering. All of the editors of the prior editions except for two (Jack Watts and John Hall) have retired, and a new editorial team has taken their place. Additionally, Springer has assumed the role of publisher beginning with this edition. For the first four editions, the SFPE Handbook of Fire Protection Engineering was published by the National Fire Protection Association. The Society of Fire Protection Engineers owes a debt of gratitude to NFPA. Without their encouragement and confidence, this handbook might never have existed. With a new editorial team emerge many changes. The chapters relevant to human behavior in fire have been significantly refocused and augmented. The fundamental engineering chapters have been revised to provide a better foundation for the chapters that follow. Many new chapters related to fire protection system selection and design have been added. The chapters associated with fire resistance design have been modified to reflect advances over the last decade. And, this edition includes several new chapters pertinent to industrial fire protection. The editors owe a debt of gratitude to those whom they follow. Continuing a successful endeavor is much easier than launching it.
Acknowledgment of Past Authors
Name Ahrens, Martha J. Alpert, Ronald L. Atreya, Arvind Babrauskas, Vytenis Back III, Gerard G. Barry, Thomas F. Beck, Vaughan R. Beever, Paula F. Beller, Douglas K. Berlin, Geoffrey N.
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(continued) Name Kandola, B. S. Kanury, A. Murty Kersken-Bradley, Marita Klote, John H. Kodur, V. K. R. Kuligowski, Erica Kumar, Suresh Lattimer, Brian Y. Lee, K. Y. Lie, T. T. MacLennan, Hamish A. Mawhinney, Jack R. McCaffrey, Bernard McGrattan, Kevin Meacham, Brian J. Mehaffey, Jim Miles, Stewart Milke, James A. Modarres, Mohammad Morgan, Alexander Mowrer, Frederick W. Mudan, Krishna S. Mulholland, George W. Nelson, Harold E. Notarianni, Kathy A. Nowlen, Steven Ohlemiller, T. J. Parry, Gareth Pauls, Jake Phillips, William G. B. Proulx, Guyle`ne Purser, David A. Quintiere, James G. Ramachandran, G. Roby, R. J. Rockett, John A. Rosenbaum, Eric Salisbury, Matthew Scheffey, Joseph L. Schifiliti, Robert P. Simmons, Robert F. Siu, Nathan Stretton, A. J. Stroup, David W. Tanaka, Takeyoshi Tewarson, Archibald Thomas, Ian Thomas, Philip H.
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(continued) Name Tien, C. L. Titus, John J. Torero, Jose´ Walton, William D. Watts, Jr., John M. White, Derek A. White, Robert H. Wickstro¨m, Ulf Wolski, Armin Wood, Christopher Yung, David Zalosh, Robert G.
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Metrication
The editors of the SFPE Handbook of Fire Protection Engineering have worked toward the expanded use of SI units for this fifth edition. In some instances, however, US customary units have been retained. For example, when equations, correlations, or design methodologies have input variables or constants that have been developed from data originally in US customary units, those units are retained. This is also the case for certain tables, charts, and nomographs. Where equations employing US customary units are used in worked examples, the results are presented as SI units as well.
xi
Contents
Volume I 1
Introduction to Fluid Mechanics . . . . . . . . . . . . . . . . . . . . Bart Merci
1
2
Conduction of Heat in Solids . . . . . . . . . . . . . . . . . . . . . . . Ofodike A. Ezekoye
25
3
Convection Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . Arvind Atreya
53
4
Radiation Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . Revised by C. Lautenberger, Original chapter authored by C.L. Tien, K.Y. Lee, and A.J. Stretton
102
5
Thermochemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D.D. Drysdale
138
6
Chemical Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . Raymond Friedman
151
7
Thermal Decomposition of Polymeric Materials . . . . . . . . Artur Witkowski, Anna A. Stec, and T. Richard Hull
167
8
Structural Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . Luke A. Bisby
255
9
Properties of Building Materials . . . . . . . . . . . . . . . . . . . . V.K.R. Kodur and T.Z. Harmathy
277
10
Chemical Kinetics and Fire . . . . . . . . . . . . . . . . . . . . . . . . Gregory T. Linteris and John F. Griffiths
325
11
Diffusion Flames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ali S. Rangwala
350
12
Fundamentals of Premixed Flames . . . . . . . . . . . . . . . . . . Grunde Jomaas
373
13
Fire Plumes, Flame Height, and Air Entrainment . . . . . . . Gunnar Heskestad
396
xiii
xiv
Contents
14
Ceiling Jet Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ronald L. Alpert
429
15
Vent Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Takeyoshi Tanaka
455
16
Effect of Combustion Conditions on Species Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Daniel T. Gottuk and Brian Y. Lattimer
486
Flammability Limits of Premixed and Diffusion Flames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Craig Beyler
529
17
18
Ignition of Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D.D. Drysdale
554
19
Smoldering Combustion . . . . . . . . . . . . . . . . . . . . . . . . . . Guillermo Rein
581
20
Spontaneous Combustion and Self-Heating . . . . . . . . . . . . Brian F. Gray
604
21
Flaming Ignition of Solid Fuels . . . . . . . . . . . . . . . . . . . . . Jose´ Torero
633
22
Electrical Fires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vytenis Babrauskas
662
23
Surface Flame Spread . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yuji Hasemi
705
24
Smoke Characterization and Damage Potentials . . . . . . . . Jeffrey S. Newman, Geary G. Yee, and Paul Su
724
25
Heat Transfer from Fires to Surfaces . . . . . . . . . . . . . . . . Brian Y. Lattimer
745
26
Heat Release Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vytenis Babrauskas
799
27
Calorimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Marc Janssens
905
28
The Cone Calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vytenis Babrauskas
952
29
Compartment Fire Modeling . . . . . . . . . . . . . . . . . . . . . . . James G. Quintiere and Colleen A. Wade
981
30
Estimating Temperatures in Compartment Fires . . . . . . . William D. Walton, Philip H. Thomas, and Yoshifumi Ohmiya
996
31
Zone Computer Fire Models for Enclosures . . . . . . . . . . . William D. Walton, Douglas J. Carpenter, and Christopher B. Wood
1024
Contents
xv
32
33
34
Modeling Fires Using Computational Fluid Dynamics (CFD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kevin McGrattan and Stewart Miles
1034
Enclosure Smoke Filling and Fire-Generated Environmental Conditions . . . . . . . . . . . . . . . . . . . . . . . . . Frederick W. Mowrer
1066
Methods for Predicting Temperatures in Fire-Exposed Structures . . . . . . . . . . . . . . . . . . . . . . . . Ulf Wickstro¨m
1102
35
Fire Load Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mario Fontana, Jochen Kohler, Katharina Fischer, and Gianluca De Sanctis
36
Combustion Characteristics of Materials and Generation of Fire Products . . . . . . . . . . . . . . . . . . . . Mohammed M. Khan, Archibald Tewarson, and Marcos Chaos
1131
1143
Volume II 37
Performance-Based Design . . . . . . . . . . . . . . . . . . . . . . . . Morgan J. Hurley and Eric R. Rosenbaum
1233
38
Fire Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . George V. Hadjisophocleous and Jim R. Mehaffey
1262
39
Engineering Considerations for Fire Protection System Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Milosh Puchovsky and Craig Hofmeister
1289
40
Design of Detection Systems . . . . . . . . . . . . . . . . . . . . . . . Robert P. Schifiliti, Richard L.P. Custer, and Brian J. Meacham
1314
41
Hydraulics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kenneth E. Isman
1378
42
Automatic Sprinkler System Calculations . . . . . . . . . . . . . Russell P. Fleming
1423
43
Halon Design Calculations . . . . . . . . . . . . . . . . . . . . . . . . . Casey C. Grant
1450
44
Clean Agent Total Flooding Fire Extinguishing Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . Philip J. DiNenno and Eric W. Forssell
1483
45
Carbon Dioxide Systems . . . . . . . . . . . . . . . . . . . . . . . . . . Jeff Harrington and Joseph A. Senecal
1531
46
Water Mist Fire Suppression Systems . . . . . . . . . . . . . . . . Jack R. Mawhinney and Gerard G. Back III
1587
xvi
47
Contents
Foam Agents and AFFF System Design Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Joseph L. Scheffey
48
Foam System Calculations . . . . . . . . . . . . . . . . . . . . . . . . . Hamid R. Bahadori
49
Considerations for Coordinating and Interfacing Fire Protection and Life Safety Systems . . . . . . . . . . . . . . David Jacoby, David LeBlanc, Jeffrey Tubbs, and Andrew Woodward
1646 1707
1740
50
Smoke Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . John H. Klote
51
Smoke Control by Mechanical Exhaust or Natural Venting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . James A. Milke
1824
Structural Fire Engineering of Building Assemblies and Frames . . . . . . . . . . . . . . . . . . . . . . . . . . . Jean-Marc Franssen and Nestor Iwankiw
1863
Analytical Methods for Determining Fire Resistance of Steel Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . James A. Milke
1909
Analytical Methods for Determining Fire Resistance of Concrete Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . Charles Fleischmann, Andy Buchanan, and Anthony Abu
1949
Analytical Methods for Determining Fire Resistance of Timber Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Robert H. White
1979
52
53
54
55
56
Egress Concepts and Design Approaches . . . . . . . . . . . . . . Richard W. Bukowski and Jeffrey S. Tubbs
57
Selecting Scenarios for Deterministic Fire Safety Engineering Analysis: Life Safety for Occupants . . . . . . . Daniel Nilsson and Rita Fahy
58
Human Behavior in Fire . . . . . . . . . . . . . . . . . . . . . . . . . . Erica D. Kuligowski
59
Employing the Hydraulic Model in Assessing Emergency Movement . . . . . . . . . . . . . . . . . . . . . . . . . . . . Steven M.V. Gwynne and Eric R. Rosenbaum
1785
2012
2047 2070
2115
60
Computer Evacuation Models for Buildings . . . . . . . . . . . Erica D. Kuligowski
2152
61
Visibility and Human Behavior in Fire Smoke . . . . . . . . . Tokiyoshi Yamada and Yuki Akizuki
2181
Contents
xvii
62
Combustion Toxicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . David A. Purser
2207
Volume III 63
Assessment of Hazards to Occupants from Smoke, Toxic Gases, and Heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . David A. Purser and Jamie L. McAllister
2308
64
Engineering Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S.M.V. Gwynne and K.E. Boyce
2429
65
Liquid Fuel Fires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D.T. Gottuk and D.A. White
2552
66
Fire Hazard Calculations for Large, Open Hydrocarbon Fires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Craig L. Beyler
67
Vapor Clouds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nicolas F. Ponchaut, Francesco Colella, and Kevin C. Marr
68
Effects of Thermal Radiation on People: Predicting 1st and 2nd Degree Skin Burns . . . . . . . . . . . . Christopher J. Wieczorek and Nicholas A. Dembsey
2591 2664
2705
69
Flammable Gas and Vapor Explosions . . . . . . . . . . . . . . . Robert Zalosh
2738
70
Dust Explosions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Robert Zalosh
2766
71
BLEVES and Fireballs . . . . . . . . . . . . . . . . . . . . . . . . . . . Alfonso Ibarreta, Hubert Biteau, and Jason Sutula
2792
72
Introduction to Fire Risk Analysis . . . . . . . . . . . . . . . . . . . John M. Watts Jr. and John R. Hall Jr.
2817
73
Probability and Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . John R. Hall Jr. and Francisco Joglar
2827
74
Reliability, Availability, and Maintainability . . . . . . . . . . . Francisco Joglar
2875
75
Building Fire Risk Analysis . . . . . . . . . . . . . . . . . . . . . . . . Brian J. Meacham, David Charters, Peter Johnson, and Matthew Salisbury
2941
76
Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kathy A. Notarianni and Gareth W. Parry
2992
77
Decision Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H.A. Donegan
3048
xviii
Contents
78
Data for Engineering Analysis . . . . . . . . . . . . . . . . . . . . . . Marty Ahrens and John R. Hall Jr.
3073
79
Measuring Consequences in Economic Terms . . . . . . . . . . G. Ramachandran and John R. Hall Jr.
3098
80
Computer Simulation for Fire Risk Analysis . . . . . . . . . . . William G.B. Phillips and Rita F. Fahy Revised by Douglas K. Beller
3117
81
Engineering Economics . . . . . . . . . . . . . . . . . . . . . . . . . . . John M. Watts, Jr. and Robert E. Chapman
3137
82
Fire Risk Indexing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . John M. Watts Jr.
3158
83
Risk-Informed Industrial Fire Protection Engineering . . . Thomas F. Barry
3183
84
Product Fire Risk Analysis . . . . . . . . . . . . . . . . . . . . . . . . John R. Hall Jr.
3211
85
Health Care Application of Quantitative Fire Risk Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ha˚kan Frantzich
3226
The Building Envelope: Fire Spread, Construction Features and Loss Examples . . . . . . . . . . . . . . . . . . . . . . . Daniel J. O’Connor
3242
86
87
Wildland Fires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Albert Simeoni
3283
88
Fires in Vehicle Tunnels . . . . . . . . . . . . . . . . . . . . . . . . . . Ricky Carvel and Haukur Ingason
3303
89
Fire Risk Analysis for Nuclear Power Plants . . . . . . . . . . . Nathan O. Siu, Nicholas Melly, Steven P. Nowlen, and Mardy Kazarians
3326
90
Fire Risk in Mass Transportation . . . . . . . . . . . . . . . . . . . Armin Wolski and Jarrod Alston
3370
Appendix 1
Conversion Factors . . . . . . . . . . . . . . . . . . . . . . .
3397
Appendix 2
Thermophysical Property Data . . . . . . . . . . . . . .
3425
Appendix 3
Fuel Properties and Combustion Data . . . . . . . .
3437
Appendix 4
Configuration Factors . . . . . . . . . . . . . . . . . . . . .
3476
Appendix 5
Piping Properties . . . . . . . . . . . . . . . . . . . . . . . .
3483
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3493
1
Introduction to Fluid Mechanics Bart Merci
Fluid Properties In this section, a number of fluid properties are defined. An implicit assumption in the classical fluid mechanics is the ‘continuum hypothesis’, implying that we treat fluids as continuous media, not as an ensemble of individual molecules [1]. This is justified in ‘normal’ circumstances. This way, the fluid and flow quantities are continuous and local quantities to be interpreted as averages over a volume V* which is very small (but still very large when compared to distances between molecules). This assumption allows to define local fluid and flow properties (e.g. velocity vectors). The continuum hypothesis is adopted here. A fluid can be a liquid or a gas (vapour).
Density The mass density is the amount of fluid mass inside a volume: m ρ¼ : V
certain time is defined as in Equation 1.1, taking the local limit for a small volume. In an incompressible flow, the density does not vary. In general, liquids can be considered ‘incompressible’. In gases, the density can vary due to variations in pressure or temperature (see below: ideal gas law). The reciprocal of density is the ‘specific volume’ (m3/kg).
Viscosity Fluids can flow. The viscosity is the fluid property that indicates how easily molecules can move with respect to each other. Fluid particles with different velocity have the tendency to evolve to the same common velocity, through exchange of momentum. In other words, fluid layers with different velocities exert a shear stress τ onto each other. Most technically relevant fluids are ‘Newtonian’: the shear stress increases linearly with the strain rate (or velocity gradient):
ð1:1Þ
Its unit is kg/m3. In a variable density flow, the density can vary in space and time and the local density at a
B. Merci (*) Department of Flow, Heat and Combustion Mechanics, Ghent University, Ghent, Belgium
τ¼μ
dv : dy
ð1:2Þ
The unit of τ is Pa (¼ N/m2). The proportionality factor, relating the velocity gradient to the shear stress, is the dynamic viscosity μ (unit: Pa.s). In gases, μ typically increases with temperature, whereas in liquids it decreases with increasing temperature.
M.J. Hurley (ed.), SFPE Handbook of Fire Protection Engineering, DOI 10.1007/978-1-4939-2565-0_1, # Society of Fire Protection Engineers 2016
1
2
B. Merci
Sometimes, the kinematic viscosity is used: μ ν¼ : ρ
ð1:3Þ
Its unit is m2/s. The shear stress, Equation 1.2, causes friction losses in case of flow. The higher the viscosity, the larger the flow losses become for the same velocity gradient. In other words, the resistance of the fluid against (imposed) flow increases with increasing viscosity. The viscosity of a fluid is never zero. The important implication is that, whenever there is a solid boundary, this boundary always exerts an influence on the flow field (e.g. causing the development of a boundary layer).
Specific Heat The specific heat or thermal capacity, c, is the amount of energy required to cause a temperature rise of 1 K (or 1 C) in 1 kg of the fluid. Its unit is J/(kg.K). In gases the value of the specific heat depends on the circumstances under which the energy is supplied. If the pressure is kept constant, the notation is cp. If the volume is kept constant, the notation is cv. The difference between the two values is called the gas constant R (also in J/(kg.K)): c p ¼ cV þ R:
ð1:4Þ
For liquids and solids, cp cv.
Conduction Coefficient
q_ ¼ k∇T ¼ λ∇T:
α¼
k ρc
ð1:6Þ
The unit of α is m2/s.
Diffusion Coefficient In a mixture of fluids (see below), one species can diffuse in the mixture due to concentration gradients of that species in the mixture. It is common practice to apply Fick’s law for many flows: ! Jk
¼ ρDk ∇Y:
ð1:7Þ
The diffusion coefficient D thus provides the relation between the diffusion flux Jk (kg/(m2s)) of species k and the spatial gradient of the local mass fraction Yk (i.e. the amount of mass of species k per kg mixture) of that species. The minus sign expresses that the diffusion flux is always from higher concentration to lower concentration. The unit of D is m2/s.
Dimensionless Groups of Fluid Properties
The conduction coefficient expresses how easily heat flows inside a material. Its value indicates the heat flux per unit area (W/m2) related to a spatial temperature gradient (K/m): !
This is Fourier’s law. The minus sign indicates that the heat flux is always from high temperature to low temperature. The unit of the conduction coefficient (k or λ) is W/(m.K). The conduction coefficient, specific heat and density can be combined to obtain the thermal diffusivity:
ð1:5Þ
By combining the fluid properties, dimensionless groups can be constructed. Indeed, the units of ν, α and D are the same (m2/s). Physically, the interpretation is that ν tries to make the velocity field uniform inside a fluid
1
Introduction to Fluid Mechanics
3
(through exchange of momentum), α tries to make the temperature field uniform (through heat exchange by conduction) and D tries to make the concentration field in a mixture homogeneous (through concentration gradient driven diffusion). The resulting dimensionless groups read: – The Prandtl number: Pr ¼
ν μc p μc p ¼ ¼ : α λ k
ð1:8Þ
– The Schmidt number: ν : D
ð1:9Þ
α Le ¼ : D
ð1:10Þ
Sc ¼
Internal Energy The local motion of molecules in a fluid is related to the internal energy (e or u, with unit J/kg). This is a measure for the thermal energy.
Enthalpy The quantity (static) enthalpy (h, with unit J/kg) is related to the internal energy through addition of pressure, divided by mass density: h¼uþ
p p ¼eþ : ρ ρ
ð1:11Þ
– The Lewis number:
Clearly, these numbers are connected: Le ¼ Sc:Pr1 . It is important to note that the dimensionless numbers Equations 1.8, 1.9, and 1.10 are still fluid properties, not flow properties. As long as no mixtures are considered, the Prandtl number is the most relevant dimensionless fluid property, when heat transfer is an issue.
Entropy The entropy is a measure for the disorder in the fluid. It is related to the second law of thermodynamics. This quantity is typically not particularly relevant for fire related issues.
Equation of State Liquids
State Properties State properties describe the state of the fluid, not the material properties of the fluid.
Pressure The pressure (p) can be defined as the normal force per unit area at a certain point. The unit is Pa. Pressure differences are the driving force for fluid flows.
Temperature The unit of temperature (T) is Kelvin (K). The temperature must not be confused with heat (the unit of which is Joule, J).
In liquids, the density is essentially constant, relatively very weakly dependent on pressure and temperature. Yet, the general expression that provides the equation of state defines the relation between density, temperature and pressure: ρ ¼ f ð p; T Þ
ð1:12Þ
Gases: Ideal Gas Law In gases, it is common practice to specify Equation 1.12 as the ‘ideal gas law’: p ¼ ρRT
ð1:13Þ
For fire related flows, this is justified. Most gases behave as air would do and air behaves as an ideal gas (with the exception of extremely low or
4
high pressure or temperature, but this is not relevant for real-life fire applications). The gas constant R (J/(kg.K)) has been introduced in Equation 1.4 and the temperature T is expressed in Kelvin (K).
Mixtures In fire related flows, the fluid can be a mixture. Obvious examples are smoke or flames. A distinction must be made between chemical and physical issues. If toxicity is an issue, chemical aspects are important. As long as the flow itself is concerned, the physical behaviour of many gaseous mixtures resembles very much the behaviour of hot air. One reason is that the species most often encountered, have comparable diffusivities (with the important exception of hydrogen, which has a much higher diffusivity). Another reason is that typically by far mixtures in fire related flows consist mainly of air. As a consequence, the simplification is made very commonly to treat a mixture of hot gases as hot air, applying the ideal gas law (Equation 1.13) with the gas constant for air and using the (temperature dependent) viscosity for hot air. Therefore, mixtures of gases do not receive much attention when fluid mechanics aspects are considered in case of fire. Yet, a few definitions are introduced here. The mass fraction Yi of species i is the ratio of the local amount of mass of species i to the local amount of mass of mixture. It is therefore a non-dimensional quantity. Conservation of mass leads to the statement that, everywhere in physical space, the sum of all mass fractions of all X N species equals unity: i¼1 Y i ¼ 1. Using the notion of mass fractions, the fluid properties of mixtures can be determined from the fluid properties of their constituent species. E.g. the specific heat becomes X N c¼ i¼1 Y i ci . Also state properties can be defined as such. X N E.g. static enthalpy becomes: h ¼ i¼1 Y i hi .
B. Merci
Conservation Equations Figure 1.1 visualises a streamline through a surface of a (control) volume. This concept will be used to develop the conservation equations in the integral formulation. A streamline is defined such that locally the velocity vector is tangent to the streamline. A collection of streamlines is called a stream tube.
Conservation of Mass—Continuity Equation Conservation of mass expresses the following principle: The amount of mass that flows into a stationary volume per unit time, equals the outflow of mass per unit time out of that same volume plus the amount of mass accumulation per unit time in that same volume. Mathematically, this is formulated as follows: • The net outflow per unit time is given by a closed surface integral over the entire area of the manifold ∂V, enclosing the volume V: ðð !! ! ρ v :n dA; in this expression, v is the local ∂V
!
velocity vector at a certain position on ∂V, n the local normal vector on the surface (i.e. the vector with length equal to 1, locally perpendicular to the surface and pointed outward) and dA the area of an infinitesimal element
dA
n
θ
v
Fig. 1.1 Streamline through a surface. Notation: dA is the area of an infinitesimal part of the surface; n is the normal vector, with length equal to unity, perpendicular to dA and pointing ‘outward’ of the control volume, spanned by the surface; v is the local flow velocity vector at position dA; θ is the angle between vectors n and v
1
Introduction to Fluid Mechanics
5 !!
A2, v2, ρ2
on the surface; note that the inner product v :n !!
> 0 for outflow, while v :n < 0 for inflow; • The accumulation of mass per unit time is obtained from a derivation with respect to time of the integral of the mass density over
A1, v1, ρ1
∂ the entire volume: ∂t ∭ ρdV. V
The conservation of mass thus reads: ðð ∂ !! ∭ ρdV þ ρ v :n dA ¼ 0: ð1:14Þ ∂t V ∂V
This equation is also called the continuity equation. An important simplification is found in the case of permanent (or ‘steady’) motion. In that case, the time derivative disappears in Equation 1.14: ðð !! ρ v :n dA ¼ 0: ð1:15Þ
Fig. 1.2 Illustration of conservation of mass for steady flow (Equation 1.15) through a pipe expansion. Dashed lines: boundary of control volume. Bold vectors: normal vectors (unity length, perpendicular to surface and pointing outward). The other vectors indicate velocity vectors
The integral in Equation 1.14 in fact refers to the total net mass flow rate (kg/s) through a surface with area A: ðð !! ð1:17Þ m_ ¼ ρ v :n dA A
∂V
A further simplification concerns incompressible fluids (e.g. water in a pipe under normal conditions). In that case, density does not change, so that not only Equation 1.15 applies, but it further simplifies to read: ðð !! v :n dA ¼ 0: ð1:16Þ ∂V
A very simple illustration of Equation 1.15 is provided on the basis of Fig. 1.2. There is no flow through the solid boundaries (solid lines in ðð !! Fig. 1.2), so the only contributions to ρ v :n dA ∂V
stem from surfaces 1 and 2. In surface 1, the velocity vector is pointing inward, while the normal vector is by definition pointing outward, so the contribution (under the simplified assumption of uniform flow through the cross-section) becomes: ρ1 v1 A1 . On surface 2, the velocity and the normal vectors are pointing outward, leading to: þρ2 v2 A2 . Equation 1.15 thus provides: ρ1 v1 A1 þ ρ2 v2 A2 ¼ 0 ! ρ1 v1 A1 ¼ ρ2 v2 A2 . In case of incompressible flow (Equation 1.16) this further simplifies to: v1 A1 ¼ v2 A2 .
If the mass density is not included, the total net volume flow rate (m3/s) through a surface with area A is found: ðð !! V_ ¼ v :n dA: ð1:18Þ A
Expression (1.14) can also be formulated in differential form, applying Green’s theorem: ! ∂ρ þ ∇: ρ v ¼ 0: ∂t
ð1:19Þ
The symbol ∇ is the divergence operator:
!
∇: v ¼ ¼
! ! ∂! ∂ ! ∂! ! 1x þ 1 y þ 1 z : vx 1 x þ v y 1 y þ vz 1 z ∂x ∂y ∂z
∂vx ∂v y ∂vz þ þ : ∂x ∂y ∂z
ð1:20Þ !
In Equation 1.20, 1 x is the notation for the unity vector, i.e. a vector with length equal to unity, in the x-direction. Expression (1.15), for steady flow, reads in differential form:
6
B. Merci
! ∇: ρ v ¼ 0;
ð1:21Þ
σyy (y+dy)
y
τyx (y+dy)
while expression (1.16), for incompressible fluids, becomes: !
∇: v ¼ 0:
ð1:22Þ
This shows that the velocity field for any flow of an incompressible fluid is ‘divergence free’, or ‘solenoidal’.
σxx (x)
τxy (x+dx) dy
σxx (x+dx)
τxy (x) dx
τyx (y) σyy (y) x
Total Momentum Now the integral formulation for the conservation of total momentum is discussed. Figure 1.1 again serves as the basic sketch. Conservation of total momentum refers to the expression of Newton’s second law, applied to flows. The net change in momentum of a system per unit time in a certain sense and direction equals the net force on that system in that sense and direction. Expressed for a stationary volume, this becomes: The total force onto a stationary volume equals the sum of the net outflow of momentum per unit time out of that same volume plus the accumulation of momentum per unit time in that same volume. The local amount of momentum per unit vol!
ume is ρ v (kg/(m2s)). Newton’s second law thus reads: ∂ ! ∭ ρ v dV þ ∂t V
ðð
! ! !! ρ v v :n dA ¼ F tot : ð1:23Þ
∂V
Note that Equation 1.19 is a vector equation, i.e. the equation is valid for each component/ direction individually. For a permanent (or ‘steady’) motion, expression (1.19) simplifies to: ðð ! ! !! ρ v v : n dA ¼ F tot : ð1:24Þ ∂V
Fig. 1.3 Definition of normal stresses and shear stresses (2D)
The total force consists of: • Surface forces: – Pressure (Pa); – Viscous stresses (Pa); • Body forces: – Gravity (N); – Others (not relevant for fire related flows). These forces are discussed now, in differential formulation: 8 ∂σ xx ∂τxy ∂τxz > > F þ þ þ ρgx ¼ > > tot, x ∂x ∂y ∂z > > > < ∂τ yx ∂σ yy ∂τ yz þ þ þ ρg y ð1:25Þ Ftot, y ¼ > ∂x ∂y ∂z > > > > > > : Ftot, z ¼ ∂τzx þ ∂τzy þ ∂σ zz þ ρgz ∂x ∂y ∂z The final terms in Equation 1.25 refer to the gravity acceleration vector, multiplied with the local mass density. Figure 1.3 shows how the normal stresses and shear stresses are defined. The shear stresses are found from Stokes’ law: ∂vx ∂v y τxy ¼ τ yx ¼ μ þ ∂y ∂x ∂vx ∂vz ð1:26Þ þ τxz ¼ τzx ¼ μ ∂z ∂x ∂vz ∂v y þ τ yz ¼ τzy ¼ μ : ∂y ∂z
1
Introduction to Fluid Mechanics
7
The shear stresses are thus proportional to the dynamic viscosity and the local velocity gradients. The normal stresses contain contributions from stresses due to fluid dilatation (for variable density flows only) and pressure:
2 ∂vx 1 ! σ xx ¼ p þ μ ∇: v 3 ∂x 3 2 ∂v y 1 ! ∇: v σ yy ¼ p þ μ 3 ∂y 3 2 ∂vz 1 ! ∇: v : σ zz ¼ p þ μ 3 ∂z 3 The above equations:
results
in
ð1:27Þ
Navier–Stokes
the
8 ∂τxy ∂τxz ∂ ∂vx ∂vx ∂vx ∂p 2 ∂ ∂vx 1 ! > > þ μ þ ρv y þ ρvz ¼ ∇: v þ þ ρgx ðρvx Þ þ ρvx þ > > > ∂t ∂x 3 ∂x ∂x ∂y ∂z ∂x 3 ∂y ∂z > > > < ∂v y ∂v y ∂v y ∂v y 1 ! ∂τxy ∂τ yz ∂ ∂p 2 ∂ ρv y þ ρvx þ μ þ ρv y þ ρvz ¼ ∇: v þ þ ρg y þ > ∂t ∂y 3 ∂y 3 ∂x ∂y ∂z ∂y ∂x ∂z > > > > >∂ ∂vz ∂vz ∂vz ∂p 2 ∂ ∂vz 1 ! ∂τxz ∂τ yz > > : ðρvz Þ þ ρvx þ μ þ ρv y þ ρvz ¼ ∇: v þ þ ρgz þ ∂t ∂z 3 ∂z ∂x ∂y ∂z ∂z 3 ∂x ∂y ð1:28Þ Note that the presence of the gravity force is essential in order to account for the Archimedes force. This is essential for buoyancy-driven forces, which is important in the context of fire. Also note that pressure gradients (or pressure differences) are the driving force for flows, not the absolute pressure level.
Energy Conservation of energy refers to the first law of thermodynamics:
∂ ∂t
The change (per unit time) of the total internal energy of a system equals the sum of the heat added (per unit time) to the system and the work (per unit time) exerted onto that system. The total internal energy consists of: • Static internal energy e (J/kg) or ρe (J/m3); • Kinetic energy ρv2/2 (J/m3). The mathematical formulation of the first law of thermodynamics for a stationary open system can be found in many textbooks (e.g. [2–9]). It reads:
ð 1 1 !! !! ρe þ ρv2 dV ¼ ∮ ρe þ ρv2 v :n dS ∮ p v :n dS þ ∮ 2 2 ∂V ∂V ∂V V
ð ð !! !! þ ρg : v dV þ ρSh dV ∮ q :n dS V
V
The terms on the right hand side are: • First term: Net inflow of total internal energy into the control volume (‘convection’); the minus sign is necessary to comply with the
∂V
!
! ! !
!
τ : v :n dS ð1:29Þ
sign convection (see previous sections: the normal vector is pointing outward). • Second term: Work of the flow against pressure. This is work from a force (pressure),
8
B. Merci
exerted onto the surface. The work by the pressure onto the flow is positive for inflow and negative for outflow, which explains the minus sign. • Third term: Work by the viscous stresses. This is work from a force (viscous stresses, Equations 1.26 and 1.27, exerted onto the surface. With the sign conventions used (Fig. 1.3 and outward pointing normal vector), this is a term with a plus sign. • Fourth term: Work by gravity. This is work by a volume force, exerted inside the volume. This work is positive for a downward flow,
∂ ∂t
!
y
required in this term (if the y-direction is positive vertically upward). • Fifth term: Volumetric source term of heat / internal energy (e.g. radiation). This term can be positive or negative. • Final term: Net incoming flux of heat/internal energy (e.g. conduction). The flux with the flow cannot be added to this term (as it is already included in the convection term). The energy equation can also be formulated, using enthalpy Equation 1.11:
ð ð 1 ∂ 1 !! ρh þ ρv2 dV ¼ pdV ∮ ρh þ ρv2 v :n dS þ ∮ 2 ∂t 2 ∂CV ∂CV
CV
CV
ð
!!
ð
ρ g : v dV þ
þ CV
!
so that with g ¼ g1 no minus sign is
! ! !
! !
τ : v :n dS
!!
ρSh dV ∮ q :n dS:
ð1:30Þ
∂CV
CV
In differential formulation, this reads: ! ! N X ∂ 1 2 1 2 ! ∂p !! ! !! ρh þ ρv þ ∇: ρ h þ v v ¼ þ ∇: τ : v þ ρSh þ ρ Y i g : v i ∇:q ð1:31Þ ∂t 2 2 ∂t i¼1 The (static) enthalpy is the mass-weighted sum of the enthalpies of species i: h¼
N X
Y i hi :
ð1:32Þ
i¼1
The enthalpy hi is the sum of a reference enthalpy (the chemical standard formation enthalpy of species i) and a ‘sensible’ (thermal) enthalpy [5–9]. For ideal gases this reads: ðT hi ðT Þ ¼ hre f , i þ c p, i ðT ÞdT; ð1:33Þ T re f
with cp,i the specific heat of species i, defined above. Note that in Equation 1.31, expressed in terms of enthalpy, the source term ρSh contains e.g. radiation, but not a heat release rate due to
combustion. Combustion reactions transform chemically bound enthalpy into sensible enthalpy and as such cause a temperature rise, but the sum of sensible and chemical enthalpy does not change locally. If the energy equation is expressed in terms of temperature (or sensible enthalpy), a source term due to the combustion heat release rate does appear. The final term in Equation 1.31 reads: !
∇: q ¼ ∇:ðλ∇T Þ ∇: ρ
N X
! hi Di ∇Y i
þ D:E:
i¼1
ð1:34Þ The abbreviation ‘D.E.’ stands for the ‘Dufour effect’, i.e. and additional enthalpy flux due to species concentration differences. This effect is
1
Introduction to Fluid Mechanics
9
ignored in fire related flows. The first terms in Equation 1.34 refer to Fourier’s law for heat conduction, Equation 1.5. The middle terms refer to an enthalpy flux due to diffusion, using Fick’s law, Equation 1.7. The general expression, Equation 1.31, can often be simplified. Many fire-induced flows are
low-Mach number flows (note: this is not true for explosions). The time derivative of pressure can often be ignored. Also the work done by gravity, by the viscous shear stresses and by the normal stresses becomes very small and the kinetic energy is negligible. Using Equations 1.8 and 1.9, the energy equation becomes:
! N ! X ∂ μ 1 1 ðρhÞ þ ∇: ρh v ¼ ∇: ∇h þ μ hi ∇Y i þ ρSh ∂t Pr Sci Pr i¼1
For unity Lewis number (Lei ¼ 1 for all i, Equation 1.10) fluids, this further simplifies to:
μ ! ∂ ðρhÞ þ ∇: ρh v ¼ ∇: ∇h þ ρSh : Pr ∂t ð1:36Þ
ð1:35Þ
Buoyancy The main relevance of the fundamental law of hydrostatics, Equation 1.37, lies in the fact that in many fire related flows, buoyancy plays a dominant role. This can be learnt from the Navier–Stokes equations, Equation 1.28, combining the forces due to pressure gradients and grav!
!
ity. In the vertical direction (still with g ¼ g1 y), using Equation 1.38, the resulting force per unit area reads:
Hydrostatics Hydrostatics From the general Navier–Stokes equations (1.28), the basic law for hydrostatics is immediately recovered. Indeed, setting all velocities in a certain environment equal to zero, the only terms remaining are: !
∇ p ¼ ρamb g :
ð1:37Þ
Equation 1.37 is valid at any time (in the absence !
!
of motion). For the special case where g ¼ g1 y , with g ¼ 9.81 m/s2, Equation 1.37 reads (in the y-direction): dp ¼ ρamb g dy
ð1:38Þ
Note that Equation 1.37 in such circumstances also implies that pressure does not vary in the horizontal directions. Equation 1.38 can be integrated: p ¼ pre f ρamb g y yre f : ð1:39Þ
dp ρg ¼ ðρamb ρÞg: dy
ð1:40Þ
In the process of getting to expression (1.40), the implicit assumption is made that pressure differences in the horizontal directions are small. Equation 1.40 reveals that the driving force in situations where buoyancy dominates, stems from density differences, in the presence of a gravity field. This is known as Archimedes’ law. Note that, since gravity acts in the vertical direction only, buoyancy forces by definition also act in the vertical direction only. For small density differences, the approximation ρ ρamb is typically made in the Navier–Stokes equations, except that the difference ðρamb ρÞ is accounted for in combination with gravity (Equation 1.40). This is called Boussinesq’s approximation. In the context of small density differences, expression (1.40) can be developed further, using a Taylor series
10
B. Merci
∂ρ ρ ¼ ρðT; pÞ ) ρ ρamb þ ∂T p ∂ρ ðT T amb Þþ ∂ p ð p pamb Þ. Typically the expansion:
T
pressure correction is much smaller than the
temperature correction. Using the thermal volumetric expansion coefficient: 1 ∂ρ β¼ ; ð1:41Þ ρ ∂T p the Archimedes force becomes:
ðρamb ρÞg ¼ ρamb βðT T amb Þg , if βðT T 1 Þ 1:
The basic expression is thus Equation 1.40, based on density differences, while Equation 1.42 is only valid for small enough temperature differences.
Scaling Laws—Dimensionless Flow Numbers In this section, starting from the governing equations, some scaling laws and nondimensional flow numbers are introduced. The characteristic length scale is L, the characteristic velocity is u.
Dimensionless Flow Numbers Examination of the terms in the Navier–Stokes equations, Equations 1.28 and 1.26, leads to the following proportionalities: ρut ρuL ΔLp Δρg μLu2 . Several non-dimensional flow numbers can be derived now, as follows. The importance of each of the numbers mentioned, depends on the importance of the corresponding terms in the Navier–Stokes equations. The convection term/ inertia term is always important, as it characterizes the flow. Depending on the flow configuration, one or more terms are in competition with (or determine) the inertia term (or thus the flow). This is explained next. When the viscous stresses prevail, the
number, which is the ratio of inertial forces to viscous forces: Re ¼
ρuL uL ¼ : μ ν
ρu2 L
μLu2 leads to the Reynolds
ð1:43Þ
The viscous forces tend to damp the inherent instabilities in the non-linear convection terms in the Navier–Stokes equations, while these instabilities can evolve towards fully-developed turbulence for large enough Reynolds number. This is addressed in the next section. When buoyancy is dominant, the proportionality ρuL Δρg leads to the Froude number, which is the ratio of inertial forces to the Archimedes force: 2
Fr ¼
ρu2 : ΔρgL
ð1:44Þ
In the fire community, this is often simplified to:
2
proportionality
ð1:42Þ
Fr ¼
u2 : gL
ð1:45Þ
Expression (1.44) resembles the underlying physics more than Equation 1.45. On the other hand, the difference between expressions (1.44) and (1.45) is no more than a numerical factor, depending on the densities at hand. Moreover, in many experiments it is much more straightforward to measure velocities than mass densities, so that it is easier to characterize the experimental set-up through formulation (1.45). This explains why the use of Equation 1.45 is popular in diagrams and correlations.
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Introduction to Fluid Mechanics
11
If large (imposed) pressure differences occur, sometimes the Euler number comes into play, through ρuL ΔLp: 2
Eu ¼
Δp : u2
ð1:46Þ
In fire related flows, this is often not relevant. In buoyancy driven flows, applying Boussinesq’s hypothesis, the driving force (Equation 1.42) can also be made dimensionless as: Ra ¼
L3 gβΔT : αν
ð1:47Þ
This is the Rayleigh number. Alternatively, the Grashof number can be used: Gr ¼
L3 gβΔT : ν2
ð1:48Þ
The relation between the two is: Ra ¼ Gr:Pr, with the Prandtl number as defined in Equation 1.8. The Grashof number can be interpreted as a ratio of buoyancy forces (with Boussinesq’s approximation) to the viscous forces. This is relevant in boundary layers (see below).
Scaling In this section, scaling is briefly discussed in the context of fluid mechanics. As such, only the momentum equation is considered, albeit that at the end of this section, some remarks are formulated on the fire heat release rate (using the energy equation) and the study of unsteady phenomena (using the mass conservation equation). As a consequence, no comments are formulated on e.g. convective heat transfer or conduction through solids, nor on radiation. For an extensive discussion on scaling, the reader is referred to [10, 11]. The main non-dimensional numbers in low-Mach number flows are the Reynolds number Equation 1.43 and the Froude number Equation 1.44 (or Equation 1.45). Firstly, it is mentioned that the only way to preserve both numbers when scaling (up or down) a flow in a
certain configuration, is through the use of different fluids. Indeed, assume that the fluid does not change (and that the densities do not change). Then preservation of Re reveals that: Re1 ¼ Re2 ) u1νL1 ¼ u2νL2 ) u2 ¼ uL1 L2 1 . Preservation of the Froude number (still with the assumption that densities do not change) leads to: qffiffiffiffi u2 u2 Fr 1 ¼ Fr 2 ) gL11 ¼ gL22 ) u2 ¼ u1 LL21 . Clearly, this is inconsistent with the requirement, stemming from the preservation of the Reynolds number. Both numbers can be preserved if, starting from the requirement for preservation of the Froude number, the fluid’s viscosity is modified such that also the Reynolds number is preserved. This is not straightforward. Fortunately, both the Reynolds number and the Froude number have the property that, as soon as they are large enough, their actual value becomes irrelevant. In other words, as soon as they are sufficiently high, the qualification ‘high’ is sufficient, not the exact number. This is due to turbulence, overwhelming molecular phenomena (see next section). This can also be understood intuitively. The Reynolds number is the ratio of inertia to viscous damping forces. Either the damping force is strong enough to overcome the inherent instabilities in the non-linear convection terms in the Navier–Stokes equations (laminar flow), almost strong enough (transitional flow) or not strong enough (turbulent flow). When turbulence is fully developed, the strength of the viscous stress becomes irrelevant, i.e. the true value of the Reynolds number becomes irrelevant. For the Froude number, it is most instructive to examine expression (1.44). The driving force for buoyancy is in the denominator. If density differences become small, buoyancy becomes irrelevant and the Froude number is high. As such, high values of the Froude number implies that buoyancy is not important and thus that the error is small when the Froude number is not preserved (as long as it stays sufficiently high). Knowing this, it is instructive to examine the order or magnitude of Reynolds number and Froude number in fire related flows. Indeed, if one of the numbers can be expected to be high,
12
B. Merci
that number need not be preserved in scaling. Typical dimensions are in the order of 1 m: L ¼ OðmÞ. Typical velocities are in the order of 1 m/s: u ¼ Oðm=sÞ. Densities are in the order of 1 kg/m3: ρ ¼ Oðkg=m3 Þ. The dynamic viscosity in gases is in the order of 106 Pa.s: μ ¼ O 106 Pa:s . Using these numbers, the Reynolds number Equation 1.43 is: Re ¼ O 1:1:1 ¼ 106 6 O 10 , while the Froude number Equation 1.44 1:1 is: Fr ¼ O 1:10:1 ¼ Oð0:1Þ. Obviously, these are rough order of magnitude analyses, but it is clear that in fire related flows, the choice will be made to preserve the Froude number, not the Reynolds number, when scaling is applied. The energy equation also provides information regarding scaling laws. The simplified formulation (1.36) can be used for fire-related flows. Yet, temperatures are very important in fire related flows, so the energy equation should be interpreted in terms of sensible enthalpy, in _ in W) which case the fire heat release rate ( Q, comes into play. Knowing that, in terms of dimensions, (sensible) enthalpy differences can be re-written as the product of specific heat and temperature differences, Equation 1.36 leads to ρc ΔT ρc ΔTu the following proportionalities: pt pL Q_ L3
kΔT . L2 This reveals that: Q_ uρc p ΔTL2 :
ð1:49Þ
It is common practice to scale configurations such that the temperatures remain the same. This also implies that densities do not change (if the same fluid is applied). As has just been explained, the Froude number Equation 1.44 is preserved, so pffiffiffi that the velocity scales as L . As a consequence, the fire heat release rate scales as: pffiffiffiffiffi 2 L1 L Q_ 1 ¼ pffiffiffiffiffi 12 ) Q_ L5=2 : ð1:50Þ _ L2 L2 Q2 Finally, it is noteworthy that the conservation of mass, Equation 1.19, reveals that: t L=u:
ð1:51Þ
Applying Froude scaling, the velocity scales as pffiffiffi L, so that expression (1.51) reveals that the
temporal evolution of quantities (e.g. temperature) depends on the dimensions of the configupffiffiffi ration as t L. This is relevant when unsteady phenomena are studied.
Turbulence There are numerous text books on turbulence and turbulent flows, e.g. [12, 13]. Only some introductory comments are presented here.
Reynolds Number In the previous section it has been mentioned that the Reynolds number Equation 1.43 is the ratio on inertia to viscous forces. It is well-known that the convection term in the Navier–Stokes equations (1.28) is inherently unstable and that the flow becomes turbulent when the viscous forces are not strong enough to damp the instabilities, i.e. when the Reynolds number becomes sufficiently high. Below a certain threshold number, the flow remains ‘laminar’. There is no sudden change from ‘laminar’ to ‘turbulent’: there is a ‘transition’ zone in between. Care must be taken in the definition of this ‘critical’ Reynolds number, in the sense that the length scale must be defined. In flows over flat plates, it is common practice to use the distance from the leading edge and Rec is in the order of 500.000. In pipe flows, it is common practice to use the pipe diameter as characteristic length scale and Rec is in the order of 2.000. It is important to stress that the Reynolds number is a flow property, not a fluid property. Turbulence is typically defined on the basis of a number of properties [13]: • Randomness: there are fluctuations in the flow; • Three-dimensionality: even if the mean flow is 2D or axisymmetric, the vortices or ‘eddies’ are always three-dimensional; • There is a wide range of length scales and time scales in the flow. The largest scales are determined by the configuration at hand,
1
Introduction to Fluid Mechanics
while the smallest scales are determined by the Reynolds number. The smallest scales can easily be 10,000 times smaller than the largest scales. • Turbulent mixing is very effective. • There is a lot of diffusion and dissipation. Turbulence dies out quickly if not sustained by velocity gradients in the mean flow. • There is vortex stretching, transferring energy from the mean flow to turbulent fluctuations. It is instructive to briefly explain the randomness in the flow. Indeed, knowing that the Navier–Stokes equations (Equation 1.28) are deterministic, one may pose the question how it is possible that randomness occurs when applying deterministic boundary and initial conditions. The reason is that there are always small fluctuations, i.e. the boundary and initial conditions are never known with infinite precision. Due to the unstable convection terms in the Navier–Stokes equations, turbulent flows are extremely sensitive to details and this creates randomness in the instantaneous flow fields. This makes it impossible to make long-term predictions of instantaneous turbulent flow fields and explains why turbulent flows are tackled in simulation through statistical approaches (see below). Obviously, the mean flow can still be deterministic (see below).
13
‘same’ turbulent flow are made, repetitive measurements of the quantity are made at the same location, and the average value of the measurements is determined. In a simplified manner, though, one can think of this procedure as a time averaging, where the averaging period Δt is sufficiently long, compared to the largest turbulent time scales, but sufficiently short compared to time scales associated with possible variations in the mean flow: 1 vx ðtÞ ¼ Δt
ðt tΔt
1 vx ðtÞdt; T ðtÞ ¼ Δt
ðt T ðtÞdt: tΔt
ð1:52Þ It is clear that this is only possible if the turbulent time scales are short, compared to time scales in the mean flow. The ‘integral’ turbulent time scale is typically less than 1 s, so in many fire related flows this concept of Reynolds averaging is possible. Using Equation 1.52, the instantaneous value can be expressed as the sum of the (Reynolds) averaged value and the instantaneous fluctuation around that value: vx ðtÞ ¼ vx ðtÞ þ v,x ðtÞ; T ðtÞ ¼ T ðtÞ þ T , ðtÞ: ð1:53Þ Note that:
Reynolds Averaging As mentioned in the previous section, the fluctuations in a turbulent flow make a direct analysis through the Navier–Stokes equations (Equation 1.28) impossible. Therefore, a statistical approach is adopted. The primary interest is often the mean flow. To that purpose, the Navier–Stokes equations are averaged. The concept of Reynolds averaging is explained first. Consider a turbulent flow. Measuring a velocity component (or e.g. a temperature) at a certain location will then yield a fluctuating signal, as explained. One can now determine the ‘average’ of that signal. The true definition of a Reynolds average [12, 13] is that many realizations of the
v,x ðtÞ ¼ 0; T , ðtÞ ¼ 0; vx ðtÞ ¼ vx ðtÞ; T ðtÞ ¼ T ðtÞ:
ð1:54Þ
Applying this averaging technique to the conservation equations (1.19), (1.28) and (1.36), the equations are obtained for the Reynoldsaveraged quantities. They are very similar to the instantaneous equations, but some additional terms appear: • Reynolds stresses in the momentum equations; • Turbulent heat fluxes in the energy equation. This is explained next. For the sake of ease, the energy equation is simplified here: it is expressed in terms of temperature and no chemical reactions, nor radiation, are considered. The
14
B. Merci
averaging of the chemical and radiative source terms is a separate problem, not addressed here. The additional terms appear as a consequence of the presence of products in the instantaneous
Equations 1.28 and 1.36. The mean value of the product is not equal to the product of the mean values:
, , , , , , vx v y ¼ ðvx þ v,x Þ v y þ v,y ¼ vx v y þ vx v y þ vx v y þ vx v y ¼ vx v y þ vx v y vx T ¼ ðvx þ v,x Þ T þ T , ¼ vx T þ vx T , þ v,x T þ v,x T , ¼ vx T þ v,x T , :
Simplifying further to a steady boundary layer flow of an incompressible fluid over a flat plate without external pressure gradient, the main remaining dominant terms are: ∂vx ∂v y þ ¼0 ∂x ∂y ∂vx ∂ ∂vx ∂vx ∂ ðv,x v,y Þ ν þ vy ¼ vx ∂y ∂y ∂x ∂y ∂y ð1:56Þ
vx
∂T ∂T ∂ ∂T ∂ , , þ vy ¼ α vyT ∂x ∂y ∂y ∂y ∂y
Clearly, the final terms, stemming from turbulence, are similar in nature to the molecular viscous stresses and the molecular thermal diffusion terms. The main question is now what the turbulent correlations look like. Indeed, terms like v,x v,y are only non-zero if the velocity fluctuations in Fig. 1.4 Sketch of turbulent fluctuations (eddies) in a flow with a mean velocity gradient
ð1:55Þ
the difference directions are statistically correlated. This is the case, explained from Fig. 1.4, showing a situation in a flow with a mean velocity gradient. The discussion is given here for the top left eddy, but it prevails for all eddies. At the left side of the top left eddy, the instantaneous motion is downward, as indicated by the arrow. Knowing that the mean velocity in the vertical direction equals zero, this implies that v’ < 0. In its downward motion, the eddy brings along fluid with a higher (mean) velocity in the horizontal direction into a region with lower (mean) velocity. Thus, the impact is a local increase in horizontal velocity, in other words u’ > 0. Clearly, from a statistical point of view the velocity fluctuations in both directions are correlated, in such a manner that u0 v0 < 0. At the right side of the top left eddy, the instantaneous motion is upward (v’ > 0) and (in the mean) lower horizontal velocity is brought into a region with (in the mean) higher U
v’ < 0
v’ > 0
v’ < 0
y v’ > 0
x
v’ < 0
v’ > 0
1
Introduction to Fluid Mechanics
15
horizontal velocity, causing u’ < 0. Thus, again u0 v0 < 0. A similar reasoning can be built up for the temperature fluxes. Additionally, it is clear that the fluctuations, caused by the turbulent eddy motion, will be larger as the mean velocity (or temperature) gradients are larger. The above led to the following ‘eddy viscosity’ modeling concept, introduced by Boussinesq: v,x v,y ¼ νt
∂vx ∂y
ð1:57Þ
In other words, a ‘turbulent’ or ‘eddy’ viscosity is simply added to the molecular viscosity in Equation 1.56. This reflects the physical observation that momentum transfer increases in turbulent flows through the turbulent motion of eddies. These cause ‘large scale’ momentum transfer. Similarly, this concept can be applied to the heat fluxes: v,y T , ¼ αt
∂T ∂y
ð1:58Þ
In other words, the addition of the turbulent thermal diffusivity to the molecular thermal diffusivity reflects the physical observation that heat transfer increases in turbulent flows through the turbulent motion of eddies. These cause ‘large scale’ heat transfer.
Turbulence Modeling As mentioned above, there is always a wide range of length scales and time scales in turbulent flows. The higher the Reynolds number, the wider this range, because the smallest scales become smaller and smaller. The largest turbulence scales are called the ‘integral’ scales. The smallest scales are called the ‘Kolmogorov’ scales. A detailed discussion of the spectrum is considered beyond the scope of this section, but it is important to appreciate that most of the turbulent kinetic energy is in the integral scale range (‘energy containing range’), while turbulence is dissipated at scales around
the Kolmogorov scales. Indeed, at those scales, viscous damping ‘kills’ turbulence, i.e. dissipates the turbulent kinetic energy into heat. The notion of energy cascade, introduced by Richardson, is worth mentioning. The basic mechanism is as follows: • Energy is taken from the mean flow and transferred to kinetic energy of turbulent eddies; this occurs around the integral scales; • The turbulent eddies break up, transferring their energy to the eddies of smaller scale; only little energy is dissipated in this breakup process; • The break-up process of eddies continues (‘cascade process’) until the eddies become so small that they cannot survive the damping action of viscosity anymore; • The dissipation takes place at the smallest turbulence scales. It is important to appreciate that, whereas the dissipation takes place at the smallest scales, the dissipation rate is determined by the production rate of turbulence from the mean flow in the energy containing range (in equilibrium conditions). This phenomenology is reflected in the choice for turbulence modeling in CFD (Computational Fluid Dynamics). One extreme approach is not to model turbulence, i.e. to completely resolve all turbulent motions, down to the smallest scales. Knowing that these small scales can easily be in the order of 0.1 mm or less, and realizing that the computational mesh needs to be sufficiently fine to resolve the smallest eddies, it is immediately clear that this approach is not feasible in typical fire related flow simulations, where dimensions are in the order of 1 m. Worse than that, in addition to unacceptable computing time and memory requirements, most of the time and memory would be devoted to simulating the smallest scales [13], whereas the primary interest is typically in the large scale flow phenomena (or in the mean flow). The other extreme is RANS (ReynoldsAveraged Navier–Stokes) turbulence modeling. In this approach, Reynolds averaging (see previous section) is applied and all turbulent motions, i.e. the entire turbulent spectrum, are modeled. Only the mean flow is resolved. The k-ε model
16
belongs to this class of models. The advantages of the RANS approach are clear: the computational mesh only needs to be fine enough to resolve the mean flows; the time step (in transient calculations) can be chosen on the basis of mean flow phenomena; one immediately gets a solution for the mean flow. There are major disadvantages, though. Firstly, all turbulence is modeled. Knowing that the largest turbulent scales are configuration dependent, it cannot be expected that a single RANS model can deal with arbitrary configurations in a reliable manner. Second, in fire related flows large scale flow unsteadiness often plays an important role, e.g. in the entrainment process of air into flames or smoke. Such unsteadiness is not captured in (unsteady) RANS and must be modeled. Again, being configuration dependent, RANS models cannot be expected to be as accurate as approaches where this unsteadiness is resolved. This explains the popularity of the LES (Large-Eddy Simulations) technique in CFD for fire related flows. In this technique, the large scale eddies are resolved and only the effect of the small scale eddies is modeled. This technique offers the advantage of resolving the large-scale flow unsteadiness (and buoyancy effects). Also, the unacceptable fineness of the computational mesh as required in DNS is avoided. Yet, there is a very important caveat. Indeed, in order to guarantee the quality of LES results, 80 % of the turbulent kinetic energy must be resolved [13]. It is common practice to use the computational mesh as filter in the LES approach, i.e. the size of the computational mesh cells determines the size of the eddies still resolved. In many CFD simulations performed on today’s computers, the mesh size is in the order of 10 cm or more. Very often, it cannot be guaranteed that 80 % of the turbulent kinetic energy is effectively resolved, so that care must be taken in the interpretation of the CFD results. In other words, blind belief in the exactness of under-resolved LES must be avoided. Also, it must be understood that if the computational mesh is used as filter for the instantaneous Navier–Stokes equations, as is common practice in the fire safety science community, no grid independent results can be expected from LES. Indeed, as the filter of the
B. Merci
equations itself is modified, the results inevitably change. This is not the case in RANS simulations, where the results become independent of the mesh applied, provided it is fine enough. For more discussion on turbulence modeling, in the context of reacting flows, the reader is also referred to [14].
Boundary Layers—External Flows In section “Scaling”, it was mentioned that the absolute value of the Reynolds number Equation 1.43 becomes irrelevant as Re becomes high. In other words, the flow can be considered ‘inviscid’, i.e. μ ¼ 0. Stated in another manner: viscosity becomes irrelevant in the Navier–Stokes equations. This, however, is only true in the absence of solid boundaries. Indeed, since viscosity is never really equal to zero, there is a ‘no-slip’ boundary condition at any solid boundary: due to the viscous forces, the fluid locally takes the velocity of the solid boundary, at the solid boundary. In fire-related flows, the solid boundaries typically stand still, so that the no-slip boundary condition implies that the fluid velocity equals zero. In fire related flows, boundary layers appear as ‘external’ flows or in ‘internal flows’. ‘Internal’ flows are discussed in the next section. Examples of fire related boundary layers in external flows are: the flow over surfaces (horizontal or vertical) with e.g. flame spread, flow of smoke underneath a ceiling, atmospheric boundary layers in forest fires, etc. An ‘external flow’ is a flow where a ‘free stream velocity’ can be defined, i.e. a velocity that is not affected by the presence of the solid boundary. Both the boundary layer flow itself and the corresponding (convective) heat transfer can be of importance in the context of fire. Consider first the situation of a flow with free stream velocity U1 over a smooth flat plate, without external pressure gradient, schematically shown in Fig. 1.5. At the flat plate, U ¼ 0 (no slip boundary condition), whereas ‘sufficiently far away’ from the plate U ¼ U1. The notion
1
Introduction to Fluid Mechanics
17
Fig. 1.5 Schematic representation of flow over a flat plate (Source: http://www.cortana.com)
‘sufficiently far away’ is related to the thickness of the boundary layer, which can be defined as: y ¼ δ : vx ¼ 0:99U 1 :
ð1:59Þ
In words: the boundary layer thickness δ is the distance from the plate where the velocity equals 99 % of the free stream velocity. Other measures, such as displacement thickness and momentum thickness, can also be used to characterize the boundary layer thickness, but this is not essential for the present discussion. Two flow regions can be defined: • y < δ: Strong velocity gradients and viscous shear stresses; • y > δ: Negligible velocity gradients and viscous shear stresses. From an order of magnitude analysis, in the assumption that δ x, with x the distance from the leading edge of the flat plate, and in the assumption of laminar flow in the boundary layer, it can be shown that the boundary layer thickness grows as: δlam
μx ρU 1
1=2 :
Using x as characteristic distance, the following Reynolds number can be defined:
ð1:60Þ
In words: the laminar boundary layer thickness grows with the square root of the distance from the leading edge. It is thicker as the kinematic viscosity is higher. The latter shows that the influence region of the flat plate is larger for fluids with higher viscosity.
Rex ¼
U1 x : ν
ð1:61Þ
The viscous shear stress at the plate then becomes: ∂vx U1 τs ¼ μ ρν ∂y y¼0 δ 1=2 U1 x ρU 21 : ð1:62Þ ν This can be expressed in a non-dimensional manner, by introducing the friction coefficient: C f,x
τs, x ¼1 2 2ρU 1
U 1 x 1=2 ¼ Re1=2 : x ν ð1:63Þ
The ‘Blasius’ solution for laminar boundary layers over smooth flat plates indeed yields: δlam ¼ 4:92xRe1=2 ; C f , x:lam ¼ 0:664Re1=2 x x ð1:64Þ However, as mentioned, there are inherent instabilities in the convection terms in the Navier–Stokes equations. These instabilities are damped near the flat plate, primarily due to the blocking effect and the viscous forces, so that turbulent vortices (eddies) cannot develop.
18
B. Merci
However, as the laminar boundary layer thickness grows with the distance from the leading edge (Equation 1.60), turbulence can start to develop. There is a critical Reynolds number Rex,crit (Equation 1.61) beyond which there is transition from laminar to turbulent flow. For a smooth flat plate, Rex,crit is in the order of 500.000. As mentioned in the previous section, the momentum (and heat) transfer strongly increase in turbulent motions, as compared to the aligned laminar flow, since momentum (and heat) are transferred on a larger scale through the turbulent eddies. As a result, the surface friction (and heat transfer) increase and the boundary layer becomes thicker. It can be shown that: τs δturb ¼ 0:37xRe1=5 ; C f , x, turb ¼ 1 2 x ρU 1 2 ¼ 0:0592Re1=5 : x
ð1:65Þ
Thus, a turbulent boundary layer grows more rapidly than a laminar boundary layer. Before discussing the turbulent boundary layer in more detail, it is worth mentioning that, very similar to boundary layers at the level of velocities, thermal boundary layers can be defined. Indeed, the thermal diffusivity α plays the same role for heat transfer as the kinematic viscosity ν does for momentum transfer, as mentioned before. The thermal boundary layer thickness is defined as: y ¼ δT : T T s ¼ 0:99ðT 1 T s Þ;
rffiffiffiffi τs ; u* ¼ ρ
ð1:67Þ
and the non-dimensional distance from the solid boundary, expressed in ‘viscous’ units: yþ ¼
yu* : ν
ð1:68Þ
Three regions can be distinguished inside the boundary layer: • Laminar (or ‘viscous’) sub-layer, y+ < 5: very close to the solid boundary, all turbulence is damped (due to blocking effect and viscous forces) and the flow is essentially laminar. The velocity increases linearly with the distance from the solid boundary. • Logarithmic layer, 30 < y+ < 300: the motion is turbulent and there is a logarithmic relation between the mean velocity and the distance from the solid boundary. • Buffer layer: 5 < y+ < 30: transitional region between the laminar sub-layer and the logarithmic layer. It must be stressed that the discussion above refers to smooth surfaces. Roughness on a surface will affect the transition to turbulence and the turbulent boundary layer structures. This can be important, e.g. when the wind load on buildings is considered in built environment or when wind effects are considered in the context of e.g. forest fires. This, however, is considered beyond the scope of the present chapter.
ð1:66Þ
with Ts the surface temperature at the flat plate. The Prandtl number (Equation 1.8) then determines whether the thermal boundary layer is thicker or not than the flow boundary layer: • Pr ¼ 1: δ ¼ δT; • Pr < 1: δ < δT; example: air; • Pr > 1: δ > δT; example: water. Now the turbulent layer is discussed in more detail. Figure 1.6 presents a profile as measured in a pipe (which is in fact an internal flow, see next section), but the boundary layer near the solid boundary is very similar. The results are expressed in a nondimensional manner, introducing the friction velocity:
Internal Flows—Flows in Pipes— Pressure Losses A major difference from the previous section on external flows, is that in internal flows the notion ‘free stream velocity’ does not exist. In fully developed flow conditions, the flow is entirely affected by the presence of the solid boundary and, consequently, by the fluid’s viscosity. The discussion is based here on flows through pipes, since pipes are a common configuration (e.g. water through pipes for sprinklers or water hoses in fire service intervention). Some comments are formulated for flows through ducts in the end.
1
Introduction to Fluid Mechanics
19
35
30
Laminar sublayer
Transition buffer zone
Turbulent core
25
20 u — u*
u
λu log10 ——* v
—= u*
yu 5.75 log10 ——*+ 5.5 v
15
10
u yu* — = —– u* v Nikuradse
5
Reichardt
1
2
3
4
5
yu log10 ——* v
Fig. 1.6 Turbulent velocity profiles as measured in a pipe: different regions in boundary layer
When the entrance region of a smooth pipe is considered, a boundary layer develops from the solid boundary, very similar to what has been described in the previous section. However, since this boundary layer grows on the entire surface, there is a point where the entire crosssection is covered by a ‘boundary layer’. This point determines the ‘entrance length’. From that point onward, the boundary layers do not evolve and the flow becomes fully developed. Depending on the Reynolds number, the flow is again laminar or turbulent. It is clear that the distance from the entrance is not a useful characteristic length, since in fully developed flow conditions, the velocity profiles are independent of that distance. Clearly, the pipe diameter is a useful quantity. At the same time, there is no free stream velocity. A mean velocity Um can be computed from the volume flow rate and the cross-sectional area. Thus, the Reynolds number is now defined as:
When the cross-section is not round, the diameter D is replaced by the hydraulic diameter Dh, defines as four times the cross-sectional area divided by the cross-section perimeter:
Um D : ð1:69Þ ν The critical Reynolds number beyond which the flow becomes turbulent is around Recrit ¼ 2300.
• Friction factor:
Re ¼
Dh ¼
4A : P
ð1:70Þ
It is straightforward to show that for fully developed laminar flows, the following expressions hold (with R ¼ D/2 the radius of the pipe and r the radial distance from the pipe symmetry axis): • Parabolic velocity profile: u r 2 ¼2 1 ; Um R • Wall shear stress (friction): ∂u Um τs, lam ¼ μ ¼ 4μ ; ∂r r¼R R
τs, lam 16 f lam ¼ 1 2 ¼ ; ReD 2ρU m
ð1:71Þ
ð1:72Þ
ð1:73Þ
20
B. Merci 64 Laminar flow f = — R 0.1 0.09
Laminar flow
Critical zone
Transition zone
0.08
Complete turbulence, rough pipes 0.05 0.04
0.07 0.06
0.03 0.02
0.01 0.008 0.006
Rcr 0.03
∈
0.015 0.04
0.004 0.025
0.002
0.02
0.015
0.01 0.009 0.008
Riveted steel Concrete Wood stove Cast iron Galvanized iron Asphalted cast iron Commercial steel or wrought iron Drawn tubing
∈ (ft)
0.003–0.03 0.001–0.01 0.0006–0.03 0.00085 0.0005 0.0004
0.00015 0.000005
0.001 0.0008 0.0006 0.0004
∈(mm)
0.9–9.0 0.3–3.0 0.18–0.9 0.25 0.15 0.12
Relative roughness — D
hL Friction factor f = ————— (Lv 2/D2g)
0.05
0.0002 0.0001 Smooth pipes
0.046 0.0015
0.000,001 0.000,005
0.000,05
0.000,01 7 9 103 2(103) 3 4 5 6 7 9 104 2(104) 3 4 5 6 7 9 105 2(105) 3 4 5 6 7 9106 2(106) 3 4 5 67 9 107 2(107) 3 4 5 67 9 108 vD Reynolds number R = —– v
Fig. 1.7 Moody diagram
• Pressure loss over a distance L in the pipe: 1 4L Δ plam ¼ f lam ρU 2m : 2 D
ð1:74Þ
Note that the pressure loss is linear with the length of the pipe and, with Equation 1.73, linear with the mean velocity and inversely proportional with the square of the pipe’s diameter. Recall that this is only true for laminar flows. For turbulent flows, the expressions become more complex. The velocity profile can be approximated as: u U max
r 1=7 Um : ¼ 1 , Umax ¼ R 0:817
ð1:75Þ
Expression (1.74) still holds for the pressure losses, but the friction factor is no longer obtained from Equation 1.73. The Moody diagram [14] (Fig. 1.7) reveals that, for large enough Reynolds number, the friction factor is determined by the relative roughness of the pipe, independent of the Reynolds number. As a consequence, for turbulent flows, the
pressure loss is still linear with the length of the pipe, but proportional to the mean velocity squared and inversely proportional with the pipe diameter. In duct flows, essentially the same reasoning holds. The major difference is in the values for the friction factor f, important to estimate pressure losses. Secondary flows appear in the corners of duct, transporting momentum from the center to the corners and leading to a relative increase in velocity near the corners. It is instructive to quantify pressure losses for internal flows as: 1 Δ pL ¼ CL ρU 2m : 2
ð1:76Þ
The loss coefficient CL must be defined, depending on the situation (geometry and flow type—laminar/turbulent). All pressure losses must be accounted for in the design. This holds for e.g. the design of the piping system for sprinklers (i.e. what pump must be chosen) or the design of a smoke extraction system
1
Introduction to Fluid Mechanics
21
(i.e. what extraction fans are required to overcome all pressure losses, including the ones in the exhaust system). Some examples are briefly mentioned here: • Straight sections: Moody diagram, see above. • Curves/bends: CL is determined by the total angle and the radius of the bend (e.g. CL ¼ 0.14 for an angle of 90o with radius 2D, but it is about 1.2 for the same angle of 90o but with radius ¼ 0, i.e. a sharp bend). Curves and bends are always important to consider in calculations of pressure losses. 2 • Sudden pipe expansion: CL ¼ 1 AA12 . A special case concerns the flow into a large space, i.e. A2 ! 1. Then CL ¼ 1. • Sudden pipe constriction: the flow is constricted and then widens again behind the constriction. A good estimate for a sudden constriction is CL ¼ 0.5, while CL goes down to 0 for a very gentle constriction. • Flows through openings: CL primarily depends on the edges of the opening. The most typical situation is that the edges are Sharp. In that case CL typically varies between the values CL ¼ 0.4 and CL ¼ 0.7.
V
1 Static pressure hole
(p1 – p)
Fig. 1.8 Sketch of Pitot tube
principle of a Pitot tube. The flow is stagnated. By measuring the pressure increase cause by this stagnation, the velocity can be computed. Indeed, applying Bernoulli’s Equation 1.77 at constant height z yields: 1 1 ptot þ ρ02 ¼ pstat þ ρv2 ) v ¼ 2 2
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ð ptot pstat Þ : ρ
ð1:78Þ
Bernoulli Equation The Bernoulli equation is of fundamental importance. The equation, valid on any streamline, has been developed for incompressible flows (liquids). Yet, it can also be applied to low-Mach number flows where the density hardly changes (gas flows in fire related flows, as long as the density along the streamline does not vary strongly). With the notation now that z is the height (i.e. the z-direction is vertically upward), Bernoulli’s equation reads: 1 p þ ρv2 þ ρgz ¼ const: 2 A few application mentioned.
examples
ð1:77Þ are
Application Example 2: Venturi Flowrate Meter Figure 1.9 shows the basic principle of a Venturi meter. It is essentially a converging cone, from which the flowrate through a pipe can be calculated. Indeed, applying Bernoulli’s Equation 1.77 at constant height z yields: 1 1 p1 þ ρv21 ¼ p2 þ ρv22 : 2 2
ð1:79Þ
Conservation of mass allows elimination of v1: v1 ¼ v2 AA21 . Insertion in Equation 1.80 and introducing V_ ¼ v2 A2 yields: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2A21 ð p1 p2 Þ : V_ ¼ A2 ρ A21 A22
ð1:80Þ
briefly
Application Example 1: Velocity Measurement with a Pitot Tube Figure 1.8 shows the basic
Application Example 3: Flow Out of a Large Tank Figure 1.10 sketches the situation. A large tank is considered, so that the liquid surface can be approximated as standing still, i.e. v1 ¼ 0.
22
B. Merci
P1, V1
sffiffiffiffiffiffiffiffiffi 2Δ p : V_ ¼ Cd A ρ
P2, V2
ð1:82Þ
This can be interpreted as a ‘correction’ to the cross-section area that is effectively used for outflow (or inflow). For an orifice, the value of Cd is around 0.6 for e.g. open doors or windows, going up to about 0.7 for flows through small gaps [10]. Finally, it is mentioned that, when pressure losses are considered (see previous section), Bernoulli’s equation can be extended to:
Manometer
1 1 p1 þ ρv21 þ ρgz1 ¼ p2 þ ρv22 þ ρgz2 2 2 þ Δ pL, 12 : ð1:83Þ
Fig. 1.9 Sketch of Venturi meter
In Equation 1.84, the final term reflects the pressure loss between points 1 and 2 on the streamline.
p1V1 1
Z p2,V2
z1
Wind
2
z2 Datum
Fig. 1.10 Outflow out of a large tank
Approximating p1 ¼ p2 ¼ patm, the flow is generated by the gravity force: pffiffiffiffiffiffiffi 1 2 ρv2 ¼ ρgz ) v2 ¼ 2gz: 2
ð1:81Þ
The assumption p1 ¼ p2 ¼ patm is a reasonable assumption if the tank is open and if the liquid density is much higher than the density of air (the latter is practically always fulfilled). Application Example 4: Flow Through an Orifice In the previous example, the pressure driving the fluid out of the tank stems from gravity. In general, the pressure difference (Δp) over an opening determines the flow through the opening. From the (mean) velocity and the cross-sectional area (A) of the opening, the volume flow rate through that opening can be computed. A discharge coefficient Cd is introduced, though:
Wind is an important factor in fire protection engineering. An obvious example is the effect of wind on the development of forest fires, where convection strongly affects the direction and speed of fire spread. Another examples concerns smoke and heat control (SHC) in case of fire inside a building, where wind will exert a pressure load onto the building. The distribution of the load (positive and negative) affects the performance of the SHC system. The wind can also induce internal flows into the building, depending on leakages or open windows or doors. It is common practice to consider steady wind conditions. Clearly, wind gusts can have an impact in the course of the fire. This is not considered in the discussion below.
Natural Wind Characteristics A classical method to characterize the boundary layer, when there is no detailed information of surface roughness, is the use of a power law:
1
Introduction to Fluid Mechanics
23
Fig. 1.11 Schematic representation of wind flow, interacting with a tall building
–
Plan
Rear
Eddy
Wind
+
–
–
S Side
vðzÞ ¼ v zre f
z zre f
α
:
ð1:84Þ
The exponent α is given the value α ¼ 1/7 for ‘smooth’ surfaces. This is related to turbulent boundary layer velocity profiles. Other values apply for ‘rough’ surfaces, i.e. when ‘obstacles’ such as trees or buildings disturb the boundary layer. An alternative option is then the use of a log law expression: v* z vðzÞ ¼ ln : ð1:85Þ zo κ In expression (1.86), v* is the friction velocity Equation 1.67, κ is the von Karman coefficient (κ ¼ 0.4) and zo is the aerodynamic roughness length. The reader is referred to specialized literature for more details (e.g. [15]).
Interaction of Wind with Buildings It is well-known that wind, impinging in a perpendicular direction onto a rectangular building, causes over-pressure on the windward side and
Wake
under-pressure on all other sides (including the roof). This is illustrated in Fig. 1.11. This pressure load distribution affects the performance of SHC systems and can cause internal flows (e.g. through open windows or doors), as mentioned. However, it must be stressed that Fig. 1.11 is a strong simplification of reality. Not only is the wind assumed steady and perpendicular to one side of the building, it is also not supposed to be affected by the environment. In reality, tall buildings are situated in a built environment, so the oncoming wind profile need not obey expressions like (1.85) or (1.86) and need not be unidirectional. For obvious reasons, the direction of the oncoming wind, even if not disturbed by the environment, varies in time, depending on atmospheric pressure distributions. Finally, modern buildings are not necessarily rectangular in shape. All these factors indicate the need for either smallscale wind tunnel experiments or extensive CFD studies. For the time being, since it is necessary to consider many wind directions and velocities and the (built) environment can be complex and hard to characterize as boundary conditions in CFD simulations, wind tunnel experiments seem
24
B. Merci
preferable. The model scale can then be built on a table that can be turned around in the wind tunnel to examine various angles of oncoming wind. To finalize this section, it is recalled that wind-induced over-pressure and under-pressure are proportional to the wind velocity squared. This is to be expected from Bernoulli’s equation 1.77. Clearly, the flow does not stagnate entirely over the entire surface and thus pressure coefficients are introduced: 1 Δ pw ¼ Cw ρamb v2w : 2
ð1:86Þ
The wind coefficient can be positive (overpressure at the windward side) or negative (under-pressure). In e.g. [16] more info is found on this topic.
Nomenclature Av Cp Cv D Eav L m Mliq P R s T td u V WTNT Xf Xg
Vent area (m2) Specific heat at constant pressure (kJ. kg1.K1) Specific heat at constant volume (kJ. kg1.K1) Fireball diameter (m) Total expansion energy (kJ) Latent heat of vaporization (kJ.kg1) Flammable mass (kg) Liquid mass (kg) Pressure (Pa) Distance from explosive material (m) Specific entropy (kJ.kg1.K1) Temperature (K) Duration of the fireball (s) Internal energy (kJ.kg1) Vessel volume (m3) Equivalent mass of TNT (kg) Mass fraction of the initial liquid mass that flashes to vapor Mass fraction of the initial vapor mass that does not condense during expansion
Greek Symbols β
Fraction of energy released converted into the blast wave.
γ
Ratio of specific heats γ ¼
ν ρ
Specific volume (m3.kg1) Density (kg.m3)
Cp Cv
Subscripts atm gas liq
Atmospheric Gas Liquid
References 1. G.K. Batchelor (1967) An introduction to fluid dynamics, Cambridge University Press. 2. H.D. Baehr (1978) Thermodynamik, Springer Verlag. 3. A. Bejan (1993) Heat transfer, John Wiley and Sons. 4. W.M. Rohsenhow, J.P. Hartnett and E.N. Ganic´ (1985), Handbook of Heat Transfer Fundamentals (2nd ed.), McGraw–Hill Book Company. 5. K.K. Kuo (1986) Principles of combustion, John Wiley and Sons. 6. T. Poinsot and D. Veynante (2001) Theoretical and numerical combustion, Edwards. 7. P.A. Libby and F.A. Williams (1980) Turbulent reacting flows, Springer Verlag. 8. N. Peters (2000) Turbulent combustion, Cambridge University Press. 9. G. Cox (1995) Combustion fundamentals of fire, Academic Press. 10. B. Karlsson and J.G. Quintiere (2000) Enclosure fire dynamics, CRC Press. 11. J.G. Quintiere (2006) Fundamentals of fire phenomena, John Wiley and Sons. 12. H. Tennekes and J.L. Lumley (1972) A first course in turbulence, MIT Press 13. S.B. Pope (2000) Turbulent flows, Cambridge University Press. 14. L.F. Moody (1944), “Friction factors for pipe flow”, Transactions of the ASME 66 (8): 671–684. 15. B. Blocken and J. Carmeliet (2004) “Pedestrian wind environment around buildings: Literature review and practical examples.” Journal of Thermal Envelope and Building Science 28(2): 107-159. 16. J.H. Klote and J.A. Milke (2002) Principles of smoke management, American Society of Heating, Refrigerating & Air-Conditioning Engineers, Inc. Bart Merci is a Professor at Ghent University (Belgium). He is Head of the research unit “Combustion, Fire and Fire Safety”. Having completed a PhD (Ghent University, 2000) on turbulence modeling in CFD simulations of nonpremixed combustion, he is an expert in fluid mechanics aspects in reacting flows, more particularly related to fire and smoke dynamics.
2
Conduction of Heat in Solids Ofodike A. Ezekoye
Introduction Heat transfer is an area of thermal engineering that focuses on the transport, exchange, and redistribution of thermal energy. The three modes or ways that heat can be transferred have been termed conduction, convection, and radiation. In this chapter, the basic physics associated with conduction heat transfer will be presented, and it will be shown through examples how the tools and analysis typically used for conduction problems can be applied to design and analysis when fire occurs. Conduction heat transfer only occurs in a medium. This is a distinction between conduction and radiation, which does not require a medium. The medium or state of matter in which conduction takes place can be a gas, liquid, or solid. The distinction between conduction and convection heat transfer is associated with whether the medium has some ordered flow or bulk motion. Heat transfer, when there is a mass averaged velocity, is termed convection. Heat transfer that takes place in a stationary frame of reference is called conduction. More details will be presented on the mechanisms that allow heat transfer to occur in a stationary medium as we proceed through this discussion. Solutions will be provided for selected configurations and O.A. Ezekoye (*) Department of Mechanical Engineering, University of Texas at Austin, ETC 7.130, MS C2200, TX 78712, Austin
scenarios. The treatise of Carslaw and Jaeger [1] covers most solutions for conduction phenomena. Other useful texts that discuss conduction phenomena are readily available [2, 3]. It is useful to build up this discussion by first identifying where conduction heat transfer ties into overall energy conservation and energy transfer.
Energy Conservation The fundamental laws that allow us to analyze and predict fire phenomena are often termed conservation laws. Conservation laws are essentially balance equations that allow us to model how variables that describe the physical world dynamically evolve. In fire systems, we typically model the physical world using mass conservation, momentum conservation, energy conservation, and chemical species conservation. For this chapter, we are interested in describing how heat is transferred in media that are not deforming (i.e., are in rigid body motion with no unbalanced forces) or reacting (fixed chemical species and mass). We do assume, however, that the medium can possibly have heat transferred to it either through interactions with its surrounding or through some other energy input into it. Also, we assume that the medium may have different amounts of thermal energy stored within it at different locations. To more precisely describe energy transfer processes, we rely on the first law of thermodynamics. The energy conservation principle is the basis for heat transfer.
M.J. Hurley (ed.), SFPE Handbook of Fire Protection Engineering, DOI 10.1007/978-1-4939-2565-0_2, # Society of Fire Protection Engineers 2016
25
26
O.A. Ezekoye
Thermodynamic Properties The first law of thermodynamics is a statement of energy conservation [4, 5]. It states that the change in energy for an identifiable set of matter can only result from heat transferred across the material’s boundary or work done either by or on the material. The thermodynamic property or energy function that best describes the molecular, atomic, electronic, and nuclear energy of a material is the internal energy. In terms of the internal energy, U, the first law is dU ¼ Q_ net, in þ W_ net, in dt U is the internal energy, Q is heat added to the system and W is work done on the system. The total internal energy U is a system integrated value that represents the total thermal energy of the material system of interest. We can describe the local internal energy in terms of a mass specific internal energy, u, that is simply the total internal energy, U, for a region of matter divided by the mass of that region. The internal energy, like any other thermodynamic variable can be defined in terms of other thermodynamic variables. There is an approximation used in thermodynamics that states that the internal energy for an incompressible material can be specified in terms of the temperature. The thermodynamic property specific heat capacity at constant volume, cv, relates differential changes in the mass specific internal energy to differential changes in temperature. cv ¼
du and mcv dT ¼ dU dT
The mass is defined as the product of density and volume. The control-mass statement of the first law for a case with no net work done becomes: ρVc
dT ¼ Q_ net, in dt
This form of the first law neither provides information about spatial variations in energy within the medium nor describes how energy is transferred. Experience tells us that the heat transfer into some identifiable mass element likely depends on temperature differences. It will be
necessary to define the heat transfer rate in terms of temperature differences. The empirical law defining the heat transfer rate to a body immersed in a fluid is called Newton’s law of cooling. When Newton’s law of cooling is used, the heat transfer rate to the body is Q_ net, in ¼ hAðT T 1 Þ If we apply Newton’s law of cooling to the first law, we arrive at a result called the lumped thermal approximation in conduction analysis.
Lumped Thermal Analysis Briefly, the lumped thermal approximation allows one to model the overall transient thermal response of a body at some initial temperature subjected to either a change to the external fluid temperature or as a result of some local heating within the object. The validity of this approximation will be discussed in more detail in later sections. For the purposes of this discussion, we will say that the approximation is valid when the time scales for internal energy transfer and subsequent homogenization of the temperature field within an object are much smaller than the time scales for energy transfer from the surface of the body to an external thermal reservoir. In short, the lumped thermal approximation is reasonable when temperature differences within a body are relatively small when compared to temperature differences between the surface of the body and a characteristic temperature of the exterior fluid. It can be shown that a nondimensional heat transfer parameter called the Biot number (Bi) which represents the ratio of the internal conductive resistance to the external convective resistance should be small for the lumped thermal approximation to be valid. A mathematical statement of the energy equation in the lumped approximation is (Fig. 2.1): dT hc A ¼ ðT T 1 Þ dt ρVc This first order ordinary differential equation can be integrated and one form of the solution is: T Te ¼ eðhc A=ρVcÞt ¼ et=tc T0 Te
2
Conduction of Heat in Solids
27
heat transfer coefficient is proportional to the fluid velocity h ¼ Cu1=2 . This results in: tACT u1=2 ρLc ¼ RTI ¼ T0 Te C ln T ACT T e Fig. 2.1 Schematic showing convective flow over an object that will be analyzed using a lumped thermal approximation
This combination of parameters is the well known response time index for sprinklers.
Fourier’s Law of Conduction In the above, T0 is the initial temperature of the body and Te is the external fluid temperature surrounding the object. There is a characteristic time in the problem defined as: tc ¼
ρVc hA
The characteristic time provides an estimate of the time required for the nondimensional temperature to relax to its steady value. This relatively simple solution is useful in characterizing a large number of important problems in fire systems [6]. Example 1 The lumped thermal approximation is frequently used to analyze the response of a sprinkler head as it activates due to a change in the environment temperature because of a fire. A sprinkler head fuse can be modeled as a cylinder of diameter 4 mm and length 12 mm. The density can be approximated as being 1000 kg/m3. The specific heat capacity is approximately 1 kJ/kgK. The heat transfer coefficient of the smoke gases is 20 W/m2K. If the smoke gases are 200 C and the fuse is initially at 20 C, how long will it take for the fuse to open if the activation temperature is 80 C? The solution is arrived at from inverting: T Te ¼ eðhc A=ρVcÞt ¼ et=tc T0 Te tACT ¼
ρLc T0 Te ln hc T ACT T e
For the values that we specified, we find that the fuse opens in 243 s. Chapter 3, shows that the
As previously noted, the lumped approximation does not allow one to predict the spatial variation of temperature within a body. In some sense, it provides an average or lumped temperature response. To be able to predict the spatial variation of temperature, it is necessary to introduce another physical law that models how heat is transported when temperatures differences exist within a body. We expect heat to flow across a body in proportion to the temperature difference across the body, and perhaps inversely related to the distance across the body. Fourier’s law states that the heat flux is proportional to the temperature gradient (the spatial derivative of the temperature). For a one dimensional homogeneous and isotropic object this reduces to the simple expression: q} ¼ k
dT dx
We use the notation q00 to indicate a heat transfer rate per unit area. The proportionality between the heat flux and the spatial derivative of temperature is the thermal conductivity.
Thermal Conductivity For materials like air, water, glass, and copper, the thermal conductivity is isotropic (i.e., does not depend on orientation), but it has a temperature dependence. Under conditions in which the overall thermal conductivity difference across the body is small relative to the any particular value of the thermal conductivity in the body, we
28
O.A. Ezekoye
can consider k to be essentially a constant. In fire applications, this is often not the case, but for the sake of analysis we will often use this approximation when generating analytical solutions. There are materials for which the thermal conductivity depends both on the local temperature and also on the orientation. In contrast to isotropic materials for which there is no directional effect, anisotropic materials have this directional dependence. The most commonly encountered anisotropic material in fire applications is wood. The grain structure of wood is the source of the anisotropy. Practically, we would find that for the same temperature difference across a given thickness of wood, the heat transfer rate depends on whether this temperature difference is aligned with the grains or aligned perpendicular to the grains. Of course, as one heats wood, there are also chemical changes to the wood. So, the thermal conductivity depends on the temperature, composition, and orientation. For a simple analysis, the effects of decomposition are often neglected for the initial ignition process. Again, Fourier’s law states that the heat flux !00
vector, q , is proportional to the temperature gradient, where the proportionality constant is the thermal conductivity, k. In general, k is a second order tensor and has different values depending on the face and orientation of a differential volume [1–3]. For a general anisotropic material 2 3 kxx kxy kxz 00 ! q ¼ 4 k yx k yy k yz 5∇T kzx kzy kzz This suggests that the component of the heat flux vector in the x-direction depends on all components of the temperature gradient. ∂T ∂T ∂T þ kxy þ kxz qx ¼ kxx ∂x ∂x ∂x For some materials that are frequently dealt with in fire analyses, such as wood, there is some simplification in the dependence of thermal conductivity on orientation. Laminates like wood are said to be orthotropic. For an orthotropic material, the off-diagonal elements of the thermal conductivity tensor are zero and the diagonal elements are not equal to each other.
2
kxx k¼4 0 0
0 k yy 0
3 0 0 5 kzz
For metals, many crystalline solids, many amorphous solids, liquids, and gases, the conduction process is considered to take place in an isotropic medium. For such materials, the thermal conductivity can vary spatially and with temperature, but does not have an orientation effect. 2 3 1 0 0 k ¼ kðT ðx; yÞÞ4 0 1 0 5 0 0 1
Homogeneous Systems Most obvious in gases, it is known that random molecular motion transfers heat from hot molecules to cooler ones. For solids other wave like effects are important. There is a relatively simple theory that describes the physics of thermal conductivity. Conduction heat transfer can be thought of in terms of a carrier particle with a characteristic velocity and characteristic length scale over which it acts. The development of this perspective of thermal conductivity, based on the properties of notional particles is described by Kaviany [7, 8]. In some sense, this description is a simple generalization of the kinetic theory description of thermal conductivity for gases. For gases, we understand that the kinetic theory of gases describes how k varies in terms of a characteristic gas velocity, u, the number density of molecules, n, the mean free path, l, and the molecular internal energy described by the molecular mass and heat capacity (mc). 1 k ffi mcv nul 3 In the following table adapted from Kaviany [7, 8], the characteristic parameters for various types of conduction systems are provided (Table 2.1). Examples of Homogenous Materials In fire analysis, most solid materials are approximated as being homogeneous. Examples of homogeneous systems in fire applications are
2
Conduction of Heat in Solids
29
Table 2.1 Characteristic quantities used in microscale carrier model of conduction
Regimes
Fluid particle (random motion) Dilute gases
Mean free path Carrier concentration Carrier speed
Interparticle spacing Fluid density Thermal speed
Microscale carrier
Phonon (quantal lattice vibration)
Electron
Acoustic phonon and optical phonon Lattice dimension Solid density Speed of sound
Free electrons and valence electrons Lattice dimension Free electron density Electron drift velocity
Fig. 2.2 Range of thermal conductivities for different materials (Adapted from [2])
simple polymeric materials, metals, and various types of insulating materials (Fig. 2.2).
Composite Systems Treatment of composite material thermal conductivity is somewhat more complicated than the treatment for homogeneous materials. With increased use of composite materials like polymer impregnated concrete as structural components, it is useful to discuss how to construct an effective thermal conductivity for such materials. The key to constructing an effective thermal conductivity is to develop a meaningful way to average the thermal properties for the system. A representative averaging volume is the term used to describe the volume over which one can meaningfully average the properties of the composite in order to properly thermally characterize the material. The simplest treatments of composite media thermal conductivity use either series or parallel
resistance models. For a mixed medium that is comprised of several different conducting elements, the parallel approximation provides an upper bound on an effective thermal conductivity, while the series approximation provides a lower bound. Examples of Composite Materials Examples of composite materials include many types of insulating materials in which at least two types of materials are mixed in various mass fractions. The mass or volume fractions of the constituents can then be used along with their individual conductivities to define an effective conductivity for the system. Various mixing rules have been developed for the effective thermal conductivity. Gebhart [9] discusses a general way of classifying the effective thermal conductivity of a binary system comprised of a matrix material a and added material b as:
30
O.A. Ezekoye
ke kb Li ¼ f ; Φb ; ; Bi : ka ka L Depending on the ratio of the thermal conductivities, the ratios of the characteristic lengths of the a and b segments within the medium, and the relative volumetric ratios, different correlations exist for the effective conductivity. Kaviany [7] presents a correlation for the effective conductivity for random porous solids (e.g., continuous solid and fluid phases) as might occur for a wound insulation material, hk i ¼ kf
0:2800:757 logðεÞ0:057 logðks =k f Þ ks kf
which is valid for fluid porosity (volume fraction) in the range of 0:2 < ε < 0:6.
Heat Equation Formulations The heat equation is the name given to the differential equation that models heat conduction in materials. The heat equation is most generally developed in a three dimensional, unsteady form. Depending on the scenario of interest, it is not always necessary to solve the full formulation of the heat equation. By formulating an appropriate reduced form of the heat equation, one can generally compute an accurate representation of the temperature profile and heat flux distribution in the material. In the following sections, several reduced model forms for the heat equation will be discussed.
Steady One Dimensional Models Under conditions in which there is a primary heat transfer direction, it is appropriate to formulate a one-dimensional form of the heat equation. Further, when the time scale for changes in boundary conditions and sources are large relative to the time scale over which the thermal system equilibrates, the analysis can be treated as being steady. A discussion of how to define the time to equilibrate in conduction systems will follow in a later section.
Fig. 2.3 Schematic of differential volume in which steady one dimensional heat equation is developed
Q
Q
x
x
x+Δx
x + Δx
To develop the one dimensional conduction model, we consider an elemental volume, ΔV, located between spatial locations x and x + Δx for a heat transfer process that is in steady state. We can apply the first law of thermodynamics to the elemental volume and consider a case in which there is no internal generation (Fig. 2.3). Q = Q x
x+Δx
= Constant
dT Q = q″A = −kA dx d dT kA =0 dx dx
Application of Fourier’s law leads to an energy equation specified in terms of temperature gradients defined within the solid. The solution can be found by simple integration. If the thermal conductivity, k, is nearly constant over the temperature range of interest to the problem, then we see that a very simple relationship holds between the temperature difference across the solid, the thermal conductivity, and the thickness of the solid. It is apparent that an analogy holds between this form and Ohm’s law, where the heat transfer rate is identified as a current, the temperature difference, ΔT is identified as a potential change, and L/kA is identified as a generalized resistance.
Cylindrical Shells This same type of analysis can be formulated for cylindrical shells. The difference in the analysis is that the cylindrical shell has variable surface area (Fig. 2.4). Applying Fourier’s law over concentric cylindrical elements yields dT Q_ ¼ Aq ¼ 2πrL k dr
2
Conduction of Heat in Solids
Similar to the development for the planar slab geometry, an effective resistance can be defined for the cylindrical system. Integrating the equation twice yields: 2πkLðT 1 T 2 Þ Q_ ¼ lnðr 2 =r 1 Þ We can extract a resistance from this expression to be: R¼
lnðr 2 =r 1 Þ 2πkL
Fin Approximation The fin approximation refers to one dimensional conduction analysis where heat transfer has a predominant direction, there is no transverse temperature gradient, and the heat transfer in the transverse direction is simply defined through Newton’s law of cooling. The simplest example of use of the fin approximation is in the development of the pin fin model. A pin fin is slender rod of length L and diameter D with convective heat transfer taking place over most of the rod’s
Fig. 2.4 Schematic of cylindrical shell in which one dimensional, steady cylindrical formulation of heat equation is developed
31
surface. At least one end of the rod is assumed to be fixed at a temperature different from the environmental fluid temperature. For one dimensional heat transfer to be valid, the length of the fin divided by the diameter should be large and a Biot number Bi ¼ hD/k for the fin should be small. In a fire scenario, a fully exposed beam might be modeled as being a fin [10]. Development of the pin fin equation begins with a power balance on a differential section of the fin, as shown below (Fig. 2.5). One dimensional analysis (radially lumped) is valid when d/L 20 μm What is its total irradiation?
Surface Properties Thermal radiation may be absorbed at, reflected by, or transmitted through a surface. Imprecisely, absorptivity (α) is the fraction absorbed at the surface, reflectivity (ρ) is the fraction reflected by the surface, and transmissivity (τ) is the fraction transmitted through the surface. It follows from a radiation balance: αþρþτ ¼1
ð4:19Þ
where each property in Equation 4.29 may exhibit spectral and directional characteristics
110
Revised by C. Lautenberger
(but such dependency is not explicitly shown). Additionally, emissivity (ε) is the ratio of the actual amount of radiation emitted by a surface to the maximum possible amount of radiation that could be emitted by that surface if it was a blackbody. These properties are defined more precisely in the sections that follow.
ελ ðλ; T Þ ¼
εð T Þ ¼
ελ ðλ; θ; ϕ; T Þ ¼
I λ, e ðλ; θ; ϕ; T Þ I λ, b ð T Þ
ð4:20Þ
As described earlier, hemispherical radiation quantities are usually applied in engineering applications. The spectral hemispherical emissivity is defined in terms of the blackbody emissive power at wavelength λ and is obtained by integrating Equation 4.20 over all directions with the result:
ð4:21Þ
Spectral normal emissivity (very close to hemispherical emissivity) is shown for several materials in Fig. 4.5 [4]. Total emissivity is obtained by integrating Equation 4.21 over all wavelengths:
Emissivity Since no surface can emit more thermal radiation than a blackbody, a logical tool for normalizing thermal emission from real surfaces is the blackbody. Spectral surface emissivity is defined as the ratio of the actual spectral intensity of radiation emitted by a surface to the blackbody spectral intensity:
Eλ ðλ; T Þ Eλ, b ðλ; T Þ
Eð T Þ Eb ð T Þ
ð4:22Þ
By definition, the emissivity of a blackbody (whether ελ(λ, θ, ϕ, T ), ελ(λ, T), or ε(T )) is unity. Total normal emissivity (very close to hemispherical emissivity) is shown graphically in Fig. 4.6 for several materials [4]. Representative values of total hemispherical emissivity are tabulated for several materials in Table 4.2 [7] (metals) and Table 4.3 [7] (non-metals).
Absorptivity In a fire, one of the most important radiative characteristics of a material or surface is its absorptivity, defined loosely as the fraction of the incident radiation that is absorbed by the material. The absorptivity is strongly
1
Spectral normal emissivity (-)
0.8 Silicon carbide (1000 K)
0.6
Aluminum oxide (1400 K)
0.4
Stainless steel (1200 K) heavily oxidized
0.2
Stainless steel (800 K) Tungsten (2800 K) lightly oxidized Tungsten (1600 K)
0 0.1
1
10 Wavelength (mm)
Fig. 4.5 Spectral normal emissivity of several materials [4]
100
4
Radiation Heat Transfer
111
1 Silicon carbide
Total normal emissivity (-)
0.8 Stainless steel heavily oxidized
0.6
0.4 Aluminum oxide Stainless steel lightly oxidized
0.2
0 300
Tungsten
600
900
1200
1500
1800
2100
Temperature (K)
Fig. 4.6 Total normal emissivity of several materials [4].
Table 4.2 Representative total hemispherical emissivity of several metals [7] Material Aluminum
Bismuth Brass
Chromium Cobalt Copper
Gold
Description Crude Foil, bright Highly polished Ordinarily rolled Oxidized Roughed Unoxidized Unoxidized After rolling Browned Polished Polished Unoxidized Unoxidized Black oxidized Highly polished Molten Matte New Oxidized Polished Rolled Polished Electroytically deposited
Emissivity 0.07–0.08 (0–200 C) 0.01 (9 C), 0.04 (1 C), 0.087 (200 C) 0.04–0.05 (1 C) 0.035 (100 C), 0.05 (500 C) 0.11 (200 C), 0.19 (600 C) 0.044–0.066 (40 C) 0.022 (25 C), 0.06 (500 C) 0.048 (25 C), 0.061 (100 C) 0.06 (30 C) 0.5 (20–300 C) 0.03 (300 C) 0.07 (150 C) 0.08 (100 C) 0.13 (500 C), 0.23 (1000 C) 0.78 (40 C) 0.03 (1 C) 0.15 0.22 (40 C) 0.07 (40–100 C) 0.56 (40–200 C), 0.61 (200 C), 0.88 (540 C) 0.04 (40 C), 0.05 (260 C), 0.17 (1100 C) 0.64 (40 C) 0.02 (40 C), 0.03 (1100 C) 0.02 (40 C), 0.03 (1100 C) (continued)
112
Revised by C. Lautenberger
Table 4.2 (continued) Material Inconel
Inconel X Iron
Lead Magnesium Mercury Molybdenum Monel Nichrome Nickel
Platinum Silver Steel
Stellite Tantalum Tin Tungsten Zinc
Description Sandblasted Stably oxidized Untreated Rolled Stably oxidized Cast Cast, freshly turned Galvanized Molten Plate, rusted red Pure polished Red iron oxide Rough ingot Smooth sheet Wrought, polished Oxidized Unoxidized
Oxidized Oxidized Polished Rolled Sandblasted Electrolytic Oxidized Wire Oxidized Unoxidized Polished Calorized Cold rolled Ground sheet Oxidized Plate, rough Polished Rolled sheet Type 347, oxidized Type AISI 303, oxidized Type 310, oxidized & rolled Sandblasted
Unoxidized Filament Oxidized Polished
Emissivity 0.79 (800 C), 0.91 (1150 C) 0.69 (300 C), 0.82 (1000 C) 0.3 (40–260 C) 0.69 (300 C), 0.88 (1150 C) 0.89 (300 C), 0.93 (1100 C) 0.21 (40 C) 0.44 (40 C), 0.7 (1100 C) 0.22–0.28 (0–200 C) 0.02–0.05 (1100 C) 0.61 (40 C) 0.06 (40 C), 0.13 (540 C) 0.96 (40 C), 0.67 (540 C) 0.95 (1100 C) 0.6 (1100 C) 0.28 (40–260 C) 0.28 (00–200 C) 0.05 (100 C) 0.13 (260 C), 0.18 (310 C) 0.09 (0 C), 0.12 (100 C) 0.78–0.81 (300–540 C) 0.43 (20 C) 0.09 (20 C) 0.36 (800 C), 0.8 (1150 C) 0.81 (800 C), 0.87 (1150 C) 0.04 (40 C), 0.1 (540 C) 0.31–0.39 (40 C), 0.67 (540 C) 0.1 (260 C), 0.19 (1100 C) 0.07 (260 C), 0.11 (540 C) 0.04 (25 C), 0.05 (100 C), 0.15 (1000 C) 0.01 (40 C), 0.02 (260 C), 0.03 (540 C) 0.5–0.56 (40–540 C) 0.08 (100 C) 0.61 (1100 C) 0.79 (260–540 C) 0.94–0.97 (40–540 C) 0.07 (40 C), 0.1 (260 C), 0.14 (540 C), 0.23 (1100 C) 0.66 (40 C) 0.87–0.91 (300–1100 C) 0.74–0.87 (300–1100 C) 0.56 (800 C), 0.81 (1150 C) 0.82 (800 C), 0.93 (1150 C) 0.18 (20 C) 0.19 (1300 C) 0.04–0.05 (25–100 C) 0.18 (40 C), 0.11 (540 C), 0.39 (2800 C) 0.11 (260 C) 0.02 (40 C), 0.03 (260 C)
4
Radiation Heat Transfer
Table 4.3 Representative total hemispherical emissivity of several non-metals [7] Material Bricks
Building materials
Carbon
Ceramics
Cloth
Emissivity 0.94 (540 C), 0.98 (1100 C) Fire clay 0.75 (1400 C) Light buff 0.8 (540 C) Magnesite refractory 0.38 (1000 C) Sand lime red 0.59 (1400 C) Silica 0.84 (1400 C) Various refractories 0.71–0.88 (1100 C) White refractory 0.89 (260 C), 0.68 (540 C) Asbestos, board 0.96 (40 C) Asphalt pavement 0.85–0.93 (40 C) Clay 0.39 (20 C) Concrete, rough 0.94 (0–100 C) Granite 0.44 (40 C) Gravel 0.28 (40 C) Gypsum 0.9 (40 C) Marble, polished 0.93 (40 C) Mica 0.75 (40 C) Plaster 0.89 (40 C), 0.48 (540 C) Quartz 0.76 (40 C) Sand 0.83 (40 C) Sandstone 0.83 (40 C) Slate 0.67 (40–260 C) Baked 0.52–0.79 (1000–2400 C) Filament 0.95 (260 C) Graphitized 0.76–0.71 (100–500 C) Rough 0.77 (100–320 C) Soot (candle) 0.95 (120 C) Soot (coal) 0.95 (20 C) Unoxidized 0.8 (25–500 C) Alumina coating 0.65 (430 C), 0.45 on inconel (1100 C) Zirconia coating 0.62 (430 C), 0.45 on inconel (1100 C) Earthenware, glazed 0.9 (1 C) Earthenware, matte 0.93 (1 C) Procelain 0.92 (40 C) Refractory, black 0.94 (100 C) Refractory, light buff 0.92 (100 C) Refractory, white 0.9 (100 C) Al2O3 Cotton 0.77 (20 C) Silk 0.78 (20 C)
113
Material Glass
Description Chrome refractory
Description Convex D Fused quartz Nonex Pyrex Smooth
Ice Oxides
Waterglass Smooth Al2O3 C2O Cr2O3 Fe2O3 MgO NiO ZnO
Paints
Paper Roofing materials
Aluminum Enamel, snow white Lacquer Lampblack Oil White White Aluminum surfaces Asbestos cement Bituminous felt Enameled steel, white Galvanized iron, dirty Galvanized iron, new Roofing sheet, brown Roofing sheet, green Tiles, uncolored Tiles, brown Tiles, black Tiles, asbestos cement Weathered asphalt
Emissivity 0.8–0.76 (100–500 C) 0.75–0.8 (100–500 C) 0.82–0.78 (100–500 C) 0.8–0.9 (40 C) 0.92–0.95 (0–200 C) 0.96 (20 C) 0.92 (0 C) 0.35–0.54 (850–1300 C) 0.27 (850–1300 C) 0.73–0.95 (850–1300 C) 0.57–0.78 (850–1300 C) 0.29–0.5 (850–1300 C) 0.52–0.86 (500–1200 C) 0.3–0.65 (850–1300 C) 0.27–0.7 (1–100 C) 0.91 (40 C) 0.85–0.93 (40 C) 0.94–0.97 (40 C) 0.89–0.97 (0–200 C) 0.89–0.97 (40 C) 0.95 (40 C), 0.82 (540 C) 0.22 (40 C) 0.65 (1400 C) 0.89 (1400 C) 0.65 (1400 C) 0.90 (1400 C) 0.42 (1400 C) 0.8 (1400 C) 0.87 (1400 C) 0.63 (1400 C) 0.87 (1400 C) 0.94 (1400 C) 0.66 (1400 C) 0.88 (1400 C) (continued)
114
Revised by C. Lautenberger
Table 4.3 (continued) Material Rubber
Description Hard, black, glossy Soft, gray Fine Frost Granular Black loam Plowed field
Snow
Soils Water Wood
Beech Oak, planed Sawdust Spruce, sanded
Emissivity 0.95 (40 C) 0.86 (40 C) 0.82 (10 C) 0.98 (0 C) 0.89 (10 C) 0.66 (20 C) 0.38 (20 C) 0.92–0.96 (0–40 C) 0.91 (70 C) 0.91 (40 C) 0.75 (40 C) 0.82 (100 C)
Spectral hemispherical absorptivity, a directionally-averaged property that is obtained by integrating over all incident angles, is the ratio of the spectral irradiation absorbed by the surface (Gλ,abs) to the spectral irradiation of the surface Gλ: ð 2π ð π=2
Iλ, i, abs ðλ; θ; ϕÞ cos ðθÞ sin ðθÞdθdϕ αλ ðλÞ ¼ 0ð 2π 0ð π=2 Iλ, i ðλ; θ; ϕÞ cos ðθÞ sin ðθÞdθdϕ 0
0
Gλ, abs ðλÞ ¼ Gλ ðλÞ
ð4:24Þ wavelength–dependent. For example, at wavelengths below 1 μm the absorptivity of clear Polymethylmethacrylate is close to zero, but at wavelengths above 3 μm it approaches unity. A blackbody absorbs all incident radiation with no spectral or directional dependency. As with emissivity, the idealized blackbody behavior is used as a normalization tool to quantify the amount of radiation absorbed by a surface relative to the maximum possible amount the surface may absorb (i.e., if it was a blackbody). Spectral radiant intensity incident on a surface is denoted Iλ,i; it is, in general, a function of λ, θ, and ϕ. Spectral, directional absorptivity is the ratio if the spectral directional radiant intensity absorbed by a surface Iλ,i,abs(λ, θ, ϕ) to the spectral directional radiant intensity incident on that surface Iλ,i(λ, θ, ϕ) (because the latter is the maximum possible radiation that could be absorbed by that surface, i.e. if it was a blackbody): αλ ðλ; θ; ϕÞ ¼
ð1 αðT e Þ ¼
0
I λ, i, abs ðλ; θ; ϕÞ I λ, i ðλ; θ; ϕÞ
αλ ðλÞEλ, b ðλ; T e Þdλ ð1 ¼ Eλ, b ðλ; T e Þdλ 0
ð4:23Þ
ð3
Finally, total hemispherical absorptivity is obtained by integrating spectral hemispherical absorptivity over all wavelengths: ð1
Gλ, abs ðλÞdλ α ¼ 0ð 1 ¼ Gλ ðλÞdλ
ð1 0
αλ ðλÞGλ ðλÞdλ ð1 Gλ ðλÞdλ
0
¼
0
Gabs G ð4:25Þ
Example 5 A particular diffuse material is idealized as having a spectral absorptivity of zero for wavelengths less than 3 μm and unity for wavelengths greater than 3 μm. Calculate its total hemispherical absorptivity for a blackbody at 800, 1200, and 2000 K. Solution Assume Gλ(λ) ¼ Eλ,b(λ,Τe) where Te is the temperature of the emitter (800, 1200, and 2000 K) and use Equation 4.25:
0 Eλ, b ðλ; T e Þdλ þ
ð1
0
3
σT 4e
1 Eλ, b ðλ; T e Þdλ
ð1 ¼
Eλ, b ðλ; T e Þdλ
3
σT 4e
4
Radiation Heat Transfer
115
It is possible to put this in a form that allows use of the radiation fraction tabulated in Table 4.1: ð1 α¼
¼
Eλ, b ðλ; T e Þdλ
ð3
0
σT 4e ð3
¼1
Eλ, b ðλ; T e Þdλ
0
ð3
σT 4e Eλ, b ðλ; T e Þdλ
0
σT 4e Eλ, b ðλ; T e Þdλ
0
σT 4e
¼ 1 F0!3 ð3T e Þ
For Te ¼ 800 K, λTe ¼ 2400 μm K and from Table 4.1 F0!3 ¼ 0:14 so α ¼ 0.86. For Te ¼ 1200 K, λTe ¼ 3600 μm K and from Table 4.1 F0!3 ¼ 0:40 so α ¼ 0.60. For Te ¼ 2000 K, λTe ¼ 6000 μm K and from Table 4.1 F0!3 ¼ 0:76 so α ¼ 0.24. It is seen that, for this idealized material, the effective absorptivity is a strong function of emitter temperature. In a fire we are usually interested in the total hemispherical absorptivity defined in Equation 4.25. However, as demonstrated above, the total hemispherical absorptivity depends on the spectral energy distribution of the radiation source. Therefore, a material technically cannot be assigned a single absorptivity value because the spectral distribution of the incoming radiation depends on the temperature of the emitter. Due to Wien’s displacement law and the Planck distribution, this is true even if the emitter behaves as a blackbody. In fires, the temperature of radiation sources ranges from approximately ~600 K (smoke layer, hot surfaces) to ~2000 K (flames). Additionally, certain bench–scale fire tests use tungsten–filament heaters that operate at temperatures near 3000 K. Thus, the effect of source temperature on the integrated (or effective) absorptivity has relevance for both real fires and bench-scale fire testing. Hallman’s 1971 Ph.D. dissertation [8] and subsequent publications [9, 10] remain some of the most comprehensive sources of information on the change of polymers’ total hemispherical absorptivity with the temperature of the emitter. Hallman measured the spectral absorptivity of
several solids and then determined the integrated surface absorptivity of different solids irradiated by hexane flames, blackbodies between 1000 and 3500 K, and solar energy. His absorptivity data are reproduced in Table 4.4. Note that the total hemispherical absorptivity of some materials is relatively insensitive to the temperature of the radiation source (black PMMA) but others are quite sensitive. For example, the absorptivity of clear PMMA decreases from 0.85 for a 1000 K blackbody to 0.25 for a 3500 K blackbody. Similar measurements were made by Wesson et al. [11] for undegraded wood. Their results are reproduced in Table 4.5. More recently, Fo¨rsth and Roos [12] conducted similar measurements for wood products (Table 4.6), carpet (Table 4.7), painted plywood (Table 4.8), and plastics (Table 4.9). During a fire, a material’s radiative characteristics may change. Although the integrated absorptivities from Wesson et al. [11] (reproduced in Table 4.5) are relatively low, the absorptivity of charred wood is generally not the same as that of virgin wood. Janssens [13] suggested that blackening causes the absorptivity of wood to increase from ~0.76 (based on Reference [11]) to approximately unity as the surface temperature approaches the ignition temperature. He therefore used an average value of 0.88 in his ignition analyses, and recommends using an integrated absorptivity of 1.0 during flaming combustion [14]. Interestingly, Fo¨rsth and Roos [12] noted the opposite trend, i.e. a reduction in effective absorptivity as wood darkens. More research is needed in this area. Wood is not the only class of materials that exhibits a change in radiative characteristics during a fire. Under nonflaming conditions, low density polyethylene has been observed to change from visually opaque to transparent, eventually followed by a darkening of the surface [15]. This indicates that a change in the material’s radiative characteristics occurred (at least in the visible range). Modak and Croce [16] reported that for clear PMMA, 39 % of flame radiation is transmitted through the surface, but for “charred” PMMA (previously exposed to a fire environment and then cooled) no radiation penetrates in depth. Bubbling
116
Revised by C. Lautenberger
Table 4.4 Integrated surface absorptivities for polymers from Hallman [9] Generic name Acrylonitrile butadiene styrene Cellulose acetate butyrate Cork Melamine/formaldehyde Nylon 6/6 Phenolic Polycarbonate (rough surface) Polyethylene (low density) Polymethylmethacrylate (black) Polymethylmethacrylate (clear) Polymethylmethacrylate (white) Polyoxymethylene Polyphenylene oxide Polypropylene Polystyrene (clear) Polystyrene (white) Polyurethane thermoplastic Polyvinyl chloride (clear) Polyvinyl chloride (gray) PVC/acrylic (gray, rolled) PVC/acrylic (red cast) Rubber (Buna–N) Rubber (Butyl IIR) Rubber (natural, gum) Rubber (neoprene) Rubber (silicone)
Trade name Cycolac® Uvex® Formica® Bakelite Lexan® Plexiglas® Plexiglas® Plexiglas® Delrin®
Styrolux® Texin®
Kydex® Kydex®
Blackbody emitter temperature (K) 1000 1500 2000 2500 0.91 0.86 0.77 0.71 0.84 0.71 0.56 0.43 0.64 0.56 0.49 0.46 0.91 0.88 0.85 0.82 0.93 0.90 0.86 0.82 0.90 0.86 0.81 0.77 0.87 0.83 0.78 0.75 0.92 0.88 0.82 0.77 0.94 0.94 0.95 0.95 0.85 0.69 0.54 0.41 0.91 0.86 0.78 0.70 0.92 0.86 0.78 0.71 0.86 0.78 0.70 0.63 0.87 0.83 0.78 0.74 0.75 0.60 0.46 0.35 0.86 0.75 0.63 0.53 0.92 0.89 0.83 0.77 0.81 0.65 0.49 0.38 0.90 0.90 0.89 0.89 0.88 0.87 0.86 0.85 0.91 0.90 0.89 0.88 0.92 0.93 0.93 0.93 0.92 0.93 0.94 0.94 0.88 0.82 0.76 0.72 0.91 0.92 0.93 0.93 0.79 0.66 0.58 0.54
Table 4.5 Integrated surface absorptivity for wood from different emitters (From Wesson et al. [11]) Wood Alaskan cedar Ash Balsa Birch Cottonwood Mahogany Mansonia Maple Oak Redgum Redwood Spruce White pine Masonite
Flame radiation 0.76 0.76 0.75 0.77 0.76 0.76 0.76 0.76 0.77 0.77 0.77 0.76 0.76 0.75
Tungsten lamp radiation 0.44 0.46 0.41 0.47 0.48 0.49 0.47 0.49 0.56 0.52 0.51 0.45 0.49 0.52
Solar radiation 0.36 0.36 0.35 0.39 0.40 0.52 0.51 0.44 0.49 0.56 0.55 0.35 0.43 0.61
3000 0.65 0.34 0.44 0.80 0.75 0.75 0.72 0.72 0.95 0.31 0.62 0.64 0.57 0.70 0.28 0.45 0.72 0.30 0.89 0.84 0.87 0.93 0.95 0.69 0.93 0.52
3500 0.61 0.27 0.44 0.79 0.71 0.75 0.71 0.68 0.95 0.25 0.56 0.59 0.53 0.68 0.22 0.40 0.68 0.24 0.89 0.83 0.86 0.93 0.95 0.68 0.93 0.53
Flame 0.92 0.88 0.60 0.91 0.93 0.91 0.88 0.93 0.94 0.89 0.92 0.93 0.88 0.86 0.78 0.88 0.93 0.85 0.91 0.88 0.92 0.92 0.92 0.89 0.91 0.79
occurring near the surface of polymers can change their radiative characteristics, but this effect is has not yet been reliably quantified. In a real fire, materials may become coated in soot from flames or a smoke layer, causing their absorptivities to approach unity.
Reflectivity A fraction of radiation incident on a surface may be reflected. One complicating factor is that reflection may be diffuse, specular, or (most likely) some combination of these two idealizations. A diffuse reflector is a surface for which, analogous to a diffuse emitter, the intensity of reflected radiation is equal in all directions and does not depend on the angle of incoming
4
Radiation Heat Transfer
117
Table 4.6 Effective absorptivities for different grey body temperatures for various wood products (From Fo¨rsth and Roos [12]) Grey body emitter T (K) Cone calorimeter irradiation (kWm2) Product Plywood Dark heat-treated lacquered ash tree floor Dark heat-treated non-lacquered ash tree floor Light lacquered ash tree flooring Light non-lacquered oak flooring Medium dark lacquered oak flooring Medium dark non-lacquered oak flooring
674 10 αeff 0.86 0.89 0.83 0.90 0.86 0.91 0.86
852 25
1025 50
1153 75
1300 100
5777 Sun
0.84 0.88 0.81 0.88 0.84 0.89 0.84
0.81 0.85 0.79 0.86 0.81 0.87 0.82
0.79 0.83 0.77 0.84 0.80 0.85 0.80
0.76 0.80 0.74 0.82 0.77 0.83 0.77
0.40 0.63 0.62 0.40 0.37 0.56 0.50
Table 4.7 Effective absorptivities for different grey body temperatures for various carpets (From Fo¨rsth and Roos [12]) Grey body emitter T (K) Cone calorimeter irradiation (kWm2) Product Beige PVC carpet Pink PVC carpet Red PVC carpet Blue PVC carpet Grey PVC carpet Black PVC carpet Grey rubber mat Black rubber mat White vinyl carpet Beige vinyl carpet Brown vinyl carpet Grey vinyl carpet Black vinyl carpet Beige linoleum carpet
674 10 αeff 0.92 0.90 0.92 0.89 0.90 0.93 0.91 0.90 0.88 0.91 0.90 0.92 0.93 0.92
radiation. This contrasts to a specular emitter which is an idealized surface where the angle of reflected radiation is equal to the angle of incident radiation, like a billiard ball bouncing off the rail. Rough surfaces approximate diffuse emitters, and polished surfaces are close to specular surfaces. It is seen that, in its most general form, surface reflection is a bidirectional process meaning the intensity of reflected radiation depends not only on the angle of incident radiation, but also on the angle of reflected radiation. As a simplification, we look only at hemispherically-integrated reflection. Then the
852 25
1025 50
1153 75
1300 100
5777 Sun
0.91 0.88 0.92 0.87 0.88 0.93 0.91 0.90 0.86 0.90 0.89 0.91 0.93 0.91
0.90 0.86 0.91 0.85 0.86 0.93 0.91 0.91 0.83 0.89 0.88 0.89 0.93 0.89
0.89 0.84 0.90 0.83 0.84 0.93 0.91 0.91 0.81 0.87 0.88 0.88 0.93 0.88
0.87 0.81 0.89 0.80 0.82 0.93 0.91 0.91 0.79 0.85 0.87 0.87 0.93 0.86
0.60 0.39 0.80 0.43 0.43 0.92 0.82 0.95 0.44 0.51 0.77 0.57 0.94 0.55
spectral directional reflectivity is defined as the ratio of the reflected spectral radiant intensity to the incident spectral radiant intensity: ρλ ðλ; θ; ϕÞ ¼
I λ, i, re f ðλ; θ; ϕÞ I λ, i ðλ; θ; ϕÞ
ð4:26Þ
note that in Equation 4.26, θ and ϕ refer to the direction of the incident radiation, not the reflected radiation (since, for simplification, no consideration is given to the direction of reflected radiation). Spectral hemispherical reflectivity is obtained by integrating over all incident angles:
Table 4.8 Effective absorptivities for different grey body temperatures for various paints painted on plywood (From Fo¨rsth and Roos [12]) Grey body emitter T (K) Cone calorimeter irradiation (kWm2) Product White ceiling water paint White floor water paint Mid gray floor water paint White priming water paint Red priming water paint Red priming water paint White top water paint Yellow top water paint Red top water paint Blue top water paint White wall water paint Black wall water paint Blue wall water paint White lacquer paint Blue lacquer paint Black lacquer paint Red ceiling lacquer paint Black ceiling lacquer paint
674 10 αeff 0.86 0.86 0.90 0.86 0.90 0.89 0.87 0.90 0.89 0.89 0.84 0.93 0.92 0.86 0.90 0.92 0.87 0.92
852 25
1025 50
1153 75
1300 100
5777 Sun
0.83 0.84 0.89 0.83 0.89 0.87 0.84 0.88 0.88 0.87 0.81 0.93 0.91 0.84 0.89 0.92 0.84 0.93
0.81 0.81 0.89 0.81 0.87 0.85 0.81 0.86 0.86 0.85 0.77 0.93 0.91 0.81 0.88 0.92 0.82 0.93
0.78 0.78 0.89 0.78 0.86 0.83 0.78 0.84 0.84 0.83 0.74 0.93 0.90 0.79 0.88 0.92 0.79 0.93
0.75 0.75 0.88 0.75 0.83 0.80 0.75 0.82 0.81 0.81 0.71 0.93 0.90 0.76 0.87 0.93 0.77 0.93
0.30 0.24 0.76 0.27 0.71 0.70 0.25 0.44 0.55 0.73 0.23 0.95 0.75 0.26 0.74 0.95 0.70 0.95
Table 4.9 Effective absorptivities for different grey body temperatures for various plastics and other materials (From Fo¨rsth and Roos [12]) Grey body emitter T (K) Cone calorimeter irradiation (kWm2) Product White ABS Black ABS Nature acetal Nature PA-6 Clear PC Clear PC Ultra UV Brown PC Nature PE Yellow PE Black PE Clear PMMA G Yellow PMMA G Brown PMMA G Clear PMMA XT Grey PP Nature PTFE Clear PVC White PVC White PVC expostandard (foamed) Grey PVC Black PVC Nature PVDF
674 10 αeff 0.91 0.92 0.93 0.93 0.92 0.92 0.93 0.93 0.93 0.93 0.93 0.94 0.94 0.93 0.92 0.84 0.91 0.91 0.82 0.91 0.93 0.94
852 25
1025 50
1153 75
1300 100
5777 Sun
0.90 0.92 0.93 0.93 0.91 0.91 0.93 0.93 0.92 0.93 0.92 0.93 0.94 0.92 0.92 0.78 0.90 0.89 0.80 0.90 0.93 0.94
0.88 0.92 0.93 0.94 0.89 0.90 0.93 0.93 0.92 0.93 0.91 0.93 0.94 0.91 0.91 0.73 0.88 0.87 0.78 0.90 0.93 0.94
0.86 0.92 0.92 0.94 0.87 0.88 0.93 0.93 0.91 0.93 0.89 0.93 0.94 0.89 0.91 0.70 0.86 0.85 0.76 0.90 0.93 0.94
0.84 0.92 0.91 0.94 0.85 0.85 0.93 0.93 0.90 0.93 0.87 0.92 0.94 0.87 0.90 0.66 0.84 0.82 0.73 0.90 0.93 0.94
0.31 0.94 0.46 0.74 0.24 0.46 0.93 0.62 0.53 0.95 0.23 0.62 0.94 0.21 0.66 0.10 0.27 0.31 0.31 0.88 0.95 0.78
4
Radiation Heat Transfer
ð 2π ð π=2
Iλ, i, re f ðλ; θ; ϕÞ cos ðθÞ sin ðθÞdθdϕ
ρλ ðλÞ ¼ 0ð 2π 0ð π=2 0
¼
119
Iλ, i ðλ; θ; ϕÞ cos ðθÞ sin ðθÞdθdϕ
0
Gλ, re f ðλÞ Gλ ð λ Þ
ð4:27Þ Final, total hemispherical reflectivity is obtained by integrating over all wavelengths: ð1
Gλ, re f ðλÞ
ρ ¼ 0ð 1
Gλ ðλÞ
Kirchhoff’s Law: Relation Between Emissivity and Absorptivity Kirchoff’s law is used extensively in radiation heat transfer calculations. In its most general form, Kirchoff’s law states that in order to maintain thermal equilibrium, the spectral directional absorptivity must be equal to the spectral directional emissivity: αλ ðλ; θ; ϕÞ ¼ ελ ðλ; θ; ϕ; T Þ
¼
Gre f G
ð4:28Þ
0
ð4:32Þ
Using the relations presented earlier in the chapter, it can be shown that if the irradiation is diffuse or the surface is diffuse, then Kirchoff’s law has no directional dependency, i.e.:
Transmissivity Directional spectral transmissivity is defined in an analogous manner to the other radiation properties discussed here: τλ ðλ; θ; ϕÞ ¼
I λ, i, trans ðλ; θ; ϕÞ I λ, i ðλ; θ; ϕÞ
ð4:29Þ
Hemispherical spectral transmissivity is:
αλ ðλÞ ¼ ελ ðλ; T Þ
ð4:33Þ
If Equation 4.33 applies (i.e., the irradiation is diffuse or the surface is diffuse), then if the surface is also gray (meaning αλ and ελ are invariant with λ) or the surface is irradiated only by radiation emitted from a blackbody at the same temperature as the surface, its total absorptivity is equal to its total emissivity:
ð 2π ð π=2 τ λ ðλ Þ ¼
0
I λ, i, trans ðλ; θ; ϕÞ cos ðθÞ sin ðθÞdθdϕ 0 ð 2π ð π=2 Iλ, i ðλ; θ; ϕÞ cos ðθÞ sin ðθÞdθdϕ 0
¼
0
Gλ, trans ðλÞ G λ ðλ Þ
ð4:30Þ And total transmissivity is then obtained by integrating over all wavelengths: ð1 τ¼
0ð
Gλ, trans ðλÞ 1
0
G λ ðλÞ
¼
Gtrans G
ð4:31Þ
α¼ε
ð4:34Þ
For engineering calculations, Equation 4.34 is most commonly applied for the special case of diffuse and gray surfaces. Fortunately, this is a reasonable approximation for many radiation heat transfer engineering models for participating media in fire applications. Although real surfaces may exhibit an emissivity that varies with wavelength (see Fig. 4.7), an effective emissivity can be selected so that the integrated emissive power of the gray surface matches the integrated emissive power of the real surface at a particular temperature.
120
Revised by C. Lautenberger 4500 Blackbody
Spectral emissive power (Ebλ, W/m2•μm)
4000 3500
Gray body, ε = 0.8
3000 Gray body, ε = 0.6
2500 2000 1500 Real surface
1000 500 0 0
5
10
15
Wavelength (l, mm)
Fig. 4.7 Monochromatic emissive power for black body, two gray bodies, and real surface
Radiant Heat Transfer in Nonparticipating Media In this section, cases are examined where the surfaces are separated by a medium that does not emit, absorb, or scatter radiation. A vacuum meets this requirement exactly, and common diatomic gases of symmetric molecular structure such as N2, O2, and H2 are very nearly nonparticipating media within the thermal radiation spectrum. The radiative energy transfer between the surfaces depends on the geometry, orientation, temperature, and radiation properties of the surfaces. In practice, surfaces are usually idealized as isothermal, diffuse, and gray to make engineering calculations tractable. The geometry and orientation of each surface is commonly accounted for in calculations by one or more configuration factors, also known as view factors, shape factors, angle factors, and geometric factors [1–7, 17–19].
View Factors A view factor, or configuration factor, is a purely geometrical relation between two surfaces. It is
A2
dA2
b2 n2 R
n1
b1
A1 dA1
Fig. 4.8 Coordinate system for shape factors
defined as the fraction of radiation leaving one surface which is intercepted by the other surface. Consider the two arbitrarily oriented surfaces A1 and A2 in Fig. 4.8. Assuming that the radiosity from differential area dA1 is diffuse, the
4
Radiation Heat Transfer
121
X
configuration factor from dA1 to the finite area A2, Fd1 2, is given by ð Fd12 ¼ A2
cos ðβ1 Þ cos ðβ2 Þ dA2 !2 πR
ð4:35Þ
where the separation distance between the two ! surfaces is R , β is the angle between the line of !
!
sight R and the surface normal n , and A2 is the area of surface 2. If the radiosity from all of surface A1 (not just differential are dA1) is diffuse, then the configuration factor for the finite area A1 to A2, F1 2, is calculated as: F12 ¼
1 A1
ð ð A1 A2
All configuration factors can be derived using the multiple integration of Equations 4.35 and 4.36, but this is generally very tedious except for simple geometries. Several cases have been tabulated with the numerical results or algebraic formulas available in various references [1–7, 17, 18]. Several configuration factors are provided in Appendix D. The configuration factors in Appendix D can be extended to other geometries by using configuration factor algebra and the method of surface decomposition. In surface decomposition, unknown factors can be determined from known factors for convenient areas or for imaginary surfaces which can extend real surfaces or form an enclosure [1, 6]. When the radiant fluxes from both surfaces are uniformly and diffusely distributed (a common engineering assumption), a reciprocity relation for any given pair of configuration factors in a group of exchanging surfaces is: Ai Fi j ¼ A j F ji
ð4:37Þ
The summation rule is another useful relation for calculating unknown configuration factors
ð4:38Þ
where Fij relate to surfaces that subtend a closed system. It is possible for a concave surface to “see” itself, which can make Fii important in certain situations. In many cases, it is advantageous to define a single surface ( j) as a composite surface consisting of multiple (real or imaginary) surfaces (k), i.e.: Aj ¼
X
Ak
ð4:39Þ
For a composite surface j, made up of multiple surfaces k, since view factors are additive:
cos ðβ1 Þ cos ðβ2 Þ dA1 dA2 !2 πR ð4:36Þ
Fi j ¼ 1
j
Fi j ¼
X
Aik
ð4:40Þ
Example 6 For the geometry shown below, use shape factor algebra to develop an expression for the view factor between surface 1 and surface 4 that could be evaluated from the shape factor relations provided in Appendix D.
4
3 2
1
Solution The desired view factor is F14. For simplicity of nomenclature, denote surface A as a composite surface made up of surfaces 1 and 2. Similarly, denote surface B as a composite surface made up of surfaces 3 and 4. Then, from the additive property of shape factors: AA FAB ¼ A1 F1B þ A2 F2B Both FAB and F2B can be calculated from the appropriate shape factor in Appendix D. Note that
122
Revised by C. Lautenberger
F1B ¼ F13 þ F14 F13 ¼ FA3 F23 Combining these two equations gives an expression for F1B:
A convenient method to analyze radiative energy exchange in a diffuse gray enclosure relies on the concepts of radiosity and irradiation introduced earlier. The irradiation of surface i (Gi) is the radiative flux reaching the ith surface regardless of its origin:
F1B ¼ FA3 F23 þ F14 Substituting this expression into the first equation above: AA FAB ¼ A1 ðFA3 F23 þ F14 Þ þ A2 F2B ¼ A1 FA3 A1 F23 þ A1 F14 þ A2 F2B Solving for F14: 1 ðAA FAB A2 F2B A1 FA3 þ A1 F23 Þ A1 1 ¼ ðAA FAB A2 F2B Þ þ F23 FA3 A1
F14 ¼
Note that all of the view factors in the above example can be evaluated from the shape factor relations provided in Appendix D.
Gray Diffuse Surfaces For engineering applications, thermal emission from most surfaces is treated as having diffuse directional characteristics independent of wavelength and temperature. Real surfaces exhibit radiation properties that are so complex that information about these property measurements for many common materials is not available. The gray diffuse surface is a useful model that alleviates many of the complexities associated with a detailed radiation analysis, while providing reasonably accurate results in many practical situations. The advantage of diffuse surface analysis is that radiation leaving the surface is independent of the direction of the incoming radiation, which greatly reduces the amount of computation required to solve the governing equations. Discussions for specularly reflecting surfaces and nongray surfaces can be found in the literature [1, 6].
Gi ¼
X
ð4:41Þ
Fi j J j
j
where Jj is the surface radiosity, defined as the total radiative flux leaving the jth surface including both emitted and reflected radiation: J i ¼ Ei þ ρi Gi ¼ εi Ebi þ ρi Gi
ð4:42Þ
The net rate at which radiation leaves surface i is given by Qi ¼ Ai ðJ i Gi Þ ¼ Ai ðEi þ ρi Gi Gi Þ ¼ Ai ðEi Gi ð1 ρi ÞÞ ¼ Ai ðEi αi Gi Þ ð4:43Þ since, for a diffuse gray opaque surface ρi ¼ 1 αi. It must be emphasized that the radiosityirradiation formulation is based on the assumption that each surface has uniform radiosity and irradiation (or equivalently, uniform temperature and uniform heat flux). Physically unrealistic calculations can result if each surface does not approximately satisfy this condition. Larger surfaces should be subdivided into smaller surfaces if necessary. The radiosity-irradiation formulation allows a more physical and graphic interpretation using the resistance network analogy. Eliminating the irradiation Gi from Equations 4.41, 4.42 and 4.43, and substituting ρi ¼ 1 εi gives Qi ¼
X Ji J j Ebi J i ¼ 1 ð4:44Þ ð1 εi Þ=ðεi Ai Þ Ai Fi j j
Note that the second equality in Equation 4.44 can be written as: Qi ¼
X j
X Ai Fi j J i J j ¼ Qi j j
ð4:45Þ
4
Radiation Heat Transfer
123 Eb2
Fig. 4.9 Network analogy for radiative exchange
1
——— 1– Refractory wall
A2F23
∈2
∈2 A2
Eb3
J2
1
1
——— 3
2
A1F12
——— J1
A1F13
1 – ∈1 1
∈1 A1 Eb1
The denominator in the rightmost term of Equation 4.44 corresponds to resistance in electric circuits. This electrical resistance analogy was first proposed by Oppenheim [20]. As illustrated in Fig. 4.9, the diffuse-gray surface has a radiation potential difference (Ebi Ji) and a resistance (1 εi)/εiAi. This example also illustrates that an adiabatic surface, such as a reradiating or refractory wall, exhibits a surface temperature that is independent of the surface emissivity or reflectivity.
and scattering within the medium. The intensity, Iλ(S), is coupled with the spatial distribution of the extinction coefficient and with temperature through conservation of energy in the medium. The contributions of intensity passing through an area must be integrated over all directions to calculate a net radiative energy flux. The integral nature of radiation makes analysis difficult and simplifications necessary for engineering practice.
Spectral Emissivity and Absorptivity
Thermal Radiation in Participating Media The Equation of Transfer The equation of transfer describes the variation in intensity of a radiant beam at any position along its path in an absorbing-emitting-scattering medium. This equation is the foundation upon which detailed radiation analyses are based, and the source of approximate solutions when simplifying assumptions are made. For a given direction line in the medium, the equation of transfer is 1 dI λ ðSÞ þ I λ ðSÞ ¼ I λ, b ðT Þ κλ ðT; SÞ dS
ð4:46Þ
where S represents the physical pathlength and κλ represents the spectral extinction coefficient, which includes the effects of both absorption
From a microscopic viewpoint, emission and absorption of radiation is attributed to changes in energy levels of atoms and molecules caused by interactions with photons. Tien [21] discusses these effects in gases from an engineering perspective. Consider a monochromatic beam of radiation passing through a radiating medium of thickness L. For the special case where the temperature and properties of the medium are uniform along this path, the intensity of radiant beam at point x is obtained by integrating Equation 4.46: I λ ðxÞ ¼ I λ ð0Þexpðκλ xÞ þ I λ, b ð1 expðκ λ xÞÞ
ð4:47Þ
which accounts for the loss of intensity by absorption and the gain by emission, and where κλ denotes the extinction coefficient. The extinction coefficient is generally the sum of two parts:
124
Revised by C. Lautenberger
the absorption coefficient and the scattering coefficient. In many engineering applications, the effects of scattering are negligible and the extinction coefficient represents only absorption. The spectral emissivity for pathlength S in a uniform gas volume can be readily expressed by considering the case of no incident radiation (or Iλ(0) ¼ 0): ελ ¼
Iλ ¼ 1 expðκ λ SÞ I λ, b
ð4:48Þ
which compares the fraction of energy emitted to the maximum (blackbody) emission at the same temperature for the pathlength S through the material. The term κ λS in Equation 4.48 is called optical pathlength or opacity and is denoted τλ (not to be confused with transmissivity). It can be defined more generally for nonhomogeneous media as: τλ ¼
ðS
κλ ðxÞdx
terms of mean (gray-gas) absorption coefficients representing average properties over the whole spectrum of wavelengths. The appropriate mean absorption coefficients are the Planck mean, κP, for optically thin media, and the Rosseland mean, κR, for optically thick media [5, 6, 21]. The Planck mean absorption coefficient is defined as ð1
ð I λ, b κ λ dλ π 1 0 ð κP 1 ¼ 4 I bλ κ λ dλ σT 0 I λ, b dλ
ð4:50Þ
0
This form of the absorption coefficient is a function of temperature alone and is independent of pressure. The effect of the beam source temperature (e.g., a hot or cold wall) in the gas absorptivity is approximated by a ratio correction [21, 22] κm ¼ κP ðT s Þ
ð4:49Þ
Ts Tg
ð4:51Þ
0
If τλ > 1, which implies that the mean penetration distance is much less than the characteristic length of the medium. In optically thick media, as will be described below, the local radiant intensity results only from local emission and the equation of transfer can be approximated by a diffusion equation.
where Ts is the source temperature and Tg is the gas temperature. When the Planck mean absorption coefficient is used to estimate the emissivity of a gas, the source temperature is set equal to the gas temperature. The formulation of radiative transfer is simplified when the medium is optically thick. In this case, the radiative transfer can be regarded as a diffusion process (the Rosseland or diffusion approximation), and the governing equation is approximated by: 4 1 ∂Eλ, b 4 1 ∂ σT 4 qr ¼ 3 κ R ∂x 3 κ R ∂x 00
Planck and Rosseland Mean Absorption Coefficients The mean absorption coefficient is often useful when radiative energy transport theory must be used to describe the local state of a gas at various locations. The mathematical complexity involved in the calculations often dictates a solution based on the gray-gas assumption, where all radiation parameters are considered to be wavelength independent. Thus solutions are given in
¼
16σ 3 1 ∂T T 3 κ R ∂x
ð4:52Þ
Evaluation of the total heat flux in an optically thick medium is simplified by defining the Rosseland mean absorption coefficient which is independent of wavelength: 1 κR
ð1 0
1 ∂Eλ, b dλ κλ ∂Eb
ð4:53Þ
4
Radiation Heat Transfer
125
In Equation 4.53, ∂Eλ, b =∂Eb is evaluated from the 1=4
Planck distribution after setting T ¼ ðEb =σ Þ . The Rosseland mean absorption coefficient is not well defined for gases under ordinary conditions because astronomically long pathlengths are required to make the windows between the bands optically thick. However, the Rosseland limit is useful when dealing with gases in the presence of soot particles, which are characterized by a continuous spectrum. The source temperature effect is accounted for by using Equation 4.51 in the same manner as for the Planck mean absorption coefficient. The radiating gas in many actual fire systems is neither optically thin nor optically thick, so it may be necessary to use band theory to rigorously calculate a mean absorption coefficient, κ m. However, with a reasonable estimate of the mean absorption coefficient, radiative transport calculations are much more convenient.
Mean Beam Length for Homogeneous Gas Bodies The concept of mean beam length is a powerful and convenient tool to calculate the energy flux from a radiating homogeneous gas volume to its boundary surface. It may also be used to approximate radiative energy flux for a nonhomogeneous gas, especially when more elaborate calculations are not feasible. Consider the coordinate system given in Fig. 4.3, where dA is a differential area on the boundary surface of the gas body. The radiative heat flux from the gas body to dA is 00
q_ r ¼
ð1 ð 0
Ω
ελ ðXÞI λ, b cos ðθÞdλdΩ
ð4:54Þ
where the spectral emissivity, ελ, is a function of pressure pathlength: X
ðS 0
Pa xðξÞdξ
ð4:55Þ
which in turn varies with solid angle Ω according to the gas body geometry. In practical situations, 00 the calculation of q_ r is more convenient in terms of total emissivity, which is often available in chart form. From the definition of total emissivity, Equation 4.54 can be expressed as: 00
q_ r ¼
σT 4 π
ð Ω
εðXÞ cos ðθÞdΩ σT 4 εðLÞ ð4:56Þ
which gives the definition of mean beam length, L, for a gas body, where ε(L ) has the same functional form as ε(X). Physically, the mean beam length represents the equivalent radius of a hemispherical gas body such that it radiates a flux to the center of its base equal to the average flux radiated to the boundary surface by the actual volume of gas. The determination of the mean beam length is simplified when the gas is optically thin and only the geometry of the gas body enters the calculation. In the optically thin limit, it is convenient to define L ¼ L0
1 π
ð Ω
X cos ðθÞdΩ
ð4:57Þ
where L0 is called the geometric mean beam length. In the optically thick limit, a correction factor (C) can be used to obtain reasonable radiative heat flux estimates: L CL0
ð4:58Þ
In Table 4.10, L0 and C have been provided for a variety of gas body shapes. For an arbitrarily shaped gas volume, the geometric beam length from the gas volume to the entire boundary surface can be estimated by: L0 ¼
4V A
ð4:59Þ
where V and A are the volume and the area of the boundary surface of the gas body, respectively. The correction factor C is approximately 0.9.
126
Revised by C. Lautenberger
Table 4.10 Mean beam lengths for various gas body shapes Geometry of gas body Sphere
Radiating to Entire surface
Geometric mean beam length L0 0.66 D
Correction factor C 0.97
Cylinder H ¼ 0.5 D
Plane and surface Concave surface Entire surface
0.48 D 0.52 D 0.50 D
0.90 0.88 0.90
Cylinder H¼D
Center of base Entire surface
0.77 D 0.66 D
0.92 0.90
Cylinder H¼2D
Plane end surface Concave surface Entire surface
0.73 D 0.82 D 0.80 D
0.82 0.93 0.91
Semi-infinite cylinder H!1
Center of base Entire base
1.00 D 0.81 D
0.90 0.80
Infinite slab
Surface element Both bounding planes
2.00 D 2.00 D
0.90 0.90
Cube D D 4D
1 4 face 1 1 face Entire surface
0.90 D 0.86 D 0.89 D
0.91 0.83 0.91
Thermal Radiation Properties of Combustion Products Radiation Properties of Gases The emissivity of any gas is a strong function of wavelength, varying by as much as several orders of magnitude over small changes in wavelength. However, the level of accuracy required in engineering calculations, where many of the parameters are difficult to measure or estimate, seldom requires high resolution emissivity spectra. Where wavelength dependence of radiative
heat flux is a concern, gas properties may be calculated using the exponential wide-band model [23]. The uncertainties involved in estimating parameters to calculate radiative heat flux make average properties such as total emissivity a useful tool. The first comprehensive total emissivity charts were formulated by Hottel and coworkers to summarize work performed up to about 1945. Modern formulations for the emissivity of gases have been summarized by Edwards [22]. Total emissivity charts for water vapor and carbon dioxide [22] are provided in Figs. 4.10 and 4.11, respectively. Gas emissivity can be
4
Radiation Heat Transfer
127
1.0
1.0 PaL (atm – m)
PaL (atm – m)
4.0 2.0 1.0
0.1
Gas emissivity, ∈t
Gas emissivity, ∈t
4.0 2.0 1.0 0.4
0.1
0.4 0.2
0.1
0.2 0.1
0.04
0.04
0.01
0.02
0.01
0.01 0.02
0.004
H2O, Pe = 1
CO2, Pe = 1
0.01
0.002 0.001
0.001 100
200
500
1000
0.004 0.002
2000
5000
Gas temperature, T (K)
0.001
0.001 100
200
500
1000
2000
5000
Gas temperature, T (K)
Fig. 4.10 Total emissivity of water vapor
Fig. 4.11 Total emissivity of carbon dioxide
read off these charts from the partial pressure and temperature of each gas and the mean beam length for the gas volume geometry. Correction factors for the chart emissivities are available in the literature for the pressure effect on water vapor emissivity [24], the pressure effect on carbon dioxide emissivity [5, 6], and the band overlap for mixtures of the two gases [25]. For most fire protection engineering applications, the pressure correction factors are 1.0 and the band overlap correction is approximately Δε 12εCO2 for medium to large fires. Assuming the carrier gas is transparent (e.g., air), the emissivity is:
in Figs. 4.10 and 4.11, and the use of wide-band models is advised to estimate the band overlap correction instead of using the correction charts at these lower temperatures [26]. For crucial engineering decisions, wide-band model block calculations as detailed by Edwards [22] are recommended over the graphical chart method to determine total emissivity. Other gases such as sulfur dioxide, ammonia, hydrogen chloride, nitric oxide, and methane have been summarized in chart form [5]. The carbon monoxide chart by Hottel is not recommended for use [27] due to uncertainties most likely introduced by traces of carbon dioxide in the original experiments. Spectral and total properties have been published for some of the important hydrocarbon gases, e.g., methane, acetylene, and propylene [28–30]. Mixtures of several hydrocarbon gases are subject to band
1 2
εg ¼ CH2 O εH2 O þ CCO2 εCO2 Δε εH2 O þ εCO2
ð4:60Þ At temperatures below 400 K, the older charts by Hottel [5, 6] may be more reliable than the charts
128
Revised by C. Lautenberger
overlapping, and appropriate corrections must be made to avoid overestimating total emissivity of a mixture of fuels. The total emissivity for a gas in the optically thin limit can be calculated from the Planck mean absorption coefficient. Graphs of the Planck mean absorption coefficient for various gases that are important in fires are shown in Fig. 4.12, which can be used with Equation 4.48 to estimate the total emissivity (by assuming that total properties represent a spectral average value).
Radiation Properties of Soot In a nonhomogeneous (e.g., with soot) medium, scattering becomes an important radiative mechanism in addition to absorption and emission. The absorption and scattering behavior of a single particle can be described by solving the electromagnetic field equations; however, many physical idealizations and mathematical approximations are necessary. The most common assumptions include perfectly spherical particles, uniformly or randomly distributed particles, and
Fig. 4.12 Planck mean absorption coefficient for various gases
interparticle spacing so large that the radiation for each particle can be treated independently. Soot particles are produced as a result of incomplete combustion and are usually observed to be in the form of spheres, agglomerated chunks, and long chains. They are generally very small ˚ where 1 A ˚ ¼ 1010 m ¼ 104 μm) (50–1000 A compared to infrared wavelengths, so that the Rayleigh limit is applicable to the calculation of radiation properties [31, 32]. Soot particles are normally characterized by their optical properties, size, shape, and chemical composition (hydrogen-carbon ratio). From a heat transfer viewpoint, radiation from a soot cloud is predominantly affected by the particle size distribution and can be considered independent of the chemical composition [31]. Soot optical properties are relatively insensitive to temperature changes at elevated temperatures, but as shown in Fig. 4.13, room temperature values representative of soot in smoke do show appreciable deviations. By choosing appropriate values of optical constants for soot, the solution for the electromagnetic field equations gives [33]
100
H2O Planck mean absorption coefficient (atm·m)–1
50
CO2
20 10
C2H2
CH4
5
2
CO
1 0.5
0.2 0.1 250
500
1000
Temperature (K)
1500
2000
4
Radiation Heat Transfer
129
Fig. 4.13 Optical constants for soot
6
4 n
Refractive index
2
k
1 0.8 0.6
1600 K 1000 K 300 K
0.4
0.2 0.2
0.4
0.6 0.8 1
2
4
6
8 10
20
Wavelength, λ (μ)
kλ ¼
C0 f λ v
ð4:61Þ
where fv is the soot volume fraction (generally about 106 in flames) and C0, a constant between 2 and 6 dependent on the complex index of refraction m ¼ n ik, is given by C0 ¼
n2
36πnk 2 k þ 2 þ 4n2 k2 2
ð4:62Þ
Equations 4.61 and 4.62 can be used to evaluate the Planck mean absorption coefficient in the optically thin limit [34], giving: κP ¼ 3:83
C0 f T C2 v
C0 f T C2 v
κ R ¼ 3:72
C0 f T C2 v
ð4:65Þ
to be used in Equation 4.66 for the soot radiation calculations. Typical temperatures, volume fractions, and mean absorption coefficients for soot particles in the luminous flames of various fuels are tabulated in Table 4.11.
Radiation Properties of Gas-Soot Mixtures
ð4:63Þ
where C2 is Planck’s second constant (1.4388 102 m-K). The Rosseland mean absorption coefficient in the optically thick limit is κR ¼ 3:6
A mean coefficient that may be used for the entire range of optical thickness is suggested as
ð4:64Þ
The calculation of the total emissivity of a gas-soot mixture requires information on basic flame parameters such as soot volume fraction, soot absorption coefficient, temperature and geometric length of the flame, and partial pressure of the participating gas components [35]. These parameters can be estimated for various types of
130
Revised by C. Lautenberger
Table 4.11 Radiative properties for soot particles Gas fuels
Solid Fuels
κS (m1) 6.45 6.39 13.32 16.81 11.92 24.07 12.59 30.72 45.42 0.8 0.5 1.2
Fuel, composition Methane, CH4 Ethane, C2H6 Propane, C2H8 Isobutane, (CH3)3CH Ethylene, C2H4 Propylene, C3H6 n-butane, (CH3)(CH2)2(CH3) Isobutylene, (CH3)2CCH2 1,3-butadiene, CH2CHCHCH2 Wood, (CH2O)n Plexiglas, (C5H8O2)n Polystyrene, (C8H8)n
Fig. 4.14 Mean absorption coefficients for luminous flames and smoke
fv 106 4.49 3.30 7.09 9.17 5.55 13.6 6.41 18.7 29.5 0.362 0.272 0.674
Ts(K ) 1289 1590 1561 1554 1722 1490 1612 1409 1348 1732 1538 1486
Mean absorption coefficients κ/(C0fv × 105) (m–1)
8
X
PCO2
PH2O
C0fv
C0fv
104 atm 6
105 4
103 104 103
2
κR κP
0
500
1000
1500
2000
Temperature (K)
fuel when actual measurements are unavailable for a particular situation. The following equation is a good approximation [36] for total emissivity of homogeneous gas-soot mixtures: εt ¼ ð1 expðκSÞÞ þ εg expðκs SÞ
ð4:66Þ
where S is the physical pathlength, εg is the total emissivity of the gas alone, and κ s is the effective absorption coefficient of the soot. The Planck mean absorption coefficients for gas-soot mixtures in luminous flames and smoke are shown in Fig. 4.14.
4
Radiation Heat Transfer
131 00
dq_ r ¼ dλ
Application to Flame and Fire
ð
I λ ! ! ! n R dΩ Ω R
ð4:68Þ
Heat Flux Calculation from a Flame !
Where n is a unit vector normal to the target
Prediction of the radiative heat flux from a flame is important in determining ignition and fire spread hazard, and in the development of fire detection devices. The shape of flames under actual conditions is transient, which makes detailed radiation analysis cumbersome. In most calculations, flames are idealized as simple geometric shapes such as plane layers or axisymmetric cylinders and cones. A cylindrical geometry, shown in Fig. 4.15, will be analyzed here and used in a sample calculation. Assuming κ λ is independent of pathlength, integration of the transport equation (Equation 4.48) yields [37]
!
element dA and R is the line-of-sight vector extending between dA and the far side of the flame cylinder. Evaluation of Equation 4.68 is quite lengthy, but under the condition of L/r 3, it can be simplified to [37] 00
dq_ r ¼ πI λ, b ελ ðF1 þ F2 þ F3 Þ dλ
ð4:69Þ
where the shape factor constants and emittance are defined as
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2κλ I λ ¼ I bλ 1 exp r 2 L2 cos 2 ðϕÞ sin ðθÞ ð4:67Þ where θ, ϕ. r, and L are geometric variables defined in Fig. 4.15. The monochromatic radiative heat flux on the target element is given by
F1 ¼
u r 2 ðπ 2θ0 þ sin ð2θ0 ÞÞ 4π L
ð4:70aÞ
F2 ¼
v r ðπ 2θ0 þ sin ð2θ0 ÞÞ 4π L
ð4:70bÞ
F3 ¼
w r cos 2 ðθ0 Þ π L
ð4:70cÞ
ελ ¼ 1 expð0:7μλ Þ
ð4:71Þ
Fig. 4.15 Schematic of a cylindrical flame R H
S z
q
q0 Y
n
dA
r
n dA x
f L
y
132
Revised by C. Lautenberger Detector
1.2 m
Flames y x
1.8 m
~ 0.5 m φ
z
1m
3.6 m 1.4 m
2.4 m
Fig. 4.16 Example calculation for flux to target element from flame
The parameters in the definitions are given by θ0 ¼ tan 1 ðL=H Þ μλ ¼ 2r !
sin
!
κλ θ 0
2
þ
!
π 4
ð4:72aÞ
ð4:72bÞ
!
n ¼ u i þ v j þ wk
Solution First, the condition of L/r 3 should be checked to verify that the previous analysis is applicable. L r
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1:22 þ 1:82 ¼ 8:65 > 3 0:25
ð4:74Þ
ð4:72cÞ
The unit normal vector to the detector is given
If the flame is considered to be homogeneous and Equation 4.69 is integrated over all wavelengths, the total heat flux is:
by n ¼ k , the polar angle θ0 ¼ tan1(1.818) ¼ 1.068 is determined from Equation 4.72a, and the shape factors are evaluated from Equations 4.70a, 4.70b, and 4.70c:
00
q_ r ¼ εm Eb
3 X
Fj
ð4:73Þ
j¼1
Example 7 As shown in Fig. 4.16, a fire detector is located at the center of the ceiling in a room (2.4 3.6 2.4 m) with wood wall linings. The sprinkler system is capable of extinguishing fires smaller than 0.5 m in diameter 1.0 m high. For this example, determine the appropriate heat flux setting for the detector, using a worst case scenario of ignition in one of the upper ceiling corners.
!
!
F1 ¼ 0
ð4:75aÞ
F2 ¼ 0
ð4:75bÞ
1 0:25 cos 2 ð1:068Þ ¼ 0:0102 F3 ¼ π 1:818 ð4:75cÞ From Equation 4.73, the radiant heat flux can be calculated as:
4
Radiation Heat Transfer 00
q_ r
133
¼ ð1 expðκ m SÞÞσT 4f F3 ¼ ð1 expð0:8 0:5ÞÞ 5:67 108 17324 0:0102 ¼ 1:7 kW=m2
Hot upper gas layers are composed of strongly participating media such as carbon dioxide, water vapor, and soot particles. Heat flux from the smoke layer is directly related to ignition of remote surface locations such as furniture or floor carpets. The schematic in Fig. 4.17 will be considered in a radiative transport analysis and example calculation. The calculation is based on a considerably simplified formulation which provides reasonable results with only a small penalty in accuracy. Integration of Equation 4.46 over the pathlength S through the smoke layer yields
where wood flame properties were taken from Table 4.11. If the geometry of the example had been L/r < 3, it would have been necessary to interpolate between the L/r ¼ 3 case and the L/r ¼ 0 case, which has been obtained accurately [6, 37]. If the detector is pointed directly !
at the burning corner in this example (i.e., n ¼ !
!
0:55 i þ 0:83 j ), the calculated heat flux jumps to 9.0 kW/m2, showing the strong influence of direction in calculations of radiation heat transfer.
4 ! σT 4 Tw I ð SÞ ¼ 1 expðκSÞ π T
Heat Flux Calculation from a Smoke Layer Consider the situation shown below in Fig. 4.17 involving radiative heat transfer in a compartment fire with a hot gas layer located below the ceiling. Fig. 4.17 Example calculation for flux to target element from smoke layer
ð4:76Þ
The monochromatic radiative heat flux on a differential target element is again given by Equation 4.68. However, for the present geometry of
SMOKE LAYER
0.5 m
R q
1.9 m
3.6 m
y z
n x
R sin f
2.4 m
DIFFERENTIAL TARGET AREA
ð4:77Þ
θ
134
Revised by C. Lautenberger
the ceiling layer and enclosure surface, integration of Equation 4.68 is quite time-consuming since the upper and lower bounds of the integral vary with the angle of the pathlength. The calculation can be simplified by assuming as a first order approximation that the lower face of the smoke layer is an isothermal surface. Using this assumption, the problem can be handled using the simple relations of radiative exchange in a nonparticipating medium between gray surfaces (the absorption of the clear air below the smoke layer is negligible). The radiosity and irradiation of each surface in the enclosure is: J i ¼ εi σT 4i þ ð1 εi ÞGi Gi ¼
X
Fi j J j
ð4:78aÞ ð4:78bÞ
j
After solving the simultaneous equations for all Ji and Gi, the net heat flux on any of the surfaces can be calculated from 00
q_ r, i ¼ J i Gi
ð4:79Þ
This situation is considered in Example 8 below. Example 8 A smoke layer 0.5 m thick is floating near the ceiling of a room with dimensions of 3.6 2.4 2.4 m. (See Fig. 4.17.) The floor is made from wood (emissivity ¼ 0.9), and the four side walls are painted concrete (emissivity ¼ 0.94). The calculation will determine the heat flux in a bottom corner of the room, assuming that each surface in the enclosure is kept at constant temperature: the smoke layer at 1400 K, the side walls at 800 K, and the floor at 300 K. Assume there is a differential target area 0.01 m2 in one of the corners of the floor, and also at the floor temperature of 300 K. Solution The bottom of the smoke layer will be designated surface 1, the floor will be surface 2, and the differential target area in the bottom corner will be surface 3. Only four surfaces are required since the four side walls can be treated as a single surface 4. Shape factors F12 and F31 can be found in Appendix D, and from these two
factors, the remaining shape factors are determined by shape factor algebra: F12 ¼ 0:3242 F31 ¼ 0:1831 F13 ¼
A3 F31 ¼ 0:0002 A1
F14 ¼ 1 F12 F13 ¼ 0:6756 Continuing in a similar fashion, the other shape factors are obtained as: F21 F22 F23 F24
¼ 0:3242 ¼ 0:0000 ¼ 0:0000 ¼ 0:6758
F31 F32 F33 F34
¼ 0:1831 ¼ 0:0000 ¼ 0:0000 ¼ 0:8169
F41 F42 F43 F44
¼ 0:2560 ¼ 0:2561 ¼ 0:0003 ¼ 0:4876
The emissivity for the smoke layer can be estimated from the mean absorption coefficient for a wood flame (Table 4.11) as: ε1 ¼ 1 expðκ m SÞ ¼ 1 expð0:8 0:5Þ ¼ 0:33 The blackbody emissive power of each surface is calculated as σT4, for example: 4 σT 1 ¼ 5:6696 108 14004 ¼ 217:8 kW=m2 From Equations 4.78a and 4.78b, the radiative fluxes to and from each surface are determined by solving the eight simultaneous equations: J1 J2 J3 J4
¼ 88:7 kW=m2 ¼ 4:7 kW=m2 ¼ 3:9 kW=m2 ¼ 23:9 kW=m2
G1 G2 G3 G4
¼ 17:7 kW=m2 ¼ 43:3 kW=m2 ¼ 34:8 kW=m2 ¼ 34:3 kW=m2
The net radiative heat flux on the target element from Equation 4.79 is 00
q_ r, 3 ¼ J 3 G3 ¼ 30:9 kW=m2 where the negative sign indicates that heat must be removed from the target element so it remains
4
Radiation Heat Transfer
135 Eb1
Fig. 4.18 Equivalent resistance network for an enclosure 1 – e1 e1 A1
J1
1 ——— A1F12 1 ——— A1F13
J2
Eb 2
1 ——— A1F14
J4
1 – e2
1 ——— A2F24
e2 A 2 1 ——— A2F23
Eb 4 1 – e4 e4 A 4
J3
1 – e3 e3 A 3 Eb 3
in equilibrium. This example also could have been solved by the resistance network method shown in Fig. 4.18)
n Pa Pe Q
Radiation intensity (W/m2) Cartesian coordinate direction vectors Radiosity or radiative heat flux leaving surface (W/m2) Boltzmann constant (1.3806 1023 J/K), or infrared optical constant of soot (imaginary component), or thermal conductivity (W/m K) Mean beam length or distance (m) Geometrical mean beam length (m) Index of refraction (c0/c) orinfrared optical constant of soot (real component) Unit normal vector Partial pressure of absorbing gas (Pa) Effective pressure (Pa) Energy rate (W)
q˙00
Heat flux (W/m2)
R r S T t u, v, w
Line of sight vector Radius of cylinder (m) Pathlength (m) Temperature (K) Time (s) ! Cartesian components of unit vector n
V
Volume (m3)
I! ! ! i , j, k J k
Nomenclature A C C0 C2 c c0 E Fij fv G H h
Area (m2) Correction factor for mean beam length Soot concentration parameter Planck’s second constant (1.4388 102 m K) Speed of light in the medium (m/s) Speed of light in a vacuum (2.998 108 m/s) Radiative emissive power (W/m2) Configuration factor from surface i to surface j Soot volume fraction Irradiation or radiative heat flux received by surface (W/m2) Height (m) Planck’s constant (6.6256 1034 J s)
L L0 n !
!
136
X
Revised by C. Lautenberger
ðs Pressure pathlength,
Pa xðξÞdðξÞ
References
0
x
(atm-m) Spatial coordinate (m)
Greek Symbols α β ε θ κ λ μ μλ ν ξ ρ Ω σ τ ϕ χ
Absorptivity or thermal diffusivity k/pcp (m2/s) Angle from normal (radians) Emissivity Polar angle (radians) Extinction coefficient or absorption coefficient (m l) Wavelength (m) Micron (106 m) Defined parameter, Equation 4.73 Frequency (st) Integration dummy variable Reflectivity or density (kg/m3) Solid angle (steradians) Stefan-Boltzmann constant (5.6696 10B W/m2K4) Transmissivity or optical pathlength Azimuthal angle (radians) Fractional measure
Subscripts a b e f g i j m 0 P R s t w λ ν 1
Actual Blackbody or base External Flame Gas Initial or ith surface Summation variable or jth surface Mean value Original Planck mean Rosseland mean Surface or soot Total Wall Spectral wavelength Spectral frequency Ambient
1. J. deRis, 17th Symposium (International) on Combustion, 1003, Combustion Institute, Pittsburgh, PA (1979). 2. S.C. Lee and C.L. Tien, Progress in Energy and Combustion Science, 8, 41 (1982). 3. G.M. Faeth, S.M. Jeng, and J. Gore, in Heat Transfer in Fire and Combustion Systems, American Society of Mechanical Engineers, New York (1985). 4. Incropera, F.P. and DeWitt, D.P., Fundamentals of Heat and Mass Transfer, John Wiley & Sons, New York, 2002. 5. H.C. Hottel and A.F. Sarofim, Radiative Heat Transfer, McGraw-Hill, New York (1967). 6. R. Siegel and H.R. Howell, Thermal Radiation Heat Transfer, McGraw-Hill, New York (1981). 7. Bejan, A., Heat Transfer, John Wiley & Sons, New York, 1993. 8. Hallman, J.R., “Ignition characteristics of plastics and rubber,” Ph.D. Dissertation, University of Oklahoma, 1971. 9. Hallman, J.R., Welker, J.R., and Sliepcevich, C.M., “Polymer surface reflectance–absorptance characteristics,” Polymer Engineering and Science 14: 717–723 (1974). 10. Hallman, J.R., Sliepcevich, C.M., and Walker, J.R., “Radiation absorption for polymers: The radiant panel and carbon arcs as radiant heat sources,” Journal of Fire & Flammability 9: 353–366 (1978). 11. Wesson, H.R., Welker, J.R., and Sliepcevich, C.M., “The piloted ignition of wood by thermal radiation,” Combustion and Flame 16: 303–310 (1971). 12. Fo¨rsth, M. and Roos, A., “Absorptivity and its Dependence on Heat Source Temperature and Degree of Thermal Breakdown,” Fire and Materials 35: 285–301 (2011). 13. Janssens, M., “Piloted ignition of wood: a review,” Fire and Materials 15: 151–167 (1991). 14. Janssens, M. and Douglas, B., “Wood and wood products,” in Handbook of Building Materials for Fire Protection, Ed. Harper, C.A., pp. 7.1–7.58, McGraw–Hill, New York, 2004. 15. Kashiwagi, T. and Ohlemiller, T.J., “A study of oxygen effects on nonflaming transient gasification of PMMA and PE during thermal irradiation,” Proceedings of the Combustion Institute 19: 815–823 (1982). 16. Modak, A.T. and Croce, P.A., “Plastic pool fires,” Combustion and Flame 30: 251–265 (1977). 17. E.M. Sparrow and R.D. Cess, Radiation Heat Transfer, McGraw-Hill, New York (1978). 18. J.R. Howell, A Catalog of Radiation Configuration Factors, McGraw-Hill, New York (1982). 19. C.L. Tien, in Handbook of Heat Transfer Fundamentals, McGraw-Hill, pp 14.36, New York (1985).
4
Radiation Heat Transfer
20. Oppenheim, A.K, Trans. ASME, 65, 725, 1956. 21. C.L. Tien, Advances in Heat Transfer, 5, 253 (1968). 22. D.K. Edwards, in Handbook of Heat Transfer Fundamentals, McGraw-Hill, pp 14.53, New York (1985). 23. D.K. Edwards, Advances in Heat Transfer, 12, 115 (1976). 24. G.B. Ludwig, W. Malkmus, J.E. Reardon, and J.A.L. Thompson, Handbook of Radiation from Combustion Gases, NASA SP- 3080, Washington (1973). 25. T.F. Smith, Z.F. Shen, and J.N. Friedman, Journal of Heat Transfer, 104, 602 (1982). 26. J.D. Felske and C.L. Tien, Combustion Science and Technology, 11, 111 (1975). 27. M.M. Abu-Romia and C.L. Tien,, Journal of Quantitative Spectroscopy and Radiative Transfer, 107, 143 (1966). 28. M.A. Brosmer and C.L. Tien, Journal of Quantitative Spectroscopy and Radiative Transfer, 33, 521 (1985). 29. M.A. Brosmer and C.L. Tien, Journal of Heat Transfer, 107, 943 (1985). 30. M.A. Brosmer and C.L. Tien, Combustion Science and Technology, 48, 163 (1986).
137 31. S.C. Lee and C.L. Tien, 18th Symposium (International) on Combustion, Combustion Institute, 1159, Pittsburgh (1981). 32. C.L. Tien, in Handbook of Heat Transfer Fundamentals, McGraw-Hill, pp 14.83, New York (1985). 33. G.L. Hubbard and C.L. Tien, Journal of Heat Transfer, 100, 235 (1978). 34. J.D. Felske and C.L. Tien, Journal of Heat Transfer, 99, 458 (1977). 35. J.D. Felske and C.L. Tien, Combustion Science and Technology, 7, 25 (1977). 36. W.W. Yuen and C.L. Tien, 16th Symposium (International) on Combustion, Combustion Institute, 1481, Pittsburgh (1977). 37. A. Dayan and C.L. Tien, Combustion Science and Technology, 9, 41 (1974).
Chris Lautenberger is a fire protection engineer at Reax Engineering Inc. in Berkeley, CA. He is also an Instructor in Cal Poly’s Fire Protection Engineering program where he co-teaches courses on Fire Modeling and Fire Dynamics.
5
Thermochemistry D.D. Drysdale
Introduction Thermochemistry is the branch of physical chemistry that is concerned with the amounts of energy released or absorbed when a chemical change (reaction) takes place [1–3]. Inasmuch as fire is fundamentally a manifestation of a particular type of chemical reaction, viz., combustion, thermochemistry provides methods by which the energy released during fire processes can be calculated from data available in the scientific and technical literature. To place it in context, thermochemistry is a major derivative of the first law of thermodynamics, which is a statement of the principle of conservation of energy. However, while concerned with chemical change, thermodynamics does not indicate anything about the rate at which such a change takes place or about the mechanism of conversion; this falls within the topic of chemical kinetics [4]. Consequently, the information it provides is normally used in association with other data, for example, to enable the rate of heat release to be calculated from the rate of burning.
The First Law of Thermodynamics It is convenient to limit the present discussion to chemical and physical changes involving gases; D.D. Drysdale (*) BRE Centre for Fire Safety Engineering, University of Edinburgh, Scotland, UK
this is not unreasonable, as flaming combustion takes place in the gas phase. It may also be assumed that the ideal gas law applies, that is, PV ¼ n RT
ð5:1Þ
where P and V are the pressure and volume of n moles of gas at a temperature, T (in degrees Kelvin); values of the universal gas constant (R) in various sets of units are summarized in Table 5.1. At ambient temperatures, deviations from “ideal behavior” can be detected with most gases and vapors, while at elevated temperatures such deviations become less significant. In this context, it should be noted that whereas the terms gas and vapor are sometimes used interchangeably, it is best to make a distinction. Both are in the gaseous state, but as a general rule a vapor at normal temperatures can be made to liquefy if the pressure of the vapor is increased sufficiently. Thus, propane can be stored as a liquid under a relatively low pressure (approximately 8.4 bar at 293 Kelvin) whereas the permanent gases (particularly hydrogen, helium, oxygen, and nitrogen) can only be stored as gases at ambient temperatures, typically in pressure cylinders at 2000 psi (c. 138 bar). Again, as a general rule, vapors tend to deviate more strongly from ideal gas behavior than do the permanent gases.
Internal Energy As a statement of the principle of conservation of energy, the first law of thermodynamics deals
M.J. Hurley (ed.), SFPE Handbook of Fire Protection Engineering, DOI 10.1007/978-1-4939-2565-0_5, # Society of Fire Protection Engineers 2016
138
5
Thermochemistry
139
Table 5.1 Values of the ideal gas constant, R Units of pressure Pa (N/m2) atm
Units of volume m3 cm3
atm
l
atm
m3
Units of R J/Kmol cm3atm/ Kmol latm/ Kmol m3atm/ Kmol
Value of R 8.31431 82.0575 0.0820575 8.20575 10–5
dx ¼ Distance through which the piston is moved; the increment in volume is therefore dV ¼ A · dx The total work done is obtained by integrating Equation 5.5 from the initial to the final state; that is, ð final w ¼ P dV ð5:6Þ initial
Combining Equations 5.3 and 5.5, the differential change in internal energy can be written with the relationship between work and heat. Confining our attention to a “closed system”— for which there is no exchange of matter with the surroundings—it is known that there will be a change if heat is added or taken away, or if work is done on or by “the system” (e.g., by compression). This change is usually accompanied by an increase or decrease in temperature and can be quantified if we first define a function of state known as the internal energy of the system, E. Any change in the internal energy of the system (ΔE) is then given by ΔE ¼ q w
ð5:2Þ
where q is the heat transferred to the system, and w is the work done by the system. This can be expressed in differential form dE ¼ dq dw
ð5:3Þ
Being a function of state, E varies with temperature and pressure, that is, E ¼ E(T, P). According to the standard definition, work, w, is done when a force, F, moves its point of application through a distance, x, thus, in the limit dw ¼ F dx
ð5:4Þ
The work done during the expansion of a gas can be derived by considering a cylinder/piston assembly (Fig. 5.1); thus dw ¼ P A dx ¼ P dV where P ¼ Pressure of the gas A ¼ Area of the piston
ð5:5Þ
dE ¼ dq P dV
ð5:7Þ
This shows that if the volume remains constant, as P · dV ¼ 0, then dE ¼ dq; if this is integrated, we obtain ΔE ¼ qv
ð5:8Þ
where qv is the heat transferred to the constant volume system; that is, the change in internal energy is equal to the heat absorbed (or lost) at constant volume.
Enthalpy With the exception of explosions in closed vessels, fires occur under conditions of constant pressure. Consequently, the work done as a result of expansion of the fire gases must be taken into account. At constant pressure, Equation 5.5 may be integrated to give w ¼ P ðV 2 V 1 Þ
ð5:9Þ
where V1 and V2 are the initial and final volumes, respectively. Equation 5.2 then becomes ΔE ¼ E2 E1 ¼ q p þ PV 1 PV 2
ð5:10Þ
or, rearranging, q p ¼ ðE2 þ PV 2 Þ ðE1 þ PV 1 Þ ¼ H2 H1
ð5:11Þ
where qp is the heat transferred at constant pressure, and H is known as the enthalpy (H E + PV). The change in enthalpy is therefore the heat
140 Fig. 5.1 Cylinder/piston assembly
D.D. Drysdale Gas pressure P
dx
Force F
Area A
absorbed (or lost) at constant pressure (provided that only P V work is done), and consequently it is the change in enthalpy that must be considered in fire-related problems.
Specific Heat Specific heat, or heat capacity, of a body or “system” is defined as the amount of heat required to raise the temperature of unit mass by 1 C; the units are J/kg K, although for most thermochemical problems the units J/mol K are more convenient. The formal definition of the “mole” is the amount of a substance (solid, liquid, or gas) that contains as many elementary units (atoms or molecules) as there are carbon atoms in exactly 0.012 kg of carbon-12 (C12). This number—known as Avogadro’s number— is actually 6.023 1023; in its original form, Avogadro’s hypothesis was applied to gases and stated that equal numbers of molecules of different gases at the same temperature and pressure occupy the same volume. Thus, the quantity of a substance that corresponds to a mole is simply the gram-molecular weight, but expressed in kilograms to conform with SI units. For example, the following quantities of the gases N2, O2, CO2, and CO represent 1 mole of the respective gas and, according to Avogadro’s hypothesis, will each occupy 0.022414 m3 at 273 K and 760 mmHg (101.1 kPa):
0.028 kg nitrogen (N2) 0.032 kg oxygen (O2) 0.044 kg carbon dioxide (CO2) 0.028 kg carbon monoxide (CO) 0.016 kg methane (CH4) 0.044 kg propane (C3H8) The concept of specific heat is normally associated with solids and liquids, but it is equally applicable to gases. Such specific heats are required for calculating flame temperatures, as described below. Values for a number of important gases at constant pressure and a range of temperatures are given in Table 5.2. It is important to note that there are two distinct heat capacities; at constant pressure, Cp, and at constant volume, Cv. Thus, at constant pressure dq p ¼ dH ¼ C p dT
ð5:12Þ
while at constant volume dqv ¼ dE ¼ Cv dT
ð5:13Þ
For an ideal gas, C p ¼ Cv þ R:
Heats of Combustion Chemical Reactions and Stoichiometry When chemical reactions occur, they are normally accompanied by the release or absorption of heat. Thermochemistry deals with the
5
Thermochemistry
141
Table 5.2 Heat capacities of selected gases at constant pressure (101.1 kN/m2) [5] Cp (J/mol K) Temperature (K) Species CO CO2 H2O(g) N2 O2 He CH4
298
500
1000
1500
2000
29.14 37.129 33.577 29.125 29.372 20.786 35.639
29.79 44.626 35.208 29.577 31.091 20.786 46.342
33.18 54.308 41.217 32.698 34.878 20.786 71.797
35.22 58.379 46.999 34.852 36.560 20.786 86.559
36.25 60.350 51.103 35.987 37.777 20.786 94.399
quantification of the associated energy changes. This requires a definition of the initial and final states, normally expressed in terms of an appropriate chemical equation, for example, C3 H8 þ 5O2 ! 3CO2 þ 4H2 O
ð5:R1Þ
in which the reactants (propane and oxygen) and products (carbon dioxide and water) are specified. This balanced chemical equation defines the stoichiometry of the reaction, that is, the exact proportions of the two reactants (propane and oxygen) for complete conversion to products (no reactants remaining). Note that the physical states of the reactants and products should also be specified. In most cases, the initial conditions correspond to ambient (i.e., 25 C and atmospheric pressure) so that there should be no doubt about the state of the reactants. In this case both are gaseous, but it is more common in fires for the “fuel” to be in a condensed state, either liquid or solid. As an example, the oxidation of nhexane can be written C6 H14 þ 9:5O2 ! 6CO2 þ 7H2 O
ð5:R2Þ
but the fuel may be in either the liquid or the vapor state. The consequences of this will be discussed below. Reaction 5.R1 may be used to calculate the mass of oxygen or air required for the complete oxidation of a given mass of propane. Thus, we deduce that 1 mole of propane (44 g) reacts completely with 5 moles of oxygen (5 32 ¼ 160 g); that is, 1 g propane requires 3.64 g oxygen. If the propane is burning in air, then the presence of nitrogen needs to be taken
into account, although it does not participate to any significant extent in the chemical change. As the ratio of oxygen to nitrogen in air is approximately 21:79 (or 1:3.76), Reaction 5.R1 can be rewritten C3 H8 þ 5O2 þ 18:8N2 ! 3CO2 þ 4H2 O þ 18:8N2
ð5:R3Þ (where 18.8 ¼ 5 3.76), showing that 44 g propane requires (160 + 18.8 28), or 686.4 g of “air” for complete combustion, that is, 15.6 g air/g propane. Calculations of this type are valuable in assessing the air requirements of fires. Thus, on the assumption that wood has the empirical formula [5] CH1.5O0.75, it can be shown that its stoichiometric air requirement is 5.38 g air for each gram of fuel, assuming complete combustion of wood to CO2 and H2O. The relevant stoichiometric equation is CH1:5 O0:75 þ O2 þ 3:76N2 ¼ CO2 þ 0:75H2 O þ 3:76N2
ð5:R4Þ
In this calculation no distinction is made of the fact that flaming combustion of wood involves oxidation of the volatile gases and vapors produced by the pyrolysis of wood, while the residual char burns much more slowly by surface oxidation.
Measurement of Heats of Combustion The heat of combustion of a fuel is defined as the amount of heat released when unit quantity is oxidized completely to yield stable end products.
142
D.D. Drysdale
In the present context, the relevant combustion processes occur at constant pressure so that we are concerned with an enthalpy change, ΔHc. By convention, for exothermic reactions such as oxidation, values of ΔHc are negative; that is, the reaction produces energy that can then be lost from the system. (By contrast, an endothermic reaction such as the conversion of water to hydrogen and oxygen will take place only if energy is provided in a suitable form.) Heats of combustion are measured in the combustion bomb calorimeter in which a precise amount of fuel is burned in pure oxygen inside a pressure vessel whose temperature is strictly monitored. The apparatus is designed to reduce heat losses from the calorimeter to a minimum so that the amount of heat released can be calculated from the rise in temperature and the total thermal capacity of the system; corrections can be made for any heat loss. In the past, combustion bomb calorimetry received a great deal of attention within physical chemistry [1, 6] as the technique was able to provide a wealth of data of relevance to thermochemistry. However, the experiment gives the heat released at constant volume; that is, the change in internal energy, ΔE (Equation 5.8). The change in enthalpy is given by ΔH ¼ ΔE þ ΔðPV Þ
ð5:14Þ
where Δ(PV) is calculated using the ideal gas law ΔðPV Þ ¼ ΔðnRT Þ
ð5:15Þ
The method gives the gross heat of combustion—that is, in which the reactants and products are in their standard states. The net heat of combustion, on the other hand, refers to the situation in which the products are in the sate in which they are formed. For Reaction 5.R1, for example, water is formed in the gaseous phase so that the amount of energy released is less than the gross heat of combustion by an amount equivalent to the latent heat of evaporation of water (2.26 kJ/ g). The net heat of combustion is the value that should be used in fire calculations. This is illustrated in the next section: see Reactions 5.R5a and 5.R5b. It should also be remembered
that there is a heat of gasification associated with any condensed fuel (liquid or solid); a correction must be made for this if the heat of combustion of the fuel vapor is required. Table 5.3 contains the heats of combustion (ΔHc) of a number of combustible gases, liquids, and solids, expressed in various ways, viz., kJ/mole (fuel), kJ/g (fuel), kJ/g (oxygen), and kJ/g (air). The first of these is the form normally encountered in chemistry texts and reference books, whereas the second is more commonly found in sources relating to chemical engineering and fuel technology and is more useful to the fire protection engineer. However, the third and, particularly, the fourth have very specific uses in relation to fire problems. It is immediately apparent from Table 5.3 that ΔHc (O2) and ΔHc (air) are approximately constant for most of the fuels listed, having average values of 13.1 kJ/g and 3 kJ/g, respectively. (See the section on “Rate of Heat Release in Fires”.) The data quoted in Table 5.3 refer to heats of combustion measured at ambient temperature, normally 25 C. These data will be satisfactory for virtually all relevant fire problems, but occasionally it may be necessary to consider the heat released when combustion takes place at higher temperatures. This requires a simple application of the first law of thermodynamics. If the reaction involves reactants at temperature T0 reacting to give products at the final temperature TF, the process can be regarded in two ways: 1. The products are formed at T0, absorb the heat of combustion, and are heated to the final temperature TF. 2. The heat of combustion is imagined first to heat the reactants to TF, then the reaction proceeds to completion, with no further temperature rise. By the first law, we can write ðΔH c ÞT 0 þ CPrp ðT F T 0 Þ ¼ ðΔHc ÞT F þ C Rp ðT F T 0 Þ
ð5:16Þ
where CpPr and CpR are the total heat capacities of the products and reactants, respectively. This may be rearranged to give
5
Thermochemistry
143
Table 5.3 Heats of combustion of selected fuels at 25 C (298 K) [7] Fuel Carbon monoxide (CO) Methane (CH4) Ethane (C2H6) Ethene (C2H4) Ethyne (C2H2) Propane (C3H8) n-Butane (n-C4H10) n-Pentane (n-C5H12) n-Hexane c-Hexane (c-C6H12) n-Octane (n-C8H18) Benzene (C6H6) Methanol (CH3OH) Ethanol (C2H5OH) Acetone (CH3COCH3) D-glucose (C6H12O6) Cellulosec Polyethylene Polypropylene Polystyrene Polyvinylchloride Polymethylmethacrylate Polyacrylonitrile Polyoxymethylene Polyethyleneterephthalate Polycarbonate Nylon 6,6 Polyester Wool Wood (European beech) Wood volatiles (European beech) Wood char (European beech) Wood (Ponderosa pine)
ΔHc (kJ/mol) 283 800 1423 1411 1253 2044 2650 3259 3861 3680 5104 3120 635 1232 1786 2772 — — — — — — — — — — — — — — — — —
ΔHc (kJ/g) 10.10 50.00 47.45 50.53 48.20 46.45 45.69 45.27 44.90 43.81 44.77 40.00 19.83 26.78 30.79 15.40 16.09 43.28 43.31 39.85 16.43 24.89 30.80 15.46 22.00 29.72 29.58 23.8 20.5 19.5 16.6 34.3 19.4
ΔHcb (kJ/g[O2]) 17.69 12.54 11.21 14.74 15.73 12.80 12.80 12.80
ΔHc (kJ/g[air]) 4.10 2.91 2.96 3.42 3.65 2.97 2.97 2.97
12.80 12.80 13.06 13.22 12.88 14.00 13.27 13.59 12.65 12.66 12.97 12.84 12.98 13.61 14.50 13.21 13.12 12.67 — — — — — —
2.97 2.97 3.03 3.07 2.99 3.25 3.08 3.15 2.93 2.94 3.01 2.98 3.01 3.16 3.36 3.06 3.04 2.94 — — — — — —
a
Apart from the solids (D-glucose, et seq.), the initial state of the fuel and of all the products is taken to be gaseous ΔHc(O2) ¼ 13.1 kJ/g is used in the oxygen consumption method for calculating rate of heat release c Cotton and rayon are virtually pure cellulose and can be assumed to have the same heat of combustion b
ðΔHc ÞT F ðΔH c ÞT 0 ¼ ΔC p TF T0
ð5:17Þ
or, in differential form, we have Kirchoff’s equation dðΔH c Þ ¼ ΔC p dT
ð5:18Þ
where ΔC p ¼ CPrp -C Rp . This may be used in integrated form to calculate the heat of combustion at temperature T2 if ΔHc is known at temperature T1 and information is available on the heat capacities of the reactants and products, thus ð T2 ðΔH c ÞT 2 ¼ ðΔH c ÞT 1 þ ΔC p dT ð5:19Þ T1
144
D.D. Drysdale
H2 ðgÞ þ 0:5O2 ðgÞ ! H2 OðgÞΔH f ½H2 OðgÞ
Where ΔC p ¼
X
C p ðproductsÞ
X
C p ðreactantsÞ
¼ 241:84 kJ=mol
ð5:20Þ
ð5:R5bÞ
and Cp is a function of temperature, which can normally be expressed as a power series in T, for example,
By definition, the heats of formation of all the elements are set arbitrarily to zero at all temperatures. This then allows the heats of reaction to be calculated from the heats of formation of the reactants and products, thus
C p ¼ a þ bT þ cT 2 þ . . .
ð5:21Þ
Information on heat capacities of a number of species and their variation with temperature may be found in Stull and Prophet [7] and Strehlow [8]. Some data are summarized in Table 5.2.
Heats of Formation The first law of thermodynamics implies that the change in internal energy (or enthalpy) of a system depends only on the initial and final states of the system and is thus independent of the intermediate stages. This is embodied in thermochemistry as Hess’s law, which applies directly to chemical reactions. From this, we can develop the concept of heat of formation, which provides a means of comparing the relative stabilities of different chemical compounds and may be used to calculate heats of chemical reactions that cannot be measured directly. The heat of formation of a compound is defined as the enthalpy change when 1 mole of that compound is formed from its constituent elements in their standard state (at 1 atm pressure and 298 K). Thus, the heat of formation of liquid water is the enthalpy change of the reaction (at 298 K) H 2 ðgÞ þ 0:5O2 ðgÞ ! H2 OðlÞΔH f ¼ 285:8kJ=mol
ð5:R5aÞ
so that ΔHf (H2O) (l) ¼ 285.8 kJ/mole at 25 C. This differs from the heat released by the reaction if the product is water vapor rather than liquid (“The heat of formation of water vapor” kJ/mol [ΔHf {H2O(g)} ¼ –241.84 kJ/ mol]) by the latent heat of evaporation of water at 25 C (43.96 kJ/mol). Thus
ΔH ¼ ΔH f ðproductsÞ ΔH f ðreactantsÞ ð5:22Þ where ΔH is the heat (enthalpy) of the relevant reaction. However, most heats of formation cannot be obtained as easily as heats of combustion. The example given in Reaction (5.R5a) is unusual in that the heat of formation of water also happens to be the heat of combustion of hydrogen. Similarly, the heat of combustion of carbon in its most stable form under ambient conditions (graphite) is the heat of formation of carbon dioxide. Combustion calorimetry can be used indirectly to calculate heats of formation. The heat of formation of ethyne (acetylene), which is the enthalpy change of the reaction 2CðgraphiteÞ þ H2 ! C2 H2
ð5:R6Þ
can be deduced in the following way: the heat of combustion of ethyne has been determined by bomb calorimetry as 1255.5 kJ/mol at 25 C (298 K). This is the heat of the reaction C2 H2 þ 2:5O2 ! 2CO2 þ H2 O
ð5:R7Þ
which, by Hess’s law (see Equation 5.22), can be equated to 298 ðΔHc Þ298 ðC2 H2 Þ ¼ 2 ΔH f ðCO2 Þ 298 298 þ ΔH f ðH2 OÞ ΔH f ðC 2 H 2 Þ 298 2:5 ΔH f ðO2 Þ ð5:23Þ We know that (ΔHc)298 (C2H2) ¼ 1255.5 kJ/mol (ΔHf)298 (CO2) ¼ 393.5 kJ/mol
5
Thermochemistry
145 Table 5.4 Heats of formation at 25 C (298 K)
(ΔHf)298 (H2O) ¼ 241.8 kJ/mol (ΔHf)298 (O2) ¼ 0.0 kJ/mol (by definition) so that by rearrangement, Equation 5.23 yields (ΔHf)298 (C2H2) ¼ +226.7 kJ/mol This compound has a positive heat of formation, unlike CO2 and H2O. This indicates that it is an endothermic compound and is therefore less stable than the parent elements. Under appropriate conditions, ethyne can decompose violently to give more stable species. The heats of formation of a number of compounds are given in Table 5.4. The most stable compounds (CO2 and H2O) have the largest negative values, while positive values tend to indicate an instability with respect to the parent elements. This can indicate a high chemical reactivity, and indeed heats of formation have been used in preliminary hazard assessment to provide an indication of the risks associated with new processes in the chemical industry. It should be noted that the heats of combustion of endothermic compounds do not give any indication of any associated reactivity (compare ethane, ethene, and ethyne in Tables 5.3 and 5.4).
Rate of Heat Release in Fires Although thermochemistry can give information relating to the total amount of energy that can be released when a fuel is burned to completion, it is rarely (if ever) possible to use heats of combustion directly to calculate the heat released in “real” fires. Indeed, it can be argued that the rate of heat release is more important than the total available [10]. When a single item is burning in isolation, the rate of burning and the rate of heat release in the flame are coupled. It has been common to express the rate of heat release as the product of the burning rate (i.e., the rate of mass ˙ [kg/s]) and the net heat of combustion of loss m the fuel (ΔHc kJ/kg). Q_ c ¼ m_ ΔH c
ð5:24Þ
However, this assumes that combustion is complete, although it is known that this is never so in
Compound Hydrogen (atomic) Oxygen (atomic) Hydroxyl (OH) Chlorine (atomic) Carbon monoxide Carbon dioxide Water (liquid) Water (vapor) Hydrogen chloride Hydrogen cyanide (gas) Nitric oxide Nitrogen dioxide Ammonia Methane Ethane Ethene Ethyne (acetylene) Propane n-Butane Iso-butanea Methanol
(ΔHf)298 (kJ/mol) +218.00 +249.17 +38.99 +121.29 –110.53 –393.52 –285.8 –241.83 –92.31 +135.14 +90.29 +33.85 –45.90 –74.87 –84.5 +52.6 +226.9 –103.6 –124.3 –131.2 –242.1
a
Heats of formation of other hydrocarbons are tabulated in Weast [9]
natural fires, which involve diffusion flames rather than premixed flames. Air and fuel have to mix by the process of diffusion (laminar or turbulent, depending on the size of the fire) before combustion can occur. The mixing process is relatively inefficient, and despite the fact that excess air is drawn (or entrained) into the flame, the products of combustion will contain some species that are only partially oxidized, such as carbon monoxide, aldehydes, ketones, and particulate matter in the form of soot or smoke. Their presence indicates that not all the available combustion energy has been released. The “combustion efficiency” is likely to vary from around 0.3–0.4 for heavily fire-retarded materials to 0.9 or higher in the case of oxygencontaining products (e.g., polyoxymethylene) [10, 11]. This is discussed in detail by Tewarson [12]. Fires burning in compartments present a completely different problem. In the first place, there is likely to be a range of different fuels present, each with a different stoichiometric air
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requirement. These will burn at different rates, dictated not just by the nature of the fuel but also by the levels of radiant heat existing within the compartment during the fire. The rate of heat release during the fully developed stage of a compartment fire is required for calculating postflashover temperature-time histories for estimating fire exposure of elements of structure, as in the method developed by Pettersson et al. [13]. To calculate the rate of heat release within the compartment, it is assumed that the fire is ventilation controlled and that all combustion takes place within the compartment. The rate of heat release ( Q_ c ) can be obtained from the expression Q_ c ¼ m_ air ΔH c ðairÞ
ð5:25Þ
where ΔHc (air) is the heat of combustion per unit mass of air consumed (3 kJ/g; see Table 5.3), ˙ air is the mass flow rate of air into the and m compartment, given approximately by the expression 1=2
m_ air ¼ 0:52A0 H 0
ð5:26Þ
where A0 is the effective area of ventilation (m2) and H0 is the height of the ventilation opening (m) [14]. The compartment temperature (as a function of time) is then obtained from heat balance calculations, as described in Drysdale [3], Tewarson [12], and Walton and Thomas [14]. The assumption behind Equation 5.25 is that the burning process is stoichiometric and that all the fuel vapors are burned within the compartment—air is supplied at exactly the rate required to consume the fuel vapors, that is, Rate of supply of air ¼r Rate of supply of fuel where r is the stoichiometric air-fuel ratio and the maximum possible temperatures will be achieved. However, it is worth noting that this does not take into account the fact that the rate of heat release is not instantaneous. Although (in principle) the ideal stoichiometric mixture is created within the compartment, burning gases will emerge from the opening(s) simply because the reaction takes time to reach completion.
Burning gases (i.e., flames) are carried outside the compartment, indicating that not all of the heat of combustion is released within the compartment. For a fully developed (postflashover) ˙ air/ fire, it is perhaps more likely that the ratio m ˙ fuel (the “equivalence ratio”) is less than the m stoichiometric ratio r—that is, insufficient air is entering the compartment to burn all the fuel vapors. Under these circumstances, excess fuel vapors will escape from the compartment and burn outside as they mix with external air. The external flame length will depend inter alia on the equivalence ratio [15]. Regardless of whether the equivalence ratio is equal to or greater than the stoichiometric ratio, fuel vapor will burn outside the compartment and temperatures based on Equation 5.25 will be high. The method will also overestimate the temperatures achieved if the equivalence ratio is much greater than the stoichiometric ratio. Under these conditions, excess air is drawn into the compartment and will act as a diluent and reduce the average temperatures—if the ventilation is high enough, the rate of heat release will be controlled by the area of the burning surface [3, 16]. Note that the concept of equivalence ratio is used elsewhere in this handbook, specifically by Tewarson [12] and by Gottuk and Lattimer [17] in discussing the yields of products generated in the upper layer during the preflashover fire. Much useful data on the fire behavior of combustible materials can be obtained by using the technique of “oxygen consumption calorimetry.” This is the basis of the “cone calorimeter,” in which the rate of heat release from a small sample of material burning under an imposed radiant heat flux is determined by measuring the rate of oxygen consumption [18]. The latter can be converted into a rate of heat release using the conversion factor 13.1 kJ/g of oxygen consumed. (A small correction is required for incomplete combustion, based on the yield of CO.) This technique can be used on a larger scale to measure the rate of heat release from items of furniture, wall lining materials, and so on [19, 20] and is now used routinely in both fire research and fire testing facilities.
5
Thermochemistry
147 Table 5.5 Thermal capacity of the products of combustion of a stoichiometric propane/air mixture
Calculation of Adiabatic Flame Temperatures In the previous sections, no consideration has been given to the fate of the energy released by the combustion reactions. Initially it will be absorbed within the reaction system itself by (1) unreacted reactants, (2) combustion products, and (3) diluents, although it will ultimately be lost from the system by various heat transfer processes. This is particularly true for natural fires in enclosed spaces. However, if we consider a premixed reaction system, such as a flammable vapor-air mixture, and assume it to be adiabatic, that is, there is no transfer of heat (or mass) to or from the system, then we can calculate the maximum theoretical temperature, the adiabatic flame temperature. Consider a flame propagating through a stoichiometric propane-air mixture of infinite extent (i.e., there are no surfaces to which heat may be transferred) and that is initially at 25 C. The appropriate equation is given by Reaction 5.R8: C3 H8 þ 5O2 þ 18:8N2 ! 3CO2 þ 4H2 O þ 18:8N2
ð5:R8Þ
This reaction releases 2044 kJ for every mole of propane consumed. This quantity of energy goes toward heating the reaction products, that is, 3 moles of carbon dioxide, 4 moles of water (vapor), and 18.8 moles of nitrogen for every mole of propane burned. The thermal capacity of this mixture can be calculated from the thermal capacities of the individual gases, which are available in the literature (e.g., JANAF) [7]. The procedure is straightforward, provided that an average value of Cp is taken for each gas in the temperature range involved, giving 942.5 kJ/K as the total thermal capacity of the products per mole of propane consumed (see Table 5.5). As 2044 kJ are released at the same time as these species are formed, the maximum temperature rise will be
CO2 H2O N2
Thermal capacity at 1000 K No. of moles (J/molK) (J/K) 3 54.3 162.9 4 41.2 164.8 18.8 32.7 614.8 Total thermal capacity ¼ 942.5 J/K (per mole of propane)
ΔT ¼
2044000 ¼ 2169 K 942:5
giving the final (adiabatic) temperature as 2169 + 298 ¼ 2467 K. In fact, this figure is approximate for the following reasons: 1. Thermal capacities change with temperature, and average values over the range of temperatures appropriate to the problem have been used. 2. The system cannot be adiabatic as there will be heat loss by radiation from the hot gases (CO2 and H2O). 3. At high temperatures, dissociation of the products will occur; as these are endothermic processes, there will be a reduction in the final temperature. Of these, (2) and (3) determine that the actual flame temperature will be much lower than predicted. These effects can be taken into account. Thus, with propane burning in air, the final temperature may not exceed 2000 K. If the propane were burning as a stoichiometric mixture in pure oxygen, then in the absence of nitrogen as a “heat sink,” much higher temperatures would be achieved. The total thermal capacity would be (942.5 614.8) ¼ 327.7 J/K. However, the amount of heat released remains unchanged (2044 kJ) so that the maximum temperature rise would be ΔT ¼
2044000 ¼ 6238K 327:7
predicting a final temperature of 6263 C. Because dissociation will be a dominant factor,
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D.D. Drysdale
this cannot be achieved and the temperature of the flame will not exceed approximately 3500 K. The occurrence of dissociation at temperatures in the region of 2000 K and above makes it necessary to take dissociation into account. Dissociation is discussed in Chap. 6. However, the simple calculation outlined above can be used to estimate the temperatures of near-limit flames, when the temperature is significantly lower and dissociation can be neglected. It is known that the lower flammability limit of propane is 2.2 %. The oxidation reaction taking place in this mixture can be described by the following equation: 0:022C3 H8 þ 0:978ð0:21O2 þ 0:79N2 Þ ! products
Dividing through by 0.022 allows this to be written C3 H8 þ 9:34O2 þ 35:12N2 ! 3CO2 þ 4H2 O þ 4:34O2 þ 35:12N2 ð5:R9Þ showing that the heat released by the oxidation of 1 mole of propane is now absorbed by excess oxygen (4.34 moles) and an increased amount of nitrogen as well as the combustion products. Carrying out the same calculation as before, it can be shown that the total thermal capacity of the products per mole of propane consumed is 1627.6 kJ/K, which gives the adiabatic flame temperature for this limiting mixture is 1281 C (1554 K). If the same calculation is carried out for the other hydrocarbon gases, it is found that the adiabatic limiting flame temperature lies in a fairly narrow band, 1600 100 K (Table 5.6). This can be interpreted by assuming that the limit exists because heat losses (by radiation from the flame) exceed the rate of heat production (within the flame). As a consequence, flame cannot sustain itself. This concept can be applied to certain practical problems relating to the lower flammability limit. Example 1 It is recognized that the leak of propane into a test cell could lead to a flammable
Table 5.6 Adiabatic flame temperature of lowerlimiting hydrocarbon/air mixtures Gas Methane Ethane Propane n-Butane n-Pentane n-Heptane n-Octane
Adiabatic flame temperature at lower flammability limit (K) 1446 1502 1554 1612 1564 1692 1632
atmosphere, and it is decided to keep the atmosphere inert by the addition of nitrogen. Calculate the percentage of nitrogen necessary to prevent ignition of a mixture in which the propane and air are in stoichiometric proportions. Solution The stoichiometric reaction for propane in air is C3 H8 þ 5O2 þ 18:8N2 ! 3CO2 þ 4H2 O þ 18:8N2
ð5:R10Þ
and the heat of combustion of propane is 2044 kJ/mole. It is assumed that the heat of combustion is absorbed by the products 3CO2 + 4H2O + 18.8 N2. It was shown above that the adiabatic flame temperature (i.e., the temperature of the product gases, assuming no heat losses) will be 2169 K. If the flame temperature can be held below 1600 K (or 1554 K, according to Table 5.6), then flame propagation will not be possible and the introduction of an ignition source will not lead to an explosion. Suppose that the extra quantity of nitrogen required to form an “inert atmosphere” corresponds to X moles per mole of propane. Then C3 H8 þ 5O2 þ 18:8N2 þ XN2 ! 3CO2 þ 4H2 O þ ð18:8 þ XÞN2 ð5:R11Þ Following the procedure illustrated in Table 5.5, the thermal capacity of the product gases— 3CO2 + 4H2O + (18.8 + X)N2—will be 3 54.3 + 4 41.2 + (18.8 + X) 32.7 ¼ ΣCp. If sufficient nitrogen has been added to reduce the adiabatic flame temperature to 1554 K, then the
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Thermochemistry
149
thermal capacity of the product gases will be given by X
2044000 1554 298 ¼ 1627:4 kJ=mole of propane
Cp ¼
If we consider that 1 mole of fuel passes through each of the six cylinders, but of the 6 moles only three are burned, we have overall 6CH4 þ 12O2 þ 45:12N2 ! 3CH4 þ 3CO2 þ 6H2 O þ 6O2 þ 45:12N2 ð5:R13Þ
Thus 3 54:3 þ 4 41:2 þ ð18:8 þ XÞ 32:7 ¼ 1627:4
Dividing through by 3 gives 2CH4 þ 4O2 þ 15:04N2 ! CH4 þ 2O2 þ CO2 þ 2H2 O þ 15:04N2
X ¼ 20:9 Consequently, the amount of nitrogen added to the air in the test cell to render the atmosphere “inert” with respect to a leak of propane corresponds to 20.9 moles of N2 for every (5 + 18.8) ¼ 23.8 moles of air, that is, the mixture in the cell must be 47 % nitrogen, the balance being air. (Experimentally, a significantly lower figure is obtained—c. 40 %. It should be remembered that in the above calculation it is assumed that the adiabatic temperature assumption is valid and that the reaction will go to completion.) Example 2 A mechanical engineering research laboratory contains a six-cylinder internal combustion engine that is being used for research into the performance of spark plugs. The fuel being used is methane, CH4, and the fuel-air mixture can be adjusted at will. The combustion products are extracted from the exhaust manifold through a 30 cm square duct, 20 m long. It is found that the engine will continue to operate with a stoichiometric mixture when only three of the cylinders are firing. If under these conditions the average temperature of the gases entering the duct from the manifold is 700 K, is there a risk of an explosion in the duct? Solution The stoichiometric reaction for methane in air is CH4 þ 2O2 þ 7:52N2 ! CO2 þ 2H2 O þ 7:52N2
ð5:R12Þ
ð5:R14Þ The mixture discharged into the exhaust manifold has the composition given by the right-hand side of Reaction 5.R14. If this “burns” at 700 K, the final abiabatic flame temperature may be calculated on the basis of the reaction CH4 þ 2O2 þ CO2 þ 2H2 O þ 15:04N2 ! 2CO2 þ 4H2 O þ 15:04N2 ð5:R15Þ The total thermal capacity of the product gases (2CO2 + 4H2O + 15.04 N2) (at 1000 K) can be shown to be 765.3 J per mole of methane burned. Using Kirchoff’s equation (Equation 5.19), ΔHc(CH4) at 700 K is calculated as 802.8 kJ/mol, giving ΔT ¼ 802800/765.3 ¼ 1049 K. This gives a final temperature of 1749 K, which is significantly higher than the limiting flame temperature (1600 K) discussed above. This indicates that there is a risk of explosion, and measures should be applied to prevent this mixture being discharged into the duct. It should be noted that at 700 K there will be a “slow” reaction between methane and the oxygen present, which could invalidate the tacit assumption that the duct becomes completely filled with the mixture described by the right-hand side of Reaction 5.R13. However, slow oxidation of the methane will tend to make the mixture less flammable, and so the calculation gives a conservative answer.
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Nomenclature A Aw Cp E F H H ΔHc ΔHf ˙ m ˙ air m n p q Qc R T V w
Area (Equation 5.5) Area of ventilation opening Specific heat Internal energy Force (Equation 5.4) Height of ventilation opening Enthalpy Heat of combustion Heat of formation Mass rate of burning Mass flow rate of air Number of moles Pressure Energy Rate of heat release Universal gas constant Temperature Volume Work
Subscripts c F f o p v
Combustion Final Formation Initial Constant pressure Constant volume
Superscripts Pr R
Products Reactants
References 1. W.J. Moore, Physical Chemistry, 5th ed., Longman, London (1974). 2. P Atkins and J de Paula, “Atkins’ Physical Chemistry” 9th Edition (Oxford University Press, 2009) 3. D.D. Drysdale, Introduction to Fire Dynamics, 3rd ed., John Wiley and Sons, Chichester, UK (2011). 4. J.F. Griffiths, “Combustion Kinetics,” in SFPE Handbook of Fire Protection Engineering, 4th
ed. (P.J. DiNenno et al., eds.), National Fire Protection Association, Quincy, MA, pp. 1-220–1-230 (2008). 5. A.F. Roberts, Combustion and Flame, 8, p. 245 (1964). 6. G M Barrow, “Physical Chemistry” 4th Edition, McGraw-Hill Book Co. (New York, 1961) 7. NIST-JANAF Thermochemical Tables: see http:// kinetics.nist.gov/janaf/ 8. R.A. Strehlow, Combustion Fundamentals, McGrawHill, New York (1984). 9. R.C. Weast, Handbook of Chemistry and Physics, Chemical Rubber Co., Cleveland, OH (1973). 10. V. Babrauskas and R. Peacock, “Heat Release Rate: The Single Most Important Variable in Fire Hazard,” in Fire Safety Journal, 18, pp. 255–272 (1992). 11. A. Tewarson, in Flame Retardant Polymeric Materials (M. Lewin, ed.), Plenum, New York (1982). 12. M. Khan, A. Tewarson, and M. Chaos, “Combustion Characteristics of Materials and Generation of Fire Products,” in SFPE Handbook of Fire Protection Engineering, 5th ed. Springer, New York, 2015. 13. O. Pettersson, S.E. Magnusson, and J. Thor, Fire Engineering Design of Structures, Swedish Institute of Steel Construction, Publication, 50 (1976). 14. W.D. Walton and P.H. Thomas, “Estimating Temperatures in Compartment Fires,” in SFPE Handbook of Fire Protection Engineering, 4th ed. (P.J. DiNenno et al., eds.), Society of Fire Protection Engineers, Bethesda, MD, pp. 3-204–3-221 (2008). 15. M.L. Bullen and P.H. Thomas, Seventeenth Symposium (International) on Combustion, Combustion Institute, Pittsburgh, PA (1979). 16. P.H. Thomas and A.J.M. Heselden, “Fully Developed Fires in Compartments,” CIB Report No. 20; Fire Research Note No. 923, Conseil International du Batiment, France (1972). 17. D.T. Gottuk and B.Y. Lattimer, “Effect of Combustion Conditions on Species Production,” in SFPE Handbook of Fire Protection Engineering, 4th ed. (P.J. DiNenno et al., eds.), National Fire Protection Association, Quincy, MA, pp. 2-67–2-95 (2008). 18. V. Babrauskas, “The Cone Calorimeter,” in SFPE Handbook of Fire Protection Engineering, 4th ed. (P.J. DiNenno et al., eds.), National Fire Protection Association, Quincy, MA, pp. 3-90–3-108 (2008). 19. V. Babrauskas and S.J. Grayson (eds.), Heat Release in Fires, Elsevier Applied Science, London (1992). 20. M.L. Janssens, “Calorimetry,” in SFPE Handbook of Fire Protection Engineering, 5th ed. Springer, 2015.
D.D. Drysdale is professor emeritus in the BRE Centre for Fire Safety Engineering, School of Engineering, at the University of Edinburgh, Scotland. His research interests lie in fire science, fire dynamics, and the fire behavior of combustible materials.
6
Chemical Equilibrium Raymond Friedman
Introduction The temperature of a flame must be known in order to calculate convective and radiative heat transfer rates, which control pool-fire burning rates, flame spread rates, remote ignitions, damage to exposed items (e.g., structural steel, wiring), and response of thermal fire detectors or automatic sprinklers. Chapter 5 provides a simple technique for calculating flame temperature, based on ignoring the dissociations that occur at high temperature. Although the error is small for near-limit flames, this technique gives answers that are too high. For example, if propane (C3H8) burns in stoichiometric proportions with air at 300 K, and it is assumed that the only products are CO2, H2O, and N2, then the simple thermochemical calculation yields a flame temperature of 2394 K. On the other hand, if chemical equilibrium is considered, so that the species CO, O2, H2, OH, H, O, and NO are assumed present in the products, then the flame temperature, calculated by methods described in this section, comes out to be 2268 K. Flame temperature measurements in laminar premixed propane-air flames agree with the latter value. (The discrepancy in flame temperature caused by neglecting dissociation would be even greater for fires in oxygen-enriched atmospheres.)
The chemical equilibrium calculation yields not only the temperature but the equilibrium composition of the products. Thus, the generation rate of certain toxic or corrosive products such as carbon monoxide, nitric oxide, or hydrogen chloride may be calculated, insofar as the assumption of equilibrium is valid. For a fire in a closed volume, the final pressure as well as the temperature will depend on the dissociations and therefore require a calculation taking chemical equilibrium into account. From a fire research viewpoint, there is interest in correlating flammability limits, extinguishment, soot formation, toxicity, flame radiation, or other phenomena; and chemical equilibrium calculations in some cases will be a useful tool in such correlations. In a later part of this chapter, departure of actual fires from chemical equilibrium will be discussed.
The Chemical Equilibrium Constant Consider a chemical transformation, such as 2CO þ O2 ! 2CO2
ð6:1Þ
If this process can occur, presumably the reverse process can also occur (principle of microscopic reversibility, or principle of detailed balancing): 2CO2 ! 2CO þ O2
ð6:2Þ
R. Friedman (*) Retired from FM Global M.J. Hurley (ed.), SFPE Handbook of Fire Protection Engineering, DOI 10.1007/978-1-4939-2565-0_6, # Society of Fire Protection Engineers 2016
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R. Friedman
If both processes occur at finite rates in a closed system, then, after a sufficient time, a condition of chemical equilibrium will be reached, after which no further change occurs as long as the temperature and pressure remain constant and no additional reactants are introduced. This condition of equilibrium can be expressed as a mathematical constraint on the system, which, for the gaseous reaction 2CO þ O2 ⇄ 2CO2 , can be written K3 ¼
p2 CO2 p2 CO pO2
ð6:3Þ
where the pi are partial pressures (atm)1 and K3 is the equilibrium constant. This expression can be rationalized by the following argument. According to the chemical “law of mass action,” first stated a century ago, the rate of the forward reaction (Equation 6.1) at a given temperature is given by k f p2CO pO2 while the rate of the reverse reaction (Equation 6.2) is given by kr p2CO2 : At equilibrium, the forward rate must be equal to the reverse rate: k f p2CO pO2 ¼ kr p2CO2
ð6:4Þ
which may be rearranged to p2 CO2 kf ¼ ¼ K3 2 p CO pO2 kr
ð6:5Þ
Although this appears to be a satisfactory explanation, research over the past hundred years has shown that chemical reactions in fact rarely proceed as suggested by the stoichiometric equation. (This is discussed more fully in Chap. 13.) For example, the three-body collision of two CO molecules and an O2 molecule, resulting in the formation of two CO2 molecules, simply does not happen. Rather, the reaction would occur as follows: O2 þ M ! 2O þ M
ð6:6Þ
(where M is any molecule) followed by O þ CO þ M ! CO2 þ M
ð6:7Þ
Now, observe how Equation 6.3 can be obtained from this reaction sequence. The reverse of O2 + M ! 2O + M, namely 2O + M ! O2 + M, can also occur, and the equilibrium constant for this pair of reactions, which actually do occur, is K6 ¼ pO 2 pM = pO2 pM ¼ pO 2 = pO2 . (The pM term cancels.) Similarly the reverse reaction CO2 + M ! O + CO + M can occur, and the equilibrium constant is K7 ¼ pCO2 = pCO pO . If we now multiply K72 by K6, we obtain K 27 K 6 ¼
pCO2 pCO pO
2
p2 pO 2 ¼ 2 CO2 pO2 p CO pO2
¼ K3
ð6:8Þ
Thus, Equation 6.3 is perfectly valid, even if the “law of mass action” does not correctly describe the reaction process involving CO and O2. To get a further understanding of the validity of the equilibrium constant concept, consider the following facts: CO will not react with O2—even by the above mechanism involving O atoms— unless first heated to quite high temperatures. However, at least a trace of moisture is usually present, and in such cases the reaction occurs by the following process, which can occur at lower temperatures. First, H and OH are formed by dissociation of H2O. Then, the CO is converted by CO þ OH ⇄ CO2 þ H K 9 ¼
pCO2 pH pCO pOH
ð6:9Þ
while the O2 reacts with H: O2 þ H ⇄ OH þ O K 10 ¼
pOH pO pO 2 pH
ð6:10Þ
If the quantity K92K10 is now calculated, 1
In place of partial pressures, the concentrations of the species in moles/liter can be used in these formulae instead (see Chap. 13).
K 29 K 10 ¼
p2 CO2 pH pO CO pO2 pOH
p2
ð6:11Þ
6
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153
But, the reaction H + O + M ! OH + M can occur, as well as its reverse, OH + M ! H + O + M. It does not matter if these reactions are actually important in the rate of oxidation of CO in the presence of H2O. As long as these reactions can occur, then at equilibrium
Now the system is completely defined by the simultaneous solution of these three equations. The equilibrium constant varies with temperature but is independent of pressure (except at rather high pressures). It is also independent of the presence of other reactive chemical species.
k f pH pO pM ¼ kr pOH pM
Generalized Definition of Equilibrium Constant
and kf p ¼ K 12 ¼ OH kr pH pO
ð6:12Þ
aX1 þ bX2 ⇄ cY1 þ dY2
Substituting this into Equation 6.11 p2 CO2 ¼ K 29 K 10 K 12 ¼ K 3 p2 CO pO2
ð6:13Þ
Thus, the ratio p2CO2 = p2CO pO2 is a constant at equilibrium (at a given temperature) regardless of the reaction mechanism, even if other (hydrogen-containing) species are involved, because by the principle of microscopic reversibility, these other species (catalysts) affect the reverse reaction as well as the forward reaction. Let us now consider the mathematical specification of the CO–CO2–O2 system at equilibrium. The system, at a given temperature and pressure, may be described by three variables, namely the partial pressures of the three species: pCO, pO2 , and pCO2 . There are already two well-known constraints on the system: (1) The sum of the partial pressures must equal the total pressure, p pCO þ pO2 þ pCO2 ¼ p
ð6:15Þ
A third constraint, that of chemical equilibrium, provides a third equation involving pCO, pO2 , and pCO2 : p2 CO2 ¼ K3 p2 CO pO2
K would be given by K¼
ð pY1 Þc ð pY2 Þd ð pX1 Þa ð pX2 Þb
Attention should be paid to the manner in which a chemical reaction is written. For example, instead of writing 2CO þ O2 ⇄ 2CO2 one could equally well have written CO þ 1=2O2 ⇄ CO2 . The equilibrium constant for the latter formulation is K 16 ¼
pCO2
ð6:16Þ
1=2
pCO pO2
By comparison of Equation 6.16 with Equapffiffiffiffiffiffi tion 6.3, it is clear that K 16 ¼ K 3 : If the reaction was written as 2CO2 ⇄ 2CO þ O2 the equilibrium constant would be equal to 1/K3.
ð6:14Þ
and (2) the ratio of carbon atoms to oxygen atoms in the system must remain at the original, presumably known, value of C/O: pCO þ pCO2 C ¼ O pCO þ 2 pO2 þ 2 pCO2
For a generalized reaction
ð6:3Þ
Simultaneous Equilibria In most real chemical systems, one must deal with a number of simultaneous chemical equilibria. For example, air at 2500 K will contain the species N2, O2, NO, and O. The following simultaneous equilibria may be considered O2 ¼ 2O N2 þ O2 ¼ 2NO
pO 2 pO 2
ð6:17Þ
p2 NO pN2 pO2
ð6:18Þ
K 17 ¼ K 18 ¼
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R. Friedman
N2 þ 2O ¼ 2NO
K 19 ¼
p2 NO pN 2 p O 2
ð6:19Þ
It is easily seen from the above relations that K19 ¼ K18/K17. Hence, Equations 6.17, 6.18, and 6.19 are not three independent equations, and any two of these equations may be used to describe the equilibrium condition; the third would be redundant. To determine the four unknowns, pN2 , pO2 , pNO, and pO, one would solve the selected two equilibrium relations plus the following two relations: pNO þ pN 2 þ pO2 þ pO ¼ p
ð6:20Þ
pNO þ 2 pN2 ¼ 3:76 pNO þ 2 pO2 þ pO
ð6:21Þ
And
where 3.76 is the ratio of nitrogen atoms to oxygen atoms in air. If one knows the temperature, the equilibrium constants may be calculated from the thermodynamic properties of the reactants and products, as discussed in the next section. However, since the various equilibrium reactions release or absorb energy, and accordingly raise or lower the temperature of an adiabatic system respectively, the determination of equilibrium composition of an adiabatic system must proceed simultaneously with the calculation of its temperature; that is, an energy balance must be satisfied as well as the equilibrium equations, the atom-ratio equations, and the p ¼ ∑ pi equation. As a general rule, a gaseous chemical system at a given temperature, containing s kinds of chemical species involving e chemical elements, requires s-e equilibrium relations, e-1 atom-ratio relations, and a p ¼ ∑ pi equation, in order to specify it. If the temperature is unknown, an energy balance equation is also needed. (If the pressure is unknown but the volume is known, then the equation of state must be used in the pressure equation.) In order to solve an actual problem, one must select the species to be considered. The more
species one includes, the more difficult is the calculation. There is no need to include any species that will be present in very small quantity at equilibrium. Some guidelines can be provided. For combustion of a C–H–O compound in air, it is usually sufficient to include the species CO2, H2O, N2, O2, CO, H2, OH, H, O, and NO. These species are adequate if the air-fuel ratio is sufficiently large so that the O/C atomic ratio is greater than one. If the O/C atomic ratio is less than one, then solid carbon must be considered, as well as many additional gaseous species. If chlorine is present, then HCl, Cl2, and Cl must be added. If sulfur is present, then SO2 and SO3 are the primary species, unless there is a deficiency of oxygen.
The Quantification of Equilibrium Constants While a chemist might establish the numerical value of an equilibrium constant for A ⇄ B by direct measurement of the partial pressures of A and B in a system at equilibrium, this is rarely done because it is difficult to make such measurements in a high-temperature system, and it takes a long time to establish equilibrium in a low-temperature system. Instead, the equilibrium constant is generally determined from the thermodynamic relation first deduced by van’t Hoff in 1886 [1] ΔFo ¼ RT ln K
ð6:22Þ
If this equation is applied to A ⇄ 2B at absolute temperature T, then K ¼ p2B = pA ; and ΔFo is the free energy of two moles (mol) of B at 1 atm and temperature T, minus the free energy of 1 mol of A at 1 atm and temperature T. (The superscript o designates that each substance is in its “standard state,” that is, an ideal gas at 1 atm.) By definition ΔFo ¼ ΔH o TΔSo ¼ ΔEo þ ð pV o Þ TΔSo
ð6:23Þ
Accordingly, if ΔSo, the entropy difference, and either ΔHo, the enthalpy difference, or ΔEo, the
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energy difference, are known for the substances involved in an equilibrium at temperature T, then the equilibrium constant, K, may be calculated. It happens that ΔSo, ΔHo, and ΔEo are well known for almost all substances expected to be present at equilibrium in combustion gases at any temperature up to 4000 K, so the calculation of equilibrium constants is straightforward. The variation of the equilibrium constant with temperature was shown by van’t Hoff [1] to be given by d ln K ΔH o ΔH ¼ ¼ for ideal gases dT RT 2 RT 2 ð6:24Þ Thus, for an exothermic reaction occurring at temperature T, ΔH is negative and K decreases as T increases. The converse is true for endothermic reactions. It is appropriate to inquire about the underlying physical reason for the value of K to be governed by ΔFo (actually ΔHo and ΔSo). An explanation is as follows: any chemical system being held at constant temperature will seek to reduce its energy, E, and to increase its entropy, S. The reduction of energy is analogous to a ball rolling downhill. The increase of entropy is analogous to shuffling a sequentially arranged deck of cards, yielding a random arrangement. These two tendencies will often affect the equilibrium constant in opposite directions. Consider the equation ln K ¼
ΔSo ΔEo Δn R RT
ð6:25Þ
where Δn is the increase in the number of moles of product relative to reactant. Equation 6.25 is obtained by combining Equations 6.22 and 6.23 with the ideal gas law at constant temperature Δ(pVo) ¼ ΔnRT. Inspection of Equation 6.25 shows that, if ΔSo is a large positive quantity and ΔSo/R dominates the other terms, K will be large, that is, the reaction is driven by the “urge” to increase entropy. Again, if the reaction is highly endothermic, then –ΔEo/RT will be a
large negative number and can dominate the other terms to cause K to be small, that is, the reaction prefers to go in the reverse, or exothermic, direction and reduces the energy of the system. (Most spontaneous reactions are exothermic.) The Δn term is generally small compared with the other terms and represents the work done by the expanding system on the surroundings, or the work done on the contracting system by the surroundings. In summary, Equation 6.25 represents the balance of these various tendencies and determines the relative proportions of reactants and products at equilibrium. Notice that the term ΔEo/RT becomes small at sufficiently high temperature, and the entropy term then dominates. In other words, all molecules break down into atoms at sufficiently high temperature, to maximize entropy. The important conclusion from this discussion is that there is no need to consider rates of forward and reverse processes to determine equilibrium. Table 6.1 provides values of equilibrium constants for 13 reactions involving most species found in fire products at equilibrium, over a temperature range from 600 K to 4000 K. Equilibrium constants for other reactions involving the same species may be obtained by combining these constants, as in Equation 6.13, or as illustrated in the examples below. Table 6.1 does not include the ½ N2 ¼ N equilibrium, because fire temperatures are generally not high enough for significant N to form. Tables 6.2 and 6.3 present information on the degree to which various gases are dissociated at various temperatures. In performing calculations, remember that even if a relatively small fraction of dissociation occurs, a rather large amount of energy may be absorbed in the dissociation, with a corresponding large increase in the energy of the system. For example, if water vapor initially at 2800 K is allowed to dissociate adiabatically at 1 atm, only 5.7 % of the H2O molecules will dissociate, but the temperature will drop from 2800 K to 2491 K; that is, the temperature relative to a 300 K baseline is lower by 12.4 %.
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Table 6.1 Values of log10 K for selected reactions 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 3000 3100 3200 3300 3400 3500 3600 3700 3800 3900 4000
KA –18.574 –15.449 –13.101 –11.272 –9.807 –8.606 –7.604 –6.755 –6.027 –5.395 –4.842 –4.353 –3.918 –3.529 –3.178 –2.860 –2.571 –2.307 –2.065 –1.842 –1.636 –1.446 –1.268 –1.103 –0.949 –0.805 –0.670 –0.543 –0.423 –0.310 –0.204 –0.103 –0.007 0.084 0.170
KB –16.336 –13.599 –11.539 –9.934 –8.646 –7.589 –6.707 –5.958 –5.315 –4.756 –4.266 –3.833 –3.448 –3.102 –2.790 –2.508 –2.251 –2.016 –1.800 –1.601 –1.417 –1.247 –1.089 –0.941 –0.803 –0.674 –0.553 –0.439 –0.332 –0.231 –0.135 –0.044 0.042 0.123 0.201
KC 18.633 15.583 13.289 11.498 10.062 8.883 7.899 7.064 6.347 5.725 5.180 4.699 4.270 3.886 3.540 3.227 2.942 2.682 2.443 2.224 2.021 1.833 1.658 1.495 1.343 1.201 1.067 0.942 0.824 0.712 0.607 0.507 0.413 0.323 0.238
KD –2.568 –2.085 –1.724 –1.444 –1.222 –1.041 –0.890 –0.764 –0.656 –0.563 –0.482 –0.410 –0.347 –0.291 –0.240 –0.195 –0.153 –0.116 –0.082 –0.050 –0.021 0.005 0.030 0.053 0.074 0.094 0.112 0.129 0.145 0.160 0.174 0.188 0.200 0.212 0.223
KE 34.405 29.506 25.830 22.970 20.680 18.806 17.243 15.920 14.785 13.801 12.940 12.180 11.504 10.898 10.353 9.860 9.411 9.001 8.625 8.280 7.960 7.664 7.388 7.132 6.892 6.668 6.458 6.260 6.074 5.898 5.732 5.574 5.425 5.283 5.149
KF 14.318 12.946 11.914 11.108 10.459 9.926 9.479 9.099 8.771 8.485 8.234 8.011 7.811 7.631 7.469 7.321 7.185 7.061 6.946 6.840 6.741 6.649 6.563 6.483 6.407 6.336 6.269 6.206 6.145 6.088 6.034 5.982 5.933 5.886 5.841
KG –7.210 –6.086 –5.243 –4.587 –4.062 –3.633 –3.275 –2.972 –2.712 –2.487 –2.290 –2.116 –1.962 –1.823 –1.699 –1.586 –1.484 –1.391 –1.305 –1.227 –1.154 –1.087 –1.025 –0.967 –0.913 –0.863 –0.815 –0.771 –0.729 –0.690 –0.653 –0.618 –0.585 –0.554 –0.524
KH –3.814 –2.810 –2.053 –1.462 –0.988 –0.599 –0.273 0.003 0.240 0.447 0.627 0.788 0.930 1.058 1.173 1.277 1.372 1.459 1.539 1.613 1.681 1.744 1.802 1.857 1.908 1.956 2.001 2.043 2.082 2.120 2.155 2.189 2.220 2.251 2.280
KI –7.710 –6.182 –5.031 –4.133 –3.413 –2.822 –2.328 –1.909 –1.549 –1.236 –0.962 –0.720 –0.504 –0.310 –0.136 0.022 0.166 0.298 0.419 0.530 0.633 0.729 0.818 0.900 0.978 1.050 1.118 1.182 1.242 1.299 1.353 1.404 1.452 1.498 1.541
KJ –5.641 –4.431 –3.522 –2.814 –2.245 –1.799 –1.389 –1.059 –0.775 –0.527 –0.311 –0.119 0.053 0.207 0.346 0.472 0.587 0.692 0.789 0.879 0.962 1.039 1.110 1.178 1.240 1.299 1.355 1.407 1.459 1.503 1.547 1.589 1.629 1.666 1.703
KK 24.077 20.677 18.125 16.137 14.544 13.240 12.152 11.230 10.438 9.752 9.191 8.420 8.147 7.724 7.343 6.998 6.684 6.396 6.134 5.892 5.668 5.460 5.268 5.088 4.920 4.763 4.616 4.478 4.347 4.224 4.108 3.998 3.894 3.795 3.700
KL 8.530 7.368 6.494 5.812 5.265 4.816 4.442 4.124 3.852 3.615 3.408 3.225 3.062 2.916 2.785 2.666 2.558 2.459 2.368 2.285 2.208 2.136 2.070 2.008 1.950 1.896 1.845 1.798 1.753 1.710 1.670 1.632 1.596 1.562 1.529
KM 5.036 4.374 3.876 3.486 3.173 2.917 2.702 2.520 2.364 2.229 2.110 2.006 1.913 1.829 1.754 1.686 1.625 1.568 1.517 1.469 1.425 1.384 1.347 1.311 1.278 1.248 1.219 1.192 1.166 1.142 1.119 1.098 1.077 1.058 1.039
Partial pressures of all gases are expressed in atmospheres (Pascals/101,325). Graphite, C(S), is assigned a value of unity in the equilibrium expressions for KE and KF
Table 6.2 Temperature (K) at Which a given fraction of a pure gas at 1 atm is dissociated Fraction 0.001 0.004 0.01 0.04 0.1 0.4
CO2 1600 1800 1950 2200 2450 2950
H2O 1700 1900 2100 2400 2700 3200
H2 2050 2300 2450 2700 2900 3350
O2 2200 2400 2600 2900 3200 3700
N2 4000 — — — — —
Table 6.3 Temperature at which air at equilibrium contains a given fraction of nitric oxide, at 1 atm Fraction 0.001 0.004 0.01 0.04
Temperature (K) 1450 1750 2100 2800
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Carbon Formation in OxygenDeficient Systems Solid carbon (soot) may be expected to form in oxygen-deficient combustion products, under some conditions. Since solid carbon does not melt or boil until extremely high temperatures (~4000 K), we only need concern ourselves with solid carbon C(s), not liquid C(l) or gaseous carbon C(g). Consider pure carbon monoxide at 2000 K. There are three conceivable ways in which it might form solid carbon: 1=2 pCO2 1 1 α : CO ⇄ CðsÞ þ CO2 Kα ¼ 2 2 p 1=2CO pO2 1 β : CO ⇄ CðsÞ þ O2 Kβ ¼ 2 pCO p γ : CO ⇄ CðsÞ þ O Kγ ¼ O pCO Note that solid carbon does not appear in any of the equilibrium expressions. (By convention, a solid in equilibrium with gases is assigned a value of unity.) From Table 6.1, we see that, at 2000 K, 1=2
Kα ¼
KE ¼ antilog10 KF
10:353 7:469 2
¼ 5:1 103 Kβ ¼
1 ¼ antilog10 ½0 7:469 ¼ 3:4 108 KF
Kγ ¼
KA ¼ antilog10 ½3:178 7:469 KF
¼ 2:2 1011 We see that Kα, Kβ, and Kγ are all small compared with unity, so very little of the CO would decompose by any of these modes. However, Kα is much larger than either Kβ or Kγ, so it is the dominant mode for whatever decomposition may occur. Thus, from the expression pCO2 ¼ ðKa pCO Þ2 , and taking pCO as 1 atm, we calculate pCO2 ¼
2 5:1 103 ¼ 2:6 105 atm: Since, by process α, 2 mol of CO must decompose for each mole of CO2 formed, we conclude that 2 2.6 10–5 or 5.2 10–5 mol of CO will decompose to C(s) plus CO2, per mole of CO originally present, after which we will have reached an equilibrium state. In other words, about 1/20,000 of the CO will decompose. If the original mixture had consisted of CO at 1 atm plus CO2 at any pressure greater than 2.6 10–5 atm, at 2000 K, then we could conclude that no carbon whatsoever would form. It can also be shown that addition of a trace of O2 or H2O to CO at 2000 K would completely suppress carbon formation. As a general statement, for a chemical system containing fewer carbon atoms than oxygen atoms, the equilibrium condition will favor CO formation rather than that of solid carbon. For a carbon-containing system with little or no oxygen, carbon may or may not form, depending on the hydrogen partial pressure. For example, carbon may form according to C2 H2 ⇄ CðsÞ þ H2 . The equilibrium expression for this reaction is written pH2 ¼ K ð¼ 13:9 at 3000KÞ p C2 H 2 Again, note that solid carbon does not appear in the expression. If we rewrite the expression in the form pH2 > 13:9 pC2 H2 , it becomes the criterion for suppression of carbon formation at 3000 K. In other words, as long as pH2 is more than 13.9 times as large as pC2 H2 , no carbon will form at 3000 K and any carbon present will be converted to C2H2. On the other hand, pure C2H2 will decompose to C(s) plus H2 until the H2/C2H2 ratio reaches 13.9, after which no further decomposition will occur at 3000 K. Another way to view this is to say that H2, C2H2, and solid carbon at 3000 K will be in a state of equilibrium if and only if the ratio pH2 = pC2 H2 ¼ 13:9, and this is true regardless of the quantity of solid carbon present, and also regardless of the presence of other gases. For a C–H–O–N system, the threshold conditions for equilibrium carbon formation are
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R. Friedman
Table 6.4 Threshold atomic C/O ratios for carbon formation (equilibrium at 1 atm, N/O ¼ 3.76) Atomic H/C ratio 0 2 4
Temperature (K) 1600 2000 1.00 1.00 1.00 1.02 1.00 1.05
2400 1.00 1.09 1.16
2800 1.00 1.30 1.56
equilibrium condition is only a limiting case that real flames may approach. The products of a nonluminous laminar flame more than a few millimeters from any cold surface will always be very nearly in equilibrium.
Sample Problems somewhat more complicated, but the trends are illustrated by the calculated values shown in Table 6.4 for carbon formation thresholds in carbon-hydrogen-air systems at 1 atm. It must be noted that carbon forms more readily in actual flames than Table 6.4 indicates, because of nonequilibrium effects. In premixed laminar flames, incipient carbon formation occurs at a C/O ratio roughly 60 % of the values shown in Table 6.4. See the next section for further comments on nonequilibrium.
Departure from Equilibrium This procedure of specifying chemical systems by equilibrium equations will only yield correct results if the system is truly in equilibrium. If one prepares a mixture of H2 and O2 at room temperature and then ages the mixture for a year, it will be found that essentially nothing has happened and the system will still be very far from equilibrium. On the other hand, such a system at a high temperature characteristic of combustion will reach equilibrium in a small fraction of a second. For example, a hydrogen atom, H, in the presence of O2 at partial pressure 0.1 atm will react so fast at 1400 K that its half-life is only about 2 μs. (At room temperature, the half-life of this reaction is about 300 days.) Since peak flame temperatures are almost always above 1400 K, and sometimes as high as 2400 K, it would appear that equilibrium would always be reached in flames. However, luminous (yellow) flames rapidly lose heat by radiation, turbulent flames may be partially quenched by the action of steep velocity gradients, and flames burning very close to a cold wall may be partially quenched by heat transfer to the wall. Thus, the
Example 1 Given a mixture of an equal number of moles of steam and carbon monoxide, what will the equilibrium composition be at 1700 K and 1 atm? Solution We would expect the species CO, H2O, CO2, and H2 to be present. From Table 6.2, we see that the equilibria H2 ⇄ 2H, O2 ⇄ 2O, and H2 O ⇄ 1=2H2 þ OH can all be neglected at 1700 K, so the species H, O, and OH will not be present in significant quantities. Since we have four species involving three chemical elements, we will require 4—3 or 1, equilibrium relationship, for the equilibrium H2 O þ CO ⇄ H2 þ CO2 . The relationship is pH2 pCO2 ¼K pH2 O pCO
ð6:26Þ
In addition, we need 3—1, or 2, atom-ratio relations, which are H 2 pH 2 þ 2 pH 2 O : ¼2 C pCO þ pCO2
ð6:27Þ
(because the original mixture of H2O + CO contains two H atoms per C atom) and O pH2 O þ pCO þ 2 pCO2 : ¼2 C pCO þ pCO2
ð6:28Þ
(because the original mixture of H2O + CO contains two O atoms per C atom). Finally, the sum of the partial pressures equals 1 atm: pH2 O þ pCO þ pH2 þ pCO2 ¼ 1
ð6:29Þ
We now have a well-set problem, four equations and four unknowns, which may be solved as soon as K is quantified.
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159
We do not find the equilibrium H2 O þ CO ⇄ H2 þ CO2 in Table 6.1. However, if we calculate (KE/KFKC) from Table 6.1, we see that 1=2 1=2 ð1Þ pO2 p H p O2 pCO2 KE ¼ 2 K F K C ð1Þ pO2 pCO p H2 O pCO2 pH2 ¼ ¼K pCO pH2 O
From Table 6.1, log10 (KEI/KFKC) at 1700 K ¼ 12.180 – 8.011 – 4.699 ¼ –0.51, and K ¼ antilog10 (–0.51) ¼ 0.309. Upon substituting K ¼ 0.309 into Equation 6.26, and then simultaneously solving Equations 6.26, 6.27, 6.28, and 6.29, we obtain pCO2 ¼ pH2 ¼ 0:179 atm and pH2 O ¼ pCO ¼ 0:321 atm Example 2 One mole of hydrogen is introduced into a 50-L vessel that is maintained at 2500 K. How much dissociation will occur, and what will the pressure be? Solution Let α be the degree of dissociation of the hydrogen defined by ( α ¼ ð pH =2Þ=
pH2 þ ð pH =2Þ ). Thus, α ranges from zero to one. One mole of H2 partially dissociates to produce 2 α mol of H, leaving 1—α mol of H2. The total number of moles is then 2 α + 1 – α, or α + 1. In view of the definition of α, the total number of moles present is ( pH þ pH2 =
pH2 þ ð pH =2Þ ). By the ideal gas law, PV ¼ nRT.
pH þ pH2 ð50Þ ¼
pH þ pH2 ð0:08206Þð2500Þ pH2 þ ð pH =2Þ
ð6:30Þ which reduces to pH2 þ
pH ¼ 4:103 2
ð6:31Þ
The equilibrium equation is
pH 1=2 ¼ K B
pH 2
ð6:32Þ
From Table 6.1, log10KB ¼ –1.601 at 2500 K, and therefore KB ¼ 0.0251. Upon substitution into Equation 6.32 and elimination of pH2 between Equations 6.31 and 6.32, one obtains pH 2 þ 0:000316 pH 0:00258 ¼ 0
ð6:33Þ
This equation yields a positive and a negative root. The negative root has no physical significance. The positive root is pH ¼ 0:0506 atm. Then, Equation 6.32 yields pH2 ¼ 4:08 atm, and the total final pressure is 4.08 + 0.0506 ¼ 4.13 atm. The degree of dissociation, α, comes out to be 0.0062. (This is less dissociation than indicated by Table 6.2 because the pressure is well above 1 atm.) Example 3 Propane is burned adiabatically at 1 atm with a stoichiometric proportion of air. Calculate the final temperature and composition. The initial temperature is 300 K. Solution The problem must be solved by a series of iterations. The first step is to assume a final temperature, either based on experience or by selecting a temperature substantially below the value calculated by assuming that CO2 and H2O are the only products of combustion. The second step is to solve the set of equations that specify the equilibrium composition at the assumed final temperature. The third step is to consult an overall enthalpy balance equation, which will show that the assumed final temperature was either too high or too low. The fourth step is to assume an appropriate new final temperature. The fifth and sixth steps are repeats of the second and third steps. If the correct final temperature is now found to be bracketed between these two assumed temperatures, then an interpolation should give a fairly accurate value of the true final temperature. Additional iterations may be made to improve the accuracy of the results to the degree desired. As a guess, the final temperature is assumed to be 2300 K. Now the equilibrium equations at 2300 K are set up. The species to be considered are three principal species: CO2, H2O, and N2, and seven minor species: H2, O2, OH, H, O, CO, and NO.
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R. Friedman
(Based on chemical experience, the following possible species may be neglected at 2300 K when stoichiometric oxygen is present: N, C(g), NH, CN, CH, C2, HO2, HCN, O3, C3, NO2, HNO, C2H, CH2, C2O, CHO, and NH2.) Thus, we consider ten species involving four elements, so 10—4 or 6, equilibrium equations are needed. Any six independent equilibria may be selected. We can assure independence by requiring that each successive equilibrium expression we write will introduce at least one new chemical species. Observe that this requirement is met in the following list: 1 CO þ O2 ¼ CO2 2
pCO2 KE 1=2 ¼ K ¼ KF pCO pO2
p þ pOH þ 2 pH2 O þ pH2 H 8 : ¼ H N 37:6 2 pN2 þ pNO
O 10 : ¼ C 3 pO þ pOH þ pNO þ pCO þ pH2 O þ 2 pO2 þ 2 pCO2 pCO2 þ pCO
ð6:42Þ Finally, pCO2 þ pH2 O þ pN2 þ pH2 þ pO2 þ pOH þ pH þ pO þ pCO þ pNO ¼ 1 ð6:43Þ From Table 6.1 at 2300 K:
ð6:34Þ 1 O2 ¼ O 2
1 1 O2 þ N2 ¼ NO 2 2
pO 1=2 ¼ K A
pO 2
pNO pO2 pN2
ð6:35Þ
1=2 ¼ K G ð6:36Þ
1 H2 þ O2 ¼ H2 O 2
pH 2 O 1=2 ¼ K C pH2 pO2 pOH
1 H2 þ O2 ¼ H2 O 2
1 H2 ¼ H 2
pH 2 pO 2
ð6:37Þ
1=2 ¼ K D ð6:38Þ
pH 1=2 ¼ K B
pH 2
ð6:39Þ
Four additional equations are needed to determine the ten unknown partial pressures. These are three atom-ratio equations and a summation of the partial pressures to equal the total pressure. To obtain the atom ratios, we take air to consist of 3.76 parts of N2 (by volume) per part of O2, neglecting argon, and other species. Then, from stoichiometry, C3H8 + 5O2 + (5 3.76)N2 ! 3CO2 + 4H2O + 18.8 N2. H 8 pH þ pOH þ 2 pH2 O þ 2 pH2 : ¼ C 3 pCO2 þ pCO
ð6:40Þ
ð6:41Þ
KE KF KE/KF KA KG KC KD KB
log10 x 9.001 7.061 9.001–7.061 –2.307 –1.391 2.682 –0.116 –2.016
x – – 87.1 0.00493 0.0406 481 0.766 0.00964
We insert these K values into Equations 6.34, 6.35, 6.36, 6.37, 6.38, and 6.39, and then solve the set of ten equations, Equations 6.34, 6.35, 6.36, 6.37, 6.38, 6.39, 6.40, 6.41, 6.42, and 6.43, for the equilibrium values of the ten partial pressures at 2300 K. This solution may be obtained by a tedious set of successive approximations. The first approximation is obtained by solving for the three principal species N2, CO2, and H2O, assuming the partial pressures of the remaining species are zero. Then, using this trial value of pCO2 , solve for pCO and pO2 , using Equation 6.34 and assuming that pCO ¼ 2 pO2 . Next, using pH2 O and pO2 as determined, use Equation 6.37 to determine a trial value of pH2 . Then, using all the foregoing partial pressures, determine pO from Equation 6.35, pNO from Equation 6.36, pOH from Equation 6.38, and pH from Equation 6.39. Thus, ten trial values of the partial pressures are found. However, upon substitution into Equations 6.40, 6.41, 6.42, and 6.43, none of these equations will be quite satisfied. The partial
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161
pressures of the principal species must then be adjusted so as to satisfy Equations 6.40, 6.41, 6.42, and 6.43, and then a second iteration with the equilibrium equations must be carried out to establish new values for the minor species. After four or five such iterations, the results should converge to a set of partial pressures satisfying all equations. A faster method is to use a computer program to solve the equations. (See the following section.) The equilibrium partial pressures at 2300 K will come out to be: PN2 PH2 O PCO2 PCO PO2 PH2 POH PNO PH PO
0.7195 atm 0.1474 atm 0.1006 atm 0.0143 atm 0.0066 atm 0.0038 atm 0.0037 atm 0.0028 atm 0.0006 atm 0.0004 atm
Now, we must determine if 2300 K was too high or too low a guess, by writing the enthalpy balance equation (see Chap. 5). As a basis for the enthalpy balance, we assume that we have exactly 1 mol of products, at 1 atm. Then, if PCO2 ¼ 0:1006 atm (see above), we must have 0.1006 mol of CO2. Similarly, we have 0.0143 mol of CO. Since these are the only two carbon compounds in the products, and since 3 mol of CO2 + CO must form from each mole of C3H8 burned, it follows that (0.1006 + 0.0143)/3 ¼ 0.0383 mol of C3H8 must have burned. Since the original C3H8-air mixture was stoichiometric, it follows that the reactants also consisted of 5 0.0383 ¼ 0.1915 mol of O2 and 3.76 0.1915 ¼ 0.7200 mol of N2. (Thus, a total of 0.9498 mol of reactant form 1 mol of product, if the product is indeed at equilibrium at 2300 K.) The enthalpy balance equation is X X ni H i , T r ¼ n jH j, T p ð6:44Þ
reactant temperature Tr, and nj and Hj are the number of moles and the enthalpy per mol of each product species at product temperature Tp. The enthalpy of each reactant or product species x at temperature T is given by o H x, T ¼ ΔH of þ H o H 298 ð6:45Þ 298:15
(ΔHfo, 298.15)x
is the enthalpy of formation where of a mol of species x from its constituent elements in their standard states at 298 K (see Chap. 5). These constituent elements are H2, O2, N2, and C(s), so ΔHfo, 298.15 for each of these four species is zero, by definition. o 2 Values of (ΔHfo)298.15 and Ho H298 for various species are contained in Table 6.5 on page 1–109. Substitution of numerical values into Equation 6.44 yields: o
Reactant (ΔHf )298.15 species (kJ/mol) –103.85 C3H8 O2 0 N2 0
o H 2300 o o H 298 H2300 ni (kJ/mol) (kJ/mol) (mol) 0.16 –103.69 0.0383 0.05 0.05 0.1915 0.05 0.05 0.7200 Total ¼
o niHi.2300 (kJ) –3.971 +0.010 +0.036 3.925
and Product species N2 H2O CO2 CO O2 H2 OH NO H O
o H 2300 o o H2300 (Hfo)298.15 H 298 (kJ/mol) (kJ/mol) (kJ/mol) 0 66.99 66.99 –241.83 88.29 –153.54 –393.52 109.67 –283.85 –110.53 67.68 –42.85 0 70.60 70.60 0 63.39 63.39 38.99 64.28 103.27 90.29 68.91 159.20 218.00 41.61 259.61 249.17 41.96 291.13
o ni niHi.2300 (mol) (kJ) 0.7195 +48.199 0.1474 –22.632 0.1006 –28.555 0.0143 –0.613 0.0066 +0.466 0.0038 +0.241 0.0037 +0.382 0.0028 +0.446 0.0006 +0.156 0.0004 0.116 Total ¼ 1.794
The enthalpy of the products (–1.794 kJ) is seen to be 2.131 kJ larger than the enthalpy of the reactants (–3.925 kJ). To put this 2.131 kJ
o If H o H 298 is not available from a table, it may be Z T o evaluated from the equation H o H 298 ¼ C p dT: 2
where ni and Hi are the number of moles and the enthalpy per mol of each reactant species at
For C3H8, Cp ¼ 0.09 kJ/molK at 298 K.
298
N2
(ΔHfo)298.15 0.00 kJ/mol o ; H o H 298 kJ/mol Temp(K) 100 –5.77 200 –2.86 298 0.00 300 0.05 400 2.97 500 5.91 600 8.90 700 11.94 800 15.05 900 18.22 1000 21.46 1100 24.76 1200 28.11 1300 31.50 1400 34.94 1500 38.40 1600 41.90 1700 45.43 1800 48.98 1900 52.55 2000 56.14 2100 59.74 2200 63.36 2300 66.99 2400 70.64 2500 74.30 2600 77.96
Species
0.00 kJ/mol o H o H 298 ; kJ/mol –5.78 –2.87 0.00 0.05 3.03 6.08 9.24 12.50 15.84 19.24 22.70 26.21 29.76 33.34 36.96 40.60 44.27 47.96 51.67 55.41 59.17 62.96 66.77 70.60 74.45 78.33 82.22
O2
NO
249.17 kJ/mol 90.29 kJ/mol o o H o H 298 ; H o H 298 ; kJ/mol kJ/mol –4.52 –6.07 –2.19 –2.95 0.00 0.00 0.04 0.05 2.21 3.04 4.34 6.06 6.46 9.15 8.57 12.31 10.67 15.55 12.77 18.86 14.86 22.23 16.95 25.65 19.04 29.12 21.13 32.63 23.21 36.17 25.30 39.73 27.38 43.32 29.46 46.93 31.55 50.56 33.63 54.20 35.71 57.86 37.79 61.53 39.88 65.22 41.96 68.91 44.04 72.61 46.13 76.32 48.22 80.04
O
Table 6.5 Enthalpies of selected combustion productsa H2 0.00 kJ/mol o H o H 298 ; kJ/mol –5.47 –2.77 0.00 0.05 2.96 5.88 8.81 11.75 14.70 17.68 20.68 23.72 26.80 29.92 33.08 36.29 39.54 42.84 46.17 49.54 52.95 56.40 59.88 63.39 66.93 70.50 74.09
H 218.00 kJ/mol o H o H 298 ; kJ/mol –4.12 –2.04 0.00 0.04 2.12 4.20 6.28 8.35 10.43 12.51 14.59 16.67 18.74 20.82 22.90 24.98 27.06 29.14 31.22 33.30 35.38 37.46 39.53 41.61 43.69 45.77 47.85
H2O (g)
OH
–241.83 kJ/mol 38.99 kJ/mol o o H o H 298 ; H o H 298 ; kJ/mol kJ/mol –6.61 –6.14 –3.28 –2.97 0.00 0.00 0.06 0.05 3.45 3.03 6.92 5.99 10.50 8.94 14.18 11.90 17.99 14.88 21.92 17.89 25.98 20.94 30.17 24.02 34.48 27.16 38.90 30.34 43.45 33.57 48.10 36.84 52.84 40.15 57.68 43.50 62.61 46.89 67.61 50.31 72.69 53.76 77.83 57.25 83.04 60.75 88.29 64.28 93.60 67.84 98.96 71.42 104.37 75.01
CO2
CO
–393.52 kJ/mol –110.53 kJ/mol o o H o H 298 ; H o H 298 ; kJ/mol kJ/mol –6.46 –5.77 –3.41 –2.87 0.00 0.00 0.07 0.05 4.01 2.97 8.31 5.93 12.92 8.94 17.76 12.02 22.82 15.18 28.04 18.40 33.41 21.69 38.89 25.03 44.48 28.43 50.16 31.87 55.91 35.34 61.71 38.85 67.58 42.38 73.49 45.94 79.44 49.52 85.43 53.12 91.45 56.74 97.50 60.38 103.57 64.02 109.67 67.68 115.79 71.35 121.93 75.02 128.08 78.71
162 R. Friedman
81.64 85.32 89.01 92.71 96.42 100.14 103.85 107.57 111.31
F2
0.00 kJ/mol o H o H 298 ; kJ/mol –5.92 –2.99 0.00 0.06 3.28 6.64 10.11 13.66 17.27 20.91 24.59 28.30 32.03 35.77 39.54 43.32 47.11 50.91
2700 2800 2900 3000 3100 3200 3300 3400 3500
C(s)
0.00 kJ/mol o H o H 298 ; kJ/mol –0.99 –0.67 0.00 0.02 1.04 2.36 3.94 5.72 7.64 9.67 11.79 13.99 16.24 18.54 20.88 23.25 25.66 28.09
78.91 kJ/mol o H o H 298 ; kJ/mol –4.43 –2.23 0.00 0.04 2.30 4.53 6.72 8.90 11.05 13.19 15.33 17.45 19.56 21.67 23.78 25.89 27.99 30.09
F
86.14 90.08 94.04 98.01 102.01 106.02 110.05 114.10 118.16 HCl
109.81 115.29 120.81 126.36 131.94 137.55 143.19 148.85 154.54
–92.31 kJ/mol o H o H 298 ; o ; kJ/mol kJ/mol H o H 298 –4.19 –5.77 –2.10 –2.86 0.00 0.00 0.04 0.05 2.26 2.97 4.52 5.89 6.80 8.84 9.08 11.81 11.34 14.84 13.59 17.91 15.82 21.05 18.03 24.24 20.23 27.48 22.41 30.78 24.60 34.12 26.77 37.51 28.93 40.93 31.09 44.39
49.92 52.00 54.08 56.16 58.24 60.32 62.40 64.48 66.55
121.29 kJ/mol
Cl
77.72 81.37 85.04 88.74 92.46 96.20 99.96 103.75 107.55
0.00 kJ/mol o H o H 298 ; kJ/mol –6.27 –3.23 0.00 0.06 3.54 7.10 10.74 14.41 18.12 21.84 25.59 29.34 33.10 36.88 40.66 44.45 48.25 52.05
Cl2
83.76 87.49 91.23 94.98 98.73 102.48 106.24 110.00 113.77
–272.55 kJ/mol o H o H 298 ; kJ/mol –5.77 –2.86 0.00 0.05 2.97 5.88 8.80 11.73 14.68 17.64 20.64 23.68 26.76 29.87 33.04 36.24 39.48 42.76
HF
50.30 52.39 54.48 56.58 58.67 60.77 62.87 64.97 67.08 0.00 kJ/mol o H o H 298 ; kJ/mol –21.72 –16.82 0.00 0.14 34.61 38.31 42.02 45.76 49.51 53.27 57.03 60.81 64.58 68.37 72.16 75.96 79.76 83.57
Br2
78.63 82.27 85.92 89.58 93.27 96.96 100.67 104.39 108.12 111.86 kJ/mol o H o H 298 ; kJ/mol –4.12 –2.04 0.00 0.04 2.12 4.20 6.28 8.36 10.46 12.57 14.70 16.84 19.01 21.20 23.40 25.61 27.85 30.09
Br
134.26 140.44 146.65 152.86 159.09 165.33 171.59 177.85 184.12 –36.44 kJ/mol o H o H 298 ; kJ/mol –5.77 –2.86 0.00 0.05 2.97 5.90 8.87 11.88 14.96 18.10 21.30 24.56 27.87 31.24 34.65 38.10 41.59 45.11 (continued)
HBr
82.41 86.12 89.83 93.54 97.27 101.00 104.73 108.48 112.22
6 Chemical Equilibrium 163
0.00 kJ/mol o H o H 298 ; kJ/mol 54.72 58.54 62.38 66.22 70.07 73.93 77.80 81.67 85.55 89.45 93.35 97.25 101.16 105.08 109.01 112.94 116.88 120.83
0.00 kJ/mol o ; H o H298 kJ/mol 30.55 33.02 35.53 38.05 40.58 43.13 45.71 48.29 50.89 53.50 56.13 58.77 61.43 64.09 66.78 69.47 72.17 74.89
78.91 kJ/mol o H o H 298 ; kJ/mol 32.18 34.28 36.37 38.46 40.55 42.64 44.73 46.82 48.91 50.99 53.08 55.17 57.25 59.34 61.42 63.50 65.59 67.67
F –272.55 kJ/mol o H o H 298 ; kJ/mol 46.09 49.44 52.83 56.25 59.69 63.17 66.66 70.18 73.73 77.29 80.87 84.47 88.09 91.72 95.37 99.03 102.71 106.39
HF 0.00 kJ/mol o H o H 298 ; kJ/mol 55.86 59.68 63.51 67.34 71.18 75.02 78.88 82.74 86.61 90.50 94.39 98.29 102.21 106.14 110.08 114.03 118.00 121.98
Cl2
These data are taken from the JANNAF thermochemical tables [2]
a
F2
C(s)
Table 6.5 (continued) HCl
–92.31 kJ/mol o H o H 298 ; o o H H 298 ; kJ/mol kJ/mol 33.23 47.89 35.38 51.41 37.51 54.96 39.64 58.53 41.77 62.12 43.89 65.73 46.02 69.37 48.13 73.01 50.25 76.68 52.36 80.36 54.48 84.06 56.58 87.76 58.69 91.48 60.79 95.21 62.90 98.95 65.00 102.70 67.10 106.46 69.20 110.23
121.29 kJ/mol
Cl 0.00 kJ/mol o Ho H 298 ; kJ/mol 87.38 91.20 95.02 98.85 102.68 106.52 110.36 114.20 118.05 121.91 125.77 129.63 133.49 137.37 141.24 145.13 149.01 152.90
Br2 111.86 kJ/mol o H o H 298 ; kJ/mol 32.35 34.61 36.88 39.15 41.43 43.70 45.98 48.26 50.54 52.81 55.09 57.36 59.63 61.89 64.15 66.41 68.67 70.92
Br –36.44 kJ/mol o H o H 298 ; kJ/mol 48.66 52.24 55.84 59.46 63.10 66.76 70.44 74.13 77.83 81.55 85.28 89.02 92.77 96.53 100.31 104.09 107.88 111.68
HBr
164 R. Friedman
6
Chemical Equilibrium
165
difference in perspective, note that the heat of combustion of 0.0383 mol of propane at 298 K, to form 3 mol of CO2 and 4 mol of H2O per mole of propane, is 0.0383 (3 393.52 + 4 241.83 – 103.85) ¼ 78.29 kJ. Thus, the 2.131 kJ discrepancy when compared with 78.29 kJ is rather small, showing that the 2300 K “first guess” was very close. Since the products, at 2300 K, are seen to have a slightly higher enthalpy than the reactants, the correct temperature must be slightly less than 2300 K. To continue the calculation, the next step is to assume that the final temperature is 2200 K instead of 2300 K. The details will not be presented, but this will yield a new and slightly different set of values of the ten partial pressures of the products. Thus, a new enthalpy balance may be attempted, in the same manner as before. When this is done, the result will be that this time the enthalpy of the reactants will come out to be slightly higher than the enthalpy of the products, showing that the correct temperature is above 2200 K. An interpolation may be made between the 2200 K enthalpy discrepancy and the 2300 K enthalpy discrepancy, which will show that the correct final temperature is 2268 K. Furthermore, the partial pressures of each product species may be obtained by interpolating between the 2200 K partial pressures and the 2300 K partial pressures, with results as follows: T ¼ 2268 K
PN2
0.7207 atm
PH2 O PCO2
0.1484 atm 0.1026 atm
PCO PO2
0.0125 atm 0.0059 atm
PH2
0.0034 atm
POH PNO PH PO
0.0032 atm 0.0025 atm 0.0005 atm 0.0003 atm
Computer Programs for Chemical Equilibrium Calculations In view of the extremely tedious calculations needed for determination of the equilibrium
temperature and composition in a combustion process, a computer program for executing these calculations would be desirable. Fortunately, such programs have been developed. However, the user of a computer program should be warned that thorough understanding of the material in this chapter is needed to avoid misinterpreting the computer output. Further, given such understanding, simple manual calculations can be performed to obtain independent checks of the computer output. One program, entitled GASEQ, can be used with any computer using Windows. It can be downloaded from http://www.gaseq.co.uk. Alternatively, a program may be obtained from Reaction Design, 6440 Lusk Blvd, Suite D209, San Diego, CA 92121. Their e-mail address is . These programs will calculate the final equilibrium conditions for adiabatic combustion at either constant pressure or constant volume, given the initial conditions. For the constantpressure calculations, one specifies the initial temperature, the pressure, and the identities and relative proportions of the reactants. The computer programs contain the properties of selected reactants including: air, oxygen, nitrogen, hydrogen, graphite, methane, acetylene, ethylene, ethane, propane, butane, 1-butene, heptane, octane, benzene, toluene, JP-4, JP-5, methanol, ethanol, and polyethylene. If the fire only involves reactants from this list, no further input is necessary. If the fire involves a reactant not on this list, the input data must include the elemental composition and the enthalpy of formation of the reactant at 298 K, as well as enthalpy versus temperature data for the reactant over the temperature range from 298 K to the initial temperature. (If the initial temperature is 298 K, the last item is not needed.) The computer programs can handle reactants containing any of the following elements: A, Al, B, Br, C, Cl, F, Fe, H, He, K, Li, Mg, N, Na, Ne, O, P, S, Si, and Xe. Data are included in the program on all known compounds, including liquids and solids, that can form at elevated temperatures from combinations of these elements. It is not necessary for the user to
166
R. Friedman
specify which product species to consider. The program can consider them all, and will print out all equilibrium species present with mole fractions greater than 5 10–6, unless instructed to print out trace values down to some lower specified level. The program can calculate Chapman-Jouguet detonation products as well as constant-pressure or constant-volume combustion products, if desired. An addition to the program permits calculation of viscosity and thermal conductivity of gaseous mixtures, selected from 154 gaseous species, at temperatures from 300 K to 5000 K.
Nomenclature Cp ΔEo ΔFo ΔHo
Heat capacity at constant pressure (kJ/molK) Energy of products relative to energy of reactants, all at temperature T and 1 atm (kJ/mol) Free energy of products relative to free energy of reactants, all at temperature T and 1 atm (kJ/mol) Enthalpy of products relative to enthalpy of reactants, all at temperature T and 1 atm (kJ/mol)
K K n pi p R ΔSo T
Equilibrium constant (based on partial pressures expressed in atmospheres) Degrees Kelvin Number of moles (e.g., a mole of oxygen is 32 g) Partial pressure of ith species (atm) Total pressure (atm) Gas constant (kJ/mol K) Entropy of products relative to entropy of reactants, all at temperature T and 1 atm (kJ/mol) Absolute temperature (K)
References 1. J. van’t Hoff, cf. G. Lewis, M. Randall, K. Pitzer, and L. Brewer, Thermodynamics, McGraw-Hill, New York (1961). 2. D.R. Stull and H. Prophet, JANNAF Thermochemical Tables, 2nd ed., NDRS-NBS 37, National Bureau of Standards, Washington, DC (1971).
Raymond Friedman was with Factory Mutual Research from 1969 through 1993. During most of this time he was vice president and manager of their Research Division. Currently he is an independent consultant. He has past experience at Westinghouse Research Laboratories and Atlantic Research Corporation. He is a past president of The Combustion Institute, past vice chairman and past secretary of the International Association for Fire Safety Science, and an expert in fire research and combustion.
7
Thermal Decomposition of Polymeric Materials Artur Witkowski, Anna A. Stec, and T. Richard Hull
Introduction Polymers are composed of large numbers of repeat units forming very long chain molecules. Most polymers are based on carbon, and hence known as organic polymers. The long-chain structure means that polymers can exist in solid or liquid form, but are too large to be volatile. Polymers fuel the vast majority of unwanted fires, as wood, paper, fabrics, foams and plastics. Flaming combustion is a gas phase process, and it is necessary to understand the stages in the conversion of long molecular chains into volatile fragments. This is often referred to as “pyrolysis” or “gasification”, but these terms encompass a complex set of chemical and physical processes, leading to the production of volatile flammable molecules.
Polymeric Materials A polymer is a large molecule constructed from many smaller structural units called monomers, covalently bonded together in any conceivable pattern (but often, and most simply in long chains). If the material is composed of only one type of repeating structural unit, it is known as a A. Witkowski (*) • A.A. Stec • T.R. Hull Centre for Fire and Hazards Science, University of Central Lancashire (UCLan), Preston, Lancashire PR1 2HE, UK
homopolymer. If the material is composed of more than one type of repeat unit it is known as a copolymer. Thermal decomposition is “a process of extensive chemical species change caused by heat”. Thermal degradation is “a process whereby the action of heat or elevated temperature on a material, product, or assembly causes a loss of physical, mechanical, or electrical properties” [1]. Used correctly, thermal degradation may describe processes occurring before around 1 % of the mass is lost, while thermal decomposition includes the entire mass loss process.
Polymer Classification Polymers represent the largest class of combustible materials fuelling unwanted fires. The different ways they can be subdivided provides a useful introduction to this wide and important class of materials.
Natural, Synthetic, Semi-natural and Biobased Before the widespread use of synthetic polymers in the second half of the twentieth century almost all unwanted fires were fuelled by natural polymers such as wood, paper, cotton, wool etc. Synthetic polymers are generally derived from oil or coal, and share the flammability of those raw materials. The ease of manufacture and processing of synthetic polymers has driven the increase in their use. As most of the common
M.J. Hurley (ed.), SFPE Handbook of Fire Protection Engineering, DOI 10.1007/978-1-4939-2565-0_7, # Society of Fire Protection Engineers 2016
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168
synthetic polymers are more flammable then their natural counterparts, this has also increased the number and severity of unwanted fires, despite significant advances in fire prevention, detection and control. Semi-natural polymers are typically purified, and chemically modified natural polymers, such as cellulose acetate, cellophane or rayon. Drivers towards greater environmental sustainability have led to increased developments in biobased polymers, which includes the semi-natural polymers and a new polymeric materials, using raw materials derived from living, rather than the fossilised carbon sources. It seems likely that these materials, such as polylactic acid (PLA) and styrene-soya oil-divinyl benzene (SSD), will increase their market share in the next decade.
Chemical Composition of the Repeat Units Most natural polymeric materials involved in fires are cellulose based. Cellulose is a polymer with alternating repeat units of glucose (Fig. 7.1). Several of the common synthetic polymers, the so-called vinyl polymers made from vinyl monomers (CH2 ¼ CHX), have a repeat units of (CH2CHX), such as polyethylene (X is H); polypropylene (X is CH3); polyvinyl chloride (X is Cl); polystyrene (X is C6H5); polyacrylonitrile (X is C N); polyvinyl acetate (X is OCOCH3); polyvinyl alcohol
A. Witkowski et al.
(X is OH). Other “polymers” such as polyamides, polyesters, epoxy resins and polyurethanes are actually classes of materials with similar bonding between the repeat units, but different structures within each repeat unit.
Chemistry of Polymerisation Synthetic polymers are made by chemical reaction of monomers to form long polymer chains. Since the reverse process, the decomposition of polymers into smaller volatile fuel molecules, is often related to their synthesis, this can also provide insight into their decomposition behaviour. Broadly the process occurs either by step-growth, or chain-growth polymerisation. Step-growth polymerisation occurs by chemical reaction of two functional groups to form the linkage, with the release of a small molecule (such as water). This is known as step-growth polymerization as it takes place one molecule at a time. Figure 7.2 shows the familiar esterification reaction, in this case used to produce a polyester. As water is often the molecule released, this process is also known as condensation polymerization. The synthetic process is slow, and the lack of water or other secondary product in the polymer prevents decomposition being simply the reverse of polymerisation. The second process, chain-growth polymerisation, involves opening of double bonds to form consecutive links in the polymer chain. For example, styrene
Fig. 7.1 Part of a cellulose polymer chain, and a single glucose unit (monomer)
7
Thermal Decomposition of Polymeric Materials
169 H2O
COOH + HO
HOOC
HO O
OH
H O
O
O
n
Fig. 7.2 Step-growth polymerisation of polyethylene terephthalate (PET)
HC
CH2
HC
+
H C
H2 C
CH2
HC
+
H C
H2 C
CH2
HC
CH2
+
H C
HC
+
H2 C
H C
H2 C
CH2
HC
CH2
+
H C
H2 C
H C
Fig. 7.3 Chain-growth polymerisation of poly(styrene) (PS)
monomers combine to form polystyrene, without release of a secondary product (Fig. 7.3). The polymerisation reaction is known as chain-growth or addition polymerisation. Typically, once the monomer becomes activated, the chain grows extremely quickly (less than 1 s), so, during the polymerisation process, only long polymer chains and volatile monomer units will be present. It is highly likely that some monomer will remain at the end of the polymerisation process, since the final material will have very long chains and a high viscosity. During the decomposition of polystyrene, the reverse process occurs, resulting in monomer, dimer and trimer predominating in the vapour phase. Addition polymerization involves three distinct stages—initiation, propagation and termination. To start the process, an initiator is added to
the monomer. The initiator splits to form two free radicals, which attach themselves to a carbon atom of the monomer. When this occurs, the reactive site is transferred to another carbon atom in the monomer, and the chain begins to propagate (Fig. 7.4). Finally the reactivity of the propagating chain end is lost by combination of two reactive sites, or rearrangement, collectively known as termination. In order to maximise the degree of polymerization, the remaining monomers must diffuse towards the reactive chain end, before termination reactions occur. Addition polymerisation can involve free radical, cationic, anionic, catalytic, or ring opening processes. The means of polymerisation will affect the degree of branching, and the molecular weight and dispersity of the polymer (section “Molecular Mass or Polymer Chain Length”),
170
A. Witkowski et al.
I
+
X
+
I
+
I X
X
X
X
etc.
X
Fig. 7.4 Free radical polymerisation of an alkene (CH2 ¼ CHX)
which will in turn affect its decomposition (section “Decomposition Mechanisms”).
Thermoplastics and Thermosets Synthetic polymers (often referred to as plastics, because of their mouldability) can be subdivided into those which can be repeatedly deformed by heating (thermoplastics), so they are meltprocessable; and those which once the polymerisation process is complete, cannot be melted or have their shape changed by heating, and decompose directly from solid to vapour (thermosets or thermosetting polymers). Most thermosets have additional covalent bonds forming crosslinkages between the polymer chains. Common thermoplastics include polyethylene (PE), polypropylene (PP), polystyrene (PS), polymethylmethacrylate (PMMA), polyvinyl chloride (PVC), polyamides (PA) and some polyesters and polyurethanes. Thermosets are generally stronger, but more brittle than thermoplastics, have higher thermal stability, higher dimensional stability, higher rigidity, and resistance to creep and deformation under load. Epoxies, vulcanized rubbers, phenolics, unsaturated polyester resins, rigid polyurethanes, urea-formaldehyde and melamineformaldehyde are examples of thermosets. Molecular Mass or Polymer Chain Length The number of repeating units in a synthetic polymer exerts a significant influence on its physical properties. The high molecular weights of polymers increase their viscosity when molten and in solution, decrease their solubility, and of course prevent their volatilisation. Chain length can also be a controlling factor in determining the solubility, elasticity, fibre-forming capacity, tear strength, and impact strength in many polymers. The chain length of commercial polymers is optimised during synthesis for the intended application. For example, PMMA, with an average
molecular weight less than 500,000 (around 5000 repeat units) has sufficiently low viscosity to be melt-processable, whereas PMMA with molecular weight of 5,000,000 does not soften sufficiently to allow its shape to be changed on heating, hence it is known as cast PMMA. The number of repeating units will usually vary as a statistical distribution of chain lengths. This may be classified as a number-average molecular mass Mn , or a weight-average molecular mass Mw . Within most synthetic polymers, the most common unit is actually the monomer, although this only represents a tiny proportion by mass. Natural polymers often have narrower molecular mass ranges, or even identical molar masses. The ratio Mn =Mw is known as the dispersity (or heterogeneity index), providing a simple index of the range of chain lengths present. An enzyme, where all the molecules have the same molecular mass is described as monodisperse, a polymer produced by anionic polymerisation will typically have a dispersity around 1.1, a step growth polymer will have a dispersity around 2, while one produced by free radical polymerisation will usually lie between 1.5 and 10. Consequences of High Molar Mass Increasing the interaction between polymer molecules leads to increasing cohesive energy per molecule. In polymeric materials this gives rise to certain properties characteristically associated with high molar mass, regardless of their chemical structure: (i) High crystal melting point (if the polymer is crystalline) (ii) High viscosity in the melt and in solution (iii) High mechanical strength (iv) High flexibility and ductility (unless highly cross-linked) (v) High resistance to dissolution (especially crystalline polymers)
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Thermal Decomposition of Polymeric Materials
171
The average degree of polymerization, or DP, is usually defined as the number of monomeric units in a polymer [2]. For a homopolymer, there is only one type of monomeric unit and the number-average degree of polymerization is given by Number average molecular mass of polymer molecular weight of the monomer unit Mn ¼ M
DPn ¼
ð7:1Þ For most industrial purposes, degrees of polymerization in the thousands or tens of thousands are desired. Low molecular weight polymeric materials (having short chains) are generally weaker. Although sections may be crystalline, only weak Van der Waals forces hold the crystallites together. This allows the crystalline layers to slip past one another causing a break in the material. Amorphous polymers, with high DP (such as cast PMMA) have greater strength because the molecules become tangled between layers.
Physical Properties Polymers can be readily processed by forming or moulding into shapes, either once (thermosets) or repeatedly (thermoplastics). Many are important engineering materials with a wide range of properties, some of which are unattainable from any other material types, and they are generally low in cost. The desirable properties of polymer products include light weight, availability in a wide range of colours, low thermal and electrical conductivity, toughness, and good resistance to acids, bases and moisture. The applications of a polymer depend most strongly on its mechanical behaviour. The “deformability” of a polymer can be expressed as the ratio of the deformation (strain) resulting from a constant applied stress. The ratio of stress to strain is the elastic modulus. A large number of synthetic polymers now exist covering a wide range of properties. These can be grouped into three major classes:
Fig. 7.5 Typical stress—strain plots for a fibre, a flexible plastic, and an elastomer
plastics, fibres, and elastomers. Although there is no firm dividing line between the groups, some distinction between these categories can be obtained from a typical stress—strain plot (Fig. 7.5). Rigid plastics and fibres are resistant to deformation and are characterized by a high elastic modulus and low percentage elongation. Elastomers readily undergo deformation and exhibit large reversible elongations under small applied stresses, i.e., they exhibit elasticity. The flexible plastics are intermediate in behaviour, during the elastic stage of their deformation, and then yield inelastically with typical plastic deformation. During the final stages of processing, fibres are stretched to three or more times their original length (“drawing”) when in a semi-crystalline state, to produce increased chain alignment, crystallinity and strength. For amorphous materials, the temperature at which the molecules move relative to one another, known as the glass transition temperature (Tg—described in more detail in section “Glass Transition Temperature”) exerts a profound influence on the physical properties. In general, elastomers have values of Tg well below room temperature, while rigid, structural polymers have Tg values above room temperature.
172
Structural Physical and Decomposition Property Data In order to better understand the range of common polymers, their names, abbreviations, and molecular structures have been listed in Table 7.1. Where available, measurements of their crystallinity, glass transition temperature (Tg) and melting point have also been provided, in order to give the reader an instant guide to the main properties of interest. More detailed tabulations providing citable data have been published [2]. In addition, Lyon et al. [3] have tabulated the decomposition temperatures and Arrhenius parameters Ea and A (section “Kinetics of Polymer Decomposition”) for a number of common polymers from literature and the data is reproduced here. Individual polymeric materials will differ according to their method of preparation, thermal history and the definition and method of measurement of the decomposition properties. Therefore individual literature values have been provided to give an indication of the uncertainties in the reported data.
Polymers and Fire The flammable components of our built and natural environments are almost all based on organic polymers, and the vast majority of unwanted fires are fuelled by these polymers. Smouldering combustion typically occurs by reaction of atmospheric oxygen with a porous, combustible solid matrix, with a reaction zone moving through the solid, releasing gaseous products. Flaming combustion requires the fuel to be present in molecular form in the vapour phase, where it can undergo much more rapid reaction with atmospheric oxygen. Since polymers are much too large to exist in the vapour phase (because the bonding forces holding them in the condensed phase is proportional to their large surface area) they must first break down into volatile fragments. The pyrolysis of a polymer, turning molecular chains of 10,000–100,000 carbon atoms into species small enough to be volatilised, often involves breaking the polymer chain. In some cases, the
A. Witkowski et al.
chain releases groups from its ends most easily, known as end-chain scission or unzipping. In others, the chain breaks at random points along its length, known as random chain scission. A third process, where groups attached to the backbone as side chains can leave as stable molecules, is known as chain-stripping. If the polymer, or the chain resulting from chain stripping, does not undergo chain scission to form volatiles or lose further substituents, it may undergo carbonisation, resulting in char formation. Thus the conversion of an organic polymer to volatile organic molecules, and/or a char, may follow one or more of the four general mechanisms. While some polymers fall exclusively into one category, others exhibit mixed behaviour, often dependent on the decomposition conditions. The temperature of a material is a measure of the kinetic energy of its molecules. At very low temperatures (close to 0 K), molecules are almost stationary, but at all normal temperatures in the solid phase, molecules are in a state of constant vibration. As the temperature increases, the vibrations become stronger, while the strength of the chemical bonds remains constant. For a particular polymer, a critical temperature is reached where there is sufficient kinetic energy to rupture one of the bonds holding the repeat units, or the side chains, of the polymer together. If the resultant molecules are small enough to be volatile, they may escape from the surface of the polymer, or in the case of a thermoplastic, form bubbles within it. When sufficient fuel is present in the vapour phase mixed with air, it can react with oxygen, releasing heat and increasing the free radical concentration. In the presence of a pilot flame or spark, additional free radicals accelerate the ignition process. Ignition and flaming combustion occurs when there is sufficient heat from the flame to replace the gas phase fuel by further pyrolysis. As molecules are released from the decomposing polymer, particularly by chain stripping, this leaves active sites for further reaction. In many cases, such as cellulosic materials, this can result in cross-linking reactions to other polymer chains, leading to char formation. In bulk cellulosic materials such as wood, this can result in the build-up of
Poly(vinylidene fluoride)
Poly(vinyl acetate)
Poly(vinyl chloride)
Poly(vinyl alcohol)
Polyacrylonitrile
Polystyrene
Polybutadiene
Polyisoprene
Polyisobutylene
Polypropylene
Polyethylene
Chemical name
F
C
F
CH2
n
CH2
CH2
CH2
CH2
n
n
n
n
n
n
n
n
CH2
CH2
CH2
CH
CH
CH2
CH2
CH2
OOCCH3
CH
Cl
CH
OH
CH
CN
CH
CH
CH
CH3
C
CH3
C
CH3
CH3
CH
CH2
Structure
CH2
CH2
n
n
Kynar, Hylar
Acetate
“Acrylic” (wool or textile)
Butyl rubber
Natural Rubber
Polythene
Common or trade name
Table 7.1 Common properties and some of their physical/decomposition properties
PVDF
PVAc
PVC
PVAL or PVA
PAN
PS
PIB
PP
PE
343–373
413
363–378
203
200
253
175–260
Tg/K
High
313
Low 5 % 353–358 (plasticised) Med 15 % unplasticised
Low
Low
Low
–
65 %
40–80 %
Abbreviation Crystallinity
443–448
348–378 (485)
503–533
590
503
303
229
443
473–508
Melting point/K
738–758
526
563–733
na
512
637 549 606
680
596 574
621 589
687 677 679 644 649 660 624
Decomposition temperature/K
105 105 105 105 105 105 105
6.5 2.3 2.0 2.6 1.8 1.7 2.2
1020 1018 1019 1022 1019 1017 1018
105 105 105 105 105
9.4 3.5 7.3 1.3 6.7
1017 1018 1016 1017 1017
–
(continued)
2.01 105 4.9 1013
2.24 105 1.8 1020
1.34 105 7.8 1020 1.38 105 3.0 1012
–
1.30 105 1.8 1011
2.60 2.60 2.30 2.01 2.30
2.50 105 8.2 1019 2.49 105 2.3 1019
2.05 105 1.8 1015 2.05 105 1.5 1016
3.00 2.64 2.77 3.01 2.64 2.43 2.43
Kinetic parameters [3] Ea/J mol1 A/s1
High Thermal Stability Polymers Poly(phenylene oxide)
Polycarbonate
Polycaprolactam
Poly(hexamethylene adipamide)
Poly(butylene terephthalate)
Engineering thermoplastics Poly(ethylene terephthalate)
Polyformaldehyde, polyoxymethylene Poly(ethylene oxide) or Polyethylene glycol Poly(tetrafluoro ethylene)
Poly(methyl methacrylate)
Poly(methyl acrylate)
Chemical name
CH2
CH2
C
F
C
F
n
O
O
NHCO
CH3
n
CH3
C
n
n
O
O
(CH2) 4
O (CH 2) 4
CO
NHCO
(CH2)5
C
C
NH
O
n
n
O
(CH2) 6
OOC
n
CH2
n
OCH2 CH2
F
F
OCH2
OCH2
COOCH3
C
CH3
COOCH3
CH
Structure
Table 7.1 (continued)
C
O
n
n
CO n
With PS as Noryl
Nylon 6.6, Polyamide 6.6 Nylon 6, Polyamide 6 Lexan
Polyester
Polyester
Teflon
Acetal
Perspex, Plexiglass
Common or trade name
PPO
PC
PA 6
PA 6.6
PBT
PET
PTFE
PEG and PEO
POM
PMMA
Low
Medium
Medium
High
High
High
High
Low
Abbreviation Crystallinity
418–423
323–353
343–363
318–333
343–353
398
364–383
388 (synd); 378 (atact); 318 (isotac)
Tg/K
488–503
498–508
498–538
493–503
523–533
600
448–454
363–378
Melting point/K
753–758
708
703–746
681
698–713
782 773 742
618 601
633–663 591 577 514 501
Decomposition temperature/K
105 105 105 105 105
4.7 1.9 5.4 6.4 2.3
1016 1017 1017 1010 109
–
–
–
–
–
–
–
–
–
–
1.59 105 2.6 1011
3.39 105 4.4 1020 3.14 105 1.7 1019 3.37 105 5.3 1021
1.93 105 2.1 1014 1.92 105 4.9 1014
2.18 2.18 2.18 1.26 1.09
Kinetic parameters [3] Ea/J mol1 A/s1
Polyurethane
Phenol formaldehyde resin
Melamine formaldehyde resin
Urea Formaldehyde resin
Thermosets Epoxy resin
Polyether imide
Polyphenylene Sulphide
Polyether sulphone
Poly(ether ether ketone)
C H2
C H2
O
C
H2 C
O
N
C H2
(
(
(
O
N
O
O
H N
OH
H N
H2 C
R
O
N H
O
O
O
S
O
1
O
H2 C
n
H2 C
H3C
H N
NH
HN
CH3
C
CH3
S
O
C
OH
N
O
C H2
O
OH
C H
O
H N
)
CH3
H N
C
O
C
O
2
H2 C
R
)
O
C H2
O
n
O
O
)
n
CH3
C
CH3
O
N
O
O
H2 C
n
H2 C
H2 C
)
Bakelite
Melaware
PUR and PUF
PF
MF
UF
EP
PEI
PPS
PES
PEEK
490
416
Cross-linked 283–493
Cross-linked 353–393
Cross-linked 293–333
Cross-linked
Cross-linked 273–453
Low
Low
High 32 %
607
723–753
>473
673–723
800
777
853
843
–
–
–
–
–
–
–
(continued)
–
–
–
–
–
–
–
Polylactic acid
Keratin
Natural and biopolymers Cellulose
Styrene acrylonitrile copolymer
Acrylonitrilebutadiene-styrene copolymer
Copolymers Poly(ethylene co-vinyl acetate)
Chemical name
C
O
OH
HO
1
H
R
H
H N
OH
O
CH2
CH2
CH2
OH
O
C
O
H
HO
CN
CH
CN
CH
CH2
H
R
2
HO
H
N H
C
O
H
H
R
3
O
CH
CH2
H3C
CH2
OH
H O
...
n
n
...
...
n
(OCH(CH3)CO-)n
H
HO
...
...
...
Structure
Table 7.1 (continued)
O
H N
OH
H
O
C
H
H
R
4
OH
O
m
O
N H
H H
CH2
H OH
HO
...
CH
... m
CH2
CH
H OH
C
O
CH
H
O
OH
H
... m
O
CH
CH2 o
Wool
...
Common or trade name
PLA
SAN
ABS
EVA
H-bonded
High
Low
Low
Medium
Abbreviation Crystallinity
318–338
373– 393
188–378
233–293
Tg/K
423–433
Decomposes
393
383–398
303–383
Melting point/K
623–643
693
693–701
753 573
Decomposition temperature/K
–
–
–
–
–
–
–
–
–
–
3.45 105 1.27 1022 1.66 105 6.11 1011
Kinetic parameters [3] Ea/J mol1 A/s1
7
Thermal Decomposition of Polymeric Materials
the protective layer, shielding the wood from external radiation, slowing the rate of further fuel pyrolysis, and hence the rate of burning. The burning process can be viewed on either the molecular scale or the macro scale.
177
crystalline materials. As such, they all tend to have highly ordered and regular structures. Amorphous materials, by contrast, have their molecules arranged randomly and in long chains which wrap around each other, without any long
The molecular scale Stage I
Heating
An external source supplies heat causing the temperature of the substance to increase. The extent of temperature change depends on the specific heat of the material. Physical, mechanical, and thermal properties change in the case of polymers. This may include softening, melting and volatilsation Stage II Decomposition At higher temperatures the majority of the bonds reach failure point, causing the release of gaseous molecules which differ depending on the material burning. This can be accelerated by attack of oxygen on the surface of the polymer, producing carbon dioxide and carbon monoxide Stage III Oxidation In the presence of oxygen at high temperatures, oxidation of the gaseous fragments proceeds rapidly, releasing heat, and combustion products (mostly carbon dioxide and water)
The macro scale Stage I Heating Stage II Pyrolysis Stage III Ignition
Heat causes a temperature rise which will depend on the thermal inertia (kρC) of the material Heat causes decomposition of the fuel, followed by pyrolysis of fuel to the gas phase Fuel accumulates above the surface, and reacts with oxygen. Once the critical concentration of free radicals is reached, flashing will occur. When the total heat flux to the surface from fuel oxidation is sufficient to pyrolyse enough fuel to replace it, ignition will occur, the rate of reaction will increase and produce carbon dioxide and water Stage IV Flame spread As the radiant heat flux increases it will pyrolyse adjacent materials, leading to a repeated series of ignitions, resulting in fire growth Stage V Fire As the flame gets larger, it will no longer be able to been entrain sufficient oxygen, and development products of incomplete combustion such as carbon monoxide and soot will be produced, increasing the radiative component of heat transfer
Polymer Crystallinity Although most polymers are solids at room temperature they have more properties in common with glass than with crystalline solids, such as sugar or salt. Glass has an amorphous morphology with properties different to crystalline solids. When heated, it gradually changes, from a brittle solid-like material, softening, and eventually becoming a viscous liquid. In contrast, the application of heat to a crystalline solid turns it sharply to a low viscosity liquid at a particular temperature. The difference lies mainly in the structure of each phase. Crystalline materials have their molecules arranged in repeating patterns. Salt, sugar, ice and most metals are
range order. Both crystalline and amorphous phases exist in polymers. Polymers can form crystallites either by straightening out the molecules and packing as rods (extended-chain crystals), or each chain folds back and forth, so that crystallisation occurs by short segments of the same chain packing together ( folded-chain crystals) (Fig. 7.6). Chain-folding is kinetically favoured, as it is a unimolecular process, but orientation of a polymer (such as the “drawing” of a fibre) leads to chain-extension crystal structures. A complete polymer chain is likely pass through many small crystals, tying them together into a strong, coherent mass, surrounded by amorphous sections of polymer. If individual polymer molecules were
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A. Witkowski et al.
CHAIN-FOLDED CRYSTAL CHAIN-EXTENDED CRYSTAL
POLYMER CRYSTALLITE
Fig. 7.6 Schematic of chain-folded crystal, chain extended crystal, and polymer crystallite
confined to individual crystals, they would be extremely brittle. The mixtures of small crystals and amorphous material in polymers cause them to melt over a range of temperatures without a sharp melting point. In most polymers, the combination of crystalline and amorphous structures forms a material with advantageous properties of toughness and rigidity. Some polymers, such as polystyrene and PMMA, are completely amorphous, others have a combination of disordered regions and small crystallites. An amorphous polymer results from polymer chains that lack regular order. If parts of two chains do not pack well together, crystallites do not form. Shorter chains organize themselves into crystalline structures more readily than longer molecules, as those with a high degree of polymerization (DP) tend to become tangled. The DP is an important factor in determining the degree of crystallinity of a polymer. The cooling rate also influences the degree of crystallinity (section “Differential Thermal Analysis and Differential Scanning Calorimetry”). Slow cooling provides time for crystallization to occur. Fast cooling yields highly amorphous materials. When characterising the flammability of a material, in order, for example to predict its large scale fire behaviour, it is essential to ensure that all the material has the same thermal history. For example, cone calorimeter plaques prepared from the same semicrystalline polymer may have
different decomposition and burning behaviour if they were formed into plaques under different thermal conditions. This can be compensated for by subsequent annealing (heating and holding each specimen at an appropriate temperature below the crystalline melting point, followed by controlled cooling). If the polymer is cooled slowly, this will produce a significant increase in crystallinity, and relieve internal stresses. The size and shape of the side chains of monomer also influence the polymer morphology. If the monomers are large or irregular, relative to the polymer backbone, as in polystyrene, it is difficult for the polymer chains to arrange themselves in an ordered manner, resulting in a more amorphous material. Likewise, smaller monomers, such as polypropylene, and polymers that have a very regular structure, such as the rod-like structure of PTFE, will form highly crystalline polymers.
Thermal Response Characteristics of Polymers Physical Transitions The physical processes occurring during thermal decomposition depend on the material. Thermoplastics can be softened and melted by heating; once polymerisation is complete,
7
Thermal Decomposition of Polymeric Materials
thermosetting polymers are infusible and phase changes such as melting cannot occur. The melting/softening behaviour of thermoplastics on heating depends on the degree of crystallinity. For crystalline materials the intermolecular forces are usually identical, so melting occurs at a well-defined temperature; for amorphous materials a range of intermolecular forces hold the polymer chains to each other, so the polymer will soften over a wider temperature range. However, many materials cannot undergo the transition to a viscous state without undergoing thermal decomposition. Neither thermosets nor cellulosic materials have a fluid state, so they neither melt or soften. In thermosets, the 3-dimensional network of cross-linking covalent bonds prevents the polymer chains from moving relative to each other. In cellulosic polymers, the extensive hydrogen bonding between the hydroxyl groups and oxygen atoms keeps the polymer chains in place.
Glass Transition Temperature As the temperature of a polymer rises above a certain critical point, its glass transition temperature, Tg, it becomes more rubber-like. Conversely, as the temperature drops below Tg, it behaves in an increasingly brittle manner. The glass-transition temperature is the point at which the polymer chains in a non-crystalline (amorphous) material acquire sufficient thermal energy to undergo significant translational motion, characteristic of the liquid-like or rubbery state. Below Tg the chains are frozen into a glassy state, where only very localised atomic movement, such as vibration, is possible. If a molten polymer is cooled so quickly that the Tg is reached before the polymer can fully crystallise, then the polymer will remain frozen in its glassy (amorphous) state until its temperature is raised above Tg. The Tg is a transition which is characteristic of non-crystalline phases; it is an important parameter in the selection of materials for particular applications, such as whether rigid or elastomeric properties are required. Above Tg, but well below its melting point, an incompletely crystallised polymer can undergo further crystallisation
179
(section “Differential Thermal Analysis and Differential Scanning Calorimetry”).
Melting The backbone of a typical (CH2CHX)n polymer is composed of a chain of tetrahedrally bonded carbon atoms covalently bonded to each other so that the molecule can be represented as an extended zigzag chain. The repeating units in a polymer chain are often free to rotate relative to one another. If they are all in a particular position, the polymer molecule will have a linear zigzag shape. If they rotate, this will result in bends in the polymer molecule. While the linear zigzags can stack together easily, each bend will be an obstacle to crystallinity. For polyethylene (–CH2CHX)n, a typical value of the molecular weight is 1.6 105 g mol1, so the chain contains 10,000 carbon atoms; thus in the extended zigzag state, the chain would be about 1260 nm long and 0.3 nm diameter. As every group of four atoms in the chain can have three possible stable rotational positions (linear, zigzag or kinking to left or right), a total of 310,000 shapes (or additional degrees of freedom) are available to this particular chain, only one of which is the fully extended zigzag. Even though this has the lowest energy, the most probable conformation will be some kind of randomly angled amorphous shape (Fig. 7.7). The number of different possible states which can exist when leaving the crystalline state (or extended zigzag conformation), known as the entropy change, ΔS, exerts the greatest influence on the melting temperature of a polymer. A large part of this entropy is due to the additional freedom that allows the chain conformational changes to occur in the melt; i.e., the restrictions of the crystalline lattice no longer apply. In any phase transition, the free energy change involved, ΔG, is zero, since the two phases must be in equilibrium. The free energy is the sum of the chemical bonding forces, or enthalpy ΔH, and the disorder, or number of possible ways the molecule can be arranged. This is the product of the temperature and the entropy change, TΔS.
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A. Witkowski et al.
Crystalline portion
Break in crystalline region
amorphous region Fig. 7.7 Crystalline and amorphous regions of a polymer
ΔG ¼ ΔH TΔS ¼ 0
ð7:2Þ
so that during the polymer melting process; the melting temperature Tm is given by T m ¼ ΔH fusion =ΔSfusion
Table 7.2 Structures and melting temperatures of four polymers
Polymer
Tm(°C)
ð7:3Þ
The enthalpy of fusion (ΔHfusion) reflects the strength of attractive forces between the molecules. For chemically similar materials (e.g. hydrocarbon polymers) these will not vary greatly. Thus ΔSfusion, the entropy change on melting, is the only significant variable. For polymers, entropy is related to the number of degrees of freedom each polymer molecule has. A molecule in the liquid state has more potential degrees of freedom (bond rotations, bond angle flexions and inversions, translational and rotational motions) than if it is frozen in a crystal. Clearly, the more flexible the polymer chain, the more degrees of freedom it acquires on melting, and the greater is ΔSfusion. A high ΔSfusion leads to a low Tm. Conversely, the stiffer the polymer chain, the fewer degrees of freedom it acquires on melting, the lower is ΔSfusion and the higher is Tm. For completely rigid polymer chains, only
135 CH3
CH3
CH3
CH3
CH3
165 380 > 600
translational and rotational degrees of freedom are acquired on melting, leading to extremely high values of Tm, often well above the decomposition temperature of the polymer. Table 7.2 shows the variation in melting point for four polymers. In PE every bond is free to rotate; PP is constrained to a small extent by the coiling of the chain to accommodate the methyl groups in a regular manner. Aromatic rings do not allow any rotation so poly-1,4-phenylene
7
Thermal Decomposition of Polymeric Materials
ethylene (PhCH2CH2Ph)n can only rotate between the two –CH2–CH2– carbon atoms. In poly-1,4-phenylene (Ph–Ph–)n no rotation is possible (as the conjugated aromatic rings must all lie in the same plane, so the polymer molecule exists as a rigid rod), there is no “entropy advantage” to the polymer on melting. Poly-1,4phenylene decomposes before melting, so it is not melt-processable, so there is no way of forming it into shapes, and so its practical applications are limited to heat resistant fabrics, electrical insulation etc [4].
Bubble Formation As a consequence of the chemical processes of polymer decomposition, leading to volatile formation, volatile molecules will start to accumulate within the decomposing polymer. If the polymer is molten when decomposition commences, bubbles will form and migrate upwards, eventually erupting from the surface. This causes physical swelling, reducing the thermal inertia of the material, accelerating the rate of surface heating and the onset of ignition.
Chemical Transformations In the case of thermosets and cellulosic materials, the polymer molecule starts to decompose before the chains have acquired sufficient energy to overcome the forces holding them in place. These materials tend to produce carbonaceous chars on thermal decomposition. The physical structure of these chars will profoundly affect the heat transfer, volatile release, and access of oxygen, all of which will impact on the thermal decomposition processes. The char can undergo glowing combustion in the presence of oxygen. However, it is unlikely that both glowing combustion of the char and significant flaming can occur simultaneously in the same zone above the surface, since the flame will consume all the available oxygen, and the flow of volatiles through the char will tend to drive oxygen away from the char surface. Therefore, in general, char oxidation will only occur after flaming has subsided.
181
Influence of Oxygen The thermal decomposition of polymers may proceed by heat alone, or by the combined action of heat and oxygen. In many polymers, the thermal decomposition processes are accelerated by oxygen, lowering the minimum decomposition temperatures. Prior to ignition, thermo-oxidative decomposition results in pyrolysis of fuel and other species. After ignition, during steady flaming, even in well-ventilated conditions, pyrolysis of the condensed phase (pyrolysis zone) is essentially anaerobic, with all the oxidation taking place in the gas phase (flame zone) [5]. Thus, the mass loss, resulting from pyrolysis, the residue formation etc., of a flaming sample corresponds to a decomposition of the material under an inert atmosphere [6]. Unfortunately, there are several published studies of the development of fire retarded materials which appear oblivious to this fundamental principle of fire science. Only for ignition, non-intense flaming, samples near and after extinction, and non-igniting samples will thermo-oxidative decomposition be relevant to the behaviour in a fire. Indeed the observation of bubbles of volatile fuel in decomposing polymers, around the time to ignition (which have been characterised by immersing the test specimen in liquid nitrogen), showed that for many thermoplastics, even prior to ignition, most volatile formation comes from the bulk of the polymer, not its surface, and hence the critical decomposition condition remains anaerobic [7]. The thermal decomposition of polymers has been broken into for general chemical mechanisms. The first three essentially describe the conversion of an involatile polymer molecule into fragments small enough to be volatile. In many cases the decomposition follows more than one of the mechanisms. (i) Random-chain scission, in which chain scissions occur at apparently random locations in the polymer chain. (ii) End-chain scission, in which individual monomer units are successively removed at the chain end. (iii) Chain-stripping, in which atoms or groups not part of the polymer chain (or backbone) are cleaved.
182
A. Witkowski et al.
(iv) Cross-linking, in which bonds are created between polymer chains. These are discussed further in section “Decomposition Mechanisms”.
Influence of Chemical Structure on Thermal Stability The combustion behaviour of a polymeric material can be interpreted in terms of the properties of the volatiles, particularly their composition, reactivity and rate of formation. Thermal stability can be quantified from the temperature dependence of decomposition. Detailed studies by Madorsky [8] in the 1960s of the effects of chemical structure on the thermal stability of polymeric materials underpin our understanding of the factors controlling the thermal decomposition of polymers. These experiments investigated the thermal stability by determining the temperature, Th, at which 50 % of a small polymer sample will volatilise in 30 min in an inert atmosphere. Table 7.3 summarises the effects of chemical structure on the thermal stability of polymers, and provides examples of that behaviour. The individual effects are discussed below.
Chain Branching With two chain branches on every other carbon atom in the chain, polyisobutylene (CH2C (CH3)2)n has the lowest thermal stability, followed by polypropylene (CH2CH(CH3))n with one branching point on every other carbon atom. Commercial polyethylene is not composed only of straight polymer chains. It actually contains a number of branches of its linear chains, either of small groups such as CH3– or longer side chains, which occur randomly during the polymerisation process. These are the most reactive parts of otherwise unreactive structures. Polymethylene (CH2)n is the name given to the special, unbranched form of polyethylene. The number of branching points in normal polyethylene also affects its crystallinity. Low density polyethylene (LDPE) has around 60 branching points per 1000 carbon atoms. An intermediate density, linear low density polyethylene (LLDPE) is actually a copolymer of ethane and an alkene such as oct-1-ene, so the regularity of the polymer chain is deliberately disrupted by the presence of side chains, 6 carbon atoms in length. High density polyethylene (HDPE) is closer to the idealised polymethylene with around 7 branching points per 1000 carbon atoms. During thermal decomposition, the
Table 7.3 Factors affecting the thermal stability of polymers (From Madorsky [8]) Factor Chain branching
Effect on thermal stability Weakens
Double bonds in polymer backbone
Weakens
Aromatic ring in polymer backbone
Strengthens
High molecular weight
Strengthens
Cross-linking
Strengthens
Oxygen in the polymer backbone
Weakens
Examples Polymethylene Polyethylene Polypropylene Polyisobutylene Polypropylene Polyisoprene Poly-1,4-phenylene methylene Polystyrene PMMA B (MW ¼ 5.1 l06) PMMA A (MW ¼ 1.5 l05) Polydivinyl benzene Polystyrene Polymethylene Polyethylene oxide Polyoxymethylene
Th/K 688 679 660 621 660 596 703 637 600 556 672 637 688 618 heat of gasification per unit mass) are replicated in the criteria for extinction. However, while ignition requires a source (whose energy input will affect the result), extinction has no such dependence. The dilution of the flame by nitrogen causes the flame to swell, reducing the amount of heat fed back to the sample below the flame. As a rule of thumb, there is generally some correlation between the time to ignition in the cone calorimeter and the LOI, but none between LOI and heat release rate.
Bench-Scale Measurement of Heat Release The Cone Calorimeter The Cone Calorimeter [180, 189] (Fig. 7.52) was developed specifically to determine the rate of heat release and effective heat of combustion of building materials (ISO 5660–1). It was subsequently modified to determine smoke generation (ISO 5660–2) and later applied to furniture. A horizontal specimen, 100 mm square, typically 3–6 mm, but up to 50 mm, thick is mounted under a steel frame, such that only the surfaces, but not the edges are exposed to a conical radiator pre-set to between 10 and 100 kW m2 mounted beneath an instrumented hood and duct. A spark ignition is used and the specimen is mounted on a load cell. Heat release is quantified by oxygen depletion calorimetry. Measurement of heat release from real fires by oxygen depletion calorimetry is well established, and gives sensible values which relate to the
Fig. 7.52 Diagram of cone calorimeter Exhaust duct, leading to gas sampling
Conical Radiant Heater
Spark igniter
Sample holder
Load cell
7
Thermal Decomposition of Polymeric Materials
extent of burning. Provided the effluent flow through the exhaust is carefully controlled, the heat release will be proportional to the oxygen depletion. A sample of the effluent is cooled to remove water and analysed using a paramagnetic analyser and non-dispersive infrared CO and CO2 analysers. It will not take into account the reduction in heat release due to the endothermic decomposition of metal hydroxide fire retardants, such as aluminium hydroxide (ATH), although this can be compensated for separately. (For PMMA containing 60 % ATH this would result in an overestimation of total heat release by ~8 %). A detailed description of the use and interpretation of data from the cone calorimeter for fire retardant materials development has been published [193]. The cone calorimeter monitors a comprehensive set of fire properties in a well defined fire scenario. The results can be used to evaluate material specific properties, setting it apart from many of the established fire tests which are designed to monitor the fire response of a certain specimen. The cone calorimeter covers ignition followed by essentially penetrative flaming combustion, where the flame front moves through the bulk of the sample. The ignition parameter measured in the cone calorimeter is the time to ignition, which depends on the thermal inertia, critical heat flux and critical mass loss for ignition, or alternatively the critical surface temperature for ignition. Fire response parameters measured in the cone calorimeter include mass loss, heat release rate (HRR), total heat release (THR), smoke production and CO production. Fire response properties more typical of fully developed or post flashover fire scenarios are not replicated in the cone calorimeter. There are three distinct uses of cone calorimeter data: – To compare the fire response of materials: to assess their fire performance; to perform screening for materials development; or to develop pyrolysis and burning models. – To determine data for input to simulations or predictions of full-scale fire behaviour. – To determine characteristic parameters such as the maximum HRR (peak heat release rate,
239
pHRR), fire growth rate index (FIGRA), THR etc., for regulatory purposes. These applications of the cone calorimeter define different techniques and data evaluation. For regulatory purposes, its strengths are its welldefined conditions, reproducibility and unambiguous data evaluation of one or two characteristic values. The use of defined, and in some way ideal, burning behaviour is suitable for developing pyrolysis and burning models and for obtaining reasonable input values for the simulation of fires. However, as a fire scenario, it is not representative of most real fires. Small fires are not usually initiated with radiation from above, piloted by a spark ignition source, and surrounded by a frame which acts as a large heat sink, producing an unusual gas flow field around the flame zone, and where the effects of sample dripping are negligible. Heat Release Curves from Cone Calorimetry The heat release rate (HRR) during the cone calorimeter experiment gives rise to a characteristic heat release rate curves versus the time (Fig. 7.53) [174, 190].
Microscale Measurement of Heat Release Microscale Combustion Calorimetry [192] (MCC) (section “Microscale Combustion Calorimetry”) evaluates the combustibility of milligram samples by separately reproducing the solid state and gas phase processes of flaming combustion by controlled pyrolysis of the sample in an inert gas stream, followed by high temperature oxidation of the volatile pyrolysis products. Oxygen consumption calorimetry is used to measure the heat of combustion of the pyrolysis products. The maximum amount of heat released per unit mass per degree of temperature (J g1 K1) is a material property that appears to be a good predictor of “flammability”. The heat release capacity (HRC) and total heat release (THR), obtained by MCC, are related to the char yield and the heat of complete combustion of the volatiles. It takes no account of physical effects, such as dripping, wicking, and sample thickness; or chemical effects such as flame inhibition, because the conditions force
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Thermally thick non-charring (or non-residue forming) samples show a strong initial increase after ignition up to a steady HRR191. This plateau remains until near the end of the test, when an additional pHRR occurs. This peak is caused by reduction in heat transfer by conductivity through the increasingly thin sample, since the glass wool supporting the sample prevents heat transfer to the sample holder as the pyrolysis zone approaches it.
HRR Thick Sample (Non Charring)
time HRR For intermediate thermally-thick, non-charring samples the plateau vanishes. The averaged or steady HRR is only marked by a shoulder. The pHRR increases in comparison with thermally thick non-charring samples since its origin is half way between the thermally-thick non-charring and thermally-thin behaviour.
Intermediate Thickness (Non Charring)
time HRR Thick Sample (Charring)
time HRR Thin Sample (Charring/ Non Charring)
Thermally-thick charring (residue forming) samples show an initial increase in HRR until an effective char layer is formed. As the char layer thickens, this results in a decrease in HRR. The maximum reached at the beginning is the steady HRR and the pHRR. Some thermally thick charring materials, such as wood, show a pHRR at the beginning, typical for charring, and a second pHRR at the end. The second peak may be caused by cracking char or increase in effective pyrolysis temperature, as observed with the thick non-charring materials. Thermally-thin samples are characterized by a sharp peak in HRR, since the whole sample is pyrolysed at the same time. In this case, the pHRR is determined by their total fire load.
time Fig. 7.53 Types of heat release curves from cone calorimetry [191]
pyrolysis and combustion to completion [193]. However, varying the combustion temperature or oxygen concentration results in incomplete combustion as occurring in real fires. The THR results have been correlated to LOI; HRC and char residue to LOI; and HRC and THR with peak heat release rate (pHRR) in the cone calorimeter. It has been used as a screening test for efficacy of flame retardant additives [194].
Influence of Physical Properties on Flammability The following factors affect polymer combustion in real fires, and should therefore influence the outcome of a suitably designed test. Fuel production—when the fuel in the gas phase reaches a critical concentration, ignition and flaming can occur. While the fuel production rate during heating is essentially a
7
Thermal Decomposition of Polymeric Materials
material property, the air flow around the sample may profoundly alter the ignition temperature. Presence of inhibitors or diluents—Cl · or Br · or PO · are stable radicals which will reduce the critical concentration of active radicals such as H · and OH·, in the flame zone. The effect is most pronounced at ignition, and least evident under developed fire conditions. Rheology of decomposing polymer—Some polymers depolymerise during decomposition reducing their viscosity. This allows better dispersion of heat, and material flow away from the source of heat. This can result in harmless dripping away from the flame zone, or flaming drips allowing flaming to spread downwards. Some additives (e.g. high surface area fillers, such as nanofillers) will increase the viscosity reducing dripping resulting in a more rapid increase in the surface temperature. This will reduce the time to ignition. In some cases free radical initiators are added purely to promote dripping to remove the fuel from the source of heat. Char formation—the formation of a char on the surface of the polymer will reduce the flow of heat to and fuel from the sample. Intumescent chars bubble up and provide a more effective barrier. However, in a typical fire test, the direction of swelling is often towards the heat source, increasing the radiant flux to the sample. Orientation of sample—as flames rise, flame spread is easiest from below (going upwards) and hardest from above (going downwards). Because of flow of molten material and ultimately dripping, it is very difficult to correlate vertical burning behaviour with horizontal burning behaviour. Absorption of radiation—radiation from flames or a radiant panel must be absorbed by the polymer. The presence of absorbing centres (conjugated double bonds, or black pigments) can increase the localisation of the heating. Conversely, a highly reflective surface can significantly lengthen the time to ignition in certain tests.
241
Smoke Formation—Smoke can act as both the source of radiation (a sooty yellow diffusion flame radiates much more than a blue premixed flame) or block radiation from the flame back to the polymer.
Char Formation Classifying polymers by the structural units they contain has been used to calculate various flammability parameters and predict burning behaviour [195, 196]. The char-forming tendency (CFT) of polymers may be estimated from the contributions from each structural group, referred to as “molar group contributions”. Van Krevelen has taken the char-forming tendency of the individual structural units of polymers as an additive quantity, and based on this, the following relationship has been created: X ðCFT Þi CR
1200 ð7:50Þ M Where CR ¼ Char Residue ð%Þ CFT ¼ Char Forming Tendency ðno unitsÞ M ¼ Molecular Weight of repeat unit g mol1 Each structural group is assigned a value. This is known as the char-forming tendency (CFT) shown in Table 7.15. Aliphatic groups are generally assigned a value of zero, although if they are connected to aromatic nuclei they can have negative values (Table 7.16). Char forming tendency cannot be calculated for polymers which contain halogenated species as their soot-forming tendencies would significantly affect the char formation. The char-forming tendency is a statistical concept. For example the phenyl group has a CFT value of 1 C equivalent, which means that on average only 1 in 6 phenyl groups in the polymer forms a char, where the other 5 contribute to tar and gas formation. If the benzene ring contains 4 non-hydrogen, non-aliphatic substituents, all the rings will contribute to the char.
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Table 7.15 Molar group contributions for char formation
Group “All” aliphatic groupsa
Contribution to residue per structural in unit CFT C-equiv. Group 0 0 N
Contribution to residue per structural in unit CFT C-equiv. 12 1
N
C
C O
-CHOH-(exception)
4
1/3 C
36
3.5
42
3.5
42
3.5
84
7
84
7
108
9
132
11
120
10
144
12
C
N
NH CH
12
1
CH S C
C N 24
2
CH CH N
C N
36
3
48
4
60
5
H N N O N N
N
72
6
O
N N O
60
5
96
8
H N
H N
N
N
O
N
O
O
N
O
(continued)
7
Thermal Decomposition of Polymeric Materials
243
Table 7.15 (continued) Contribution to residue per structural in unit CFT C-equiv. Group 72 6 N
Group
N
N
N
O
120
168
Contribution to residue per structural in unit CFT C-equiv. 120 10
O
10
180 N
N
N
N
15
14
a
Without halogen groups
Table 7.16 Molar group contributions for char formation of aliphatic groups, connected to aromatic nuclei supplying hydrogen for the disproportionation reaction (H shift) Group >CH2 and >CH-CH2-CH3 -C(CH3)2 -CH(CH3)2
Contribution to residue per structural unit CFT 12
in C-equivalent 1
18 36 48
3/2 3 4
Example: Calculation of Char Forming Tendency (CFT) Figure 7.54 shows the values assigned to the structural groups which make up the monomer unit in polyetheretherketone (PEEK) [197]: These values are summarised in Table 7.17. The CFT of PEEK has been determined as 12 and therefore the char residue will amount to
144 g per structural unit of PEEK. The molecular weight of the PEEK monomer unit is 288.3 g mol1. These can be used to estimate the mass of the char residue (CR) to give: CR
12 1200 ¼ 50% 288
The calculated char residue (CR) is 50 %. This is slightly greater than char yields determined by experimental methods which give values ranging from 41 % [198] to 47 % [199, 200].
Calculating Polymer Flammability from Molar Group Contributions Recently, another useful method has been developed to calculate the heat release capacity (HRC) from additive molar group contributions. As a material flammability parameter [201–203] the
244
A. Witkowski et al. O
4
C
O
4
4
n
O
Fig. 7.54 PEEK assigned contributions for char
with structural group
Table 7.17 Summary of structural group contributions and their char-forming tendencies Chemical group
O O
Value 4
N 3
CFT 12
0
2
0
0
1
0
C Total
12
HRC has been recognized as a tool for analysing fire response and flammability of polymers. A quantitative laboratory pyrolysis-combustion method for directly measuring the heat release capacity has been established [204–206], and experimental data are presented which indicate that HRC can be used to correlate polymer structure with fire behaviour. The contribution of over 40 M groups has been correlated to HRC [207, 208] as shown in Table 7.18. The measured and estimated heat release capacities for over 80 polymers agree to within 15 %, demonstrating a capability for prediction of polymer flammability from chemical structure. Specific heat release rate is a molecular-level fire response parameter of a burning polymer. Lyon et al. determined the specific heat release rate using the MCC (section “Microscale Combustion Calorimetry”). Dividing the specific heat release rate (W g-1) by the rate of temperature rise (K s1) gives a material fire parameter with the units (J g1 K1) representing the HRC. They argue that the HRC is a true material property that is rooted in the chemical structure of the polymer, and is calculable from additive molar group contributions [199].
Example: Calculating Heat Release Capacity (HRC) The calculation of heat release capacity is illustrated by example of molar group contributions for a diglycidylether of bisphenolA (BPA epoxy) cured by anionic ring opening polymerization. The chemical structure of the repeat unit of the polymer is shown in Fig. 7.55. The polymer repeat unit is comprised of six basic chemical groups, and the heat release capacity is calculated from the associated Ni, Mi, and ψi for these groups, which are listed in Table 7.19. The molar heat release capacity (ηc) is obtained by summing the group contributions according to their mole fraction in the repeat unit, then dividing by the molar mass of the repeat unit to give the heat release capacity on a mass basis in units of J g1 K1. X X i ni Ψ i iNiΨ i Ψ ¼X ηc ¼ ¼ X M i ni M i i N i Mi ¼
204:5 kJ=mole K ¼ 601 J g1 K 1 340g=mole
The predicted value of 601 J g1 K1 compares favourably with the measured value of 657 J g1 K1 for this polymer.
Conclusions Polymeric materials fuel nearly all unwanted fires. All polymeric materials contain large molecular chains, giving them greater strength and resilience, than either small molecules or metallic structures. However, as almost all contain carbon and hydrogen they are easily oxidised and burn readily. The diversity in the range of polymeric materials is huge and polymers may be classified in several ways: natural, biobased or synthetic; means of polymerization; thermoplastics or thermosets; molecular mass distribution; or physical properties. Each has impacts on their burning behaviour. Some polymers, such as polyamide 6, polyvinyl chloride and polyacrylonitrile differ
Table 7.18 Structural groups and their molar contribution to the heat release capacity (molar group contributions derived from a single polymer are marked*) Structural group
Contribution/ kJ mol1 K1 118*
Structural group H
77.0
O
7.6
CH3
P
Contribution/ kJ mol1 K1 8.1
HO
Contribution/ kJ mol1 K1 19.8
Br
22.0
Structural group
NH
69.5
CH2
4.18
O
22.0
O C
30.6
23.2*
1.8
CF2 C
29.5
H3C
Cl
O
0.1
Cl
25.5
O
C N
H3C
C O
28.8
8.8
H N
34.7
Cl
N
28.3
10.9*
S
O
C
O
N
N
O
26.6
11.6
O
O
Pendant: 39.5 Backbone: 13.7
O
CH
C
22.5
H3C
43.0* N
P
N
O
13.8
O
36.4*
O
19.0
H2N
13.9*
F3C
14.8
O
18.7 N
49.0
O O
C
53.5* Si
16.7
C
17.6
N
66.7
N
CH2 N
N
15.1
N
N
18.9*
74.5
O N
O
O
O
N N O
9.7
C
C
O S O
19.2
76.7
O O
P O
O
246
A. Witkowski et al.
O
H3C
CH2 CH
CH2
O
O
*
CH2
HC CH2 O
H3C
*
Fig. 7.55 Repeat unit of diglycidylether bisphenol A
Table 7.19 Group contributions used in the calculation of the heat release capacity of bisphenol-A epoxy Molar mass Molar heat release capacity Chemical group, i Number of moles N Mi/g mol1 Ψ/kJ mol1 K1 NiMi/g mol1 Ni ψ/kJ mol1 K1 1 12 28.3 12 28.3
C 2
13
26.6
26
53.2
2
15
22.5
30
45.0
2
76
28.8
152
57.6
4
14
16.7
56
66.8
4
16
11.6
64
46.4
340
204.5
CH H3C
CH2
O
Total:
only in their average molecular mass, its distribution and any impurities arising from manufacture. Others such as polyethylene, differ as a result of the polymerization process, so free radical polymerised low-density polyethylene (LDPE) has the most branching points (or starting points for decomposition), catalytically polymerised linear low-density polyethylene (LLDPE) has a smaller number of identical branching points, and high density polyethylene (HDPE) has the least of branching points and hence the highest decomposition temperature. Many polymers, such as polyamides, polyesters, polyurethanes and epoxies represent diverse classes, having only the chemistry of the linkages (e.g. esters or urethanes) between repeat units in common. Both the physics and chemistry of polymers affect their thermal decomposition and burning behaviour. Depending on their thermal history,
most polymers exert a degree of crystallinity, increasing with the duration of cooling, giving a sharper transition between solid and liquid phases. The chemical composition of the molecular chains exerts a profound influence on the thermal decomposition of the polymers, with chain branching, double bonds, or oxygen in the polymer backbone reducing the thermal stability, and aromatic rings and crosslinking of the polymer backbone increasing the thermal stability. Polymer decomposition can best be studied on a microscale by thermogravimetric analysis, which provides fundamental information about gaseous fuel production rates, quantified by the Arrhenius parameters A and Ea. Other techniques, such as DSC, DTA, DMTA, and rheology provide additional information on the physical transformations occurring, while evolved gas analysis, using FTIR or GCMS, or
7
Thermal Decomposition of Polymeric Materials
oxygen depletion calorimetry, and char analysis, illuminate the chemical processes. The thermal decomposition of polymers is thermodynamically driven, as higher temperatures favour the formation of gaseous molecules, and is controlled by a frequently complex array of competing kinetic processes. Attempts to identify individual reactions have generally failed, and there is a broad consensus that predicting the rate of fuel gasification will suffice as input to pyrolysis models, and fire models that include condensed phase processes. The breakdown of individual polymers can follow up to four competing pathways: end chain scission (PMMA, PTFE, PS); random chain scission (PE, PP, PS, PA, polyisoprene etc.); chain-stripping (PVC, PAN, PVA, cellulose etc.); and char formation (PAN, PEEK, cellulose etc.), with a significant variation from individual polymers. Fire retardants are added to our around a third of plastic materials in order to meet regulatory requirements. In general, these apply to high risk applications, such as construction products, upholstered furnishings, electrical and electronic goods, and materials for mass transport applications. There is considerable diversity in the different fire retardant mechanisms, from the gas phase flame inhibitors, using halogens or organophosphorus compounds, to condensed phase processes ranging from intumescents and char formation, to endothermic dehydration and formation of a refractory shield. Fire behaviour may be quantified on a bench scale using ease of ignition tests such as the UL 94, or the much criticised limiting oxygen index, or using more sophisticated apparatus such as the cone calorimeter or microscale combustion calorimeter. The physical properties of polymers exert an influence on this process, with perhaps the greatest benefit being conferred by char formation, reducing the rate of thermal attack.
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254 Polymeric Materials (C.A. Wilkie and A.F Grand, eds.), Marcel Dekker, Inc., NY (2000). 202. R.E. Lyon, “Heat Release Capacity,” Proceedings of the 7th International Conference on Fire and Materials, San Francisco, CA, pp. 285–300 (2001). 203. R.E. Lyon, “Heat Release Kinetics,” Fire and Materials, 24, pp. 179–186 (2000). 204. R.N. Walters and R.E. Lyon, “A Microscale Combustion Calorimeter for Determining Flammability Parameters of Materials,” Proceedings 42nd International SAMPE Symposium and Exhibition, 42(2), pp. 1335–1344 (1997). 205. R.N. Walters and R.E. Lyon, “A Microscale Combustion Calorimeter for Determining Flammability Parameters of Materials,” NISTIR 5904 (K. Beall, ed.), pp. 89–90 (1996). 206. R.E. Lyon and R.N. Walters, U.S. Patent 5981290, Microscale Combustion Calorimeter, 11/09/1999. 207. R.N. Walters and R.E. Lyon, “Molar Group Contributions to Polymer Flammability,” PMSE Preprints, 83, 86, ACS National Meeting, Washington, D.C. (August 2000).
A. Witkowski et al. 208. R.N. Walters and R.E. Lyon, “Calculating Polymer Flammability from Molar Group Contributions,” Proceedings of the BCC Conference on Flame Retardancy of Polymeric Materials, Stamford, CT (May 22–24, 2000).
Dr Witkowski is a Lecturer at the University of Central Lancashire (UCLan), UK. His work focuses on thermal decomposition of solids and pyrolysis mechanisms, and numerical modelling. Dr Stec is an Associate Professor in Fire Chemistry and Toxicity at UCLan. Her work focuses on quantification of combustion products and the factors affecting fire toxicity from bench- and largescale tests. Prof Hull is a Professor of Chemistry and Fire Science at the University of Central Lancashire (UCLan). He obtained his PhD in 1987 in Fire Retardant Mechanisms from the University of Salford, UK. His current research interests include the development of fire retardant materials and the assessment of fire toxicity.
8
Structural Mechanics Luke A. Bisby
Introduction Structural mechanics, sometimes called ‘solid mechanics’ or ‘mechanics of materials’ is concerned with describing the behavior of structural members under loading, as occurs in all buildings and other structures due to the effects of gravity and other forces (e.g. wind, earthquake, etc.). A detailed understanding of structural mechanics is essential for anyone seeking to perform structural fire engineering analysis or design. It is not possible within this brief chapter to provide a complete treatment of the topic; however when reviewed in conjunction with Chap. 9 of this handbook, the current chapter provides a basic description of structural mechanics as is required for an initial understanding of the means by which structural stability, and to a certain extent integrity, against fire spread and insulation during fire, are engineered through careful selection and design of building materials.
Philosophy of Structural Design Structural design is both a creative art and a science, and structural engineers may use considerable creativity in determining the load bearing system for a particular building. In general, the process of structural design under normal L.A. Bisby (*) School of Engineering, University of Edinburgh, UK, The King’s Buildings, Mayfield Road, Edinburgh, UK EH93JL
(ambient) temperature conditions takes little (if any) explicit account of the possible effects of fire; it typically consists of the following steps: 1. The architect and the engineer establish the aesthetic, general structural layout, and functional requirements for the building. 2. The overall structural framing system and building materials are selected and a structural concept is proposed, based on the competing interests of architectural, functional, economic, and sustainability considerations. At this stage only approximate sizes of structural elements are known. 3. The likely loads which will act on the structure are estimated in accordance with structural engineering principles (discussed below), with due consideration given to all possible loads and their likelihood of acting (on their own or in combination with other loads). 4. A structural analysis is performed to determine the load path by which all loads are transferred through the structure from the location where they act and into the structure’s foundations. The internal forces and stresses acting within the various structural elements are subsequently determined. 5. The likely stresses and forces acting in each structural element (the design loads) are checked against the capacities of the respective structural elements (the design resistances) to ensure that the structural elements have sufficient strength and stiffness to (a) resist the applied loads without collapse
M.J. Hurley (ed.), SFPE Handbook of Fire Protection Engineering, DOI 10.1007/978-1-4939-2565-0_8, # Society of Fire Protection Engineers 2016
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(called ultimate design considerations), and (b) provide a suitable level of in-service performance of the structure (called serviceability considerations; for instance deflections, vibrations, durability, etc.). 6. Steps 3–5 are repeated as necessary, until the structural elements satisfy both ultimate and serviceability design requirements and the building is deemed to satisfactorily achieve the functional requirements set out in the early stages of the design process. It is clear from the above steps that the structural design process fundamentally involves a comparison between the loads acting on and within the structure, and the resistances or capacities of the structural elements from which the structure is made. This chapter focuses on how a structural element’s resistance to load can be determined using basic structural mechanics; however a description of the means by which the loads acting on a structure are typically estimated by structural engineers is instructive and is briefly treated first.
Structural Design at Ambient Temperature To understand the goals of structural fire engineering and the means by which these goals are met during design it is first necessary to understand the general framework through which structures are designed to resist the full suite of potential loads to which they might be subjected during their lifetime, as well as the probabilistic basis of this framework which is intended to provide a suitably low probability of failure.
Loads and Load Combinations Throughout a structure’s lifetime it will be subjected to a wide variety of loads. During the structural design process it is essential that all credible loading scenarios be considered and addressed. Loads to be used in structural design are typically specified in design codes, which provide empirically determined and statistically
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characterized worst case credible loads to be assumed in the particular jurisdiction in which the design code is in force. The most common loads for which typical structures are designed are given below. 1. Dead Loads: These are loads which are always present, and include the self weight of the structure as well as loads arising from permanent fixtures and equipment. Dead loads may include the weight of floor coverings, walls, doors, suspended ceilings, etc., and are usually estimated based on the dimensions and construction materials of the trial structure under analysis. 2. Live Loads: Sometimes called Imposed Loads, these are typically specified by design codes on the basis of data obtained from surveys of real buildings and account for the weight of people and moveable fixtures and equipment. It is important to recognize that live loads are likely to be variable throughout the life of a structure, and thus the specified values of live loads given in codes may be considerably higher than those which are actually experienced on a day-to-day basis. 3. Snow Loads: As the name implies, these are loads due to the weight of snow and ice which can accumulate on structures in cold climates. Snow loads are estimated based on geographic and climatic data which has been collected and calibrated over many decades. In some design codes loads due to snow may be treated as live loads. 4. Wind Loads: Wind loads may cause lateral forces which act on the vertical surfaces of a building, but may also cause uplift on horizontal surfaces such as roofs and slabs. Wind loads are highly variable and again are treated in design codes using empirical correlations based on geography, topography, and the form of the building. Wind loads are particularly important during the design of tall buildings, for which lateral load resistance often governs the design of the overall structural system. Modern tall building design typically includes complex wind tunnel tests to determine the possible distributions of wind pressures over the building’s surface given its
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geometry and the surrounding climate and topography. 5. Seismic Loads: In many parts of the world, loads arising form both vertical and horizontal ground acceleration during earthquake must be considered during design. Design earthquake loads are given in design codes and account for geography, probability and magnitude of possible earthquakes, soil conditions, etc. It is worth noting that the statistical likelihood of a fire and earthquake occurring simultaneously is very low. It is clear that there is uncertainty associated with the likely magnitude of each of the different loads, and also with the likelihood that each of the loads might be acting at its full (or some lesser) value at any given point in time during the life of a structure. For instance, the self weight of a structure, once designed, is reasonably well known and can be assumed to always be acting, whereas the weight of the people in a structure has large variability and may not ever be known with any degree of certainty either spatially or temporally. Furthermore, it is highly unlikely that all of the noted loads will be acting at their full value at any given time (i.e. the chances are low that a building will be completely full of people, in the middle of winter, with the wind blowing a gale, and during an earthquake). Most modern building codes deal with the uncertainty around loading using a series of load combinations which seek to statistically account for the variability in magnitude and occurrence of the respective loads when acting in combination. These load combinations help engineers to decide which combinations of loads they must consider in designing a structure; any given structure may need to be checked under a variety of potential load combinations to determine the worst possible case which must be used in designing the individual structural elements. As an illustrative example, some of the loading combinations required by The American Society of Civil Engineers’ Minimum Design Loads for Buildings and Other Structures (ASCE-7-05) [1], assuming that
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only those loads noted previously might be acting, include: 1:4D 1:2D þ 1:6L þ 0:5S 1:2D þ 1:6S þ ðL or 0:8W Þ 1:2D þ 1:6W þ L þ 0:5S
ð8:1Þ
1:2D þ E þ L þ 0:2S
and so on, where: D ¼ dead load; L ¼ live load; S ¼ snow load; W ¼ wind load; and E ¼ earthquake load. The various load combinations are based on the philosophy that, under any given set of circumstances, the worst case loads on a structure will be described by one of these combinations of loads—with a selected level of statistical confidence as described in the following sections.
Working Stress Design Once the worst case load acting on a structural element at any given instant is determined using the procedures described above, the structural engineer must assess whether or not the performance of the candidate structural element design is satisfactory under that load. There are a number of means by which this can be accomplished so as to ensure a reasonable level of confidence that the design will not fail. Most modern structural design codes use a procedure which is called Load and Resistance Factor Design (LRFD), or in some codes Limit States Design (described in detail in the next section). However, some older codes still use an approach called Working Stress or Allowable Stress Design. It is important to recognize that all building materials have their own distinct response under loading (refer to Chap. 9), and that this specific response under loading profoundly influences
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their ability to resist deformation and eventual failure. The key parameters of interest are a material’s strength (usually described in terms of its failure stress) and its resistance to deformation (usually referred to as its stiffness). Strength and stiffness are described in the following sections, but it should be noted that there are differing amounts of uncertainty associated with both of these properties—for all building materials. For instance, timber, which is a naturally occurring material with associated defects, has a relatively high level uncertainty associated with its mechanical properties, since these depend on numerous factors including the species of tree, the climate in which the tree was grown, the grade of lumber, the in-service humidity condition, etc., whereas structural steel has relatively little uncertainty since it is manufactured under well controlled factory conditions and is relatively insensitive to humidity, etc. LRFD and Working Stress design provide alternative means by which this variability and uncertainty in material response to loading can be accounted for during design. In Working Stress Design, the loads expected to be acting on the structure during service are compared against the permissible stress levels which are considered safe for the structural elements under long term loads. The loads to be considered in Working Stress design are determined based on guidance given in building codes, and are intended to represent a conservative estimate of the most likely in-service loading on the structure. The analysis of the structure is subsequently performed under these loads, and the stresses in the structural elements are calculated (using principles presented later). The resulting stresses are compared against the allowable stresses for the materials in question; these are also specified in building codes. Working stress design loads and allowable stresses have been calibrated over time to provide safe designs by implicitly building a relatively large safety factor into the allowable stress values specified in codes. These methods have now fallen out of favour in most jurisdictions, and all modern building codes are moving towards a Limit States design approach.
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Limit States Design Limit States Design is now the preferred method of design in most national building codes, largely because it (1) removes some of the unnecessary conservatism which is inherent in Working Stress Design and (2) attempts to rationally assess and account for the statistical variability of both the loads acting on a structure and the resistance of the structural elements, including variability associated with material response. Limit States Design accomplishes this by applying reliability concepts to both loads and resistances such that a consistent level of safety or safety index is achieved for all designs. As the name implies, Limit States Design uses a variety of so-called ‘limit states’ which represent the functional requirements for a structure. Ultimate Limit States (ULS) are those associated with structural failure or collapse, and are addressed by checking the capacity of the structural element, with material and member strengths artificially (statistically) reduced to account for known variability in material properties, errors and uncertainties in construction, etc., against the credible worst case loads which might act on the structure. The most likely (mean) loads are artificially increased to account for their spatial and temporal variability. Serviceability Limit States (SLS) are those associated with the in-service performance of the structure and are checked against the loads assumed to be acting in service. Since serviceability limit states are not associated with life safety, the service loads need not be unduly increased during design. The design checks which are made in Limit States Design can be expressed in general as: αE ϕR
ð8:2Þ
where: E ¼ the specified effect of loads acting on the structure; α ¼ load factors applied to the specified loads which take into account the variability of the load and load patterns and, to some extent, inaccuracy in the structural analysis;
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Structural Mechanics
R ¼ the calculated resistance of a member based on specified material properties and crosssectional dimensions; and ϕ ¼ the resistance factor applied to the calculated resistance or to specified properties and dimensions, workmanship, type of failure (e.g. brittle versus ductile) and uncertainty in the prediction of resistance.
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build from steel, the resistance factor is typically reduced somewhat to ensure that member failure occurs before connection failure; this is preferred because connection failures can occur with little warning whereas member failures generally give some warning prior to failure. Concrete tends to have lower specified material resistance factors in the range of 0.60–0.65 to reflect its higher variability; designers and codes are statistically less confident of its nominal strength.
Serviceability Limit States For the serviceability limit states, the factored resistance on the right side of Equation 8.1 is replaced with a serviceability criterion such as an allowable deflection, acceleration, etc. The load factors, α, are assigned different values, as described for example in ASCE-7-05 (ASCE 2005); typically close to or less than 1.0.
Material or Member Resistance Factors As indicated in the definitions of ϕ and R, for ultimate strength design the resistance, R, is scaled by a resistance factor, ϕ, which is typically less than 1.0 to reflect the probability that the full theoretical value of R may not be achieved at all times (i.e., in some cases the structural members and materials may not be as strong as we calculate them to be based on nominal material properties, dimensions, tolerances, and construction qualities). This results from a statistical consideration of the likely ability of a structural member to resist load. In some jurisdictions these resistance factors are applied to structural elements of different types based on the member type (e.g. beam, column, wall, etc.) and materials of construction (e.g. steel, concrete, timber, etc.). Values may vary between about 0.60 and about 0.95. In other jurisdictions resistance factors may be applied to materials rather than to structural elements. Values of resistance factors for structural materials also vary depending on the particular building code and jurisdiction. For structural steel, the value of ϕ is typically in the range of 0.85–0.95. Interestingly, for connections (i.e., bolts, welds, etc.)
Safety Index In Limit States Design, the values of both the load factors, α, and the material or member resistance factors, ϕ, in a given building code have been calibrated to provide the desired level of safety (or rather to give an acceptable probability of failure). This is generally accomplished using the concept of a safety index, β. In reality, both E and R in Equation 8.1 are random statistical variables with an associated probability distribution about a mean value. This is shown schematically in Fig. 8.1, where the probability that either the load, E, or the resistance, R, take on given values is plotted. Clearly, the mean resistance must be greater than the mean load effect to prevent failure; however, because both load and resistance are probabilistic in nature there is always a small chance of failure (occurring when then resistance is less than the applied load). The probability of failure is represented by the shaded overlapping area in Fig. 8.1. Frequency
Resistance Load Failure
E
R
Design Variable
Fig. 8.1 Probabilistic nature of load effect, E, and structural resistance, R
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It is clear that the probability of failure can be reduced by artificially increasing the true (nominal) resistance, R, of a structure by imposing smaller values of ϕ (i.e. by shifting the R-curve to the right in Fig. 8.1) or by artificially decreasing the true loads by imposing larger values of α (i.e. by shifting the E-curve to the left). The target safety index, β, allows building code developers to determine what these values should be based on known (or approximated) probability distributions for both the loads and the material or member resistances. Since failure will occur if R < E, the probability of failure can be represented by the distribution of Z ¼ RE. This is shown schematically in Fig. 8.2, where failure is again represented by the shaded region. This failure probability distribution also has a mean value and an associated standard deviation. The goal of Limit States Design is to ensure that the mean value is sufficiently above zero. As shown in Fig. 8.2, the Safety Index is simply the number of standard deviations that the mean value of the Z curve is greater than zero. In most international codes this value is set between 2 and 3. The safety Index can be quantified, provided that the mean and standard deviations of the load and resistance distributions are known, using: β¼
Z RE ffi ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi σz σR 2 þ σE 2
ð8:3Þ
Clearly, to be able to quantify the safety index, it is necessary to have good statistical data for both the applied loads on a structural member and its resistance; in many cases these Frequency
Failure
b × sZ Z
Z=R-E
Fig. 8.2 Probabilistic nature of Z ¼ R–E, and definition of the Safety Index, β
data are not very well known—particularly during fire.
Structural Design Under Fire Conditions Structural design for fire conditions generally follows the same approach as for structural design under ambient conditions, however because a severe fire in most buildings is a statistically ‘rare’ event, the load and resistance factors specified in building codes for the fire limit state change to reflect this fact.
Philosophy and Goals The design equation during fire is similar to Equation 8.2, and can be expressed in general as: αθ Eθ ϕθ Rθ
ð8:4Þ
where the subscript θ is added to denote the effects of elevated temperature. Elevated temperature may have an effect on each of the terms in Equation 8.4. For instance: Eθ ¼ the specified effect of loads acting on the structure at elevated temperature. It should be noted that thermal expansion of structural elements may introduce new loads into the structure due to restraint to thermal expansion, and these should be considered; αθ ¼ load factors applied to the specified loads for the elevated temperature condition. These are typically reduced as compared with the ambient temperature values to reflect the most likely load condition at the time of a fire (service loading condition). Typical load combinations for fire are given later in this chapter; Rθ ¼ the calculated resistance of a member at elevated temperature, based on material properties (and in some cases reduced cross-sectional dimensions) which have been reduced due to the damaging effects of heating. The resistance of a structural element will reduce during the course of a fire as it heats up; and
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261
ϕθ ¼ the resistance factor applied to the calculated resistance or to specified properties and dimensions, workmanship, type of failure, and uncertainty in the prediction of resistance at high temperature. These factors are typically set to 1.0 such that the nominal member or material strength at elevated temperature is used in calculations. It is also important to recognize that structural design for fire typically considers three distinct modes of failure which must be prevented when satisfying Equation 8.4. Recognizing that ensuring that fire does not spread beyond the compartment of origin for the requisite period of time is a fundamental goal of fire safety engineering, these failure modes are: 1. loss of load bearing capacity (i.e. structural collapse); 2. passage of flame or hot gas through a building element (e.g. wall or floor), which would represent a breach of fire compartmentation; and 3. excessive temperature rise at the exposed face of the structural element, which may also represent a breach of fire compartmentation.
Structural Fire Design Loads and Load Combinations Load combinations for use in Limit States Design for ultimate capacity at ambient conditions were given previously. In the case of structural fire analysis, the load combinations are altered to reflect the statistical unlikelihood of a severe fire occurring in the first place, as well as the fact that the actual likely loads acting on a structure on a day-to-day basis are typically much less than those used for ultimate strength design. Various countries apply slightly different load combinations for fire. As one example, ASCE-7-05 [1] suggests the following load combination for fire: 1:2D þ Ak þ ð0:5L or 0:25Þ
ð8:5Þ
It should be noted that other codes may also include the effects of snow and wind loads during fire, however again at reduced levels as compared with ambient temperature design. The
most important outcome of assuming these reduced loads during fire is the realization that, und er day-to-day conditions which are typically used to assess structural performance in fire, most structures are subjected to loads of 50 % or less of their ultimate design capacities [2]. It should be noted that the value of the load or load effect resulting from the extraordinary event (fire) should be included and is denoted by Ak in Equation 8.5.
Structural Mechanics Thus far, this chapter has concerned itself with the method that structural engineers use to quantify the likelihood of failure of, and hence design, structural members under the influence of the various combinations of loads to which they might be subjected. Structural mechanics is the branch of physics which allows structural engineers to determine the strength, or load bearing capacity, and deformation of structural elements of various types (e.g. beams, columns, slabs) under load. To provide a basic overview of the procedures used, the following sections give a brief summary of the necessary concepts; the steps in any analysis typically include: 1. Calculation of external reaction (support) forces; 2. Determination of internal forces (axial, bending, shear, and torsion); and 3. Prediction of failure modes depending on the materials of construction, the geometry, the support conditions, and the loads.
Statics With the previous issues in mind, we now move to a discussion of the physics which are used to evaluate the capacities of various types of structural elements. The first of these topics is statics. Statics provides the means by which both the external reactions and internal forces within a structural element can be determined. If a structure is in equilibrium (i.e. it is not moving but ‘static’) then the algebraic sum of all of the forces
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and moments acting on that structure is equal to zero. Otherwise the structure would be accelerating.
Static Equilibrium and Reaction Forces The first step in the analysis of structural element under load is the determination of its support reactions. For simple two-dimensional (i.e. planar) structures, static equilibrium can be applied using an orthogonal coordinate system, such that the algebraic sum of the forces in the x (horizontal) and y (vertical) directions must be zero, and also the sum of the moments acting on the structure must be zero. These equations can be expressed as follows: X X X Fx ¼ 0, F y ¼ 0, Mz ¼ 0 ð8:6Þ In reality structures are three-dimensional, and in this case there would be six equations governing static equilibrium; three translations along x, y and z-axes and moments about all three axes. As is typical in elementary structural mechanics this chapter considers only planar structures for simplicity. To illustrate the use of these equations consider the planar beam structure shown in Fig. 8.3; this is similar to the example structure used in the previous edition of this handbook [3, 4]. The structure is a solid beam of constant crosssectional area and materials of construction along its length. The beam is supported on an idealized pin support at Location B and an idealized roller support at Location C. It is loaded by a diagonal tension force at Location A, as well as a distributed load of varying magnitude along its length. Figure 8.3b shows a free body diagram of the beam, where the supports have been replaced by the unknown reaction forces which they would generate (in the directions in which they prevent motion). Note that there are three unknown reaction forces in this case, and since three equations of equilibrium are available in two dimensions, the unknowns can be determined. Such structures are referred to as statically determinate. The equations are applied as follows (with units of kN and m):
L.A. Bisby
X
X
F y ¼ 0 : 6 þ RBy þ RCy 1ð24Þ 2ð18Þ=2 ¼ 0 Mz ¼ 0 : 6ð6Þ þ 1ð24Þð6Þ RCy ð18Þ þ 2ð18Þð9Þ=2 ¼ 0
∴RCy ¼ 18; RBy ¼ 30 Note that if this structure had one or more additional supports there would not have been sufficient equilibrium equations to solve for all of the unknown reactions, and the structure would have been referred to as statically indeterminate. Unknown support reactions for statically indeterminate structures can only be obtained by considering compatibility of their deformation under load in addition to equilibrium; such methods are beyond the scope of this introductory discussion.
Internal Forces Once the support reactions for a statically determinate structure are known the internal forces can be determined at any desired location. Again, for a two-dimensional planar structure there are three internal forces which must be considered: Axial force, N(x), shear force, V(x), and moment, M(x). The internal forces are found by taking a section through the structure, which leads to the development of three unknown internal forces. Again the three equations of equilibrium can be applied to solve for the unknowns. As an example, for the two-dimensional planar structure shown in Fig. 8.3c, the internal forces at any location between B and C can be determined from the following equilibrium equations (again with units of kN and m): X Fx ¼ 0 : 8 þ 8 þ N ¼ 0 ! N ¼ 0 X
F y ¼ 0 : 6 1ð6 þ xÞ þ 30 ð2x=18ÞðxÞ=2 þ V ¼ 0 ∴V ðxÞ ¼ x2 =18 x þ 18 X
Mz ¼ 0 : M þ 6ð6 þ xÞ þ 1ð6 þ xÞð6 þ xÞ=2 30ðxÞ þ ð2x=18ÞðxÞðx=3Þ=2 ¼ 0
∴MðxÞ ¼ x3 =3 x2 =2 þ 18x 54
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263
a w = 3 kN/m
w = 1 kN/m A
C B
53.13° 10 kN
6m
18 m w = 2 kN/m
b
w = 1 kN/m
A
C RBx
8 kN
B
c
RCy
RBy
6 kN
w = 2x/18 kN/m
w = 1 kN/m
M(x)
A
N(x) 6 kN
8 kN
B 30 kN
6 kN
d
8
V(x)
8
0
0
Axial Force Diagram (kN) (tension +ive)
18
e
Shear Force 0 Diagram (kN)
0 −6 −12
−18 58.9
f 0
0
Bending Moment Diagram (kN·m)
−54
Fig. 8.3 (a) Example structure, (b) free body diagram, (c) section to the left of location x, (d) axial force diagram, (e) shear force diagram, and (f) bending moment diagram
By taking sections at successive locations along the length of the beam and calculating the internal forces it is possible to develop diagrams which plot the variation of the respective internal
forces along the length of the structure; these are called the axial force, shear force, and bending moment diagrams, respectively, and are shown in Fig. 8.3d–f for the structure in question.
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L.A. Bisby
Strength of Simple Structural Elements Once the internal forces within a structural element are known using the principles briefly presented above (or using more advanced techniques for statically indeterminate structures) the effects of these forces must be determined so as to check the capacity of the structural element in question against the loading demand. To do this the likely failure mode for the structural element must be determined. There are a variety of failure modes which must be considered, depending on the type of structural element (i.e. beam, column, etc.) and the material from which it is constructed (some materials are more prone to certain types of failures than other materials). The most important failure modes in buildings are typically tension failure, compression failure, and bending failure. For some structures or structural elements under certain conditions shear failure may also be important; however shear is not treated in this introductory discussion.
Tension Members (Cables and Ties) Tension members are much less common in buildings that compression elements (columns) or flexural (bending) elements (beams and slabs), however tension members are the simplest structural element because their failure mode can be described in relatively simple terms. Tension elements in real buildings include diagonal bracing, cable-supports and ties, and hangar bars. Consider a cylindrical steel bar of a given material and length L and cross-sectional area A which is subjected to a tensile axial load, P, in the direction of its longitudinal axis (Fig. 8.4). Using the principles of the preceding section, if the bar is sectioned at any internal location, a tension force, P, will be acting internally (Fig. 8.5). The force is tensile as it acts to elongate the bar. The average tensile stress in the bar, which is a measure of the intensity of force in a material, can be determined from: σ¼
P A
ð8:7Þ
A P
P
Fig. 8.4 Tensile loading of cylindrical bar of crosssectional area, A
σ=
P
P A
Fig. 8.5 Determination of average axial stress, σ, of cylindrical bar of cross-sectional area, A, under tensile load, P
s sy
eultimate > 5%
E = 200GPa
E
σy ≈ 250-450MPa
1 ey
e
Fig. 8.6 Idealized axial stress, σ, versus axial strain, ε, for typical structural steel
This shows that stress in the bar is proportional to the internal force and is given in units of force per unit area (in this case N/mm2 or MPa). Using Hooke’s Law the strain, ε, and hence elongation, δ, of the bar can be determined from the following expressions (within the linear-elastic range of material response) from: σ ¼ εE δ ε¼ L
ð8:8Þ
In the above expressions, E is the modulus of elasticity of the material from which the bar is made (a material characteristic, see below and Fig. 8.6), and the strain, ε, represents the intensity of deformation. To determine if the bar will fail under this load (and hence stress) the stress versus strain response of the material from which the bar is
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made must be known. As an example, for structural steel a typical idealized plot of stress versus strain is given in Fig. 8.6. Note that in practice this curve would be determined experimentally. Figure 8.6 shows that the loading response of steel is characterized by a linear increase in stress with increasing strain, with slope E providing the definition of Hooke’s Law used previously, up to a given stress, σ y, which is called the yield stress. Beyond the yield stress the strain increases linearly with no further increase in stress. Hence, the steel can be assumed to fail in tension when it reaches its yield stress, and its load carrying capacity (resistance), R, can be easily determined under this condition from: R ¼ σ yA
ð8:9Þ
Calculation of tensile strength at elevated temperature can be performed in a similar manner provided that the temperature of the structural element and the effect of this temperature on the stress versus strain response of the material are known. Chapter 9 provides information on the probable reductions in mechanical properties of various structural materials at elevated temperature. For the purposes of illustration, if it is assumed that the yield strength of steel is reduced from σ y at ambient temperature to σ yθ at elevated temperature, then the tensile strength at elevated temperature, Rθ, can be determined from: Rθ ¼ σ yθ Aθ
ð8:10Þ
It should be noted that the cross-sectional area at elevated temperature, Aθ, may also be reduced in applying Equation 8.10 to reflect a reduction in cross-sectional area due to heating, as would occur for example due to charring of wood for timber elements in fire. It must be recognized that all structural materials display distinct differences in mechanical response to loading and widely varying strength and stiffness. For example, a typical stress versus strain response for ‘normal’ strength concrete is shown in Fig. 8.7, where drastic differences in both the qualitative and quantitative aspects as compared with steel are obvious.
s
fc’ ≈ 25-60MPa
fc’
≈ 0.002
ecc ≈ 0.003
e
Fig. 8.7 Idealized axial stress, σ, versus axial strain, ε, for typical ‘normal’ strength concrete
a
P
b
P
σ =
P A
P
Fig. 8.8 (a) Compressive loading of short (stocky) cylindrical bar of cross-sectional area, A, and (b) determination of average axial stress, σ
Compression Members (Columns and Struts) Compression elements are common in buildings and include columns and struts. The strength of these elements can be determined in a similar manner as for tension elements, with the exception that compression elements may also be susceptible to buckling failure. Consider the short, stocky compression element shown in Fig. 8.8. As for the tension element discussed previously, the column has height L, cross-sectional area A, and is subjected to an axial load P (in this case compressive). Provided that the element is not prone to buckling failure, its compressive (crushing) strength at ambient or elevated temperature can be approximated using Equations 8.9 and 8.10, respectively. However, in reality all compression elements in buildings are susceptible to buckling
266 Fig. 8.9 (a) Compressive loading of long (slender) bar of cross-sectional area, A, (b) determination of average axial stress, σ, of the bar under compressive load, P, (c) buckling failure of the bar under load, P, and (d) equilibrium of half the bar under buckling failure
L.A. Bisby
a
P
c
P
δ
ε=
δ
d
L b
L
σ=
y P
P A
y M
L 2
P
failure and to the combined effect of axial load and the inevitable bending which also occurs; failure by buckling must therefore also be checked. To illustrate the alternative compressive failure mode by buckling, Fig. 8.9 shows a vertical column of height L, cross-sectional area A, and applied load P. The column is assumed to be pin-supported at both ends, such that there is no rotational restraint of its extremities (note that this is not the case for most real columns in buildings). When the load is applied to the column (Fig. 8.9a) the column experiences an axial compressive stress of σ (Fig. 8.9b), and the column’s length will reduce by an amount δ (Fig. 8.9a). However, because in reality it is impossible to apply a perfectly concentric compressive load, and because all structural elements contain small imperfections and irregularities, the column will inevitably also experience a small amount of bending (Fig. 8.9c); the result is a lateral deflection, y. Figure 8.9d shows the bottom half of the column when it is sectioned at its mid-height. If we consider the section’s equilibrium under this condition, taking moments at the section the following moment equilibrium equation is obtained:
P
P
X
Mz ¼ 0 :
P
M Py ¼ 0 ! M
¼ Py
ð8:11Þ
The elastic deformation of an element in bending can be described by the following equation: M d2 y ¼ EI dx2
ð8:12Þ
where y is the displacement perpendicular to the axis of the element, x is the distance along the element, and M is the internal moment which is acting at the section. I is the moment of inertia of the element and is a measure of its resistance to flexural deformation. The moment of inertia it is a function of the element’s crosssectional geometry and can be considered as a flexural analogue of area, A, for calculating tensile strength. Substituting Equation 8.12 into Equation 8.11 and rearranging gives: d2 y P y¼0 dx2 EI
ð8:13Þ
This is a second order differential equation which has the following solution:
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Structural Mechanics
267
rffiffiffiffiffi ! rffiffiffiffiffi ! P P v ¼ C1 sin x þ C2 cos x EI EI ð8:14Þ If the ends of the column are pinned (as in this case), then Equation 8.14 is only satisfied when: rffiffiffiffiffi ! rffiffiffiffiffi P P sin L ¼ 0 or L ¼ nπ ð8:15Þ EI EI Rearranging for P, the critical buckling load, Pcritical, is obtained; this is the theoretical load which will cause global buckling failure: R ¼ Pcritical ¼
n2 π 2 EI L2
where : n ¼ 1, 2, 3 . . . ð8:16Þ
It is clear that the lowest value of Pcritical will govern and that this occurs for n ¼ 1. Whilst this equation is only valid for linear elastic materials, as it depends on the assumptions of elastic beam theory (i.e. Equation 8.12), it is instructive for studying the propensity of elements to buckling failure under compressive loads. An interesting feature of Equation 8.16 is that it shows buckling strength to be proportional to the inverse of the square of the buckling length. Thus, if the length of a column is doubled then its buckling strength decreases by a factor of four, and so on. This can be important for the response of columns in fire in cases where lateral support from beams and slabs is removed by heating of the floorplate. The preceding section has given two means of calculating the strength of a structural element subjected to compressive axial load. Figure 8.10 plots these two methods versus column length. For very short columns, the crushing strength given by Equation 8.9 will govern, whereas for slender columns buckling (Equation 8.16) will govern. In reality, the transition between the two failure modes is more gradual due to column imperfections and inadvertent load eccentricities, and for intermediate column lengths a combined buckling crushing failure mode will be observed in reality. Building codes contain structural
R
p 2EI/L2
syA
Real Column Lcritical
L
Fig. 8.10 Column compressive strength versus buckling length
design procedures which have been calibrated to take account of the necessary factors. Calculation of compressive strength at elevated temperature is similar to at ambient temperature, however several additional important considerations are required; these are that: 1. the strength of materials is reduced at elevated temperature, such that the crushing strength will be less than at ambient temperature (see Chap. 9), according to Equation 8.10; 2. the stiffness (i.e. elastic modulus, E) is reduced at elevated temperature (possibly more or less severely than the material’s strength), thus reducing the critical buckling load, Pcritical to: n 2 π 2 Eθ I θ Lθ 2 where : n ¼ 1, 2, 3;
Rθ ¼ Pcritical,
θ
¼
ð8:17Þ
3. the effective size of the column’s cross section may be reduced, thus reducing the moment of inertia of the section from I to Iθ; 4. local increases in temperature may result in additional loads and moments due to interactions with the rest of the structure during fire; for instance thermal restraint to expansion of columns by the cool surrounding structure can increase the compressive loads on a column by 20–30 % in some cases; and 5. thermal expansion of the floorplate may result in lateral forces and displacements being imposed on columns, resulting in unexpected shear forces and so-called second-order bending moments.
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L.A. Bisby
o
M Compressive Strain and stress
r
M
Tensile Strain and stress
M Fig. 8.12 Segment of a beam in bending
Fig. 8.11 Segment of a beam in bending
Flexural Elements (Joists, Beams and Girders) Flexural elements in buildings are those which resist the applied loads primarily by bending; these include joists, beams, girders, and slabs. The variation of internal moment in a structural element under a set of loads, E, can be determined using the techniques discussed previously with reference to Fig. 8.3. The resistance of an element to bending, R, must be determined using structural mechanics. When a structural element is subjected to bending it experiences curvature. This is shown in Fig. 8.11, where a short segment of beam is subjected to a moment couple (i.e. an internal bending moment) which causes the segment to bend in a concave-up direction. Lines which were previously vertical drawn on the side of the beam would now both point towards a distant origin called the center of curvature (denoted by O in Fig. 8.11). The distance to the center of curvature is called the radius of curvature, r. This concave up condition is typically referred to as a positive or sagging moment. When an internal moment causes bending in a concave down direction it is referred to as a negative or hogging moment. When the segment is subjected to a sagging moment, material at the top of the beam’s cross section is compressed whereas material at the bottom of the beam is elongated, as shown in Fig. 8.12. At one specific location on the beam’s cross section it is neither being compressed nor
stretched; this location is called the neutral plane, and occurs at the mid-height for sections which are symmetric about a horizontal axis of bending (such as the I-shaped cross section shown in Fig. 8.13). If it is assumed that the beam is homogenous and fabricated from a linear elastic material (a helpful simplification for illustrative purposes), the distribution of strains over the cross section is linear as shown in Fig. 8.13. Applying Hooke’s Law the stress distribution over the cross section is therefore also linear, with maximum compressive stress at the top fibre of the cross section and maximum tensile stress at the bottom fibre. These assumptions can be expressed as: εy ¼
εtop εbottom y¼ y ytop ybottom
ð8:18Þ
σy ¼
σ top εtop E y¼ y ytop ytop
ð8:19Þ
If the beam is in equilibrium, then at any section to the total compressive forces must be equal to the total tensile forces. For any small area, dA, located anywhere on the cross section, the resultant force is determined as the stress multiplied by its area: dF ¼ σdA
ð8:20Þ
Applying equilibrium in the horizontal direction and integrating over the cross section:
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Structural Mechanics
269
etop ey
ytop
stop sy
y
Neutral Axis
ybottom
ebottom Beam Cross-section
sbottom
Strain distribution
Stress Distribution
Fig. 8.13 Beam cross-section, strain distribution, and stress distribution for a homogenous, linear elastic beam in bending
X
ð
ð
Fx ¼ 0 : 0 ¼ dF ¼ σdA ðA ¼ A
A
y ytop
σ top dA ¼
ð σ top ydA ytop A
ð8:21Þ Since the term in front of the integrand is non-zero, then for equilibrium it is required that: ð 0 ¼ ydA ð8:22Þ A
This is equivalent to stating that the axis of zero strain, called the neutral axis, must pass through the centroid of the cross section. Stresses in the beam can also be determined using equilibrium, which requires that the internal moment, M, be equal to the moment produced by integrating the moment contributions of the individual areas over the cross section. This can be expressed as: ð ð X M ¼M : M ¼ ydF ¼ yðσdAÞ A
ð ¼
y A
y ytop
σ top
!
A
ð ð8:23Þ σ top 2 y dA dA ¼ ytop A
The term inside the integrand represents the moment of inertia (or second moment of area), I, of the cross section, and can be found using
simple techniques or tables given in solid mechanics textbooks. Rearranging and incorporating Equation 8.19, an equation for the stress at any location in a cross section is obtained: σy ¼
My I
ð8:24Þ
This is referred to as The Flexure Formula, and can be used (for linear elastic materials) to check that the stress in a cross section is less than the failure stress for the material from which a beam is made; and hence to define the resistance of an element, R, with respect to bending failure. This approach works for most statically determinate structures, because for these types of structures the formation of a single flexural failure point (called a plastic hinge) is sufficient to cause failure. Statically indeterminate structures are more complicated as they require the formation of more than one location of flexural failure, as discussed below. The above approach to flexural analysis can also be used for elevated temperature analysis provided that the likely reductions in mechanical properties of a structural member’s constituent materials are known, and also provided that reductions in cross sectional area are accounted for. Similar mechanics can be used to develop equations for stress in sections made from
270
inelastic or non-linear materials, however these are considerably more involved and are not discussed here. For beams made from steel, which is often considered to be elastic-plastic, as previously shown in Fig. 8.6, or for reinforced concrete which is built up from a combination of steel and concrete (refer to Fig. 8.7), specialist texts should be consulted for information in this area.
Lateral Instability of Beams The above equations assume failure of a beam by excessive bending stresses. This is analogous to crushing failure of a column in compression. However, in certain cases beams may fail due to instability failures which are akin to buckling failures in compressively loaded columns. Lateral instability failures result when a beam’s compression fibre has insufficient lateral support, allowing it to buckle in a direction perpendicular to its longitudinal axis. Obviously, this is more of a problem for slender beams or beams built up from thin plates. In design the propensity of an element to lateral instability is accounted for by limiting the maximum stresses which are permitted in the cross section; this is particularly an issue for structural steel beams (and columns). In structural fire design it is important to recognize that any members which provide lateral bracing to beams must have sufficient fire resistance to be able to continue to provide this bracing in the event of a fire. This is an important consideration for both beams and, as already noted, for columns. Specialist texts should be consulted for additional information on lateral instability of beams in bending.
Continuity and Full Structure Response As already noted, most real structures are too complicated to use equilibrium alone to determine all of the external and internal forces which may be acting. In these case more advanced methods of analysis must be used which generally account also for the deformations of structures under loading (in addition to static equilibrium). Such methods are beyond the
L.A. Bisby
scope of the current chapter, however the implications of static indeterminacy for real structural response, both at ambient and at elevated temperature, are worthy of brief discussion.
Continuous Beams Continuous beams are statically indeterminate due to their being, as the name implies, continuous over multiple supports. An example of a relatively simple continuous beam is given in Fig. 8.14. This figure shows that unlike simplysupported beams, which require only a single location of flexural failure for collapse to occur, continuous beams require multiple failure locations before a failure mechanism can form; three failure locations in the case of the beam shown. Continuous beams are therefore redundant structures, and they can benefit from beneficial structural actions such as moment redistribution, both at ambient temperature and during fire. Techniques to account for moment redistribution during fire are described in detail elsewhere (e.g. [2]). Frames The structural response of building frames, for instance the idealized two-dimensional portal frame and moment resisting frame shown in Figs. 8.15 and 8.16, respectively, under gravity loads is complex, and for most real structures requires the use of detailed computer analysis techniques to determine the internal forces and moments. In fire the response of frames is even further complicated; for instance by the effects of thermal expansion and thermal restraint at elevated temperature. To illustrate some of the important behaviors which may occur in statically indeterminate frame structures during fire, Fig. 8.15 shows a possible sequence of deformation that is likely to occur in a simple planar portal frame structure subjected to a fire in its interior. The initial geometry of the structure is shown in Fig. 8.15a, where the well-known shape of an industrial building such as a warehouse is evident. Under ambient conditions the stability of the structure is assured by moment
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271
w
A
B
C
D
E
w RAx RAy
RBy
RCy
RDy
REy
Bending Moment Diagram
Simply-supported beam
Equivalent beam with built-in ends
Single-hinge failure mechanism
Three-hinge failure mechanism
Fig. 8.14 Bending moment diagram and failure mechanism for a continuous beam as compared with a simplysupported beam under a uniformly distributed load
resisting connections at locations B, C, and D (i.e. these connections resist relative rotational displacements between the structural elements framing into the joints). Without moment resisting connections at these locations the structure would be a mechanism and would immediately collapse. The connections to the foundations at A and E are not strictly required to be moment resisting for stability under ambient conditions. Under ambient conditions this structure resists loads by a combination of bending and axial compression in its structural elements. Figure 8.15b shows how this portal frame might react during the early stages of a fire.
The roof elements (B-C and C-D) would initially be heated by the fire, and two important actions would occur: 1. The beams would experience an overall longitudinal thermal expansion, which would tend to increase the length of the beams under heating by amount ΔT, as a function of the constituent materials’ coefficient of thermal expansion, αT. This thermal expansion, if occurring without any axial restraint, would be described by the following expressions: εT ¼ αT ΔT
or
ΔLT ¼ αT ΔTL
ð8:25Þ
The result of this thermal expansion would be to push the columns outwards, and hence to
272
L.A. Bisby
a
a C B
D
A
E
b
c
Fig. 8.15 Schematic showing complexities of structural response and possible failure mode of a statically indeterminate portal frame in fire
increase the moments in the columns and in the connections to the foundation. In reality there would be some restraint to axial thermal expansion, which would also tend to increase the mechanical compressive loads in the beams on heating. 2. The beams, which when heated from below would experience greater heating at their bottom fibre than at their top, would undergo thermal curvature and thermal bowing, to various degrees depending on the materials of
b
Fig. 8.16 Schematic showing complexities of structural response of a statically indeterminate multi-floor moment resisting frame in fire (Reproduced after Buchanan [2])
construction, the roofing system, etc. The result of this is that the roof beams would bow toward the fire and begin to sag purely as a consequence of the thermal gradient. As a consequence of the thermal elongation and thermal bowing, combined with reductions in the mechanical properties of the beam on further heating, the peak in the roof would gradually displace downwards under the influence of gravity loads. At some point the peak of the roof, Point C, may displace below the height of points B and D, and the roof would snap-through forming a catenary. Figure 8.15c shows the structure once the roof has snapped through. Under this condition the roof acts in tension (rather than bending and compression) to support the load under a severely deformed geometry. In addition, the moments on the column bases would be reversed and stability of the structure would be assured
8
Structural Mechanics
only by the moment capacity of the columns and their base connections to the foundations. Eventual failure of the structure would occur with the columns pulled inward leading to collapse. This relatively simple example clearly illustrates that thermal expansion, thermal bowing, large deflections, and alternative load carrying mechanisms can all be expected to play pivotal roles in the structural mechanics of a real, however simplified, structure during fire. A more complicated, yet still highly idealized structure is shown in Fig. 8.16; this is a two-dimensional moment resisting frame. Again, Fig. 8.16a shows the frame supporting gravity loads under ambient conditions. Again, the structure resists both vertical (e.g. gravity) and possibly lateral (e.g. wind) loads through a combination of bending and compressive loading. Figure 8.16b shows a highly exaggerated idealization of the possible deformation of this moment resisting frame under exposure to a fire which is localized to a single internal bay at the ground floor level. This suggests that the response of the structure is far more complex than the response of a single isolated beam presented earlier, and that the effects of continuity, axial restraint, thermal elongations and rotations, and reductions in mechanical properties of the constituent materials will all profoundly affect the forces, stresses, deformations, and ultimately the failure mode of the structure during fire. As a result of the heating during a fire, elements are subjected to loads which may never have been considered during ambient design (for example shearing or unexpected bending of the perimeter columns due to being pushed laterally by the expanding floor plate). Such factors must be considered during design in order for structures to be rationally engineered to resist the effects of fire. Such analysis is extremely complex and requires the use of specialized computer analysis software.
Slabs and Shells (Membrane Actions) An additional structural action which often plays an important role in the response of real structures during fire is membrane action.
273
Fig. 8.17 Schematic representation of compressive and tensile membrane actions in a reinforced concrete slab
Membrane action, which can be either compressive or tensile, manifests itself in planar structures such as reinforced concrete floor slabs or steel-concrete composite deck slabs. Figure 8.17 shows two-dimensional idealizations of both tensile and compressive membrane actions, where compressive membrane action can be though of as arching action, and tensile membrane action can be thought of as catenary action. In reality these actions normally manifest themselves in three dimensions; think of a dome (compressive membrane) or a net (tensile membrane). Compressive membrane action is particularly important in continuous reinforced concrete structures during the early stages of a fire, where restrained thermal expansion of concrete slabs can lead to the development significant lateral restraint forces resulting in arching action during fire (provided of course that the thrust forces have a line of action below the neutral axis of bending of the slabs). Tensile membrane action is particularly important during the late stages of fires for structures with relatively thin concrete or
274
L.A. Bisby
axial restraint as in Fig. 8.18b) then the bar is prevented from expanding and as a result it experiences zero thermal strain (i.e. zero elongation) but an increase of thermal stress. By invoking Hooke’s Law (Equation 8.8 presented previously) the thermal stress, σ T (or thermal force FT), in the bar will be:
a L
b
DL = aTDTL
c
FT = EAaTDT
FT = EAaTDT
DL = aTDTL
Fig. 8.18 Schematic representation of the possible effects of restraint to thermal expansion of a cylindrical steel bar
steel-concrete composite slabs. In these cases tensile membrane action can prevent structural collapse (however under large vertical deflections) for durations of fire exposure much greater than would be expected on the basis of single element analysis. Membrane actions are discussed in considerable detail in specialized structural fire engineering references (e.g. [2, 5, 6]).
Thermally-Induced Loading As discussed previously, thermal expansion (and more importantly restraint to thermal expansion) may significantly affect the deformation and eventual failure of real structures in real fires. To illustrate the possible importance of thermal expansion, consider a simple cylindrical steel bar of length L which is uniformly heated an amount ΔT (Fig. 8.18). If the bar is free to expand as in Fig. 8.18a then the change in length during heating is described by Equation 8.25 given previously. If however, the bar is rigidly supported between two immovable walls (i.e. a case of perfect
σ T ¼ EεT ¼ EαT ΔT FT ¼ σ T A ¼ EAαT ΔT
ð8:26Þ
If it is assumed that the bar is made from structural steel, with a typical yield strength, σ y, of 350 MPa and modulus of elasticity E of 200,000 MPa (refer to Fig. 8.6), and if it is further assumed that the coefficient of thermal expansion of steel, αT, is 13 106/K then the increase of temperature required to cause the bar to yield can be determined as follows: ε ¼ εT ¼ αT ΔT σ y ¼ EεT ¼ EαT ΔT σy 350 ¼ ¼ 134 C ∴ΔT ¼ EαT 200;000 13 106 ð8:27Þ In other words, a change in temperature of the perfectly restrained steel bar of +134 C can cause the bar to reach its failure stress. This simple example, whilst clearly not representative of a real structure, shows that a relatively mild increase of temperature can have a profound influence on the forces and deformations within a structure during heating. Only recently has the significance of thermal interaction within a structure been widely acknowledged within the structural fire engineering community in terms of its possible influences on the overall stability, and likely failure modes, of a building during fire (e.g. [6]).
Other Considerations There are a host of other important structural mechanics issues which must be considered in the analysis and design of structures to resist the
8
Structural Mechanics
damaging effects of fire and elevated temperature; it is not possible to discuss all of these here. There are many failure modes and structural interactions which could occur in any given structure, and hence structural fire analysis and design should only be undertaken by individuals with specialist knowledge in this area.
Connections One area which has not traditionally been explicitly considered within mainstream structural design for fire is the specific performance of connections at elevated temperature. Under ambient conditions structures are generally designed under the assumption that structural members will fail before their connections. Indeed, as already noted more onerous strength reduction factors are typically applied during connection design to ensure that this is the case. The performance in fire of connections of various types is currently a topic of considerable research interest; however a detailed discussion of this topic is avoided here. It is sufficient for the reader to be aware that connection performance in fire should be considered during the fire safe structural design of a building.
Disproportionate Collapse Disproportionate collapse refers to a situation where localized failure of a single structural element can lead to major or global collapse of a large, or disproportionate, portion of a structure [2]. There have been numerous real examples of disproportionate structural failure due to extreme loading events such as blast, earthquake, and even fire. The most notable case of a disproportionate structural collapse resulting from fire is probably the collapse of Building 7 of the World Trade Center complex in New York on September 11th, 2001. Design to avoid disproportionate collapse, termed design for redundancy or resilient design, requires the provision of structural redundancy and alternative load paths. Again, this topic is beyond
275
the scope of this introductory discussion; additional guidance is available elsewhere (e.g. [7]).
Summary This chapter has provided a brief, introductory summary of basic structural mechanics, as is relevant to a surface level understanding of the response of structural elements and structures to fire. In conjunction with Chap. 9 of this handbook, it provides a basic understanding of the means by which structural stability, and to a certain extent integrity and insulation during fire, can be engineered through careful selection and design of building materials. Acknowledgements The overall structure and format of this chapter of the SFPE Handbook has been based on the previous (4/e) version, which was authored by Robert W. Fitzgerald. The significant contribution of Prof. Fitzgerald to the development of this handbook must therefore be gratefully acknowledged.
Nomenclature A
Area (nm2)
Ak
Load or load effect resulting from an extraordinary event (e.g. fire) Integration constant Integration constant Distance from the extreme compression fiber to the neutral axis of bending (mm) Dead load Earthquake load Load effect, or modulus of elasticity (Young’s modulus) (GPa) Force (kN) Compressive strength of concrete (MPa) Moment of inertia (mm4) Live load Length (mm) Moment (kN∙m) 0, 1, 2. . . Center of curvature Load (kN) Member resistance, or reaction force (kN)
C1 C2 c D E E F f c’ I L L M n O P R
276
r S V W x y Z α αT β ε εcc εy ΔL ΔT δ σ σy ϕ π θ ω
L.A. Bisby
Radius of gyration (mm) Snow load Shear force (kN) Wind load Coordinate parallel to the axis of the structural element (mm) Coordinate normal to the axis of the structural element (mm), or lateral deflection (mm) Difference between resistance and load demand Load factor Coefficient of thermal expansion (K1) Safety index Strain (no units) Compressive failure strain of concrete (no units) Yield strain (no units) Change in length (mm) Change in temperature (K) Deformation (mm) Stress (MPa) Yield stress (MPa) Resistance factor Pi Subscript denoting elevated temperature Uniformly distributed loading (kN/m)
References 1. ASCE, Minimum Design Loads for Buildings and Other Structures (ASCE-7-05), American Society of Civil Engineers (2005).
2. A.H. Buchanan, Structural Design for Fire Safety, Wiley, New York, NY (2001). 3. R.W. Fitzgerald, Mechanics of Materials, AddisonWesley, Reading, MA (1982). 4. Fitzgerald, R. “Structural Mechanics,” SFPE Handbook of Fire Protection of Engineering, National Fire Protection Association, Quincy, MA (2008). 5. J.A. Purkiss, Fire Safety Engineering Design of Structures, Butterworth-Heinemann, New York, NY (2007). 6. Y. Wang, I. Burgess, F. Wald, M. Gillie, PerformanceBased Fire Engineering of Structures, Spon Press (2012). 7. Scott et al., 2002 Prevention of Progressive Collapse, Multihazard Mitigation Council Of the National Institute of Building Sciences, Washington, D.C., July.
Professor Luke Bisby is Arup Chair of Fire and Structures, and Royal Academy of Engineering Research Chair, within the BRE Centre for Fire Safety Engineering at the University of Edinburgh. Educated in Canada as a structural engineer, his research and teaching are focused predominantly in the area of Fire Safety Engineering. His reasearch is broadly in the areas of structural engineering and the provision of fire safety across the built environment, with an emphasis on the mechanical response of buildings and construction materials during fire. He has published widely in areas related to the fire behaviour of reinforced concrete structures, and on fibre-reinforced polymers in structural engineering applications. His current reasearch is interested in the response of novel structural materials to heating, including high performance and high strength concretes, polymers and polymer composites for construction, fire protection materials (including reactive fire protection coatings), and structural cross-laminated timber. He is also involved in research projects seeking to better understand and unpick sociological and psychological issues in fire safety engineering and regulation.
9
Properties of Building Materials V.K.R. Kodur and T.Z. Harmathy
Introduction Building components are to be designed to satisfy the requirements of serviceability and safety limit states. One of the major safety requirements in building design is the provision of appropriate fire resistance to various building components. The basis for this requirement can be attributed to the fact that, when other measures of containing the fire fail, structural integrity is the last line of defense. In this chapter, the term structural member is used to refer to both load-bearing (e.g., columns, beams, slabs) and non-load-bearing (e.g., partition walls, floors) building components. Fire resistance is the duration during which a structural member exhibits resistance with respect to structural integrity, stability, and temperature transmission. Typical fire resistance rating requirements for different building components are specified in building codes. In the past, the fire resistance of structural members could be determined only by testing. In recent years however, the use of numerical methods for the calculation of the fire resistance of various structural members is gaining acceptance because these calculation methods are far less costly and time consuming. The fire performance of a structural member depends, in part, on
the properties of the materials the building component is composed of. The availability of material properties at high temperature and temperature distributions permits a mathematical approach to predicting the performance of building components exposed to fire. When a structural member is subjected to a defined temperature-time exposure during a fire, this exposure will cause a predictable temperature distribution in the member. Increased temperatures cause deformations and property changes in the materials. With knowledge of the deformations and property changes, the usual methods of structural mechanics can be applied to predict fire resistance performance. In recent years, significant effort has been undertaken to develop material properties of various construction materials at elevated temperatures. In this chapter, the characteristics of materials are outlined. The various properties that influence fire resistance performance, together with the methods used to develop these properties, is discussed. The trends on the variation of thermal, mechanical, and other materialspecific properties with temperature of commonly used construction materials are presented.
Material Characteristics
V.K.R. Kodur (*) Civil and Environmental Engineering, Michigan State University, East Lansing, Michigan, USA
Classification
T.Z. Harmathy
Materials, based on composition, can be classified as either a homogeneous or heterogeneous type.
M.J. Hurley (ed.), SFPE Handbook of Fire Protection Engineering, DOI 10.1007/978-1-4939-2565-0_9, # Society of Fire Protection Engineers 2016
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Homogeneous materials have the same composition and properties throughout their volume and are rarely found in nature. Heterogeneous materials have different composition and properties. Most construction materials are heterogeneous, yet their heterogeneity is often glossed over when dealing with practical problems. The heterogeneity of concrete is easily noticeable. Other heterogeneities related to the microstructure of materials, that is, their grain and pore structures, are rarely detectable by the naked eye. The microstructure depends greatly on the way the materials are formed. In general, materials formed by solidification from a melt show the highest degree of homogeneity. The result of the solidification is normally a polycrystalline material, comprising polyhedral grains of crystals, which, in general, are equiaxial and randomly oriented. Severe cold working in metals may produce an elongated grain structure and crystals with preferred orientations. Noncrystalline solids are called amorphous materials. Gels and glasses are amorphous materials. Gels are formed by the coagulation of a colloidal solution. Glasses (vitreous materials) are solids with a liquid-like, grainless submicroscopic structure with low crystalline order. On heating, they will go through a series of phases of decreasing viscosity. Synthetic polymers (plastics) are made up of long macromolecules created by polymerization from smaller repeating units (monomers). In the case of thermoplastic materials, the mobility of the molecular chains increases on heating. Such materials soften, much like glass. In some other types of plastics, called thermosetting materials, polymerization also produces cross-bonds between the molecular chains. These crossbonds prevent the loosening of the molecular structure and the transition of the material into a liquid-like state. Some building materials (e.g., gypsum, brick) are formed from a wet, plastic mass or from compacted powders by firing. The resulting product is a polycrystalline solid with a welldeveloped pore structure. Two important building materials, concrete and gypsum, are formed by mixing finely ground powders (and aggregates) with water. The mixture solidifies
V.K.R. Kodur and T.Z. Harmathy
by hydration. The cement paste in a concrete has a highly complex microstructure, interspersed with very fine, elaborate pores. Most building materials can be treated as isotropic materials, that is, as though they possessed the same properties in all directions. An exception to this is some of the advanced composite materials, such as fiber-reinforced polymers (FRP), which might possess varying properties in different directions and are classified as anisotropic materials. Among the material properties, those that are unambiguously defined by the current composition and phase are referred to as structure-insensitive. Some others depend on the microstructure of the solid or on its previous history. These properties are structure-sensitive.
Porosity and Moisture Sorption The fire performance of a material is dependent on the chemical composition and molecular structure of the material. The presence of water in the material composition influences the properties of materials at elevated temperatures. The two commonly associated terms to describe the composition and the extent of water present in a material are porosity and moisture sorption. What is commonly referred to as a solid object is actually all the material within its visible boundaries. Clearly, if the solid is porous—and most building materials are—the so-called solid consists of at least two phases: (1) a solid-phase matrix and (2) a gaseous phase (namely, air) in the pores within the matrix. Usually, however, there is also a liquid or liquid-like phase present: moisture either absorbed from the atmosphere to the pore surfaces or held in the pores by capillary condensation. This third phase is always present if the pore structure is continuous; discontinuous pores (like the pores of some foamed plastics) are not readily accessible to atmospheric moisture. The pore structure of materials is characterized by two properties: porosity, P (m3.m–3), the volume fraction of pores within the visible boundaries of the solid; and specific surface, S (m2.m–3), the surface area of the pores per unit volume of the material. For a solid with
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Properties of Building Materials
continuous pore structure, the porosity is a measure of the maximum amount of water the solid can hold when saturated. The specific surface and (to a lesser degree) porosity together determine the moisture content the solid holds in equilibrium with given atmospheric conditions. The sorption isotherm shows the relationship at constant temperature between the equilibrium moisture content of a porous material and the relative humidity of the atmosphere. A sorption isotherm usually has two branches: (1) an adsorption branch, obtained by monotonically increasing the relative humidity of the atmosphere from 0 to 100 % through very small equilibrium steps; and (2) a desorption branch, obtained by monotonically lowering the relative humidity from 100 to 0 %. Derived experimentally, the sorption isotherms offer some insight into the nature of the material’s pore structure [1, 2]. For heterogeneous materials consisting of solids of different sorption characteristics (e.g., concrete, consisting of cement paste and aggregates), the sorption isotherms can be estimated using the simple mixture rule (with m ¼ 1; see Equation 9.1). Building materials, such as concrete (or more accurately, the cement paste in the concrete) and wood, because of their large specific surfaces, can hold water in amounts substantial enough to be taken into consideration in fire performance assessments.
Mixture Rules Some properties of materials of mixed composition or mixed phase can be calculated by simple rules if the material properties for the constituents are known. The simplest mixture rule is [3] X πm ¼ vi π im ð9:1Þ i
where π ¼ Material property for the composite πi ¼ Material property for the composite’s ith constituent vi (m3.m–3) ¼ Volume fraction of the ith constituent
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m (dimensionless) ¼ Constant that has a value between 1 and +1 Hamilton and Crosser recommended the following rather versatile formula for two-phase solids [4]: v1 π1 þ γv2 π2 v1 þ γv2
ð9:2Þ
nπ1 ðn 1Þπ1 þ π2
ð9:3Þ
π¼ where γ¼
Here phase 1 must always be the principal continuous phase. n (dimensionless) is a function of the geometry of phase distribution. With n ! 1 and n ¼ 1, Equations 9.2 and 9.3 convert into Equation 9.1 with m ¼ 1 and m ¼ 1, respectively. With n ¼ 3, a relation is obtained for a two-phase system where the discontinuous phase consists of spherical inclusions [5]. By repeated application, Equations 9.2 and 9.3 can be extended to a three-phase system [6], for example, to a moist, porous solid that consists of three essentially continuous phases (the solid matrix, with moisture and air in its pores).
Survey of Building Materials There are burnable (combustible) and nonburnable (noncombustible) building materials. The reason for preferring the use of the words burnable and nonburnable has been discussed by Harmathy [2]. To a designer concerned with the structural performance of a building during a fire, the mechanical and thermal properties of these materials are of principal interest. Yet burnable building materials may become ignited, and thereby the positive role assigned to these materials by design (i.e., functioning as structural elements of the building) may change into a negative role—that is, becoming fuel and adding to the severity of fire. Those properties of burnable building materials that are related to the latter role are discussed in other chapters of this handbook.
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From the point of view of their performance in fire, building materials can be divided into the following groups: 1. Group L (load-bearing) materials. Materials capable of carrying high stresses, usually in tension or compression. With these materials, the mechanical properties related to behavior in tension and/or compression are of principal interest. 2. Group L/I (load-bearing/insulating) materials. Materials capable of carrying moderate stresses and, in fire, providing thermal protection to Group L materials. With Group L/I materials, the mechanical properties (related mainly to behavior in compression) and the thermal properties are of equal interest. 3. Group I (insulating) materials. Materials not designed to carry load. Their role in fire is to resist the transmission of heat through building elements and/or to provide insulation to Group L or Group L/I materials. With Group I materials, only the thermal properties are of interest. 4. Group L/I/F (load-bearing/insulating/fuel) materials. Group L/I materials that may become fuel in fire. 5. Group I/F (insulating/fuel) materials. Group I materials that may become fuel in fire. The number of building materials has been increasing dramatically during the past few decades. In the last decade or so, a number of high-performing materials, such as FRP and high-strength concrete (HSC), have been developed to achieve cost-effectiveness in construction. Although many of these high-performing materials possess superior properties at ambient temperatures, the same cannot be said of their performance at elevated temperatures. In materials such as HSC, additional complexities such as spalling arise, which may severely impact the fire performance of a structural member. By necessity, only a few of those materials that are commonly used will be discussed in this chapter in some detail. These materials are as follows: in Group L—structural steel, lightgauge steel, and reinforcing/prestressing steel; Group L/I—concrete and brick (including fiber-reinforced concrete); Group L/I/F
V.K.R. Kodur and T.Z. Harmathy
(or Group I/F and L/F)—wood and FRP; and Group I—gypsum and insulation.
Material Properties at Elevated Temperatures The behavior of a structural member exposed to fire is dependent, in part, on the thermal and mechanical properties of the material of which the member is composed. While calculation techniques for predicting the process of deterioration of building components in fire have developed rapidly in recent years, research related to supplying input information into these calculations has not kept pace. The designer of the fire safety features of buildings will find that information on the properties of building materials in the temperature range of interest, 20–800 C is not easy to come by. Most building materials are not stable throughout this temperature range. On heating, they undergo physicochemical changes (“reactions” in a generalized sense), accompanied by transformations in their microstructure and changes in their properties. For example, concrete at 500 C is completely different from the material at room temperature. The thermophysical and mechanical properties of most materials change substantially within the temperature range associated with building fires. In the field of fire science, applied materials research faces numerous difficulties. At elevated temperatures, many building materials undergo physicochemical changes. Most of the properties are temperature dependent and sensitive to testing method parameters such as heating rate, strain rate, temperature gradient, and so on. Harmathy [7] cited the lack of adequate knowledge of the behavior of building materials at elevated temperatures as the most disturbing trend in fire safety engineering. There has been a tendency to use “notional” (also called “typical,” “proprietary,” “empirical,” etc.) values for material properties in numerical computations—in other words, values that ensure agreement between experimental and analytical results. Harmathy warned that this practice might lead
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Properties of Building Materials
to a proliferation of theories that lack general validity. Clearly, the generic information available on the properties of building materials at room temperature is seldom applicable in fire safety design. It is imperative, therefore, that the fire safety practitioner knows how to extend, based on a priori considerations, the utility of the scanty data that can be gathered from the technical literature. Also, knowledge of unique materialspecific characteristics at elevated temperatures, such as spalling in concrete or charring in wood, is critical to determine the fire performance of a structural member. These properties are discussed in the following sections.
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Stress-Strain Relationships The mechanical properties of solids are usually derived from conventional tensile or compressive tests. The strength properties are usually expressed in stress-strain relations, which are often used as input data in mathematical models calculating the fire resistance. Figure 9.1 shows, for a metallic material, the variation of stress, σ (Pa), with increasing strain (deformation), ε (mm–1), while the material is strained (deformed) in a tensile test at a more or less constant rate (i.e., constant crosshead speed), usually of the order of 1 mmmin–1. Generally, because of a decrease in the strength and ductility of the material, the slope of the stress-strain curve decreases with increasing temperature.
Reference Condition Modulus of Elasticity, Yield Strength, Ultimate Strength The modulus of elasticity is a measure of the ability of the material to resist deformation and is expressed as the ratio of the deforming stress to the strain in the material. Generally, the modulus of elasticity of a material decreases gradually with increasing temperature. The tensile or compressive strength of the material is generally expressed by means of yield strength and ultimate strength. Often the σu σy Stress, σ
Most building materials are porous and therefore capable of holding moisture, the amount of which depends on the atmospheric conditions. Because the presence of moisture may have a significant and often unpredictable effect on the properties of materials at any temperature below 100 C, it is imperative to conduct all property tests on specimens brought into a moistureless “reference condition” by some drying technique prior to the test. The reference condition is normally interpreted as that attained by heating the test specimen in an oven at 105 C until its weight shows no change. A few building materials however, among them all gypsum products, may undergo irreversible physicochemical changes when held at that temperature for an extended period. To bring them to a reference condition, specimens of these materials should be heated in a vacuum oven at some lower temperature level (e.g., at 40 C in the case of gypsum products).
u r y
e
Mechanical Properties The mechanical properties that determine the fire performance of structural members are strength, modulus of elasticity, and creep of the component materials at elevated temperatures.
0 0.2%
Strain, ε
Fig. 9.1 Stress-strain curve (strain rate is roughly constant)
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Fig. 9.2 Variation of strength with temperature for different materials
100 90
Strength (% of initial)
80 70 60 50 40
Concrete
30 FRP
20
Wood Structural steel
10 0
0
100
200
300
400
500
600
700
800
Temperature (°C)
strength at elevated temperature is expressed as a percentage of the compressive (tensile) strength at room temperature. Figure 9.2 shows the variation of strength with temperature (ratio of strength at elevated temperature to that at room temperature) for concrete, steel, wood, and FRP. For all four materials, the strength decreases with increasing temperature; however, the rate of strength loss is different. For materials such as concrete, compressive strength is of main interest because it has very limited tensile strength at higher temperatures. However, for materials such as steel, both compressive and tensile strengths are of equal interest. Section 0-e of the curve in Fig. 9.1 represents the elastic deformation of the material, which is instantaneous and reversible. The modulus of elasticity, E (Pa), is the slope of that section. Between points e and u the deformation is plastic, nonrecoverable, and quasi-instantaneous. The plastic behavior of the material is characterized by the yield strength at 0.2 % offset, σy (Pa), and the ultimate strength, σu (Pa). After some localized necking (i.e., reduction of cross-sectional area), the test specimen ruptures at point r. The modulus of elasticity is more or less a structure-insensitive property.
For metals of similar metallurgical characteristics, the stress-strain curve can be reproduced at room temperature at a reasonable tolerance, and the shape of the curve does not depend significantly on the crosshead speed. At sufficiently high temperatures, however, the material undergoes plastic deformation even at constant stress, and the e-r section of the stressstrain curve will depend markedly on the crosshead speed.
Creep Creep, often referred to as creep strain, is defined as the time-dependent plastic deformation of the material and is denoted by εt (mm–1). At normal stresses and ambient temperatures, the deformation due to creep is not significant. At higher stress levels and at elevated temperatures, however, the rate of deformation caused by creep can be substantial [8]. Hence, the main factors that influence creep are the temperatures, the stress level, and their duration. In a creep test the variation of εt is recorded against time, t (h), at constant stress (more accurately, at constant load) and at constant (elevated) temperature T (K). A typical strain-time
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Properties of Building Materials
283
a
b
Creep stress, εt
Strain, ε
r
s2 tan–1εts •
s1
tan–1z
εt s E
e
Time, t
0
0
Temperature-compensated time, θ
Fig. 9.3 (a) Creep strain vs. time curve (T ¼ constant; σ constant); (b) creep strain vs. temperature-compensated time curve (σ constant)
curve is shown in Fig. 9.3a. The total strain, ε (mm–1), is ε¼
σ þ εt E
ð9:4Þ
The 0-e section of the strain-time curve represents the instantaneous elastic (and reversible) part of the curve; the rest is creep, which is essentially nonrecoverable. The creep is fast at first (primary creep, section e-s1 in Fig. 9.3a, then proceeds for a long time at an approximately constant rate (secondary creep, section s1-s2), and finally accelerates until rupture occurs (tertiary creep, section s2-r). The curve becomes steeper if the test is conducted either at a higher load (stress) or at a higher temperature. Dorn’s concept is particularly suitable for dealing with deformation processes developing at varying temperatures [9]. Dorn eliminated the temperature as a separate variable by the introduction of a new variable: the “temperaturecompensated time,” θ (h), defined as θ¼
ðt
eΔHc =RT dt
ð9:5Þ
0
where ΔHc (Jkmol–1) is the activation energy of creep, and R (Jkmol1K–1) is the gas constant. From a practical point of view, only the primary and the secondary creeps are of importance. It has been shown that the creep strain in
these two regimes can be satisfactorily described by the following equation [10] εt0 cosh1 2Zθ=εt0 ðσ ’ constantÞ ð9:6Þ εt ¼ ln 2 or approximated by the simple formula [11] εt εt0 þ Zθ
ðσ ’ constantÞ
ð9:7Þ
where Z (h–1) is the Zener-Hollomon parameter, and εt0 (mm–1) is another creep parameter, the meaning of which is explained in Fig. 9.3b. The Zener-Hollomon parameter is defined as [12] Z ¼ ε_ ts eΔH=RT
ð9:8Þ
where ε_ ts (mm–1h–1) is the rate of secondary creep at a temperature, T. The two creep parameters, Z and εt0, are functions of the applied stress only (i.e., they are independent of the temperature). For most materials, creep becomes noticeable only if the temperature is higher than about one-third of the melting temperature (on the absolute scale). The creep of concrete is due to the presence of water in its microstructure [13]. There is no satisfactory explanation for the creep of concrete at elevated temperatures. Anderberg and Thelandersson [14], and Schneider [15] suggested techniques for the calculation of the deformation of concrete under conditions characteristic of fire exposure.
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Thermal Properties The material properties that influence the temperature rise and distribution in a member are its thermal conductivity, thermal expansion, specific heat, thermal diffusivity, and mass loss. These properties depend on the composition and characteristics of the constituent materials.
Thermal Expansion The thermal expansion characterizes the expansion (or shrinkage) of a material caused by heating and is defined as the expansion (shrinkage) of unit length of a material when it is raised 1 in temperature. The expansion is considered to be positive when the material elongates and is considered negative when it shortens. In general, the thermal expansion of a material is dependent on the temperature. The dilatometric curve is a record of the fractional change of a linear dimension of a solid at a steadily increasing or decreasing temperature. With mathematical symbolism, the dilatometric curve is a plot of Δ‘ against T ‘0 where Δ‘ ¼ ‘ – ‘0 and ‘0 (m) and ‘ (m) are the changed and original dimensions of the solid, respectively, the latter usually taken at room temperature. Δ‘ reflects not only the linear expansion or shrinkage of the material, but also the dimensional effects brought on by possible physicochemical changes (i.e., “reactions”). The heating of the solid usually takes place at a predetermined rate, 5 Cmin–1 as a rule. Because the physicochemical changes proceed at a finite rate and some of them are irreversible, a dilatometric curve obtained by heating rarely coincides with that obtained during the cooling cycle. Sluggish reactions may bring about a steady rise or decline in the slope of the dilatometric curve. Discontinuities in the slope indicate very fast reactions. Heating the material at a rate higher than 5 Cmin–1 usually causes the
reactions to shift to higher temperatures and to develop faster. The coefficient of linear thermal expansion, β (mm–1K–1), is defined as β¼
1 d‘ ‘ dT
ð9:9Þ
Since ‘ ¼ ‘0 the coefficient of linear thermal expansion is, for all intents, the tangent to the dilatometric curve. For solids that are isotropic in a macroscopic sense, the coefficient of volume expansion is approximately equal to 3β. The thermal expansion is measured with a dilatometric apparatus, capable of producing curves that show the expansion of the materials with temperature in the range from 20 to 1000 C. Harmathy [7, 16], using a horizontal dilatometric apparatus, recorded dilametric curves for various types of concrete and brick, some of which are presented in later sections. The sample was 76.2 mm long and about 13 by 13 mm in cross section. It was subjected to a small spring load that varied during the test. Unfortunately, even this small load caused creep shrinkage with those materials that tended to soften at higher temperatures. Furthermore, because the apparatus did not provide a means for placing the sample in a nitrogen atmosphere, in certain cases oxidation may also have had some effect on the shape of the curves.
Mass Loss The mass loss is often used to express the loss of mass at elevated temperatures. The thermogravimetric curve is a record of the fractional variation of the mass of a solid at steadily increasing or decreasing temperature. Again, with mathematical symbolism, a thermogravimetric curve is a plot of M against T M0 where M and M0 (kg) are the changed and original masses of the solid, respectively, the latter usually taken at room temperature.
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Properties of Building Materials
285
Fig. 9.4 Mass loss of various concrete types as a function of temperature [18]
105 100 95
Mass (%)
90 85 80
Fiber-reinforced siliceous concrete
75
Fiber-reinforced carbonate concrete
70
Plain carbonate concrete
65
0
100 200 300 400 500 600 700 800 900 1000
Temperature (°C)
Generally a heating rate of 5 Cmin–1 is used in the measurements. A thermogravimetric curve reflects reactions accompanied by loss or gain of mass but, naturally, it does not reflect changes in the materials’ microstructure or crystalline order. M/M0 ¼ 1 is the thermogravimetric curve for a chemically inert material. Again, an increase in the rate of heating usually causes those features of the curve that are related to chemical reactions to shift to higher temperatures and to develop faster. The thermogravimetric curves to be shown were obtained by a DuPont 951 thermogravimetric analyzer [17], using specimens of 10–30 mg in mass, placed in a nitrogen atmosphere [7]. The rate of temperature rise was 5 Cmin–1. Figure 9.4 shows the variation of mass loss for concrete in the temperature range from 20 to 1000 C.
Density, Porosity The density, ρ (kgm–3), in an oven-dry condition, is the mass of a unit volume of the material, comprising the solid itself and the air-filled pores. Assuming that the material is isotropic
with respect to its dilatometric behavior, its density at any temperature can be calculated from the thermogravimetric and dilatometric curves. ðM=M0 ÞT ρ ¼ ρ0 1 þ ððΔ‘Þ=ð‘0 ÞÞT
ð9:10Þ
where ρ0 (kgm–3) is the density of the solid at the reference temperature (usually room temperature), and the T subscript indicates values pertaining to temperature T in the thermogravimetric and dilatometric records. The density of composite solids at room temperature can be calculated by means of the mixture rule in its simplest form (Equation 9.1 with m ¼ 1). X p¼ v i pi ð9:11Þ i
where the i subscript relates to information on the ith component. At elevated temperatures, the expansion of the components is subject to constraints, and therefore the mixture rule can yield only a crude approximation. If, as usual, the composition is given in mass fractions rather than in volume fractions, the volume fractions can be obtained as
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V.K.R. Kodur and T.Z. Harmathy
where wi is the mass fraction of the ith component (kgkg–1). True density, ρt (kgm–3), is the density of the solid in a poreless condition. Such a condition is nonexistent for many building materials and, therefore, may be a theoretical value derived on crystallographic considerations, or determined by some standard technique, for example, ASTM C135 [19]. The relationship between the porosity and density is P¼
ρt ρ ρt
ð9:13Þ
The overall porosity of a composite material consisting of porous components is X P¼ v i Pi ð9:14Þ i
where, again, the i subscript relates to the ith component of the material.
Specific Heat The specific heat of a material is the characteristic that describes the amount of heat required to raise a unit mass of the material at unit temperature. A calorimetric curve describes the variation with temperature of the apparent specific heat of a material at constant pressure, cp (Jkg–1K–1). The apparent specific heat is defined as cp ¼
δh δT p
c p ¼ c p þ Δh
ð9:12Þ
ð9:15Þ
where h is enthalpy (Jkg–1), and the p subscripts indicate the constancy of pressure. If the heating of the solid is accompanied by physicochemical changes (i.e., “reactions”), the enthalpy becomes a function of the reaction progress variable, ξ (dimensionless), that is, the degree of conversion at a particular temperature from reactant(s) into product(s). For any temperature interval where physicochemical change takes place [2, 6, 20], 0 ξ 1, and
dξ dT
ð9:16Þ
where cp (Jkg–1K–1) is the specific heat for that mixture of reactants and (solid) products that the material consists of at a given stage of the conversion (as characterized by ξ), and Δ hp (Jkg–1) is the latent heat associated with the physicochemical change. As Equation 9.16 and Fig. 9.5 show, in temperature intervals of physicochemical instability, the apparent specific heat consists of sensible heat and latent heat contributions. The latter contribution will result in extremities in the calorimetric curve: a maximum if the reaction is endothermic, a minimum if it is exothermic. In heat flow studies, it is usually the ρcp product (Jm–3K–1) rather than cp that is needed as input information. This product is referred to as volume specific heat. Until the 1980s, adiabatic calorimetry was the principal method to study the shape of the cp versus T relationship. Since the 1980s, differential scanning calorimetry (DSC) has been the most commonly used technique for mapping the curve in a single temperature sweep at a desired rate of heating. Unfortunately, the accuracy of the DSC technique in determining the sensible heat contribution to the apparent specific heat may not be particularly good (sometimes it may be as low as 20 %). The rate of temperature rise was usually 5 Cmin–1. At higher heating rates, the peaks in the DSC curves tend to shift to higher
Apparent specific heat, cp
w i = pi vi ¼ P i wi = pi
dξ Δhp ⎯ dT
cp
0
Temperature, T
Fig. 9.5 The apparent specific heat
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Properties of Building Materials
temperatures and become sharper. For temperatures above 600 C, a high-temperature differential thermal analyzer (DTA) is also used. Harmathy, with the aid of a DuPont 910 differential scanning calorimeter, developed calorimetric curves for a number of materials by placing the samples, 10–30 mg in mass, in a nitrogen atmosphere [7, 21]. Materials that undergo exothermic reactions may yield negative values in the calorimetric curve. A negative value for cp indicates that, at the applied (and enforced) rate of heating, the rate of evolution of reaction heat exceeds the rate of absorption of sensible heat by the material. In natural processes, the apparent specific heat can never be negative, because the heat evolving from the reaction is either scattered to the surroundings or, if absorbed by the material, causes a very fast temperature rise. If the heat of reaction is not very high, obtaining nonnegative values for cp can be achieved by suitably raising the scanning rate. For this reason, some materials undergoing exothermic reactions must be tested at rates of heating higher than 5 Cmin–1, often as high as 50 Cmin–1. If experimental information is not available, the cp versus T relationship can be calculated from data on heat capacity and heat of formation for all the components of the material (including reactants and products), tabulated in a number of handbooks [22, 23]. Examples of calculations are presented in Harmathy [2, 6], where information is developed for the apparent specific heat versus temperature relation for a cement paste and four kinds of concrete.
Thermal Conductivity The temperature rise in a member, as a result of heat flow, is a function of the thermal conductivity of the material. Heat transmission solely by conduction can occur only in poreless, nontransparent solids. In porous solids (most building materials), the mechanism of heat transmission is a combination of conduction, radiation, and convection. (If pore size is less than that about 5 mm, the contribution of pores to convective heat transmission is negligible.) The thermal
287
conductivity of porous materials is, in a strict sense, merely a convenient empirical factor that makes it possible to describe the heat transmission process with the aid of the Fourier law. That empirical factor will depend not only on the conductivity of the solid matrix but also on the porosity of the solid and the size and shape of the pores. At elevated temperatures, because of the increasing importance of radiant heat transmission through the pores, conductivity becomes sensitive to the temperature gradient. Because measured values of the thermal conductivity depend to some extent on the temperature gradient employed in the test, great discrepancies may be found in thermal conductivity data reported by various laboratories. A thermal conductivity value yielded by a particular technique is, in a strict sense, applicable only to heat flow patterns similar to that characteristic of the technique employed. Experimental data indicate that porosity is not a greatly complicating factor as long as it is not larger than about 0.1. With insulating materials, however, the porosity may be 0.8 or higher. Conduction through the solid matrix may be an insignificant part of the overall heat transmission process; therefore, using the Fourier law of heat conduction in analyzing heat transmission may lead to deceptive conclusions. If the solid is not oven-dry, a temperature gradient will induce migration of moisture, mainly by an evaporation condensation mechanism [24]. The migration of moisture is usually, but not necessarily, in the direction of heat flow and manifests itself as an increase in the apparent thermal conductivity of the solid. Furthermore, even oven-dry solids may undergo decomposition (mainly dehydration) reactions at elevated temperatures. The sensible heat carried by the gaseous decomposition products as they move in the pores adds to the complexity of the heat flow process. At present there is no way of satisfactorily accounting for the effect of simultaneous mass transfer on heat flow processes occurring under fire conditions. The thermal conductivity of layered, multiphase solid mixtures depends on whether the phases lie in the direction of, or normal to, the direction of heat flow and is determined
288
using the simple mixture rule [4, 25]. At higher temperatures, because of radiative heat transfer through the pores, the contribution of the pores to the thermal conductivity of the solid must not be disregarded [26]. The thermal conductivity of solids is a structure-sensitive property. For crystalline solids, the thermal conductivity is relatively high at room temperature and gradually decreases as the temperature rises. For predominantly amorphous solids, on the other hand, the conductivity is low at room temperature and increases slightly with the rise of temperature. The conductivity of porous crystalline materials may also increase at very high temperatures because of the radiant conductivity of the pores. The thermal conductivity of materials such as concrete or brick can be measured, in the temperature range between 20 and 800 C, using a non-steady-state hot wire method [27, 28]. The thermal conductivity values at discrete temperature levels can be plotted to obtain a curve. Unfortunately, no scanning technique exists for acquiring a continuous thermal conductivity versus temperature curve from a single temperature sweep. Special problems arise with the estimation of the thermal conductivity for temperature intervals of physicochemical instability. Both the steady-state and variable-state techniques of measuring thermal conductivity require the stabilization of a pattern of temperature distribution (and thereby a certain microstructural pattern) in the test sample prior to the test. The test results can be viewed as points on a continuous thermal conductivity versus temperature curve obtained by an imaginary scanning technique performed at an extremely slow scanning rate. Because each point pertains to a more or less stabilized microstructural pattern, there is no way of knowing how the thermal conductivity would vary in the course of a physicochemical process developing at a finite rate and varying microstructure. On account of the nonreversible microstructural changes brought about by heating, the thermal conductivity of building materials (and perhaps most other materials) is usually different in the heating and cooling cycles. Open and solid circles are used in the
V.K.R. Kodur and T.Z. Harmathy
figures to identify thermal conductivity values obtained by stepwise increasing and stepwise decreasing the temperature of the sample, respectively. Also, often the thermal conductivity of a material is taken as invariant with respect to the direction of heat flow.
Thermal Diffusivity The thermal diffusivity of a material is defined as the ratio of thermal conductivity to the volumetric specific heat of the material. It measures the rate of heat transfer from an exposed surface of a material to the inside. The larger the diffusivity, the faster the temperature rise at a certain depth in the material. Similar to thermal conductivity and specific heat, thermal diffusivity varies with temperature rise in the material. Thermal diffusivity, α, can be calculated using the relation α¼
k ρc p
ð9:17Þ
where k ¼ Thermal conductivity ρ ¼ Density cp ¼ Specific heat of the material
Special (Material-Specific) Properties In addition to thermal and mechanical properties, certain other properties, such as spalling in concrete and charring in wood, influence the performance of a material at elevated temperature. These properties are unique to specific materials and are critical for predicting the fire performance of a structural member.
Critical Temperature In building materials, such as steel and FRP, the determination of failure in a structural member exposed to fire is simplified to the calculation of critical temperature. The critical temperature is defined as the temperature at which the material
9
Properties of Building Materials
loses much of its strength and can no longer support the applied load. When this temperature is reached, the safety factor against failure becomes less than 1. North American standards (ASTM E119) assume a critical or failure temperature of 538 C (1000 F) for structural steel. It is a typical failure temperature for columns under full design load. This temperature is also regarded as the failure temperature in the calculation of fire resistance of steel members. If a load is applied to the member, the test is continued until the member actually fails, which, depending on the load intensity, may occur at a higher or lower steel temperature. This concept of critical temperature is also used for reinforced and prestressed steel in concrete structural members for evaluating the fire resistance ratings. These ratings are generally obtained through the provision of minimum member dimensions and minimum thickness of concrete cover. The minimum concrete cover thickness requirements are intended to ensure that the temperature in the reinforcement does not reach its critical temperature for the required duration. For reinforcing steel, the critical temperature is 593 C, whereas for prestressing steel the critical temperature is 426 C [29]. Fig. 9.6 Spalling in NSC and HSC columns after exposure to fire [32]: (a) normal-strength concrete column and (b) high-strength concrete column
289
Spalling Spalling is defined as the breaking of layers (pieces) of concrete from the surface of the concrete elements when the concrete elements are exposed to high and rapidly rising temperatures, such as those experienced in fires. Spalling can occur soon after exposure to heat and can be accompanied by violent explosions, or it may happen when concrete has become so weak after heating that, when cracking develops, pieces fall off the surface. The consequences may be limited as long as the extent of the damage is small, but extensive spalling may lead to early loss of stability and integrity due to exposed reinforcement and penetration of partitions. Although spalling might occur in all concretes, high-strength concrete (HSC) is believed to be more susceptible than normalstrength concrete (NSC) because of its low permeability and low water-cement ratio. In a number of test observations on HSC specimens, it has been found that spalling is often of an explosive nature [30, 31]. Hence, spalling is one of the major concerns in the use of HSC and should be properly accounted for in evaluating fire performance. Spalling in NSC and HSC columns is compared in Fig. 9.6 using the data
290
obtained from full-scale fire tests on loaded columns [32]. It can be seen that the spalling is quite significant in the HSC column. Spalling is believed to be caused by the buildup of pore pressure during heating. The extremely high water vapor pressure, generated during exposure to fire, cannot escape due to the high density (and low permeability) of HSC, and this pressure buildup often reaches the saturation vapor pressure. At 300 C, the pressure reaches approximately 8 MPa; such internal pressures are often too high to be resisted by the HSC mix having a tensile strength of approximately 5 MPa [33]. The drained conditions at the heated surface, and the low permeability of concrete, lead to strong pressure gradients close to the surface in the form of the so-called “moisture clog.” [2, 34] When the vapor pressure exceeds the tensile strength of concrete, chunks of concrete fall off from the structural member. The pore pressure is considered to drive progressive failure; that is, the lower the permeability of concrete, the greater the spalling. This falling off can often be explosive in nature, depending on the fire and concrete characteristics. However, other researchers explain the occurrence of spalling on the basis of fracture mechanics and state that the spalling results from restrained thermal dilatation close to the heated surface [35]. This leads to compressive stresses parallel to the heated surface, which are released by brittle fractures of concrete, in other words, spalling. Spalling, which often results in the rapid loss of concrete during a fire, exposes deeper layers of concrete to fire temperatures, thereby increasing the rate of transmission of heat to the inner layers of the member, including the reinforcement. When the reinforcement is directly exposed to fire, the temperatures in the reinforcement rise at a very high rate, leading to a faster decrease in strength of the structural member. The loss of strength in the reinforcement, added to the loss of concrete due to spalling, significantly decreases the fire resistance of a structural member. In addition to strength and porosity of concrete mix, density, load intensity, fire intensity, aggregate type, and relative humidity are the
V.K.R. Kodur and T.Z. Harmathy
primary parameters that influence spalling in HSC. The variation of porosity with temperature is an important property needed for predicting spalling performance of HSC. Noumowe et al. carried out porosity measurements on NSC and HSC specimens, using a mercury porosimeter, at various temperatures [36].
Charring Charring is the process of formation of a layer of char at the exposed surface of wood members during exposure to fire. The charring process also occurs in other members, such as FRP and some types of plastics. When exposed to heat, wood undergoes thermal degradation (pyrolysis), the conversion of wood to char and gas, resulting in a reduction of the density of the wood. Studies have shown that the charring temperature for wood lies in the range of 280–300 C [29]. The charred layer is considered to have practically no strength. The fire resistance of the member depends on the extent of charring and the remaining strength of the uncharred portion. The charring rate, a critical parameter in determining the fire resistance of a structural wood member, is defined as the rate at which wood is converted to char. In the standard fire resistance test, it has been noted that the average rate of charring transverse to the grain is approximately 0.6 mm/min [29]. The charring rate parallel to the grain of wood is approximately twice the rate when it is transverse to the grain. Detailed studies on the charring rates for several specimen and timber types are reported by various researchers [37–39] and are summarized in a report [40]. These charring rates were constant (in each study) and ranged from 0.137 to 0.85 mm/min. The assumption of a constant rate of charring is reasonable for thick wood members. Charring is influenced by a number of parameters, the most important ones being density, moisture content, and contraction of wood. The influence of the moisture content and density of the wood on the charring rate is illustrated in Fig. 9.7 for Douglas fir exposed to the standard
9
Properties of Building Materials
291
0.9 0.8
Rate of charring (mm/min)
0.7
Moisture content (by weight) 5% 10% 15% 20%
0.6 0.5 0.4 0.3 0.2 0.1 0 300
400 Density
500 (kg/m3
600
)
Fig. 9.7 Rate of charring in Douglas fir as a function of its density (dry condition) for various moisture contents when exposed to ASTM standard fire [29]
fire [29]. It can be seen that the charring rate decreases with increasing density of the wood and also with increasing moisture content. It is important to recognize that the charring rate in real fires depends on the severity of fire to which the wood is exposed. It should be noted that the charring rate is a function of the imposed radiant heat flux. This depends on the fuel load and the ventilation factor of the compartment (for full details see Chap. 30, in this book). Detailed information on the charring of untreated wood— with expressions for charring rate in terms of the influencing factors of density, moisture content, external heat flux, and oxygen concentration— when exposed to real fires is given by Hadvig [41] and Mikkola [42].
Sources of Information Information on the properties of building materials at elevated temperatures is scattered throughout the literature. There are a few publications, however, that may be particularly valuable for fire safety practitioners. A book by
Harmathy [2] and the ASCE manual on structural fire protection [29] present a wealth of information on concrete, steel, wood, brick, gypsum, and various plastics. The thermal properties of 31 building materials are surveyed in an NRCC report [7]. The mechanical and thermal properties of concrete are discussed in an ACI guide [43], and in reports by Bennetts [44] and Schneider [45]. Those of steel are surveyed in the ACI guide, in Bennetts’s report, and in a report by Anderberg [46]. Information on the thermal conductivity of more than 50 rocks (potential concrete aggregates) is presented in a paper by Birch and Clark [47]. The relationships for thermal and mechanical properties, at elevated temperatures, for some building materials are listed in the ASCE structural fire protection manual [29]. In most cases these properties are expressed, in the temperature range of 0–1000 C, as a function of temperature and other properties at ambient temperature. These values can be used as input data in mathematical models for predicting cross sectional temperatures and fire performance of structural members.
Steel Steel is a Group L material. The steels most often used in the building industry are either hot-rolled or cold-drawn. The structural steels and concrete reinforcing bars are hot-rolled, low-carbon, ferrite-pearlite steels. They have a randomly oriented grain structure, and their strength depends mainly on their carbon content. The prestressing steel wires and strands for concrete are usually made from cold-drawn, high-carbon, pearlitic steels with an elongated grain structure, oriented in the direction of the cold work. In addition, light-gauge steel, made from cold-formed steel, finds wide applications in lightweight framing, such as walls and floors. Information on the mechanical properties of two typical steels (a structural steel [ASTM A36] and a prestressing wire [ASTM A421]) is presented in Figs. 9.8, 9.9, and 9.10 and in Table 9.1 [48]. Figures 9.8 and 9.9 are stressstrain curves at room temperature (24 C and
292
V.K.R. Kodur and T.Z. Harmathy
Fig. 9.8 Stress-strain curves for a structural steel (ASTM A36) at room temperature and elevated temperatures [48]
1 2 3 4 5 6
700 600
= = = = = =
24°C 99°C 149°C 204°C 260°C 316°C
7 8 9 10 11 12
= = = = = =
368°C 427°C 482°C 536°C 593°C 649°C 54 67 3 21 8
σ (MPa)
500 400 1 2
300
9 10
200 11 12
100
0
0
0.02
0.04
0.06
0.08
0.10
0.12
ε (m·m–1)
Fig. 9.9 Stress-strain curves for prestressing steel (ASTM A421) at room temperature and elevated temperatures [48]
1 2 3 4 5 6
2000
= = = = = =
7 8 9 10 11 12
21°C 93°C 149°C 204°C 257°C 310°C
= = = = = =
377°C 432°C 488°C 538°C 593°C 649°C 4 5
σ (MPa)
1500 2 1
3 6
1000
7 8 9
500
10 11 12 0
0
0.02
0.04
0.06
0.08
0.10
0.12
ε (m·m–1)
21 C, respectively) and at a number of elevated temperature levels. Figure 9.10 shows the effect of temperature on the yield and ultimate strengths of the two steels. Table 9.1 presents information on the effect of stress on the two creep parameters, Z and εt0 (see Equation 9.7). Because creep is a very
structure-sensitive property, the creep parameters may show a substantial spread, even for steels with similar characteristics at room temperature. The application of the creep parameters to the calculation of the time of structural failure in fire is discussed in Hamilton and Crosser [4, 8].
9
Properties of Building Materials
293
The modulus of elasticity (E) is about 210 103 MPa for a variety of common steels at room temperature. Figure 9.11 shows its variation with temperature for structural steels [50] and steel reinforcing bars [49]. (E0 in Fig. 9.11 is the modulus of elasticity at room temperature.) The density (ρ) of steel is about 7850 kgm–3. Its coefficient of thermal expansion (β) is a structure-insensitive property. For an average carbon steel, β is 11.4 106 mm–1K–1 at room temperature. The dilatometric curve shown in Fig. 9.12 is applicable to most of the common steels. The curve reveals substantial contraction of the material at about 700 C, which is associated with the transformation 1750
1500
σu
σy or σu (MPa)
1250 σy 1000
ASTM A421
750 σu
500
ASTM A36
250 σy 0
0
100
200
300
400
500
600
700
Temperature (°C)
Fig. 9.10 The ultimate and yield strengths for a structural steel (ASTM A36) and a prestressing steel (ASTM A421) at elevated temperatures [48]
(phase change of steel) of the ferrite-pearlite structure into austenite. Being a structure-sensitive property, the thermal conductivity of steel is not easy to define. For carbon steels it usually varies within the range of 46–65 Wm–1K–1. Equations for various properties of steel, as functions of temperature, are available in the ASCE structural fire protection manual [29] and in Eurocode 3 [51, 52]. In the ASCE manual, the same set of relationships is applicable for thermal properties of both structural and reinforcing steel. However, separate relationships for stress-strain and elasticity are given for the two steels with slightly conservative values for structural steel. Recently, Poh proposed a general stress-strain equation that expresses stress explicitly in terms of strain in a single continuous curve [53, 54]. The critical temperature of steel is often used as a benchmark for determining the failure of structural members exposed to fire. This ensures that the yield strength is not reduced to less than that of 50 % of ambient value. The critical temperature for various types of steels is given in Table 9.2. The above discussed high temperature properties are generally applicable to conventional carbon (mild) steel whose chemical composition consist of iron, carbon, manganese, sulfur and phosphorous. In recent years, a number of new steels are available and these steel are made by adding alloys, such as nickel, titanium, boron and chromium. These alloys influence durability characteristics, as well mechanical properties of steel. For example, molybdenum, chromium and niobium can increase the fire resistance property of steel, while chrome and nickel can enhance the corrosion resistance of steel [56]. Current design rules on fire resistance of steel structures (EC3 2005b [51], BS:5950
Table 9.1 Creep parameters for a structural steel and a prestressing steel [48] Steel ASTM A36
ΔHc/R (k) 38,890
εt0(σ) (m m–1) 3.258 10–17σ1.75
ASTM A421
30,560
8.845 10–9σ0.67
σ is measured in Pa
Z(σ) (h–1) 2.365 10–20σ4.7 if σ 103.4 106 1.23 1016 exp (4.35 10–8σ) if 103.4 106 σ 310 106 1.952 10–10σ3 if σ 172.4 106 8.21 1013 exp (1.45 10–8σ) if 172.4 106 σ 690 106
294
V.K.R. Kodur and T.Z. Harmathy
Fig. 9.11 The effect of temperature on the modulus of elasticity of (1) structural steels and (2) steel reinforcing bars [49]
1.0 1
0.8
2
E/E 0
0.6
0.4
0.2
0
0
100
200
300
400
500
600
700
Temperature (°C)
Fig. 9.12 Dilatometric curve for steel
0.014 0.012
Δ /
0
0.010 0.008 0.006 0.004 0.002 0
0
Table 9.2 Critical temperature for various types of steel Steel Structural steel Reinforcing steel Prestressing steel Light-gauge steel
Standard/reference ASTM ASTM ASTM EC 3 [51]
Temperature ( C) 538 593 426 350
Gerlich et al. [55]
400
2003 [57]) are mainly based on experimental data on mild steel and do not account for specific property variations in new types of alloy steels. Recent research by Wang et al. [58] clearly show that high strength (Q460) steel exhibits
100 200 300 400 500 600 700 800 900 1000 Temperature (°C)
slower loss of strength and modulus throughout 20–800 C temperature range as compared to mild steel. This is mainly due to the presence of chromium and niobium, which improves fire resistance properties of steel. Furthermore, tests by Kodur et al. [59] have shown that type of heat treatment has significant influence on strength properties of steel e.g. annealing and normalizing produces normal strength steel, whereas quenching and tempering produces high strength steel. High strength steel, produced using quenching and tempering process, and that is used in bolts (A490 bolts) possesses slightly lower thermal conductivity than that of conventional mild steel.
Properties of Building Materials
Fig. 9.13 Reduction of the yield strength of coldformed light-gauge steel at elevated temperatures [57–61]
295 1.0
Strength retension factor, FyT /Fy
9
0.9
BS 5950: Part 856 2.0% strain
0.8
1.5% strain
0.7
0.5% strain
0.6 0.5
Gerlich54 0.4 0.3 0.2
Makelainen and Miller 55 0.1 0.0
0
100
200
300
400
500
600
700
Temperature (°C)
1.0
Makelainen and Miller55 Steady-state tests
0.9
Normalized modulus elasticity, ET /E
Fig. 9.14 Modulus of elasticity of cold-formed light-gauge steel at elevated temperatures [57–61]
0.8 0.7 0.6 0.5
Gerlich54
0.4 0.3 0.2
Makelainen and Miller55 Transient tests
0.1 0.0
0
100
200
300
400
500
600
700
Temperature (°C)
The properties of cold-formed light-gauge steel are slightly different from those of hot-rolled structural steel. Gerlich [60] and Makelainen and Miller [61], based on steadystate and transient tests on cold-formed steel tension coupons (cut from studs) and galvanized sheets, proposed relationships for yield strength and modulus of elasticity. Figure 9.13 shows the variation of yield strength of light-gauge steel at
elevated temperatures, corresponding to 0.5 %, 1.5 %, and 2 % strains based on the proposed relationships and on the relationship in BS 5950 [57]. The BS 5950 curves represent a conservative 95 % confidence limit (i.e., a 5 % chance that strength would fall below the curve), whereas the other two curves are representative of mean test data. Figure 9.14 shows the variation of modulus of elasticity of light-gauge steel at elevated
296
Concrete Concrete is a Group L/I material. The word concrete covers a large number of different materials, with the single common feature that they are formed by the hydration of cement. Because the hydrated cement paste amounts to only 24–43 volume percent of the materials present, the properties of concrete may vary widely with the aggregates used. Traditionally, the compressive strength of concrete used to be around 20–50 MPa, which is referred to as normal-strength concrete (NSC). In recent years, concrete with a compressive strength in the range 50–100 MPa has become widely used and is referred to as high-strength concrete (HSC). Depending on the density, concretes are usually subdivided into two major groups: (1) normal-weight concretes with densities in the 2150- to 2450-kgm–3 range and (2) lightweight concretes with densities between 1350 and 1850 kgm–3. Fire safety practitioners again subdivide the normal-weight concretes into silicate (siliceous) and carbonate aggregate concrete, according to the composition of the
principal aggregate. Also, a small amount of discontinuous fibers (steel or polypropylene fibers) is often added to the concrete mix to achieve superior performance; this concrete is referred to as fiber-reinforced concrete (FRC). In this section, the properties of concrete are discussed under three groups: namely, NSC, FRC, and HSC.
Normal-Strength Concrete A great deal of information is available in the literature on the mechanical properties of various types of normal-strength concrete. This information is summarized in reports by Bennetts [44] and Schneider [45], the ACI guide [43], the ASCE fire protection manual [29], and in Harmathy’s book [2]. Figure 9.15 shows the stress-strain curves for a lightweight concrete with expanded shale aggregate at room temperature (24 C) and a few elevated temperature levels [63]. The shape of the curves may depend on the time of holding the test specimen at the target temperature level before the compression test. The modulus of elasticity (E) of various concretes at room temperature may fall within a very wide range, 5.0 103–35.0 103 MPa, 16 24°C 14
260°C
538°C
12 σ (MPa)
temperatures. The modulus ET represents the tangent modulus at low stress levels (or initial tangent modulus), because steel stress-strain relationships become increasingly nonlinear at elevated temperatures. The effect of zinc coating on the mechanical properties of steel is of little significance. The light-gauge steel has somewhat lower thermal expansion when compared to similar expressions for other steels [61]. The other thermal properties of steel, such as specific heat and thermal conductivity, are of little importance for the thermal modeling of light-gauge steel because steel framing plays a minor role in the heat transfer mechanism. A review of some of these properties is presented in a review paper [62]. The critical temperature of light-gauge steel is much lower than for other types of steels. Although Eurocode 3 limits this to a conservative value of 350 C, in other cases a critical temperature of 400 C is used (see Table 9.2).
V.K.R. Kodur and T.Z. Harmathy
760°C
8
4
0
0
0.004
0.008 ε (m • m
0.012
–1)
Fig. 9.15 Stress-strain curves for a lightweight masonry concrete at room and elevated temperatures [63]
9
Properties of Building Materials
297
dependent mainly on the water-cement ratio in the mixture, the age of concrete, the method of conditioning, and the amount and nature of the aggregates. Cruz found that the modulus of elasticity decreases rapidly with the rise of temperature, and the fractional decline does not depend significantly on the type of aggregate [64] (in Fig. 9.16, E0 is the modulus of elasticity at room temperature). From other surveys [2, 44], it appears, however, that the modulus of elasticity
1.0 Carbonate (E0 = 34 000 MPa)
0.8
E/E0
0.6
0.4
Lightweight (E0 = 19 000 MPa)
0.2
0
Sulicate (E0 = 38 000 MPa)
0
100
200
300 400 500 Temperature (°C)
600
Fig. 9.16 The effect of temperature on the modulus of elasticity of concretes with various aggregates [61]
Fig. 9.17 The effect of temperature on the compressive strength of a normal-weight concrete with silicate aggregate [65]
of normal-weight concretes decreases faster with the rise of temperature than that of lightweight concretes. The compressive strength (σu) of NSC may also vary within a wide range. Compressive strength is influenced by the same factors as the modulus of elasticity. For conventionally produced normal-weight concretes, the strength at room temperature is usually between 20 and 50 MPa. For lightweight concretes, the strength is usually between 20 and 40 MPa. Information on the variation of the compressive strength with temperature is presented in Fig. 9.17 (for a silicate aggregate concrete), Fig. 9.18 (for a carbonate aggregate concrete), and Fig. 9.19 (for two lightweight aggregate concretes, one made with the addition of natural sand) [65]. ([σu]0 in the figures stands for the compressive strengths of concrete at room temperature.) In some experiments, the specimens were heated to the test temperature without load (see curves labeled “unstressed”). In others they were heated under a load amounting to 40 % of the ultimate strength (see curves labeled “stressed”). Again, in others they were heated to the target temperature without load, then cooled to room temperature and stored at 75 % relative humidity for six days, and finally tested at room temperature (see curves labeled “unstressed residual”).
1.0 Stressed 0.8
σu /(σu )0
Unstressed 0.6 Unstressed residual 0.4 Avg. initial σu = 26.9 MPa
0.2
0 0
200
400 Temperature (°C)
600
800
298
V.K.R. Kodur and T.Z. Harmathy
Fig. 9.18 The effect of temperature on the compressive strength of a normal-weight concrete with carbonate aggregate [65]
1.0 Stressed Unstressed
σu /(σu)0
0.8
0.6
Unstressed residual
0.4 Avg. initial σ = 26.9 MPa
0.2
0 0
200
400
600
800
Temperature (°C)
Fig 9.19 The effect of temperature on the compressive strength of two lightweight concretes (one with natural sand) [65]
1.0 Stressed (sanded)
σu /(σu)0
0.8 Unstressed residual (sanded)
0.6
Unstressed (unsanded)
0.4
0.2
Unstressed (sanded)
Avg. initial σu of "unsanded" concrete = 17.9 MPa Avg. initial σu of "sanded" concrete = 26.9 MPa
0 0
200
400
600
800
Temperature (°C)
Some information on the creep of concrete at elevated temperatures is available from the work ˆ chal [67], Gross [68], and of Cruz [66], MareA Schneider et al. [69] The creep curves shown in Fig. 9.20 are those recorded by Cruz for a normalweight concrete with carbonate aggregates. Because the aggregates amount to 60–75 % of the volume of concrete, the dilatometric curve usually resembles that of the principal aggregate. However, some lightweight aggregates, for example, pearlite and vermiculite, are unable to resist the almost continuous shrinkage of the cement paste on heating, and therefore their
dilatometric curves bear the characteristic features of the curve for the paste. The dilatometric curves of two normal-weight concretes (with silicate and carbonate aggregates) and two lightweight concretes (with expanded shale and pumice aggregates) are shown in Fig. 9.21 [20]. These curves were obtained in the course of a comprehensive study performed on 16 concretes. The results of dilatometric and thermogravimetric tests were combined to calculate the volumetric heat capacity (ρcp) versus temperature relation for these four concretes, as shown in
9
Properties of Building Materials
299
Fig. 9.22. The partial decomposition of the aggregate is responsible for a substantial drop (above 700 C) in the density of concretes made with carbonate aggregate. The aggregate type and moisture content have significant influence on the specific heat of concrete. The usual ranges of variation of the volumespecific heat (i.e., the product ρcp) for normal0.004 649°C
0.002
0
∈t, mm–1
0.002 482°C
0 0.001
316°C
0 0.001
149°C
0 0.001 24°C 0
0
1
2
3
4
5
Time, t
Fig. 9.20 Creep of a carbonate aggregate concrete at various temperature levels (applied stress: 12.4 MPa; compressive strength of the material at room temperature: 27.6 MPa) [66]
0.015 2 0.010
1
0
0.005
Δ /
Fig. 9.21 Dilatometric curves for two normalweight and two lightweight concretes [20]. (1) normalweight concrete with silicate aggregate, (2) normal-weight concrete with carbonate aggregate, (3) lightweight concrete with expanded shale aggregate, (4) lightweight concrete with pumice aggregate
weight and lightweight concretes are shown in Fig. 9.23. This information, derived by combining thermodynamic data with thermogravimetric observations [2, 6], has since been confirmed by differential scanning calorimetry [7]. Experimental data are also available on a few concretes and some of their constituents [2, 7]. The thermal conductivity (k) of concrete depends mainly on the nature of its aggregates. In general, concretes made with dense, crystalline aggregates show higher conductivities than those made with amorphous or porous aggregates. Among common aggregates, quartz has the highest conductivity; therefore, concretes made with siliceous aggregates are on the whole more conductive than those made with other silicate and carbonate aggregates. Derived from theoretical considerations [6], the solid curves in Fig. 9.24 describe the variation with temperature of the thermal conductivity of four concretes. In deriving these curves, two concretes (see curves 1 and 2) were visualized to represent limiting cases among normal-weight concretes, and the other two (see curves 3 and 4), limiting cases among lightweight concretes. The points in Fig. 9.24 stand for experimental data. They reveal that the upper limiting case is probably never reached with aggregates in common use and that the thermal conductivity of lightweight concretes may be somewhat higher than predicted on theoretical considerations.
0
–0.005
3
–0.010
4
–0.015 0
100 200 300 400 500 600 700 800 900 1000 1100 1200 Temperature (°C)
300 2100 2000 1900
ρcp (MJ·m–3·K–1)
Fig. 9.22 Volumetric heat capacity of two normalweight and two lightweight concretes [20]. (1) normalweight concrete with silicate aggregate, (2) normal-weight concrete with carbonate aggregate, (3) lightweight concrete with expanded shale aggregate, (4) lightweight concrete with pumice aggregate
V.K.R. Kodur and T.Z. Harmathy
1800 1700
1
1600 1500 2
1400 1300
3
4 1200 1100
100 200 300 400 500 600 700 800 900 1000 1100 1200
0
Temperature (°C)
7 6
–3
ρcp , MJ·m ·K
–1
Fig. 9.23 Usual ranges of variation for the volumespecific heat of normalweight and lightweight concretes [6]
5 4 Normal weight
3 2 1 0
Lightweight 0
200
400
600
800
Temperature (°C)
1
2.0
–1
k (W·m ·K )
2.5
–1
Fig. 9.24 Thermal conductivity of four “limiting” concretes and some experimental thermal conductivity data. 6,19 Symbols: ▼, ∇—various gravel concretes; ●— expanded slag concretes; ■, □—expanded shale concretes; ○—pumice concrete
1.5 2 1.0 3 0.5 4 0 0
200
400
600
Temperature (°C)
800
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Further experimental information on the thermal conductivity of some normal-weight and many lightweight concretes is available from the literature [6, 7, 20]. In reinforced concrete structures, the bond between rebars and concrete (at elevated temperatures) plays a major role in determining the fire endurance of structural members. Diederichs and Schneider investigated the variation of bond strength between deformed and plain rebars and concrete as a function of temperature [70]. They found that the bond strength reduction follows the same pattern as compressive strength for deformed and rusted plain bars. However, higher reduction in bond strength was observed for new plain bars. They also found that the bond strength at elevated temperature increases with decreasing coefficient of thermal expansion of concrete, which is significantly influenced by the type of aggregate. Diederichs and Schneider also concluded that the water-cement ratio and the bar diameter have a minor effect on the bond strength between steel and concrete [70]. Figure 9.25 illustrates the variation of bond strength as a function of temperature for reinforced and prestressed concrete.
Fiber-Reinforced Concrete Steel and polypropylene discontinuous fibers are the two most common fibers used in the concrete mix to improve structural properties of concrete. 1.0 Strength (proportion of ambient)
Fig. 9.25 Variation of bond strength as a function of temperature for reinforced and prestressed concrete [70]
Studies have shown that polypropylene fibers in a concrete mix are quite effective in minimizing spalling in concrete under fire conditions [71, 72]. The polypropylene fibers melt at a relatively low temperature of about 170 C and create channels for the steam pressure in concrete to escape. This prevents the small explosions that cause the spalling of the concrete. Based on these studies, the amount of polypropylene fibers needed to minimize spalling is about 0.1–0.25 % (by volume). The polypropylene fibers were found to be most effective for HSC made with normal-weight aggregate. The addition of fibers improves certain mechanical properties, such as tensile strength, ductility, and ultimate strain, at room temperature. However, there is very little information on the high-temperature properties of this type of concrete [73]. Steel fiber–reinforced concrete (SFRC) exhibits, at elevated temperatures, mechanical properties that are more beneficial to fire resistance than those of plain concrete. There is some information available on SFRC’s material properties at elevated temperatures. The effect of temperature on the compressive strength for two types of SFRC is shown in Fig. 9.26. The strength of both types of SFRC exceeds the initial strength of the concretes up to about 400 C. This is in contrast to the strength of plain concrete, which decreases slightly with temperatures up to 400 C. Above approximately
0.8 Reinforcing steel 0.6 Prestressing steel 0.4
0.2
0
0
200
400 Temperature (°C)
600
800
302 140 120 Compressive strength (% of initial strength)
Fig. 9.26 Effect of temperature on compressive strength of steel fiber–reinforced concrete
V.K.R. Kodur and T.Z. Harmathy
Fiber-reinforced concrete
100 80 60 40
Plain concrete
20 0
Fig. 9.27 Effect of temperature on tensile strength of steel fiber–reinforced concrete
0
200
400 Temperature (°C)
600
800
600
800
120
Tensile strength (% of initial strength)
100
Fiber-reinforced concrete
80 60 40
Plain concrete
20 0
0
400 C, the strength of SFRC decreases at an accelerated rate [74]. The effect of temperature on the tensile strength of steel fiber–reinforced carbonate concretes is compared to that of plain concrete in Fig. 9.27 [75]. The strength of SFRC decreases at a lower rate than that of plain concrete throughout the temperature range, with the strength being significantly higher than that of plain concrete up to about 350 C. The increased tensile strength delays the propagation of cracks in fiber-reinforced concrete structural members and is highly beneficial when the member is subjected to bending stresses.
200
400 Temperature (°C)
The type of aggregate has a significant influence on the tensile strength of steel fiber–reinforced concrete. The decrease in tensile strength for carbonate aggregate concrete is higher than that for siliceous aggregate concrete [75]. The thermal properties of SFRC, at elevated temperatures, are similar to those of plain concrete. Kodur and Lie [27, 73] have carried out detailed experimental studies and developed dilatometric and thermogravimetric curves for various types of SFRC. Based on these studies, they have also developed expressions for thermal and mechanical properties of steel fiber–reinforced concrete in the temperature range 0–1000 C [18, 76].
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High-Strength Concrete The strength of concrete has significant influence on the properties of HSC. The material properties of HSC vary differently with temperature than those of NSC. This variation is more pronounced for mechanical properties, which are affected by these factors: compressive strength, moisture content, density, heating rate, percentage of silica fume, and porosity [77]. The available information on the mechanical properties of HSC at elevated temperatures is presented in a review report by Phan [30]. The loss in compressive strength with temperature is higher for HSC than that for NSC up to about 450 C. Figure 9.28 shows the comparison of strengths for NSC and HSC types, together with CEB and European design curves for NSC. The difference between compressive strength versus temperature relationships of normalweight and lightweight aggregate concrete is not significant. However, HSC mixture with silica fume have higher compressive strength loss with increasing temperature than HSC mixture without silica fume. Based on a series of hightemperature material property tests, Kodur et al. have proposed a set of stress-strain relationships for HSC as a function of temperature [78, 79]. The variation, with temperature, of modulus of elasticity and tensile strength of HSC is similar to that of NSC. Fig. 9.28 Comparison of design compressive strength and results of unstressed tests of lightweight aggregate concrete [30]
Kodur and Sultan have presented detailed experimental data on the thermal properties of HSC (for both plain and steel fiber–reinforced concrete types) [80]. The type of aggregate has significant influence on the thermal properties of HSC at elevated temperatures. Figure 9.29 shows the thermal conductivity and specific heat of HSC, with siliceous and carbonate aggregates, as a function of temperature. Based on the test data, Kodur and Sultan have proposed relationships for thermal conductivity, specific heat, thermal expansion, and mass loss of HSC as a function of temperature [81]. The variation of thermal expansion with concrete temperature for siliceous and carbonate aggregate HSC is similar to that of NSC, with the aggregate having a strong influence. Overall, the thermal properties of HSC, at elevated temperatures, are similar to those of NSC [82]. HSC, due to low porosity, is more susceptible to spalling than NSC, and explosive spalling may occur when HSC is exposed to severe fire conditions. Hence, one of the major concerns for the use of HSC is regarding its behavior in fire, in particular, the occurrence of spalling at elevated temperatures. For predicting spalling performance, knowledge of the variation of porosity with temperature is essential. Figure 9.30 shows the variation of porosity with temperature for NSC and HSC. The data in this figure are taken from the measurements
1.2 1
NSC
Fc /Fc (20°C)
0.8 0.6 HSC
0.4
CEB design curve 0.2 Eurocode design curve 0
0
200
400
600
Temperature (°C)
800
1000
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V.K.R. Kodur and T.Z. Harmathy
a
b
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Thermal conductivity (W/m°C)
2.5
1.5 1.0
Siliceous aggregate HSC
0.5
Carbonate aggregate HSC
0
10 8
Siliceous aggregate HSC
6
Carbonate aggregate HSC
4 2 0
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400 Temperature (°C)
600
800
0
200
400
600
800
1000
Temperature (°C)
Fig. 9.29 Thermal conductivity and specific heat capacity of HSC as a function of temperature: [80] (a) thermal conductivity of high-strength concrete and (b) specific heat of high-strength concrete
Fig. 9.30 Porosity of HSC and NSC as a function of temperature [36]
10 NSC
Porosity (%)
8
HSC
6
4
2
0
0
100
200
300
400
500
600
Temperature (°C)
of porosity after exposure to different temperatures [36]. The spalling in HSC can be minimized by creating pores through which water vapor can be relieved before vapor pressure reaches critical values. This is usually done by adding polypropylene fibers to the HSC [71, 72, 83]. Also, Kodur et al. have reported that spalling in HSC columns can be minimized to a significant extent by providing bent ties as lateral confinement [77, 84]. Figure 9.31 illustrates conventional and improved tie configuration for minimizing spalling in HSC columns [84].
a
b
Conventional tie configuration
Modified tie configuration
Fig. 9.31 Tie configuration for achieving higher fire resistance in concrete structures [79]
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305
Brick Building brick belongs in the L/I group of materials. The density (ρ) of bricks ranges from 1660 to 2270 kgm–3, depending on the raw materials used in the manufacture, and on the molding and firing technique. The true density of the material (ρt) is somewhere between 2600 and 2800 kgm–3. The modulus of elasticity of brick (E) is usually between 10 103 and 20 103 MPa. Its compressive strength (σu) varies in a very wide range, from 9 to 110 MPa—50 MPa may be regarded as average [85]. This value is an order
Fig. 9.32 Dilatometric and thermogravimetric curves for a clay brick [7]
of magnitude greater than the stresses allowed in the design of grouted brickwork. Because brick is rarely considered for important load-bearing roles in buildings, there has been little interest in the mechanical properties of bricks at elevated temperatures. At room temperature, the coefficient of thermal expansion (α) for clay bricks is about 5.5 106 mm–1 K–1. The dilatometric and thermogravimetric curves for a clay brick of 2180 kgm–3 density are shown in Fig. 9.32 [7]. The variation with temperature of the specific heat and the thermal conductivity of this brick is shown in Figs 9.33 and 9.34, respectively [7].
0.015
Δ /
0
0.010
0.005
0
1.05 1.00
M/M 0
0.95 0.90 0.85 0.80 0.75 0.70
0
100 200 300 400 500 600 700 800 900 1000 Temperature (°C)
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Fig. 9.33 Apparent specific heat of a clay brick [7]
3500 3000
Cp (J·kg–1·K–1)
2500 2000 1500 1000 500 0
Fig. 9.34 Thermal conductivity of a clay brick. Symbols: ○—heating cycle, ●—after cooling [7]
0
100 200 300 400 500 600 700 800 900 1000 Temperature (°C)
1.75 1.50
k, W·m–1·K–1
1.25 1.00 0.75 0.50 0.25 0
0
Wood Wood is a Group L/I/F or I/F material. As structural members, wood is widely used in residential and low-rise constructions. Although about 180 wood species are commercially grown in the United States, only about 25 species have been assigned working stresses. The two groups most extensively used as structural lumber are the Douglas firs and the southern pines. The oven-dry density (ρ) of commercially important woods ranges from 300 kgm–3 (white cedar) to 700 kgm–3 (hickory, black
100 200 300 400 500 600 700 800 900 1000 Temperature (°C)
locust). The density of Douglas firs varies from 430 to 480 kgm–3 and that of southern pines from 510 to 580 kgm–3. The true density of the solid material that forms the walls of wood cells (αt) is about 1500 kgm–3 for all kinds of wood. The density of wood decreases with temperature; the density ratio (ratio of density at elevated temperature to that at room temperature) drops to about 0.9 at 200 C and then declines sharply to about 0.2 at about 350 C [40]. Wood is an orthotropic material, so the strength and stiffness in longitudinal and transverse directions are influenced by grain orientation. The mechanical properties of wood are
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307
Fig. 9.35 The effect of temperature on the modulus of elasticity and compressive strength of wood [87–89]
1.0
E/E0, or σu /(σu)0
0.8
E/E0
0.6
σu/(σu)0
0.4
0.2
0
0
50
100
150
200
250
300
Temperature (°C)
affected by temperature and are influenced by moisture content, rate of charring, and grain orientation. The modulus of elasticity (E) of air-dry, clear wood along the grain varies from 5.5 103 to 15.0 103 MPa, and its crushing strength (σu) varies from 13 to 70 MPa. These properties are related and roughly proportional to the density, regardless of the species [86]. Figure 9.35 shows the variation of the modulus of elasticity and compressive strength of oven-dry, clear wood with temperature [87–89]. (E0 and [σu]0 in the figure are modulus of elasticity and compressive strength at room temperature, respectively.) The modulus of elasticity decreases slowly with temperature up to about 200 C, when it reaches about 80 %, and then the decline is more rapid. The compressive strength also drops linearly to about 80 % at about 200 C, and then the drop is more rapid— to about 20 % around 280 C. The tensile strength exhibits behavior similar to that of compressive strength, but the decline in tensile strength with temperature is less rapid. The moisture content plays a significant role in determining the strength and stiffness, with increased moisture content leading to higher reduction. There is very little information on stress-strain relationships for wood. The formulas for reduced stiffness and design strength can be found in Eurocode 5 [90] (Part 1.2).
The coefficient of linear thermal expansion (β) ranges from 3.2 10–6 to 4.6 10–6 mm–1K–1 along the grain and from 21.6 10–6 to 39.4 10–6 mm–1K–1 across the grain [91]. Wood shrinks at temperatures above 100 C, because of the reduction in moisture content. Lie [29] reported that the amount of shrinkage can be estimated as 8 % in the radial direction, 12 % in the tangential direction, and an average of 0.1–0.2 % in the longitudinal direction. The dilatometric and thermogravimetric curves of a pine with a 400 kgm–3 oven-dry density are shown in Fig. 9.36 [7]. The thermal conductivity (k) across the grain of this pine was measured as 0.86–1.07 Wm–1K–1 between room temperature and 140 C [14]. The thermal conductivity increases initially up to a temperature range of 150–200 C, then decreases linearly up to 350 C, and finally increases again beyond 350 C. Figure 9.37 shows the apparent specific heat for the same pine, as a function of temperature [7]. The accuracy of the curve (developed by differential scanning calorimeter [DSC]) is somewhat questionable. However, it provides useful information on the nature of decomposition reactions that take place between 150 and 370 C. Charring is one of the main high-temperature properties associated with wood and should be considered in predicting performance under fire
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V.K.R. Kodur and T.Z. Harmathy
Fig. 9.36 Dilatometric and thermogravimetric curves for a pine of 400 kgm–3 density [7]
0.02 0.01
Δ /
0
0 –0.01 –0.02 –0.03 –0.04 –0.05
1.2 1.0
M/M 0
0.8 0.6 0.4 0.2 0
Fig. 9.37 Apparent specific heat for a pine of 400 C density [7]
0
100 200 300 400 500 600 700 800 900 1000 Temperature (°C)
0
100 200 300 400 500 600 700 800 900 1000
3500 3000
Cp (J·kg–1·K–1)
2500 2000 1500 1000 500 0
Temperature (°C)
9
Properties of Building Materials
conditions. The rate of charring is influenced by the radiant heat flux or, alternatively, the fire severity. Generally, a constant transverse-tograin char rate of 0.6 mm/min can be used for woods subjected to standard fire exposure [29]. The charring rate parallel to the grain of wood is approximately twice the rate when it is transverse to the grain. These charring rates should be used only when attempting to model the performance of wood sections in the fire resistance furnace. Charring is influenced by a number of parameters, the most important ones being density, moisture content, and contraction of wood. It is reasonable to modify the 0.6 mm/min to approximately 0.4 mm/min for moist dense wood or to 0.8 mm/min for dry and light wood. The fire retardants often used to reduce flame spread in wood may only slightly increase the time until ignition of wood. Specific charring rates for different types of wood can be found in “Structural Fire Protection” [29] and Be´nichou and Sultan [40]. Eurocode [90] gives an expression for charring depth in a wood member exposed to standard fire. The dependence of charring rate on the radiant heat flux is discussed in Wood Handbook [87]. In recent years different types of engineered wood is widely used in residential construction. These engineered wood products (ex: joists and studs) capitalize on the strength of wood and the efficiency of the sectional shapes (ex: I-shaped joists) to enhance load bearing capacity at ambient conditions, while at the same time reducing the mass and cost of the structural member. However, there is very limited data on high temperature thermo-mechanical properties of engineered lumber and fire resistance of engineered joists and studs. Limited research has clearly shown that fire resistance of engineered joists to be significantly lower than that of conventional wood joists [92]. This was mainly attributed to poor thermal, mechanical and charring properties of engineered lumber as compared to conventional wood products. Typically, room temperature thermal conductivity and modulus of elasticity of engineered lumber is higher than other types of wood due to the
309
presence of compressed plies [92]. Comparison of charring rates indicate that engineered lumber has higher rate of charring rate as compared to conventional wood [92].
Fiber-Reinforced Polymers In recent years, there has been a growing interest in the use of fiber-reinforced polymers (FRPs) in civil engineering applications due to the advantages, such as high strength and durability (resistance to corrosion), that FRP offers over traditional materials. FRP composites consist of two key elements, namely the fibers (glass, carbon, or aramid) and a thermosetting polymer matrix such as epoxy, vinyl ester, phenolic, or polyester resin. The commonly used types of FRP composite materials are glass fiber–reinforced plastic (GFRP), carbon fiber–reinforced plastic (CFRP), and aramid fiber–reinforced plastic (AFRP) composites. FRPs are similar to wood in that they will burn when exposed to fire and can be classified as an L/I/F type material. FRP is used as an internal reinforcement (reinforcing bars as an alternative to traditional steel reinforcement) and as external reinforcement in forms, such as wrapping and sheeting for the rehabilitation and strengthening of concrete members. One of the main impediments to using FRPs in buildings is the lack of knowledge about the fire resistance of FRP [93, 94]. There are some major differences associated with FRP as a material. The properties depend on the type and composition of FRP, and the availability of various types of FRP makes it difficult to establish the properties at elevated temperatures. The material properties are controlled by the fibers in the longitudinal direction and by the matrix in the transverse direction. In addition to thermal and mechanical properties, factors such as burning, charring, evolution of smoke, and toxicity in fire also play a significant role in determining the fire performance. A summary of typical mechanical properties for various types of FRPs, in comparison to other commonly used construction materials, at room temperature, is presented in Table 9.3.
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Table 9.3 Properties of various FRP composites and other materials
Material GFRP (glass/ epoxy) GFRP (glass/ epoxy) unidirectional CFRP (carbon/ epoxy) unidirectional CFRP (graphite/ epoxy) Boron/epoxy ARP (aramid/ epoxy) unidirectional Mild steel Concrete (normal strength) Wood (Douglas fir)
Modulus Modulus Tensile of elasticity of elasticity strength σt1 E1 (MPa) E2 (MPa) (MPa) 55,000 18,000 1050
Comp. strength σc1 (MPa) 1050
Shear modulus G (MPa) 9000
Shear strength S (MPa) 42
Poisson’s Tensile ratio strength ν 0.25
Comp. strength σc2 σ2 (MPa) (MPa) 28 140
42,000
12,000
700
—
5000
72
0.30
30
—
180,000
10,000
1500
—
7000
68
0.28
40
—
207,000
5200
1050
700
2600
70
0.25
40
120
207,000 76,000
21,000 8000
1400 1400
2800 —
7000 3000
126 34
0.30 0.34
84 12
280 —
200,000 31,000
— —
550 4
240 40
— —
380 7
— — 0.15–0.20 —
— —
9800
—
69
—
—
—
—
—
—
E1 ¼ modulus of elasticity in longitudinal direction E2 ¼ modulus of elasticity in transverse direction
There is very little information on the material properties of FRPs at elevated temperatures [93]. The impact of high temperatures on the behavior of FRP composites is severe degradation of their properties: reduction of strength and stiffness, and increase in deformability, thermal expansion, and creep. Above 100 C temperature, the degradation can be quite rapid as the glass transition temperature of the matrix is reached. The glass transition temperature, which is often considered the upper use temperature, varies with the type of resin used and was found to be as low as 100 C in some resins and as high as 220 C in others. From the limited studies, it appears that as much as 75 % of the GFRP strength and stiffness is lost by the time the temperature reaches 250 C [93, 95]. The stress-strain relationships, from the studies conducted by Gates [95], for a CFRP composite (IM7/5260) are shown in Fig. 9.38 for various temperatures. It can be seen that the tensile strength of IM7/5260 composite reduces to approximately 50 % at about 125 C and to
about 75 % at a temperature of 200 C. The strain level, for a given stress, is also higher with the increase in temperature. Recently, Wang and Kodur reported high temperature strength and stiffness properties of glass and carbon FRP rebars; full details of the tests are reported in Wang and Kodur [96]. The variation of strength with temperature (ratio of strength at elevated temperature to that at room temperature) for FRP along with that of other traditional construction materials is shown in Fig. 9.2. The curve showing the strength degradation of FRP is based on the limited information reported in the literature [93, 95]. The rate of strength loss is much greater for FRP than for concrete and steel, resulting in a 50 % strength loss by about 200 C. The bond between FRPs and concrete (or between FRP layers or lap splices in multiply layup applications) is essential to transfer loads. This load transfer occurs through the polymer resin matrix and thus relies heavily on the mechanical properties of the polymer.
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311
Fig. 9.38 Tensile stressstrain curves for CFRP at various temperatures [95] − (MPa) Effective stress σ
200 IM7/5260 IM7/8320
23°C
150 Tension
70°C
100 125°C 150°C 175°C
50
200°C
23°C–70°C 125°C–150°C 175°C
0
200°C
0
200
400
600
Effective plastic strain ε–p
Deterioration of the mechanical properties of the matrix material at temperatures above the specific polymer’s glass transition temperature, Tg, have the potential to cause loss of bond at only modestly increased temperatures, resulting in loss of interaction between FRP and concrete. The glass transition temperature of commonly used polymer matrix materials is typically in the range of 65–140 C. No specific research has yet been reported on the bond between concrete and externally bonded FRP strengthening systems at high temperature, although limited data on the high-temperature residual performance of the FRP concrete bond has recently been presented [97]. Research on the bond properties of FRP bars for concrete reinforcement applications (internal reinforcement) at elevated temperature has been reported in the literature [98–101]. This work has indicated that dramatic decreases in bond strength can be expected, to values of about 10 % of room temperature strength, at temperatures between 100 and 200 C (i.e., at temperatures close to or above Tg). The observed bond strength reductions have been attributed to changes in the properties of the polymer matrix at the surface of the FRP bars. It seems clear that temperature effects on the FRP–FRP and FRP–concrete bond are critical, both in FRP internal reinforcement and in externally bonded FRP applications, and a great deal of additional research is required in this area.
Thus, bond degradation at elevated temperature is a critical factor to be considered in the design of FRP-reinforced or -strengthened concrete members. This was observed in full-scale fire tests on FRP-strengthened reinforced concrete columns [102]. The critical temperature of FRP is much lower than that for steel and depends on the composition of fibers and matrix. Kodur and Baingo have assumed a critical temperature of 250 C in modeling the behavior of FRP-reinforced concrete slabs [93]. Recently, Wang and Kodur have developed critical temperature information for glass and carbon FRP reinforcing rebars [103, 104]. They carried out a series of tensile strength tests at high temperatures on two types of commercially available FRP rebars. This included both carbon FRP and glass FRP bars of different diameters. Conventional steel rebars were also tested for comparison. The data were used to determine the variation of average failure strength and elastic modulus for each type of reinforcement with increasing temperature. Full details of experimental studies, including specimen preparation, test setup, test procedure, and observations as well as test data, are described elsewhere [96, 104]. A summary of the results of these studies are shown in Fig. 9.39. For the GFRP and CFRP bars, observed failure strengths were used, whereas for the steel bars, the 0.2 % proof stress was used. The elastic modulus was taken as the
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V.K.R. Kodur and T.Z. Harmathy
Fig. 9.39 Effect of strength degradation as a function of temperature for FRP [96]
9.5 mm CFRP rebar 9.5 mm GFRP rebar
1.2
10 mm steel rebar 12.7 mm GFRP rebar
Normalized strength
1.0
15 mm steel rebar
0.8
0.6
0.4
0.2 250
0 0
100
200
325
300
550
400
500
600
700
800
Temperature (°C)
Table 9.4 Thermal properties of various FRPs and other materials at room temperature
Material Glass/epoxy (S-glass) Glass/epoxy (E-glass: 63 % fiber) Carbon/epoxy (high modulus) Carbon/epoxy (ultra-high modulus) Boron/epoxy Aramid/epoxy (Kevlar 49) Concrete Steel Epoxy
Coefficient of thermal expansion (unidirectional) (β: 10–6 m m–1 C) Longitudinal αL Transverse αΤ 6.3 19.8 7.13 — –0.9 27 –1.44 30.6 4.5 14.4 –3.6 54 6.16 10.8–18 — 54–90
slope of a straight line fitted to the initial linear portion of the recorded stress-strain relationship for each specimen. The critical temperature for the FRP reinforcement was derived based on a 50 % tensile strength reduction, as is the case for steel reinforcement. This resulted in critical temperatures of about 325 C and 250 C for GFRP and CFRP reinforcing bars, respectively. These critical temperatures are significantly less than 593 C, the critical temperature for steel reinforcement, thus highlighting the presumed susceptibility of FRP reinforcement to fire. Figure 9.39 also shows that the steel reinforcing bars in these tests lost about 50 % of their roomtemperature yield strength at about 550 C, a
Thermal conductivity k (W m–1 C–1) Longitudinal kL Transverse kT 3.46 0.35 — — 48.4–60.6 0.865 121.1–129.8 1.04 1.73 1.04 1.73 0.73 1.36–1.90 15.6–46.7 — 0.346
result that agrees well with published data available in the literature. The variation of elastic moduli of FRP with temperature is different in each direction. Typical values for various types of FRP are given in Table 9.3 [93]. The three values represent the longitudinal, transverse, and shear moduli, respectively, of different unidirectional FRPs. At high temperature, the elastic moduli of FRPs decreases at a faster rate than that for concrete or steel. Similar to mechanical properties, the thermal properties of FRP are also dependent on direction, fiber type, fiber orientation, fiber volume fraction, and laminate configuration. Table 9.4 shows thermal properties for various types of
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FRP at room temperature. In the longitudinal direction, the thermal expansion of FRPs is lower than that of steel. However, in the transverse direction, it is much higher than that of steel. Some of the information available in the literature can be found in a review report by Kodur and Baingo [93]. At room temperatures, FRPs in general have low thermal conductivity, which makes them useful as insulation materials. With the exception of carbon fibers, FRPs have a low thermal conductivity. Information on the thermal properties of FRP at elevated temperatures is very scarce, which
a
is likely due to the fact that such information is proprietary to the composite materials’ manufacturers. Also, there is not much information on evolution of smoke and toxins in FRP composites exposed to fire. Thermal expansion of FRP reinforcement varies in longitudinal and transverse directions, and the coefficient of thermal expansion highly depends on type of fiber, resin, and volume fraction of fiber. The longitudinal coefficient of thermal expansion is dominated by properties of the fiber, while the transverse coefficient is dominated by properties of the resin. Figure 9.40
25 GFRP100-T1
GFRP100-T2
CFRP200-T1
CFRP200-T2
Thermal strain (10−3)
20
15
10
5
0 0
50
100
150
200
250
300
350
250
300
350
−5 Temperature (°C)
b
1 0.5
Thermal strain (10−3)
0 −0.5
0
50
100
150
200
−1 −1.5 −2 −2.5 −3
GFRP100-L1
GFRP100-L2
CFRP200-L1
CFRP200-L2
−3.5 −4
Temperature (°C)
Fig. 9.40 Variation of thermal strain in GFRP and CFRP in (a) longitudinal and (b) transverse directions as a function of temperature
314
(a and b) shows longitudinal and transverse coefficients of thermal expansion for typical GFRP and CFRP bars. It can be noted that usually there is a change in expansion rate at around glass transition temperature (Tg), indicating FRP reinforcement experiences different coefficients of thermal expansion before and after phase change (Tg). In transverse direction, the dimension of GFRP and CFRP rebars increase with temperature, and GFRP undergoes higher thermal expansion than that of CFRP. However, in longitudinal direction, GFRP rebar slightly expands with temperature, but CFRP rebar contracts with increase in temperature. The coefficients of thermal expansion in transverse direction for GFRP and CFRP rebars can be taken to be 64.5 and 7.79 106/ C, respectively, while the corresponding coefficients of thermal expansion in longitudinal direction are 2.48 and 7.6 106/ C, respectively [105]
Gypsum Gypsum (calcium sulfate dihydrate: CaSO4 2H2O) is a Group I material. Gypsum board is produced by mixing water with plaster of paris (calcium sulfate hemihydrate: CaSO41/2H2O) or with Keene’s cement (calcium sulfate anhydrite: CaSO4). The interlocking crystals of CaSO4 2H2O are responsible for the hardening of the material. Gypsum products are used extensively in the building industry in the form of boards, including wallboard, formboard, and sheathing. The core of the boards is fabricated with plaster of paris, into which weight- and set-controlling additives are mixed. Furthermore, plaster of paris, with the addition of aggregates (such as sand, pearlite, vermiculite, or wood fiber) is used in wall plaster as base coat, and Keene’s cement (neat or mixed with lime putty) is used as finishing coat. Gypsum board, based on composition and performance, is classified into various types, such as regular gypsum board, type X gypsum board, and improved type X gypsum board. A gypsum board with naturally occurring fire resistance from the gypsum in the core is defined as
V.K.R. Kodur and T.Z. Harmathy
regular gypsum. When the core of the gypsum board is modified with special core additives or with enhanced additional properties, to improve the natural fire resistance from regular gypsum board, it is classified as type X or improved type X gypsum board. There might be significant variation in fire performance of the gypsum board based on the type and the formulation of the core, which varies from one manufacturer to another. Gypsum is an ideal fire protection material. The water inside the gypsum plays a major role in defining its thermal properties and response to fire. On heating, it will lose the two H2O molecules at temperatures between 125 and 200 C. The heat of complete dehydration is 0.61 106 J/kg gypsum. Due to the substantial absorption of energy in the dehydration process, a gypsum layer applied to the surface of a building element is capable of markedly delaying the penetration of heat into the underlying loadbearing construction. The thermal properties of the gypsum board vary depending on the composition of the core. The variation with temperature of the volume specific heat (ρcp) of pure gypsum has been illustrated in Harmathy [106], based on information reported in the literature [107, 108]. The thermal conductivity of gypsum products is difficult to assess, owing to large variations in their porosities and the nature of the aggregates. A typical value for plaster boards of about 700 kgm–3 density is 0.25 Wm–1K–1. Figures 9.41 and 9.42 illustrate the typical variation of the thermal conductivity and the specific heat, respectively, of the gypsum board core with temperature. The plots reflect the expressions proposed recently by Sultan [109], based on tests conducted on type X gypsum board specimens. The specific heat measurements were carried out at a heating rate of 2 C/min. The dehydration of gypsum resulted in the two peaks that appear in the specific heat curve at temperatures around 100 C and 650 C. The peak values are slightly variant to those reported earlier by Harmathy [16]; this may be due to the differences in gypsum composition. The coefficient of thermal expansion (β) of gypsum products may vary between
Properties of Building Materials
Fig. 9.41 Thermal conductivity of type X gypsum board core as a function of temperature [109]
315 0.6
Thermal conductivity [W/(m°C)]
9
0.5 0.4 0.3
0.1 0
Fig. 9.42 Specific heat of type X gypsum board core as a function of temperature [109]
Sultan [109]
0.2
100 200 300 400 500 600 700 800 900 1000 Temperature (°C)
0
Specific heat [kJ/(kg°C)]
20
15
10
5
0
Sultan (1996) Heating rate: 2°C/min
0
100 200 300 400 500 600 700 800 900 1000 Temperature (°C)
11.0 10–6 and 17 10–6 mm–1K–1 at room temperature, depending on the nature and amount of aggregates used. The dilatometric and thermogravimetric curves of a so-called fire-resistant gypsum board of 678 kgm–3 density are shown in Fig. 9.43. There is not much information about the mechanical properties of the gypsum board at elevated temperatures because these properties are difficult to obtain experimentally. The strength of gypsum board at an elevated temperature is very small and can be neglected. The Gypsum Association [110] lists typical mechanical properties, at room temperature, for some
North American gypsum board products. The attachment details (screw spacing, orientation of gypsum board joints, stud spacing, etc.) may have a noticeable effect on the fire performance of the gypsum board.
Insulation Insulation is a Group I material and is often used as a fire protection material both for heavy structural members such as columns and beams and for lightweight framing assemblies such as floors and walls. The insulation helps delay the
316
V.K.R. Kodur and T.Z. Harmathy
Fig. 9.43 Dilatometric and thermogravimetric curves for a gypsum board of 678 kgm–3 density [7]
0.02 0.01
Δ / 0
0 –0.01 –0.02 –0.03 –0.04 –0.05 1.05 1.00
M/M 0
0.95 0.90 0.85 0.80 0.75 0.70 0
100 200 300 400 500 600 700 800 900 1000 Temperature (°C)
temperature rise of structural members, thereby enhancing fire resistance. There are a number of insulation materials available in the market. Mineral wool and glass fiber are the two most widely used insulation materials in walls and floors. Other insulation materials used for fire protection include intumescent paints, spray mineral fibers, insulation boards, and compressed fiber board. The thermal properties of insulation play an important role in determining the fire resistance. However, there is not much information available on the thermal properties of various types of insulation. Figure 9.44 shows the variation of thermal conductivity with temperature for glass and rock fiber insulation types. The differences in thermal conductivity values at higher
temperatures are mainly due to variation in the chemical composition of fiber. Full-scale fire resistance tests on walls and floors have shown that the mineral fiber insulation performs better than glass fiber insulation. This is mainly because glass fiber melts in the temperature range of 700–800 C and cannot withstand direct fire exposure. The melting point for mineral fiber insulation is higher. The density of glass fiber is about 10 kg/m3 and is much lower than that of rock fiber, which is about 33 kg/m3. The mineral wool insulation, when installed tightly between the studs, can be beneficial for the fire resistance of non-load-bearing steel stud walls because it acts as an additional fire barrier
Properties of Building Materials
Fig. 9.44 Thermal conductivity of insulation as a function of temperature [40]
317 2 Rock fiber Thermal conductivity (W/m°C)
9
Glass fiber
1.6
Rock fiber 1.2
0.8
0.4
0
200
0
400
600
800
1000
Temperature (°C)
Table 9.5 Properties of some commonly used insulation materials [105]
Material Spray Sprayed mineral fibers Perlite or vermiculite plaster High-density perlite or vermiculite plaster Boards Fiber silicate or fiber calcium silicate Gypsum plaster Compressed fiber boards Mineral wool, fiber silicate
Density ρ (kg/m3)
Thermal conductivity k (W/mK)
Specific heat c (J/kgK)
Equilibrium moisture content %
300 350 550
0.12 0.12 0.12
1200 1200 1200
1 15 15
600 800
0.15 0.2
1200 1700
3 20
150
0.2
1200
2
after the fire-exposed gypsum board falls off [111]. On the other hand, cavity insulation slows down the flow of heat through the wall assembly and can cause an accelerated temperature rise in the fire-exposed gypsum board. Another common form of fire insulation applied on steel structural members to achieve required fire resistance is spray applied fire resistive materials (SFRM), which work by delaying temperature rise in steel. SFRM, available under different trade names, offers several advantages over other types of fire insulation such as cost effectiveness, ease of application, and light weight, and therefore is widely used as fire proofing material for steel structures. SFRM is mainly composed of base materials such as
gypsum, cementitious and mineral fiber and other additives such as vermiculite. The thermal properties of some of the commonly used insulation systems are given in Table 9.5 [112]. It should be noted that these values are average property values and can vary depending on the manufacturer and on the proportions of different constituent materials. Also the moisture content of the insulation material has an effect on the thermal properties. The above listed thermal properties for fire insulation are at room temperature and they can vary significantly with temperature and also with insulation composition, which can vary for different trade names (from different commercial manufactures) among the same type of insulation
318
V.K.R. Kodur and T.Z. Harmathy
(ex: SFRM). However, in practice fire resistance of insulated structural (steel) members is evaluated by considering only room temperature thermal properties of fire insulation [113]. This is mainly due to lack of reliable data on the effect of temperature on thermal properties of fire insulation. Further, there is no data on relative thermal performance of similar fire insulation products (ex: SFRM) produced from different commercial manufactures. Figure 9.45a shows variation of thermal conductivity with temperature for three types of commercially available SFRM (A, B, and C) generated in a recent research study [114]. The thermal conductivity of three SFRM types at room temperature is in the range of 0.07 and 0.2 W/m.K. This variation of thermal
a
0.3
Thermal Conductivity (W/mK)
SFRM A SFRM B
0.25
SFRM C 0.2
0.15
0.1
0.05
0
0
100
200
300
400
500
600
700
800
Temperature (°C) Temperature (°C)
b 5
0
200
0 −5
Strain(ΔL/L)x10-3
Fig. 9.45 Effect of temperature on (a) thermal conductivity and (b) thermal contraction, of different SFRMs
conductivity among three types of SFRM well pertains to the variation in their densities and also to composition of ingredients in each type. The trends in the figure further indicate that temperature has significant effect on thermal conductivity of SFRM. This variation in thermal conductivity at higher temperatures is primarily governed by changes in moisture content and density of different SFRM types. Insulation materials such as SFRM experience shrinkage at higher temperatures, as opposed to expansion phenomenon in materials such as steel, concrete and wood. The variation of thermal strain for three types of SFRM is plotted as a function of temperature in Fig. 9.45b [114]. This variation of thermal strain with temperature is also linked to changes in moisture content.
−10 −15 −20 −25
SFRM A
−30
SFRM B
−35
SFRM C
−40 −45 −50
400
600
800
1000
1200
9
Properties of Building Materials
319
Table 9.6 Density of SFRM at room temperature and after exposure to 700 C
Summary
main inputs needed in these models is the material properties at elevated temperatures. The thermal and mechanical properties of most materials change substantially within the temperature range associated with building fires. Even to date, there is lack of adequate knowledge of the behavior of many building materials at elevated temperatures. Although there is sufficient information available for some materials, such as normal-strength concrete and steel, there is a complete lack of information on certain properties for widely used materials, such as wood, insulation, and so on. Often, traditional materials are being modified (e.g., high-strength concrete) to enhance their properties at room temperatures without giving due consideration to elevated temperatures. In many cases, these modifications will cause the properties to deteriorate at elevated temperatures and introduce additional complexities, such as spalling in HSC. In the field of fire science, applied materials research faces numerous difficulties. At elevated temperatures, many building materials undergo physicochemical changes. Most of the properties are temperature dependent and sensitive to testing method parameters such as heating rate, strain rate, temperature gradient, and so on. One positive note is that in the last two decades, there has been significant progress in developing measurement techniques and commercial instruments for measuring the properties. This will likely lead to further research in establishing material properties. The review on material properties provided in this chapter is a broad outline of the available information. Additional details related to specific conditions on which these properties are developed can be found in cited references. Also, when using the material properties presented in this chapter, due consideration should be given to the material composition and other characteristics, such as fire and loading, because the properties at elevated temperatures depend on a number of factors.
The use of numerical methods for the calculation of the fire resistance of various structural members is gaining acceptance. One of the
Disclaimer Certain commercial products are identified in this paper in order to adequately specify the experimental procedure. In no case does such identification imply
Insulation type SFRM A SFRM B SFRM C
Density (Kg/m3) Room temp. (20 C) 700 C 298 241.3 423.2 349.8 451.8 381.2
Decrease in density (%) 19.0 17.3 15.6
However, the loss of moisture content only account for the shrinkage phenomenon that occurs in 100–400 C range. The intermediate expansion resulting in increase in thermal strains in 400–800 C range is dictated by the expansion of intumescent material, such as, vermulite, which is added to SFRM to counteract shrinkage and the percentage of Vermiculite in SFRM has major influence on the level of contraction. The change in density for three types of SFRM at ambient conditions and after exposure to 700 C is presented in Table 9.6 [114]. There is a decrease in density in all three types of SFRM at 700 C, which is predominantly due to the loss of moisture. This decrease in density in SFRM is comparable to that in gypsum, and attributed to dehydration reactions, which takes place with increase in temperature [115].
Other Miscellaneous Materials Further information is available from the literature on the dilatometric and thermogravimetric behavior, apparent specific heat, and thermal conductivity of a number of materials in Group I, including asbestos cement board, expanded plastic insulating boards, mineral fiber fireproofing, arborite, and glass-reinforced cement board [7]. The properties of plastics and their behavior in fire are discussed in other chapters of this handbook and in Harmathy [2].
320
V.K.R. Kodur and T.Z. Harmathy
recommendations or endorsement by the authors, nor does it imply that the product or material identified is the best available for the purpose.
Nomenclature a b c c E h Δh ΔHc k Lv ‘ Δ‘ m M n P qn R S t T v w Z
Material constant, dimensionless Constant, characteristic of pore geometry, dimensionless Specific heat (Jkg–1K–1) Specific heat for a mixture of reactants and solid products (Jkg–1K–1) Modulus of elasticity (Pa) Enthalpy (Jkg–1) Latent heat associated with a “reaction” (Jkg–1) Activation energy for creep (Jkmol–1) Thermal conductivity (Wm–1K–1) Heat of gasification of wood Dimension (m) ‘ – ‘0 Exponent, dimensionless Mass (kg) Material constant, dimensionless Porosity (m3m–3) Net heat flux to char front Gas constant (8315 Jkmol–1K–1) Specific surface area (m2.m–3) Time (h) Temperature (K or C) Volume fraction (m–3.m3) Mass fraction (kgkg–1) Zener-Hollomon parameter (h–1)
Greek Letters α β γ β0 δ ε ε εt0
Thermal diffusivity Coefficient of linear thermal expansion (mm–1) Expression defined by Equation 9.3, dimensionless Charring rate (mm/min) Characteristic pore size (m) Emissivity of pores, dimensionless Strain (deformation) (mm–1) Creep parameter (mm–1)
ε_ ts θ ξ π ρ σ σ
Rate of secondary creep (m.m–1h–1) Temperature-compensated time (h) Reaction progress variable, dimensionless Material property (any) Density (kgm–3) Stress; strength (Pa) Stefan-Boltzmann constant (5.67 10–8 Wm–2K–4)
Subscripts g a I p s t t T u y 0
Glass transient (temperature) Of air Of the ith constituent At constant pressure Of the solid matrix True Time-dependent (creep) At temperature T Ultimate Yield Original value, at reference temperature
References 1. T.Z. Harmathy, Technical Paper No. 242, National Research Council of Canada, Ottawa (1967). 2. T.Z. Harmathy, Fire Safety Design and Concrete, Longman Scientific and Technical, Harlow, UK (1993). 3. D.A.G. Bruggeman, Physik. Zeitschr., 37, p. 906 (1936). 4. R.L. Hamilton and O.K. Crosser, Industrial & Engineering Chemistry Fundamentals, 7, p. 187 (1962). 5. J.C. Maxwell, A Treatise on Electricity and Magnetism, 3rd ed., 1, Clarendon Press, Oxford, UK (1904). 6. T.Z. Harmathy, Journal of Materials, 5, p. 47 (1970). 7. T.Z. Harmathy, DBR Paper No. 1080, NRCC 20956, National Research Council of Canada, Ottawa (1983). 8. V.K.R. Kodur and M.M.S. Dwaikat, “Effect of high temperature creep on fire response of restrained steel beams”, J. of Materials and Structures, 43, 10, pp. 1327–1341 (2010) 9. J.E. Dorn, Journal of the Mechanics and Physics of Solids, 3, p. 85 (1954). 10. T.Z. Harmathy, in ASTM STP422, American Society for Testing and Materials, Philadelphia (1967). 11. T.Z. Harmathy, “Trans. Am. Soc. Mech. Eng.,” Journal of Basic Engineering, 89, p. 496 (1967).
9
Properties of Building Materials
12. C. Zener and J.H. Hollomon, Journal of Applied Physics, 15, p. 22 (1944). 13. F.H. Wittmann (ed.), Fundamental Research on Creep and Shrinkage of Concrete, Martinus Nijhoff, The Hague, Netherlands (1982). 14. Y. Anderberg and S. Thelandersson, Bulletin 54, Lund Institute of Technology, Lund, Sweden (1976). 15. U. Schneider, Fire and Materials, 1, p. 103 (1976). 16. T.Z. Harmathy, Journal of the American Concrete Institute, 65, 959 (1968). 17. 951 Thermogravimetric Analyzer (TGA), DuPont Instruments, Wilmington, DE (1977). 18. T.T. Lie and V.K.R. Kodur, “Thermal and Mechanical Properties of Steel Fibre-Reinforced Concrete at Elevated Temperatures,” Canadian Journal of Civil Engineering, 23, p. 4 (1996). 19. ASTM Test Method C135 86, 2007 Annual Book of ASTM Standards, 15.01, American Society for Testing and Materials, Philadelphia (2007). 20. T.Z. Harmathy and L.W. Allen, Journal of the American Concrete Institute, 70, p. 132 (1973). 21. 910 Differential Scanning Calorimeter (DSC), DuPont Instruments, Wilmington, DE (1977). 22. J.H. Perry (ed.), Chemical Engineers’ Handbook, 3rd ed., McGraw-Hill, New York (1950). 23. W. Eitel, Thermochemical Methods in Silicate Investigation, Rutgers University, New Brunswick, Canada (1952). 24. T.Z. Harmathy, Industrial & Engineering Chemistry Fundamentals, 8, p. 92 (1969). 25. D.A. DeVries, in Problems Relating to Thermal Conductivity, Bulletin de l’Institut International du Froid, Annexe 1952–1, Louvain, Belgique, p. 115 (1952). 26. W.D. Kingery, Introduction to Ceramics, John Wiley and Sons, New York (1960). 27. T.T. Lie and V.K.R. Kodur, “Thermal Properties of Fibre-Reinforced Concrete at Elevated Temperatures,” IR 683, IRC, National Research Council of Canada, Ottawa (1995). 28. Thermal Conductivity Meter (TC-31), Instruction Manual, Kyoto Electronics Manufacturing Co. Ltd., Tokyo, Japan (1993). 29. ASCE, “Structural Fire Protection: Manual of Practice,” No. 78, American Society of Civil Engineers, New York (1993). 30. L.T. Phan, “Fire Performance of High-Strength Concrete: A Report of the State-of-the-Art,” National Institute of Standards and Technology, Gaithersburg, MD (1996). 31. U. Danielsen, “Marine Concrete Structures Exposed to Hydrocarbon Fires,” Report, SINTEF—The Norwegian Fire Research Institute, Trondheim, Norway (1997). 32. V.K.R. Kodur and M.A. Sultan, “Structural Behaviour of High Strength Concrete Columns Exposed to Fire,” Proceedings, International Symposium on High Performance and Reactive Powder Concrete, Concrete Canada, Sherbrooke, Canada (1998).
321 33. U. Diederichs, U.M. Jumppanen, and U. Schneider, “High Temperature Properties and Spalling Behaviour of High Strength Concrete,” in Proceedings of Fourth Weimar Workshop on High Performance Concrete, HAB, Weimar, Germany (1995). 34. Y. Anderberg, “Spalling Phenomenon of HPC and OC,” in International Workshop on Fire Performance of High Strength Concrete, NIST SP 919, NIST, Gaithersburg, MD (1997). 35. Z.P. Bazant, “Analysis of Pore Pressure, Thermal Stress and Fracture in Rapidly Heated Concrete,” in International Workshop on Fire Performance of High Strength Concrete, NIST SP 919, NIST, Gaithersburg, MD (1997). 36. A.N. Noumowe, P. Clastres, G. Debicki, and J.-L. Costaz, “Thermal Stresses and Water Vapor Pressure of High Performance Concrete at High Temperature,” Proceedings, Fourth International Symposium on Utilization of High-Strength/High-Performance Concrete, Paris, France (1996). 37. J.A. Purkiss, Fire Safety Engineering Design of Structures, Butterworth Heinemann, Bodmin, Cornwall, UK (1996). 38. E.L. Schaffer, “Charring Rate of Selected Woods— Transverse to Grain,” FPL 69, U.S. Department of Agriculture, Forest Service, Forest Products Laboratory, Madison, WI (1967). 39. B.F.W. Rogowski, “Charring of Timber in Fire Tests,” in Symposium No. 3 Fire and Structural Use of Timber in Buildings, HMSO, London (1969). 40. N. Be´nichou and M.A. Sultan, “Fire Resistance of Lightweight Wood Frame Assemblies: State-of-theArt Report,” IR 776, IRC, National Research Council of Canada, Ottawa (1999). 41. S. Hadvig, Charring of Wood in Building Fires— Practice, Theory, Instrumentation, Measurements, Laboratory of Heating and Air-Conditioning, Technical University of Denmark, Lyngby, Denmark (1981). 42. E. Mikkola, “Charring of Wood,” Report 689, Fire Technology Laboratory, Technical Research Centre of Finland, Espoo (1990). 43. Guide for Determining the Fire Endurance of Concrete Elements, ACI-216–89, American Concrete Institute, Detroit, MI (1989). 44. I.D. Bennetts, Report No. MRL/PS23/81/001, BHP Melbourne Research Laboratories, Clayton, Australia (1981). 45. U. Schneider (ed.), Properties of Materials at High Temperatures—Concrete, Kassel University, Kassel, Germany (1985). 46. Y. Anderberg (ed.), Properties of Materials at High Temperatures—Steel, Lund University, Lund, Sweden (1983). 47. F. Birch and H. Clark, American Journal of Science, 238, p. 542 (1940). 48. T.Z. Harmathy and W.W. Stanzak, in ASTM STP464, American Society for Testing and Materials, Philadelphia (1970).
322 49. Y. Anderberg, “Mechanical Properties of Reinforcing Steel at Elevated Temperatures,” Tekniska Meddelande, 36, Sweden (1978). 50. “European Recommendations for the Fire Safety of Steel Structures,” European Convention for Construction Steelwork, Tech. Comm. 3, Elsevier, New York (1983). 51. Eurocode 3, Design of steel structures, Part 1-2: General rules-structural fire design, Document CEN, European Committee for Standardization, UK (2005). 52. T. Twilt, “Stress-Strain Relationships of Reinforcing Structural Steel at Elevated Temperatures, Analysis of Various Options and European Proposal,” TNORep. BI-91-015, TNO Build. and Constr. Res., Delft, Netherlands (1991). 53. K.W. Poh, “General Stress-Strain Equation,” ASCE Journal of Materials in Civil Engineering, Dec. (1997). 54. K.W. Poh, “Stress-Strain-Temperature Relationship for Structural Steel,” ASCE Journal of Materials in Civil Engineering, Oct. (2001). 55. J.T. Gerlich, P.C.R. Collier, and A.H. Buchanan, “Design of Light Steel-Framed Walls for Fire Resistance,” Fire and Materials, 20, 2 (1996). 56. G.Q. Li, S.C. Jiang, and Y.Z. Yin, “Experimental studies on the properties of constructional steel at elevated temperatures.” J. Struct. Eng., 129, 12, pp. 1717–1721 (2003). 57. BS 5950, “Structural Use of Steelwork in Building,” Part 8, in Code of Practice for Fire Resistant Design, British Standards Institution, London (2003). 58. W. Wang, L. Bing and V.K.R. Kodur, “Effect of temperature on strength and elastic modulus of high strength steel”, in Press: ASCE Journal of Materials in Civil Engineering, pp. 1–24 (2012). 59. V.K.R. Kodur and W. Khaliq, “Effect of temperature on thermal and mechanical properties of steel bolts”, ASCE Journal of Materials in Civil Engineering, 24, 6, pp. 765–774 (2012). 60. J.T. Gerlich, “Design of Loadbearing Light Steel Frame Walls for Fire Resistance,” Fire Engineering Research Report 95/3, University of Canterbury, New Zealand (1995). 61. P. Makelainen and K. Miller, Mechanical Properties of Cold-Formed Galvanized Sheet Steel Z32 at Elevated Temperatures, Helsinki University of Technology, Finland (1983). 62. F. Alfawakhiri, M.A. Sultan, and D.H. MacKinnon, “Fire Resistance of Loadbearing Steel-Stud Walls Protected with Gypsum Board: A Review,” Fire Technology, 35, 4 (1999). 63. T.Z. Harmathy and J.E. Berndt, Journal of the American Concrete Institute, 63, p. 93 (1966). 64. C.R. Cruz, Journal, PCA Research and Development Laboratories, 8, p. 37 (1966). 65. M.S. Abrams, in ACI SP 25, American Concrete Institute, Detroit, MI (1971).
V.K.R. Kodur and T.Z. Harmathy 66. C.R. Cruz, Journal, PCA Research and Development Laboratories, 10, p. 36 (1968). ˆ chal, in ACI SP 34, American Concrete 67. J.C. MareA Institute, Detroit, MI (1972). 68. H. Gross, Nuclear Engineering and Design, 32, p. 129 (1975). 69. U. Schneider, U. Diedrichs, W. Rosenberger, and R. Weiss, Sonderforschungsbereich 148, Arbeitsbericht 1978–1980, Teil II, B 3, Technical University of Braunschweig, Germany (1980). 70. U. Diederichs and U. Schneider, “Bond Strength at High Temperatures,” Magazine of Concrete Research, 33, 115, pp. 75–84 (1981). 71. V.K.R. Kodur, “Fibre-Reinforced Concrete for Enhancing the Structural Fire Resistance of Columns,” ACI-SP (2000). 72. A. Bilodeau, V.M. Malhotra, and G.C. Hoff, “Hydrocarbon Fire Resistance of High Strength Normal Weight and Light Weight Concrete Incorporating Polypropylene Fibres,” in Proceedings, International Symposium on High Performance and Reactive Powder Concrete, Sherbrooke, Canada (1998). 73. V.K.R. Kodur and T.T. Lie, “Fire Resistance of Fibre-Reinforced Concrete,” in Fibre Reinforced Concrete: Present and the Future, Canadian Society of Civil Engineers, Montreal (1997). 74. U.-M. Jumppanen, U. Diederichs, and K. Heinrichsmeyer, “Materials Properties of F-Concrete at High Temperatures,” VTT Research Report No. 452, Technical Research Centre of Finland, Espoo (1986). 75. J.A. Purkiss, “Steel Fibre-Reinforced Concrete at Elevated Temperatures,” International Journal of Cement Composites and Light Weight Concrete, 6, 3 (1984). 76. T.T. Lie and V.K.R. Kodur, “Effect of Temperature on Thermal and Mechanical Properties of Steel Fibre-Reinforced Concrete,” IR 695, IRC, National Research Council of Canada, Ottawa (1995). 77. V.K.R. Kodur and R. McGrath, “Effect of Silica Fume and Confinement on Fire Performance of High Strength Concrete Columns,” Canadian Journal of Civil Engineering, p. 24 (2006). 78. F.P. Cheng, V.K.R. Kodur, and T.C. Wang, “StressStrain Curves for High Strength Concrete at Elevated Temperatures,” ASCE Journal of Materials Engineering, 16, 1, pp. 84–90 (2004). 79. V.K.R. Kodur, T.C. Wang, and F.P. Cheng, “Predicting the Fire Resistance Behaviour of High Strength Concrete Columns,” Cements and Concrete Composites Journal, 26, 2, pp. 141–153 (2003). 80. V.K.R. Kodur and M.A. Sultan, “Thermal Properties of High Strength Concrete at Elevated Temperatures,” CANMET-ACI-JCI International Conference, ACI SP-170, Tokushima, Japan, American Concrete Institute, Detroit, MI (1998). 81. V.K.R. Kodur and M.A. Sultan, “Effect of Temperature on Thermal Properties of High Strength
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Properties of Building Materials
Concrete,” ASCE Journal of Materials in Civil Engineering, 15, 8, pp. 101–108 (2003). 82. V.K.R. Kodur and W. Khaliq, “Effect of temperature on thermal properties of different types of high strength concrete”, ASCE Journal of Materials in Civil Engineering, 23, 6, pp. 793–801 (2011). 83. V.K.R. Kodur, “Spalling in High Strength Concrete Exposed to Fire—Concerns, Causes, Critical Parameters and Cures,” in Proceedings: ASCE Structures Congress, Philadelphia (2000). 84. V.K.R. Kodur, “Guidelines for Fire Resistance Design of High Strength Concrete Columns,” Journal of Fire Protection Engineering, 15, 2, pp. 93–106 (2005). 85. J.W. McBurney and C.E. Lovewell, ASTM— Proceedings of the Thirty-Sixth Annual Meeting, Vol. 33 (II), American Society for Testing and Materials, Detroit, MI, p. 636 (1933). 86. Wood Handbook: Wood as an Engineering Material, Agriculture Handbook No. 72, Forest Products Laboratory, U.S. Government Printing Office, Washington, DC (1974). 87. C.C. Gerhards, Wood & Fiber, 14, p. 4 (1981). 88. E.L. Schaffer, Wood & Fiber, 9, p. 145 (1977). 89. E.L. Schaffer, Research Paper FPL 450, U.S. Department of Agriculture, Forest Products Lab., Madison, WI (1984). 90. “Structural Fire Design,” Part 1.2, in Eurocode 5, CEN, Brussels, Belgium (1995). 91. F.F. Wangaard, Section 29, in Engineering Materials Handbook (C.L. Mantell, ed.), McGrawHill, New York (1958). 92. V.K.R. Kodur, J. Fike, R. Fike, and M. Tabaddoor, “Factors governing fire resistance of engineered wood I-joists”, Proceedings of the Seventh International Conference on Structures in Fire, Zurich, Switzerland, pp. 417–426 (2012). 93. V.K.R. Kodur and D. Baingo, “Fire Resistance of FRP Reinforced Concrete Slabs,” IR 758, IRC, National Research Council of Canada, Ottawa (1998). 94. V.K.R. Kodur, “Fire Resistance Requirements for FRP Structural Members,” Proceedings—Vol I, 1999 CSCE Annual Conference, Canadian Society of Civil Engineers, Regina, Saskatchewan (1999). 95. T.S. Gates, “Effects of Elevated Temperature on the Viscoelastic Modeling of Graphite/Polymeric Composites,” NASA Technical Memorandum 104160, NASA, Langley Research Center, Hampton, VA (1991). 96. Y.C. Wang and V.K.R. Kodur, “Variation of Strength and Stiffness of Fibre Reinforced Polymer Reinforcing Bars with Temperature,” Cement and Concrete Composites, 27, pp. 864–874 (2005). 97. SK. Foster, “High Temperature Residual Performance of Externally-Bonded FRP Systems for
323 Concrete,” MSc Thesis, Kingston, Canada, Department of Civil Engineering, Queen’s University (2006). 98. A. Katz and N. Berman, “Modeling the Effect of High Temperature on the Bond of FRP Reinforcing Bars to Concrete,” Cement and Concrete Composites Journal, 22, pp. 433–443 (2000). 99. A. Katz, N. Berman, and L.C. Bank, “Effect of High Temperature on the Bond Strength of FRP Rebars,” Journal of Composites for Construction, 3, 2, pp. 73–81 (1999). 100. A. Sumida, T. Fujisaki, K. Watanabe, and T. Kato, “Heat Resistance of Continuous Fiber Reinforced Plastic Rods,” Proceedings, Fifth Annual Symposium on Fibre-Reinforced-Plastic Reinforcement for Concrete Structures, Thomas Telford, London, pp. 557–565 (2001). 101. N. Galati, B. Vollintine, A. Nanni, L.R. Dharani, and M.A. Aiello, “Thermal Effects on Bond Between FRP Rebars and Concrete,” Proceedings, Advanced Polymer Composites for Structural Applications in Construction, Woodhead Publishing Ltd., Cambridge, UK, pp. 501–508 (2004). 102. V.R. Kodur, L.A. Bisby, and M.F. Green, “Experimental Evaluation of the Fire Behavior of FibreReinforced-Polymer-Strengthened Reinforced Concrete Columns,” Fire Safety Journal, 41, 7, pp. 547–557 (2005). 103. V.R. Kodur and L.A. Bisby, “Evaluation of Fire Endurance of Concrete Slabs Reinforced with FRP Bars,” ASCE Journal of Structural Engineering, 131, 1, pp. 34–43 (2005). 104. Y.C. Wang, P.M.H. Wong, and V.K.R. Kodur, “An Experimental Study of Mechanical Properties of FRP and Steel Reinforcing Bars at Elevated Temperatures,” Composite Structures, 80, 1, pp. 131–140 (2007). 105. B. Yu, and V.K.R. Kodur, “Effect of Temperature on Strength and Stiffness Properties of Near-Surface Mounted FRP Reinforcement,” Journal of Composites, Part B: Engineering, 58, pp. 510–517 (2014). 106. T.Z. Harmathy, in ASTM STP301, American Society for Testing and Materials, Philadelphia (1961). 107. R.R. West and W.J. Sutton, Journal of the American Ceramic Society, 37, p. 221 (1954). 108. P. Ljunggren, Journal of the American Ceramic Society, 43, p. 227 (1960). 109. M.A. Sultan, “A Model for Predicting Heat Transfer Through Noninsulated Unloaded Steel-Stud Gypsum Board Wall Assemblies Exposed to Fire,” Fire Technology, 32, 3 (1996). 110. “Gypsum Board: Typical Mechanical and Physical Properties,” GA-235–98, Gypsum Association, Washington, DC (1998).
324 111. M.A. Sultan, “Effect of Insulation in the Wall Cavity on the Fire Resistance Rating of Full-Scale Asymmetrical (1 2) Gypsum Board Protected Wall Assemblies,” in Proceedings of the International Conference on Fire Research and Engineering, Orlando, FL, SFPE, Boston (1995). 112. A.H. Buchanan, Structural Design for Fire Safety, John Wiley & Sons Ltd., Chichester, UK (2002). 113. V.K.R. Kodur, M. Dwaikat and R. Fike, “High-temperature properties of steel for fire resistance modeling of structures,” Journal of Materials in Civil Engineering, 22, 5, pp. 423–434 (2010). 114. V.K.R. Kodur and A. Shakya, “Effect of temperature on thermal properties of fire insulation”, Fire Safety Journal, 61, pp. 314–323 (2013). 115. S. Park, S.L. Manzello, D.P. Bentz, and T. Mizukami, “Determining thermal properties of gypsum board at elevated temperatures”, Fire and Materials (2009).
V.K.R. Kodur and T.Z. Harmathy V.K.R. Kodur is a Professor in the department of Civil and Environmental Engineering and also serves as Director of the Center on Structural Fire Safety and Diagnostics at the Michigan State University (MSU). Dr. Kodur’s research has focused on the evaluation of fire resistance of structural systems through large scale fire experiments and numerical modelling; characterization of materials under high temperature; and non-linear design and analysis of structural systems. He is a Fellow of the Canadian Academy of Engineering, a Foreign Fellow of Indian National Academy of Engineering and Fellow of ASCE, ACI and SEI. He is an Associate Editor of Journal of Structural Engineering, Chairman of ACI Fire Protection Committee, and Chairman of ASCE-29 (Fire) Standards Committee. T.Z. Harmathy was head of the Fire Research Section, Institute of Research in Construction, National Research Council of Canada, until his retirement in 1988. His research centered on materials science and the spread potential of compartment fires.
Chemical Kinetics and Fire
10
Gregory T. Linteris and John F. Griffiths
Introduction The purpose of this chapter is to set out the principles of chemical kinetics as they apply to combustion in flames and fires. Chemical equilibrium, which was discussed in a previous chapter, deals with the final preferred state of a given set of reactants after an infinite time has passed. In contrast, chemical kinetics deals with the rate at which the system proceeds to the equilibrium state, i.e., the specific participating chemical reactions and their rates. Chemical equilibrium and chemical kinetics are related in that the thermodynamic, equilibrium state provides the driving force for chemical reaction. The material in this chapter is covered briefly; more detailed descriptions can be found in chemistry [1] and combustion [2–4] text books, upon which much of the material is based. The foundations of chemical kinetics have validity in gas, liquid or solid phases, but for fires, the gas phase has the greatest relevance because the main heat release normally occurs during flaming combustion. The role of solidand liquid-phase chemical kinetics in fires is discussed in Chap. 7. Similarly, smoldering combustion is a surface combustion process and the chemical kinetic description is closely related to G.T. Linteris (*) National Institute of Standards and Technology, 100 Bureau Dr. Stop 8665; Gaithersburg, MD, 20899 J.F. Griffiths University of Leeds, School of Chemistry, Leeds, LS2 9JT UK
that of pyrolyzing materials. The specialized fields of propellants, explosives, and material synthesis also require solid-phase chemical kinetic descriptions, but these are beyond the scope of the present chapter. Nonetheless, many of the fundamental principles of chemical kinetics discussed here are relevant regardless of the phase of the reacting system. Gas-phase chemical kinetics is of interest in fires for many reasons. The heat release in a fire typically occurs in the gas phase, and is responsible for the gas-phase temperature field, and hence the heat flux to the burning materials (a feedback loop which controls the fuel supply rate in the fire, and hence the geometric growth in fire size with time). Some fundamental fire phenomena, such as ignition and extinction, are clearly controlled by the gas-phase chemical kinetics. Fire suppression is controlled by the rates of chemical reaction, both for the relatively inert agents (e.g., CO2, water) which reduce the temperature (and hence overall reaction rate) to the point of extinction, and for chemically acting agents (e.g., CF3Br and hydrofluorocarbons) which interfere with the normal chemistry of the fuels with air. Similarly, the action of the most commonly used fire retardants in polymers is controlled by their gas-phase chemical behavior. In general, chemical reaction rates must be fast enough to match the local residence time for transport (either convective or diffusive); if not, the flame will extinguish. The formation of soot, the major radiating species from fire plumes, is controlled by gas-phase chemical kinetics, as is the formation
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of CO, which is the major toxic compound responsible for fire deaths. In fires, the formation of other toxic compounds, for example of HCN, as well as environmental pollutants (polycyclic aromatic hydrocarbons, dioxins, etc.) is controlled by the chemical kinetics of reactions occurring in the gas-phase. Clearly, understanding chemical kinetics is central to controlling unwanted fires and their deleterious effects. It is of great value if the Fire Scientist can answer the question: “Is the process at hand controlled by the rate of chemical reactions or by some other physical process?” The goal of the present chapter is to provide some fundament materials for approaching such a question. The reaction of a fuel (for example methane) with air to products can be represented by an expression such as: CH4
•CH3
•O
•CH3
CH2O
•H
CH3CO
•M
•O,OH
CH3,CH2O,CHO
•H
CHO
C2H3
•M,O2,H
•H
CO
•M,H,O2
C2H2 •O
•O,O2
•H,O,OH
•M,O2
C2H4
•H,O,OH
CH
CH3CHO
C2H5
•H
CH2
ð10:2Þ
but again, the details are missing. Figure 10.1 shows reaction pathways for a premixed methane-air flame (initial pressure P0 and temperature T0 of 1 bar and 298 K). The
•O
•H
CH3
CO
CH4 ! CH3 ! CH2 O ! CHO ! CO ! CO2 ;
•H,O,OH
•CH3
ð10:1Þ
which is an example of a global (or overall) reaction. While reaction (10.1) shows the reactants and products, it does not represent the detailed chemical interactions which actually occur. Rather, the conversion of CH4 to CO2 and H2O is a multi-step process involving many species and many reactions. A more complete representation might include some intermediate species along the path:
C2H6 •H,O,OH
•H
CH4 þ 2O2 ! CO2 þ H2 O
•O
•OH
•H
CH2CO
CH3
•OH
CH2O,CHO
•O,O2
CO,CO2
Fig. 10.1 Reaction pathway analysis for premixed stoichiometric methane-air flame (From [5])
CH3
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the decomposition of methane proceeds mostly through the sequence shown in Equation 10.2, with the molecule oxidized to smaller and smaller fragments. In contrast, Fig. 10.2 shows that under rich conditions, reaction of CH3 proceeds largely through its reaction with other CH3 molecules, in pyrolysis reactions which tend to form larger molecules, and finally, acetylene C2H2, which is a precursor for soot. Pictures such as those in Figs. 10.1 and 10.2 are very useful tools for understanding the role of chemistry in the physical behavior of combustion systems. Indeed, the widespread availability of numerical codes for performing the simulations, chemical databases for the mechanisms, and fast computers have made such simulations integral design tools in many chemical and engineering fields. These include the design of propulsion devices (gas turbines, diesel and spark ignition
arrows connect the initial, intermediate, and product species for the major reaction steps involved in the consumption of methane. For each species in the figure, the major reactants and products are at the ends of the arrows, while participating reaction partners are listed next to the arrow. The thickness of the arrows indicates the fraction of the total reaction flux which proceeds through that particular reaction path (normalized, in this case, by the total reaction rate of CH4.) The purpose of such a figure is to provide not only detailed knowledge of the important steps in the consumption of a reactant, but also to provide a heuristic understanding of the general features of the chemical system. For example, Fig. 10.2 shows the chemical reaction pathways for methane in the same configuration (a premixed laminar flame), but at a different fuel-air ratio, in this case, fuel rich. In Fig. 10.1,
CH6
C2H6 O •H,CH
•H
•H,O,OH
•CH3 •CH3
•O
CH3
C2H5
CH3CHO
•H,O,OH
CH3CO
•H •O
•M,O2
•CH3 •H
CH2O
C2H6
CHO
CO
CH3,CHO
•H2OH
•H,O,OH
•M,O2,K
•O,OH
C2H3 •H
•M,H,O2
•O
•OH
C2H2
•H
CH2CO
CH3
•OH
CH2O,CHO
Fig. 10.2 Reaction pathway analysis for premixed fuel-rich methane-air flame (From [5])
•M
CH3
328
engines, etc.) and new power plants and incinerators, particularly in regard to understanding the efficiency and pollutant formation. In fire safety, detailed chemical kinetic descriptions are primarily used in research. As computer models, kinetic mechanisms, and computer speed all improve, however, the contributions of chemical kinetics to the understanding of fire safety will increase, as it has in other fields. A reaction mechanism (such as that used to produce the reaction pathway analyses in Figs. 10.1 and 10.2) starts with a list of species believed to be participating in chemical reactions for the physical system and conditions of interest. Thermodynamic properties of the species are required, as are the rates of the reaction of each species with all others in the list, and the temperature and pressure dependence on the rates of reaction. The development of such mechanism, and validation of the mechanisms, is a timeconsuming and arduous task. Fortunately, there are many combustion and chemical kinetics researchers worldwide working in this area [6–9]. The databases are constantly in development, and versions are freely available, as discussed below. The remainder of this chapter describes the fundamental concepts used in developing chemical mechanisms, and some examples of their application.
Fundamentals Radical Reactions In a combustion system, the consumption of a fuel molecule (and its decomposition products) is driven largely by attack from radicals. A radical (or free radical) is an atom, molecule, or ion with one or more unpaired electron or an open shell configuration. A radical can be formed by breaking the bond of a stable molecule, for example due to a high-energy collision: CH4 + M ¼> ∙CH3 + ∙H + M. In this reaction, M (discussed further below) represents any other molecule in the system which can act as a collision partner with CH4, and thereby supply the energy to break
G.T. Linteris and J.F. Griffiths
the C-H bond. In this case, the fragments, ∙H and ∙CH3, are radicals. The unpaired electron is typically shown by “∙”. Radicals tend to be highly reactive, and are responsible for promoting the chemistry occurring in combustion systems. The unpaired electron in a radical attacks bonds in stable molecules, leading to their decomposition. The energy barrier in radical reactions tends to be very low, which is why their reactions are so fast. In high-temperature gaseous combustion systems, the equilibrium concentration of radicals increases with temperature, and peak radical concentrations can be quite high, with a volume fraction on the order of 1 % in the primary reaction zone of premixed flames. While this number may appear low, recall that radicals are highly reactive: their concentrations do not build up higher because they are consumed so fast. Typical radicals in combustion are: ∙H, ∙O∙, ∙OH, ∙CH, ∙C2, ∙CH2, ∙CHO, ∙CH3, ∙R, etc. Here, ∙R denotes any hydrocarbon molecule with an unpaired electron at one site. For example, ∙R can be ∙CH3, ∙C2H5, ∙C3H7, for the methyl, ethyl, and propyl radicals, formed by the abstraction (removal) of H atom from CH4, C2H6, and C3H8. In these cases, the stable molecules can also be represented generically as RH; for example: C2H6 + OH ! C2H5∙ + H2O, which can be written as RH + OH ! R∙ + H2O . In the context of combustion kinetics, explosive behavior corresponds to extremely rapid reaction. There are two types of explosive behavior: thermal explosions, and chain branched explosions. The former is due to temperature rise, while the latter is due to an exponential build-up in radical concentrations. In combustion, the radical pool refers to the chain-carrying radicals which are involved in the branching reactions, for example H, OH, O, and HO2. It often takes time for this pool to develop, which leads to an induction time for ignition (also called the ignition delay). The buildup, maintenance, and decay of the radical pool in combustion is determined by the relative rates of the production and destruction of radicals, and relies upon certain key branching steps in the reactions scheme, as described below.
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The typical steps of radical chain reactions, initiation, propagation, branching, and termination, are described here in the context of ignition of H2/O2 systems (following Ref. [2]). The initial radicals required to start the process come from the breaking of a bond of a stable molecule (either thermally through collisional energy transfer, or through photolytic interactions, for example in the presence of UV light). Since the bond strengths of most stable molecules relevant to combustion systems tend to be high, the process is slow (photolytic bond breaking is typically unimportant in combustion). Initiation steps, for example reaction 10.3 in Table 10.1, are those in which two reactive radicals are formed from stable species. Propagation steps (reaction 10.4) involve radicals, changing the type, but not the total number of radicals. These reactions tend to have very low activation energies, and hence are very fast. Propagation steps are mostly responsible for the consumption of the fuel and its decomposition products in combustion system. Chain branching steps (e.g., reaction 10.6) increase the number of radicals, and hence are responsible for the explosive growth in the radical concentration, which leads to rapid reaction in the system as a whole. Termination steps reduce the number of radicals, and thereby shut down the overall combustion. Reaction 10.7, while it technically is a propagation step, is usually thought of as a termination step because at low temperatures the radical HO2• is relatively unreactive, and its fate is often to be destroyed at walls (as in the reconciling of the explosion limits of the H2–O2 system [2–4]). In reaction 10.7, a non-reacting third body (M) takes away energy from the radical-radical combination. In this example, after the reaction of H• + O2, HO2• would have Table 10.1 Radical reactions important in H2/O2 ignition Initiation Propagation Branching Termination
H2 þ O2 ! 2OH OH þH2 ! H2 O þ H O þH2 ! OH þH H þO2 ! OH þO H þO2 þ M ! HO2 þ M H ! ½H2
(10.3) (10.4) (10.5) (10.6) (10.7) (10.8)
too much energy stay together (since it is a relatively small molecule and cannot absorb the energy in vibrational or rotational modes of energy storage). Another example of such a three-body termination reaction is: H + H + M ! H2 + M, which is important in flames. Reaction 10.8 represents the destruction of a radical without another interacting gas molecule (for example through radical quenching at a wall), which can be very important in many situations where solid surfaces are available to the gas-phase reactants. Although it looks as if reaction 10.5 is a propagation step (because there is no increase in the number of unpaired electrons) this is classified as a chain branching reaction since the number of active reaction chains has been multiplied. There is another class of overall termination steps: the gas-phase catalytic cycles involving flame inhibitors such as FeO, HBr, and HOPO. These catalytic cycles serve to reduce radical concentrations in flames, and are discussed in more detail below.
Law of Mass Action The rate of disappearance of a reactant is generally proportional to the concentrations of participating reactants. For an arbitrary chemical reaction: A þ B ! products;
ð10:9Þ
the proportionality is represented by the Law of Mass Action: d ½ A ¼ ω_ A ¼ k ½A1 ½B1 dt
ð10:10Þ
Here, the brackets denote concentration (for example with units of mol cm3), d[A]/dt is the rate of change in the concentration of A with time (t), and k is a proportionality constant. This expression was phenomenologically developed, based on empirical results, but there is a theoretical basis for it. Molecules of A and B must collide to react. Their collision rate depends upon their concentrations (which depend upon the total concentration via the ideal gas law and their volume fraction). Today, k is known as the
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specific reaction rate constant (or often just the rate constant). The magnitude of k is usually a function only of temperature, and that dependence is often significant. Note that the concentration C of species i, Ci, or [i] can be expressed as Ci ¼ Xi ∙ CT, where the total concentration is given by the ideal gas law CT ¼
NT P ¼ RT V
ð10:11Þ
in which NT is the total number of moles in the volume, V, at the given pressure P and temperature T, and R is the universal gas constant (8.314 J mol1 K1) The mole fraction Xi (known also as the volume fraction), is Xi
Ni Ni ¼ ¼ X NT Ni
ð10:12Þ
i
in which Ni is the number of moles of species i, and the summation is over all species in the system.
The Law of Mass Action can be written for either global or elementary reactions. An example of a global reaction (also called a net reaction or overall reaction) is ð10:13Þ
in which 2 moles of hydrogen reacts with 1 mole of oxygen to form 2 moles of water; the Law of Mass Action would be:
1 d ½H 2 d ½H 2 O d ½O 2 ¼ ¼ 2 dt dt dt ¼ kG ½H2 n ½O2 m
OH þ H2 ! H2 O þ H
ð10:14Þ
where kG is the global rate coefficient, n is the reaction order with respect to H2, m is the order with respect to O2, and m + n is the overall order. Note that a distinction is made on the left hand side of the equation between reactant removal and product formation. Reaction 10.13 with 10.14 describe what happens to the reactants globally. Relations such as these are typically
ð10:15Þ
are believed to represent an actual interaction between molecules: an OH molecule collides with an H2 molecule, and (if there is sufficient energy involved in the collision) they react to form one H2O molecule and an H atom. The Law of Mass Action for this elementary reaction would be: d ½H 2 ¼ k15 ½OH 1 ½H 2 1 dt
Global vs. Elementary Rates
2H2 þ O2 ! 2H2 O
obtained experimentally, and are valid only for that experiment and the range of conditions from which it was developed. The expressions are usually complex; the empirical reactions orders are typically not integers, can be negative, and depend upon time and the reaction conditions. Extrapolation to other experimental conditions can be unreliable or incorrect. Note that reaction 10.13 is not believed to actually occur; detailed experiments have shown that on the molecular level, two molecules of hydrogen do not collide with one molecule of oxygen to form two molecules of water. In contrast, elementary reactions, such as
ð10:16Þ
and the specific reaction rate constant k15 describes the probability of reaction. The dependence (i.e. reaction order) on the concentrations of H and OH (1 in this example) are the molecularity with respect to that reactant, and the overall molecularity is the sum of individual molecularities of the reactants. Generally, for elementary reactions, the determination of reaction orders is easy: they correspond to the molecularities. An overall reaction such as reaction 10.13 is the result of a large number of elementary reactions. For example the reaction of hydrogen and oxygen, in a simple but satisfactory form, can be described through a sequence of reactions involving about 8 species and 40 reactions; that for methane 30 species and 400 reactions, and hexane, 450 species 1500 reactions. Comprehensive representations of mechanisms for the combustion of hydrocarbon fuels run into many hundreds of species involved in many
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thousands of reactions, the complexity increasing with their size or the number of compounds in the fuel mixture [6]. Describing a chemical system in terms of elementary reactions is a difficult and time consuming task, but has many advantages. The reaction order of elementary reactions is constant (does not change with system or conditions, as the global orders might), and the specific reaction rate constant varies only with temperature; hence, the rate expressions should be valid over a wider range of conditions than those of one-step global reactions.
Type of Reactions There are three types of elementary reactions actually observed in gaseous combustion systems: unimolecular, bimolecular, and termolecular (depending upon the number of species involved).
Bimolecular Reactions Bimolecular reactions are those given by AþB!C
ð10:17Þ
AþB!CþD
ð10:18Þ
d ½ A ¼ ω_ A ¼ k ½A1 ½B1 dt
ð10:19Þ
or
with
These are the most common types of reactions; the molecularity is one for each reactant and two overall (a so-called second-order reaction). Common examples would be H + H2O ! OH + H2, CO + OH ! CO2 + H, or C4H10 + ∙OH ! ∙C4H9 + H2O. This last reaction is called an abstraction reaction because the ∙OH radical abstracts a hydrogen atom from the butane molecule.
Unimolecular Reactions Unimolecular reactions are given by A ! B or A ! B þ C with
ð10:20Þ
d ½A ¼ kuni ½A1 dt
ð10:21Þ
Some bimolecular reactions behave as though they were unimolecular. For example, in the bimolecular reaction 10.17 above, A + B ! products, if the concentration of B is present in large excess as compared to A, its concentration will not change appreciably, so the rate expression Equation 10.19 would be: d ½ A ¼ keff ½A1 dt
ð10:22Þ
in which the effective rate constant is determined by keff ¼ k[B]1. Hence, this second-order reaction is pseudo-first order in A. A special example of a pseudo first-order reaction is the decomposition of the butyl radical ∙C4H9 (formed after abstraction of a hydrogen atom from C4H10) after a collision with another molecule M: C4 H9 þ M ! C3 H6 þ CH3 þ M
ð10:23Þ
The collision partner M, represents any other molecule in the system. It is called a chaperone molecule or a third body (as in reaction 10.7). Conceptually, its role is to provide the energy needed (via a collision) to break the necessary bonds in reactions 10.23, but it does not otherwise participate in the reaction. In reaction 10.7, it serves the opposite role: to carry away the excess energy resulting from the joining of two free radicals. The role of M can be recognized in the following way. Reaction 10.23 constitutes the breaking of a C–C bond. In order for this to happen it is necessary for sufficient energy to be accumulated at the appropriate part of the C4H9∙ radical. The energy required is approximately equal to the bond dissociation energy (see Chap. 5). C4H9∙ is able to gain the necessary thermal energy via kinetic energy transfer from another species during a collision. So M can be any molecule in the system and the concentration [M] represents the total concentration of species in the system. As a result of this special function of “M” the order of reaction 10.23 can vary, with keff showing a complex experimental dependence
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G.T. Linteris and J.F. Griffiths
on concentration. The reaction is second order overall at low concentrations of species in the system (signifying low pressures), which arises from a first order dependence with respect to both the reactant, C4H9∙ and M, e.g. d ½C4 H 9 ¼ k0 ½C4 H 9 ½M dt
ð10:24Þ
where the subscript o signifies the rate constant at the low pressure limit, and represents the second order case. However, as the concentration (or pressure) of the system is raised the reaction changes to eventually achieve a first order dependence on the principal reactant and with no dependence on M, e.g. d ½C 4 H 9 ¼ k1 ½C4 H 9 ; dt
ð10:25Þ
where the subscript 1 signifies the rate constant at the high (infinite) pressure limit, and is strictly a first order rate constant. There is a complex dependence of the rate constant on concentration between the two limits, and the overall reaction order varies between 2 and 1. There are sophisticated theories applied in combustion chemistry to interpret these data, but the two limiting conditions can be derived on the basis of simple algebraic analysis as is found in chemical kinetic texts (e.g. [1]).
Termolecular Reactions Termolecular reactions are described by AþBþM!CþM
ð10:26Þ
with d ½ A ¼ k ter ½A ½B1 ½M1 dt
ð10:27Þ
Examples of such reactions are the radical recombination reactions OH + H + M ! H2O + M
and H + H + M ! H2 + M. (Note that for the latter of these reactions, a factor of two would have to be added to Equation 10.27 for the change in [H] with time, since both A and B (i.e. H) are the same. The rates of these third-order reactions are pressure dependent (each concentration in Equation 10.27 is proportional to P via Equation 10.11). Also, via Le Chaˆtelier’s principle, the equilibrium is affect by pressure since there is a change in the number of moles in reaction 10.26. Finally, the efficiency of different species as third bodies can vary substantially. For example, in the reaction OH + H + M ! H2O + M, the efficiency of N2, CO, H2, CO2, and H2O, as a third body is enhanced by a factor or 1, 1.8, 2, 3.6, and 6.3 relative to N2. These different third-body efficiencies are usually accounted for in detailed reaction mechanisms.
Units of Reaction Rate Constant Since the derivative of the concentration with time d[A]/dt always has the units (concentration/time), but since the number of terms on the right hand side of a rate equation varies with the reaction order n (c.f. Equations 10.19, 10.21, 10.27), the units of the specific reaction rate constant k must change accordingly. The units of k are: (concentration)(n1)∙s1 (or, for example, (mol cm3)(n1) s1) which yields the units shown in Table 10.2 for reaction orders of 0 to 3.
Arrhenius Rate Expression Specific reaction rate constants can be a strong function of temperature (and show no pressure dependence, except in the situations described above). In the late 1800s, Svante Arrhenius discovered empirically that the rate of chemical reactions is described well by an exponential
Table 10.2 Units of the rate constant for various reaction orders Units of k Reaction order 0 1 2
Rate expression, single component, A d½A=dt ¼ ko d½A=dt ¼ k1 ½A
3
d½A=dt ¼ k3 ½A2 ½M
d½A=dt ¼ k2 ½A2
conc time1 time1 conc1 time1
(in cgs) mol cm3 s1 s1 cm3 mol1 s1
conc2 time1
cm6 mol2 s1
10
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333
function of temperature. The equation which bears his name is kðT Þ ¼ A0 eðEa =RT Þ
ð10:28Þ
in which A0 is the pre-exponential factor and Ea is the activation energy. Later, the pre-exponential factor A0 was found, for many reactions, to have some temperature dependence, and today, a modified version of the Arrhenius equation is more commonly used: kðT Þ ¼ AT b eðEa =RT Þ
ð10:29Þ
Potential Energy
In combustion, Ea is typically given in units of kcal mol1 or kJ mol1; alternatively, Ea is divided by R to give an activation temperature Ta (¼ Ea/R), with units of K. The kinetic theory of gases has provided a theoretical basis for the modified Arrhenius equation. For a bimolecular reaction (10.18, 10.19), the reaction rate is proportional to the concentrations of reactants present. The rate constant k represents the probability of reaction, which in turn depends upon the rate of molecular collisions (embodied in the pre-exponential term ATb). Not all collisions will have sufficient energy for reaction, however, and the exponential term describes the fraction of molecules in the gas with sufficient energy to overcome a barrier to reaction. Figure 10.3 shows the chemical potential energy diagram for a hypothetical reaction. For the forward reaction, the activation energy is Ea,f, while for the reverse reaction, it is
Un-catalyzed
Ea,f
Ea,r
Reactants
Catalyzed
Products Reaction Progress Fig. 10.3 Energy diagram for a chemical reaction
Ea,r. For this exothermic reaction, the products have less chemical energy than the reactants (and for an adiabatic system, this difference is typically manifested as an increase in temperature of the products). The reverse reaction has a higher activation energy by an amount corresponding to the exothermicity of the forward reaction. Note that potential energy curves are shown for un-catalyzed (solid line) and catalyzed (dashed line) reactions. A catalyst does not change the energy states of the products or reactants, but lowers the effective activation energy (for both forward and reverse reaction), so the system can more rapidly achieve the equilibrium state. The collision term ATb in the modified Arrhenius expression represents the frequency of collisions, times the probability of collision—the so-called steric factor, with a typical upper limit of 1013–1014 cm3 mol1 s1. (Note that the units of ATb are the same as those of k). Nonetheless, steric factors are often quite low, representing the need for the molecules to have the correct orientation, and have the energy in the molecule (vibrational, rotational, translational) to be distributed optimally for reaction to occur. For unimolecular reactions, A represents the vibrational energy in the molecule which leads to its decomposition. Termolecular reactions are actually two bimolecular reactions in rapid sequence; grouping them together can lead to unusual values for the A and Ea.
Effect of Temperature on Reaction Rates The parameters for the reaction rate expression are mostly determined through, or validated in, experimental measurements in devices such as shock-tubes, static reactors, flow reactors, premixed and diffusion flames, rapid combustion machines, and combustion bombs. In determining the Arrhenius parameters experimentally, one approach, adopted very early, is to measure the reaction progress for a given set of initial reactant concentrations. By performing experiments over a range of temperatures, it is possible to construct the plot of as ln(k) vs. 1/T as in Fig. 10.4. The activation energy Ea is obtained from the negative slope of the line, while the pre-exponential (as ln (A0 )) is obtained from the intercept. The results
334
G.T. Linteris and J.F. Griffiths
Fig. 10.4 Arrhenius plot from the experimentally determined rate constant for the reaction H + O2
1000
2000
28
600 T / K
ln (k / mol−1 cm3 s−1)
26
24
22
20 0.5
1.0
103
Fig. 10.5 Dependence of reaction rate constant k on temperature for various reactions important in combustion
1.5
K/T
log (k / cm3mol-1s-1)
14 H + HBr = H2 + Br
13
C3H8 + OH = iC3H7 + H2O
12 CH4+ OH = CH3 + H2O
11
CO + OH = CO2+H
10
9 H + O2 = OH + O
8
7 H + H2O = H2 + OH
6 0.0
1000 K/T
0.2
0.4
presented in the figure were obtained over a very wide temperature range by many different research groups using a number of different experimental techniques.
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
Figure 10.5 shows the rate constant for various important reactions in combustion with data from Ref. [10]. As indicated, the reactions CO + OH ! CO2 + H and H + HBr ¼ H2 + Br have
10
Chemical Kinetics and Fire
very low activation energies (E/R ¼120 K and 290 K respectively), and show very little temperature sensitivity, typical of a radical propagation reactions. The chain-branching reaction H + O2 ¼ OH + O has a somewhat higher temperature sensitivity (Ea/R ¼ 9,860 K) as does the propagation reaction H + H2O ! H2 + OH (for which the activation energy, Ea ¼ 82 kJ mol1), both of which are endothermic. The lines in Fig. 10.5 that exhibit curvature require the rate constant to be interpreted over the full temperature range using the three parameter representation (Equation 10.29). Otherwise, a different activation energy would have to be applied within more restricted sections of the temperature range, as is reflected in the varying gradient.
Effect of Pressure on Reaction Rates Pressure manifests itself primarily through its effect on concentration via the Law of Mass Action (Equation 10.10) with the ideal gas law (Equation. 10.11), and in three-body reactions (Equations. 10.26 and 10.27) which are very pressure dependent. In the context of fire, these considerations are most important with regard to the laboratory experiments used to: measure elementary rates, understand a phenomenon, or validate a chemical mechanism. For example, many reaction rates for three-body reactions are in the fall-off regime at ambient pressure. Hence, in specifying the relevant rate, pressure plays a role. Nonetheless, in actual fires, while small pressure differences have a major effect on the flow of gases, the magnitude of pressure changes typically has little effect on combustion kinetics. Some effect of pressure may be relevant at high altitude, or in aircraft fire safety considerations. Of course, pressure rise in explosions can influence the kinetics. For typical atmospheric pressure fires, however, the limited changes in pressure have little effect on the combustion kinetics.
335
Important Concepts in Hydrocarbon Combustion Kinetics Applications of combustion kinetics to fire will be illustrated in examples below.
Ignition Ignition is defined as the initiation of combustion. Generally, this involves bringing the gas-phase reactants to the point of rapid, exothermic reaction (i.e., explosive behavior). As described above, this high rate of reaction can be induced via thermal or radical chain branching mechanisms. And these, in turn, can be induced by a spark, a local hot spot (due to a hot wire or surface), or a pilot flame. Alternatively, spontaneous (or auto-) ignition occurs when a fuel and air mixture, for example in a uniformly heated chamber or next to a hot surface, by itself reaches the explosive reaction conditions. Gas-phase reactions lead to increasing radical concentrations (either due to thermal or chain branching mechanisms), which eventually are high enough for sustained gas-phase flame propagation. A special category of spontaneous ignition takes place when a uniformly mixed gas mixture, at constant initial temperature, is raised instantaneously to a uniformly high temperature after passage of a shock wave, as in a shock tube experiment. This configuration, while not experienced often in fire research, is of significance since most of the experimental and calculated data on ignition delay are obtained using this technique. In fire research however, the term “ignition” is often used in the context of the initiation of flaming combustion over a solid or liquid material. This process, while also dependent upon the behavior of the gas-phase reactants, largely involves the thermodynamic behavior of the solid material as it heats and decomposes (typically when exposed to an external infrared heat flux, for example from the hot upper layer in a
336 1000
φ = 1.0, P = 1 bar
100
τign / ms
room fire). Of course, gas-phase reaction and solid material ignition are related in that the solid material ignites when: (1) it is producing gas-phase reactants fast enough, (2) the fuel molecules mix with the oxidizer gas in proportions which are within the flammability limits, and (3) the radical concentrations build up sufficiently, due to heat release, chainbranching, etc. Nonetheless, this last part of the process (ignition, by an externally imposed source, of the gas-phase reactants which are within the flammability limits) is distinctly different from the spontaneous ignition of gas-phase reactants described in the previous paragraph. For the purposes of the discussion below, when discussing “ignition”, it is gas-phase spontaneous ignition (not material ignition) with which we are concerned. Spontaneous ignition is a gas-phase chemical process well described by the detailed kinetic models described above (and below)—provided that the reaction mechanism embraces processes that are relevant to an appropriately wide range of temperatures. For example, if a reactive gas mixture is exposed to a hot surface (or container), and (for the purposes of discussion) uniformly heated, it will reach an explosive condition (i.e., rapid reaction) after some length of exposure time to the heated condition. The parameter of interest is the ignition time or ignition delay τign, which is the time it takes for a mixture at a given temperature, to reach the state of rapid reaction. To define the ignition delay, a criterion for the condition of rapid reaction is required. Often, a characteristic temperature rise, the maximum rate of temperature (or pressure) rise, or some minimum radical concentration is used (e.g., XOH > ¼ 104) is used. Figure 10.6 shows the calculated ignition delay of a stoichiometric H2/air mixture. As indicated, the ignition delay is a strong function of the initial temperature: it drops by about three orders of magnitude as the initial temperature rises from 925 to 1025 K. Given a comprehensive kinetic mechanism, ignition delay is readily calculated. The chemistry of homogeneous ignition is often different from that in a flame. Ignition delays are a strong function of the reactants, stoichiometry, initial
G.T. Linteris and J.F. Griffiths
10
1
0.1 900
950 1000 Temperature K
1050
Fig. 10.6 Ignition delay of a stoichiometric H2/air mixture as a function of initial gas temperature
temperature and pressure, and the presence of trace species. Figure 10.7 shows the H-atom volume fraction and temperature as a function of time for an H2.air system at an initial temperature of 1000 K. As indicated, the ignition delay is about 1.6 104 s. The build-up in H radical concentration is exponential in time, and increases drastically for times greater than about 10-5 s. Hence, the explosive behavior is predominantly due to a chain-branching mechanism rather than thermal initiation. Some fuels decompose forming H-atoms more readily, and these promote a short ignition delay. Additives which consume H-atoms retard ignition, while those that create H-atoms accelerate ignition.
Competition Between Reactions The macroscopic behavior in combustion systems is often determined by which of two (or more) possible reaction paths dominate. Reactions proceed in parallel, and which reaction dominates depends upon the temperature and the concentrations of reactants (which can change with time and location in the system), and the pressure. Some examples of combustion reactions in which the competition between alternate reactions are given below.
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337
Fig. 10.7 H-atom and temperature increase with time for stoichiometric H2/air mixture at 1000 K
Initiation Reactions: Thermal Decomposition vs. Oxidation The homogeneous ignition above requires the buildup in radical concentrations. To get this process started, there must be radical initiation reactions. Two possible initiation routes are the dissociation reaction of H2, reaction (10.30) and the molecular reaction between H2 and O2. reaction (10.31). Figure 10.8 shows the rate constants
and the ratio of the rate constants for these two competing reactions. As indicated, reaction (10.31) is 4 and 9 orders of magnitude higher at 2000 K and 1000 K, respectively. Hence, for any reasonable concentration of O2, the rate of the molecular reaction (10.31) (i.e., the rate constant times the relevant concentrations as in Equation 10.19) will be much higher, making it the favored initiation route.
H2 þ M ! H þH þM
k ¼ 6:7 1014 eð51000=TÞ s1
ð10:30Þ
H2 þ O2 ! HO2 þH
k ¼ 1:5 1014 eð28, 500=TÞ s1
ð10:31Þ
Relative Rates of Oxidation and Degradation of the Primary Fuel Radical As described above, the propagation reactions are the principal means of reactant consumption through, for example, RH þ OH ! R þH2 O
ð10:32Þ
where R. represents an alkyl radical generated from an alkane (e.g. an ethyl radical (C2H5) from ethane (C2H6)). Whether or not the alkyl radical then decomposes or oxidizes depends upon the temperature and the concentration of oxygen. Consider normal undecane (n-C11H24), a component of kerosene. The undecyl radical formed from it in a reaction such as (10.32) may undergo the competitive reactions
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G.T. Linteris and J.F. Griffiths
T/K 2000 1500
1000
500
10
20
kH2 + O2
18
kH2 + O2/kH2 + M
6
kH2 + M
4
log (k / cm3mol-1s-1)
16 14
2
12
0
10
−2
8
−4
6
−6
4
−8
2
−10
log (kH2 + O2 / kH2 + M)
8
0
0.0
0.5
1.0
1.5
2.0
1000 K/T Fig. 10.8 Rate constant (left scale) and ratio of the rate constants (right scale) for H2 + O2 abstraction reaction and H2 + M dissociation reaction, as a function of temperature (top scale) and inverse temperature (bottom scale)
n C11 H23 alkyl radical
! n C6 H12 þ n C5 H11 k ¼ 2:5 1013 eð14433=TÞ s1 alkene lower alkyl radical
ð10:33Þ
n C11 H23 þ O2 ! n C11 H22 þ HO2 k ¼ 1:0 1012 eð1000=TÞ mol1 cm3 s1 hydroperoxy ð10:34Þ alkyl radical alkene radical
Examining the activation energy for the two competing reactions reveals that the first, the thermal decomposition route (Ea/R ¼ 14,443 K), is very temperature sensitive, whereas the second route (Ea/R ¼ 1,000 K), H-atom abstraction by O2 (a radical propagation reaction), is less temperature sensitive. Figure 10.9 shows the ratio of the rate constant for the two reactions. As indicated, the relative importance of the
decomposition reaction to the consumption of n-C11H23∙ increases at higher temperature by many orders of magnitude. To compare the rates of disappearance of the fuel radical d[n-C11H23∙]/dt by the two routes, it is necessary to use Equation 10.21 and Equation 10.19 for unimolecular and bimolecular reactions, so that the ratio of rates is ωdec/ω+O2 ¼ kdec/(k+O2[O2]) in which the concentration of [O2] is determined
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Chemical Kinetics and Fire
339 T/K 2000 1500
1000
500 5
0
ωdec / ω+O2
-1
3
kdec / k+O2
-3
2
-4
1
-5
0
−6
−1
−7
−2
−8
−3
−9 0.0
log (ωdec/ω+O2)
log (kdec/k+O2/ cm3mol-1s-1)
-2
4
−4 0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
1000 K/T Fig. 10.9 Ratio of the rate constant (left scale) and reaction rate (right scale) for decomposition (dec) vs. H abstraction by O2 (+O2) reactions for n-C11H23 , as a function of temperature (top scale) and inverse temperature (bottom scale)
at each temperature via Equations 10.11 and 10.12, with XO2 ¼ 0.21 in air. As shown in the figure, the reaction rates are about equal at 850 K; whereas the decomposition rate is 1000 times slower at 600 K, and 1000 times faster at 1500 K, then the abstraction route. The competition between radical abstraction and thermal decomposition reactions has several consequences. The relative rate of reaction is dependent upon the oxygen concentration, so in fuel rich conditions, thermal decomposition will be favored, leading to the build-up of small fuel radicals, and ultimately acetylene, which is a precursor for soot. Also, at temperatures below 1000 K, the combustion chemistry tends to be specific to the primary fuel structure; whereas at higher temperatures the large fuels will tend to decompose to smaller hydrocarbon fragments, so that ultimately, the important reactions for heat release all involve combustion of the same, much smaller (e.g., one- and two-carbon) hydrocarbon species. This explains why the macroscopic
combustion behavior of different hydrocarbons can be very similar in flames.
Relative Rates of Reaction of OH with CO vs. Hydrocarbon The reaction of carbon monoxide, an intermediate species in hydrocarbon-air flames, controls two of the most important features of fires. (1) Most of the heat release in a flame occurs via conversion of CO to CO2, and (2) residual CO, the most important toxic by-product of flames (and the species responsible for most fire deaths) is often controlled by its reaction rate. As described below, the consumption of CO in flames occurs almost entirely by its reaction with OH. Hence, it is of interest to compare the rate of OH reaction with CO to that of OH reaction with other hydrocarbon species (for example, the fuel itself). Figure 10.10 shows the reaction rate constant for OH reaction with n-C4H10 or CO. As the figure indicates, the reaction of OH with n-C4H10 is on the order of 140 times faster than
340
G.T. Linteris and J.F. Griffiths T/K 2000 1500
1000
500 200
14
180
kC4H10+OH
160
120
kC4H10
+ OH /
kCO+OH 100
12
80
kCO+OH
kC4H10+OH / kCO+OH
log (k / cm3mol-1s-1)
140
60 40 20 10 0.0
0 0.5
1.0
1.5
2.0
1000 K/T
Fig. 10.10 Rate constant k (left scale) and ratio of rate constants (right scale) for reaction of OH with CO or n-C4H10, as a function of temperature (top scale) and inverse temperature (bottom scale)
its reaction with CO at 1800 K. This illustrates that in many flames, the burnout of CO will be kinetically limited until the hydrocarbon content is much lower than the CO concentration; i.e., for n-C4H10 (and many other hydrocarbons) concentrations of 1/140 that of CO, the rate of consumption will be about equal. The burnout of the CO is typically the last stage of reaction sequence and occurs after the hydrocarbon is essentially gone.
H-Atom Reaction with O2 vs. Reaction with Fuel The reaction of H + O2 ! OH + O (reaction 10.6) is the most important chain branching reaction in combustion, and greatly increases radical concentrations in the flame. Nonetheless, as described above, reactions of hydrocarbon species with radicals (chain propagation processes such as reaction 10.32) are largely responsible for the consumption of the fuel species and its
decomposition products. Hence, it is of interest to compare the rates of these two processes. Figure 10.11 shows the rate constant (left scale) for the H-atom abstraction reaction n-C4H10 + H ! C4H9 + H2 and for the reaction the H + O2 ! OH + O (using the rate expressions: k ¼ 3.1 1014 exp(4320/T) / mol1cm3 s1; and k ¼ 1.99 1014 exp(8460/T)/ mol1 cm3 s1, respectively). The ratio of the rate constants is also shown (right scale). As indicated, both reactions have a comparatively high temperature sensitivity, so they become increasingly important at high temperatures. Furthermore, the abstraction reaction is roughly 20 times faster at typical flame temperatures (1200–2000 K) and in the range of 50–1000 times faster at temperatures between 650 and 1000 K. Hence, the chain branching reaction is most influential after the hydrocarbon is consumed. This property of the kinetics has a large influence on flame structure. The regime of the
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Chemical Kinetics and Fire
341 T/K
2000 1500
1000
500 1000
14 kH+C4H10
800
log (k / cm3mol-1s-1)
kH+O2 12
600
400
kH + C4H10/ kH + O2
kH+C4H10 / kH+O2
10 200
8 0.0
0 0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
1000 K/T
Fig. 10.11 Rate constant k (left scale) and ratio of rate constants (right scale) for reaction of H with O2 or n-C4H10, as a function of temperature (top scale) and inverse temperature (bottom scale)
chain-branching reactions is separated, either physically or temporally, from the regime of fuel consumption, and one cannot have a large build-up in radical concentrations until the fuel species are significantly depleted. Nonetheless, in the context of spatial structure of a flame, the effect is mitigated somewhat by the diffusion of radicals (especially H atoms) which are transported to regions where they are needed for propagation reactions.
Flame Configuration/Structure Effects on Chemistry As described above, there often exists competition between possible reaction paths in combustion systems, controlled largely by the temperature and chemical environment. The chemical environment can vary due to different initial conditions, changes with time, or the structure of the flame itself. (“Flame structure” constitutes the profile of concentrations of species, temperature, and flow velocities over space
and time.) For example, in a co-flow laminar diffusion flame burner, the high-temperature reaction zone (i.e., the flame sheet) forms a conical shape around the fuel stream above the exit jet of the burner. Figure 10.12 shows of the volume fraction profiles for some of the species as a function of radial position across the high-temperature reaction zone in a cup-burner flame. The peak temperature occurs at r ¼ 8.5 mm, and the concentration of O2 and CH4 decrease near that location. On the fuel side of the reaction zone (i.e., r < 8.5 mm), the species consist mostly of the fuel (CH4) and its decomposition products (e.g., CH3); while on the oxidizer side, the major species present are O2 and the products of combustion (e.g., H2O, CO2) which are diffusing radially out from the flame. Due to diffusion, there is some mixing of species from each side. One notable feature is that the peak of the radical pool occurs on the oxidant side of the reaction zone, nearly coincident with the peak temperature. These results can be explained as follows. First, the major chain branching reaction H + O2 ! OH + O (reaction 10.6) has a relatively high
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G.T. Linteris and J.F. Griffiths
Fig. 10.12 Calculated species volume fraction, temperature, and heat release rate at a height of 11 mm above a cup-burner flame of CH4 and air
activation energy (E ~ 70 kJ mol-1), so its occurrence requires high temperature; but more importantly, it requires O2, so that reaction must occur primarily on the air side of the flame. Secondly, the rate of reaction of H with CH4 is much faster than with O2, so reaction 10.6 cannot dominate on the fuel side. Similarly, the reaction CO + OH ! CO2 + H, which is responsible for CO consumption (as discussed above), must also be on the oxidant (air) side of the reaction zone: it needs OH, which would be consumed preferentially by the hydrocarbons on the fuel side. Since the CO + OH reaction, forming CO2, is also responsible for a large fraction of the heat release, its location also dominates the location of the heat release and peak temperature. The structure of a premixed flame (Fig. 10.13) also results from the hydrocarbon kinetics described above. As illustrated, the CO consumption and the peak of the chain-branching reaction 10.6 are both retarded until the CH4 is nearly gone (since, as described above, the
radicals required in both reactions react faster with CH4). The consumption flux of CH4 creates a dilemma: it needs both CH4 and H, but they cannot both co-exist at high concentration because the chain-branching reactions producing H will not occur until hydrocarbons are considerably depleted. This is solved by species transport: H atoms are produced at a high rate near the peak temperature, but diffuse rapidly upstream where they are consumed by reaction with CH4.
Super Equilibrium Chemical equilibrium is an idealized state, which is sometimes achieved for select conditions in fires, but often is not realized in practice. In premixed and diffusion flames of hydrocarbons with air, for example, the radical pool species H, OH, and O, can achieve concentrations several orders of magnitude higher than those calculated at thermodynamic equilibrium. For example,
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343
Fig. 10.13 Major species profiles and reaction fluxes for laminar premixed methane-air flame (From [3])
Fig. 10.14 shows the ratio of peak to equilibrium H-atom volume fraction in a methane-air counterflow diffusion flame; the results are plotted as a function of strain rate, which is proportional to the jet velocities of the methane and air streams
forming the opposing flows in the burner. As indicated, super-equilibrium ratios range from 1 at zero strain, to 400 at a strain rate of 190 s-1. The super-equilibrium concentrations occur because the reactions which form the radicals
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G.T. Linteris and J.F. Griffiths
Fig. 10.14 Ratio of peak to final equilibrium H-atom volume fraction as a function of strain rate in a methane-air counterflow diffusion flame
(typically, the chain-branching reactions such as H + O2 and O + H2) are much faster than the reactions which recombine radicals (typically, the three-body recombination reactions such as H + OH + M). The species do not reside long enough in the main reaction zone for the recombination reaction to establish thermodynamic equilibrium at the prevailing temperature. The result is that radical pool species are present in very high concentration, leading to the rapid attack on the fuel species, and fast overall reaction. If the radicals are controlled to be closer to equilibrium levels (even at the elevated temperatures of the flames), the overall reaction rate is greatly reduced. Premixed flames also have large superequilibrium of radicals. For example, in a stoichiometric methane-air flame, the peak volume fraction of H, O, and OH (which occur near the location of the peak of the H + O2 reaction flux) are 17, 14, and 2.6 times the final equilibrium value, respectively. Note that it is generally accepted that the chemical action of fire suppressants is to decrease the peak radical concentration towards the final equilibrium level.
Role of Trace Species There are several classic examples in combustion in which very low concentrations of reactants completely change both the route for fuel decomposition, as well as the overall rate of reaction. While they are sometime esoteric, they demonstrate the principles which are important for more practical situations.
Moisture in CO Oxidation In early research, it was found that the oxidation rate of CO to CO2 is highly dependent on the presence of trace quantities of water in the system. In fact, many hydrogen containing compounds (e.g., H2, or a hydrocarbon) can supply the trace hydrogen atom necessary for the faster reaction. In the bone-dry system, the reaction of CO proceeds as follows. The initiation step CO þ O2 ! CO2 þ O is slow. It is believed to be followed by O þO2 þ M ! O3 þ M
ð10:35Þ
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345
O3 þ CO ! CO2 þ 2 O
ð10:36Þ
CO þ O þM ! CO2 þ M
ð10:37Þ
Fe(CO)5
+O2
Fe
which are all slow at combustion temperatures. In contrast, in the presence of water, the reaction proceeds via: CO þ O2 ! CO2 þ O
ð10:38Þ
O þH2 O ! 2OH
FeO +H +H2O
+H FeOH
+H
Fe(OH)2
Fig. 10.15 Schematic diagram of reaction pathways of Fe(CO)5 in premixed methane-air flames
CO þ OH ! CO2 þ H
ð10:39Þ
H þO2 ! OH þ O
ð10:40Þ
with the subsequent build-up of the radical pool, followed by fast reaction in the system. A similar mechanism exists if H2 is present rather than H2O. At an H2 content of 0.1 %, the moist reaction route accounts for about 70 % of the CO reaction. Indeed, for a premixed CO-air flame, the presence of only 2000 μL/L (ppmv) of H2 can increase the burning velocity by factor of two.
Flame Inhibition by Iron-Containing Compounds In early work with premixed CO-air flames, it was also found that trace contamination of the CO with iron pentacarbonyl strongly affected the reaction mechanism. It was found that iron in the high-pressure steel bottle containing the CO reacted with the CO to form Fe(CO)5, which had high enough vapor pressure to enter the reactant stream (at trace quantities) with the CO. Later work showed that the iron enters into catalytic gas-phase reactions which have a very strong inhibiting effect on the build-up in the radical pool. The inhibiting effect acts similarly for all hydrocarbon flames. Indeed, it has been found that iron compound concentrations as low as 1 μL/L can reduce the burning velocity of premixed hydrocarbon-air flames by 1 %. The mechanism is as follows. The Fe(CO)5 readily decomposes, via a sequence of steps, to form Fe and 5 CO: FeðCOÞ5 ! Fe þ 5CO:
+O FeO2
ð10:41Þ
This is followed by the formation of the inhibiting species FeO, Fe(OH)2, and FeOH via the sequence shown in Fig. 10.15: Once formed, the three reactions (forming a triangle on the right side of Fig. 10.15) enter into a gas-phase catalytic cycle: FeO þ H2 O ! FeðOHÞ2 FeðOHÞ2 þ H ! FeOH þ H2 O FeOH þ H ! FeO þ H2 ————————————— Net : H þH ! H2
(10.42) (10.43) (10.44)
which effectively recombines H atoms into H2, thereby greatly reducing the radical concentrations and essentially suppressing the flame propagation chemistry. (Recall that the radicals are typically present at super-equilibrium quantities, so the effect of reactions 10.42 to 10.44 is to drive the system to equilibrium more rapidly.) In the rate constant expression Equation 10.28, the activation energy (Ea/R) for these reactions is low (0 K, 302 K, and 604) K, and the pre-exponential factor A’ is high (1013.2 s1, 1014.3 s1, and 1012.1 s1), so these reactions proceed at nearly gas-kinetic rates: that is, as fast as the molecules can collide, they react. In fact, further analysis has shown that these reactions of iron in flames approach the ideal gas-phase catalytic radical recombination rate [11].
Flame Inhibition by Bromine-Containing Compounds Similar catalytic cycles are present for bromine added to hydrocarbon flames. For example, the
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G.T. Linteris and J.F. Griffiths
catalytic cycle of HBr in a methane-air flame can be represented by: H þHBr ¼ H2 þ Br H þBr2 ¼ HBr þ Br Br þBr þM ¼ Br2 þ M ————————————— Net : H þH ! H2
(10.45) (10.46) (10.47)
The net effect of adding HBr to a flame typically is to recombine H atoms into H2 (as in the iron mechanism above), and thereby reduce the overall reaction rate. It should be noted that in actual methane-flames, several regeneration steps for the inhibiting molecule HBr are also important, such as CH2O + Br∙ ¼ ∙HCO + HBr, and CH4 + Br∙ ¼ ∙CH3 + HBr. These reactions contribute to cycles like reactions 10.45 to 10.47; however, they are not so easy to outline in a concise list because there are many reactions involved in the consumption of other radicals, such as ∙CH3 and ∙HCO. This basic mechanism is believed to occur also during the action of other bromine-containing additives such as CF3Br (halon 1301).
Chemical Kinetic Models Overview A chemical kinetic model starts with a list of species and the reactions between them. The thermodynamic data for the species are required, as are the parameters for the specific reaction rate constants of all reactions. Either the forward or reverse reaction data are required, with the equilibrium relationship usually then providing the rate parameters for the counterpart reaction. The relevant reactions necessary for inclusion depend upon the environment, and the desired information. For example, a mixture of hydrocarbons and air would have a different chemical mechanism for understanding the atmospheric chemistry at 298 K as opposed to flame chemistry at 2000 K. In the former, only reactions prevalent at low temperature are important, whereas in the latter, high-temperature process are considered; the participating species can
be different. Of course, since the reactions are elementary, they should apply to both situations, and the two mechanisms could be combined into a larger, comprehensive unit. Nonetheless, the run time of a simulation depends on the size of the chemical mechanism, so it is usually desirable to minimize the number of species (i.e., the number of variables) and reactions in a model. Selecting the right chemical model, and its complexity, are an essential first step for understanding the chemical behavior of a system. Often, one will eliminate chemistry that is not important for the present problem. For example, while the chemistry for the formation of NOx is always occurring in high-temperature flames of hydrocarbons with air, the NOx species are relatively trace compounds, and have a minor effect on the development and overall energetics of flames. Hence, those reactions can be eliminated if the goal of a study is to understand a feature such as the rate of heat release, rather than pollutant (i.e., NOx) formation. In combustion, detailed chemical kinetic models are hierarchical: a mechanism for a larger reactant will contain the entire kinetic model of each of the smaller species which are present in the larger model. The simplest kinetic model is that of the H2/O2 system, and this is contained in all larger mechanisms; the H2/O2 kinetic model is followed in complexity by those for CO, CH2O, CH4, and C2H6. As a result, a mechanism for cetane (C16H34) can have 1200 species and more than 7000 reactions [6]. Usually, each of the smaller, simpler mechanisms is experimentally validated prior to development of the next most complex model, so the reaction sets are internally consistent. Because all the mechanisms are based on elementary rates, the mechanisms should be widely applicable. Unlike the example of NOx chemistry, the chemistry of smaller hydrocarbon species cannot be eliminated from kinetic models of larger species; rather, they are essential. Even for a kinetic model based on elementary rates, one still needs to exercise caution in its application. The species and reaction set of a mechanism are developed for a specific range of conditions (e.g., reactant composition and
10
Chemical Kinetics and Fire
stoichiometry, flame type, temperature range, etc.). It is incumbent upon the user to understand the conditions for which the mechanism was developed, and interpret if those conditions are close enough to the condition of interest for the mechanism to be useful. An example of this is the NIST chemical kinetic mechanism for hydrofluorocarbon (HFC) inhibition of hydrocarbon flames. The mechanism was developed based on the assumption that the flame inhibitors (for example C2HF5) would be added in small amounts (a few percent) to hydrocarbon-air flames. Recently, it has become of interest to understand the flammability of pure refrigerants with air, as well as the reaction of flame inhibitors at very high loading. For these conditions, additional species are likely to participate, and the mechanism will need to be extended. The important reaction pathways can sometimes be very similar for different fuels. As outlined by Warnatz [12], in combustion at high temperatures (i.e., near 2000 K), larger fuel molecules quickly break down to C1 and C2 species, and once these form, their decomposition pathways are similar for all hydrocarbon flames. Similarly, as outlined by Babushok and Tsang [13], the burning velocity of hydrocarbons tends to be controlled by a small set of reactions involving small decomposition products of the larger fuel molecules (and other common species such as O2). Also, the mechanism of flame inhibition of halogenated compounds also tends to be very similar for different hydrocarbon fuels [13]. The reactions which form and destroy the radical pool are similar, so the effect of the flame inhibitors (which act to reduce radical concentrations) are also related.
Databases There are many sources, both in publications and online, for thermodynamic data, elementary reaction rates, and comprehensive kinetic models. Some thermodynamic data can be found in [14] and [15], and reaction rate (and other) data in [6–8, 10].
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Role of Gas-Phase Kinetics in Some Fire Problems Understanding Standard Fire Tests Through Kinetic Modeling: The Cup Burner Test The cup burner method is a standard test [16] used for specifying the amount of fire suppressant to be used in full-scale applications. In this test, a small cup (28 mm dia) holds the liquid fuel, which is supplied to the burner so as to maintain the level of the fuel to the top edge of the cup. For gaseous fuels, a fine screen distributes the low velocity gas evenly over the exit nozzle of the burner. A chimney (10 cm diameter) holds the gaseous oxidizer, which is usually air mixed with fire suppressant. By increasing the volume fraction of the fire suppressant, its extinguishing concentration is determined as the volume fraction in air at which the flame is extinguished. As with any standard test method, there is always the question as to how the results obtained in small laboratory experiments corresponds to full-scale fires. Insight into this question can be gained by numerically modeling the test method, interpreting the controlling physics, and then comparing those with the parameters believed to be controlling at full scale. Since flame extinction is intimately connected with flame chemistry (and overall reaction rate) a good chemical kinetic description of the flame is necessary. It is possible to model cup-burner flames using direct numerical simulation, in which the momentum, energy, and species conservation equations are solved directly. Using available chemical kinetic mechanisms, the numerical calculation (2-D axi-symmetric) produces detailed information on the flame structure: i.e., the species concentrations, gas velocity and temperature, at all locations in the calculation domain, as a function of time. Using postprocessing techniques on the data to generate the reactive and diffusive flux of species, and heat transfer properties of the flame, great insight can be gained (for example, Ref. [17]).
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Fig. 10.16 Calculated species profiles at a height of 16 mm above a cup-burner flame of CH4 and air, with C2HF5 added to the air stream at a volume fraction of 9.3 % (From [17])
Figure 10.16 show the calculated flame structure for a cup-burner flame of methane, with C2HF5 added to the air stream at a volume fraction just below extinguishment (0.093). Results such as these have been used to answer such questions as: 1. Why do cup-burner flames always extinguish due to flame lift-off, rather than extinction elsewhere? 2. Does a particular fires suppressant work by thermal or chemical kinetic mechanisms? 3. Does a fire suppressant in the air stream add to the heat release in cup-burner flame? 4. Why are cup-burner flames in low gravity harder to extinguish than those in normal gravity? Analysis of cup-burner flames has shown that: 1. The flame is stabilized at the base, by a partially-premixed region which has a much higher reactivity than the rest of the flame. Addition of the fire suppressant to the air stream lowers the reactivity (either thermally or kinetically) at the flame base. The base can find a new stabilization point if it lifts off further: higher lift-off allows more time for mixing of the fuel and air streams, which leads to more
premixed character and a higher reactivity. At the extinguishment agent volume fraction, further lift-off does not sufficiently increase the reactivity to overcome the loss of reactivity caused by agent addition, and the premixed flame base cannot stabilize in the flow field. 2. Simulations have shown that essentially inert agents (such as CO2, N2, Ar, He, etc.) act by lowering the temperature at the flame base, reduce reaction rates there, and cause lift off (as described above). For other agents (such as CF3Br, Br2, CF3H, C2HF5, etc.) the peak temperature (as well as the temperature in the stabilization region) is actually increased with agent addition; hence, the mechanism cannot be thermal in origin. Further analysis has shown that chemical reactions at the flame base reduce radical concentrations more there than further up in the flame, causing flame extinguishment preferentially at the base. 3. By integrating the heat of reaction for all reactions over the entire calculation domain, it has been demonstrated that, for agent volume fractions just above that for extinguishment, CF3Br reduces the total heat release, whereas C2HF5 increases (i.e. nearly doubles) it.
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4. Fire safety in spacecraft requires an understanding of the behavior of flames in zero gravity (0-gn). Experiments and simulations have shown that despite 0-gn flames being much weaker, they require more fire suppressant for extinguishment. Simulations have explained this unexpected behavior. The normal-gravity (1-gn) flames have buoyancy-induced flicker, which causes the flame base to oscillate strongly. This creates a more difficult flow field for flame base stabilization, and causes the flame to blow off earlier than it would without the flame flicker. Hence, the better-stabilized 0-gn flames require more suppressant to lower the reaction rate at the base and cause blow-off. The significance of the work to understand the chemical kinetic behavior of laboratory flames goes beyond the goal of understanding standard test methods. Twenty years ago, such 2-D timedependent simulations with full chemistry were not possible, even for cup-burner flames; but today they are common. As computer speed, numerical methods, and chemical kinetic models all improve, it will not be long before such simulations with detailed chemistry are possible for the larger domains typical of fires. When that happens, the full potential of chemical kinetics for understanding fire problems will start to be realized—as has occurred in other areas of combustion.
8. H. Wang, Available Reaction Models, University of Southern California, Los Angeles, CA; http://ignis. usc.edu/Mechanisms/Model%20release.html, 2012. 9. F.L. Dryer, Kinetic Models, Princeton University, Princeton, NJ; http://www.princeton.edu/mae/people/ faculty/dryer/homepage/kinetic_models/, 2012. 10. J.A. Manion, R.E.L.R.D. Huie, D.R. Burgess, V.L. Orkin, Tsang, W.S. McGivern, V.S. Hudgens, V.D. Knyazev, D.B. Atkinson, E. Chai, A.M. Tereza, C.-Y. Lin, T.C. Allison, W.G. Mallard, F. Westley, J.T. Herron, R.F. Hampson, D.H. Frizzell, NIST Chemical Kinetics Database, NIST Standard Reference Database 17, Version 7.0 (Web Version), Release 1.4.3, Data Version 2008.12, National Institute of Standards and Technology, 2012. 11. V.I. Babushok, W. Tsang, G.T. Linteris, D. Reinelt, Combust. Flame 115 (1998) 551–560. 12. J. Warnatz, Pure and Applied Chemistry 72 (2000) 2101–2110. 13. V.I. Babushok, W. Tsang, Combust. Flame 123 (2000) 488–506. 14. A. Burcat, B. Ruscic, Third Millennium Ideal Gas and Condensed Phase Thermochemical Database for Combustion With Updates From Active Thermochemical Tables, ANL-05/20 and TAE 960 Technion-IIT; ftp://ftp.technion.ac.il/pub/supported/ aetdd/thermodynamics/BURCAT.THR, Argonne National Laboratory, 2012. 15. in: P.J. Linstrom, W.G. Mallard (Eds.), NIST Chemistry WebBook, NIST Standard Reference Database Number 69, National Institute of Standards and Technology, Gaithersburg MD, 20899 (http://webbook. nist.gov), 2001. 16. NFPA 2001 Standard on Clean Agent Fire Extinguishing Systems 2008 Edition, NFPA, 2007. 17. F. Takahashi, G.T. Linteris, V.R. Katta, O. Meier, Proc. Combust. Inst. 34 (2012) 2707–2717.
References
Gregory T. Linteris is a mechanical engineer in the Flammability Reduction Group of the Fire Research Division of the Engineering Laboratory at the National Institute of Standards and Technology. Dr. Linteris is a project leader for research on material flammability in the Flammability Reduction Group. He also conducts research to understand the detailed mechanisms of chemically acting fire suppressants. In 1997, Dr. Linteris served as a payload specialist astronaut on two NASA space shuttle missions, conducting microgravity combustion, fluid mechanics and material science experiments while in earth orbit for 20 days.
1. S. Benson, The Foundations of Chemical Kinetics, McGraw-Hill, New York, 1960. 2. J. Warnatz, U. Maas, R.W. Dibble, Combustion, Springer-Verlag, Berlin, 2010. 3. S.R. Turns, An Introduction to Combustion, McGrawHill, Boston, 2000. 4. I. Glassman, Combustion, Academic Press, San Diego, CA, 1996. 5. J. Warnatz, in: W.C. Gardiner (Ed.), Combustion Chemistry, Springer-Verlag, New York, 1984. 6. C.K. Westbrook, Pitts, LLNL Chemical Kinetic Mechanisms for Combustion, https://www-pls.llnl. gov/?url ¼ science_and_technology-chemistry-com bustion-mechanisms, Lawrence Livermore National Laboratory, 2012. 7. C.K. Law, Law Combustion Group: Chemical Kinetic Database, Princeton University, Princeton, NJ, http:// www.princeton.edu/~cklaw/kinetics/, 2012.
John F. Griffiths is emeritus professor of combustion chemistry at the University of Leeds in the United Kingdom. His main research interest is the gas-phase combustion of hydrocarbons, which is related both to combustion hazards which may arise from spontaneous ignition processes in the chemical industry and to the efficiency of reciprocating engines.
Diffusion Flames
11
Ali S. Rangwala
Fires involve reactants, usually fuel and air, not intimately mixed at a molecular level before combustion. Usually, the fuel is in the solid or liquid state so transfer of material across a phase boundary (phase change) must also occur. The vaporized fuel must combine with oxygen from air to form a flammable mixture, which when ignited forms the flame zone. In most fire problems, this mixing of fuel vapor and oxygen takes place mostly by diffusion and takes orders of magnitude longer time compared with that of a chemical reaction. Therefore, diffusion of species is the primary controlling process during such burning behavior. A fundamental understanding of diffusion flames then involves exploring the mechanisms associated with the transport of the reactants and the resulting flame structure. In Fire Protection Engineering, diffusion flame theory is used in calculating flame-length, flamelocation, and rates of burning. The flame-length, is used for hazard analysis as it provides information to estimate the heat transfer to surrounding surfaces. Knowledge of flame location is necessary for suppression, and finally, the rate of burning provides an estimate of the “size” of the fire and in combination with the heat of combustion is used to calculate the heat release rate.
A.S. Rangwala (*) Associate Professor, Department of Fire Protection Engineering, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609-2280
The Diffusion Coefficient Diffusion is the phenomena of migration of mass. The mass can be in the form of atoms, molecules, ions, or other particles because of spatial gradient of some quantity (concentration, temperature, pressure etc.). Similar to conduction heat transfer (Fourier’s law) and momentum transfer (Newton’s law), mass transfer is governed by a law called as Fick’s law of diffusion. In a simplified context, Fick’s law of diffusion describes the movement of one chemical species A through a binary mixture of A and B because of concentration gradient of A. In most fire problems A is usually fuel vapor, oxidizer or products of combustion, while B represents air. To explain this further, let us consider the example of a candle flame shown in Fig. 11.1. The paraffin of the candle melts because of heat from the flame; it travels by capillary forces through the wick where it then evaporates to become paraffin vapor, a gaseous fuel. Let F represent fuel vapor, O represent oxygen and P represent products. Fuel vapor will issue out of the wick because of the heat received from the flame. If one traverses along the path X-X’ (shown by dashed red line in Fig. 11.1) the concentration of fuel vapor is highest at the wick and reduces until it reaches a concentration most suitable for chemical reaction with oxygen at X’. The concentrations of the various species involved, can be given by the mass fractions, YF, YO and YP, where YF denotes the mass of fuel vapor divided by the total mass of
M.J. Hurley (ed.), SFPE Handbook of Fire Protection Engineering, DOI 10.1007/978-1-4939-2565-0_11, # Society of Fire Protection Engineers 2016
350
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Fig. 11.1 The candle flame
gas-mixture in a given volume and the subscripts O and P denote oxidizer and products, respectively. Initially the mass fraction of F at the wick is 1 at the wick and zero just outside the wick, and this gradient drives the fuel vapor out of the wick. On approaching the flame zone, the mass fractions of the fuel and oxidizer should be such that a stoichiometric mixture should be formed. Now, Fick’s law states that the mass transport of fuel vapor along XX’ due to mass diffusion can be described by: J F ¼ ρDFA
Y F, X Y F, X0 : XX0
ð11:1Þ
JF is the mass flow rate of fuel vapor per unit area (or mass flux) and is proportional to the mass fraction difference divided by the distance from the wick to the flame (XX’). ρ is the density of the gas-mixture system and DFA is a proportionality factor called as the binary mass diffusivity of fuel vapor with respect to air. In differential form, Equation 11.1 can be written as: J F ¼ ρDFA
dY F : dx
ð11:2Þ
The negative sign denotes that the mass fraction of fuel vapor will decrease as one moves along
XX’, represented as x-direction. This is logical because the fuel vapor originates at the wick (location X). Equation 11.2 is also called the Ficks law of diffusion and forms the starting point of our discussion on diffusion flames. Note that similar relationships can be written for oxygen (diffusing towards the flame) and products of combustion (diffusing on either side of the flame). Table 11.1 gives the binary diffusion coefficients D for many common gases. Values refer to atmospheric pressure. The first part of the table gives data for several gases in the presence of a large excess of air. The mass diffusivity D, is an important transport property such as thermal diffusivity α and momentum diffusivity (kinematic viscosity) υ, and all three have dimensions of (length)2/time. The ratios of these quantities, taken as a pair, form three important nondimensional numbers that play a prominent role in analyzing most fire problems. They are Prandtl number, Pr ¼ υ/α, Schmidt number, Sc ¼ υ/D and Lewis number, Le ¼ α/D. Equation 11.2 assumes that the driving force for diffusion is concentration gradient. However, it has been observed, as well as predicted by the kinetic theory of gases, that mass diffusion can occur in the presence of a temperature gradient and pressure gradient. Further, the value of the binary
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Table 11.1 Diffusion coefficients of common gases at 0 C, 760 mmHg. Assuming ideal gas behavior, D can be calculated for other pressures and temperatures using the relation D / P1 T 3=2 Gas-pair O2—air CO2—air H2—air H2O—air Methane (CH4)—air Ethane (C2H6)—air Propane (C4H10)—air Butane (C3H8)—air Pentane (C5H12)—air n-Octane (C8H18)—air Benzene (C6H6)—air Toluene (C7H8)—air Napthalene (C10H8)—air Anthracen (C14H10)—air Methyl alcohol (CH3OH)—air Ethyl alcohol (C2H5OH)—air
D (cm2/s) 0.178 0.138 0.611 0.220 0.196 0.108 0.0878 0.0750 0.0671 0.0505 0.077 0.051 0.0513 0.0421 0.1325 0.102
mass diffusivity itself depends on temperature and pressure (D P1T3/2). The diffusion coefficient of common gas-mixtures at various temperatures and pressures can be obtained using this equation in combination with values listed in Table 11.1. However, this effect is usually neglected in fire problems. Further details on the subject can be found in Ref. [1].
Structure of Diffusion Flame The zoomed inset of the part of the flame zone in Fig. 11.1 shows an illustrative sketch of the structure of a diffusion flame. It consists of a flame separating a fuel-rich zone and an oxidizer-rich zone. The flame or reaction zone incorporates the location of the maximum temperature. For example, for a methane-air flame, this temperature is experimentally observed to be around 1950 K [2]. As shown in Fig. 11.1, fuel and oxidizer both almost disappear in the flame zone, although there is some fuel and oxidizer leakage outside the designated flame zone as
shown by the dashed lines. Products of combustion and heat diffuse outwards from the flame zone to both the sides. One of the characteristics of typical hydrocarbon diffusion flames is their yellowness, especially when the fuel can emit soot, and it’s appearance can be explained using Fig. 11.2 [3]. The reaction zone usually has a blue emission, especially when the fuel and oxidizer have been mixed in proper proportions. This is mainly due to radiation due to excited CH radicals. The reddish glow arises from radiation from CO2 and water vapor radiation. Most importantly, the intense yellow radiation which is a characteristic of most fires is due to the presence of carbon particles or soot. Figure 11.2a illustrates a simplified illustrative sketch of three prominent zones in a diffusion flame. Note that emphasis is given to the fuel side. The cracking zone is a region on the fuel side of the reaction zone before the soot formation zone. This where the molecules crack and polymerize forming lighter fuel molecules which chemically react with the oxygen in the reaction zone and rest convert to carbonaceous and tarry substances in a soot formation zone that exists just before the reaction zone. Soot generally forms as particles with diameters of the order of several nanometers by a process called as inception or nucleation. These particles then undergo surface growth. One mechanisms attributed to the surface growth is called as the Hydrogen Abstraction by C2H2 Addition (HACA) mechanism [6] where H-atoms impacting on the soot surface activate acetylene addition thereby increasing the mass of soot particles. The process of nucleation occurs concurrently with coagulation, where small particles coalesce to form larger primary particles, and agglomerations where multiple primary particles line up end-to-end to form larger structures resembling a string of pearls as shown in Fig. 11.2b [5]. When the soot particles pass through the flame front they oxidize whereby the mass of soot is decreased by heterogeneous surface reactions between soot particles and oxidizing species. Incandescent soot results in the
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Fig. 11.2 (a) Zones in a diffusion flame [4] (b) soot particle observed under a scanning electron microscope—resemblance to string of pearls [5]
Fig. 11.3 Upward propagating flame on a PMMA surface
characteristic yellow-color of most hydrocarbon diffusion flames. The processes leading to cracking and soot formation are dependent on fuel type and ambient conditions and form an important research topic in fire safety [7–9]. This is mainly because most of the flame radiation from fires originates from soot particles. The luminous radiation from soot often makes it difficult to observe the blue emission from the reaction zone. The blue radiation is observable for small flames (less than 15 cm) as shown in Fig. 11.3 where the initial stages of a wall fire (PMMA, 1.2 cm thick, 5 cm wide, 50 cm long) are shown. The size of the soot particles depends on the time allowed for their
growth, the fuel composition and temperature of the flame zone. Since time increases with linear dimensions longer flames are usually yellower, smokier than shorter flames, indicating the escaping of the soot particles out of the flame zone. Large carbon particles will radiate more heat as shown in Fig. 11.3 [10]. A laminar natural convection flame is blue at the base, yellow in the center and red/orange at the tip. The latter condition means that so much heat has been lost by radiation from the carbon particles, that when it does cross the reaction zone into a region where oxygen is available for combustion, it is too cold to burn. The result is emission of smoke.
354
A useful material-property called smokepoint of a fuel can be defined based on this radiative heat loss mechanism by soot. A fuels smoke point is the maximum height of its laminar flame (or fuel mass flow rate) burning in air at which soot is just released from the flame tip. Another definition (and more applicable to fire safety) is the heat release rate at which smoke just begins to be released from the flame tip. Smoke point is a simplified ranking scheme for soot production and was first introduced by Kent and Wagner [11]. Smoke-point can be easily determined for gases and vapors by adjusting the flow rate of the fuel from a simple burner. For liquid fuels a wick-fed lamp (ASTM D1322) is used. Determining the smoke point for solid fuels is difficult, although some progress has been made in this direction by de Ris and Cheng [12]. It has been shown [12–14] that smoke point can provide a convenient measure of the flame radiant fraction. A comprehensive review on the development of an engineering model capable of predicting the release of soot and radiation given the smoke point of the fuel, stoichiometric mass ratio of the reactants and the adiabatic stoichiometric flame temperature is discussed by Lautenberger [15].
Diffusion Flame Theory The theory of diffusion flames consists of an analysis of factors controlling the mixing of fuel and oxidizer. Main factors controlling the mixing are mass diffusivity (D), gradient of species mass fraction (dY/dn) normal to the condensed fuel surface and the flow field. Unlike premixed flame analysis, the rates of the reaction mechanisms do not dominate the burning behavior in diffusion flames. As discussed earlier, in diffusion flames, fuel and oxidizer come together in a reaction zone through diffusion. This diffusion can be just molecular transport (candle flame, laboratory flames) or be enhanced several times by convection, which may be even turbulent (most large-scale fires such as pool, building, forest etc.) The theoretical solution of
A.S. Rangwala
the diffusion flame is best approached by considering a candle flame once again. Focus on a control volume in the gas phase as shown by the dashed boxed. The fuel vapor and oxidizer diffuse from opposite directions and approach the flame in a normal direction (Fig. 11.1, LHS). The concentrations of fuel and oxidizer at the flame are in stoichiometric proportion. In other words, the diffusion flame surface is defined as the locus of all points in space where the fuel and oxygen meet at stoichiometric proportions. A one-step chemical reaction given by Equation 11.3 can be used to represent the overall chemical process. 1 g½FUEL þ s g½OXIDIZER ! ð1 þ sÞ g½PRODUCTS þ Heat
ð11:3Þ
The assumption made here is that the net disappearance rate of the reactants (fuel and oxidizer) is infinitely fast. This is represented by the zoomed inset in Fig. 11.1, where solid lines are used to indicate the profiles of temperature and mass fractions of the reactants. The flame zone is infinitesimally thin, and both fuel and oxygen are consumed at this “zero-thickness” flame sheet. However, in the actual scenario, the assumption of infinitely fast reaction is not true as indicated by the profiles in dashed lines in the flame structure inset in Fig. 11.1, where the flame zone has finite thickness and both the oxygen and the fuel leak through this flame zone. The details of flame broadening are beyond the scope of this chapter. However, an interested reader may refer to a book related to the topic [16]. For our purposes, the infinite rate chemistry assumption is sufficient in predicting parameters such as the mean flame zone location and mass burning rate. The one-step and infinitely fast reaction 000
assumptions also imply that ω_ F ¼ 000
000
ω_ O s
¼
000
ω_ P 1þs ,
denotes the nonlinear rate term where ω_ representing the rate of formation or destruction of a species per unit volume. Subscripts F, O and P, denote fuel, oxidizer and products, respectively. The conservation equations for the control volume are given by:
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Species Conservation
ρ
∂Y F ∂Y F ∂ ∂Y F 000 þ ρui ¼ ρD ω_ F ; ð11:9Þ ∂xi ∂t ∂xi ∂xi
Assumption: binary diffusion coefficients are equal for all species.
ρ
∂½Y P =ð1 þ sÞ ∂ ½ Y P =ð 1 þ s Þ þ ρui ∂t ∂xi
ρ
∂Y O ∂Y O ∂ ∂Y O 000 þ ρui ¼ ρD ω_ O ; ð11:4Þ ∂xi ∂t ∂xi ∂xi
ρ
∂Y F ∂Y F ∂ ∂Y F 000 þ ρui ¼ ρD ω_ F ; ð11:5Þ ∂xi ∂t ∂xi ∂xi
ρ
∂Y P ∂Y P ∂ ∂Y P 000 þ ρui ¼ ρD þ ω_ P : ð11:6Þ ∂xi ∂t ∂xi ∂xi
000
¼
∂T ∂T ∂ ∂T λ þ ρui cp ¼ ∂t ∂xi ∂xi ∂xi " # 000 000 ω_ O ΔH c ω_ P ΔHc 000 : ð11:7Þ or þ ω_ F ΔH c or s 1þs
In the above equations, ρ represents the gas phase density, cp represents the specific heat and λ equals the thermal conductivity. ΔHc represents the heat of combustion of the fuel and D equals the diffusion coefficient which is assumed to be the same for oxygen—air, fuel—air and product—air 000 The nonlinear rate terms ( ω_ ) can be eliminated from the equations by suitable subtractions and assuming that the Lewis number is unity Le ¼ ρcλp D ¼ 1 . Multiply Equation 11.4 by 1s , c
1 Equation 11.6 by 1þs and Equation 11.7 by ΔHp c to get the modified conservation equations.
ð11:10Þ
Modified Energy Conservation Equation ∂ Tcp =ΔH c ∂ Tcp =ΔH c þ ρui ρ ∂t ∂xi ∂ λ ∂ Tcp =ΔH c 000 ¼ þ ω_ F : ∂xi cp ∂xi
Energy Conservation ρcp
∂ ∂½Y P =ð1 þ sÞ ω_ ρD þ P : ∂xi ∂xi 1þs
ð11:11Þ
Equations 11.8, 11.9, 11.10, and 11.11 can be combined into a single equation given by LðβÞ ¼ 0;
ð11:12Þ
where β can take several values as shown in Table 11.2 and the operator L is expressed as, LðβÞ ρ
∂β ∂β ∂ ∂β þ ρui ρD : ð11:13Þ ∂t ∂xi ∂xi ∂xi
In the operator L, the first term represents the accumulation of thermal energy or chemical species, the second term represents the convection efflux thorough the control surfaces and the third represents the diffusion efflux. The non-linear volumetric reactive effects are eliminated using Table 11.2 Different forms of the coupling function b introduced in Equation 11.12
Modified Species Conservation Equations ∂ðY O =sÞ ∂ðY O =sÞ þ ρui ρ ∂t ∂xi 000
¼
∂ ∂ðY O =sÞ ω_ O ; ρD ∂xi ∂xi s
ð11:8Þ
β βFO
Y F YsO
βFP
YP Y F þ 1þs
βFT
Y F þ ΔHpc
βOP
YP Y O þ 1þs
βOT
Y O þ ΔHpc
βPT
Y P þ ΔHpc
Value
Tc
Tc
Tc
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A.S. Rangwala
Fig. 11.4 The onedimensional diffusion flame mathematical model
the coupling function β, which can take 6 forms as shown in Table 11.2. This methodology is referred to as the Shvab-Zeldovich transformation after two classical papers by Shvab [17] and Zeldovich [18] that first used the coupling function. Note that although Shvab-Zeldovich proposed a general solution, the original idea was first proposed by Burke-Schumann [19] in 1928. Equation 11.12 can be solved with knowledge of initial and boundary conditions. However, this is not an easy task! For example, the convective term is also non-linear unless the velocity is constant. Further, many added assumptions such as constant, ρD, steady state ( ∂β ¼ 0), ∂t one-dimensional system, constant pressure and low speed flow are required before analytical solutions to some problems can be obtained. Nevertheless the coupling function β is a powerful tool that is used extensively in diffusion flame problems. One example is considered below.
apparent, then, that each accidental flame is dependent on the details of the environment in which it burns. Thus the possible variations in behavior are endless. The one-dimensional flame structure discussed earlier will be used once again to describe the problem. A further set of assumptions will be imposed to simplify the math and facilitate physical understanding.
Assumptions 1. The oxidizer enters the system at x ¼ 0 with a temperature Ti, a concentration of YO,i and a velocity of u ¼ U which is a constant. 2. The fuel enters the system at x ¼ 1 with a temperature Ti, a concentration of YF,i and a velocity of u ¼ U Fig. 11.4. 3. The reaction occurs at x ¼ xf in a zone with thickness, ε ! 0: 4. All reactants are consumed at the reaction x < x f YF ¼ 0 zone so for: x > x f YO ¼ 0
Diffusion Flame Location The diffusion flame surface is defined as the locus of all points in space where the fuel and oxygen meet at stoichiometric proportions. The position of the flame front of a diffusion flame is dependent on the surrounding geometry and the flow rates of the various gas streams. It is
Conservation Equations Since the flow field is assumed to be known and constant (u ¼ U), there is no need to solve the overall mass and momentum conservation equations. Thus,
11
Diffusion Flames
357
Species Conservation 2 000 d ðY O =sÞ d ðY O =sÞ ω_ F ð11:14Þ ¼ þD U dx dx2 sρ
dY F U dx
2 000 d YF ω_ F þD ¼ ρ dx2
ð11:15Þ
Energy conservation u
000 d T= ΔH c =c p d2 T= ΔH c =cp ω_ ¼ F þα dx dx2 ρ
! ;
ð11:16Þ where α ¼ ρcλ p represents the thermal diffusivity. Boundary Conditions x¼0
T ¼ Ti
Y O ¼ Y O, i
YF ¼ 0
x¼1
T ¼ Ti
YO ¼ 0
Y F ¼ Y F, i ð11:17Þ
The conservation equations are coupled using Equation 11.12. Note that with the steady, 1-D system discussed in the example, the L operator
As shown above, the coupling function or the Shvab-Zedovich transformation eliminates the nonlinear reaction rate terms from the conservation equations. We are still left with 6 boundary conditions for the three linear equations that can be obtained with βOF, βOT and βFT. We can further decrease the difficulty in the solution procedure without altering the nature of the solution by replacing β with a new normalized varið0Þ able, Z ¼ ββðð1xÞβ Þβð0Þ ; which is called as a mixture
fraction. Note that β (0) and β (1) are constants obtained from the boundary conditions. Since the boundary conditions for the variable Z at the boundaries x ¼ 0 and x ¼ 1 are Z ¼ 0 and Z ¼ 1, respectively, irrespective of the β-variable that defines Z, the solution is unique and we need to obtain the solution to one mixture fraction equation only. This simple algebraic manipulation allows us to obtain a single differential equation with normalized boundary conditions given by: 2 dZ d Z U ¼α dx dx2
where
ð11:20Þ
d β reduces to LðβÞ ρU dβ dx ρD dx2 : This gives, 2
2 dβ d β U ¼α : dx dx2
The solution to this differential equation is ð11:18Þ
Three β-variables will be selected such that the values of temperature and mass fractions of fuel and oxygen (three variables obtained by solving three equations) can be evaluated later. The choices are βOF, βOT and βFT. The variables and the boundary conditions are listed below: βOF ¼
YO YF s
and
βOT ¼
Y O Tcp þ s ΔH c
and
Tcp ΔHc
and
βFT ¼ Y F þ
Y O, i s βOF ¼ Y F, i Y O, i Tcp þ βOT ¼ s ΔHc Tcp βOT ¼ ΔHc Tcp βFT ¼ ΔHc Tcp βFT ¼ Y F, i þ ΔH c
x ¼ 0, βOF ¼ x ¼ 1, x ¼ 0, x ¼ 1, x ¼ 0, x ¼ 1,
x¼0!Z¼0 x¼1!Z¼1
ð11:19Þ
ex=δ 1 Z ¼ 1=δ ð e 1Þ
where
δ¼
α U
ð11:21Þ Going back to the dimensional values (oxygen concentration, fuel concentration and temperature) requires the determination of the flame location. Based on the assumption that the flame will place itself where fuel and oxidizer arrive in stoichiometric proportions, the flame location can be expressed by: β x f ¼ YsO Y F ¼ 0. Substituting the appropriate expression for Ζ(x) in terms of β and evaluating x=δ Y O, i Y O, i e 1 þ Y F, i βOF ðxÞ ¼ ; s s e1=δ 1 ð11:22Þ
358
A.S. Rangwala
the flame location, xf, is obtained as 2
3 1=δ e 1 Y O, i þ 15 : x f ¼ δ Ln4 s Y O , i þ Y F, i
ð11:23Þ
s
Finally, assuming there is no oxidizer in the fuel zone and no fuel in the oxidizer zone the fuel and oxygen concentrations can be defined as: x < x f Y O ¼ sβOF ðxÞ x > x f YO ¼ 0
and and
YF ¼ 0 Y F ¼ βOF ðxÞ ð11:24Þ
A similar method can be followed when determining the temperature distribution, from f2 for x < xf and f3 for x > xf. This is explained in the worked example. There are several advantages in introducing the mixture fraction. The mixture fraction (Z) should satisfy the balance equation LðZÞ ρ
∂Z ∂Z ∂ ∂Z þ ρui ρD ¼ 0; ∂t ∂xi ∂xi ∂xi ð11:25Þ
based on the definition of the operator L of Equation 11.10. The boundary condition equation is Z ¼ 1 in the fuel stream and Z ¼ 0 in the oxidizer stream. This equation converts all the Shvab-Zeldovich variables (β) into a single parameter. Equation 11.25 greatly simplifies the modeling of diffusion flames. Note that there is no source term in Equation 11.25.
Comments on the Formulation and Analysis It is important to reiterate the assumptions used in working out the solution discussed earlier. 1. One-step and infinitely fast reaction, 2. Lewis number ¼ 1, 3. Binary diffusion coefficients are equal for all species, 4. ρD ¼ constant, 5. Velocity (U) is constant, 6. Steady state, 7. One-dimensional, and 8. Constant specific heat, thermal diffusivity and density. Assumptions 1, 2 and 3 are necessary for implementing the Shvab-
Zeldovich transformation. This is because Z couples the transport of heat and species into a single variable. In some cases, heat and different species may have different diffusivities and therefore can be transported at different rates. Consequently, β and Z are no longer conserved. However, by making the equal diffusivity and Le ¼ 1 assumption, we are requiring that these diffusive fluxes are transported at the same rate and hence preserving the conserved nature of Z. Assumption 4 is used in most fire problems, however, can be relaxed. Assumptions 5–8 were used to solve our specific example of a one-dimensional flame. Of these 5 can be most questionable. This is because the flow-field plays a significant role in diffusion problems. An exact representation of the flow-field can be obtained by solving the overall mass and momentum conservation or the Navier–Stokes equations, which require proper pressure–velocity coupling since most fires are incompressible in nature. Assumption 6 is reasonable mainly because of the slow regression rates observed for most condensed fuels. Assumption 7 facilitated an analytical solution. Assumption 8 is reasonable so long as the properties are chosen correctly. The correct choice of properties is hugely important in all problems of this nature. This is further discussed below.
Property Estimation Most theoretical and empirical expressions to solve fire problems usually rely on the assumption of constant thermophysical properties. An important issue in using these expressions in practice therefore necessitates a proper method to evaluate the thermophysical properties such that results obtained through them match with experimental data. A first step in property estimation is obtaining certain average temperature. For a diffusion flame, the temperature can vary from a few hundred degrees at the fuel side to around 1500–2000 K at the flame zone. Surrounding temperature can also be of the order of a few tens to a few hundred degrees based on the problem. Composition of the gas mixture within this range varies from a pure fuel vapor near the interface to pure air in the far field.
11
Diffusion Flames
Within this range, there exists many gas species formed because of thermal cracking of the fuel vapor as well as combustion products such as CO2, CO and H2O. Therefore the process of arriving at an “average” mixture property based on specific mixture composition and average temperature is a nontrivial issue. This problem of an average gas-composition at an average temperature whose properties can be used for correlations with constant property assumptions has been investigated by several researchers (c.f. Rangwala et al. [20] for a list of references related to the topic). The main method reported in most combustion textbooks is by Law and Williams [21] and employs flame, ambient (or surrounding) and interface temperature to arrive at an average temperature. The average mixture composition is calculated using some proportions of fuel and air. The disadvantage of using the Law and Williams [21] scheme in fire problems is the need to know the fuel-vapor composition which is difficult to evaluate for complex materials usually involved. A much simpler scheme using only properties of air was recently developed by Rangwala et al. [20]. The scheme has been tested in several diffusion controlled problems involving burning behavior of both gaseous liquid and solid fuels. The scheme considers forced convection and variable oxygen concentration. This scheme is simpler to use and recommended for fire problems. In this scheme, the average thermal conductivity is estimated as the thermal conductivity of air calculated at a temperature given as one third the sum of ambient and the adiabatic flame temperature. The gas phase specific heat is estimated as the specific heat of air at adiabatic flame temperature. Adiabatic flame temperatures for several fuels are tabulated in standard fire dynamics textbooks [22, 23].
359
Ethane and 20 % nitrogen as fuel (all percentages are in volume) do the following: (1) Plot the mixture fraction as a function of “x”. (2) Find the flame location (xF). (3) Plot the fuel and oxygen concentrations as a function of “x”. (4) Plot the temperature as a function of “x”. Solve for two situations of U ¼ 1 mm/s and U ¼ 0.1 mm/s and U ¼ 1 mm/s. Comment on what is the meaning of the “characteristic length scale δ” and what is the effect of U on δ, the flame location and the flame temperature. Assume thermal properties as those of air at 1000 K.
Part 1: Mixture Fraction x
A plot of Z ðxÞ ¼ e1δ 1 is shown in Fig. 11.5. eδ 1
The value for delta ( δ ¼ Uα ) based on U of 1 mm/s equals 0.168 m. It is assumed that the thermal diffusivity is that of air at 1000 K (α ¼ 168 106 m2 =s).
Part 2: Flame Location The flame is located at the position where βOF ¼ YO s Y F ¼ 0: This corresponds to a stoichiometric mixture. The flame location can be found using Equation 11.23. Based on the problem 0:2230 statement, Y O, i ¼ 0:2232þ0:7828 ¼ 0:244 and Y F, i 0:830 ¼ 0:830þ0:228 ¼ 0:811; where, the molecular weight of ethane is 30 g/mol. s ¼ YYFo is stoic
Solved Example On a geometrical configuration identical to that of the one-dimensional non-viscous problem presented earlier, a mixture of 22 % oxygen and 78 % nitrogen as oxidizer and a mixture 80 %
Fig. 11.5 Mixture fraction (Z) vs. x
360
A.S. Rangwala
Fig. 11.6 Profiles of oxygen, fuel and temperature
obtained assuming a one step overall reaction of ethane reacting with oxygen C2 H6 þ 72O2 ! 2CO2 þ 3H 2 O and equals s ¼ 112 30 ¼ 3:73. Substituting these values in Equation 11.23 gives, 1 1 e0:168 1 þ 1A ¼ 0:57: x f ¼ 0:168 ln@ 0:811 þ 0:244 3:73 0
0:244 3:73
The location of the flame is shown in Fig. 11.6. It occurs at a location where the concentration of fuel (YF) and oxidizer (YO) are zero. Note that since the chemical reaction is assumed to be infinitely fast, there is no fuel or oxidizer leakage on either side of the flame. Further, the flame location occurs at the location of maximum temperature.
Profiles of fuel, oxidizer and temperature are evaluated in Part 3 and 4 discussed next.
Part 3 and 4: Profiles of Oxygen, Fuel and Temperature First assume that there is no oxygen in the fuel zone and no fuel in the oxidizer zone. Use f1 to find the fuel and oxygen mass fractions. x < x f Y o ¼ ϕ f 1 ðxÞ and Y f ¼ 0 x > x f Y o ¼ 0 and Y f ¼ f 1 ðxÞ Since the oxygen and fuel mass fractions are known, the temperature can be plotted using f2 or f3.
! Ti Ti Ti þ f 3 ðxÞ ¼ ΨðxÞð f 3 ð1Þ f 3 ð0ÞÞ þ f 3 ð0Þ ¼ 1 Y f,i þ ΔH c =cp ΔHc =cp ΔH c =cp eδ 1 ! ! exδ 1 Ti Ti Ti þ Y f ðxÞ T ðxÞ ¼ ΔH c =cp Y f,i þ 1 δ ΔH =c ΔH =c ΔH e 1 c p c p c =cp
x
eδ 1
The specific heat, cp ¼ 1:14gJ @ 1000K and the heat of combustion is equal to ΔH c ¼ The temperature profile is shown in Fig. 11.6.
47500 gJ .
The characteristic length scale δ represents the ratio of the mass diffusion to the velocity of the gas stream. This characteristic distance
11
Diffusion Flames
represents the extent that heat mass is diffusing against the gas flow into the gas stream.
361
Mass Burning Rate 00
Final Note The example discussed uses constant surface boundary conditions at fuel and oxidizer side. For the case of condensed fuels at the interface between fuel and air, specifying a constant mass fraction for the species as the boundary condition at the interface provides great simplicity in formulating an analytical solution. However, determining an approximate value of YF,x ¼ surface, the fuel mass fraction at the interface, is complicated as it involves solving a heat and mass balance at the fuel surface [24]. Further complication is that typically the species concentrations are discontinuous at the interface between two materials, whereas temperature is continuous. To take an example, consider a heptane pool fire. If we are interested in determining the rate at which heptane vapor is transferred to the gas-phase, we would need to specify the vapor concentration of heptane in the gas-phase side of the heptane-air interface. The mass fraction of heptane inside the pool is unity (neglecting the small amount of oxygen or nitrogen dissolved in heptane). However, it would be incorrect to assume YF,x ¼ surface ¼ 1 for the gas-phase mass fraction of heptane vapor at the interface. This value primarily depends on the interface temperature besides the pressure. Interface temperature is determined by the heat balance analysis between gas-phase to interface. The conditions at the interface are based on relationships that are theory-based or deduced from experiments. An additional nondimensional number called as B-number arises during the solution of establishing the mass fraction of fuel vapor at the interface. The B-number is an important derived property, which is dependent on the thermo-physical properties of the system, that provides an expression for the mass burning rate eventually. This leads us to the next section which discusses an important parameter usually used to quantifying the fire-hazard associated with a given material—its mass burning rate as a function of time.
The mass burning rate per unit area (m_ ) or mass burning flux is an important parameter to quantify the hazard associated with fire. As mentioned earlier, this mass flux varies with B-number [3], which accounts for the thermodynamic effects, and the Nusselt number to account for the gas-phase convective effects. A general relationship will be derived in this section to account for a variety of physical flow conditions. In fire problems, the fuel is usually a solid or liquid burning in free convective conditions. The fuel vaporizes first, then diffuses toward the oxygen from the ambient. To solve such problems one needs to have information on the velocity, temperature and mass fraction profiles. The solution can be initiated by writing down a heat balance at the surface of the burning fuel, 00
00
m_ L ¼ q_ ;
ð11:26Þ
where L represents the latent heat of vaporization (for a liquid) or the heat of gasification (for a 00 solid). q_ is the net heat flux to the surface and depends on the nature of the flow field and boundary conditions (free stream temperature, ambient oxygen concentration etc.). It also 00 depends on m_ , an effect called as the “blocking effect [22].” If the net heat flux to the surface increases, then logically mass flux or mass loss rate per unit area will also increase. This causes the boundary layer to thicken causing reduction in gradients. The burning rate therefore does not increase linearly with external heat flux and to develop a general solution requires generalization of the heat flux to the fuel. It can be assumed that the heat flux to the surface is a product of the heat transfer coefficient (h) and temperature difference between the flame and the surface. If the flame temperature is denoted by Tf and surface temperature by Ts the mass loss rate per unit area can be represented as: 00
m_ ¼
00 h T f Ts h q_ ¼B ; ¼ cp L L
ð11:27Þ
362
A.S. Rangwala
Table 11.3 B-number values for different fuels [25] Solids Polypropylene Polyethylene Polystyrene Nylon 6/6 Polycarbonate PMMA PVC Fir wood α-cellulose Polyoxymethylene
Formula C3H6 C2H4 C8H8 C12H22N2O2 C6H14O3 C5H8O2 C2H3Cl C4.8H8O4 C6H10O5 CH2O
B-number 1.29 1.16 1.55 1.27 1.41 1.78 1.15 1.75 6.96 1.47
cp ðTf Ts Þ where B ¼ is nondimensional and L represents the mass transfer number. L in Equation 11.27 denotes the latent heat of gasification, h represents the convective heat transfer coefficient, Tf and Ts denote an average flame temperature and temperature of the fuel surface and cp denotes the specific heat of the gas. The B-number (also called the Spalding mass transfer number) was first introduced by Spalding [3] in 1950 to characterize liquid fuel droplet burning and physically relates the heat release related to combustion (the numerator) to the losses associated with combustion (the denominator). The heat transfer coefficient (h) is expressed in terms of a nondimensional Nusselt number, defined as Nu ¼ hxλ , where λ denotes the thermal conductivity of the gasmixture at the interface between the condensed fuel and air and x is a characteristic length scale. In case of a flat fuel surface x can be defined as the distance from the leading edge and in the case of a sphere or cylinder refers to the diameter. The earlier expression is now equal to:
00
m_ ¼ B
λ Nu xcp
ð11:28Þ
In order to account for the blocking effect, the Nusselt number is first evaluated without the
Liquids Methanol Ethanol Propanol Butanol n-pentane n-hexane n-heptane n-octane (gasoline) iso octane n-nonane n-decane n-undecane n-dodecane (kerosene) Acetone
Formula CH3OH C2H5OH C3H7OH C4H8OH C5H12 C6H14 C7H16 C8H18 C8H18 C9H20 C10H22 C11H24 C12H26 C3H2O
B-number 2.53 2.89 3.29 3.35 7.63 6.67 5.92 5.42 6.59 4.89 4.61 4.43 4.13 7.28
blocking effect and then corrected for this effect through the ratio Nu/Nuo 00
m_ ¼ B
λ Nu Nuo xcp Nuo
ð11:29Þ
Nondimensionalizing both sides by ρU 1 , where U 1 is a characteristic velocity representing the flow-field subjected to or induced by the diffusion flame, the above expression can be re-written as: 00
λ μ Nu m_ Nuo ¼B cp μ ρU1 x Nuo ρU 1 ¼ BðPr ReÞ1 Nuo
Nu Nuo
ð11:30Þ ð11:31Þ
The quantity cpλμ equals 1/Pr where Pr ¼ Prandtl Nu number. The ratio Nu , the blocking effect can be o calculated for several laminar flows and equals lnð1þBÞ B
for small B. For turbulent flows it can be calculated empirically only. Typical values of B for many fuels are listed in Table 11.3. Expressions for Nuo for many geometrical configurations are available in standard heat and mass transfer textbooks and shown in Table 11.4. For example, using Table 11.4, an expression for
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Diffusion Flames
363
Table 11.4 Nuo values for some standard geometries and flow conditions. Re ¼ U1υ X, and Gr ¼ Flow field type Free convective flow Vertical plate (laminar, Gr < 109)
Illustration
gX3 ðT f T o Þ T o υ2
Nuo 0.59 (GrPr)1/4
Vertical plate (turbulent, Gr > 109)
Horizontal plate burning face up (laminar, Gr < 107)
0.54 (GrPr)1/4
Horizontal plate burning face up (turbulent, Gr > 107)
0.14(GrPr)1/3
Horizontal plate burning face down (turbulent)
0.27(GrPr)1/4
Horizontal cylinder
0.525(GrPr)1/4
Sphere
2 + 0.6 Gr1/4Pr1/3
Forced flow Horizontal flat plate (laminar)
0.332Re1/2 Pr1/3
Horizontal flat plate (turbulent Re > 105)
0.036Re0.8 Pr0.3
Pool fire (laminar and axisymmetric)
0.11 Re1/2 Pr2/3
(continued)
364
A.S. Rangwala
Table 11.4 (continued) Flow field type Droplet (laminar)
Illustration
Nuo 0.37Red0.6
Cylinder (laminar)
0.891Re1/2
Cylinder (turbulent, Re > 40,000)
0.27 (GrPr)1/4
mass loss rate of a vertical plate in a laminar free convective flow can be calculated as: 00
m_ ¼ Co Bm
λ ðGr PrÞ1=4 cp x
ð11:32Þ
A mass burning rate for the same plate in a turbulent natural convective flow-field is: 00
m_ ¼ Co Bm
λ ðGr PrÞ1=3 cp x
ð11:33Þ
The constant Co can take different values and usually lies between 0.5 and 1.5. The value of the exponent m on B is 0.5. Recently Ali et al. [26] have extended the correlation (laminar case) to include several orientation angles. The mass burning rate of a plate oriented at an angle θ with respect to the vertical for a plate in a free convective flow-field is given by [26]: 00
m_ ¼ 0:737ðGr x Prx Þ0:25
lnð1 þ BÞ ; B0:15
ð11:34Þ
where Gr x ¼ geff βΔTx and geff ¼ g cos θ for 0 < υ2 θ < 90 and geff ¼ gðcos θ sin θÞ for 90 < θ 0 . Note that 0 represents the vertical case, 90 denotes a pool fire and 90 denotes a ceiling configuration. The mass loss rate per 00 unit area m_ can also be expressed as a regression 00 rate m_ /ρs where ρs is the density of the fuel 3
(condensed phase). Typical regression rates of most fuels (solids/liquids shown in Table 11.3) vary between 0.02 and 0.4 mm/s. The regression rates are very small and are essentially due to the diffusion controlled nature of the problem.
Diffusion Flame Height When gaseous fuel issues out of a tube into ambient atmosphere of air and the gas is ignited a flame is established as shown in Fig. 11.7. The question we will try to answer is how high is the resulting diffusion flame? The problem can be solved using conservation equations with certain approximations as was first shown by Burke and Schuman [19]. However, for practical purposes a simple physical reasoning exercise will be adopted here. It will be shown later that the relationship obtained is similar to that obtained using the more rigorous approach. Imagine a fuel molecule, shown in Fig. 11.7 by the red circle, initially located at the center of the burner tube. The molecule can traverse two extreme paths (depicted by o-x and o-y) to meet with oxygen at the flame surface. The time taken to traverse horizontally along o-x is given by d2/4D, where D is the diffusion coefficient between methane and air. The relationship is obtained by a dimensional analysis of the two parameters: distance over which diffusion must occur (m) and diffusion coefficient (m2/s).
11
Diffusion Flames
365 Table 11.5 Flame height correlations (all quantities in SI m, m3/s etc.) Flame height (Hf) 0:67 QF ðT 1 =T F Þ T 1 H f ¼ 4πDln ð1þ1sÞ T f 0:67 QF ðT 1 =T F Þ T1 Hf ¼ 0:5 2 16D½inverf ð1þsÞ Tf 2 0:33 Tf bβ2 QF T1 H fm ¼ hIDY TF T1 Fstoic h 4 4 4 i1=3 h i2=9 Tf QF T 1 H f B ¼ 9β T1 8D2 ah4 T 4
Geometry Circular Square Slot
F
β ¼ 4inverf1 1þ1 ð sÞ QF volumetric fuel flow rate (m3/s), D diffusivity (m2/s), T 1 ambient temperature (K), Tf mean flame temperature (K), TF fuel temperature (K), s molar stoichiometric oxidizer-fuel ratio, inverf inverse error function, ω ¼ inverf[erf(ω)], buoyant acceleration a ¼ mean
0:6g
Fig. 11.7 The diffusion jet-flame
The only way of obtaining a time scale from these two quantities is to divide the square of the distance by the diffusion coefficient. The length of the flame will correspond to the condition that a point on the stream axis where combustion is complete, the average depth of penetration of air into gas must equal to the radius of the burner tube. Similarly, the time taken to traverse vertically along O-Y is given by Hf /V, where Hf is the flame height and V is the velocity of the gas issuing of the burner. Equating the two times gives, Hf /V d2/4D or Hf d2V/4D. This simple result is reflected in all the correlations (developed by Roper [27, 28]) related to diffusion flame height shown in Table 11.5. An important element in the expression developed is the influence of fuel properties, geometry (of the duct). The influence of fuel properties is usually incorporated in the flame temperature and stoichiometric coefficient (s) shown in Table 11.5. The inverse error function is generated in the same way as inverse trigonometric functions and is tabulated in standard textbooks (For example see Table 9.4 in Turns [29]). The parameter, I typically takes values between 1 and 1.5. I ¼ 1 for uniform flow and I ¼ 1.5 for fully
Tf T1
1 (m2/s)
developed parabolic exit velocity profile. The subscript “m” denotes that the flow-field is momentum controlled and subscript “b” denotes buoyancy controlled. To determine if the flame is momentum or buoyancy controlled the flame Froude number Fr must be calculated as Fr f ¼
ðV e IY F, stoic Þ2 : aH f
ð11:35Þ
If Fr f 1 then flame is momentum controlled and if Fr f 1 then the flame is buoyancy controlled. If Fr f 1, then the flame lies in a transitional zone which is both momentum and buoyancy controlled. In this case, 4 H fT ¼ H fm 9
H fB H fm
8 3 ‘b
Confined Ceilings Channel Configuration Previous discussions of ceiling jets in this chapter have all dealt with unconfined radial spread of the gas flow away from a ceiling impingement point. In practice this flow may be interrupted by ceiling beams or corridor walls, creating a long channel that partially confines the flow. Knowledge of the resultant ceiling jet flows is important in determining fire detector response times. For the channel configuration, the flow near the impingement point will remain radial (i.e., axisymmetric), but after spreading to the walls or beams that bound the ceiling, the flow will become generally parallel with the confining boundary. Delichatsios [35] has developed correlations for steady-state ceiling jet temperature and velocity, which apply to the channel flow between beams and down corridors. In the case of corridors, the correlations apply when the corridor half-width, ‘b, is greater than 0.2 times the ceiling height, H, above the fire source. Note that this value of ‘b corresponds approximately to the outer radius of the ceiling jet turning region. In the case of beams, the flow must also be contained fully so that only a flow in a primary channel results, without spillage under the beams to the adjoining secondary channels. For the latter condition to be satisfied, the beam
hb =H > 0:1ð‘b =H Þ1=3 ‘b =H > 0:2 Y ‘b 1=3 < 3:0 0:5 < H H where ΔTp ¼ Excess temperature on the plume centerline defined previously in Equation 14.17 Y ¼ Distance along the channel measured from the plume impingement point St ¼ Stanton number, whose value is recommended to be 0.03 Based on the minimum value of ‘b/H ¼ 0.2, the limit on hb/H implies that the beam depth to ceiling height ratio must be at least 0.17 for the fire gases to be restricted to the primary channel. The constant a in Equation 14.59 is determined by Delichatsios to be in the range 0.24–0.29. This equation is based on the concept that the channel flow has undergone a hydraulic jump, which results in greatly reduced entrainment of cooler, ambient air from below. Reductions in ceiling jet temperature or velocity are then mainly due to heat losses to the ceiling and would thus be dependent on ceiling composition to some extent. Additional detailed measurements of the ceiling jet flow in a primary beamed channel have been obtained by Koslowski and Motevalli [36]. Their data generally validate the
446
R.L. Alpert
Delichatsios beamed ceiling correlation (Equation 14.61) and ceiling jet flow behavior, but additional measurements for a range of beam depth to ceiling height ratios has allowed the correlation to be generalized. Furthermore, Koslowski and Motevalli recast the correlation in terms of the nondimensional heat release rate defined by Heskestad and Delichatsios (Equations 14.9 and 14.10), instead of centerline plume conditions at the ceiling, with the following result: 1=3 " # H Y ‘b 1=3 * ΔT 0 ¼ C exp 6:67 St ‘b H H ð14:61Þ where the Stanton number is recommended to be 0.04, rather than 0.03, and the constant, C, has the following dependence on the ratio of beam depth, hb, to ceiling height, H: 2 hb hb C ¼ 25:38 þ 13:58 þ 2:01 H H ð14:62Þ Y for 0:5 1:6 H To derive Equation 14.62, Koslowski and Motevalli vary the hb/H ratio from 0.07 up to 0.28. In so doing, they note that C increases steadily with this ratio until leveling off near hb/H ¼ 0.17, determined by Delichatsios as the condition for the fire gases to be restricted to the primary channel. Between values of hb/H of 0.07 (or even much less) and 0.17, spillage from the primary channel to adjacent secondary channels is steadily reduced, thereby increasing temperatures in the primary channel. Characteristics of the ceiling jet flow in the secondary channels, as well as the primary channel, have also been studied by Koslowski and Motevalli [37].
Corner Configuration with Strong Plumes An open configuration of two walls at a 90 angle to form a corner, covered by a ceiling, with a fire source at the base of and in close contact with the
corner, is often used as a hazardous environment in which to test the flammability of wall and ceiling linings. This wall-ceiling-corner configuration also occurs naturally in many types of enclosures (see below) where hot gases from the fire source may be partially or completely confined by more than just the ceiling and corner walls themselves, resulting in the formation of a hot gas layer near the ceiling. In this section, the environment of an open corner with inert lining surfaces is discussed, where a ceiling jet develops due to impingement of a fire plume or flames from the source fire at the base of the wall corner onto the ceiling covering the wall-corner. A careful study of this environment based on full-scale tests was conducted by Lattimer and Sorathia [38]. These tests used a ceiling clearance of 2.25 m above the surface of a 0.17–0.50 m2 or L-shaped line (each leg being 0.17–0.50 m) sand burner having propane heat release rates from 50 to 300 kW. Thermocouple measurements [38] of excess gas temperature at a radial distance from the corner, r, in the ceiling jet could be correlated (with a regression coefficient of 0.85) by the following formulas: T T 1 ¼ 950
T T1
for
r þ H 2 ¼C L f , tip
rþH 0:55 ð14:63Þ L f , tip
for
rþH > 0:55 L f , tip ð14:64Þ
The specific value of 950 for the maximum excess of corner fire gas temperature above ambient in Equation 14.63 may vary for fire sources other than the propane burner or for corner walls having thermal characteristics different from those used in these specific tests. However, it is expected that the functional dependencies for ceiling jet temperature should be preserved. Note that the constant, C, in Equation 14.64 is 288 for the square burner of side, D, and 340 for the L-shaped line burner, each leg of which is length, D and that Lf,tip is the flame length from the surface of either type burner to the flame tip, the furthest location where flame
14
Ceiling Jet Flows
447
tips are observed visually, as determined from the correlation [38], qffiffiffiffiffiffi L f , tip ¼ 5:9 Q* ð14:65Þ D where Q* is based on actual fire heat release rate and the burner length-scale, D (instead of the usual ceiling clearance, H). Lattimer and Sorathia [38] also used twenty Schmidt-Boelter gauges to measure heat flux to the bounding surfaces of the corner configuration from the propane sand burner flames. Their 00 measurements of total heat flux, q_ , to the ceiling surface from the ceiling jet flames and/or hot gases could be correlated by the following for either the square or L-shaped line burner: 00
q_ ¼ 120 00
q_ ¼ 18
for
rþH L f , tip
rþH 0:58 L f , tip
3:5 for
ð14:66Þ
rþH > 0:58 L f , tip ð14:67Þ
where the flame tip total length is given by Equation 14.65, above. This same formula is found also to predict the maximum heat flux to the top portion of the wall from the ceiling jet flow, where now the variable, r, represents distance from the corner along the top of the wall. Again, the specific maximum heat flux of 120 kW/m2 that was measured in the corner configuration by Lattimer and Sorathia [38] may vary for fuels with thermal radiation characteristics much different from those of propane or for different burner configurations. For example, it is well known that peak heat fluxes in pool and solid fuel fires can exceed 140–160 kW/ m2, as discussed by Coutts [39].
General Enclosure Configurations The analyses in preceding sections for unconfined ceiling jet flows may be sufficient for large industrial or commercial storage facilities. In smaller rooms, or for very long times after fire ignition in larger industrial facilities, a quiescent,
heated layer of gas will accumulate in the upper portion of the enclosure. This heated layer can be deep enough to totally submerge the ceiling jet flow. In this case, temperatures in the ceiling jet can be expected to be greater than if the ceiling jet were entraining gas from a cooler, ambienttemperature layer. It has been shown by Yu and Faeth [10] that the submerged ceiling jet also results roughly in a 35 % increase in the heat transfer rate to the ceiling. There are analytical formulas to predict temperature and velocity in such a two-layer environment, in which the ceiling jet is contained in a heated upper layer and the fire is burning in a lower, cool layer. This type of prediction, which has been developed by Evans [40, 41], Cooper [42], and Zukoski and Kubota [43], can best be used to check the proper implementation of readily available numerical models (e.g., zone or field/CFD) of fire-induced flows in enclosures. An example of a zone model to predict activation of thermal detectors by a ceiling jet submerged in a heated layer is the algorithm developed by Davis [44]. This model, which assumes that thermally activated links are always located below the ceiling at the point of maximum ceiling jet temperature and velocity, is based partly on a model and thoroughly documented software developed by Cooper [45]. Formulas to predict the effect of the heated upper layer in an enclosure are based on the assumption that the ceiling jet results from a fire contained in a uniform environment at the heated upper-layer temperature. This substitute fire has a heat release rate, Q_ 2 , and location below the ceiling, H2, differing from those of the real fire. Calculation of the substitute quantities Q_ 2 and H2, depends on the heat release rate and location of the real fire, as well as the depths and temperatures of the upper and lower layers within the enclosure. Following the development by Evans [41], the substitute source heat release rate and distance below the ceiling are calculated from Equations 14.68, 14.69, 14.70, and 14.71. Originally developed for the purpose of sprinkler and heat detector response time calculations, these
448
R.L. Alpert
equations are applicable during the growth phase of enclosure fires. 0
* Q_ I, 2
ZI, 2 ¼
* 1 þ CT Q_ I, 1 @ ¼ ξCT
8 > >
* 1=3 > :Q_ I, 2
92=5 > > =
ξQ_ I, 1 CT 2 * 2=3 > > ; ðξ 1Þ β þ 1 þ ξCT Q_ I, 2 *
ð14:68Þ
Z I, 1
ð14:69Þ * 5=2 Q_ c, 2 ¼ Q_ I, 2 ρ1, 2 c p1 T 1, 2 g1=2 Z I, 2
ð14:70Þ
H 2 ¼ H 1 ZI, 1 þ ZI, 2
ð14:71Þ
Further explanation of variables is contained in the nomenclature section. Cooper [42] has formulated an alternative calculation of substitute source heat release rate and distance below the ceiling that provides for generalization to situations in which portions of the time-averaged plume flow in the lower layer are at temperatures below the upper-layer temperature. In these cases, only part of the plume flow may penetrate the upper layer sufficiently to impact on the ceiling. The remaining portion at low temperature may not penetrate into the hotter upper layer. In the extreme, when the maximum temperature in the lower-layer plume flow is less than the upper-layer temperature, none of the plume flow will penetrate significantly into the upper layer. This could be the case during the decay phases of an enclosure fire, when the heat release rate is small compared to earlier in the fire growth history. In this calculation of substitute firesource quantities, the first step is to calculate the fraction of the plume mass flow penetrating the upper layer, m2*, from Equations 14.72 and 14.73. m*2 ¼
1:04599σ þ 0:360391σ 2 1 þ 1:37748σ þ 0:360391σ 2
ð14:72Þ
where σ¼
3 2 1 þ C Q_ * 2=3 T I , 1 ξ 7 6 15 ð14:73Þ 4 ξ1 ξ
Then, analogous to Equations 14.69, 14.70, and 14.71 of the previous method: 2=5 1 þ σ 1=3 Z I, 2 ¼ ZI, 1 ξ3=5 m*2 σ σm*2 Q_ c, 2 ¼ Q_ c, 1 1þσ H 2 ¼ H 1 ZI, 1 þ ZI, 2
ð14:74Þ ð14:75Þ ð14:76Þ
The last step is to use the substitute source values of heat release rate and distance below the ceiling, as well as heated upper-layer properties for ambient conditions, in the correlations developed for ceiling jet flows in uniform environments. To demonstrate the use of the techniques, the previous example in which a sofa was imagined to be burning in a showroom may be expanded. Let all the parameters of the problem remain the same except that at 200 s after ignition (t ti ¼ 120 s), when the fire heat release rate has reached 2.5 MW, a quiescent heated layer of gas at a temperature of 50 C is assumed to have accumulated under the ceiling to a depth of 2 m. For this case, the two-layer analysis is needed to determine the ceiling jet maximum temperature at the same position as calculated previously (a radial distance of 4 m from the plume impingement point on the ceiling). All of the two-layer calculations presented assume quasi-steady conditions. From Equation 14.47 with the values of parameters in the single-layer calculation, it can be shown that the time after sofa ignition must be at least 31 s for a quasi-steady analysis to be acceptable. Since the actual time after ignition is 120 s, such an analysis is appropriate. It will be assumed that this finding will carry over to the two-layer case. Using Equations 14.68, 14.69, 14.70, and 14.71 from the work of Evans [41], values of the heat release rate and position of the substitute fire source that compensates for the two-layer effects on the plume flow can be calculated. The dimensionless heat release rate of the real fire source evaluated at the position of the interface between the upper and lower layers is as follows:
14
Ceiling Jet Flows
* Q_ I, 1 ¼
449
Q_ 5=2 ρ1 c p1 T 1 g1=2 ZI, 1
ð14:77Þ
For an actual heat release rate of 2500 kW, ambient temperature of 293 K, and distance between the fire source and the interface between the lower and upper layers of 3 m, Equation 14.77 becomes * Q_ I, 1
2500 ¼ 1:204 1 293 9:81=2 35=2 ¼ 0:1452
Using the ratio of upper-layer temperature to lower-layer temperature, ξ ¼ 323/293 ¼ 1.1024, and the constant, CT ¼ 9.115, the dimensionless heat release rate for the substitute fire source is * Q_ I, 2 ¼ 0:1179
Using the value for the constant β2 ¼ 0.913, the position of the substitute fire source relative to the two-layer interface is Z I, 2 ¼ 3:161 Now, from Equations 14.76 and 14.77, the dimensional heat release rate and position relative to the ceiling are found to be Q_ 2 ¼ 2313 kW H 2 ¼ 5:161 m The analogous calculations for substitute firesource heat release rate and position following the analysis of Cooper [42], Equations 14.72, 14.73, 14.74, 14.75, 14.76, and 14.77, are σ ¼ 23:60 m*2 ¼ 0:962 ZI, 2 ¼ 3:176 Q_ 2 ¼ 2308 kW H 2 ¼ 5:176 m These two results are essentially identical for this type of analysis. Since it has been shown that the quasi-steady analysis is appropriate for this example, the dimensionless maximum temperature in the ceiling jet flow, 4 m from the impingement point, can now be calculated from (ΔT2*)qs in Equation 14.48.
Using the ceiling height above the substitute source, this equation yields the result
ΔT *2
qs
¼
11:40 0:126 þ 0:210ð4=5:161Þ
4=3
¼ 134:4 For the given time after ignition of 120 s and the assumed fire growth, the calculated Q_ 2 value implies that α equals 0.1606, instead of the original sofa fire growth factor of 0.1736. Substitution of this new α in Equation 14.42, along with H2 and the upper-layer temperature as the new ambient value, yields the following dimensional excess temperature at the 4-m radial position in the ceiling jet: ΔT ¼
134:4 323 ð0:0278 :01606Þ2=5 9:8 5:1613=5
ΔT ¼ 190 K T ¼ 190 K þ 323 K ¼ 513 K ¼ 240 C This is 73 C above the temperature calculated previously using the quasi-steady analysis and a uniform 20 C ambient, demonstrating the effect of flow confinement on gas temperature.
Ceiling Jet Development At the beginning of a fire, the initial buoyant flow from the fire must spread across the ceiling, driven by buoyancy, to penetrate the cooler ambient air ahead of the flow. Research studies designed to quantify the temperatures and velocities of this initial spreading flow have been initiated [46]. At a minimum, it is useful to become aware of the many fluid mechanical phenomena embodied in a description of the ceiling jet flow in a corridor up to the time when the ceiling jet is totally submerged in a quiescent, warm upper layer. Borrowing heavily from a description of this flow provided by Zukoski et al. [46], the process is as follows. A fire starts in a small room with an open door to a long corridor having a small vent near the floor at the end opposite the door. As the fire
450 Fig. 14.6 Transient ceiling jet flow in a room and corridor [45]
R.L. Alpert
a
b
c
Vf
Hydraulic jump
d
Vf
e
Vw
f
Vw
g
starts, smoke and hot gases rise to form a layer near the fire room ceiling. The layer is contained in the small room by the door soffit (Fig. 14.6a). As the fire continues, hot gas from the room begins to spill out under the soffit into the hallway. The fire grows to a relatively constant heat release rate. The outflowing gas forms a short, buoyant plume (Fig. 14.6b) that impinges on the hallway ceiling, producing a thin jet that flows away from
the fire room in the same manner that the plume within the room flows over the interior ceiling. The gas flow in this jet is supercritical, analogous to the shooting flow of liquids over a weir. The velocity of the gas in this flow is greater than the speed of gravity waves on the interface between the hot gas and the cooler ambient air. The interaction of the leading edge of this flow with the ambient air ahead of it produces a hydraulic, jumplike condition, as shown in Fig. 14.6c.
14
Ceiling Jet Flows
A substantial amount of ambient air is entrained at this jump. Downstream of the jump, the velocity of the gas flow is reduced and mass flow is increased due to the entrainment at the jump. A head is formed at the leading edge of the flow. Mixing between this ceiling-layer flow and the ambient cooler air occurs behind this head. The flow that is formed travels along the hallway ceiling (Fig. 14.6c, d) with constant velocity and depth until it impinges on the end wall (Fig. 14.6e). A group of waves are reflected back toward the jump near the fire room, traveling on the interface. Mixing occurs during the wall impingement process (Fig. 14.6f), but no significant entrainment occurs during the travel of the nonbreaking reflected wave. When these waves reach the jump near the fire room door, the jump is submerged in the warm gas layer, eliminating the entrainment of ambient lower-layer air at this position (Fig. 14.6g). After several wave reflections up and down the corridor along the interface, the wave motion dies out, and a ceiling layer uniform in depth is produced. This layer slowly grows deeper as the hot gas continues to flow into the hallway from the fire room. It is clear from the preceding description that quantification of effects during development of a submerged ceiling jet flow is quite complex. Analyses and experiments have been performed to better understand the major features of a developing ceiling jet flow in a corridor [47, 48]. One such study [49] contains a description somewhat different from that already given.
451
beams or corridor walls, are very useful for verifying that detailed numerical models of fire phenomena (e.g., Hara and Shinsuke [50]) have been implemented properly. The predictive techniques are the basis for acceptable design of fire detection systems, as exemplified by Appendix B of NFPA 72®, National Fire Alarm Code [33].
Nomenclature A a b CT cp D Deff f g H h hb Lf,tip ‘b ‘T
Summary m 2* Reliable formulas are available to predict maximum gas temperatures and velocities and approximate temperature/velocity profiles in fire-driven ceiling jet flows beneath unobstructed ceilings for both steady and power-law fire growth. These predictive formulas, which also apply to certain situations where the ceiling jet flow is confined by
p
Pr Q_ Q_ c
g/(ρ1cpT1)(m2/kg) Constant in Equation 14.59, equal to 0.24–0.29 Effective plume radius at the intersection with the ceiling elevation (m) Constant [17], related to plume flow, equal to 9.115 heat capacity at constant pressure (J/kg K) Burner dimension (m) Effective diameter of the base of the flame zone or the burning fuel Ceiling friction factor Gravitational acceleration (m/s2) Ceiling height above fire source; for sloped ceiling, on the fire axis (m) Heat transfer coefficient (kW/m2 K) Depth of beams in a primary beam channel (m) Visible flame length from burner to furthest flame tip (m) Half-width for corridor or primary beam channel (m) Ceiling jet thickness based on 1/e depth of excess temperature profile (m) Fraction of fire-plume mass flux penetrating upper layer Ambient air pressure (Pa); also, as exponent of time for general powerlaw fire growth Prandtl number Total heat release rate (kW) Convective heat release rate (kW)
452 * Q*, Q_ 0
Q00c* q_
R R^ Ra Re r rup St T T1 Tp ΔT t U Uup Vp Y ZI z zH zo zv _ dQ=dt
R.L. Alpert
_ ρ1 c p T 1 pffiffigffiH 5=2 Q= p ffiffi ffi Q_ c = ρ1 c p T 1 gH 5=2
ν θ
Rate of heat transfer per unit area (heat flux) to the ceiling surface (kW/m2) Radial distance to detector (m) r/(H zo) Rayleigh number Reynolds number Radial distance from axis of fire plume (m) Radial distance in steepest upward direction from axis of fire plume (m) Stanton number, h/(ρUcp) Ceiling jet gas temperature (K) Ambient air temperature (K) Peak gas temperature in plume at the intersection with ceiling elevation (K) Excess gas temperature, T T1 (K) or ( C) Time (s) Ceiling jet gas velocity (m/s) Maximum ceiling jet gas velocity in the steepest upward direction (m/s) Maximum plume velocity at the intersection with ceiling elevation (m/s) Distance along channel or corridor, measured from plume axis (m) Distance of layer interface above the real or substitute fire source (m) Vertical distance above the base of the flame zone Distance of ceiling above the base of the flame zone Virtual origin elevation in a transient rack storage fire Distance of virtual plume origin above the base of the flame zone Rate of change of heat release rate with time (kW/s)
ρ σ ξ
Greek Letters α β2
Growth parameter for t2 fires (kW/s2) Constant [17] related to plume flow, equal to 0.913
Kinematic viscosity (m2/s) Angle of inclination of the ceiling with respect to the horizontal (degrees) Gas density (kg/m3) Parameter defined in Equation 14.73 Ratio of temperatures, T1,2/T1,1
Subscripts 0 1 2 1
c f I i p qs
Based on steady-state fire source Associated with lower layer Associated with upper layer; or parameter associated with t2 fire growth Ambient, outside ceiling jet or plume flows Convective fraction Associated with gas travel time delay Value at the interface position between the heated upper layer and cool lower layer Reference value at ignition Associated with plume flow Quasi-steady flow condition
Superscripts * ^
Dimensionless quantity Quantity related to transient rack-storage fire
References 1. R.W. Pickard, D. Hird, and P. Nash, “The Thermal Testing of Heat-Sensitive Fire Detectors,” F.R. Note 247, Building Research Establishment, Borehamwood, UK (1957). 2. P.H. Thomas, “The Distribution of Temperature and Velocity Due to Fires Beneath Ceilings,” F.R. Note 141, Building Research Establishment, Borehamwood, UK (1955). 3. R.L. Alpert, “Calculation of Response Time of Ceiling-Mounted Fire Detectors,” Fire Technology, 8, p. 181 (1972) 4. R.L. Alpert, “Turbulent Ceiling Jet Induced by LargeScale Fires,” Combustion Science and Technology, 11, 197 (1975) 5. H.Z. Yu (You), “An Investigation of Fire-Plume Impingement on a Horizontal Ceiling: 2-Impingement and Ceiling-Jet Regions,” Fire and Materials, 9, 46 (1985) 6. G. Heskestad and T. Hamada, “Ceiling Jets of Strong Fire Plumes,” Fire Safety Journal, 21, 69, (1993)
14
Ceiling Jet Flows
7. G. Heskestad, “Physical Modeling of Fire,” Journal of Fire & Flammability, 6, p. 253 (1975). 8. L.Y. Cooper, “Heat Transfer from a Buoyant Plume to an Unconfined Ceiling,” Journal of Heat Transfer, 104, p. 446 (1982). 9. L.Y. Cooper and A. Woodhouse, “The Buoyant PlumeDriven Adiabatic Ceiling Temperature Revisited,” Journal of Heat Transfer, 108, p. 822 (1986). 10. H.Z. Yu (You) and G.M. Faeth, “Ceiling Heat Transfer during Fire Plume and Fire Impingement,” Fire and Materials, 3, 140 (1979) 11. C.C. Veldman, T. Kubota, and E.E. Zukoski, “An Experimental Investigation of the Heat Transfer from a Buoyant Gas Plume to a Horizontal Ceiling—Part 1: Unobstructed Ceiling,” NBS-GCR77–97, National Bureau of Standards, Washington, DC (1977). 12. V. Motevalli and C.H. Marks, “Characterizing the Unconfined Ceiling Jet Under Steady-State Conditions: A Reassessment,” Fire Safety Science, Proceedings of the Third International Symposium (G. Cox and B. Langford, eds.), Elsevier Applied Science, New York, p. 301 (1991). 13. R.L. Alpert, “Fire Induced Turbulent Ceiling-Jet,” Technical Report Serial No. 19722–2, Factory Mutual Research Corporation, Norwood, MA, p. 35 (1971). 14. D.D. Evans and D.W. Stroup, “Methods to Calculate the Response Time of Heat and Smoke Detectors Installed Below Large Unobstructed Ceilings,” Fire Technology, 22, 54 (1986). 15. R.L. Alpert, “The Fire Induced Ceiling-Jet Revisited,” in The Science of Suppression, Proceedings of Fireseat 2011 at the National Museum of Scotland, 9 November 2011, The University of Edinburgh, Edinburgh, Scotland, pp. 1–21. 16. A. Tewarson, “Generation of Heat and Gaseous, Liquid and Solid Products in Fires,” SFPE Handbook of Fire Protection Engineering, this volume, (p. 3–142 in 4th Edition). 17. E.E. Zukoski, T. Kubota, and B. Cetegen, “Entrainment in Fire Plumes,” Fire Safety Journal, 3, 107 (1981) 18. G. Heskestad and M.A. Delichatsios, “The Initial Convective Flow in Fire,” 17th International Symposium on Combustion, Combustion Institute, Pittsburgh, PA (1978). 19. C.L. Beyler, “Fire Plumes and Ceiling Jets,” Fire Safety Journal, 11, p. 53 (1986). 20. G.T. Atkinson and D.D. Drysdale, “Convective Heat Transfer from Fire Gases,” Fire Safety Journal, 19, p. 217 (1992). 21. Y. Hasemi, S. Yokobayashi, T. Wakamatsu, and A. Ptchelintsev, “Fire Safety of Building Components Exposed to a Localized Fire: Scope and Experiments on Ceiling/Beam System Exposed to a Localized Fire,” AsiaFlam 95—1st International Conference, Interscience Communications, Ltd., London, p. 351 (1995). 22. M.A. Kokkala, “Experimental Study of Heat Transfer to Ceiling from an Impinging Diffusion Flame,” Fire
453 Safety Science, Proceedings of the Third International Symposium (G. Cox and B. Langford, eds.), Elsevier Applied Science, New York, p. 261 (1991). 23. R.L. Alpert, “Convective Heat Transfer in the Impingement Region of a Buoyant Plume,” ASME Journal of Heat Transfer, 109, p. 120 (1987). 24. H.C. Kung, R.D. Spaulding, and P. Stavrianidis, “Fire Induced Flow Under a Sloped Ceiling,” Fire Safety Science, Proceedings of the Third International Symposium (G. Cox and B. Langford, eds.), Elsevier Applied Science, New York, p. 271 (1991). 25. O. Sugawa, T. Hosozawa, N. Nakamura, A. Itoh and Y. Matsubara, “Flow Behavior under Sloped Ceiling,” in Fifteenth Meeting of UJNR Panel on Fire Research and Safety, NISTIR 6588, National Institute of Standards and Technology, Gaithersburg, MD USA, March 2000. 26. Y. Oka, M. Ando and K. Kamiya, “Ceiling Jet Flow Properties for Flames Impinging on an Inclined Ceiling,” Fire Safety Science, Proceedings of the Tenth International Symposium, International Association for Fire Safety Science, London, 2012. 27. Y. Oka and M. Ando, “Temperature and Velocity Properties of a Ceiling Jet Impinging on an Unconfined Inclined Ceiling,” accepted for publication in Fire Safety Journal, 2012. 28. H.C. Kung, H.Z. Yu (You), and R.D. Spaulding, “Ceiling Flows of Growing Rack Storage Fires,” 21st Symposium (International) on Combustion, Combustion Institute, Pittsburgh, PA, p. 121 (1986). 29. R.P. Schifilliti, Use of Fire Plume Theory in the Design and Analysis of Fire Detector and Sprinkler Response, Thesis, Worcester Polytechnic Institute, Worcester, MA (1986). 30. G. Heskestad, “Similarity Relations for the Initial Convective Flow Generated by Fire,” ASME Paper No. 72-WA/HT-17, American Society of Mechanical Engineers, New York (1972). 31. G. Heskestad and M.A. Delichatsios, “Environments of Fire Detectors,” NBS-GCR-77-86 and NBSGCR77-95, National Bureau of Standards, Washington, DC (1977). 32. G. Heskestad and M.A. Delichatsios, “Update: The Initial Convective Flow in Fire,” Short Communication, Fire Safety Journal, 15, p. 471 (1989). 33. NFPA 72®, National Fire Alarm Code®, National Fire Protection Association, Quincy, MA (1999). 34. H.Z. Yu and P. Stavrianidis, “The Transient Ceiling Flows of Growing Rack Storage Fires,” Fire Safety Science, Proceedings of the Third International Symposium (G. Cox and B. Langford, eds.), Elsevier Applied Science, New York, p. 281 (1991). 35. M.A. Delichatsios, “The Flow of Fire Gases Under a Beamed Ceiling,” Combustion and Flame, 43, 1 (1981). 36. C. Koslowski and V. Motevalli, “Behavior of a 2-Dimensional Ceiling Jet Flow: A Beamed Ceiling Configuration,” Fire Safety Science, Proceedings of the Fourth International Symposium (T. Kashiwagi,
454 ed.), International Association of Fire Safety Science, Bethesda, MD, p. 469 (1994). 37. C.C. Koslowski and V. Motevalli, “Effects of Beams on Ceiling Jet Behavior and Heat Detector Operation,” Journal of Fire Protection Engineering, 5, 3, p. 97 (1993). 38. B. Lattimer and U. Sorathia, “Thermal Characteristics of Fires in a Noncombustible Corner,” Fire Safety Journal, 38, p. 709 (2003). 39. D. Coutts, “An Emissive Power Correlation for Solid Fuel Packages,” Journal of Fire Protection Engineering, 21, p. 133, 2011. 40. D.D. Evans, “Thermal Actuation of Extinguishing Systems,” Combustion Science and Technology, 40, p. 79 (1984). 41. D.D. Evans, “Calculating Sprinkler Actuation Time in Compartments,” Fire Safety Journal, 9, 147 (1985). 42. L.Y. Cooper, “A Buoyant Source in the Lower of Two Homogeneous, Stably Stratified Layers,” 20th International Symposium on Combustion, Combustion Institute, Pittsburgh, PA (1984). 43. E.E. Zukoski and T. Kubota, “An Experimental Investigation of the Heat Transfer from a Buoyant Gas Plume to a Horizontal Ceiling—Part 2: Effects of Ceiling Layer,” NBS-GCR-77-98, National Bureau of Standards, Washington, DC (1977). 44. W.D. Davis, “The Zone Fire Model Jet: A Model for the Prediction of Detector Activation and Gas Temperature in the Presence of a Smoke Layer,” NISTIR 6324, National Institute of Standards and Technology, Gaithersburg, MD (1999). 45. L.Y. Cooper, “Estimating the Environment and the Response of Sprinkler Links in Compartment Fires with Draft Curtains and Fusible Link-Actuated
R.L. Alpert Ceiling Vents—Theory,” Fire Safety Journal, 16, pp. 137–163 (1990). 46. E.E. Zukoski, T. Kubota, and C.S. Lim, “Experimental Study of Environment and Heat Transfer in a Room Fire,” NBS-GCR-85-493, National Bureau of Standards, Washington, DC (1985). 47. H.W. Emmons, “The Ceiling Jet in Fires,” Fire Safety Science, Proceedings of the Third International Symposium (G. Cox and B. Langford, eds.), Elsevier Applied Science, New York, p. 249 (1991). 48. W.R. Chan, E.E. Zukowski, and T. Kubota, “Experimental and Numerical Studies on Two-Dimensional Gravity Currents in a Horizontal Channel,” NISTGCR-93-630, National Institute of Standards and Technology, Gaithersburg, MD (1993). 49. G. Heskestad, “Propagation of Fire Smoke in a Corridor,” Proceedings of the 1987 ASME/JSME Thermal Engineering Conference, Vol. 1, American Society of Mechanical Engineers, New York (1987). 50. T. Hara and K. Shinsuke, “Numerical Simulation of Fire Plume-Induced Ceiling Jets Using the Standard κ – ε Model,” Fire Technology, 42, p. 131 (2006). Dr. Ronald L. Alpert received his undergraduate and graduate education at the Massachusetts Institute of Technology, where he majored in mechanical engineering. For nearly 35 years, he was with FM Global in various technical and managerial positions, ending his career there as an assistant vice president and manager of the Flammability Technology Research Program. Dr. Alpert was editor in chief of the Journal of Fire Protection Engineering for 10 years and a section editor of the NFPA Fire Protection Handbook, 20th edition. He has published numerous papers in refereed journals and technical reports.
15
Vent Flows Takeyoshi Tanaka
Introduction Fire releases a great amount of heat that causes the heated gas to expand. The expansion produced by a fire in a room drives some of the gas out of the room. Any opening through which gas can flow out of the fire room is called a vent. The most obvious vents in a fire room are open doors and open or broken windows. Ventilation ducts also provide important routes for gas release. A room in an average building may have all of its doors and windows closed and, if ventilation ducts are also closed, the gas will leak around normally closed doors and windows and through any holes made for pipes or wires. These holes will act as vents. (If a room were hermetically sealed, a relatively small fire would raise the pressure in the room and burst the window, door, or walls.) Gas will move only if it is pushed. The only forces acting on the gas are the gas pressure and gravity. Since gravity acts vertically, it might seem that gas could only flow through a hole in the floor or ceiling. Gravity, however, can produce horizontal pressure changes, which will be explained in detail below. A gas flow that is caused directly or indirectly by gravity is called a buoyant flow.
When a pressure difference exists across a vent, fluid (liquid or gas) will be pushed through. Precise calculation of such flows from the basic laws of nature can only be performed today by the largest computers. For fire purposes, and all engineering purposes, calculations are carried out with sufficient precision using the methods of hydraulics. Since these formulas are only approximate, they are made sufficiently accurate (often to within a few percent) by a flow coefficient. These coefficients are determined by experimental measurements.
Calculation Methods for Nonbuoyant Flows If a pressure drop, Δp ¼ p1 p2, exists across a vent of area, A, with a fluid density, ρ, the flow through the vent has (Fig. 15.1) [1] rffiffiffiffiffiffiffiffiffi 2Δ p ð15:1Þ Velocity u ¼ ρ rffiffiffiffiffiffiffiffiffi 2Δ p ρ
ð15:2Þ
and Mass flow
T. Tanaka (*) Fire Science and Technology, Kyoto University
V_ ¼ CA
Volume flow
pffiffiffiffiffiffiffiffiffiffiffiffi m_ ¼ CA 2ρΔ p
ð15:3Þ
In these formulas C is flow coefficient and the SI units are Δ p ¼ ðPaÞ ¼ ðN=m2 Þ, A ¼ ðm2 Þ, ρ ¼ ðkg=m3 Þ, u ¼ ðm=sÞ, V_ ¼ ðm3 =sÞ, m_ ¼ ðkg=sÞ.
M.J. Hurley (ed.), SFPE Handbook of Fire Protection Engineering, DOI 10.1007/978-1-4939-2565-0_15, # Society of Fire Protection Engineers 2016
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Fig. 15.1 Most fire vents are orifices
a
b Area A
Area A
Orifice
where A is area of vent and A1 is area of supply pipe. The factor 6895 converts pressure in lb/in.2 h i to Pascals while the factor 1 ðA=A1 Þ2
pg Area A
corrects Δp for the dynamic effect of the inlet velocity in the supply hose or pipe. In the atmosphere, the pressure at the ground, pa, is just sufficient to support the weight of the air above. If the air density is ρa, the pressure, p, at height, h, is less than pa by the weight of the air below height, h. Thus the pressure difference is
Area A1
pg
Area A1
Δ p ¼ pa p ¼ ρa gh
Area A
Fig. 15.2 A hose nozzle and a sprinkler nozzle
If the flow of water from a fire hose or sprinkler (Fig. 15.2) is to be calculated and the pressure, pg, is read on a gauge (in lb/in.2) at the entrance to the nozzle where the area is A1, the previous formulas provide the velocity, volume flow, and mass flow by using Δp ¼
6895 pg 1 ðA=A1 Þ2
Nozzle
ð15:4Þ
ð15:5Þ
It is sometimes convenient when considering fire gases to use h ¼ Δ p=ρa g, the pressure head, in meters of ambient air, in the velocity and flow rate formulas given above. The previous discussion supposes that the flowing fluid is of constant density. For liquids this is true for all practical situations. The density of air or fire gases will not change significantly during the flow through the vent so long as the pressure change is small, so they can also be treated as constant density fluids. If the pressure drop is large, the equations become more complicated [2]. If the pressure and density upstream of the vent are p1 and ρ1 while the pressure after the vent is p2, the equations for velocity and mass flow become
sffiffiffiffiffiffiffiffi( 2=γ " ðγ1Þ=γ #)1=2 2 p1 γ p2 p2 u¼ 1 ρ1 γ 1 p 1 p1
ð15:6Þ
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pffiffiffiffiffiffiffiffiffiffiffiffi m_ ¼ CA 2ρ1 p1
(
2=γ " ðγ1Þ=γ #)1=2 γ p2 p2 1 γ 1 p1 p1
where γ ¼ c p =cv . The value of γ depends on the complexity of the molecules of the flowing gas. For fire gases (which always contain a large amount of air) the value of γ will fall between 1.33 and 1.40. For most fire purposes the diatomic gas value (air) of 1.40 is sufficiently accurate. The mass flow given by the previous equation has a maximum at p2 ¼ p1
2 γþ1
γ=ðγ1Þ
ð15:8Þ
For γ ¼ 1.40, the maximum flow is reached for a downstream pressure p2 ¼ 0:528 p1 . For all lower back pressures the flow remains constant at its maximum " ðγþ1Þ ðγ1Þ #1=2 2 pffiffiffiffiffiffiffiffiffiffi m_ ¼ CA ρ1 p1 γ γþ1 ð15:9Þ With these equations, the mathematical description of the rate of flow of liquids and gases through holes is complete as soon as the appropriate flow coefficients are known. The coefficients, found by experiment, correct the formulas for the effect of the fluid viscosity, the nonuniformity of the velocity over the vent, turbulence and heat transfer effects, the details of nozzle shape, the location of the pressure measurement points, and so forth. The corrections also depend on the properties and velocity of the fluid. The most important coefficient correction for any given vent geometry is the dimensionless combination of variables called the Reynolds number, Re, and Re ¼
uDρ μ
ð15:7Þ
ρ ¼ Density of the fluid approaching the vent μ ¼ Viscosity of the fluid approaching the vent A door or window vent is almost always rectangular, not circular. The D to be used in the Reynolds number should be the hydraulic diameter D¼
4A P
ð15:11Þ
where A ¼ Area of the vent P ¼ Perimeter of vent For a rectangular vent, a wide and b high, A ¼ ab, P ¼ 2ða þ bÞ. D¼
2ab ð a þ bÞ
ð15:12Þ
The experimental values of the flow coefficients for nozzles and orifices, C, are given in Fig. 15.3 [2]. Flow coefficients for nozzles are near unity while for orifices are approximately 0.6, as can be seen in Fig. 15.1, where the flow from an orifice separates from the edge of the orifice and decreases to a much smaller area, in fact about 0.6 of the orifice area. For most fire applications the Reynolds number will be about 106. Sprinklers and fire nozzles are small but the velocity is quite high. Conversely, ventilation systems of buildings are larger but have a lower velocity. Finally, doors and windows in the areas of a building not too near the fire are still larger but the velocity is still smaller. For most purposes the flow coefficient can be set as C ¼ 0:98 for a nozzle and C ¼ 0:60 for an orifice.
ð15:10Þ
where u ¼ Velocity of the fluid given by the previous equations D ¼ Diameter of the nozzle or orifice
Buoyant Flows Through Vertical Vents A fire in a room causes gases to flow out through a vent by two processes. The heating of the air in a room causes the air to expand, pushing other air
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Fig. 15.3 Orifice and nozzle flow coefficients
1.0 Nozzle
Flow coefficient
0.9 P1 P2
0.8
P1 P 2
0.7
Orifice
0.6 0.5 104
Fig. 15.4 Pressure gradients: (a) each side of a door; (b) superimposed on a pressure versus height graph
105 106 Reynolds number (Re)
a
107
b h
hv hn
pf
out through all available vents and hence throughout the entire building. At the same time, the heated air, with products of combustion and smoke, rises in a plume to the ceiling. When the hot layer of gas at the ceiling becomes deep enough to fall below the top of a vent, some hot gas will flow out through the vent. As the fire grows, the buoyant flow out will exceed the gas expansion by the fire. Thus the pressure in the fire room at the floor will fall below atmospheric, and outside air will flow in at the bottom. A familiar sight develops, where smoke and perhaps flames issue out the top of a window while fresh air flows in near the bottom. This buoyant flow mechanism allows a fire to draw in new oxygen so essential for its continuation. For these buoyantly driven flows to occur, there must be a pressure difference across the vent. Figure 15.4 illustrates how these pressure differences are produced. The pressure difference at the floor is
p
pa
pf
Δ p f ¼ p f pa
pa
ð15:13Þ
where pf ¼ Pressure at the floor inside the room in front of the vent pa ¼ Pressure at the floor level outside of the room just beyond the vent The pressure at height y is less than the pressure at the floor and can be found by the following hydrostatic equations: ðy Inside p1 ¼ p f ρ1 gdy ð15:14Þ 0
Outside
p2 ¼ pa
ðy
ρ2 gdy
ð15:15Þ
0
The pressure difference at height, h, is Δ p ¼ p1 p2 ðh ¼ Δ p f þ ðρ2 ρ1 Þg dy 0
ð15:16Þ
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Since the outside density, ρ2, is greater than the inside density, ρ1, the integral is positive so that Δp is often positive (outflow) at the top of the vent and negative (inflow) at the bottom. The flow properties at the elevation, h, are the same as previously given. sffiffiffiffiffiffiffiffiffi 2Δ p u¼ ð15:17Þ ρ V_ ¼C A
sffiffiffiffiffiffiffiffiffi 2Δ p ρ
pffiffiffiffiffiffiffiffiffiffiffiffi m_ ¼ C 2ρΔ p A
ð15:18Þ
ð15:19Þ
Since they are not the same at different heights in the vent, the volume and mass flow are given as flow per unit area.
Measuring Vent Flows in a Fire Experiment Sufficient measurements must be made to evaluate ρ and Δp to allow use of Equation 15.19. There are four different available methods that differ in simplicity, accuracy, and cost. Method 1 The dynamic pressure distribution can be measured in the plane of the vent. This measurement requires a sensitive pressure meter. The pressure difference is almost always less than the atmospheric pressure difference between the floor, pf, and the ceiling, pc. For a room 2.5 m in height the atmospheric pressure difference is p f pc ¼ ρa gH ¼ 1:176 9:81 2:5 ¼ 28:84 Pascals
ð3:0 mm H2 OÞ
This is only p f pc 28:84 ¼ 101, 325 pa ¼ 0:00028 fraction of atmospheric pressure
Thus the buoyantly driven flow velocities induced by a room fire could be as high as rffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2Δ p 2 28:84 u¼ ¼ ¼ 7:00 m=s ρ 1:176
ð23 ft=sÞ
Since the pressure varies with height and time, a series of pressure probes is required and each should have its own meter or a rapid activation switch. Although standard pitot tubes are the most accurate dynamic pressure probes, they are sensitive to flow direction and would have to be adjusted at each location for the direction of the local flow, especially for outflow and inflow. The probe orientation would need to be continually changed as the fire progressed. A single string of fixed-orientation pressure probes arranged vertically down the center of the door increases convenience of the measurement but forces a decrease in accuracy. The out-in flow problem is avoided by use of bidirectional probes in place of pitot tubes [3] (Fig. 15.5). These probes give velocities within 10 % over an angular range of 50 degrees of the probe axis in any direction. Determination of the local velocity also requires the measurement of the local gas density. The density of fire gases can be determined from measured gas temperatures with sufficient accuracy by the ideal gas law ρ¼
Mp RT
ð15:20Þ
where M ¼ Average molecular weight of flowing gas R ¼ 8314
J ¼ Universal gas constant kg mol K
As noted previously, the pressure changes only by a very small percentage throughout a building so its effect on gas density is negligible. Fire gases contain large quantities of nitrogen from the air and a variety of other compounds. The average molecular weight of the mixture will be close to but somewhat larger than that of air. Incomplete knowledge of the actual composition of fire gas prevents high-accuracy calculations. For most fire calculations, it is accurate enough
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Fig. 15.5 A bidirectional flow probe
Support tubes (Connect press taps to indicating instrument)
0.572D
0.286D
Press. taps
Barrier 0.143D
0.857D
( )
D 7" 8
2D
to neglect the effect of the change of molecular weight from that of air (Ma ¼ 28.95). Density of gas is determined primarily by its temperature (which may vary by a factor of 4 in a fire). Thus ρ¼
352:8 kg T m3
ð15:21Þ
where T is temperature in Kelvin (¼ C + 273). A string of thermocouples must be included along with the bidirectional probes to measure vent flows. For higher accuracy, aspirated thermocouples must be used or a correction made for the effect of fire radiation [3]. The temperature and, hence, the gas density will vary over the entire hot vent outflow. To determine the temperature distribution so completely would require an impracticably large number of thermocouples. Fortunately, the temperature in the vent is a reflection of the temperature distribution in the hot layer inside the room, which normally is stratified, and hence varies most pffiffiffiffiffiffiffiffiffiffi u ¼ 0:070 TΔ p pffiffiffiffiffiffiffiffiffiffi u ¼ 5:81 TΔ p
N Δp 2 m lb Δp in:2
strongly with the distance from the ceiling. Thus a string of thermocouples hanging vertically on the centerline of the vent is usually considered to be the best that can be done in a practical fire test. Special care must be exercised to keep the test fire some distance away from the entrance to the vent. Since a fire near a vent has effects at present unknown, fire model calculations of real fire vent flows under such conditions will be of unknown accuracy. The velocity distribution vertically in the vent is given by sffiffiffiffiffiffiffiffiffi 2Δ p u ¼ 0:93 ð15:22Þ ρ where ρ follows from Equation 15.21 using the temperature distribution in the vent with a calibration factor of 0.93 for the bidirectional probes [4]. Using ρ from Equation 15.21 gives the directly useful forms
pressure measured with bidirectional probe
ð15:23Þ
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where
If the bidirectional probe pressures are measured in psi, the coefficient 16.79 must be replaced by 1394.
u is in ðm=sÞ T is in ðKÞ Except for very early stages of a room fire, there will be flow out at the top (u, Δp > 0) and flow in at the bottom (u, Δp > 0).1 Thus there is a position in the vent at which u ¼ 0, which is the vertical location where the pressure inside is equal to that outside. This elevation, hn, is called the neutral axis. Defining the elevation of the vent sill as hb (hb ¼ 0 for a door) and the elevation of the soffit as ht, the flows are given by ð ht ð15:24Þ Flow out m_ u ¼ C ρub dy hn
Flow in
ð hn _ m d ¼ C ρub dy
Δ p ¼ Δ p f þ 3461 ð15:25Þ
hb
where b ¼ Width of the vent C ¼ Experimentally determined flow coefficient (¼ 0.68) [5] Using Equations 15.21 and 15.22 and C ¼ 0.68 into these equations, the most convenient forms are ð ht rffiffiffiffiffiffiffi Δp Flow out m_ u ¼ 16:79 b dy ðkg=sÞ Tv hn ð15:26Þ Flow in
m_ d ¼ 16:79
Method 2 A somewhat simpler but less accurate procedure to measure vent flows requires the measurement of the pressure difference at the floor (or some other height). One pressure difference measurement together with the vertical temperature distribution measurement, T1, inside the room (about one vent width in from the vent) and T2, outside the vent (well away from the vent flow), provides the density information required to find the pressure drop at all elevations (Equation 15.16).
ð hn rffiffiffiffiffiffiffi Δp dy ðkg=sÞ b Tv hb ð15:27Þ
where Δp ¼ Pressure drop in Pascals measured with bidirectional probe as a function of y b ¼ Width of the vent in m TV ¼ Temperature (K) in the vent measured as a function of y 1 Equation 15.23 should be written u ¼ (sign Δp)K pffiffiffiffiffiffiffiffiffiffiffiffiffi TjΔ pj since when Δp < 0 the absolute value must be used to avoid the square root of a negative number and the sign of the velocity changes since the flow is in and not out.
ðy 0
1 1 dy ð15:28Þ T2 T1
For most fires, Δpf will be negative; that is, the pressure at the floor inside the fire room will be less than the pressure outside. This is only true for a fire room with a normal size vent (door, window). For a completely closed room the inside pressure is well above the outside pressure. Since the temperature inside the fire room is higher than that outside, Equation 15.28 gives a Δp that becomes less negative, passes through zero at the neutral axis, hn, and becomes positive at higher levels in the fire room. The vertical location of the neutral axis is, therefore, readily found from Equation 15.28. The calculation of the pressure distribution requires measurement of the temperature distribution both inside, T1, and outside, T2, of the vent. However, calculation of the flow requires a knowledge of the density distribution in the vent itself. Thus a third thermocouple string is required to measure the temperature distribution, Tu, in the vent. The desired flow properties [6] are Velocity sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffi ðy 2Δ p 1 1 u¼ dy ðm=sÞ ¼ 4:33 T v ρ T1 hn T 2
ð15:29Þ
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Fig. 15.6 Buoyant flow out of the window of a fire room
ρ u
y hV
δ hn hi
ρa
ht
d hb
Room 1
Flow out ð ht m_ u ¼ C ρbu dy hn
¼ 1063
1=2 ð ht ð y 1 1 1 b dy dy T v hn T 2 T 1 hn ð15:30Þ
Flow in ð hn m_ d ¼ C ρbu dy hb
1=2 ð ht ð y 1 1 1 dy dy ¼ 1063 b T v hb T 2 T 1 hn ð15:31Þ where b ¼ Width of the vent at height y Δp ¼ Calculated from Equation 15.16 using the temperatures (and thus densities) inside and outside of the room ρ ¼ Density computed from the temperature in the vent (Note that for inflow Δp is negative. Therefore, the equation takes the square root of the magnitude |Δp| while its sign gives the flow direction.) Method 3 The use of a sensitive pressure meter can be avoided entirely by visually (or better,
Room 2
photographically) locating the bottom of the outflow in the vent during the test at the position of the neutral axis, hn, where Δp ¼ 0. Method 3 is the same as Method 2 except that the neutral axis location is found directly by experiment rather than being deduced from the pressures. The distribution of pressure drop across the vent is found by integrating Equation 15.16 above (Δp > 0) and below (Δp < 0) hn using the density distribution inside, ρ1, and outside, ρ2, the room. The flow properties are computed as before from Equations 15.29, 15.30 and 15.31. Method 4 A simpler but less accurate method uses the fair assumption that the gas in the fire room soon separates into a nearly uniform hot layer of density, ρ, with a nearly uniform cold layer below of density, ρd. This separation with appropriate notation is shown in Fig. 15.6. In this approximation the appropriate flow formulas [5] are Outflow
ρa ρ 1=2 uu ¼ 2g y ρ
ð15:32Þ
where y is distance above the neutral plane 2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi m_ u ¼ Cb 2gρðρa ρÞðhv hn Þ3=2 ð15:33Þ 3 The inflow by this two-layer method depends on δ, which is small and cannot be determined
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463
with sufficient accuracy because of the effect of gas motions in the fire room. The neutral axis may be found in several ways: 1. It may be located visually or photographically during the test. 2. It may be found from the vent temperature distribution by locating [visually on a plot of TV( y)] the position just below the most rapid temperature rise from bottom to top of the vent. The lower-layer temperature, Td, of the two-layer model is taken as the gas temperature just above the vent sill. The upper-layer temperature, Tu, is chosen so that the two-layer model has the same total mass (i.e., the same mean density) in the vent as the real flow.2 ð 1 1 hv dy hn hv hn ¼ þ ¼ T hv 0 T hv T d hv T u
ð15:34Þ
The densities ρa and ρ are found using Equation 15.21 from the temperatures Ta and Tu, respectively. The outflow velocity and mass flow are found from Equations 15.32 and 15.33. An estimate of the air inflow rate can be found if the test has included the measurement of the oxygen concentration in the gases leaving the fire room. The gas outflow rate is equal to the inflow rate plus the fuel vaporized, except for the effect of transient variations in the hot layer depth. Thus 1 þ yO2 λ m_ d ¼ m_ u ð15:35Þ 1 þ 0:23λ where λ is the effective fuel-air ratio.
2
Sometimes the mean temperatures, T of the two-layer model and the real flow are also used and both hn and Tu are determined (using Td as above). The requirement of identical T is arbitrary, sometimes leads to impractical results, and is not recommended.
The flow coefficient to be used for buoyant flows is 0.68 as determined by specific experiments designed for the purpose. For nonbuoyant flows (nozzles and orifices), the flow coefficients are determined to better than 1 % and presented as a function of the Reynolds number as in Fig. 15.3. This accuracy is possible because the fluid can be collected and measured (by weight or volume). For buoyant flows the experiments are much more difficult because the hot outflow and cold inflow cannot be collected and weighed. The best fire-gas vent flow coefficient measurements to date [6, 7] have 10 % accuracy with occasional values as bad as 100 % (for inflow). The most accurate buoyant flow coefficients were measured not for fire gases but for two nonmiscible liquids (kerosene and water) [7]. In this case the two fluids could be separated and measured, and the value 0.68 was found except for the very low flow rates (near the beginning of a fire). When buoyant flow coefficients can be measured within a few percent accuracy, they will be a function of the Reynolds number, Re ¼ uhvρ/μ; the Froude number, Fr ¼ u2ρa/ghv(ρ ρa); and the depth parameter, hn/hv. The best option now available is to use C ¼ 0.68 and expect 10 % errors in flow calculations. Note that the above four methods require a knowledge of hn, the dividing line between outflow above and inflow below. It would be useful to have a simple formula by which hn could be calculated without any special measurements. What determines hn? The fire at the start sends a plume of heated gas toward the ceiling and, by gas expansion, pushes some gas out of the vent. The hot plume gases accumulate at the ceiling with little, if any, flowing out the vent. After a time, depending on the size of the room, the hot layer depth becomes so large that its lower surface falls below the top of the vent. Hot gas begins to flow out. When a fire has progressed to a second room, there is a hot layer on each side of a connecting vent. Thus (with two layers on each side) there
464 Fig. 15.7 Some selected two-layer vent pressure drop distributions. Dotted line is pressure distribution in room 1; solid line is pressure distribution in room 2
T. Tanaka
a
b
c
d
e n
n
n
n n
n n
are as many as four different gas densities: ρd1 is greater than ρ1, densities below and above in room 1, and ρd2 is greater than ρ2, densities below and above in room 2. There are also four pertinent levels: hb, sill height (0 if the vent is a door); ht, soffit height; hi1 , interface height in room 1; hi2 , interface height in room 2. There are many different flow situations possible depending on these eight values. The pressure variation from floor to ceiling in each room depends on the densities and layer heights in the room. In addition, the pressure difference between the two rooms (at the floor, for example) may have any value depending on the fire in each room, all the room vents, and especially the vent (or vents) connecting the two rooms. Figure 15.7 shows a few of the possible pressure distributions. The pressure distribution in room 1 is shown with a dotted line while that in room 2 is shown as a solid line. In Fig. 15.7a, there are no hot layers, the pressure in room 1 at every level is higher than that in room 2, and the flow is everywhere out (positive) (room 1 to room 2). In Fig. 15.7b, a common situation exists. The density in room 2 is uniform (perhaps the outside atmosphere). Room 1 has a hot layer and a floor pressure difference such that there is outflow at the top, inflow at the bottom, and a single neutral axis somewhat above the hot-cold interface in the room. In Fig. 15.7c, the flow situation is similar to that in Fig. 15.7b, although there are hot layers in both rooms (but with a neutral axis above the interface in room 1 and below the interface in room 2).
In Fig. 15.7d, the densities (slopes of pressure distribution lines) are somewhat different than those in Fig. 15.7c (the hot layer in room 2 is less deep but hotter than that in room 1). Consequently, there are two neutral axes with a new small inflow layer at the top, three flow layers in all—two in and one out. In Fig. 15.7e, the densities and floor level pressure difference are such that there are four flow layers, two out and two in, with three neutral axes. These five cases do not exhaust the possible vent flow situations. Figure 15.7a, b accounts for all cases early in a fire and all cases of vents from inside to outside of a building. They are also the only cases for which experimental data are available. The case illustrated in Fig. 15.7c is common inside a building after a fire has progressed to the point that hot layers exist in the two rooms on each side of a vent. The cases illustrated in Fig. 15.7d, e have not been directly observed but probably account for an occasional confused flow pattern. (In fact, the above discussion assumes two distinct layers in each room.) The layers are seldom sharply defined and in this case there may be many neutral axes, or regions, with a confusing array of in-out flow layers. These confused flow situations are probably not of much importance in a fire since they seldom occur and when they do they don’t last very long. The previous discussion of the possible two-layer flow situation is very important for the zone modeling of a fire. Fire models to date are all two-layer models (a three- or more layer model will present far more complex vent flows than those pictured in Fig. 15.7). In fire computation by a zone model, cases such as (d) and
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Fig. 15.8 Sample fire room and doorway temperature distributions Height above floor (m)
1.85 In doorway
1.5
1
In room 0.5
300
(e) in Fig. 15.7 will be unimportant to fire development. However, since these situations can arise, they should be handled via fire computation, that is, by computing the flow layer by layer. Each layer has a linear pressure variation from sill, interface, or neutral axis up to the next interface, neutral axis, or soffit. By use of the pressure drop at the floor and the room densities on each side of the vent in Equation 15.16, the position, hi, of all layers and the sill, interfaces, neutral axes, and soffit will be known. Thus, for each layer (defined as j) the pressure drop at the bottom, Δpj, and at the top, Δpj+1, will be known. Since the room densities are constant in each room for each layer, the vent pressure drop will vary linearly from Δpj to Δpj+1. The flow in each layer from room 1 to room 2, found by integration [8], is given by pffiffiffiffiffi 2 m_ i ¼ ðsign αÞC b h jþ1 hj 2ρ 3 0 q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 1 Δ pj þ Δ pj Δ pjþ1 þ Δ pjþ1 C B q ffiffiffiffiffiffiffiffiffiffiffi q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi @ A Δ pj þ Δ pjþ1 ð15:36Þ where Δ pj þ Δ pjþ1 whose sign determines α¼ 2 the in‐out direction of the flow ρ ¼ Density of the gas flowing in the flow layer i
350
Thus ( ρ¼
400 Temperature (K)
450
Density in room 1 at height hþj
if α > 0
Density in room 2 at height hþ i
if α < 0
This flow calculation appears complex but can be coded quite easily for computer use and then used to calculate all the possible cases. Although all vent flows can now be calculated, the path of each layer of gas flow when it enters a room is still needed for fire modeling. If the two-layer model is to be preserved, each inflow must mix with the hot layer or the cold layer, or be divided between them. No information is yet available as to the best solution to this problem. To illustrate these various methods of flow calculation, some test data from a steady burner fire in a room at the U.S. Bureau of Standards [6] are used. Some typical data are shown in Fig. 15.8. Accurate results, even in a steadystate fire, are difficult to obtain and questions about the data in this figure will be noted as appropriate. The vent temperatures were measured by small-diameter bare thermocouples for which there is some unknown radiation correction. This unknown correction may account for the top vent temperature being higher than that in the fire room. The vent was 1.83 m high, 0.737 m wide, and the outflow measured with bidirectional probes (not corrected for flow angle) was 0.588 kg/s for a fire output of 0.63 kW. The ambient
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T. Tanaka
temperature was 21.3 C (¼ 294.3 K). This flow was determined by using Method 1. Method 2 uses the known location of the neutral axis and requires the integration of Equations 15.30 and 15.31. In this way the data of Fig. 15.8 gives outflow of 0.599 kg/s, 1.8 % higher compared to Method 1 and inflow of 0.652 kg/s. A measured (by bidirectional probes) inflow is not given, but it seems odd that the inflow is greater than the outflow since inflow must be smaller than the outflow by the mass rate of fuel burned at steady state. Data for use of Method 3 are not available. Method 4 requires the selection from Fig. 15.8 of a neutral axis location and inlet temperature.
In the figure the rapid temperature rise in the vent begins at about 1 m. Hence this height is chosen as the neutral axis. The lowest inlet temperature is Td ¼ 308 K. By computing (1/Tv) the average value was found to be (1/Tv) ¼ 2.875 103. Now by Equation 15.34 2:875 103 ¼
1:00 0 1:83 1:00 þ 1:83 308 1:83 T u
Thus Tu ¼ 411.9 K. The corresponding density is ρ ¼ 352.8/411.9 ¼ 0.8565 kg/m3. From the ambient temperature, Ta, we find ρa ¼ 352.8/ 294.3 ¼ 1.199 kg/m3. Thus the outflow by Equation 15.33 is
2 m_ u ¼ 0:68 0:737½2 9:81 0:8565ð1:199 0:8565Þ1=2 3 ð1:83 1Þ3=2 ¼ 0:607 kg=s This value is 3.2 % higher compared to Method 1.
Buoyant Flows Through Horizontal Vents Unlike flows through vents in a vertical wall or non-buoyant flows through orifices, not ample quantitative works have been done on buoyant flows through vents in horizontal or slightly
Fig. 15.9 Possible scenarios of horizontal vent flow in fire where the standard Bernoulli’s flow equation becomes inadequate
sloped surfaces. Such buoyant flows through horizontal vents can become issue in some situations associated with fire, particularly in such a configuration as exemplified in Fig. 15.9, which may arise in fires in basements of buildings, holds in ships and multi-floor building containing rooms closed to the outdoors. The flow rate through a horizontal opening can be treated, as done in vertical vents, by using Bernoulli’s equation if there is no temperature difference between the connecting spaces
VENT
VENT
FIRE
FIRE
15
Vent Flows
467
or if there is a large enough pressure difference across the vent. Let Δp be the pressure difference across the vent defined by Δ p ¼ pU pL
ð15:37Þ
where
pU and pL ¼ Pressures at the vent elevation in the upper and lower spaces, respectively. The standard vent flow model using Bernoulli’s equation would predict the flow rate through a horizontal vent as follows according to the value of Δp, illustrated in Fig. 15.10:
ðaÞ when Δ p < 0 : V_ U ¼ CAV ð bÞ
when Δ p ¼ 0 :
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2Δ p=ρL ; V_ L ¼ 0
V_ U ¼ 0; V_ L ¼ 0
ðcÞ when Δ p > 0 : V_ U ¼ 0; V_ L ¼ CAV
where V_ U and V_ L ¼ Volume rates of flows to upper and lower spaces through the vent, respectively AV ¼ Vent area C ¼ Vena contracta ρL and ρU ¼ Air densities in lower and upper spaces, respectively. However, this method will fail, over certain ranges of pressure difference, when temperature difference exists between the spaces due to the antagonistic effect of buoyancy to pressure gradient. Consider the situation where the lower space temperature is higher than upper space temperature, for example. There is a flow across the vent due to the air density difference Δρð¼ ρU ρL Þ even if the pressure difference, Δp, is basically zero. In such a case as mentioned earlier in Fig. 15.9, where a pace has no other air passage besides the vent between the connecting spaces, a bidirectional flow will occur through the vent in a certain range around Δp ¼ 0 and the upward and downward flow rates will become equal due to continuity. The horizontal vent flows under zero pressure difference, Δp ¼ 0, was investigated by Epstein [9], Tan and Jaluria [10] and others, using brinewater scale models. In these experiments, the effects of vent configuration on the flow characteristics were investigated for a large range of opening size and aspect ratio. Also, Heiselberg [11] conducted the experiments for the same purpose using a single opening test
ð15:38aÞ ð15:38bÞ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2jΔ pj=ρU
ð15:38cÞ
room set in a full-scale thermostatic chamber, where the air in the test room was heated by an electric heating system while the temperature in the thermostatic chamber was controlled by an air conditioning system. While circular orifices were used in the brine-water experiments by Estein and others, square openings were adopted in the Heiselberg’s experiments as the vent. The conceptual configuration of the vents in their experimental setup is illustrated in Fig. 15.11.
a
Δp < 0 : VU > 0; VL = 0 b Δp = 0 : VU = 0; VL = 0 c
Δp > 0 : VU = 0; VL > 0 Fig. 15.10 The standard vent flow model for horizontal vents
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T. Tanaka
TU, rU
D VENT
L
TL, rL
Fig. 15.11 Schematic configuration of vents in the existing experiments for horizontal vent flow
The flow through a horizontal vent under Δp ¼ 0 condition is often unstable. Epstein [9] identified four regimes of the exchange flow as a function of aspect ratio of the vent as follows: Regime I (L/D < 0.15): Oscillatory exchange flow
Fr ¼
8 > > 0:055 > > > > > > > > 1=2 > > > 0:147 DL > >
> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi q 0:093 < 3:25 0:4 < > > 3 > D > 1 þ 0:084 DL 0:4 > > > > > > > L 3=2 L > > : 0:32 D 3:25 < < 10 D
where V_ EX ¼ Exchange volume flow rate TL ¼ Temperature in lower space TU ¼ Temperature in upper space g ¼ acceleration due to gravity Heiselberg, adopting the same Fr as Equation 15.39, developed a similar formula based on his experimental data using the airs at different temperature as follows:
8 > > 0:050 > > > > > > > 1=2 < L Fr ¼ 0:147 > D > > > > 1=2 > > L > > : 0:077 D
ð15:40Þ
L < 0:115 D
L 0:115 < < 0:55 D
0:55
> ...........................> > ; f N ð p1 , . . . , pi . . . , pN Þ ¼ 0
ð15:86Þ
A multidimensional Newton–Raphson method may be used for the solution of Equation 15.86. The iteration procedure is expressed by
f (p) f (p (1)) f (p (3))
p (2) p (1)
p p (3)
f (p (2))
15
Vent Flows
483
49 0.38
0.41
21
1.63
41
27 1.74
1.27
1.38 1.99
20
0.76
20 1.46
0.79
20
0.61
39
25 1.10
0.90
0.69
20
0.75
20
0.77
25
20 23 1.35
0.34
1.37
0.55
35 1.17
0.04 0.70
0.30
20
0.71
0.54
0.24
20
0.34
0.41
21 0.65
391
102
0.11
2.21
1.29 0.18
38
0.96
4.57
207
226
1.08
1.14 0.97
0.31
0.93 38
0.69 0.69
0.69
0.69
20
20
20
21
3.29 20
Fig. 15.26 An example of smoke movement prediction by a two-layer zone model (Number: temperature [ C], number !: vent flow rate or plume flow rate [kg/s])
h i1 h i pðkþ1Þ ¼ pðkÞ JðkÞ f pðkÞ
ð15:87Þ
where p ¼ ( p1,. . ., pi,. . ., pN) and f ¼ ( f1,. . ., f2,. . ., fN) and [J] is the Jacobian matrix defined by 2
∂ f 1 =∂ p1 6 ... 6 ½J ¼ 6 6 ∂ f i =∂ p1 4 ... ∂ f N =∂ p1
... ... ... ... ...
∂ f 1 =∂ p j ... ∂ f i =∂ p j ... ∂ f N =∂ p j
... ... ... ... ...
3 ∂ f 1 =∂ pN 7 ... 7 ∂ f j =∂ pN 7 7 5 ... ∂ f N =∂ pN
ð15:88Þ In actual calculation, the inverse matrix of the Jacobian matrix, [J(k)]1, is not calculated but the coupling linear equations h i h i J ðkÞ Δ p ¼ f pðkÞ ð15:89Þ are directly solved using an appropriate method such as Gaussian elimination for correction pressure increments Δp and the new estimate is calculated as
pðkþ1Þ ¼ pðkÞ þ Δ p
ð15:90Þ
Figure 15.26 shows an example of smoke movement in a building predicted using the two-layer zone model BRI2, in which vent smoke and air flows were calculated using the above multidimensional Newton–Raphson method.
Summary Most of the equations for vent flows in this chapter are basically derived from Bernoulli’s equation for steady flow of ideal and incompressible fluid. The mass and volume vent flows are given as a function of the flowing gas density, area of the vent, and the pressure difference across the vent with a coefficient called flow coefficient or opening coefficient. The value of the flow coefficient, C, varies depending on the size and shape
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of a vent. For usual doorway openings and windows in a building, the value of the C is known to be from 0.6 to 0.7 from many experimental measurements. In a building fire, the heat release and the flows induced by the fire cause temperature distributions in spaces in the building, which then cause vertical pressure difference distribution across a vent. When such a vertical temperature distribution exists across a vent, it is often convenient for calculation of the vent flow rates to first obtain the neutral plane height, which is given as a function of the pressure difference at a reference height and gas density difference in the spaces at both sides of the vent. The equation to control the space (room) pressures at a reference height in building spaces can be obtained by considering the mass and heat conservations in the spaces and the equation of gas state. In general, the equation is a function of the vent flow rates, the temperatures of the spaces, and the heat addition and loss, but at steady state, it is reduced to be the mass conservations of the spaces. When multiple spaces are involved in a calculation of the flows in fire, analytical solutions are only possible for very limited conditions, so generally some numerical calculation method must be invoked to solve the coupling nonlinear equations for the space pressures.
Nomenclature A a b C cp cv D Fr g Gr h [J] L M ˙ m
Area (m2) Length (m) Width (m) Flow coefficient () Specific heat at constant pressure (kJ/kg K) Specific heat at constant volume (kJ/kg K) Orifice diameter (m) Froude number () Gravity constant (m/s2) Grashof number () Height (m) Jacobian matrix Orifice length (m) Molecular weight (kg/kg mol) Mass flow rate (kg/s)
P p Q_ Q_
h
R Re T u V V_ VR y αK Δ δ γ ¼ cp/cv Π ρ μ
Perimeter (m) Pressure (Pa) Heat release rate of fire source (kW) Heat loss by heat transfer (kW) Gas constant (J/kg mol K) Reynolds number () Temperature (K) Velocity (m/s) Volume (m3) Volume flow rate (m3/s) Room volume (m3) Vertical coordinate (m) Effective heat transfer coefficient (kW/m2K) Increment of Depth (see Fig. 15.6) (m) Isentropic exponent () Non-dimensional pressure () Density (kg/m3) Viscosity (Ns/m2)
Subscripts a b c d f g i ij j L, l n O2 t u, U v, V 0 1 2
Atmosphere Sill of vent Ceiling of room Lower Floor Gauge Hot-cold interface From room (layer) i to room (layer) j Index of layer Lower Neutral axis Oxygen Soffit of vent Upper Vent, in the vent Reference height Upstream of orifice Downstream of orifice
References 1. H. Rouse, Fluid Mechanics for Hydraulic Engineers, McGraw-Hill, New York (1938). 2. Mark’s Mechanical Engineers Handbook, McGrawHill, New York (1958).
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Vent Flows
3. J.S. Newman and P.A. Croce, Serial No. 21011.4, Factory Mutual Research Corp., Norwood, MA (1985). 4. D.J. McCaffrey and G. Heskestad, “Robust Bidirectional Low-Velocity Probe for Flame and Fire Application—Brief Communications,” Combustion and Flame, 26, pp. 125–127 (1976). 5. J. Prahl and H.W. Emmons, “Fire Induced Flow Through an Opening,” Combustion and Flame, 25, pp. 369–385 (1975). 6. K.D. Steckler, H.R. Baum, and J. Quintiere, 20th Symposium on Combustion, Pittsburgh, PA (1984). 7. J. Quintiere and K. DenBraven, NBSIR 78–1512, National Bureau of Standards, Washington, DC (1978). 8. H.E. Mitler and H.W. Emmons, NBS-GCR-81-344, National Bureau of Standards, Washington, DC (1981). 9. M. Epstein, “Buoyancy-driven exchange flow through small openings in horizontal partition, with special reference to flows in multicompartment enclosures”, Journal of Heat Transfer, 110, pp.885–893 (1988) 10. Q. Tan and Y. Jaluria, NIST-G&R-92-607, National Institute of Standards and Technology, Gaithersburg, MD (1992). 11. Heiselberg, P. and Li, Z., (2007), "Experimental study of buoyancy driven natural ventilation through horizontal openings", Proceedings of Roomvent 2007 : Helsinki 13–15 June 2007.. 12. M. Epstein and M.A. Kenton, “Combined Natural Convection and Forced Flow Through Small Openings in a Horizontal Partition, with Special Reference to Flows in Multicompartment Enclosures,” Journal of Heat Transfer, 111, pp. 980–987 (1989). 13. G. Heskestad and R. D. Spaulding, “Inflow of air required at wall and ceiling apertures to prevent escape of fire smoke”, Proceeding of the 3rd International Symposium on Fire Safety Science, pp.919–928 (1991)
485 14. L. Y. Cooper, “Combined buoyancy- and pressuredriven flow through a shallow, horizontal, circular vent”, HTD-Vol. 299, Heat Transfer With Combined Modes, ASME, Chicago (1994). 15. T. Tanaka, “A Model of Multiroom Fire Spread,” Fire Science and Technology, 3, p. 105 (1983). 16. S. Yamada and T. Tanaka, “Reduced Scale Experiments for Convective Heat Transfer in the Early Stage of Fires,” International Journal on Engineering Performance-Based Codes, 1, 3, pp. 196–203 (1999). 17. T. Tanaka and T. Yamana, “Smoke Control in Large Scale Spaces (Part 1, Analytic theories for simple smoke control problems),” Fire Science and Technology, 5, 1, pp. 31–40 (1985). 18. T. Tanaka, “Performance-Based Fire Safety Design Standards and FSE Tools for Compliance Verification,” International Journal on Engineering Performance-Based Codes, 1, 3, pp. 104–117 (1999). 19. B.J. McCaffrey, J.G. Quintiere, and M.F. Herkeleroad, “Estimating Room Temperature and Likelihood of Flashover Using Fire Test Data Corrections,” Fire Technology, 17, 2, pp. 98–119 (1981). 20. T. Tanaka and K. Nakamura, “A Model for Predicting Smoke Transport in Buildings,” Report of the Building Research Institute, No. 123, Ministry of Construction, Tsukuba, Japan (1989). 21. T. Tanaka and S. Yamada, “BRI2002: Two Layer Zone Smoke Transport Model,” Fire Science and Technology, 23, Special Issue (2004).
Takeyoshi Tanaka is a professor emeritus at Kyoto University. His performance–based areas of expertise are fire modeling, smoke control, and fire safety design. His professional experience includes research for the Building Research Institute of Japan’s Ministry of Construction.
Effect of Combustion Conditions on Species Production
16
Daniel T. Gottuk and Brian Y. Lattimer
Introduction A complete compartment fire hazard assessment requires a knowledge of toxic chemical species production. Although combustion products include a vast number of chemical species, in practical circumstances the bulk of the product gas mixture can be characterized by less than 10 species. Of these, carbon monoxide (CO) represents the most common fire toxicant (see Chap. 63). Over half of all fire fatalities have been attributed to CO inhalation [1, 2]. Concentrations as low as 4000 ppm (0.4 % by volume) can be fatal in less than an hour, and carbon monoxide levels of several percent have been observed in full-scale compartment fires. A complete toxicity assessment should not only include the toxicity of CO but also include the synergistic effects of other combustion products, such as elevated CO2 and deficient O2 levels. The transport of combustion products away from the room of the fire’s origin is of the utmost importance, because nearly 75 % of the fatalities due to smoke inhalation occur in these remote locations [3]. However, conditions close to the compartment of origin will govern the levels that are transported to remote locations. The research in this area has focused on characterizing species levels produced under a variety of conditions, both inside and nearby the compartment of fire origin. D.T. Gottuk (*) • B.Y. Lattimer Jensen Hughes, 3610 Commerce Drive, Suite 817, Baltimore, MD 21227, USA
Species product formation is affected by the compartment geometry, ventilation, fluid dynamics, thermal environment, chemistry, and mode of burning. The mode of burning and ventilation are two of the key conditions that dictate product formation. These conditions can be used to classify fires into three general categories: (1) smoldering, (2) free- (or open-) burning fires, and (3) ventilation-limited fires. Smoldering is a slow combustion process characterized by low gas temperatures and no flaming. Under these conditions, high levels of CO can be generated. Chapters 63, 19, and 36 discuss this mode of burning in detail; thus, it will not be discussed further here. Free-burning fires are flaming fires that have an excess supply of air. These well-ventilated fires (discussed in Chap. 36) are generally of little concern in terms of generating toxic species. This chapter focuses primarily on the third category, ventilation-limited flaming fires. These fires consist of burning materials inside an enclosure, such as a room, in which airflow to the fire is restricted due to limited ventilation openings in the space. As a fire grows, conditions in the space will transition from overventilated to underventilated (fuel rich). It is normally during underventilated conditions that formation of high levels of combustion products, including CO, creates a major fire hazard. This chapter discusses the production of species within a compartment fire and the transport of these gases out of the fire compartment to adjacent areas. Engineering correlations are presented along with brief reviews of pertinent work on
M.J. Hurley (ed.), SFPE Handbook of Fire Protection Engineering, DOI 10.1007/978-1-4939-2565-0_16, # Society of Fire Protection Engineers 2016
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Effect of Combustion Conditions on Species Production
species production in compartment fires. These sections provide the background and basis for understanding the available engineering correlations and the range of applicability and limitations. An engineering methodology is presented to utilize the information given in this chapter. This chapter is organized according to the following outline: Basic Concepts Species Production Within Fire Compartments Hood Experiments Compartment Fire Experiments Chemical Kinetics Fire Plume Effects Transient Conditions Species Transport to Adjacent Spaces Engineering Methodology
Basic Concepts In a typical compartment fire, a two-layer system is created. The upper layer consists of hot products of combustion that collect below the ceiling, and the lower layer consists of primarily ambient air that is entrained into the base of the fire (Fig. 16.1). Initially, the fire plume is totally in the lower layer, and the fire burns in an overventilated mode similar to open burning. Due to excess air and near-complete combustion, little CO formation is expected in this mode. (See Chap. 36, for yields.) As the fire grows, ventilation paths in the room restrict airflow, creating underventilated (fuel-rich) burning conditions.
487
It is generally under these conditions that products of incomplete combustion are created. Typically, the fire plume extends into the upper layer, such that layer gases recirculate through the upper part of the plume. Depending on both the size of the room and the size of the fire, it is possible to have a fire plume that cannot be contained within the room, resulting in flame extension out of windows or doors. Flame extension can occur when the fire plume impinges on the ceiling and the ceiling jets are longer than the distance from the plume to outside vent openings (Fig. 16.2). Flame extension is different from a second burning phenomenon outside of the fire compartment, called external burning, which is discussed below. The main point to understand is that flame extension outside of the fire compartment is a result of a fire that is too large to be contained in the room. Flame extension can occur during both overand underventilated burning conditions. To estimate when flame extension may occur, the maximum heat release rate that can be supported by the compartment ventilation needs to be determined. Flame length correlations can then be used to determine whether flames will extend outside of the compartment. As a fire progresses and the upper layer descends, the layer will spill below the top of doorways or other openings into adjacent areas. The hot, vitiated, fuel-rich gases flowing into adjacent areas can mix with air that has high O2 concentrations to create a secondary burning zone outside of the compartment (Fig. 16.3). This is referred to as external burning. External
Upper layer Flame extension
Lower layer Air
Fig. 16.1 An overventilated compartment fire with the fire plume below the layer interface
Upper layer
Fig. 16.2 A fire compartment with flame extension out of the doorway
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D.T. Gottuk and B.Y. Lattimer
External burning Air Layer burning Air
nprod ¼ Number of moles of products of complete combustion per mole of reactants (stoichiometric mixture of fuel and oxidant streams) Cp ¼ Heat capacity of products of complete combustion (kJ/gmol K) The use of the ignition index is discussed in detail in Chap. 17, of this book. An ignition index greater than 1.0 indicates that ignition is expected if the mixture contains sufficient fuel.
Fig. 16.3 An underventilated compartment fire with external burning of fuel-rich upper layer gases
burning can also be accompanied by layer burning. Layer burning is the ignition of fuel-rich upper-layer gases at the interface between the upper and lower layers. External burning and layer burning occur due to the buildup of sufficient fuel in an atmosphere that is able to mix with available oxygen. These phenomena can only occur during underventilated burning conditions. In some circumstances, external burning can decrease human fire hazard through the oxidation of CO and smoke leaving the fire compartment (see the section in this chapter, “Species Transport to Adjacent Spaces”). The occurrence of external burning has been predicted using a compartment layer ignition model developed by Beyler [4] (see Chap. 17). Beyler derived a relationship called the ignition index to predict the ignition of gases at the interface of the upper and lower layers inside a compartment. The ignition index, I, is defined as X C j =100 ΔH c, j I¼ 1:0 ð16:1Þ ð T SL, j j nprod C p dT To
where j ¼ Fuel species of interest Cj ¼ Volume concentration of fuel j when fuel stream is stoichiometrically mixed with oxidant stream ΔHc,j ¼ Heat of combustion of the species j (kJ/gmol) TSL,j ¼ Adiabatic flame temperature at the stoichiometric limit for fuel species j (K) To ¼ Temperature of the gas mixture prior to reaction (K)
Species Yields The generation of fire products in compartment fires can be quantified in terms of species yields, Yi, defined as the mass of species i produced per mass of fuel burned (g/g): Yi ¼
mi mf
ð16:2Þ
Similarly, oxygen is expressed as the depletion of O2 (i.e., DO2), which is the grams of O2 consumed per gram of fuel burned: DO2 ¼
mO2 mf
ð16:3Þ
The normalized yield, fi, is the yield divided by the theoretical maximum yield of species i for the given fuel, ki. For the case of oxygen, f O2 is the normalized depletion rate, where ki is the theoretical maximum depletion of oxygen for the given amount of fuel. As a matter of convenience, the use of the term yield throughout this chapter will also include the concept of oxygen depletion. As in Chap. 36, the normalized yield is also aptly referred to as the “generation efficiency” of compound i. By definition, the normalized yields range from 0 to 1, and are thus good indicators of the completeness of combustion. For example, under complete combustion conditions the normalized yields of CO2, H2O, and O2 are 1. As a fire burns more inefficiently, these yields decrease. The use of normalized yields is also useful for establishing mass balances. The conservation of carbon requires that
16
Effect of Combustion Conditions on Species Production
f CO þ f CO2 þ FTHC þ f resid:C ¼ 1
ð16:4Þ
where fTHC is the normalized yield of gas-phase total hydrocarbons and fresid.C is the normalized yield of residual carbon, such as soot in smoke or high molecular weight hydrocarbons that condense out of the gas sample. For two-layer systems the yield of all species except oxygen can be calculated as follows: Xiwet m_ f þ m_ a Mi Yi ¼ ð16:5Þ m_ f Mmix where Xiwet ¼ The wet mole fraction of speciesi m_ a ¼ The mass air entrainment rate
489
depending on conditions, is typically 10–20 % by volume. Xiwet ¼ ð1 XH2 Owet ÞXidry
ð16:8Þ
Reliable water concentration measurements are difficult to obtain. Therefore, investigators have calculated wet species concentrations using the above relationship with the assumption that the molar ratio, C, of H2O to CO2 at any equivalence ratio is equal to the calculated molar ratio at stoichiometric conditions [5, 6]. Based on this assumption, Equation 16.9 can be used to calculate wet species concentrations from dry concentration measurements. Xiwet ¼
into the upper layer
Xidry 1 þ CXCO2dry
ð16:9Þ
m_ f ¼ The mass loss rate of fuel Mi ¼ The molecular weight of speciesi
Equivalence Ratio
Mmix ¼ The molecular weight of the mixture ðtypically assumed to be that of airÞ The depletion rate of oxygen is calculated as DO2 ¼
0:21m_ a MO2 =Ma XO2wet m_ f þ m_ a MO2 =Mmix m_ f
ð16:6Þ The normalized yield, fi, is simply calculated by dividing the yield by the maximum theoretical yield fi ¼
Yi ki
ð16:7Þ
Typical operation of common gas analyzers requires that water be removed from the gas sample before entering the instrument. Consequently, the measured gas concentration is considered dry and will be higher than the actual wet concentration. Equation 16.8 can be used to calculate the wet mole fraction of species Xiwet , from the measured dry mole fraction, Xidry . As can be seen from Equation 16.8, the percent difference between Xidry and Xiwet is on the order of the actual H2O concentration which,
The concept of a global equivalence ratio (GER) can be used to express the overall ventilation of a control volume, such as a fire compartment. However, due to the complex interaction between the plume and the upper and lower layers, as well as the potential extension of the fire beyond the initial compartment, a unique definition for the GER does not exist. Therefore, if one uses the term GER, it must be associated with a defined control volume. The first efforts in developing the GER concept were based on hood experiments [7–11] (e.g., as in Fig. 16.4) in which the idea of a plume equivalence ratio was introduced. The plume equivalence ratio, ϕp, is the ratio of the mass of fuel burning, mf, to the mass of oxygen entrained, ma, into the fire plume (below the upper layer) normalized by the stoichiometric fuel-to-oxygen ratio, r O2 . ϕp ¼
m f =mO2 r O2
ð16:10aÞ
Since oxygen is typically entrained into a fire plume via air, ϕp is commonly defined as
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D.T. Gottuk and B.Y. Lattimer
Fig. 16.4 Schematic of the two-layer system created in the hood experiments of Beyler [8, 9]
Layer interface
Exhaust and gas sampling
Air Burner
m f =ma ð16:10bÞ r where ma is the mass of air entrained into the plume (in the lower layer) and r is the stoichiometric mass fuel-to-air ratio. As discussed in the section on species production within fire compartments, this simple characterization of the equivalence ratio well represented the global conditions that existed in the first hood and compartment fire experimental configurations. In order to more accurately describe the time integrated conditions within the upper layer, a second equivalence ratio was defined for this control volume [7, 10, 11]. The upperlayer equivalence ratio, ϕul, is the ratio of the mass of the upper layer that originates from fuel sources, to the mass of the upper layer that originates from any source of air into the upper layer, divided by the stoichiometric fuel-to-air ratio. The two equivalence ratios (ϕp and ϕul) are not necessarily the same. As a fire grows, the upper-layer composition represents a collective time history of products. In an ideal two-layer fire, where all air enters the upper layer through the plume, ϕul is the same as ϕp only during steady burning conditions. If the burning rate of the fire changes quickly compared to the residence time of the gases in the upper layer, the upper-layer equivalence ratio lags behind the plume equivalence ratio. The residence time, tR, ϕp ¼
can be defined as the time required for a unit volume of air to move through the upper-layer volume, and can be characterized according to Equation 16.11. tR ¼
V ul ρul m_ exhaust
ð16:11Þ
where m_ exhaust ¼ Mass flow rate of gases out of the layer ðkg=sÞ ρul ¼ Density of the upper‐layer gases ðkg=m3 Þ V ul ¼ Volume of the upper layer ðm3 Þ
For example, consider a compartment fire burning with a plume equivalence ratio of 0.5 with upper layer gases that have a residence time of 20 s. If the fire grows quickly such that ϕp increases to a value of 1.5 in about 5 s, ϕul would now lag behind (less than 1.5). The fuel rich (ϕp ¼ 1.5) gas mixture from the plume is effectively diluted by the upper-layer gases since there has not been sufficient time (greater than 20 s) for the layer gases to change over. The result is that ϕul will have a value between 0.5 and 1.5. Another instance when ϕul can differ from ϕp is when additional fuel or air enters the upper layer directly. An example of this would be the burning of wood paneling in the upper layer. The calculation of ϕul can be a complex task. Either a fairly complete knowledge of the gas composition is needed [7] or time histories of ventilation flows and layer residence times are needed to be able to calculate ϕul. Toner [7] and Morehart [12] present detailed methodologies
16
Effect of Combustion Conditions on Species Production
for calculating ϕul from gas composition measurements. Equation 16.12 can be used to calculate ϕul if the mass flow rates can be expressed as a function of time. ðt 1 m_ f ðt0 Þdt0 ttR ϕul ¼ ð t ð16:12Þ 0 0 r m_ a ðt Þdt ttR
Although termed the upper-layer equivalence ratio, ϕul actually represents the temporal aspect of the equivalence ratio no matter what the control volume. For instance, the control volume may be the whole compartment, as shown in Fig. 16.1. In this case, the compartment equivalence ratio, ϕc, is defined as the ratio of the mass, mf, of any fuel entering or burning in the compartment to the mass, ma, of air entering the compartment normalized by the stoichiometric fuel-to-air ratio. In a compartment fire, air is typically drawn into the space through a door or window style vent. If all of the air drawn into the compartment is entrained into the lower layer portion of the plume, then the plume equivalence ratio can be an adequate representation of the fire environment. However, if layer burning occurs, or multiple vents cause air to enter the upper layer directly, the use of a compartment equivalence ratio is more appropriate. As a practical note, for fires within a single compartment, the equivalence ratio is calculated (and experimentally measured) based on the instantaneous fuel mass ˙ f, and air flow rate, m ˙ a, into the loss rate, m compartment (Equation 16.13a). ϕ¼
m_ f m_ a r
ð16:13aÞ
As noted previously, r is defined as the stoichiometric fuel-to-air ratio. Unfortunately, the ratio r is sometimes defined as the air-to-fuel ratio, ra. Therefore, consideration must be given to values obtained from tabulated data. Keeping with the nomenclature of this chapter, the equivalence ratio can also be expressed as
491
ϕ¼
m_ f m_ f r o ra ¼ m_ a m_ a Y O2, air
ð16:13bÞ
where r a ¼ Mass air‐to‐fuel ratio r o ¼ Oxygen‐to‐fuel mass ratio Y O2, air ¼ Mass fraction of oxygen in air ð0:23Þ The formulation of Equation 16.13b allows direct use of values tabulated for various fuels in Appendix 3, Table 3.2, of this handbook. Another useful expression for ϕ can be derived from Equation 16.13b by multiplying the numerator and denominator by the fuel heat of combustion, Δhc, and recognizing that the heat release per mass of oxygen consumed, E, is equal to Δhc over ro, yielding ϕ¼
1 1 Q_ Q_ ¼ m_ a EY O2, air m_ a 3030
ð16:13cÞ
where Q_ ¼ Ideal heat release rate of the fire ðkWÞ m_ a ¼ Air flow rate ðkg=sÞ E 13,100 kJ/kg (Drysdale [13]) Note that Q is the ideal heat release rate, which is determined by multiplying the mass loss rate by the heat of combustion, and is not limited by the amount of air flowing into the compartment or control volume. To date, Equation 16.13c has not been utilized in the literature and therefore has not been well established. However, it offers a convenient means to calculate the equivalence ratio without the need to know the fuel chemistry. The equivalence ratio is an indicator of two distinct burning regimes, overventilated (fuel lean) and underventilated (fuel rich). Overventilated conditions are represented by equivalence ratios less than one, while underventilated conditions are represented by equivalence ratios greater than one. An equivalence ratio of unity signifies stoichiometric burning, which, in an ideal process, represents complete combustion of the fuel to CO2 and H2O with no
492
D.T. Gottuk and B.Y. Lattimer
excess oxygen. During underventilated conditions there is insufficient oxygen to completely burn the fuel; therefore, products of combustion will also include excess fuel (hydrocarbons), carbon monoxide, and hydrogen. It follows that the highest levels of CO production in flaming fires is expected when underventilated conditions occur in the compartment on fire. This basic chemistry also suggests that species production can be correlated with respect to the equivalence ratio. Although the not-so-ideal behavior of actual fires prevents accurate theoretical prediction of products of combustion, experimental correlations have been established. A simple model for the most complete combustion of a fuel can be represented by the following expressions: [8] f CO2 ¼ f O2 ¼ f H2 O ¼ 1
for ϕ < 1
CH1.74O0.323 N0.07. Calculate the stoichiometric fuel-to-air ratio, the maximum yields of CO, CO2, and H2O, and the maximum depletion of O2. Solution For complete combustion of the fuel to CO2 and H2O, the following chemical equation can be written CH1:74 O0:323 N0:07 þ 1:2735ðO2 þ 3:76 N2 Þ ! 1:0CO2 þ 0:87H2 O þ 4:823N2 The molecular weight of the fuel, M f , ¼ 1ð12Þ þ1:74ð1Þ þ 0:323ð16Þ þ 0:07ð14Þ ¼ 19:888. The stoichiometric fuel-to-air ratio is ð1 mole fuelÞ M f 19:888 r¼ ¼ ðmoles of airÞ ðMa Þ 1:2735 ð4:76Þ ð28:8Þ r ¼ 0:1139 The stoichiometric air-to-fuel ratio is
ð16:14aÞ f CO2 ¼ f O2 ¼ f H2 O ¼ 1=ϕ
for ϕ > 1 ð16:14bÞ
f CO ¼ f H2 ¼ 0 f THC ¼ 0 f THC ¼ 1 1=ϕ
for all ϕ
ð16:14cÞ
for ϕ < 1
ð16:14dÞ
for ϕ < 1
1 ¼ 8:78 r
ð16:14eÞ
These expressions assume that for ϕ greater than 1, all excess fuel can be characterized as unburned hydrocarbons. Since compartment fire experiments have shown that significant levels of both CO and H2 are produced at higher equivalence ratios, Expression 16.14c is not always representative, and reveals a shortcoming of assuming this simple ideal behavior. However, for the products of complete combustion (CO2, O2, and H2O), this model serves as a good benchmark for comparison of experimental results. Example 1 Consider a piece of cushioned furniture to be primarily polyurethane foam. The nominal chemical formula of the foam is
The maximum yield of CO (i.e., kCO), is calculated by assuming that all carbon in the fuel is converted to CO. Therefore, the number of moles of CO formed, nCO, equals the number of moles of carbon in one mole of fuel. For the polyurethane foam, nCO ¼ 1. nCO ðMCO Þ ð1Þ ð28Þ ¼ 1:41 ¼ n f ðMfuel Þ ð1Þ ð19:888Þ
kCO ¼
Similarly, kCO2 and kH2 O are calculated as ð1Þ ð44Þ ¼ 2:21 19:888 ð0:87Þ ð18Þ ¼ 0:787 ¼ 19:888
kCO2 ¼ k H2 O
The maximum depletion of oxygen, kO2 , refers to the mass of oxygen needed to completely combust one mole of fuel to CO2 and H2O. This is the same as the stoichiometric requirement of oxygen. kO2 ¼
nO2 ðMO2 Þ ð1:2735Þ ð32Þ ¼ 2:05 nfMf ð1Þ19:888
16
Effect of Combustion Conditions on Species Production
Example 2 The fuel specified in Example 1 is burning at a rate of 9 g/s and entraining air at a rate of 56 g/s. Measurements of the upper layer gas composition reveal dry concentrations of 3.7 % by volume CO, 14.3 % CO2, and 0.49 % O2. Correct the concentrations for the water removed during the gas analysis process (i.e., calculate the wet concentrations). Solution In order to use Equation 16.9 to calculate the wet mole fractions, the stoichiometric molar ratio of H2O to CO2 for C needs to be calculated. This ratio is simply obtained from the stoichiometric chemical equation in Example 1. C¼
nH2 O 0:87 ¼ 0:87 ¼ 1 nCO2
Once C is obtained, the wet mole fractions can be calculated as 0:037 ¼ 0:033 1 þ 0:87ð0:143Þ 0:143 ¼ 0:127 XCO2wet ¼ 1 þ 0:87ð0:143Þ 0:0049 ¼ 0:0044 XO2wet ¼ 1 þ 0:87ð0:143Þ XCOwet ¼
The estimated mole fraction of water is XH2 O ¼ CXCO2wet ¼ 0:87ð0:127Þ ¼ 0:11 Therefore, the corrected gas concentrations on a percent volume basis are 3.3 % CO, 12.7 % CO2, and 0.44 % O2. Example 3 Continuing from Example 2, calculate the yields and normalized yields for each species measured. The wet mole fractions are XCOwet ¼ 0:033, XCO2wet ¼ 0:127, and XO2wet ¼ 0:0044. Solution Using Equations 16.5 and 16.7, the yield and normalized yield of CO, CO2, and H2O can be calculated. The maximum yields calculated in Example 1 are kCO ¼ 1:41, kCO2 ¼ 2:21, kH2 O ¼ 0:787, and kO2 ¼ 2:05.
493
Y CO
XCOwet m_ f þ ma MCO ¼ m_ f Ma
ð0:033Þ ð9 þ 56Þ ð28Þ ¼ 0:23 9ð28:8Þ Y CO 0:23 ¼ 0:16 f CO ¼ ¼ kCO 1:41 ð0:127Þ ð9 þ 56Þ ð44Þ ¼ 1:40 Y CO2 ¼ 9ð28:8Þ 1:40 ¼ 0:63 f CO2 ¼ 2:21 ð0:11Þ ð9 þ 56Þ ð18Þ ¼ 0:50 Y H2 O ¼ 9ð28:8Þ 0:50 f H2 O ¼ ¼ 0:63 0:787 ¼
The depletion of oxygen is calculated using Equation 16.6, assuming the molecular weight of the gas mixture, Mmix, to be approximately that of air. 0:21m_ a MO2 =Ma XO2wet m_ f þ m_ a MO2 =Mmix DO2 ¼ m_ f 0:21ð56Þ32=28:8 0:0044ð9 þ 56Þ32=28:8 DO2 ¼ 9 DO2 ¼ 1:42
The normalized yield is calculated as f O2 ¼
DO2 1:42 ¼ 0:69 ¼ 2:05 k O2
Species Production Within Fire Compartments Hood Experiments Beyler [8, 9] was the first to publish major species production rates in a small-scale twolayer environment. The experiments performed consisted of situating a burner under a 1-m-diameter, insulated collection hood. The result was the formation of a layer of combustion products in the hood similar to that found in a two-layer compartment fire (see Fig. 16.4). By varying the fuel supply rates and the distance between the burner and layer interface, and, consequently, the air entrainment rate, a range of
494
D.T. Gottuk and B.Y. Lattimer
equivalence ratios was obtained. Layer gases were exhausted at a constant, metered flow rate from the periphery of the hood at a depth of 15 cm below the ceiling. The general procedure was to allow steady-state burning conditions to develop, so the layer maintained a constant depth below the exhaust flow location. Tests revealed a reasonably well-mixed uniform layer both in temperature and chemical composition during the steady-state conditions. Gas analysis was performed on samples taken from the exhaust stream. Table 16.1 shows the physicochemical properties of the fuels tested. Beyler’s results show that species yields correlate very well with the plume equivalence ratio. Figure 16.5 shows normalized yields of major species for propane fires plotted against the plume equivalence ratio. The trends seen in these plots for propane are fairly representative of the other fuels tested. For overventilated conditions, the yield of CO2 and H2O and depletion of O2 are at a maximum, and there is virtually no production of CO, H2, or unburned hydrocarbons (THC). As underventilated burning conditions ðϕ 1Þ are approached, products of incomplete combustion (CO, H2, and THC) are generated.
For comparison, the expressions for ideal complete combustion (Equations 16.14a, 16.14b, 16.14c, 16.14d, and 16.14e) are shown on each plot in Fig. 16.5. The CO2 yield departs from Equation 16.14b as CO production increases at higher equivalence ratios. This departure, which is fairly independent of ϕ for ϕ > 1, has been described by the yield coefficient [5]. The ratios of the normalized yield of CO2, H2O, or normalized depletion of O2 to the theoretical maximums expressed by Equations 16.14a, 16.14b, 16.14c, 16.14d, and 16.14e are defined as the yield coefficients, BCO2 , BH2 O , and BO2 respectively [5]. BCO2 ¼
f CO2 1
for ϕ < 1
ð16:15aÞ
BCO2 ¼
f CO2 1=ϕ
for ϕ > 1
ð16:15bÞ
BH 2 O ¼
f H2 O 1
for ϕ < 1
ð16:16aÞ
BH 2 O ¼
f H2 O 1=ϕ
for ϕ > 1
ð16:16bÞ
for ϕ < 1
ð16:17aÞ
BO2 ¼
f O2 1
Table 16.1 Physicochemical data for selected fuels
Fuel Acetone Ethanol Hexane Isopropanol Methane Methanol Propane Propene Polyurethane foam Polymethylmethacrylate Toluene Wood (ponderosa pinea) Wood (spruceb)
Empirical chemical formula of volatiles C3H6O C2H5OH C6H14 C3H7OH CH4 CH3OH C3H8 C3H6 CH1.74O0.323 N0.0698 C5H8O2 C7H8 C0.95H2.4O CH3.584O1.55
Empirical molecular weight 58 46 86 60 16 32 44 42 20 100 92 30 40
From Beyler [9] chemical formula estimated from ϕ < 1 yield data Gottuk et al. [5] c r ¼ stoichiometric fuel-to-air ratio a
b
Maximum theoretical yields kCO kCO2 kO2 kH2 O 1.45 2.28 2.21 0.93 1.22 1.91 2.09 1.17 1.95 3.07 3.53 1.47 1.40 2.20 2.40 1.20 1.75 2.75 4.00 2.25 0.88 1.38 1.50 1.13 1.91 3.00 3.64 1.64 2.00 3.14 3.43 1.29 1.41 2.21 2.05 0.79 1.40 2.20 1.92 0.72 2.13 3.35 3.13 0.78 0.89 1.40 1.13 0.73 0.69 1.09 0.89 0.80
1/rc 9.45 8.94 15.1 10.3 17.2 6.43 15.6 14.7 8.78 8.23 13.4 4.83 3.87
a
d
CO2 Yield
0.2
0.6
1.0
0.2
0.6
1.0
1.0
XX X
Equivalence ratio
0.6
XXXX
0.2
1.0
Equivalence ratio
0.6
X X XXX X X XXXX X XXX X XX XXX X XX XX XXXXX X X X X XXX XXX
0.2
XXXX X XXX XX XX X X XX X X X XX X X
1.4
X XXXXXX X XX
1.4
XXXXX X XXX
1.8
X
1.8
X
b
e
0.2
0.6
1.0
1.4
1.8
0.02
0.06
0.10
0.14
0.18
0.22
0.26
0.30
0.34
0.38
0.2
XXX X XX X XX XX
0.2
1.0
X
1.0
X XXX
Equivalence ratio
0.6
X
X XX XX
Equivalence ratio
0.6
X X XX X X X X X X X X XX X XXX
1.4
X XX XXX X XX
1.4
X X X X X X X XXX X XX XXX X X
1.8
1.8
X
X
c
f
0.04
0.12
0.20
0.28
0.36
0.44
0.2
0.6
1.0
0.2
X
0.2
1.0
X XXX X XX X
1.0
Equivalence ratio
0.6
X X X XX XX
X X X X X
X X XX
Equivalence ratio
0.6
X XX X X XX XX XXXX X X X XXX XXX XX
1.4
X XX XX XX X X X X
1.4
XXX X XXX XX
X
1.8
1.8
X
Fig. 16.5 Normalized yields of measured chemical species as a function of the equivalence ratio for propane experiments using a 13 cm (o) or 19 cm (x) burner with supply rates corresponding to 8 to 32 kW theoretical heat release rate [8]
H2O Yield
CO Yield H2 Yield
O2 Yield THC Yield
16 Effect of Combustion Conditions on Species Production 495
496
D.T. Gottuk and B.Y. Lattimer
BO 2 ¼
f O2 1=ϕ
for ϕ > 1
ð16:17bÞ
These terms are useful in discussing characteristics of the combustion efficiency. For example, an O2 yield of 1 indicates complete utilization of available O2. In the case of CO2 and H2O, deviation from the model (as indicated by BCO2 or BH2 O < 1) is a measure of the degree of incomplete combustion. It can be seen from Fig. 16.5 that the production of CO is primarily at the expense of CO2 (i.e., BO2 and BH2 O remain nearly 1, while BCO2 is about 0.8). Table 16.2 shows average yield coefficients for underventilated fires. Figure 16.6 shows unnormalized CO yields plotted against the plume equivalence ratio for fuels tested by Beyler [8, 9]. The correlations agree quite well for all fuels. Below an equivalence ratio of 0.6, minimal CO production is observed. Above ϕp equal to 0.6, carbon monoxide yield increases with ϕp and, for most fuels, tends to level out at equivalence ratios greater than 1.2. Toluene, which creates large amounts of soot, is anomalous compared to the other fuels studied. As can be seen in Fig. 16.6, the CO
yields from toluene fires remain fairly constant at about 0.09 for both overventilated and underventilated burning conditions. It should be noted that Beyler originally presented all correlations with normalized yields, fCO. However, better agreement is found between unnormalized CO yield-equivalence ratio correlations for different fuels, YCO (shown in Fig. 16.6), rather than normalized yields. One point of interest, though, is that when CO production is correlated as normalized yield, a more distinct separation of the data occurs for ϕp greater than 1. The degree of carbon monoxide production (represented as fCO) during underventilated conditions can be ranked by chemical structure according to oxygenated hydrocarbons greater than hydrocarbons greater than aromatics. This ranking is not observed for unnormalized yield correlations. Toner et al. [7] and Zukoski et al. [10, 11] performed similar hood experiments with a different experimental setup. The hood used was a 1.2 m cube, insulated on the inside with ceramic fiber insulation board. The layer in the hood formed to the lower edges where layer gases were allowed to spill out. Gas sampling was done using an
Table 16.2 Average yield coefficients and upper-layer temperatures for underventilated firesa (values in parentheses are standard deviations) Fuel Acetone Ethanol Hexane Hexane Isopropanol Methane Methane Methanol Propane Propene Polyurethane foam Polymethylmethacrylate Polymethylmethacrylate Toluene Wood (ponderosa pine) Wood (spruce) a
BCO2 0.78 (0.03) 0.79 (0.01) 0.61 (0.10) 0.83 (0.05) 0.75 (0.01) 0.80 (0.05) 0.69 (0.03) 0.79 (0.03) 0.78 (0.05) 0.77 (0.08) 0.87 (0.04) 0.77 (0.06) 0.93 (0.04) 0.57 (0.04) 0.85 (0.05) 0.90 (0.00)
BO2 0.92 (0.04) 0.97 (0.01) 0.82 (0.02) 0.96 (0.06) 0.89 (0.01) 1.00 (0.04) 0.87 (0.07) 0.99 (0.00) 0.97 (0.03) 0.92 (0.08) 0.97 (0.02) 0.92 (0.19) 0.98 (0.04) 0.62 (0.05) 0.89 (0.03) 0.95 (0.00)
BH2 O 0.99 (0.04) 1.00 (0.04) 0.87 (0.03) NA 0.96 (0.01) 1.01 (0.03) 0.86 (0.06) 0.94 (0.02) 1.05 (0.04) 1.02 (0.10) NA 0.72 (0.04) NA 0.78 (0.03) 0.79 (0.10) NA
Temperature (K) 529 (76) 523 (72) 529 (25) 1038 (62) 513 (33) 713 (101) 547 (12) 566 (53) 557 (62) 629 (51) 910 (122) 525 (37) 1165 (126) 509 (23) 537 (37) 890 (0)
Reference Beyler [8] Beyler [8] Beyler [8] Gottuk et al. [5] Beyler [8] Toner et al. [7] Morehart et al. [12] Beyler [8] Beyler [8] Beyler [8] Gottuk et al. [5] Beyler [9] Gottuk et al. [5] Beyler [8] Beyler [9] Gottuk et al. [5]
Values have been calculated from data found in the cited references. Values for Toner et al. [7], Beyler [8], Beyler [9], and Morehart et al. [12] are from hood experiments, and values for Gottuk et al. [5] are for a reduced-scale enclosure
Effect of Combustion Conditions on Species Production
Fig. 16.6 Unnormalized carbon monoxide yields as a function of the plume equivalence ratio for various fuels studied by Beyler in a hood apparatus [8, 9]
497
0.4
Unnormalized CO yield
16
Notes: = Methanol = Ethanol = Isopropanol X = Propane = Acetone
0.3
X
0.2
X
0.1
XX X XX X XX X X
X X X XX X XX X X X X XXXX X X XXX X X X XX X X X XXX X XX X X
0 0
X XXX X X XXX X X
0.5
X
X XX XX X X XX X
1.0
X X X X XX X X XX X X XX XX X XXXXXXX XXXX XX XX X X
X
X
1.5
Unnormalized CO yield
0.4 Notes: X = Prop ane = Propene = Hexane + = Toluene • = PMMA = Equation 14
0.3
0.2
X
XX X X X X • •• X X X XXX
•
XXX
••
0.1 +
+
+
X X X XX XX X X • X XX XXX XX XX X X X X X • XX ••XXXX•
0 0
uncooled stainless-steel probe inserted into the layer. Detailed gas species measurements were made using a gas chromatograph system. The upper-layer equivalence ratio was determined from conservation of atoms using the chemical species measurements, the measured composition of the fuel, and the metered fuel flow rate. Natural gas flames with heat release rates of 20–200 kW on a 19-cm-diameter burner were studied. The layer in the hood was allowed to form and reach a steady-state condition before gas sampling was performed. It was concluded that species concentrations were well correlated to the upper-layer equivalence ratio, ϕul, and insensitive to temperatures for the range studied (490–870 K). Since these experiments were conducted during steady-state
0.5
+ X+
XX • X XX X • XXX X
++
X
X
X X X XX X X X XX X X XX XX X X XXX X XXX X• X XX
•
X
X
•
X
+ +
1.0 Plume equivalence ratio
1.5
conditions, with mean upper-layer residence times of about 25–180 s, it can be concluded that ϕp and ϕul were equal. The data of Toner et al. [7] have been used to plot CO and CH4 yields versus upper-layer equivalence ratio in Figs. 16.7 and 16.8, respectively. The correlations are qualitatively similar to the correlations obtained by Beyler for different fuels. An analysis of these test results also showed that normalized CO2 and O2 yield versus equivalence ratio data is represented reasonably well by Equations 16.15, 16.16, and 16.17. Similar to Beyler’s propane results, the average BO2 value is about 1 and BCO2 is 0.8 for underventilated burning conditions (the use of yield coefficients is discussed further in the section on engineering correlations).
498 0.4
Unnormalized CO yield
Fig. 16.7 Unnormalized carbon monoxide yields as a function of equivalence ratio for methane fires studied by Toner et al. [7] and Morehart et al. [12] in hood experiments
D.T. Gottuk and B.Y. Lattimer
Notes: = Toner + = Morehart
0.3
Equation 22 0.2 Equation 21 0.1
0 0
0.5
1.0
1.5
2.0
2.5
3.0
Equivalence ratio
1.0 Notes: + = Toner = Morehart
0.8 Normalized CH4 yield
Fig. 16.8 Normalized yields as a function of equivalence ratio for methane fires studied by Toner et al. [7] and Morehart et al. [12] in hood experiments
1 – 1/φ
0.6
0.4 + + + +++
0.2
+ + + + ++
+
+
0 0
+ +++ + ++ + + ++ ++ ++ + 0.5 1.0
1.5
2.0
2.5
3.0
Equivalence ratio
Toner compared the measured species concentrations to the calculated equilibrium composition of the reactants at constant temperature and pressure. The layer composition was modeled quite well by the chemical equilibrium composition for very overventilated conditions but not for underventilated conditions. His observance of CO production for near-stoichiometric and underventilated fires, at the expense of CO2 production, led them to suggest that the oxidation of CO was “frozen out” before completion. (At low temperatures, there is insufficient energy for CO to chemically react to CO2.) [7] Since the results showed that species production was independent of temperature for the range studied
(490–870 K), Toner et al. concluded that, if a freeze-out temperature existed, it must be higher than 900 K. Work by Pitts [14] and by Gottuk et al. [15], discussed later, shows that a freezeout temperature does exist in the range of 800–900 K, depending on other factors. Zukoski, Morehart, et al. [11] performed a second series of tests similar to that described above for Zukoski et al. [10] and Toner et al. Much of the same apparatus was used except for a different collection hood. The hood, 1.8 m square by 1.2 m high, was larger than that used by Toner et al. and was uninsulated. Morehart et al. [12] experiments consisted of establishing steady-state burning conditions such
16
Effect of Combustion Conditions on Species Production
that the burner-to-layer interface height was constant. A constant ϕp was maintained based on this constant interface height in conjunction with the fact that the mass burning rate of fuel was metered at a constant rate. Additional air was then injected into the upper layer at a known flow rate until a new steady-state condition was achieved. This procedure established a ϕul that was lower than the ϕp, since ϕp was based on the ratio of the mass burning rate to the mass of air entrained into the plume from room air below the layer interface. By increasing the air supply rate to the upper layer, a range of ϕul was established while maintaining a constant ϕp. Although similar, the correlations obtained by Morehart et al. deviated from those obtained by Toner et al. Figs. 16.7 and 16.8 compare the CO and CH4 yields calculated from the data of Morehart et al. with the yields calculated from the data of Toner et al. For overventilated conditions, Morehart et al. observed higher CO and CH4 yields, signifying that the fires conducted by Morehart et al. burned less completely. For underventilated methane fires, Morehart et al. observed lower CO, CO2, and H2O and higher CH4 and O2 concentrations than Toner et al. The only apparent differences between experiments was that Morehart found layer temperatures were 120–200 K lower for fires with the same equivalence ratio as those observed by Toner, that is, they ranged from 488 to 675 K. Due to the similarity in experimental apparatus, except for the hood, Morehart concluded that the temperature difference resulted from having a larger uninsulated hood. Morehart studied the effect of increasing temperature on layer composition by adding different levels of insulation to the hood. Except for the insulation, the test conditions (e.g., ϕ of 1.45 and layer interface height) were held constant. Residence times of layer gases in the hood were in the range of 200–300 s. For the range of temperatures studied (500–675 K), substantial increases in products of complete combustion (i.e., CO2 and H2O) and decreases in fuel and oxygen occurred with increasing layer temperature. Upper-layer oxygen mass fraction was reduced by approximately 70 % and methane
499
was reduced by 25 % [11, 12]. Excluding one outlier data point, CO concentrations increased by 25 %. This is an important result. Although the gas temperatures were well below 800 K, an increase in the layer temperature resulted in more fuel being combusted to products of complete combustion and additional CO (see the section “Chemical Kinetics” later in this chapter).
Compartment Fire Experiments The hood experiments performed by Beyler and Zukoski et al. differ from actual compartment fires in several ways. The hood setup allowed considerable radiation to the lab space below. Conversely, a real compartment would contain most of the radiation, thus resulting in higher wall and upper-layer temperatures. Consequently, higher fuel mass loss rates for pool fires would be expected for an actual compartment fire. Also, the hood setup results in a lower layer that has an infinite supply of air which is neither vitiated nor heated. In a real compartment fire, the air supply is limited by ventilation openings (doors, windows, etc.) and the depth of the upper layer. The air that is entrained into the lower layer of an actual compartment fire can be convectively heated by hot compartment surfaces prior to fire plume entrainment. The hood experiments did not include any significant ceiling and wall flame jets. These dynamic flame structures enhance mixing of the upper layer in actual compartment fires and extend the flame zone beyond the plume. Lastly, the hood experiment correlations were developed from sustained steady-state burning conditions. Actual fires of interest are usually in a continual growth stage, and, thus, are more transient in nature. Tewarson reported that CO and CO2 yields and O2 depletion were correlated well by the air-to-fuel stoichiometric fraction (i.e., the reciprocal of the equivalence ratio) for wood crib enclosure fires [16]. Enclosure fire data was taken from previous work in the literature for cellulosic-base fiberboard and pine wood cribs burned in various compartment geometries, 0.21–21.8 m3 in volume, with single and dual
500
horizontal and vertical openings centered on the end walls. Additional data were obtained for pine wood cribs burned in a small-scale flammability apparatus that exposed the samples to variable external radiant heat fluxes with either natural or forced airflow from below. The characteristics of the correlations presented by Tewarson are similar to the correlations developed by Beyler. The CO2 yield and O2 depletion are relatively constant for low equivalence ratios and decrease sharply as the equivalence ratio increases for underventilated conditions. The CO yield correlates with the equivalence ratio but with a fair amount of scatter in the data. Due to the lack of measurements, the air entrainment rate used to calculate the mass airto-fuel ratio was estimated from the ventilation parameter, Ah1/2, where A is the cross-sectional area and h is the height of the vent. Although the general shape of the correlations are valid, the use of the ventilation parameter assumption causes the equivalence ratio data to be suspect. In addition, the elemental composition of the fuel volatiles for the wood was not corrected for char yield. A correction of this sort would tend to decrease the calculated equivalence ratio and increase the CO and CO2 yields. Gottuk et al. [5, 17] conducted reduced-scale compartment fire tests specifically designed to determine the yield-equivalence ratio correlations that exist for various fuels burning in a compartment fire. A 2.2 m3 (1.2 m 1.5 m 1.2 m high) test compartment was used to investigate the burning of hexane, PMMA, spruce, and flexible polyurethane foam. The test compartment was specially designed with a two-ventilation path system that allowed the direct measurement of the air entrainment rate and the fuel volatilization rate. The setup created a two-layer system by establishing a buoyancydriven flow of air from inlet vents along the floor, up through the plume, and exhausting through a window-style exhaust vent in the upper layer. There was no inflow of air through the exhaust vent. The upper-layer gas mixture was sampled using an uncooled stainless steel probe placed into the compartment through the center of the
D.T. Gottuk and B.Y. Lattimer
exhaust vent. This location for the probe was chosen after species concentration and temperature measurements, taken at several locations in the upper layer, showed a well-mixed, uniform layer. Table 16.1 shows the physicochemical properties used for the four fuels. It should be noted that in determining properties of a fuel, such as maximum yields or the stoichiometric fuel-to-air ratio, the chemical formula must characterize the volatiles, not necessarily the base fuel. For liquid fuels or simple polymers, such as PMMA, the composition of the volatiles is the same as the base fuel. However, more complex fuels can char or contain nonvolatile fillers, as found in polyurethane foams. As a result, the composition of the volatiles differs from that of the base material. As an example, the composition of the wood volatiles used in this study was obtained by adjusting the analyzed wood composition for an observed average of 25 % char [5]. The results of these compartment tests showed similarities to Beyler’s hood experiments. However, some significant quantitative differences exist. Figure 16.9 compares the CO yield correlations from Beyler’s hood study and that of these compartment tests for hexane fires. This plot illustrates the primary difference observed between the hood and compartment hexane and PMMA fire test results. An offset exists between the rise in CO yield for the two studies. For the hood experiments, higher CO production was observed for overventilated (ϕp < 1) and slightly underventilated burning conditions. For the compartment fire experiments, negligible CO was produced until underventilated conditions were reached. Consistent with the increased CO production and the conservation of carbon, CO2 yields were lower for the hood experiments compared to the compartment fires. The spruce and polyurethane compartment fires produced similar CO yieldequivalence ratio correlations to those observed by Beyler in hood experiments (i.e., high CO yields were observed for overventilated fires). The differences in CO formation can be explained in terms of temperature effects. For the region of discrepancy between equivalence
Effect of Combustion Conditions on Species Production
Fig. 16.9 Comparison of unnormalized CO yield correlations for hexane fires in a compartment and under a hood apparatus. (Figure taken from Gottuk et al. [5])
501
0.4
Unnormalized CO yield
16
Notes: = Gottuk et al. + = Beyler
0.3
0.2
+ +
Equation 22
+ +++ + + + +
+
+
Equation 21 +
0.1
+ +
0 0
0.5
1.0
1.5
2.0
2.5
3.0
Equivalence ratio
ratios of 0.5 and 1.5, upper-layer temperatures in Beyler’s hood experiments and the spruce and polyurethane compartment fire experiments were typically below 850 K, whereas temperatures for the hexane and PMMA fires were above 920 K (temperatures typically associated with postflashover fires) [18]. As is detailed in the section on chemical kinetics, the temperature range between 800 and 900 K is a transition range over which the oxidation of CO to CO2 changes from a very slow to a fast reaction. That is, for upper-layer temperatures below 800 K, the conversion of CO to CO2 does not occur at an appreciable rate to affect CO yields. Since the oxidation of a fuel first results in the production of CO, which then further reacts to form CO2, the low temperatures ( 1.5), carbon monoxide concentrations in the front of the compartment were approximately 30–60 % higher than in the rear. Temperature gradients of 200–300 C were observed from the back to the front of the compartment. Due to the nonuniform air entrainment at the base of the fire and possible mixing of additional air near the front, it is difficult to determine the local equivalence ratio for each region. The concentration gradient from front to rear of the compartment may have been due to differences in the local equivalence ratios. Nonetheless, plots of concentration measurements in the rear of the compartment versus equivalence ratio are quite similar to the data of Zukoski
502
et al. and Toner et al. Yield data for these results have not been reported. A second set of experiments was performed by NIST to investigate the generation of CO in wood-lined compartments [19]. Douglas fir plywood (6.4 mm thick) was lined on the ceiling and on the top 36 cm of the walls of the compartment described above. Natural gas fires ranging from 40 to 600 kW were burned in the compartment. The results showed that, for tests in which wood pyrolysis occurred, increased levels of CO were observed compared to burning the natural gas alone. Carbon monoxide concentrations (dry) reached levels of 7 % in the front and 14 % in the rear of the compartment. These are extremely high concentrations compared to the peak levels of 2–4 % observed in the unlined compartment fire tests with the methane burner only. Typical peak CO concentrations observed for a range of fuels (including wood) in hood experiments [8–11] and the compartment fire experiments of Gottuk et al. [5] also ranged from 2 % to 4 %. However, concentrations greater than 5 % have also been reported for cellulosic fuels burning in enclosures [16, 20]. Since wood is an oxygenated fuel, it does not require additional oxygen from entrained air to form CO. This enhances the ability of the wood to generate CO in a vitiated atmosphere. Therefore, there are two reasons that high CO concentrations can result in fires with oxygenated fuels in the upper layer. First, the fuel-bound oxygen allows the fuel to generate CO during pyrolysis. Second, due to preferential oxidation of hydrocarbons over CO, the limited oxygen in the upper layer reacts with the pyrolyzing wood to form additional CO. Aspects of this chemistry are discussed in the next section. These initial test results for fires with wood on the walls and ceiling emphasized the importance of adding additional fuel to the upper layer. The practical implications are significant, as many structures have cellulosic-based wall coverings and other combustible interior finishes. Because of the initial studies by NIST, Lattimer et al. [21] conducted a series of tests to evaluate the effect on species production from the addition of wood in
D.T. Gottuk and B.Y. Lattimer
the upper layer of a reduced-scale enclosure fire. The enclosure was the same as used by Gottuk et al. [5], measuring 1.5 m wide, 1.2 m high, and 1.2 m deep. Two primary sets of tests were conducted for cases with and without Douglas fir plywood suspended below the ceiling, with (1) a 0.12 m2 window vent opening and (2) a 0.375 m2 doorway opening, both leading to a hallway. In the compartment with a window opening and wood burning in the upper layer, Lattimer et al. measured CO concentrations of 10 % on average, which is nearly three times greater than the levels measured without the wood. Peak concentrations were as high as 14 %, the same as measured by Pitts et al. [19] CO concentrations were similarly high when the doorway opening was used. In this case, the quasi-steady state average CO concentrations were 8 % with peaks greater than 10.6 % with wood compared to approximately 5.7 % average levels with a doorway vent and no wood. Regardless of the vent opening, these tests showed that wood in the upper layer resulted in CO concentrations increasing dramatically (10.1 %, vs. 3.2 % without wood) with only small increases in the CO2 concentrations (11.6 %, vs. 10.4 % without wood). These trends are summarized in Table 16.3, which presents the Table 16.3 Summary of quasi-steady state average species concentrations (percent volume dry) for underventilated reduced-scale compartment fire tests with and without wood in the upper layer [21, 22] Window vent tests [21] CO CO2 O2 Doorway vent test [21] CO CO2 O2 Doorway vent CO CO2 O2 a
No wood in upper layer 3.2 10.3 0.2
Wood in upper layer 10.1 11.6 0.04
5.7 8.7 0.2 NIST results [22]
8.0 9.6 0.1
2.6/1.8a 6.5/7.5a 0.1/0a
5.5/11.5a 10/15.5a 0/0.5a
Front and back, respectively
16
Effect of Combustion Conditions on Species Production
average upper-layer species concentrations for tests with and without wood for both window and doorway vent conditions. For comparison, the data from the NIST research has also been included. The compartment equivalence ratio was calculated for both the tests with and without wood in the upper layer when the window vent was used. Figures 16.10, 16.11, and 16.12 show the corresponding calculated yields of CO2, O2, and CO plotted as a function of equivalence ratio. Also
included in these plots are the data from the compartment fires of Gottuk et al. [5] The results show that the global equivalence ratio concept is capable of predicting the CO2, O2, and CO yields, although somewhat fortuitously, in a compartment with wood pyrolyzing in the hot, vitiated upper layer. These tests also indicate that the correlations hold to fairly high equivalence ratios of about 5.5, as observed for the tests with wood. More work is needed to determine whether the global equivalence ratio concept can predict species levels when
1.2 1.1 Normalized CO2 yield [(kg of CO2/kg of fuel)/YCO2, max]
Fig. 16.10 The normalized CO2 yield data of Gottuk et al. [5] (○), data from Lattimer et al. [21] with no wood in the compartment upper layer (●), and data from Lattimer et al. [21] with wood in the upper layer (~). Also shown in this plot is the normalized CO2 yield estimated using the complete combustion model of Equation 16.14 (—)
503
1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 1
2 3 4 Compartment equivalence ratio, φc
5
6
0
1
3 4 2 Compartment equivalence ratio, φc
5
6
1.2 1.1 1.0 Normalized O2 yield [(kg of O2/kg of fuel)/YO2, max]
Fig. 16.11 The normalized O2 yield data of Gottuk et al. [5] (○), data from Lattimer et al. [21] with no wood in the compartment upper layer (●), and data from Lattimer et al. [21] with wood in the upper layer (~). Also shown in this plot is the normalized O2 yield estimated using the complete combustion model of Equation 16.14 (—)
0
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0
504 0.30
0.25 CO yield (kg of CO/kg of fuel)
Fig. 16.12 The unnormalized CO yield data of Gottuk et al. [5] (○), data from Lattimer et al. [21] with no wood in the compartment upper layer (●), and data from Lattimer et al. [21] with wood in the upper layer (~)
D.T. Gottuk and B.Y. Lattimer
0.20
0.15
0.10
0.05
0.00 0
nonoxygenated fuels are in the upper layer. It is also unclear whether other oxygenated fuels will follow the correlations as well as the available wood fire data. The data in Table 16.3 should provide an assessment of the effect of the ventilation opening on species generation. However, it is uncertain whether the differences are due more to differences in sampling locations relative to the flame regions. In the tests with a doorway vent, the larger opening resulted in larger air flow rates and, thus, larger fires in the compartment (approximately 500 kW vs. 220 kW with the window vent). The larger fires increased the flame zone within the compartment. Consequently, the sampling probe was probably within the flame zone at times, which would yield higher CO and lower CO2 concentrations than measurements from the window vent tests in which the sampling probe was not sampling from a flame zone. With the window vent, the fires were small enough such that there were no ceiling jets at the level of the sampling probe. The research discussed thus far has concentrated on reduced-scale enclosures. Limited full-scale studies have been reported in the literature to date. One study by NIST systematically examined the production of species in light of the global equivalence ratio concept. NIST conducted a set of tests using a standard
1
2 3 4 Compartment equivalence ratio, φc
5
6
enclosure (as defined by ISO 9705) to compare the results from the NIST reduced-scale enclosure tests to fires conducted in a full-scale enclosure [23–26]. The enclosure measured 2.44 m wide, 3.67 m deep, and 2.44 m tall, with a door (0.76 m by 2 m) centered at one end of the compartment. The fires consisted of a 35-cmdiameter natural gas burner centered in the enclosure. The burner was scaled to provide the same exit gas velocities as in the reduced-scale enclosure tests. Twelve tests were conducted, with fires ranging in size from 0.5 to 3.4 MW. In one test, the ceiling and upper portions of the walls were lined with 12.7 mm thick plywood. In the full-scale enclosure, fires greater than 1250 kW created underventilated conditions. The NIST researchers concluded that although the reduced-scale and full-scale enclosures were geometrically similar, with good agreement between predicted mass flows, the differences in measured gas concentrations indicated that the generation of combustion products is not entirely controlled by the ventilation within the compartment. CO concentrations (upwards of 6 % by volume) were as much as two times higher in the full-scale enclosure than in the reduced-scale tests. These results also coincided with higher upper-layer temperatures, approaching 1400–1500 K. The variation in CO concentrations from front to back in the
16
Effect of Combustion Conditions on Species Production
enclosure was reversed in the full-scale enclosure compared to the reduced-scale enclosure. In the full-scale enclosure, higher CO concentrations were observed in the back of the compartment. In the reduced-scale enclosure, higher concentrations were measured in the front. Pitts primarily associates the higher CO concentrations with the high layer temperatures that are in the range that strongly favor the formation of CO toward equilibrium concentrations (values can approach 16 % at ϕ of 3) [26]. One full-scale enclosure test was conducted with wood in the upper layer. This test resulted in high CO concentrations of 8 % in the front and 12 % in the rear for a 2 MW fire. The temperatures were lower than those observed in the full-scale tests without wood. These results are similar to those observed in the NIST reduced-scale enclosure.
Chemical Kinetics The field of chemical kinetics can be used to describe the changes in gas composition with time that result from chemical reactions. The kinetics of actual combusting flows are dependent on the initial species present, temperature, pressure, and the fluid dynamics of the gases. Due to the inability to adequately characterize the complex mixing processes and the significant temperature gradients in turbulent flames, the use of kinetic models is restricted to simplified combusting flow processes. Consequently, the fire plume in a compartment fire is beyond current chemical kinetics models. However, the reactivity of the upper-layer gas composition can be reasonably modeled if one assumes that the layer can be characterized as a perfectly stirred reactor, or that the layer gases flow away from the fire plume in a plug-flow-type process [14, 15]. Pitts has shown that no significant differences between results exist for either modeling approach when applied to these upper layers [14]. Several kinetics studies have been performed to examine aspects of the reactivity of upperlayer gases [12, 14, 15]. Comparisons between
505
different hood experiments and between hood and compartment fire experiments have indicated that upper-layer temperatures have an effect on CO production. The results of these chemical kinetics studies provide insights into CO generation in compartment fires, which also serve to explain the differences in CO yields between experiments with respect to temperature effects. These studies primarily focused on the question “What would the resulting composition be if the upper-layer gases in the hood experiments existed at different isothermal conditions (constant temperature)?” A particular focus was to examine the resulting compositions for cases modeled under the high temperatures characteristic of compartment fires. Chemical kinetics models calculate the change in species concentrations with respect to time. Calculations are dependent on the reaction mechanism (i.e., the set of elementary reactions and associated kinetic data) and the thermodynamic data base used. Thermodynamic data are fairly well known and introduce little uncertainty into the modeling. However, reaction mechanisms do vary. Pitts presents a comparison of the use of various mechanisms in the literature [14]. The comparison indicates that reaction kinetics for high temperatures (greater than 1100 K) are fairly well understood. However, the elementary reactions for the range of 800–1000 K are not as certain; therefore, quantitative modeling results in this range may be suspect. Nevertheless, the general trends presented below are valid despite any uncertainty associated with the mechanisms used. Chemical kinetics modeling shows that significantly different trends occur for overventilated and underventilated burning conditions. This can be seen in Figs. 16.13 and 16.14, which present major species concentrations with respect to time for an overventilated and underventilated condition, respectively. Figure 16.13 shows a modeled case for ϕ equal to 0.91 and a temperature of 900 K. The initial composition is taken from Beyler’s data for a fire with a layer temperature of 587 K. The temperature of 900 K corresponds to the temperature observed by Gottuk et al. for a
506 10 Upper-layer concentrations (% vol)
Fig. 16.13 Chemical kinetics model calculated species concentrations versus time for an overventilated (ϕ ¼ 0.91) burning condition with an upper-layer temperature of 900 K [15]
D.T. Gottuk and B.Y. Lattimer
8
H2 O/2
6
CO2 /2
4 O2
2 C2 H4 H 2
0 0
Fig. 16.14 Chemical kinetics model calculated species concentrations versus time for an underventilated (ϕ ¼ 2.17) burning condition with an upper-layer temperature of 1300 K [14]
CO 10
20 Time (s)
30
40
1300 K
0.05
H2O/4
Mole fraction
0.04
CH4/2
CO2/2
H2
0.03
CO 0.02
0.01 O2
0
0.4
0.8
1.2
1.6
2
Time (s)
hexane compartment fire at the same global equivalence ratio. For overventilated conditions, increased temperatures cause CO concentrations to initially increase. As can be seen in Fig. 16.13, this is due to the incomplete oxidation of hydrocarbons (modeled as C2H4). Once the hydrocarbons are consumed, available O2 is used in the oxidation of CO to CO2. Since overventilated conditions indicate excess oxygen, CO concentrations are reduced to zero
given sufficient time. This is representative of the case of the overventilated hexane and PMMA compartment fires studied by Gottuk et al., in which the higher compartment temperatures, compared to the hood tests of Beyler, resulted in near-zero CO yields for ϕ less than 1. Figure 16.14 shows an underventilated case for ϕ equal to 2.17 and a temperature of 1300 K. The initial composition is taken from Morehart et al.
Effect of Combustion Conditions on Species Production
507
1300 K 0.026 1200 K
1100 K
K
0.022
10 00
Fig. 16.15 Carbon monoxide concentrations as a function of time for a range of isothermal conditions. Initial concentrations from a methane hood fire at ϕ ¼ 2.17 [14]
CO mole fraction
16
0.018
900 K
800 K
700 K 0.014 0
4
12
8
16
20
Time (s)
for a methane hood experiment [12]. Similar to the overventilated conditions, CO increases due to the oxidation of hydrocarbons (CH4). However, the available oxygen is depleted before the hydrocarbons are fully oxidized. The resulting composition consists of higher levels of CO and H2 and decreased levels of unburned fuel. Carbon dioxide levels remain virtually unchanged. The much higher temperature studied in this case results in much quicker reaction rates, as is reflected in the 2 s time scale for Fig. 16.14 compared to 30 s for Fig. 16.13. It is clear from Figs. 16.13 and 16.14 that hydrocarbon oxidation to CO and H2 is much faster than CO and H2 oxidation to CO2 and H2O, respectively. This is a result of the preferential combination of free radicals, such as OH, with hydrocarbons over CO. Carbon monoxide is oxidized almost exclusively by OH to CO2 [27]. Therefore, it is not until the hydrocarbons are consumed that free radicals are able to oxidize CO to CO2. The formation and consumption of CO in a reactive gas mixture is dependent on both the temperature of the mixture and the amount of time over which the mixture reacts. This point is illustrated in Fig. 16.15, which shows the resulting CO concentrations at different isothermal conditions from an initial gas mixture taken from
an underventilated fire (ϕ ¼ 2.17). Pitts noted that there are three distinct temperature regimes. At temperatures under 800 K, the gas mixture is unreactive and the CO to CO2 reactions are said to be “frozen out.” As the temperature increases in the range of 800–1000 K, the mixture becomes more reactive and CO is formed at faster rates, due to the oxidation of unburned hydrocarbons. For the time period shown, it is interesting to note that the ultimate concentration is approximately constant1 for each case in this temperature range. The third regime of high temperatures above 1100 K is characterized by fast reaction rates and much higher CO production for the 20 s reaction time shown. With sufficient time, the ultimate CO concentration for the 800–1000 K conditions would approach the same value as that seen for the higher temperatures. Results of Zukoski et al. [10] and Gottuk et al. [15] indicated that layer temperatures of 850–900 K or higher are needed for the layer gases to be reactive. Considering that the
1 Note that although the ultimate CO concentration is roughly constant, the value of 2.1 % for this illustration is not to be taken as a universal limit for this temperature range. In general, the resulting CO concentration will depend on the initial gas composition and the time over which the mixture is allowed to react.
508
minimum (freeze out) temperature above which a gas mixture is reactive is dependent on the time scale evaluated. These values are consistent with the results shown in Fig. 16.12. In terms of compartment fires, the time over which the gases react can be taken as the residence time of the gases in the upper layer, which is calculated according to Equation 16.11. In many practical cases of high-temperature compartment fires, it would be reasonable to assume that the residence time of layer gases would be longer than the time needed for the gas mixture to react fully.
Fire Plume Effects Although a fire plume is too complex to adequately model the chemistry, the hood experiments discussed earlier provide significant insights with respect to the fire plume and species production in compartment fires. Results of Beyler’s hood experiments suggest that the production of upper-layer gases is independent of the structure and fluid dynamics of the flame. Beyler modified a 19 cm propane burner by including a 2.8 cm lip to enhance turbulence and the large-scale structure of the flame [8]. Compared to the no-lip burner, the flame was markedly changed, and air entrainment was increased by 30 %. Yet, the upper-layer species-equivalence ratio correlations were the same for both burners. Additionally, as shown in Fig. 16.5, correlations for different size burners are also identical. The insensitivity of species yields to the details of the flame structure is also suggested by the compartment fire hexane results of Gottuk et al. [5] The correlations include data from fires utilizing various size burn pans and with a wide range of air entrainment rates. In several cases, nearly equal steady-state equivalence ratio fires were obtained with quite different burning rates and air entrainment rates. Although the conditions varied significantly, the positive correlation between yields and equivalence ratio suggests that the yields are not sensitive to the details of the flame structure.
D.T. Gottuk and B.Y. Lattimer
The temperature of the fire plume has a significant effect on species production from the fire plume. It is reasonable to assume that differences in upper-layer temperature are also reflective of a similar trend in the average temperature of the fire plume gases. An increase in the upper-layer temperature can increase the fire plume temperature in two ways. For plumes that extend into the upper layer, entrainment of hotter upper-layer gases will result in increased plume temperatures compared to plumes in layers with lower temperature gases. Secondly, an increase in the surrounding temperature (both gases and compartment surfaces) reduces the radiant heat loss from the plume, thus resulting in a higher plume temperature. The effect of temperature on species generation in a fire plume can be found in the methane hood experiments of Morehart et al. [12] and Zukoski et al. [11] Morehart studied the effect of increasing temperature on layer composition by adding different levels of insulation to his hood. Except for the insulation, the test conditions (e.g., ϕ of 1.45 and layer interface height) were held constant. For the range of temperatures studied (500–675 K), substantial increases in products of complete combustion and decreases in fuel and oxygen occurred with increasing layer temperature. Upper-layer oxygen mass fraction was reduced by approximately 70 % and methane was reduced by 25 %. Excluding one outlier data point, CO concentrations increased by 25 %. The temperatures of the Morehart et al. upper layer were well below 700 K. Therefore, based on kinetics modeling, these layers were unreactive at these low temperatures. It follows that the change in layer composition must have been due to changes in the plume chemistry. The more complete combustion can be attributed to an extension of the flammability limits (or reaction zone) in the plume due to raising the flame temperature. The above discussion demonstrates that increasing the plume temperature substantially increases the consumption of O2 and fuel, and primarily increases the levels of products of complete combustion.
16
Effect of Combustion Conditions on Species Production
The effect of changing temperature on a compartment fire upper-layer composition is twofold: (1) the generation of species in the fire plume is changed, and (2) oxidation of post-flame gases in the layer is affected. Elevated compartment temperatures correlate with increased fire plume temperatures and more complete oxidation of the fuel to CO2 and H2O within the fire plume. The layer temperature dictates post-flame oxidation in the upper layer. Upper-layer temperatures below about 800 K indicate chemically unreactive layers. As such, combustion within the fire plume controls the final CO levels that would be measured in the upper layer. At these low temperatures significant levels of CO can be generated even for some overventilated conditions (0.5 < ϕ < 1). The yield of CO is inversely proportional to temperature for overventilated conditions and directly proportional to temperature for underventilated conditions. Upper-layer temperatures of about 900 K and higher indicate chemically reactive layer gases. As such, reactions in the layer dictate final CO production. Temperatures above 900 K allow nearly complete oxidation of CO to CO2 for overventilated conditions. For underventilated fires, chemical kinetics modeling indicates that higher temperature environments may result in slightly higher CO yields due to preferentially accelerated hydrocarbon oxidation compared to CO oxidation. During underventilated conditions, two mechanisms affecting net CO formation compete (i.e., CO and hydrocarbon oxidation). Increasing gas temperatures above 900 K depletes CO by accelerating the CO to CO2 conversion. However, incomplete oxidation of unburned hydrocarbons increases the CO production. Since hydrocarbon oxidation is much faster than CO oxidation, net CO levels increase until all available oxygen is consumed.
Transient Conditions Transient conditions cause the upper-layer equivalence ratio to differ from the plume equivalence ratio. A fast-growing fire will tend to have
509
a ϕul that is less than ϕp. Conversely, a fire that is dying down quickly, such that ϕp is decreasing rapidly, will have a ϕul that is higher than ϕp. These trends result due to the upper layer being a temporary collection reservoir for the gases from the fire plume. In an effort to characterize transient conditions, Gottuk et al. defined a steady-state time ratio, τSS, as the ratio of the residence time, tR, to a characteristic growth time of the fire. Since fire growth is directly related to the fuel volatilization rate, a representative growth time of the fire was defined as the ratio of the fuel mass ˙ f, to the derivative of the fuel volatililoss rate, m € f . An increase in τSS is indicative of zation rate, m more transient conditions. τSS ¼
tR €f m_ f =m
ð16:18Þ
An analysis of the transient nature of the compartment fires studied by Gottuk et al. showed that values well below 1 indicated near steadystate conditions, such that the plume and upperlayer equivalence ratios could be considered equal. Investigation of individual fires showed that the steady-state time ratio decreased below 1.0 at very early times in the fire. Typically, the ratio was 0.1 or less for the quasi-steady-state periods over which data was averaged. For some fires, during the highly transient transition from overventilated to underventilated conditions, the τSS increased quickly, approaching a value of 1. The correlations presented in the engineering methodology represent data that have been averaged over steady-state (hood experiments) or quasi-steady-state (compartment fires) periods. For the purpose of modeling fires with respect to time it is of interest to know how the species yields correlate with the equivalence ratio during transient conditions (i.e., as the fire is growing). Determining this correlation was accomplished by plotting the yield to equivalence ratio data for individual fires from the time of ignition to the steady-state period. These transient correlations were compared to the steady-state correlations obtained from steady-state averaged data from all tests (e.g., the CO yield correlation shown in
510
1.0
• • ••
0.3
Notes: = Steady-state yield + = Transient yield • = τ ss
•
+
0.2
+
++ + ++ + + + ++ + •
••• • •• • • •••• •• • •• • • • • ••• • • • • • •• • • • •• •• ••••• ••• •
+ ++ + +++++++++++++ + + +
0 0
Fig. 16.9). An example of one comparison is shown in Fig. 16.16. Figure 16.16 shows the steady-state hexane CO yield correlation along with the transient yield vs. equivalence ratio data for a hexane compartment fire that obtained a steady-state average ϕp of 3. The solid dots in Fig. 16.16 represent the steady-state time ratio data, τSS. For this example, τSS remained fairly constant at about 0.1 for the entire fire. And as can be seen, the agreement between the transient and steady-state correlations is quite good, even for the transition to underventilated conditions. Good agreement between transient and steadystate data was also observed for CO2 and O2 yield correlations. Although more transient in nature than the hood experiments, the compartment fires are characterized as primarily quasi-steady and, therefore, do not differ significantly from Beyler’s hood experiments in this respect. This analysis also shows that the species yield correlations developed for steady-state conditions are representative of the transient growth periods of these fires. In terms of full-scale application, these results suggest that ϕp and ϕul are approximately equal for compartment fires characterized by relatively slow growth compared to the upper-layer residence time (i.e., τSS 1). However, the low τSS values observed in the reduced-scale compartment fires may not always be representative of full-scale fires. The reduced-scale compartment fires had residence times typically between 4 and 20 s. These short residence times were a result of
0.5
+ + + ++ ++ +
+
0.6
0.4
+
+
0.1
++ +
+ +
+ •
0.8
•• • •
•• ••••• • •
0.2 •
• •
•
1.0 1.5 2.0 Equivalence ratio
••
•
• • • • ••
2.5
•
Steady-state time ratio
0.4
Unnormalized CO yield
Fig. 16.16 Comparison between a transient, unnormalized CO yield correlation for a hexane fire with an average steadystate ϕp of 3 and the steadystate correlation for all hexane fires studied by Gottuk et al. The steadystate time ratio, τSS, data are shown as solid dots [17]
D.T. Gottuk and B.Y. Lattimer
0 3.0
having relatively large fires compared to the compartment volume. Until flashover conditions are approached, a full-scale compartment fire will most likely have smaller fires compared to the volume of the space. As a result, the residence time of gases in the upper layer of a fullscale fire may be much longer. Times on the order of 5–10 min may not be unrealistic in some cases. Therefore, in the case of a fastgrowing full-scale fire, values of ϕp could increase relative to ϕul. The application point is that the control volume used for the equivalence ratio must be considered with respect to the residence time of gases in the upper layer.
Species Transport to Adjacent Spaces The species levels transported from a compartment depend on a variety of conditions produced during the course of the fire. As compartment fire gases exit the compartment, they entrain the gases present in the adjacent space (Fig. 16.17). If a fuel-rich mixture is produced in the compartment, the gases flowing out may ignite, causing burning in the adjacent space. This burning is an indication that oxidation reactions are taking place, which ultimately affects the species levels transported to remote areas. As the gases continue to flow through the adjacent space, they are cooled by mixing with surrounding gases and heat losses to the boundaries. Eventually, gases are cooled to a temperature below which
16
Effect of Combustion Conditions on Species Production
511 Lf,tip
Fig. 16.17 Phenomena controlling species transport to remote locations
Oxidation reactions
mair •
•
Qloss
Transport to remote locations Reaction is frozen
mair •
mfuel •
oxidation reactions do not readily occur. At this point the reactions are said to be frozen. The amount of combustion products that exist at this point will continue to flow throughout the rest of the structure. As a result, combustion product levels in the overall structure will accumulate as the fire inside the compartment persists and/or additional items in the structure begin to burn. Conditions inside the fire compartment and in the directly adjacent space will govern the species levels transported to remote locations. The primary consideration is the conditions that develop inside the compartment. If burning outside of the fire compartment occurs due to either flame extension or external burning, gases will continue to react outside of the compartment influencing the species levels transported to remote areas. The degree to which gases react outside the compartment depends on the mixing of oxygen with the fuel-rich gases flowing out of the compartment, and the addition of fuel to the gases flowing along the adjacent space.
General Effects of Burning Outside the Compartment Species levels transported to remote locations will be equivalent to those formed inside the compartment unless burning occurs outside. Chemical kinetics indicate that oxidation reactions cannot occur efficiently outside the compartment unless gas temperatures are near those produced at the onset of flashover (775–875 K) (see the section
“Chemical Kinetics” in this chapter). In the presence of oxygen, hydrocarbons begin to react efficiently when temperatures are above 700 K [14]. Perhaps more importantly, the oxidation of CO to CO2 does not readily occur until temperatures rise above 800 K. The occurrence of burning outside the compartment, either from flame extension or the onset of flashover, will result in local temperatures in excess of 1300 K [4]. At these temperatures, oxidation reactions for both hydrocarbons and CO occur in the presence of available oxygen. The occurrence of burning outside the compartment has been shown, in most situations, to reduce the incomplete combustion products (including smoke and CO levels) transported to remote locations [5, 28–30]. The burning in unconfined adjacent areas (e.g., open surroundings) has been measured to decrease incomplete combustion products more efficiently than burning in confined adjacent areas (e.g., a corridor). In addition, the consumption of incomplete combustion products during burning in confined areas was found to be sensitive to the air entrainment into the plume/ceiling jet flow. This entrainment is a function of the mass flow from the compartment, the geometry of the opening between the compartment of fire origin and the adjacent space, and the geometry of the adjacent space itself. Smoke layers that develop in confined adjacent spaces can cause lower oxygen levels to be entrained into the plume/ceiling jet flow in the adjacent space, increasing the incomplete combustion product levels transported to remote areas.
512
D.T. Gottuk and B.Y. Lattimer
Burning in Unconfined Adjacent Areas
Burning in Confined Adjacent Areas
Unconfined adjacent areas are those areas where the flame extending from the compartment of origin is not redirected by the boundaries of the adjacent area, and the gases are allowed to burn as a buoyant plume. Examples of unconfined adjacent areas include outdoor surroundings, atriums, and corridors with high ceilings relative to the door height of the burning compartment. Gottuk et al. [15, 31] investigated the impact of external burning on combustion products downstream of an unconfined jet. The compartment was connected to its surroundings through a window opening. Tests were performed with compartment fires with and without external burning. In these tests, a compartment equivalence ratio of 1.6 was the lowest ϕc where external burning was noted to occur. The effects of external burning on the CO levels downstream of the fire are shown in Fig. 16.18. With a compartment equivalence ratio greater than 1.6, CO levels were measured decreasing below the fire compartment levels. The CO yield is shown to decrease to a minimum of 0.02 at ϕ greater than 2.0. The decrease in CO represents a 75–90% reduction of the CO generated in the fire compartment.
Burning in a confined adjacent area, such as a corridor or room, causes the external flame to impinge on a ceiling, and possibly on walls. Compared with flow in an unconfined area, the ceiling and walls in the confined area will reduce the amount of air entrainment into the gas jet exiting the fire compartment. The effects of burning in confined areas on species transport have been investigated by Ewens et al. [28, 32] and Lattimer et al. [29, 30] using the same fire compartment design in the unconfined external burning study (Figs. 16.19 and 16.20) [17, 31]. The transport of species to remote locations is geometry dependent and can be affected by smoke layers that develop in the confined area. However, species levels transported to remote areas can be predicted by defining an equivalence ratio for a control volume involving both the fire compartment and the burning in the adjacent space. Species transport has been evaluated for two common compartment-hallway configurations. Ewens [28] and Lattimer et al. [30] evaluated species transport in a configuration with the fire compartment on the end of a hallway (see
0.40 0.35 Unnormalized CO yield
Fig. 16.18 Effect of external burning on CO levels downstream of an unconfined adjacent area. CO yield versus compartment equivalence ratio for hexane compartment fires with an exhaust jet to the open atmosphere through a window opening; (○) compartment levels, (☉) downstream levels [17, 31]
0.30 0.25 0.20 0.15 0.10 0.05 0.00 0.0
0.5
1.0
1.5
2.0
2.5
3.0
Compartment equivalence ratio, φc
3.5
4.0
16
Effect of Combustion Conditions on Species Production
1.52 m Air
513
Inlet soffit Compartment
Fire location
Hallway Exhaust duct
1.22 m Adjustable size opening
1.22 m Air plenum
1.67 m 3.66 m 1.22 m
Fig. 16.19 Compartment on the end of a hallway [28, 30, 32]
Compartment
1.22 m
1.52 m 5.18 m
Exhaust duct
Hallway
1.22 m
Fire location
1.67 m
Air plenum Air inlet duct
Inlet soffit Adjustable size opening
Air
1.22 m Exit soffit
Fig. 16.20 Compartment on the side of a hallway [29, 30]
Fig. 16.19). Lattimer et al. [29, 30] performed a study with the fire compartment on the side of a hallway (see Fig. 16.20). In both studies, most tests were performed with a window connecting the compartment and hallway.
Using the apparatus shown in Fig. 16.19, Ewens [28] evaluated the effects of different geometric variables and compartment stoichiometry on CO levels (in addition to other species) downstream of the external burning where
514 0.40 0.35
Unnormalized CO yield
Fig. 16.21 Effect of external burning on CO levels downstream of a postflashover compartment fire. Adjacent hallway with a (~) 0 m inlet soffit and (∎) 0.20 m inlet soffit. (☉) Unconfined area and (○) inside the compartment [17, 28, 31, 32]
D.T. Gottuk and B.Y. Lattimer
0.30 0.25 0.20 0.15 0.10 0.05 0.00
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Compartment equivalence ratio, φc
1e + 0
Mass flow rate (kg/s)
Fig. 16.22 The mass flow rates in a space adjacent to a postflashover fire with external burning plotted versus the ratio of the distance down the hall, x, to the length of the flame to its tip, Lf,tip. Opening of 0.12 m2, no inlet soffit above the opening, and an average compartment ϕ ¼ 2.0 [28]
O2 CO2 CO THC Total
1e – 1 1e – 2
1e – 3 1e – 4 1e – 5 0.0
0.5
1.0
1.5
2.0
x/Lf,tip
reactions were considered frozen. As shown in Fig. 16.21, Ewens [28] demonstrated that burning in confined areas outside the compartment decreases incomplete combustion product levels, but not always to the same extent as when the fire gases spill into an unconfined space. The degree of oxidation was found to be dependent on both air entrainment into the gases exiting the compartment and the fuel flowing out of the compartment. The data of Ewens show that both fire size and geometric parameters will affect species production. The two important results to understand are that geometries which increase air entrainment in the adjacent space (e.g., an inlet soffit
vs. no soffit) or reduce the layer depth in the adjacent space will enhance the oxidation reactions and result in lower levels of incomplete combustion products, such as CO. Fire gases flowing into and through the adjacent space entrain surrounding gases as they flow away from the fire compartment. These gases can undergo chemical reactions, particularly as they are within the flaming region. A sample plot of the species variation along the flame length in the hallway is shown in Fig. 16.22 [28]. Results shown in Fig. 16.22 are from postflashover hexane fire tests with an average compartment equivalence ratio of ϕ ¼ 2.0, a 0.12 m2 opening
16
Effect of Combustion Conditions on Species Production
(0.50 m wide 0.24 m high) connecting the compartment and adjacent space, and no inlet soffit above the opening in the hallway. These data represent time-averaged conditions 0.025 m below the ceiling along the hallway during the quasi-steady-state period of the fire, when external burning was occurring. Gases entered the adjacent space as a ceiling jet, but were allowed to expand horizontally until intersecting the walls of the hallway. For this geometry, the largest increase in the total mass flow rate was during the first half of the flame length, which was 2.7 m (on average) from the compartment. By x/Lf,tip ¼ 0.75, the total mass flow rate had reached a maximum. This indicated that all of the entrainment into the ceiling jet flow occurred by x/Lf,tip ¼ 0.75. The majority of the oxidation reactions had also occurred by x/Lf,tip ¼ 0.75. The mass flow rates of CO, CO2, and O2 were essentially constant downstream of x/Lf,tip ¼ 0.75. This indicates that the oxidation of CO to CO2 was frozen by an x/Lf,tip ¼ 0.75. Small amounts of total hydrocarbons (THC) continued to react from 0.75 < x/Lf,tip < 1.0; however, this was not measured to significantly increase CO levels. Analysis of data in Fig. 16.22, as well as other data by Ewens et al. [28, 32] and Lattimer et al. [29, 30], indicates that by the flame tip all of the oxidation reactions have occurred. As a result, the mass flow rates of the major combustion products beyond the flame tip will be transported to remote locations. The mass flow rate levels will be influenced by the oxygen availability in the flaming region. Based on test results from Ewens et al. [28, 32] and Lattimer et al. [29, 30], mixing near the compartment has been shown to have the most significant influence on the combustion products transported to remote areas.
Predicting Species Levels Lattimer [33] performed additional analysis on Ewens’ data to develop a correlation between species transported and ϕ for a control volume consisting of part of the area in the adjacent space
515
where burning occurred. In this set of data, the mixing in the adjacent space (hallway) was varied by using windows with different areas and aspect ratios to connect the compartment to the adjacent space, and by adding a 0.20 m soffit above the window. The equivalence ratio in this analysis was calculated using a control volume that extended to the sampling point located in the adjacent space. Using this control volume, the mass flow rate of air for the ϕcv calculation in Equation 16.13 was the air flow rate into the compartment plus the air entrainment into the plume/ceiling jet flow in the adjacent space, up to the sampling location. In these experiments, gas sampling was always performed in or just downstream of the flame within the hallway. In Figs. 16.23, 16.24, 16.25, and 16.26 the species yields are plotted vs. the control volume equivalence ratio, ϕcv. Note that CO yields are not normalized because for various fuels unnormalized CO yields were found to correlate best with ϕ. The lines in the normalized O2 depletion and CO2 and THC yield plots represent the results from the complete combustion model presented in Equation 16.14. Due to limited data near the compartment, there are few data points at high ϕcv. The trends in the species data were similar to those observed in the hood experiments by Beyler [8, 9] and in the compartment experiments by Gottuk et al. [5] The normalized O2 depletion is approximately unity at ϕcv less than 1.0 and decays at the rate prescribed by the complete combustion model at higher ϕcv. CO2 normalized yields are near unity up to a ϕcv of approximately 0.8. At ϕcv greater than 0.8, the CO2 levels begin to decay and are consistently less than the level predicted by the complete combustion model. This behavior is consistent with the rise in incomplete combustion products, such as CO and THC, at ϕcv ranging from 0.6 to 0.8. These results indicate that species levels in adjacent spaces can be adequately correlated by the same global equivalence ratio correlations obtained for species production in fire compartments as long as ϕcv is calculated using the appropriately defined control volume. ϕcv accounts for the effects of external burning on
516 1.6 1.4 Normalized O2 yield
Fig. 16.23 Normalized O2 depletion of gases in a space adjacent to a postflashover compartment fire. Control volume includes fire compartment and a portion of the adjacent space where burning occurs
D.T. Gottuk and B.Y. Lattimer
1.2 1.0 0.8 0.6 0.4 0.2 0.0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
2.5
3.0
2.5
3.0
Control volume equivalence ratio, φ cv
1.6 1.4 Normalized CO2 yield
Fig. 16.24 Normalized CO2 yields of gases in a space adjacent to a postflashover compartment fire
1.2 1.0 0.8 0.6 0.4 0.2 0.0 0.0
1.0
0.5
1.5
2.0
Control volume equivalence ratio, φ cv
0.40 0.35 Unnormalized CO yield
Fig. 16.25 Unnormalized CO yields of gases in a space adjacent to a postflashover compartment fire.
0.30 0.25 0.20 0.15 0.10 0.05 0.00 0.0
0.5
1.0
1.5
2.0
Control volume equivalence ratio, φcv
Effect of Combustion Conditions on Species Production
Fig. 16.26 Normalized THC yields of gases in a space adjacent to a postflashover compartment fire
517
0.50 0.45 Normalized THC yield
16
0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 0.0
0.5
1.0
1.5
2.0
2.5
3.0
Control volume equivalence ratio, φcv
species levels and can be used with Equations 16.19, 16.20, 16.21, 16.22, 16.23, 16.24, and 16.25 to estimate species transported to remote areas.
Effects of Oxygen-Deficient Smoke Layers in Adjacent Spaces The development of hot, oxygen-deficient smoke layers in the adjacent space affects both the entrainment into the plume/ceiling jet and the amount of oxygen mixing with the fuel-rich gases flowing from the fire compartment. Ewens et al. [28, 32] demonstrated that layers as thin as 0.20 m may have an impact on incomplete combustion products being transported to adjacent areas. Lattimer et al. [29, 30] performed a series of tests with different oxygen-deficient layer depths in the space directly adjacent to a postflashover fire (see Fig. 16.20). Tests were performed with three different opening sizes connecting the compartment to the adjacent space, but the compartment stoichiometry was approximately the same in all tests. In each test, the layer depth was kept at a constant level by the use of an exit soffit. In order to change the layer depth from test to test, the height of the exit soffit was adjusted for each test. Except for cases with a deep smoke layer in the adjacent space, external burning occurred in all tests. Figure 16.27 contains a plot of time to
ignition for tests with different layer depths. Layer depth is represented as a dimensionless depth, γ ¼ δ/z, which relates the distance between the ceiling and the bottom of the visible smoke layer, δ, to the distance between the ceiling and the bottom of the gases flowing out of the compartment, z. (For a window configuration, z is measured to the bottom of the window.) As shown in Fig. 16.27, the smoke layer did not affect the time to ignition until the visible smoke layer was nearly deep enough to prevent ignition altogether (indicated by the infinite time to ignition). At layer depths greater than γ ¼ 1.7, external burning did not occur since the exiting fire gases were not able to entrain sufficient fresh air to provide the necessary oxygen for combustion. Rather, the gases exiting the fire compartment entrained primarily vitiated gases in the upper layer of the adjacent space. The CO, CO2, and THC yields measured at a remote location (in the exhaust duct) for the different window opening sizes are shown plotted in Figs. 16.28, 16.29, and 16.30 with respect to the smoke layer depth. Each data point is the time-averaged yield during the quasi-steady-state part of the fire. For this geometry, combustion product levels were not significantly affected by the smoke layer until it fell below the bottom of the opening (γ > 1.0). As the layer depth increased from γ ¼ 1.0–1.8, the burning outside the compartment became increasingly less efficient. This resulted in an increase in CO and
518
500 Time to external burning (s)
Fig. 16.27 Time for external burning in tests with a range of layer depths in the adjacent space with a 6.32 m2 floor plan area [30]
D.T. Gottuk and B.Y. Lattimer
450 400 350 300 250 200 A vent = 0.12 m2 A vent = 0.08 m2 A vent = 0.04 m2
150 100 50 0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
Dimensionless smoke layer depth, δ/z
0.5
3.0 CO THC CO2
0.4
2.5 2.0
0.3 1.5 0.2 1.0 0.1
Normalized CO2 yield
Normalized THC yield and unnormalized CO yields
Fig. 16.28 The effect of an oxygen-deficient upper layer on downstream species yields from a postflashover fire extending into a hallway. Opening of 0.12 m2, 0.20 m soffit above the opening, and an average ϕc ¼ 3.1. Open symbols are tests with no external burning. γ > 1 indicates layer is below the bottom of the vent [28, 29]
0.5 0.0
0.0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
Dimensionless layer depth, γ = δ/z
0.5
1.0 CO THC CO2
0.4
0.8
0.3
0.6
0.2
0.4
0.1
0.2
0.0 0.0
0.5
1.0
1.5
2.0
2.5
Dimensionless layer depth, γ = δ/z
0.0 3.0
Normalized CO2 yield
Normalized THC yields and unnormalized CO yields
Fig. 16.29 The effect of an oxygen-deficient upperlayer on downstream species yields from a postflashover fire extending into a hallway. Opening of 0.08 m2, 0.20 m soffit above the opening, and an average ϕc ¼ 2.8. Open symbols are tests with no external burning [30]
Effect of Combustion Conditions on Species Production
519
0.5
1.0 CO THC CO2
0.4
0.8
0.3
0.6
0.2
0.4
0.1
0.2
Normalized CO2 yield
Fig. 16.30 The effect of an oxygen-deficient upper layer on downstream species from a postflashover fire extending into a hallway. Opening of 0.04 m2, 0.20 m soffit above the opening, and an average ϕc ¼ 2.8. Open symbols are tests with no external burning [29, 30]
Normalized THC yields and unnormalized CO yields
16
0.0
0.0 0.0
THC yields and a decrease in the CO2 yield. The increase in CO and THC yields was attributed to reducing the oxygen available to oxidize the combustion products. When the smoke layer was increased to a dimensionless layer depth of γ ¼ 1.7–1.8, external burning was not observed and downstream species yields were consistent with levels inside the fire compartment. External burning in some tests with deep oxygen deficient upper layers actually caused additional CO formation in the adjacent space. As shown in Fig. 16.28, in tests with the largest opening, 0.12 m2, and a dimensionless layer depth of γ ¼ 1.3–1.5, CO yields increased to approximately 0.27 kg/kg, which is approximately 0.05 kg/kg higher than compartment levels. In addition, corresponding normalized THC yields were on average 0.06 kg/kg lower than compartment levels. These results indicate that available oxygen is being used to preferentially oxidize THC instead of CO. This oxidation of THC forms additional CO, causing an increase in CO levels transported to remote locations. The exact conditions in the adjacent space necessary to produce these results have not been fully established.
Other Considerations There are other variables that may influence the combustion product levels being transported to remote locations that have not been fully
1.0 1.5 2.0 2.5 0.5 Dimensionless layer depth, γ = δ/z
3.0
explored. These variables include the effects of air addition through forced ventilation, additional fuel decomposition in the adjacent space, and heat losses to the ceiling and walls. The addition of air to the system through forced ventilation may have an influence on species levels, depending on where the air is added relative to the external burning. Forced ventilation in the region where external burning is occurring will introduce additional oxygen into the flow, and possibly induce additional mixing. This may result in better oxidation of incomplete combustion products, such as CO. Addition of air to the system downstream of the external burning will dilute the gases, but will not reduce the amount (in terms of mass) of incomplete combustion products being transported to remote locations. Decomposition of fuel in the adjacent space may affect species levels transported to remote locations. This effect may be sensitive to the location of the decomposing fuel, the type of fuel, whether it is flaming or smoldering, and the conditions surrounding the fuel. Heat losses to the ceiling and walls can cause gas temperatures in the adjacent space to decrease more readily for some materials, compared to well-insulated boundaries. An example of this may be steel decks and bulkheads on ships. A decrease in gas temperature may cause temperatures to reach levels where no reactions can occur sooner than those observed in wellinsulated cases. As a result, higher heat loss to
520
the boundaries may result in higher incomplete combustion products, including CO, to be transported to remote areas. Species concentrations may not always be transported away from the compartment in a uniform manner. In experiments performed by Lattimer et al. [29, 30] with the compartment located on the side of a hallway, the bulk flow from the compartment was measured to flow across the hallway and down the side of the hallway opposite the fire compartment. This resulted in higher CO, CO2, and THC levels (and lower O2) flowing along the side of the hallway opposite the fire compartment. For example, CO levels were measured to be as high as 1.9 % along the side of the hallway opposite the fire compartment, while on the side of the hallway with the fire compartment the maximum CO level was measured to be 1.0 %. As these gases flow farther from the compartment, they are expected to become more uniform across the hallway. However, the distance away from the compartment where mostly uniform flow occurs was not quantified.
Engineering Methodology In light of the experimental work and chemical kinetics considerations discussed previously, several correlations can be used as guidelines for fire protection engineering. The production of chemical species in compartment fires has been shown to be correlated with the control volume equivalence ratio, ϕcv. For most purposes, the equivalence ratio can be calculated using instantaneous fuel burning rates and air mass flow rates assuming quasi-steady-state conditions. The following methodology presents a guide to determining bounds on species production as well as comments on the limits of this approach. The methodology for estimating species transported to remote locations is provided in Fig. 16.31. This approach considers the occurrence of external burning outside the compartment. In general, the primary steps in the analysis are:
D.T. Gottuk and B.Y. Lattimer
1. Determine the compartment equivalence ratio, ϕc. 2. If ϕc is less than 1, estimate species levels using the global equivalence ratio-yield correlations presented in Equations 16.19, 16.20, 16.21, 16.22, 16.23, 16.24, and 16.25 with the ϕc. 3. If ϕc is greater than 1, determine whether external burning will occur outside of the compartment. External burning can be assumed to occur at a ϕc (plume or compartment) of 1.6, or by calculating the ignition index using Equation 16.1. 4. If there is no external burning, use the ϕc and Equations 16.19, 16.20, 16.21, 16.22, 16.23, 16.24, and 16.25 to calculate the species transported. 5. If external burning is occurring, determine the effect of the smoke layer using the dimensionless smoke depth, γ ¼ δ/z, where δ is the depth of the layer below the ceiling and z is the lowest elevation of gases exiting the compartment. 6. If γ is greater than 1.0 and external burning is predicted, the smoke layer can be assumed to inhibit oxidation in the adjacent space. CO and other incomplete-combustion products are not reduced. The ϕc and Equations 16.19, 16.20, 16.21, 16.22, 16.23, 16.24, and 16.25 can be used to estimate the species transported to remote locations. 7. If γ is less than 1.0 and external burning is predicted, the smoke layer does not inhibit the oxidation in the adjacent space and incomplete-combustion products, such as CO, will be reduced. The species transported can be estimated using Equations 16.19, 16.20, 16.21, and 16.22 and the equivalence ratio for a control volume, ϕcv, that incorporates the compartment and the adjacent space out to the flame tip (see Fig. 16.17). It should be noted that this methodology may not provide the maximum levels of incomplete combustion products that can be produced in a fire. Equations presented in this methodology for species yields as a function of equivalence ratio have been shown to provide good correlations
16
Effect of Combustion Conditions on Species Production
Fig. 16.31 General methodology for predicting species levels transported to remote locations from a fire compartment
521
Calculate φc
φc > 1.0?
No
Yes External burning?
No
Yes Calculate smoke layer depth, δ, relative to lowest elevation of gases exiting compartment, z, (γ = δ/z)
γ = δ/z < 1.0?
No
External burning has no effect
Yes Calculate φcv with control volume out to flame tip in adjacent space
Use φc to determine species yields
Use φcv to determine species yields
even for wood as a secondary fuel pyrolyzing in the hot upper layer. However, it is not clear whether these correlations will hold for nonoxygenated fuels in the upper layer or how well they will represent other oxygenated fuels. Several empirical correlations have been developed to predict species levels at a range of equivalence ratios. Different correlations are given in the following paragraphs to accommodate analyses of various levels of complexity. Due to its toxicity, CO production is of primary importance. Four correlations (see Equations 16.19, 16.20, 16.21, and 16.22) are presented, representing varying degrees of complexity. In each case, the correlations basically represent a lower bound for the yield of
CO. Equations 16.19a and 16.19b represents a “zeroth order” correlation between CO yield and equivalence ratio. For overventilated burning conditions, there is no CO production and for underventilated conditions CO is produced at a yield of 0.2 g per gram of fuel burned. This correlation applies best to fires with average upper-layer temperatures greater than 900 K. f CO ¼ 0 f CO ¼ 0:2
for ϕ < 1 for ϕ > 1
ð16:19aÞ ð16:19bÞ
Equations 16.20a, 16.20b, and 16.20c accounts for some of the temperature effect by including a linear rise in CO yield over the transition region from ϕ of 0.5 to 1.5.
522
D.T. Gottuk and B.Y. Lattimer
f CO ¼ 0
for ϕ < 0:5
f CO ¼ 0:2ϕ 0:1
ð16:20aÞ
for 0:5 < ϕ < 1:5 ð16:20bÞ
f CO ¼ 0:2
for ϕ > 1:5
ð16:20cÞ
The temperature effect on CO production is best represented in the following two correlations. Equation 16.21, which represents a fit to the hexane data of Beyler’s hood experiments, is suggested for compartment fires with average upper-layer temperatures below 800 K. Equation 16.22 is used for fires with upper-layer temperatures above 900 K. Equation 16.15 is an approximate fit to the compartment fire hexane data of Gottuk et al. For the most part, CO yields from hexane fires represent lower limits observed for the fuels studied to date [5, 8]. Therefore, these equations provide a minimum CO production that can be used for hazard analysis. 1
Y CO ¼ð0:19=180Þ tan ðXÞ þ 0:095 for T < 800 K
ð16:21Þ
whereX ¼ 10ðϕ 0:8Þ and tan1 (X) is in degrees Y CO ¼ð0:22=180Þ tan 1 ðXÞ þ 0:11 for T > 900 K
ð16:22Þ
where X ¼ 10ðϕ 1:25Þ and tan1(X) is in degrees The figures presented earlier of CO yield versus equivalence ratio also show plots of Equations 16.21 and 16.22. Figure 16.7 shows the CO yield data for methane hood experiment fires in which upper-layer temperatures ranged from 490 to 870 K. The CO yield data of Zukoski et al. and Toner et al. lie between the curves of Equations 16.21 and 16.22, particularly for slightly overventilated and stoichiometric conditions. This is consistent with the fact that these fires had temperatures that were higher than those represented by Equation 16.14 and some were within the transition range of 800–900 K.
The simple model presented as Equations 16.14a, 16.14b, 16.14c, 16.14d, and 16.14e with the inclusion of the empirically determined yield coefficients, is fairly adequate for predicting CO2, O2, and H2O normalized yields (see Equations 16.23, 16.24, and 16.25). Suggested average yield coefficients for compartment fires of elevated temperatures (T > 900 K) are 0.88 for BCO2 and 0.97 for BO2 [5]. Suggested values for low upper-layer temperatures (T < 800 K) are 0.77 for BCO2 , 0.92 for BO2 , and 0.95 for BH2 O . Average yield coefficients for underventilated fires are shown in Table 16.2. f CO2 ¼ 1
for ϕ < 1
f CO2 ¼ BCO2 =ϕ f O2 ¼ 1
for ϕ < 1
f O2 ¼ BO2 =ϕ f H2 O ¼ 1
for ϕ > 1
for ϕ > 1
for ϕ < 1
f H2 O ¼ BH2 O =ϕ
for ϕ > 1
ð16:23aÞ ð16:23bÞ ð16:24aÞ ð16:24bÞ ð16:25aÞ ð16:25bÞ
As presented in Equations 16.23, 16.24, and 16.25, normalized chemical species yields, f, can be correlated quite well by the global equivalence ratio. This is true for a wide range of fuel types. However, it is worthwhile to point out that for different fuels, the CO2, O2, and H2O yields to equivalence ratio correlations only collapse down to a single curve when the yields are normalized by the maximum possible yield for a given fuel (i.e., presented as f rather than Y ). Although complete combustion does not occur, combustion efficiencies with respect to equivalence ratio are similar enough between fuels that the stoichiometry of a particular fuel will dictate the generation of CO2 and the depletion of O2. Therefore, the species associated with complete combustion (CO2, O2, and H2O) are not expected to have equal yields for different fuels, since varying fuel compositions will dictate different limits of CO2 and H2O that can be generated and O2 that can be consumed for a gram of fuel burned. By normalizing the yields, the variability of fuel composition is removed.
16
Effect of Combustion Conditions on Species Production
523
Y i m_ f Mmix m_ f þ m_ a Mi
ð16:26Þ
0:21m_ a MO2 =Ma DO2 m_ f m_ f þ m_ a MO2 =Ma
ð16:27Þ
concentrations in Fig. 16.32) represent a reasonable lower bound for a range of typical fuels. Higher concentrations of CO can be created, particularly when additional fuel is added to a vitiated upper layer. Corresponding to Fig. 16.32, CO2 and O2 concentrations for hexane compartment fires are shown in Figs. 16.33 and 16.34, respectively. Even though the peak concentrations of CO2 will be dependent on the fuel type, the oxygen concentration as a function of will be similar for most hydrocarbons [5]. The ratio of CO to CO2 concentrations can be used as an indicator of the combustion mode. Higher combustion efficiency is obtained as more fuel is burned completely to CO2 and H2O and is indicated by a ratio of CO to CO2 near zero. Since CO is a product of incomplete combustion, the ratio of CO to CO2 concentrations will increase as fires burn less efficiently. The ratio increases with equivalence ratio even for underventilated conditions, as evidenced by experimental data (e.g., Gottuk et al. [5]) and the engineering correlations presented above.
The yield-equivalence ratio correlations shown in Fig. 16.9, which are also represented by Equations 16.21 and 16.15, have been replotted as CO concentration vs. equivalence ratio in Fig. 16.32. As indicated previously, the yield correlations in Fig. 16.9 (and thus, the
Example 4 Consider that the piece of furniture described in Example 1 is burning in a room such that a two-layer system develops. The only ventilation to the room is an open doorway through which 217 g/s of air is being entrained. The material is burning at a rate of 37 g/s, and the
On the other hand, carbon monoxide production is best correlated by the equivalence ratio when represented as a simple yield, YCO, rather than a normalized yield, fCO. This is one indicator that CO production is not strongly dependent on fuel type, as is production of CO2 and O2. The reason for this is believed to be due to the fact that CO is effectively an intermediate product that depends more on the elementary chemistry than on fuel composition, which determines products of complete combustion. Once yields are determined using the above correlations, species gas concentrations can be calculated. Equation 16.26 can be used to calculate the concentration of species i for all species except oxygen. Oxygen concentrations can be calculated from the depletion of oxygen using Equation 16.27.
XO2wet ¼
Fig. 16.32 Carbon monoxide concentrations as a function of equivalence ratio for hexane fires in a compartment (o) and under a hood (+). Data represent the same tests shown in Fig. 16.9 as unnormalized yields
5
CO concentration (% vol wet)
Xiwet ¼
Notes: = Gottuk et al. + = Beyler
4
3
2
1 ++ +
0 0
0.5
++
++ ++
+++
+
+ 1.0
1.5 Equivalence ratio
2.0
2.5
3.0
524
D.T. Gottuk and B.Y. Lattimer 20 CO2 concentration (% vol wet)
Fig. 16.33 CO2 concentrations as a function of equivalence ratio for hexane compartment fires [5]
15
10
5
0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
2.5
3.0
Plume equivalence ratio
20 O2 concentration (% vol wet)
Fig. 16.34 O2 concentrations as a function of equivalence ratio for hexane compartment fires [5]
15
10
5
0 0.0
0.5
1.0
1.5
2.0
Plume equivalence ratio
average temperature of the upper layer is 700 C. Calculate the plume equivalence ratio and determine the yield of CO and depletion of O2. Solution The plume equivalence ratio is calculated using Equation 16.10b. The stoichiometric fuel-to-air ratio, r, has already been calculated in Example 1. ϕp ¼
m_ f =m_ a 37=217 ¼ 1:5 ¼ 0:1139 r
Because the average upper-layer temperature ð700 C þ 273 ¼ 973 KÞ is above 900 K, Equation 16.22 is used to calculate the yield of CO. The argument, X, of the inverse tangent is
X ¼ 10 ϕ p 1:25 ¼ 10ð1:5 1:25Þ ¼ 2:5 0:22 Y CO ¼ tan 1 ðXÞ þ 0:11 180 0:22 Y CO ¼ tan 1 ð2:5Þ þ 0:11 180 Y CO ¼ 0:19 Therefore, 0.19 g of CO are produced for every gram of polyurethane foam that burns. The production rate of CO is equal to that yield, YCO, multiplied by the fuel burning rate (0.19 37 g/s ¼ 7.0 g/s). The normalized yield of oxygen is determined using Equation 16.24, and the recommended yield coefficient, BO2 , of 0.97.
16
Effect of Combustion Conditions on Species Production
f O2 ¼
BO2 0:97 ¼ 0:65 ¼ 1:5 ϕ
From Example 1, we obtain the maximum theoretical depletion of oxygen, kO2, and calculate the depletion of oxygen as DO2 ¼ f O2 kO2 ¼ 0:65 ð2:05Þ ¼ 1:33 g of O2 per gram of fuel burned The depletion rate of oxygen is 49.2 g/ s (1.33 37 g/s). Example 5 For the piece of furniture burning in Example 4, calculate the CO and O2 concentrations in the upper layer. Solution Gas concentrations can be calculated from the yields determined in Example 4 using Equation 16.26 for CO and Equation 16.27 for O2. XCOwet ¼ X O2 ¼
Y CO m_ f Mmix 0:19ð37Þ ð28:8Þ ¼ 0:028 ¼ m_ f þ m_ a MCO ð37 þ 217Þ ð28Þ
0:21m_ a MO2 =Ma DO2 m_ f m_ a þ m_ f MO2 =Ma
0:21ð217Þ 32=28:8 1:33ð37Þ ð32 þ 217Þ 32=28:8 ¼ 0:005 ¼
X O2
The resulting concentrations of CO and O2 are 2.8 and 0.5 % by volume, respectively. Example 6 A fire is burning in a room that has one door open and no other ventilation. The room is 7 m wide and 4 m deep with a 2.43 m high ceiling. The door measures 0.76 m wide and 2.05 m high (area ¼ 1.56 m2). The peak heat release rate of the fire has been estimated to be 4.5 MW. Determine how much CO can be transported to other rooms in the building. Solution The first step is to calculate the compartment equivalence ratio, ϕc. Since details of the fire are not provided, the mass burning rate of the fuel is not known. Therefore, ϕc is estimated via Equation 16.13c using the heat release rate, Q, of 4.5 MW. ϕc ¼
Q 1 4, 500 kW ¼ m_ a 3030 m_ a 3030
525
˙ a, into the room is The mass flow rate of air, m estimated using the ventilation parameter [33] as follows: pffiffiffiffiffiffiffiffiffi pffiffiffi m_ a ¼ 0:5A h ¼ 0:5 1:56 2:05 ¼ 1:12 kg=s ˙ a into the equation above for the Substituting m compartment equivalence ratio yields a ϕc of 1.3. Since ϕc is greater than 1, the occurrence of external burning must be considered. However, using the criteria that ϕc is less than 1.6, it is assumed that no external burning will occur. Species levels inside the room are calculated by Equations 16.19, 16.20, 16.21, 16.22, 16.23, 16.24, and 16.25 using ϕc. The yield of CO is calculated using Equation 16.21 or 16.22, depending on the temperature of the upper layer. The upper-layer temperature can be estimated using the McCaffrey, Quintiere, and Harkleroad (MQH) correlation [34] that is presented in Chap. 30 of this book. According to the MQH correlation, the upper-layer gas temperatures exceed 900 K for fires above 1100 kW. For temperatures above 900 K, Equation 16.22 is used to calculate the CO yield as Y CO ¼ ð0:22=180Þ tan 1 ½10ðϕ 1:25Þ þ 0:11 ¼ 0:14 Since there is no external burning, the CO generated in the compartment (0.14 kg of CO per kg of fuel burned) will flow to other parts of the building. Before dilution occurs away from the fire compartment, the initial concentration of CO in the gases from the fire compartment can be calculated using Equation 16.26: XCOwet
0:14 m_ f 28:8 Y CO m_ f Mmix ¼ ¼ m_ f þ 1:12 28 m_ f þ m_ a MCO
Since there is no information on the contents burning in the room, an accurate assessment of ˙ f, cannot be the fuel mass burning rate, m ˙ f can be made using obtained. An estimate of m Equation 16.13a, with an assumed value of r, the stoichiometric fuel-to-air ratio. Values of r are presented in Table 16.1 for various fuels as 1/r. In order to bound the possible CO
526
D.T. Gottuk and B.Y. Lattimer
concentrations, values of 1/r of 4–15 are chosen to represent a reasonable range of hydrocarbon fuels that may be burning in the room. The fol˙ f calculation lowing shows an example of the m using Equation 16.13a and 1/r ¼ 4: m_ f ¼
ϕ m_ a 1:3ð1:12 kg=sÞ ¼ 0:36 kg=s ¼ 4 1=r
The corresponding calculation for 1/r of 15 yields ˙ f of 0.097 kg/s. Substituting the values for m ˙f an m into the above equation for XCOwet results in CO concentrations of 3.5 and 1.1 %, respectively.
Nomenclature Bi C Cj Cp DO2 E F ΔHc,j j k Lf,tip M ma ˙a m mf ˙f m €f m ˙ exhaust m n nprod
yield coefficients of species i stoichiometric molar ratio of water to carbon dioxide volume concentration of fuel j when fuel stream is stoichiometrically mixed with oxidant stream heat capacity of products of complete combustion, (kJ/g mol K) mass depletion of oxygen per gram of fuel burned (g/g) energy released per kg of oxygen consumed normalized yield or generation efficiency heat of combustion of the species j, (kJ/g mol) fuel species of interest maximum theoretical yield length of flame tip for flame extending down a corridor ceiling molecular weight mass of air mass flow rate of air mass of fuel mass loss rate of fuel derivative of the fuel mass loss rate mass flow rate out of the layer molar quantity number of moles of products of complete combustion per mole of
Q r ra rO2 T TSL,j To t tr τSS Vul X Xidry Xiwet Y YO2 , air z γ δ ϕ ϕc ϕcv ϕp ϕul ρul
reactants (stoichiometric mixture of fuel and oxidant streams) ideal heat release rate stoichiometric fuel-to-air ratio stoichiometric air-to-fuel ratio stoichiometric fuel-to-oxygen ratio temperature adiabatic flame temperature at the stoichiometric limit for fuel species j (K) temperature of the gas mixture prior to reaction (K) time residence time of gases in the upper layer steady-state time ratio volume of the upper layer mole fraction dry mole fraction of species i (H2O removed from sample) wet mole fraction of species i yield (g/g) also refers to DO2 mass fraction of oxygen in air distance between the bottom of the compartment outflow and the ceiling in the adjacent space dimensionless layer depth in adjacent space ðγ ¼ δ=zÞ layer depth in the adjacent space equivalence ratio compartment equivalence ratio equivalence ratio defined per a specified control volume plume equivalence ratio upper-layer equivalence ratio density of the upper layer
Subscripts A f CO O2 CO2 H 2O H2
air fuel carbon monoxide oxygen carbon dioxide water hydrogen
16
Effect of Combustion Conditions on Species Production
THC resid,C Xiwet Xidry
total unburned hydrocarbons residual carbon wet gas concentration with water in the mixture dry gas concentration with no water in the mixture
References 1. R.A. Anderson, A.A. Watson, and W.A. Harland, “Fire Deaths in the Glasgow Area: II The Role of Carbon Monoxide,” Medicine, Science, & the Law, 21, pp. 289–294 (1981). 2. B. Harwood and J.R. Hall, “What Kills in Fires: Smoke Inhalation or Burns?” Fire Journal, 83, pp. 29–34 (1989). 3. R.J. Gann, V. Babrauskas, and R.D. Peacock, “Fire Conditions for Smoke Toxicity Measurements,” Fire and Materials, 18, 3, pp. 193–199 (1994). 4. C.L. Beyler, “Ignition and Burning of a Layer of Incomplete Combustion Products,” Combustion Science and Technology, 39, pp. 287–303 (1984). 5. D.T. Gottuk, R.J. Roby, M.J. Peatross, and C.L. Beyler, “Carbon Monoxide Production in Compartment Fires,” Journal of Fire Protection Engineering, 4, pp. 133–150 (1992). 6. N.P. Bryner, E.L. Johnsson, and W.M. Pitts, “Carbon Monoxide Production in Compartment Fires— Reduced-Scale Enclosure Test Facility,” NISTIR 5568, National Institute of Standards and Technology, Gaithersburg, MD (1995). 7. S.J. Toner, E.E. Zukoski, and T. Kubota, “Entrainment, Chemistry, and Structure of Fire Plumes,” NBSGCR-87-528, National Institute of Standards and Technology, Gaithersburg, MD (1987). 8. C.L. Beyler, “Major Species Production by Diffusion Flames in a Two-Layer Compartment Fire Environment,” Fire Safety Journal, 10, pp. 47–56 (1986). 9. C.L. Beyler, Fire Safety Science—Proceedings of First International Symposium, Hemisphere, Washington, DC, pp. 430–431 (1986). 10. E.E. Zukoski, S.J. Toner, J.H. Morehart, and T. Kubota, Fire Safety Science—Proceedings of the Second International Symposium, Hemisphere, Washington, DC, pp. 295–304 (1989). 11. E.E. Zukoski, J.H. Morehart, T. Kubota, and S.J. Toner, “Species Production and Heat Release Rates in Two-Layered Natural Gas Fires,” Combustion and Flame, 83, pp. 324–332 (1991). 12. J.H. Morehart, E.E. Zukoski, and T. Kubota, “Species Produced in Fires Burning in Two-Layered and Homogeneous Vitiated Environments,” NBS-GCR90-585, National Institute of Standards and Technology, Gaithersburg, MD (1990).
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13. D. Drysdale, An Introduction to Fire Dynamics, 2nd ed., John Wiley and Sons, Chichester, UK (1999). 14. W.M. Pitts, 24th Symposium (International) on Combustion, Combustion Institute, Pittsburgh, PA (1992). 15. D.T. Gottuk, R.J. Roby, and C.L. Beyler, “The Role of Temperature on Carbon Monoxide Production in Compartment Fires,” Fire Safety Journal, 24, pp. 315–331 (1995). 16. A. Tewarson, “Fully Enveloped Enclosure Fires of Wood Cribs,” 20th Symposium (International) on Combustion, Combustion Institute, Pittsburgh, PA, p. 1555 (1984). 17. D.T. Gottuk, “The Generation of Carbon Monoxide in Compartment Fires,” NBS-GCR-92-619, National Institute of Standards and Technology, Gaithersburg, MD (1992). 18. W.D. Walton and P.H. Thomas, “Estimating Temperatures in Compartment Fires,” The SPFE Handbook of Fire Protection Engineering, National Fire Protection Association, Quincy, MA, Ch. 22 (1988). 19. W.M. Pitts, E.L. Johnsson, and N.P. Bryner, “Carbon Monoxide Formation in Fires by High-Temperature Anaerobic Wood Pyrolysis,” presented at the 25th Symposium (International) on Combustion, Combustion Institute, Pittsburgh, PA (1994). 20. D. Gross and A.F. Robertson, 10th Symposium (International) on Combustion, Combustion Institute, Pittsburgh, PA, pp. 931–942 (1965). 21. B.Y. Lattimer, U. Vandsburger, and R.J. Roby, “Carbon Monoxide Levels in Structure Fires: Effects of Wood in the Upper Layer of a Post-Flashover Compartment Fire,” Fire Technology, 34, 4 (1998). 22. W.M. Pitts, “The Global Equivalence Ratio Concept and the Prediction of Carbon Monoxide Formation in Enclosure Fires,” NIST Monograph 179, National Institute of Standards and Technology, Gaithersburg, MD (1994). 23. N.P. Bryner, E.L. Johnsson, and W.M. Pitts, “Carbon Monoxide Production in Compartment Fires: FullScale Enclosure Burns,” in Proceedings of the Annual Conference on Fire Research, NISTIR 5499, National Institute of Standards and Technology, Gaithersburg, MD (1994). 24. W.M. Pitts, N.P. Bryner, and E.L. Johnsson, “Combustion Product Formation in Under and Overventilated Full-Scale Enclosure Fires,” in Proceedings of Combustion Fundamentals and Applications, Joint Technical Meeting, San Antonio, TX (1995). 25. N.P. Bryner, E. L. Johnsson, and W.M. Pitts, “Scaling Compartment Fires—Reduced- and Full-Scale Enclosure Burns,” in Proceedings, International Conference on Fire Research and Engineering (D.P. Lund and E.A. Angell, eds.), Society of Fire Engineers, Boston (1995). 26. W.M. Pitts, “An Algorithm for Estimating Carbon Monoxide Formation in Enclosure Fires,” Fire Safety
528 Science—Proceedings of the Fifth International Symposium, International Association of Fire Safety Science,” pp. 535–546 (1997). 27. J. Warnatz, “Rate Coefficients in the C/H/O System,” in Combustion Chemistry, (W.C. Gardiner, ed.), Springer-Verlag, New York, pp. 224–232 (1984). 28. D.S. Ewens, “The Transport and Remote Oxidation of Compartment Fire Exhaust Gases,” M.S. Thesis, Virginia Polytechnic Institute and State University, Department of Mechanical Engineering, Blacksburg, VA (1994). 29. B.Y. Lattimer, U. Vandsburger, and R.J. Roby, “The Transport of Carbon Monoxide from a Burning Compartment Located on the Side of a Hallway,” 26th Symposium (International) on Combustion, Combustion Institute, Naples, Italy, pp. 1541–1547 (1996). 30. B.Y. Lattimer, U. Vandsburger, and R.J. Roby, “The Transport of High Concentrations of Carbon Monoxide to Locations Remote from the Burning Compartment,” NIST-GCR-97-713, U.S. Department of Commerce (1997). 31. D.T. Gottuk, R.J. Roby, and C.L. Beyler, “A Study of Carbon Monoxide and Smoke Yields from
D.T. Gottuk and B.Y. Lattimer Compartment Fires with External Burning,” 24th Symposium (International) on Combustion, Combustion Institute, Pittsburgh, PA, pp. 1729–1735 (1992). 32. B.Y. Lattimer, D.S. Ewens, U. Vandsburger, and R.J. Roby, “Transport and Oxidation of Compartment Fire Exhaust Gases in Adjacent Corridor,” Journal of Fire Protection Engineering, 6, 4 (1994). 33. B.Y. Lattimer, unpublished data (2000). 34. B.J. McCaffery, J.G. Quintiere, and M.F. Harkleroad, “Estimating Room Fire Temperatures and the Likelihood of Flashover Using Fire Test Data Correlations,” Fire Technology, 17, 2, pp. 98–119 (1981).
Dr. Daniel T. Gottuk is VP of Specialty Services and the Technical Director of Jensen Hughes. He is actively involved in fire hazard analyses, fire research and testing, and forensic engineering relative to fire dynamics and fire detection. Brian Y. Lattimer is a Professor in Mechanical Engineering at Virginia Tech. His research areas include fire dynamics, heat transfer from fires, and material response to fires.
Flammability Limits of Premixed and Diffusion Flames
17
Craig Beyler
Introduction It is well known that not all fuel/oxidant/diluent mixtures can propagate flame. Normal flametype combustion cannot be sustained outside certain limits definable in terms of fuel/oxidant/ diluent composition. Definition of these limits has received a great deal of attention in premixed combustion conditions, that is, in systems where the fuel and oxidant are mixed prior to combustion. Despite scientific interest in the subject dating back to the nineteenth century, the mechanism responsible for flammable limits is not yet understood. Nonetheless, a great deal has been learned that has practical application. Much less investigation into the nature and cause of limits in diffusion flames has been undertaken. Empirically, clear parallels exist between diffusion and premixed limits, and these will be explored in the latter portion of this chapter.
Premixed Combustion Premixed flame fronts can only propagate within a range of compositions of fuel and oxidant. The composition limits within which a flame can
C. Beyler (*) Jensen Hughes, 3610 Commerce Drive, Suite 817, Baltimore, MD 21227, USA
propagate are known as the upper and lower flammable limits and are expressed as concentrations of the fuel in a specified oxidant/ diluent mixture at a specified temperature and pressure. For instance, the lower flammable limit (LFL) of methane in air at normal temperature and pressure is 5 % by volume, and the upper flammable limit (UFL) is 15 % by volume. As such, only methane/air mixtures with methane concentrations between 5 % and 15 % methane will support propagation of flame. For most simple hydrocarbons, the lower and upper flammable limits in air correspond to an equivalence ratio of approximately 0.5 and 3, respectively. The lower flammable limit concentrations for these fuels is approximately 48 g/m3 (Fig. 17.1) [1]. The most widely used method of measuring flammable limits was developed by the U.S. Bureau of Mines [2]. The apparatus consists of a 1.5-m-long, 0.05-m-diameter vertical tube which is filled with the fuel/oxidant/diluent mixture to be tested. The top of the tube is closed, and the base of the tube can be closed until the start of the test to prevent diffusion of the mixture from the tube. With the base of the tube open, the mixture is ignited by a spark or small pilot flame at the base of the tube, and the travel of the flame front up the tube is observed. The mixture is deemed to be within the flammable limits if the flame can propagate halfway up the 1.5 m tube. The test is designed to identify the range of mixture compositions capable of flame propagation remote from the ignition source.
M.J. Hurley (ed.), SFPE Handbook of Fire Protection Engineering, DOI 10.1007/978-1-4939-2565-0_17, # Society of Fire Protection Engineers 2016
529
530
C. Beyler
Fig. 17.1 Effect of molecular weight on lower limits of flammability of alkanes at 25 C [1]
Lower limit of flammability (vol %)
6 X
5
50 mg/L
4 X
3
X
2 1
X
X
X
45 mg/L
X
X
X
X
X
0 0
20
40
60
80
100
120
140
160
180
200
Molecular weight (g/mol)
Methane in air (vol %)
15 X
X
X
X
X
10
X 5
0
0
4 Tube diameter (cm)
8
Fig. 17.2 Upper and lower flammable limits of methane as determined in a vertical tube apparatus for upward propagation (circles), and for downward propagation (crosses) [3]
The apparatus can be used with ignition at the top of the tube, but the flammable limits determined for downward propagation are narrower than for upward propagation. The 0.05 m diameter of the tube was chosen as the smallest diameter at which the heat losses from the flame to the tube wall had minimal effect on the flammable limits determined (Fig. 17.2) [3]. Several other methods for determining flammable limits are available [4–7]. Some methods are
designed for use in special conditions, and others simply reflect national differences. Although each method gives substantially similar results, some variations in results do exist (see, for example, Smedt et al. [8] and Goethals et al. [9]). Mixtures are capable of combustion outside the flammable limits, but external energy must be provided throughout the mixture volume in order to allow propagation of a flame [10]. An example of this behavior is shown in Fig. 17.3. A small hydrogen diffusion flame is used as a pilot source in a lean methane/air mixture. At methane concentrations less than 5 %, combustion occurs only in the wake of the pilot flame. Above 5 %, the flame can propagate away from the pilot flame, regardless of the orientation of the pilot flame. Flammable limits are a function of the oxygen and inert concentrations, as well as the mixture temperature and pressure. As the concentration of inerts is reduced and the oxygen concentration is increased, the upper flammable limit is increased, whereas the lower limit is relatively unchanged. This result can be understood by observing that at the lower flammable limit there is always more than enough oxygen present for complete combustion, but at the upper limit less than the stoichiometrically required oxygen is present. Hence, at the upper limit the additional oxygen participates in the combustion process, whereas at the lower limit the additional oxygen simply replaces inert gas.
17
Flammability Limits of Premixed and Diffusion Flames
531
a Methane flame
H2 Air
Air + 3.1% CH4
Air + 3.7% CH4
Air + 4.3% CH4
Air + 5.23% CH4
b H2
Methane flame
Air
Air + 3.1% CH4 Initial flame
Air + 3.7% CH4 Light blue
Air + 4.95% CH4
Air + 5.64% CH4 Strong blue
Fig. 17.3 A small jet diffusion flame in a coflowing (a) and contraflowing (b) stream as the concentration of the fuel in the stream is gradually increased up to ignition.
The stream velocity is 0.222 m/s, and the hydrogen jet diameter is 1.52 mm [10]
The lower flammable limit is also insensitive to the pressure, except at pressures well below atmospheric. The upper limit shares this insensitivity at subatmospheric pressures, but the upper limit increases with increasing pressure above atmospheric (Fig. 17.4) [1]. The flammable limits widen with increases in mixture temperature as illustrated in Fig. 17.5; [1] this aspect will be discussed further later in this chapter. Figure 17.5 also relates flammable limits with the saturation vapor curve and the autoignition temperature (AIT). The flashpoint of a liquid is given in the figure as TL. At that temperature, the vapor pressure at the liquid surface is at the lower flammable limit. The corresponding upper limit temperature is given as TU. If a liquid is contained within a closed vessel and the vapors are allowed to come into equilibrium at temperatures above the upper limit temperature, the vapors in the vessel will be above the upper flammable limit, for example, as typically occurs in an automobile gas tank.
If the liquid is not enclosed fully, there will be a location above the surface of the liquid where the fuel/air mixture will be diluted below the upper flammable limit and will ignite if an ignition source is present.
Predicting Lower Flammable Limits of Mixtures of Flammable Gases (Le Chatelier’s Rule) Based on an empirical rule developed by Le Chatelier in the late nineteenth century, the lower flammable limit of mixtures of multiple flammable gases in air can be determined. A generalization of Le Chatelier’s rule was given by Coward et al. [11] n X Ci 1 LFL i i¼1
ð17:1Þ
where Ci is the volume percent of fuel gas, i, in the fuel/air mixture, and LFLi is the volume
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Fig. 17.4 Effect of pressure on the limits of flammability of natural gas in air at 28 C [1]
60 % of air = 100% – % natural gas
Natural gas (vol %)
50
40
30
Flammable mixtures
20
10
0 0
Fig. 17.5 Effect of temperature on limits of flammability of a combustible vapor in air at constant initial pressure [1]
100
200
300 400 500 Initial pressure (atm)
600
700
Upper limit
Saturated vapor-air mixtures
Combustible concentration
800
Autoignition
Flammable mixtures
Mist
B Lower limit
A
TL
TU
AIT Temperature
percent of fuel gas, i, at its lower flammable limit in air alone. If the indicated sum is greater than unity, the mixture is above the lower flammable limit. This relationship can be restated in terms of the lower flammable limit concentration of the fuel mixture, LFLm , as follows: LFLm ¼ X n i¼1
100 C f i =LFLi
ð17:2Þ
where C f i is the volume percent of fuel gas i in the fuel gas mixture. Example 1 A mixture of 50 % methane, 25 % carbon monoxide, and 25 % hydrogen is mixed with air. Calculate the lower flammmable limit of this fuel gas mixture. Solution Referring to Table 17.1, LFLs of methane, carbon monoxide, and hydrogen are
17
Flammability Limits of Premixed and Diffusion Flames
533
Table 17.1 Summary of limits of flammability, Lower Temperature Limits (TL), and Minimum Autoignition Temperatures (AIT) of individual gases and vapors in air at atmospheric pressure [1] Limits of flammability (vol %) Combustible LFLa UFLa Acetal 1.6 10 Acetaldehyde 4.0 60 Acetic acid 5.4b – Acetic anhydride 2.7c 10d Acetanilide 1.0e – Acetone 2.6 13 Acetophenone 1.1e – Acetylacetone 1.7e – Acetyl chloride 5.0e – Acetylene 2.5 100 Acrolein 2.8 31 Acrylonitrile 3.0 – Acetone2.2 12 cyanohydrin Adipic acid 1.6e – Aldol 2.0e – Allyl alcohol 2.5 18 Allyl amine 2.2 22 Allyl bromide 2.7e – Allyl chloride 2.9 – o-Aminodiphenyl 0.66 4.1 Ammonia 15.0 28 n-Amyl acetate 1.0b 7.1b n-Amyl alcohol 1.4b 10b tert-Amyl alcohol 1.4e – n-Amyl chloride 1.6i 8.6b j tert-Amyl chloride 1.5 – n-Amyl ether 0.7e – Amyl nitrite 1.0e – n-Amyl propionate 1.0e – Amylene 1.4 8.7 Aniline 1.2l 8.3l
TL ( C) 37 – 40 47 – – – – – – – 6 –
AIT ( C) 230 175 465 390 545 465 570 340 390 305 235 – –
– – 22 – – 32 – – 25 38 – – 12 – – – – –
420 250 – 375 295 485 450 – 360 300 435 260 345 170 210 380 275 615
Anthracene n-Amyl nitrate
0.65e – 1.1 –
– –
540 195
Benzene Benzyl benzoate Benzyl chloride Bicyclohexyl Biphenyl 2-Biphenylamine Bromobenzene
1.3b 0.7e 1.2e 0.65b 0.70k 0.8e 1.6e
– – – 74 110 – –
560 480 585 245 540 450 565
7.9b – – 5.1m – – –
Limits of flammability (vol %) Combustible LFLa Cumene 0.88b Cyanogen 6.6 Cycloheptane 1.1 Cyclohexane 1.3 Cyclohexanol 1.2e Cyclohexene 1.2b Cyclohexyl acetate 1.0e Cyclopropane 2.4 Cymene 0.85b Decaborane 0.2 Decalin 0.74b n-Decane 0.75f Deuterium 4.9 Diborane Diesel fuel (60 cetane) Diethyl amine Diethyl analine 1,4-Diethyl benzene Diethyl cyclohexene Diethyl ether 3,3-Diethyl pentane Diethyl ketone Diisobutyl carbinol Diisobutyl ketone 2-4,Diisocyanate Diisopropyl ether Dimethyl amine 2,2-Dimethyl butane 2,3-Dimethyl butane Dimethyl decalin Dimethyl dichlorosilane Dimethyl ether n,n-Dimethyl formamide 2,3-Dimethyl pentane 2,2-Dimethyl propane Dimethyl sulfide Dimethyl sulfoxide Dioxane Dipentene Diphenylamine
UFLa 6.5b – 6.7 7.8 – – – 10.4 6.5b – 4.9b 5.6g 75
TL ( C) – – – – – – – – – – 57 46 –
AIT ( C) 425 – – 245 300 – 335 500 435 – 250 210 –
0.8 – 1.8 0.8e 0.8b 0.75 1.9 0.7b 1.6 0.82b 0.79b – 1.4 2.8 1.2 1.2 0.69b 3.4
88 – 10 – – – 36 – – 6.1h 6.2b – 7.9 – 7.0 7.0 5.3k –
– – – 80 – – – – – – – 120 – – – – – –
– 225 – 630 430 240 160 290 450 – – – – 400 – – 235 –
3.4 1.8b
27 14b
– 57
350 435
1.1 1.4 2.2 – 2.0 0.75m 0.7e
6.8 7.5 20 – 22 6.1m –
– – – 84 – 45 –
335 450 205 – 265 237 635 (continued)
534
C. Beyler
Table 17.1 (continued) Limits of flammability (vol %) Combustible LFLa UFLa Butadiene (1,3) 2.0 12 n-Butane 1.8 8.4 1,3-Butandiol 1.9e – Butene-1 1.6 10 Butene-2 1.7 9.7 n-Butyl acetate 1.4i 8.0b n-Butyl alcohol 1.7b 12b sec-Butyl alcohol 1.7b 9.8b tert-Butyl alcohol 1.9b 9.0b tert-Butyl amine 1.7b 8.9b n-Butyl benzene 0.82b 5.8b sec-Butyl benzene 0.77b 5.8b tert-Butyl benzene 0.77b 5.8b n-Butyl bromide 2.5b – Butyl cellosolve 1.1m 11h n-Butyl chloride 1.8 10b n-Butyl formate 1.7 8.2 n-Butyl stearate 0.3e – Butyric acid 2.1e – α-Butryolactone 2.0m – Carbon disulfide 1.3 50 Carbon monoxide 12.5 74 Chlorobenzene 1.4 – m-Cresol 1.1m – Crotonaldehyde 2.1 16n Gasoline 100/130 1.3 7.1 115/145 1.2 7.1 Glycerine – – n-Heptane 1.05 6.7 n-Hexadecane 0.43e – n-Hexane 1.2 7.4 n-Hexyl alcohol 1.2b – n-Hexyl ether 0.6e – Hydrazine 4.7 100 Hydrogen 4.0 75 Hydrogen cyanide 5.6 40 Hydrogen sulfide 4.0 44 Isoamyl acetate 1.1 7.0b Isoamyl alcohol 1.4 9.0b Isobutane 1.8 8.4 Isobutyl alcohol 1.7b 11b Isobutyl benzene 0.82b 6.0h Isobutyl formate 2.0 8.9
TL ( C) – 72 – – – – – 21 11 – – – – – – – – – – – – – 21 – –
AIT ( C) 420 405 395 385 325 425 – 405 480 380 410 420 450 265 245 – – 355 450 – 90 – 640 – –
– – – 4 126 26 – – – – – – 25 – 81 – – –
440 470 370 215 205 225 – 185 – 400 – – 360 350 460 – 430 –
Limits of flammability (vol %) Combustible LFLa Diphenyl ether 0.8e Diphenyl methane 0.7e Divinyl ether 1.7 n-Dodecane 0.60e Ethane 3.0 Ethyl acetate 2.2 Ethyl alcohol 3.3 Ethyl amine 3.5 Ethyl benzene 1.0b Ethyl chloride 3.8 Ethyl cyclobutane 1.2 Ethyl cyclohexane 2.0o Ethyl cyclopentane 1.1 Ethyl formate 2.8 Ethyl lactate 1.5 Ethyl mercaptan 2.8 Ethyl nitrate 4.0 Ethyl nitrite 3.0 Ethyl propionate 1.8 Ethyl propyl ether 1.7 Ethylene 2.7 Ethyleneimine 3.6 Ethylene glycol 3.5e Ethylene oxide 3.6 Furfural alcohol 1.8p 2-Monoisopropyl biphenyl 0.53h Monomethylhydrazine 4 Naphthalene 0.88s Nicotine 0.75b Nitroethane 3.4 Nitromethane 7.3 1-Nitropropane 2.2 2-Nitropropane 2.5 n-Nonane 0.85u n-Octane 0.95 Paraldehyde 1.3 Pentaborane 0.42 n-Pentane 1.4 Pentamethylene glycol – Phthalic anhydride 1.2l 3-Picoline 1.4e Pinane 0.74w Propadiene 2.16
UFLa – – 27 – 12.4 11 19n – 6.7b – 7.7 6.6o 6.7 16 – 18 – 50 11 9 36 46 – 100 16q
TL ( C) – – – 74 130 – – – – – – – – – – – – – – – – – – – 72
3.2r – 5.9t – – – – – – – – – 7.8 – 9.2v – 7.2w –
141 – – – 30 33 34 27 31 13 – – 48 – 140 – – –
AIT ( C) 620 485 – 205 515 – 365 385 430 – 210 260 260 455 400 300 – – 440 – 490 320 400 – 390 435 – 526 – – – – – 205 220 – – 260 335 570 500 – – (continued)
17
Flammability Limits of Premixed and Diffusion Flames
535
Table 17.1 (continued) Limits of flammability (vol %) Combustible LFLa UFLa Isobutylene 1.8 9.6 Isopentane 1.4 – Isophorone 0.84 – Isopropylacetate 1.7e – Isopropyl alcohol 2.2 – Isopropyl biphenyl 0.6e – Jet fuel JP-4 1.3 8 JP-6 – – Kerosene – – Methane 5.0 15.0 Methyl acetate 3.2 16 Methyl acetylene 1.7 – Methyl alcohol 6.7 36n e Methyl amine 4.2 – Methyl bromide 10 15 3-Methyl butene-1 1.5 9.1 Methyl butyl ketone S51.2 8.0b Methyl cellosolve 2.5x 20l Methyl cellosolve acetate 1.7m – Methyl ethyl ether 2.2e – Methyl chloride 7e – Methyl cyclohexane 1.1 6.7 Methyl cyclopentadiene 1.3b 7.6b Methyl ethyl ketone 1.9 10 Methyl ethyl ketone peroxide – – Methyl formate 5.0 23 Methyl 1.0e – cyclohexanol Methyl isobutyl carbinol 1.3e – Methyl isopropenyl ketone 1.8i 9.0e Methyl lactate 2.2b – α-Methyl 0.8e – naphthalene 2,Methyl pentane 1.2e – Methyl propionate 2.4 13 Methyl propyl 1.6 8.2 ketone Methyl styrene 1.0e –
TL ( C) – – – – – –
AIT ( C) 465 – 460 – – 440
– – – 187 – – – – – – – –
240 230 210 540 – – 385 430 – – – 380
46 – – –
– – – 250
49 –
445 –
40 – –
390 465 295
40
–
– – –
Limits of flammability (vol %) Combustible LFLa Propane 2.1 1,2-Propandiol 2.5e b-Propiolactone 2.9d Propionaldehyde 2.9 n-Propyl acetate 1.8 n-Propyl alcohol 2.2n Propyl amine 2.0 Propyl chloride 2.4e n-Propyl nitrate 1.8x Propylene 2.4 Propylene dichloride 3.1e Propylene glycol 2.6y Propylene oxide 2.8 Pyridine 1.8n Propargyl alcohol 2.4i Quinoline 1.0e Styrene 1.1z Sulfur 2.0aa p-Terphenyl 0.96e n-Tetradecane 0.5e Tetrahydrofurane 2.0 Tetralin 0.84b 2,2,3,3-Tetramethyl pentane 0.8 Tetramethylene glycol – Toluene 1.2b Trichloroethane – Trichloroethylene 12bb Triethyl amine 1.2 Triethylene glycol 0.9l 2,2,3-Trimethyl butane 1.0
UFLa 9.5 – – 17 8 14b –– – 100x 11 – – 37 12a – – – – – – – 5.0m
TL ( C) 102 – – – – – – – 21 – – – – – – – – 247 – – – 71
AIT ( C) 450 410 – – – 440 – – 175 460 – – – – – – – – 535 200 – 385
– – 7.1b – 40a 8.0 9.2bb –
– – – – 30 – – –
430 390 480 500 420 – – 420
2.0
12
–
–
– – 530
Trimethyl amine 2,2,4-Trimethyl pentane Trimethylene glycol Trioxane Turpentine
0.95 1.7e 3.2e 0.7b
– – – –
– – – –
415 400 – –
– – –
– – –
Unsymmetrical dimethylhydrazine Vinyl acetate
2.0 2.6
95 –
– –
– –
49
495
Vinyl chloride
3.6
33
–
– (continued)
536
C. Beyler
Table 17.1 (continued) Limits of flammability (vol %) Combustible LFLa UFLa Methyl vinyl ether 2.6 39 Methylene chloride – – Monoisopropyl bicyclohexyl 0.52 4.1r
Limits of flammability (vol %) TL ( C) AIT ( C) Combustible LFLa – – m-Xylene 1.1b – 615 o-Xylene 1.1b p-Xylene 1.1b 124 230
UFLa 6.4b 6.4b 6.6b
TL ( C) – – –
AIT ( C) 530 465 530
T ¼ 70 C T ¼ 100 C c T ¼ 75 C d T ¼ 75 C e Calculated f T ¼ 53 C g T ¼ 86 C h T ¼ 175 C i T ¼ 50 C j T ¼ 85 C k T ¼ 110 C l T ¼ 140 C m T ¼ 150 C n T ¼ 60 C o T ¼ 130 C p T ¼ 72 C q T ¼ 117 C r T ¼ 200 C s T ¼ 78 C t T ¼ 122 C u T ¼ 43 C v T ¼ 195 C w T ¼ 160 C x T ¼ 125 C y T ¼ 96 C z T ¼ 29 C aa T ¼ 247 C bb T ¼ 30 C a
b
5.0 %, 12.5 %, and 4.0 % by volume, respectively. Using Equation 17.2 we find LFLm ¼
100 ¼ 5:48% 50=5 þ 25=12:5 þ 25=4
The composition of the lower flammable limit fuel/air mixture is 2.74 % methane, 1.37 % carbon monoxide, 1.37 % hydrogen, and 94.5 % air.
Critical Adiabatic Flame Temperature at the Lower Flammable Limit As early as 1911, Burgess and Wheeler [12] noted the constancy of the potential heat release
rate per unit volume of normal alkane/air lower flammable mixtures at room temperature. Since the heat capacity of the products of complete combustion are nearly the same for all hydrocarbons, their observation also implies that the adiabatic flame temperature (AFT) at the lower flammable limit is a constant. Examination of a wide range of C,H,O-containing fuels indicates that the adiabatic flame temperature at the LFL is approximately 1600 K (150 K) for most C,H,O-containing fuels, with the following notable exceptions: hydrogen, 980 K; carbon monoxide, 1300 K; and acetylene, 1280 K. This result indicates that the adiabatic flame temperature at the lower flammable limit is an indication
17
Flammability Limits of Premixed and Diffusion Flames
of the reactivity of the fuel. The lower the adiabatic flame temperature, the more reactive the fuel. The utility of the concept of a critical adiabatic flame temperature at the lower flammable limit goes beyond that outlined above. It has been demonstrated that the adiabatic flame temperature at the lower flammable limit is relatively insensitive (100 K) to the diluent used and to the initial temperature of the mixture [13–15]. The adiabatic flame temperature at the limit is insensitive to initial temperature only so long as significant preflame combustion reactions do not occur. As such, for a mixture near or above its autoignition temperature (AIT) for a significant length of time, the adiabatic flame temperature at the limit is not expected to be constant. Weinberg [15] has shown that a mixture of 1 % methane (LFL ¼ 5 % at 293 K) in air can burn if it is preheated to 1270 K, even though the flame only increases that temperature by about 250 K, in accordance with the expected adiabatic flame temperature. This result was achieved by mixing the methane and air just before the flame so that preflame reactions were not allowed to proceed significantly. Due to the constancy of the adiabatic flame temperature at the lower limit, the concept can be
1800
utilized to predict the effect of variable mixture temperature and diluents on the flammable limits of a mixture. Coward and Jones [2] have examined variable oxygen/diluent ratios, using nitrogen, carbon dioxide, water, argon, and helium as diluents. Their work shows that the limit temperature is insensitive to the oxygen/diluent ratio. Figure 17.6, adapted from Macek [16], illustrates the change in adiabatic flame temperature at the lower flammable limit as additional nitrogen is added to decrease the oxygen/nitrogen ratio. The figure shows an increase in the adiabatic flame temperature at the lower flammable limit from 1550 K to over 1700 K as we move from normal air to the stoichiometric limit. Beyond the stoichiometric limit, no fuel-lean mixture can burn. The region beyond the stoichiometric limit can be best understood in the context of flammability diagrams and upper flammable limits. We will examine these later in the chapter. The insensitivity of the limit temperature to the chemical structure of C,H,O-containing fuels contributes significantly to the utility of the concept of a critical adiabatic flame temperature at the lower flammable limit. No systematic evaluation of the limit temperature concept for fuels containing sulfur, nitrogen, or halogens has been undertaken. Existing data indicate that
0.19
0.18
0.17
0.16
0.14
0.13
0.12 0.11
Mol fraction O2 in mixture 1700 Adiabatic flame temperature (K)
Fig. 17.6 Computed adiabatic flame temperature along the lower branch of the flammability limits of propane (Adapted from Macek) [16]. SL and NP are defined in Fig. 17.9
537
10
SL
1600 1500 LL 1400
NP
1300 1200 1100 10
20
30
Added nitrogen (vol %)
40
538
C. Beyler
halogen-containing fuels have limit temperatures several hundred degrees higher than C,H,O fuels. Since halogens are combustion inhibitors, this conclusion is consistent with the idea that the adiabatic flame temperature at the lower flammable limit is indicative of the reactivity of the fuel. Thus, possible exceptions to the generalization that the adiabatic flame temperature at the lower flammable limit is approximately 1600 K may be identifiable by considering the reactivity of the fuel gas. Egerton and Powling [17] have shown that the limit temperatures at the upper flammable limit for hydrogen and carbon monoxide are equal to their limit temperatures at the lower flammable limit. Stull [18] has reported the same result for methane. However, it is not generally possible to calculate the adiabatic flame temperature for other fuels, since the products of combustion under fuel-rich conditions include a mixture of products of combustion and pyrolysis, which cannot be predicted by assuming chemical equilibrium is achieved or by detailed chemical kinetics calculations. Equilibrium calculations indicate that the only carbon-containing species that should be produced are CO, CO2, CH4, and solid carbon. This conclusion is not generally a good approximation under fuel-rich conditions. Example 2 The lower flammable limit of propane at 20 C is 2.1 % by volume. Find the lower flammable limit at 200 C. Solution For adiabatic combustion, all the heat released is absorbed by the products of combustion: ð T f , LFL LFL nC p dT ΔH c ¼ 100 T0
ð17:3Þ
where ΔHc ¼ Heat of combustion of the fuel LFL/100 ¼ Mole fraction of fuel n ¼ Number of moles of products of combustion per mol of fuel/air mixture Cp ¼ Heat capacity of the products of combustion T0 ¼ Initial temperature of the fuel/air mixture Tf, LFL ¼ Adiabatic flame temperature of a lower flammable limit mixture
This equation uses concepts developed in Chap. 5. For the present purposes, it is suitable to use an average value of the heat capacity. This adjustment reduces Equation 17.3 to LFL ð17:4Þ ΔH c ¼ nC p T f , LFL T 0 100 We know that Tf ,LFL ¼ 1600 K, and for T0 ¼ 20 C, we also know that LFL ¼ 2.1 %. Rearranging Equation 17.4 yields T f , LFL T 0 ΔH c ¼ LFL=100 nC p 1600 K 293 K ¼ 2:1=100 ¼ 6:22 104 K Both the heat of combustion and the heat capacity are weak functions of temperature, and these effects will be ignored. As such we can use the above expression to predict the lower flammable limit for an initial temperature of 200 C. T f , LFL T 0 1600 K 473 K ¼ LFL=100 LFL=100 ¼ 6:22 104 K LFL ¼ 1:8 percent
Flammability Diagrams Whereas the flammable limits of a fuel in air can be characterized by the lower and upper flammable limits, it is necessary to represent flammable limits of more general fuel/oxidant/ inert mixtures by using flammability diagrams. Examples of flammability diagrams for methane/oxygen/nitrogen mixtures are shown in Figs. 17.7 and 17.8. Based on an extensive series of tests with a range of mixture compositions, a flammability diagram can be constructed indicating the regions of mixture compositions within the flammable limits. Two types of flammability diagrams are often used. The first type uses three axes in which each of the three constituent gases is explicitly represented, and the second diagram utilizes only two axes in which the third gas concentration is determined by the difference between the sum
17
Flammability Limits of Premixed and Diffusion Flames
539
Fig. 17.7 Three-axis flammability diagram for the system methane/ oxygen/nitrogen at atmospheric pressure and 26 C [1]
C 100
0
90
10
80
20
50
–O2
tha
40
50
60
–CH4
30
) l%
MI +N2
+O2
(vo
Me
40
+CH4 –N2
en
(vo
l%
60
rog
ne
30 Nit
)
70
70 Flammable mixtures
20
Limit line
Min O2
80
Critical C/N
10 0 O 100
90
80
70
60
50
90 40
30
20
10
0
100 H
Oxygen (vol %)
Fig. 17.8 Two-axis flammability diagram for the system methane/ oxygen/nitrogen at atmospheric pressure and 26 C [1]
C 100 %O2 = 100% – % CH4 – %N2
Methane (vol %)
80
60
+CH4 –N2 +O2
–CH4
40
20
MI +N2
Air line
Flammable mixtures Limit line Min O2
Critical C/N
N 0
20
40
60
A
80
100
Nitrogen (vol %)
of the other two gases and 100 %. Both types give the same information. Shown in Figs. 17.7 and 17.8 are the air and limit lines. Anywhere along the air line the ratio of oxygen to nitrogen is the same as in air. The limit line represents a range of mixtures with a fixed oxygen-to-nitrogen ratio which is tangent to the flammable region. Any oxygen/nitrogen
mixture with an oxygen-to-nitrogen ratio less than that of the limit line will not support flame propagation when mixed with any amount of methane. This condition is known as the limiting oxygen concentration (LOC). The LOC is an important concept in inerting. If the oxygen concentration can be maintained below the LOC, then premixed burning can be
540
C. Beyler
prevented. The LOC is a function of the temperature, pressure, fuel, and inert gas. Table 17.2 shows the LOC [19–23] of a wide range of fuels with nitrogen and carbon dioxide as the inert diluents. The tabulated values apply to diluted air/fuel mixtures at normal temperature
and pressure. Like flammable limits, the dynamics of the LOC can generally be understood using the AFT concepts. As can be seen in Table 17.2 with nitrogen diluent, the LOC is generally in the 10–12 % range. Fuels like carbon monoxide and hydrogen
Table 17.2 Limiting oxygen concentrations at normal temperature and pressure
Gas or vapor Ethane Propane n-Butane Isobutane n-Pentane Isopentane n-Hexane n-Heptane Ethylene Propylene 1-Butene Isobutylene Butadiene 3-Methyl-1butene Benzene Gasoline (73/100) (100/130) (115/145) Kerosene JP-1 fuel JP-3 fuel JP-4 fuel Natural gas (Pittsburgh) n-Butyl chloride Methylene chloride Ethylene dichloride 1,1,1Trichloroethane Trichloroethylene Acetone n-Butanol Carbon disulfide
Limiting oxidant concentration N2/air (volume % O2 above which deflagration can take place) 11 11.5 12 12 12 12 12 11.5 10 11.5 11.5 12 10.5 11.5
Limiting oxidant concentration CO2/air (volume % O2 above which deflagration can take place) 13.5 14.5 14.5 15 14.5 14.5 14.5 14.5 11.5 14 14 15 13 14
Reference Coward and Jones [19] Coward and Jones [19] Coward and Jones [19] Coward and Jones [19] Coward and Jones [19] Jones et al. [20] Coward and Jones [19] Jones et al. [20] Coward and Jones [19] Coward and Jones [19] Coward and Jones [19] Jones et al. [20] Coward and Jones [19] Zabetakis [22]
11.4
14
Coward and Jones [19]
12 12 12 10 (150 C) 10.5 (150 C) 12 11.5
15 15 14.5 13 (150 C) 14 (150 C) 14.5 14.5
Jones et al. [20] Jones et al. [20] Jones et al. [20] Zabetakis and Rosen [23] Jones et al. [20] Jones et al. [20] Jones et al. [20]
12 14 12 (100 C) 19 (30 C) 17 (100 C) 13 11.5 (100 C) 14
14.5 – – – – – – –
Coward and Jones [19] Kuchta et al. [21] Kuchta et al. [21] Kuchta et al. [21] Kuchta et al. [21] Kuchta et al. [21] Kuchta et al. [21] Kuchta et al. [21]
9 (100 C) 11.5 – 5
– 14 16.5 (150 C) 7.5
Kuchta et al. [21] Zabetakis [22] Zabetakis [22] Zabetakis [22] (continued)
17
Flammability Limits of Premixed and Diffusion Flames
541
Table 17.2 (continued) Limiting oxidant concentration N2/air (volume % O2 above which deflagration can take place) Gas or vapor Carbon monoxide 5.5 Ethanol 10.5 2-Ethyl butanol 9.5 (150 C) Ethyl ether 10.5 Hydrogen 5 Hydrogen sulfide 7.5 Isobutyl formate 12.5 Methanol 10 Methyl acetate 11 Methyl ether 10.5 Methyl formate 10 Methyl ethyl 11 ketone
Limiting oxidant concentration CO2/air (volume % O2 above which deflagration can take place) 5.5 13 – 13 5.2 11.5 15 12 13.5 13 12.5 13.5
Reference Zabetakis [22] Zabetakis [22] Zabetakis [22] Zabetakis [22] Zabetakis [22] Zabetakis [22] Zabetakis [22] Zabetakis [22] Zabetakis [22] Zabetakis [22] Zabetakis [22] Zabetakis [22]
Data were determined by laboratory experiment conducted at atmospheric temperature and pressure. Vapor-air-inert gas samples were placed in explosion tubes and ignited by electric spark or pilot flame Source: Adapted from Table C-1, NFPA 69, Standard on Explosion Prevention Systems
8 % air = 100% – % n-hexane – % inert 7
6 n-Hexane vapor (vol %)
have lower LOCs, and chlorinated fuels have higher values. These trends are expected based on AFT concepts at the LFL. For carbon dioxide as a diluent, the LOCs are generally 2–3 % higher than for nitrogen diluent. Again this is expected based on AFT concepts due to the higher molar heat capacity of carbon dioxide. Figure 17.9 is yet another representation of the flammable limits of fuel/oxidant/inert mixtures. The dilution of a fuel/air mixture is given by the percent of inert gas in excess of the nitrogen present in air. Figure 17.9 includes only mixtures that lie to the right of the air line, and as such is a magnification of a portion of the region included in Figs. 17.7 and 17.8. Also shown in Fig. 17.9 are several lines and points of specific interest. The highest concentration of nitrogen that will allow propagation of a flame is known as the nitrogen point (NP). Of course, this concept can be generalized to any inert (IP). If the concentration of the inert is greater than that at the inert point, no mixture of fuel and oxidant will propagate a flame remote from the ignition source.
5
4 N2
3 Cst CO2
2
NP
SL
1
0 0
10
20
30
40
50
Added inert (vol %)
Fig. 17.9 Limits of flammability of various n-hexane/ inert gas/air mixtures at 25 C and atmospheric pressure [1]
542
C. Beyler 16 % air = 100% – % methane – % inert 14
Methane (vol %)
12
CO2
10
8
H2O He
Cst Flammable mixtures
6
N2 4
2
0 0
10
20
30
40
50
Added inert (vol %)
Fig. 17.10 Limits of flammability of various methane/ inert gas/air mixtures at 25 C and atmospheric pressure [1]
As shown in Fig. 17.9, the stoichiometric line passes through the flammable region. The point at which the stoichiometric line intersects the boundary of the flammable region is known as the stoichiometric limit (SL). The SL is the most dilute stoichiometric mixture that will propagate a flame remote from the ignition source. In the case of methane, the peak of the flammable region occurs near the stoichiometric limit (Fig. 17.10). For longer chain alkanes, the peak shifts to the rich side of the stoichiometric line (Fig. 17.9). For C5 and higher hydrocarbons, the peak of the flammable region is bisected by the stoichiometric line defined by combustion to CO rather than to products of complete combustion. This shift has been attributed to incomplete combustion [16] and to preferential diffusion of reactants [24]. A similar shift of the maximum burning velocity to the rich side of stoichiometry is also observed. In this case, preferential diffusion of reactants has been shown to be the responsible factor.
Flammability diagrams are useful not only in determining the flammability of a given mixture, but also in developing strategies for avoiding flammable mixtures while diluting fuel-rich mixtures. In order to make use of the diagrams in this fashion, we must examine the change in position on the diagram when fuel, oxygen, or inert gas is added to the mixture. Consider a mixture given by point MI in the three-axis diagram (Fig. 17.7). The arrows indicate the change in the mixture composition with the addition or removal of each gas species. In the three-axis diagram, moving toward the vertex corresponding to 100 % of any one of the gases corresponds to the addition of that gas, since adding an infinite amount of a single gas will reduce the concentrations of the other gases to zero. Adding air corresponds to moving toward the point on the air line at which there is no fuel. Clearly, following these examples, the effect of adding any gas or gas mixture can be plotted in the three-axis diagram. In the two-axis diagram in Fig. 17.8, moving toward the vertex with 0 % inert, 0 % fuel corresponds to the addition of oxygen. In Fig. 17.9 moving toward the 0 % inert, 0 % fuel vertex corresponds to adding air. Figure 17.10 shows the effect of various inert diluents on the flammable region. As indicated by the critical adiabatic flame temperature concept, the lower flammable limit is increased in proportion to the heat capacity of the diluent (see Chap. 5). Example 3 A methane leak fills a 200 m3 room until the methane concentration is 30 % by volume. Calculate how much nitrogen must be added to the room before air can be allowed in the space. Solution The initial mixture in the room is given by the point B in Fig. 17.11. Adding nitrogen moves along the line toward pure nitrogen (the N point). Drawing the line from the air point, A, tangent to the flammable region defines the mixture C: the mixture with the least nitrogen added that, on mixing with air, will not form a flammable mixture. Referring to Fig. 17.11 we see that
17
Flammability Limits of Premixed and Diffusion Flames
543
Fig. 17.11 Graphic solution of Example 3 (Adapted from Zubetakis) [1]
C 0
100
10
90
20
80
–N2
60
+CH4
30 –O2
40
M1
50
50
+O2 +N2 –CH4
40
60
Air
30
70
B
Flammable mixtures
20
) l% (vo en rog Nit
Me tha ne (vo l% )
70
80 D
10 0 O 100
C
90
80
70
60
50
40
30
A
L
90 0
100 N
Oxygen (vol %)
point C corresponds to a methane concentration of 13 %. In order to reduce the methane concentration from 30 % to 13 %, an as yet unknown amount of nitrogen must be added. If we could remove only the initial mixture and replace it with nitrogen, the amount of nitrogen would simply be 30 13 200 m3 ¼ 113 m3 30 However, there is generally no way to prevent mixing of the initial mixture to be exhausted and the nitrogen being introduced to replace it. As such, inerting nitrogen is also lost. We can model this occurrence by assuming that the room is well mixed during nitrogen injection so that the concentrations are uniform everywhere. Under these conditions the methane concentration, C, is given by V N C ¼ C0 exp V where C0 ¼ Initial methane concentration VN ¼ Volume of nitrogen added V ¼ Volume of the room
Rearranging this equation we find C 13 3 V N ¼ V ln ¼ 200 m ln C0 30 ¼ 167 m3 Of course, the flow of gases out of the room contains methane and may burn on mixing with air. Mixing air and the initial gases in the room results in mixtures along the line AB (see Fig. 17.11), some of which are clearly flammable. As such, ignition sources must be excluded near the room exhaust, or the exhaust also needs to be inerted. Example 4 A 1 kg/s flow of methane is being dumped into the atmosphere. How much nitrogen must be mixed with methane to avoid a flammable mixture in the open? Solution In order to make the methane nonflammable, it needs to be diluted with enough nitrogen so that on further addition of air the flammable region is missed. Such a mixture of methane and nitrogen is given by extrapolating the line AC back to zero oxygen; that is, point D
544
C. Beyler
on Fig. 17.11, where the mixture is 82 % nitrogen, 18 % methane. The ratio of the flow rates of nitrogen to methane must equal the ratio of the concentrations of nitrogen and methane. Since concentrations expressed as volume percent are directly related to mole fractions, the flow rates of nitrogen and methane must be expressed as molar flow rates, n˙, CN2 n_ N2 ¼ n_ CH4 CCH4 The molar flow rate of methane is given by n_ CH4 ¼
m_ CH4 MW CH4
˙ is the where MW is the molecular weight and m mass flow rate. CN2 m_ CH4 n_ N2 ¼ MW CH4 CCH4 100 g=s 82% ¼ 16 g=mol 18% ¼ 285 mol=s m_ N2
¼ n_ N2 MW N2 ¼ ð285 mol=sÞð28 g=molÞ ¼ 7970 g=s or 7:97 kg=s
Ignition Energies and Quenching Diameters The energy required to ignite flammable mixtures is generally quite low, on the order of a few tenths of a millijoule (mJ) for nearstoichiometric mixtures in air and as low as a few thousandths of a millijoule in oxygen. Here again, preferential diffusion causes the minimum to occur for rich mixtures for fuels with molecular weights greater than that of air [24]. As the flammable limits are approached, the ignition energy increases sharply. Several methods exist for preventing the initiation of an explosion. These include avoiding flammable mixtures, excluding ignition sources whose energy is greater than the minimum ignition energy, and enclosing any ignition sources in an enclosure that will not allow the propagation
of the flame to the outside. We have already discussed the first of these. Some low-power electrical equipment can be designed such that the worst fault condition cannot produce the minimum ignition energy for a specified gas. Such equipment is termed “intrinsically safe” and may be used where there is a risk of a flammable atmosphere being formed. Where this method is not feasible, the electrical equipment may be housed in an “explosionproof” enclosure that will not allow propagation of the flame out of the enclosure, which is accomplished by making the size of the openings small enough that sufficient heat is lost by the flame as it passes through the opening that it is quenched. The quenching distance is most often determined by placing a pair of flanged electrodes in a gas mixture and attempting to ignite the gases. The flanges are parallel plates, and if the mixture can be ignited in the presence of the plates, the separation of the plates is greater than the quenching distance. The quenching distance with parallel plates, d||, is 65 % of the quenching diameter in circular tubes. Figure 17.12 [25] shows the relation of the quenching distance to the minimum ignition energy for a number of hydrocarbon/air mixtures. The relation can be expressed as Emin ¼ 0.06d||2, where Emin is the minimum ignition energy in air given in mJ and d|| is the quenching distance in air given in mm. Because the hot quenched flame gases in an enclosure will expand through the opening, they may autoignite outside the enclosure. It has been found that the minimum experimental safe gap (MESG) for most hydrocarbons is approximately half the quenching distance [25].
Dusts and Mists The lower flammable limit of dusts and mists would be expected to be higher than their gaseous counterparts due to the need to volatilize the dust or mist. For very small particles with high surface-area-to-volume ratios, the lower flammable limit is independent of particle diameter, and the limit concentrations are approximately the same as the analogous gaseous fuel for fuels that volatilize completely. Hertzberg et al. [26] have
17
Flammability Limits of Premixed and Diffusion Flames
20 10 8 6 4
Minimum ignition energy (mJ)
2 1 0.8 0.6 0.4 0.2 0.1 0.08 0.06 0.04 0.02 0.01 0.008 0.006 0.004 0.002 0.001 0.1
0.2
0.4
1.0
2.0
4.0
10.0
20.0
Quenching distance (mm)
Fig. 17.12 The relation between flat-plate quenching and spark minimum ignition energies for a number of hydrocarbon-air mixtures [25]
shown that bituminous coal dusts with particle diameters of 50 mm or less and polyethylene dusts with particle diameters of 100 μm or less have lower flammable limits in air that are independent of particle diameter. Figure 17.13 shows the measured lower flammable limit concentration for Pittsburgh bituminous coal as a function of average particle diameter and oxygen concentration. Notice that the lower flammable limit in the small-particle limit is a function of the oxygen concentration, unlike gaseous fuels. Also note that the lower flammable limit concentration is much higher than the 48 g/m3 typical of gaseous hydrocarbons. These effects are due to the fact that not all the coal dust is volatilized. The fraction of dust that is volatilized is a function of the particle diameter and the oxygen concentration. As the oxygen concentration affects the maximum flame temperature and, hence, the heat flux
545
to the particle, both the ability of heat to penetrate the particle and the rate of heating are affected. It is well known that the fraction of the material volatilized increases with the rate of heating. It is not expected that the lower flammable limit can be reduced below 50 g/m3, even at 100 % oxygen. As the particle size increases, it would be expected that the lower flammable limit would also increase due to the difficulty of getting the fuel into the gas phase where combustion will take place. This result does in fact occur, but depending on the geometry of the test, the apparent lower flammable limit of mists can actually decrease with increasing particle diameter due to the effects of gravity [27]. If the ignition source is at the bottom of the container and the aerosol is not kept well mixed, the particles can begin to settle out, causing the local concentration in the lower portions of the apparatus to be higher. This laboratory effect can also be expected to operate under actual conditions, depending on the degree of mixing of the aerosol. Although it is in principle possible for flame propagation to occur as a result of heterogeneous combustion of particles, this appears not to be an important mechanism for organic materials. Lower flammable limits of anthracite coal dusts with only a 20 % volatile yield can be explained solely on the basis of gas-phase combustion [28]. On the other hand, flame propagation by heterogeneous combustion is important for metal and graphite dusts.
Diffusion Flame Limits The limits of flammability for diffusion flames were first examined by Simmons and Wolfhard [29]. In their experiments, they determined the minimum level of dilution of the oxidant stream necessary to prevent the stabilization of a diffusion flame for a variety of gas and liquid fuels. The oxygen mole fraction, XO2 , of the oxidant stream at the flammability limit is known as the limiting oxygen index (LOI), or simply the oxygen index (OI). Simmons and Wolfhard’s results are included in Table 17.3. They observed that the oxygen index of their diffusion flames
546
C. Beyler
Fig. 17.13 Lean flammability limit data for Pittsburgh bituminous coal as a function of particle size for three oxygen concentrations [26]
Pittsburg bituminous
Lean flammable limit (g/m3)
700 600
8-Liter chamber, chemical match ignition
500
Key 15.5% O2
400
21% O2 X
300
50% O2 X
200 100
X
X
X
X
X
0 1
2
5
10
20
50
100
200
500
Mean diameter, Ds (µm)
Table 17.3 Thermodynamic equilibrium properties at extinction (Adapted from Macek [16] and Strehlow [25]) Fuel CH4 C2H2 C2H4 C2H6 C3H8 n-C4H10 n-C5H12 n-C6H14 n-C7H16 n-C8H18 n-C10H22 CH3COCH3 CH3OH C2H5OH n-C3H7OH n-C4H9OH n-C5H11OH n-C6H13OH n-C8H17OH C6H6 C6H12 H2 CO a
LFL (vol %) 5.0 2.7 2.7 3.0 2.1 1.8 1.4 1.2 1.05 0.90 2.6 6.7 3.3 2.2 1.7 1.4 1.2
T(LFL) (K) 1480
X(SL)a 0.123
T(SL) (K) 1720
X(NP)a 0.117
T(NP) (K) 1610
1530 1540 1640 1590 1610 1620 1650
0.114 0.125 0.134 0.135 0.135 0.134 0.134
1620 1730 1830 1810 1800 1770 1770
0.111 0.114 0.121 0.115 0.117 0.118 0.118
1540 1470 1490 1410 1420 1430 1440
1550 1490 1490 1510 1550 1490
0.112 0.118
1690 1700
0.085 0.106
1430 1430
1.3 1.2 4.0 12.5
Expressed as mole fraction of oxygen
OIa 0.139 0.085 0.105 0.118 0.127 – 0.1325 0.1335 – 0.134 0.1345 0.1285 0.111 0.126 0.128 0.129 0.130 0.1315 0.1315 0.133 0.134 0.054 0.076
X(OI)a 0.130
0.114 0.124 – 0.130 0.132 – 0.133 0.133 0.103 0.121 0.124 0.126 0.128 0.130 0.130
T(OI) (K) 1780 1540 1610 1630 1720 – 1760 1770 – 1780 1780 1730 1530 1670 1700 1710 1730 1740 1750 1810 1770 1080 1450
Flammability Limits of Premixed and Diffusion Flames
Fig. 17.14 Computed adiabatic flame temperatures at flammability limits for n-alkanes (Adapted from Macek) [16]
547 X
X
1800
X X
1750 Adiabatic flame temperature (K)
17
X
X
X 1700 1650 X
1600
X 1550 1500
Stoichiometric limit (premixed) Oxygen index (diffusion) Lean limit (premixed)
1450 0
1
2
3
4
5
6
7
8
9
10
C Atoms in alkane
equaled the ratio, XO2 =ðXO2 þ Xdiluent Þ, found in a premixed stoichiometric-limit mixture involving the same fuel. This result implies that the adiabatic flame temperature for the limit diffusion flame, calculated on the basis of stoichiometric combustion of the fuel and oxidant streams, is equal to the adiabatic flame temperature at the stoichiometric limit of a premixed system involving the same fuel, oxidant, and diluent. Figure 17.14 graphically illustrates the relationship of the adiabatic flame temperatures at the lean, premixed limit in air, at the stoichiometric limit (premixed), and at the oxygen index (premixed). As the figure shows, the adiabatic flame temperature at the stoichiometric limit and the oxygen index are essentially equal, and the adiabatic flame temperature at the lower flammable limit in air is approximately 150 K less. Ishizuka and Tsuji [30] verified Simmons and Wolfhard’s results for methane and hydrogen, and showed that the adiabatic flame temperature at the limit is the same whether dilution is of the fuel or oxidizer stream. The information in Fig. 17.14 forms the basis of a method for the evaluation of diffusion flame limits for fuel mixtures. In essence, the ability of a fuel and oxidant pair to react in a diffusion
flame is evaluated by examining the flammability of a premixed stoichiometric mixture of the fuel and oxidant. To do this, we assume that Le Chatelier’s rule holds at the stoichiometric limit; that is, X Ci n 1 ð17:5Þ i¼1 SLi and that the adiabatic flame temperature at the stoichiometric limit for each fuel is a constant, leading to the expression X
n i¼1
ðCi =100ÞΔH c, i 1 ð T f , SL, i n p C p dT
ð17:6Þ
T0
where Ci ¼ Volume percent of fuel species, i, when the fuel stream is mixed stoichiometrically with the oxidant stream Tf,SL,I ¼ Adiabatic flame temperature of the stoichiometric limit mixture for fuel species i ¼ 1700 K for most hydrocarbons ¼ 1450 K for carbon monoxide ¼ 1080 K for hydrogen T0 ¼ Temperature of the stoichiometric mixture prior to reaction
548
ΔHc,I ¼ Heat of combustion of fuel species ¼620 kJ/mol for hydrocarbons (per carbon, assuming H/C ¼ 2) ¼283 kJ/mol for carbon monoxide ¼242 kJ/mol for hydrogen np ¼ Number of moles of products of combustion per mole of reactants (stoichiometric mixture of the fuel and oxidant streams) Cp ¼ Heat capacity of the products of combustion This approach has been successfully used to predict the flammability of the hot gas layer formed in enclosure fires [31]. Although the hot gas layer formed in enclosure fires can become flammable, under some conditions the oxygen concentration in the hot layer can cause extinction of flames fully immersed in the hot layer. Based on the analogies between premixed and diffusion flames, one would expect the oxygen concentration in the layer at extinction to be approximately equal to the premixed LOC. In fact, comparing the nitrogen diluent in Table 17.2 with Table 17.3, one can see a very close correspondence between the LOC and the LOI. Morehart, Zukoski, and Kubota [32] examined the oxygen concentration at extinction of flames by dilution of air with combustion products. They found that flames were extinguished at oxygen concentrations of 12.4–14.3 %, with the lower value occurring for a 50-cm-diameter pool burner and the higher value occurring for a 9 cm pool burner. These results are consistent with diesel pan fire tests (0.62 m and 0.84 m diameters) conducted by Peatross and Beyler [33] in which oxygen concentrations below 14 % could not be achieved during pool burning in a compartment. It is also consistent with the results of Back et al. [34], who measured oxygen concentrations at extinction in water mist extinguishment tests in obstructed machinery space fires. They found an average oxygen concentration of 14.5 % for heptane spray fires and 13.5 % for pool fires at extinction. Since the molar heat capacity of water vapor is midway between nitrogen and carbon dioxide, one would expect water mist and combustion product extinction limits to be between nitrogen and carbon dioxide.
C. Beyler
All of the above results are for relatively quiescent conditions. It is well known that at higher strain rates, the oxygen concentration at extinction increases. This phenomenon can most easily be seen in counterflow diffusion flame extinction experiments such as Hamins et al. [35] Example 5 As part of a hazard analysis of a particular room fire, the composition of the hot layer during fire development has been estimated. The results of the analysis indicate that the following composition represents the highest concentration of fuel gases expected: Hot layer—700 K, 10 % total hydrocarbons (THC), in the form of CH2, 2 % CO, 1 % H2, 15 % CO2, 2 % O2, 70 % N2 Cold layer—300 K, 21 % O2, 79 % N2 Will the hot layer burn? Solution The working equation is Equation 17.6. The first step is to write a balanced chemical equation for stoichiometric burning: 0:1 CH2 þ 0:02 CO þ 0:01 H2 þ 0:02 O2 þ 0:7 N2 þ0:15 CO2 þ xðO2 þ 3:78 N2 Þ ! 0:27 CO2 þ0:11 H2 O þ ð0:7 þ 3:78XÞN2
We can find x by requiring that both sides of this equation have the same amount of oxygen: CO O2 CO2 air CO2 H2 O 0:02 0:11 þ 0:02 þ 0:15 þ x ¼ 0:27 þ ! x ¼ 0:145 2 2
The concentrations in the stoichiometric mixture can be determined from the balanced chemical equation: ni 100% Ci ¼ nT nT
CTHC CCO CH 2
¼ 0:1 þ 0:02 þ 0:01 þ 0:02 þ 0:7 þ 0:15 þ 0:145 þ 0:145ð3:78Þ ¼ 1:693 0:1 ¼ 100% ¼ 5:9% 1:693 0:02 ¼ 100% ¼ 1:2% 1:693 0:01 ¼ 100% ¼ 0:6% 1:693
17
Flammability Limits of Premixed and Diffusion Flames
Similarly, the number of moles of products per mole of reactants can be determined from the chemical equation ½0:27 þ 0:11 þ 0:7 þ 0:145ð3:78Þ np ¼ 1:693 ¼ 0:962 This result is lower than typical values of 1–1.1, because the unknown hydrocarbon mixture is taken as CH2 . This choice is not an error, since CH2 has been consistently used for the heat release and heat capacity as well. For convenience, we will use constant average specific heats taken from Drysdale: [3] Cp (J/mol · K) 54.3 41.2 32.7
CO2 H2O N2
C (%)a 16.2 6.6 77.2
Calculated by the same method as the fuel gas concentrations n pC p ¼ n p
X Ci 100
C p, i
¼ 0:96½ð0:162Þð54:3Þ þ ð0:066Þ ð41:2Þ þ ð0:772Þ ð32:7Þ ¼ 35:3 J=mol K Notice that the average specific heat is near that of nitrogen, since it is the major constituent of the mixture. In calculating T0 , the initial temperature of the mixture, we will ignore variations in Cp between the hot and cold layers. T0 ¼ ¼
nh Th þ nc Tc nh þ nc ¼ nT nh þ nc ð1Þ ð700 K Þ þ ð0:69Þ ð300 KÞ ¼ 537 K 1:69
where nh and nc are the number of moles originating in the hot and cold layers, respectively. Substituting into Equation 17.5,
549
X
n i¼1
ðCi =100ÞΔH c, i ð0:059Þ ð620Þ103 ¼ 35:3ð1700 537Þ C p T f , SL, i T 0
þ
ð0:012Þ ð283Þ103 35:3ð1450 537Þ
þ
ð0:006Þ ð242Þ103 ¼ 1:07 35:3ð1080 537Þ ð17:7Þ
Since the result is greater than one, the hot layer will ignite and burn. Although the approach to the onset of layer burning used in Example 5 has a great deal of generality, it requires a very detailed characterization of the upper and lower layers. It has been shown by Beyler [31] that a much simpler method can be used to evaluate the conditions required for layer burning. The method [31] is based on the very simple chemical model Fuel þ Oxidizer ( Products þ Excess oxidizer for ϕ < 1 ! Products þ Excess fuel for ϕ > 1 ð17:8Þ where the equivalence ratio, ϕ, is given by m_ f m_ air r mf r ¼ mair Stoichiometric ϕ¼
ð17:9Þ
According to this model, the fuel mass fraction in the upper layer is Yf ¼ 0 Yf ¼
1 1=ϕ 1 þ 1=ϕr
for ϕ < 1 for ϕ > 1
ð17:10Þ
Equation 17.6 can be expressed on a mass basis for this application as Y f ΔH c 1 m p C p ðT SL T 0 Þ
ð17:11Þ
550
C. Beyler
where ΔHc is the heat of combustion of the fuel, and mp is the mass of products resulting from burning a unit mass of upper layer gases. Substituting the ϕ > 1 relationship for Yf into Equation 17.6, expressing the heat release in terms of oxygen consumed using ΔH c ¼
ΔH O2 Y O2 r
ð17:12Þ
and recognizing that mp ¼ 1 þ
Yf r
ð17:13Þ
Yields 1 1=ϕ ΔHO2 Y O2 1 1þr C p ðT SL T 0 Þ
ð17:14Þ
Equation 17.14 can be solved for the equality condition to give the equivalence ratio at which layer burning begins, ϕig, ϕig ¼
k kr1
ð17:15Þ
where k¼
ΔH O2 Y O2 C p ðT SL T 0 Þ
T0 is the precombustion temperature resulting from stoichiometric mixing of the air and fuel streams. Here, the upper layer contains the fuel and the lower layer contains the air. T0 can be expressed as T u þ Y f =r T l T0 ¼ ð17:16Þ 1 þ Y f =r Using Equations 17.15 and 17.16, a relationship between the critical ignition equivalence ratio and the layer temperatures can be developed. Using normal values for the semi-universal constants, ΔHO2 ¼ 13:4 MJ=kg, Cp ¼ 1.1 kJ/kg K, TSL ¼ 1700 K. Using air properties for the lower layer, Y O2 ¼ 0:233 and Tl ¼ 300 K. Using a typical r ¼ 0.07 yields the relationship between ϕig and Tu shown in Fig. 17.15. The results shown in Fig. 17.15 are consistent with the measurements of Beyler [31], where ϕig was found to be 1.7 for Tu of 500–600 K. Gottuk [36] found that external burning was first observed in flashes at ϕ ¼ 1.4 0.4, and sustained external burning was first observed at f ¼ 1.9 0.3 when Tu was in the range 900–1100 K. While in Gottuk’s [36] experiments it was difficult to observe burning at the layer interface due to soot deposits on the viewing ports, layer interface burning was
2.2
Ignition equivalence ratio
2.0
1.8
1.6
1.4
1.2
1.0 300
500
700 900 1100 Upper layer temperature (K)
Fig. 17.15 Equivalence ratio required for upper layer ignition as a function of the upper layer temperature determined using Equations 17.15 and 17.16 with typical properties. Using normal values for the semi-universal
1300
constants, ΔH O2 ¼ 13:4 MJ=kg, Cp ¼ 1.1 kJ/kg K, TSL ¼ 1700 K. Using air properties for the lower layer, Y O2 ¼ 0:233, Tl ¼ 300 K. Using a typical r ¼ 0.07 yields the relationship between ϕig and Tu
17
Flammability Limits of Premixed and Diffusion Flames
generally observed shortly after the initiation of flashes in the exhaust. Because the exhaust flow was isolated from the inflow in the experiment, there is some issue of the availability of a pilot flame which does not arise in normal two-directional vents found in most fires. Thus, Gottuk’s work is generally consistent with Fig. 17.15.
Oxygen Index Test Method The original oxygen index test method, used to determine the oxygen index of liquid and gas fuels, utilizes a counterflow diffusion flame formed at the stagnation region of a porous cylinder or sphere through which fuel vapors are fed. A low-velocity oxidant stream passes over the porous body. This arrangement yields the most favorable aerodynamic conditions for flame stabilization. As such, fuel and oxidant streams that can burn in the low-velocity counterflow system may not burn under less favorable aerodynamic conditions characterized by higher velocities and shear. It is also important to point out the difference between the oxygen index as measured for gas and liquid fuels and the oxygen index of solids as measured using a candle-type test [37, 38]. The oxygen indexes of the gas and liquid fuels as tested by Simmons and Wolfhard [29] were governed by gas-phase effects. In the American Society for Testing and Materials test [33] for solids, the extinction can be caused by gas- and solid-phase effects. As such, the oxygen index of a solid fuel is not directly relevant to gas-phase diffusion flame limits and should not be used to calculate adiabatic flame temperature at the limit for use in the expressions presented here.
Nomenclature AIT C Cp
Autoignition temperature (C or K) Concentration (volume percent) Heat capacity (J/kg K)
551
LFL M n NP OI r SL T V X Y ΔHc ϕ
Lower flammable limit (volume percent) Mass (kg) Moles Nitrogen point Oxygen index Stoichiometric fuel/air ratio Stoichiometric limit (volume percent) Temperature (C or K) Volume (m3) Mole fraction Mass fraction Heat of combustion (J/kg) Equivalence ratio
Subscripts C i ig f l L m N O p u U
Combustion Species Ignition Flame or fuel Lower layer Liquid or lower limit Mixture Nitrogen Initial or ambient Products of combustion Upper layer Upper limit
References 1. M.G. Zabetakis, Bulletin No. 627, U.S. Bureau of Mines, Washington, DC (1965). 2. H.F. Coward and G.W. Jones, Bulletin No. 503, U.S. Bureau of Mines, Washington, DC (1952). 3. D.D. Drysdale, An Introduction to Fire Dynamics, John Wiley and Sons, New York (1999). 4. ASTM E681-94, Standard Test Method for Concentration Limits of Flammability of Chemicals, American Society for Testing and Materials, Philadelphia (1994). 5. ASTM E918-83, Standard Test Method for Concentration Limits of Flammability of Chemicals, American Society for Testing and Materials, Philadelphia (1993). 6. DIN 51 649 Teil 1, Bestimmung der Explosionsgrenzen von Gasen and Gasgemischen in
552 Luft, Deutsches Institute fur Normung, Berlin, Germany (1986). 7. VDI 2263 Part 1, Test Methods for the Determination of the Safety Characteristics of Dusts, Verein Deutscher Ingenieure (1990). 8. G. Smedt, F. Corte, R. Notele, and J. Berghmans, “Comparison of Two Standard Test Methods for Determining Explosion Limits of Gases at Atmospheric Conditions,” Journal of Hazardous Materials, A70, pp. 105–113 (1999). 9. M. Goethals, B. Vanderstraeten, J. Berghmans, G. Smedt, S. Vliegen, and E. Van’t Oost, “Experimental Study of the Flammability Limits of Toluene–Air Mixtures at Elevated Pressure and Temperature,” Journal of Hazardous Materials, A70, pp. 99–104 (1999). 10. G.A. Karim, I. Wierzba, M. Metwally, and K. Mohon, “Combustion of a Fuel Jet in a Stream of Lean Gaseous Fuel-Air Mixtures,” in 18th Symposium (International) on Combustion, Combustion Institute, Pittsburgh, PA (1981). 11. H.F. Coward, C.W. Carpenter, and W. Payman, “The Dilution Limits of Inflammability of Gaseous Mixtures. Part III. The Lower Limits of Some Mixed Inflammable Gases with Air. Part IV. The Upper Limits of Some Gases, Singly and Mixed, in Air,” Journal of the Chemical Society, 115, pp. 27–36 (1919). 12. M.J. Burgess and R.V. Wheeler, “The Lower Limit of Inflammation of Mixtures of the Paraffin Hydrocarbons with Air,” Journal of the Chemical Society, 99, pp. 2013–2030 (1911). 13. A.G. White, “Limits for the Propagation of Flame in Inflammable Gas–Air Mixtures. Part III. The Effects of Temperature on the Limits,” Journal of the Chemical Society, 127, pp. 672–684 (1925). 14. M.G. Zabetakis, S. Lambiris, and G.S. Scott, “Flame Temperatures of Limit Mixtures,” in 7th Symposium (International) on Combustion, Combustion Institute, Pittsburgh, PA. 15. F.J. Weinberg, “Combustion Temperatures: The Future?” Nature, 283, 239 (1971). 16. A. Macek, “Flammability Limits: A Re-Examination,” Combustion Science and Technology, 21, pp. 43–52 (1979). 17. A. Egerton and J. Powling, “The Limits of Flame Propagation at Atmospheric Pressure. II. The Influence of Changes in the Physical Properties,” Proceedings of the Royal Society A, 193, London, UK, pp. 190–209 (1948). 18. D.R. Stull, Fire Research Abstracts and Reviews, 13, 161 (1971). 19. H.F. Coward and G.W. Jones, “Limits of Flammability of Gases and Vapors,” Bulletin 503, U.S. Bureau of Mines, Washington, DC (1952). 20. G.W. Jones, M.G. Zabetakis, J.K. Richmond, G.S. Scott, and A.L. Furno, “Research on the
C. Beyler Flammability Characteristics of Aircraft Fuels,” Technical Report 52–35, Supplement I, Wright Air Development Center, Wright-Patterson AFB, OH (1954). 21. J.M. Kuchta, A.L. Furno, A. Bartkowiak, and G.H. Martindill, “Effect of Pressure and Temperature on Flammability Limits of Chlorinated Combustibles in Oxygen-Nitrogen and Nitrogen Tetroxide-Nitrogen Atmospheres,” Journal of Chemical and Engineering Data, 13, 3, p. 421 (1968). 22. M.G. Zabetakis, “Flammability Characteristics of Combustible Gases and Vapors,” Bulletin 627, U.S. Bureau of Mines, Washington, DC (1965). 23. M.G. Zabetakis and B.H. Rosen, “Considerations Involved in Handling Kerosene,” Proceedings AP1, 37, p. 296 (1957). 24. B. Lewis and G. Von Elbe, Combustion, Flame, and Explosions of Gases, Academic, New York (1961). 25. R.A. Strehlow, Combustion Fundamentals, McGrawHill, New York (1984). 26. M. Hertzberg, K. Cashdollar, and R. Conti, “Domains of Flammability and Thermal Ignitability for Pulverized Coals and Other Dusts: Particle Size Dependences and Microscopic Residue Analyses,” in the 19th Symposium (International) on Combustion, Combustion Institute, Pittsburgh, PA, pp. 717–729 (1981). 27. J.H. Burgoyne and L. Cohen, “The Effect of Droplet Size on Flame Propagation of Liquid Aerosols,” Proceedings of the Royal Society A, 225, 375, pp. 375–392 (1954). 28. M. Hertzberg, K. Cashdollar, and C. Lazzara, “The Limits of Flammability of Coals and Other Dusts,” 18th Symposium (International) on Combustion, Combustion Institute, Pittsburgh, PA, pp. 717–730 (1981). 29. R.F. Simmons and H.G. Wolfhard, “Some Limiting Oxygen Concentrations for Diffusion Flames in Air Diluted with Nitrogen,” Combustion and Flame, 1, pp. 155–161 (1957). 30. S. Ishizuka and H. Tsuji, “An Experimental Study of Effect of Inert Gas on Extinction of Laminar Diffusion Flames,” 18th Symposium (International) on Combustion, Combustion Institute, Pittsburgh, PA, pp. 695–703 (1981). 31. C.L. Beyler, “Ignition and Burning of a Layer of Incomplete Combustion Products,” Combustion Science and Technology, 39, pp. 287–303 (1984). 32. J. Morehart, E. Zukoski, and T. Kubota, “Characteristics of Large Diffusion Flames Burning in a Vitiated Atmosphere,” in Third International Symposium on Fire Safety Science, Elsevier Science Publishers, UK, pp. 575–583 (1991). 33. M. Peatross and C. Beyler, “Ventilation Effects on Compartment Fire Characterization,” in Fifth International Symposium on Fire Safety Science, Elsevier Science Publishers, UK, pp. 403–414 (1997). 34. G. Back, C. Beyler, R. Hansen, “A Quasi Steady-State Model for Predicting Fire Suppression in Spaces
17
Flammability Limits of Premixed and Diffusion Flames
Protected by Water Mist Systems,” Fire Safety Journal, 35, pp. 327–362. 35. A. Hamins, D. Trees, K. Seshadri, H. Chelliah, “Extinction of Nonpremixed Flames with Halogenated Fire Suppressants,” Combustion and Flame, 99, pp. 221–230 (1994). 36. D.T. Gottuk, “The Generation of Carbon Monoxide in Compartment Fires,” PhD Dissertation, Virginia Polytechnic and State University, Blacksburg, VA (1992). [Also in NIST-GCR-92-619, National Institute of Standards and Technology, Gaithersburg, MD (1992).] 37. C.P. Fenimore and F.J. Martin, “Flammability of Polymers,” Combustion and Flame, 10, 135 (1966).
553
38. ASTM D2863-97, Standard Test Method for Measuring the Minimum Oxygen Concentration to Support Candle-Like Combustion of Plastics (Oxygen Index), American Society for Testing and Materials, Philadelphia (1997). Dr. Craig Beyler earned a Ph.D. in engineering science at Harvard University under the direction of Professor Howard Emmons and served on the faculty of Worcester Polytechnic Institute’s Center for Firesafety Studies. Dr. Beyler is currently technical director of Hughes Associates, Inc., Fire Science and Engineering.
Ignition of Liquids
18
D.D. Drysdale
Introduction The purpose of this chapter is to discuss the ignition characteristics of combustible liquids that are in widespread use as fuels and solvents and are encountered as process fluids in the chemical and process industries. Ignition leads to flaming combustion in which the fuel undergoes a change of state and is converted from liquid to vapor. Unlike the flaming combustion of solid fuels, this conversion does not involve any chemical change to the fuel molecules that simply evaporate from the exposed surface.1 The flammable vapors mix with air to burn as a diffusion flame. When combustible solids exhibit flaming combustion, the change of state from solid to vapor involves chemical decomposition (see Chap. 7). Unlike liquids for which the process of evaporation is reversible (the evolved vapors can be converted back to the original liquid by cooling or by compression), the conversion is irreversible, breaking down the large polymeric molecules of which the solid is composed into fragments that are small enough to vaporize and enter the gas phase. Some solids, such as the 1 There are exceptions to this generalization. High molecular weight liquids with high flashpoints (e.g., cooking oil, flashpoint 321 C) will be undergoing some chemical decomposition at temperatures associated with vapor formation.
D.D. Drysdale (*)
thermoplastics (e.g., polypropylene and polystyrene), first soften and liquefy before producing molecular fragments that are small enough to vaporize. Others such as wood do not liquefy but release gases and vapors directly leaving behind an involatile carbonaceous char that, if permitted to do so, will undergo surface oxidation (smoldering) at a much slower rate. As a general rule, fires involving combustible liquids are associated only with flaming combustion, but there are exceptions that will be discussed later. The underlying physics of the vaporization process for liquids provides a relatively simple key to understanding the conditions under which liquids can be ignited. The vapors from combustible liquids are flammable and exhibit exactly the same properties and behavior as the common flammable gases such as methane and propane (see Chap. 17). Thus, we can identify flammability limits, autoignition temperatures, minimum ignition energies, quenching distances, and so on. Of these, the most important are the flammability limits. If the concentration of vapor above a liquid surface is below the lower flammability limit, then the vapors cannot be ignited, flame will not propagate through the vapor-air mixture, and the liquid will not “burn.” The limiting condition of the liquid at which the vapors are at the lower flammability limit is known as the flashpoint. Experimentally, this can be measured in a closed cup apparatus in which the vapor-air mixture in the closed volume above the surface (the “headspace”) is at equilibrium with the liquid—the vapor will be at a pressure (the
M.J. Hurley (ed.), SFPE Handbook of Fire Protection Engineering, DOI 10.1007/978-1-4939-2565-0_18, # Society of Fire Protection Engineers 2016
554
18
Ignition of Liquids
saturation vapor pressure) that is defined by the temperature of the liquid. This “closed cup flashpoint” provides us with a relatively simple method of ranking flammable liquids according to the hazard they present in everyday use. In principle, the concept of flashpoint can also be applied to combustible solids, but because the phase change (solid to vapor) is irreversible there is no corresponding simple method for classifying solids according to their ignition hazard. The ignition of solids depends on a large number of factors including the physical form of solid and the mode and intensity of the heat transfer process. Such issues are discussed in Chap. 21. For combustible liquids, the flashpoint is closely linked to the flammability limits of the vapor. If the liquid is in an unconfined cup or present as a pool, the minimum liquid temperature at which the vapors can be ignited and burn is found to be higher than the “closed cup flashpoint” as defined above and is called the “open cup flashpoint.” The reason for this is simply that the vapors will diffuse away from the liquid surface and for successful ignition from a “pilot” (a small flame or a spark) the pilot must be located in a region where the mixture is flammable. In general, a higher liquid temperature is required to ensure that the pilot is in a flammable zone. However, the “flash” of flame that occurs as flame propagates through the flammable mixture is not necessarily followed by sustained burning of the liquid. A criticality must be exceeded before this will occur. It is only then that the liquid can properly be said to have been ignited to flaming combustion. This is known as the firepoint, which will be discussed in a later section entitled “Measurement of Flashpoint and Firepoint.”
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Vaporization of Liquids
many solvents (e.g., acetone, diethyl ether, etc.), some paints and varnishes, and so on. Most are blends, but for convenience and clarity in the following discussion, a one-component system (such as pure n-hexane) will be considered. The classic phase diagram for a one-component system is shown schematically in Fig. 18.1. The variables are pressure and temperature and the so-called “phase space” is divided into three areas corresponding, respectively, to solid, liquid, and gas (vapor). For a pure compound at constant pressure (illustrated by the horizontal dashed line) we can identify the melting point (TM) and the boiling point (TB), which are uniquely defined at any given pressure. The values quoted in the literature refer to normal atmospheric pressure. The upper pair of lines that intersect at the point T in Fig. 18.1 represent equilibrium states between solid and liquid and between liquid and vapor, respectively.2 The line (TC) defines how the vapor pressure of the liquid varies with temperature. Thus, for n-hexane at normal atmospheric pressure, TB ¼ 69 C, which corresponds to the temperature at which the (saturated) vapor pressure is 101.3 kPa. The variation of boiling point with pressure is best illustrated using pure water as the example. At sea level (101.3 kPa) it has a boiling point of 100 C, but, as with all other liquids, this point decreases with elevation. In Banff, Scotland (at sea level), water boils at 100 C but in Banff, Alberta (elevation 1463 m), it boils at about 95 C. On the summit of Mount Everest (8848 m) where the pressure is approximately 33 kPa, or one-third of the value at sea level, it boils at about 72 C. As will be seen, the flashpoints of combustible liquids also change with a change of atmospheric pressure but for a subtly different reason, as will be discussed later. On the phase diagram, temperature and pressure may be varied independently provided that only one phase is present: there are two degrees
The liquids of general interest to the fire protection engineer are those that are stable at normal atmospheric temperatures and pressures (say, 10–30 C and 101.3 kPa). These include common liquid fuels (such as gasoline and kerosene),
2 The third line in Fig. 18.1, below the intersection at T, represents the equilibrium states between solid and vapor. Solid converts directly to vapor by the process of sublimation. It will not be considered further here.
556
D.D. Drysdale
Fig. 18.1 Typical phase diagram for a one-component system. Points on the curve TC correspond to the equilibrium (“saturated”) vapor pressure of the liquid, as given in Equation 18.3. T is the “triple point” and C defines the critical temperature and pressure (Table 18.1)
Pressure
Solid
Liquid
C
Vaporization Condensation
M
B
Melting Freezing
Gas
Sublimation
T Deposition
TM
TB
Temperature
of freedom (i.e., independent variables), which in this case are temperature and pressure. Thus, a gas can be compressed and heated at the same time and still remain a gas (no change in state). The ideal gas law encapsulates this in the equation
increase the temperature, the resulting vapor pressure is defined by the line BC and (unless atmospheric pressure is increased in step) complete conversion of liquid to vapor will occur, and the number of phases present is reduced from two to one as expressed in Gibbs’s phase rule:
PV ¼ nRT
F¼c pþ2
ð18:1Þ
where P ¼ Pressure V ¼ Volume T ¼ Temperature (K) n ¼ Number of moles of gas present (mass divided by the molecular weight) R ¼ Ideal gas constant3 However, when two phases are present and in equilibrium, corresponding to a point on one of the lines on the phase diagram, then P and T cannot be varied independently without changing the number of phases present. For example, at point B, liquid and vapor are in equilibrium, with the saturated vapor pressure of n-hexane equal to 101.3 kPa (760 mmHg, or 1 bar) at 69 C. If we
3 The numerical value of R depends on the units used for P and V (see Chap. 5).
ð18:2Þ
where f is the number of degrees of freedom (independent variables), c is the number of components, and p is the number of phases present (e.g., see Moore [2] and Atkins and de Paula [3]). For the one-component system (e.g., pure n-hexane), c ¼ 1, so that when p ¼ 2 (liquid and vapor present) the number of degrees of freedom f ¼ 1. That is, we can change either the temperature or the pressure, but we cannot change them independently without changing the number of phases present. (Note that the intersection of the three lines on the phase diagram marked T is known as the triple point, where the three phases are in equilibrium; that is, p ¼ 3. The number of degrees of freedom is, therefore, zero so that this point is uniquely defined.) In summary, the lines that divide the phases in Fig. 18.1 represent equilibrium states: the line
18
Ignition of Liquids
557
Table 18.1 Critical temperatures and pressures [1] Hydrogen (H2) Nitrogen (N2) Oxygen (O2) Methane (CH4) Ethane (C2H6) Propane (C3H8) n-Butane (n-C4H10) n-Hexane (n-C6H14)
Normal boiling point ( C) 252.9 195.8 183.0 164 88.6 42.1 0.5 69
that separates the liquid and gaseous phases defines how the saturated vapor pressure of the liquid varies with temperature. However, this line does not continue indefinitely but ceases at the critical point marked C. At temperatures and pressures above the critical point, only one phase exists—the distinction between the liquid and gas disappears. Some values of critical temperatures and pressures are given in Table 18.1. A gas such as propane (boiling point 42 C) is below its critical temperature at ambient temperatures and can be liquefied by pressurization. However, the so-called “permanent gases,” which include oxygen and nitrogen, are above their respective critical temperatures and cannot exist as liquids at ambient temperature (e.g., 25 C) regardless of the pressure. They are stored under pressure as gases in cylinders, typically at 140 bar. A single phase then exists within the cylinder. The only way that a permanent gas can be stored as a pressurized liquid is to cool it below its critical temperature. Large quantities of natural gas (mainly methane) can be stored economically as a refrigerated (cryogenic) liquid: its critical temperature is 82.3 C and its normal boiling point is 164 C as given in Table 18.1. If a liquid is in an enclosed space, such as a can, tank, or bottle, the vapor will be contained within the headspace and quickly reach equilibrium (i.e., the saturated vapor pressure will be reached). This value is predicted in the phase diagram and is a function of temperature (see Equations 18.3, 18.4, and 18.5). It represents a dynamic state in which vaporization continues but at a rate that is balanced exactly by
Critical temperature ( C) 240 146.9 118.5 82.3 32.2 96.6 152.3 234.5
Critical pressure (bar) 13 34 50.5 46.5 48.3 42.5 37 29.9
condensation of vapor back to the liquid state (see Fig. 18.1). For this reason, if the liquid is unconfined (e.g., forming a pool in the open), the liquid will eventually undergo complete evaporation as vapor continuously diffuses away from the surface of the liquid. Consequently, the vapor pressure at the surface will be less than the saturated vapor pressure and equilibrium cannot be achieved. The rate of mass loss by evaporation will be determined by the temperature of the liquid, the exposed area of the pool, and any air movement over the liquid surface (see, for example, Wade [4] and Clancy [5]). Boiling occurs when the vapor pressure is equal to atmospheric pressure, as discussed above. However, if the liquid is in a closed (sealed) container capable of withstanding high internal pressures, the two phases (liquid and vapor) will remain in equilibrium at temperatures well above the atmospheric boiling point. Thus, propane and butane (which have normal boiling points of 42.1 C and 0.5 C, respectively) can be stored as liquids at 25 C at 9.6 bar and 2.3 bar (957 and 231 kPa), respectively, in appropriate pressure vessels. These pressures correspond to the saturated vapor pressures of these two hydrocarbons at 25 C. The reduction in volume associated with condensation is very large, making liquefaction a particularly effective means of storing these and similar gases. They can be liquefied simply by compression, although this is not possible with the so-called permanent gases, as discussed above. Clearly, methane, propane, and butane cannot exist as stable liquids at normal temperatures and pressures. If liquefied methane (at 163 C) is
558
released from a refrigerated tank and spilled on the ground, it will form a pool and boil vigorously until the surface of the ground has cooled to about 163 C. Thereafter, it will behave as a stable liquid, evaporating at a rate dictated by the rate of heat transfer from the ground (see Thyer [6]). Although methane is much lighter than air at ambient temperature, the vapor that evolves from the pool will be initially at 163 C and much denser than the surrounding air. Consequently, it will spread horizontally until it gains sufficient heat from the surroundings to regain its buoyancy. Although propane is sometimes stored as a cryogenic liquid, propane and butane are more commonly stored in pressure vessels. Catastrophic release due to vessel failure gives rise to a BLEVE (boiling liquid expanding vapor explosion), a term originally coined for a pressure burst of a boiler containing superheated water (see Chap. 66). (It is defined by the Centre for Chemical Process Safety as “an explosion resulting from the failure of a vessel containing a liquid at a temperature significantly above its boiling point at normal atmospheric pressure.” [7]) The liquid boils throughout its volume once the pressure is released and a substantial quantity will convert to vapor. The heat of vaporization is taken from the remaining liquid so that the BLEVE produces a vapor cloud containing a significant proportion of the original mass as liquid droplets. These may fall to the ground, although if ignition occurs (as it will if the pressure burst has been the result of exposure of the vessel to fire), there will be a fireball that will burn out rapidly (see, for example, Abbassi and Abbassi [8]).
Calculation of Vapor Pressure If the space above the liquid is enclosed (as in a bottle or other container), evaporation will take place until the vapor pressure reaches its saturation value. This equilibrium is described by a form of the Clapeyron-Clausius equation, which gives the saturated vapor pressure ( p ) as a function of the temperature of liquid (T K).
D.D. Drysdale
dðln p∘ Þ Lv ¼ dT RT 2
ð18:3Þ
where Lv is the latent heat of evaporation of the liquid (kJ/kg) and R is the ideal gas constant. The derivation of this expression requires a number of approximations and may be found in most texts on physical chemistry [2, 3]. Integration of the equation gives the vapor pressure as a function of temperature; thus, po ¼ Cexp½Lv =RT
ð18:4Þ
or ln p∘ ¼ lnC
Lv RT
ð18:5Þ
A plot of ln p versus 1/T will be a line of slope –Lv/R, although it is not strictly linear over an extended temperature range. However, it may be assumed to be linear within the range of temperatures with which we are concerned (i.e., we can assume that Lv is constant). Values of Lv for a range of liquids are given in Table 18.2. The expression for vapor pressure is normally given in the form shown in Equation 18.5. The 53rd edition of the CRC Handbook of Chemistry and Physics [13] (and perhaps some later editions) gives an extensive table of data on p (T), but in a modified form as follows: log10 po ¼ 0:2185
A þB T
ð18:6Þ
where p is given in mmHg. Values of A and B for some typical liquid fuels are given in Table 18.3 (converting the data from log10 to loge [i.e., ln] and from mmHg to kPa is a hazardous process that has not been attempted here). Vapor pressures may also be calculated from data in Yaws [12]. Example 1 Using the data in Table 18.3, calculate the pressure in a cylinder containing liquid isobutane at 25 C. How can you determine how much fuel remains in the cylinder after drawing gas from it for a period of time? Solution For isobutane, A ¼ 5416.2 K and B ¼ 7.349085. T ¼ 25 + 273 K ¼ 298 K. Substituting these values in Equation 18.4 gives
18
Ignition of Liquids
559
Table 18.2 Selected ignition properties of some fuels in aira
Fuel Alkanes Methane Ethane Propane n-Butane i-Butane n-Pentane i-Pentane n-Hexane i-Hexane n-Heptane i-Heptane n-Octane i-Octane n-Nonane n-Decane n-Undecane n-Dodecane Kerosene{ Alkenes Ethylene Propene 1-Butene 1-Pentene Hexelene Cycloparaffins Cyclopropane Cyclobutane Cyclopentane Cyclohexane Cycloheptane Dimethyl cyclohexane Aromatics Benzene Toluene m-Xylene o-Xylene p-Xylene Styrene bi-Phenyl Naphthalene Anthracene Ethyl benzene Butyl benzene
Flammability limitsb (% by volume) AIT Lower Upper ( C)
Formula
Flashpoint ( C) Molecular Boiling Lv H weight point ( C) (kJ/kg) (MJ/kg) Closed Open
CH4 C2H6 C3H8 C4H10 – C5H12 – C6H14 – C7H16 – C8H18 – C8H20 C10H22 C11H24 C12H26 ~C14H30
16 30 44 58 – 72 – 86 – 100 – 114 – 128 142 156 170 ~198
162 89 42 0 10 36 13 69 – 98 – 125 – 151 174 196 216 ~232
298 – 288 360 308 293 ~291
50.2 47.6 46.4 45.9 – 45.5 – 45.2 – 45.0 – 44.9 – 44.8 44.7 44.6 44.6 ~44.0a
C2H4 C3H6 C4H8 C5H10 C6H12
29 42 56 70 84
104 48 6 30 67
516 437 398a 314 388
47.3 45.9 45.4 46.9 47.5
121 108 80 – –
– – – 1.8 –
2.7 2.0 1.6 1.5 –
36 11.0 9.3 8.7 –
450 457 384 273 253
C3H6 C4H8 C5H10 C6H12 C7H14 C8H16
42 56 70 84 98 112
34 13 49 81 119 119
588 483 443 358 376 300
46.3 44.8 44.3 43.9 43.7 46.3a
95 65 37 20 9a 11
– – – – – –
2.4 1.8 1.4 1.3 1.1 0.9
10.4 11.1 9.4 8.0 7.1 6.5
498 427 361 260 – 304
C6H6 C7H8 C8H10 – – C8H8 C12H10 C10H8 C13H10 C8H10 C10H14
78 92 106 – – 104 154 128 166 106 134
80 110 139 141 137 145 254 218 340 136 173
432 362 343 347 339 – – 316c 310c 320c 277c
40.7 41.0 41.3 41.3 41.3 40.5 40.6 40.3 40.0c 43.1 43.7
11 4 25 17 25 32 113 79 121 15 49
– 7 – 24 – – 124 88 196 24 63
1.4 1.2 1.1 1.0 1.1 1.1 0.8 0.9 0.7 1.0 0.8
7.1 562 7.1 536 7.0 528 6.0 464 7.0 529 6.1 490 6.7 540 5.9 587 – 540 6.7 432 5.8 412 (continued)
509 489 426 386 366 365 371 365 – 365
– – – 135 – 104 – 60 117 – – 49 – 51 22 – 29 – 4 – 18 – 13 – 12 – 31 – 44 – – 65 72 – ~49 –
5.0 3.0 2.1 1.8 1.8 1.4 1.4 1.2 1.2 1.0 1.0 0.8 1.0 0.7 0.75 0.7 0.60 (~0.6)
15.0 600 12.5 515 9.5 450 8.5 405 8.4 460 7.8 260 7.6 420 7.5 234 7.0 – 7.0 223 6.0 – 6.5 220 5.6 – 5.6 206 5.4 208 4.8 202 4.7 204 (~5.6) ~260
560
D.D. Drysdale
Table 18.2 (continued)
Fuel Alcohols Methanol Ethanol n-Propanol i-Propanol Allyl alcohol n-Butanol i-Butanol 2-Pentanol i-Amyl alcohol 3-Pentanol n-Hexanol Cyclohexanol n-Heptanol 1n-Octanol 2n-Octanol Nonanol i-Decanol Carbonyls Formaldehyde 37 % in H2O Acetaldehyde i-Butyraldehyde Crotonaldehyde Diethyl acetaldehyde Ethyl hexaldehyde Paraldehyde Salicyl aldehyde Benzaldehyde Ketones Acetone 2-Butanone Diethyl ketone Methyl i-butyl ketone Dipropyl ketone Methyl n-propyl ketone Methyl vinyl ketone Acids Formic acid Acetic acid Benzoic acid
Formula
Flashpoint ( C) Molecular Boiling Lv H weight point ( C) (kJ/kg) (MJ/kg) Closed Open
CH3OH C2H5OH C3H7OH – C3H6O C4H9OH – C5H11OH C5H11OH
32 46 60 – 58 74 – 88 88
C6H13OH – C7H15OH C8H17OH
102 – 116 130
C9H19OH C10H21OH
Flammability limitsb (% by volume) AIT Lower Upper ( C)
144 158
64 78 97 82 95 117 107 119 130 118 159 161 176 196 180 214 235
1101 837 686 667 684 621 578 575c 501 575c 458 460c 439 408 419 403 373
20.8 27.8 31.3 33.1 31.9 36.1 36.1 – 35.3 – 36.4 36.6 39.8 40.6 – 40.3 –
12 13 15 12 21 29 28 – 43 34 45 68 – 81 74 – –
16 22 29 – 24 43 – 41 46 39 74 – 71 – 82 – –
7.3 4.3 2.0 2.0 2.5 1.4 1.7 1.5 1.2 1.2 1.2a 1.2 1.0 0.9 0.8 0.8 0.7
36.0 19.0 12.0 12.6 18.0 11.2 9.8 9.7 9.0 9.0 8.2 9.3 7.2 6.4 6.5 6.1 5.5
469 423 371 399 378 343 406 343 350 435 285 300 – 282 – – –
CH2O – C2H4O C4H8O C4H6O C4H12O
30 – 44 72 70 76
97 97 21 61 102 118
826 826c 570 444c 490c 500c
18.7 – 25.1 33.8 34.8 –
93 54 38 40 13 294
– 93 – 24 – –
7.0 (7.0c) 1.6 1.6 2.1 –
73.0 – 10.4 10.6 15.5 –
430 424 185 254 232 –
C8H16O
128
163
325c
39.4
–
52
–
C6H12O3 C7H6O2 C7H6O
132 122 106
124 196 179
328 396 362
– – –
17 78 64
36 – 74
1.3 1.4 1.4
16.2 8.4 7.8
238 – 192
C3H6O C4H8O C5H10O C6H12O
58 72 86 100
56 80 101 116
521 443 380 345c
29.1 33.8 33.7 35.2
18 2 – 23
9 1 13 24
2.6 1.8 1.5 1.4
128 10.0 8.0 7.5
538 516 452 454
C7H14O C5H10O
114 86
144 375
317 376c
38.6 33.7
– 7
– 16
1.1 1.5
7.0 8.2
– 452
C4H6O
70
81
440c
–
7c
–
–
–
CH2O2 C2H4O2 C7H6O2
46 60 122
101 118 250 s
502 405 270c
5.7 14.6 24.4
69 40 121
– 57 –
18.0 5.4 1.4
–
–
–
57.0 601 16.0 427 8.0 574 (continued)
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Ignition of Liquids
561
Table 18.2 (continued)
Fuel Miscellany Camphor Carbon disulfide m-Creosol o-Creosol p-Creosol Furan Pyridine Aniline Acetal p-Cymene o-Dichloro benzene 1,1-Dichloro ethylene 1,2-Dichloro ethylene Monochloro benzene Resorcinol Ethyl formate Ethyl acetate Methyl propionate Acrolein Acrylonitrile n-Amyl acetate 1-Amyl acetate 1, 3-Butadiene n-Butyl acetate n-Butyl ether Dimethyl ether Divinyl ether Diethyl ether Gasoline{ Naptha{ Petroleum ether{
Formula
Flashpoint ( C) Molecular Boiling Lv H weight point ( C) (kJ/kg) (MJ/kg) Closed Open
C10H16O CS2 C7H8O – – C4H4O C5H5N C6H7N C6H14O2 C10H14 C6H4Cl2
152 76 108 – – 68 79 93 118 134 146
204 s 47 203 191 202 31 114 183 103 176 180
265c – – – – 399 449 434 277 283 –
C2H2Cl2
96
37
–
–
61
C6H5Cl
112
C6H6O2 C3H6O2 C4H8O2 C4H8O3 C3H4O C3H3N C7H14O2 – C4H6 C6H12O2 C8H18O C2H6O C4H4O C4H10O – – –
–
38.8 13.6 34.6 34.1 34.1 – 35.0 36.5 31.8 43.9 19.3
Flammability limitsb (% by volume) AIT Lower Upper ( C)
66 30 86 81 86 35 20 76 21 47 66
93 – – – – – – 91 – 63 74
0.6 1.3 1.1 1.4 1.1 2.3 1.8 1.3 1.6 0.7 2.2
3.5 50.0 7.6 7.6 7.6 14.3 12.4 11.0 10.4 5.6 9.2
466 90 559 599 559 – 482 617 230 436 647
–
–
10
7.3
16.0
582
–
–
6
–
5.6
12.8
460
132
–
–
32
38
1.3
7.1
638
110 74 88 104
276 54 77 80
– – – –
26.0 22.5 25.9 22.2
127 20 4 2
– 12 1 –
1.6 2.7 2.2 (2.4)
9.8 13.5 11.4 (13.0)
567 455 427 469
56 53 130 – 54 116 130 46 70 74 – – –
53 77 149 153 4 127 141 24 39 35 ~33 ~177 ~78
– – – – – – – – – – – – –
29.1 24.5 33.5 – – 30.0 39.7 31.6 – 37.4 ~44.1 – –
– – 24 25 76 22 25 41 30 45 ~45 ~41 ~ 18
26 0 27 38 – 32 38 – – – – – –
2.8 2.4 1.1 1.0 2.0 1.7 1.5 3.4 (1.7) 1.9 (~1.4) (~0.8) (~1.4)
31.0 234 17.3 481 6.8 357 7.5 360 11.5 429 7.6 421 7.6 – 18.0 350 (27) 360 48 180 (~6.8) ~371 (~5.0) ~246 (~5.9) ~288
Note: s indicates sublimes at normal pressures; Lv is latent heat of evaporation; H is heat of combustion; ~ indicates approximate values; – indicates not available; { indicates liquid blend a Adapted from Kanury [9]. The data were originally from references International Critical Tables of Numerical Data [10] and Handbook of Industrial Loss Prevention [11] but the flammability limits and autoignition temperatures have been taken from Yaws [12]. It is not clear whether the flashpoint measurements quoted in Yaws [12] refer to the closed cup or the open cup tests so these have not been adopted b The figures in brackets are taken from Kanury [9] c Estimated value
562
D.D. Drysdale
Table 18.3 Calculation of saturated vapor pressures A (K) 2128.8 4811.8 5801.2 5416.2 6595.1 7627.2 8928.8 9086.6 10,912.0 11,857.7
Methane (CH4) Propane (C3H8) n-Butane (n-C4H10) i-Butane (i-C4H10) n-Pentane (C5H12) n-Hexane (C6H14) n-Heptane (C7H16) i-Octane (C8H18) n-Decane (C10H22) n-Dodecane (C12H26)
B () 7.027729 7.392262 7.492753 7.349085 7.489673 7.717119 8.258500 8.113870 8.248089 8.150997
Data for Equation 18.5 [13]
log10( po) ¼ 3.378, or po ¼ 2386.7 mmHg, or 3.14 bar. If the temperature remains 25 C, this pressure will remain unchanged for as long as there is any liquid isobutane left in the container. Pressure is no guide to the amount of isobutane remaining. The only way to determine how much liquid is left is to weigh the container, assuming that you know the tare. Example 2 Calculate the normal boiling point of n-hexane from the data in Table 18.3, assuming the atmospheric pressure is 760 mmHg. Solution Take po ¼ 760 mmHg, so that log10(760) ¼ 2.881. For n-hexane, A ¼ 7627.2 K and B ¼ 7.717119, so by substitution and rearrangement: 2:881 ¼ 0:2185
7627:2 þ 7:717119 T
4:836T ¼ 1666:543 T ¼ 344 K ¼ 71:6∘ C which is about 2 K higher than the measured value quoted in Table 18.2. Example 3 Calculate the temperature at which the vapor pressure of n-decane corresponds to the lower flammability limit for n-decane vapor. Assume that this vapor pressure is 0.75 % by volume (Table 18.3) and that the atmospheric pressure is 760 mmHg. Solution The vapor pressure corresponding to the lower flammability limit of n-hexane is 0.75 % of
760 mmHg, or 5.7 mmHg. The calculation is exactly the same as for the previous example, except that log10( p ) ¼ log10(5.7) ¼ 0.756. Thus 0:756 ¼ 0:2185
10, 912:0 þ 8:24809 T
7:4922T ¼ 2384:272 T ¼ 318:2 K ¼ 45:2∘ C The closed cup flashpoint of n-decane is given in Table 18.2 as 317 K, or 44 C. Sources of the difference between the calculated flashpoint and that measured in a standard test will be discussed below.
Vapor Pressure of Liquid Blends Most commonly encountered fuels are in fact blends of different compounds. Gasoline, for example, contains several hundred individual hydrocarbons including a significant proportion of aromatics. The total vapor pressure is the sum of the partial vapor pressures of the individual components, which in turn depend on the concentration of the individual components in the blend. To illustrate how the vapor pressures of the components may be calculated, consider a mixture of two hydrocarbon liquids, A and B. At a given temperature, the partial vapor pressures of components A and B are given by Raoult’s Law [2, 3]: pA ¼ xA pAo
pB ¼ xB pBo
ð18:7Þ
where xA and xB are the mole fractions of A and B, respectively, given by xA ¼
nA nA þ nB
xB ¼
nB nA þ nB
ð18:8Þ
and nA and nB are the number of moles of A and B present (i.e., the mass of the component present divided by its molecular weight). Suppose that A and B are n-hexane and n-decane, respectively, and the mixture is at a temperature of 25 C. These hydrocarbons form an “ideal mixture” in that the molecules of A and B are so similar that they do not interact with one another, either physically or chemically
18
Ignition of Liquids
563
(i.e., the interactions between A and B are no different from the interactions between A and A, or B and B). As an example, consider a mixture containing 5 % hexane (by mass) in n-decane. Would its flashpoint be above or below 25 C? (The flashpoints of n-hexane and n-decane are 29 C and 44 C, respectively.) This can be ascertained by calculating the partial vapor pressures of the two components at 25 C and using Le Chatelier’s Principle (see Chap. 17) to discover if the total vapor pressure ( ptotal ¼ pn-hexane pn-decane) is above or below the lower flammability limit. The principle states that a mixture of flammable vapors in air will be at the lower flammability limit if X li ¼1 ð18:9Þ Li i where li is the percentage composition (molar proportion) of component i in the vapor-air mixture and Li is the corresponding value for the lower flammability limit of component i. To calculate the equilibrium partial vapor pressures of n-hexane and n-decane above a 5 % hexane/95 % n-decane mixture (by mass), the respective mole fractions must be calculated; thus, xnhexane ¼
0:05=MW A 0:05=MW A þ 0:95=MW B
xndecane ¼
0:95=MW B 0:05=MW A þ 0:95=MW B
xnpentane ¼ xndecane
ð18:10Þ
where the molecular weights are MWA ¼ 86 and MWB ¼ 142. According to Equation 18.6 and Table 18.3, the partial pressures of n-hexane and n-decane are 10.66 mmHg and 1.65 mmHg, respectively. Using Equation 18.8 with Ln-hexane ¼ 1.2 % and Ln-decane ¼ 0.75 % (see Table 18.2), 10:66=760 1:65=760 þ ¼ 1:46 0:012 0:0075
indicating that the mixture is above the lower flammability limit at 25 C (i.e., the flashpoint of this mixture is below 25 C). Example 4 Determine by calculation whether ndecane containing 1 % n-pentane (by volume) would be classified as a Class 1C or a Class II flammable liquid according to the NFPA Standard. [14] (This is equivalent to posing the question, “Is the flashpoint above or below 37.8 C?”) Solution This calculation is identical to that discussed previously, but the densities of the two liquids must be taken into account and the calculation carried out at 37.8 C. The mixture can be taken as 0.01 626 kg of n-pentane + 0.99 730 kg of n-decane (where the densities of n-pentane and n-decane are 626 kg/m3 and 730 kg/m3, respectively). The mole fractions are
ð0:01 626Þ=MW A ð0:01 626Þ=MW A þ ð0:99 730Þ=MW B
ð0:99 730Þ=MW B ¼ ð0:01 626Þ=MW A þ ð0:99 730Þ=MW B
where now MWA ¼ 72 (the molecular weight of pentane) and MWB ¼ 142. These give xn-pentane ¼ 0.0141 and xn-decane ¼ 0.986. From Equation 18.6 and Table 18.3, the saturated vapor pressures of n-pentane and n-decane at 37.8 C are 713.11 mmHg and 3.773 mmHg, respectively, so that the partial pressures are
ð18:11Þ
ð18:12Þ
10.05 mmHg and 3.72 mmHg. Applying the Le Chatelier Principle (with the lower flammability limit of n-pentane vapor as 1.4 %), X li 10:05=760 3:72=760 þ ¼ 1:6 ¼ 0:014 0:0075 L i i ð18:13Þ
564
D.D. Drysdale
This is above the lower flammability limit and, consequently, the mixture has a flashpoint below 37.8 C and is definitely not a Class II liquid. (Further calculation could be carried out to ascertain if the mixture is Class IB or IC; see below.) This calculation reveals that the partial vapor pressure of the more volatile component can be disproportionately high and for this reason it will evaporate from the mixture much more rapidly than the less volatile component. Consequently, care must be taken when determining the flashpoints of such mixtures. The liquid to be tested should be kept in a closed container and a sample transferred to the flashpoint apparatus as quickly as possible to minimize evaporative loss. In some circumstances, it might be wise to refrigerate the liquid and chill the apparatus. The author has experience of assessing the flashpoint of a sample of crude oil that (without refrigeration) gave a flashpoint of 28 C, but a flashpoint of 15 C occurred if the liquid (and the apparatus) was cooled to 0 C before opening the sample container. (The problem of evaporative loss is also encountered in the more extreme example of trying to identify traces of gasoline or other flammable liquids that may have been used in an arson attack.) In the examples discussed above, the vapor pressure of liquid mixtures was calculated using Raoult’s Law (Equation 18.7), which applies only to ideal mixtures such as blends of hydrocarbons. It is important to note that many other liquid mixtures, such as alcohol and water, are not ideal as there is some interaction between the molecules of the different components (A and B). Instead of Equation 18.7, it is necessary to use Equation 18.14: pA ¼ αA pAo
pB ¼ αB pBo
ð18:14Þ
where αA is known as the activity of component A in the mixture, and pAo is the saturation vapor pressure of pure A, and so on. The activity coefficient αA is the product of the mole fraction of A (Equation 18.15) and the activity coefficient γA: αA ¼ γA nA
αB ¼ γB nB
ð18:15Þ
where γA is the activity coefficient of component A in the mixture (note that for a pure liquid,
Table 18.4 Examples of data for the Van Laar equation for binary (two-component) systems [15] Component A Ethanol Methanol Acetone n-Heptane
Component B Water Water Water CCl4
CA 0.67 0.25 0.89 0.2164
CB 0.42 0.20 0.65 0.0618
γ ¼ 1). For a two-component mixture of A and B, the activity coefficients are given by the Van Laar equations: log10 γA ¼ log10 γB ¼
CA ½1 þ ðCA xA =CB xB Þ2 CB
ð18:16Þ
½1 þ ðCB xB =CA xA Þ2
Essentially the same set of calculations can be carried out to establish the flammability properties of nonideal mixtures, but the activity coefficients (Equations 18.15 and 18.16) must be calculated from Equations 18.16 using data such as those contained in Table 18.4. Another more general data set than that given in Table 18.4 is given by Babrauskas [16].
Effect of Atmospheric Pressure on Flashpoint The calculations that are provided above all refer to the standard atmosphere at sea level where the pressure is 101.3 kPa (760 mmHg), conventionally normalized as 1 bar. If the atmospheric pressure changes, this change has no significant effect on the vapor pressure, which is a function of the temperature of the liquid. At a constant temperature but a reduced pressure, the vapor-air ratio in the headspace will be increased (i.e., it will become richer in fuel). This has significant consequences for liquid fuels because it will reduce the flashpoint. Consider the following argument. In Example 3, the temperature at which the saturated vapor pressure of n-decane corresponds to the lower flammability limit was shown by calculation to be 45.2 C, which compares well with the measured value of the closed cup flashpoint (44 C). At 45.2 C, the vapor pressure was
18
Ignition of Liquids
assumed to be 5.7 mmHg, which is 0.75 % of normal atmospheric pressure (760 mmHg). If the temperature remains the same (45.2 C) but the pressure is reduced—say to the value appropriate to Denver, Colorado (at 1 mile high, 631 mmHg)—then the volumetric concentration of n-decane vapor in air becomes 5.7/631 ¼ 0.009, or 0.9 %. It has been shown that the lower flammability limit is remarkably insensitive to a reduction in pressure until it falls below 200–300 mmHg (27–40 kPa) [17, 18]. Clearly, at 45 C the saturated vapor pressure of n-decane is above the lower flammability limit. The effect on the flashpoint can be shown in the following example. EXAMPLE 5 Calculate the flashpoint of n-decane if measured in Denver, Colorado, where the atmospheric pressure is 631 mmHg. Assume that the lower flammability limit of n-decane vapor is 0.75 %. SOLUTION The vapor pressure corresponding to the lower flammability limit of n-hexane is 0.75 % of 631 mmHg, or 4.73 mmHg. The calculation is exactly the same as in Example 3, except that log10( p ) ¼ log10(4.73) ¼ 0.675. Thus, 10, 912:0 þ 8:24809 T 7:573T ¼ 2384:272
565
35–63 C [19], as measured at sea level. As an aircraft gains altitude after takeoff, the air pressure in the headspace will fall relatively rapidly, while the fuel will cool rather slowly. There is the potential for the vapor-air mixture in the headspace to become flammable. On long-haul flights, of course, the hazard will be relatively short-lived as the fuel loses heat and cools to below the local flashpoint, relevant to the pressure at cruising altitude. This phenomenon is discussed in NFPA’s Fire Protection Handbook [19].
Measurement of Flashpoint and Firepoint There are a number of standard tests available for measuring the closed cup [20, 21] and open cup [22, 23] flashpoints (Fig. 18.2). The former measurement is directly related to the lower flammability limit of the fuel vapor and is used to classify liquids according to their ignition hazard [18]. Its relationship to equilibrium vapor pressure of the liquid is discussed in an earlier section.
Closed Cup Flashpoints
0:075 ¼ 0:2185
T ¼ 314:8 K ¼ 41:8∘ C The value obtained in Example 3 at normal atmospheric pressure was 45.2 C. The difference is not insignificant and could be very important for liquids close to the boundary between two classifications (see later discussion). The issue becomes more significant at higher altitudes such as Mexico City (2240 m) and Lhasa in Tibet (3650 m). In these cities, the flashpoint of n-decane would be approximately 39.4 C and 35.9 C, respectively. An interesting consequence of this relates to the headspace in the fuel tanks of aircraft. The kerosene grades of commercial aviation fuel have closed cup flashpoints in the range of
In the closed cup test, such as the PenskyMartens apparatus [20] and the Tag tester [21], the flammability of the saturated (equilibrium) vapor-air mixture in the space above the liquid surface (i.e., the headspace) is tested by introducing a small pilot flame (see Fig. 18.2). The apparatus is designed to allow the miniature explosion within the headspace to vent through an aperture that is opened to admit the pilot ignition source, which also allows the “flash” of flame to be observed. The procedure involves raising the temperature of the liquid slowly from approximately 10–20 K below the anticipated flashpoint at a rate of 5–6 K/min, introducing the ignition source at intervals corresponding to about a 1 C (1 K) temperature rise. The slow rate of heating is intended to allow enough time for equilibrium conditions to be
566 Fig. 18.2 Four of the commonly used apparatuses for determining flashpoints of flammable or combustible liquids [19]
D.D. Drysdale
Flame tip Test flame applicator device
Sample Sample
Bath
Tag closed cup ASTM D56
Bath
Tag open cup ASTM D1310 Stirrer
Test flame applicator device
Test flame applicator device
Test cup Test cup
Cleveland open cup ASTM D92
reached within the headspace (see below). The lowest temperature at which a flash of flame is observed is recorded as the closed cup flashpoint. It is expected that it can be determined to an accuracy of better than 1 C for liquids with flashpoints below 100 C. Values of the closed cup flashpoint for a range of liquids are given in Table 18.2. All refer to standard atmospheric pressure (101.3 kPa). If the closed cup flashpoint is measured when the atmospheric pressure differs from 760 mmHg, the value may be corrected using Equation 18.17:
Pensky-Martens closed cup ASTM D93
Corrected flashpoint ¼ T 0:033 ð760 PÞ ð18:17Þ where T is the measured flashpoint ( C) and P is the ambient atmospheric (barometric) pressure (mmHg). This is intended for relatively small excursions that are commonly experienced on a day-to-day basis. No guidance is given that is relevant to high-altitude locations. In general, there is reasonable but not exact agreement between measured values and those calculated on the basis that the vapor pressure
18
Ignition of Liquids
must correspond to the lower flammability limit. The reason for this may be that the lower flammability limit is based on the ability of a flame to propagate approximately 75 cm inside a vertical tube, 5 cm in diameter [24], whereas the flashpoint is observed as a localized ignition in the vicinity of the ignition source. Similar localized ignition occurs in the flammability limit apparatus but at a concentration of fuel in air that sustains only limited flame propagation. If this explanation is accurate, the “calculated” flashpoint would be expected to be greater than the measured one—as indeed the calculation above shows (Example 3). Care should be taken when testing liquids of reduced flammability, such as certain chlorinated hydrocarbons. James and Tyler [25] investigated reports of fire and explosions that involved a commercial cleaning fluid, of which the principal component was methyl chloroform (1,1,1 trichloroethane, CCl3CH3). This compound does not give a flashpoint in the standard test, but a flashpoint of 12 C was recorded in vessels of diameter greater than 12.4 cm [26]. Babrauskas [16] draws attention to a problem with blends containing halogenated components. If these are of high volatility, the blend may give a high flashpoint as a consequence of the inhibiting effect of the halogenated component. However, if this halogenated component is lost as a result of preferential evaporation over a period of time, the effective flashpoint can decrease, which is the reverse of the effect of the preferential loss of lighter hydrocarbons from fuel blends as discussed above. The closed cup flashpoint is sometimes referred to as the “lower flashpoint.” Although not widely used, this term does emphasize the link to the lower flammability limit of the vapor and allows the concept of the “upper flashpoint” to be introduced. This term corresponds to the temperature at which the vapor concentration in the headspace is at the upper flammability limit, signifying that the mixture will not ignite when an ignition source is introduced, although a weak diffusion flame may exist briefly at the open aperture. Upper flashpoint is seldom measured, although Hasegawa and Takishi [27] have
567
obtained some results in the Setaflash apparatus [16]. It is useful in identifying the temperature range within which the vapor-air mixture in the headspace is flammable. For example, at ambient temperatures, the vapor-air mixture in the headspace of a gasoline tank is well above the upper flammability limit and cannot be ignited. However, the upper flashpoint of the lower alcohols (in particular methanol and ethanol) appears to be in the mid-20s, only 10–15 K or so above the lower flashpoint. This means that at ambient temperatures (say, 15–20 C) a partially full can of alcohol contains a flammable vapor-air mixture that can be easily ignited. This is a significant hazard that can give rise to serious consequences. For example, if an attempt is made to top-up a conventional flambe´ lamp directly from the fuel container before the flame has extinguished and if the temperature of the alcohol in the container is between the lower and upper flashpoints, flame will propagate into the container, perhaps causing it to burst or otherwise expel burning liquid. Such occurrences have led to a number of serious accidents in restaurants [28]. Provision of a flame arrester in the opening of the container would prevent such an occurrence.
Open Cup Flashpoints and Firepoints Open cup flashpoints are not routinely available in the literature although they are clearly relevant to the ignition of open pools of liquid. They are determined using an open cup, the most common of which is the Cleveland apparatus [22] as shown in Fig. 18.2. Instead of the vapor accumulating immediately above the liquid surface, it is lost to the atmosphere by diffusion. Consequently, the concentration of vapor in air deceases with height above the liquid surface. In the standard test, the ignition source (a small diffusion flame at the end of a swivel arm) is moved across the top of the cup, no more than 2 mm above its rim, in a trajectory that carries the flame over the center. The process of heating the fuel is essentially the same as for the closed cup test, but in this case the result is more strongly apparatus
568
D.D. Drysdale
a
b Decane
n -Decane
60
Decane
64 Temperature (°C)
Temperature (°C)
64
56 Firepoint Flashpoint 52
60
56 Firepoint 52
0
2
4
6
8
10
12
Height of ignition source (mm)
0
2
4
6
8
10
12
Height of ignition source (mm)
Fig. 18.3 Open cup flashpoint (o) and firepoint (•) of n-decane as a function of the height of the ignition source above the liquid surface. (a) Flashpoint, revealing how the onset of sustained burning occurs when the temperature of the liquid is above the firepoint
(61.5 C); (b) Firepoint as a function of the height of the ignition source, showing that it is relatively insensitive to heights less than about 9 mm. The arrow shows the height of the ignition source in the standard test [29]
dependent. A flash of flame is observed when the ignition source first encounters a mixture at the lower flammability limit. For this reason, the measured open cup flashpoint is very sensitive to the height of the ignition source above the surface. This was demonstrated very clearly by Glassman and Dryer [29], as shown in Fig. 18.3a. Clearly, this measurement is apparatus-specific and cannot provide information about the ignitability of the liquid that can properly be generalized—the flashpoint of an open pool of liquid will depend on the distance the vapor has to travel before meeting a suitable ignition source. Indeed, instead of observing a flashpoint, the liquid may catch fire and continue to burn (i.e., its temperature is above the firepoint [see Fig. 18.3a]). This burning will occur when fuel vapors are being released at a high enough rate to support a diffusion flame. At the flashpoint (closed cup and open cup), the mixture is fuel lean and all the fuel vapor is consumed in the premixed flame. However, if the temperature of the liquid is high enough to produce a fuel-rich vapor-air mixture, a self-sustained diffusion flame becomes possible, as illustrated clearly in Fig. 18.3a, which reveals that a minimum fuel temperature must be achieved for this result to occur. This minimum temperature at which a self-sustaining diffusion flame becomes possible is known as the
firepoint. Glassman and Dryer [29] found the firepoint to be much less sensitive to the height of the ignition source, as shown in Fig. 18.3b. In general, firepoints are not routinely measured and there is not a good database. Some values quoted by Babrauskas [16] are given in Table 18.5. A different selection is given by Kanury [9], but these are all blends that are poorly defined. Typically the firepoint is 10–20 K above the closed cup flashpoint, but one cannot rely on this generalization. The difference appears to be erratic and can be much greater and more uncertain for high-flashpoint liquids (see Babrauskas [16]). The lower alcohols seem to behave in a very different manner. Glassman and Dryer [29] found the open cup flashpoints and the firepoints of methanol and ethanol were equal and—even more surprisingly—considerably less than the closed cup flashpoint. This anomaly disappeared if a spark ignition source was used instead of a flame in the open cup measurement: the open cup flashpoint and the firepoint remained equal but were now higher than the closed cup flashpoint (see Table 18.5). This observation has still to be explained satisfactorily, but clearly the behavior of the alcohols is not typical. Several attempts have been made to define the firepoint of liquids (and indeed solids) in terms of the heat and mass transfer processes involved
18
Ignition of Liquids
569
Table 18.5 Some values of closed cup flashpoint, open cup flashpoint, and firepoint temperatures
n-Hexane n-Heptane Methanolb n-Octane Ethanolb s-Butanol m-Xylene p-Xylene n-Butanol n-Nonane o-Xylene JP-6 n-Decane Decalin Tetraline Bicyclohexyl n-Dodecane Fuel oil no. 2 Fuel oil no. 6 Glycerol Motor oil
Closed cup FP ( C) 22 4 12 12 13 24 25 25 29 31 32 NA 44 NA NA NA 74 124 146 160 216
Open cup FP ( C) a
1 1.0, 13.5b 17 6, 18.0b NA NA 31 36 37 36 38 52 57 71 74 NA NA NA 176 NA
Firepoint ( C) NA 2 1.0, 13.5b 18 6, 18.0b 29 44 44 36, 38, 50 42 42 43 61.5, 66 63 74 79 103 129 177 207 224
Unless otherwise stated, these data come from the Factory Mutual Handbook, as quoted by Babrauskas [16] NA Not available a The open cup flashpoint of n-hexane is quoted as 26 C in the original Factory Mutual Handbook and repeated in Babrauskas [16]. This is incorrect b Data from Glassman and Dryer [29]. The lower values were obtained with ignition by a pilot flame. The upper values refer to spark ignition
in the combustion of the fuel vapors close to the fuel surface. For a diffusion flame to become established at the surface of the liquid, the rate of evolution of flammable vapor must be greater than a certain critical value. It has been argued that it is determined by the need to establish a self-sustaining process whereby the energy required to maintain (and promote) the evolution of vapors comes from the flame by convective and radiative heat transfer. However, if the flow rate of vapors is too small, the flame will be too close to the surface and self-extinguish as a consequence of heat losses to the surface. Valuable contributions to the definition of firepoint as a criticality have been made by
Roberts and Quince [30], Rasbash [31], and Beyler [32]. In particular, they have used Spalding’s B-number, first used to describe the rate of burning of fuel droplets [33], to develop the concept of ignition [30, 31] and extinction [31, 32] criticalities. It is a dimensionless transfer number that can be used to express the conservation of heat (BH) or mass (BM), the values of which can be used to define the rates of heat and mass transfer, respectively. They can be expressed as follows: mog H=r c T g T ls BH ¼ ð18:18Þ Q and mfs mog =r BM ¼ 1 mfs
ð18:19Þ
where mog is the mass fraction of oxygen in the atmosphere, mfs is the mass fraction of fuel vapor immediately above the liquid surface, H is the heat of combustion of the fuel vapor, r is the stoichiometric ratio (mass of O2 required to burn unit mass of fuel), c is the specific heat, Tg is the ambient air temperature, and Tls is the temperature of the surface of the liquid. BH and BM are assumed equal when the diffusivities of heat and mass are equal (the Lewis number is unity). However, this assumption carries with it the hidden assumption that radiative heat transfer can be ignored and only convection need be considered. For small flames—particularly those associated with the burning of small droplets for which this approach was developed—this approximation is reasonable. The rate of burning can be expressed as a mass ˙ 00 , the rate of mass transfer per unit surface flux (m area) in terms of the B-number using the following equation: 00
m_ ¼
h lnð1 þ BÞ c
ð18:20Þ
where h is the (convective) heat transfer coefficient. Following the argument developed by Roberts and Quince [9], which invokes the concept that there is a critical temperature below
570
D.D. Drysdale
which a flame will extinguish (see Chap. 5), a critical B-number can be formulated as Bcrit
mog T f , max T ls ¼ r T f , max T f , crit
enough from the surface so that the quenching process does not occur. The critical flow rate of vapors at the firepoint will, therefore, be given by
ð18:21Þ
where Tf,max is the theoretical flame temperature assuming no heat losses to the surface of the liquid, Tf,crit is the critical flame temperature below which the flame will extinguish, and Tls is the surface temperature of the liquid—the firepoint temperature. Bcrit can be calculated from Equation 18.19 for BM, substituting for mfs the mass concentration of fuel vapor above the liquid surface at the firepoint (calculated from the saturation vapor pressure derived from data similar to that contained in Table 18.3), allowing the critical temperature hypothesis to be tested. The theoretical temperature Tf,max can be deduced from a heat balance at the surface, assuming that the flame loses no heat to the surface (i.e., it is adiabatic). For a range of fuels (identified in Table 18.2), Tf,crit was found to have a mean value of 1350 C (albeit 100 K), which is not inconsistent with measured and predicted values for premixed flames close to the lower flammability limit (about 1300 C) (see Chap. 5). Observations of the firepoint temperatures of a number of fuels reveal that the saturated vapor pressure at the firepoint is above stoichiometric. Roberts and Quince [9] reported values from 1.33 to 1.92 stoichiometric. Clearly, the mixture immediately above the surface is rich by a significant margin but is still within the flammability range. (Zabetakis [24] has shown that the upper flammability limit is between 2.5 and 4 the stoichiometric concentration.) The firepoint represents a criticality, the rate of evolution of vapors being just sufficient to allow the establishment of a diffusion flame at the surface. It is closely linked to the “quenching distance,” a characteristic of premixed flames that are quenched (extinguished) within 1 or 2 mm of the surface due to heat losses and (probably) the loss of free radicals (see Chap. 12). The flow rate of vapors at the firepoint must be sufficient to allow a nascent diffusion flame to form far
h 00 m_ crit ¼ lnð1 þ Bcrit Þ c
ð18:22Þ
00
˙ crit has not been determined for any liquid fuels m but values have been reported for a range of solids (see Chap. 36).
Classification of Liquid Fuels Although this chapter is entitled “Ignition of Liquids,” most of the emphasis has been on understanding the flashpoint, the minimum liquid temperature at which the vapor can be ignited. It is clear that it is the firepoint that determines whether or not sustained flaming of the liquid will occur, yet combustible liquids are classified—quite properly—in terms of their flashpoints. Measurement of the closed cup flashpoint provides a method of classifying flammable liquids according to the hazard they represent. Systems of classification have been developed in several countries, but they have as the common basis the need to identify and make provision for those liquids that can be easily ignited at ambient temperatures. Thus, in the United Kingdom under the Highly Flammable Liquids and Liquefied Petroleum Gases (HFL/LP-gas) Regulation 1972 [34], liquids with closed cup flashpoints less than 32 C were classified as “highly flammable liquids.” NFPA 30, Flammable and Combustible Liquids Code [14], assigns liquids with flashpoints less than 37.8 C (100 F) to a similar category, known as Class I. Figure 18.4 compares the U.K. and U.S. systems and shows how the Class I liquids are subdivided into three subclasses A, B, and C. The boundary between I (A and B) and IC is set at 22.8 C (73 F), whereas Class IA liquids are distinguished from Class IB in having normal boiling points less than 37.8 C (100 F). “Flammable liquids” (1972 Regulations, U.K.) and Class II liquids (U.S.) have a common upper bound of 60 C. These are liquids that must
18
Ignition of Liquids
Fig. 18.4 A comparison of the U.K. and U.S. classifications of flammable and combustible liquids with the UN Globally Harmonized System
571 U.K.
GHS
U.S.A.
Class IIIB 100°C
Combustible liquids
93.4°C
212°F 200°F
100°C
Combustible liquids
Class IIIA 60°C
50°C
60°C
140°F
Flammable liquids 32°C
Class II 37.8°C
50°C 100°F
Class IC
Flammable liquids* 23°C
73°F
0°C
Highly flammable liquids
Class IA + IB 32°F
0°C
Highly flammable liquids*
GHS—UN “Globally Harmonized System” *Liquids with flashpoint 10 % in dry weight), so it is negligible in most residential fire scenarios but important in the natural environment (see section “Smoldering Wildland Fires”). The pyrolysis subfront (Equation 19.1) follows the preheating and drying when the fuel temperature increases above a certain threshold. This threshold3 is
approximately at 200 C for polyurethane, and to 250 C for cellulose [15]; subsequent heating above this temperature increases the pyrolysis rate and char production. The oxidation subfront consumes char and oxygen, releasing heat. It involves the oxidation of the fuel and the char, but char oxidation (Equation 19.2a) is much more exothermic. The oxidation and pyrolysis subfronts may overlap in space. The extent of this overlap depends on the propagation conditions [16] and is discussed in the section “Smoldering Kinetics”. It is convenient to characterize onedimensional smoldering by its direction of propagation relative to the direction of the oxygen supply. Two one-dimensional modes exist. Forward propagation occurs when the oxygen supply is moving in the direction of the smolder front. Opposed propagation (also called reverse) occurs when the oxygen supply is moving opposite to the smolder front. These are illustrated in Fig. 19.2. The most familiar example of forward propagation is a cigarette, as seen in Fig. 19.2 (right). Although one-dimensional spread is an idealized situation, it can occasionally be found in fires, but in general, real smoldering fires are multidimensional and cannot be classified into a single mode.
3 The onset of pyrolysis or oxidation does not occur at one fixed temperature but it is known to be a function of the heating rate and start over a range of temperatures; higher onset temperatures are observed for higher heating rates. See Rein et al. [15] and the section “Smoldering Kinetics” for evidence of this.
19
Smoldering Combustion
In forward propagation, the pyrolysis subfront is located at the leading edge of the front, and the oxidation subfront at the trailing edge, where oxygen is drawn (see Fig. 19.2, right). The oxygen supply flows first through the char where it is consumed. Then the hot, oxygendepleted gases of combustion flow through the virgin fuel. This convective transport results in enhanced drying and preheating, but it also results in water condensation on the virgin fuel as the combustion gases cool down. In opposed propagation, the oxygen supply flows first through the virgin fuel, and through the preheating and evaporation subfronts before reaching the char where the oxidation subfront is located. Then the hot, oxygen-depleted gases of combustion flow through the char and ash residues. This means that heat is transferred by convection in the opposite direction to the virgin fuel, reducing the extend of the drying and preheating, which in turn results in a weaker smoldering process. Consequently, forward smolder is faster than opposed under the same fuel and oxidizer supply, and allows for more complete combustion of the fuel [17]. In opposed propagation, the pyrolysis and oxidation subfronts overlap on top of each other from the leading edge to the trailing edge [16].
585
and fuel kinetics, with the oxygen supply rate playing a secondary role. Above a critical threshold of heat supply, the temperature increase initiates endothermic pyrolysis, which is followed by the onset of oxidation. When the heat released by oxidation is high enough to balance the heat required for the endothermic processes (heat losses, pyrolysis, drying and preheating of fuel), propagation occurs and the reaction might become self-sustaining (only then oxygen supply rate will play an important role). This section discusses four types of ignition sources: radiant, conductive, ember and selfheating. For all four, it is proven that the critical energy condition needed for smoldering is significantly lesser than that for flaming. The results discussed here are on individual fuel samples. But note that a particularly important smoldering scenario, that of upholstery and bedding fires, is a composite problem with the ignition propensity of both the fabric and the substrate contributing to the overall behavior [18].
Radiant Ignition
The process of smoldering ignition requires the supply of heat, and is governed by heat transfer
The effects of exposing polyurethane foam to an external radiant heat flux of increasing magnitude is illustrated in Fig. 19.3. The heat flux needed to initiate smoldering is significantly lower than that for flaming (see Table 19.1). For instance, the critical radiation heat flux for smolder ignition of polyurethane foam is
Fig. 19.3 Images of polyurethane foam samples exposed to increasing levels of radiation (from left to right): (a) virgin foam (not exposed to radiation), (b) charred foam in which a
smoldering front did not propagate, (c) sample in which smoldering propagated, and (d) sample which underwent flaming ignition (By R. Hadden [19], CC BY license)
Ignition
586
G. Rein
7 kW/m2, while for spontaneous flaming is 30 kW/m2 [19]. For piloted flaming ignition, the critical level is 13 kW/m2 (Chap. 36). It has been shown that the onset of smoldering involves a range of threshold temperatures. A single threshold temperature is not a valid criterion for ignition but it is part of a multi-criteria signature [20]. Several experimental studies have found that the minimum temperature measured during ignition of polyurethane foam is in range from 300 C to 450 C [19–21]. This is much lower than the threshold surface temperature of 600 C required for spontaneous flaming ignition of the same material [19]. Figure 19.4 (left) shows the experimental data on the peak temperature reached inside a slab of polyurethane foam for the cases of no ignition, smoldering or flaming ignition. The same experiments (see Fig. 19.4 (right)) also show that the time to Table 19.1 Critical heat fluxes found experimentally for the ignition of smoldering and spontaneous flaming combustion in samples of different sizes (Data from Hadden et al. [19]) Sample size (mm) 50 100 140
Critical heat flux for smoldering ignition (kW m2) 18–19 8–9 7–8
Critical heat flux for flaming ignition (kW m2) 32–45 32–37 30–31
smoldering ignition by radiation depends on the heat flux level and ranges from 1 to 20 min for a heat flux of 45–7 kW/m2 respectively. Flaming ignition was observed for heat fluxes above 30kW/m2 and was fast, less than 1 min. The dependence of the time to ignition with radiant heat flux shown in Fig. 19.4 (right) resembles a an inverse square-root law with the incident heat flux. This suggests that smoldering ignition can be explained in terms of heat transfer, in the same way that a an inverse square-root law explains the flaming ignition of a thermally thick fuel (Chap. 21). This law originates from the time it takes for heat conduction to result in a critical temperature at a key location. For flaming, the key location is the free surface of the fuel, but for smoldering the key location is inside the fuel bed, at a sufficient depth such that an insulating layer of char is formed over the oxidation front [21]. The concept of a critical depth for ignition is not sufficiently studied yet but could be expected to vary for different materials and external conditions in the scale from 1 to 10 cm roughly.
Conductive Ignition The heat source that can start a smoldering fire with the lowest heat flux is the conductive type.
900
18
700
Time to ignition, min
Maximum temperature, °C
20
No ignition Smouldering Flaming
800
600 500 400 300
16 14 12 10 8 6 4
200 100
2 0
10
20
30
40
50
Heat Flux, kW/m2
Fig. 19.4 Radiant ignition of smoldering and flaming in polyurethane samples of different sizes in still air. (Left) Maximum temperatures observed. (Right) Time to
0
0
10
20
30
40
50
Heat Flux, kW⋅m−2
ignition. Red, green and blue represent 50, 100 and 140 mm side square samples respectively (Data from Hadden et al. [19])
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Smoldering Combustion
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This scenario occurs when a large and hot object is in direct contact with the fuel bed. Heat is transferred by conduction, but in porous fuels, convection also plays a role. Anthenien and Fernandez-Pello [21] studied the initiation of smoldering using an electric heater in contact with a sample of polyurethane foam under forced airflow. Ignition was reported at heat fluxes as low as 3 kW/m2 and the relationship between time to ignition and heat flux was shown to follow a an inverse square-root law. Ignition was found to be weakly dependent on the airflow. Conductive ignition has also been studied on a bed of particles [22]. A series of beds of anthracitic coal particle of uniform diameter ranging from 7 to 45 mm was investigated inside a cubic box (side of 100 mm) with the top side open to the atmosphere and multiple perforations on the other sides. The heat source was an electric wire that delivered 80 W. Figure 19.5 shows that the relationship of the time to ignition with particle diameter has a ‘U’ shape. It was not possible to ignite a bed which particle diameter was smaller than 7 mm. For very small particle sizes, the bed exhibits poor internal convection which limits the airflow and a long ignition time is required. But as the particle sizes increase, the porosity and the flow permeability of the fuel bed increase and a minimum time to ignition of 130 min (average) is required for a particle diameter of 25 mm. As particles become larger, the inter-particle
Ignition by Embers In close connection with conductive sources, a fuel bed can also be ignited by hot embers. This is related to ignition by hot works and also to the phenomenon of spotting in wildland fires, when lofted embers land downwind, leading to secondary fires in the wildland or in urban areas remote from the originating flame front. Ignition by embers is a transient phenomenon involving the loss of heat from the ember to the fuel by conduction and convection. Embers can be classified by material (metal or biomass) and thermal state (hot, smoldering or flaming). Manzello et al. [23] compared the ember ignition of three fuel types and found that a bed of shredded paper was much more prone to smoldering than pine needles or mulch. The experimental study of Hadden et al. [24] found a relationship between ember size and the critical initial temperature required for ignition of a bed of cellulose powder. They used steel spheres with diameters in the range 0.8–19 mm at initial temperatures between 500 C and 1300 C. Smaller embers require higher temperatures to initiate combustion. Their data shows two distinct boundaries as the ember temperature
300
250
Time to ignition, min
Fig. 19.5 Experimentally observed relationship between time to ignition and particle size in a bed of anthracite coal (Data from Hadden and Rein [22])
conduction rate decreases resulting in a longer time to ignition.
200
150
100
50
10
20
30
Particle size, mm
40
50
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increases, one separating no-ignition from smoldering ignition, and the other from smoldering to flaming ignitions. The minimum ember temperature at which smoldering could be initiated was 550 C, and the minimum temperature for flaming ignition occurred at 650 C. Krause and Schmidt [25] also observed a decrease of the critical temperature with ember size for a series of organic powder samples (cork, beech and cocoa), and reported a minimum temperatures of 400 C for smoldering ignition.
Self-Heating Ignition Self-heating of a solid fuel can initiate smoldering fire deep within a pile of fuel without any external source, even at ambient temperatures. Self-heating refers to the tendency of certain porous solid fuels to undergo spontaneous exothermic reactions in oxidative atmospheres at low temperatures ([2, 26], Chap. 20). It is a well-known problem in the store of large amounts of carbon-rich materials (e.g., waste, coal heaps, organic powders) and in the process industries. The process is as follows: initially, the pile of the material releases small amounts of heat by very slow oxidation at ambient temperature. Somewhere near the center of the pile, where the fuel is most insulated, the heat accumulates in the long term and results in a sustained increase of the local temperature, which in turn accelerates the oxidation rate. Large pile sizes and poor ventilation conditions facilitate the buildup of heat. The process selfaccelerates for some time (hours, days or weeks) and above a certain threshold temperature it leads to a thermal runaway. This results in a smoldering fire that can spread from the inside to the outside, and may undergo transition to flaming at a later stage when it reaches the free surface (discussed in section “Transition to Flaming”).
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generation and heat loss from the system. The rate of heat loss scales with the surface area, and the rate of heat generation scales with the volume. Consequently, as the size of a sample decreases, the surface -to-volume ratio4 of the smoldering front increases. Below a certain size, heat losses overwhelm heat generation and ignition will not occur. Palmer [27] found experimentally that the minimum thickness for smoldering of horizontal layers of sawdust was around 10 mm. Ohlemiller and Rogers [28] found the minimum thickness for cellulosic insulation to be 35 mm. A more recent experimental investigation of the effect of sample size [19] is reported in Table 19.1 and Fig. 19.4. Both the critical heat fluxes for smoldering and flaming ignition increase with decreasing sample size, with smoldering ignition being significantly more sensitive to the sample size than flaming. Krause and Schmidt [25] studied the ignition of organic dust samples by embers, and found that the larger the samples, the lower the critical ember temperature. The fact that large samples are easier to ignite than small samples has implications for testing standards and the translation of results from small-scale testing to real scale. The process of ignition is related to selfsustained propagation (as discussed in the section “Smoldering Spread”) which allows an approximate analytical treatment. The critical size Lc for self-sustained propagation in a prismatic sample of square cross-section can be estimated by Equation 19.3 provided by Rein [9] based on the energy balance by Torero and FernandezPello [14] and Bar-Ilan et al. [29, 30]. Lc ¼
4δU ðT s T 0 Þ 00 Qs m_ O2
ð19:3Þ
where δ is the smolder-front thickness perpendicular to the propagation direction, Ts is the peak temperature, and Qs is the heat of smoldering, which all depend on the fuel. The overall heat loss coefficient U, the ambient temperature T0 and
Size Effects and Ignition There is a minimum size below which a fuel sample will not undergo ignition. This is determined by the balance between the rates of heat
4 The surface-to-volume ratio of a sample is inversely proportional to its characteristic length (e.g., thickness for a very wide layer, diameter for a cylinder, side length for a prism or diameter for a sphere).
19
Smoldering Combustion 00
the supply of oxidizer m_ O2 depend on the geometry and external conditions. For polyurethane foam, Equation 19.3 says the critical size is around 160 mm [19]. If a sample is below the critical size Lc, sustained smoldering will not be achieved. Smoldering will only spread if the heat losses are reduced or the rate of heat generation is increased, or both. The former would involve insulating the reaction front or supplying additional heat from an external source, and the latter would involve increasing the supply of oxidizer.
Smoldering Spread The spread of smoldering is controlled by the oxygen supply and heat transfer [1]. Conditions sufficient to yield smolder initiation, especially near an external heat source, might not be sufficient for self-sustained spread away from the ignition region. If the external heat supply continues, assisted propagation is possible. Otherwise, once the external heat supply ceases, smoldering reaction will be self-sustained or lead to extinction. Experimental and modeling work has demonstrated that the smolder spread rate is linearly dependent on the total air supply rate to the
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smoldering front [1, 29, 30]. Some of these results are presented in Fig. 19.6. Torero and Fernandez-Pello [14] reported than this linear increase breaks down for opposed propagation at high airflows and stars decreasing (at ~3 mm/ s for polyurethane foam slabs of 150 mm square cross section). In general, air is transported to the reaction front by convection and diffusion. Convection can be natural (buoyant) or forced. In the absence of forced flow, buoyancy tends to dominate over diffusion in regions of lesser flow resistance, for example near the free surface or in a bed of large particles. The diffusion flux is dominant when deep layers of a pile of fine particles is ignited [27]. Forced convection in smoldering fires usually takes the form of an air current flowing through the fuel bed or over the free surface of the bed. Forced convection directly flowing through the bed of the fuel is often used in laboratory studies (e.g., see Fig. 19.6). The advantage is that it provides controllable conditions to investigate the phenomena also deeper into the bed. These studies have found a critical air supply rate required for self-sustaining propagation (around 0.6 g/m2s of oxygen flow for opposed mode in a 120 mm diameter slab of polyurethane foam [30]). This critical supply
Fig. 19.6 Spread rate of smoldering assisted by airflow forced through the bed in opposed mode for a variety of materials (After Ohlemiller [7])
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rate is known to be a function of the heat losses. For example, microgravity experiments on the same polyurethane samples [30] have shown that the removal of lateral heat losses by natural convection allows self-sustained propagation at significantly lower oxygen supplies (0.3 g/m2s). When a bed of fuel is ignited locally, in general the spread will be multidimensional and include both horizontal and vertical spread. Each front will be dominated by forward or opposed propagation (or a combination) depending on the roles of buoyancy, wind and diffusion. Two important configurations are presented in Fig. 19.7 where the spread is either downwards or upwards though the fuel bed. If initiation occurs on the top surface of the fuel bed, the fire will spread laterally and downward. It leads to a void or hole in the general shape of a semi-ellipsoid or pan. Downward
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spread is dominated by forward smoldering (Fig. 19.7, left), and creates a growing layer of ash that only decreases if wind carries the particles away. The horizontal spread is enhanced by a direct supply of atmospheric oxygen, which is readily available, and the rate is significantly greater than downward spread where oxygen transfer is limited by the layer of ash and char. Combustion of the uppermost layer is typically quenched due to large convective and radiant heat losses; this leaves a very thin layer of charred material on top while smoldering continues below. The fact that horizontal spread is faster a few cm below the surface leads to the formation of an overhang pointing inwards at the rim of the void (overhang not shown in figure 19.7). Horizontal spread accelerates in response to an increased wind. Palmer [27] examined this in thin horizontal layers (3–57 mm) of
Fig. 19.7 Diagrams of downward (left) and upward (right) propagation in a porous fuel bed Huand and Rein [31] Fig. 19.8 Smoldering spread rate through horizontal layers of sawdust as a function of the horizontal airflow over the topmost layer. Circles: 120 mm particle size; triangles: 190 μm particle size; squares: 480 mm particle size (Data from Palmer [27], after Ohlemiller [7])
Smoldering Combustion
various cellulosic particles (cork, pine, beech, grass). The results in Fig. 19.8 show that the horizontal airflow has a greater effect in forward propagation, but that airflow in opposed propagation and the particle size have a weaker effect. In the absence of any forced flow over the fuel layer, the flow induced by the buoyant plume supplies oxygen for the horizontal spread at the topmost fuel layer. Oxygen then penetrates into the layer mostly by diffusion [32]. If initiation occurs deep within a layer of fuel and the nearest free surface is on the top, the fire will slowly spread upwards dominated by opposed smoldering (Fig. 19.7, right). The thick layer of virgin fuel above the reaction front hinders the oxygen supply, but also reduces the rate of heat losses. Ultimately, the spread is faster towards the free surface driven by oxygen diffusion, thus leading to fronts in the shape of an elongated bell. The reaction front usually spreads without fully consuming the char left behind. The upward case was studied in Palmer’s work [27], which consists of a collection of observations from simple experiments involving the initiation of a smoldering front at the base of sawdust heaps (cork, elm and mixed wood). Some of the results are shown in Fig. 19.9. Note the scales reported in this data; the time to smolder up through a layer 1 m deep is about 2 weeks, and the process gave little hint of its presence until it was close to the surface of the fuel heap (smoke gets trapped inside the porous bed). The slope of the curve indicates that the time for upward smolder to penetrate a fuel layer is proportional to the square of the layer depth. Palmer showed that such dependence suggests the smolder front spread is proportional to the diffusion rate of oxygen from the free surface, through the unburned fuel, to the reaction front. Data from other experiments on a variety of fuels and air supply conditions are summarized in Table 19.2.
Smoldering Kinetics The spread rate of self-sustained smoldering is typically controlled by oxygen transport and heat transfer. Yet, heterogeneous chemical kinetics
591
400
200
Time for smoldering to penetrate heap (hr)
19
100 70 40
20
10 7 4
2
1 4
7
40 10 20 Depth of fuel heap (cm)
70 100
Fig. 19.9 Upward spread of smouldering through a bed driven by air diffusion. Ignition at base of the fuel bed and spread upwards in heaps of wood sawdust. Squares: layer 0.025 m deep in 0.3 m square box; diamonds: layer 0.052 m deep in 0.3 m square box; triangles: layer 0.052 m deep in 0.6 m square box; circles: layer 0.052 m deep in 0.9 m square box (Data from Palmer [27], after Ohlemiller [7])
governs the front structure and is ultimately responsible for determining the conditions under which a material ignites and extinguishes. Smoldering combustion of a solid fuel involves multiple pathways to chemical reactions, and these pathways are not yet fully understood. In spite of the complex kinetic behavior, experimental evidence suggests that mechanisms consisting of only a few global reactions capture the most important characteristics of the chemical process and allow an approximate analysis. Smoldering chemistry in its simplest form can be understood as a two-step process: pyrolysis of fuel (Equation 19.1) produces the char that is then oxidized
Table 19.2 Experimental data on smoldering in various fuels and configurations (After Ohlemiller [7]) Fuel Pressed fiber insulation board, 230–290 kg/m3
Configuration 13 mm thick horizontal strip, width large compared to thickness 13 13 mm Pressed fiber strip at varied insulation vertical board, 230–290 kg/m3 inclinations Fiber insulation 13 50 mm board strip forward smolder
Fiber insulation 13 50 mm board strip opposed smolder
Peak temperature NA
Reference Palmer [27]
Comments Smolder velocity increased 50 % for strips with width thickness
Natural 1.6–2.8 convection mm/min
NA
Palmer [27]
Airflow over 20–1500 cm/s
790 C (900 cm/s airflow)
Palmer [27]
Smolder velocity highest for upward spread; lowest for horizontal spread Some samples extinguished due to cooling at airflows >1450 cm/s
NA
Palmer [27]
NA
Brenden and Schaffer [33]
NA
Kinbara et al [34]
820 C
Egerton et al. [35]
Air supply Spread rate Natural 0.8–1.3 convection mm/min
2.1 mm/min (20 cm/s airflow) 7.8 mm/min (1400 cm/s airflow) 1.7–2.1 mm/min
Airflow over strip, 80–900 cm/s Fiber insulation 13 mm thick Airflow 1 mm/min board (pine or sheet, horizontal, over sheet, aspen) forward smolder 10–18 cm/s Cardboard Vertical rolled Natural 3–5 mm/min cardboard convection cylinder, downward propagation, diameter 1.9–3.8 mm Shredded 8 mm diameter Natural 1.8–3 mm/min tobacco cigarette, convection horizontal, in open air Cotton Double fabric Airflow ~6 mm/min upholstery layer, 2 mm over fabric thick, horizontal, fabric, forward smolder 10 cm/s Cellulosic Various weight Natural 1.8–45 mm/min upholstery fabrics convection (depends on fabric on horizontal on substrate) substrates fiberglass, PU foam, cotton 2–4 mm/min Cotton batting, 15 cm cube, hold Natural together by metal convection (decrease as densities mesh and open to density 5–100 kg/m3 the air on all increases) sides 22 cm tall Wood char, Natural Upward packed bed of densities convection ~0.4 mm/min. 290–435 kg/m3 particles, Downward diameter ~0.05 mm/min 1–3 mm Cork, beech Mesh wire Natural 0.1–1.5 and cocoa baskets with convection mm/min and powders volumes of decreasing 0.8–200 l relationship with basket volume
Extinguishment >900 cm/s
Small dia. 2 faster than large dia.; ambient temp. effect measured
770 C
Donaldson and Smolder behavior Yeadon [36] dependent on alkali metal content Reported Donaldson and Smolder fastest on values Yeadon [36], inert fiberglass suspiciously Stiefel substrate low et al. [37] 690 C
Hagen et al. [38]
Upward 530 C. Downward 800 C
He and Behrendt [39]
260–375 C and decreasing relationship with basket volume
Krause and Schmidt [25]
Lower densities or repeated heating of sample result in higher ignition temperature Downward peak temperature decreases as the height of ash layer increases Ignition sources tested include hot body, glowing nest and electric coil
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Smoldering Combustion
593
in situ (Equation 19.2a). In this section we explore more comprehensive kinetics. To begin with, the simple two-step scheme proposed in Equations 19.1 and 19.2a can be extended to include the direct oxidation of the fuel. Char oxidation (Equation 19.2a) is the principal heat source in most self-sustained smolder propagation processes; the potential for smoldering combustion thus exists with any material that
forms a significant amount of char during thermal decomposition. The fuel is oxidized as well (Equation 19.4) but the most exothermic reaction is that of char, and therefore the simplest overall mechanisms does not include fuel oxidation. Fuel oxidation is also related to self-heating when it takes place at low temperature close to ambient (see Chap. 20).
Direct heterogeneous oxidation of the fuel: Fuel ðsolidÞ þ O2 ! Heat þ CO2 þ H2 O þ other gases þ Char ðsolidÞ þ Ash ðsolidÞ ð19:4Þ The materials for which smoldering kinetics are best known are polyurethane foam and cellulose. Kashiwagi and Nambu [40] provided a quantified three-step mechanism for cellulose, including cellulose pyrolysis, cellulose oxidation and char oxidation and accounting for three solid species; cellulose, char and ash. In flexible polyurethane foam, the presence of oxygen during degradation plays another key role, because without oxygen, many foams do not form char [41]. Rein et al. [15] provided a five-step
a
mechanism for polyurethane consisting of two foam pyrolysis, two foam oxidations and one char oxidation reaction, and accounting for four solid species (foam, β-foam, char and residue). This mechanism was developed and the kinetic constants found from thermogravimetric experiments, as shown in Fig. 19.10. This multi-step mechanism allows explaining the different contributions of the pyrolysis and oxidation reaction to the degradation of the foam in the presence of air, as seen in Fig. 19.11.
b 6
6 (Nitrogen Atmosphere)
5 Mass-loss rates [1/s] x 103
5 Mass-loss rates [1/s] x 103
20°C/min
(Air Atmosphere)
20°C/min
4
3 10°C/min 2
1
0 200
3 10°C/min 2
5°C/min
1
5°C/min
100
4
300
400
Temperature [°C]
Fig. 19.10 Thermogravimetric mass loss rate of polyurethane foam in; (a) nitrogen atmosphere, and (b) air atmosphere, as a function of temperature for three heating
0
100
200
300
400
Temperature [°C]
rates (Symbols are data from experiments of Chao and Wang [42], and lines are data from numerical simulations of Rein et al. [15])
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a
b
12
10 foam
Oxidation rates ω [1/s] x 103
Pyrolysis rates ω [1/s] x 103
10
12
8
6
4
2
β-foam
0
8
β-foam char
6
4 foam 2 0
100
200
300
400
100
Temperature [°C]
Fig. 19.11 Numerical results for the different reactions rates (pyrolysis on the left, oxidation on the right) in polyurethane foam decomposition in air atmosphere.
200
300
This simulates the experimental thermogravimetric data of Fig. 19.10 (right) and allows explaining the origin of the three mass-loss peaks (Data from Rein et al. [15])
15 Heat released rate [kJ / m3]
400
Temperature [°C]
foam β-foam char
20 10 10 5 0 0 t = 900s
t = 600s
450 0.2
0.2
200 0.1
0
55
65
Distance from Igniter [mm]
75
0.1
350
40
Oxygen
Temperature [°C]
400
60
Distance from Igniter [mm]
Fig. 19.12 Numerical results for the front structure during self-propagation; (left) opposed smoldering; and (right) forward smoldering. Top figures show the heat-
released rate of each reaction (positive for oxidation, negative for pyrolysis). Bottom figures show the temperature and oxygen profiles (Data from Rein et al. [16])
The separation of pyrolysis from oxidation is essential in any smouldering kinetics scheme. It was the work of Rein et al. [16] that proved that the same kinetic mechanism was able to explain both forward and opposed smoldering. In forward smoldering propagation (Fig. 19.12,
right), the oxidation and the pyrolysis reactions form two distinct propagating sub fronts. The pyrolysis sub front arrives first to the virgin foam and then followed by the oxidation sub front. In opposed smoldering (Fig. 19.12, right), the oxidation and the pyrolysis reactions overlap
19
Smoldering Combustion
to form a single front. Previously to the work of Rein et al. [16], smoldering chemistry had been described as a function of the propagation mode: forward smoldering with two-step chemistry, and opposed smoldering with one-step chemistry. Smoldering kinetics is an immature field of solid phase chemistry due to is complexity and secondary role in fire spread. It has been the objective of few studies to date. Despite the recent advances reviewed in this section, the topic remains mostly undeveloped.
Suppression A smoldering fire can be extraordinarily difficult to suppress. Experiments on heaps of coal show that smoldering requires large amounts of water. For example, the amount of water required to suppress smoldering coal was measured to be in the range from 1 to 2 l of water per kg of burning fuel. Moreover, smoldering requires lower oxygen concentration to be smothered, around 10 % O2, compared to 16 % O2 for flaming [43, 44]. Oxygen removal is insufficient unless it is continued until the whole fuel bed is cooled to a point where oxygen readmission will not cause re-ignition. Because volumetric cooling of a fuel bed is a very slow process (long thermal response time), this means that the holding time for smothering are much longer for smoldering than for flaming5 (months vs. hours) [22]. One practical problem in suppressing a large fuel bed is the tendency of the extinguishing fluid agents to follow higher permeability channels and thereby miss significant in-depth burning zones. Channeling arises when a substantial fraction of the fluid takes the same flow path through the bed, resulting in limited contact surface area between the agent and the burning fuel. This, coupled with the lower residence times in regions of high permeability because of the high flow velocities, requires large quantities of water for suppression.
5 Avoidance of flaming re-ignition of a non-porous fuel requires cooling of the surface layer only.
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Hadden and Rein [22] investigated three water suppression methods (pipe, shower and spray) on a small-scale coal bed. They showed that the most efficient method with respect to total water required is the shower. However, using a spray results in less water runoff and thus offers a higher efficiency. The injection pipe is significantly less efficient, requiring three times more water than a spray, and resulting in >80 % lost as run-off. Tuomisaari et al. [45] tested a number of extinguishing agents (liquids: water, water with additives; gases: N2, CO2, Ar and Halon) in series of tests on a small bed of smoldering wood chips. The result was that gaseous CO2, injected from the bottom, was found to be the most effective.
Gas Emissions Gas emissions from smoldering fires differ significantly to those from flaming fires. First, the emissions rate per unit area is much lower but also the chemistry is different. Smoldering is characteristically an incomplete combustion, releasing species and quantities that substantially depart from that in stoichiometric and complete combustion. For example, the CO/CO2 ratio which can be thought of as an index of the incompleteness of combustion is ~0.4 in smoldering but ~0.1 in flaming combustion [46]. The presence of pyrolysate in the products of smouldering, significantly contributes to of a complex gaseous mixture including volatile organic compounds (VOC), polyaromatic hydrocarbons (PAH), other hydrocarbons and particulate matter (PM). While the yield of toxic species is larger in smoldering fires than in flaming fires [47], the production rate, which is proportional to the spread rate, is much lower. This means that inside an enclosure, a smoldering fire of long duration (in the range from 1 or 3 h for a single bedroom size compartment [48]) can lead to a lethal dose of toxicity, especially CO. But there are not as yet sufficient data on the toxicity of smoldering materials to definitively understand the issue of life safety. Some more information is presented in Chap. 62 and in [47].
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Limited information is available on the aerosol emitted by a smolder source. The residual char left behind the smolder front and the original porous bed act as filters for aerosol. This finding explains the observation by Palmer [27] that upward smoldering in a thick layer of fuel was not detected until it neared the surface (like in Fig. 19.7 right). The mean particle size of the aerosol in smoldering cellulose was measured to be in the range from 2 to 3 μm [49]; this is about 50–200 times larger than the sooty particulates produced by flaming combustion. The low heat release rate of smoldering fires means that the buoyant plume is weak, which has implications on the location of smoke detectors in rooms. The morphology of the smoke from smouldering is different to smoke from flaming, and this affects smoke detection. This means smoke is slow to reach the ceiling, or it may never reach it, and often the building mechanical ventilation controls the smoke movement [50] (see also Chap. 13). In the natural environment, the low buoyant strength of large smoldering fires leads to haze episodes because the plume accumulates near the ground and can slide into populated areas, choking towns and cities for weeks [5]. The composition of haze measured by Bertschi et al. [51] in the tropical savanna shows it contains 130 % more CO and 670 % more hydrocarbons in mass basis, but 15 % less CO2 and no NOx when compared to the flaming wildfires.
Smoldering Wildland Fires In the natural environment, smoldering fires burn two types of biomass: thick fuels, like tree branches or logs, and organic soil, like the duff layer or peat [5]. These are characterized by having a significantly greater thermal time compared to fine fuels like foliage. Thick fuels favor the slow burning of smoldering combustion. The persistent smoldering of thick fuels is typically observed for a few days after a flaming wildfire has passed, and it is often referred to as residual smoldering combustion. Overall, smoldering is
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responsible for up to 50 % or more of the total burned biomass during wildfires [51–53]. But it is the soil rich in organic matter, in particularly that in peatlands, which is most affected ecosystem by smoldering fires, both in frequency and size. Peat soils are made by the natural accumulation of partially decayed biomass and are the largest reserves of terrestrial organic carbon [54]. Because of this vast accumulation of fuel, once ignited, smoldering peat fires burn for very long periods of time (e.g., months, years) despite extensive rains, weather changes or fire-fighting attempts. These are the largest fires on Earth and large contributors of greenhouse gases [5, 54]. Peat fires occur with some frequency worldwide in tropical, temperate and boreal regions (e.g., in Indonesia, Australia, Alaska, Canada, Florida, British Isles, Siberia). Droughts, drainage and changes in land use are thought to be main causes leading to the high flammability conditions of dry peatlands. Possible ignition events can be natural (e.g., lightning, self-heating, volcanic eruption) or anthropogenic (land management, accidental ignition, arson). The most studied peat megafire took place in Indonesia in 1997 and led to an extreme haze event. The smoke covered large parts of SouthEast Asia, even reaching Australia and China, and induced a surge of respiratory emergencies in the population and disruption of shipping and aviation routes for weeks. It was estimated that these fires released between 0.81 and 2.57 Gton of carbon gases [55]. This is equivalent to 13–40 % of global man-made emissions of the year 1997. The 1997 megafire was not an isolated case in the region. Analysis of 1960–2006 data shows that smoldering haze episodes have drifted to South East Asian countries once every 3 years on average [56]. Rough figures at the global scale estimate that the average greenhouse gas emissions from peat fire is equivalent to >15 % of man-made emissions. Moreover, because peat is ancient carbon, and smoldering is enhanced under warmer and drier climates, it creates a positive feedback mechanism in the climate system, a self-accelerating global process [5].
19
Smoldering Combustion
597
Fig. 19.13 The data separates the ignition (bottom) from the noignition (top) limits for a mixture of peat, moisture and mineral contents. Circles and sequre symbols are experimental data by Frandsen [58]. Lines are computational simulations by [59].
Because the water content of wildland fuels like peat can vary naturally over a wide range of values (from dry to flooded in water), and because water represents a significant energy sink, moisture content is the single most important property governing the ignition and spread of smoldering wildfires. The critical moisture content for ignition (related to the moisture of extinction [57]) of boreal peat has been measured in the range 110–120 % in dry basis6 [16, 58]. Any peat drier than this is susceptible to smoldering. The prominent role of moisture is such that natural or anthropogenic-induced droughts are the leading cause of smoldering megafires. The second most important property is the mineral content.7 As found experimentally by Frandsen [58] and computationally by Huang et al [59], there is a decreasing relationship between the mineral content and the critical moisture content: higher mineral loads mean soil can only ignite at lower moistures. This is 6 The water content in dry basis is the mass of water divided by the mass of a dried sample expressed as a %. 7 The mineral content is the % of the fuel mass (on dry basis) that will not burn or react at high temperatures. It results in ash.
because the inert content is a heat sink to the fire. The results are shown in Fig. 19.13. This rule can be applied to most organic soils or fuel beds to determine if they are susceptible to smoldering. Any soil which composition is more than 80 % mineral, cannot be ignited [58, 59]. After moisture and mineral contents, other important properties are bulk density, porosity, flow permeability and organic composition. Because the fuel layers found in the natural environment (soil depths from 0.5 to 30 m) can be much thicker than those in the built environment (~0.1 m), smoldering wildfires can be classified in shallow or deep fronts. Each has significantly different dynamics because of the different role played by the controlling mechanisms of oxygen supply and heat losses. Organic material located close to the surface of the soil burns in shallow fires (roughly 90 % mass loss) and also because the long residence time of smoldering means that heat penetrates deep into the soil layers [5]. On the contrary, flames produce high temperatures above the ground for short periods of time (in the order of 15 min). This results in minimal heating of the soil below depths of a few cm, reaching peak temperatures of 300 C at superficial layers ( εF then the boundaries of integration can be changed to
00
_ P ð0; tÞ ¼ m
ð εF 0
χðx; tÞ YF, s ðx; tÞ
i¼N h X i¼1
ni Eii =RTðx;tÞ i Ai Ym O ðx; tÞYS ðx; tÞe
! i dx
ð21:4Þ
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Flaming Ignition of Solid Fuels
639
Where the chemical reactions are left in a generic form while recognizing that, due to the absence of oxygen, the reactions occurring between εO < x < εF might differ significantly from those occurring between 0 < x < εF. To summarize, the production of fuel is controlled by the following variables: Temperature Local fuel concentration Local oxygen concentration Residual fuel fraction Permeability function Oxygen penetration depth Reactive depth Kinetic constants
T(x,t) YS(x,t) YO(x,t) YF,s(x,t) χ(x,t) εO(t) εF(t) Ai, mi, ni, Ei
temperatures that can be achieved. Carbonaceous chars can reach much higher temperatures, leading in many cases to vigorous oxidation (surface glowing) that can be the catalyser for gas phase ignition. This will be part of the gas phase discussion. In what concerns the production of fuel, the differences appear mostly in-depth where temperature is controlled by heat transfer through the char and fuel production is affected by an overall permeability function. The effects of permeability were described above and temperature effects on fuel production will be discussed in the context of the calculation of the temperature distributions.
Charring
The Thermal Depth («T)
For the purpose of ignition of a solid fuel the process of charring has an impact on both heat and mass transport therefore needs to be briefly addressed. A general summary of the chemical processes leading to charring can be obtained in Chap. 7, and more details form Cullis and Hirschler [16] for polymers and in the case of wood from Drysdale [17], thus will not be described here. Instead an attempt will be made to explain the role of charring in ignition. For charring materials pyrolysis leads to the production of gaseous fuel (pyrolyzate) and a residual solid phase char. The char is mainly a carbonaceous solid that could be further decomposed. The secondary decomposition could be complete, leading to an inert ash or to a secondary char that can be further decomposed in a single or multiple steps. Non-charring materials decompose leaving no residue behind. From the perspective of ignition, the exposed surface represents the boundary between the gas and the solid. This boundary moves as the material is completely removed. The rate at which the surface moves is the regression rate (VR). For charring and non-charring materials, this will be the boundary where complete consumption of the fuel is achieved. Although, regression rates can be very different between charring and non-charring materials, at the surface, the main difference between the two material types is the
When a heat flux is applied to one of the solid surfaces, the heat travels across the solid fuel. Initially only a very small area is affected, but as the thermal wave travels through material a larger and larger fraction of the solid is heated. The velocity of the thermal wave is represented in Fig. 21.1 by VT(t). VT(t) is a function of time because it will decrease as the thermal wave moves away from the heating source and towards the cold back surface. The region that has been heated is quantified by the characteristic length εT(t). It is important to note that, given that temperature is a continuous function, εT(t) has to be arbitrarily defined simply as the end of the heated region. There is no exact mathematical definition for this length but physically it means that the temperature is approaching ambient temperature (T T0) or the gradient of the temperature is approaching zero ( dT=dx 0 ). The proximity that temperature or the gradient have to achieve when approaching these targets is only a matter of what precision is required by those making the analysis. The length scale εT(t) is extremely important because it characterizes solids into different groups. This breakdown enables the simplification of the energy equation and the generation of simple analytical expressions for the temperature distribution. For the purpose of ignition, solid fuels are classified in:
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Semi-infinite Solid (L > εT) If the thermal wave is far from the end of the sample, the heat coming from the exposed surface has still not migrated to the back end. The temperature at the back end is ambient (T0) and there are no heat losses through this surface. The thickness of the sample is no longer a relevant quantity and therefore the fuel can be treated as a semi-infinite solid (L ! 1). Materials do not show semiinfinite solid behaviour forever, as time progresses the thermal wave will eventually reach the end of the sample. In many cases materials will behave as semi-infinite solids for the period of interest, in which case the assumption of L ! 1 is valid. The boundary condition for the energy equation becomes: x¼L!1
ð21:5Þ
00
q_ N ð1; tÞ ¼ 0 T ¼ T0 Thermally-Thick and Thermally-Thin Solid (εT L) The thermal wave has reached the end of the sample and therefore heat losses at the back end need to be quantified. The thickness of the sample, L, becomes a relevant dimension of the problem and a boundary condition for x ¼ L needs to be defined. This group can be sub-divided into two different cases, thermally thick and thermally thin. A solid can be defined as thermally thick if a significant thermal gradient exists within the solid through the period of ignition. In contrast, in a thermally thin solid the gradient is negligible for most of the time before ignition. A simple criterion based on the Biot number (Bi) is generally used for the purpose of establishing if a material is thermally thin or thick. The Biot number is defined as Bi ¼ hL/k, where “h” is a global heat transfer coefficient (W/m2K) and “k” is the thermal conductivity (W/mK). If Bi < εP the solid can be considered inert, thus thermal properties can be defined as those of the original solid fuel. The thermal properties relevant to ignition are Density Thermal conductivity Specific heat
ρ(x,t) k(x,t) C(x,t)
Kg/m3 W/m.K J/kg.K
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Flaming Ignition of Solid Fuels
which are all functions of temperature. Since the temperature varies in-depth they are also functions of “x.” The evolution of these properties with temperature for common materials can be found in most heat transfer book [19], nevertheless, for materials typically present in fires (wood, complex plastics, composites, etc.) these properties are in many cases unknown [20, 21]. For x > εP the chemical reactions have initiated the decomposition of the material. The relevant properties remain the same, nevertheless pyrolysis introduces further changes to the properties. The gasification of the fuel and its transport towards the surface will strongly affect the density, while any potential voids will force to redefine thermal conductivity and specific heat to account for the existence of at least two phases. The process of pyrolysis can lead directly to gasification with no residue (non-charring) or to a carbonaceous residue (charring). Figure 21.1 shows the case of a charring material where a second front for charring (x ¼ εCH) is formed behind the pyrolysis front. The charring front will propagate at a velocity VCH and will leave behind a residue that will have a new set of properties that are potentially very different to those of the fuel. The properties are still the permeability, the density, thermal conductivity and specific heat but precise values are mostly unknown for most chars issued of materials relevant to fires. It is common to see in the char region large voids and cracks that compromise the one-dimensional treatment provided here. These have been considered when addressing materials such as wood but will not be described here.
Melting and the Evaporation of Water Melting or water evaporation have not been considered in the description of the ignition until this point. These two processes are endothermic
641
phase changes that can have a significant effect on the temperature distribution in the solid. Numerous models have been built in the past to describe the heat sinks associated to melting and several studies have attempted to quantify the impact of melting on practical situations such as dripping. Phase changes are generally incorporated to the energy equation as heat sinks where some rate function is created to describe the conversion from one phase to the other. The simplest procedure is to assign a critical temperature to the phase change (i.e. 100 C for water) and a heat of melting or evaporation (ΔHM). Once the fuel or water reaches this temperature it is converted to the high temperature phase. The phase change process is assumed to be infinitely fast and therefore the rate is defined by the available energy reaching the location where the phase change is occurring. All the energy is then used for the phase change and the thermal wave can only proceed once the transition has been completed. This approach is inappropriate if the available energy is very low, in this case thermodynamic equilibrium equations will define the rate of vaporization or melting. Other more complex models that include processes such as re-condensation can be found in the literature but will not be discussed here. The consequences of melting or water evaporation are various. Phase changes can affect the thermal properties of the fuel significantly and can result in motion of the molten fuel or water vapour. This leads to convective flow of energy or mass transfer. Understanding the physical processes behind phase change does not represent a great challenge. Furthermore, the potential impact of phase change on ignition is clear. Thus it is evident that any predictive tool for ignition should attempt to quantify the impact of phase change on ignition. Nevertheless, the formulation of a model that can describe these processes in a comprehensive manner is extremely complex and the measurements that could serve for its validation are mostly non-existent.
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kρC [W2/sm4K2]
5.0E+05 4.0E+05 3.0E+05 2.0E+05
Glass Transition Temperature
1.0E+05 0.0E+00 0
50
100
150
200
250
300
o
Temperature [ C]
Fig. 21.4 Evolution of the product of the thermal conductivity, density and specific heat (kρC) for PMMA as a function of temperature
Given that, phase change is fundamentally an additional heat sink that will have to be incorporated to the energy equation in an arbitrary manner, it is justifiable to exclude the treatment of this subject from the present analysis. Nevertheless, this is done with the clear warning that its exclusion will have a significant impact on any quantitative assessment of the ignition process. Other processes that deserve to be addressed are softening or glass transition. Many materials such as thermoplastics will undergo gradual or drastic property changes with temperature. These property changes are not endothermic but will affect the progression of heat through the sample and could lead to dripping. Softening or glass transition will be directly incorporated in the analysis through the variable properties described in section “The Pyrolysis (εP) and Charring Depths (εCH)”. An example of how these properties change with temperature is shown in Fig. 21.4. Figure 21.4 presents the evolution of the product of all three thermal properties (kρC) for PMMA as a function of temperature, indicating the abrupt change occurring at the glass transition temperature.
The Temperature Distribution As explained in section “The Production of Gaseous Fuel”, to determine the fuel production it is necessary to define the evolution of the temperature inside the solid fuel. This can be achieved by defining a comprehensive energy equation. Figure 21.4 represents a typical control volume for x < εP where all the main heat transfer mechanisms are incorporated. For the purposes of this description the coordinate system will be anchored to the regressing surface, thus “x” will move with a velocity VR. A mass flow of fuel will therefore cross the control volume presented in Fig. 21.5 carrying 00 energy in and out (q_ S ). The gaseous products of pyrolysis and oxygen diffusion will also carry 00 00 energy in and out of the control volume (q_ P , q_ O respectively) and the generic expression for the 00 00 ˙ P, m ˙ O ) incorporates mass flow of these gases (m the regression rate. Heat is conducted in and out 00 of the control volume ( q_ CND ) and for generality 000 in-depth radiative absorption is allowed ( q_ RAD ). Since for x < εP the temperature is sufficiently high to allow for chemical reactions all heat
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Flaming Ignition of Solid Fuels
643
⋅
q″P (x, t) ⋅
⋅
q″O ( x, t)
q″CND (x,t)
⋅
q″S ( x, t)
x=x
q⋅ ″′ g ( x, t)
q⋅ ″′ RAD ( x, t)
x+=x +dx
q⋅ ″O ( x+ , t)
x
q⋅ ″S ( x+ , t)
q⋅ ″CND (x+ , t)
q⋅ ″P ( x+ , t) Fig. 21.5 Typical control volume for x < εP showing the main heat transfer mechanisms
Table 21.1 Summary of all energy transport within a generic control volume for x < eP. DHP,i is the net heat resulting from each individual chemical reaction. The net heat will be endothermic for most pyrolysis processes and exothermic for oxidative reactions. The summation is not truly a summation, but as explained earlier, is the overall set of chemical reactions where some could be sequential and others competing Description In 00 Energy transported by gaseous q_ P ðxþ ; tÞ fuel traversing the control volume Energy transported by oxygen traversing the control volume
00
˙ p (x, t)CP,P(x, t)TP(x, t) m
00
_ O ðxþ ; tÞCP, O ðxþ ; tÞTO ðxþ ; tÞ m 00 ˙ O (x, t)CP,O(x, t)TO(x, t) m
00
Heat conduction
q_ CND ðx; tÞ
Radiative absorption
q_ RAD ðx; tÞ:dx
00
00
q_ P ðx; tÞ
q_ O ðx; tÞ
00
Formulation _ p ðxþ ; tÞCP, P ðxþ ; tÞTP ðxþ ; tÞ m
q_ O ðxþ ; tÞ
00 Energy transported by solid q_ S ðxþ ; tÞ fuel traversing the control volume
Chemical energy (generation/sink)
Out
00
ρS ðxþ ; tÞVR ðtÞCS ðxþ ; tÞTðxþ ; tÞ 00
ρS(x, t)VR(t)CS(x, t)T(x, t) -kS dT dx x¼x 00 dT þ q_ CND ðx ; tÞ -kS dx x¼xþ q_ S ðx; tÞ
000 000
q_ g ðx; tÞ:dx
sources and sinks associated to all chemistry need to be included. Table 21.1 summarizes all terms incorporated in Fig. 21.5. Estimation of the net heat transfer will lead to a change in the energy accumulated within the control volume. The following expression summarizes the energy balance:
000
q_ RAD ðx; tÞ:dx X mi ni i¼N i¼1 ΔHP, i ρS ðx; tÞ Ai YO ðx; tÞYF ðx; tÞe Ei =RTðx; tÞ
∂ECV ¼ ∂t
h 00 i 00 00 00 q_ S ðxþ ; tÞ þ q_ P ðxþ ; tÞ þ q_ 0 ðx; tÞ þ q_ CND ðx; tÞ h 00 i 00 00 00 q_ O ðx þ , tÞ þ q_ CND ðx þ , tÞ þ q_ S ðx; tÞ þ q_ P ðx; tÞ þ 000
000
q_ RAD ðx; tÞ dx þ q_ g ðx; tÞ dx
where ECV ¼ ρS ðx; tÞCS ðx; tÞTðx; tÞ dx, which after appropriate substitutions results in the general energy equation for the control volume.
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00 00 _ P CP, P TP _ O CP, O TO ∂ m ∂ m ∂T ∂½ρS VR CS T 000 ∂½ρS CS T ∂ þ q_ RAD þ kS þ ¼ ∂x ∂x ∂x ∂x ∂t ∂x h i X mi ni Ei =RT i¼N þ ΔH ρ A Y Y e P , i i S i¼1 O S
Given the differential nature of the equation all variables are assumed to be functions of “x” and “t” so these dependencies are no longer indicated. Many of the terms are left in a generic form and not quantified. Their quantification is complex, thus a more detailed discussion will be provided later in those cases where it is necessary. The solution to Equation 21.5 will provide the evolution of the temperature distribution along the sample and as a function of time (T(x,t)). This solution can then be incorporated in Equation 21.4 to establish the fuel production rate. It is important to note that thermal equilibrium between phases has not been assumed, thus there are three different temperatures in Equation 21.5, T, TP and TO. Expressions similar to Equation 21.5 can be defined for each phase and will have to be solved in a simultaneous manner. The boundary condition will be the exchange of heat between phases, this is generally done using empirical correlations for heat transfer in porous media [22]. The alternative approach is to demonstrate thermal equilibrium between the phases (heat transfer is much faster than mass transfer within the pores), in which case all temperatures will be the same and only Equation 21.5 will have to be solved. To summarize, and in addition to the variables established in sections “The Production of Gaseous Fuel” and “The Pyrolysis (εP) and Charring Depths (εCH)”, the temperature distribution is controlled by the following variables: Thermal conductivity Specific heat
kS(x,t) CS(x,t) CP,P(x,t) CP,O(x,t)
Density of the solid Regression rate Mass flow Temperature of the gas phase Radiative properties of the solid (absorptivity, αS(x,t)) Heat of reaction
ð21:7Þ
ρ(x,t) VR(t) 00 ˙P m 00 ˙O m TP TO αS (x,t) ΔHP,i
The Surface Boundary Conditions (x ¼ 0 and x ¼ L) Figure 21.1 shows all the different modes of heat transfer through the surface control volumes. In theory, control volumes at x ¼ 0 and x ¼ L could be represented in a generic manner that makes them identical. In practise this is generally not the case because materials tend to have an exposed face and one that is in contact with some backing. The backing will define a conductive boundary condition while the open face a convective/radiative one. For illustration purposes, this distinction will be made here and the exposed face will be defined as an open bound00 ary, thus q_ N ð0; tÞ will include convection and 00 radiation, while the back-face, q_ N ðL; tÞ, will be attached to a substrate, thus will be defined as an impermeable conductive boundary condition. It needs to be emphasized that this is an arbitrary simplification that is only done to illustrate two different types of boundary conditions because they are mutually exclusive. In many cases a material might be sandwiched between two solids or exposed at both ends. The appropriate choice of boundary conditions needs to be made
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645
q⋅ P″ (0, t)
″ (0, t) q⋅ Cv
q⋅ O″ (0, t)
q⋅ S″(0, t)
q⋅ e″ (0, t)
″ (0, t) q⋅ SR
x=0 ″′ (0, t) q⋅ RAD
q⋅ g″′( x, t) x=ε
q⋅ O″ (ε, t) q⋅ S″(ε, t)
x
q⋅ e″(ε, t)
″ (ε, t) q⋅ CND
q⋅ P″ (ε, t) Fig. 21.6 Boundary control volume for x ¼ 0 showing the main heat transfer mechanisms
but the processes to be described will not be different. Figure 21.6 shows the open boundary condition (x ¼ 0) at a specific point in time. The different components are mainly those described
in Table 21.1 leading to a very similar expression for the energy balance as that presented in section “The Temperature Distribution”. So at the x ¼ 0 surface
h 00 i ∂ECV ð0; tÞ 00 00 ¼ q_ S ðε; tÞ þ q_ P ðε; tÞ þ q_ 0 ð0; tÞ ∂t h 00 i 00 00 00 00 00 q_ O ðε; tÞ þ q_ CND ðε; tÞ þ q_ S ð0; tÞ þ q_ P ð0; tÞ þ q_ SR ð0; tÞ þ q_ Cv ð0; tÞ þ 000
000
q_ RAD ðx; tÞ ε þ q_ g ðx; tÞ ε where the terms that remain undefined are described in Table 21.2. Radiation absorption within the surface control volume is represented 00 00 00 as q_ RAD ð0; tÞε ¼ q_ e ð0; tÞ-q_ e ðε; tÞ to remain consistent with the notation of the previous section.
For the boundary control volume the characteristic thickness ε ! 0, which eliminates all energy transported by mass flow, radiation absorption and energy generation. The final expression for the exposed boundary condition is then:
∂T 0 ¼ kS εS ð0; tÞσ T4 ð0; tÞ T40 hCv ðtÞðTð0; tÞ T0 Þ ∂x x¼0þ
ð21:8Þ
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Table 21.2 Summary of all energy transport within the surface control volume. Only terms not presented in Table 21.1 are described here. The Stefan-Boltzmann Constant is: s ¼ 5.670 108 W/m2K4, eS(0,t) is the surface emissivity and hCv is the convective heat transfer coefficient. Only for illustration purposes two different approaches are used to describe radiation, absorption is allowed to happen in-depth while emission is treated as a surface process. The spectral emissivity and absorptivity of the material will define the most appropriate treatment for each specific case Description Radiation from the exposed surface to the environment
In
00
q_ SR ð0; tÞ 00
q_ Cv ð0; tÞ
Convective losses from the surface External radiative heat-flux
A similar treatment can be followed with the back end boundary condition (x ¼ L). In this case the back surface is assumed to be in direct contact with another solid. Mass transfer, convection and radiative losses to the environment are therefore precluded. The boundary condition will only include conductive terms and can be described as: ∂T ∂TB 0 ¼ kS þ kB ð21:9Þ ∂x x¼L ∂x x¼Lþ where kB is a global thermal conductivity of the backing material that could include the thermal resistance between the two solids. In most cases the contact between both solids is not perfect, leaving air gaps or requiring adhesives, in these cases it is important to define the thermal conductivity in a manner that includes the contact resistance. The variable TB is the temperature of the backing solid, these temperature will come out of a solution to an additional energy balance of the form of Equation 21.5. Note that if kB is very small the backing can be assumed as an insulator and the boundary condition can be summarized to no losses at the back. This eliminates the need to solve a second energy equation for TB. To summarize, and in addition to the variables established in sections “The Production of Gaseous Fuel”, “The Pyrolysis (εP) and Charring Depths (εCH)” and “The Temperature Distribution”, the temperature distribution is controlled by the following variables:
Out
00
q_ e ð0; tÞ
Formulation εS ð0; tÞσ T4 ð0; tÞ-T40 Þ hCv ðTð0; tÞ-T0 Þ 00
q_ e ð0; tÞ
Global thermal conductivity of the backing material Temperature of the backing material Emissivity of the solid Convective heat transfer coefficient Ambient temperature
kB(x,t) TB(x,t) εS(x,t) hCv(t) T0
The Gas Phase The sequence of events leading to the ignition of a gas phase flame will be described in this section. It will be assumed that gaseous fuel emerges from the solid following the description provided in section “The Solid Phase”. After the onset of pyrolysis gas begins to emerge from the fuel surface, initially in very small quantities, but as εF and T(x,t) increase Equation 21.4 shows that the fuel mass flux will increase. The emerging fuel will encounter the ambient oxidizer and eventually produce a flammable mixture. Given that fuel is migrating into the oxidizer flow, the definition of a flammable mixture is not a simple one. In standard test methods the ambient flow is well defined, mixed convection generated by a horizontal heated surface and the extraction system in the cone calorimeter [23], natural convection resulting from a vertical heated surface in the LIFT apparatus [24] and forced convection over the fuel surface (horizontal or vertical) in the FM Global Fire Propagation Apparatus [25]. In real fires, flow fields are defined by the flames
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Flaming Ignition of Solid Fuels
647
themselves and by the geometry of the environment (obstacles, fuel geometry, etc.) with the possibility of complex flow patterns. The only mechanisms to establish the fuel distribution within the gas phase are detailed measurements or modelling [26–28]. Nevertheless, from a phenomenological perspective, to achieve ignition, what is required is to achieve a flammable condition in at least one location in the gas phase. The definition of a flammable mixture is for the fuel concentration to be found between the Lower or Lean Flammability Limit (LFL) and the Upper or Rich Flammability Limit (UFL). Although the LFL and UFL are apparatus dependent measurements, it is clear that the precision required for flaming ignition of solids does not require a more universal description of flammability. For a more detailed discussion on flammability limits and their limitations the reader is referred to Chap. 12.
Auto-ignition Once a flammable mixture has been attained, this mixture needs to increase in temperature until a combustion reaction can occur. This process is described in great detail by Torero [29] and by Fernandez-Pello [30, 31], who cites a series of experiments by Niioka [32] where ignition is Fig. 21.7 Schematic of the characteristic times involved in the ignition of a flat plate subject to a hot stagnation point flow. This schematic is based on the work by Niioka [32] and adapted from FernandezPello [30, 31]
studied using a stagnation point flow over a solid fuel surface. In these experiments the heat to initiate the combustion reaction is provided by a hot flow impinging on a fuel surface that acts as a heat sink. Niioka [32] identifies an induction time and a pyrolysis time. The pyrolysis time corresponds to the time required to attain a flammable mixture while the induction time is the time for the mixture to reach a temperature at which ignition can occur. Given the specific configuration, the pyrolysis time decreases with the flow velocity (enhanced heat transfer to the fuel surface) while the induction time increases (reduced residence time in the gas phase). Although these observations are not universally applicable, they serve to illustrate the process of auto-ignition. Fernandez-Pello [30, 31] describes Niioka’s conclusions graphically by means of the schematic, this schematic is simplified and presented in Fig. 21.7. Figure 21.7 shows how the summation of the pyrolysis and induction times leads to an ignition time. In auto-ignition there is no hot spot that will serve as an initiation point for the reaction, thus the mixture has to absorb enough energy to reach ignition. The exact amount of energy required for ignition can be associated to a Damko¨hler number [18]. The Damko¨hler number corresponds to the ratio between a local residence and chemical time. The chemical time represents the necessary
Time
Ignition Time
Induction Time
Pyrolysis Time
Flow Velocity
648
time for the reaction chemistry to occur and is expressed as the inverse of the reaction rate. Combustion reactions can be described by expressions like that presented in Equation 21.1 thus the chemical time is directly affected by the temperature of the reactants. The higher the temperature, the greater the reaction rates and the shorter the chemical time. The residence time is a measure of the strain (or dissipation rates) or the time the reactants remain together at a specific location thus it is directly related to the velocity field. The faster the flow or the velocity gradients, the shorter the residence time. If the chemical times are shorter than the residence times the reaction has enough time to proceed and a flame can exist. A critical Damko¨hler number for ignition can then be established, above which a combustion reaction can proceed [18]. In the schematic presented in Fig. 21.7, critical Damko¨hler numbers will be attained at both sides of the ignition curve preventing ignition. This is probably the most precise way to describe ignition but it requires the full resolution of the flow and temperature fields as well as comprehensive knowledge of the kinetic constants associated to the combustion reaction. While the flow field can be resolved by means of Computational Fluid Dynamics (CFD) the chemistry of most fire related fuels still remains uncertain. Qualitative assessment of the Damko¨hler number for ignition has only been achieved for a few very well defined experimental conditions such as stagnation flows [6, 32, 33] or boundary layers [34]. Other alternative representations of the ignition conditions that rest on the same fundamental approach have been discussed by Quintiere [35] and by Gray and Lee [36]. An important aspect of the ignition process that remains to some extent unresolved is the origin of the heat that is necessary for the gaseous fuel to reach the critical Damko¨hler number. If the air flow is hot, like in Niioka’s experiments [32], then the energy will come from the oxidizer and the problem is immensely simplified. If the oxidizer is cold and there is an external radiative heat source, then solid and gas will heat at different rates. The solid will absorb heat and its
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surface temperature will change following Equation 21.5 while the gas will absorb heat based on its absorptivity and dissipate it in a manner governed by the flow field. The absorptivity of the gas is a strong function of the fuel type and concentration, thus also requires detailed knowledge of the flow field. The two possible outcomes are that the gas phase heats faster than the solid phase or the opposite. In the former case ignition will occur away from the fuel surface, since the fuel will act as a heat sink for the gas. In the latter case, ignition will occur closer to the fuel surface since the fuel acts as a heat source. This latter scenario is common with charring materials where oxidation of the char contributes to increase the surface temperature [37]. It is clear that auto-ignition is a complex process that fully involves interactions of the solid and gas phases. Therefore, to characterize auto-ignition of solid fuels it is necessary to established well defined experimental conditions and simplifications to the analysis. Data obtained from different experimental conditions and with a specific analysis will generally not be compatible with other data that was obtained from a different experiment or deduced by means of an alternative analysis. Thus, scatter in the reported data is common for auto ignition. Data on auto-ignition is generally reported as Auto-Ignition Temperatures (AIT) which corresponds to a recorded temperature at the moment where ignition of a flame is first observed. A summary of much of the data available is presented in Chap. 14 of Ref. [1] together with a series of references to relevant papers and textbooks [38, 39]. Given the complexity of the processes leading to auto-ignition, these values can only be taken as reference values that are a direct function of the specific test conditions. Generally, significant discrepancy is found in the literature where reported Auto-Ignition Temperatures can vary in more than 150 C for the same material. The greatest discrepancies tend to be found when the orientation of the solid fuel is varied and the fluid mechanics and heat transfer are significantly altered [1]. AutoIgnition Temperatures are most consistent for
21
Flaming Ignition of Solid Fuels
gaseous mixtures (Chap. 12) and liquid fuels (Chap. 18) where tests are conducted in enclosed vessels where the fuel has been fully evaporated.
Piloted Ignition As discussed in the previous section, the process of auto-ignition is extremely difficult to describe in a quantitative manner, even under simple experimental configurations. Therefore, as an example, it is not practical to rely on autoignition to describe the susceptibility of solid materials to ignite. A mechanism to simplify the process is to include a pilot flame or a hot spot. This is a practical experimental simplification that has a basis on reality, since in most ignition scenarios there will be a region of high temperature. The presence of a pilot strongly simplifies the gas phase processes and reduces the influence of environmental variables. While characterization of the flow field is still required to establish the presence of a flammable mixture, it is no longer necessary to resolve heat transfer between phases or to define the absorption of energy by the gas. In the presence of a pilot, ignition can be assumed at the moment where a flammable mixture (LFL) is attained at the location of the pilot. Currently, all standard test methods that attempt the description of the ignitability of solids use some form of a pilot. In some cases, the pilot is a large flame [24] while in others is either a small pilot flame [25] or a high energy spark [23]. Both methods have their advantages and disadvantages, sparks produce only local heating thus have a weaker tendency to influence the solid phase by acting as a heat source. Nevertheless, given their small volume, ignition is strongly influenced by the spark location. The flow field has to establish a flammable mixture at exactly the location of the pilot. In contrast, large pilot flames have a tendency to supply heat to the fuel surface, but cover a large volume, therefore are less sensitive to the flow field. Because of its practical relevance, all subsequent discussion will concern piloted ignition.
649
To attain the LFL at the pilot location it is necessary to resolve the momentum and mass transport equations simultaneously with the surface boundary conditions explained above. Figure 21.1 shows an arbitrary distribution of the fuel concentration external to the sample, YF,g. A similar representation could be made for the oxygen concentration (YO,g). The characteristic equation that describes the flow field is as follows: !
ρ0
Du ! ! ¼ ∇P þ ρ0 g þ μ0 ∇2 u Dt
ð21:10Þ
!
Where u is the velocity field, ρ0 the density of the !
air, P the pressure field, g the gravity vector and μ0 the viscosity of the air. Temperature dependencies of the properties have been omitted for simplification assuming that air is the main constituent and it will remain close to ambient temperature. Conservation of fuel and oxygen concentrations can then be defined by: DYF, g ¼ ρ0 DF, O ∇2 YF, g Dt
ð21:11Þ
DYO, g ¼ ρ0 DF, O ∇2 YO, g Dt
ð21:12Þ
ρ0 ρ0
where species transport is assumed to be non-reactive, thus the source/sink has been omitted. This is an adequate assumption for pure mixing. To obtain the solution of Equations 21.8, 21.9 and 21.10 it is necessary to add the following variables to those established in sections “The Production of Gaseous Fuel”, “The Pyrolysis (εP) and Charring Depths (εCH)”, “The Temperature Distribution” and “The Surface Boundary Conditions (x¼0 and x¼L)”: Density of air Velocity field Pressure field Viscosity of air Diffusivity of fuel in air Pilot location
ρ0 !
u P μ0 DF,0 !
r
At this point, there is no need to specify a critical Damko¨hler number for ignition because
650
of the presence of the pilot, although in absolute rigour, this assumes that the flow conditions are such that blow-off of the flame kernel does not occur, thus the pilot will allow the establishment of a flame across the flammable mixture.
“Flash Point” and “Fire Point” Once ignition has been achieved a flame can propagate through the regions where a flammable mixture is present consuming the reactants. Independent of the flow field, it is most likely that a flammable mixture will be established close to the solid fuel surface. The pyrolysis rates at the moment when the flame is established will determine if a flame can continue to exist or if the combustion reaction will cease after the gas phase mixture is consumed. The feedback from the flame will enhance pyrolysis, but usually, the relatively large thermal inertia of the solid will result in a slow response, therefore it will be necessary for pyrolysis rates to be sufficient even in the absence of the flame heat feedback. If pyrolysis rates are not sufficient, the flame will extinguish and continuous pyrolysis will lead once again to the formation of a flammable mixture and subsequent ignition. This manifests itself as a sequence of flashes that precede the establishment of a flame over the combustible solid. This process is identical to the “flash point” generally associated to liquid fuels (Chap. 18) and for solid fuels has been described in detail by Atreya [37]. The transition between the “flash point” ignition and the established flame, which could also be named the “fire point” in an analogy with liquid fuels, deserves especial attention. The characteristics of the diffusion flame established on a solid fuel surface are defined by the flow field and the supply of fuel. The rate at which both reactants reach the flame zone defines the flame temperature and thus the characteristic chemical time. If the amount of fuel reaching the flame is small, then the flame temperature will be low and the chemical time will be long. As described above, the flow field defines the residence time. A second critical Damko¨hler
J. Torero
number appears, but this time is one of extinction. This concept has been described many times explicitly in the combustion literature [18] but only implicitly in the fire literature. There are only few studies where a critical extinction Damko¨hler number has been presented to describe the “fire point” but in all cases they concern idealized flow fields that allow establishing a direct correlation between fuel production and flame temperature [33, 34]. In most discussions simplifications have been assumed leading to simpler parameters that can serve as surrogates for the Damko¨hler number. Williams [40] discusses a critical gas phase temperature below which extinction will occur. If the residence time remains unchanged, then extinction is only associated to the chemical time, thus can be directly linked to a critical gas phase temperature. It can be further argued that extinction is much more sensitive to temperature than to flow, thus only radical changes in the residence time need to be addressed making this criterion a robust one. A more practical surrogate to the Damko¨hler number is a critical fuel mass flux criterion. Under specific testing conditions the flow field will remain invariable. In this case the attainment of a critical mass flux of fuel will be the single parameter defining the flame temperature and thus the Damko¨hler number [41, 42]. Furthermore, under more restrictive conditions the critical mass flux can be associated to a critical solid phase temperature [43]. Drysdale [17] and Beyler [44] provide a detail description of the classic approaches to this subject while Quintiere and Rangwala address some of the more current studies [45]. The sequence of events relating “flash” and “fire” points is not trivial because they represent distinctively different processes. For piloted ignition, the “flash point” only requires a flammable mixture while for the “fire point” the rate of fuel supply has to be enough to achieve a chemical time shorter than the residence time. Thus a number of different scenarios can be observed that in many cases can affect the consistency of different ignition studies. A simple example will be used to illustrate this. For example; if the pilot is very close to the fuel surface then a flammable
21
Flaming Ignition of Solid Fuels
mixture will be achieved at the pilot location soon after the onset of pyrolysis. In this case fuel supply will be far from that required to sustain a flame. A significant delay will exist between flash and fire points where several flashes will be observed. If the pilot is distanced from the fuel surface it will take longer to attain a flammable mixture and therefore at the moment of the first flash the fuel supply would have increased and a smaller number of flashes will be observed before the flame is fully established. Greater separation of the pilot from the fuel surface might result in the flammable mixture being attained at the pilot location at the same time as the fuel supply is sufficient to sustain a flame. In this case the fire point will correspond with the first flash. A further increase in the distance between pilot and fuel will not change the physical manifestation but will continue to delay ignition. In this case ignition will occur when a flammable mixture is attained at the pilot but will not be related to the flash or fire points. This example has been presented to illustrate the sensitivity of ignition studies to different variables and the importance of detailed observations to the validity of conclusions and comparisons. In this case pilot location was used as the example, but a similar analysis could be made with the heat flux, the oxygen concentration, the flow field [31, 46] or the ambient pressure [47]. The only added variable required to model the “fire point” will be the critical Damko¨hler number for extinction (Dae,cr) or any equivalent way to represent the extinction condition. As mentioned above, other criteria can be used to establish the extinction condition and that are partially equivalent to the critical Damko¨hler number. Such criteria are a critical mass transfer numbers (Bcr) [34, 48], critical mass fluxes [11, 28, 30, 42] or critical temperatures (Tcr) [17, 35, 40, 43, 45].
Simplifications and Standardization To predict flaming ignition of a solid fuel is necessary to solve Equations 21.1, 21.2, 21.3, 21.4, 21.5, 21.6, 21.7, 21.8, 21.9, and 21.10. A
651
number of authors have attempted the solution to these equations for a number of materials. Furthermore, they have in some cases added further complexity by including phenomena such as intumescent behaviour [49] or bubbling [50]. Extensive reviews of these modelling efforts can be found in Refs. [4, 51–54] and some of the more recent modelling exercises have achieved significant success [55–59]. In most cases some simplifications have been necessary and in general the critical limitation of these models is associated to the inadequate definition of many of the relevant variables and parameters listed in the previous sections. As mentioned before, the current trend is to optimise parameters by fitting complex models to specific experimental results by means of sophisticated optimization techniques. The optimization process results in ranges of possible values for all parameters stipulated. The results have then been extrapolated to other experimental conditions. While success has been reported [6, 7], these optimization processes are only as good as the models whose parameters they optimize. It is therefore important to note that even in the most complex models some simplifying assumptions have been made. Currently, the use of such models remains a research subject with increasing applicability to the modelling of flaming ignition of solid fuels. This section will take the equations presented in previous sections and suggest simplifications that will lead to models commonly used in the analysis of standard test methods evaluating the flaming ignition of solid fuels.
The Inert Solid Assumption The assumption that the solid remain inert until ignition is probably the most far reaching of all proposed simplifications. As a result of this assumption the energy equation is dramatically simplified. Despite the far reaching implications of assuming that the solid remains inert until ignition there is very limited work that assesses the validity of this assumption.
652
J. Torero
Fig. 21.8 Characteristic ignition delay times (tig) and times to the onset of pyrolysis (tP) for PMMA and a wide range of external heat fluxes extracted from Ref. [60]. Onset of pyrolysis or ignition did not occur below 11 kW/m2
800 Pyrolysis Time
700
Ignition Time
600 500 t [s] 400 300 200 100 0
0
10
20
30
40
50
60
q⋅ e″ [kW/m2]
To the knowledge of the author, the only explicit studies that discuss the importance of assuming that the material is inert are those by Fereres et al. [42], Dakka et al. [60] and Beaulieu and Dembsey [61]. In the first two studies transparent Poly(methyl methacrylate) (PMMA) was used while on the latter work the detailed analysis is done with black PMMA but a number of other materials serve to confirm the conclusions. Despite the bias towards PMMA, the discussion is appropriate here to illustrate the potential errors associated to this simplification. Figure 21.8 presents characteristic ignition delay times (tig) and pyrolysis delay times (tP) for PMMA. The ignition delay time was recorded as the first flash while the pyrolysis delay time as the moment when the fuel initiates its endothermic degradation. The onset of pyrolysis was characterized by means of mass loss measurements, flow visualization and IR-Thermography. These results show that for these particular experiments there is a significant difference between the “flash point” and the
x¼0
0 ¼ kS
onset of pyrolysis (could be up to 100 %) therefore the assumption that the fuel remains inert until ignition might not be justified. The breakdown of the inert solid heating assumption is further discussed by Beaulieu and Dembsey [61] who show that an analysis following this approximation will lead to shorter ignition delay times for realistic heat fluxes. The biggest errors were observed at the higher heat fluxes. Their tests were done for a comprehensive array of materials and with heat fluxes up to 200 kW/m2. Despite these experimental results, this assumption still remains the backbone of all standard test method analyses for ignition [23–25]. If this approach is followed and the regression rate is assumed to be negligible, VR 0, Equation 21.5 is reduced to ∂½ρS CS T ∂ ∂T 000 ¼ kS þ q_ RAD ð21:13Þ ∂t ∂x ∂x And the boundary conditions to
∂T εS ð0; tÞσ T4 ð0; tÞ T40 hCv ðtÞðTð0; tÞ T0 Þ ∂x x¼0þ
ð21:14Þ
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Flaming Ignition of Solid Fuels
x¼L
653
∂T ∂TB 0 ¼ kS þ kB ∂x x¼L ∂x x¼Lþ ð21:15Þ
Absorption of Radiation and Global Properties The next major simplifications that are commonly accepted are to assume that most of the incident heat flux is absorbed at the surface (α(t) 1) and that the thermal properties of the
x¼0
x¼L
solid can be considered invariant (ρS ðx; tÞ ρS , CS ðx; tÞ CS , and kS ðx; tÞ kS ). These assumptions further simplify Equation 21.11 because it allows neglecting in-depth radiative absorption. The thermal properties can then be extracted from the differential terms and external radiation now appears in the exposed boundary condition: 2 ∂½T ∂ T ¼ kS ρS CS ð21:16Þ ∂t ∂x2
∂T 00 0 ¼ kS þ q_ e σ T4 ð0; tÞ T40 hCv ðtÞðTð0; tÞ T0 Þ ∂x x¼0þ
∂T ∂TB 0 ¼ kS þ kB ∂x x¼L ∂x x¼Lþ ð21:18Þ
There is little true justification in the literature to support these assumptions, nevertheless they are of practical use since for many fire related materials the absorptivity (or emissivity) will approach unity [62], or in the case of testing the material surface can be treated with a coating that has these properties [25]. A series of recent studies have explored the absorptivity [63] of PMMA and the interaction between the heat source and PMMA [64, 65]. Figure 21.9 shows that when using an electrical resistance (cone heater [23]) the transmissivity of PMMA can be neglected and the absorption can be assumed to occur at the surface. Instead, when using tungsten lamps (from the Fire Propagation Apparatus [25]) in-depth absorption cannot be neglected. This information allowed explaining significant differences in the piloted ignition delay times obtained with both tests but mostly emphasize the potential importance of assuming an absorptivity of unity. Furthermore, thermal properties vary with temperature, but a global set of properties can be established to provide a good fit to ignition
ð21:17Þ
data. An example of a comprehensive assessment of the impact of variable thermal properties is provided by Steinhaus [66].
The Boundary Conditions To standardize the ignition process it is important to provide a controlled environment, so that test results can be consistent between laboratories and different users of the standard. Therefore, standard test methods provide clear definition of the environmental conditions, thermal characteristics of the backing material and pilot location [23–25]. Equations 21.8, 21.9 and 21.10 do not have to be solved to obtain the fuel concentration at the pilot location. Instead the impact of the gas phase on the results is ignored. This is done on the basis that flow conditions are the same between tests thus their impact on the transport of fuel and oxidizer to the pilot is the same. Standardization of the flow conditions has a deep effect on the meaning of the results. The thermal properties associated to the analysis are no longer true thermal properties of the material but global properties that are a combination of the solid and the standardized gas phase
654
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Fig. 21.9 Transmitted to incident heat flux ratio for clear PMMA samples (Lucite and Plexiglass) exposed to a radiative source (conical resistance and tungsten lamp)
providing 10 and 20 kW/m2 for thicknesses ranging between 0.375 and 51 mm [65]
conditions. This is of critical importance, because, as a product of standardization, test results can be compared among themselves (if the same method is used), nevertheless can not be extrapolated to conditions different to those of the test. This applies to other standard tests or to real fire conditions. Cordova et al. [46] provides a graphical assessment of the effect of varying the flow conditions on the resulting thermal properties showing that small variations in the flow field can result in drastic variations of the resultant thermal properties. It is common to apply ignition data from standard tests to fire models and is only recently that CFD models such as the Fire Dynamics Simulator (Version 5 and above) allow realistic representations of the solid phase that include true thermal properties [67]. It is important to note that extrapolation is not necessarily incorrect. Nevertheless, it has to be done with great care to guarantee that the effect of the environment on the thermal properties can either be neglected or an appropriate correction is provided.
Different test methods will use different flow fields therefore values for the convective heat transfer coefficient vary with the authors. A commonly cited value is 15 W/m2K. Furthermore, it is common to linearize surface radiation to define a single total heat transfer coefficient (hT 45 W/m2K). More precise values and models are present in the literature [26–28, 31] but they correspond to very specific scenarios and therefore are hard to generalize. Most test methods define the backing material as a good insulator ( kB ! 0 ) neglecting heat losses through the back end of the sample. Finally, characteristic ignition delay times can be considered much shorter than the time required for the thermal wave to travel through the sample therefore L > εT and the solid is generally assumed as semi-infinite. These last set of simplifications are truly not necessary because a simple numerical solution can be obtained without linearizing surface radiation or assuming a semi-infinite solid. Many studies have attempted to establish the impact of these simplifications by means of numerical
21
Flaming Ignition of Solid Fuels
655
solutions that relax these assumptions, the most recent of these papers is by Mowrer [68]. If surface radiation is described by means of constant heat transfer coefficient, then a correction is necessary to account for the growth of this coefficient as the surface temperature increases. Mowrer [68] showed that a correction to the global thermal properties could be made to account for this effect. The back end boundary condition is a more difficult problem. For low heat fluxes the thermal wave reaches the end of the sample, L < εT, before ignition occurs and heat is exchanged between the sample and the insulating material. Quantification of this heat exchange can be done numerically, as indicated in section “The Surface Boundary Conditions (x¼0 and x¼L)”, but this is not a simple process because it needs to properly describe the different components associated to the way the sample is arranged during tests. The alternative solution of providing a well defined insulating boundary and neglecting back end losses has been preferred and detailed analyses have been conducted to characterize the physical arrangements of sample and insulating material. Among the most comprehensive of these studies is presented in Ref. [69]. If all these assumptions are made, Equations 21.12, 21.17, and 21.18 can be reduced to: 2 ∂T ∂ T ¼ kS ρS CS ð21:19Þ ∂t ∂x2 ∂T 00 x ¼ 0 0 ¼ kS þ q_ e hT ðTð0; tÞ T0 Þ ∂x x¼0þ ð21:20Þ x!1
∂T 0 ¼ kS ∂x x¼L
ð21:21Þ
The Ignition Condition If the solid is assumed to be inert until ignition and the gas phase can be summarized into a single total heat transfer coefficient (hT) this amounts to the assumption that ignition will
occur at the onset of pyrolysis and that these process can be simply characterized by the attainment of a characteristic surface temperature that is commonly labelled the ignition temperature, Tig. If the sample is suddenly exposed to an external heat flux, then the time delay between exposure and ignition is named the ignition delay time, tig. These two parameters represent then the entire process of ignition. A final link can be made to establish a critical ignition condition. If the ignition delay time is infinitely long, then there will be no gradients of temperature within the solid and surface heat losses will be equivalent to the heat input. This represents the minimum heat flux required to achieve Tig, and thus flaming ignition of the solid fuel. This heat flux is named the minimum 00 heat flux for ignition, q_ 0, ig . Since surface temperatures are more difficult to measure than heat fluxes, the minimum heat flux for ignition can be used to establish the ignition temperature. Equation 21.18 can then be re-written to 00
q_ 0, ig Tig ¼ T0 þ hT
ð21:22Þ
Equation 21.14 is an idealized expression that assumes that no temperature gradients exist in the solid, this can lead to errors in the calculation of Tig. To establish a relationship between external heat fluxes and surface temperature that includes in-depth heat transfer a sample can be allowed to reach thermal equilibrium and the surface temperature recorded. The obtained relationship represents a more accurate representation of Equation 21.14 and can be used to extract ignition temperatures from measured heat fluxes. A graphic representation of this relationship can be found in Ref. [34]. Again, both minimum heat flux for ignition and ignition temperature are not material properties but a combination of the material and the specific environmental conditions associated to the test [46]. Extrapolation to realistic scenarios and fire models has to be done with significant care.
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The Solution 00
Imposing a constant external heat flux ðq_ e ¼ constantÞ and using all the above assumptions allows for an analytical solution to Equation 21.13. This solution establishes the evolution of the solid temperature as a function of time. This solution can be found in any heat transfer book [19] but was first postulated for 2
00
Tðx; tÞ T0 ¼
x q_ e 6 4erfc pffiffiffiffiffiffiffiffiffiffi e 4α ð hT Þ Dt
the flaming ignition of a solid fuel by Quintiere [70] and incorporated in ASTM E-1321 [24]. Alternate solutions have been postulated for other test methods and will be briefly discussed in Chaps. 28 and 36. More detailed discussion of methodologies and nomenclature can be found in the description of the standard tests [23, 25]. The solution for T(x,t) is given by
ðhT Þ p ffiffiffiffiffiffiffiffiffi pffiffiffiffi αD kS ρ S C S
0
13
2
xþ
ð hT Þ x C7 B ð hT Þ 1 terfc@qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffit2 þ pffiffiffiffiffiffiffiffiffiffiA5 4α kS ρ S C S Dt k ρ C S S
S
ð21:23Þ "
12 !# tig tig Where αD ¼ kS =ρS CS is the global thermal diffuð21:27Þ Tig ¼ T0 þ T 1 e tc erfc tc sivity and “erfc” is the complement to the error function. To obtain the surface temperature (Ts), x is set equal to 0 and T ¼ T(0,t) ¼ Ts. There- To avoid the complex form of the error function simplified solutions have been proposed in the fore Equation 21.21 simplifies to: 2 13 literature [70, 71]. In order to solve for the ignition 0 2 delay time (tig) a first order Taylor series expansion ðhT Þ 00 t q_ 6 B ð hT Þ 1 C 7 Ts ¼ T0 þ e 41 e kS ρS CS erfc@qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffit2 A5 of Equation 21.18 is conducted. The range of ðh T Þ kS ρS CS validity of this expansion is limited, thus cannot be used over a large range of incident heat fluxes. ð21:24Þ Thus, the domain has to be divided at least in two. The first domain corresponds to high incident from Equation 21.15, heat fluxes where the ignition temperature (Tig) 00 q_ e is attained very fast, thus tig < < tc. Application ð21:25Þ T¼ ðhT Þ of the first order Taylor Series Expansion to Equation 21.18 around tig =tc ! 0 yields the can be defined as a characteristic temperature following formulation for the ignition delay and, time (tig): tc ¼
k S ρS C S 2
ð hT Þ
ð21:26Þ
is defined as a characteristic time. Equation 21.15 is the general solution to the surface temperature at all levels of incident heat flux. To obtain the ignition delay time (tig) the surface temperature (Ts) is substituted by Tig and Equation 21.15 can be rewritten as:
00
1 2 q_ e pffiffiffiffiffi ¼ pffiffiffiqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi tig π kS ρS CS Tig T0
ð21:28Þ
As can be seen from Equation 21.19, the short time solution for the ignition delay time (tig) is independent of the total heat transfer coefficient term (hT). Thus the ignition delay time (tig) is
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Flaming Ignition of Solid Fuels
657
4.5 4 Equation (29) 3.5
1/t
1/2
1/2
[1/s ]
3 Equation (28)
2.5 2 1.5 1 0.5 0 0
5
⋅″ 10 q0ig
15
20 25 ⋅q ″ [kW/m2] e
30
35
40
45
Fig. 21.10 Ignition delay time (1/tig0.5) for different external heat fluxes using PMMA as a solid fuel (Data extracted from Ref. [60])
00
only a function of the external heat flux (q_ e ) and the global properties (kS , ρS , CS) of the solid fuel and the ignition temperature (Tig). For low incident heat fluxes tig tc , the Taylor series expansion is made around tig =tc ! 1, where the first order approximation yields: " # pffiffiffi hT T ig T 1 π hT 1 ð21:29Þ pffiffiffiffiffi ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 tig q_ }e kS ρS CS Equations 21.19 and 21.20 establish the relationship between ignition delay time and external heat flux. It is convenient to express the ignition pffiffiffiffiffi delay time data presented in Fig. 21.7 as 1= tig where Tig is obtained from the experimental minimum heat flux for ignition and Equation 21.14. Such a plot is presented in Fig. 21.8. Substituting Tig in Equation 21.19 allows extracting the product of the three thermal properties (kS ρS CS ) as a single experimental parameter representing the global material properties controlling flaming ignition of solid fuels that can be considered semi-infinite. Quintiere terms this product the thermal inertia [70] (Fig. 21.10).
When describing ignition propensity of solid fuels is customary to summarize the description of the materials on the basis of only two parameters, the ignition temperature, Tig, and the thermal inertia, kS ρS CS . Several tables have been produced in the past with comprehensive lists of materials typical of fires. As an example, Table 21.3 presents the data as compiled by Quintiere [70]. A comprehensive list is not presented here because a comprehensive compilation of data is provided in Appendix 3 or in Refs. [1] and [2].
Thermally Thin Materials A very similar analysis can be conducted for thermally thin materials where in the absence of thermal gradients and after all relevant simplifications Equations 21.13, 21.20, and 21.21 can be combined into a single energy equation and a boundary condition ρS C S L
∂T 00 ¼ q_ e hT ðTðtÞ T0 Þ ∂t
ð21:30Þ
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J. Torero
Table 21.3 Ignition data from ASTM E-1321 per Quintiere [72] Material Wood fiber board Wood hardboard Plywood PMMA Flexible foam plastic Rigid foam plastic Acrylic carpet Wallpaper on plasterboard Asphalt shingle Glass reinforced plastic
x¼L
Tig [ C] 355 365 390 380 390 435 300 412 378 390
00
q_ N ðL; tÞ ¼ 0
kS ρS CS [(kW/m2K)2.s] 0.46 0.88 0.54 1.00 0.32 0.03 0.42 0.57 0.70 0.32
ð21:31Þ
when the external heat flux is much larger than the losses this equation can be integrated to deliver Equation 21.22 [73]. ρS CS L Tig T0 tig ¼ 00 q_ e
ð21:32Þ
This is once again not a necessary assumption but has the practical advantage of leaving the product ρS CS as a single experimental parameter that can be extracted from the slope of a simple plot 00 presenting 1/tig vs q_ e . ρS CS represents then the global material properties controlling flaming ignition of thermally thin solid fuels. A comprehensive data review of this product is provided in Refs. [1] and [2].
Summary A review of flaming ignition of solid fuels has been presented. Emphasis has been given to a comprehensive description of all processes involved. Some minor simplifications have been made to the original formulation leading to approximately 30 variables and parameters controlling flaming ignition of a solid fuel. A section follows where the common simplifications associated to the methodologies of interpretation of standard test methods are
applied. Analytical solutions are obtained showing that the description of the ignition process can be summarized to two material related parameters and two specified environmental 00 conditions (T0, q_ e ). The material related parameters are as follows: Thermally thin materials
Tig
ρS CS
Thermally thick materials
Tig
kS ρ S C S
It is important to insist that these parameters are a function of the material and the environmental conditions at which they were obtained. They can be directly applied for comparison between materials (flammability assessment) but extrapolation to conditions beyond the tests where they were obtained is not always possible and if performed, has to be done with great care.
References 1. Babrauskas, V., “Ignition Handbook,” Fire Science Publishers & Society of Fire Protection Engineers, 2003. 2. Engineering Guide: Piloted Ignition of Solid Materials Under radiant Exposure, Society of Fire Protection Engineers, Bethesda, Maryland, USA, 2002. 3. Hirata, T., Kashiwagi, T. and Brown, J.E., “Thermal and oxidative degradation of Poly (methyl methacrylate): Wight loss,” Macromolecules, 18, 1410–1418, 1985. 4. Di Blasi, C., “Modeling and Simulation of Combustion Processes of Charring and Non-Charring Solid Fuels,” Progress in Energy and Combustion Science, 19, 71–104, 1993. 5. Ohlemiller, T.J., “Modeling of Smoldering Combustion Propagation,” Progress in Energy and Combustion Science, 11, 277–310, 1986. 6. Rein, G., Lautenberger, C., Fernandez-Pello, A.C., Torero, J.L. & Urban, D.L., “Application of Genetic Algorithms and Thermogravimetry to Determine the Kinetics of Polyurethane Foam in Smoldering Combustion,” Combustion and Flame 146 95–108 (2006). 7. Lautenberger, C., Rein, G. & Fernandez-Pello, A.C., “The Application of a Genetic Algorithm to Estimate Material Properties for Fire Modeling from BenchScale Fire Test Data,” Fire Safety Journal 41 204–214 (2006). 8. Bal, N., “Uncertainty and complexity in pyrolysis modelling,” PhD Dissertation, University of Edinburgh, 2012. 9. Bal, N. and Rein, G., “Uncertainty and Calibration in Polymer Pyrolysis Modelling,” Recent Advances in
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Flame Retardancy of Polymeric materials, vol. 23, C. Wilke (Editor), BCC, May 2012. 10. Chao, Y.H. and Wang, J.H., “Comparison of the Thermal Decomposition Behavior of a Non-Fire Retarded and a Fire Retarded Flexible Polyurethane Foam,” Journal of Fire Science, 19, pp. 137–155, 2001. 11. Lautenberger C. and Fernandez-Pello, A.C., “Optimization algorithms for material pyrolysis property estimation,” Fire Safety Science, 10, 751–764, 2011. 12. Chaos, M. Khan, M.M., Krishnamoorthy, N., De Ris, J.L. and Dorofeev, S.B. “Evaluation of optimization schemes and determination of solid fuel properties for CFD fire models using bench-scale pyrolysis tests,” Proceedings of the Combustion Institute, 33, 2599–2606, 2011. 13. Bruns, M.C., Koo, J.H. and Ezekoye, O.A., “Population-based models of thermoplastic degradation: Using optimization to determine model parameters,” Polymer degradation and stability, 94, 1013–1022, 2009. 14. Lyon, R.E., Safronava, N. and Oztekin, E., “A simple method for determining kinetic parameters for materials in fire models,” Fire Safety Science, 10, 765–777, 2011. 15. Kashiwagi, T. and Nambu, H., “Global Kinetics constants for thermal oxidative degradation of a cellulosic paper,” Combustion and Flame, 88, 345–368, 1992. 16. Cullis, C.F. and Hirschler, M.M., “The Combustion of Organic Polymers,” International Series of Monographs in Chemistry, Oxford Science Publications, Oxford, United Kingdom, 1981. 17. Drysdale, D., An Introduction to Fire Dynamics. Second Edition. John Wiley and Sons, New York, 1999. 18. Williams, F.A., Combustion Theory, 2nd Edition, Addison-Wesley Publishing Company, Inc., 1985. 19. Incropera, F.P., Dewitt, D.P., Bergman, T.L., Lavine, A.S., Fundamentals of Heat and Mass Transfer, 6th Edition, John Wiley and Sons, 2006. 20. Oztekin, E.S., Crowley, S.B., Lyon, R.E., Stoliarov, S. I., Patel, P. and Hull, T.R., Sources of variability in fire test data: a case study on poly(aryl ether ether ketone) (PEEK), Combustion and Flame, 159, 1720–1731, 2012. 21. Stoliarov, S.I., Safronava, N. and Lyon, R.E., “The effect of variation in polymer properties on the rate of burning,” Fire and Materials, 33, 257–271, 2009. 22. Nield, D.A. and Bejan, A., “Convection in Porous Media,” Springer-Verlag, 1992. 23. ASTM E-1354-03, Standard Test Method for Heat and Visible Smoke Release Rates for Materials and Products Using an Oxygen Consumption Calorimeter, American Society for Testing and Materials, Philadelphia, 2003. 24. ASTM 1321-97a, Standard Test Method for Determining Material Ignition and Flame Spread Properties, American Society for Testing and Materials, Philadelphia, 1997.
659 25. ASTM E-2058-03, “Standard Method of Test for Measurement of Synthetic Polymer Material Flammability Using the Fire propagation Apparatus (FPA),” American Society for Testing and Materials, Philadelphia, 2003. 26. Staggs, J.E.J., “Convection heat transfer in the cone calorimeter,” Fire Safety Journal, 44, 469–474, 2009. 27. Staggs, J.E.J., “A reappraisal of convection heat transfer in the cone calorimeter,” Fire Safety Journal, 46, 125–131, 2011. 28. Zhang, J. and Delichatsios, M.A., “Determination of the convective heat transfer coefficient in threedimensional inverse heat conduction problems,” Fire Safety Journal, 44, 681–690, 2009. 29. Torero, J.L. “Scaling-Up Fire,” Proceedings of the Combustion Institute, 34 (1), 99–124, 2013. 30. Fernandez-Pello, A.C., “The Solid Phase,” In Combustion Fundamentals of Fire, Ed. G. Cox, Academic Press, New York, pp. 31–100, 1995. 31. Fernandez-Pello, A.C. “On fire ignition,” Fire Safety Science, 10, 25–42, 2011. 32. Niioka, T., Takahashi, M., Izumikawa, M., 1981, “Gas-phase ignition of a solid fuel in a hot stagnation point flow”, 18th Symposium on Combustion, The Combustion Institute, Pittsburgh, PA, pp. 741–747. 33. Delichatsios M A and Delichatsios M M, “Critical Mass Pyrolysis rates for Extinction of Fires over solid Materials” Fifth Symposium on Fire Safety Science, 153–164, 1996. 34. Torero, J.L., Vietoris, T., Legros, G., Joulain, P. “Estimation of a Total Mass Transfer Number from Stand-off Distance of a Spreading Flame,” Combustion Science and Technology, 174 (11–12), pp. 187-203, 2002. 35. Quintiere, J.G., “Fundamentals of Fire Phenomena,” John Wiley and Sons, 2006. 36. Gray, P. and Lee, P. R. “Thermal Explosion Theory,” Oxidation and Combustion Reviews, 2, 3–180, 1967. 37. Atreya, A., “Ignition of Fires,” Philosophical Transactions of the Royal Society A: Mathematical, Physical, and Engineering Sciences 356 2787–2813 (1998). 38. Horrocks, A.R., Gawande, S., Kandola, B. and Dunn, K. W., “Recent Advances in Flame Retardancy of Polymeric Materials,” Business Communications Co., Norwalk, Connecticut, USA, 2000. 39. Backer, S., Tesoro, G.C., Toong, T.Y. and Moussa, N. A., “Textile Fabric Flammability,” The MIT Press, Cambridge, Massachusetts, USA, 1976. 40. Williams, F.A., “A Review of Flame Extinction,” Fire Safety Journal, 3, 163–175, 1981. 41. Rasbash D J, Drysdale D D, and Deepak D, “Critical Heat and Mass Transfer at Pilot Ignition and Extinction of a Material,” Fire Safety Journal, 10, 1–10, 1986. 42. Fereres, S., Lautenberger, C., Fernandez-Pello, A.C., Urban, D. and Ruff, G., “Mass flux at ignition in reduced pressure environments,” Combustion and Flame, 158, 1301–1306, 2011.
660 43. Thomson H E, Drysdale D D, and Beyler C L, “An Experimental Evaluation of Critical Surface Temperature as a Criterion for Piloted Ignition of Solid Fuels,” Fire Safety Journal, 13 185–196, 1988. 44. Beyler, C., “A Unified Model of Fire Suppression,” Journal of Fire Protection Engineering, 4 (1), 5–16, 1992. 45. Quintiere, J.G. and Rangwala, A.S., “A theory for flame extinction based on flame temperature,” Fire and Materials, Volume 28, Issue 5, September/ October, Pages: 387–402, 2004. 46. Cordova, J.L., Walther, D.C., Torero, J.L. and Fernandez-Pello, A.C. “Oxidizer Flow Effects on the Flammability of Solid Combustibles,” Combustion Science and Technology, 164, No. 1–6, pp. 253–278, 2001. 47. McAllister, S., Fernandez-Pello, A.C., Urban, D. and Ruff, G., “The combined effect of pressure and oxygen concentration on piloted ignition of a solid combustible,” Combustion and Flame, 157, 1753–1759, 2010. 48. Roberts, A.F. and Quince, B.W., “A Limiting Condition for Burning of Flammable Liquids,” Combustion and Flame, 20, 245–251, 1973. 49. Lautenberger, C. and Fernandez-Pello, A.C. “A generalized pyrolysis model for combustible solids,” 5th International Seminar on Fire and Explosion Hazards, April, 23–27, Edinburgh, UK. 50. Butler, K. M. Mixed Layer Model for Pyrolysis of Bubbling Thermoplastic Materials, National Institute of Standards and Technology, Gaithersburg, MD, NISTIR 6242; October 1998. 51. Kashiwagi, T., “Polymer Combustion and Flammability-Role of the Condensed Phase,” Proceedings of the Combustion Institute, 25, 1423–1437, 1994. 52. Di Blasi C., “The state of the art of transport models for charring solid degradation,” Polymer International 49 1133–1146, 2000. 53. Moghtaderi, B., “The State-of-the-Art in Pyrolysis Modeling of Lignocellulosic Solid Fuels,” Fire and Materials 30 1–34, 2006. 54. Lautenberger, C. & Fernandez-Pello, A.C., “Pyrolysis Modeling, Thermal Decomposition, and Transport Processes in Combustible Solids,” to appear in Transport Phenomena in Fires, Ed. M. Faghri & B. Sunden, WIT Press, 2008. 55. Lautenberger, C., Kim, E., Dembsey, N. and Fernandez-Pello, A.C., “The role of decomposition kinetics in pyrolysis modelling – Application to a fire retardant polyester composite,” Fire Safety Science, 9, 1201–1212, 2009. 56. Stoliarov, S.I., Crowley, S., Walters, R.N. and Lyon, R. E., “Prediction of the burning rates of charring polymers,” Combustion and Flame, 157, 2024–2034, 2010. 57. Stoliarov, S.I., Crowley, S., Lyon, R.E. and Linteris, G.T., “Prediction of the burning rates of non-charring
J. Torero polymers,” Combustion and Flame, 156, 1068–1083, 2009. 58. Bal, N. and Rein, G., “Numerical investigation of the ignition delay time of a translucent solid at high radiant heat fluxes,” Combustion and Flame, 158, 1109–1116, 2011. 59. Wasan, S.R., Rauwoens,P., Vierendeels, J. and Merci, B., “An enthalpy-based pyrolysis model for charring and non-charring materials in case of fire,” Combustion and Flame, 157, 715–734, 2010. 60. Dakka, S.M., Jackson, G. S. and Torero, J.L., “Mechanisms Controlling the Degradation of Poly (methyl methacrylate) Prior to Piloted Ignition” Proceedings of the Combustion Institute, 29, 281–287, 2002. 61. Beaulieu, P.A., and Dembsey, N.A., “Flammability Characteristics at Applied Heat Flux Levels up to 200 kW/m2”, Fire and Materials, 2007. 62. Hallman. J., “Ignition Characteristics of Plastics and Rubber,” Ph. D. Thesis, University of Oklahoma, Norman, OK, USA, 1971. 63. Jiang, F., deRis J.L. and Khan, M.M. “Absorption of thermal energy in PMMA by in-depth radiation,” Fire Safety Journal, 44, 106–112, 2009. 64. Girods, P., Bal, N., Biteau, H., Rein, G. and Torero, J. L., “Comparison of pyrolysis behaviour results between the Cone Calorimeter and the Fire Propagation Apparatus heat sources,” Fire Safety Science, 10, 889–901, 2011. 65. Bal, N., Raynard, J., Rein, G., Torero, J.L., Fo¨rsth, M., Boulet, P., Parent, G., Acem, Z. and Linteris, G., “Experimental study of radiative heat transfer in a translucent fuel sample exposed to different spectral sources,” International Journal of Heat and Mass Transfer, (in press), 2013. 66. Steinhaus, T. 1999 “Evaluation of the Thermophysical Properties of Poly(Methyl Methacrylate): A Reference Material for the Development of a Flammability Test for Micro-Gravity Environments,” Masters Thesis, University of Maryland. 67. McGrattan, K., Klein, B., Hostikka, S., Floyd, J., “Fire Dynamics Simulator (Version 5), User’s Guide,” NIST Special Publication 1019–5, October 1, 2007. 68. Mowrer, F.W., “An analysis of effective thermal properties of thermally thick materials,” Fire Safety Journal, Volume 40, Issue 5, Pages 395–410, July 2005. 69. deRis, J. L. and Khan, M. M., “A Sample Holder for Determining Material Properties,” Fire and Materials, 24, 219–226, 2000. 70. Quintiere, J.G., “A Simplified Theory for Generalizing Results from a Radiant Panel Rate of Flame Spread Apparatus,” Fire and Materials, Vol. 5, No. 2, 1981. 71. Wickman, I. S., “Theory of Opposed flame Spread,” Progress in Energy and Combustion Science, 18, 6, pp. 553–593, 1993.
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72. Quintiere, J.G., “Principles of Fire Behavior,” Delmar Publishers, 1997. 73. Lautenberger, C. Torero, J.L. and Fernandez-Pello, A.C., “Understanding Materials Flammability,” Chapter 1, Flammability Testing of Materials in Building, Construction, Transport and Mining Sectors, V. B. Apte Editor, pp. 1-21, CRC Press, 2006.
661 Jose´ Torero is the Head of the School of Civil Engineering at The University of Queensland. He holds a BSc for the Pontificia Universidad Cat olica del Peru´ (1989), and an MSc (1991) and PhD (1992) from the University of California, Berkeley. Jose is a Chartered Engineer (UK), a fellow of the Australian Academy of Technological Sciences and Engineering, the Royal Academy of Engineering (UK) and the Royal Society of Edinburgh (UK).
22
Electrical Fires Vytenis Babrauskas
Introduction An electrical fire is generally understood to be a fire that is caused by the flow of an electric current or by a discharge of static electricity. It is not defined as a fire involving an electrical device or appliance. For example, a fire on an electric range that occurs due to overheating and ignition of the oil in a deep-fry pan is not classed as an electrical fire, even though it involves an electrical appliance. Conversely, an electrical device or appliance is not always needed for an electrical fire to occur. Lightning-caused fires are a form of electrical fires and these can ignite, for example, a dry bush, which is not an electrical device. As with other categories of fires, there are three main aspects of electrical fires to be considered: ignition, combustion behavior, and suppression. This chapter deals mostly with the ignition aspects. Combustion behavior of electrically initiated fires is normally dominated by the fuel characteristics of the primary combustibles that are involved. These will most commonly be cellulosic or plastic fuels, although with some sustained electrical faults combustion of aluminum (e.g., busbars) can play a significant role. Copper and steel generally do not burn even in worst-case electrical fires. Sustained burning of aluminum generally does not take place except in installations of at least 480 V and of high current
V. Babrauskas (*) Fire Science and Technology Inc., San Diego, CA, USA
capacity. The traditional segregation of electrical fires as Class C fires has been based primarily on concerns of potential shock hazard to firefighting personnel. But research studies [1, 2], show that this would be a realistic concern only for high-voltage installations. Even for these, the hazard is minimal. For example, the most recent study on this topic [3] showed that a fire fighter would have to be holding a straight-stream nozzle 1.0 m from a 45 kV power line for a shock hazard, defined as 10 mA passing through the body, to be created. For a fog nozzle, no hazard could be produced at a 2.0 m distance even with a 200 kV line (smaller distances were not measured) and current with the 200 kV line was only 0.35 mA. This chapter discusses the differences between electric current and static electricity, outlines the various forms of heating that can take place due to electrical activity, and discusses how ignition of various substances may take place due to electrical activity. The electrical characteristics of lightning are also discussed, since this is a form of electrical discharge. Several reviews of electrical fires have been published by Babrauskas [4–6]; these provide additional details on the status of research and practical applications.
Static Electricity and Electric Current In the simplest terms, electricity is a form of energy associated with the movement of
M.J. Hurley (ed.), SFPE Handbook of Fire Protection Engineering, DOI 10.1007/978-1-4939-2565-0_22, # Society of Fire Protection Engineers 2016
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electrons. The movement can be sustained (i.e., electric current) or not. Sustained movement requires a conductive path to be established, but the limited movement of electrons possible in insulators can allow charge separation to occur. Once this happens and a certain amount of charge is accumulated, a discharge may be possible and this whole process is known as static electricity. Static electricity, however, does not mean an absence of electric current, since current (flow of electrons) occurs both in charging and in discharging. Instead, static electricity is a somewhat imprecise concept implying that the primary flow of electrons is either in insulators or in conductors that are not connected into the form of a closed circuit.
Electrical Discharges Breakdown Phenomena Electrical breakdown means that a substance that is normally an insulator suddenly (and possibly just temporarily) breaks down, and becomes a conductor. The process is somewhat different in gases, liquids, and solids. In a gas, the medium is self-healing—if the driving force is removed, the medium restores itself essentially to its original condition, although a slight chemical change may occur (e.g., some ozone can be created by an electrical discharge in air). Liquids are also largely self-healing, but the chemical changes entailed may have some long-term implications. The best example of this is oil-filled transformers that can withstand a certain amount of discharges if these are not too energetic. But each discharge causes degradation of the liquid and eventually the transformer may suffer a catastrophic failure due to this degradation. Discharges in solids, on the other hand, are usually highly destructive. With most solid materials, an electrical discharge creates a path that is permanently damaged or destroyed. The majority of insulating solids are organic substances and a discharge through an organic solid has the effect of carbonizing the material, but a portion of the material may also be ablated.
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A more detailed explanation [7] of the breakdown process is as follows. Due to cosmic radiation and other factors, a small number of free electrons are always present in air. If an electric field is applied, the electrons move in the direction opposite to the electric field (i.e., to the positive electrode). If the electric field is sufficient, an electron can travel only a short distance before it collides inelastically with an atom/molecule and ionizes it, now leaving two free electrons. Both of these electrons now continue to travel and each one will again collide, and create a new pair of electrons (original electron, plus electron removed from an atom) at this collision. It can be seen that this process leads to exponential growth and one electron, starting at the cathode, will result in n electrons reaching the anode, where n ¼ eαd , with d ¼ gap distance and α ¼ Townsend’s first ionization coefficient, with has the units of 1/distance. The value 1/α then represents the distance between successive ionizing collisions. The generation of electrons is further augmented by the positive ions which are created in the process and which move, much more slowly, towards the cathode. When a positive ion collides with the cathode, it then liberates γ electrons, with γ being known as Townsend’s second ionization coefficient. If only electrons that naturally get liberated from the cathode enter into this process, augmented by electrons liberated due to collisions with neutral species along the path, then the discharge (a discharge is the flow of a detectable amount of current) is called a Townsend discharge, named after J. S. Townsend, an early researcher of gas discharges. A Townsend discharge is nonluminous and the current flow is small. If the process increases so that a sizable current starts to flow, term breakdown is applied, and the two main types of breakdown modes are: electric arc (if sustained) and electric spark (if not). An electric arc requires that a sufficiently high current (more than approximately 0.1 A) be available. As soon as a conducting path gets established across the gap, the delivery of energy into the arc channel rapidly increases, but the rate of current growth is largely determined by the external circuit parameters. The actual arc channel starts out
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small, then grows rapidly in diameter. This radial growth is so fast that it is modeled as a shock wave propagation [8]. The shock front, however, does not correspond identically with the channel boundary. The channel expands in two stages. Initially it expands by means of the expanding shock wave until the shock wave detaches from the luminous core. After that point it detaches more slowly until an ultimate value is reached. During the initial expansion phase, the channel conductivity [9] is 1.5 104 S m1 and the channel radius r (mm) increases [10] according to: r ¼ 294
I 1=3 t1=2 1=6
ρo
where I ¼ current (A), t ¼ time (s), and ρo ¼ ambient density of air (kg m3).
Paschen’s Law The kinetic energy W gained by an electron when accelerated by an electric field E over a distance L is: W ¼ EeL where e is the charge of the electron (1.6022 1019 C). The simplest estimate of breakdown would be that a self-sustained avalanche is created when W attains a sufficient value so that a traveling electron can knock off an outer-shell electron from molecules of the gas through which it is traveling. The distance L is the mean free path (average distance between two collisions) for an electron in ambient air, which is experimentally found to be about 0.4 μm. This value is not to be confused with the mean free path of the molecules of air, which is around 0.068 μm, a smaller distance to the fact that air molecules are much larger than electrons. The energy required to ionize an oxygen molecule is 13.5 eV, while for nitrogen it is somewhat higher at 15.8 eV. An electron volt (eV) is a unit of energy equal to 1.6022 1019 J. Thus, the simple estimate would be that breakdown would occur when
E¼
W 13:5 1:6022 1019 ¼ eL 1:6022 1019 0:4 106
¼ 34 106 Vm1 ¼ 34MVm1 This estimate is about a factor of 10 too high, and this is because this simplest effort at estimating ignored the electron avalanche effect. In actual fact, breakdown in air at 1 atm requires a field of roughly 3 MV m1, and Paschen’s paper of 1889 [11] is credited with defining a relation between breakdown voltage, spacing of electrodes, and gas pressure, which has become known as Paschen’s Law. According to Paschen’s Law, the pressure gap distance product is the controlling variable and the breakdown voltage V is given by: V¼
c1 pd c2 þ lnð pd Þ
where p ¼ pressure, d ¼ gap distance, and c1 and c2 are constants. Thus, when the electric field exceeds about 3 MV m1, breakdown is estimated to occur. Modern measurements [12] of Paschen’s Law curves for air and for nitrogen are shown in Fig. 22.1. For gaps greater than about 0.1 mm, it can be seen that the curve is essentially a straight line. For smaller gaps, however, the breakdown voltage does not go to zero and, instead, a minimum breakdown voltage is found. This minimum of the Paschen curve is approximately 340 V, and it occurs at a Pd product of 0.007 atm-mm. In other words, in ambient air, the minimum breakdown voltage occurs for a gap of 0.007 mm (7 μm). This is an exceedingly small distance, and two conductors this far apart would appear to be touching to the naked eye. For practical applications, it can be more convenient to present results in the form of the dielectric strength (MV m1), which is the breakdown voltage divided by the distance between the electrodes. This is shown in Fig. 22.2 and indicates that for larger distances, the dielectric strength of air is approximately 3.0 MV m1; the value for nitrogen is quite similar. Paschen’s Law is not absolute but rather depends on experimental conditions. These
Electrical Fires
Fig. 22.1 The breakdown voltage (Paschen’s Law) between spherical electrodes in air and nitrogen. The voltage refers either to DC voltage or to the peak value, for AC voltage (From Ignition Handbook [7], used by permission)
665 100,000 Nitrogen Air Breakdown voltage (V)
22
10,000
1,000
100 0.001
0.010
0.100
1.000
10.000
100.000
Pressure-distance product (atm-mm)
35 Nitrogen Air
30 Dielectric strength (MV m–1)
Fig. 22.2 The dielectric strength at 1 atm, as a function of distance (From Ignition Handbook [7], used by permission)
25 20 15 10 5 0 0.01
0.10
1.00
10.00
100.00
Distance (mm)
include electrode shape, the material of the electrodes, electrode surface contamination, humidity, and the polarity (if electrodes are not identical). The law also assumes that the impressed electric field is uniform and deviations occur if the field has nonuniformities. Paschen’s Law curves are identical for both AC and DC voltages. But since AC voltages are normally described by their root-mean-square
(rms) values and not the peak values, if results are to be applied to AC voltages, then the values pffiffiffi indicated in Fig. 22.1 need to be divided by 2. Thus, on an rms basis, the minimum AC breakdown voltage is 340/1.414 ¼ 240 V(rms). It must be emphasized that Paschen’s Law is not used in the design of low-voltage equipment. There are many standards worldwide that govern gap sizes (clearances) required for low- or medium-
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Fig. 22.3 Breakdown voltage for mica as a function of gap distance
100,000
Breakdown voltage (V)
Austen and Whitehead8 Lewis et al.9 Fitted line 10,000
1,000
100 0.0001
voltage equipment, but they all mandate values much larger than the minimum that would suffice to prevent breakdown. This is for serviceability reasons and also takes into account surges.
Dielectric Strength of Solid or Liquid Insulators The dielectric strength of solids and liquids can also be characterized by similar graphs, but only limited specialized references exist [13]. Most of this literature covers solely the HV regime, and data for voltages below 1 kV are extremely scarce. Mica is one of the rare insulators for which low-voltage data are available, with the results of Austen and Whitehead [14] and Lewis et al. [15] being shown in Fig. 22.3. For polymers, some data obtained by Abed [16] on polystyrene, PVC, and PTFE are shown in Fig. 22.4. Also shown are data on polyethylene obtained by Mason [17] and a single data point given by Austen [18]. The latter indicates that breakdown occurs at 150 V when the insulation thickness is reduced to 0.003 mm. The most common insulator for low-voltage1 wiring is
1 Low voltage is defined by various institutions as being lower than 600, 660, or 1,000 V.
0.001
0.01 Distance (mm)
0.1
1
poly(vinyl chloride), PVC. A more recent review paper [19], however, indicated that no breakdown data for PVC are available below 0.07 mm, at which thickness the breakdown voltage is still in the kV range (approximately 7 kV). The available data suggest that plastics most likely show a relationship where the breakdown voltage approaches zero as the electrode spacing becomes infinitesimal. But the available data are too few to establish this quantitatively.
Arcs Definitions of Arc and Spark Both an electric arc and an electric spark fall under the general definition of a continuous, luminous discharge of electric current crossing a gap or an insulating surface between two conductors [7]. They are distinguished in that an arc is a sustained event while a spark is transient. Matters are clouded by the fact that some researchers refer to a “spark phase” of an arc, but this type of definition is not widely held and is not used in fire safety engineering. Spark, however, also has another very different definition: a small incandescent particle. For clarity, the latter can be referred to as a mechanical spark.
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Fig. 22.4 Breakdown voltage for several polymers as a function of gap distance Breakdown voltage (kV)
100
10
1
Arc
Abnormal glow
Normal glow discharge
Dark discharge
0.1 0.001
Voltage (V)
Polystyrene PVC PTFE PE (Mason)11 PE (Austen)12
0.01
0.1 Distance (mm)
1
10
theoretical predictions, are shown in Fig. 22.6. Also shown is the following empirical data fit: T ¼ 6, 500I a 4:5 A T ¼ 4, 010 þ 1, 658 ln I a I a > 4:5 A The theoretical predictions are only loosely obeyed, so the empirical data fit should be sufficient for calculation purposes.
10–10 10–5 10–4 10–3 10–2 10–1 Current (A)
1
10
102
Fig. 22.5 Schematic representation of steady-state voltage and current for several discharge types (From Ignition Handbook, used by permission)
Characteristics of an Arc An arc is actually only one of several types of steady electrical discharges that are possible, as shown in Fig. 22.5. But, of these, only the arc is important from a safety viewpoint, and it corresponds to discharges of the highest current and the lowest voltage. The temperature of an arc can vary widely. Under ambient pressure conditions, it is commonly 6,500–12,000 K but can reach 50,000 K. The primary factor governing arc temperature is the arc current. Experimental data, along with some
Means of Creating Arcs An arc can be created by a variety of means, primarily the following: • Raising the voltage across a fixed pair of electrodes until breakdown occurs • Opening or closing the contacts in a currentcarrying circuit • Transitioning from arcing across a carbonized path (arc tracking) • Glow-to-arc transition • Introducing ionized gases in between two electrodes (e.g., from a flame) Creating an arc by raising the voltage across a fixed pair of electrodes is very common for testing purposes. It also occurs in some accidental circumstances, as discussed below. Contact arcs regularly occur in electric switches, relays, and similar devices. They also occur inadvertently, when, for example, two bare
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30,000
Temperature (K)
25,000
20,000
15,000
10,000
5,000
0 1
10
100
1,000
10,000 100,000
Arc current (A)
Fig. 22.6 Temperature of arcs in ambient-pressure air, along with predictions from theory (light lines) and an experimental data fit (bold line) (From Ignition Handbook, used by permission)
current-carrying conductors are accidentally shorted. When considering electric switch contacts, the arc caused by closing the switch is called a make-arc (or closing arc), whereas the arc caused in opening the switch is a break-arc (or opening arc, or parting arc). The process of creating an arc (at voltages that may be much less than Paschen’s Law minimum of 340 V) is quite similar for both types of contact arcs. In the case of a break-arc the steps involved are the following: 1. The electrodes that were originally touching at numerous spots start to touch at only a few very small spots. 2. A high current density passes through the small metal diameter of contact area that is available. 3. The metal bridge joining the two contacts starts to melt. 4. The bridge elongates and rises in temperature. 5. The bridge reaches the metal’s boiling point, becomes unstable, and ruptures. 6. Voltage rises rapidly across the gap, thermionic emission from the hot cathode starts, and eventually the gap becomes ionized and an arc forms. 7. The diameter of the arc expands from that of the bridge to its eventual free-burning diameter.
The voltage across the gap at the moment of rupture is only approximately 1 V. The reason Paschen’s Law does not apply is that it describes the characteristics of room-temperature, nonionized gases, and the space between the contacts is ionized and at high temperature. Even though 10–15 V is needed for the steadystate operation of an arc, the arc is able to initiate with only a 1 V drop due to inductive effects of the wiring. In closing switch contacts (a make-arc), the sequence of events is very similar. Contact is initially made at only a few high spots. These have limited current-carrying capacity and proceed to melt and rupture, at which point an arc develops. That arc is normally extinguished by heat losses when the contacts close together more tightly. Arcing across a carbonized path (arc tracking) is arcing that is supported by a carbonized path on a solid, as discussed below, and this is a low-current process. If this process continues and accelerates, one possible outcome is a normal, high-current arc across air. The conditions leading to this have not been explored in detail, however. Glow-to-arc transition is a rare phenomenon not normally encountered in fires [20]. The dielectric strength of a hot, ionized gas is tiny compared to that of normal ambient air. Thus, when the distance between two conductors is such that there would be no possibility of breakdown in normal air, introducing ionized gases in between two electrodes (e.g., from a flame) can lead to arcing. This is why, in many fires, a large number of artifacts are found suggesting that an arc occurred there. It is not because several different places arced simultaneously and each erupted into fire [21]. Instead, a single fire introduced flames into various locales where conductor-to-conductor spacing was such that arcing could not be supported in ambient air but could be supported in an ionized, hot medium. Arc Flash The thermal radiation from an arc is referred to as arc flash and a sustained, high-current arc can lead to severe injury or death of an individual so exposed. IEEE Std 1584 [22] provides a
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calculational method for estimating arc flash radiation, whereas ASTM F 1506 [23] and ASTM F 1959 [24] provide procedures for assessing the actual effectiveness of protective clothing. Arc Extinguishment A DC arc will extinguish only if the power supply is removed or if enough material erodes to make the gap too large. In an AC circuit, an arc will self-extinguish 2 60 times (2 50 times with 50 Hz power) per second, each time the current goes to zero. But it may reignite thereafter if conditions are right. Whether or not the arc reignites afterwards depends on whether the arc channel can recover so that it will not break down again with the new imposed voltage. Arcs in circuits of less
than 150 V tend to extinguish and not reignite when the waveform goes through the zero crossing. Arcs in circuits of over 600 VAC tend to draw very high currents and, consequently, may be relatively safer since a circuit protection device is likely to open. Voltages between 150 and 600 V are considered the most hazardous in regard to fires being ignited from arcing [25]. This is because the arcs tend to not be extinguished, yet the current flows are small enough that circuit protection devices operate slowly. Typical waveforms [26] for arcing in 120 VAC circuits are shown in Fig. 22.7. Note the intermittent nature of the arc as it extinguishes and reignites.
Voltage
Current
Fig. 22.7 Typical waveforms during a branch-circuit arcing event
670
Ignition Modes Involving Electric Current Sparking or Arcing Electric sparking or arcing can ignite materials in all phases: gases, liquids, solids, liquid aerosols, and dust clouds. Ignition in gaseous and dust cloud media has been studied extensively. Ignition in bulk liquids is rare, apart from oil-filled transformers and other HV devices. Ignition of liquid sprays, fogs, or aerosols is problematic in some industries, however. Ignition of solids from arcing or sparking is common but has not been researched to any satisfactory degree. Gases If an atmosphere exists where a flammable gas has been dispersed into an oxidant gas (commonly air) and the mixture is within its flammable limits, spark ignition is generally very easy. Arc ignition has normally not been studied. Since a very low-energy transient energy discharge ignites such mixtures, a sustained energy discharge will be much more capable of ignition. For this reason, the phenomenon is referred to as spark ignition rather than arc ignition. Flammability limits for a number of gases are given in Chap. 17. A larger collection of data is provided in the Ignition Handbook [7]. Some values for minimum ignition energy (MIE) are given in Table 22.1; more extensive tables are available in the Ignition Handbook [7]. It should be observed that these energies are exceedingly small and are tabulated in millijoules. To appreciate the magnitude, one can consider the fact that if a coffee mug is raised by 0.3 m, its potential energy is increased by roughly 1.0 J. Dust Clouds Dust clouds are significantly more difficult to ignite than gases, but explosions due to this cause remain an important concern in manufacturing, mining, and agricultural industries. The lower flammability limit of dust clouds has generally been erroneously reported in most data compilations because apparatuses used to measure the lower flammability limit (LFL) of dust clouds have had gross, systematic
V. Babrauskas Table 22.1 Minimum ignition energy (MIE) of some common gases and vapors Substance Acetone Acetylene Ammonia Benzene Butane Carbon disulfide Cyclohexane Ethane Ethylene Ethylene oxide Furan Heptane Hexane Hydrogen Hydrogen sulfide Iso-octane Methane Methanol Pentane Propane Propylene Toluene Vinyl acetylene p-Xylene
Energy (mJ) 2.15 0.03 680 0.91 0.26 0.039 2.65 0.42 0.114 0.105 0.328 1.15 0.29 0.03 0.077 2.9 0.71 0.3 0.82 0.5 0.418 2.5 0.095 0.2
From Ignition Handbook, used by permission
errors, leading to reported values for many substances being much lower than their true value [7]. But, as a very rough rule, dust clouds will not reach their LFL unless visibility is down to zero in that location. The upper flammability limit (UFL) for dust clouds is rarely measured, simply because it is generally very difficult to generate a dust cloud that exceeds the UFL. Minimum ignition energies have been tabulated and it is believed that those are more reliable. Some typical values are shown in Table 22.2. Unlike gases, where MIE values are typically below 1 mJ, MIE values for dust clouds are typically some two orders of magnitude higher. Nonetheless, these are all still low, even though they are higher than for gases. Solids Ignition of solids from electric sparks or arcs is unfortunately common. The cause can be
22
Electrical Fires
671
Table 22.2 Minimum ignition energy for various dust clouds Substance Aluminum Aspirin Black powder Coal Cocoa Coffee Cornstarch Cotton linters Dextrin Flour, cake Grain dust Magnesium Manganese Nitrostarch Nylon Paper dust Phenol formaldehyde Polyethylene Polyethylene terephthalate Polystyrene Rice Silicon Soap powder Sugar, powdered Tantalum Tin Titanium TNT Urea formaldehyde Wheat starch Wood flour Zinc
MIE (mJ) 50 25–30 320 250 100–180 160 30–60 1,920 40 25–80 30 40 305 40 20–30 20–60 10–6,000 70 35 40–120 40–120 100 60–120 30 120 80 25 75 80–1,280 25–60 30–40 960
From Ignition Handbook, used by permission
either static electricity or circuits carrying an electric current. Some of the mechanisms have been studied, and these are discussed later. However, the problem of understanding the response of solid materials to a spark or arc ignition source has been neglected. Apart from metals and some other rare substances, there are no combustible solids with an ignition temperature over 1,000 C. Figure 22.6 shows that the temperature of an electric arc is at least 6,500 K and may be much higher. Yet, an electric arc impinging onto a combustible solid is not necessarily assured of
igniting it. There are two primary factors operating in such cases: (1) The arc impingement may be very brief, many combustible materials can resist enormous heat fluxes if these are sustained only briefly. (2) The material may ablate too rapidly to allow ignition. These mechanisms, however, are understood only qualitatively—there have not been research studies to successfully quantify them.
Arcing Across a Carbonized Path Many electrical fires are due to arcing across a carbonized path. If a carbonized path is created where current may potentially flow, arcing may then occur along this path, possibly leading to ignition either of the combustible insulator itself, or some other nearby fuel. A carbonized path can be created in at least three ways [27], such as the following: 1. Arc tracking 2. Overheating (by electrical overcurrent, external radiant heating, etc.) 3. Impingement of fire on solid electrical insulation material Arc Tracking Of these three possibilities, substantive research has been done only on arc tracking. Arc tracking is a progressive creation by electrical means of a carbonized path along the surface of an insulator that separates two current-carrying conductors. Arc tracking is subdivided into two types: dry tracking and wet tracking. Dry tracking can be induced by causing an electric arc to impinge onto the surface of an organic material. Wet tracking can occur if a film of water covers the surface of the insulator and spans between two conductors. The electric conductivity of pure water is very low, but when ionic contaminants are dissolved in water, its conductivity increases and it becomes possible to create a current flow if the layer of moisture has access to conductors from both sides of the line. The flow of current then has a drying effect on the moisture layer. The drying is nonuniform, and eventually dry patches
672
tracking will normally not be initiated unless a conductive moisture film exists that has electrical contact to two conductors that have a voltage difference between them. This may happen if a cable is mechanically damaged so that two current-carrying conductors are exposed. Moisture then collects on the damaged area, and pollutants are present that ionize the layer. But on some materials, arc tracking does not require a direct contact between an electrode and the surface of the insulator; tracking over phenolic and melamine surfaces can be initiated even when the electrodes are separated by gaps of about 0.25 mm from the insulator surface. In general, in low-voltage circuits, a carbonized path is probably most commonly created by a poor connection or other source of locally elevated temperatures, but moisture or pollutants can also be of significant importance. Oba [32] conducted experiments where he damaged the insulation on Japanese PVC-insulated power cable to expose the conductors and then sprayed electrolyte onto the area to initiate arc tracking. By varying the AC voltage supplied to the cord, he obtained a char length relation as a function of voltage (Fig. 22.8). Below 50 V, progress of charring
8 7 Char length developed (mm)
start to be formed along the current path. With buildup of carbonization along the path, small electrical discharges, called scintillations, can then occur. Since part of the current flow is through an electrolyte of significant resistance, these scintillations represent a very small current flow and would not trip any overcurrentprotection devices. The ultimate event, if it occurs, is the actual flaming ignition of the material over which tracking is occurring. If the tracking is dry, the processes that occur along the surface are similar. Although an overcurrent-protection device cannot be expected to protect against arcing across a carbonized path (unless this escalates to a high-current fault), arc fault circuit interruption (AFCI) devices, which have been developed in recent years [28], are intended to respond to this condition; because they are relatively new, however, fieldperformance data do not yet exist, although it is known that some models of first-generation devices have not been highly successful [29]. Surprisingly, temperatures up to 1,000 C can be generated by such surface leakage discharges. These elevated temperatures then continue the process of polymer carbonization. Thus, in the tracking process, a carbon track is laid down along the surface, and that track has a low enough resistivity that current can subsequently start to flow along the carbonized track, which, in turn, causes more carbonization and more heating. A runaway situation can then develop. Scintillations can vary widely in their discharge energy, with the low end of the scale being mild events that would not be expected to damage metals (although they might ignite some potential targets). Nakamura et al. [30] measured scintillations on PVC and reported values that ranged from 100 to 3,000 J. But, they did not endeavor to set up their experiments to elicit the lowest possible discharge energy. To create arc tracking, a vastly lower voltage can suffice than for breakdown in air between two electrodes. For example, with many plastics, Yoshimura et al. [31] found that 600 VAC was sufficient to cause an arc discharge across a 4 mm gap. By contrast, breakdown across a 4 mm gap in air requires about 10,000 VAC. On cables, wet
V. Babrauskas
6 5 4 3 2 1 0 0
50
100
150
200
250
Voltage (V)
Fig. 22.8 Char length developed after 70 h in the wet arc-tracking experiments of Oba (From Ignition Handbook, used by permission)
22
Electrical Fires
was very limited. He repeated the experiments by depositing powdered carbon onto the damaged area and found, in that case, for arc tracking to occur, the applied voltage had to exceed 24 V. Below 50 V, small incandescent spots could be produced but not flaming ignition. Flaming ignition was readily possible for voltages of 100–150 V. Above 200 V, flaming ignition readily occurred, but increased char lengths were not obtained since the events were explosively forceful and blew off the carbonized material and the melted conductor portions. Under other conditions, much less than 24 V is sufficient to cause arc tracking. Bernstein [33] reports that arc tracking can occur in 6 V battery circuits, provided the battery has sufficient current capacity to sustain the arc. Arc-tracking problems have been troublesome in a variety of models and types of motor vehicles in circuits operating at around 14 VDC (nominal 12 V) [7]. For polymers, the molecular structure is the main determinant of arc-tracking propensity [34]. Aliphatic polymers (e.g., polyethylene, PTFE) tend not to undergo arc tracking, whereas aromatic ones or ones containing alternating double bonds (e.g., phenolic, polyethylene terephthalate, polystyrene) do because the latter, when pyrolyzed, leave residues that are electrically conductive or semiconductive. Also tending to exhibit arc tracking are polymers that, although lacking aromatic rings or double bonds originally, form rings or double bonds during thermal degradation; PVC and polyacrylonitrile are examples. It was also found that oxygen is not a requisite for the formation of arc tracks and that materials can be made to arc-track in a nitrogen atmosphere. Generally, arc tracking can only happen if a polymer can char, since a conductive track can only be established in char. Practical difficulties arise in evaluating this because charring is not an absolute property of polymers but, rather, depends on environmental details. It has also been found [35] that arc tracking is promoted by the presence of halogen atoms in the polymer. Conversely, alumina trihydrate (Al2O33H2O), a common filler for many polymers, is highly
673 d1
Metal conductor d2
Plastic insulator
Fig. 22.9 Simplified view illustrating clearance and creepage distances (From Ignition Handbook, used by permission)
effective in reducing the arc-tracking propensity in certain polymers [36, 37]. Most research studies have not focused on the time element and none have done so in a systematic way. The minimum current needed, however, has been studied. Wilkins and Billings [38] obtained the following minimum values: PVC 0.15–0.20 mA, PVA 0.3 mA, Ebonite (butadiene/methylstyrene rubber) 1.1 mA, phenolic/paper 1.15 mA, polycarbonate 1.2 mA, and PTFE 2.3 mA. Creepage In design, the resistance to arc tracking is controlled by two means: (1) selection of well-performing insulation materials, and (2) observing adequate creepage distances. The latter concept is illustrated in Fig. 22.9. For arcing in air from metal to metal, the governing distance is called the clearance distance, d1. But since arc tracking proceeds only along solid surfaces, the distance across which arc tracking must travel, if failure is to occur, is called the creepage distance, d2. Creepage distances are set down in numerous military and industrial specifications, but the rationale is usually empirical and not much scientific research is available on the topic.
Surface Flashover Fire protection engineers need to be aware that the term flashover is used in a very different way in electrical engineering, where it means “a discharge which occurs over the surface of a solid dielectric in a gaseous or liquid medium.” [39]
674
V. Babrauskas
Gross Overloads Excessive overload can lead to fires, but this condition is much rarer than is an arcing fault. It can arise if either a circuit breaker is faulty or a cable is used that is of much smaller gauge than is the rating of the circuit breaker. Both of these situations are relatively uncommon. Ampacity ratings of wires and cables are conservative enough that an overload of roughly 2 is not expected to create any significant problems, at least in the short term (long-term thermal degradation of insulation material is a separate issue).
Ignition in the excessive-overload mode is unlikely to occur if the cable is in a circuit that is protected by a circuit breaker/fuse correctly matched to the rating of the cable, since tripping would occur rapidly under 3 and greater overloads. But ignitions can readily occur if a much smaller gauge cable is used than corresponds to the rating of the circuit breaker. An overload may not directly ignite an insulated wire but may significantly raise the temperature of both the wire and the insulator. Old-style rubber-insulated wires used to be prone to a sleeving effect, whereby insulation closest to the wire is thermally degraded and shrinks back from the conductor. For wires insulated with thermoplastic insulation (including the majority of today’s common cable types), a somewhat different effect is found. Elevated temperatures cause copper to elongate but the insulation to shrink. As a result, copper wires readily “pop out” of the softened insulation. A direct metallic contact can then occur, with this short circuit being a localized place of ignition [7]. By contrast, if a PVC-insulated cable is externally heated (by fire or otherwise), it usually chars rather than melts. But melting, rather than charring, may occur if the external heating is with a very low heat flux [40], below about 15 kW m2. Bubbling of thermoplastic insulation has been experimentally found only to occur from overcurrent and not due to external heating [40].
If a sufficiently overloaded condition persists, then cables may be able not just to ignite but also to create a propagating, self-sustained fire. Experimental studies [7] indicate that, for this event to occur, the current carried must be 300–700 % of the rated current (ampacity). However, all existing tests have been short-term. Even a current at 200 % of rated ampacity, if sustained for a protracted period of time, may deteriorate the insulation enough so that carbonization can begin. Eventually, failure may not be the melting and shorting commonly involved in ignitions from short-term overloads but, rather, some form of tracking damage.
Excessive Thermal Insulation Ampacity ratings for cables are based on a certain amount of convective cooling being available, which can be defeated by thermal insulation. Thus, even if the current passed through a cable is within its rating, embedding it in thermal insulation can cause the temperature to rise to values that are no longer reasonable for the particular class of insulation used. If, in addition, an overload condition is created, the heating can be greatly exacerbated. Bunching of cables together can also lead to overheating, since ampacity ratings envision only a limited aggregation of adjacent conductors. Goodson et al. [41] observed a house
The dielectric strength of air is lower than that of any commonly used electrical insulators, so if the path through air and the path through a solid insulator are of similar length and breakdown occurs, it will go through air, not through the solid insulator. The surface of an insulator may become polluted so that its breakdown strength becomes low; this problem is common in locales exposed to salty air near the sea. The material with the lowest breakdown strength may be this pollutant film and, if breakdown occurs along this film, it is referred to as “surface flashover.” This reaction does not constitute arcing across a carbonized path, since the path, although of low breakdown strength, is not carbonized. The problem is relevant only to high-voltage (HV) circuits and would be a source of ignition only in the vicinity of HV installations.
Overloads and Related Phenomena
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Electrical Fires
during construction where charring damage was already found on bunched NM cables. Thus, they ran wall-cavity tests using bunched, 90 C-rated NM cables and obtained charring when the stud cavity was insulated with polyurethane foam insulation. Prior to World War II, knob-and-tube wiring was common in the United States. This form of wiring uses two separate conductors that are not grouped into a cable but are individually strung on widely spaced porcelain knobs. The currentcarrying capacity of this form of wiring is dependent on there being unobstructed air cooling of the wires. Fires have occurred when the wires were buried in thermal insulation. A similar problem can be encountered when extension cords, which are rated for exposed-air use, are buried under thermally insulating objects or else are coiled in multiple layers on a cord reel while carrying a high current but one still within the nominal rating. Stray Currents and Ground Faults Stray currents occur when circumstances cause current to flow through paths not intended to carry current. Ground faults are a well-known example [42]. They can occur if a conductor is abraded or damaged and contacts metal siding, roofing, and so on. Kinoshita et al. [43] documented that a current of only 5 A was required for ignition when a three-conductor, PVC-insulated cable contacted a galvanized iron roof. The Consumer Product Safety Commission (CPSC) has hypothesized that the Beverly Hills Supper Club fire, one of the deadliest U.S. fires of the twentieth century, was made possible by improper wiring of the neutral conductors and triggered by a ground fault that occurred [44]. If a building has conductive components throughout it, such as metal lath, aluminum siding, an electric fault can result in an electrified house, leading to multiple ignitions [7]. The fault is commonly contact with HV wiring. An unusual mode of ignition from a ground fault is where current flows through a gas line.
675
The current can cause overheating of the metal and lead to a rupture of the pipe [45]. In recent years, a related problem has been fires or explosions in houses due to use of CSST (lightweight corrugated stainless steel tubing) gas piping instead of black iron [46]. These products proved to be particularly susceptible to puncturing by lightning strikes, which do not need to be direct enough to cause other damage. Gas escapes from the small holes created and a gas explosion or a house fire ensues. In cold climates, it is not rare for individuals to thaw a frozen water pipe by attaching a welding transformer and passing current through it. Fires have resulted due the very large currents that are involved [47]. Overvoltage, Floating Neutrals, and Surges Ignitions from an overvoltage is relatively rare, as concerns branch-circuit wiring. The materials used for wires and wiring devices are well able to withstand the normal surges that are a regular event in a power distribution system. To experience ignitions, one of the following events is generally needed: 1. Lightning strike 2. Accidental delivery of high voltage into low-voltage wiring 3. A floating neutral 4. A large voltage spike (surge) Lightning strikes can result in massive ignitions, not just of wiring but also of all sorts of combustibles. Occasional fire reports are encountered in which, due to some malfunction in the power distribution network, high voltage got applied to wiring intended to carry only 120/240 V. A case is documented [48] in which a utility transformer fault caused all the ground-fault circuit interrupter devices in a house to fail, along with igniting a fire due to an explosion of a TV set. In another case, a faulty transformer caused the service entrance wires to ignite and burn inside a house. A systematic study of such fires does not exist, but ignition should be considered very likely any time that such a failure occurs.
676
V. Babrauskas L1 120 V Break in neutral
N
120 V
R1
Rx
R2 L2
Fig. 22.10 Floating neutral (From Ignition Handbook, used by permission)
A floating neutral (sometimes called open neutral) can lead to ignition in 120/240 V wiring circuits due to a special nature of that circuit topology.2 In a single-phase service entrance, there are three current-carrying wires: two hot wires and one neutral. Figure 22.10 illustrates the normal feed from an outdoor transformer to a building. Inside the building, the system becomes effectively a four-wire system, since a safety grounding wire is also run that is connected to the neutral and terminates at a ground rod.3 All 240 V loads are directly connected across L1 and L2 and do not depend on the presence of the neutral. But 120 V loads are connected across N and either L1 or L2. If a neutral is in place, the loads will receive the intended 120 V voltage. However, if a break occurs in the neutral, the voltage delivered to 120 V loads can swing widely, in principle from barely above 0 to almost 240 V, although in practice the range is not quite as large. Figure 22.10 shows the circuit arrangement. The voltage present across a particular load Rx will be determined by the voltage divider action of other loads in the system, designated as R1 and R2. The voltage across Rx will be Vx ¼
240 R2 R2 1þ þ R1 Rx
Most electrical or electronic equipment can ignite if a voltage much in excess of the intended
2
The discussion here is based on electrical practice in North America. 3 Mobile homes normally have a four-wire service from pole to building.
one is fed to it. Conversely, most devices will not ignite if the voltage delivered to them is too low. Electric motors, however, are an exception, and flaming fires can result from certain motors running at a sufficiently undervoltage condition. An ignition due to undervoltage can also occur if one hot leg of a 240 V circuit is disconnected. If the circuit has any 240 V appliances and these are energized, then they can transfer power from the live leg to the disconnected leg. But the delivery will be through a sizeable resistance and much less than 120 V will be delivered. The preceding discussion ignored the presence of the ground wire. According to The National Electrical Code [49], a grounding electrode must be connected from the neutral to an earth ground at the service entrance. But, provided that the neutral is functioning properly, this ground wire serves no observable function. Consequently, there may be little to prevent its deterioration or abuse over the years. If a break in the neutral then occurs, a sizable current can flow through the ground wire. If the ground wire passes near or through combustibles, and an excess current ends up flowing through it, then an ignition might occur at that place. Fires have also been reported [50] in installations using armored cable when a floating neutral occurred and current that would normally flow through the neutral instead flowed through the armor. Surprisingly large voltage spikes can be found on 120/240 V systems. Without any overt fault conditions, simply the operation of a motor controller can create a 2,000–3,000 V spike [51]. The majority of voltage surges, however, are due to external—not in-premises—factors. The primary causes are lightning, electrical utility switching transients, and failures of components in the high-voltage electrical transmission system [19]. To evaluate the role of voltage surges, it is essential to recognize that there is a fundamental dividing-line voltage. Surges above approximately 6,000 V(peak) lead to a “sparkover of clearances” widely throughout the house. In other words, the householder will typically find the majority of outlets and other electrical devices have suffered calamitous damage, and
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677
Fig. 22.11 Surge voltages experienced in branchcircuit wiring
100
Occurrences per year
10
1
0.1
Breakdown over normal clearance distances
0.01
0.001 100
1,000
10,000
Peak voltage (V)
possibly multiple fires were ignited. Conversely, surges below about 6,000 V(peak) will generally appear benign. But appearances may be deceiving in the case of surges that are in the kilovolt range but below 6,000 V. The 6,000 V value corresponds to the level at which wiring devices4 that are properly designed, installed, and operated will typically suffer a breakdown. But devices that have a manufacturing or installation defect may break down at less than 6,000 V. The hazard comes about if that breakdown is not visually obvious (e.g., concealed inside a wall or within plastic). A breakdown of plastic insulation will lead to the formation of a carbonized path along which the discharge occurred. As explained earlier, once a carbonized path is formed that extends electrode to electrode, arc tracking can start. The process is slow, although an exact time frame has not been established. In one documented case, electrical fires due to this cause occurred after a modest lightning strike struck a house that did not initially lead to fire or widespread visible
4 This refers to outlets, plugs, and similar devices. Electric and electronic appliances are often designed to much less stringent standards and may fail or start burning at significantly smaller surge levels.
electrical damage. The fires erupted about 4 months after the lightning strike [19]. In the case of breakdown of insulation due to below6,000 V surges or spikes, a delayed fire can occur in the following two ways: 1. The initial fault clears itself and the circuit breaker is not tripped (or fuse not blown). 2. The circuit breaker trips, but the householder resets it, and operation seems “normal.” In either case, after a certain period in which arc tracking progresses unnoticed, fire breaks out. It should be noted that applying Paschen’s Law to clearances typically specified by electrical standards, it would be expected that widespread sparkover of clearances would require about 6,500 V(rms) or 9,200 V(peak). The empirical observation that 6,000 V(peak) is typically sufficient evidently reflects the fact that devices in the field do not quite behave as ideally as their laboratory testing would suggest. The 6,000 V(peak) value is vastly greater than pffiffiffi the operating voltage of 120 2 ¼ 170 V(peak). But such peak voltages are not rare, as indicated by several field studies. Figure 22.11 indicates that an individual house would expect to suffer such a surge roughly once every 100 years [19]. Thus, the risk for an individual house is
678
V. Babrauskas
Overheating
Cu2O breeding
Increase of temperature
Initiation of glowing
Increase of contact resistance
Surface oxidation Oxidation on contact spot
Creep and relaxation
Vibration
Breathing
Current flow
Electric arc erosion
Migration of contact
Softening
Surging in current
Thermal expansion contraction
Work hardening
Current cycling ON/OFF
Heat cycling
Stress
Fig. 22.12 Mechanisms for overheating at electrical connections, as outlined by Kuroyanagi et al [52] (From Ignition Handbook, used by permission)
low, but within a given community there can be a number of such events every year. It must be noted that the field studies were all completed before the current era of widespread use of surge suppressors. Thus, houses where a sizable number of surge-suppression devices are used can be expected to be at lower risk than these statistics indicate.
Overheating Connections Failures of electrical connections are generally due to manufacturing defects, installation defects, design defects, abuse, damage, or environmental effects. In addition, it can be expected that much like any other mechanical device, an electrical connection will have a finite lifetime, but—apart from the aluminum-wiring problem
discussed later—there currently exist no useful studies on this point.5 The physics and chemistry of electrical connections are very complex, as illustrated by the phenomenological flowchart put forth by Kuroyanagi and coworkers [52]. From Fig. 22.12 it can be seen that numerous phenomena are involved, but not all have been studied systematically and in detail. In the simplest terms, failure can be understood to involve the following factors: • Localized heating takes place, due to smaller effective area available for current flow compared to a bulk, undamaged conductor. 5 The NFPA Research Foundation is currently conducting a study on aging electrical wiring and there may be conclusions obtained from it concerning the potential lifetime of electrical connections.
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679
• Heating accelerates oxidation and promotes creep. • Creep causes relaxation of the mechanical forces restraining the connection, leading to fewer micro-areas through which effective current flow can take place. • This relaxation further raises the temperature, which further accelerates oxidation. • Oxidation diminishes the area through which current can readily flow. • Expansion and contraction from thermal cycling may cause further loosening. This may cause certain areas of micro-contact to make and break, while a more severe effect entails irrecoverable plastic deformations. Thermal cycling may be due to ambient temperature fluctuations, or due to fluctuations in current, leading to changes in I2R heating. • The presence of moisture or corrosive gases in the environment can accelerate failure due to additional chemical degradation. In the case of PVC insulation, once sufficient overheating takes place, HCl gas will get liberated from the plastic, and this is highly corrosive. • The presence of vibrations also serves to make and break micro-contact areas, resulting in worsening of the connection. The simplest theoretical model of an overheating connection is obtained by assuming that heat is produced at a constant rate in an infinitesimally thin plane section across the wire. The wire is represented as a cylinder without any change of geometry at the point of connection [53]. The solution for the temperature of that cross section is sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r 1 ΔT ðtÞ ¼ q γ , t=τ 2πλh 2 00
where q00 ¼ Power density at the plane section (W m2) r ¼ Radius of the wire (m) λ ¼ Thermal conductivity of the wire (W m1 K1) h ¼ Effective heat transfer coefficient from the surface of the wire (W m2 K1) γ ¼ Incomplete gamma function [54]
and the time constant τ (s) is given by τ¼
r ρC 2 h
where ρ ¼ density (kg m3) and C ¼ heat capacity of copper (J kg1 K1). The equilibrium value of the temperature rise is rffiffiffiffiffiffiffi r 00 lim ΔT ðtÞ ¼ q t!1 2λh As an example, for a copper wire of 14 AWG, r ¼ 1.63/2 ¼ 0.815 mm, ρ ¼ 8,890 kg m3, C ¼ 385 J kg1 K1, and λ ¼ 400 W m1 K1. Assuming that h ¼ 50 W m2 K1, and that 10 W is dissipated in the connection, giving q00 ¼ 10/pr2 ¼ 4.8 106 W m2. Then sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0:815 103 ΔT ð1Þ ¼ 4:8 106 ¼ 685 2 400 50 If the ambient temperature ¼ 20 C, then the temperature at the overheating connection will be 20 + 685 ¼ 705 C, which is much higher than the ignition temperature of most combustibles. This theoretical treatment is highly simplified; nonetheless, it indicates that very high temperatures can be anticipated. In the early stages of failure, bad connections give little external evidence of their deteriorating condition. It is sometimes considered the infrared (IR) thermal imaging can be used as a preventive maintenance operation, since the technique can graphically show hot spots. However, research studies have shown that this is not possible until very late in the process [55]. In the earlier stages, the cool metalwork surrounding the overheated spot essentially preclude finding and identifying the spot. Evidence of overheating is clear when mechanical connections between two currentcarrying conductors start to show glowing. Normally, good electric connections should not be subject to a temperature rise much in excess of that for the conductors themselves. This depends on the connection having a very low resistance. Most metals that are used for carrying electrical current are subject to oxidation when exposed to
680
V. Babrauskas
atmosphere. The metal oxide film formed on the surface has a very high resistivity. Thus, a connection where the mating parts are oxidized will be a high resistance connection and will overheat if significant current is passed through it. Temperatures of a glowing connection vary widely, but peak values at the hottest point have been measured from 1,100 C [56] to 1,500 C [57, 58], for copper connections. Temperatures up to approximately 300 C have been measured on metal parts some distance away from the hot point [54]. Even though copper melts at 1,083 C, much higher temperatures can be found, since the hottest portion is on the metal oxide which is being formed and not on the metallic copper. One of the earliest studies on glowing connections was published [59] in 1961 (Fig. 22.13) and it was found that the connection acts as a nonlinear circuit element. For currents over 10 A, drops of around 2 V were found. But for small currents, voltage drops in the tens of volts can be found. At a maximum current of 20 A, 50 W is dissipated in a copper/brass connection and around 35 W for copper/iron. The study also noted that the power dissipation
60
30
Cu/Brass
Power dissipated (W)
50
40
25
20 Cu/Fe
30
15
20
10
10
5
Cu/Brass Cu/Fe
0
0 0
5
10 Current (A)
15
20
Voltage drop (V)
Fig. 22.13 Power dissipation and voltage drop across glowing connections of two types (From Ignition Handbook, used by permission)
depends only on the materials involved and not on the nominal size of the contacts. The Cu2O breeding process at a glowing connection has been studied by several Japanese research groups [60, 61], that provided numerous details of this complex process [7]. One of the things learned was that the process is primarily confined to solid conductors; significant currents are hard to sustain at a glowing connection of a stranded wire—the wire tended to break at the point of heating. Overheating can occur in electrical connections of all types, but historically the most notorious case was that of aluminum wiring during the early 1970s. In the late 1960s some U.S. house builders introduced a cost-cutting measure whereby aluminum was substituted for copper conductors in house-wiring branch circuits. This substitution was done without adequate research or field-testing and the outcome was a rash of house fires. The Consumer Products Safety Commission and the National Institute of Standards and Technology (NIST) conducted extensive studies on the phenomenon and found that the problem occurs due to a combination of metallurgical factors including creep, hardness,
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and oxide characteristics [7]. The outcome is that small-diameter aluminum wires6 cannot be reliably terminated by a screw connection and show rapid deterioration and failure. Details concerning the failures of various specific types of electrical connections can be found in the Ignition Handbook [7].
Ejection of Hot Particles Electrical short circuits and arcs sometimes eject incandescent metal particles (i.e., mechanical sparks, sometimes called ‘ejecta’). These particles can then ignite nearby combustible materials, especially if the material is low density or smolder-prone. The particles can be propelled a modest distance in a residential wiring situation; for instance, in one study [62] particles were found up to 1.5 m away. It has also been documented [7] that ignition-causing particles can be ejected from openings in a receptacle (which can superficially appear to be undamaged) and from within a metal box with a metal cover (since small holes are invariably contained).
Miscellaneous Phenomena Some additional phenomena have been documented but are rare. These include harmonic distortion-caused overload, eddy currents, and dendrites [7]. Slightly less rare is the formation of adventitious batteries, which involves a potential difference created by electrochemical action when an electrolyte is present in conjunction with two dissimilar metals. This process sometimes leads to a hydrogen explosion, since the electrolysis process separates water into hydrogen and oxygen [7]. Numerous studies have been published examining the possibility of very strong radio-frequency fields causing sparks and
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ignition of flammable atmospheres, but it does not appear that any actual incidents have been reported [7].
Time for Fire to Initiate from an Electrical Cause One area in which research is seriously lacking is for the time frame associated with electrical fires. In some cases, such as a major lightning strike or a high-current arcing fault in a 480 VAC busbar, the ignition may be essentially immediate. But in the case of the most common faults—a bad connection or arcing across a carbonized path— overt ignition usually takes a long time after the initial conditions were established for the fault. These processes are qualitatively known to be of long term, but means for quantification do not currently exist.
Static Electricity General Principles Static electricity represents electric charges that are notionally static; that is, they are collected on a surface and are not continuously flowing in an electrical current. The steps involved in a static electricity discharge are schematically illustrated in Fig. 22.14. For significant charge separation (sometimes loosely called charge generation) to
Charge separation
Charge accumulation Dissipation of charge Discharge
Ground
Ignition 6 The problem is only pertinent to small-diameter, 10 AWG (2.588 mm) or smaller, conductors; serviceentrance cables and other large-diameter aluminum conductors can generally be reliably terminated.
Flammable mixture
Fig. 22.14 Static electricity fundamentals (From Ignition Handbook, used by permission)
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occur, at least one material must be involved that is an electrical insulator. An electrical insulator is considered to be a substance that has a resistivity above about 108 Ω-m, which includes most organic substances.
Means by Which Charge Separation Occurs Electric charge may be separated by the following means [7]: 1. Contact and separation or friction between solids 2. Relative motion at a phase interface (liquid–solid, liquid–gas, or between two liquid phases) 3. Induction (whereby charge is moved due to the presence of an electric field), also sometimes termed polarization 4. Ion collection from a discharge process (e.g., from corona discharge) 5. Double-layer charging 6. Fragmentation of solids having nonuniform surface charge densities 7. Mechanical fracture (electron emission due to strained or ruptured bonds within solids), also termed piezoelectrification 8. Thermal cycling (e.g., charging by freezing), also sometimes termed pyroelectrification Contact or friction between two dissimilar substances can produce a charge separation if either of the two substances is an insulator. The contact may be solid-solid, solid–liquid, or liquid-liquid. The most common modes pertinent to fire ignitions are the following: 1. Contact and separation between dissimilar solids 2. Flowing powders 3. Flowing liquids A mild amount of charging can be created simply when two surfaces come into firm contact and are then separated. Friction merely enhances the charging by increasing the effective area of contact. Traditional wisdom is that not only must the materials be dissimilar, but that sizable charging will take place only if they are far apart on the triboelectric series, which is a
V. Babrauskas
rank-order listing of materials according to how much of a negative or positive charge they tend to collect [63]. The triboelectric series is determined by the material’s dielectric constant [64], however, current understanding is that electrification is not precluded in contact between objects made of the same material. Thus, plastic chips falling down a chute made of the same plastic are known to be able to undergo electrostatic charging [65]. It is believed that this may involve both physical factors (e.g., stresses at the surface) and chemical factors (contamination). Electrification due to ionized gases flowing past surfaces can arise, but if the gas is at normal temperatures (i.e., not a hot plasma) and is not contaminated with solid or liquid particles, then the charging that can be achieved is trivial, amounting to less than a volt [66]. Gases that contain solid–liquid aerosols or gas streams that generate liquid or solid particulates (e.g., the discharge of a CO2 extinguisher, the rapid evaporation of liquid propane) can pick up a sizable charge, however. For certain materials, moisture in the air promotes the dissipation of charge since it decreases the electrical resistivity of some materials; it never affects the separation of charge. For many other materials, however, the resistivity is not lowered due to atmospheric moisture. Adding vapor-phase moisture does not actually change the electrical conductivity of the air; adding a mist or spray, however, raises the conductivity [67].
Discharge Types Discharges of static electricity can involve the following geometries: • Discharge between two conductive electrodes • Discharge involving one conductive electrode and a diffuse insulating medium • Discharge from one mist or cloud to another Apart from events taking place solely in the atmosphere (which are considered later in the section called “Lightning”), discharges involved in accidental ignitions are classified as the following:
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1. 2. 3. 4. 5.
Spark Corona discharge Brush discharge Powder heap discharge Propagating brush discharge (Lichtenberg discharge) 6. Lightning-like discharge Additional details on discharges are given in the Ignition Handbook [7] and by Britton [68].
Spark A normal electric spark discharge occurs through the air separating two electrodes when the electric field reaches a value of approximately 3 MV m1. Thus, for a gap distance d, the voltage V required is 3d, where V is in megavolts and d is in meters. For a spark to be incendive, the gap distance normally must be equal to or greater than the quenching distance. Considering 2 mm as a typical quenching distance, the voltage required is on the order of 6 kV. Up to about 1,000 mJ can be delivered in a static-discharge spark. This is a sizeable amount of energy, well beyond the minimum ignition energy (MIE) of most substances. Spark discharges are distinguished from other electrostatic discharges in that breakdown occurs across the whole gap separating two electrodes. Corona Discharge A corona discharge (sometimes called point discharge) is a slow, diffuse discharge that originates at a metallic electrode and branches out in a diffuse manner into space or towards poorly conducting surfaces. A corona discharge requires an electrode that has a needle-like point, typically less than 5 mm diameter. Charging such an electrode results in an electric field which is distorted, being generally low, but much greater near the point. When the electric field exceeds the local dielectric strength, breakdown occurs. Corona discharge has the lowest energy of the electrostatic discharge types. It is visible as a violet glow in a darkened room. A corona discharge can also occur in the presence of second electrode, but is still considered a ‘one-electrode’ discharge since the discharge does actually reach the second electrode. A minimum voltage of
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about 2–6 kV is necessary for a corona discharge to occur, with smaller potentials needed for finerpointed needles. The maximum energy normally realizable from a corona discharge—not much over 0.01 mJ—would even theoretically suffice to ignite only the most ignitable of gases, such as CS2 or H2. However, actual ignition requires that the energy be delivered into a small kernel, and the diffuse nature of a corona discharge precludes that. Corona discharges are often used in processes and machinery as a safety measure for lowering charge accumulation.
Brush Discharge When a grounded conductor is brought into an electric field that is near its dielectric breakdown strength, a gas discharge can occur in the form of a brush discharge. The discharge is able to occur because of electric field distortion introduced by the electrode, which locally raises the field above its breakdown value. The name comes from the brush-like shape of the discharge. It differs from a corona discharge, in that the latter is visually observed to be diffuse. A brush discharge is similar to corona discharge in being a low-energy, one-electrode discharge, but whereas a corona discharge requires a needlelike electrode, a brush discharge occurs when electrodes have a radius of 5–50 mm. The incendivity of brush discharges is proportional to the radius—larger-radius conductors are more likely to lead to ignition than ones of smaller radius. Commonly, the high electric field will occur due to the presence of a charged insulator. It is estimated that the energy from a brush discharge will not exceed about 4 mJ. In addition, most of the energy released during a brush discharge does not contribute to incendivity, since the energy is not just localized at the place where a flame kernel is formed. The high electric fields necessary for a brush discharge are readily found in many powder operations, in mists, and also with movement of plastic films. Circumstances leading to a brush discharge can include: • approaching a highly-charged insulator such as plastic films or plastic pipes with a finger or a metal tool;
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• discharging of solids from plastic bags in the vicinity of metal parts; • filling a tank at a high velocity with an insulating liquid, with the charged liquid surface approaching an internal fitting that can act as an electrode; • lowering a conductive cup, etc., into a highly charged liquid; • projection of metal parts into a cloud of highly charged dust or aerosol; • pouring of insulating powders into silos when the fill surface approaches a conductive fitting; • projection of ships’ masts, flagpoles, or antennas into a powerful atmospheric electric field—this is known as St. Elmo’s fire. Even though about 3.6 mJ can be delivered in a brush discharge [69] and there are dust clouds that have an MIE 1 mJ, most studies have concluded that brush discharges will not ignite dust clouds [70], provided that the cloud is not a hybrid dust/gas mixture.
Powder Heap Discharge In some cases, when rapidly filling large containers such as silos or flexible intermediate bulk containers (FIBC) with powders, a much higher charge can build up in the settled powder than was present in the air through which the material moved and a discharge can then take place. This occurs because a growing volume of powder is aggregated, plus when the powder is compacted, its charge likewise gets compacted if the powder is insulating and charge cannot get dissipated. The powder heap discharge is also called a cone discharge or a bulking discharge. It occurs along the exposed surface of the powder. A minimum particle size [71] of ca. 0.1 mm is needed for powder heap discharge to occur, but the majority of the actual incidents have
Fig. 22.15 Double-layer charging (charge pairing) occurring when a charged insulator is adjacent to a grounded conductor
V. Babrauskas
involved polymeric resin particles in the 1–10 mm range. Early recommendations used to state that up to 10 mJ can be delivered in a single discharge step. Some indirect evidence suggests that discharges as large as 1,000 mJ may be anticipated for large particles flowing into a large silo. A minimum product feed rate is needed for a powder heap discharge to occur. This has been estimated at 3,000–5,000 kg h1 for 3 mm particles, rising to 25,000–30,000 kg h1 for 0.8 mm particles [81]. Powders having a resistivity of less than 1010 Ω-m are conservatively judged to not be susceptible to explosions from powder heap discharges [72]; powders which have caused explosions have had resistivities > 1012 Ω-m.
Propagating Brush Discharge A very vigorous discharge can occur when certain conditions are met for the charging of a surface. There is a limit to the amount of surface charging that can be sustained on a surface without discharging by ionizing the air (2.65 105 C m-2). This limit can be increased if a double layer of charges of opposite polarity is accumulated. A way for this to occur is when an insulating layer is directly on top of a grounded metallic layer. This allows opposite polarity charges to build on the second side of the insulating layer (Fig. 22.15). Under those conditions, the maximum surface charge is governed by the breakdown strength of the insulator, which may be on the order of 20–40 MV m-1, instead of the 3 MV m-1 for air. In addition, the dielectric constant of many common insulators is 2–4 times that of air. These two factors combine to give maximum surface charges of around 5 104 C m-2, and
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it is considered that 2.5 104 C m-2 is the minimum surface charge needed for a propagating brush discharge. With very thin films of certain plastics, surface charge densities up to 8 103 C m-2 have been measured [73]. A propagating brush discharge can ignite most flammable mixtures, including dust clouds. A discharge occurs in one of two ways: (1) a grounded electrode is brought near the charged insulator surface; or n a dielectric breakdown of the insulating layer, resulting in a local puncture. A minimum voltage of ca. 4 kV is needed for a propagating brush discharge to occur with very thin films (10–20 μm) rising to 8 kV for 0.2 mm thick ones. Up to ca. 1,000 mJ can be delivered in a propagating brush discharge. Circumstances leading to a propagating brush discharge can include: • conveying an insulating powder at high velocity through plastic pipes or bins that are grounded on their exterior; • conveying an insulating liquid at high velocity through plastic pipes that are grounded on the outside, or metallic pipes that have an insulating interior coating; • loading of insulating powders into large, non-conductive silos; • high velocity operation of conveyor belts that have metallized outer surfaces and an insulating core; • repeated collisions of dust particles on an insulating surface atop a grounded layer. • In some cases, a propagating brush discharge can occur without an overt grounded layer, for instance when rain is falling on a plastic pipe conveying an insulating powder [74].
accidents have been blamed on such discharges, but the details of the circumstances have never been clear. Lightning-like discharges would presumably be able to ignite almost any combustible matter, so the conditions—if any—that might lead to such lightning would be important to quantify.
Lightning-Like Discharge Lightning in the atmosphere can occur when water droplets and ice particles are charged to very high potentials. Since particles in dust clouds will also pick up an electric charge, lightning-like discharges have been observed to occur in the dust clouds formed during volcanic eruptions. What is unanswered is whether such discharges can occur on a smaller scale, to wit, in connection with storage silos. A number of
V ¼ Emax r ¼ 3:0 106 r
Electrostatic Charging and Discharging of Solids For simple geometries, the amount of charge that an isolated solid can accumulate and the voltage to which it can be charged can be computed [7]. The maximum charge density, σmax (C m2), that can be built up on the isolated object is given by: σmax ¼ εεo Emax where ε ¼ dielectric constant (–), εo ¼ permittivity of vacuum (8.854 1012 S s m1), and the abbreviation C denotes coulombs, whereas S denotes Siemens. Since the dielectric constant for air ¼ 1.0 and Emax, the breakdown strength of air, is approximately 3 MV m1, then σmax, the maximum charge density possible for an isolated object in air ¼ 26.5 μC m2. If the object is spherical, then its area ¼ 4πr2, where r ¼ radius (m), and the maximum charge that can accumulate on it is Qmax ¼ 4πr 2 26:5 ¼ 333 r 2 μC Now, since voltage V is, by definition, equal to the field strength E times distance,
which gives the maximum voltage to which the spherical object can be charged in air. But capacitance C is defined as ¼ Q/V, V¼
Q Q ¼ ¼ Emax r ¼ 3:0 106 r C 4πεεo r
Then the capacitance with respect to ground of an isolated sphere can evaluated as
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V. Babrauskas
C ¼ 4πεεo r where C ¼ capacitance (farads; F), and the symbol C here must not be confused with the unit C denoting coulombs. Assuming that no losses occur, the energy W (joules) that can be delivered from a spark discharge is 1 W ¼ CV 2 2 Substituting the above gives W ¼ 501r 3 For many hydrocarbon vapors, a value of MIE 0.25 mJ is applicable. Then, to cause an incendive discharge from a charged, isolated body, its radius must be at least 1=3 0:25 103 r¼ ¼ 0:008 m 501 Since this limit is only 8 mm, it would be very difficult to develop a safety measure on limiting the physical size of bodies that pick up a charge. In practice, somewhat higher minimum sizes will pertain, since ideally efficient conditions will not be present for discharge. For a propane-air mixture (MIE ¼ 0.26 mJ), a minimum radius of 12 mm was found necessary in order to have an incendive discharge [75]. Capacitance values for some common objects are given in Table 22.3.
A mild shock due to electrostatic discharge is common for human beings. Such discharges can also be incendive. Shoes charge the wearer because each time the foot is raised, the capacitance to ground is decreased and charge accumulates on the person. Charging readily occurs when apparel is worn that is highly insulating and the apparel contacts and separates from external objects. The charge picked up on the apparel then induces a similar charge in the body. Although standard values are sometimes proposed for the capacitance of a human being, the actual capacitance [76] varies with the thickness of the footwear, as shown in Fig. 22.16. The resistance of the human body [77], measured to a fingertip, is about 1,300–2,000 Ω, but if the person undergoes a discharge via a grasped metallic object, the body’s effective resistance may be only 360–700 Ω. Table 22.3 The estimated capacitance of some objects Object Buckets, small drums 55-gal drum Automobile Tank truck Large tractor-trailer
Capacitance (pF) 5 100 500 1,000 3,000
10,000
Capacitance (pF)
Fig. 22.16 Effect of footwear thickness on the capacitance of a person (assumed standing on a floor of moderate conductivity) (From Ignition Handbook, used by permission)
Electrostatic Charging and Discharging of Persons
1,000
100
0.1
1 10 100 Distance between bare feet and floor (mm)
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In dry air, the body can charge up to 5–25 kV, although voltages toward the high end of this range are uncommon and are limited by corona discharge. Thus, under the worst circumstances, the energy that is stored and is available for release in a spark is 2 1 1 CV 2 ¼ 300 1012 25 103 2 2 ¼ 94 mJ
W¼
If this much energy could be effectively applied, it would be enough to ignite all common ignitable vapors and also many dusts. However, more typical values of stored energy due to friction of apparel are 5–20 mJ. A value of 25 mJ has been adopted by a British standard [78] as the maximum practical value needing to be considered. At an RH of 50 %, a person walking on a carpet will generate no more than about 3 kV, and for RH greater than or equal to 60 % it is impossible to create a significant voltage [79]. Thus, the problem is limited to dry atmospheric conditions. Guidelines are also available (Table 22.4) which relate the energy discharge from a person to the sensation [68, 80]. A perceptible sensation corresponds requires that the person be charged to about 2 kV [64]. In view of the above results, discharges that are perceptible but not severe are likely to lead to ignition if the person is in a space containing a gas in its flammable range. However, since people do not generally walk around in flammable atmospheres, it is found that electrostatic discharge from humans is actually a rare cause of unwanted ignition of gases [81]. Table 22.4 Human responses corresponding to various levels of discharge energy Energy 1 mJ 10 mJ 30 mJ 100 mJ 250 mJ >1J > 10 J
Response Perceptible Prick Sharp prick Slight jerk Severe shock Possible unconsciousness Possible cardiac arrest
Electrostatic Charging and Discharging of Granular Materials When granular materials—powders, dusts, grains, and so on—are in motion, they can pick up a charge. Insulating powders—those with a resistivity greater than about 1012 Ω-m—do not easily dissipate a surface charge they may acquire and, thus, can be prone to spark discharges. This is especially a problem if they are conveyed or stored in insulating pipes or silos. The tendency for powders to pick up a charge is roughly proportional to their surface/ mass ratio (or inversely proportional to particle diameter). The resistivity of powders changes drastically with moisture. At conditions of RH greater than 60–65 %, any charge formed is rapidly leaked away and hazardous conditions would not be expected [82]. Discharging of dry chemical (sodium bicarbonate or ammonium phosphate/ammonium sulfate) fire extinguishers can cause static electricity buildup. It was found experimentally that this can result in charging voltages that would correspond to discharge energies of up to 54 mJ [83]. Energies of this magnitude may ignite many dusts, not just gases. Pneumatic transport systems cause a buildup of charge largely due to bends in the pipeline, but within a few meters of travel distance a steadystate value of charge is reached [84]. For a given air velocity, increasing the product mass flow rate decreases the charging tendency. Charging tendency is also reduced by reducing air velocity and by increasing particle size of the granular material. Electrostatic discharges commonly occur whenever granular materials are pneumatically conveyed. These are typically nonincendive corona discharges. It is the possibility of spark discharges or other more energetic forms that forms the crux of the fire safety problem in these applications. Silos can build up very high potentials when granular materials are conveyed into them; in one study [84], up to 150 kV was measured.
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During loading or conveying of powders, local non-incendive discharges (corona and possibly brush discharges) may occur which are helpful, rather, than deleterious, since they serve to reduce the charge buildup. Based on this observation, to reduce the incendivity of bulking discharges, it is commonly recommended that a grounded wire be strung through the center of a container receiving insulating powders. This causes small coronalike discharges to occur to the grounding wire, instead of large sparks to the container itself. A ground wire is equally effective if the container is insulating, instead of conductive [85]. The ground wire must be thin (around 1 mm) in order to ensure a corona-like discharge.
Electrostatic Charging and Discharging of Liquids Many liquids are prone to undergo charge separation when they move past either a solid surface
or the interface with another liquid. If a sufficiently high charge is accumulated, an electric discharge may occur. This discharge may cause an ignition under appropriate fuel-air ratio conditions. Charge relaxation readily occurs if the liquid has a high electric conductivity and for such liquids a high charge does not build up. Unfortunately, many organic liquids (i.e., aliphatic, aromatic, and cyclic hydrocarbons; ethers; some silicones) are good insulators (Table 22.5). Liquids with conductivities less than 5 1011 S m1 are considered to be of low enough conductivity that electrostatic hazards must be carefully guarded against. However, if the conductivity is extremely low, then ionized species that could cause charge buildup are also largely absent. Liquids with a conductivity of less than 1013 S m1 are considered to be in the latter category. Thus, the peak hazard involves liquids with conductivities from 1013 to 5 1011 S m1. Pure hydrocarbons do not exhibit electrostatic charging; however, even impurities at the 0.001 ppm level change this
Table 22.5 Electrical conductivity of common liquids [7] Hazard Low: Conductivity less than 1013
High: Conductivity of 1013–5 1011
Low: Conductivity greater than 5 1011
Example substances Hexane Carbon disulfide Benzene Heptane Xylene Dioxane Toluene Cyclohexane Styrene Kerosene Hexamethyldisilazane Jet-A fuel Gasoline Turpentine Crude oils Halogenated hydrocarbons Methyl alcohol Ethyl alcohol Cetones Water: deionized Iso-propanol Water: acid rain
Typical electrical conductivity (S m1) 1017 8 1016 5 1015 3 1014 1013 1013 1012 2 1012 1011 1.5 1011 2.9 1011 2–3 1011 1010 4 1010 109 to 107 108 107 1.4 107 105 105 104 102
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situation [86]. The presence of a small amount of water in the product can increase the electrostatic charging effect up to 50-fold. For insulating liquids flowing in conducting pipes, the charge density (C m3) picked up is linearly proportional to the liquid’s flow velocity, and the charge density reaches a steady-state value after a certain distance down the pipe, with the charging voltage being roughly proportional to the flow velocity. However, when liquids flow in insulating pipes, little streaming current occurs because the charge induced in the pipe walls does not get dissipated to ground. Flows that consist of two-phase liquids, liquids with suspended solids, or mixtures of immiscible liquids tend to build up higher charges than single-phase liquids. Charge buildup can especially increase if the liquid flows through a fine-pore filter. When a low-conductivity liquid is in motion in a conducting pipe, not just separation but also an actual flow of charge occurs. This flow is called a streaming current and it arises because ions in the liquid tend to move with the flow, while the opposite charge on the wall dissipates to earth. For it to occur, the liquid must have a conductivity in the range of about 1013–107 S m1. Experimental studies [87] indicate that, for these liquids, the streaming current I (amperes) can be estimated as I ¼ 9:42 106 ðuDÞ2 where u ¼ velocity (m s1) and D ¼ diameter (m). An empirical expression [88] for the charge density is 000
Q ¼ 5 107 u=D Moisture and impurities can greatly increase the charge density, but experiments have to be set up carefully to illustrate this. The effect is not found unless the liquid is pumped through filters [89]; charge generation associated with tankloading in the absence of filtering does not show deleterious effects of impurities. Metallic trash in tanks can act as ‘charge collectors’ and greatly reduce the charge density necessary to cause an electrostatic discharge [89]. The effect takes place since small metallic objects can be
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buoyed up by turbulence or by foaming of the product. The combination of filtering and splash loading was found to be highly conducive to discharges; removing either of the two factors greatly diminished the potential for a discharge. In low-viscosity liquids, splash loading by itself produces a charged foam in the tank which can lead to discharges even when the inflowing liquid has little charge on it. Liquid sprays can cause intense static electrification; this was first observed near waterfalls in the nineteenth century and is called spray electrification [90]. The process occurs due to the presence of a double layer of charge at the liquid surface. Small pieces of material in the form of droplets removed from the surface can then possess an unbalanced charge. By this process, a water stream may ignite a flammable atmosphere, and this concern arises in operations, for example, where a water spray is used to clean equipment that was used to store flammable liquids.
Lightning Electrical Characteristics Lightning becomes possible because electric charge can become separated and accumulated in clouds. Clouds are highly complex entities and, even today, the physicochemical environment of clouds is by no means comprehensively understood. One theory by Ermakov and Stozhkov [91] is illustrated in Fig. 22.17. Thundercloud formation begins when a cold air mass meets a warm one. Ionized, warm, moist air rises but is then progressively cooled at higher elevations and condensation of water vapor on nucleation centers begins. In the initial phase, condensation proceeds faster on negatively charged nuclei than on positive ones, and the upward air flux produces large-scale separation of charge and a resultant electric field. The latent heat released in condensation assists the buoyancy of the upward air current. Cosmic rays produce ionized showers of particles.
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V. Babrauskas J– 9
6
5
5 4
1 3
2
2
1 3 7 10
Initial phase
Maturity
8
Decay
Fig. 22.17 Formation of thunderclouds as described by Ermakov and Stozhkov [91]. 1, warm air front; 2, cold air front; 3, ascending flux of wet ionized air; 4 and 5, extensive air showers produced by primaries with energies over 1014 eV or 1015 eV, respectively; 6, cloud-to-cloud
lightning; 7, cloud-to-ground lightning; 8, ground-tocloud lightning; 9, negative screen layer; 10, positive charge at cloud base; J current of negative ions from the ionosphere to the top of the cloud
When the electric field exceeds 0.2–0.3 MV m1, electron avalanches occur; ionized tracks link with each other and form a conducting tree structure, which allows cloud-to-cloud discharges to occur. In the mature phase, droplets grow and coagulate. There are ascending and descending airflows and the cloud becomes asymmetric with an excess of negative charge at its base. The electric field between the cloud and earth’s surface increases, leading to cloudto-ground discharges. Thunder is an acoustic shock wave that originates in the gas breakdown region and then propagates out through the air. The origins of a lightning strike are due to a separation of charges in clouds. Lightning becomes possible when a potential of 10–100 MV with respect to the ground has been reached. A lightning flash is composed of several events. The actual discharge begins with the formation of the first stepped leader, which is a localized gas breakdown of about 50 m length. The process continues in a stair-step fashion until a leader gets to within about 50 m of the ground (or an object on the ground). The negative charge of the
stepped leader induces a positive charge in the earth below. Protruding grounded objects start to conduct heavier point-discharge currents. A streamer then arises from one of these objects or from the earth itself, connects to the leader, and starts a return stroke. The return stroke is the brightly visible lightning stroke. After the first return stroke, a dart leader may descend directly to the ground without stairstepping. This dart leader is ball shaped. It will be followed by a second return stroke. There may be three or four, but occasionally many more, strokes per the total event, comprising the lightning flash. The total lightning flash may last from 0.01 to 2 s, with 0.2 to 0.4 s being typical, but each individual stroke only lasts about 30 μs. The interval between strokes may be around 40 ms. The current carried by the stepped leader is small, only on the order of 100 A. But each return stroke will typically carry 10–20 kA of current, and peak currents in excess of 100 kA are occasionally recorded. A cloud-to-ground stroke may discharge about 25 C per stroke. The average length of a stroke is 3 km, and the average energy
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released is 105 J m1, making an average energy release of 3 108 J per stroke [92]. In electrical circuit terms, a lightning stroke can be considered a constant-current source. Therefore, the energy dissipated in the object along its path is ð I 2 Rdt where I ¼ current (A), R ¼ resistance (Ω), and t ¼ time (s). This accounts for the much greater damage found for objects of poor conductivity than for metals. Design values for the current of 100–200 kA are commonly used [93] since only about 1 % of lightning strokes give currents in excess of 200 kA [92]. The current from a second or subsequent stroke is typically less than half that of the first one. When a lightning strike occurs, nearby metallic objects can have a current induced in them, including not only electrical wiring but also other metallic objects such as building beams. The electric field induced by a lightning strike of a known current value can be estimated [94] according to: E ¼ 33
I r
where E ¼ electric field (V m1), I ¼ current (kA), and r ¼ distance from strike (km). Thus, for example, a strike with a current of 100 kA is expect to induce a field of 1,100 V m1 at a distance of 3 km. A direct strike to a building or structure is one where the ground-side termination of the lightning bolt attaches to any part of the building. A side flash is a strike where the lightning bolt terminates on a nearby object, but a secondary flash occurs from that locale to the building. A side flash is considered to also be a type of direct strike. An indirect strike is one where the main bolt terminates elsewhere, but some energy from the bolt is delivered to the building by means of power lines, metallic underground pipes, or other conductive paths.
Ignitions from Lightning The primary damages [95] to residences from lightning are the following: • Brick, concrete, and other solid surfaces moved or cracked • Plumbing pipe punctures • Holes burned or punctures in roofs • Arc damage to metal structures such as window frames • Arcs across wiring The last three of these, of course, may also be accompanied by ignition of combustible materials. Because the temperature rise in an object is proportional to its resistance, a metallic object (e.g., a lightning rod) may sustain limited temperature rise, whereas a poor conductor such as wood may become ignited. Multiple ignitions from a single strike are not rare. Whether combustibles will be ignited from a lightning flash or not depends critically on whether there is a flow of continuing current in the channel after the stroke. About 25–50 % of lightning strikes exhibit this characteristic— these are sometimes called hot bolts. Lightning strikes that are positive (i.e., the cloud being positive with respect to the ground) are much rarer than the converse, but these are precisely the ones that are most likely to cause ignitions, since their peak currents and total charge transfer are much larger. Positive flashes do not have the stepped-leader characteristic of the common, negative strikes, and consist of a single stroke, followed by a period of continuing current flow. The probability [96] of igniting a house fire from a lightning strike is much higher if the house has plastic plumbing pipes as opposed to metallic ones. This is because the lightning current may flow to ground through a metallic pipe network, but if electric wiring is the only substantive metallic path, the current is likely to go through electric wiring, where heating will be much greater due to the smaller area of the conductors.
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Safety Measures Against Lightning The lightning rod was invented by Benjamin Franklin in 1752. This is a metallic rod which is grounded at one end and raised in the air at the other. When the initial streamers from the cloud start to form, there is not a highly specific place along the ground level where the initial return stroke is preferentially located. By providing a ground-potential conductor in the air, a preference is established, and the lightning current flows down the rod (which must be of adequate dimension in order not to overheat). Franklin recommended that the tip of the rod (air terminal, in the jargon of the lightning protection industry) be pointed, because this leads to a point discharge. In earlier times, this point discharge (corona discharge) was considered necessary to ‘attract’ the lightning stroke. More recently, experiments showed that a smoothly rounded tip is more successful in attracting lightning to itself and avoid strikes to nearby objects [97]. The first comprehensive engineering guide to proper installation of lightning protection systems was published by Anderson [98] in 1879 and, perhaps surprisingly, few of his recommendations have been overturned by more modern research. Mu¨ller-Hillebrand [99] reviewed some of the early concepts of lightning protection. A lightning protection system basically comprises three main components: • air terminals • downconductors • ground terminals.
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Franklin recommended that each air terminal provides a downward ‘cone of protection,’ with the cone’s angle from vertical being 58 . The origin of this recommendation is unclear and it was evidently not evolved from experiments. Subsequent experience suggested that this angle is much too large, and during the nineteenth century the recommendations slowly went downward to about 30 . However, even using a 30 angle of protection, failures were documented [100]. In more recent times, Lee [100] synthesized a design method for protecting buildings, evolved from advanced calculations used by electric utilities for protection of power lines. The method is applicable only to structures of 45 m height or less and is described in the following way: Imagine a rolling sphere of 45 m radius (Fig. 22.18). The sphere starts rolling along the ground from a distance far away from the structure in question, then roll up to and over the structure and its protective air terminal(s). If the sphere only ends up touching the air terminal(s) and the ground and cannot come into contact with the structure to be protected, then air terminals of sufficient height and quantity have been erected, otherwise additional protection is needed. This more realistic protection concept is more liberal than the 30 fixed-angle scheme for low structures and more conservative for high structures. The 45 m dimension is used because it corresponds to the typical length of the stepped leader, which is about 50 m. In view of the enormous currents of around 20,000 A that are involved in a lightning strike, it is perhaps surprising that gigantic-size
Fig. 22.18 Sphere of protection from an air terminal: structure A is protected, structure B is not
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downconductors are not required to safely conduct the electricity. The minimum size of conductor does not need to be huge since the flow of current is so brief—much less than 1 s—and heating is proportional to the time of current flow. The simplest model that can predict this is the adiabatic lumped-capacitance model: W ¼ I 2 Rt ¼ ρ C p V T f T o where W ¼ energy (J) flowing into a piece of metal, I ¼ current (A), R ¼ resistance (Ω), t ¼ time (s), ρ ¼ density (kg m-3), Cp ¼ heat capacity (J kg1 K1), V ¼ volume (m3), Tf ¼ final temperature ( C), and To ¼ initial temperature ( C). This assumes that the current flow is constant over the time t; if the current flow is varying, then the expression becomes: ð W ¼ R I 2 dt ¼ ρ C p V T f T o where R is assumed to be time-invariant and has been taken outside the integral. Applying the above relation to copper wire, ρ ¼ 8,890 kg m3, Cp ¼ 385 J kg1 K1, V ¼ A · L, where A ¼ cross-sectional area (mm) and L ¼ length (m). The resistance of a copper wire can be expressed as: R ¼ ρe
L A
where ρe ¼ electrical resistivity of copper ¼ 1.7241 108 Ω · m. The initial temperature To can be taken as 20 C, while the final (allowable) temperature Tf must be set to some reasonable value below the melting point. Since the downconductor may come into contact with combustibles such as dry leaves, it seems appropriate to limit Tf to 200 C. Based on studies of ð lightning discharges, I 2 dt ¼ 5 106 A2 · s is commonly used. The equation can then be evaluated as: 8 L 1:7241 10 5 106 A ¼ 8890 385 ðA LÞ180
and it can be noted that the actual length of the wire sensibly cancels out of the equation. This gives A2 ¼ 1.4 1010 m4, or A ¼ 1.18 105 m2 ¼ 11.8 mm2. If the temperature criterion were the melting point of copper (1,083 C), then A ¼ 4.9 mm2, using the same ‘action integral’ of 5 106 A2 · s. In US practice, however, a more conservative approach is taken, with conductor areas being greater than 11.8 mm2, in order to allow for mechanical damage, some unusually potent lightning strikes, etc. The most commonly followed guidance is that published by NFPA [101]. NFPA 780 divides structures into two Classes, Class I being those up to 75 ft (22.9 m), with Class II being those higher. For Class I structures, the required downconductor area is 29 mm2 for copper and 50 mm2 for aluminum. The cross-sectional area required for copper conductors in Class II service is 2 that for Class I. Generally, stranded or braided conductors are used, to minimize loss of current-carrying capacity due to skin effect (this electromagnetic effect pertains to transient current flows and leads to current flowing disproportionately near the surface). A lead coating is often used to minimize loss of metal due to corrosion from flue gases. Properly-installed and maintained lightning protection systems are highly effective, with one report [102] quoting old US studies giving 99.3 % and 99.9 % effectiveness values. For configuration of the air terminal, modern studies by Moore et al. [103] concluded that the optimum tip-height to tip-radius ratio is about 680. Thus, a rod erected at 10 m height ought to have a tip of 14.7 mm radius.
Ignition and Values of Voltage, Current, or Power Are there minimum values of voltage, current, or power that must be exceeded for ignition to be possible? Sometimes the stance is taken that, under certain circumstances, an energized electrical device cannot be the source of a fire.
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This stance is usually couched in terms of power but has also been couched in terms of current or voltage. For example, some authors [104] claim that ignition is not possible for devices that cannot consume more than 20 W. Certain UL standards [105] consider the limit to be 15 W. A more conservative view [106] is “several watts.” Such a limit would be attractive in that it can simplify such standards, but there does not exist a research basis that would support these notions. Instead, research findings indicate that minuscule values may suffice, ones that are so low as to not form a useful criterion. For example, some flammable gas mixtures can be ignited by arcing from a resistive circuit having only 4–5 V, whereas in inductive circuits, a 0.5 V power supply may suffice [7]. In terms of power, it has been documented that breaking an 0.95 W incandescent lamp can suffice to cause an explosion of a methane/air mixture, whereas a broken 3 W lamp can cause an explosion of coal dust in air [107]. Although solids are generally harder to ignite than gases or dust clouds, very limited testing indicates that exceedingly low values can also suffice for solids. For example, a Dacron comforter was ignited from a 6 W night-light lamp, bamboo decorations from a 25 W lamp, and cellulose attic insulation from a 50 W lamp [7]. Notebook paper was ignited [7] from a resistor rated at 1/8 W that was dissipating 1.25 W at the time. Power values associated with arc-tracking ignitions have rarely been explored, but in one study it was found that 4.8 W sufficed to ignite PBT plastic [108]. This should be interpreted in the context that PBT is one of the more arc-tracking resistant plastics and plastics more prone to arc-tracking (such as PVC) would presumably require less. Finally, it must be noted that the values cited above are values that sufficed to cause an ignition or explosion during limited testing. These values are not intended to imply lower-value limits. Ignitions, in fact, may occur under conditions or regimes not encompassed in the research that has been published to date.
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Electrical Explosions Most explosions in which electricity plays a role can be grouped into three categories: 1. Pure arc explosions 2. Pure fuel explosions 3. Mixed mode explosions. In a pure electrical arc explosion, the main source of explosion energy is the arc itself. Combustion, i.e., oxidation, plays only a modest role, if any. In the case of copper or steel conductors, oxidation is generally negligible, while in the case of aluminum conductors some of the exothermicity comes from oxidation of the aluminum. For such explosions to be damaging, significant arc power is normally required. Thus pure arc explosions are mostly of interest in high voltage transmission and distribution equipment, in industrial facilities, or in commercial installations where significant short-circuit currents are available. Pure fuel explosions are ones where the only role of electricity is to provide a spark or a low-energy arc, with the explosion energy corresponding to burning of fuel. The most common example is spark from an electrical switch causing an explosion in a house which filled with natural gas. This category also includes electrically initiated explosions of solid or liquid explosives, for example, by use of an exploding bridgewire. Pure fuel explosions are treated in depth in the Ignition Handbook [7] but are outside the scope of this Chapter. In addition, there are numerous monographs which discuss the physical, chemical, or civil engineering aspects of explosions of all types [109–113]. Mixed mode explosions are explosions which are initiated by an electric spark, arc, or hot surface, and where the fuel was delivered due to an electrical fault. The best known mixed mode explosions are explosions of oil-filled transformers and explosions of underground electric distribution cables, including manhole explosions. In these explosions, an electrical fault gasifies the dielectric liquid or solid,
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which is then ignited by a localized source of energy. Mixed mode explosions are also experienced when lead-acid batteries explode and in other cases of adventitious generation of hydrogen. In recent years, explosions of residential dishwashers have been identified as an additional example of mixed mode explosions. (Explosions in a purposive hydrogen-production facility initiated by an electric spark are categorized as pure fuel explosions, since an electric fault does not play a role in generating the fuel.)
Basic Phenomena Electric arc explosions involve complicated phenomena, and none of the standard monographs on explosions cover this specialized topic. The only review of the topic has been by Babrauskas [114], and here some of the main findings will be summarized. Electric arcing in circuits with sizable maximum short-circuit current capacity can be a highly energetic effect. In fact, buildings have collapsed due to arc pressure, since in an enclosed space some surprisingly large pressures can be built up. For instance, in one test explosion overpressures of 83 atm were obtained. The magnitude of this can best be appreciated by considering that a fuel-air deflagration will typically attain only around 7–8 atm, barring pressurepiling effects or other turbulence enhancements. During normal operation of a circuit breaker, arc pressures of roughly 3 atm magnitude can be expected [115], but these devices are designed to sustain the pressures generated by the normal arcing associated with circuit opening. Arc explosions are not rare in industry, and in other situations where 480 V, or higher, voltages are utilized, but published case histories are scarce. Neither of the two large electrical accident compilations [116, 117] mentions the subject. Lee [118] published four brief case histories, Crawford et al. [119] documented seven case histories of arc explosions inside motor terminal boxes, including one fatality, while Heberlein et al. [120] described two non-fatal explosions inside motor control
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centers. The best-known incident was in an Atlanta high-rise building that took place on 30 June 1989. The fumbling of an electrician replacing a fuse caused a 480 VAC bus duct explosion [121] and the explosion and subsequent fire led to five fatalities. Lightning strikes can lead to arc explosions in any type of premises. In 1773, Lind demonstrated that if a conductor from a lightning arrester is run down through a house, but with a small gap in this conductor, this can form a spark gap and a strike to the arrester can result in an arc explosion capable of destroying the house [122]. Individuals have been bodily knocked over when in proximity both to electrical fault arcs and lightning strikes, although interestingly often there have been negligible injuries to the individual knocked over [123]. But in cases where roofs collapse, the outcome may be traumatic if persons are present underneath. Eardrum rupture can be expected at explosion overpressures of 19 kPa (10 % probability) or 45 kPa (50 % probability), while death due to lung damage is 120 kPa (10 % probability) or 141 kPa (50 % probability). The above values come from an extensive statistical study by Eisenberg et al. [124]; older data are somewhat different, but not greatly. In any case, they indicate that it does not take large overpressures for injury or death to result from explosion pressures. An arc explosion arises due a very rapid heating of air or other medium. In the process, electrical energy is converted into other forms of energy: dissociation, ionization, and heating of the gas, including its compression; thermal radiation; and conduction losses into adjacent solids such as electrodes. In addition, some electrode metal is vaporized and this contributes to the total volume which is being explosively heated, yet, the role of chemical reactions has only recently been explored. When an arc breakdown is initiated, energy gets deposited into the arc channel at a rate much greater than can be removed from the area by the shock wave that is created. This causes a rapid pressure rise and, if the arc energy is sufficiently high, this will be perceived as an explosion.
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For a low-energy arc, the perceived sound may simple be a ‘snap,’ ‘crackle,’ or ‘pop.’ But within the scientific community there is not an agreedupon, quantitative definition of the term ‘explosion,’ nor are there studies to quantify the fraction of the arc energy that gets delivered as sound energy, i.e., vibrations in the 20–20 kHz range. In an open environment, arc pressures will rarely be highly destructive. Theoretical modeling suggests that very high pressures may be created, but experimental studies do not bear this out, which only show overpressures below about 10 kPa. However, if arc explosions occur within enclosures which are sealed, or nearly so, then, as mentioned above, huge overpressures may be found. Electric arc explosions are not combustion phenomena—they are predominantly physical explosions, due to very rapid conversion of electrical energy into heat. Chemical reactions play a role, but only a supporting role, in such explosions. Recent studies suggest that chemical reactions are mainly ones which convert air to species such as O3 and NOx. While these may comprise oxidation, they are very different from a fuel-air explosion of a normal sort. Some of the electrode metal is also vaporized in an arc explosion, and arc temperatures are high enough so that presumably much of this metal vapor may get oxidized. However, the electrode oxidation effect is quantitatively only a small part of the heat balance in an arc explosion. Thus, first-order estimates of arc explosions treat the process solely as converting electrical energy to heat and ignore chemical reaction contributions.
Shock Waves from Electric Arcs If in a gaseous medium there is an abrupt change in pressure, temperature, or volume created at some location, a wave will be generated which will propagate through the medium. The wave can be a sound wave, a shock wave, or both, depending on the characteristics of the source. In the case of an electric arc, while a shock wave will be generated and it is audibly perceived as an explosion (unless of very small scale), the shock
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wave does not constitute a detonation, which would require that the shock wave be supported by an exothermic reaction occurring behind the shock front. For subsonic sound waves in air, the decay in pressure with distance from the source pffiffi goes as 1= r for the infinite-cylinder geometry and 1/r for the sphere. But for shock waves, these simple wave-equation relationships are not applicable. A reasonably short arc will be represented by a short cylinder, but this is not a geometry that lends itself to simple theoretical solutions. Baker presented calculated data on a point sources [125], along with experimental data on bursting explosions of short cylindrical vessels and spherical vessels. His results showed that, unless only examined over small intervals, the actual relationship is not even of a power-law type. In an electric arc, when breakdown is initiated, a narrow conducting filament first bridges the gap, and then grows rapidly in diameter until it reaches an ultimate value and the ‘arc channel’ is fully established. In the course of this, there are two disturbances that a propagated: a sound wave propagating at the speed of sound and a shock wave propagating at two or three times that. Flowers [126] made detailed measurements and found velocities of 1,000–2,000 m s1 for the radial expansion of the arc channel; these are well above the 340 m s1 of sound speed, indicating that shock waves are being generated in all cases. The arc channel eventually reaches a steady-state diameter and no longer expands, and Flowers found that a time of 3–35 μs was required for the final diameter to be attained in his experiments, but the actual value is dependent on external circuit parameters which limit the current growth rate. When the final diameter is achieved, Flowers found that the arc channel cross-sectional area is linearly proportional to the current, with the proportionality being 11 A mm2. Later Vanyukov et al. showed that the expanding shock front and the channel are initially of the same diameter, but subsequently the channel typically approaches a maximum diameter, while the shock front continues expanding outwards
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Fig. 22.19 Results of Vanyukov et al. on the expansion of the arc channel and growth of the shock wave
[127] (Fig. 22.19). Intermediate between these is the ‘envelope,’ which is the boundary between compressed gas (outside the boundary) and rarefied gas (inside). In some cases, however, arc channel diameter growth continues for a protracted period, especially at higher current values [128].
Pressures from Arcs in the Open Baker [125] treated arc explosions in the open using results from acoustical theory. The pressure rise Δ p ¼ ð p1 po Þ is assumed to be due to the arc effectively generating a certain volume V of air at the ambient density ρo. Then from acoustical theory, the pressure rise at any particular distance r (m) from the arc is: Δp ¼
γ 1 P_ γ 4π r po
where P_ ¼ first derivative of electrical power developed in the arc (W s1), and γ is defined as: γ ¼ c p =cv . Air can assumed to be an ideal
diatomic gas, giving γ ¼ 7/5 ¼ 1.4. This equation predicts that the pressure rise will vary linearly with P_ and decrease with distance proportionally to 1/r. The only extensive series of experiments available to examine the relationship between P_ and the pressure rise has been that of Drouet and Nadeau [129]. Unfortunately Fig. 22.20 suggests that there was a systematic error in the measurements. The slightly different than expected slope for long arcs could well be due to a limitation of theory, but the short-arc results are most likely erroneous, not only because they have a dissimilar slope, but mainly because they imply that in excess of 100 % of the power of the arc is realized as compression of air.
Pressures from Arcs in an Enclosure If an arc discharge occurs within an enclosure which is of modest size, then the whole enclosure will get measurably pressurized. In addition, of course, there will be local shock wave propagation,
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Fig. 22.20 The results of Drouet and Nadeau compared to Baker’s theory
and also reflections of shock waves from compartment walls. Modeling such details in the system would require numerical calculations. But, for many practical purposes, what is of most interest is the peak, quasi-steady overpressure that is achieved, and this can be approximated in a simple way. Neglecting all transient and hydrodynamic effects, the discharge of an arc in a single, closed compartment can be treated as an ideal gas within a isolated, isochoric (constant volume) system. If an amount of heat or energy ΔW is injected into the volume, the change in pressure Δp is [130]: Δp ¼
R ΔW Mcv V
where M ¼ molar mass, R ¼ universal gas constant ¼ 8.314 J mol1 K1, and cv constantvolume heat capacity (J kg1 K1). Using the relations between cv, cp, and γ, the relation is more usefully written as: Δ p ¼ ð γ 1Þ
ΔW V
This shows that, all else being equal, the overpressure is inversely proportional to the volume.
Consistent with the theoretical prediction, when using very small enclosures and large arc currents, some exceedingly large pressures can be obtained. Graneau [122] conducted experiments in a tiny cubical cavity, 12.7 mm on a side (2 106 m3), with the electrode gap also being 12.7 mm. For a spark discharge of 40 kV and a peak current of 38 kA, he measured an average pressure of 409 atm in the cavity, with even higher pressures during the peak of the discharge. Baldrey and Hudson [131] conducted tests within a small pressure vessel and got an overpressure of 83 atm in the worst case. Numerous other studies have also been published [114]. The analysis is complicated since not all of the electrical energy delivered actually goes into heating the gas. Conversely, in the case of aluminum electrodes, an additional energy term comes from the combustion of the aluminum. Thus, because of differing experimental conditions, published results tend to lack generality. An additional complication is that many studies were done not on fully sealed enclosures, but on ones with certain small openings. This makes the results highly dependent on the specifics of the geometry.
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Fig. 22.21 Arc pressure rise, as function of electrode material, measured by Tanaka et al. in an 0.32 m3 enclosure for 0.1 s duration AC arcs
In addition, many studies were at very low overpressures. Such results are more readily amenable to analysis, but do not necessarily reflect on more damaging explosion incidents. An example of results where at least moderately high overpressures were achieved is the study of Tanaka et al [132]. Figure 22.21 shows their results obtained for AC arcs of fixed 0.1 s duration. The higher values obtained for aluminum electrodes reflect the contribution of the combustion of electrode metal. Efforts have been made to use commercial CFD codes for computing pressure rises in enclosures, but the validity of such efforts has been problematic. Capelli-Schellpfeffer et al. published two CFD modeling studies intended to simulate an experimental arc fault in 480 VAC switchgear in which an arc energy of 20 kJ was delivered and a peak overpressure of 2.6 atm was measured [133]. In the first study [133], a peak of 0.2 atm was computed, while in the second [134] a peak of 16,000 atm was predicted. Interestingly, the same 20 kJ value of arc energy was used by Caillard et al. [135] but in a capacitive discharge circuit and they predicted a peak overpressure of 1,700 atm while
measuring a peak of 0.26 atm. Other researchers [136] obtained reasonable agreement, but only by using a custom-designed CFD code.
Summary Fires arising due to static electricity or electric current can be difficult to understand for the nonspecialist because, apart from fire science, the separate discipline of electrical science is invoked. Partly because of this disciplinestraddling nature of the phenomenon, research has not been as vigorously pursued as in some other aspects of fire science. But at the present time, the fundamentals have been well enough established that general guidance can be given. The ways by which the “heat” leg of the fire triangle is produced in electrical fires has been outlined in this chapter. The most highly specialized of these mechanisms is the electrical arc, and its characteristics have been reviewed in this chapter. Electric arc explosions are a highly specialized phenomenon and are primarily physical explosion, rather than chemical, although some chemical reactions may occur.
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Nomenclature A C Cp Cv c1 c2 D d d1 d2 e E h I L M p P P_ q00 Q Q000 r R R t T u V V W α ε εo γ γ γ λ ρ
Area (m2) Capacitance (F) Heat capacity, constant-pressure (J kg1 K1) Heat capacity, constant-volume (J kg1 K1) Constant (-) Constant (-) Diameter (m) Distance (m) Clearance distance (m) Creepage distance (m) Charge of the electron (C) Electric field (V m1) Heat transfer coefficient (W m2 K1) Current (A) Distance (m) Molar mass (kg/mol) Pressure (Pa) Power (W) First derivative of electrical power (W s1) Power density (W m2) Charge (C) Charge density (C m3) Radius (m) Resistance (W) Universal gas constant (8.314 J mol1 K1) Time (s) Temperature (K) Velocity (m s1) Potential difference (“voltage”; V) Volume (m3) Energy (J) Townsend’s first ionization coefficient, (m1) Dielectric constant (–) Permittivity of vacuum (S s m1) Ratio Cp/Cv (—) Incomplete gamma function (–) Townsend’s second ionization coefficient (-) Thermal conductivity (W m1 K1) Density (kg m3)
ρe σ τ
Electrical resistivity of copper (Ω · m) Charge density (C m2) Time constant (s)
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14. A.E.W. Austen and S. Whitehead, “The Electric Strength of Some Solid Dielectrics,” in Proceedings Royal Society A, 176, pp. 33–49 (1940). 15. A.B. Lewis, E.L. Hall, and F.R. Caldwell, “Some Electrical Properties of Micas,” Journal of Research NBS, 7, pp. 403–418 (1931). 16. Y. Abed, “Experimental and Digital Determination of Breakdown Voltage of Different Synthetic Insulating Materials,” in Conference Record of the 1982 I.E. International Symposium on Electrical Insulation, IEEE, New York, pp. 123–126 (1982). 17. J.H. Mason, “Breakdown of Solid Dielectrics in Divergent Fields,” IEE Proceedings, 102C, pp. 254–263 (1955). 18. A.E.W. Austen and H. Pelzer, “The Electric Strength of Paraffins and Some High Polymers,” Journal of IEE, 93, pp. 525–532 (1946). 19. V. Babrauskas, “Mechanisms and Modes for Ignition of Low-Voltage, PVC-Insulated Electrotechnical Products,” Fire & Materials (2005). 20. J.D. Cobine, Gaseous Conductors: Theory and Engineering Applications, Dover, New York (1958). 21. L. West and D.A. Reiter, “Full-Scale Arc Mapping Tests,” in Fire & Materials 2005, Interscience Communications Ltd., London, pp. 325–339 (2005). 22. Guide for Performing Arc-Flash Hazard Calculations (IEEE Std 1584), IEEE, New York, 2002. 23. Standard for Performance Specification for Flame Resistant Textile Materials for Wearing Apparel for Use by Electrical Workers Exposed to Momentary Electric Arc and Related Thermal Hazards (ASTM F 1506), ASTM, West Conshohocken, PA, 2012. 24. Standard Test Method for Determining the Arc Thermal Performance Value of Materials for Clothing (ASTM F 1959), ASTM, West Conshohocken, PA, 2006. 25. T. Bernstein, “Electrical Fires: Causes, Prevention, and Investigation,” in Electrical Hazards and Accidents: Their Cause and Prevention (E.K. Greenwald, ed.), Van Nostrand Reinhold, New York, pp. 116–134 (1991). 26. J. Engel, M. Walz, and J. McCormick, “Arc Fault Circuit Interrupters,” Third Joint FAA/DoD/NASA Conference on Aging Aircraft, Albuquerque, NM (1999). 27. T. Bernstein, “Electrocution and Fires Involving 120/240-V Appliances,” IEEE Transactions on Industry Applications, IA-19, pp. 155–159 (1983). 28. G. Gregory, “AFCIs Target Residential Electrical Fires,” NFPA Journal, 94, pp. 69–71 (Mar./Apr. 2000). 29. A.C. Eberhardt, “Testing and Performance of Line Interrupters in Structure Fires,” presented at Defense Research Institute, Product Liability Conference, New Orleans (2004). 30. S. Nakamura, H. Kaneda, M. Ieda, and G. Sawa, “Correlation between Resistance to Tracking and Energy of Scintillation Discharge for Polyvinylchloride Doped with Aluminium
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702 46. Rousseau, A., Validation of Installation Methods for CSST Gas Piping to Mitigate Lightning Related Damage - Phase 1, Prepared by SIFTIM, Fire Protection Research Foundation, Quincy MA (2011). 47. B. Be´land, “Some Fires of Electrical Origin,” Fire & Arson Investigator, 37, 2, pp. 37–38 (Dec. 1986). 48. K.F. Davis, “Building Fires Attributed to Be Caused by Electrical Wiring Faults,” in Proceedings of the 27th International Conference on Fire Safety, Product Safety Corp., Sissonville, WV, pp. 101–110 (1999). 49. NFPA 70, National Electrical Code, National Fire Protection Association, Quincy, MA, 2014. 50. P. Cushing, “BX Cable and Fire Cause Determination,” Fire Engineering, 153, p. 46 (July 2000). 51. S. Turkel, “In Search of Transients,” EC&M, 99, 16, p. 18 (Oct. 2000). 52. T. Kuroyanagi, S. Inoue, and H. Suzuki, “Glowing Phenomena of Copper and Copper Materials and Their Electrical Characteristics,” Copper Promotion Technical Research Group Journal, 20, pp. 198–204 (1981). 53. O. Keski-Rahkonen and J. Mangs, “Electrical Ignition Sources in NPPs: Statistical, Modelling, and Experimental Studies,” International Atomic Energy Agency, Technical Committee Meeting on “Fire Experience in NPPs and Lessons Learned” (J7-TC2001.7), Vienna (July 9–13, 2001). 54. M. Abramovitz and I.A. Stegun, Handbook of Mathematical Functions (AMS55), NBS, Gaithersburg, MD (1964). 55. Wilson, C., McIntosh, G., and Timsit, R. S., Contact Spot Temperature and the Temperature of External Surfaces in an Electrical Connection, Proc. ICECICREPEC2012 – Joint Conf. of the 26th Intl. Conf. on Electrical Contacts and 4th Intl. Conf. on Reliability of Electrical Products and Electric Contacts, Beijing, China (2012). 56. W.J. Meese and R.W. Beausoliel, “Exploratory Study of Glowing Electrical Connections” (NBS BSS 103), NBS, Gaithersburg, MD (1977). 57. D. Newbury and S. Greenwald, “Observations on the Mechanisms of High Resistance Junction Formation in Aluminum Wire Connections,” Journal of Research NBS, 85, pp. 429–440 (1980). 58. Shea, J. J., Glowing Contact Physics, pp. 48–57 in 52nd IEEE Holm Conference on Electrical Contacts, IEEE, New York (2006). 59. “Tests of Insulating Materials for Resistance to Heat and Fire,” Report of CEE Working Group “Hot Mandrel Test,” CEE (031) D126/61, Deutsches Komitee der CEE beim Verband Deutscher Elektrotechniker, Frankfurt am Main (1961). 60. T. Kawase, “The Breeding Process of Cu2O,” IAEI News, 47, pp. 24–25 (July/Aug. 1975); Second Report, 49, pp. 45–46 (Nov./Dec. 1977). 61. Y. Hagimoto, K. Kinoshita, and T. Hagiwara, “Phenomenon of Glow at the Electrical Contacts of
V. Babrauskas Copper Wires,” National Research Institute of Police Science Reports—Research on Forensic Science, 41, pp. 30–37 (Aug. 1988). 62. J. Aronstein, “Fire Due to Overheating AluminumWired Branch Circuit Connections,” Wright Malta Corp., Ballston Spa NY (1983). 63. Guest, P. G., Static Electricity in Nature and Industry (Bulletin 368), Bureau of Mines, US Government Printing Office, Washington (1933). 64. Lu¨ttgens, G., and Glor, M., Understanding and Controlling Static Electricity, Expert Verlag, Ehningen (1989). 65. Pratt, T. M., Electrostatic Initiation of Explosions in Dusts, Cereal Foods World 23, 601–605 (1978). 66. L.B. Loeb, “Static Electrification-I,” in Progress in Dielectrics, vol. 4, Academic, New York, pp. 249–309 (1962). 67. E.M. Cohn and P.G. Guest, “Influence of Humidity upon the Resistivity of Solid Dielectrics and upon the Dissipation of Static Electricity” (IC 7286), Bureau of Mines, Pittsburgh (1944). 68. Britton, L. G., Avoiding Static Ignition Hazards in Chemical Operations, AIChE (1999). 69. Glor, M., Ignition of Gas/Air Mixtures by Discharges between Electrostatically Charged Plastic Surfaces and Metallic Electrodes, J. Electrostatics 10, 327–333 (1981). 70. Bartknecht, W., Dust Explosions: Course, Prevention, Protection, Springer-Verlag, Berlin (1989). 71. Glor, M., Conditions for the Appearance of Discharges during the Gravitational Compaction of Powders, J. Electrostatics 15, 223–235 (1984). 72. Glor, M., Overview of the Occurrence and Incendivity of Cone Discharges with Case Studies from Industrial Practice, J. Loss Prevention in the Process Industries 14, 123–128 (2001). 73. Maurer, B., Glor, M., Lu¨ttgens, G., and Post, L., Hazards Associated with Propagating Brush Discharges on Flexible Intermediate Bulk Containers, Compounds and Coated Materials, pp. 217–222 in Electrostatics ‘87—7th Intl. Conf. on Electrostatic Phenomena (Conf. Series No. 85), Institute of Physics, London (1987). 74. Cross, J. A., Electrostatics: Principles, Problems and Applications, Adam Hilger, Bristol, England (1987). 75. Y. Tabata and S. Masuda, “Minimum Potential of Charged Insulator to Cause Incendiary Discharges,” IEEE Transactions on Industry Applications, IA-20, pp. 1206–1211 (1984). 76. P.G. Guest, V.W. Sikora, and B. Lewis, “Static Electricity in Hospital Operating Suites: Direct and Related Hazards and Pertinent Remedies” (RI 4833), Bureau of Mines, Pittsburgh (1952). 77. Fisher, R. J., A Severe Human ESD Model for Safety and High Reliability System Qualification Testing (SAND89-0194C), Sandia Natl. Labs., Albuquerque NM (1989).
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78. Code of Practice for Control of Undesirable Static Electricity (BS 5958 Part 1), British Standards Institution, London (1980). 79. G.W. Brundrett, “A Review of Factors Influencing Electrostatic Shocks in Offices,” Journal of Electrostatics, 2, pp. 295–315 (1976/77). 80. Klinkenberg, A., and van der Minne, J. L., Electrostatics in the Petroleum Industry, Elsevier, Amsterdam (1958). 81. Lu¨ttgens, G., and Wilson, N., Electrostatic Hazards, Butterworth-Heinemann, Oxford (1997). 82. P. Boschung and M. Glor, “Methods for Investigating the Electrostatic Behaviour of Powders,” Journal of Electrostatics, 8, pp. 205–219 (1980). 83. S.J. Collocott, V.T. Morgan, and R. Morrow, “The Electrification of Operating Powder Chemical Fire Extinguishers,” Journal of Electrostatics, 9, pp. 191–196 (1980). 84. S. Singh, P. Cartwright, and D. Thorpe, “Silo Electrostatic Hazards” (SMS-84-052), National Grain and Feed Association, Washington, DC (1984). 85. Blythe, A. R., and Reddish, W., Charges on Powders and Bulking Effects, pp. 107-114 in Electrostatics 1979 (Conf. Series No. 48), The Institute of Physics, London (1979). 86. A. Klinkenberg and J.L. van der Minne, Electrostatics in the Petroleum Industry, Elsevier, Amsterdam (1958). 87. L.B. Britton and J.A. Smith, “Static Hazards of Drum Filling,” Paper 54e, 21st Loss Prevention Symposium, AIChE (1987). 88. H.L. Walmsley and J.S. Mills, “Electrostatic Ignition Hazards in Road Tanker Loading: Part 1. Review and Experimental Measurements,” Journal of Electrostatics, 28, pp. 61–87 (1992). 89. Bachman, K. C., Variables Which Influence Spark Production Due to Static Electricity in Tank Truck Loading, Lightning and Static Electricity Conf., Royal Aeronautical Society, London (1975). 90. L.B. Loeb, “Static Electrification-I,” in Progress in Dielectrics, vol. 4, Academic, New York, pp. 249–309 (1962). 91. V.I. Ermakov and Y.I. Stozhkov, “New Mechanism of Thundercloud Electricity and Lightning Production,” in 11th International Conference on Atmospheric Electricity (NASA/CP-1999-209261) (H.J. Christian, ed.), NASA, Marshall Space Flight Center, AL, pp. 242–245 (1999). 92. W.C. Hart and E.W. Malone, Lightning and Lightning Protection, Don White Consultants, Gainesville, VA (1979). 93. M.M. Frydenlund, Lightning Protection for People and Property, Van Nostrand Reinhold, New York (1993). 94. Frey, O., The Origin, the Effects and the Simulation of Transients, as Well as Their International Standardization, Electro 82, Boston (1982).
703 95. Recommended Practice for Protecting Residential Structures and Appliances against Surges (Document # PEAC.0545.R), EPRI PEAC Corp., Knoxville, TN (1999). 96. M.M. Frydenlund, Lightning Protection for People and Property, Van Nostrand Reinhold, New York (1993). 97. Frydenlund, M. M., Lightning Protection for People and Property, Van Nostrand Reinhold, New York (1993). 98. Anderson, R., Lightning Conductors: Their History, Nature and Mode of Application, E&FN Spon, London (1879). 99. Mu¨ller-Hillebrand, D., The Protection of Houses by Lightning Conductors—An Historical Review, J. Franklin Institute 274, 34–54 (1962). 100. Lee, R. H., Protection Zone for Buildings against Lightning Strikes using Transmission Line Protection Practice, IEEE Trans. Industry Applications IA-14, 465–470 (1978). 101. Standard for the Installation of Lightning Protection Systems (NFPA 780), NFPA. 102. The Basis of Conventional Lightning Protection Technology: A Review of the Scientific Development of Conventional Lightning Protection Technologies and Standards, Federal Interagency Lightning Protection User Group, [n.p] (2001). 103. Moore, C. B., Rison, W., Mathis, J., and Aulich, G., Lightning Rod Improvement Studies, J. Applied Meteorology 39, 593–609 (2000). 104. T.E. Eaton, Notes on Electrical Fires, 3rd ed. and 1990 supplement, Eaton Engineering Co., Nicholasville, KY (1989). 105. Safety of Information Technology Equipment, Including Electrical Business Equipment (UL 1950), Underwriters Laboratories Inc., Northbrook IL, 2006. 106. J. Sletback, R. Kristensen, H. Sundklakk, G. Na˚vik, and R. Munde, “Glowing Contact Areas in Loose Copper Wire Connections,” in Proceedings 37th IEEE Holm Conference on Electrical Contacts, IEEE, New York, pp. 244–248 (1991). 107. E.L. Litchfield, T.A. Kubala, T. Schellinger, F.J. Perzak, and D. Burgess, “Practical Ignition Problems Related to Intrinsic Safety in Mine Equipment: Four Short-Term Studies” (RI 8464), Bureau of Mines, Pittsburgh (1980). 108. M. Saito and W. Sakurai, “An Evaluation Method of Electrical Fire Hazard Caused by Tracking Breakdown,” in Proceedings Electrical/Electronics Insulation Conference, IEEE, New York, pp. 137–141 (1979). 109. Me´dard, L. A., Accidental Explosions, 2 vols., Ellis Horwood, Chichester, England (1989). 110. Crowl, D. A., Understanding Explosions, CCPS/ AIChE, New York (2003). 111. Bodurtha, F. T., Industrial Explosion Prevention and Protection, McGraw-Hill, New York (1980).
704 112. Hattwig, M., and Steen, H., eds., Handbook of Explosion Protection and Prevention, WileyVCH, Weinheim, Germany (2004). 113. Baker, Wilfred E., Cox, P. A., Westine, P. S., Kulesz, J. J., and Strehlow, R. A., Explosion Hazards and Evaluation, Elsevier, Amsterdam (1983). 114. Babrauskas, V., Electric Arc Explosions, pp. 1283–1296 in Interflam 2010—Proc. 12th Intl. Conf., Interscience Communications Ltd, London (2010). 115. Lindmayer, M., and Paulke, J., Arc Motion and Pressure Formation in Low Voltage Switchgear, IEEE Trans. on Components, Packaging, and Manufacturing Technology A21, 33–39 (1998). 116. Nabours, Robert E., Fish, R. M., and Hill, P. F., Electrical Injuries: Engineering, Medical and Legal Aspects, 2nd ed., Lawyers & Judges Publishing Co. (2004). 117. Mazer, W. M., Electrical Accident Investigation Handbook, 3 vols., Electrodata, Inc., Glen Echo MD (var. dates). 118. Lee, R. H., Pressures Developed by Arcs, IEEE Trans. on Industry Applications IA-23, 760–764 (1987). 119. Crawford, K. S., Clark, D. G., and Doughty, R. L., Motor Terminal Box Explosions due to Faults, IEEE Trans. on Industry Applications 29, 257–267 (1993). 120. Heberlein, G. E. jr., Higgins, J. A., and Epperly, R. A., Report on Enclosure Internal Arcing Tests, IEEE Industry Applications Magazine 2:3, 35–42 (May/June 1996). 121. Jennings, C., Fire-Fatality High-Rise Office Building Fire, Atlanta, Georgia (June 30, 1989), US Fire Admin., [Emmitsburg MD], (1989). 122. Graneau, P., The Cause of Thunder, J. Physics D: Applied Physics 22, 1083–1094 (1989). 123. Lee, R. H., The Shattering Effect of Lightning— Pressure from Heating of Air by Stroke Current, IEEE Transactions on Industry Applications 22, 416–419 (1986). 124. Eisenberg, N. A., Lynch, C. J., and Breeding, R. J., Vulnerability Model: Assessing Damage from Maritime Spills by Computer Simulation (CG-D-136-75), US Coast Guard, Washington (1975). 125. Baker, W. E. et al., Explosion Hazards and Evaluation, Elsevier, Amsterdam (1983).
V. Babrauskas 126. Flowers, J. W., The Channel of the Spark Discharge, Physical Review 64:7/8, 225–235 (1943). 127. Vanyukov, M. P., Isaenko, V. I., and Khazov, L. D., Investigation of Light Phenomena Related to the Development of the Spark-Discharge Channel, Zhurnal tekhnicheskoι fiziki 25, 1248 (1955). 128. Higham, J. B., and Meek, J. M., The Expansion of Gaseous Spark Channels, Proc. Physical Society B 63, 649–661 (1950). 129. Drouet, M. G., and Nadeau, F., Pressure Waves due to Arcing Faults in a Substation, IEEE Trans. on Power Apparatus and. Systems PAS-98, 1632–1635 (1979). 130. Dasbach, A., and Pietsch, G., Investigation of the Power Balance of High Current Faults, pp. 15–18 in Proc. 9th Intl. Conf. on Gas Discharges and Their Applications (GD88), Venice (1988). 131. Baldrey, H. W., and Hudson, A. A., Pressures Generated by Fault Arcs in Small Enclosures (Ref. Z/T134), The British Electrical and Allied Industries Research Assn., Leatherhead, Surrey, England (1961). 132. Tanaka, S., Miyagi, T., Ohtaka, T., Iwata, M., Amakawa, T., and Goda, Y., Influence of Electrode Material on Pressure-rise due to Arc in a Closed Chamber, IEEJ Trans. PE 128, 1561–1568 (2008). 133. Capelli-Schellpfeffer, M.,, Miller, G. H., and Humilier, M., Thermoacoustic Energy Effects in Electrical Arcs, pp. 19–32 in Occupational Electrical Injury: An Intl. Symp., / Annals of the New York Academy of Sciences, Vol. 888, New York Academy of Sciences, New York (1999). 134. Bowen, J. E., Wactor, M. W., Miller, G. H., and Capelli-Schellpfeffer, M., Catch the Wave: Modeling the Pressure Wave Associated with Arc Fault, IEEE Industry Applications Magazine 10:4, 59–67 (Aug. 2004). 135. Caillard, J., de Izarra C., Brunet, L, Valle´e, O., and Gillard, P., Assessment of the Blast Wave Generated by a Low-Energy Plasma Igniter and Spectroscopic Measurements, IEEE Trans. on Magnetics 39, 212–217 (2003). 136. Friberg, G., and Pietsch, G. J., Calculation of Pressure Rise due to Arcing Faults, IEEE Trans. on Power Delivery 14, 365–370 (1999)
Surface Flame Spread
23
Yuji Hasemi
Introduction Surface flame spread is a process of a moving flame in the vicinity of a pyrolyzing region on the surface of a solid or liquid that acts as a fuel source. It is distinct from flame propagation in a premixed fuel and oxygen system in that the surface spread of flame occurs as a result of the heating of the surface due to the direct or remote heating by the flame generated from the burning surface. The surface flame spread is very often critical to the destiny of fires in natural and built environments. This spread applies whether the fire is an urban conflagration or is the first growth after ignition of a room’s draperies. This chapter provides fire safety engineers with an overview of surface flame spread during the growth of a fire and the modeling of different modes of flame spread to improve understanding of their effects on the outcomes of fires.
Surface Flame Spread Basics Flame Spread Process The surface flame spread is caused as a result of the cycle of the following processes: This chapter is based in part on material by Professor J. Quintiere appearing in previous editions of this handbook. Y. Hasemi (*) Wasada University
1. Vaporization of solid or liquid due to the heating from flame over the fuel’s surface 2. Mixing of the pyrolized gas and oxygen in the vicinity of the fuel surface 3. Combustion of the pyrolized gas and formation of the diffusion flame 4. Heating of the unburnt fuel surface to ignition temperature from the diffusion flame The oxygen and fuel concentrations together with the heat transfer between the flame and the solid phase strongly affect the process. Taking the surface flame spread as a successive ignition front over a combustible object, the speed of spread and its sustainability are controlled by the balance of the flame heating and the rise of surface temperature (see Chap. 21). If the flame ignites the virgin surface of the area larger than that of the burning surface before local extinction, the spread will accelerate. From this point of view, relative configuration of the flame to the surface is critical for the dynamics and the hazard of surface flame spread. Flame spread in the direction of the mean flow due to wind or buoyancy is called wind-aided or concurrent spread, and, on the contrary, flame spread occurring in a direction opposite to that is called opposed-flow spread. Difference of the significance of the mode of flame spread for fire safety can be illustrated through the typical process of fire growth in a room with highly combustible lining ignited on the floor, as shown in Fig. 23.1. The spread of fire over the floor is a typical opposed-flow spread because the flame induces unheated air along the
M.J. Hurley (ed.), SFPE Handbook of Fire Protection Engineering, DOI 10.1007/978-1-4939-2565-0_23, # Society of Fire Protection Engineers 2016
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706
a
Y. Hasemi
b
c
Fig. 23.1 Orientation of combustible surface and the modes of flame spread over (a) floor, (b) wall, and (c) ceiling
carpet surface in the direction against the spread of the flame (Fig. 23.1a). The surface flame spread at the initial stage of a room fire is generally slow and can even be unstable; but once the wall lining is ignited, the buoyancy makes the flame develop along its surface and exposes the lining surface above the burning region to the flame (Fig. 23.1b). This condition generally makes the flame spread much faster than on the floor, even if the floor and the wall are lined with identical material. If not extinguished at this stage, fire may finally reach and ignite the ceiling. The buoyancy makes the flame spread laterally beneath the ceiling toward the opening, exposing the overall surface of the ceiling to the flame heating (Fig. 23.1c). As widely recognized, flame spread beneath the ceiling is generally fast and could cause flashover by igniting remaining furniture and wall surface far from the ignition source within the room. The Bradford Stadium fire disaster in the United Kingdom (1985) is one of the most significant examples of lateral flame spread beneath a combustible roof or ceiling. During lateral flame spread beneath the ceiling, downward flame spread over the wall lining is often observed within the smoke layer. It is an opposed-flow spread, yet its spread velocity is generally fast due to the additional heating from the smoke layer. As seen in the growth of room fire, the windaided flame spread presents a number of key processes escalating the hazard of building and
mass fires. In mass fires such as urban conflagrations and forest fires, fire brands have an additional but sometimes essential role in enhancing fire spread in the wind direction. The importance of opposed-flow flame spread can become significant when the temperature of the fire environment has been raised enough to preheat the wide range of surfaces of combustibles. Although the two modes of flame spread are apparently distinct from each other, there is notable ambiguity in fires on an inclined combustible surface. On an upward inclined surface, the angle between the flame flow and the surface is reduced with an increase of the angle of inclination, and finally the flame begins to crawl over the surface [1] (Fig. 23.2). This change occurs generally at 15–30 , depending on the width, side confinements, and other conditions; inclination of roofs, escalators, and slopes for wheelchairs are generally within the range where wind-aided flame spread is anticipated. The escalator fire at the Kings Cross Subway Station Fire Disaster (1987) is a significant example of wind-aided flame spread along an inclined configuration under the enhancement of buoyancy due to the confinement of air supply by the side walls [2].
Research Background Large numbers of experiments on and models of surface flame spread with diverse levels of theoretical sophistication and practical relevance
23
Surface Flame Spread
Fig. 23.2 Change of the mode of surface flame spread according to the slope angle
707 Vertical θ = 90° θ = 60°
θ = 30°
Horizontal θ = 0°
have been conducted, and it is impossible to make a precise review of all the important research on this subject. It is recommended to seek comprehensive reviews such as Drysdale [3], Quintiere [4], Fernandez-Pello and Hirano [5], Hirano [6], and Williams [7]. However, as long as surface flame spread is discussed for the assessment of fire safety of natural or artificial composites, the phenomena are generally modeled as a thermal process causing the successive piloted ignition on the surface due to the heating from the burning of the material itself under the gravity and the atmospheric conditions of the earth. Active research on thermal modeling of surface flame spread has occurred since the late 1960s, and significant progress was made in the basic understanding of flame spread through theoretical sophistication and laboratory experiments throughout the 1970s. Later, during the 1980s, the approach was extended to turbulent flames for the application to the fire hazard assessment of lining materials. In the 1990s, further studies were conducted to analyze and assess the general behavior of room fires through input from and validation against large-scale tests with
around one-story-high wall specimens or with standard and larger-scale room tests. These studies have revealed the importance of the surface configurations on the general behavior of flame spread; examples of acceleration of flame spread on grooved combustible surfaces, in corner walls, and in a vertical, inclined, or downward channel lined with combustible material show the significance of the configuration effect. Together with the substantial progress in the measurement technology of the combustibility of materials through the 1980s and the 1990s, these studies have made it possible to predict surface flame spread in a room to some extent using material properties obtained from benchscale tests.
Wind-Aided Flame Spread The wind-aided flame spread is the most important mode of surface flame spread for fire hazard assessment. In this section, modeling and assessment are introduced regarding the two most significant examples of wind-aided flame spread in building fires: upward wall flame spread and
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flame spread beneath the ceiling. Upward wall flame spread along a wall has drawn the particular interest of fire safety engineers for its primary importance in the determination of the destiny of a room fire and for the rich variety of configurations of wall surfaces that may influence the general behavior of flame spread. In this section, theories of wind-aided flame spread developed essentially for wall fires are applied to provide technical insight in the assessment of room fires or the combustibility of lining materials in general.
direction normal to the wall surface can be reasonably assumed and evolution of the surface temperature at x above the fire origin at time t, T(x,t), is formulated as ðt
00
T ðx; tÞ T o ¼ q_ f ðx; τÞϕðt τÞdτ
ð23:1Þ
0
where T0 ¼ Initial surface temperature q_00 ¼ Flame heat flux f
ϕ(t τ) ¼ Impulse response of the surface temperature at timet t to the surface heat flux at τ ϕ(t τ) ¼ [πkρc(t τ)]1/2 and ϕ(t τ) ¼ [ρcδ(t τ)]1 apply for a thermally thick wall and for a thin wall with thickness of δ respectively with k, ρ, and c thermal conductivity, density, and specific heat of the solid. Equation 23.1 can be solved for flame spread velocity, Vp ¼ dxp /dt, for simple conditions by further introducing engineering relations on the flame heat flux, 00 q_ f ¼ Fðx; τÞ. Flame heat flux is normally represented as relative location to the flame length, xf; that is, 00 q_ f ¼ F x=x f , Applying the Froude modeling for the flame height (see Chap. 21) to a line fire along a wall, xf is generally expressed as function of heat release rate per unit width as
Upward Turbulent Wall Flame Spread Figure 23.3 is a schematic of upward flame spread typical of wind-aided flame spread. The flame spread is thus perceived in two different manners: first by the advancement of flame front and second by the advancement of the ignition front of the solid surface. The rate of movement of the ignition front is normally defined as the flame spread velocity for modeling purpose. The location of the ignition front of a burning surface, xp(t), is identified as the location where surface temperature has reached the ignition temperature, Tig. Flame Heat Transfer For Fig. 23.3, one-dimensional thermal conduction in the
Fig. 23.3 Upward wall flame spread [9] Tw (x,y ) Flame
xp
xp
δfc
x xp
Tig Tw (x,0) Wall temperature
qf ″(x ) •
Heat flux
Y Model
Preheat distance Ignition front
23
Surface Flame Spread
709
*n x f =D ¼ kQ_ ‘
ð23:2Þ
Where D ¼ Characteristic lengthof the burning area * (normally height or depth), Q_ ‘ ¼ Q_ ‘ =cT 0 ρ1 g1=2 D2=3 :
k ¼ Empirical coefficient Q_ ‘ ¼ Heat release rate per unit width of fire source Figure 23.4 illustrates a relation between heat release rate per unit width and flame length for line burners against a constant temperature inert wall. It shows that k ¼ 6.0 for intermittent flame and n ~ 2/3 for Q_ ‘ 1:0, as anticipated for an ideal line source by dimensional analysis [8]. The value of k depends on the definition and measurement of flame length, and experimental k values range from 4.65 to 7.0 [8–11]. Newman and Wieczorek reviewed reported values for k and n [12]. With n ¼ 2/3 in Equation 23.2, flame length is found to be independent of the dimension of the burning region and is represented as
Fig. 23.4 Relation between the length of intermittent wall flame and dimensionless heat release rate per unit width [9]
2=3 2=3 x f ¼ k3=2 =c p T o ρ1 g1=2 Q_ ‘ 0 2=3 ¼ k Q_ ‘
ð23:3Þ
The k0 value is roughly 0.01 k; for Fig. 23.3, k0 value is found to be k0 ¼ 0.057 m1/3 kW2/3, whereas k0 values in literature range from 0.043 m1/3 kW2/3 to 0.067 m1/3 kW2/3 [8, 9, 12, 13]. For a limited range of Q_ ‘ , flame length can be linearized against heat release rate or the characteristic length of burning region for engineering purposes as 00
x f k f Q_ ‘ ¼ k f Q_ ‘ D ¼ aD
ð23:4Þ
00
where Q_ ‘ is the characteristic heat release rate 00 per unit width, kf, and ak f Q_ ‘ depends on heat release rate, but kf ~ 0.006–0.01 m2/kW is suitable for lining materials in practice [14–16]. Figure 23.5 is a general relation between the total incident heat flux from wall flame to wall surface and the distance from the lower edge of the burning surface normalized by xf. It is a summary of experiments on wall flames
Flame length / fuel length, xf /D (–)
100
0.0375D × 0.270 0.082D × 0.270 0.075D × 0.270 3
Solid; laminar 2
10
1 0.1
1 Dimensionless heat release rate per unit width, Q */(–)
10
710
Y. Hasemi
10
Small fire Laminar methanol fire x0 = 1.1 cm, xf = 5.3 cm x x
0
xf
Pyrolysis region
x0
x
Turbulent moderate fires x > x0
1 2 5
•
Total incident heat flux, qw ″ (W/cm2)
0
Large fire PMMA wall fire x < x0 x0 = 3.56 m, xf = 6.06 m
Ahmad and Faeth19 •
qw ″ × PR = k(Grx *)n μ∞ LB
(
(
Hasemi9
Grx * = Lgx 3/(4CpT∞v∞2) 0.1 Laminar, x < x0 Laminar, x0 < x < xf Turbulent, x0 < x < xf x < 10 cm Laminar x > 10 cm Turbulent
k 0.24–0.28 0.5–0.6 0.035–0.04
n 0.25 0.25 0.4
1 1.3
Data region (xf : 0.3–1.4 m)
0.01 0.01
0.1
1.0
10
x /xf Fig. 23.5 Wall flame incident heat flux for materials [17], for laminar flames [19], and for a large PMMA wall fire [18]
from steady porous burners, vertical wicks, and burning of specimens of finite-surface area of materials in practice [9, 17–19]. For more detailed flame heat flux data and correlations on different configurations, see Chap. 25. As thermal conduction theories suggest, response of surface temperature to heat input depends significantly on the thickness of the solid; modeling of surface flame spread requires different approaches for thermally thick solid and thin materials. Except for items such as paper, garments, or draperies in a room, in practice most solids should behave as thermally thick under flame spread conditions. Engineering treatment of surface flame spread might appear to regard solids thicker than 1 mm as thermally thick. Up to a thickness of 1–2 cm, flame spread could
depend on thickness and on the substrate material adjacent to the solid. Based on these factors, it is apparent that the thermally thick case is more significant. With the unique dependence of flame heat flux on dimensionless height, x/xf, Equation 23.1 can be solved to provide a characteristic steady flame spread velocity Vp ¼ xp /t for a thermally thick solid as ð 1 pffiffiffiffiffiffiffi 2 2 00 Vp ¼ q_ f ξ þ x p = ξdξ =πkρc T ig T o 0
ð23:5Þ The numerator has the dimension of (kW/m2)2 m, and Equation 23.5 can be 00 represented more simply as q_ fc 2δfc with charac00
teristic flame heat flux, q_ fc , and characteristic
23
Surface Flame Spread
711
preheat distance, δfc. Equation 23.5 is thus expressed as . . 00 2 ¼ xfc x p Vp ¼ 4q_ fc2 δfc t*ig πkρc T ig T o ð23:6Þ where
characteristic time to ignition, it will become difficult to sustain successive thermal ignition on the surface. Taking the linearized flame length approximation (Equation 23.4), we introduce the following dimensionless flame spread acceleration factor: [14] b ¼ ða 1Þ tig *=tb
xfc ¼ x p þ δfc 2 00 t*ig πkρc T ig T o =4q_ fc2 Equation 23.6 is essentially in the same form with the flame spread velocity obtained for flame heat flux decaying exponentially with distance from the ignition front [20]. The preheat distance, δfc, is essentially the distance between the flame front and the ignition front.
Heat release rate, Qc″
Controlling Parameters of Upward Wall Flame Spread In Equation 23.6, it is important that the characteristic preheat distance, δfc, is essentially controlled only by the heat release rate in a one-dimensional flame configuration, and kρc(Tig T0)2 is the central part of material property to control ignitability. Another important parameter that may control the general behavior of flame spread is the local burnout. Consider local burnout occurring at tb after the local ignition (Fig. 23.6), D ¼ Vptb. If the local burnout time is short compared to the
ð23:7Þ
where (a 1) represents the significance of flame heating, and if tig*/tb is large, it will become difficult for successive ignition to sustain. Obviously, b ¼ 0 stands for Equation 23.6 and is the condition for the achievement of steady-state spread. The sign of b dictates the general behavior of wind-aided flame spread: b > 0 will lead to the acceleration of spread, whereas b < 0 will result in the deceleration of spread and finally autonomous extinction. There is more sophisticated discussion on the general behavior of wind-aided flame spread [15, 16, 21–24], which may still await future validation. But every kind of thermal model and analysis based on the linearized flame length approximation (Equation 23.4) finally eventuates the recognition of b as the central parameter for the assessment of hazard of flame spread. Figure 23.7 is a summary of the correlation between the time to flashover in ISO 9705 roomcorner tests with combustible linings and b [14]. The elements of b, namely a, tig*, and tb, are all material properties that can be quantified with bench-scale tests such as the cone calorimeter. Although there is still some discussion on what external heat flux level should be chosen for the quantification, use of 30–50 kW/m2 external radiant flux seems to lead to reasonable explanation of the growth of room fire from Equation 23.7. For a charring material, heat release rate generally decays with time after the sharp peak just after the ignition and can be more suitably represented by an exponential function 00 00 of time, namely Q_ ðtÞ ¼ Q_ expðt=tc Þ. Analmax
tig
tb Time
Fig. 23.6 Time history of heat release rate from fixed area burning surface
ysis of the results of room-corner tests and the cone calorimeter on wood-based materials suggests use of k f Q_ max and tc for a and tb respectively leads to a result consistent with Fig. 23.7 [15, 22] for such materials.
712
∞ Time to flashover, tig (s)
Fig. 23.7 Time to flashover in the ISO 9705 room-corner test versus the flame spread acceleration factor [14]
Y. Hasemi
800 700 600 500 400 300 200 100 0 –8
Equation 23.7 is simple but provides useful insights in the overall understanding of windaided flame spread. It is especially noteworthy that material properties are not the single factor to quantify this equation. Time to ignition and time to burnout are dependent on the ambient temperature and external heating; and a, essentially the flame-length to pyrolysis-length ratio, can be augmented not only by external heating through enhancement of vaporization but also by increase of pyrolizing surface area due to any finishing treatment such as roughness and grooves. Existence of the source of external heating has thus two implications for the acceleration of flame spread: first through the increase of the temperature of the unburnt surface and second through the promotion of vaporization of fuel due to additional heating of the burning surface [25]. Grooves or trench-like configurations of the burning surface can reduce air entrainment to the vaporizing region and extend the flame length. Configuration effect is as important as material properties in the fire safety assessment of any assembly with a combustible surface. Flame spread can be significantly enhanced in parallel wall configuration, where the flame on either wall stimulates pyrolysis and preheating of the other surface and generates mutual acceleration of flame spread. If the wall distance is small compared to the wall width, the air supply to the burning surface will be restricted and further prolong the flame length. Even though parallelwall configuration is not common in building
–6
–4 –2 0 2 4 Flame spread acceleration factor, b(–)
6
8
design, commodities or cargoes piled in warehouses or in mass merchandise outlets often make “valleys with combustible cliffs,” which can be considered as parallel walls from the flame spread point of view. A number of fire tests of cargoes and commodities in typical warehouse configuration demonstrate significant acceleration of fire growth in such a configuration [24, 26]. A cavity within a wall or a roof sandwiched by combustible surfaces is another significant example capable of showing the parallel-wall effect. Surface flame spread can be further enhanced in a vertical or inclined cavity by the stack effect due to general temperature rise within the cavity. The fast fire spread throughout whole high-rise building at the Beijing Television Cultural Center fire (2009) is partly attributed to these configuration effects. The vertical long cavity lined with polymer insulation within the facades on both sides of the building should have helped acceleration of fire spread once the fire penetrated into the cavity. Also, in a corner of walls, flame is generally prolonged due to the restriction of entrainment and the mutual radiation between the walls, which can result in faster flame spread. There are experiments and measurements of upward turbulent flame spread on nearly full-scale specimens of various materials in practice [11, 18, 26–29]. These reports would provide valuable information necessary for consideration in running large-scale flame spread tests with materials in practice.
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Fig. 23.8 Area covered by ceiling flame versus effective heat release rate [30, 31]
3
Flame area, Sf (m2)
2.5
d = 0.09 m Sf = 0.069 Q
2 1.5
d = 0.16 m Sf = 0.062 Q
1 One-dimensional ceiling fire Sf = 0.023 Q
0.5
0 0
10
20
30
40
50
Heat release rate (oxygene consumption method, Q(kW)
Surface Flame Spread Beneath Ceiling Although fewer studies have been conducted on the ceiling fires, the mechanism of the surface spread is essentially similar to the upward wall spread. Flame spreading beyond the pyrolysis front is the dominant force for the successive ignition of unburnt ceiling surface. According to the measurements of flame size and flame heat flux for one-dimensional ceiling flames in a corridor-like configuration and for circular ceiling flames from downward porous propane sources [30] (Fig. 23.8), the area covered by a visible ceiling flame is nearly proportional to the heat release rate, and the heat release rate per unit flame area is significantly larger for one-dimensional flames than for circular flames. This situation indicates uniform entrainment of air beneath a ceiling flame, but the rate of entrainment could depend on the configuration. Flame length is thus proportional to heat release rate per unit width in corridor configuration, xf ¼ 0.0122 Q_ le with Q_ le as the effective heat release rate per unit width (kW/m) for corridor ceiling configuration [31] and proportional to the half power of heat release rate beneath an unconfined ceiling. As shown in Chap. 25, total heat flux from the ceiling flame to the ceiling surface can be
represented as a unique function of distance from the windward edge of the burning surface divided by the flame length. From these facts, the engineering framework for the assessment of surface flame spread on a wall applies suitably for the flame spread beneath a combustible ceiling, whereas such physical constants as a should be different from the wall fire configuration. Under an unconfined ceiling, heat flux within the solid ceiling flame is decreased weakly with distance within the range of 20–30 kW/m2, and is generally weaker than in upward wall flames of similar heat output, because of the buoyancy reducing the thickness of ceiling flame. Ambient thermal conditions and surface configurations of the ceiling could also affect the general behavior of flame spread beneath the ceiling. One of the important issues to be considered in the understanding and fire hazard assessment of flame spread beneath the ceiling in a room is the effect of preheating due to ceiling jet and smoke layer, which normally come in contact with the ceiling earlier than flame in a likely fire growth scenario in a room. Corridor ceiling flame spread tests lined with mediumdensity fiberboard (MDF) with uniform external radiation to the ceiling surface demonstrate significant sensitivity of the ultimate burn length to pilot flame length ratio, xpoff/xpo, to the ceiling
714 Initial surface temperature versus xpoff ≠ xpo
14 12
xpoff / xpo (–)
Fig. 23.9 Relation between the surface temperature due to external heating at piloted ignition to ceiling and the ultimate burnt length to pilot flame length ratio for MDF [31]
Y. Hasemi
10 8 6 4 2 0 0
100
200
300
400
Initial surface temperature (°C)
surface temperature just prior to the ignition by pilot flame, To (Fig. 23.9) [31]. To was controlled by the upward radiant panel. In the tests resulting in xpoff/xpo > 10, almost the whole ceiling surface was finally pyrolyzed and flame spread itself was strongly accelerated. Flame spread was less sensitive to heat flux within the range of 0–10 kW/m2. The remarkably fast flame spread beneath a nearly unconfined roof/ceiling observed at the event of the Bradford Stadium fire disaster (1985) is attributed partly to the use of roof material of low ignition temperature. Increase of the effective combustible surface area due to beams, decorations, and so forth can also increase a value and accelerate flame spread. Stenstad and Karlsson have demonstrated a significant example of such effect by a large-scale experiment [32].
Opposed-Flow Flame Spread Mechanism of Opposed-Flow Flame Spread In the opposed-flow spread, the front of the pyrolyzing region moves in the opposite direction of the flame flow. As seen in Fig. 23.10, the unburnt surface beyond the pyrolysis front is heated by remote flame; the flame spread velocity is less dependent on flame length or heat release rate, and the distance that the flame heating covers should be quite limited. For this
reason, in the modeling of opposed-flow flame spread, spread velocity is normally assumed as steady state. Consider that the pyrolysis front traverses Δ within the time interval τ on a combustible solid of the thickness δ small enough to ensure practically uniform temperature across the thickness with no heat loss from the back surface. The flame spread velocity can be given by Vp ¼ Δ/τ, and the energy conservation for the control volume Δ distance from the pyrolysis front can be described as ρcδV p T ig T o ¼ q_00 Δ ð23:8Þ The net flame heat flux due to the gas-phase conduction can be given by q_00 kg T f T r =Δ ð23:9Þ where kg, Tf, and Tr are gas-phase conductivity, flame temperature, and reference temperature for the control volume. Tr can be correlated with either Tig or To. From these equations, the flame spread velocity can be represented as a function of thermal properties and the configuration condition as V p ¼ kg T f T r =ρcδ T ig T s
ð23:10Þ
The flame temperature, Tf, should ideally be taken as that due to adiabatic stoichiometric combustion but, in general, could be thought of as less due to heat losses and chemical kinetic effects. Under these ideal theoretical considerations, it can be shown that
23
Surface Flame Spread
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Fig. 23.10 Energy conservation in opposedflow spread
Boundary layer
Vg
Flame
Control volume δ
Ts
V
Pyrolysis region
Tig Δ
T 1 T ig þ Y ox, 1 =rcg ðΔH LÞ T f T ig ¼ 1 Y ox, 1 =r
ð23:11Þ where ΔH and L are heat of combustion and heat of gasification of the solid fuel, respectively. T1 and Yox,1 are gas-phase ambient temperature and oxygen concentration, respectively, and r and cg are stoichiometric mass ratio of oxygen to fuel and specific heat of the gas phase, respectively. Because ΔH/L and Yox,1/r are large, and heat of combustion per unit mass of consumed oxygen, ΔHox, is nearly constant for most of combustible solids in practice (13 kJ/g), the flame temperature can be approximated as T f T ig Y ox, 1 ΔH ox =cg
ð23:12Þ
and we realize that the flame temperature is primarily sensitive to only the ambient oxygen concentration. This suggests that flame spread over a ceiling would be reduced in a room as the oxygen within the smoke layer near it is reduced. For a thermally thin solid, δ can be taken as constant. Combining Equations 23.8 and 23.9, flame spread velocity is given as V p ¼ Δ=τ ¼ kg T f T o =ρcδ T ig T r ð23:13Þ For a thermally thick solid, δ should represent the depth of thermal penetration, which depends on time; that is, from the heat conduction equapffiffiffiffiffiffiffiffiffiffiffiffi tion for a semi-infinite thick slab as δ ¼ kτ=ρc. Substituting this into Equation 23.8, we have
2 2 V p ¼ q_00 Δ=kρc T ig T o
ð23:14Þ
In Equations 23.13 and 23.14, the flame spread velocity is apparently independent of the opposed-flow velocity, Vg. However, the independence is only the case as long as chemical effects are unimportant. Chemical kinetic effects become important when the time for chemical reactions to be completed in the flame, tchem, becomes long compared to the fluid flow transit time through the flame, tflow . If the flow is too fast, chemical reaction will be incomplete. Because the flow transit time is proportional to V g -1 and mixing should be enhanced by the decrease of Vg, the flow transit time to chemical reaction time ratio, normally referred to as the Damko¨hler number, Da, can be represented as Da ¼ tflow =tchem / 1=V 2g
ð23:15Þ
The flame spread velocity is reduced with an increase of Da. Taking the flame spread velocity given by Equation 23.10 as Vp,ideal, the actual flame spread velocity to Vp,ideal ratio can be illustrated qualitatively as shown in Fig. 23.11. However, for a thermally thick solid, the relation between flame spread velocity and opposed-flow velocity is more complicated. Figure 23.12 is a significant such example showing either increase or decrease of V with Vg depending on the ambient oxygen concentration [33]. This illustration suggests the dependence of Vp,ideal on Vg in the flame spread over a
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Fig. 23.11 Qualitative dependence of opposedflow flame spread with Damko¨hler number, Da
10
l ica em tics h C ne ki Y ox,∞
V/ Vpideal
1
Fast High Low
h Hig
10–1
Slo Low w
Vg
Extinction
10–2 10–2
10–1
1
10
Da
Fig. 23.12 Effect of opposed-flow velocity and oxygen concentration of flame spread speed for thick PMMA (Taken from Fernandez-Pello et al.) [33]
100
Vp (cm/s)
10–1
Y0 1.00 0.727 0.533 0.432 0.329 0.276 0.247 0.233 0.211
10–2
10–3 101
102 Vg (cm/s)
103
23
Surface Flame Spread
717
Fig. 23.13 Outline of the heating and flame spread in the LIFT apparatus
Radiant panel
V
Sample
155 mm
280 mm
800 mm
483 mm
thermally thin solid. Attributing this effect to the dependence of the preheat distance, which is the length of the control volume shown in Fig. 23.10, and assuming the balance of gas-phase heat conduction with convection due to the opposed flow has the velocity of Vg, ρgcgVg∂T/∂x kg∂2T/∂x2, then the following estimate can be derived: Δ kg =ρg cg V g
ð23:16Þ
By substituting Equations 23.9 and 23.16, Equation 23.14 yields the expression first derived by de Ris: [34] 2 2 V p V g kg ρg cg T f T r =kρc T ig T o ð23:17Þ
2 V p Φ=kρc T ig T o
ð23:18Þ
with Φ, a parameter depending on Vg and Yox,1 that could be quantified with a bench-scale test for practical materials. Quintiere and Harkleroad [14] examined this approach using the lateral ignition and flame spread test (LIFT) apparatus (Fig. 23.13) and have quantified the effective opposed-flow flame spread properties as summarized in Table 23.1. See Chap. 21 for more detail on the ignitability parameters. Equation 23.18 also suggests the importance of the ignitability parameter, kρc(Tig–To)2 for the fire hazard assessment of any material. Existence of a source of external heating, such as exposure to smoke layer, flame sheet spreading beneath the ceiling, and the like, may have a significant influence on the spread velocity.
Modeling of Opposed-Flow Flame Spread
Mass Fires
Significant progress has been made on the understanding and modeling of opposed-flow flame spread, but most of the research has concentrated on poly(methyl methacrylate) (PMMA) and other rather ideal materials from the viewpoint of combustion and pyrolysis modeling. Few models have been attempted on the opposedflow turbulent flame spread over charring materials and composites in practice. Because it is the numerator of Equation 23.17 that is hard to quantify for materials in practice, Equation 23.17 can be rewritten as
Urban fires, wildland fires, and forest fires are serious fire disasters in various districts. The conflagrations at the Great Hanshin earthquake (1995) revealed significant risk of earthquake urban fires in Japan and other districts featuring urban areas densely inhabited with buildings with relatively weak fire protection. Land development of wildland near urban districts in North America and Australia has caused a risk of occurrence of urban–wildland interface fire disasters. Albini reviewed research resources for forest and wildland fires [35]. Recent investigation
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Table 23.1 Effective opposed-flow flame spread properties [14] Material PMMA polycast (1.59 mm) Polyurethane (S353M) Hardboard (6.35 mm) Carpet (acrylic) Fiberboard, low density (S119M) Fiber insulation board Hardboard (3.175 mm) Hardboard (S159M) PMMA type g (1.27 cm) Asphalt shingle Douglas fir particle board (1.27 cm) Wood panel (S178M) Plywood, plain (1.27 cm) Chipboard (S118M) Plywood, plain (0.635 cm) Foam, flexible (2.54 cm) GRP (2.24 mm) Mineral wool, textile paper (S160M) Hardboard (gloss paint) (3.4 mm) Hardboard (nitrocellulose paint) GRP (1.14 mm) Particle board (1.27 cm stock) Gypsum board, wallpaper (S142M) Carpet (nylon/wool blend) Carpet #2 (wool, untreated) Foam, rigid (2.54 cm) Polyisocyanurate (5.08 cm) Fiberglass shingle Carpet #2 (wool, treated) Carpet #1 (wool, stock) Aircraft panel epoxy Fiberite Gypsum board, FR (1.27 cm) Polycarbonate (1.52 mm) Gypsum board, (common) (1.27 mm) Plywood, FR (1.27 cm) Polystyrene (5.08 cm)
Tig ( C) 278 280 298 300 330 355 365 372 378 378 382 385 390 390 390 390 390 400 400 400 400 412 412 412 435 435 445 445 455 465 505 510 528 565 620 630
kρc (kW2s/m4K2) 0.73 — 1.87 0.42 — 0.46 0.88 — 1.02 0.70 0.94 — 0.54 — 0.46 0.32 0.32 — 1.22 0.79 0.72 0.93 0.57 0.68 0.25 0.03 0.02 0.50 0.24 0.11 0.24 0.40 1.16 0.45 0.76 0.38
Φ (kW2/m3) 5.4 — 4.5 9.9 — 2.2 10.9 — 14.4 5.3 12.7 — 12.9 — 7.4 11.7 9.9 — 3.5 9.8 4.2 4.2 0.79 11.1 7.3 4.0 4.9 9.0 0.8 1.8 * 9.2 14.7 14.4 * *
Ts,min ( C) 120 105 170 165 90 210 40 80 90 140 210 155 120 180 170 120 80 105 320 180 365 275 240 265 335 215 275 415 365 450 505 300 455 425 620 630
Φ/kρc (mK2/s) 8 82 2 24 42 5 12 18 14 8 14 43 24 11 16 37 31 34 3 12 6 5 1 16 30 141 201 18 4 17 * 23 13 32 * *
Note: Values are only significant to two places *Flame spread was not measurable
witnesses the increase of the frequency and the hazard of forest fires in polar Russia, Alaska, and Canada since about the 1990s [36]. Flame spread in a forest or in an urban district depends on radiant heat transfer, convective heating, and leeward spread of fire brands due to wind or the slope of the terrain. Figure 23.14 is a
summary of the fire spread velocity for urban and wildland fires superimposed on the correlation between fire spread velocity and wind velocity summarized on Japanese urban fires from the 1910s to the 1950s [37, 38]. The significant fire spread velocity recorded in past urban and wildland fires, from the order of 100 m/h to 10 km/h,
23
Surface Flame Spread
719
Fig. 23.14 Comparison of rates of fire spread for urban and wildland fires as a function of wind speed (From Kawagoe [38] and Thomas [37])
Cribs Gorse and heather Urban fires in Japan
Spread velocity (m/mm)
20
15
10 8 6 4 2
0
cannot be explained by convective or radiant heating and suggests the importance of the role of fire brands in the wind-aided spread of mass fires. In urban fires, collapse of wooden buildings due to fire is the typical and most significant source of fire brands. In wildland and forest fires, the porous bush along the terrain is involved, and dried bush, fallen bark and pine needles, and so forth can be typical sources of fire brands. Even though weight per area of bush, bark, and dried leaves is small and their flaming might not last so long, they are quick to ignite by fire brand due to the large surface area to weight ratio of these materials. In that sense, fire brands should have primary importance in the growth of forest fires. However, in more severe fires, the crowns of the trees may also be involved.
5
10
15 20 Wind velocity (m/s)
25
30
Flame Spread Over Liquids Flame spread over a horizontal pool of liquid fuels is essentially opposed flow, but its spreading velocity is very often significantly larger than estimated from the thermal theory [39]. The difference is attributed to the convective flow within the liquid moving concurrently with the flame. The convection is due to the surface tension, which is reduced with increase of temperature and pulls the flame toward the unburnt surface of the liquid. This is illustrated in Fig. 23.15 for a thin liquid layer, δ. Under steady conditions, the viscous forces on the control volume are balanced by the surface tension forces. Thus, the shear stress, τ, at the bottom surface equals the surface tension gradient (dσ/dx) along the free surface:
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Fig. 23.15 Enhanced flame spread speed in liquids due to surfacetension induced flow
Flame
Tig, Flashpoint
Control volume
V Liquid fuel layer
δ
x Ts
y Δ
Fig. 23.16 Relationship between the liquid temperature and the rate of plane flame spread of methanol, based on Akita [40]
Liquid-phase effects
Gas-phase effects
Stoichiometric condition
Flashpoint
V (cm/s)
100
10
Pulsating spread
1 –20
–10
0
10
20
30
Ts (°C)
τ ¼ dσ=dx ¼ ðdσ=dT Þ ð∂T=∂xÞ
ð23:19Þ
For a thin liquid layer, the surface tension effect results in nearly a Couette flow (constant shear) over the layer thickness, δ. Hence, it can be approximated that τ ¼ ðμ∂u=∂yÞ y¼0 μV=δ
ð23:20Þ
where μ is the liquid viscosity. By further approximating the surface tension gradient as a difference over length Δ, the flame speed can be estimated as
σðT s Þ σ T ig δ V¼ ð23:21Þ μΔ
provided σ(T ), the surface tension, is known as a function of temperature for the liquid, and Δ can be estimated for the conditions of speed. Also, δ, as in the thermally thick case for solids, is only the physical liquid depth for pools less than about 1 mm and, therefore, must be reinterpreted for pools of larger depth. For example, one might pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi estimate δ as ðμ=ρÞ ðΔ=V Þ for the deeppool case. Typical flame spread characteristics over a liquid fuel are sketched in Fig. 23.16 for liquid methanol from the data of Akita [40]. Below the flashpoint, Ts < Ti g ~ 11 C, the spread is governed by transport phenomena within the liquid fuel. For initial liquid bulk temperatures above the flashpoint, a flammable mixture
23
Surface Flame Spread
always exists everywhere above the surface so that propagation is governed by gas-phase effects. Above a liquid temperature, which corresponds to stoichiometric conditions above the surface, the flame speed remains constant and usually above the normal premixed laminar flame speed. A study by Ito and Kashiwagi [41] used holographic interferometry to examine the liquid phase for subflashpoint liquid bulk temperatures. They examined the pulsating region depicted in Fig. 23.16, and the adjacent uniform region of spread just below the flame; both appear to contribute to flame spread rate in the uniform region.
Summary This chapter has provided the practicing engineer with some insight into the nature of fire spread over materials. In general, surface flame spread depends on the heat transfer processes at the flame front. These transport processes depend not only on the fuel but also on the fuel’s configuration and orientation and on ambient environmental conditions. Thus, estimates of flame spread require complex analysis and specific material data. The current state of knowledge does provide limited formulas and material data to make some estimates. In this chapter, the full scope of flame spread phenomena has not been addressed. For example, flame spread in mines, ducts, and buildings presents an entirely new and complex array of conditions. Thus, flame spread on materials must be evaluated in the context of their use, and appropriate data must be made available for proper assessments of materials.
Nomenclature a b c cg cp
00
k f Q_ ‘ flame spread acceleration factor (¼ (a 1) tig*/tb) specific heat of solid specific heat of gas specific heat of air
721
δ δfc D Da Δ ΔH ΔHox g k k0 k kg L μ q00 00 qf 00 qfc Q_ ‘ * Q_ ‘
* Q_ ‘e r ρ ϕ Φ
σ t tb tc tig* τ Tf Tig To Tr Ts T1 Vg Vp xf xp xpo xpoff Yox,1 x, y
fuel thickness characteristic preheat distance characteristic length of the burning area (height, etc.) Damko¨hler number distance from the pyrolysis front heat of combustion ΔH/r gravitational acceleration *n x f =Q_ ‘ 2=3 2=3 constant k3=2 =c p T o g1=2 Q_ ‘ x f =Q_ ‘ gas thermal conductivity heat of gasification viscosity heat flux due to gas-phase conduction flame heat flux characteristic flame heat flux heat release rate per unit width dimensionless heat release rate per unit width effective heat release rate per unit width stoichiometric mass ratio oxygen/fuel density impulse response function opposed-flow preheat factor (numerator in n) surface tension time time to local burnout characteristic decay time of pyrolysis characteristic time to ignition time flame temperature ignition temperature initial surface temperature reference temperature surface temperature ambient temperature gas velocity flame spread velocity flame length pyrolysis front length pilot flame length maximum pyrolysis front length mass fraction of oxygen coordinates
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Superscripts · 0 00
per unit time per unit length per unit area
References 1. T. Hirano, S. Noreikis, and T. Waterman, “Measured Velocity and Temperature Profiles of Flames Spreading over a Thin Combustible Solid,” Combustion and Flame, 23, p. 83 (1974). 2. D.D. Drysdale, A.J.R. Macmillan, and D. Shilitto, “King’s Cross Fire: Experimental Verification of the “Trench Effect,” Fire Safety Journal, 18 (1992). 3. D.D. Drysdale, An Introduction to Fire Dynamics, 2nd ed., John Wiley and Sons, New York (1999). 4. J.G. Quintiere, Fundamentals of Fire Phenomena, John Wiley and Sons, New York (2006). 5. A.C. Fernandez-Pello and T. Hirano, “Controlling Mechanism of Flame Spread,” Combustion Science and Technology, 32, pp. 1–31 (1983). 6. T. Hirano, “Physical Aspects of Combustion in Fires,” in Proceedings of the 3rd International Symposium on Fire Safety Science, International Association for Fire Safety Science, Boston, MA, pp. 27–44 (1991). 7. F. Williams, “Mechanism of Fire Spread,” in Proceedings of the 16th Symposium (International) on Combustion, Combustion Institute, Pittsburgh, PA, pp. 1281–1294 (1976). 8. M.A. Delichatsios, “Modeling of Aircraft Cabin Fires,” Technical Report, Factory Mutual Research Corp. (1984). 9. Y. Hasemi, “Thermal Modeling of Upward Wall Flame Spread,” in Proceedings of the First International Symposium on Fire Safety Science, International Association for Fire Safety Science, Boston, MA, pp. 87–96 (1985). 10. T.I. Eklund, “A Vortex Model for Wall Flame Height,” Journal of Fire Science, 4, pp. 4–14 (1986). 11. M. Kokkala, D. Baroudi, and W.J. Parker, “Upward Flame Spread on Wooden Surface Products: Experiments and Numerical Modelling,” in Proceedings of the 5th International Symposium on Fire Safety Science, International Association for Fire Safety Science, Boston, MA, pp. 309–320 (1997). 12. J.S. Newman and C.J. Wieczorek, “Chemical Flame Heights,” Fire Safety Journal, 39, pp. 375–382 (2004). 13. K.-M. Tu and J.G. Quintiere, “Wall Flame Heights with External Radiation,” Fire Technology, pp. 195–203 (Aug. 1991). 14. J.G. Quintiere and M. Harkleroad, “New Concepts for Measuring Flame Spread Properties,” in Proceedings of Fire Safety: Science and Engineering, a symposium sponsored by ASTM Committee E-5 on Fire
Standards and the Society of Fire Protection Engineers, ASTM STP 882, ASTM International, W. Conshohocken, PA, pp. 239–267 (1985). 15. B. Karlsson, “Models for Calculating Flame Spread on Wall Lining Materials and the Resulting Heat Release Rate in a Room,” Fire Safety Journal, 23, pp. 365–386 (1994). 16. D. Baroudi, “A Discrete Dynamical Model for Flame Spread over Combustible Flat Solid Surfaces Subject to Pyrolysis with Charring—An Application Example to Upward Flame Spread,” Fire Safety Journal, 38, pp. 53–84 (2003). 17. J.G. Quintiere, M. Harkleroad, and Y. Hasemi, “Wall Flames and Implications for Upward Flame Spread,” Combustion Science and Technology, 48, 3–4, pp. 191–222 (1986). 18. L. Orloff, A.T. Modak, and R.L. Alpert, “Burning of Large-Scale Vertical Surfaces,” in Proceedings of the 16th Symposium (International) on Combustion, Combustion Institute, Pittsburgh, PA, pp. 1345–1354 (1976). 19. T. Ahmad and G.M. Faeth, “Turbulent Wall Fires,” in Proceedings of the 17th Symposium (International) on Combustion, Combustion Institute, Pittsburgh, PA, pp. 1149–1160 (1979). 20. M. Sibulkin and J. Kim, “The Dependence of Flame Propagation on Surface Heat Transfer ii. Upward Burning,” Combustion Science and Technology, 17, pp. 39–49 (1977). 21. K. Saito, J.G. Quintiere, and F.A. Williams, “Upward Turbulent Flame Spread,” in Proceedings of the 1st International Symposium on Fire Safety Science, International Association for Fire Safety Science, London, pp. 75–86 (1985). 22. D. Baroudi and M. Kokkala, “Analysis of Upward Flame Spread,” VTT Publications, 89 (1992). 23. Y. Hasemi and N. Yasui, “A Strategy to Develop Engineering Upward Flame Spread Evaluation Methodology Based on the Linearized Flame Height Approximation,” Fire Science and Technology, 15, 1–2, pp. 17–28 (1995). 24. G. Grant and D.D. Drysdale, “Numerical Modelling of Early Flame Spread in Warehouse Fires,” Fire Safety Journal, 24, pp. 247–278 (1995). 25. A.C. Fernandez-Pello, “Upward Laminar Flame Spread Under the Influence of Externally Applied Thermal Radiation,” Combustion and Flame, 17, p. 87 (1977). 26. H. Ingason and J. de Ris, “Flame Heat Transfer in Storage Geometries,” Fire Safety Journal, 31, pp. 39–60 (1998). 27. Y. Hasemi, M. Yoshida, N. Yasui, and W.J. Parker, “Upward Flame Spread along a Vertical Solid for Transient Local Heat Release Rate,” in Proceedings of the 4th International Symposium on Fire Safety Science, International Association for Fire Safety Science, Boston, MA, pp. 385–396 (1994). 28. M.M. Delichatsios, P. Wu, M.A. Delichatsios, G.D. Lougheed, G.P. Crampton, C. Qian, H. Ishida, and K. Saito, “Effect of External Radiant Heat Flux on
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Upward Fire Spread: Measurements on Plywood and Numerical Predictions,” in Proceedings of the 4th International Symposium on Fire Safety Science, International Association for Fire Safety Science, Boston, MA, pp. 421–432 (1994). 29. B.Y. Lattimer, S.P. Hunt, M. Wright, and C. Beyler, “Corner Fire Growth in a Room with a Combustible Lining,” in Proceedings of the 7th International Symposium on Fire Safety Science, International Association for Fire Safety Science, Boston, MA, pp. 419–430 (2002). 30. Y. Hasemi, D. Nam, and M. Yoshida, “Experimental Flame Correlations and Dimensional Relations in Turbulent Ceiling Fires,” in Proceedings of the 5th Asia Oceania Symposium on Fire Science and Technology, International Association for Fire Safety Science, Boston, MA, pp. 379–390 (2001). 31. Y. Hasemi, M. Yoshida, Y. Yokobayashi, and T. Wakamatsu, “Flame Heat Transfer and Concurrent Flame Spread in a Ceiling Fire,” in Proceedings of the 5th International Symposium on Fire Safety Science, International Association for Fire Safety Science, Boston, MA, pp. 379–390 (1997). 32. V. Stenstad and B. Karlsson, “Flame Spread on a Solid Wooden Ceiling,” Conference Proceedings of Interflam 2007, 1, Interscience Communications, London, UK, pp. 45–57 (2007). 33. A.C. Fernandez-Pello, S.R. Ray, and I. Glassman, in Proceedings of the 18th Symposium (International) on Combustion, Combustion Institute, Pittsburgh, PA (1981). 34. J. de Ris, “Spread of a Laminar Diffusion Flame,” in Proceedings of the 12th Symposium (International) on
723 Combustion, Combustion Institute, Pittsburgh, PA, pp. 241–252 (1968). 35. F.A. Albini, “An Overview of Research on Wildland Fire,” in Proceedings of the 5th International Symposium on Fire Safety Science, International Association for Fire Safety Science, Boston, MA, pp. 59–74 (1997). 36. H. Hayasaka, “Recent Large-Scale Fires in Boreal and Tropical Forests,” Journal of Disaster Research, 2, 4, pp. 276–283 (2007). 37. P.H. Thomas, “Rates of Spread of Some Wind-Driven Fires,” Forestry, 44, 2 (1971). 38. K. Kawagoe (ed.), Fire Safety in Buildings, Architectural Studies and Engineering Series, 21, Shokokusha (1970) (in Japanese). 39. I. Glassman and F.L. Dryer, “Flame Spreading Across Liquid Fuels,” Fire Safety Journal, 3, pp. 123–138 (1980). 40. K. Akita, “Some Problems of Flame Spread Along a Liquid Surface,” in Proceedings of the 14th Symposium (International) on Combustion, Combustion Institute, Pittsburgh, PA, pp. 1075–1083 (1973). 41. A. Ito and K. Kashiwagi, “Characterization of Flame Spread over PMMA Using Holographic Interferometry Sample Orientation Effects,” Combustion and Flame, 71, pp. 189–204 (1988).
Yuji Hasemi is professor in the Department of Architecture, Faculty of Science and Engineering, Waseda University, Tokyo, Japan.
Smoke Characterization and Damage Potentials
24
Jeffrey S. Newman, Geary G. Yee, and Paul Su
Introduction Smoke is a mixture of (1) particulates consisting of soot, semi-volatile organic compounds (SVOC), and solid inorganic compounds; and (2) non-particulates consisting of very volatile organic compounds, volatile organic compounds, and liquid and gaseous inorganic compounds. Soot creates bridging between electrical conductors and conveys corrosive products, resulting in damage to electronics and electrical circuits through leakage current and corrosion, while SVOC and non-particulates stain and impart malodor to surfaces. Soot is also a very effective adsorbent and transport mechanism for SVOC, non-particulates and inorganic compounds. The smoke problem (exclusive of toxicity or escape potential considerations) is ultimately characterized by the quantification of damage due to the deposition of combustion products onto building surfaces and contents (e.g., equipment, furnishings, and commodities). It is instructive to categorize the assessment of smoke damage potentials into two regimes: “far-field” at some distance away from the fire/smoke source and “near-field” close to the source, where it is likely to have simultaneous heat damage (and J.S. Newman (*) Retired from FM Global, 1151 Boston Providence Turnpike, Norwood, MA 02062 USA G.G. Yee • P. Su FM Global, 1151 Boston Providence Turnpike, Norwood, MA 02062 USA
water damage such as in the case of fire sprinkler protection). In general, fire damage in the “nearfield” is dominated by heat/water damage with smoke of a much lesser impact, while smoke can often be the governing damage mechanism in the “far-field” and, due to extent of travel and area coverage, of far greater impact. Figure 24.1 illustrates, for example, the various components that are necessary to evaluate smoke damage potentials, especially in the “farfield”. As shown in the figure, the impact of the smoke deposition profile resulting from smoke release, typically from a fire event, is quantified by the comparison of a defined damage function with its associated damage threshold. As will be subsequently discussed, the damage function can represent a variety of types of smoke damage including leakage current, corrosion and stain/ odor. The deposition profile is assessed through the coupling of smoke generation, the characterization of pertinent smoke properties and the transport of smoke resulting in time and spatially resolved concentration profiles. Detection and active response both affect and are affected by these concentration profiles. Knowledge of the smoke deposition velocity is also an important component for the quantification of the resulting smoke deposition profile. For reference, the solid gray-shaded blocks shown in Fig. 24.1 will be covered in detail in this Chapter while the three unshaded blocks labeled Concentration Profile, Transport and Generation are place holders that are outside of this Chapter’s scope. In should be noted that
M.J. Hurley (ed.), SFPE Handbook of Fire Protection Engineering, DOI 10.1007/978-1-4939-2565-0_24, # Society of Fire Protection Engineers 2016
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Fig. 24.1 Outline of components to evaluate smoke damage potentials
Generation refers to heat and gas species’ production and is a function of the prescribed fire scenario with the content of Chap. 36 of this Handbook providing useful specific smoke and heat generation properties for a variety of materials. Transport and Concentration Profile data can be obtained from any number of physical correlations [1] or computer models [2, 3] coupled with the prescribed Generation information. Finally, Detection/Response is shown in light gray as it is covered only as an overview of important considerations as relating to the smoke Deposition Profile with details on detection given in Chap. 40 of this Handbook.
Deposition Profile Deposition Velocity The process by which smoke can deposit on various surfaces is often complex and can result from either a single dominant physical mechanism or a combination of mechanisms including particle inertia, sedimentation or gravitational settling, Brownian diffusion, thermophoresis or
thermodiffusion, and electrostatic precipitation [4]. For electrically neutral aerosols, the governing mode of smoke deposition is primarily dependent on whether the transport flow is laminar or turbulent and the particle size. The flow regime for smoke particle motion can be characterized by the magnitude of the particle Reynolds number, i.e., Rep ¼
ρg d p V η
ð24:1Þ
where ρg is the gas density, dp the particle diameter, V the particle velocity and η is the gas viscosity.
Laminar Flow (Rep < 1) 1. For smoke particles >1 μm in diameter, the deposition is primarily due to gravitational settling. Stokes’s Law applies to particle motion when inertial forces are negligible compared with viscous forces, and gives the particle terminal settling velocity, VTS as V TS ¼
ρ p d2p g 18η
where g is gravitational acceleration.
ð24:2Þ
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2. For smoke particles LC > 108 LC > 106
Class Very low Low High
current damage thresholds, while defined broadly, are relatively well-specified. Conversely, stain and odor thresholds are primarily driven by perception. Suggested specific thresholds are covered in the following discussion for leakage current and stain. A methodology for setting of odor thresholds is also proposed. The classification or ranking of leakage current (LC) has been proposed in an ASTM draft, as shown in Table 24.8 [47]. Leakage currents less than 108 A are classified as very low,
20
25
(10-3)
currents between 108 and 106 A are classified as low, while currents greater than 106 A are classified as high. This classification system can be used as one of the criteria for evaluating smoke damage of electrical circuits by measuring the value of LC for targets exposed to different materials as given previously in Table 24.3. The specific application would be used to denote the target LC levels, with smoke exposure to highly sensitive electronic components most likely in the very low range (e.g., semiconductor fabrication facilities and data centers) and machine components in the low range (e.g., machine shops and printing facilities). As noted above, stain and odor damage thresholds are driven by human sensory perception unlike damage thresholds for leakage current. The field of psychophysics [48], for example, attempts to quantitatively study perception through the functional relationships between the physical properties of stimuli and the psychological responses to them. In particular, one important quantifier is the “Difference Threshold” (or “Just Noticeable Difference” often abbreviated as JND). The JND is the minimum amount by which stimulus intensity must be changed in order to produce a noticeable variation in sensory experience. Weber’s Law
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Smoke Characterization and Damage Potentials
Table 24.9 Weber fractions for various stimuli Stimuli Brightness Loudness Finger span Heaviness Line length Taste Electric shock Odor
Weber fraction 0.079 0.048 0.022 0.020 0.029 0.083 0.013 0.25
[48] (also known as the Weber–Fechner law) states that the JND depends on a percentage of change in a stimulus rather than on a fixed amount of change: kW ¼ ΔS=S
ð24:18Þ
where ΔS represents the difference threshold (JND), S represents the initial stimulus intensity and kW signifies that the proportion on the right side of the equation remains constant despite variations in the S term. kW is typically referred to as the Weber fraction and is given in Table 24.9 for sensory perception response to a number of different stimuli [49, 50]. The Weber fractions for brightness and odor, i.e., 0.079 and 0.25, respectively, are of particular interest for assessing smoke damage thresholds for stain and odor. Applying a brightness threshold of 0.079 [corresponding to a % Brightness Change of 7.9 % in Equation 24.16] to the smoke deposition data in Fig. 24.8, results in a smoke damage threshold of ~0.015 g/m2 for smoke stain. Odor thresholds for smoke damage are somewhat more difficult to assess than those for stain. A useful approach is first to establish a reasonable odor baseline without smoke deposition for the target surface. If, for example, the target surface is a typical packaging material, then the inherent concentration of volatile organic compounds (VOCs) of the packaging would be relevant. For instance, odor in recycled packaging papers has been related to several VOCs such as phenols and aldehydes [51]. The typical average concentration is about 100 ppm (or 1.0 104 g VOC per g paper). Similar or higher
739
VOC concentrations have been found for other types of papers and plastic packaging materials [52–54]. The food and pharmaceutical industries are particularly concerned with odor and/or taste transfer from VOCs contained in product packaging. For example, the sources of VOCs in paper packaging can be from the original paper manufacturing process, including the paper itself, inks, binders, adhesives and coatings. Recycled paper, especially from newspaper, can have VOC contents of up to 4000 ppm (or 4.0 103 g VOC per g paper) [55]. As a further illustration, the baseline odor threshold for a typical paper boxed commodity stored in a warehouse can be determined by a combination of three factors: (1) the packaging VOC content, (2) the paper density (often referred to as basis weight or grammage in g/m2) and (3) the odor difference threshold or Weber fraction (i.e., 0.25). Typical paper densities for liner board used to construct the paper box range from a low of 125 g/m2 to a high of over 440 g/m2. Using 100 ppm as a typical average VOC content with a paper density of, for instance, 200 g/m2, the baseline volatile organic content of the target paper surface can be estimated as: 100 x 106 g VOC 200 g paper g paper m2 paper 0:020 g VOC ¼ m2 paper The odor threshold corresponding to the JND would be 25 % higher or 0.025 g VOC/m2.
Example Application to Semiconductor Fabrication Facilities Semiconductor fabrication facilities are highvalue properties that contain very expensive process equipment and related support equipment. During semiconductor fabrication, process liquid heating and other electrical sources present potential ignition hazards. Note that semiconductor fabrication cleanrooms are always provided
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with sprinkler protection, and the likely fire scenario involves combustible plastics resulting in complete equipment loss due to heat damage in the vicinity of the fire origin, and partial or complete loss at some distance from the fire origin due to smoke damage. The majority of smoke damage is due to surface contamination, leading to leakage current and long-term corrosion on electronic products and equipment. As previously described, this type of damage can be linked to smoke deposition by the use of damage functions. Therefore, the estimation of smoke damage in semiconductor cleanrooms requires a methodology that connects the fire source and the damage function, and allows for mapping the damage area for a given facility size.
Damage Estimation Model The general model for estimating smoke damage is described in detail in Ref. [56], and includes the definition of the fire source based on experiments, simulation of smoke transport and deposition using numerical models, and calculation of smoke damage based on measurements. When fire scenarios involve fire growth and sprinkler suppression, current theories and models can not predict either the burning rate or the smoke generation rate and the fire source needs to be defined based on experimental data. Figure 24.13 illustrates the procedures and data sources for this general model. It should be noted that an important assumption and limitation of the transport model is that CO2 is an adequate surrogate for smoke, with smoke particles transporting as the gas phase. This assumption may not hold for larger smoke particles.
Fire Scenario and Results The selected fire scenario [56] uses a numerical simulation following the geometry of a typical bay-and-chase cleanroom configuration. Figure 24.14 shows a cleanroom module used in the numerical simulation. This module stands for a section of four pairs of clean bays in the
Fig. 24.13 General methodology for modeling smoke damage
middle of the left half of the cleanroom. The clean bays with wet bench and etch tools (two right bays) were duplicated to create a four-bay long module. The simulated fire source consists of a growing polycarbonate fire within a cleanroom stocker which peaks at a heat release rate of about 300 kW. (Stockers are selfcontained units used for the storage of in-process and finished semiconductor wafers, which are commonly stored in plastic boxes in open shelves within the stocker.) Figure 24.15 plots the maximum expected smoke deposition versus radial distance from the stocker fire. The damage functions for polycarbonate (i.e., leakage current from Table 24.3 and corrosion from Table 24.5) can be used to convert the smoke deposition values in the figure into the corresponding expected leakage currents and corrosion rates. These results are given in Fig. 24.16. Finally, applying the proposed leakage current damage thresholds as given in Table 24.8, yields expected smoke damage potentials as illustrated in Fig. 24.17.
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Fig. 24.14 Cleanroom module used in numerical simulation [56]
0.04
Smoke Deposition (g/m2)
Fig. 24.15 Smoke deposition versus radial distance [56]
0.03
0.02
0.01
0.00 0
10
20
30
Radial Distance from Fire (m)
10
Leakage Current (10-8A)
2.0
8
1.5
6
Corrosion Rate 1.0
4
Leakage Current 0.5
2 0
0.0 0
10
20
Radial Distance from Fire (m)
30
Corrosion Rate (10-12mpy)
Fig. 24.16 Leakage current and corrosion rate versus radial distance [56]
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Fig. 24.17 Estimated smoke damage potentials [56]
Nomenclature c Cc Co Cs da dag dg dp D fv g η I Io kad kB kd kW K KTH l LC λ Λ ni N ρg ρo ρs
Average coefficient of smoke extinction Slip correction factor Reference concentration Smoke mass concentration Aerodynamic equivalent mass diameter Aerodynamic equivalent geometric mean mass diameter Geometric mean diameter Particle diameter Diffusion coefficient Smoke volume fraction Gravitational acceleration Gas viscosity Transmitted light intensity Initial light intensity Adsorption rate constant Boltzmann’s constant Desorption rate constant Weber fraction Overall rate constant Thermophoretic velocity coefficient Pathlength Leakage current Wavelength of light Mean free path Number of particles with diameter di Total number of particles Gas density Standard particle density Smoke particle density
σg Rep ODλ S ΔS t τ T V VTH VTS
Geometric standard deviation Particle Reynolds number Optical density at wavelength λ Stimulus Change in stimulus Time Time constant Temperature Particle velocity Thermophoretic deposition velocity Terminal settling velocity
References 1. J.S. Newman and Y. Xin, “Characterization of Room Environments in Growing Enclosure Fires,” Fire Safety Journal, 39, pp. 239–253 (2004). 2. K. McGrattan, S. Hostikka, J. Floyd, H. Baum and R. Rehm, “Fire Dynamics Simulator (Version 5) Technical Reference Guide,” National Institute of Standards and Technology, NIST Special Publication 1018–5, October 2007. 3. Y. Wang, P. Chatterjee, and J.L. de Ris, “Large Eddy Simulation of Fire Plumes,” Proceedings of the Combustion Institute, 33, pp. 2473–2480 (2011). 4. W.C. Hinds, Aerosol Technology – Properties, Behavior, and Measurement of Airborne Particles, 2nd edition, John Wiley & Sons, Inc., New York, 1999. 5. E. Cunningham, “On the Velocity of Steady Fall of Spherical Particles through Fluid Medium,” Proceedings of the Royal Society A, 83, pp. 357–365 (1910). 6. S.K. Friedlander and H.F. Johnstone, “Deposition of Suspended Particles from Turbulent Gas Streams,” Industrial and Engineering Chemistry, 49, 7, pp. 1151–1156 (1957).
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7. A. Einstein, “On the Kinetic Molecular Theory of Thermal Movements of Particles Suspended in a Quiescent Fluid,” Annalen der Physik, 17, pp. 549–560 (1905). 8. W.C. Hinds, A. Ashley, N.J. Kennedy, N.J. and P. Bucknam, “Conditions for Cloud Settling and Rayleigh-Taylor Instability,” Aerosol Science and Technology, 36, 12, pp. 1128–1138 (2002). 9. J.S. Newman, P. Su. and G.G. Yee, “Smoke Deposition Velocity in Industrial Fire Environments,” Fire Safety Science: Proceedings of the Tenth International Symposium, International Association for Fire Safety Science, London, UK, pp. 655–668 (2011). 10. J.R. Brock, "On the Theory of Thermal Forces Acting on Aerosol Particles," Journal of Colloid Science, 17, pp.768-780 (1962). 11. L. Waldmann and K.H. Schmitt, "Thermophoresis and Diffusiophoresis of Aerosols," In Aerosol Science (C. N. Davies, ed.), Academic Press, London, pp. 137–162 (1966). 12. L. Talbot, R.K. Cheng, R. Schefer, R. and D. Willis, “Thermophoresis of Particles in a Heated Boundary Layer,” Journal of Fluid Mechanics, 101, 4, pp. 737–758 (1980). 13. S. Riahi, C.L. Beyler and J. Hartman, “Wall Smoke Deposition from a Hot Smoke Layer,” Fire Technology, (2012). 14. S. Suzuki, K. Kuwana and R. Dobashi, “Effect of Particle Morphology on Thermophoretic Velocity of Aggregated Soot Particles,” International Journal of Heat and Mass Transfer, 52, pp. 4695–4700 (2009). 15. K.M. Butler and G.W. Mulholland, “Generation and Transport of Smoke Components,” Fire Technology, 40, pp. 149–176 (2004). 16. H. Ono, R. Dobashi and T. Sakuraya, “Thermophoretic Velocity Measurements of Soot Particles under a Microgravity Condition,” Proceedings of the Combustion Institute, 29, pp. 2375–2382 (2002). 17. J.S. Newman, “Prediction of Fire Detector Response,” Fire Safety Journal, 12, pp. 205–211 (1987). 18. J.S. Newman, “Principles for Fire Detection,” Fire Technology, 24, 12, pp. 116–127 (1988). 19. J.S. Newman and J. Steciak, “Characterization of Particulates from Diffusion Flames,” Combustion and Flame, 67, pp. 55–64 (1987). 20. K.J. Rockne, G.L. Taghon and D.S. Kosson, “Pore Structure of Soot Deposits from Several Combustion Sources,” Chemosphere, 41, pp. 1125–1135 (2000). 21. P.F. DeCarlo, J.G. Slowik, D.R. Worsnop, P. Davidovits and J.L. Jimenz, “Particle Morphology and Density Characterization by Combined Mobility and Aerodynamic Diameter Measurements. Part 1: Theory,” Aerosol Science and Technology, 38, pp. 1185–1205 (2004). 22. J.G. Slowik, K. Stainken, P. Davidovits, L.R. Williams, J.T. Jayne, C.E. Kold, D.R. Worsnop, Y. Rudich, P.F. DeCarlo and J.L. Jimenz, “Particle Morphology and Density Characterization by
743 Combined Mobility and Aerodynamic Diameter Measurements. Part 2: Application to CombustionGenerated Soot Aerosols as a Function of Fuel Equivalence Ratio,” Aerosol Science and Technology, 38, pp. 1206–1222 (2004). 23. F-X. Ouf, J. Vendel, A. Coppalle, M. Weill and J. Yon, “Characterization of Soot Particles in the Plumes of Over-Ventilated Diffusion Flames,” Combustion Science and Technology, 180, pp. 674–698 (2008). 24. I. Colbeck, B. Atkinson and Y. Johar, “The Morphology and Optical Properties of Soot Produced by Different Fuels,” Journal of Aerosol Science, 28, 5, pp. 715–723 (1997). 25. G.W. Mulholland and M.Y. Choi, “Measurement of the Mass Specific Extinction Coefficient for Acetylene and Ethene Smoke Using the Large Agglomerate Optics Facility,” Proceedings of the 27th International Symposium on Combustion, pp. 1515–1522 (1998). 26. G.W. Mulholland and C. Croarkin, “Specific Extinction Coefficient of Flame Generated Smoke,” Fire and Materials, 24, pp. 227–230 (2000). 27. S. Riahi, “New Tools for Smoke Residue and Deposition Analysis,” PhD Dissertation, George Washington University, Washington D.C., January 2011. 28. R.A. Martin and D.L. Fenton, “Full-Scale Measurements of Smoke Transport and Deposition in Ventilation System Ductwork,” Los Alamos National Laboratory, Los Alamos, NM, NUREG/ CR-4321 (LA-10478-MS), 1985. 29. D.W. Weinert, T.G. Cleary, G.W. Mulholland and P.F. Beever, “Light Scattering Characteristics and Size Distribution of Smoke and Nuisance Aerosols,” Fire Safety Science: Proceedings of the Seventh International Symposium, International Association for Fire Safety Science, London, UK, pp. 209–220 (2003). 30. G.W. Mulholland, “Smoke Production and Properties,” SFPE Handbook of Fire Protection Engineering, 4th edition, National Fire Protection Association, Quincy, MA, pp. 2–291 to 2–302, 2008. 31. T.J. Tanaka, “Measurements of the Effects of Smoke on Active Circuits,” Fire and Materials, 23, pp. 103–108 (1999). 32. IEC/TS 60695-5-3 Ed. 1, “Fire Hazard Testing-Part 5.3: Corrosion Damage Effects of Fire EffluentLeakage Current and Metal Loss Test Method,” 89/545/DTS, 2002. 33. R.P. Frankenthal, D.J. Siconolfi and J.D. Sinclair, "Accelerated Life Testing of Electronic Devices by Atmospheric Particles: Why and How," Journal of the Electrochemical Society, 140, 11, pp. 3129–3134 (1993). 34. J.S. Newman, P. Su, G.G. Yee and S. Chivukula, “Development of Smoke Corrosion and Leakage Current Damage Functions,” Fire Safety Journal, 61, pp. 92–99 (2013) J.S. Newman, P. Su, G.G. Yee, K.L.T. Jamison and S. Chivukula, “Strategic Smoke
744 Damage Program: Development of Smoke Damage Functions for the Semiconductor Industry,” FM Global Technical Report, Project ID 0003038685, September 2010. 35. T.J. Tanaka and S.P. Nowlen, “Results and Insights on the Impact of Smoke on Digital Instrumentation and Control”, Sandia National Laboratories, Albuquerque, NM, NUREG/CR-6597 (SAND99-1320), 2001. 36. R.D. Peacock, T.G. Cleary, P.A. Reneke and D.C. Murphy, “A Literature Review of the Effects of Smoke from a Fire on Electrical Equipment,” National Institute of Standards and Technology, Gaithersburg, MD, NUGEG/CR-7123, 2012. 37. TAPPI Technical Association of the Paper Industry Test Method T 452 om-08, “Brightness of Pulp, Paper and Paperboard (Directional Reflectance at 457 nm),” Norcross, GA, 1998. 38. J.S. Newman, G.G. Yee and P. Su, “Development of Smoke Damage Functions for Warehouse Applications,” Fire and Materials, Proceedings of the 13th International Conference Exhibition, San Francisco, CA (2013); J.S. Newman, G.G. Yee and P. Su, “Strategic Smoke Damage Program: Development of Smoke Damage Functions for Warehouse Applications,” FM Global Technical Report, Project ID 0003043053, April 2012. 39. C.C. Austin, D. Wang, D.J. Ecobichon and G. Dussault, “Characterization of Volatile Organic Compounds in Smoke at Experimental Fires,” Journal of Toxicology and Environmental Health, Part A,” 63, pp. 191–206 (2001). 40. B-J. De Vos, M. Froneman, and E.R. Rohwer, “Organic Vapors Emitted from the Plumes of Pool Fires on Carpet Materials,” Journal of Fire Sciences, 17, pp. 383–420 (1999). 41. P. Dalton, “Odor Perception and Beliefs about Risk,” Chemical Senses, 21, pp. 447–458 (1996). 42. V.I. Berezkin, I.V. Viktorovsii, L.V. Golubev, V.N. Petrova and L.O. Khoroshko, “A Comparative Study of the Sorption Capacity of Activated Charcoal, Soot, and Fullerenes for Organochlorine Compounds,” Technical Physics Letters, 28, pp. 885–888 (2002). [Translated from Pis’ma v Zhurnal Tekhnicheskoi Fiziki, 28, pp. 11–21 (2002).] 43. I. Langmuir, “The Constitution and Fundamental Properties of Solids and Liquids. Part I. Solids,” Journal of the American Chemical Society, 38, pp. 2221–2295 (1916). 44. C.L. Chuang, P.C. Chiang, E.E. Chang and C.P. Huang, “Adsorption-Desorption Rate of Nonpolar Volatile Organic Compounds onto Activated Carbon Exemplified by C6H6 and CCl4,” Practice Periodical of Hazardous, Toxic, and Radioactive Waste Management, 7, pp. 148–155 (2003). 45. W.R. Zeng, S.F. Li and W.K. Chow, “Preliminary Studies on Burning Behavior of Polymethylmethacrylate (PMMA),” Journal of Fire Sciences, 20, pp. 297–317 (2002). 46. F. Delage, P. Pre and P. Le Cloirec, “Effects of Moisture on Warming of Activated Carbon Bed during
J.S. Newman et al. VOC Adsorption,” Journal of Environmental Engineering, 125, pp. 1160–1167 (1999). 47. BSR/ASTM Z0334Z-200x Draft Standard, “Test Method for Measurement of the Leakage Currents from Smoke Deposited on Electric Circuits,” ASTM International, West Conshohocken, PA, 2003. 48. G.A. Gescheider, Psychophysics: The Fundamentals, 3rd edition, Psychology Press, London, 1997. 49. R. Teghtsoonian, “On the Exponents in Steven’s Law and the Constant in Ekman’s Law,” Psychological Review, 78, pp. 71–80 (1971). 50. H. Stone, “Factors Influencing Behavioral Responses to Odor Discrimination – A Review,” Journal of Food Science, 31, pp. 784–790 (1966). 51. E. Martinez Martin and D. Ramirez MartinCorbalan, “Chemical Substances Content in Recycled Packaging Papers,” AIDIMA Furniture, Wood and Packaging Technology Institute, Paterna, Spain, 2005. 52. P.A. Tice, and C.P. Offen, “Odors and Taints from Paperboard Food Packaging,” Tappi Journal, 77, p. 149–154 (1994). 53. H. Kim-Kang, “Volatiles in Packaging Materials,” Critical Reviews in Food Science and Nutrition, 29, 4, pp. 255–271 (1990). 54. P. Landy, S. Nicklaus, E.Semon, P. Mielle and E. Guichard, “Representativeness of Extracts of Offset Paper Packaging and Analysis of the Main OdorActive Compounds,” Journal of Agricultural and Food Chemistry, 58, pp. 2326–2334 (2004). 55. M. Biedermann, Y. Uematsu and K. Grob, “Mineral Oil Contents in Paper and Board Recycled to Paperboard for Food Packaging,” Packaging Technology and Science, 24, 2, pp. 61–73 (2011). 56. Y. Xin and J.S. Newman, “Numerical Simulation of Smoke Damage in a Semiconductor Cleanroom,” Proceedings of the 9th International Conference on Performance-Based Codes and Fire Safety Design Methods, the Excelsior, Hong Kong, June 20–22, 2012.
Jeffrey S. Newman, retired, was an assistant vice president and principal engineer for FM Global. He specialized in characterization of fire environments including modeling, flammability of materials, smoke damage, full-scale fire testing, and smoke and fire detection. Dr. Geary G. Yee is a physical chemist and senior research specialist for FM Global. He has specialized in polymer pyrolysis, microbial corrosion, small lab-scale fire testing, smoke characterization, and material failure analysis. Dr. Paul Su is a senior research specialist and technical team leader for FM Global. He has specialized in materials and corrosion research including corrosion testing and control, failure analysis, smoke corrosivity, nanomaterials research, and chemical product development.
Heat Transfer from Fires to Surfaces
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Brian Y. Lattimer
Introduction The heat transfer from fires to adjacent surfaces is an important consideration in many fire analyses. Some example applications that may require knowledge of the heat transfer from a flame include heating and failure of structural beams, heat transfer through walls and ceilings, and the ignition and flame spread along combustible surfaces. Flames transfer heat to adjacent surfaces primarily through convection and radiation. Techniques for efficiently modeling the heat transfer from flames are still being developed; however, experimental data and empirical correlations have been generated to predict flame heat transfer for a number of common geometries. This chapter will focus on the data and empirical correlations that have been developed. Empirical correlations for predicting heat transfer from flames are typically simple to use; however, their use is usually limited to a particular type of fire or the geometry of the surface being heated. The types of fires considered in this chapter include • Exposure area fires (burning objects) • Wall and ceiling fires • Window flames Exposure area fires are burning objects located adjacent to or near the surface being heated. Wall and ceiling fires are those fires B.Y. Lattimer (*) Virginia Tech, Mechanical Engineering, 635 Prices Fork Road, Goodwin Hall413C, Blacksburg, VA 24060, USA
produced by a burning wall or ceiling. Window flames are flames extending outside of a compartment containing a fire. The heat transfer from fires has been characterized for a range of different surface geometries. The geometries included in this chapter are • Flat vertical wall • Flat unconfined and confined ceilings • Parallel flat vertical walls • Corner walls at 90 • Corner walls at 90 with a ceiling • Horizontal I-beams beneath a ceiling The majority of the data presented in this chapter is from water-cooled heat flux gauge measurements. Using these data, correlations were developed from tests where important parameters were varied (i.e., heat release rate, fire base dimension, etc.). The range of the data and the correlating parameters need to be taken into consideration before applying the correlations. For example, the heat flux along the length of the flame has historically been correlated with flame length measured in that particular study. Measured flame lengths can vary depending on the measurement technique, definition, and surrounding geometry. For the studies considered in this chapter, the data were nondimensionalized with either the average (50 % intermittent) flame length or the flame tip length. Therefore, heat flux correlations should be applied using either the flame length correlation developed in the study or one that has been demonstrated to predict the flame length in that study.
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Heat Transfer Boundary Condition The heat flux boundary condition for a material surface exposed to a fire includes the exposure heat flux from the fire and the reradiation losses from the surface. The exposure heat flux from the fire is composed of a radiative heat flux plus a convective heat flux. The heat flux boundary condition for a fire heating an adjacent surface is k
dT 00 00 ¼ qs ¼ εs qrad þ h T f T s εs σT 4s dx ð25:1Þ
assuming negligible heating from the surroun ding environment.
Heat Flux Gauges
the radiation from the fire in Equation 25.2, the equation for the boundary condition in Equation 25.1 becomes i εs h 00 00 qs ¼ qh f g h T f T h f g þ εh f g σT 4h f g εh f g þ h T f T s εs σT 4s ð25:3Þ Assuming the heat transfer coefficient at the heat flux gauge is the same as the heat transfer coefficient at the material surface, Equation 25.3 can be reorganized resulting in εs 00 εs 00 qs ¼ q þ 1 hT f εh f g h f g εh f g εs h Ts T h f g εs σ T 4s T 4h f g εh f g ð25:4Þ
The radiation and convective heat flux terms in Equation 25.1 are difficult to accurately calculate due to the dependence of these terms on geometry and fire properties. As a result, water-cooled total heat flux gauges are commonly used to measure the maximum total exposure heat flux (or cold surface heat flux) from fires in different configurations. The maximum total exposure heat flux measured using the gauge can be used to quantify the heat flux into the material surface. The total heat flux onto a water-cooled heat flux gauge is described by the following equation: 00 00 qh f g ¼ εh f g qrad þ h T f T h f g εh f g σT 4h f g :
As a result, the need to determine the radiation heat flux from the fire has been removed. However, this expression still requires the gas temperature near the surface to be measured, Tf, and the emissivity of the adjacent surface, εs, to be known in order to calculate the net heat flux into the surface. Assuming the emissivity of the adjacent surface is equal to the heat flux gauge emissivity εs ¼ εh f g , Equation 25.4 reduces to the following: 00 00 qs ¼ qh f g h T s T h f g εh f g σ T 4s T 4h f g ð25:5Þ
ð25:2Þ
Through Equation 25.5, the net heat flux into an adjacent surface can be determined using the heat flux from a water-cooled gauge, gauge temperature, gauge emissivity, and heat transfer coefficient. The gauge temperature and emissivity are typically known; therefore, the only unknown is the convective heat transfer coefficient. An estimate of the local heat transfer coefficient, h, is needed to calculate the heat flux into the material. The heat transfer coefficient is dependent on the local velocity, gas temperature, and geometry. For natural convection on
These gauges are cooled so that their surface temperatures remain near ambient (20–80 C), and they are coated with a high emissivity paint ðε 0:95Þ to maximize the absorbed radiation. Cooling the gauge surface maximizes the convective heat transfer and minimizes the radiative losses; thus, the cooled heat flux gauges measure the maximum total exposure heat flux. The heat flux measured using the gauge can be used to determine the heat flux to an adjacent surface being heated by a fire. By solving for
Heat Transfer from Fires to Surfaces
Fig. 25.1 Magnitude of the radiative and convective terms in Equation 25.5: radiation (—); convection with h ¼ 0.015 kW/(m2-K) ( ); and convection with h ¼ 0.050 kW/(m2-K) ( )
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200
400
Surface temperature (°F) 600 800 1000 1200 1400 1600 1800
60 50
Heat flux (kW/m2)
25
40 30 20 10 0 0
horizontal and vertical surfaces, the heat transfer coefficient varies from approximately 0.010 to 0.020 kW/m2-K. These coefficients apply to fires flowing against walls or along ceilings. Higher heat transfer coefficients are expected in areas where fires impinge on surfaces. Based on data from Kokkala [1, 2] and You and Faeth [3, 4], the local convective heat transfer coefficient where a diffusion flame impinges on a ceiling is on the order of 0.050 kW/(m2-K). Figure 25.1 contains a plot of the radiative and convective heat flux terms in Equation 25.5 that are subtracted from the measured heat flux. The convective term is plotted using convective heat transfer coefficients of 0.015 kW/m2-K and 0.050 kW/m2-K. The radiative term is larger than the convective term at temperatures higher than 300 C with a heat transfer coefficient of 0.015 kW/m2-K and at temperatures greater than 600 C with a heat transfer coefficient of 0.050 kW/m2-K. Based on results in this plot, a non-conservative boundary condition will result if the heat transfer coefficient is over estimated. The following examples are provided to illustrate how the heat flux into the material varies as the material surface temperature increases and how different assumptions (i.e., surface emissivity, heat transfer coefficient) affect the heat flux into the material surface.
100 200 300 400 500 600 700 800 900 1000 Surface temperature (°C)
Example 1 A water-cooled heat flux-gauge is used to measure the total incident heat flux from a fire against a wall painted black. The measured heat flux is 30 kW/m2 and the water cooling the gauge is measured to be 350 K. Both the wall emissivity and the heat flux gauge have a surface emissivity of 0.95, and the heat transfer coefficient is 0.01 kW/m2-K. Determine the net heat flux into the wall when the wall surface temperature is 600 K, 700 K, and 800 K. Solution Equation 25.5 can be used to determine the heat flux into the wall when the wall is at different temperatures. 00 00 qs ¼ qh f g h T s T h f g εh f g σ T 4s T 4h f g 00 qs ¼ 30 0:01ðT s 350Þ ð0:95Þ 5:67 1011 4 T s 3504
• Wall surface temperature of 600 K 00 qs ¼ 30 0:01ð600 350Þ ð0:95Þ 5:67 1011 6004 3504 00
qs ¼ 21:3 kW=m2
• Wall surface temperature of 700 K 00 qs ¼ 30 0:01ð700 350Þ ð0:95Þ 5:67 1011 6004 3504 00
qs ¼ 14:4 kW=m2
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• Wall surface temperature of 800 K 00 qs ¼ 30 0:01ð800 350Þ ð0:95Þ 5:67 1011 8004 3504 00
qs ¼ 4:2 kW=m2
Example 2 A water-cooled heat flux gauge is used to measure the total incident heat flux from a fire against a wall. The heat flux gauge measured a heat flux of 30 kW/m2 while the gas temperature was measured to be 1173 K. The water cooling the gauge was measured to be 350 K. The heat flux gauge has a surface emissivity of 0.95, and the
heat transfer coefficient is 0.01 kW/m2-K. With a wall surface temperature of 700 K, determine the net heat flux into the wall if the surface emissivity is 0.94, 0.90, 0.70, and 0.50. In each case, what is the percent error associated with assuming the wall surface emissivity is equal to the heat flux gauge surface emissivity? Solution Due to the surface emissivity of the wall being different from that of the heat flux gauge, the heat flux into the wall is determined using Equation 25.4:
εs εs 00 qh f g þ 1 þ T h f g εs σ T 4s T 4h f g hT f h T s εh f g εh f g εh f g εs εs εs 00 30 þ 1 350 qs ¼ 0:01ð1173Þ 0:01 700 0:95 0:95 0:95 εs 567 1011 7004 3504 00
qs ¼
εs
The heat flux into the surface where the wall and the gauge have the same emissivity is taken from 00 Example 1b and is qs ¼ 14:4 kW=m2 . • Surface emissivity of 0.94 00
qs ¼ 14:2 kW=m2 The assumption of equal surface emissivity results in a heat flux 0.7 % higher. • Surface emissivity of 0.90
Example 3 A water-cooled heat flux gauge is used to measure the total incident heat flux from a fire against a wall painted black. The measured heat flux is 30 kW/m2 and the water cooling the gauge is measured to be 350 K. Both the wall emissivity and the heat flux gauge have a surface emissivity of 0.95. With a wall surface temperature of 700 K, determine the net heat flux into the wall with heat transfer coefficients of 0.01 kW/ m2-K, 0.015 kW/m2-K, and 0.02 kW/m2-K.
00
qs ¼ 13:9 kW=m2 The assumption of equal surface emissivity results in a heat flux 3.8 % higher. • Surface emissivity of 0.70 00
qs ¼ 11:8 kW=m2 The assumption of equal surface emissivity results in a heat flux 17.7 % higher. • Surface emissivity of 0.50 00
qs ¼ 9:8 kW=m
2
The assumption of equal surface emissivity results in a heat flux 31.8 % higher.
Solution Equation 25.5 can be used to determine the heat flux into the wall when the wall is at different temperatures. 00 00 qs ¼ qh f g h T s T h f g εh f g σ T 4s T 4h f g 00
qs ¼ 30 hð700 350Þ ð0:95Þ 5:67 1011 7004 3504 • Heat transfer coefficient of 0.01 kW/m-K 00
qs ¼ 14:4 kW=m2 • Heat transfer coefficient of 0.015 kW/m-K 00
qs ¼ 12:6 kW=m2
25
Heat Transfer from Fires to Surfaces
• Heat transfer coefficient of 0.02 kW/m-K 00
qs ¼ 10:9 kW=m2
Adiabatic Surface Temperature The adiabatic surface temperature has been proposed as a means for quantifying the thermal boundary condition in fire environments [5–8]. The adiabatic surface temperature is the surface temperature that would exist if the surface were perfectly insulated. From Equation 25.1, the adiabatic flame temperature is defined as 00 0 ¼ εs qrad þ h T f T ast εs σT 4ast ð25:6Þ Combining with Equation 25.1, a relationship between the heat flux at the surface and the adiabatic surface temperature is 00 qs ¼ εs σ T 4ast T 4s þ hðT ast T s Þ ð25:7Þ The expression provides a relationship between the adiabatic surface temperature and the heat flux to the surface. Equation 25.7 has a form similar to Equation 25.1 when the radiation 00 term, qrad , is taken as the radiation from a black4 body source, σTrad . Based on this, adiabatic surface temperature can be thought of as an effective gas temperature that embodies the radiation and convection gas temperatures. The adiabatic surface temperature can then be used as the boundary surface temperature for calculating the thermal response of materials exposed to fire conditions, knowing the heat
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transfer coefficient and surface emissivity. The adiabatic surface temperature has been successfully used as an effective gas temperature to quantify the thermal boundary condition for thermo-structural analysis [6, 8]. Analysis has not been reported on whether the boundary condition using the adiabatic surface temperature provides the same results as using cold surface 00 heat flux measurement, qhfg , and Equation 25.5. Plate thermometers have been used to measure the adiabatic surface temperature in furnace environments [5–8]. Due to the time constant of the devices [5–8], the adiabatic surface temperature measurement provided by plate thermometers need to be carefully considered in applications where the fire environment is transient.
Objects Immersed in Flames Some of the highest heat fluxes measured from diffusion flames have been measured in tests with objects immersed in large, open hydrocarbon pool fires. In these tests, small and large objects (relative to the fire size) were placed within the pool fires. These tests were performed to evaluate the heat transfer from fires to large objects such as fuel tanks, weapons, and nuclear containers. The maximum heat fluxes measured in these tests are summarized in Tables 25.1 and 25.2. From data in these tables [9–19], the size of the object relative to the pool fire has a significant impact on the incident heat flux to the object.
Table 25.1 Heat fluxes to objects immersed in large pool fires [9–19] Test AEA Winfrith [9] US DOT [9] USCG [9] US DOT [9] Sandia [9] HSE Buxton [9] Shell Research [9] Large cylinder [10] Small cylinder [10] Russell and Canfield [10]
Pool size 0.5 9.45 m Not listed Not listed Not listed Not listed Not listed 4.0 7.0 m 9.1 18.3 m 9.1 18.3 m 2.4 4.8 m
Fuel Kerosene Kerosene Kerosene Kerosene Kerosene Kerosene Kerosene JP-4 JP-4 JP-5
Peak heat flux (kW/m2) 150 138 110–142 136–159 113–150 130 94–112 100–150 150–200 175
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B.Y. Lattimer
Large calorimeters were measured to be exposed to heat fluxes of 100–150 kW/m2. McLain [17] and Taylor et al. [18] measured slightly lower heat fluxes (75–85 kW/m2) in their tests with large items that were similar in size to the pool fire. In studies with small calorimeters, peak heat fluxes were measured to range from 150 to 200 kW/m2. The difference in the heat fluxes measured for small and large items immersed in pool fires has been attributed to the difference in the convective heat transfer coefficient, the flame thickness, and the impact of the object on the flame temperature. Small-scale calorimeter data provide a bound for heat fluxes to an item immersed in a pool fire. Based on the available data, a bounding heat flux of 175 to 200 kW/m2 is possible. Table 25.2 Heat fluxes to different size objects immersed in fires [10–19] Object Large calorimeter [10] Large calorimeter [12] Large calorimeter [13] Large calorimeter [14] Large calorimeter [15] Large calorimeter [16] Large calorimeter [17] Large calorimeter [18] Large wall (3.0 0.6 m) [19] Small calorimeter [11] Small calorimeter [10]
Peak heat flux (kW/m2) 100–150 85 100 110 100 105 85a 75a 80–120 175 150–200
a
Object size comparable to pool fire size
Fires Adjacent to Flat Walls Heat fluxes from exposure fires adjacent to flat walls have been experimentally studied using propane sand burners and characterized for various burning objects. The experimental study provides a systematic approach of calculating heat fluxes for this geometry. An extensive experimental study was performed by Back et al. [20] to characterize the heat transfer from a fire to a directly adjacent wall. In this study, fires were generated using square propane sand burners with edge lengths of 0.28, 0.37, 0.48, 0.57, and 0.70 m. Heat flux fields were measured for fires ranging from 50 to 520 kW. A plot of the peak heat fluxes measured for each type of fire evaluated is shown in Fig. 25.2. Peak heat fluxes for the different fires evaluated were determined to be a function of fire heat release rate. This dependence was attributed to the larger size fires resulting in thicker boundary layers, which is related to the radiation pathlength. Based on gray-gas radiation theory, the authors found the following relation adequately represented the data: 00
00
qcl ¼ qpeak
z=L f 0:4
ð25:8Þ
These peak heat fluxes were measured in the lower part of the fire (z/Lf 0.4) along the
120 Maximum wall heat flux (kW/m2)
Fig. 25.2 Peak heat release rates measured in square propane burner fires against a flat wall [20]
Exposure Fires
100 80 60 40 Aspect ratio ~ 3 Aspect ratio ~ 2 Aspect ratio ~ 1
20 0 0
100
200 300 400 Heat release (kW)
500
600
25
Heat Transfer from Fires to Surfaces
Fig. 25.3 Vertical heat flux distribution along the centerline of a square propane burner fire adjacent to a flat wall [20]
751 1000
q øcl (kW/m2)
100
Q ≈ 59 kW Q ≈ 121 kW Q ≈ 212 kW Q ≈ 313 kW Q ≈ 523 kW Correlation for Q = 59 kW Correlation for Q = 523 kW
10
1 0.01
0.1
1
10
z /Lf
centerline, with the flame length taken from Heskestad [21]: L f ¼ 0:23Q2=5 1:02D
ð25:9Þ
Above this region, the heat fluxes were measured to decrease with distance above the fire. The heat flux data measured along the centerline is shown in Fig. 25.3. Lines in this plot are a general correlation of the centerline data: 00
00
qcl ¼ qpeak
z=L f 0:4
ð25:10aÞ
00 5 z=L f 2=5 qpeak 20 3 0:4 < z=L f 1:0 00
00
qcl ¼ qpeak
ð25:10bÞ 5=3 00 qcl ¼ 20 z=L f
z=L f > 1:0
ð25:10cÞ
Heat fluxes were measured to decrease with horizontal distance from the centerline, as shown in Fig. 25.4. The normalized lateral heat flux distribution data shown in Fig. 25.4 was found to be half-Gaussian in shape over the half width of the burner. The line in the plots is a fit to the data in Fig. 25.4a:
x 2 x 00 00 1:0 ð25:11aÞ q ¼ qcl exp 0:5D 0:5D 00
00
q ¼ 0:38qcl
x 1=7 0:5D
x > 1:0 ð25:11bÞ 0:5D
Heat fluxes from burning objects to an adjacent wall have been measured for a variety of items; however, limited data have been published on this work [22, 23]. Heat fluxes at the rim of wastebasket fires were reported by Gross and Fang [22]. At the rim, heat fluxes as high as 50 kW/m2 were measured; however, the authors noted that peak heat fluxes for these fires occurred approximately 0.22 m above the rim. Mizuno and Kawagoe [23] performed experiments with upholstered chair fires against a flat wall. In these tests, Mizuno and Kawagoe measured heat fluxes to the wall of 40–100 kW/m2 over the continuous flaming region (~z/Lf < 0.4). All of these tests were performed using foampadded chairs.
Fires in a Corner Fires in a corner of a room lined with a combustible material have been shown to cause more
752
B.Y. Lattimer
b 1.4
1.4
1.2
1.2
6 6 6
1.0
1.0
5 5 3 3 3 3 5 5
0.8 0.6 0.4
2 8
9 9 9 5 9 6 9 5 9 83 83 7 85 7 5 7 5
0.2 0.0 0.0
0.5
7
3 6 6
q / qcl
q / qcl
a
0.8 0.6
9 9 9 9 9 9 4 7 4 7 7
0.4 8 8 8 8 8
1.0
6 5 6 6 5 5 5 7 6 7 6 5 7 2 7
8 8 8 89 9 9 9 2 7
5 6 6 6 5 6 6 5
2 2 7 2 7 8 2 8 7 2 2 2 2
0.2 98 8 8 9 9 91 2 7
1.5 2.0 x / 0.5D
6 8 6 4 8 4 6 6 4 64
2.5
4 1 4 1 4 8 8
3.0
3.5
0.0 0.0
5 6 6 6 5 5 5 5
7 8 5 7 2 7 4 7 7 2 2
8 1 8 1 1
2 3 5 5
3 5 37 9 3 2 7 7 7 2 2 2 2
3 5 8 8 2 9 9 9 3 7 2 7
0.5
1.0
65 5 6 6 6
8 21 8 2 2 7
1.5 2.0 x / 0.5D
6 6 8 6 8 4 527
2.5
1 4 3 8
3.0
3.5
Fig. 25.4 Lateral heat flux distribution with distance from the centerline of square propane burner fires against a flat wall [20] (a) in the flaming region and (b) in the plume
rapid flame spread and growth to flashover compared to cases with fires in other locations within the room. For these reasons, a significant amount of work has been performed to characterize the heat fluxes produced by corner fires. Heat flux measurements have been performed both in an open environment to quantify the heat flux due to the exposure fire alone and within rooms to measure the heat flux due to the exposure fire and the room environment. The heat flux from the exposure fire has been quantified in several studies performed in an open laboratory environment [24–29]. All the studies were performed in a noncombustible corner with a ceiling except the study of Kokkala [26], which was performed in a noncombustible corner without a ceiling. A comparison of the heat flux fields measured in the study with a ceiling [29] and the study without a ceiling [26] is shown in Fig. 25.5. Note that the contour plot of Lattimer and Sorathia is relative to the floor, while the plot of Kokkala is relative to the top of the burner. Lattimer et al. used a burner 0.15 m high. Up to approximately 1.8 m above the floor, the heat flux distributions are similar. In the case with the ceiling, the ceiling jet and the radiation from the fire flowing along the ceiling were
heating the top part of the wall. This resulted in higher heat fluxes farther out from the corner along the top part of the wall. A series of fire tests were performed by Lattimer and Sorathia [29] to develop empirical correlations to estimate heat fluxes from an exposure fire to the walls and ceiling of a corner. Tests were performed using 0.17-, 0.30-, and 0.50-m square propane burners placed directly against the corner. Heat flux fields were measured for fires ranging from 25 to 300 kW. Correlations were developed for three regions in the corner: along the height of the walls in the corner, along the top of the walls near the ceiling, and along the ceiling. The region containing the walls in the corner extended from the top of the fire to approximately 1.8 m above the floor, which is approximately the ceiling height minus twice the ceiling jet thickness (δ ¼ 0.1H ). Correlations for the top part of the walls, which are heated by the ceiling jet, were developed using data at locations greater than 1.8 m above the floor. Along the height of the walls in the corner, the peak heat fluxes were typically measured near the base of the fire. The peak heat fluxes along the height of the walls in the corner were measured to be a function of the fire diameter, as shown in Fig. 25.6. The curve in Fig. 25.6 is a
25
Heat Transfer from Fires to Surfaces
753
a
b 4
1.8 10
1.6
•
Distance from corner, y (m)
1.4
Q = 300 kW D = 0.17 m
10 10
1.2
10
20
1.0 40
30 20
0.8 60
20
50
30
0.6
3
40
70
0.4 70
20
30
50 80
60
40
0.2
0.2
0.4
0.6 1.2 0.8 1.0 1.4 Distance from corner, x (m)
1.6
1.8
Ceiling
2.2 70
70
80
1.8 Distance above floor, z (m)
20
30
40
10
80
1.6
50
40
30
20
10 kW/m2
60
2
20
70
1.4
50 60
2.0
Distance above burner, z (m)
Burner
0.0 0.0
50 40
60
10
30
5
60 50
10
20
1.2
50 60
40 30
5
1
1.0 60
0.8
10
20 50
0.6
60
40
5
30
50
0.4 40
20
10 5
30
0.2
Burner
0.0 0.0
0.2
0.4
0.6 0.8 1.4 1.2 1.0 Distance from corner, x (m)
1.6
1.8
0 0
0.2
Fig. 25.5 A comparison of the heat flux fields produced in a corner (a) with a ceiling [29] and (b) without a ceiling [26]. The fire was produced by a 0.17-m-square propane burner with a heat release rate of 300 kW. Note data of
00
0.6
Lattimer and Sorathia [29] are plotted relative to the floor, and the data of Kokkala [26] are plotted relative to the top of the burner
correlation to the data and is expressed using the following relation: qpeak ¼ 120½1 expð4:0 DÞ
0.4
Distance from corner, x (m)
Wall
ð25:12Þ
The vertical distribution in the maximum heat flux along the walls near the corner is shown in Fig. 25.7 plotted with the vertical distance normalized with respect to the flame tip,
*1=2
L f , tip =D ¼ 5:9QD
ð25:13Þ
where Q*D ¼
Q pffiffiffi ρ1 C p T 1 gD5=2
ð25:14Þ
Peak heat flux levels were measured in the lower part of the flame (z/Lf,tip 0.4) and decreased
754
B.Y. Lattimer
Fig. 25.6 Peak heat flux along the height of the walls in the corner [29]
120 110
Peak heat flux, q ″peak (kW/m2)
100 90 80 70 60 50 40 30 20 10 0 0.0
Fig. 25.7 Maximum heat fluxes to the walls near the corner with square burner sides of 0.17 m (○), 0.30 m (Δ), 0.30 m (elevated) (∇), and 0.50 m (□), and fire sizes ranging from 50 to 300 kW [29]
0.1
0.2 0.3 0.4 0.5 0.6 Length of area burner side, D (m)
0.7
0.8
Maximum heat flux in corner, q ″max (kW/m2)
1000
100
10
1 0.01
0.1
1
10
z / Lf,tip
with distance above z/Lf,tip ¼ 0.4. A general correlation to represent this behavior is 00
00
qmax ¼ qpeak 00
00
qmax ¼ qpeak 4
z=L f , tip 0:4
z 2 L f , tip 5
ð25:15aÞ 00
qpeak 30
0:4 < z=L f , tip 0:65 ð25:15bÞ
00
qmax ¼ 7:2
z L f , tip
10=3
z=L f , tip 0:65 ð25:15cÞ
This is similar to the form used by Back et al. [20] to correlate heat fluxes from an exposure fire to a wall (see Equations 25.10a, 25.10b, and 25.10c), except the constants are different. The horizontal distribution in the heat flux along the wall is shown in Fig. 25.8 to best
Heat Transfer from Fires to Surfaces
Fig. 25.8 Lateral distribution in the heat flux along the walls with distance from the corner with square burner sides of 0.17 m (○), 0.30 m (Δ), 0.30 m (elevated) (∇), and 0.50 m (□), and fire sizes ranging from 50 to 300 kW [29]
755 1.1 1.0 0.9 0.8 0.7 q ″/q ″max
25
0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0
0.4
00
1.8
2.0
10
correlate with actual distance from the corner [29]. This was attributed air being entrained in the corner, pushing the fire into the corner. Near the corner the shape is half-Gaussian; however, heat fluxes outside of this decrease slower. The trend in the data, which is shown as the line in Fig. 25.8, can be represented using the following relations: 00
1.6
100
1 0.1
q ¼ qmax exp½7:5x2
0.6 0.8 1.0 1.2 1.4 Distance from corner, x (m)
1000
Maximum heat flux, q ″max (kW/m2)
Fig. 25.9 Maximum heat flux along the top of the walls during a corner fire test with square burner sides of 0.17 m (○), 0.30 m (Δ), 0.30 m (elevated) (∇), and 0.50 m (□), and fire sizes ranging from 50 to 300 kW [29]
0.2
x 0:4 m ð25:16aÞ
1 (x + H ) /Lf,tip 00
00
q ¼ 0:058qmax x1:8
x > 0:4 m
10
ð25:16bÞ
It has not been established whether this correlation holds for fire sources larger than 0.50 m in length on a single side. Along the top part of the wall the maximum heat fluxes were measured at locations less than 0.15 m below the ceiling. The maximum heat fluxes are shown in Fig. 25.9 plotted against the
756
B.Y. Lattimer
normalized distance along the flame (x + H)/Lf, tip, where x is the distance from the corner. These heat fluxes can be estimated using the following relations: xþH 00 qmax ¼ 120 0:52 ð25:17aÞ L f , tip 00
qmax
x þ H 3:5 x þ H ¼ 13:0 > 0:52 L f , tip L f , tip ð25:17bÞ
The assumed plateau in the correlation was based on the maximum heat flux expected from a flame, according to Equation 25.12. The heat fluxes to the ceiling were determined to be a function of normalized distance along the flame length, (r + H)/Lf,tip. All of the ceiling heat flux data taken in the study with a square burner in the corner are shown in Fig. 25.10. Heat fluxes along the ceiling due to the exposure fire were similar to those measured along the top of the wall. This resulted in similar correlations to estimate the heat flux to the ceiling:
q ¼ 120 00
q ¼ 13:0
rþH 0:52 L f , tip
ð25:18aÞ
x þ H 3:5 r þ H > 0:52 L f , tip L f , tip ð25:18bÞ
Again, the assumed plateau in the correlation was based on the maximum heat flux expected from a flame, according to Equation 25.12. Similar levels were measured by Hasemi et al. [25] with an exposure fire in the corner, simulated burning corner walls, and an exposure fire and simulated burning corner walls in the corner. Room Environment Effects Corner fires are currently used to evaluate fire growth potential of a combustible lining material. As such, several studies have been conducted to characterize the heat flux from an exposure fire inside a room [30–33]. In these cases, the heat flux to the surface will be due to both the exposure fire and the room environment.
1000
Heat flux to ceiling, q ″ (kW/m2 )
Fig. 25.10 The heat flux along the ceiling above a fire located in a corner for tests with square burner sides of 0.17 m (○), 0.30 m (Δ), 0.30 m (elevated) (∇), and 0.50 m (□), and fire sizes ranging from 50 to 300 kW [29]
00
100
10
1
0.1 0.1
1 (r + H ) /Lf,tip
10
25
Heat Transfer from Fires to Surfaces
The effect of the room environment on the heat fluxes was clearly demonstrated through the work performed by Dillon [33] in an ISO 9705 room [34]. The incident heat fluxes from the fire were determined by measuring the temperature rise at several locations on an insulated steel plate. Heat fluxes were calculated using a two-dimensional heat balance on the plate. Heat fluxes included contributions from both the exposure fire and the room environment. Using the surface temperature measurements and initial heat flux measurements after the burner was ignited, the heat fluxes to the hot steel plate were corrected for both reradiation from surfaces in the room and heating by the hot gas layer. The effects of the room environment on the heat fluxes to the corner boundaries is discussed here for the case with a 300 kW fire in the corner, produced using a 0.17-m square burner. The heat fluxes shown in Fig. 25.11a represent the heat flux from the fire only, as measured using a heat flux gauge (i.e., cold surface). Note that the top of the burner is 30 cm above the floor. In general, the heat fluxes in Fig. 25.11a compare well with the total heat flux data shown in Fig. 25.5a. Heat fluxes shown in Fig. 25.11b correspond to heat fluxes due to the fire and the room environment (i.e., hot gas layer and reradiation from walls), as measured using a heat flux gauge. For this room environment, the heat fluxes including the room environment were higher than the heat fluxes from the exposure fire to a cold wall. The magnitude of the increase depends on the elevation inside the room. Measurements in the lower part of the room showed less of an increase compared with those near the ceiling. Heat fluxes in the upper part of the room increased by as much as 20 kW/m2, an increase largely attributed to the hot gas layer that forms inside the room during the fire. For the 300-kW fire inside the ISO 9705 compartment, average gas temperatures in the upper part of the room were measured to be approximately 680 K. Note that the heat flux due to the room environment is dependent on the gas layer temperature, which is dependent on the fire size, room geometry, ventilation, and thermal properties of the
757
boundaries. A room or fire different from that used to produce the data in Fig. 25.11b may result in a different gas layer temperature, which will result in a different heat flux contribution due to the room environment. Heat fluxes due to the hot layer environment inside a room were measured by Tanaka et al. [35]. In tests conducted in a 3.3-m-wide, 3.3-m-deep, 2.35-m-high room with the propane fire in the center of the room, heat fluxes were measured at different locations on one of the side walls. The average heat flux measured in the upper layer formed inside of the room is shown in Fig. 25.12 versus the layer temperature for different compartment door widths. The line in the plot represents the blackbody heat flux 00 using the layer gas temperature, q ¼ σT 4g . As seen in the Fig. 25.12, the blackbody heat flux using the layer gas temperature provides a reasonable estimate of the incident heat flux to the walls inside a compartment; however, the measured heat fluxes are generally higher than the blackbody heat flux. A more detailed investigation of the heat flux to compartment fire surfaces was performed by Toflio et al. [36] Through this study, it was determined that the higher heat flux was attributed to convection between the hot gas layer and the wall. In addition, as fires became large in size, radiation exchange between the fire and the walls could also increase the heat flux to wall surfaces. Effects of Fire Standoff Distance Several researchers have investigated the effects of moving the exposure fire away from the corner (i.e., standoff distance) [24, 30, 37]. As one might expect, moving the fire away from the corner decreases the heat fluxes to the room boundaries. Tests were performed by Williamson et al. [30] in a full-scale ISO 9705 room using a 0.30-m-diameter burner. Heat fluxes to the wall were strongly dependent on whether the flame was attached to the corner walls or burned freely near the wall. At a heat release rate of 40 kW, with the burner against the corner walls, the flame was attached to the walls and heat fluxes were measured to be as high as 50 kW/m2. When
758
B.Y. Lattimer
a
b 232.5
232.5 217.5
80 70
217.5
100
202.5
202.5
60
90
50
187.5
187.5 30
40
80
172.5
20
127.5 112.5 97.5
40
50
157.5
60
142.5
30 20
127.5
10 kW/m2
112.5 97.5
82.5
82.5
67.5
67.5
52.5
52.5
37.5
37.5
22.5
22.5
Burner
Burner
7.5
7.5 97.5
82.5
67.5
52.5
37.5
22.5
7.5
97.5
52.5
37.5
97.5
82.5 67.5 52.5 70
37.5
80 90
Distance from corner, y (cm)
97.5
50
82.5 40
kW/m2
67.5
50 60
70
80 100
67.5
52.5
37.5
22.5
7.5
Distance from corner, x (cm)
110
37.5 22.5
Burner
90
100 90
110
7.5 82.5
52.5 90
22.5 Burner
97.5
7.5 112.5
40
112.5
22.5
112.5
kW/m2
60
67.5
Distance from corner, x (cm)
Distance from corner, x (cm)
30
82.5
112.5
97.5
82.5
67.5
52.5
37.5
22.5
Distance from corner, y (cm)
112.5
112.5
Distance above floor, z (cm)
142.5 kW/m2
Distance above floor, z (cm)
157.5
10
172.5
70
7.5
7.5
Distance from corner, x (cm)
Fig. 25.11 Heat fluxes to corner boundaries from (a) 300-kW, 0.17-m square propane sand burner exposure fire alone to a “cold” surface and from (b) the 300-kW exposure fire and the room environment [33]
the fire was moved 50 mm from the walls, the flames were observed to be detached from the walls with the highest heat fluxes measured to be approximately 25 kW/m2. In tests with a heat release rate of 150 kW, the fire was observed to
be attached to the walls and heat fluxes of 40–60 kW/m2 were measured at the walls. Additional work needs to be performed to investigate distances at which fires attach to nearby surfaces, such as a flat wall or walls in a corner.
25
Heat Transfer from Fires to Surfaces
759
Fig. 25.12 Heat flux to the walls inside a compartment containing a hot gas layer [35]
200
100 80
Heat flux to wall (kW/m2)
50
30 20
10 8 Width (cm) 29 45 59 89
5
3 2 1 400
Fires Beneath Unconfined Ceilings There have been several experimental and theoretical studies performed on fires impinging on an unbounded ceiling [1–4, 38–41]. Total heat fluxes from fires and fire plumes impinging on the ceiling were measured by Hasemi et al. [38], You and Faeth [3, 4], and Kokkala [1, 2]. Hasemi et al. [38] conducted a series of fire tests using propane gas burners located at different distances beneath a noncombustible ceiling. Fires as large as 400 kW (approximated) were considered in the study. Heat flux gauges were used to measure the incident heat flux along the ceiling at different distances away from the fire centerline, or stagnation point. The measured heat flux at the stagnation point is shown in Fig. 25.13 to plateau at approximately 90 kW/m2. In order to collapse the data, the flame tip length was normalized with respect to the distance
500 600 800 1000 Hot layer average temperature (K)
1400
between the ceiling and fire, H, plus the virtual source location, z0 . The virtual source location for this geometry was determined using the following relations: 0 *2=5 *2=3 z ¼ 2:4D QD QD Q* < 1:0 ð25:19aÞ 0 *2=5 z ¼ 2:4D 1 QD
Q* 1:0
ð25:19bÞ
where QD* is defined as in Equation 25.14 with D being the diameter of the exposure fire. The length of the flame, Lf,tip , in this geometry is defined as the distance between the fire and the ceiling, H, plus the radial extension of the flame out from the center of the fire, LH. The location of the flame tip in this geometry was found to correlate with QH*, which is defined the same as in Equation 25.14 except D is replaced by H. The flame tip correlation was determined to be
760
B.Y. Lattimer
Fig. 25.13 Stagnation point heat fluxes on an unbounded ceiling with a fire impinging on it [38]
100
Heat flux, q s (kW/m2)
80
60 D = 1.0 m H = 1.0 m H = 1.2 m H = 0.8 m H = 0.6 m H = 0.4 m D = 1.0 m H = 0.64 m H = 0.8 m H = 1.0 m D = 0.3 m H = 1.0 m H = 0.8 m
40
20
0 0
2
3
4
5 6 Lf /(H + z )
7
8
9
10
11
100
Heat flux, q (kW/m2)
Fig. 25.14 Heat fluxes to a ceiling due to a propane fire impinging on the surface [38]
1
D = 0.5 m H = 1.0 m H = 1.2 m H = 0.8 m H = 0.6 m H = 0.4 m D = 1.0 m H = 0.64 m H = 0.8 m H = 1.0 m D = 0.3 m H = 1.0 m H = 0.8 m
10
1 0.1
1
10
(r + H + z) / (LH + H + z)
ðLH þ H Þ *1=3 ¼ L f , tip =H ¼ 2:89QH H
ð25:20Þ
The heat flux was measured to decrease with distance from the fire stagnation point.
Figure 25.14 contains a plot of the heat flux to the ceiling as a function of location within the flame. The correlation recommended by Wakamatsu [42] can be used to predict the heat fluxes:
25
Heat Transfer from Fires to Surfaces
Fig. 25.15 A comparison of the best fit curve proposed by Wakamatsu [42] ( ) and a bounding fit to the data (—). The unbounded ceiling data of Hasemi et al. [38] is represented as the outlined area
761
Heat flux, q (kW/m2)
1000
100
10
1 0.1
1
10
w = (r + H + z )/(LH + H + z ) 00
q ¼ 518:8e3:7w
ð25:21aÞ
0 0 w ¼ r þ H þ z = LH þ H þ z
ð25:21bÞ
where
Figure 25.15 contains a plot of Equation 25.21a (dashed line) along with a representation of the data of Hasemi et al. [38] for a flat unbounded ceiling. Equation 25.21a adequately estimates the data when w is greater than 0.45 but significantly overestimates heat flux levels for smaller values of w. Based on the data from Hasemi et al. [38] and other data from fires impinging on I-beams mounted to a ceiling [43], a correlation was developed to predict the bounding heat flux levels to an unconfined ceiling: 00
q ¼ 120 00
w 0:5
q ¼ 682expð3:4wÞ
w > 0:5
ð25:22aÞ ð25:22bÞ
where w is defined in Equation 25.21b. This correlation is shown in Fig. 25.15 as the solid line. The peak heat flux of 120 kW/m2 at w less than or equal to 0.5 bounds nearly all of the heat flux measurements made in this range for the studies of Hasemi et al. [38] and Myllymaki and Kokkala [43]. Heat flux measurements with smaller fires ( = 0.25 H = 1.1 m H = 0.6 m
100
10
1 0.01
0.1
1
10
(x + H )/Lf, tip
Fires Beneath I-Beams Three studies have evaluated the heat flux incident onto an I-beam mounted to a ceiling with an exposure fire impinging on the beam [38, 43, 49]. These studies all measured the heat flux to the four surfaces shown in Fig. 25.22 on the I-beam: downward face of the lower flange, upward face of the lower flange, the web, and downward face of the upper flange. For each of these surfaces, heat fluxes were measured from the stagnation point of the fire (centerline of the fire) past the location of the flame tip. The study by Wakamatsu et al. [49] provides a framework for determining heat fluxes to different parts of the I-beam. The I-beam evaluated in the study was 3.6 m long, a web 150 mm high and 5 mm thick, and flanges 75 mm wide and 6 mm thick. Tests were performed using fires from 0.5- or 1.0-m propane burners with heat release rates ranging from 100 to 900 kW. The distance between the fire source and I-beam was also varied. When the fire impinges on the I-beam, the flame length is different on the lower flange compared to the flame length on the upper flange (Fig. 25.23). Flame lengths along the lower flange, LB, were shorter than those observed
Ceiling Downward face of upper flange Web
Upward face of lower flange
Downward face of lower flange Fire
Fig. 25.22 Location of heat flux measurements on I-beams
near the upper flange, LC. Heat fluxes along the lower flange were taken to be a function LB while heat fluxes to other surfaces were related to LC. Flame lengths were related to the dimensionless Q*, as defined in Equation 25.14, with D being replaced by the appropriate distance between the fire and the flange, Q*HB ¼
Q pffiffiffi 5=2 ρ1 C p T 1 g H B
ð25:26Þ
Q*HC ¼
Q pffiffiffi 5=2 ρ1 C p T 1 g H C
ð25:27Þ
766
B.Y. Lattimer
a 10.0 y = 2.3x 0.3
(LB + HB) /HB
Fig. 25.23 Flame lengths (a) along the lower flange (Equation 25.28a) and (b) along the upper flange in I-beam tests performed by Wakamatsu et al. [49]
1.0
0.1 0.0
0.1
1.0
10.0
1.0
10.0
Q*HB
b
(LC + HC) /HC
10.0
1.0
0.1 0.0
0.1 Q*HC
Correlations were developed to predict the flame tip length along the lower and upper flanges: ðLB þ H B Þ=H B ¼ 2:3Q*0:3 HB
ð25:28aÞ
ðLC þ H C Þ=H C ¼ 2:9Q*0:4 HC
ð25:28bÞ
The heat flux measured at the stagnation point on the downward face of the lower flange was found to be the same as that measured for a fire beneath a ceiling (Fig. 25.24). The location of the
virtual origin, z0 , was determined using Equation 25.19. The variation in the heat flux along the downward face of the lower flange with horizontal distance, r, from the stagnation point is shown in Fig. 25.25. The data appear to fall between the range of the data measured in the unconfined ceiling tests, which are represented by the dashed and solid lines. These heat fluxes were the highest measured on the I-beam assembly and can be estimated using the following correlation:
25
Heat Transfer from Fires to Surfaces
767
Fig. 25.24 Heat flux at the stagnation point on the downward face of the lower flange [49]
100 Lower flange downward Free flame
Heat flux, qs (kW/m2)
80
Ceiling test Beam test
60
H = 1.0 (m) H = 0.6 (m) H = 1.0 (m) H = 0.6 (m) HB = 1.0 (m) HB = 0.6 (m) HB = 1.2 (m)
40
20
0 0
4
2
6
8
10
Lf /(H + z ¢ )
Fig. 25.25 Heat flux along the downward face of the lower flange [49]
Heat flux, q (kW/m2)
100
10
Flame tips 1 0.1
10.0
1.0 (r + HB + z¢ )/(LB + HB + z¢ ) H = 1.0 m Q = 100 kW
H = 1.2 m Q = 540 kW
Q = 150 kW
Q = 750 kW
Q = 200 kW
Q = 900 kW
H = 0.6 m Q = 95 kW Q = 130 kW
Flat ceiling maximum
Q = 160 kW
Flat ceiling minimum
768
B.Y. Lattimer
Fig. 25.26 Heat flux along the upward face of the lower flange (key same as in Fig. 25.25) [49] Heat flux, q (kW/m2)
100
10
1 0.1
Fig. 25.27 Heat flux along web (key same as in Fig. 25.25) [49]
1.0 (r + HC + z ¢ )/(LC + HC + z¢ )
10.0
1.0 (r + HC + z¢ )/(LC + HC + z¢ )
10.0
Heat flux, q (kW/m2)
100
10
1 0.1
00
q ¼ 518:8e3:7w
ð25:29aÞ
where 0 0 w ¼ r þ H B þ z = LB þ H B þ z ð25:29bÞ The heat fluxes to the upward face of the lower flange and the web are shown in Figs. 25.26 and 25.27 to be lower than those on the downward face of the lower flange. This was attributed to the lower flange shielding these parts of the I-beam from radiative and convective heat transfer. These data can be represented by the following expression: 00
q ¼ 148:1e2:75w
ð25:30aÞ
where 0 0 w ¼ r þ HC þ z = LC þ HC þ z ð25:30bÞ The lowest heat fluxes on the I-beam were measured on the downward facing part of the upper flange. As seen in Fig. 25.28, heat fluxes to this part of the I-beam are slightly less than those measured on an unconfined ceiling. Heat fluxes to the downward face of the upper flange can be estimated using the following fit to the data: 00
q ¼ 100:5e2:85w where
ð25:31aÞ
25
Heat Transfer from Fires to Surfaces
769
Fig. 25.28 Heat flux along the downward face of the upper flange (key same as in Fig. 25.25) [49] Heat flux, q (kW/m2)
100
10
1 0.1
0 0 w ¼ r þ HC þ z = LC þ HC þ z ð25:31bÞ Myllymaki and Kokkala [43] evaluated the use of the approach and data of Wakamatsu et al. [49] to estimate heat fluxes onto I-beams exposed to fires as large as 3.9 MW. They found that for fires over 2.0 MW, the correlations suggested for the upward face of the lower flange, web, and downward face of the upper flange underestimate the heat flux to these areas on the I-beam. For these large fires, the I-beam becomes completely engulfed in fire. As a result, heat fluxes on all parts of the I-beam follow the correlation suggested for the downward face of the lower flange provided in Equation 25.29. Heat fluxes to the downward face of the lower flange, the upper flange, and the web are shown in Fig. 25.29, along with the correlations recommended by Wakamatsu [42]. The highest heat fluxes measured in the tests performed by Myllymaki and Kokkala [43] were approximately 130 kW/m2 and were along the downward face of the upper flange. Data from these studies demonstrate that the heat flux to the I-beam can be conservatively estimated using the bounding heat flux correlation in Equation 25.32: 00
q ¼ 120 00
w 0:5
q ¼ 682expð3:4wÞ
ð25:32aÞ
w > 0:5 ð25:32bÞ
1.0 (r + HC + z ¢ )/(LC + HC + z ¢ )
10.0
using the appropriate expression for w provided in Equations 25.29b, 25.30b, and 25.31b. Figure 25.30 provides a plot of this correlation along with the I-beam data [43].
Burning Walls and Ceilings Fires from burning boundaries typically produce thinner flames than those generated by exposure fires. As a result, heat fluxes from burning boundary flames are typically lower than those measured for exposure fires in a similar geometry. As was the case with heat fluxes from exposure fires, heat fluxes from burning boundaries are dependent on the geometry of the burning surfaces.
Wall Fires Heat fluxes from a burning wall flame back to the surface have been studied fairly extensively. Most of the work in this area has been performed with smaller fires. Though the data indicate that these heat fluxes are dependent on both fire size and smoke production, no reported study has fully characterized this behavior. Much of the detailed heat flux measurements for fires produced by burning flat surfaces have been done with smaller-scale fires ( 0:5 ð25:34bÞ
A more conservative fit that bounds this data set was developed: 00 ð25:35aÞ q ¼ 30 z=L f 0:7 2:5 00 q ¼ 12:3 z=L f
z=L f > 0:7 ð25:35bÞ
Line burners have been used by some researchers to simulate a fire produced by a burning surface such as a wall. Hasemi [55, 59, 60] measured the heat flux from a methane line burner fire to an incombustible wall. In this study, the fire heat release rate per unit length of burner (0.30 m) was varied from 16.7 to 218.2 kW/m and two different liner burner widths (0.037 m and 0.082 m). For the test conditions considered, the heat fluxes along the flame are seen in Fig. 25.31 to be similar for each test condition. In addition, heat fluxes measured in this study are shown in Fig. 25.32 to be similar
772
B.Y. Lattimer
Fig. 25.32 The heat fluxes from methane line burners against a flat wall [29, 55, 61]
100
Heat flux (kW/m2)
Methane57 Propane63 Propane31 Equation 34 Equation 35
10
1
0.1 0.01
to those shown in Fig. 25.31. The correlations presented in Equations 25.34 and 25.35 adequately bound the data. Line burner experiments using propane as fuel have resulted in higher heat fluxes than those measured with methane as the fuel. In tests using propane with Q0 ¼ 83 167 kW/m, Kokkala et al. [61] and Lattimer [29] both measured heat fluxes of approximately 45 kW/m2 in the lower half of the flame (z ¼ 0.5 Lf). Though not shown on the plot, Foley and Drysdale [62] measured 40–50 kW/m2 from propane line burners with Q0 ¼ 11.6 and 20.9 kW/m. These data indicate that the radiation from the fire to the surface is dependent on fuel smoke production. Slightly larger-scale fire tests were performed by Kulkarni et al. [63, 64] In this study, heat flux measurements were made along the length of different 0.3-m-wide, 1.2-m-high samples of solid combustibles. Fires were initiated using a line burner at the bottom of the sample, and heat fluxes were continuously measured during the test. Heat fluxes and flame lengths were continuously monitored as the fire spread along the combustible material. These transient heat flux and flame length measurements were averaged over particular time periods and plotted to determine the heat flux at different locations along the flame length.
0.1
1 z /Lf
10
100
Figure 25.33 provides the heat flux data for the different materials included in the study. Peak heat fluxes measured for the different materials were measured to range from 25 to 60 kW/m2. Heat fluxes from burning masonite board, cardboard, and white pine board were in the 20 to 30-kW/m2 range, similar to that measured in experiments by Ahmad and Faeth [50, 51] and Quintiere et al. [52]. However, fires involving PMMA, polyurethane foam, and velour fabric were all measured to produce heat fluxes greater than 30 kW/m2. The PMMA and polyurethane foam had the highest flame lengths of all the materials (~1.75 m), which is comparable to the flame lengths reported by Quintiere et al. [52] for similar materials (PMMA and flexible foam). This indicates that the heat release rates for the PMMA and polyurethane foam are comparable in the two studies. The reason for the differences in the peak heat fluxes (e.g., 30–60 kW/m2 in tests by Kulkarni et al. [63, 64] with PMMA, while 20–26 kW/m2 in tests by Quintiere et al. [52] ) is not known. Less detailed heat flux measurements have been reported in the literature for larger fires. Orloff et al. [65] and Delichatsios [54] reported data on heat fluxes from flames produced by a 3.6-m-high burning PMMA wall. Total heat fluxes incident on the PMMA were calculated
25
Heat Transfer from Fires to Surfaces
773
Fig. 25.33 Heat fluxes for different materials [64, 64]
Heat flux (kW/m2)
100 Cardboard PMMA (black) Masonite board Polyurethane foam White pine board Velour fabric Equation 34 Equation 35
10
1
0.1 0.1
1
10
100
z /Lf
Fig. 25.34 Heat flux from a PMMA wall flame back to the fuel surface [53, 54, 65]
60
Heat flux (kW/m2)
50 40 30 20 H = 1.2 m55 H = 3.6 m67 H = 3.6 m56
10 0 0
using theory and mass loss rate data. Heat fluxes are shown in Fig. 25.34 to increase with height. All the data in this plot were at positions where z/Lf is less than 0.5. This behavior is different than that observed with smaller fires, where heat flux is relatively constant over this region. Markstein and de Ris [66] also explored the effects of larger fire size and soot production on the heat flux incident on the burning surface. The apparatus used in the study was 0.38 m wide and 1.98 m high, with the bottom 0.79 m of the wall being a sintered metal gas burner. Heat flux data
1
2 3 4 Distance along burning wall, z (m)
5
6
for methane, ethane, ethylene, and propylene fires were reported. The impact of fire size on the heat flux distribution along the height of the panel is shown in Fig. 25.35. Similar to the PMMA results, the heat fluxes were measured to increase with height in the test with the higher heat release rate (816 kW/m). The heat flux from the flame is shown in Fig. 25.36 to also be a function of fuel smoke production rate. Methane and ethane have low smoke yields (less than 0.013 g/g) [67] and are measured to produce heat fluxes as high as
774 70
Q = 88 kW/m Q = 816 kW/m
60 Heat flux (kW/m2)
Fig. 25.35 Heat fluxes along a propylene gas wall fire at different heat release rates per unit width [66]. Burning wall height was 0.79 m
B.Y. Lattimer
50 40 30 20 10 0 0.0
1.0 1.5 Height, z (m)
2.0
2.5
70 Heat flux at z = 1.25 m (kW/m2)
Fig. 25.36 Heat flux at a height of z ¼ 1.25 m for different size fires and different fuels [66]. Burning wall height was 0.79 m
0.5
60 50 40 30 Methane Ethane Ethylene Propylene
20 10 0 0
35–38 kW/m2. The smoke yield of ethylene (0.043) [67] is less than that of propylene (0.095), but similar heat fluxes were measured with height along the apparatus. Peak heat fluxes of 59 kW/m2 were measured for the largest propylene fire considered in the study. Heat fluxes were measured in tests on large (2.4-m-high, 0.60-m-wide) plywood walls [68]. The peak heat fluxes measured in these tests are provided in Table 25.3 for various preheat levels. As the heat release rate per unit width increases, the heat flux from the fire to the wall increases. Though heat fluxes are not as high as those measured for a burning PMMA wall, the heat flux is 8–20 kW/m2 higher than the 30-kW/m2 peak level measured in the smallerscale tests.
200 400 600 800 Heat release rate per unit width, Q (kW/m)
1000
Table 25.3 Peak heat flux from flames measured in 2.4-m-high, 0.60-m-wide plywood wall experiments [68] (measurements up to 1.8 m above floor)
Fuel Plywood (Finished side exposed) Plywood (Unfinished side exposed)
Radiant exposure (kW/m2) 4.8 5.2
Heat release rate per unit width Q0 (kW/m) 175 197
Peak heat flux (kW/m2) 38 40
7 7.5 11
292 217 417
45 45 50
Similar experiments were performed by Ohlemiller and Cleary [69] on composite panels. The peak heat fluxes measured in this study are provided in Table 25.4. Similar to
25
Heat Transfer from Fires to Surfaces
775
the results of Delichatsios et al. [68], heat fluxes were measured to increase with an increase in heat release rate (i.e., increase in external heat flux). Data presented in this section demonstrate that both heat release rate and smoke production rate of the fuel can influence the heat flux levels produced by wall flames back onto the burning surface. Larger fires with high smoke production rates can result in heat fluxes to the walls of approximately 60 kW/m2. Additional research needs to be performed to better quantify the transition between the smaller-fire experiments and the large-fire results.
Table 25.4 Heat fluxes from 1.2-m-High, 0.3-m-wide Composite panel fires [69] Radiant exposure Fuel (kW/m2) Fire-retarded 2.5 vinyl ester 7.5 11 Polyester 0
Heat release rate per unit width Q0 (kW/m) — — — —
Fig. 25.37 Heat flux from burning PMMA corner walls (1.6 m high and 0.20 m wide) [71]
Peak heat flux (kW/m2) 35 48 52 35
Corner Wall Fires Limited work has been performed to quantify the heat fluxes from burning boundaries in a corner. In general, the heat fluxes produced by burning corner walls are higher than those produced by a wall flame. Qian et al. [70, 71] measured heat fluxes produced in a corner of burning PMMA walls beneath an incombustible ceiling. In these experiments, a 1.6-m-high corner was lined with 12.7-mm-thick PMMA 0.20 m in width. During the tests, the walls were ignited using a torch at the bottom of the corner and were allowed to burn until flames had spread to the top of the walls. The peak heat release rate of the fire was estimated to be 80 kW. The heat fluxes measured during the growing fire are shown in Fig. 25.37. In the lower half of the flame, heat fluxes were measured to be, on average, 33 kW/m2. Above this, the heat fluxes were measured to decay similarly to heat fluxes measured for wall fires (see Equations 25.35 and 25.36). A series of experiments were conducted by Hasemi et al. [25] using L-shaped sintered
10 •
q
= 0.822 (x /xf )–2.294
Heat flux, q (kW/m2)
R ^2 = 0.926 1 q
~ (x /xf)–1.8
0.1
0.01 0.1
1 Normalized height, z /Lf
10
776
B.Y. Lattimer
a
b 100 Q = 15 kW Q = 20 kW Q = 25 kW Q = 30 kW Q = 40 kW Q = 50 kW Q = 60 kW
10
Q = 40 kW Q = 50 kW Q = 60 kW
Heat flux, q (kW/m2)
Heat flux, q (kW/m2)
100
1
10
1
Z/d = 4
Z/d = 2
0.1
0.1 0.1
1
10
100
0.1
1
10
z/Lf
z/Lf
d = 0.225 m, Z = 0.45 m
d = 0.225 m, Z = 0.90 m
100
Fig. 25.38 Heat fluxes to a corner from a simulated burning corner fire using propane as fuel [25]
metal burners mounted to the walls of the corner to simulate burning corner walls. Using propane gas as fuel, experiments were conducted using two different burner sizes (0.23 m wide and 0.45 m high, 0.23 m wide and 0.90 m high) mounted to an open corner of walls with no ceiling. The heat fluxes above the burners in these fires are provided in Fig. 25.38 for fire heat release rates of 15–60 kW. The line on the plots represents the decay in the heat flux of a wall fire. Peak heat fluxes in the lower part of the flame were measured to range from 28 to 38 kW/m2 and were constant up to approximately half the flame length. Above this, heat fluxes were measured to decay in a manner similar to that determined for burning walls. Hasemi et al. [72] also performed tests in a 1.8-m-high corner with a ceiling. Tests were performed with the top 1.35 m of the corner lined with 0.23-m-wide sintered metal burners and with the top 0.45 m of the corner lined with sintered metal burners. Heat fluxes to the ceiling were measured to be as high as 40 kW/m2, while heat fluxes as high as 60 kW/m2 were measured along the top of the walls near the ceiling. Lattimer et al. [29] performed a detailed study using L-shaped propane line burners in the
corner. Burners were placed in a 2.4-m-high corner with a ceiling, with all surfaces constructed of noncombustible materials. In this study, heat fluxes were measured for different size burners (single side length of 0.17 m, 0.30 m, and 0.50 m) and various heat release rates (50–300 kW). Similar to the approach used to develop the heat flux correlations for area burners, burning boundary correlations were developed for three regions in the corner: along the height of the walls in the corner, along the top of the walls near the ceiling, and along the ceiling. The region containing the walls in the corner extended from the top of the fire to approximately 1.8 m above the fire, which is approximately the ceiling height minus twice the ceiling jet thickness (δ ¼ 0.1H ). Above 1.8 m was considered to be the region along the top of the wall, or the wallceiling interface region. Heat flux data for these fires were normalized with respect to the flame tip location. The flame tip was the farthest distance at which flaming was visually observed. In cases where the fire impinged and flowed along the ceiling, the flame tip length was taken to be the corner height plus the flame extension along the ceiling. Lattimer et al. [29] developed the following
25
Heat Transfer from Fires to Surfaces
777
correlation to predict the flame tip of a burning boundary fire: *1=2
L f , tip =d ¼ 5:9Qd
ð25:36Þ
where dimensionless Qd* is Q*d ¼
Q pffiffiffi ρ1 C p T 1 gd 5=2
ð25:37Þ
00
qmax ¼ 70
Equations 25.35b and 25.36 are similar to those used in predicting flame heights from area burners in a corner except the length scale is d, which is the width of the burning area on the wall or the side of a single L-shaped burner. In the L-shaped line burner tests, d is the length of a single side; however, in a burning corner d was found to be the average width of the burning on the walls. For fires in a 2.4-m-high corner, the width of the burning 0.90 m above the floor was found to adequately represent the average burning width [29]. The vertical distribution in the maximum heat flux along the walls near the corner is shown in Fig. 25.39 plotted with the vertical distance
z=L f < 0:5
2:8 00 qmax ¼ 10 z=L f
ð25:38aÞ
z=L f > 0:5 ð25:38bÞ
Heat fluxes in the decay region (z/Lf ) > 0.5 decrease with dimensionless height raised to the 2.8 power, which is a slightly lower power than the decay for wall fires (2.5). Peak heat fluxes in the corner are shown in Fig. 25.40 to have some dependence on the heat release rate of the fire. The increase in the peak heat flux with increase in fire size was attributed to an increase in radiative pathlength. Assuming the gases to be gray, the following curve fit was developed:
1000
Maximum heat flux in corner (kW/m2)
Fig. 25.39 Heat flux from simulated corner wall fires back to the corner walls at a height less than 1.8 m above the floor. L-shaped line burner with single side lengths of 0.17 m (○), 0.30 m (Δ), 0.30 m (elevated) (∇), and 0.50 m (□) and fire sizes ranging from 50 to 300 kW [29]
normalized with respect to the flame tip. Peak heat fluxes were measured over the initial half of the flame length. Above this, heat fluxes decayed in a fashion similar to that observed for wall fires. The line in the plot represents a fit to the data, which can be described by the following expressions:
100
10
1
0.1 0.01
1
0.1 z/Lf,tip
10
778
B.Y. Lattimer
Fig. 25.40 Peak heat flux to the walls in the corner as a function of wall heat release rate less than 1.8 m above the floor. L-shaped line burner with single side lengths of 0.17 m (○), 0.30 m (Δ), 0.30 m (elevated) (∇), and 0.50 m (□) and fire sizes ranging from 50 to 300 kW [29]
140 130
q peak = 70 q peak = 120 [1 – exp(–0.1Q1/2)]
120 Peak heat flux in corner (kW/m2)
110 100 90 80 70 60 50 40 30 20 10 0 0
h i 00 qpeak ¼ 120 1 exp 0:1Q1=2
ð25:39Þ
Based on Equation 25.38b, a more conservative fit to the data in Fig. 25.39 was developed: 00 00 qmax ¼ qpeak z=L f 0:5 ð25:40aÞ 00
00
qmax ¼ qpeak 5 z=L f 0:5
00
qpeak 27 0:5 < z=L f 0:7
ð25:40bÞ 2=8 00 qmax ¼ 10:0 z=L f z=L f > 0:7 ð25:40cÞ The maximum heat fluxes along the height of the corner shown in Figs. 25.39 and 25.40 were measured approximately 0.05–0.10 m outside of the corner. Heat fluxes decrease with horizontal distance from the corner. The horizontal heat flux distributions at heights less than 1.8 m above the floor are shown in Fig. 25.41 to be half-Gaussian in shape over the flame, but decays slower than predicted by a half-Gaussian curve outside of the flaming region. The line in this plot is a fit to the data, which can be represented by the following expressions:
50
100
150 200 250 300 Heat release rate, Q (kW)
350
400
h i x q < 1:3 ¼ exp 1:0ðx=dÞ2 00 d qmax
ð25:41aÞ
x 1:8 q ¼ 0:30 00 d qmax
ð25:41bÞ
00
00
x 1:3 d
Burning boundary beneath a ceiling will form a ceiling jet that will heat the top part of the walls and the ceiling. The maximum heat flux along the top part of the walls is shown in Fig. 25.42. The line in the plot represents a fit to the data, which can be represented by the following expressions: xþH 00 qmax ¼ 120 0:52 ð25:42aÞ L f , tip 00
qmax
x þ H 3:5 x þ H ¼ 13:0 > 0:52 L f , tip L f , tip ð25:42bÞ
The assumed plateau in the correlation is based on the maximum heat flux expected from a flame in this configuration. This correlation is the same as that determined for area fires in a corner. The heat flux to the ceiling was correlated to the dimensionless distance away from the burner,
25
Heat Transfer from Fires to Surfaces
779
Fig. 25.41 Horizontal heat flux distribution on the walls out from the corner at a height less than 1.8 m above the floor [29]
1.2
1.0
Heat flux, q /q
max
0.8
0.6
0.4
0.2
0.0 0.0
1.0
1.5
2.0
2.5 x /d
3.0
3.5
4.0
4.5
5.0
1000
Maximum heat flux, q max (kW/m2)
Fig. 25.42 Maximum heat flux along the top of the walls with a simulated burning boundary fire in the corner. L-shaped line burner with single side lengths of 0.17 m (○), 0.30 m (Δ), 0.30 m (elevated) (∇), and 0.50 m (□) and fire sizes ranging from 50 to 300 kW [29]
0.5
100
10
1 0.1
1 (x + H ) /Lf,tip
10
780
B.Y. Lattimer 1000
Heat flux to overhead, q (kW/m2)
Fig. 25.43 Heat flux along the ceiling with a simulated burning boundary fire in the corner. L-shaped line burner with single side lengths of 0.17 m (○), 0.30 m (Δ), 0.30 m (elevated) (∇), and 0.50 m (□) and fire sizes ranging from 50 to 300 kW [29]
100
10
1
0.1 0.1
(r + H )/Lf,tip. A plot of the heat flux versus this dimensionless parameter is shown in Fig. 25.43. The line in this plot is a fit to the data, which are represented through the following relations: rþH 00 q ¼ 120 0:52 ð25:43aÞ L f , tip r þ H 3:5 r þ H > 0:52 q ¼ 13:0 L f , tip L f , tip 00
ð25:43bÞ This is the same relation used for the top of the corner walls, except the length scale in the overhead data is r. In addition, this is the same relation determined using the ceiling heat flux data from tests with an area burner.
Ceiling Fires Heat fluxes from burning ceilings have been evaluated for both unconfined ceilings and ceilings in a corridor. Due to buoyancy effects, flames from burning ceilings tend to be relatively thin. As a result, peak heat fluxes from burning
1 (r + H ) /Lf,tip
10
ceilings range from 20 to 30 kW/m2, which is similar to those measured for small wall fires. Unconfined Ceiling Fires Heat fluxes from unconfined ceiling fires were measured by Hasemi et al. [73] using different sizes of sintered metal propane gas burners mounted into a 1.8-m-square incombustible ceiling. Using two different circular burner sizes (D ¼ 0.09 and 0.16 m), heat flux to the ceiling was measured for fire heat release rates of 2.5–38 kW. The radius of the flame (intermittent) measured using the two burners is shown in Fig. 25.44 to be slightly dependent on burner size, with the larger burner having a lower radius. However, as the fires become larger, the dependence on burner diameter becomes small. Flame lengths are proportional to the heat release rate raised to the one-half power. Hasemi et al. [73] also measured the heat fluxes as a function of distance from the center of the burner. The measured heat fluxes are shown in Fig. 25.45 to be at peak levels in the first 0.4Lf and then decay with distance from the burner. Peak heat fluxes were measured to range from
25
Heat Transfer from Fires to Surfaces
781
Fig. 25.44 Flame radius produced by a simulated burning ceiling in an unconfined area [73]
0.8 0.7 φ = 0.09 m y = 0.1324x 0.4465
Flame radius (m)
0.6 0.5
φ = 0.16 m y = 0.0848x 0.5644
0.4 0.3 0.2 0.1 0 0
Fig. 25.45 Heat flux from fires beneath an unconfined ceiling [73]
5
10
15 20 25 30 Heat release rate (kW)
35
40
45
100
Total heat flux (kW/m2)
d = 0.09 m d = 0.16 m
One dimensional ceiling flames
10
Wall fires
1
0.1 0.1
16 to 27 kW/m2, with the smaller burner producing higher heat fluxes. These peak heat fluxes were similar to those measured for burning ceilings in a corridor (i.e., one-dimensional ceiling flames) and for small wall fires. Heat fluxes from the unconfined ceiling fires were measured to decay at a rate between that measured for wall fires and that observed for a burning ceiling in a corridor.
1 r /Lf (calculation)
10
Ceiling Fires in a Corridor Heat fluxes from flames produced by burning ceilings in a corridor were investigated by Hasemi et al. [72]. Tests were performed beneath a 2.73-m-long ceiling with two 0.10-m-high soffits mounted along the length of the ceiling to form a 0.30-m-wide channel. At the closed end of the channel, a 0.30-m-wide, 0.04-m-long porous propane burner was mounted in the ceiling. Heat flux distributions along the
782
B.Y. Lattimer
Fig. 25.46 Flame length produced by a burning ceiling in a corridor [72]
3
LH = 0.0122QL
LH (m)
1
1
0 0
50
100
150
200
250
Qᐉ (kW/m)
corridor were measured for fire heat release rates ranging from 10 to 50 kW (33–166 kW per meter of corridor width). The intermittent flame lengths from these fires are seen in Fig. 25.46 to increase linearly with heat release rate per unit hallway width. A fit to these data produced the following relation to predict flame length due to a burning ceiling in a corridor: L f ¼ 0:0122Q
0
ð25:44Þ
The heat flux distributions along the center of the corridor are shown in Fig. 25.47 for the different fires considered in the study. The line in the plot represents a best fit to the methane line burner data of Hasemi [55]. Heat fluxes were measured to be constant at approximately 20 kW/m2 up to 0.4 Lf. Above this, heat fluxes were measured to decay at a slower rate than that previously measured for wall fires. Heat fluxes along a flame from a burning ceiling in a corridor (not shown in the figure) can be determined using the following expressions: 00 ð25:45aÞ q ¼ 20 x=L f 0:4 5=4 00 q ¼ 6:36 x=L f
x=L f > 0:4 ð25:45bÞ
Burning Parallel Vertical Surfaces A common configuration encountered when commodities are being stored in rooms or warehouses is parallel vertical surfaces. As a result, several studies have focused on both experimentally and analytically characterizing this configuration [62, 74, 75]. Ingason and de Ris [76] also performed experiments in a rack storage configuration with a fire between four equally spaced storage towers. Part of the work by Tamanini [74, 75] investigated the effects of wall spacing on the fuel mass loss rate of combustible parallel vertical walls. Walls were 0.94 m high and 0.460 m wide with the spacing varied from 0.470 to 0.025 m and no floor at the base of the walls. The average fuel mass loss rate was measured to increase (i.e., the average heat flux to the wall increased) with an increase in spacing until the spacing was less than 0.076 m. At a spacing of 0.038 m or less, the average mass loss rate was less than that measured with no parallel wall. At a spacing of 0.038 m (or wall height divided by spacing of 25 with a fire size of approximately 180 kW), the flames from the two burning surfaces were observed to merge together approximately two-thirds the distance up the walls.
25
Heat Transfer from Fires to Surfaces
783
Fig. 25.47 Heat fluxes to the ceiling of a corridor [72]
100
Heat flux, q (kW/m2)
Solid line: wall fire correlation
Q = 10 kW Q = 15 kW Q = 20 kW Q = 25 kW Q = 30 kW Q = 35 kW Q = 40 kW Q = 45 kW Q = 50 kW
10
1 0.01
0.1
1
10
x /Lf
Though not evaluated in this study, the presence of a floor may cause the flames to merge together at larger spacings. Heat fluxes due to a fire between two parallel vertical surfaces were measured by Foley and Drysdale [62]. The study was performed using two 0.61-m-wide, 0.81-m-high walls separated by a gap of 0.06, 0.10, or 0.14 m. The fire was a 0.60-m-long propane line burner that had either a 11.6-kW/m or a 20.9-kW/m heat release rate per unit length. One of the walls was instrumented with four heat flux gauges that could be moved to measure the heat flux distribution on the walls. Heat fluxes were measured as far as 0.150 m from the centerline of the wall. For the different gap and heat release rate fires, heat fluxes were measured with the burner against the instrumented wall and with the fire in the center of the gap between the two walls. The effect of air entrainment flow path was also evaluated by performing tests with and without a floor between the panels. Results were correlated using a/d where the spacing between the walls, a, is divided by the burner length, d, and the dimensionless quantity Qd*, as defined in Equation 25.14, with d being the burner length.
The heat flux distributions measured with the fire against the instrumented wall are shown in Fig. 25.48. As seen in Fig. 25.48a, heat fluxes reached as high as 80 kW/m2 with an open base (no floor between the walls). Heat fluxes on the panel can be estimated using the following expression:
0 0:38 1:47 00 *2=3 q ¼ 67:38 zða=d Þ0:36 = Qd d y =d ð25:46Þ where y0 ¼ 0.5d y with y being the horizontal distance from the burner centerline. With the base of the walls closed (a floor between the walls) and the fire against the instrumented wall, the heat flux data in Fig. 25.48b were seen to be as high as 70 kW/m2. Heat fluxes for this case are slightly lower than the open-base case. A similar expression to that in Equation 25.45b was developed by Foley and Drysdale [62] to predict heat fluxes with the base of the walls closed:
0 2=3 1:2 00 *2=3 q ¼ 23:31 zða=dÞ0:905 = Qd d y =d ð25:47Þ
784
B.Y. Lattimer Heat transfer from flames
a
b
10
100
8 6
8 6
4
4
2
2
Heat flux, q (kW/m2)
Heat flux, q (kW/m2)
100
8 6 4 2
1
10
8 6 4 2
1 8 6
8 6
4
4 8
1
2 [z(a/d )
4 0.36
/Q d
* 2/3
6
8
d(y¢/d )
2
10 0.38
]
0.1
2
4 [z(a/d )
6 8 0.905
2 4 6 8 1 10 2/3 0.67 /Q d * d(y¢/d ) ]
Fig. 25.48 Heat fluxes measured with the fire against the instrumented wall with (a) an open base (no floor in the gap) and (b) a closed base (a floor in the gap): 0.140-m
spacing (✯), 0.10-m spacing (○), 0.060-m spacing (Δ); open symbols, Q0 ¼ 11.6 kW/m; closed symbols, Q0 ¼ 20.9 kW/m [62]
Heat fluxes were also measured with the fire in the center of the gap between the two walls. In the case with an open base (no floor), the heat fluxes were measured to be 50 % lower than those measured with the fire against the instrumented wall. As seen in Fig. 25.49a, the peak heat flux was measured to be approximately 30 kW/m2. This decrease was attributed to the air being drawn up at the base of the walls, preventing the fire from attaching to the instrumented wall. The line in the figure is the best fit to the data, which are given by the following expression:
0 0:806 0:797 00 q ¼ 22:71 zða=d Þ1:04 = Q*d d y =d
into the fire through the sides of the gap. The following expression can be used to estimate the heat flux to the walls for this case:
0 1:34 1:04 00 q ¼ 23:94 zða=d Þ1:7 = Q*D d y =d
ð25:48Þ The case with the base closed and the fire in the center of the gap resulted in the highest heat fluxes measured in the study. As seen in Fig. 25.49b, heat fluxes greater than 100 kW/m2 were measured in this case. In the tests with the high heat fluxes, the flames were observed to occupy the width of the gap. This behavior was attributed to only allowing air to be entrained
ð25:49Þ Additional research needs to be performed with this configuration to further validate the results. Larger-scale tests need to be conducted to verify the results of Foley and Drysdale [62]. In addition, the transition from wall fire heat fluxes to gap fire heat fluxes needs to be identified. Heat fluxes produced by area fires between parallel walls also need to be quantified.
Exposure Fires and Burning Walls and Ceilings A series of tests were performed by Lattimer et al. [77] to investigate the use of steady-state heat flux correlations, developed using burners
25
Heat Transfer from Fires to Surfaces
785
a
b 2
2 100
8 6 4 Heat flux, q (kW/m2)
Heat flux, q (kW/m2)
100
2 10
8 6 4 2
1
2 10
6 8
2 1
4
6 8
2
4
10 [z(a/d ) 1.04 /Q*d d(y/d ) 0.86 ]
8 6 4 2
1
8 6 4
8 6 4
8 6 4 68 0.1
2
4 68
2 4 68 1 10 [z(a/d ) 1.7 /Q*d d(y/d) 1.34 ]
2
Fig. 25.49 Heat fluxes measured with the fire in the center of the gap with (a) an open base (no floor in the gap) and (b) a closed base (a floor in the gap): 0.140-m
spacing (✯), 0.10-m spacing (○), 0.060-m spacing (Δ); open symbols, Q0 ¼ 11.6 kW/m; closed symbols, Q0 ¼ 20.9 kW/m [62]
and noncombustible boundaries, for estimating the heat fluxes in growing fires. Three tests were performed in an 2.4-m-high, 2.0-m-wide open corner lined with a combustible material. A single test was performed on three different lining materials: 12-mm-thick Douglas fir plywood, 12-mm-thick E-glass fire-retarded vinyl ester, and 88-mm-thick sandwich composite (76-mm-thick balsa wood with 6-mm-thick E-glass fire-retarded vinyl ester facings). The initiating fire in the test was a square propane sand burner with a 0.17 m side length and a heat release rate of 100 kW for 10 min followed by 300 kW for 10 min, total test time of 20 min. Total heat release during the test was measured by performing oxygen calorimetry on the gases collected in an exhaust hood, and flame lengths were measured through visual observation. Heat fluxes were measured 0.075 m from the corner along at eight different elevations, 0.15 m below the ceiling along the top of the wall, and along the ceiling on a 45 diagonal out from the corner. Due to mounting the heat flux gauges along the top of the wall too far below the ceiling, no
comparison between predicted and measured heat fluxes was done for the region along the top of the wall. Transient data were averaged every 30 s to create a reasonable amount of data to compare to the developed correlations. A comparison of the flame length predicted using Equations 25.13 and 25.36 and the measured flame length is shown in Fig. 25.50. The dimensionless length used in this calculation was the width of the burner, D, while the burning had spread laterally less than the width of the burner. When the average lateral flame spread 0.90 m above the floor exceeded the burner width, the dimensionless length was taken to be the horizontal flame front location 0.9 m above the floor. The flame front at 0.9 m above the floor was approximately the average flame front on the wall. Heat fluxes to the walls near the corner are provided in Fig. 25.51. Measured heat fluxes were slightly higher than values predicted by both the initiating fire correlation and the burning boundary correlation (assuming the heat flux is
786 28
24
20
16 Lf,tip /d
Fig. 25.50 Flame lengths measured in combustible corner fire tests compared with the flame length correlations developed for initiating and burning boundary fires in Equations 25.13 and 25.36: plywood (□), E-glass FR vinyl ester (○), sandwich composite (Δ) [77]
B.Y. Lattimer
12
8
4
0 0
2
4
6
8
10
12
Q *d = Q /(ρ∞CρT∞g
16
d
18
20
22
)
1000
Heat flux in corner, q (kW/m2)
Fig. 25.51 Heat fluxes along the height of the corner in tests with different combustible boundaries compared with the heat flux predicted using Equation 25.38 (—) and Equation 25.15 ( ): plywood (□), E-glass FR vinyl ester (○), sandwich composite (Δ) [77]
14 1/2 5/2
100
10
1
0.1 0.01
1
0.1 z /Lf,tip
10
Heat Transfer from Fires to Surfaces
Fig. 25.52 Heat fluxes to the ceiling during open corner tests with the corner lined with a combustible material compared with the heat flux predicted using Equation 25.43: plywood (□), E-glass FR vinyl ester (○), sandwich composite (Δ) [77]
787 1000
Heat flux to ceiling, q (kW/m2)
25
100
10
1
0.1 0.1
independent of the wall heat release rate). Inspection of the data indicates better agreement between the data and the correlations can be achieved using the initiating fire correlation up to when ignition occurs in the corner. After this, the corner wall heat flux correlations in Equations 25.38b and 25.40 can be used to estimate heat fluxes in the corner. A comparison of the heat fluxes along the ceiling and the heat fluxes predicted using Equation 25.43 is shown in Fig. 25.52. In general, heat fluxes are adequately predicted by the correlation, with heat fluxes as high as 130 kW/m2 measured during a test. This indicates that Equation 25.43 can be used to estimate heat fluxes to the ceiling near the corner containing the fire.
Fires from Windows Fires that have reached flashover conditions typically result in burning outside of the actual burn room. Flames from postflashover fires extending out of a building through a window will buoyantly rise along the exterior of the building. Experiments characterizing the heat fluxes to the wall above the
1 (r + H ) /Lf,tip
10
window of a postflashover compartment fire have been performed by Oleszkiewicz [78, 79], Thomas and Bullen [80], and Beitel and Evans [81]. In these studies, heat fluxes as high as 200 kW/m2 have been measured. Experiments performed by Oleszkiewicz [78, 79] were conducted using two differently sized full-scale rooms with a wall above the window that extended as much as two stories above the burn room (Fig. 25.53). The effects of window size, window aspect ratio, and fire size inside the compartment were evaluated in the study. Heat fluxes from the flames extending outside the burn room for different door sizes and different fires sizes are shown in Figs. 25.54 and 25.55 for propane gas fires. Note that the heat release rate of the fires stated in Figs. 25.54 and 25.55 is the ideal heat release rate of the compartment fire, which was determined from the gas flow rate and the heat of combustion for propane. Data in Fig. 25.54 show the effect of fire heat release rate and window size on the heat flux 0.5 m above the window. The distribution in the heat flux along the height exterior wall is shown in Fig. 25.55 for the case with a window 2.6 m wide and 1.37 m high.
788
B.Y. Lattimer
Vertical channel test apparatus Target wall
Quintiere and Cleary [32] found that flame lengths for this situation can be estimated using the relation developed by Yokoi [82]. With Lf being the distance from the bottom of the opening to the average flame height, the heat release rate outside of the compartment, Q, and the effective diameter of the window, D, can be used to predict the flame length above the window with the following expression: 2=3 Q L f ¼ 0:0321 ð25:50aÞ D where
rffiffiffiffiffiffiffiffiffiffiffiffi Ho W o D¼2 2π
ð25:50bÞ
Window
Heat Fluxes in Standard Tests
Burn room
Fig. 25.53 Exterior wall fire test facility used by Oleszkiewicz [79]
200
Heat flux (kW/m2)
Fig. 25.54 Heat fluxes from a window flame 0.5 m above the top of the window for different size propane fires inside the compartment [79]
Heat fluxes in some standard tests are provided in this section to compare with heat fluxes measured in realistic geometries presented in this chapter. Heat fluxes in room-corner tests such as ISO 9705 and NFPA 286, Standard Methods of Fire Tests for Evaluating Contribution of Wall and Ceiling Interior Finish to Room
0.94 × 2.00 0.94 × 2.70 2.60 × 1.37 2.60 × 2.00 2.60 × 2.70 (width × height)
150
100
50
0 5
6
7 8 9 Heat release rate (MW)
10
11
Heat Transfer from Fires to Surfaces
Fig. 25.55 Heat fluxes from window flames along the exterior wall above a 2.6-m-wide, 1.37-m-high window [79]
789
200
Heat flux (kW/m2)
25
10.3 MW 8.6 MW 6.9 MW 5.5 MW
150
100
50
0 0
Fire Growth, can be determined using heat flux data previously presented in the section on heat fluxes from exposure fires in a corner. This section will focus on heat fluxes produced in other tests including fire resistance test furnaces and the ASTM E84 flame spread test. Note that these heat fluxes, along with most data previously presented for room-corner tests, were typically measured with a noncombustible, insulating surface mounted to the test apparatus. The heat flux to actual test specimens could be different depending on specimen thermal properties, the occurrence of sample ignition and burning, as well as other factors.
Fire Resistance Tests Several furnace fire exposures are used throughout the world to evaluate the fire resistance of products. These fire exposures have peak temperatures ranging from 1050 C to 1350 C after a 3-h exposure (Fig. 25.56). The type of exposure used depends on the end-use application of the product. Tunnel and offshore oil rig applications have the highest temperature, most severe fire exposures, whereas less severe exposures are used for different building applications. The ASTM E119 [83] and ISO 834 [84] timetemperature curves are perhaps the most common furnace exposures used in fire resistance testing.
1
2 3 Height above window (m)
4
These furnace exposures are utilized to evaluate the fire resistance of structural elements on buildings, on ships, and in some transportation applications (e.g., railcars). ASTM E119 is primarily used in North America whereas ISO 834 is used more internationally (e.g., Europe and Australia). As seen in Fig. 25.56, the two timetemperature curves are similar, with the ISO 834 temperatures being slightly higher at times greater than 1 h. The ASTM E119 furnace exposure is measured using shielded thermocouples, whereas the ISO 834 furnace exposure is measured using sheathed thermocouples. Though the time-temperature curves in these tests are similar, the actual heat flux exposure early in the ASTM E119 fire exposure is more severe due to the type of thermocouples used to control the furnace [85, 86]. The European standard EN1363-1 [87] uses the ISO 834 timetemperature curve, but the furnace is controlled using plate thermometers, which provide a more severe exposure compared with ISO 834 thermocouples for the test duration [88, 89]. Compared with ASTM E119 shielded thermocouples, Sultan [90] measured that plate thermometers resulted in a slightly less severe exposure during the first 10 min of the test, but thereafter the thermal exposures were the same. The total heat flux measured in an ASTM E119 furnace test is provided in Fig. 25.57 for a wall and floor furnace. Total heat fluxes were measured using a water-cooled Gardon gauge.
790
B.Y. Lattimer
Fig. 25.56 Furnace timetemperature exposure curves
1400
Furnace temperature (°C)
1200 1000 UL 1709 EN1363-2 HC Modified HC RABT-ZTV(train) RABT-ZTV(car) RWS ASTM E119 ISO 834
800 600 400 200 0 0
2 Time (hr)
3
4
180 160
Heat flux (kW/m )
140 2
Fig. 25.57 Heat flux measured during ASTM E119 furnace exposure in floor and wall furnaces. Blackbody heat flux was calculated from the ASTM E119 furnace temperature curve
1
120 100 80 60 Measured-floor Measured-wall Blackbody
40 20 0 0
20
40
60
80
100
120
140
Time (min)
In this test, gaseous fuel was used and the temperature was controlled with ASTM E119 shielded thermocouples [91]. The wall furnace was lined with ceramic fiber while the floor furnace was lined with brick. The same furnace controlled with a plate thermometer provided similar heat flux levels at times after 10 min. Also provided in the plot is the blackbody heat flux based on the furnace temperatures specified in ASTM E119. As seen in the figure, the blackbody heat flux is similar to heat fluxes measured in the furnace except during the initial 10 min. The higher temperature fire exposure curves in Fig. 25.56 are used to evaluate products used in petrochemical, offshore oil platform, and some tunnel applications. The UL 1709 [92]
hydrocarbon pool fire exposure and the EN1363-2 [93] hydrocarbon curve (HC) are typically used for offshore oil platform applications, whereas the other higher-temperature curves are used to represent a large hydrocarbon fire inside a tunnel. The UL 1709 and EN1363-2 [93] both have a maximum gas temperature of 1100 C; however, the UL 1709 exposure reaches 1100 C faster than does the EN1363-2 exposure (in 5 min versus after 25 min, respectively). Unique to this fire exposure curve, the UL 1709 fire exposure also has a heat flux requirement. During a calibration test with a UL 1709 exposure, the heat flux as measured from a water-cooled heat flux gauge mounted to a calibration specimen must be
25
Heat Transfer from Fires to Surfaces
791
204 16 kW/m2 while the furnace temperature is 1093 111 C. This heat flux is approximately equal to the blackbody heat flux at the furnace temperature (i.e., 1093 C results in a blackbody flux of 197 kW/m2). The curves for tunnel applications have peak temperatures that range from 1200 to 1350 C. The RABT-ZTV curves were developed in Germany to represent different vehicle fires in tunnels. These curves reach a peak temperature of 1200 C in 5 min and remain at that temperature for 30–60 min. Thereafter, the temperatures decrease linearly with time to ambient conditions after 2.5–3.0 h. Estimated peak heat fluxes, as the blackbody flux using the peak furnace temperature, in these tests are 267 kW/m2. A modified version of the EN1363-2 HC curve has been used in France to represent fires in tunnels. The Modified HC curve peaks at 1300 C instead of 1100 C. Estimated peak heat flux in this test, based on the blackbody flux using the peak furnace temperature, is 347 kW/m2. The RWS fire curve was developed by the Rijkswaterstaat, Ministry of Transport, in the Netherlands based on results from testing conducted by TNO in the Netherlands. The RWS curve peaks at a temperature of 1350 C, which is the highest of all timetemperature curves. Estimated peak heat flux in this test, based on the blackbody flux using the peak furnace temperature, is 393 kW/m2. The potential for these temperatures in tunnel fires was validated through vehicle testing in the Fig. 25.58 Heat flux at the ASTM E84 burner impingement point
Runehamar test series, where temperatures ranging from 1280 C to 1365 C were measured [48].
ASTM E84 Tunnel Test The ASTM E84 test is a “tunnel” test that provides flame spread and smoke production data from wall and ceiling lining materials. The test chamber is approximately 18 in. (0.46 m) wide, 12 in. (0.30 m) high, and 25 ft (7.63 m) long, with a gas burner located at one end and exhaust ducting located at the other. The test material is oriented on the “ceiling” of the tunnel by attaching a 24-ft (7.32-m) long sample of the test material to the underside of the removable lid of the test chamber. A flow of 240 ft/min (1.22 m/s) is established through the test chamber. The initiating fire is an 88 kW gas burner located at one end of the sample. The flames from the two burner pipes impinge on the sample at two off-center locations, producing a flame that flows 1.2 m down the sample. Parker [94] measured heat fluxes from the initiating fire with a noncombustible ceiling in the tunnel. The highest heat fluxes were measured where the burner flames impinge on the ceiling. A plot of heat flux, measured using a watercooled heat flux gauge, at this location is shown in Fig. 25.58. The heat flux during the initial 2 min of the test was 20–30 kW/m2. By 4 min, the heat flux increased to 50–60 kW/m2 where it
70
Heat flux (kW/m2)
60 50 40 30 20 10 0
2
4
6 Time (min)
8
10
12
792
B.Y. Lattimer
Fig. 25.59 Calculated incident heat flux along the length of the ASTM E84 tunnel
50
Heat flux (kW/m2)
40
30
20
10
0 0
remained for the duration of the test (10 min). The increase in heat flux with time was attributed to reradation from the tunnel surfaces. Incident heat fluxes along the center of the tunnel length were calculated using surface temperature measurements. Figure 25.59 provides the heat fluxes after a 20-min exposure, which is 10 min longer than the actual test. Heat fluxes near the burner are approximately 40 kW/m2 and then decrease rapidly with distance along the tunnel. In a test with flames along the entire length of the tunnel, heat fluxes were calculated to be 70 kW/m2 at 2.0 m from the burner and 30 kW/ m2 at the end of the tunnel 7.3 m from the burner.
Cable Tests Gandhi et al. [95] measured heat fluxes due to the exposure fire in three different standard cable tests : UL 910, UL 1666, and UL 1685. Heat fluxes were measured using water-cooled Gardon gauges. The UL 910 test is conducted in the ASTM E84 tunnel apparatus to evaluate low power cables without conduit in air handling spaces. The sample is in a horizontal orientation for this test with the flame impinging on the underside of the cables. Average heat flux measurements along the length of the ASTM E84 tunnel where the cable would be located over the test
2
4 6 Distance along tunnel (m)
8
period are shown in Fig. 25.60. The peak heat flux was measured to be 49 kW/m2 approximately 1.0 m down the tunnel. The heat fluxes are similar to those determined by Parker [94], except the Gandhi et al. [95] measured the peak heat flux location 0.5 m further down the tunnel. Gandhi et al. [95] stated that this difference may be due to using actual heat flux gauges instead of using an inverse method as well as the sample location differences. Transient heat fluxes measured by Gandhi et al. [95] determined that the heat fluxes increase during the test by approximately 10 kW/m2 at locations 0.13–1.65 m along the tunnel. A UL 1666 test is used to evaluate cables used in high rise buildings installed in riser shafts or floor-to-floor installations. The sample is in a vertical orientation in this test adjacent to a diffusion burner. The exposure fire in this test produces a peak heat flux of 43 kW/m2 0.30 above the burner and decays to 6 kW/m2 by 1.5 m above the burner. A UL 1685 test is performed to evaluate cables used in applications other than air handling or floor-to-floor. The sample is located in a vertical orientation during the test with a propane gas-air premix burner impinging on the bottom of the cables. The exposure fire produced peak heat fluxes of 46 kW/m2 at the burner elevation and decayed to 2 kW/m2 by 1.5 m above the burner.
Heat Transfer from Fires to Surfaces
Fig. 25.60 Test average heat fluxes measured in the UL 910 experiment by Gandhi et al. [95] compared with the ASTM E84 measurements made by Parker [94]
793
60 ASTM E84 UL 910
50
Heat Flux (kW/m2)
25
40
30
20
10
0 0
2
4
6
8
Distance Along Tunnel (m)
Effects of Other Variables
Nomenclature
The environment in which a fire is burning can affect the heat flux levels incident on the surface. Studies have been conducted by Atreya and Mekki [96], Santo and Tamanini [97], Mekki et al. [98], and Chao and Fernandez-Pello to evaluate the impact of oxygen concentration on the heat fluxes transferred by flames to surfaces. In tests with methane fires, Atreya and Mekki [96] found that flame radiation (and the total heat flux to the surface) was increased by increasing the oxygen concentration. More important for most problems in fire is the effect of decreasing the oxygen concentration on heat fluxes from the flame. Santo and Tamanini [97] found that decreasing the surrounding oxygen concentration from 20.9 % to 18.0 % the radiative flux to an external target was decreased to an external target by 40 %. This decrease was attributed to a decrease in lower soot concentrations in flames in lower oxygen environments. Chao and Fernandez-Pello [99] found that this reduction in heat transfer to the surface reduces the flame spread rate along combustible panels.
a Cp d
D g H HB HC Ho h k LB LC Lweb
spacing between parallel walls (m) specific heat capacity of air at 300 K (0.998 kJ/[kg-K]) length of single side on L-shape burner, length of line burner, width of burning area on corner wall (m) length of single side of square burner, diameter (m) acceleration of gravity (9.81 m/s2) distance between fire and ceiling (m) distance between fire and lower flange of I-beam (m) distance between fire and upper flange of I-beam (m) height of room window (m) convective heat transfer coefficient (kW/[m2 -K]) thermal conductivity (kW/m-K) flame tip length along lower flange of I-beam (m) flame tip length along upper flange of I-beam (m) flame tip length along center of web on I-beam (m)
794
Lf Lf,tip LH Q Q0 Q*
B.Y. Lattimer
average flame length (m) flame tip length (m) flame extension along ceiling away from stagnation point (m) fire heat release rate (kW) fire heat release rate per unit width (kW/m) dimensionless parameter, Q*D ¼ Q pffiffi 5=2 , with D being length scale gD ρ C T 1
r 00
q Tf Tg Ts T1 Wo w
x y y0 Z z z0
material surface emissivity () ambient density of air (1.2 kg/m3) constant (3.14159) Stefan-Boltzman constant 5:67 2 11 4 10 kW= m K
Subscripts cl conv d D H hfg B C
defined using Hweb as length scale incident measured max level net peak radiative reradiated material surface
p 1
distance from corner or stagnation point to measurement location (m) heat flux (kW/m2) local gas temperature (K) room gas temperature (K) material surface temperature (K) ambient temperature (300 K) width of room window (m) dimensionless distance along ceiling or I-beam, 0 0 w ¼ r þ HB þ z = LHB þ HB þ z horizontal coordinate (m) horizontal coordinate (m) distance from center of line burner, 0 y ¼ 0:5d y ðmÞ burner height (m) vertical coordinate (m) virtual source location (m)
Greek Letters ε ρ1 π σ
web inc m max net peak rad rr s
centerline convective defined using d as length scale defined using D as length scale defined using H as length scale heat flux gauge defined using HB as length scale defined using HC as length scale
References 1. M. Kokkala, “Heat Transfer to and Ignition of Ceiling by an Impinging Diffusion Flame,” VTT Research Report 586, Technical Research Centre of Finland, Escopo, Finland (1989). 2. M. Kokkala, “Experimental Study of Heat Transfer to Ceiling from an Impinging Diffusion Flame,” Fire Safety Science—Proceedings of the 3rd International Symposium, Elsevier Applied Science, New York, pp. 261–270 (1991). 3. H.Z. You and G.M. Faeth, “Ceiling Heat Transfer During Fire Plume and Fire Impingement,” Fire and Materials, 3, 3, pp. 140–147 (1979a). 4. H.Z. You and G.M. Faeth, “An Investigation of Fire Impingement on a Horizontal Ceiling,” NBS-GCR79-188, U.S. Department of Commerce, Washington, DC (1979b). 5. Wickstrom, U., “Adiabatic Surface Temperature and the Plate Thermometer for Calculating Heat Transfer and Controlling Fire Resistance Furnaces,” Fire Safety Science -Proceedings of the Ninth Fire Safety Science, 2008, pp.1227–1238 6. Wickstrom, U. Dathinh, D., and McGrattan, K., “Adiabatic Surface Temperature for Calculating Heat Transfer to Fire Exposed Structures,” Proceedings of the 11th International Conference on Fire Science and Engineering Interflam, 2007 7. Wickstrom, U., “The Plate Thermometer-A Simple Instrument for Reaching Harmonized Fire Resistance Tests,” Fire Technology 2:195–208 8. Duthinh, D., McGrattan, K., and Khaskia, A., (2008) “Recent Advances in Fire-Structural Analysis,” Fire Safety Journal 43:161–167 9. L.T. Cowley, “Behaviour of Oil and Gas Fires in the Presence of Confinement and Obstacles,” Miscellaneous Report TNMR.91.006, Shell Research Limited, Thornton Research Center, Combustion and Fuels Department, Chester, UK (Feb. 1991). 10. J.J. Gregory, R. Mata, and N.R. Keltner, “Thermal Measurements in a Series of Large Pool Fires,” Sandia Report Number SAND85-0196, Sandia National Laboratories, Albuquerque, NM (1987). 11. L.H. Russell and J.A. Canfield, “Experimental Measurements of Heat Transfer to a Cylinder
25
Heat Transfer from Fires to Surfaces
Immersed in a Large Aviation Fuel Fire,” Journal of Heat Transfer, pp. 397–404 (Aug. 1973). 12. G. Wachtell and J. Langhaar, “Fire Test and Thermal Behavior of 150-Ton Lead-Shielded Casks,” DP 1070, Engineering and Equipment, TID-4500, E.I. DuPont De Nemours and Co., Wilmington, DE (1966). 13. C. Anderson et al., “Effects of a Fire Environment on a Rail Tank Car Filled with LPG,” Report No. FRA-OR&D 75–31, U.S. Department of Transportation, Federal Railroad Administration, Washington, DC (1974). 14. National Academy of Science, Committee on Hazardous Materials, Division of Chemistry, and Chemical Technology (National Research Council), PressureRelieving Systems for Marine Cargo Bulk Liquid Containers, National Academy of Sciences, Washington, DC (1973). 15. K. Moodie et al., “Total Pool Fire Engulfment Trials on a 5-Tonne LPG Tank,” HSE Internal Report No. IR/L/FR/87/27, Health and Safety Executive, London, UK (1987). 16. M. Tunc and J. Venart, “Incident Radiation from an Engulfing Pool Fire to a Horizontal Cylinder, Part I and II,” Fire Safety Journal, 8, pp. 81–95 (1985). 17. W. McLain, “Investigation of the Fire Safety Characteristics of Portable Polyethylene Tanks Containing Flammable Liquids,” Report No. CG-M1-88, U.S. Coast Guard, Washington, DC (1988). 18. A. Taylor et al., “Engulfment Fire Tests on Road Tanker Sections,” Rarde Technical Report 7/75, Controller HMSO, London (1975). 19. M. Schneider and L. Kent, “Measurement of Gas Velocities and Temperatures in a Large Open Pool Fire,” Fire Technology, pp. 51–81 (Feb. 1989). 20. G. Back, C.L. Beyler, P. DiNenno, and P. Tatem, “Wall Incident Heat Flux Distributions Resulting from an Adjacent Fire,” Fire Safety Science— Proceedings of the 4th International Symposium, International Association of Fire Safety Science, Ottawa, Canada, pp. 241–252 (1994). 21. G. Heskestad, “Luminous Heights of Turbulent Diffusion Flames,” Fire Safety Journal, 5, pp. 103–108 (1983). 22. D. Gross and J.B. Fang, “The Definition of a Low Intensity Fire,” in NBS Special Publication 361, Volume 1: Performance Concept in Buildings, Proceeding of the Joint RILEM-ASTM-CIB Symposium, National Bureau of Standards, Washington, DC, pp. 677–686 (1972). 23. T. Mizuno and K. Kawagoe, “Burning Behaviour of Upholstered Chairs, Part 2: Burning Rate of Chairs in Fire Tests,” Fire Science and Technology, 5, 1, pp. 69–78 (1985). 24. M. Daikoku and K. Saito, “A Study of Thermal Characteristics of Vertical Corner Wall in Room Fire,” Proceedings of the ASME/JSME, Thermal Engineering, Book No. H0933C-1995 (L.S. Fletcher and T. Aihara, eds.), pp. 83–90 (1995). 25. Y. Hasemi, M. Yoshida, S. Takashima, R. Kikuchi, and Y. Yokobayashi, “Flame Length and Flame Heat Transfer Correlations in Corner-Wall and Corner-
795 Wall-Ceiling Configurations,” in Proceedings of Interflam ‘96 (Franks and Grayson, eds.), Interscience Communications Ltd., London, pp. 179–188 (1996). 26. M. Kokkala, “Characteristics of a Flame in an Open Corner of Walls,” in Proceedings from Interflam ‘93, Interscience Communications, Ltd., London, pp. 13–24 (1993). 27. T. Ohlemiller, T. Cleary, and J. Shields, “Effect of Ignition Conditions on Upward Flame Spread on a Composite Material in a Corner Configuration,” Fire Safety Journal, 31, pp. 331–344 (1998). 28. T.J. Ohlemiller and J.R. Shields, “The Effect of Surface Coatings on Fire Growth Over Composite Materials in a Corner Configuration,” Fire Safety Journal, 32, 2, pp. 173–193 (1999b). 29. B.Y. Lattimer and U. Sorathia, “Thermal Characteristics of Fires in a Noncombustible Corner,” Fire Safety Journal, 38, pp. 709–745 (2003). 30. R.B. Williamson, A. Revenaugh, and F.W. Mowrer, “Ignition Sources in Room Fire Tests and Some Implications for Flame Spread Evaluation,” Fire Safety Science—Proceedings of the 3rd International Symposium, Elsevier Applied Science, New York, pp. 657–666 (1991). 31. H. Tran and M. Janssens, “Modeling the Burner Source Used in the ASTM Room Fire Test,” Journal of Fire Protection Engineering, 5, 2, pp. 53–66 (1993). 32. J.G. Quintiere and T.G. Cleary, “Heat Flux from Flames to Vertical Surfaces,” Fire Technology, 30, 2, pp. 209–231 (1994). 33. S.E. Dillon, “Analysis of the ISO 9705 Room/Corner Test: Simulations, Correlations and Heat Flux Measurements,” NIST-GCR-98-756, U.S. Department of Commerce, National Institute of Standards and Technology, Washington, DC (1998). 34. International Standards Organization, ISO 9705:1993 (E), International Standard for Fire Tests—Full-Scale Room Test for Surface Products, International Organization for Standardization (ISO), Geneva, Switzerland (1993). 35. T. Tanaka, I. Nakaya, and M. Yoshida, “Full Scale Experiments for Determining the Burning Conditions to Be Applied to Toxicity Tests,” Fire Safety Science—Proceedings of the 1st International Symposium, Hemisphere Publishing, Gaithersburg, MD, pp. 129–138 (1985). 36. Tofilo, P., Delicatsios, M.A., and Silcock, G.W.H., (2005), “Effect of Fuel Sootiness on the Heat Fluxes to the Walls in Enclosure Fires,” Fire Safety Science-Proceedings of the Eighth International Symposium, Beijing, China, pp. 987–998. 37. W. Takashi et al., “Flame and Plume Behavior in and Near a Corner of Walls,” Fire Safety Science— Proceedings of the 5th International Symposium (Y. Hasemi, ed.), International Association for Fire Safety Science, Melbourne, Australia, pp. 261–271 (1997). 38. Y. Hasemi, S. Yokobayashi, T. Wakamatsu, and A. Ptchelintsev, “Fire Safety of Building Components Exposed to a Localized Fire—Scope and Experiments
796 on Ceiling/Beam System Exposed to a Localized Fire,” Proceedings from ASIAFLAM, Kowloon, Hong Kong, pp. 51–361 (1995). 39. R.L. Alpert, “Convective Heat Transfer in the Impingement Region of a Buoyant Plume,” Transactions of ASME, 109, pp. 120–124 (1987). 40. H.Z. You, “An Investigation of Fire-Plume Impingement on a Horizontal Ceiling 2— Impingement and Ceiling-Jet Regions,” Fire and Materials, 9, 1, pp. 46–56 (1985). 41. L.Y. Cooper, “Heat Transfer from a Buoyant Plume to an Unconfined Ceiling,” ASME Journal of Heat Transfer, 104, pp. 446–452 (1982). 42. T. Wakamatsu, personal communication (Sept. 1999). 43. J. Myllymaki and M. Kokkala, “Thermal Exposure to a High Welded I-Beam Above a Pool Fire,” First International Workshop on Structures in Fires, Copenhagen, pp. 211–226 (2000). 44. P.L. Hinkley, H.G.H. Wraight, and C.R. Theobald, “The Contribution of Flames under Ceilings to Fire Spread in Compartments,” Fire Safety Journal, 7, pp. 227–242 (1984). 45. P.L. Hinkley, H.G.H. Wraight, and C.R. Theobald, “The Contribution of Flames under Ceilings to Fire Spread in Compartments, Part I: Incombustible Ceilings,” Fire Research Note No. 712, Fire Research Stations, Borehamwood, Herts, UK (1968). 46. P.L. Hinkley, H.G.H. Wraight, and C.R. Theobald, “The Contribution of Flames under Ceilings to Fire Spread in Compartments, Part II: Combustible Ceiling Linings,” Fire Research Note No. 743, Fire Research Stations, Borehamwood, Herts, UK (1969). 47. B. Lattimer, J. Beitel, and C. Mealy, “Heat Fluxes to a Corridor Ceiling,” unpublished data (2006). 48. A. Lonnermark and H. Ingason, “Fire Spread and Flame Length in Large-Scale Tunnel Fires,” Fire Technology, 42, pp. 283–302 (2006). 49. T. Wakamatsu, Y. Hasemi, Y. Yokobayashi, and A.V. Ptchelintsev, “Experimental Study on the Heating Mechanism of a Steel Beam Under Ceiling Exposed to a Localized Fire,” in Proceedings from Interflam ’96 (Franks and Grayson, eds.), Interscience Communications, Ltd., London, pp. 509–518 (1996). 50. T. Ahmad and G.M. Faeth, “Fire Induced Plumes Along a Vertical Wall, Part III: The Turbulent Combusting Plume,” NBS Report for Grant No. 5–9020, U.S. Department of Commerce, Washington, DC (1978). 51. T. Ahmad and G.M. Faeth, “Turbulent Wall Fires,” in 17th Symposium (International) on Combustion, Combustion Institute, Pittsburgh, PA, pp. 1149–1160 (1979). 52. J.G. Quintiere, M. Harkelroad, and Y. Hasemi, “Wall Flames and Implications for Upward Flame Spread,” AIAA-85-0456, American Institute of Aeronautics and Astronautics, Reno, NV (1985). 53. L. Orloff, J. de Ris, and G.H. Markstein, “Upward Turbulent Fire Spread and Burning of Fuel Surface,” in 15th Symposium (International) on Combustion,
B.Y. Lattimer Combustion Insititute, Pittsburgh, PA, pp. 183–192 (1975). 54. M.A. Delicatsios, “Flame Heights in Turbulent Wall Fires with Significant Flame Radiation,” Combustion Science and Technology, 39, pp. 195–214 (1984). 55. Y. Hasemi, “Experimental Wall Flame Heat Transfer Correlations for the Analysis of Upward Wall Flame Spread,” Fire Science and Technology, 4, 2, pp. 75–90 (1984). 56. H. Mitler, “Predicting the Spread Rates on Vertical Surfaces,” in 23rd Symposium (International) on Combustion, Combustion Institute, Pittsburgh, PA, pp. 1715–1721 (1990). 57. C.L. Beyler, S.P. Hunt, N. Iqbal, and F.W. Williams, “A Computer Model of Upward Flame Spread on Vertical Surfaces,” in Fire Safety Science— Proceedings of the 5th International Symposium (Y. Hasemi, ed.), International Association for Fire Safety Science, Melbourne, Australia, pp. 297–308 (1997). 58. F.W. Williams, C.L. Beyler, S.P. Hunt, and N. Iqbal, “Upward Flame Spread on Vertical Surfaces,” NRL/ MR/6180—97-7908, Navy Technology for Safety and Survivability, Chemistry Division (1997). 59. Y. Hasemi, “Thermal Modeling of Upward Wall Flame Spread,” Fire Safety Science—Proceedings of the 1st International Symposium, Hemisphere Publishing, Gaithersburg, MD, pp. 87–96 (1986). 60. Y. Hasemi, “Deterministic Properties of Turbulent Flames and Implications on Fire Growth,” Interflam ’88, John Wiley and Sons, Cambridge, UK, pp. 45–52 (1988). 61. M. Kokkala, D. Baroudi, and W.J. Parker, “Upward Flame Spread on Wooden Surface Products: Experiments and Numerical Modelling,” Fire Safety Science—Proceedings of the Fifth International Symposium, International Association for Fire Safety Science, Melbourne, Australia, pp. 300–320 (1997). 62. M. Foley and D.D. Drysdale, “Heat Transfer from Flames Between Vertical Parallel Walls,” Fire Safety Journal, 24, pp. 53–73 (1995). 63. A.K. Kulkarni, C.I. Kim, and C.H. Kuo, “Heat Flux, Mass Loss Rate and Upward Flame Spread for Burning Vertical Walls,” NIST-GCR-90-584, U.S. Department of Commerce, Washington, DC (1990). 64. A.K. Kulkarni, C.I. Kim, and C.H. Kuo, “Turbulent Upward Flame Spread for Burning Vertical Walls Made of Finite Thickness,” NIST-GCR-91-597, U.S. Department of Commerce, Washington, DC (1991). 65. L. Orloff, A.T. Modak, and R.L. Alpert, “Burning of Large-Scale Vertical Surfaces,” in 16th Symposium (International) on Combustion, Combustion Institute, Pittsburgh, PA, pp. 1345–1354 (1977). 66. G.H. Markstein and J. de Ris, “Wall-Fire Radiant Emission, Part 2: Radiation and Heat Transfer from Porous-Metal Wall Burner Flames,” in 24th Symposium (International) on Combustion, Combustion Institute, Pittsburgh, PA, pp. 1747–1752 (1992).
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67. Kahn, M., et al. “Combustion Characteristics of Materials and Generation of Fire Products” SFPE Handbook of Fire Protection Engineering, 5th ed. (M. J. Hurley, ed.), Springer (2015). 68. M.M. Delichatsios, P. Wu, M.A. Delichatsios, G.D. Lougheed, G.P. Crampton, C. Qian, H. Ishida, and K. Saito, “Effect of External Radiant Heat Flux on Upward Flame Spread: Measurements on Plywood and Numerical Predictions,” Fire Safety Science— Proceedings of the 4th International Symposium, International Association of Fire Safety Science, pp. 421–432 (1994). 69. T.J. Ohlemiller and T.G. Cleary, “Upward Flame Spread on Composite Materials,” Fire Safety Journal, 32, pp. 159–172 (1999a). 70. C. Qian, H. Ishida, and K. Saito, “Upward Flame Spread Along PMMA Vertical Corner Walls, Part II: Mechanism of M Shape Pyrolysis Front Formation,” Combustion and Flame, 99, pp. 331–338 (1994a). 71. C. Qian and K. Saito, “An Empirical Model for Upward Flame Spread over Vertical Flat and Corner Walls,” in Fire Safety Sceince—Proceedings from the 5th International Symposium (Y. Hasemi, ed.), Melbourne, Australia, pp. 285–296 (1994b). 72. Y. Hasemi, M. Yoshida, Y. Yokobayashi, and T. Wakamatsu, “Flame Heat Transfer and Concurrent Flame Spread in a Ceiling Fire,” in Fire Safety Science—Proceedings from the 5th International Symposium (Y. Hasemi, ed.), International Association for Fire Safety Science, Melbourne, Australia, pp. 379–390 (1997). 73. Y. Hasemi, M. Yoshida, and R. Takaike, “Flame Length and Flame Heat Transfer Correlations in Ceiling Fires,” poster at Fire Safety Science—6th International Symposium, International Association for Fire Safety Science, Poitiers, France (1999). 74. F. Tamanini, “Calculations and Experiments on the Turbulent Burning of Vertical Walls in Single and Parallel Configurations,” FMRC J.I.OAOE7.BU-2, FMRC Technical Report, Factory Mutual Research Corporation, Norwood, MA (1979). 75. F. Tamanini and A.N. Moussa, “Experiments on the Turbulent Burning of Vertical Parallel Walls,” Combustion Science and Technology, 23, pp. 143–151 (1980). 76. H. Ingason and J. de Ris, “Flame Heat Transfer in Storage Geometries,” Fire Safety Journal, 31, pp. 39–60 (1998). 77. B.Y. Lattimer and H. Sorathia, “Thermal Characteristics of Fires in a Combustible Corner,” Fire Safety Journal, 38, pp. 747–770 (2003). 78. I. Oleszkiewicz, “Heat Transfer from a Window Fire Plume to a Building Fac¸ade,” ASME HTD, 23, pp. 163–170 (1989). 79. I. Oleszkiewicz, “Fire Exposure to Exterior Walls and Flame Spread on Combustible Cladding,” Fire Technology, 26, 4, pp. 357–375 (1990). 80. P.H. Thomas and M.L. Bullen, “Compartment Fires with Non-Cellulosic Fuels,” in 17th Symposium (International) on Combustion, Combustion Institute, Pittsburgh, PA, pp. 1139–1148 (1979).
797 81. J.J. Beitel and W.R. Evans, “Multi-Story Fire Evaluation Program,” SwRI Project 01–6112, Final Report, Volume 1, Southwest Research Institute, San Antonio, TX, and Society of the Plastics Industry, Inc., New York (1980). 82. S. Yokoi, “Study on the Prevention of Fire Spread Caused by Hot Upward Current,” Report No. 34, Building Research Institute, Tokyo, Japan (1960). 83. ASTM E119, Standard Test Method for Fire Tests of Building Construction and Materials, American Society for Testing and Materials, West Conshohocken, PA. 84. ISO, ISO 834, Fire-Resistance Tests—Elements of Building Construction, International Organization for Standardization, Geneva, Switzerland (1999). 85. T. Harmathy, M. Sultan, and J. MacLaurin, “Comparison of Severity of Exposure in ASTM E119 and ISO 834 Fire Resistance Tests,” Journal of Testing and Evaluation, pp. 371–375 (Nov. 1987). In Handbook of Experimental Mechanics (A.S. Kobayashi, ed.), Society for Experimental Mechanics, PrenticeHall, Inc., Englewood Cliffs, NJ (1987). 86. V. Babrauskas and B. Williamson, “Temperature Measurement in Fire Test Furnaces,” Fire Technology, 13, 3, pp. 226–238 (1978). 87. EN1363-1, Fire Resistance Tests, Part 1: General Requirements, European Committee for Standardization (CEN), Brussels, Belgium (1999). 88. P. Fromy and M. Curtat, “Application of a Zone Model to the Simulation of Heat Transfer in Fire Resistance Furnaces Piloted with Thermocouples or Plate Thermometers,” in Fire Safety Science— Proceedings of the 6th International Symposium, International Association for Fire Safety Science, pp. 531–542 (1999). 89. P.H. van de Leur and L. Twilt, “Thermal Exposure in Fire Resistance Furnaces,” Fire Safety Science— Proceedings of the 6th International Symposium, International Association for Fire Safety Science, pp. 1087–1098 (1999). 90. M. Sultan, “Fire Resistance Furnace Temperature Measurements: Plate Thermometers vs. Shielded Thermocouples,” Fire Technology, 42, pp. 253–267 (2006). 91. M. Sultan, N. Benichou, and Y. Byung, “Heat Exposure in Fire Resistance Furnaces: Full-Scale vs. Intermediate-Scale,” Fire and Materials, 27, pp. 43–54 (2003). 92. UL 1709, “Rapid Rise Fire Tests of Protection Materials for Structural Steel,” Underwriters Laboratories, Northbrook, IL (1991). 93. EN1363-2, Fire Resistance Tests, Part 2: Alternative and Additional Procedures, European Committee for Standardization (CEN), Brussels, Belgium (1999). 94. W. Parker, “An Investigation of the Fire Environment in the ASTM E84 Tunnel Test,” NBS Technical Note 945, U.S. Department of Commerce, National Bureau of Standards, Washington, DC (1977). 95. Gandhi, P., Caudill, L., Hoover, J., and Chapin, T., (1996), “Determination of Fire Exposure Heat Flux in
798 Cable Fire Tests,” Fire Safety Science-Proceedings of the Fifth International Symposium, Portier, France, pp. 141–152. 96. A. Atreya and K. Mekki, “Heat Transfer During Wind-Aided Flame Spread on a Ceiling Mounted Sample,” in 24th Symposium (International) on Combustion, Combustion Institute, Pittsburgh, PA, pp. 1677–1684 (1992). 97. G. Santo and F. Tamanini, “Influence of Oxygen Depletion on the Radiative Properties of PMMA Flames,” in 18th Symposium (International) on Combustion, Combustion Institute, Pittsburgh, PA, pp. 619–631 (1981). 98. K. Mekki, A. Atreya, S. Agrawal, and I. Wichman, “Wind-Aided Flame Spread over Charring and
B.Y. Lattimer Non-Charring Solids: An Experimental Investigation,” in 23rd Symposium (International) on Combustion, Combustion Institute, Pittsburgh, PA, pp. 1701–1707 (1990). 99. Y.H. Chao and A.C. Fernandez-Pello, “Flame Spread in a Vitiated Concurrent Flow,” Heat Transfer in Fire and Combustion Systems, ASME HTD, 199, pp. 135–142 (1992).
Brian Y. Lattimer is a Professor in Mechanical Engineering at Virginia Tech. His research areas include fire dynamics, heat transfer from fires, and material response to fires.
26
Heat Release Rates Vytenis Babrauskas
Introduction Calculations of fire behavior in buildings are not possible unless the heat release rate of the fire is known. This chapter on heat release rates provides both theoretical and empirical information. The chapter is organized so that theory and basic effects are considered first, then a compendium of product data is provided, which is arranged in alphabetic order.
Definitions The essential characteristic that describes quantitatively How big is the fire? is the heat release rate. This is so important that it has been described as the single most important variable in fire hazard [1]. The heat release rate (HRR) of a burning item is measured in kilowatts (kW). It is the rate at which the combustion reactions produce heat. The term “burning rate” is also often found. This is a less specific term, and it may either denote the HRR or the mass loss rate. The latter is measured in units of kg s1. It is best to reserve ‘burning rate’ for non-quantitative fire descriptions and to use either HRR or mass loss rate, as appropriate. The relationship of these two quantities can be expressed as:
V. Babrauskas (*) Fire Science and Technology Inc.
HRR ¼ Δhc MLR
ð26:1Þ
where hc is the effective heat of combustion (kJ kg1) and MLR is the mass loss rate (kg s1). Such an equation implies that HRR and MLR are simply related by a constant. This is not in general true. Figure 26.1 shows the results obtained from a test on a 17 mm sample of Western red cedar. It is clear that the effective heat of combustion is not a constant; it is roughly 12 MJ kg1 for the first part of the test, but increases to around 30 MJ kg1 during the charring period at the end of the test. In principle, the effective heat of combustion can be determined by theory or by testing. In practice, if the effective heat of combustion is not a constant, then experimental techniques normally involve directly measuring the HRR, rather than using Equation 26.1.
Measuring the HRR, Full-Scale The simplest case is when full-scale HRR can be directly measured. This can be grouped into two types of techniques: • Open-burning HRR calorimeters • Room fire tests. Open-burning HRR calorimeters were developed in the early 1980s at NIST by Babrauskas and colleagues [2] and at FMRC by Heskestad [3]. The operating principles of these calorimeters are described in Chap. 27. Based on this work, a large number of different test
M.J. Hurley (ed.), SFPE Handbook of Fire Protection Engineering, DOI 10.1007/978-1-4939-2565-0_26, # Society of Fire Protection Engineers 2016
799
800
V. Babrauskas 40 35 Effective heat of combustion (MJ kg-1)
Fig. 26.1 Effective heat of combustion for 17 mm thick Western red cedar, tested at an irradiance of 65 kW m2
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Baffles To exhaust gas cleaning
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Fig. 26.2 NORDTEST NT FIRE 032 calorimeter
standards have been issued, for example [4–8]. A discussion of a number of other standards can be found [9]. The NORDTEST furniture calorimeter [7] is shown in Fig. 26.2. Open-burning HRR measurements are simpler to make since a test room does not need to be constructed. The HRR within a room and under open conditions are, clearly, identical at very low HRR. What happens at higher values of HRR depends on the situation at hand. If the fire is so large that room flashover can be reached (about 1.5–1.75 MW if ventilation is through a single
normal-sized door opening) then actual room HRR values post-flashover can be drastically different from their open-burning rates. This is due primarily to additional radiant heat flux contribution from the hot gas layer and the hot room surfaces, although ventilation effects can also play a role. For upholstered chairs, extensive studies have shown that room effects are only at the 20 % level up to a 1 MW fire [10]. The same study, however, showed that for mattresses, a room presence effect shows up at much lower HRR values. For liquid pools, the HRR is strongly
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Heat Release Rates
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Gas and smoke instrumentation in duct Exhaust duct 400 dia To exhaust gas cleaning Hood 3000 x 3000
Doorway 800 x 2000
2400
3600
Front view
Side view
Fig. 26.3 ISO 9705 room HRR test
affected by the surrounding room [11]. For most other commodities, this issue has not been studied. The degree by which the room affects the HRR is largely determined by how ‘open’ the fuel package itself is. A liquid pool on the floor has a view factor of 0 to itself and 1.0 to the room. By contrast, the reason that chairs tend to be little-affected by the room is that the chair ‘sees’ its own surfaces to a significant extent, rather than being fully-exposed to the room. Some useful error analyses of large open calorimeter measurements have been reported [12]; a theoretical discussion of the ‘ideal’ large scale calorimeter has also been presented [13]. Room fire tests should be commissioned when room effects are anticipated to be strong, or when a more precise estimate is needed. Apart from cost, there is a drawback to room fire testing. This is because the HRR measured in a room fire cannot be extrapolated to any rooms with larger ventilations. Open-burning HRR data could, by contrast, be applicable to such well-ventilated rooms. The development of the modern room HRR test took place at several institutions, including Fisher and Williamson at the University of California [14], Lee at NIST [15], and Sundstro¨m at the Swedish National Testing and Research
Institute [16]. Room test standards include [17, 18] and also [4, 5]. A typical standard room fire test, ISO 9705 is shown in Fig. 26.3; a similar room fire test is ASTM E 2257 [19]. This test equipment is available for commercial testing in North America, Europe, Asia, and other places.
Measuring the HRR, Bench-Scale To measure the HRR in a bench-scale test is nowadays an easy task. Most commonly, the Cone Calorimeter [20] developed at NIST by Babrauskas will be used (Fig. 26.4). These instruments are available at commercial and research laboratories worldwide. The procedures for conducting Cone Calorimeter tests are described in ASTM E 1354 [21] and ISO 5660 [22]. Other HRR calorimeters, such as the Ohio State University apparatus or the Factory Mutual Research Corp. Flammability Apparatus are also in use at some laboratories. A textbook is available which discusses many of the details of HRR measuring technology [23]. Thus, the modeler can assume that if at least enough material is available to run several small samples (100 mm 100 mm, in the case of the Cone calorimeter), an empirical HRR curve can be obtained by running bench-scale tests.
802 Fig. 26.4 The cone calorimeter
V. Babrauskas Laser photometer beam including temperature measurement Temperature and differential pressure measurements taken here
Soot sample tube Exhaust hood
Exhaust blower
Soot collection filter Controlled flow rate
Gas samples taken here
Cone heater Spark igniter Specimen
Load cell
Vertical orientation
Measuring the HRR, IntermediateScale The newest experimental technology for determining the HRR is intermediate-scale calorimetry. Various earlier efforts have been made, but the first instrument to receive standards support is the ICAL, developed at Weyerhaeuser [24] (Fig. 26.5). It has been standardized as ASTM E 1623 [25]. This test method accommodates 1.0 m by 1.0 m specimens, which allows for complex or highly non-homogenous constructions to be tested. However, since the data are still not of full scale, some additional analysis is needed to be able to utilize the test data in fire modeling.
Modeling Implications for Using FullScale HRR Data If access is available to full-scale HRR data, then the task of defining the fire is on a solid basis. Even here, however, there are a number of problems and caveats. Apart from the obvious issue that the available full-scale data must be known to describe the specific fuel source in
question (and not some possibly very differently performing ‘similar’ item), there are some additional concerns. Supposing one finds full-scale test results on one’s exact commodity, can the data simply be used unquestioningly? The answer, of course, is not. There are two main issues: • The available data may be open-burning calorimetry data. One must then determine if there is an enclosure effect to be accounted. • The available data may be room fire data, but the test enclosure may not correspond to the room for which modeling is to be done. The first of these issues was briefly touched on above already. The availability of quantitative guidance is lacking. For upholstered chair fires in a room of about the size of the ISO 9705 room, one can estimate a 20 % augmentation over the open-burn rates when considering fires in the 100–1000 kW range. For mattresses, the effect is large and without adequate guidance. For liquid pools, a pool sub-model must be specifically present in the fire model used, since no simple approximation is adequate. For wood cribs, there are formulas for guidance [26], although of course wood cribs are hardly a feature of most real fires. For other combustibles, neither data nor guidance is available.
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Heat Release Rates
803
Fig. 26.5 Intermediate scale (ICAL) calorimeter
A very similar problem is faced when the modeler has available full-scale HRR data, but the test was run in a room of rather different size or ventilation conditions than is the intended application. Only two studies on this topic have been published in the literature. Kokkala and colleagues compared [27] some room wall/ceiling linings in a large room to the values obtained in the ISO 9705 room. Also, during the CBUF project some furniture fires were done in rooms of two scales [10]. Neither of these studies looked at this issue comprehensively enough to yield numerical guidance. Some European designers have proposed that 250 or 500 kW m2 of floor area is an appropriate peak value of HRR according to which to design buildings of almost any kind [28]. It is not clear how these values were obtained, but one must consider whether they are conservative. Figure 26.48 gives HRR data for one pallet and half a pallet loads of some elastomer pellets. While these are ‘industrial’ materials,
nonetheless substances of similar heat of combustion and state of aggregation can readily be found in shops, storage rooms, and various other places in diverse building types. The test data showed that the whole-pallet test had to be extinguished at about 4500 kW m2; the fire was still growing, and its ultimate HRR would have been higher. Growth curves for the FM data listed in Table 26.8 are not available; nonetheless the peak values of roughly 2,000–20,000 kW m2 are sobering. Goods of this kind cannot occupy anywhere close to 100 % of the floor area, of course, but even assuming coverage at ¼ to ½, the actual HRR values are enormous. Now, there are clearly occupancies where it is impossible to introduce high fuel loads—swimming facilities may be an example. But other facilities, even if designed to be spartan in actual use (e.g., ceremonial lobbies) may sustain large fuel loads during construction, remodeling, expansion, and similar activities.
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V. Babrauskas
Fig. 26.6 Effect of ignition source on the HRR of PVC foam wall coverings
1000 900 30
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Effect of Ignition Source on Full-Scale HRR Full-scale tests for HRR usually do not impose an overall radiant heat flux and are ignited with localized flame sources. But locally, the heat fluxes from various ignition sources will differ both in their magnitude and in the size of the area subjected to the heat flux. Most plastic commodities that do not contain fire retardants (and are not made from an intrinsically-FR plastic) can be ignited with very small flame sources, often no bigger than a paper match. FR commodities, however, will resist ignition from small flames, but may be ignited from a largeflame ignition source. Commonly, such products show an all-or-nothing behavior. That is, ignition sources below a certain size will cause essentially no heat release from the test article, while a larger ignition source may cause a large fraction of, if not the total, combustible mass of the article. For example, it was shown [29] that a television cabinet made from a plastic fire retarded to
40
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140
0 160
the extent of obtaining a V-0 classification in the UL 94 [30] test gave no heat release when using a 10 kW burner, but burned well when exposed to a 30 kW burner. Dembsey [31] conducted room tests on rooms partially lined with a PVC-foam wall covering. His results are shown in Fig. 26.6. Note that the curve is very steep and could be represented reasonably by a step-function. Apart from a few examples, this type of data, unfortunately, is very rarely available for practical commodities of engineering interest.
Effects of Other Variables Some thermoplastic materials have a highly pronounced tendency to melt and flow. Consequently, commodities made from these materials, when burning, will often exhibit object burning above the floor and an accompanying pool fire at the floor, formed by the melt material. Sherratt and Drysdale [32] studied the problem in intermediate scale, by burning vertical polypropylene sheets above various floor materials.
26
Heat Release Rates
Major differences were found both in the peak HRR and in the time-resolved HRR curve, depending on the floor type. The differences were largely attributable to thermal characteristics (thickness, density, thermal conductivity, etc.) of the floor materials. Upholstered furniture using plastic foam padding often burns with a secondary pool fire underneath, however, this behavior occurs only in some cases.
Modeling with Bench-Scale HRR Data If full-scale data on HRR are available, then these are simply used in the fire model. In many cases, however, such data are not available, often due to cost of testing or unavailability of large size specimens. In such cases, it is desirable to be able to use bench-scale data, denoted as and measured in units of kW m2. With the benchscale HRR, there are two main questions: (1) can it be predicted from some more fundamental measurements? and (2) how can the full-scale HRR be predicted from the bench-scale HRR?
Predicting Bench-Scale HRR from Fundamental Considerations The former question has been of considerable interest to fire researchers, but practical engineering methods are not yet at hand. This task is often described as creating a ‘pyrolysis model,’ since the degradation of a material when it is exposed to heat is known as pyrolysis. When a material heats up, degrades, ignites, and burns, some very complicated physical and chemical phenomena are taking place. In addition to a change of phase, there is often flow of moisture simultaneously with heat flow. The material may undergo several different types of phase changes during the decomposition process, each accompanied by changes in density and porosity. Bubbles may be created within the bulk of the material and migrate to the surface. These may be accompanied by molten flow
805
ejection at the surface. Oxygen may or may not directly interact with the surface to create a glowing combustion. The chemical reactions being undergone are commonly several in number and occurring at different temperature regimes. Finally, the material may undergo large-scale cracking, buckling, or sloughing. Each of these physical phenomena may significantly affect the rate of specimen decomposition. From even this very brief description, it is clear that computing the pyrolysis of a material may be a difficult task. Thus, today for any fire hazard analysis purposes, HRR is invariably measured, rather than being computed from more fundamental theory. Readers wishing to look more closely at the type of modeling needed to represent the pyrolysis process can refer to the dissertation of Parker [33] as a good example of how charring materials need to be treated. Some half-dozen other dissertations have been written on the same topic. Melting type materials have proven to be even more interesting as a subject of advanced research. Several hundred of papers have been published on various aspects of modeling the pyrolysis behavior of just one common material, poly(methylmethacrylate). References [34–40] can provide an introduction to this research.
Predicting Full-Scale HRR from Bench-Scale Data: Overview Prediction of full-scale HRR is probably the single most important engineering issue in successful modeling of fires. Schematically, we may write that: ð q_ ¼ q_ 00 dA ð26:2Þ This representation does not fully reveal the difficulties involved. More explicitly, ð q_ ðtÞ ¼ q_ 00 ðt; x; y; zÞdAðtÞ ð26:3Þ
806
This makes more clear that the instantaneous per-unit-area HRR is a function of time and also of the location of the burning element. The instantaneous burning area, A(t), is also a function of time. In addition, while we have not 00 written this explicitly, q_ ðtÞ depends on the heating boundary conditions to the element. This quantity usually identified as the heat flux or irradiance incident upon the element. The latter term is commonly used since in full-scale fires the heating is dominated by the radiant component. By examining the nature of dA(t), we can also identify the role of flame spread in characterizing the HRR of full-scale fires. A bench-scale HRR test specimen is usually ignited nearly-instantaneously over its entire surface. Full-scale fire, by contrast, nearly always exhibit finite spread rates. The flame spread velocity in a full-scale fire can be identified with the movement of the boundaries of the flame-covered area dA(t). Flame spread may occur in several directions over walls, ceilings, floors, and over individual surfaces of discrete commodities burning in a space. Consequently, it can be seen that tracking flame spread and dA(t) is a major undertaking. This task, by its nature, is incompatible with zonetype of fire models, since it presumes that a mechanism is in place to track very small surface elements. Such mode line is variable with CFO models [41] the quality of production is dependent on fuel type and the user needs to verify the permanent details. Our approach will have to be restricted to identifying some of the attempts which have been made to simplify the problem in order to make it tractable for zone modeling. Simplifications are not yet possible for the ‘general’ case. Instead, we must examine specific combustibles, for which appropriate flame spread representations have been established. This is illustrated in a number of the sections below. Before we do this, however, it is important to examine in more detail some of the variables which influence the HRR.
V. Babrauskas
Predicting Full-Scale HRR from BenchScale Data: The Role of Irradiance Engineering variables such as HRR, ignitability, flame spread, etc. are sometimes viewed as material fire properties. This is a useful view, but it must be kept in mind that such ‘properties’ are not solely properties defined by the physical/ chemical nature of the substance. Instead, they are also determined by the boundary conditions of exposure. The boundary conditions can be divided into two types: (1) intended, and (2) unintended. The intended boundary conditions include irradiance (since the heat fluxes in room fires are dominated by the radiant component, the terms irradiance and imposed heat flux are used interchangeably) and thickness. Unintended boundary conditions, sometimes known as apparatus-dependencies, include such factors as edge effects, perturbations due to non-uniform heating, drafts and uncontrolled air velocities, etc. The latter are usually small if a welldesigned test apparatus was used for measuring the response of the specimen. The most significant intended boundary condition is the heat flux imposed on the specimen. This variable is crucial and no reduced-scale HRR results have meaning without knowing the irradiance. A test apparatus can impose a very wide range of specimen irradiances. For example, the Cone Calorimeter is capable of irradiances from zero to 100 kW m2. For the user of the data, the crucial question becomes what irradiance to select when requesting a test. There are no simple answers to this, but we summarize here the main conclusions of an extensive study [42]. The major consideration in the selection of the test irradiance must come from a knowledge of heat fluxes associated with real fires. In theory, this could range from zero to an upper value which would be εσ T 4f T 4o , where ε ¼ emissivity (–), σ ¼ Stefan-Boltzmann constant (5.67 1011 kW m2 K4), Tf ¼ flame temperature (K), and To ¼ ambient temperature (K). But the
26
Heat Release Rates
ε 1 for larger flames, and the ambient temperature contribution is insignificant, since To to, Equations 26.8 through 26.11 are used. The heat release rate is determined from Equation 26.1. For plastics, the heat of combustion is commonly fairly constant and can be taken from tabulations or from Cone Calorimeter testing. For wood cribs, commonly the heat of combustion is taken to be 12 103 kJ kg1. However, as illustrated in Fig. 26.1, the heat of combustion of wood is a varying function of time. A better procedure would be to either predict the HRR of wood cribs directly, without going through Equation 26.1, or else to be able to have recourse to a realistic value of Δhc (t). Neither of these possibilities have currently been developed. Room Fire Effects Experimentally, it has long been observed [94] that, unlike a pool fire, which can burn in a room in a highly fuel-rich manner, a wood crib does not burn more than approximately 30–40 % fuel rich. Conditions more fuel rich than that are not sustained, presumably, because of the highly vitiated air being supplied to the crib under those conditions. The stoichiometric fuel pyrolysis rate can be estimated as [11] m_ p ðstÞ ¼
pffiffiffiffiffi 1 0:5Av hv r
ð26:14Þ
where the stoichiometric air/fuel mass ratio, r, for wood can be taken as r ¼ 5.7. Comparing, then, the maximum pyrolysis rate given by Equation 26.11 with the stoichiometric rate given by Equation 26.14, it can be seen that a limit of approximately 37 % fuel rich is reached when Equation 26.11 becomes the governing limit to the burning rate. Similar limits may possibly exist for other classes of combustibles, but experimental data are only available for wood cribs.
Curtains Thermoplastic curtains often do not sustain any appreciable burning when ignited by a flame. Instead, a small piece ignites, but it falls off and the rest of the material still in place does not burn. The dropped-down material will usually continue burning, but its HRR will be trivial. There is no systematic study available that would elucidate under what conditions curtains will burn in place (and release a significant amount of heat), versus burning only to a trivial extent. Even if curtains ignite and burn in place, the heat content and HRR are generally moderate, but curtains can contribute to the severity of a fire by quickly propagating fire over large surfaces. Moore has done the most extensive study of curtains and draperies [100]. His test specimens were ignited with a match along the bottom. The results are summarized in Table 26.5 and Fig. 26.38. His results show primarily the effect of fabric weight. Lightweight fabrics, of weight around 125 kg m2, can show heat release rate peaks almost as high as heavy ones (around 300 kg m2); however, their potential to ignite surrounding objects is much smaller, as demonstrated in Fig. 26.38. These conclusions hold for both thermoplastic and cellulosic materials, but not for constructions using foam backings, for which insufficient data were available. Whether the curtain was in the closed or in the open position seemed to make little difference. The reason for the more severe fire performance of the heavyweight curtains was largely due to their increased burning time, which was typically about twice that for the lightweight curtains. Additional data on the HRR of curtains have been published by VTT [156] and by SP [101]. Yamada et al. [102] conducted full-scale tests on curtains of 0.9–1.2 m width and 2.0 m length. They tried 10, 30 and 50 kW square burners and found that generally at least the 30 kW burner needed to be used if full flame development was to be reached. Polyester curtains, both FR and non-FR, melted and failed to show a sustained
26
Heat Release Rates
831
Table 26.5 HRR data for curtains. Nominal curtain size: two curtains each, 2.13 m high by 1.25 m wide. Wall area covered: 2.13 m high by 1.0 m wide (in closed position)
Type of fiber Cotton Cotton Cotton Cotton Cotton Rayon/cotton Rayon/cotton Rayon/cotton Rayon/cotton Rayon/cotton Rayon/acetate Acetate Cotton/polyester Cotton/polyester Cotton/polyester Rayon/polyester Rayon/polyester Rayon/polyester Cotton/polyester Polyester Acrylic Acrylic Acrylic Acrylic Cotton/polyester/foam Rayon/polyester/foam Rayon/fiberglass Rayon/fiberglass
Weight (g/m2) 124 260 124 260 313 126 288 126 288 310 296 116 117 328 117 367 268 53 328 108 99 354 99 354 305 284 371 371
Configuration Closed Closed Open Open Closed Closed Closed Open Open Closed Closed Closed Closed Closed Open Closed Closed Closed Open Closed Closed Closed Open Open Closed Closed Closed Closed
Peak HRR (kW) 188 130 157 152 600 214 133 176 191 177 105 155 267 338 303 658 329 219 236 202 231 1177 360 NA 385 326 129 106
Number of wall and ceiling panels igniteda 1 7 0 7 3 0 6 0 2 8 4 0 1 5 0 2 7 0 7 0 0 8 0 7 1 0 5 5
Maximum possible number of panels to ignite ¼ 10
a
fire, as did FR cotton and FR rayon. Acrylic, modacrylic, non-FR rayon and non-FR cotton showed sustained burning, attaining 100–250 kW peak HRR values when subjected to the 50 kW ignition source.
and various all-plastic constructions. For samples sized 0.61 0.61 m, a redwood deck gave a peak HRR of 12 kW. Wood/plastic composites ranged between 10 and 394 kW, while all-plastic products ranged from 10 to 1055 kW.
Decks
Desks
The California Office of State Fire Marshal reported some HRR tests [103] done on outdoor decks, comparing wood, wood/plastic composite,
Chow et al. [104] measured the HRR of a small wooden office desk. The desk was 0.6 1.2 0.8 m high The ignition source
832
V. Babrauskas
Fig. 26.38 Effect of fabric weight on number of curtain panels ignited
400
Weight (g/m2)
300
200
Construction type 100
Fabric only Fabric and foam
0
Fig. 26.39 HRR of a wooden desk tested by Chow et al.
0
1
2 3 4 5 6 Number of panels ignited
7
8
700
600
HRR (kW)
500
400
300
200
100
0 0
was a pool of 0.5 L gasoline which, by itself, produced a peak HRR of 40 kW. These results are shown in Fig. 26.39.
Dishwashers VTT tested [105] European dishwashers using a propane burner of 1 kW. The specimens are
500
1000 Time (s)
1500
2000
described in Table 26.6, while test results are shown in Fig. 26.40. These results must not be applied to appliances used in North America, since European appliance styles are different from North American ones and also because local standards are such as to permit appliances of greater flammability in Europe. HRR data on North American dishwashers are not available.
26
Heat Release Rates
833
Dressers
Electric Cable Trays
A test of a wooden dresser has been conducted by NIST [106], see Fig. 26.41.
Cable tray fires present almost an endless plethora of combinations of cable materials, tray construction, stacking, ignition sources, etc. Only a very few of these have been explored. The most systematic studies available are those from Tewarson et al. [107] and Sumitra [108]. A useful engineering analysis of their data has been prepared by Lee [109]. Lee provided a basic correlation of Tewarson’s and Sumitra’s data (see Fig. 26.43), which shows that the peak fullscale heat release rate q_ fs (kW m2) can be predicted according to bench-scale heat release rate measurements:
Dryers Results for a small European clothes dryer (40 kg) have been published [70]. Even though use of plastics in North American clothes dryers has been increasing, nonetheless it would appear that the unit was more typical of the European market than the American one. In the test (Fig. 26.42), 11 kg of mass was lost and 253 MJ of heat was released.
Table 26.6 European dishwashers tested by VTT Specimen Initial mass (kg) Mass loss (kg) Peak HRR (kW) Total heat (MJ)
D1 35.6 6.1 476 165
Fig. 26.40 HRR of European dishwashers tested by VTT
D2 47.5 8.4 347 206
q_ fs ¼ 0:45q_00bs A where q_00bs is the peak bench-scale HRR (kW m2), measured under 60 kW m2 irradiance, and A is the exposed tray area actively pyrolyzing (m2). The active pyrolysis area, in turn, is estimated from Fig. 26.44, which gives dA/dt as a function of q_00 . Thus, at any given bs
time, t,
600 D1 D2
HRR (kW)
400
200
0 0
600
1200
1800 Time (s)
2400
3000
834
V. Babrauskas
Fig. 26.41 HRR of wooden dresser
2000 1800
Heat release rate (kW)
1600 1400 1200 1000 800 600 400 200 0 0
300
600
900
Time (s)
Fig. 26.42 HRR for a small European clothes dryer
600
500
HRR (kW)
400
300
200
100
0 0
300
600
900
1200
1500
1800
Time (s)
Að t Þ ¼ Ao þ
dA t dt
Finally, Table 26.7 gives a selection of measured values of q_00 for various cable types. bs
Foodstuffs SP reported on a test [110] to simulate the burning of snack foods in a shop. Retail bags of two
types of snacks were tested in a single test— potato chips and cheese nibbles. A total fuel load of 275 kg was set up in a tightly-packed, three-shelf high shelving unit, 5.4 m long. The HRR results are shown in Fig. 26.45. Visual observations indicated that potato chips burned more vigorously than cheese nibbles. NIST [111] ran two full-scale tests on bags of potato chips on a rack with open-wire-mesh shelves. Each shelf had 20 bags of potato chips. The bags were arranged five across and four
26
Heat Release Rates
835
Fig. 26.43 HRR prediction for cable trays (numbers at data points identify full-scale tests)
15
Cable tray correlation
10
n
17
qfs = 0.45 qbs • A
9
16
Measured qfs (MW)
8 7 7 6 5 4
14
13
3
5
1 0
6 PE/PVC PE, PP/CI • S • PE (Hypalon) Silicone/asbestos
2
Fig. 26.44 Effect of bench-scale cable heat release rate on full-scale rate of flame coverage
8
0
1
2
3
4 5 6 7 Predicted qfs (MW)
8
9
10
2.4 2.2
Rate of flame coverage (m2/min)
2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0 0
100
200
300
400
Bench-scale rate of heat release (kW
500 m2)
600
836
V. Babrauskas
Table 26.7 Heat release rates of typical cables in benchscale tests Specimen number 20 21 10 14 22 16 18 19 15 11 8 17 3 12 2 6 4 13 5 1 20
q_00bs IEEE 383 test (kW m2) Pass 98 Pass 128 Pass 177 Pass 178 Pass 182
Cable sample Teflon Silicone, glass braid PE, PP/Cl · S · PE XPE/XPE Silicone, glass braid asbestos XPE/Cl · S · PE PE, nylon/PVC, nylon PE, nylon/PVC, nylon FRXPE/Cl · S · PE PE, PP/Cl · S · PE PE, PP/Cl · S · PE XPE/Neoprene PE/PVC PE, PP/Cl · S · PE XPE/Neoprene PE/PVC PE/PVC XPE/FRXPE PE/PVC LDPE Teflon
Pass
204 218 231 258 271 299 302 312 345 354 359 395 475 589 1071 98
a a
Pass Pass Pass Pass a
Pass a a
Fail Pass Fail a
Pass
a
Test not conducted
Fig. 26.45 HRR of potato chips and cheese nibbles set up in a shop display unit
deep, with a total fuel load of 27.1 kg. Each bag of chips was approximately 200 mm wide by 100 mm (thick) by 360 mm high. Each bag weighed 33.8 g, of which chips accounted for 32.5 g and the plastic bag for the rest. The potato chip ingredients were listed by the manufacturer as: potatoes, sunflower oil and salt. Two replicate heat release rate experiments were conducted (Fig. 26.46). It is interesting to note that the NIST tests showed the same peak HRR (6 MW) as the SP test, albeit with a much shorter duration time due to the fact that the fuel load was 1/10 of SP amount.
Industrial Stored Commodities Pallet loads of plastic-based commodities are commonly stored in factories, warehouses, and wholesale establishments. Most tests have involved multiple pallets being tested, and most of these have also involved some manner of water application being done during the test. But there have been a few tests reported where single pallet-loads were tested, without water. SP [112] tested single pallet-loads of four kinds:
7000
6000
HRR (kW)
5000
4000
3000
2000
1000
0 0
600
1200 Time (s)
1800
2400
26
Heat Release Rates
837
Fig. 26.46 Potato chip bags tested at NIST
• FM Group A plastic standard commodity (see Table 26.10) • CEA standard commodity. Each corrugatedcardboard box is 450 550 370 mm and each (wood) pallet holds 12 boxes in a 2 2 3 array. Each box weighs 805 g and is filled with 340 g of polystyrene chips. The pallet-load is 800 1200 mm with a height of 1110 mm, excluding the pallet itself. • SCEA standard commodity. This is a Swedish version of the CEA, with each box being 380 570 380 mm. Each box weighs 700 g and holds 420 g of chips. The palletload is 800 1200 mm with a height of 1140 mm, excluding the pallet itself. • Large SCEA standard commodity. This is a variant where the box is 800 600 500 mm. Each box weighs 1470 g and contains 1220 g of chips. Each pallet holds a 1 2 2 array of boxes. The HRR results for these tests are shown in Fig. 26.47. Despite the intention being that Group A plastics represent a severe fire hazard, some plastic commodities produce significantly more HRR. In tests by Babrauskas [113], pellets of SBR (styrene-butadiene rubber) were packed in paper bags and loaded on a wooden pallet, with a
total weight of 680 kg of pellets. The pallet was over-wrapped with clear plastic film and spillage did not occur during the test. The full-pallet test was ignited with a propane torch at the bottom. The half-pallet test was ignited with a propane torch at the top. The full-pallet test (Fig. 26.48) showed a HRR of close to 7 MW when conditions required that the commodity be extinguished; peak HRR conditions had not been reached. Heskestad [114, 115] analyzed a large series of palletized1 storage tests conducted at FM in 1975 by Dean [116]. These experiments pre-dated the availability of HRR calorimeters, so Heskestad obtained peak HRR values by using mass loss rate data and values of effective heat of combustion. The test arrangement was 2 2 3 pallets high, with a flue space running in only one direction. Heskestad also analyzed a later series of rack-storage tests by Yu and Kung [117, 118]. The test arrangement was 2 2, with heights being two, three, or four pallets, and with flue spaces running in both directions.
1
‘Palletized’ denotes a storage configuration where pallets are stored directly on top of each other, without use of shelving.
838
V. Babrauskas
Fig. 26.47 HRR of single pallet-loads of various commodities tested at SP
4500
Group A std. CEA std. SCEA std. Large SCEA std.
4000 3500
HRR (kW)
3000 2500 2000 1500 1000 500 0 0
300
600
900
1200
1500
1800
Time (s)
Fig. 26.48 HRR of pallets holding bags of SBR pellets
7000 Extinguished Full pallet Half pallet
6000
HRR (kW)
5000
4000
3000 Extinguished
2000
1000
0 0
300
600
900
1200
Time (s)
Heskestad’s tabulated peak HRR values are given in Table 26.8. The peak HRR values were obtained by dividing the value in kilowatts by the floor area occupied by the commodity. The palletized test commodities occupied a floor
area of 2.44 2.59 m, while the rack storage tests were 2.29 2.29 m. The cardboard cartons with metal liner are ‘FM Standard Class II Commodity’ (Table 26.10 [119, 122]) while the PS cups are ‘FM Standard Plastic Commodity’
26
Heat Release Rates
839
Table 26.8 HRR values of palletized and rack-storage commodities tested at FM Test SP-4 SP-13 SP-23 SP30A SP-35 SP-44 SP-15 SP-22 SP-43 SP-6 SP-19 SP-34 SP-41 RS-1 RS-2 RS-3 RS-4 RS-5 RS-6 RS-7 RS-8 RS-9 RS-10 RS-11
Commodity PS jars in compartmented CB cartons PS foam meat trays, wrapped in PVC film, in CB cartons PS foam meat trays, wrapped in paper, in CB cartons PS toy parts in CB cartons PS foam insulation PS tubs in CB cartons PE bottles in compartmented CB cartons PE trash barrels in CB cartons PE bottles in CB cartons PVC bottles in compartmented CB cartons PP tubs in compartmented CB cartons PU rigid foam insulation Compartmented CB cartons, empty CB cartons, double tri-wall, metal liner 00 00 00 00 00 00 00 00 00 00
PS cups in compartmented CB cartons 00 00 00 00 00 00 00 00
Storage ht. (m) 4.11 4.88
Peak HRR (kW m2) 16,600 10,900
Time of peak (s) 439 103
4.90 4.48
11,700 5,210
113 120
4.21 4.17 4.20 4.51 4.41 4.63 4.26 4.57 4.51 2.95 2.95 2.95 4.47 4.47 5.99 2.90 2.90 2.90 4.42 5.94
26,000 6,440 5,330 28,900 4,810 8,510 5,870 1,320 2,470 1,680 1,490 1,680 2,520 2,250 3,260 4,420 4,420 4,420 6,580 8,030
373 447 434 578 190 488 314 26 144 260 89 180 120 240 210 95 100 120 100 148
CB cardboard, PE polyethylene, PP polypropylene, PS polystyrene, PU polyurethane
Table 26.9 Miscellaneous stored commodities tested by FM Commodity Fiberglass (polyester) shower stalls, in cartons Mail bags, filled PE letter trays, filled, stacked on cart PE and PP film in rolls
Storage ht. (m) 4.6
Peak HRR (kW m2) 1,400
1.52 1.5
400 8,500
4.1
6,200
(Group A Plastic). Note that there does not exist a scaling rule that would enable HRR values to be computed for stack/rack heights other than those tested. Thus, the reported values could conservatively be applied to shorter heights, but cannot be extrapolated to greater heights. Some older data
[120] are listed in Table 26.9. These have not been re-analyzed by Heskestad. The effect of storage height [121] on the HRR growth curve for Class II commodities is shown in Fig. 26.49. An initial period of limited fire growth has been removed from these curves. These results are from FM testing in the 1980s. Also shown is the HRR curve for a 2 2 2 array tested in 2005. For much of the time, the HRR exceeded the earlier results. This is because FM identified that the standard Class II commodity supplied in 2005 is somewhat different than that supplied earlier [125]. The early fire growth period [122] for Class I, III, and IV commodities is shown in Fig. 26.50. The early fire growth period for the FM Standard Plastic Commodity is shown in Fig. 26.51. These results are based on early FM studies [123, 124] which were
Products Essentially noncombustible; may be in light cardboard cartons and may be on wood pallets
Class I products with more or heavier packaging and containers
Combustible products in combustible wrapping or containers on wood pallets. May contain a limited amount of plastic.
Class I, II, or III with considerable plastic content in product, packaging or pallets
Commodities containing a greater amount of plastic than would be permitted in Class IV commodities
Class Class I
Class II
Class III
Class IV
Standard plastic (Group A Plastic)
Table 26.10 FM Commodities and standard test commodities
Typewriters and cameras of metal and plastic parts
Products of wood, paper, leather, and some foods
Class I products in multiwall cartons, boxes, or barrels.
Examples Glass, minerals, metals, ceramics
Test commodity Single-wall corrugated cardboard carton measuring 2100 (0.533 m) on side, divided into five horizontal layers by corrugated cardboard sheets. Each layer was divided by interlocking cardboard partitions forming a total of 125 compartments. Each compartment occupied by one 16-oz (0.47 l) glass jar, without lid, open side facing down to prevent collection of water. A pallet load consists of one wood pallet and eight of the above-described cartons. Double triwall (approx. 25 mm thick total) corrugated cardboard carton measuring 42" (1.07 m) on a side containing a 24 ga. (0.56 mm) sheet metal liner box measuring 3800 3800 3600 (1.07 1.07 1.02 m) high. A pallet load consisted of one wood pallet and one the above described cartons. Single-wall corrugated cardboard carton measuring 2100 (0.533 m) on a side, divided into five horizontal layers by corrugated cardboard sheets. Each layer divided by interlocking corrugated cardboard partitions forming a total of 125 compartments. Each compartment occupied by one 16-oz (0.95 l) paper jar (wide mouth container/ cup), without lid, open side facing down to prevent the collection of water. A pallet load consists of one wood pallet and eight of the above described cartons. Single-wall corrugated cardboard carton measuring 2100 (0.533 m) on a side, divided into five horizontal layers by corrugated cardboard sheets. Each layer divided by interlocking corrugated cardboard partitions forming a total of 125 compartments. Each compartment occupied by forty 16-oz (0.95 l) polystyrene and eighty-five 16-oz (0.95 l) paper jars (wide mouth container/ cup), without lids, open side facing down to prevent the collection of water. A pallet load consists of one wood pallet and eight of the above described cartons. Single-wall corrugated cardboard carton measuring 2100 (0.533 m) on a side, divided into five horizontal layers by corrugated cardboard sheets. Each layer divided by interlocking corrugated cardboard partitions forming a total of 125 compartments. Each compartment occupied by one 16-oz (0.95 l) polystyrene jar, without lids, open side facing down to prevent the collection of water. A pallet load consists of one wood pallet and eight of the above described cartons.
840 V. Babrauskas
Fig. 26.49 Effect of storage height for Class II commodities
FM Class II Commodity on 4 Tier Rack Storage (5.99 m.high) FM Class II Commodity on 3 Tier Rack Storage (4.47 m. high) FM Class II Commodity on 2 Tier Rack Storage (2.95 m. high) FM Class II commodity on 2 Tier (2005 data) 10,000 9,000 8,000
HRR (kW)
7,000 6,000 5,000 4,000 3,000 2,000 1,000 0 0
50
100
150
200
250
Time (s)
Fig. 26.50 The early firegrowth period for Class I, III, and IV commodities
FM Class I Commodity on 2 Tier Rack Storage (2.95 m. high) FM Class III Commodity on 2 Tier Rack Storage (2.95 m. high) FM Class IV Commodity on 2 Tier Rack Storage (2.95 m. high)
250
HRR (kW)
200
150
100
50
0 0
50
100 Time (s)
150
200
842
V. Babrauskas FM Plastic Commodity on 5 Tier (2x2x5) Rack Storage (7.50 m. high) FM Plastic Commodity on 4 Tier (2x2x4) Rack Storage (5.95 m. high) FM Plastic Commodity on 3 Tier (2x2x3) Rack Storage (4.48 m. high) FM Plastic Commodity on 2 Tier (2x2x2) Rack Storage (2.93 m. high) FM Plastic Commodity on 2 Tier (2x2x2) 2005 data 20000 18000 16000 14000
HRR (kW)
12000 10000 8000 6000 4000 2000 0 0
50
100
150
200
250
Time (s)
Fig. 26.51 The early fire-growth period for FM Standard Plastic commodity, as a function of storage height
conducted in their Norwood MA facility. Also shown are the results obtained in 2005 at their West Gloucester RI facility for the 2 2 2 configuration [125]. Additional FMRC data for different commodities loaded onto wooden pallets are shown in Fig. 26.52. The egg carton test [126] used foam-polystyrene egg cartons of 12-egg capacity. Polyethylene bags were used to hold 200–216 of these egg cartons, open and nested into each other. Each pallet held about 20.4 kg of egg cartons. Each pallet contained about 22.7 wood, and the load also contained about 0.4 kg polyethylene. In this test, a low density of water extinguishment was applied, but this did not appear to significantly reduce the HRR of the commodity. Only the convective portion of the HRR was measured. Polystyrene shows a very
high radiant heat release fraction, thus, to account for the radiant fraction and for the diminution due to water spraying, the total HRR curve shown in Fig. 26.52 was estimated by multiplying the measured convective portion by a factor of 2. The polyurethane foam results [127] are for a three-tier (4.27 m high) stack of foam in cardboard boxes and used a PUR foam of high HRR; other results (not shown) were also obtained by FM for fire-retardant grades. The PET (polyethylene terephthalate) bottles test [128] used 46 bottles of a 2 L size packed into single-wall corrugated cardboard boxes. Each box contained 2.55 kg of plastic and 1.29 kg of cardboard. Total test arrangement comprised eight pallet loads arranged in a 2 2 2 arrangement. Each pallet contained eight cartons of the size 0.53 0.53 0.53 m. The
26
Heat Release Rates
843
Fig. 26.52 FMRC HRR results for several additional commodities
PS egg cartons PUR Foam in Cardboard Boxes 3 Tier (4.27m. high) PET bottles Newsprint FM Class II commodity (1.07 x 1.07 x 1.02 m high)
20,000 18,000 16,000 14,000
HRR (kW)
12,000 10,000 8,000 6,000 4,000 2,000 0 0
300
600
900
1200
Time (s)
Table 26.11 Boxed computer items tested by Hasegawa et al. Code P1 P8 P5 P6 P10 P3 P7 P9 P11
Items Boxed monitors, one pallet of 12 Boxed monitors, one pallet of 12, point-source ignition Boxed monitors, one pallet of 12 (stabilized from collapse) Boxed monitors, two pallets (side-by-side) of 12 each Boxed monitors, stack of two pallets high, 10 per pallet Boxed desktop computers, one pallet of 16 Boxed desktop computers, pallet of 16 + boxed accessory boxes on top polystyrene foam in boxes Monitor boxes, one pallet of 12
newspaper test [129] comprised 8.2 kg of shredded newsprint placed in a 0.53 0.53 0.51 m single-wall corrugated cardboard box of 2.73 kg. Eight cartons comprised one pallet load. The pallets were arranged in a 2 2 2 arrangement. The newsprint test [130] used a 2 2 2 arrangement of pallets, each load being 1.07 1.07 1.02 m high. The Class II commodity results are from Khan [130].
Peak HRR (kW) 4700 5030 6400 17,300 14,100 1400 8190 6730 4600
Packaged computers and computer accessories were tested by Hasegawa et al. [131, 132]. They tested pallet-loads of packaged goods and also individual items, as packaged and boxed in individual cardboard boxes. The items were ignited using a line burner placed near the bottom edge of the package or stack. Ignition sources in the range of 50–200 kW were used. Table 26.11 identifies the specimens tested, while Figs. 26.53 through
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V. Babrauskas
Fig. 26.53 HRR of single, packaged and boxed computers and monitors
400 Desktop (boxed) Laptop (boxed) Monitor (boxed)
350 300
HRR (kW)
250 200 150 100 50 0 0
120
240
360
480
600
Time (s)
Fig. 26.54 HRR of a stack of polystyrene foam boards
2000 1800 1600
HRR (kW)
1400 1200 1000 800 600 400 200 0 0
300
600
900
Time (s)
26.57 show the results. The monitors were 16.8 kg each, while the desktop computers were 4.9 kg ea. The pallet load in test P1 collapsed during test and the full HRR was not registered, consequently, it was re-tested with supported sides. A stack of expanded polystyrene boards was burned by Dahlberg at SP and results are reported
by Sa¨rdqvist [97]. The total stack size was 1.2 1.2 1.2 m, with a mass of 1.4 kg. Ignition was with a 1 MW burner at the side of the stack. The HRR curve is shown in Fig. 26.54. Numerous other example data are tabulated by Sa¨rdqvist [97]. Dillon et al. [133] tested several commodities in a furniture calorimeter: acrylic yarns in boxes,
26
Heat Release Rates
845
Fig. 26.55 HRR of pallets of packaged, boxed computer monitors
7000 P1 P5 P8 P11
6000
HRR (kW)
5000
4000
3000
2000
1000
0 0
60
120
180
240
300
360
420
Time (s)
Fig. 26.56 HRR of pallets of packaged, larger arrays of computer monitors
20000 P6 P10
18000 16000
HRR (kW)
14000 12000 10000 8000 6000 4000 2000 0 0
10
20
30
40
50
60
Time (s)
computer monitors (US models, 430 mm [1700 ] screen) packed in shipping boxes, plastic coolers, and potato chip bags packed in cardboard boxes. The coolers with both insulated with
polyurethane foam and had polyethylene outer shells; the #1 sample had a polystyrene liner while the #2 sample had a polypropylene liner. The computer monitors were padded with
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Fig. 26.57 HRR of pallets of miscellaneous computer items
9000 P3 P7 P9 P11
8000 7000
HRR (kW)
6000 5000 4000 3000 2000 1000 0 0
20
40
60
80
100
120
Time (s)
Table 26.12 HRR of packaged household commodities tested by Dillon et al. Mass Commodity (kg) Acrylic yarn 8.7 skeins Computer 24.6 monitor Cooler #1 6.4 Cooler #2 5.2 Potato chips 8.3
Peak HRR Time to (kW) peak (s) 263 210
Total HR (MJ) 127
140
398
70
400 276 322
648 702 230
147 128 139
expanded polystyrene foam, as is customary for shipping. Their results are summarized in Table 26.12. A study has been reported on burning pallet loads of organic peroxides [134]. Liquids were packaged in plastic containers within cardboard boxes, while solids were packaged in cardboard drums. The data are given only for a few packaging configurations with sufficient data not being available to generalize HRR predictions to other configurations. For all rack storage tests, the times are very strongly affected by the ignition source location. Not enough data exist to make general correlations, but Fig. 26.58 illustrates the basic
effect. The storeroom test [135] comprised a mocked-up small storeroom in a retail shop, with miscellaneous goods boxed in cardboard boxes, placed on shelving 2.4 m high. A small amount of additional shelving was provided across an aisle 1.4 m wide. The FMRC test involved pallets in a 2 2 2 arrangement. In the storeroom test, ignition was at the base of the face of the ‘main’ storage rack. The FMRC test [136] used the standard FMRC procedure whereby an igniter is also placed at the base, but is located internally, at the two-way intersection of flue spaces between piles. The data for the storeroom test are plotted as real time, while the FMRC test data were shifted 470 s to make the steep HRR rise portions coincide. From a comparison of this kind, one can roughly estimate that igniting a rack at the front face causes events to occur 470 s later than would happen if ignition were at the center of the flue spaces.
Kiosks NIST have reported [137] some HRR results on full-scale tests of kiosks. These are the booths used in shopping malls, exhibitions, and other
26
Heat Release Rates
847
Fig. 26.58 Effect of ignition source location on fire development
18,000 Storeroom test
16,000
FMRC plastic commodity, shifted by 470 s
14,000
HRR (kW)
12,000 10,000 8,000 6,000 4,000 2,000 0 300
350
400
450
500
550
600
Time (s)
Fig. 26.59 HRR of display kiosks
2000 Test 1 Test 2 Test 3 Test 4 Test 5
1800 1600
HRR (kW)
1400 1200 1000 800 600 400 200 0
0
600
1200
1800
2400
Time (s)
places wherein a small amount of merchandise display or sales occur. Some HRR curves are illustrated in Fig. 26.59 for a kiosk, built largely of wood, which measured 1.2 m 1.2 m 2.1 m high. Tests 2–5 are all of the same sized kiosk,
but refer to various configurations of the openable panels. Test 5 appears to have been more severe since all the panels were closed. Test 1 involved the same kiosk placed in a room, rather than in the furniture calorimeter.
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V. Babrauskas
Luggage At the LSF Laboratories, Messa [138] tested the HRR of two suitcases filled with clothes. Ignition was with a square-ring burner applying approximately 5.5 kW. The test articles are described in Table 26.13 and the results are given in Fig. 26.60.
Fig. 26.61. The larger ignition source used Test 2 led to much greater HRR, despite the fact that the mass of paper goods was smaller than in Test 3. While all tests were conducted in an ISO 9705 room, the large HRR in Test 2 was evidently attributable to room-effect radiant heat flux reinforcement, which was of less significance for the other tests. Thus, for design purposes, only Tests 1 and 3 should be considered, unless the end-use environment is a relatively small room.
Magazine Racks Chow et al. [139] conducted full-scale tests on several steel magazine racks, holding magazines, newspapers, and books. Ignition was with a small pool of gasoline. Test details are given in Table 26.14, while HRR results are shown in
Table 26.13 Test description for suitcases tested at LSF Condition Mass empty (kg) Mass filled (kg) Burner HRR (kW) Burner application time (s) Total heat released (MJ)
Soft suitcase 0.98 3.06 5.5 180 33.4
Fig. 26.60 HRR of suitcases
Hard suitcase 5.20 10.34 5.5 240 139.0
Mattresses Despite the relatively simple shape of mattresses, the prediction of mattress HRR from bench-scale data is difficult. Even the use of full-scale HRR data is problematic, due to a peculiarity of mattress fires. Most other combustibles interact only modestly with their environment, until large HRR values are reached or until room flashover is being approached. Liquid pools on the other hand, as discussed below, interact very strongly with a room, if either the room size or the available ventilation are not very large in comparison to the pool’s HRR. The identical phenomenon is
140 Hard suitcase Soft suitcase
120
HRR (kW)
100
80
60
40
20
0 0
600
1200
1800 Time (s)
2400
3000
3600
26
Heat Release Rates
849
Table 26.14 Details of magazine rack tests Test no. 1 2 3
Size of each rack (WxH), m 1 2.2 2 2.2 2 2.2
Location of racks in room Left, back Back, right Left, back, right
Mass of paper goods (kg) 15 60 90a
Ignition source, quantity of gasoline (L) 2 15 3
a
Of which 15 kg was placed on floor, in front of racks
Fig. 26.61 HRR of magazine racks loaded with magazines, newspapers, and books
9000 Test 1 Test 2 Test 3
8000 7000
HRR (kW)
6000 5000 4000 3000 2000 1000 0 0
300
600
900
1200
1500
1800
Time (s)
Table 26.15 Some mattress HRR data; full-scale data are for small or no room effect, bench-scale data are peak values, taken at 25 kW m2 irradiance Padding material Latex foam Polyurethane foam Polyurethane foam Polyurethane foam Polyurethane foam Neoprene Cotton/jute
Ticking material PVC PVC PVC Rayon Rayon FR cotton FR cotton
Combustible mass (kg) 19 14 6 6 4 18 13
observed with mattresses. Thus, there may not be a single value of the HRR of a mattress, the HRR having to be considered related to the room itself. Some example data are compiled in Table 26.15 to illustrate the peak full-scale
Peak HRR, full-scale (kW) 2720 2630 1620 1580 760 70 40
Bench-scale HRR (kW m2) 479 399 138 179 NA 89 43
HRR values that are found for common material combinations [45]. The full-scale test protocol used a complete set of bedding; ignition was achieved with a wastebasket. Figure 26.62 illustrates the relation of bench-scale to full-scale
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Fig. 26.62 HRR of mattresses predicted from bench-scale results. Fullscale tests under conditions of negligible room effect; bench-scale HRR measured at 25 kW m2 irradiance
3000
Peak full-scale HRR (kW)
2500
2000
1500
1000
500
0 0
100
200
300
400
500
Peak bench-scale HRR (kW m−2)
Table 26.16 Some mattress HRR data; full-scale data include room effect of small bedroom Padding material Polyurethane foam Melamine-type PUR/cotton batting/polyester fiber pad Polyurethane foam/cotton batting/ polyester fiber pad Polyurethane foam/polyester fiber pad Melamine-type PUR FR cotton batting FR cotton batting Neoprene
Ticking material Unidentified fabric Polyester/ polypropylene Unidentified fabric
Combustible mass (kg) 8.9 NA
Peak HRR, full-scale (kW) 1716 547
180 s avg HRR, bench-scale (kW m2) 220 169
NA
380
172
PVC
NA
335
195
FR fabric PVC Polyester PVC
15.1 NA 15.7 14.9
39 17 22 19
228 36 45 31
data from the same data set, where full-scale testing was done under conditions not leading to significant room fire effect. Not enough specimens were tested to develop a usable correlation, so the results should be taken only as indicative. King-size mattresses dating from before the Federal HRR regulations can produce very high HRR values, even absent a room effect. NIST [140] tested a king-size bed assembly which contained box springs and an innerspring mattress consisting of polyurethane foam and felted
cotton padding. Additional bedding included two pillows, pillowcases, two sheets, and a comforter. Two tests were run in an open calorimeter—in one test, an electric match was used to ignite the bed, while in the other test a newspaper-filled wastebasket was the ignition source. Unlike the typical findings in the case of upholstered furniture, here the ignition source type had a major effect, with the larger ignition source resulting in a peak HRR over 5000 kW, while the smaller only showed about 3500 kW and burner a longer
26
Heat Release Rates
851
Fig. 26.63 HRR of mattresses predicted from bench-scale results. Fullscale tests under conditions of significant room effect; bench-scale HRR measured at 35 kW m2 irradiance
1750
Peak full-scale HRR (kW)
1500 1250 1000 750 500 250 0 0
50
100
150
180 s avg. bench-scale HRR (kW
Fig. 26.64 Effect of ignition source on king-size bed assemblies
200
250
m−2)
6000 Wastebasket ignition Match ignition
5000
HRR (kW)
4000
3000
2000
1000
0 0
200
400
600
800
1000
1200
Time (s)
time at a slower rate (Fig. 26.64). In either case, however, the HRR values would suffice to cause flashover in a bedroom environment, especially in view of the fact that the HRR would be much higher due to room effect augmentation. Some full-scale data obtained under conditions where a strong room interaction effect was seen are shown in Table 26.16 [141, 142].
The full-scale test setup was different for this data set, in that no bedding was used and ignition was with a burner flame at the edge of the mattress. Thus, some mattresses were able to show essentially zero HRR since bedding was not available to sustain burning, and the ignition source could be ‘evaded’ by receding specimens. A relation between full-scale and bench-scale
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Table 26.17 Results on mattress from the CBUF study Pk. HRR furn. calor. (kW) 26 31 47 47 275 348 313 917
Pk. HRR room (kW) 42 45 61 NA NA 471 1700 2550
Springs Sofabed N Y Y N Y N N
Thick. (mm) 22 50 10 20 90 20 100 140
results from this study is shown in Fig. 26.63. The behavior in that study was found to be: • Mattresses with a bench-scale HRR (180 s average value) of < 165 kW m2 led to room fires of less than 100 kW. • Mattresses with a bench-scale HRR (180 s average value) of > 165 kW m2 generally led to room fires on the order of 1–2 MW. • The transition between those extremes was very abrupt. The sharp transition between trivial fires and room flashover conditions can be attributed to the details of the test room, but also to the use of an ignition source which specimens of intermediate characteristics could ‘evade.’ Additional data on mattress HRR have been published by SP [143], Lund University [144], and in the CBUF project [10]. The CBUF study included full-scale room fire tests, open-burning furniture calorimeter tests, and Cone Calorimeter tests. The mattress results are given in Table 26.17. In both of the full-scale test environments, no bedding was used, but a square-head burner was applied to the top surface of the specimen, precluding complications from any receding-surface behavior. The bench-scale test data presented were obtained at a 35 kW m2 irradiance. The results indicate that, when tested in the standard ISO 9705 room, a very drastic room effect occurs for open-air HRR values over about 300 kW. The bench-scale data indicated that when widely varying mattress thicknesses exist, a simple relation of bench-scale to full-scale HRR cannot be sought, even if only predictions of open-burning (furniture calorimeter) results
Thick. factor 0.44 1.00 0.20 0.40 1.00 0.40 1.00 1.00
00
q_ 60 162 136 225 111 111 327 256 232
00
q_ 180 135 82 227 118 118 159 191 198
00
q_ 180 th. fac. 59 82 45 47 118 64 191 198
00
qtot 50 21 43 45 45 30 62 37
Prop. fire N N N N Y Y Y Y
would be desired. As a first cut, it was concluded that mattresses can be grouped into two groups— those leading to propagating fires (the mattress being consumed in flaming combustion during a relatively short time), and those that do not. The former can be considered to be of the highest hazard, while the latter present only trivial hazard. Since, for practical reasons, all mattress composites must be tested in the Cone Calorimeter using a 50 mm thickness, to take into account effects due to thin mattresses, a thickness factor is defined: Th: f ac: ¼ min
thickness, mm , 1:0 50
For mattresses where the innersprings are used, the thickness is measured from the top of the mattress down to top of the metal springs; it is not the total thickness. To determine whether the mattress fire will propagate or not, the following rules were developed: 00 If q_ 180 ðTh: f ac:Þ < 100 kW m2 and 00
q_ 60 < 250 kW m2 then, Q_ < 80 kW (non-propagating fire) else, Q_ > 80 kW (propagating fire) The HRR values over 80 kW in fact are flashover values of up to 2.5 MW, but the scheme does not assign a specific HRR number. Qualitatively, this scheme reflects the type of abrupt behavior change found in earlier studies
26
Heat Release Rates
853
(Fig. 26.63), but here some more refined rules were developed that avoid non-predictions which would occur from simple correlation. During the same CBUF project, a more sophisticated mattress fire model has been developed by Baroudi et al.; this model is not easy to use, but details are available [10, 145]. In the US, mattresses made after July 1, 2007 have been required by law to conform to the 16 CFR 1633 standard of the Consumer Product Safety Commission. The latter augments the previous standard (16 CFR 1632) for smoldering by a flaming test procedure. The primary requirement for the new standard is that the peak HRR not exceed 200 kW; in addition the total heat release during the first 10 min of test must not exceed 15 MJ. NRCC [72] tested an example of one such mattress and did confirm a peak HRR < 200 kW. However, a room fire test run with this same model of mattress, an equally-conforming mattress foundation, and a set of bedding produced a peak HRR of 1812 kW. This would likely lead to flashover in a room of the ISO 9705 room size and doorway dimensions. Another test run by NRCC Fig. 26.65 HRR for two types of mining equipment
showed an extreme radiant feedback effect, since mattresses not made to the Federal standard typically showed HRR values in excess of 3000 kW even for small mattress sizes, while a bunk bed attained > 6000 kW in the room test.
Mining Equipment Hansen and Ingason [146] tested two pieces of mining equipment, burning them in an underground mine facility. The first item was a Toro 501 DL diesel-powered wheel loader. The machine weighs 36,000 kg and stands 2.85 m tall. The structure is steel, but it also contains rubber tires, hydraulic oil, diesel fuel, and smaller components, including driver’s seat, cables, etc., for an estimated fuel content of 76 GJ, the majority of this being the giant tires. The second item was a Rocket Boomer 322 drilling rig. This item weighs 18,400 kg and stands 2.95 m tall. Its fuel content was estimated at 46 GJ, with the fuel comprising hydraulic oil, hoses, tires, diesel fuel, cables, and
30,000 Drilling rig Loader
Heat release rate (kW)
25,000
20,000
15,000
10,000
5,000
0 0
2000
4000 6000 Time (s)
8000
10000
854
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miscellaneous smaller items. With both items, the fuel tank was partly emptied and poured out to create a pool fire under the specimen, and this pool was ignited to start the fire. Figure 26.65 shows the HRR results, with loader achieving a peak value of 15.9 MW, while the drilling rig showing 29.4 MW.
Office Furniture Office worker cubicles (‘workstations’) have been tested in several projects at NIST [147–149]. Figure 26.66 show that severe fire conditions can be generated by these arrangements. In some cases, fires of nearly 7 MW were recorded from the burning of a single
person’s workstation. The identification of the main conditions in these tests is given in Table 26.18. In one test series [147] replicates were tested in an open furniture calorimeter, then the configuration was tested again in a room test; this is illustrated in Fig. 26.67. In 2004, NIST [150] reported results of some tests of modern office furniture, i.e., primarily plastics-based. Two full-scale tests were conducted, a single person cubicle, and a fourperson cluster of cubicles. The one-person cubicle was tested in an open environment, while the four-person cluster was in a semi-open arrangement: three walls and a ceiling were present, but not the fourth wall. The results (Fig. 26.68) indicate both a radiant augmentation due to the ceiling and an augmentation due to multiple fuel
Table 26.18 Workstations tested by NIST in 1988 and 1992 Code A B C D E F
Combustible mass (kg) 291 291 335 NA 291 NA
Number of sides w. acoustic panels 0 1 2 3 4 4
Description Mostly old-style wood furniture Semi-modern furniture Modern furniture Modern furniture Modern furniture Modern furniture
Fig. 26.66 HRR of office workstations tested by NIST in 1988 and 1992
Ref. 146 146 148 148 146 148
7000 A B C D E F
Heat release rate (kW)
6000 5000 4000 3000 2000 1000 0 0
500
1000 Time (s)
1500
2000
26
Heat Release Rates
855
Fig. 26.67 NIST results for workstation tests of 1988 and 1992
3000 Open test
2500
Open test, repeat
Heat release rate (kW)
Room test
2000
1500
1000
500
0
0
300
600
900
1200
1500
1800
2100
Time (s)
Fig. 26.68 NIST results for workstation tests of 2004
20,000 1 workstation 4 workstations
18,000 16,000
HRR (kW)
14,000 12,000 10,000 8,000 6,000 4,000 2,000 0 0
200
400
600
800
1000
1200
1400
Time (s)
loads being present in direct proximity. In that same study, NIST also ran open calorimeter tests on two office chairs, a swivel chair and a chair with a fixed metal frame (Fig. 26.69). The gross mass for the chairs were 20.5 kg, and 11.8 kg, respectively, but the mass of the combustible portions was not evaluated, although the major fraction of the total mass was the mass of the
steel components. The swivel chair had major components comprising hard-plastic shell material, and the fire involvement of these components was the cause of the second HRR peak. Additional tests were conducted by Kakegawa et al. [151] at Japan’s National Research Institute of Fire and Disaster. Each test was started by a
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Fig. 26.69 HRR results for the two office chairs tested
500 Swivel chair Metal frame chair
450 400
HRR (kW)
350 300 250 200 150 100 50 0 0
200
400
600
800
1000
1200
1400
Time (s)
Fig. 26.70 HRR of fourunit workstations tested at NRIFD
3000
Test 1 Test 2 Test 3 Test 4
2500
HRR (kW)
2000
1500
1000
500
0 0
300
600
900
1200
1500
Time (s)
polypropylene wastebasket filled with 0.2 kg of paper. The wastebasket, by itself, was found to show a peak HRR of 50–60 kW. The desks were of modern metal-frame construction, with
plastic trim parts. In addition, the workstations contained small filing cabinets, telephones, chairs, computers, and a modest amount of office paper. The HRR results for the four-unit
26
Heat Release Rates
857
Table 26.19 Workstations tested by NRIFD Test 1 2 3 4 11 12 14
Combustible mass (kg) 570 597 1054 1086 272 264 263
Type of workstation Clerical Clerical Engineering Engineering Engineering Engineering Engineering
Fig. 26.71 HRR of one-unit workstations tested at NRIFD
No. of desk units 4 4 4 4 1 1 1
Partition panels N Y N Y Y N N
Peak HRR (kW) 3035 2476 2957 2271 1602 1870 1219
Time to peak (s) 508 616 793 732 441 412 601
2000 Test 11 Test 12 Test 14
1800 1600
HRR (kW)
1400 1200 1000 800 600 400 200 0 0
300
600
900
1200
1500
Time (s)
workstations are shown in Fig. 26.70, while those for the one-workstation units are shown in Fig. 26.71. Even though the four-unit workstations had a very high fuel load, the HRR values were lower than the American units studied at NIST. This is presumably due to a more protected arrangement of the fuel, plus the fact that only short (0.45 m high) partition panels were used (Table 26.19).
Pallets Conceptually, a wood pallet is a similar arrangement to a wood crib. The geometry, however, is different. Instead of being composed of
identical rows of square-section sticks, pallets are made up of rectangular elements in a traditionally dimensioned configuration as shown in Fig. 26.72. The fire safety concern with pallets arises when they are idle and stacked many units high. Krasner [152] has reported on a number of tests where the burning rate of pallets was measured. A typical experimental heat release rate curve is shown in Fig. 26.73. This curve shows that, much like for a wood crib, a substantially constant plateau burning can be seen if the stack is reasonably high. The results for a standard pallet size of 1.22 1.22 m can be given as a general heat release rate expression
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Fig. 26.72 The geometric arrangement of a stack of wood pallets
hc
P.
1.2
2m
2m
TY
1.2
P.
4000 3500 Heat release rate (kW)
Fig. 26.73 HRR of a typical wood pallet stack (1.22 1.22 1.22 m high)
TY
3000 2500 2000 1500 1000 500 0 0
200
400
600
800
Time (s)
q_ ¼ 1368 1 þ 2:14h p ð1 0:03MÞ
00 q_ ¼ 919 1 þ 2:14h p ð1 0:03MÞ
where hp is stack height (m), M is moisture (%), and a net heat of combustion of 12 103 kJ kg1 has been assumed. For convenience in applying to nonstandard pallet sizes, this can be expressed on a per-unit-pallet-floorarea basis as:
The agreement between the above equations and experimental data is seen to be good over a wide range of pallet heights (Fig. 26.74), but the expressions do somewhat overpredict the burning rates if applied to short stacks, with stack height hp < 0.5 m.
26
Heat Release Rates
859
Fig. 26.74 Dependence of pallet HRR on stack height
14
Wood pallet stacks 1.22 m × 1.22 m × 0.14 m each pallet Assumed: Δhc (net) = 12 MJ/kg
Peak HRR (MW)
12 10
4 points
8 6 4
Mean of 8 points
2 0 0
1
2
3
4
5
6
7
Pile height (m)
Fig. 26.75 HRR of pillows
120 PUR, 527 g Polyester, 430 g Latex, 1003 g
100
PUR, 650 g
Heat release rate (kW)
PUR, 630 g Polyester, 602 g
80
Feathers, 966 g
60
40
20
0 0
300
600
900
Time (s)
Pillows Pillow tests have been reported by NIST [153] and SP10. The results are given in Fig. 26.75.
a variant of ISO 9705 especially configured for pipe insulation testing [154]. Data on this configuration have been published by Wetterlund and Go¨ransson [155] and by Babrauskas [156].
Pipe Insulation
Plants and Vegetation
The available data are from the configuration where pipe insulation is used to entirely cover the ceiling of a test room. The test method used is
Trees, Natural Some tests on Christmas trees were reported by VTT [157] and by Damant and Nurbakhsh [158].
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Fig. 26.76 The peak HRR for Douglas-fir Christmas trees, as a function of moisture and mass
400
Peak HRR/mass (kW kg−1)
350
300
250
200
150
100
50
0 0
20
40
60
80
100
120
140
160
Foliar moisture content (%)
Newer studies, however, indicated that these tests, which examined only a few trees, did not capture the full range of HRR values associated with Christmas trees. The main variables that govern the HRR of Christmas trees are the following: • Moisture content of the needles • Mass of the tree • Species • Ignition source used Moisture is the dominant variable and this had not been studied previously. The results of an extensive series of fire tests [159] on Douglas-fir (Pseudotsuga menziesii) trees are shown in Fig. 26.76, while the HRR of a typical test is illustrated in Fig. 26.77. The trees were about 2.1 m tall, had an average mass of 11 kg. The trees were cut, placed in a watering stand, and watered according to various watering programs. The average tree was kept for 10 days prior to testing. The relation of the curve fit in Fig. 26.76 is: _ q=mass ¼
400 1 þ 0:0538MC
where MC ¼ foliar moisture (%) and the units of _ q=mass are kW kg1. Moisture is measured on a
dry basis, so values can readily exceed 100 %; also note that it is the needle (foliar) moisture that governs the burning behavior—trunk moisture is not a relevant variable. The mass of the tree used here is the entire mass; Evans et al. [160] suggested that if data are available only for the foliar mass, but not the mass of the entire tree, the approximation be used: mass ¼ 2 massfoliar To ignite trees with a small flame requires that the moisture content be below 50–60 %. Otherwise, ignition is still possible if using larger combustible objects. In the work reported, the trees which could not be ignited by a small flame were all ignited by first igniting wrapped gift packages placed under the tree. For design purposes, it should be adequate to assume that the heat release curve is a triangle. This requires knowing only the peak HRR and the total heat released. To estimate the latter, it was found in the tests that the Christmas trees showed an effective heat of combustion of 13.1 MJ kg1. Thus, from knowing the mass of the tree and the effective heat of combustion, the total heat
26
Heat Release Rates
release may be estimated. The needle moisture may not be known for design purposes. It is governed both by the watering program and by the innate biology, e.g., the species, of the tree. No model is available at the present time that can predict the moisture. However, the research indicated that Douglas-firs are a notably shortlasting species. The data points shown in Fig. 26.76, with one exception, represent trees that had been on display for less than 16 days; some were watered carefully and regularly, while others were not. Other species of Christmas trees, such as Noble fir or Fraser fir are considered to be longer-lasting, but are less commonly bought. A smaller test series on Scotch pine trees was tested at NIST by Stroup et al. [161]. They examined trees of 2.3–3.1 m height and mass between 9.5 and 20.0 kg; with one exception, the trees were of mass 12.7 kg or greater. Apart from one tree, which is not considered here since it was not successfully ignited, the trees were left without water for 3 weeks in a room at 50 % RH and 23 C. Ignition was with an electric match to a lower branch of the tree. The Scotch pines were substantially taller and heavier than the Douglas-firs, so it is not surprising that higher peak HRR values were attained. The peak HRR values ranged from 1620 to 5170 kW. Normalized per mass, the average was 183 kW kg1, with the range being 103–259 kW kg1. The moisture of the branches was not recorded, but presumably was 1.0
Burning mode Convective, laminar Convective, turbulent Radiative, optically thin Radiative, optically thick
heat of evaporation Δhv, which is the enthalpy required to change a unit mass of liquid to a gas at 25 C. The relation between these two quantities is: Δhg ¼ Δhv þ ðT b 25Þ Cpv where we have taken the simplification that Cpv, the heat capacity of the vapor (kJ kg1 K1) is a constant. An extensive tabulation of these constants is provided by Babrauskas [173]. Hottel’s analysis of Blinov and Khudiakov’s data showed two basic regimes are possible: radiatively dominated burning for large pool diameters, D, and convectively dominated burning for small D. Furthermore, in the convective regime the flow can be either laminar or turbulent (being always turbulent for radiatively driven pools), while in the radiative regime the flames
26
Heat Release Rates
865
can be optically thin or thick. These distinctions can, in the simplest analysis, be made solely on the basis of pool diameter. Such a simple classification is possible if the pool is strictly circular, radiant heating is only from the pool’s flames and not augmented by external sources, and there are no interferences to the flow streamlines which could trip the onset of turbulence. In such a simplified case, the regimes can be identified as in Table 26.20. In the convective limit (small pools), one may make the following approximation:
Δhc q_ ¼ q_ c Δhg 00
A
however, the values of q_00c to be taken are not easily determined. Some additional details are given in [174]. For fire hazard analysis purposes, liquid pool fires will rarely be significantly dangerous if they are smaller than about 0.2 m in diameter. Thus, it will often only be necessary to treat pools burning in the radiative regime. In the radiative regime, it is found that data for most organic liquids can be well correlated by:
Table 26.21 Pool burning: thermochemical and empirical constants for a number of common organic fuels Material Cryogenics Liquid H2 LNG (most CH4) LPG (mostly C3H8) Alcohols Methanol (CH3OH) Ethanol (C2H5OH) Simple organic fuels Butane (C4H10) Benzene (C6H6) Hexane (C6H14) Heptane (C7H16) Xylenes (C8H10) Acetone (C3H6O) Dioxane (C4H8O2) Diethyl ether (C4H10O) Petroleum products Benzine Gasoline Kerosene JP-4 JP-5 Transformer oil, hydrocarbon Fuel oil, heavy Crude oil Solids Polymethylmethacrylate Polyoxymethylene (CH2O)n Polypropylene (C3H6)n polystyrene (C8H8)n a
See text
Density (kg m3)
Δhg (kJ kg1)
00
Δhc (MJ kg1)
m_ 1 (kg m2 s1)
kβ (m1)
0.017 (0.001) 0.078 (0.018) 0.099 (0.009)
6.1 (0.4) 1.1 (0.8) 1.4 (0.5)
70 415 585
442 619 426
120.0 50.0 46.0
796 794
1195 891
20.0 26.8
a
a
a
a
573 874 650 675 870 791 1035 714
362 484 433 448 543 668 552 382
45.7 40.1 44.7 44.6 40.8 25.8 26.2 34.2
0.078 (0.003) 0.085 (0.002) 0.074 (0.005) 0.101 (0.009) 0.090 (0.007) 0.041 (0.003) 0.018 0.085 (0.018)
2.7 (0.3) 2.7 (0.3) 1.9 (0.4) 1.1 (0.3) 1.4 (0.3) 1.9 (0.3) 5.4 0.7 (0.3)
740 740 820 760 810 760 940–1000 830–880
– 330 670 – 700 – – –
44.7 43.7 43.2 43.5 43.0 46.4 39.7 42.5–42.7
0.048 (0.002) 0.055 (0.002) 0.039 (0.003) 0.051 (0.002) 0.054 (0.002) 0.039 0.035 (0.003) 0.060
3.6 (0.4) 2.1 (0.3) 3.5 (0.8) 3.6 (0.1) 1.6 (0.3) 0.7 1.7 (0.6) 0.62
24.9 15.7 43.2 39.7
0.020 (0.002)
3.3 (0.8)
1184 1425 905 1050
1611 2430 2030 1720
866
V. Babrauskas
00 q_ ¼ Δhc m_ 1 1 ekβ D A
00
This requires determining two empirical 00 constants: m_ 1 and the term (kβ); the first of these is the asymptotic mass loss rate per unit area as the pool diameter increases towards infinity; the second is the product of the extinctionabsorption coefficient k and the beam-length corrector β. These constants are given in Table 26.21 for a number of common fuels. The net heat of combustion, Δhc, is also listed in the table. In principle, a slightly lower value, the effective heat of combustion, should be used instead of the net heat of combustion that is determined with oxygen bomb calorimetry. Some bench-scale values of a combustion efficiency factor to convert oxygen bomb values into experimentally-measured values are given in Chap. 36, “Combustion Characteristics of Materials and Generation of Fire Products.” For most liquids, however, the bench-scale values are not greatly below unity and realistic large-scale measurements are not available, thus the improvement in accuracy by extrapolating from bench-scale results may be nil. Alcohol fuels show minimal radiative flux, in comparison to other fuel types. Thus, the best recommendation previously had been to use Fig. 26.81 HRR of plastic house plants
constant values of m_ , independent of diameter. Based on some newer test results [175], it is clear that a diameter effect does exist, although it cannot be expressed in standard form. Thus, it is recommended that for methanol or ethanol the 00 00 values be used: m_ ¼ 0.015 (D < 0.6 m); m_ ¼ 00 0.022 (0.6 < D < 3.0 m); and m_ ¼ 0.029 (D > 3.0 m). The above discussion implicitly assumed that the pool depth is at least several millimeters. If liquids are spilled on a horizontal surface that has no low spots and no diking, then a liquid layer will form that is less than 1 mm thick. Thin-layer pools of this nature (which can occur in arson cases) show a lower HRR than do pools of greater depths. Putorti et al. [176] studied gasoline spills on wood parquet, vinyl floor tiles and carpeting. When a specified volume of liquid is spilled, the problem to be solved can be separated into two components: (1) determining the area of the spill, or, equivalently, the spill thickness; and (2) determining the HRR per unit area. For wood floors, Putorti found the A ¼ 1.5 V, where A ¼ area (m2) and V ¼ volume (L). For vinyl tile, a similar relation was also found, but the constant being 1.8. Converted into layer thicknesses, the thickness for wood was 0.67 mm
200 Palm, bushy Palm, slim Ficus
Heat release rate (kW)
150
100
50
0 0
60
120 Time (s)
180
240
26
Heat Release Rates
and for vinyl tile it was 0.56 mm. Earlier work has indicated that a relation of this kind should only be applied to smooth floor surfaces. For rough, absorptive surfaces a constant thickness is not obtained, and larger spill volumes produce, effectively, greater layer thicknesses [177]. Putorti’s study with carpets both indicated large differences between carpet types and also showed that the data could not be represented as a constant layer thickness. The HRR per unit area values are shown in Fig. 26.82. For the solid surface pours, the spill areas were in the range 0.4–1.8 m2. As presented above, pools of large depths in this size range would show HRR values of 1900–2400 kW m2. Thus, the carpet-surface values are about 70–80 % of values that would have been computed using the normal pool fire formulas. The smooth-surface values, however, are only about 1/5 of the values that would be found for pools of sizable depths. A similar study by Gottuk et al. [178] also describes HRR values for spills on hard surfaces that are, very roughly, about 1/5 of those for ‘normal’ pools. The relationships found by Putorti can only be expected to hold on deadflat surfaces. If surfaces are crooked, then ponding at low spots will occur and uniform spill depths should never be anticipated. DeHaan [179] conducted two tests using 1.9 L of Coleman camping fuel. This is a straight-run petroleum distillate containing normal and iso-alkanes ranging from hexane to undecane. When poured on an unpadded carpet, a HRR peak of 1150 was found, with a burning time of roughly 3 min. When poured upon a carpet that had an pad underneath it, a lower HRR peak (890 kW) was found, the peak was slightly delayed (85 s, versus 65 s) and there was a long tail to the HRR curve. The discussion above pertains only to openburning fires. Thus, the literature-derived burning rates can be used only in the case of a very large, well-ventilated room (compared to the size of the fire). If calculations show that the ‘freeburning’ pool would cause a temperature rise of more than, say, 100 C, then it is clear that radiative feedback will start being important and such an approximation cannot be made. No
867 Table 26.22 HRR of European refrigerators Specimen Initial mass (kg) Mass loss (kg) Peak HRR (kW) Extinguishment time (s) Total heat (MJ)
R1 70.0 18.0 2125 925 537
R2 67.2 14.3 1816 722 404
R3 43.7 18 852 – 432
simple formulas exist for computing the enhanced burning rates when a pool receives significant room radiation. If computations under these conditions are necessary, the theoretical study of Babrauskas and Wickstro¨m [11] should be consulted. The computer program COMPF2 [180] can also be used to treat this case. The problem of pool burning is interesting from a combustion science point of view, and over the years there has been a very large number of studies which attempted to go beyond empirical predictions [181–184]. In addition, work is occurring to provide more detailed experimental measurements for specific fuels [185, 186].
Refrigerators VTT tested [105] two European refrigerators using a propane burner of 1 kW (designated R1, R2), while EFRA tested a single refrigerator (R3), ignited with a needle-flame burner. The specimens are described in Table 26.22, while test results are shown in Fig. 26.83. The VTT specimens were extinguished before the ultimate peak burning would have occurred, while the EFRA specimen was not. These results must not be applied to appliances used in North America, since European appliance styles are different from North American ones and also because local standards are such as to permit appliances of greater flammability in Europe.
Shop Displays Chow [187] tested shop displays of three types: clothing display, compact disc (CD) display, and
868
V. Babrauskas 2000 1800
HRR per unit area (kW m−2)
1600 1400 1200
Wood Vinyl
1000
Carpet 1 Carpet 2
800 600 400 200 0 0
0.25
0.5
0.75
1
1.25
Spill volume (L)
Fig. 26.82 HRR of thin pools of gasoline over various surfaces
Table 26.23 Shop-display commodities tested by Chow Display type Clothing Compact discs Newsstand
Combustible mass (kg)
Size (m)
15
2 ea, 1.5 m wide 1.6 m high 2 ea, 1 m wide 2.2 m high
Fig. 26.83 HRR of European refrigerators tested by VTT and EFRA
Ignition source (kW) 470 1100 400
Peak HRR (kW) 2400 3600
2500 R1 R2
HRR (kW)
2000
R3
1500
1000
500
0 0
500
1000
1500
Time (s)
2000
2500
26
Heat Release Rates
869
Fig. 26.84 HRR of various shop-display commodities tested by Chow
4000 Newsstand CD rack Clothes rack
3500 3000
HRR (kW)
2500 2000 1500 1000 500 0 0
200
400
600
800
1000
Time (s)
newsstand. The clothing display comprised all-cotton T-shirts arranged on four small display racks. The CD display contained a total of 240 discs. The ignition source in each case was a small pool of gasoline, to represent an arson fire. The results are shown in Table 26.23 and Fig. 26.84.
Television Sets The burning characteristics of TV sets depend greatly on whether they have been made for the North American market, following the requirements of UL, or not. In countries where UL standards do not apply, plastic TV cabinets are generally highly flammable, commonly being made of plastics that only have an HB rating according to the UL 94 [30] procedures. These are readily ignitable from small-flame ignition sources and burn vigorously when ignited [44, 188]. By contrast, sets made for the North American market have to obtain a V-0 classification under UL 94 and will resist ignition from small flame sources.
Babrauskas et al. [88] tested at NIST small polystyrene television cabinets of two types, fireretarded and not. Since the circuit components contribute negligible HRR in comparison to the outer shell, only the cabinets were tested. Two very small (“personal size”) units were tested side-by-side in each test. This can represent either two appliances or simply the mass of one larger set. SP tested two television sets [29], a US-market set with housing having a V-0 rating, and a Swedish set with a housing having an HB rating. The US set was a 690 mm (27 in.) model, while the Swedish one was 710 mm (28 in.). The US set had a total combustible mass of 6.5 kg, with 2.9 kg comprising the enclosure, while the Swedish set had 6.0 and 2.7 kg, respectively. The Swedish set was successfully ignited and burned with a small flame the size of a match flame. The US set resisted ignition from this source and was then subjected to a 10 kW burner. With this challenge, the set burned, but showed little HRR beyond the 10 kW of the source. Finally, the test protocol chosen was a 30 kW burner. The burner HRR was subtracted out from the data shown in Fig. 26.85.
870
V. Babrauskas
Fig. 26.85 HRR of various television sets tested by NIST and SP
600 NIST, non-FR NIST, FR SP, Swedish TV SP, US TV
Heat release rate (kW)
500
400
300
200
100
0 0
300
Table 26.24 European televisions tested by VTT Specimen Type Size (inches) Initial mass (kg) Mass loss (kg) Peak HRR (kW) Total heat (MJ)
TW1 Wood 24 32.7 10.2 230 146
TW3 Wood 26 39.8 10.2 290 150
TP1 Plastic 28 31.8 5.2 274 140
TP2 Plastic 25 24.4 4.6 239 116
TP3 Plastic 28 30.5 5.3 211 137
VTT conducted two projects where TV sets were tested. In the first study [156], they tested two old, 1960s vintage (black-and-white) televisions with large wood cabinets; these were ignited with a small cup of alcohol. In a newer study [105], they tested modern plasticcabinet televisions using a propane burner of 1 kW. The specimens are described in Table 26.22, while test results are shown in Fig. 26.86. Nam et al. [189] tested a modern TV set (plastic cabinet) together with a wood stand for it. They obtained peak HRR values of 200–300 kW, although the peak took 20–40 min to reach. The most recent results come from Hoffmann et al. [190] who tested TV sets in a wooden
600
900 Time (s)
1200
1500
1800
entertainment center. The ignition source was a small amount of alcohol for HB-rated cabinets. For the V-0 rated cabinets, some small consumer goods, HB rated, were first ignited and these were then used to ignite the test TV sets (Tables 26.24 and 26.25). After the initial peak (Fig. 26.87), the burning involved the wood entertainment center, thus the latter portion of these HRR curves is not germane to TV sets per se.
Transport Vehicles and Components Passenger car HRR was measured at the Fire Research Station [191] and VTT [192]. The FRS laboratory examined a 1982 Austin Maestro and a 1986 Citroe¨n BX, while VTT examined a Ford Taunus, a Datsun 160, and a Datsun 180. The dates of manufacture were only stated as late 1970s. These results are shown in Fig. 26.88. Additional tests were reported by MFPA [193] and SP [194]. MFPA tested a Citroe¨n, a Trabant, and a Renault Espace, while SP tested a Fiat 127 of unspecified vintage. These results are shown in Fig. 26.89. The peak values range
26
Heat Release Rates
871
Table 26.25 Characteristics of TV sets tested by Hoffmann et al. Test No. 1A
TV Screen Size 510 mm (20 in.)
Rating V0
2A
510 mm (20 in.)
V0
3A 1B
480 mm (19 in.) 510 mm (20 in.)
HB V0
2B
510 mm (20 in.)
V0
Other HB Devices 1 cordless Phone, 1 small radio 1 telephone None 1 cordless phone, 1 small radio 1 telephone
Fig. 26.86 HRR of European television sets tested by VTT
Ignition Source 5 mL IPA
Peak HRR (kW) 363
Time to Peak (s) 273
5 mL IPA adjacent to phone 5 mL IPA 5 mL IPA
199
594
>1450 >1000
615 216
299
975
5 mL IPA adjacent to phone
300 TP1 TP2 TP3 TW1 TW3
250
HRR (kW)
200
150
100
50
0 0
300
600
900
1200
1500
1800
Time (s)
from 1.5 to 8.5 MW. These numbers are rather widely disparate and it is not fully clear why, except that this is not due to the fraction of polymer content onboard. Some very extensive testing was conducted at CTICM, as shown in Fig. 26.90. Test 2 was a Renault 18 (951 kg), Test 3 a Renault 5 (757 kg), Test 4 another Renault 18 (955 kg), while the specimens for the remaining tests were only identified as a “Large car, 1303 kg” (Test 7), and “Small car, 830 kg” (Test 8). Additional
tests were run in a two-car configuration, involving one small car (790 kg) side-by-side to a large car (1306 kg). These results are shown in Fig. 26.91, but test details were not published. The mass loss values are shown in Table 26.26. Okamoto et al. [195] ran a series of experiments where they tested replicates of the same vehicle (Toyota Cressida, also known as Mark2 GX81) but varied the test conditions (Table 26.27). Figure 26.92 shows the HRR results; spikes judged to be spurious were
872
V. Babrauskas
Fig. 26.87 HRR of TV sets tested by Hoffmann et al.
800 Test 1A Test 2A
700
Test 3A Test 1B
600
Test 2B
HRR (kW)
500 400 300 200 100 0 0
Fig. 26.88 HRR of cars tested at FRS and VTT
200
400
600 Time (s)
800
1000
1200
9000 8000
Citroen BX Austin Maestro Ford Taunus Datsun 160 Datsun 180
7000
HRR (kW)
6000 5000 4000 3000 2000 1000 0 0
500
removed from these data. In Test B, an explosion occurred at 1517 s, when pyrolysates accumulated in the passenger compartment suddenly ignited. Explosions did not occur with the other tests. The tests are especially valuable since, in their paper, the authors documented
1000
1500 Time (s)
2000
2500
3000
many details of fire development in these experiments. The results suggest that small differences in test conditions can affect the time scale of fire development in an automobile quite notably, also that windows should be open if maximum HRR conditions are to be elicited. It
Fig. 26.89 HRR of cars tested at MFPA and SP
7000 Citroen Steinert Trabant Steinert Renault Espace Fiat 127
6000
HRR (kW)
5000
4000
3000
2000
1000
0 0
1000
2000
3000
4000
5000
Time (s)
Fig. 26.90 HRR results of CTICM one-car tests
9000 Test 2 Test 3 Test 4 Test 7 Test 8
8000 7000
HRR (kW)
6000 5000 4000 3000 2000 1000 0 0
1200
2400
3600
Time (s)
Table 26.26 Results of CTICM car tests Test 2 3 4 7 8 9 10
Peak HRR (kW) 1208 3476 2159 8310 4073 7500 8230
Total heat released (MJ) 1758 2100 3080 6670 4090 8890 8380
Mass loss of car #1 (kg) 185 138 145 278 184 124 175
Mass loss of car #2 (kg) – – – – – 172 166
874
V. Babrauskas
Table 26.27 Test conditions for sedan vehicles tested by Okamoto et al. Test A B C D
Windows Open Closed Closed Closed, exc. part of left-front window
Amount of fuel in tank (L) 10 10 20 10
Fig. 26.91 HRR results of CTICM two-car tests
Ignition point Rear wheel splashguard 00 00
Left front seat
Peak HRR (kW) 3512 3034 1856 2395
Total HR (MJ) 4950 4860 4930 5040
9000 Test 9
8000
Test 10
7000
HRR (kW)
6000 5000 4000 3000 2000 1000 0 0
600
1200 Time (s)
Table 26.28 Test conditions for minivan vehicles tested by Okamoto et al. Test A B C D
Windows Closed Closed Closed Closed, exc. part of left-front window
Amount of fuel in tank (L) 10 10 10 10
Ignition point Rear wheel splashguard Right front bumper Center of the second row seat Center of the third row seat
is also noteworthy that the total HR values were nearly identical for all tests. Okamoto et al. [196] later ran tests on minivan type vehicles, using only one model of vehicle (Nissan Serena), but four different test conditions (Table 26.28). The vehicle weighed 1440 kg and had a 2.0 L gasoline-powered engine. Same as for the sedan vehicles, the HRR development
Peak HRR (kW) 3603 3144 – 4094
Total HR (MJ) 5367 5006 – 5153
was ragged and not approximately triangular or constant (Fig. 26.93). In Test C, the fire selfextinguished due to dropping oxygen levels since no windows broke. Ohlemiller and Shields [197] tested a number of individual components from a passenger vehicle (a minivan). The components that has a mass of around 2 kg or less all showed small HRR
26
Heat Release Rates
875
Fig. 26.92 HRR results for automobiles tested by Okamoto et al.
Fig. 26.93 HRR results for minivans tested by Okamoto et al.
4500 Test A Test B Test D
4000
Heat release rate (kW)
3500 3000 2500 2000 1500 1000 500 0 0
1000
2000
3000
4000
5000
6000
7000
Time (s)
values, typically less than 80 kW. Three components, however, showed substantial HRR values—an empty plastic fuel tank (8.5 kg), a passenger seat (8 kg), and an instrument panel (10.6 kg). The HRR curves for these items are shown in Fig. 26.94. In a separate study, Ohlemiller [198] tested one production version of an automotive HVAC unit, along with two experimental versions containing fire-retardant
agents. The non-FR version showed HRR in excess of 200 kW, while the FR versions developed only about 5 kW. Railway car results were reported by SP [197] and by Steinert [198]. Figure 26.95 shows a passenger railway car (European type IC train) reported by SP and an ICE train car by Steinert, who also published the data labeled as “two halves.” The latter comprised two half cars, one being aluminum
876
V. Babrauskas
Fig. 26.94 HRR of some larger components from a passenger vehicle
800 Instrument panel 700 Passenger seat
600
HRR (kW)
500 400
Plastic fuel tank (empty)
300 200 100 0 0
200
400
600
800
1000
1200
1400
Time (s)
Fig. 26.95 HRR of railway cars
50,000 Railway car (ICE train) Railway car (IC train) Railway car (two halves)
45,000 40,000
HRR (kW)
35,000 30,000 25,000 20,000 15,000 10,000 5,000 0 0
1000
2000
3000
4000
5000
6000
7000
Time (s)
and the other steel. These were abutted to form one test specimen. A fire was ignited in the aluminum car, but did not become rapid until windows failed at around 40 min. SP also reported results on two
subway cars [205] and half a tram car [169]; these results are shown in Fig. 26.96. Data on school buses from SP [199] and Steinert [200] are shown in Fig. 26.97.
26
Heat Release Rates
877
Fig. 26.96 HRR of subway cars and half a tram car
40,000 Subway car, F4 Subway car, F42 Half of a tram car
35,000 30,000
HRR (kW)
25,000 20,000 15,000 10,000 5,000 0 0
500
1000
1500
2000
2500
3000
3500
Time (s)
Fig. 26.97 HRR of school buses
35,000 School bus, SP School bus, Steinert
30,000
HRR (kW)
25,000
20,000
15,000
10,000
5,000
0 0
1000
A number of researchers have tested portions of various heavy vehicles. Tests on transport seating were done at SP [201]. They measured an array of four double bus seats and a similar arrangement of train seats. The foam was HR
2000
3000 4000 Time (s)
5000
6000
7000
polyurethane, while the cover was a viscose/wool/polyester/polyamide blend for the bus seats and 100 % wool fabric for the train seats. These HRR results are shown in Fig. 26.98.
878
V. Babrauskas
Fig. 26.98 HRR of seating components of heavy vehicles
2500 Bus seating Train seating
2000
HRR (kW)
1500
1000
500
0 0
200
400
600
800
1000
1200
1400
1600
Time (s)
600 Test 11, TB 133 burner ignition Test 12, TB 133 burner ignition Test 13, Trash bag ignition Test 14, Round gas burner ignition
500
HRR (kW)
400
300
200
100
0 0
200
400
600
800
1000
1200
1400
Time (s)
Fig. 26.99 HRR of Amtrak seats (pair), as tested by NIST, exposed to various ignition sources
NIST conducted tests [202] on a pair of Amtrak seats, presented with various ignition sources; these results are shown in Fig. 26.99. In the same research study, NIST also tested sleeping Amtrak berths; these results are shown in Fig. 26.100. Quite high HRR values were seen
from Amtrak wall/soffit carpeting tested in the same study (Fig. 26.101). These test specimens were only 1.0 m wide by 1.5 m high for wall carpeting, while the test that also added soffit carpeting had an 0.5 m deep carpeted soffit. Additional test results were obtained for Amtrak
26
Heat Release Rates
879
Fig. 26.100 HRR of Amtrak sleeping berths
1000 Test 15, Lower berth Test 16, Lower berth
HRR (kW)
800
Test 17, Lower and upper berths
600
400
200
0 0
200
400
600
800
1000
Time (s)
Fig. 26.101 HRR of Amtrak wall carpet and wall/soffit carpet specimens
800 Test 18, Wall carpet Test 19, Wall carpet Test 20, Wall and soffit carpet Test 21, Wall and soffit carpet
HRR (kW)
600
400
200
0 0
100
200
300
400
500
Time (s)
window drapes (Fig. 26.102) and compartment door privacy curtains (Fig. 26.103). Amtrak window assemblies are made from polycarbonate glazing material and also have polymeric gasketing and trim; these show substantial HRR (Fig. 26.104). Vehicle tires can ignite from an overheated axle and can release a substantial amount of heat if they burn. There is one study in the literature which documents such a fire. Hansen [203] burned a pair of 285/80 R22.5 truck tires
mounted on a tandem wheel arrangement. The HRR curve is given in Fig. 26.105. Vehicle tires are also prone to be ignited and to burn in tire dumps. The HRR will depend directly on the geometry and on the amount of tires involved. Some quantitative HRR experiments have been reported [204] on experiments done at the Fire Research Station. These experiments were for flaming tires, but most recent tire dump problems have been associated with a smoldering condition and no
880
V. Babrauskas 180 Test 22, Extended Test 23, Contracted Test 24, Contracted
160 140
HRR (kW)
120 100 80 60 40 20 0 0
100
200
300
400
500
Time (s)
Fig. 26.102 HRR of Amtrak window drapes
180 Test 25, Extended 160
Test 26, Contracted Test 27, Contracted
140
HRR (kW)
120 100 80 60 40 20 0 0
100
200
300
400
500
Time (s)
Fig. 26.103 HRR of Amtrak privacy curtains
HRR quantification under these conditions has been reported. Tests were also reported on two plastic mud guards [205], as used on large tanker trucks. One specimen failed to get ignited from a
100 kW burner, while the HRR for the second specimen is shown in Fig. 26.105. The ignition source was a 100 kW burner, and its HRR has not been subtracted from the results shown.
26
Heat Release Rates
881
Fig. 26.104 HRR of Amtrak coach window assembly
500 Test 28, 50 kW gas burner Test 29, Trash bag
HRR (kW)
400
300
200
100
0 0
200
400
600
800
Time (s)
Table 26.29 Characteristics of the SP Runehamer Tunnel tests
Test Load T1 380 wood pallets, 74 polyethylene pallets T2 216 wood pallets, 240 PUR foam mattresses T3 Mixed goods, comprising plastic and wood furniture, fixtures, and toys; also 10 large tires T4 600 cardboard cartons with 18,000 polystyrene cups, 40 wood pallets
Fire growth rate during Total Peak HRR Time to Total heat linear-growth period mass (kg) (MW) peak (s) release (MJ) (MW s1) 11,010 201.9 1110 242,000 0.335 6,930
156.6
846
141,000
0.438
8,550
118.6
600
131,000
0.273
2,850
66.4
444
57,000
0.282
For heavy-goods vehicles, the heat content of the combustibles being hauled is likely to greatly exceed the heat content of the vehicle itself. Thus, a recent research program at SP conducted by Ingason and Lo¨nnermark [206] (“Runehamer Tunnel tests”) characterized the HRR of some typical commodities of this type. Four large-scale tests were conducted (Table 26.29), with the results shown in Fig. 26.106. The commodities were arranged as volume 10.45 m long, 2.9 m wide, and 4.5 m high, but were not enclosed by a trailer body. In many cases, the trailer body is aluminum or tarpaulin, thus nearly-free burning may be expected in such worst-case situations.
For all except T4, the goods themselves were wrapped with polyethylene film. The authors especially noted that the primary period of fire growth in each case, up to ca. 100 MW (66 MW in the case of test T4), was linear and not of a t2 type. These linear-growth rates are given in Table 26.29. These results are especially noteworthy since they represent the highest HRR fires, of realistic products thus far studied. An earlier European research program [207–209] estimated the HRR of a truck loaded with 2,000 kg of modern upholstered furniture; however, these estimated HRR values, as derived by several investigators, varied widely.
882
V. Babrauskas
Fig. 26.105 HRR for truck tires and mud guard
1000 900 800
HRR (kW)
700 600 500 400 300 Truck tires Mud guard
200 100 0 0
500
1000
1500
2000
2500
Time (s)
Table 26.30 Some data obtained at VTT on 14 L polyethylene wastebaskets showing effect of packing density and basket construction Basket sides Solid Netted Solid Netted
Basket mass (kg) 0.63 0.63 0.53 0.53
Filling type Shredded paper Milk cartons Shredded paper Milk cartons
Filling mass (kg) 0.20 0.41 0.20 0.41
Trash Bags and Containers Bench-scale measurements of trash are not readily feasible, due to the naturally irregular arrangement of these combustibles. There are full-scale test results available, however, that can suggest appropriate values to be used in different circumstances. A small “bathroom size” (6.6 L) plastic wastebasket stuffed with 12 milk cartons used at NIST as an ignition source in early HRR testing [45] was found to show a HRR of about 50 kW, sustained for about 200 s. This value evidently represents a worst-case condition, since most researchers have measured
Filling density (kg m3) 14 29 14 29
Peak HRR (kW) 4 13 18 15
Total heat released (MJ) 0.7 3.0 7.3 5.8
significantly lower HRR rates. For example, Mehaffey et al. [210] tested a similar wastebasket filled with mixed paper/plastic fuel load and obtain a HRR curve which can be approximated as being 30 kW for 60 s. NIST [140] tested slightly larger, 8.5 L “office style” round polypropylene wastebaskets, filled with sheets of newspaper, totaling about 300 g of newspaper in a 315 g container. These gave peak HRR values of 28–35 kW and an active burning time of ca. 800 s. Table 26.30 shows some additional data [156], where, over a certain range, increasing packing density is seen to increase the heat release rate. Some typical trash-bag fires are shown in Fig. 26.107 [109].
26
Heat Release Rates
883
Fig. 26.106 HRR of representative heavy-goods vehicle cargo, as determined in SP’s Runehamer Tunnel tests
200
T1 T2 T3 T4
HRR (MW)
150
T3
T2
T1
100
T4
50
0 0
500
1000
1500
2000
2500
3000
Time (s)
Fig. 26.107 HRR of trash bags
400 Three sacks, 3.51 kg Two sacks, 2.34 kg One sack, 4.1 kg One sack, 1.17 kg
350
Heat release rate (kW)
300 250 200 150 100 50 0 0
100
200
300
400
500
600
Time (s)
Lee has correlated the peak heat release values according to the effective base diameter and packing density [109]. Figure 26.108 shows that the total burning rate (kW) increases with effective base diameter, but decreases with the tighter packing densities. Figure 26.109, conversely, illustrates
that when the results are normalized per unit base area, a downward trend is seen. The correlations according to packing density should only be considered rough observations, and not firm guidelines. For design purposes, the range of 50–300 kW appears to cover the bulk of the expected fires
884
V. Babrauskas
Fig. 26.108 Peak HRR of trash fires
600 Packing density values (kg/m3) about 30 kg/m3
500
about 100 kg/m3
Peak qfs (kW)
400
30 kg/m3
UC R 35
300
UC A3 29
UC A2 29
200
100 kg/m3
UC A1 29 100
0
UC6.6 102
0
0.1
0.2
0.3
SNL 4, 11 SNL 5, 109 10 84
NBS–C 51 NBS–F 30 0.4
0.5
0.6
0.7
0.8
0.9
Effective diameter (m)
Table 26.31 Peak HRR of small wastebaskets Wastebasket material Steel Polyethylene Polypropylene Polystyrene
Fuel load PS 12 50 50 37
paper 8 30 40 22
from normal residential, office, airplane, or similar occupancy trash bags and trash baskets. Yamada et al. [102] measured the HRR of 6.5–11.8 L wastebaskets made of steel and plastic and filled with paper and polystyrene foam trash. The peak HRR values found are shown in Table 26.31. The authors concluded that the HRR characteristics could be reasonably well represented by one of two paradigms: (1) 30 kW for 600 s; or (2) 50 kW for 300 s. NIST conducted tests [200] on trash bags collected from Amtrak overnight trains. The bags were about 450 mm diameter and 800 mm high and were ignited with a 25 kW burner. Test results are shown in Fig. 26.110. Based on these results, NIST researchers endeavored to create a ‘standard’ trash bag by filling the bag with
110 sheets (2.7 kg) of crumpled newspaper; these results are shown in Fig. 26.111. NIST also tested [211] 30-gal size (136 L) plastic trash containers made from high-density polyethylene (HDPE) and filled with construction-site debris. The debris included cut pieces of lumber, sawdust, cardboard, paper, cups, food wrappers and pager bags. The containers were 515 mm diameter, 700 mm tall and had a mass of 3.6 kg. The debris totaled 10 kg for each test. Figure 26.112 shows the results for two test replicates. Tests have been reported on some very large (364 L, 96 gal) polyolefin garbage cans (wheeled, household type) [212]. These were tested empty, and they were ignited with the wood crib specified in UL 1975 [213]. That particular crib weighs 340 g and is ignited with 20 g of excelsior. Three tests were conducted; two gave fairly similar peak HRR values (2383 and 1942 kW), while the third one was much lower at 977 kW (Fig. 26.113). Such variability is typical of polyolefin products, when they are tested in an arrangement where the product can melt and recede from the ignition source.
26
Heat Release Rates
885
Fig. 26.109 Trash heat release rates, normalized per unit base area
500
Trash bag fires
· Peak qfs″ (kW/m2)
400
UC 6.6 UC R UC A2
300
UC A1 UC A3
200
100
SNL 5, 10
NBS–C NBS–F SNL 4, 11
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Effective diameter (m)
300 Test 1, 1.8 kg Test 2, 9.5 kg Test 3, 5.4 kg Test 4, 6.8 kg Test 5, 7.3 kg Test 6, 5.0 kg
250
HRR (kW)
200
150
100
50
0 0
200
400
600
800
1000
1200
1400
Time (s) Fig. 26.110 HRR of Amtrak trash bags in NIST tests
Upholstered Furniture The HRR of upholstered furniture can be determined in three different ways: (1) by room fire testing; (2) by testing in the furniture calorimeter; (3) by conducting bench-scale tests in the Cone Calorimeter and then using a mathematical
method to predict the full-scale HRR. Of all the occupant goods that can be found in a normal residence, upholstered furniture normally has the highest HRR, thus knowledge of its performance is essential for many applications. Until the 1970s, upholstered furniture used to be made from ‘traditional’ materials. Thus,
886
V. Babrauskas 300 Test Data 250
Average of 3 replicates
HRR (kW)
200
150
100
50
0 0
200
400
600
800
1000
1200
1400
Time (s) Fig. 26.111 HRR of ‘standard’ Amtrak trash bag, based on crumpled newspaper
500 Trash Container 1 Trash Container 2
450 400
HRR (kW)
350 300 250 200 150 100 50 0 0
200
400
600
800
Time (s)
Fig. 26.112 HRR of 136-L HDPE trash containers filled with construction-site debris
1000
26
Heat Release Rates
887
Fig. 26.113 HRR of 364 L (96 gal) PE garbage cans
2500 Test 1 Test 2 Test 3
HRR (kW)
2000
1500
1000
500
0 0
200
during the 1950s and 60s, in the US furniture commonly had a wood frame, steel springs, cotton batting padding, and an upholstery fabric which was commonly a natural fiber such as wool, silk, or cotton. A fraction of the furniture used latex foam padding instead of cotton batting. In earlier-yet times, furniture was commonly stuffed with rubberized horse hair. By the 1970s, however, the predominant padding material became polyurethane foam, and fabric selection became very wide, including both thermoplastic synthetics and natural fibers. The HRR of the modern furniture were found to be many times that of traditional types [214], apart from the special case of latex foam. The latter shows HRR values distinctly higher than for polyurethane foam, but the material has a finite life and few specimens would survive to this day. Figure 26.114 illustrates several furniture items tested at NIST [2]. Chair F21 used polyurethane foam complying with the 1975 California TB 117 standard [215] and polyolefin fabric. A specimen using ordinary polyurethane foam gave essentially identical results. This level of performance represents a very common, but unfortunately worst-performance furniture item
400
600
800 1000 Time (s)
1200
1400
1600
widely bought by consumers. Specimen F32 is a sofa made from the same materials. Chair F24 illustrates the large improvement in HRR when cotton fabric is substituted for polyolefin fabric. The peak HRR decreases by about 2/3, from 2 MW to 700 kW. Further improvements, at present, are not readily available on the retail market. Contract furniture can be procured to advanced specifications, however, notably California TB 133 [213]. The latter limits the peak HRR to values less than 80 kW, which will present negligible fire hazard in almost any circumstance. In the case of the tests discussed above, ignition was from the flame of a 50 kW burner placed at the side of the specimen, representing the burning of a small trash can. Such an ignition source provides the minimum time between ignition and peak HRR. The effect of ignition source on the HRR curve has been found to be almost exclusively that of time shifting—use of smaller flames, non-flaming sources, or placing of ignition sources in less vulnerable locations results in an increase of time to peak HRR (Fig. 26.115), but otherwise does not have a statistically significant effect on the HRR curve [216–218].
888
V. Babrauskas
Fig. 26.114 HRR of several upholstered furniture items tested at NIST
3500 F32
3000
F21
Heat release rate (kW)
F24
2500 2000 1500 1000 500 0 0
200
400
600
800
1000
1200
Time (s)
Seat (C1) 880 s 1349 kw
Heat Release Rote (Kw)
Back (C2) 820 s 1237 kw
Side (C3) 1280 s 1346 kw
Front (C4) 2520 s 1271 kw
1000
500
(C2) (C1)
0 0
1000
2000
3000
4000
Time (s) Fig. 26.115 Effect of ignition source location on the HRR curve of upholstered chairs [214]
Foams with fire retardant chemical additives (FR) improve the fire performance only if large loadings are used. Furniture made for the State of California had been required to use FR foams since 1975, but the loading of FR chemicals used was very small (3–5 %). For furniture with a HRR high enough to be a room fire hazard, such minimal FR levels have no effect on HRR
[219]. A recent study with a very small ignition source compared the performance of furniture with non-FR foams and with TB117 foams using cotton upholstery [220]. Using specially constructed, non-commercial furniture for testing, no effect was found for three-seater sofas, and an effect was only seen for single-seat chairs. But the latter were of a design where even the
26
Heat Release Rates
889
non-FR version showed HRR values so low (approx. 400 kW) as to not comprise a room fire hazard. Interestingly, the same study reported test results for a large number of commercial chairs and sofas burned for comparison. With few exceptions, the latter showed peak HRR values in the range of 900–2500 kW (Fig. 26.115), indicating that the custom-made furniture was not representative of the retail residential furniture market. Furniture made to the 1975 TB117 standard was actually not intended to have lower HRR values but, rather, to resist small-flame ignitions. However, studies also showed that it was ineffective for that purpose [221]. During recent years, concerns have emerged that the 1975 TB117 standard, while ineffective from a fire safety point of view, resulted in use of noxious chemicals which have been found to have environmental toxicology problems [222]. Consequently, in 2012 the State of California replaced the 1975 TB117 regulation with TB117-2012. The latter is a cigarette-ignition (smolder resistance) test and will not require use of toxic FR chemicals to meet test requirements. A Cone Calorimeter-based prediction method was proposed by Babrauskas and Walton, based on data obtained in 1982 [223]. This was the earliest effort, and was based on a data set comprising materials primarily from the 1970s.
ðx1 > 115Þ or
then Else, If x1 < 56 then Else,
00
Since that time, the materials in use by the furniture makers changed substantially and, especially, some highly improved materials became available to the contract furniture market. In addition, predictive techniques readily available in the early 1980s were less sophisticated than those developed more recently. Thus, during the course of the European fire research program CBUF, two new predictive models were developed [10, 145]. ‘Model I’ is a relatively simple model and is described below briefly. A more advanced model was also developed and its details are provided in the above references. To use the CBUF Model I, Cone Calorimeter data must first be obtained at an irradiance of 35 kW m2. A well-controlled specimen preparation method is needed, and this is provided in ASTM E 1474 [224]. Then, one determines if the furniture item is likely to sustain a propagating fire, or whether a moderate external flame source will simply result in limited burning and no propagation. This is determined from the 180 s average of Cone Calorimeter HRR results. 00 If q_ 180 < 65 kW m2, then no propagation is assumed to occur; otherwise further calculations are made to estimate the peak HRR. The scheme is as follows: If
q35tot > 70 and x1 > 40
q_ fs ¼ x2
q_ fs ¼ 14:4 x1 q_ fs ¼ 600 þ 3:77x1
1:25 where x1 ¼ msoft ðstyle factor AÞ q_0035 pk þ q_0035300 0:7 15 þ tig35 0:7 and the subscript 35 denotes that the Cone Calorimeter HRR tests run at a 35 kW m2 irradiance. The msoft is the mass of the ‘soft’ ¼
or ðstyle ¼ f3; 4g and x1 > 70Þ
combustible parts of the item (kg); it includes fabric, foam, interliner, dust cover, etc., but does not include the frame nor any rigid support pieces. 0:7 And, x2 ¼ 880 þ 500 msoft ðstyle factor AÞ Δhc, eff 1:4 00 q35tot Here, Δhc,eff is the test-average effective heat of combustion in the Cone Calorimeter 00 (MJ kg1), and q35tot is the total heat released
890
V. Babrauskas
Table 26.32 Style factors used in the CBUF model for predicting upholstered furniture heat release rates Type of furniture Armchair, fully upholstered, average amount of padding Sofa, 2-seat Sofa, 3-seat Armchair, fully upholstered, highly padded Armchair, small amount of padding Wingback chair Sofa-bed (convertible) Armchair, fully upholstered, metal frame Armless chair, seat and back cushions only Two-seater, armless, seat and back cushions only
at a flux of 35 kW m2. Another correlation predicts the total heat release: 1:5 qtot ¼ 0:9 msoft Δhc, eff þ 2:1 mcomb, tot msoft
Style factor A 1.0 1.0 0.8 0.9 1.2 1.0 0.6 1.0 1.0 1.0
Style factor B 1.0 0.8 0.8 0.9 0.8 2.5 0.75 0.8 0.75 1.0
mass of the item (kg), that is, everything except metal parts. Finally, the time to peak, tpk (s) for the fullscale item is estimated as:
where mcomb,tot denotes the total combustible 0:5 00 0:5 0:3 00 0:2 t pk ¼ 30 þ 4900ðstyle factor BÞ msoft t pk# 1 þ 200 q_ pk#2 q_ trough
where the ‘peak’ and ‘trough’ notations refer to the fact that, in the general case, the Cone Calorimeter HRR of furniture composites shows two main peaks and one trough in between them. The style factors are obtained from Table 26.32. With these values computed, a triangular HRR curve can then be constructed. The peak HRR and the time to peak are given directly, while the base width of the triangle is determined from the calculated total heat release of the furniture item.
Video Games Edenburn [225] tested the joystick controller from video game console having a plastic enclosure made from ABS (UL 94 V-2 rated). When ignited with a needle flame, the unit showed a peak HRR of 6.7 kW and a total heat release of 2.52 MJ. HRR results for the main portion (console) were not provided.
Wall/Ceiling Lining Materials Combustible interior finish materials are substantially more difficult to treat than free-standing combustibles. They cannot be measured in a device such as the furniture calorimeter, and require any full-scale study to be a room fire. The materials cover a large area, but the area of active flame involvement is generally not predictable, except after flashover, when in many cases it can be assumed that all surfaces are involved. In the early 1980s, a series of wall materials was studied by Lee at NIST [15] in full-scale room fires, and also in bench-scale, with the Cone Calorimeter. This work comprised the first attempted correlation between bench scale and full scale for wall lining materials. For several materials in the test series, which included both cellulosics and plastics, it was found that, after flashover, the per-unit-area full-scale heat release rates, were approximately
26
Heat Release Rates
the same as the values obtained from the Cone Calorimeter. Lee’s work did not yet lead to a predictive method, since no technique for estimating the flame-covered area, A(t) was found. At about the same time, Babrauskas found that full-scale fire development on wall/ceiling linings could be approximated [226] by the 00 expression q_ bspk =tig , where the HRR value and the ignition time were obtained from the Cone Calorimeter. The 1/tig factor effectively represented the growth of A(t), but such a scheme was only semi-quantitative. The first successful quantitative method came with the work of Wickstro¨m and Go¨ransson in 1987 [227]. The model was based on the premise that the full-scale scenario involves the combustible materials located on the walls and ceiling of the ISO 9705 room. Note that the same material is expected to be placed on both walls and ceiling. The model uses the principle of area convolution and elaborates on Babrauskas’ assumption that 1/tig controls the growth of the burning area. The model was later extended and extensively validated in the European research program EUREFIC, EUropean REaction to FIre
891
Classification [228]. The primary assumptions in the model are: 1. The burning area growth rate and the HRR are decoupled. 2. The burning area growth rate is proportional to the ease of ignition, i.e. the inverse of the time to ignition in small scale. 00 3. The history of q_ at each location in the full scale is to be the same as in the Cone Calorimeter test. The model pays mind to the observation that burning patterns on wall/ceilings can be very different and, especially, that some products stop spreading fire under certain conditions, while others continue. The basic area growth regimes are illustrated in Fig. 26.117, where the regimes are marked in Roman numerals. The fire spread may follow three different routes. At points ‘A’ and ‘B’ fire spread may or may not continue, based on whether a calculated fictitious surface temperature is higher than a critical value. The calculation is based on data from the Cone Calorimeter. Within the different flame spread regimes, the burning area growth rate depends on ignitability, i.e. time to ignition in the Cone Calorimeter. Once the flame spread rate
Fig. 26.116 SwRI test results on commercial residential furniture showing that peak HRR values are primarily in the range of 900–2500 kW
892
is determined, the HRR is calculated assuming 00 that q_ is the same in small and large scale. This is understood to be a simplification. The HRR depends on the actual heat flux level received by the product as a function of time. Experience showed, however, that the errors average out and can be included in empirical constants. The method is only of moderate difficulty to apply, but the description is somewhat lengthy. Details are available [23]. This reference also contains graphs illustrating the kind of agreement that is obtained between predictions and experiments. While highly successful for its intended purpose, the EUREFIC model does have notable limitations. It: • Can only treat the standard ISO 9705 room, with the standard doorway for ventilation • Only predicts the ISO 9705 100/300 kW burner • Requires that the material be on both walls and ceiling • Cannot deal with products that do not ignite in the Cone Calorimeter at a 25 kW m2 irradiance. It must be remembered that the primary purpose for developing this model was to predict product performance categories to be obtained in the ISO 9705 test, while only using benchscale Cone Calorimeter data. For its intended purpose, it has been an unquestionable success. The above limitations indicate that the EUREFIC model, while a major breakthrough, was certainly not the final answer to modeling needs for wall/ceiling products. Two extensions have been proposed to generalize the applicability of this model. Go¨ransson, one of the developers of the EUREFIC model, proposed an extension [229] to encompass a ‘huge-scale’ room. Such a test room was constructed at VTT. Its dimensions were 6.75 m by 9.0 m, with a ceiling height of 4.9 m. The door opening, 0.8 by 2.0 m high, however, was the same as for the ISO 9705 room. The burner operation was at the 100 kW level for 10 min, then at 300 kW for another 10 min, finally at 900 kW for 10 more minutes. An extended model was created for this situation by introducing a new set of regimes to
V. Babrauskas
correspond to the 900 kW burner level. In addition, it was found that the constant had to be modified for the 100 and 300 kW time periods. The agreement between model and prediction was very good, but only five tests were available for validation at the huge scale. A second extension was developed by Sumathipala and coworkers [230, 231]. This model extends the applicability to the case of the room fire test studied by Lee [15]. The dimensions of that room are almost identical to the ISO room. The differences arise because (a) the two burner regimes are 40 and 160 kW, (b) the burner face size is different, and (c) the product is normally mounted on walls only, rather than walls and ceiling. The authors, however, in their development work, included tests of both rooms in both mounting configurations. The success of these extension confirms that the basic ideas behind the EUREFIC model are sound and can potentially have flexibility. On the other hand, it must be borne in mind that even the extensions are ‘hard-wired’ configurations and do not yet approach a technique which could be applicable towards userselected room sizes, burner levels, and product configurations. Perhaps the most ambitious model so far for wall/ceiling products has been one developed by Karlsson and coworkers [232–234]. Karlsson’s model incorporates much more of current concepts of plumes, flame length calculations, ceiling jets, and similar constructs than does the EUREFIC model. The model has the same ‘hardwired’ limitations that the EUREFIC model has in terms of ignition sources, product configuration, and room size being fixed. Another wall/ ceiling model was developed by Quintiere and Cleary [235–237] and extended by Janssens and coworkers [238].
Wardrobes Information on the HRR of wardrobes is available from a NIST study [239]. The test wardrobes are illustrated in Fig. 26.118; data
Fig. 26.117 EUREFIC fire spread regimes
Burning area (m2)
15
10
V
II
B
VI
5
A 2
IV III
I 0 0
5
10
15
20
Time (min) Table 26.33 The HRR properties of wardrobes Wardrobe combustible Test No. Construction mass (kg) 21 Steel 0 43 Plywood, 12.7 mm thick 68.3 41 Plywood, 3.2 mm thick, unpainted 36.0 42 Plywood, 3.2 mm thick, 1 coat FR 37.3 paint 44 Plywood, 3.2 mm thick, 2 coats FR 37.3 paint 61 Particleboard, 19 mm thick 120.3
Clothing and paper (kg) 1.93 1.93 1.93 1.93
Peak HRR (kW) 270 3100 6400 5300
Total heat released (MJ) 52 1068 590 486
Avg. heat of combustion (MJ kg1) 18.8 14.9 16.9 15.9
1.93
2900
408
14.2
0.81
1900
1349
17.5
0.61 m
1.22 m
Door
Hanger rod 1.78 m Hinged door
Hinged door
Front
Fig. 26.118 Configuration of the tested wardrobes
Side
894
V. Babrauskas 7000 Test 21
6000
Test 41 Test 42 Test 43
Heat release rate (kW)
5000
Test 44 Test 61 4000
3000
2000
1000
0 0
300
600
900
1200
Time (s) Fig. 26.119 HRR of various wardrobes
Table 26.34 European by VTT Specimen Ignition source (kW) Initial mass (kg) Mass loss (kg) Peak HRR (kW) Total heat (MJ)
washing W1 1 69.3 10.1 345 259
machines W2 1 69.9 10.4 431 245
tested
W3 300–550 63.3 12.3 221 383
specimen mass is seen). Thus, while the total heat content of the 19 mm particleboard specimen is high (see Table 26.33), its peak HRR is quite low, since flame spread and fire involvement proceed more slowly over a thick material (Fig. 26.120).
Washing Machines are given in Table 26.33 and Fig. 26.119. The wardrobes were outfitted with a small amount of clothing, or simulated clothing, and some paper. Tests were not run on the clothes items by themselves. However, since in the case of the steel wardrobe, the only other combustible present was the paint on the metal, it is reasonable to assign a value of about 270 kW peak for the 1.93 kg clothes load. The most important conclusion, however, was that, for combustible constructions, the peak HRR is inversely dependent on wardrobe panel thickness (and, by contrast, no simple connection to combustible
VTT tested [105] European washing machines. The specimens are described in Table 26.34, while test results are shown in Fig. 26.120. The specimens were extinguished before the ultimate peak burning would have occurred. These results must not be applied to appliances used in North America, since European appliance styles are different from North American ones and also because local standards are such as to permit appliances of greater flammability in Europe (Fig. 26.120). HRR data on North American washing machines are not available.
26
Heat Release Rates
895
Fig. 26.120 HRR of European washing machines tested by VTT
500 W1 W2
HRR (kW)
400
W3
300
200
100
0 0
600
1200
1800
2400
3000
3600
Time (s)
Windows, Plastic In applications where vandal resistance is needed, polycarbonate windows are sometimes used. This material is combustible, and limited testing was reported by Peacock et al. [240]. The tests indicated that it is hard to derive an ‘innate’ HRR value. The windows do not burn unless a sustained flame or heat source is applied. In that case, the HRR of the product increases with increasing severity of the ignition source. For a 50 kW exposure source, a test window showed an additional 50 kW HRR, with a burning time of ca. 80 s. For a 200 kW exposure source, the window peak HRR was about an additional 250 kW, but with a longer duration of about 200 s, at progressively diminishing HRR values.
some very simplified assumptions, especially that flame spread could, in the first approximation, be ignored. Further experience gained with additional classes of combustibles, as discussed above, suggests that such a condition will only very rarely hold. Furthermore, the user has no way of knowing when it might hold. Thus, prudent design practice should now demand that first recourse be made to the specific sections above which may address the modeler’s needs. If they do not, then testing is indicated. For the modeler wishing to start up a major research activity, the schemata outlined for upholstered furniture, mattresses, and wall/ceiling lining should serve as illustrations of appropriate starting points in theory and practice. It must be pointed out, however, that such research programs have proven to be complex and that quick or inexpensive results cannot be expected.
Estimating the HRR for General Combustibles
Uncertainty of HRR Measurements
The previous edition of the Handbook suggested a hypothetical method for estimating the HRR for general combustibles. This was based on
As in any engineering measurement, uncertainty in HRR measurements can be subdivided into: 1. Bias,
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Table 26.35 The 95 % confidence limits for HRR test apparatuses as determined from recent round robins Apparatus Cone calorimeter ICAL SBI Room calorimeter
Year 2000 1999 1997 1994
Labs 4 3 16 12
Levels 16 8 30 5
2. Random error, sometimes termed ‘precision uncertainty.’ Bias is properly minimized by use of calibration standards; for HRR testing this often comprises a metered flow of a calibration gas of high purity. Another source of bias that can be minimized, when appropriate, is specific to oxygen-consumption calorimetry bases measurements. For most testing, a standard oxygen consumption constant value of 13.1 MJ per kg of oxygen consumed is used. A small number of substances of fire-safety interest show oxygen consumption constants substantially different from this standard value. If the molecular composition of the substance is known, a correction can always be made to eliminate this source of bias. Most of the instruments in which the HRR measurements are made have been subjected to round robins (“inter-laboratory trials”) to quantify the magnitude of random error that can be expected. Comparative values have been compiled by Janssens [241], as shown in Table 26.35. For a number of them, several round robins have been conducted, thus the data shown are identified by year. SBI denotes the European Single Burning Item test [242], which is a regulatory HRR test for building products that uses two wall panels in a corner configuration, without ceiling. The values tabulated refer to the 95 % confidence intervals; standard deviations can be obtained by dividing the figures shown by 2.8.
References 1. Babrauskas, V., and Peacock, R. D., Heat Release Rate: The Single Most Important Variable in Fire Hazard, Fire Safety J. 18, 255-272 (1992).
Peak HRR r (%) 17 56 38 65
R (%) 23 67 54 79
Total HRR r (%) 8 72 47 25
R (%) 15 118 71 41
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V. Babrauskas 120. Guide for Smoke and Heat Venting (NFPA 204), National Fire Protection Assn., Quincy MA (1998). 121. Kung, H.-C., Spaulding, R. D., and You, H.-Z., Response of Sprinkler Links to Rack Storage Fires. FMS J.I.0G2E7.RA(2). FMRC (1984). 122. Chicarello, P. J., and Troup, J. M. A., Fire Collector Test Procedure for Determining the Commodity Classification of Ordinary Combustible Products. FMRC J.I. 0R0E5.RR. FMRC (1990). 123. Yu, H.-Z., and Stavrianidis, P., The Transient Ceiling Flows of Growing Rack Storage Fires. FMRC J.I. 0N1J0.RA(3). FMRC (1989). 124. Yu, H.-Z., A Sprinkler-Response-Prediction Computer Program for Warehouse Applications. FMRC J.I. 0R2E1.RA. FMRC (1992). 125. Newman, J., and Troup, J. M. A., The Building Calorimeter: FM Global’s Novel Approach to Large-Scale Fire Testing, NFPA World Safety Conf. and Expo., Las Vegas (2005). 126. Yu, H.-Z., RDD and Sprinklered Fire Tests for Expanded Polystyrene Egg Crates, FMRC J.I. 0R2E3.RA(1), Factory Mutual Research Corp., Norwood MA (1990). 127. Sleights, J. E., SPRINK 1.0—A Sprinkler Response Computer Program for Warehouse Storage Fires (M.S. thesis), Worcester Polytechnic Institute, Worcester MA (1993). 128. Lee, J. L., and Dean, R. K., Fire Products Collector Tests of Polyethylene Terephthalate (PET) Plastic Bottles in Corrugated Carton, FMRC J.I. 0N0J6. RA070(A), Factory Mutual Research Corp., Norwood MA (1986). 129. Lee, J. L., Combustibility Evaluation of Shredded Newsprint Commodity and an Improved Polyurethane Foam Packaging Product Using the Fire Products Collector, FMRC J.I. 0K0E6.RANS, Factory Mutual Research Corp., Norwood MA (1984). 130. Khan, M. M., Evaluation of the Fire Behavior of Packaging Materials, presented at Defense Fire Protection Symp., Annapolis (1987). 131. Hasegawa, H., Alvares, N. J., and White, J. A., Fire Tests of Packaged and Palletized Computer Products, Fire Technology 35, 294-307 (1999). 132. Hasegawa, H., private communication (2000). 133. Dillon, S. E., Janssens, M. L., and Garabedian, A. S., A Comparison of Building Code Classifications and Results of Intermediate-Scale Fire Testing of Stored Plastic Commodities, pp. 593-604 in Interflam 2001—Proc. 9th Intl. Conf., Interscience Communications Ltd., London (2001). 134. Roberts, T. A., Merrifield, R., and Tharmalingam, S., Thermal Radiation Hazards from Organic Peroxides, J. Loss Prevention in the Process Industries 3, 244-252 (1990). 135. Babrauskas, V., unpublished test data (1997). 136. Yu, H.-Z., and Stavrianidis, P., The Transient Ceiling Flows of Growing Rack Storage Fires, FMRC J.I. 0N1J0.RA(3), Factory Mutual Research Corp., Norwood MA (1989).
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137. Mitler, H. E., Input Data for Fire Modeling, pp. 187-199 in Thirteenth Meeting of the UJNR Panel on Fire Research and Safety, March 13-20, 1996 (NISTIR 6030, vol. 1), Nat. Inst. Stand. and Technol., Gaithersburg MD (1997). 138. Messa, S., Designing Fires for FIRESTARR, LSF Fire Laboratories, Montano Lucino, Italy (2000). 139. Chow, W. K., Zou, G., Dong, H., and Gao, Y., Necessity of Carrying out Full-Scale Burning Tests for Post-Flashover Retail Shop Fires, Intl. J. on Engineering Performance-Based Fire Codes 5, 20-27 (2003). 140. Madrzykowski, D., and Kerber, S, Fire Fighting Tactics under Wind Driven Conditions: Laboratory Experiments (TN 1618), Nat. Inst. Stand & Technol., Gaithersburg MD (2009). 141. Babrauskas, V., Bench-Scale Predictions of Mattress and Upholstered Chair Fires, pp. 50-62 in Fire and Flammability of Furnishings (ASTM STP 1233). American Society for Testing and Materials, Philadelphia (1994). 142. Damant, G. H., and Nurbakhsh, S., Heat Release Tests of Mattresses and Bedding Systems, State of California, Bureau of Home Furnishings and Thermal Insulation, North Highlands, CA (1991). 143. Holmstedt, G., and Kaiser, I., Brand I va˚rdba¨ddar (SP-RAPP 1983:04), Swedish National Testing and Research Institute, Bora˚s, Sweden (1983). 144. Andersson, B., Fire Behaviour of Beds and Upholstered Furniture--An Experimental Study (LUTVDG/ISSN 0282-3756),Lund University, Dept. of Fire Safety Engineering, Lund, Sweden (1985). 145. Babrauskas, V., Baroudi, D., Myllyma¨ki, J., and Kokkala, M., The Cone Calorimeter Used for Predictions of the Full-scale Burning Behaviour of Upholstered Furniture, Fire and Materials 21, 95-105 (1997). 146. Hansen, R., and Ingason, H., Heat Release Rate Measurements of Burning Mining Vehicles in an Underground Mine, Fire Safety J. 61, 12-25 (2013). 147. Walton, W. D., and Budnick, E. K., Quick Response Sprinklers in Office Configurations: Fire Test Results (NBSIR 88-3695), [U. S.] Natl. Bur. Stand., Gaithersburg, MD (1988). 148. Madrzykowski, D., and Vettori, R. L., Sprinkler Fire Suppression Algorithm for the GSA Engineering Fire Assessment System (NISTIR 4833), Natl. Inst. Stand. Technol., Gaithersburg, MD (1992). 149. Madrzykowski, D., Office Work Station Heat Release Rate Study: Full Scale vs. Bench Scale, pp. 47-55 in Interflam ‘96, Interscience Communications Ltd., London (1996). 150. Madrzykowski, D., and Walton, W. D. Cook County Administration Building Fire, 69 West Washington, Chicago, Illinois, October 17, 2003: Heat Release Rate Experiments and FDS Simulations (NIST SP 1021), Nat. Inst. Stand. & Technol., Gaithersburg MD (2004).
901 151. Kakegawa, S., et al., Design Fires for Means of Egress in Office Buildings Based on Full-scale Fire Experiments, pp. 975-986 in Fire Safety Science— Proc. 7th Intl. Symp., International Association for Fire Safety Science (2003). 152. Krasner, L. M., Burning Characteristics of Wooden Pallets as a Test Fuel (Serial 16437), Factory Mutual Research Corp., Norwood (1968). 153. Babrauskas, V., Pillow Burning Rates, Fire Safety J. 8, 199-200 (1984/85). 154. Pipe Insulation: Fire Spread and Smoke Production-Full-scale Test (NT FIRE 036), NORDTEST, Espoo, Finland (1988). 155. Wetterlund, I., and Go¨ransson, U., A New Test Method for Fire Testing of Pipe Insulation in Full Scale (SP Report 1986:33), Swedish National Testing Institute, Bora˚s (1986). 156. Babrauskas, V., Toxic Fire Hazard Comparison of Pipe Insulations: The Realism of Full-scale Testing Contrasted with Assessments from Bench-scale Toxic Potency Data Alone, pp. 439-452 in Asiaflam ‘95, Interscience Communications Ltd, London (1995). 157. Ahonen, A., Kokkala, M. and Weckman, H., Burning Characteristics of Potential Ignition Sources of Room Fires (Research Report 285), Valtion Teknillinen Tutkimuskeskus, Espoo, Finland (June 1984). 158. Damant, G., and Nurbakhsh, S., Christmas Trees-What Happens When They Ignite? Fire and Materials 18, 9-16 (1994). 159. Babrauskas, V., Chastagner, G., and Stauss, E., Flammability of Cut Christmas Trees, IAAI Annual General Meeting and Conference, Atlantic City NJ (2001). 160. Evans, D. D., Rehm, R. G., Baker, E. S., McPherson, E. G., and Wallace, J. B., Physics-Based Modeling of Community Fires, pp. 1065-1076 in Interflam 2004, Interscience Communications Ltd., London (2004). 161. Stroup, D. W., DeLauter, L., Lee, J., and Roadarmel, G., Scotch Pine Christmas Tree Fire Tests (FR 4010), Nat. Inst. Stand. and Technol., Gaithersburg MD (1999). 162. Madrzykowski, D., Impact of a Residential Sprinkler on the Heat Release Rate of a Christmas Tree Fire (NISTIR 7506), Nat. Inst. Stand & Technol., Gaithersburg MD (2008). 163. Jackman, L., Finegan, M., and Campbell, S., Christmas Trees: Fire Research and Recommendations (LPR 17:2000), Loss Prevention Council, London (2000). 164. Stephens, S. L., Gordon, D. A., and Martin, R. E., Combustibility of Selected Domestic Vegetation Subjected to Desiccation, pp. 565-571 in Proc. 12th Intl. Conf. on Fire and Forest Meteorology, Society of American Foresters, Bethesda MD (1994).
902 165. Etlinger, M. G., Fire Performance of Landscape Plants (M.S. thesis), Univ. California, Berkeley (2000). 166. Outline of Investigation for Artificial Christmas Trees (Subject 411), 2nd ed., Underwriters Laboratories Inc., Northbrook IL (1991). 167. Babrauskas, V., to be published. 168. McCaffrey, B., Flame Height, pp. 2-1 to 2-8 in SFPE Handbook of Fire Protection Engineering, 2nd ed., National Fire Protection Assn., Quincy MA (1995). 169. McCaffrey, B. J. Momentum Implications for Buoyant Diffusion Flames, Combustion and Flame 52, 149-167 (1983). 170. Sa¨rdqvist, S., Initial Fires: RHR, Smoke Production and CO Generation from Single Items and Room Fire Tests (LUTVDG/TVBB-3070-SE), Lund University, Dept. of Fire Safety Engineering, Lund, Sweden (1993). 171. Blinov, V. I., and Khudiakov, G. N., Diffusion Burning of Liquids. U.S. Army Translation. NTIS No. AD296762 (1961). 172. Hottel, H.C., Review Certain Laws Governing Diffusive Burning of Liquids, by V. I. Blinov and G. N. Khudiakov, Fire Research Abstracts and Reviews 1, 41-44 (1958). 173. Babrauskas, V., Tables and Charts, pp. A-1 to A-17 in Fire Protection Handbook, 18th ed., National Fire Protection Assn., Quincy, MA (1997). 174. Babrauskas, V., Estimating Large Pool Fire Burning Rates, Fire Technology 19, 251-261 (1983). 175. Gosse, A., BG Technologies Ltd., private communication (2000). 176. Putorti, A. D. jr., Flammable and Combustible Liquid Spill/Burn Patterns (NIJ 604-00), National Institute of Justice, U.S. Department of Justice, Washington (2001). 177. Modak, A. T., Ignitability of High-Fire-Point Liquid Spills (EPRI NP-1731), Electric Power Research Inst., Palo Alto, CA (1981). 178. Gottuk, D. T., Scheffey, J. L., Williams, F. W., Gott, J. E., and Tabet, R. J., Optical Fire Detection (OFD) for Military Aircraft Hangars: Final Report on OFD Performance to Fuel Spill Fires and Optical Stresses (NRL/MR/6180--00-8457), Naval Research Lab., Washington (2000). 179. DeHaan, J. D., The Dynamics of Flash Fires Involving Flammable Hydrocarbon Liquids, Amer. J. Forensic Medicine and Pathology 17, 24-31 (1996). 180. Babrauskas, V., COMPF2—A Program for Calculating Post-Flashover Fire Temperatures (Tech Note 991), [U. S.] Natl. Bur. Stand., Gaithersburg MD (1979). 181. Gore, J. P., Klassen, M., Hamins, A., and Kashiwagi, T., Fuel Property Effects on Burning Rate and Radiative Transfer From Liquid Pool Flames, pp. 395-404 in Fire Safety Science—Proc. 3rd Intl. Symp., International Association for Fire Safety Science, Elsevier Applied Science, New York (1991).
V. Babrauskas 182. Hamins, A., Fischer, S. J., Kashiwagi, T., Klassen, M. E., and Gore, J. P., Heat Feedback to the Fuel Surface in Pool Fires, Combustion Science and Technology 97, 37-62 (1994). 183. Adiga, K. C., Ramaker, D. E., Tatem, P. A., and Williams, F. W., Modeling Pool-Like Gas Flames of Propane, Fire Safety J. 14, 241-250 (1989). 184. Adiga, K. C., Ramaker, D. E., Tatem, P. A., and Williams, F., Modeling Thermal Radiation in Open Liquid Pool Fires, pp. 241-250 in Fire Safety Science—Proc. 2nd Intl. Symp., International Association for Fire Safety Science, Hemisphere Publishing Corp., New York (1989). 185. Koseki, H., and Mulholland, G. W., Effect of Diameter on the Burning of Crude Oil Pool Fires, Fire Technology 27, 54-65 (1991). 186. Koseki, H., Boilover and Crude Oil Fire, J. Applied Fire Science 3, 243-272 (1993/1994). 187. Chow, W. K., Necessity of Testing Combustibles under Well-developed Fires, J. Fire Sciences (2005). 188. Troitzsch, J. H., Flammability and Fire Behaviour of TV Sets, pp. 979-990 in Fire Safety Science—Proc. 6th Intl. Symp., Intl. Assn. of Fire Safety Science (2000). 189. Nam, D.-G., Hasemi, Y., and Kamikawa, D., Investigation of an Apartment Fire—Experiments for Estimating the Cause and Mechanism of the Fire, pp. 389-400 in Fire & Materials 2005, Interscience Communications Ltd., London (2005). 190. Hoffmann, J. M., Hoffmann, D. J., Kroll, E. C., and Kroll, M. J., Full Scale Burn Tests of Television Sets and Electronic Appliances, Fire Technology 39, 207-224 (2003). 191. Shipp, M., and Spearpoint, M., Measurements of the Severity of Fires Involving Private Motor Vehicles, Fire and Materials 19, 143-151 (1995). 192. Mangs, J., and Keski-Rahkonen, O., Characterization of the Fire Behaviour of a Burning Passenger Car. Part I: Car Fire Experiments, Fire Safety J. 23, 17-35 (1994). 193. Steinert, C., Experimentelle Untersuchhungen zum Abbrand-und Feuerubersprungsverhalten von Personenkraftwagen, VFDB-Zeitschrift, No. 4, 63-172 (2000). 194. Ingason, H., Gustavsson, S., and Werling, P., Brandfo¨rso¨k i en bergtunnel—Naturlig ventilation. Delrapport II (SP AR 1995:45), Swedish National Testing and Research Institute, Bora˚s (1995). 195. Okamoto, K., Watanabe, N., Hagimoto, Y., Chigira, T., Masano, R., Miura, H., Ochiai, H., Tamura, Y., Hayano, K., Maeda, Y., and Suzuki, J., Burning Behavior of Sedan Passenger Cars, Fire Safety J. 44, 301-310 (2009). 196. Okamoto, K., Otake, T., Miyamoto, H., Honma, M., and Watanabe, N., Burning Behavior of Minivan Passenger Cars, Fire Safety J. 62, 272-280 (2013). 197. Ohlemiller, T. J., and Shields, J. R., Burning Behavior of Selected Automotive Parts from a Minivan
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(NISTIR 6143), Nat. Inst. Stand. & Technol., Gaithersburg MD (1998). 198. Ohlemiller, T. J., Influence of Flame-Retarded Resins on the Burning Behavior of a Heating, Ventilating and Air Conditioning Unit from a Sports Coupe (NISTIR 6748), Nat. Inst. Stand. & Technol., Gaithersburg MD (2003). 199. Ingason, H., Gustavsson, S., and Dalhberg, M., Heat Release Rate Measurements in Tunnel Fires (SP Report 1994:08), Swedish National Testing & Research Institute, Bora˚s (1994). 200. Steinert, C., Smoke and Heat Production in Tunnel Fires, pp. 123-137 in Proc. Intl. Conf. on Fires in Tunnels (SP Report 1994:54), Swedish National Testing & Research Institute, Bora˚s (1994 201. Go¨ransson, U., and Lundqvist, A., Fires in Buses and Trains: Fire Test Methods (SP Report 1990:45). Swedish National Testing and Research Institute, Bora˚s (1990). 202. Peacock, R. D., Reneke, P. A., Averill, J. D., Bukowski, R. W., and Klote, J. H., Fire Safety of Passenger Trains. Phase II: Application of Fire Hazard Analysis Techniques (NISTIR 6525), Nat. Inst. Stand. & Technol., Gaithersburg MD (2002). 203. Hansen, P. A., Fire in Tyres: Heat Release Rate and Response of Vehicles (STF25 A95039). SINTEF NBL, Norwegian Fire Research Laboratory, Trondheim (1995). 204. Shipp, M. P., Fire Spread in Tyre Dumps, pp. 79-88 in Interflam ‘96. Interscience Communications Ltd., London (1996). 205. Murrell, J., and Briggs, P., Developments in European and International Fire Test Methods for Composites Used in Building and Transport Applications, pp. 21-32 in Proc. 2nd Intl. Conf. on Composites in Fire, Conference Design Consultants, Newcastle upon Tyne, England (2001). 206. Ingason, H., and Lo¨nnermark, A., Heat Release Rates from Heavy Goods Vehicle Trailer Fires in Tunnels, Fire Safety J. 40, 646-668 (2005). 207. Fires in Transport Tunnels. Report on Full-Scale Tests (EUREKA Project EU 499: FIRETUN), Studiengesellschaft Stahlanwendung e.V., Du¨sseldorf, Germany (1995). 208. Proceedings of the International Conference on Fires in Tunnels, SP - Swedish National Testing and Research Institute, Bora˚s (1994). Distributed by Interscience Communications Ltd, London. 209. Ingason, H., An Overview of Vehicle Fires in Tunnels, pp. 425-434 in Intl. Conf. on Tunnel Fires and Escape from Tunnels, Madrid (2001). 210. Mehaffey, J. R., Craft, S. T., Richardson, L. R., and Batista, M., Fire Experiments in Furnished Houses, pp. 163-174 in Proc. 4th Intl. Symp. on Fire and Explosion Hazards, FireSERT, Univ. Ulster, Northern Ireland (2004). 211. Stroup, D. W., and Madrzykowski, D., Heat Release Rate Tests of Plastic Trash Containers (FR 4018),
903 Nat. Inst. Stand. & Technol., Gaithersburg MD (2003). 212. Zicherman, J. B., Fire Cause Analysis, Berkeley CA; unpublished tests conducted at the Western Fire Center, Inc. (2008). 213. Fire Tests for Foamed Plastics Used for Decorative Purposes (UL 1975), Underwriters Laboratories Inc., Northbrook IL. 214. Babrauskas, V., Upholstered Furniture Heat Release Rates: Measurements and Estimation, J. Fire Sciences 1, 9-32 (1983). 215. Flammability Information Package (Contains Technical Bulletins 116, 117, 121, 133, 106 and 26). Bureau of Home Furnishings, Dept. of Consumer Affairs, State of California, North Highlands (1987). 216. Babrauskas, V., Full-Scale Burning Behavior of Upholstered Chairs (Tech Note 1103), [U. S.] Natl. Bur. Stand., Gaithersburg MD (1979). 217. Mitler, H. E., and Tu, K.-M., Effect of Ignition Location on Heat Release Rate of Burning Upholstered Furniture, pp. 121-122 in Annual Conf. on Fire Research. Book of Abstracts. October 17-20, 1994 (NISTIR 5499), Nat. Inst. Stand. & Technol., Gaithersburg MD (1994). 218. Collier, P. C. R., and Whiting, P. N., Timeline for Incipient Fire Development (Study Report 194), BRANZ, Judgeford, New Zealand (2008). 219. Babrauskas, V., Lawson, J. R., Walton, W. D., and Twilley, W. H., Upholstered Furniture Heat Release Rates Measured with a Furniture Calorimeter (NBSIR 82-2604), [U. S.] Natl. Bur. Stand., Gaithersburg MD (1982). 220. Janssens, M. L., Gomez, C., Huczek, J. P., Overholt, K. J., Ewan, D. M., Hirschler, M. M., Mason, R. L., and Sharp, J. M., Reducing Uncertainty of Quantifying the Burning Rate of Upholstered Furniture (SwRI Project No. 01.15998), Prepared for National Institute of Justice, Southwest Research Institute, San Antonio TX (2012). 221. Medford, R. L., and Ray, D. R., Upholstered Furniture Flammability: Fires Ignited by Small Open Flames and Cigarettes, CPSC, Washington (Oct. 24, 1997). 222. Babrauskas, V., Blum, A., Daley, R., and Birnbaum, L., Flame Retardants in Furniture Foam: Benefits and Risks, pp. 265-278 in Fire Safety Science— Proc. 10th Intl. Symp., Intl. Assn. for Fire Safety Science, London (2011). 223. Babrauskas, V., and Walton, W. D., A Simplified Characterization for Upholstered Furniture Heat Release Rates, Fire Safety J. 11, 181-192 (1986). 224. Standard Test Method for Determining the Heat Release Rate of Upholstered Furniture and Mattress Components or Composites Using a Bench-Scale Oxygen Consumption Calorimeter (E 1474-96a). American Society for Testing and Materials, Philadelphia (1996). 225. Edenburn, D., Burning Video Game System (Technical Report), Albemarle Corp., [n.p.] (2003).
904 226. Babrauskas, V., Bench-Scale Methods for Prediction of Full-Scale Fire Behavior of Furnishings and Wall Linings, SFPE Technical Report 84-10, Society of Fire Protection Engineers, Boston (1984). 227. Wickstro¨m, U., and Go¨ransson, U., Prediction of Heat Release Rates of Surface Materials in LargeScale Fire Tests Based on Cone Calorimeter Results, J. Testing and Evaluation 15, 364-370 (1987). 228. Proceedings of the International EUREFIC Seminar 1991, Interscience Communications Ltd, London (1991). 229. Go¨ransson, U., Model, Based on Cone Calorimeter Results, for Explaining the Heat Release Rate Growth of Tests in a Very Large Room, pp. 39-47 in Interflam ‘93: Sixth Intl. Fire Conf. Proc., Interscience Communications Ltd., London (1993). 230. Sumathipala, K., Kim, A. K., and Lougheed, G. D., A Comparison of ASTM and ISO Full-scale Room Fire Test Methods, pp. 101-110 in Proc. Fire and Intl. Conf., Interscience Materials, 2nd Communications Ltd, London (1993). 231. Sumathipala, K., Kim, A. K., and Lougheed, G. D., Configuration Sensitivity of Full-scale Room Fire Tests, pp. 237-246 in Proc. Fire and Materials, 3rd Intl. Conf., Interscience Communications Ltd, London (1994). 232. Karlsson, B., and Magnusson, S.-E., An Example Room Fire Model, pp. 159-171 in Heat Release in Fires, op cit. 233. Karlsson, B., Models for Calculating Flame Spread on Wall Lining Materials and the Resulting Heat Release Rate in a Room, Fire Safety J. 23, 365-386 (1994). 234. Magnusson, S. E., and Sundstro¨m, B., Combustible linings and room fire growth – A first analysis, pp. 45-69 in Fire Safety Science and Engineering (ASTM STP 882), American Society for Testing and Materials, Philadelphia (1985).
V. Babrauskas 235. Cleary, T. G., and Quintiere, J. G., A Framework for Utilizing Fire Property Tests, pp. 647-656 in Fire Safety Science--Proc. of the 3rd Intl. Symp., Elsevier Applied Science, London (1991). 236. Quintiere, J. G., A Simulation Model for Fire Growth on Materials Subject to a Room-Corner Test, Fire Safety J. 20, 313-339 (1993). 237. Quintiere, J. G., Haynes, G., and Rhodes, B. T., Applications of a Model to Predict Flame Spread over Interior Finish Materials in a Compartment, J. Fire Prot. Engineering 7, 1013 (1995). 238. Janssens, M., Grexa, O., Dietenberger, M., and White, R., Predictions of ISO 9705 Room/corner Test Using a Simple Model, pp. 73-83 in Proc. 4th Intl. Fire and Materials Conf., Interscience Communications Ltd., London (1995). 239. Lawson, J. R., Walton, W. D., and Twilley, W. H., Fire Performance of Furnishings as Measured in the NBS Furniture Calorimeter. Part 1 (NBSIR 83-2787), U.S. Natl. Bur. Stand., Gaithersburg MD (1983). 240. Peacock, R. D., Reneke, P. A., Averill, J. D., Bukowski, R. W., and Klote, J. H., Fire Safety of Passenger Trains, Phase II: Application of Fire Hazard Analysis Techniques (NISTIR 6525), Nat. Inst. Stand. and Technol., Gaithersburg MD (2002). 241. Janssens, M. L., Heat Release Rate, FORUM Workshop on Measurement Needs for Fire Safety, Nat. Inst. Stand. and Technol., Gaithersburg MD (2000). 242. Smith, D. A., and Shaw, K., Single Burning Item (SBI) Test: The Euroclasses and Transitional Arrangements, pp. 1-9 in Interflam ’99, Interscience Communications Ltd., London (1999).
Dr. Vytenis Babrauskas is the President of Fire Science and Technology Inc., Issaquah, WA, a company specializing in fire safety research, fire testing issues, and fire science applications to fire investigations and litigations.
27
Calorimetry Marc Janssens
Introduction Heat release rate is the single most important variable in fire hazard assessment [1]. Various test methods for measuring the heat release rate of materials and products under different conditions have therefore been developed. This chapter is dedicated to these test methods. An apparatus used for measuring heat release rate is referred to as a calorimeter and the measurement of heat release rate is called calorimetry. The importance of heat release rate in fire hazard assessment was first recognized in the early 1970s by Smith at Ohio State University [2]. Smith and coworkers developed one of the first small-scale test methods for measuring the heat release rate of planar products exposed to radiant heat [3]. They also proposed various procedures to assess compartment fire hazard on the basis of the small-scale data. These procedures ranged from simple calculation methods [4] to a relatively complex computer model [5]. This work was initiated at a time when the most accurate measuring techniques for heat release rate were not available and when computer fire modeling was still in its infancy. Moreover, Smith advocated a practical approach based on engineering judgment rather than detailed science. Hence, his test and fire
M. Janssens (*) Southwest Research Institute, San Antonio, TX 78238, USA
hazard assessment methods were far from perfect and received major criticism [6, 7]. Nevertheless, Smith deserves recognition as one of the pioneers of heat release rate calorimetry. With compartment fire hazard assessment as the primary application, there is a need for high-quality heat release rate data and, consequently, for devices and methods to measure it accurately. The first of two basic approaches to assess the fire hazard of a material consists of an experimental evaluation in full scale. Typically, this approach requires multiple large-scale fire tests covering all relevant fire scenarios and end-use conditions. The second option is the use of small-scale data, primarily heat release rate, in conjunction with a calculation procedure to estimate full-scale fire performance. The second approach is significantly more versatile, and time- and cost-effective. With the continuous improvement of the predictive capability and accuracy of fire models and calculation methods, the latter has become the preferred approach. This chapter begins with a brief discussion of the oxygen bomb calorimeter, which is used to measure the maximum amount of heat that can be released from combustion of a material. The oxygen bomb calorimeter has significant limitations. For example, materials and products are not evaluated under realistic fire conditions. Also, the total heat released is measured as opposed to the heat release rate as a function of time, that is, no information is obtained concerning the dynamic behavior of the material.
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Various heat release tests have been developed to address these limitations. These test methods all rely on one of four measuring techniques, which are described in detail in the next section. This is followed by a discussion of the effect on the measurements of various smallscale calorimeter features and construction details. In the next section a brief description is provided of commonly used calorimeters ranging in size from small to industrial scale. The chapter concludes with a discussion of the use and application of heat release rate data and a section on uncertainty of heat release rate measurements.
M. Janssens
19
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18 17
2
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Oxygen Bomb Calorimetry
1
Oxygen Bomb Calorimeter Test The maximum amount of heat that can be released during combustion of a material can be determined in an oxygen bomb calorimeter. An oxygen bomb calorimeter consists of a sealed stainless steel container (the “bomb”) in which a small quantity of material (approximately 1 g) is combusted at high pressure (30 bar) in pure oxygen (Fig. 27.1). The heat released is measured on the basis of the temperature rise of the surrounding water vessel (adiabatic method) or the heat loss needed to keep the water temperature constant (isoperibol method). Standard procedures for measuring the gross heat of combustion of solid materials are described in ASTM D5865 and ISO 1716. The building and life safety codes promulgated by the National Fire Protection Association (NFPA) make a distinction between noncombustible and limited combustible materials. Limited combustible materials must have a potential heat of 8.2 MJ/kg or less as determined by NFPA 259, Standard Test Method for Potential Heat of Building Materials. According to this method, the potential heat of a material is determined as the difference between the gross heat of combustion of the material measured with an oxygen bomb calorimeter and the gross heat of combustion of its residue after heating in a muffle furnace at 750 C for 2 h.
9
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13 8 5
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1 High pressure cylinder 2 Oxygen admission valve 3 Pressure release valve 4 Base cap 5 Rubber washer 6 Pillar 7 Pillar 8 Support ring 9 Fuse wire 10 Quartz crucible
11 Water container 12 Calorimeter mount 13 Wire 14 Plug and socket 15 Outer can 16 Wooden platform 17 Cover plate 18 Stirrer 19 Thermometer
Fig. 27.1 Oxygen bomb calorimeter
Gross Versus Net Heat of Combustion The gross heat of combustion of a solid or liquid fuel is measured in an oxygen bomb calorimeter as described in the previous section. Because the cooling water temperature remains close to ambient during a test, all water vapor generated in the combustion process fully condenses. The measured gross heat of combustion therefore includes the heat released due to condensation
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of the water vapor. In practice, combustion products are usually removed from the system at a temperature above the dew point. It is therefore more realistic to quantify the potential heat released in a fire assuming that all water vapor remains in the gaseous state. The corresponding heat released per mass unit of fuel burnt is referred to as the net heat of combustion. It is equal to the gross heat of combustion measured in an oxygen bomb calorimeter minus the heat of vaporization of the water in the products of combustion, which is a function of the moisture and hydrogen content of the fuel:
me = ma + mv, Te
ma, Ta
Qf,l mv
Tv
Fig. 27.2 Gas-phase energy balance
Δhc, net ¼ Δhc, gross ð8:936Y H þ Y W ÞΔhv ð27:1Þ where Δhc,net ¼ Net heat of combustion (kJ/g) Δhc,gross ¼ Gross heat of combustion (kJ/g) YH ¼ Mass fraction of hydrogen in the fuel (g/g) YW ¼ Moisture content of the fuel (g/g) Δhv ¼ Latent heat of vaporization of water (2.442 kJ/g at 25 C) ASTM has developed test standards to determine the moisture content and hydrogen content in a variety of solid fuels, e.g., ASTM D3173 and ASTM D5373, respectively. The gross heat and net heat of combustion are usually reported at a standard temperature of 25 C. Gross heat and net heat of combustion values for a wide range of materials can be found in Appendix C, “Fuel Properties and Combustion Data.”
Techniques for Measuring Heat Release Rate The development of the oxygen consumption technique in the late 1970s was a major breakthrough in the accurate measurement of heat release rate in fire tests. Inferior methods had been used prior to that. The most practical of the older methods is still used today for applications that do not require the highest accuracy. The older methods and the oxygen consumption technique (and the related carbon oxide generation technique) are described in this section.
Sensible Enthalpy Rise Method Consider the energy balance of a gas-phase control volume enclosing the flame of a burning specimen (Fig. 27.2). Air enters the control vol˙ a and temperature Ta. The ume at a flow rate m enthalpy of this air can be written as ha ¼ h0a þ cp ðT a T 0 Þ
ð27:2Þ
where ha ¼ Enthalpy of air at temperature T a ðkJ=gÞ h0a ¼ Enthalpy of air at reference temperature T 0 ðkJ=gÞ cp ¼ Average specific heat of air between T 0 and T a ðkJ=g KÞ T a ¼ Temperature of the air entering the combustion zoneðKÞ T 0 ¼ Reference temperature ðKÞ Part of the heat flux that strikes the exposed surface is conducted into the specimen. The resulting heat flow raises the temperature of the solid and decomposes some fraction into combustible fuel vapors. The vapors are ˙ v and enter the control generated at a rate m volume at temperature Tv. Assuming that the specific heat of all gases is approximately constant and temperature independent (a reasonable approximation), the enthalpy of the fuel vapors can be written as hv ¼ h0v þ cp ðT v T 0 Þ
ð27:3Þ
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where hv ¼ Enthalpy of volatiles at temperature Tv (kJ/g) hv0 ¼ Enthalpy of volatiles at reference temperature T0 (kJ/g) Tv ¼ Temperature of volatiles entering the combustion zone (K) The fuel vapors mix with air and are converted in the flame to products of combustion. ˙ e, of combustion products, The total flow rate, m which includes some excess air, has a temperature Te and enthalpy given by he ¼ h0e þ cp ðT e T 0 Þ
ð27:4Þ
where he ¼ Enthalpy of combustion products at temperature Te (kJ/g) 0 he ¼ Enthalpy of combustion products at reference temperature T0 (kJ/g) Te ¼ Temperature of combustion products leaving the control volume (K) Te is higher than the mass-weighted average of Ta and Tv because of the heat released by combus_ However, only a fraction of tion in the flame, Q. this heat contributes to the temperature rise of the gases. This fraction is referred to as the convective fraction of the heat release rate. The remaining fraction of Q_ is lost and is denoted as Q_ f , 1 . For the most part Q_ f , 1 is lost in the form of thermal radiation to the walls of the calorimeter (closed configuration) or to the environment (open configuration). A small part of Q_ f , 1 consists of convective and radiative feedback to the fuel surface. Assuming that gas-phase transients and pressure gradients can be neglected, application of the first law of thermodynamics for the control volume in Fig. 27.2 results in Q_ f , 1 ¼ m_ a ha þ m_ v hv m_ e he
ð27:5Þ
where Q_ f , 1 ¼ Convection and radiation heat loss rate from the flameðkWÞ m_ a ¼ Mass flow rate of air entering the combustion zoneðg=sÞ m_ v ¼ Generation rate of fuel volatilesðg=sÞ m_ e ¼ Mass flow rate of combustion products leaving the control volumeðg=sÞ
Q
ma ,T0 Combustion chamber mv ,T0
me ,T0 Gas phase
Fig. 27.3 Hypothetical combustion chamber
Suppose now that the same flow rates of air and volatiles, both at temperature T0, are mixed in a hypothetical combustion chamber. Furthermore, assume the combustion reactions in the chamber are identical to those in the flame in Fig. 27.2, and the products of combustion are cooled down to the reference temperature T0 without condensing water. This hypothetical situation is shown in Fig. 27.3. Application of the first law of thermodynamics for the combustion chamber control volume in Fig. 27.3 leads to Q_ ¼ m_ a h0a þ m_ v h0v m_ e h0e
ð27:6Þ
where Q_ is the total rate of heat released by combustion in the flame (kW). Q_ is identical in Figs. 27.2 and 27.3 but is distributed in different ways. By expressing the heat released per unit mass of volatiles, an effective heat of combustion can be defined as m_ v Δhc, eff Q_
ð27:7Þ
or per unit exposed area 00 m_ v Δhc, eff Q_
00
ð27:8Þ
where 00
m_ v
¼ Generation rate of fuel volatiles per unit area of fuel surfaceðg=m2 sÞ Δhc, eff ¼ Effective heat of combustionðkJ=gÞ 00 Q_ ¼ Total rate of heat released per unit area of fuel surfaceðkW=m2 Þ Δhc,eff is for the combustion reactions as they take place in the calorimeter. Δhc,eff must be
27
Calorimetry
909
distinguished from the net heat of combustion, Δhc,net. The difference between Δhc,eff and Δhc,net is very significant for charring materials such as wood. In an oxygen bomb calorimeter; nearly all the mass of wood is consumed, leaving a small fraction of noncombustible ash (usually less than 1 % by mass). The net heat of combustion, Δhc,net, of dry wood is in the range of 16–18 MJ/kg. When exposed under real fire conditions, only 70–80 % of the mass is converted to volatiles that burn almost completely. The heat of combustion of the volatiles, Δhc,eff, measured in a small-scale calorimeter is only 12–13 MJ/kg. A solid char residue remains, primarily consisting of carbon, with a net heat of combustion of approximately 30 MJ/kg. In an oxygen bomb calorimeter, most of this char is also burnt, explaining why Δhc,net exceeds Δhc,eff by 25–50 %. Even for materials that do not form a char, Δhc,eff can be significantly lower than Δhc,net if combustion of the volatiles in the small-scale calorimeter is incomplete. In this case, the products of combustion contain measurable amounts of combustible components such as CO, soot, unburnt hydrocarbons, and so forth. The ratio of Δhc,eff to Δhc,net is defined as combustion efficiency, χ. For clean-burning gaseous fuels, such as methane, χ is close to unity. For fuels that produce sooty flames, including gases, χ can be significantly lower. For example, χ for acetylene is approximately 0.75. χ values for a number of gases, liquids, and solids are listed in Chap. 36, “Combustion Characteristics of Materials and Generation of Fire Products.” Substitution of Equations 27.2, 27.3, 27.4, and 27.6 into Equation 27.5 leads to Q_ Q_ f , 1 ¼ c p m_ e ðT e T 0 Þ cp m_ a ðT a T 0 Þ c p m_ v ðT v T 0 Þ ð27:9Þ The stoichiometric air-to-fuel ratio ranges between 3 and 16 for most fuels. Moreover, small-scale calorimeters are usually operated with excess air. For example, the standard initial flow rate in the cone calorimeter is 30 g/s. Based on the oxygen consumption principle (see below), the stoichiometric flow rate of air for a 10 kW fire (practical upper limit in the cone
Stack with TC hot junction
ΔT Specimen Heater
TC cold junction
Fan and flow control
Fig. 27.4 Sensible enthalpy rise calorimeter
calorimeter) can be calculated as 10 kW/3 kJ per g of air ¼ 3.3 g/s. Thus, the air supply in the cone calorimeter is at least nine times stoichiometric, or at least 9 3 ¼ 27 times the generation rate of volatiles. Usually, the ratio is ˙ v is negligible compared much greater. Hence, m ˙ a and Equation 27.9 can be approximated as to m Q_ Q_ f , 1 m_ a cp ðT e T a Þ
ð27:10Þ
This equation is the basis for the sensible enthalpy method. Heat release rate is calculated from the temperature rise Te Ta of the gases flowing through a calorimeter. A schematic of a calorimeter based on this principle is shown in Fig. 27.4. There are a few problems with the practical implementation of this technique. The main concern is that only a fraction of the heat released in the flame is used to raise the sensible enthalpy or temperature of the gases. Therefore, it is necessary to recover or measure the loss term Q_ f , 1 . Some calorimeters have water-cooled walls that trap most of the losses. These losses can be estimated by measuring the enthalpy rise of the cooling water. However, due to the additional
910
M. Janssens
hardware and instrumentation, such calorimeters are rather complex and difficult to operate. A more popular method relies on a gas burner calibration to determine Q_ f , 1 in the assumption that the losses are fuel independent. Defining the loss fraction, χr, by Q_ Q_ f , 1 ð1 χr ÞQ_
ð27:11Þ
where χr is the fraction of total heat release rate lost by radiation. The symbol χr is chosen for this fraction because Q_ f , 1 consists primarily of radiation. If the calorimeter is operated with a constant ˙ a, Equation 27.11 can be written as airflow rate m m_ e c p ðT e T a Þ kðT e T a Þ Q_ 1 χr
ð27:12Þ
where k is the calibration constant (kW/K). The calibration factor, k, is determined from a _ By repeatgas burner calibration with known Q. ing the calibration over a range of heat release rate levels, k can be determined as a function of Q_ or Te. If the specimen is enclosed with the heater, Equation 27.12 is still valid, provided a reference temperature Tr is used instead of Ta. The temperature difference Tr Ta results from the heat transfer between the heater and the airflow through the enclosure. Tr is therefore a function of heater setting, to be determined via calibration. Ed Smith’s rate of heat release test developed at Ohio State University is the most well-known and most widely used calorimeter based on the sensible enthalpy rise method [3]. The test method is described in detail in a separate section.
Substitution Method For practical reasons, calorimeters based on the sensible enthalpy rise method use a closed configuration. The specimen and heater(s) are located inside a metal box, which may be (partly) insulated. The dynamic response of the enclosure to changes in the thermal environment creates problems in the practical implementation of the
sensible enthalpy rise method. After ignition, part of the heat released by a burning specimen is transferred by radiation to the enclosure walls. A fraction of this heat is stored in the walls, causing an increase of their temperature, in turn resulting in an enhanced heat transfer with the air flowing through the box. The result is that, for a material that quickly reaches steady burning conditions, there is a delay for Te to reach the corresponding steady temperature. A similar phenomenon occurs when the heat release rate from the specimen decreases or after the specimen burns out and the heat release rate goes back to zero. Under unsteady burning conditions, Te constantly lags behind the temperature corresponding to the instantaneous heat release rate. Several methods have been suggested to mathematically address this problem, but none are completely satisfactory [8–12]. The substitution method was developed to eliminate problems associated with thermal lag. The method requires two runs to determine the heat release rate of a material under a given set of conditions. The first run uses a similar arrangement as shown in Fig. 27.4. The temperature difference Te Ta is measured as a function of time. The second run uses the same apparatus, airflow rate, and radiant heat flux. However, the specimen is replaced by a noncombustible dummy specimen and a substitution gas burner. The flow of gas to the burner is controlled in such a way that the temperature difference Te Ta closely follows the curve measured during the first run. Figure 27.5 shows a schematic of the substitution run. Presumably, the dynamics are identical in both runs. Hence, problems with thermal lag have been eliminated, and the heat release rate of the specimen can be determined from the fuel flow rate to the burner in the second run. Unfortunately, implementation of this method is not trivial, because a sophisticated control system is needed for the second run. Moreover, due to the addition of substitution runs, the number of tests required to evaluate a material is doubled. The substitution method was first implemented at Factory Mutual [13]. The apparatus was designed to measure the heat release
27
Calorimetry
911 Stack with TC hot junction
Stack with TC hot junction
Noncombustible dummy specimen
ΔT
Constant ΔT
Compensation gas burner Heater
Substitution gas burner
Heater
Specimen
TC cold junction
TC cold junction
Fan and flow control
Fig. 27.5 Second run with substitution burner
rate from roof assemblies. A small-scale substitution calorimeter was developed at the Forest Products Laboratory [14].
Compensation Method A compensation calorimeter is similar to a substitution calorimeter, except that the burner is operated while a specimen is exposed. A schematic is shown in Fig. 27.6. Initially, the burner flow rate is chosen so that the corresponding heat release rate exceeds that of any material to be tested. During a test, the gas flow rate to the burner is controlled so that Te Ta remains constant. The heat release rate corresponding to the reduction in flow rate to the burner is equal to the heat release rate from the specimen. The compensation method also eliminates problems with the dynamic response of the calorimeter enclosure. In theory, a compensation calorimeter is operated at a constant temperature. This would resolve another problem associated with the assumption that Q_ f , 1 is fuel independent, whereas in reality it is not (Q_ f , 1 is a strong function of the sootiness of the flame).
Fan and flow control
Fig. 27.6 Compensation calorimeter
In practice, however, the specimen and burner have to be separated to avoid that radiation from the burner flame enhances radiant heat flux to the specimen. Hence, the calorimeter enclosure is not truly isothermal, and the problem remains unresolved. As with substitution calorimeters, the burner flow control system makes compensation calorimeters rather complex and difficult to operate. As a result, they are suitable only for research and not for routine testing. Compensation calorimeters were developed at the National Bureau of Standards [15, 16] and Stanford Research Institute [17].
Oxygen Consumption Method In 1917, Thornton showed that for a large number of organic liquids and gases, a nearly constant net amount of heat is released per unit mass of oxygen consumed for complete combustion [18]. Huggett found this also to be true for organic solids and obtained an average value for this constant E of 13.1 MJ/kg of oxygen [19]. This value may be used for practical applications and is accurate with very few exceptions to within 5 %. Thornton’s rule
912
M. Janssens
implies that it is sufficient to measure the oxygen consumed in a combustion system in order to determine the net heat released. This is the basis for the oxygen consumption method for measuring heat release rate in fire tests. The first application of the oxygen consumption technique in fire research was by Parker on the ASTM E84 tunnel test. [20] During the late 1970s and early 1980s, the oxygen consumption technique was refined at the National Bureau of Standards (NBS, currently the National Institute of Standards and Technology, or NIST). The oxygen consumption method is now recognized as the most accurate and practical technique for measuring heat release rates from experimental fires. It is widely used throughout the world, for both small-scale and large-scale applications.
Thornton’s Rule The exact value of E for a specific fuel is equal to the net heat of combustion of the fuel divided by the mass of oxygen needed for complete combustion of a mass unit of fuel. The mass of oxygen required for complete combustion of a mass unit of fuel can be determined from the stoichiometry of the combustion reactions. Consider, for example, the following equation to describe complete combustion of methane: CH4 þ 2O2 ! CO2 þ 2H2 O
ð27:13Þ
This equation indicates that 64 g of oxygen are required for complete combustion of 16.04 g of methane. Hence, the mass of oxygen needed to burn 1 g of methane is r0 ¼ 64/16.04 ¼ 3.99 g O2/g CH4. Because the net heat of combustion of methane is 50.04 kJ/g, the net heat released per mass unit of oxygen consumed is equal to E ¼ Δhc,net/r0 ¼ 50.04/3.99 ¼ 12.54 kJ/g O2. An extensive list of E values can be found in Chap. 36; in Tables C2–C4 and in the literature [21, 22]. A summary of average values for different categories of fuels and polymers based on the data in Chap. 36 is given in Table 27.1. This table also lists values for the amount of heat released per mass unit of CO2 and CO generated
(E0 and E00 , respectively). Although there is more variation between different categories, these values are also reasonably constant within a given category of fuels or polymers.
Volatiles or Condensed Phase? An interesting question is whether the oxygen consumption technique measures heat release rate for the volatiles or the solid fuel. Thermal methods approximately measure heat release rate from the volatiles. However, Huggett’s constant of 13.1 kJ/g is based on the average net heat of combustion for a large set of materials. Hence, one would expect that oxygen consumption calorimetry gives the heat released by the fuel in its natural state at ambient temperature, because that is how the fuel is supplied in an oxygen bomb calorimeter. The question can be examined in more detail for some synthetic polymers by comparing the net heat of combustion of the polymer to that of the corresponding monomer. If one were to burn a monomer in an oxygen consumption calorimeter, the products of complete combustion would be the same as for the corresponding polymer, provided test conditions are identical. Therefore, measured heat release rate would be the same in the two cases. However, the net heat of combustion is higher for the monomer. The difference with the net heat of combustion of the polymer is the net heat released in the polymerization process. Table 27.2 gives values for the net heat of combustion of nine polymers and their monomers. The former are taken from Huggett; [19] the latter are obtained by adding the heat of polymerization as reported in the literature [23]. Table 27.2 confirms that the oxygen consumption technique measures net heat release rate of a solid fuel. The heat release rate from the volatiles is always higher, but not by as much as indicated in the last column of the table, because only a fraction of polymeric fuels decomposes back into the monomer (see Chap. 7, “Thermal Decomposition of Polymeric Materials”).
27
Calorimetry
913
Table 27.1 E, a, E0 and E00 values for different fuel and polymer categories Category Fuels containing C and H Normal alkanes Substituted alkanes Cyclic alkanes Normal alkenes Cyclic alkenes Dienes Normal alkynes Arenes Fuels containing C, H and O Alcohols Aldehydes Ketones Acids Esters Others Fuels containing C, H, N and S C-H-N fuels C-H-S fuels Polymeric materials C and H in the structure C, H, O and N in the structure C, H and Cl in the structure C, H and F in the structure C, H and Si in the structure
E (kJ/g O2)
α
E0 (kJ/g CO2)
E00 (kJ/g CO)
12.7 12.6 12.7 13.2 13.0 13.5 13.3 13.0
1.079 1.076 1.069 1.070 1.062 1.057 1.060 1.049
14.6 14.6 13.8 14.2 13.4 13.5 14.0 12.4
12.9 12.8 11.6 12.4 11.1 11.2 12.0 9.4
13.3 14.2 13.2 14.2 13.0 13.9
1.104 1.108 1.088 1.245 1.118 1.076
14.5 13.3 13.2 9.7 12.5 12.2
12.8 10.6 11.1 5.4 9.7 8.9
11.5 11.3
1.063 1.055
15.4 13.1
14.1 11.5
12.5 12.5 12.8 11.3 13.7
1.051 1.085 1.124 1.293 1.083
12.4 10.9 12.1 9.2 14.8
9.5 7.2 9.6 – 13.3
Table 27.2 Net heat of combustion of some polymers and their monomers Polymer Polyethylene Polypropylene Polybutadiene Polystyrene Polyvinylchloride Polyvinylidene chloride Polyvinylidene fluoride Polymethylmethacrylate Polyacrylonitrile Average
Δhc,net (kJ/g fuel) 43.3 43.3 42.8 39.9 16.4 8.99 13.3 24.9 30.8
E (kJ/g O2) 12.65 12.66 13.14 12.97 12.84 13.61 13.32 12.98 13.61 13.09
Implementation of the Oxygen Consumption Method The basic requirement to use the oxygen consumption technique is that all combustion products are collected and removed through an
Monomer (state) C2H4 (g) C3H6 (g) C4H6 (L) C8H8 (L) C2H3Cl (g) C2H2Cl2 (L) C2H2F2 (g) C5H8O2 (L) C3H3N (L)
Δhc,net (kJ/g fuel) 47.2 45.8 44.1 40.5 18.0 9.77 15.6 25.4 32.2
E (kJ/g O2) ΔE (%) 13.78 8.9 13.39 5.8 13.56 3.2 13.19 1.7 14.10 9.8 14.79 8.7 15.61 17.2 13.26 2.2 14.25 4.7 13.99 6.9
exhaust duct. At a distance downstream sufficient for adequate mixing, both flow rate and composition of the gases are measured. A schematic of an oxygen consumption calorimeter is shown in Fig. 27.7. It is not necessary to measure the inflow of air, provided the flow rate is
914
M. Janssens
measured in the exhaust duct. Therefore, oxygen consumption calorimeters are typically open, to avoid that part of Q_ f , 1 that is reflected by the calorimeter walls and reaches the specimen surface. This would result in an uncontrolled radiant heat flux, in addition to that from the heater. The practical implementation of the oxygen consumption technique is not straightforward. Application of Thornton’s rule to the combustion system shown in Fig. 27.8 leads to the following equation for the heat release rate: Flow measurement and fan
O2 analyzer
Specimen Heater
Fig. 27.7 Oxygen consumption calorimeter
Q_ ¼ E m_ a Y Oa 2 m_ e Y Oe 2
ð27:14Þ
where E ¼ Heat release per mass unit of oxygen consumed ð 13:1kJ=gÞ Y Oa 2 ¼ Mass fraction of oxygen in the combustion airð0:232 g=g in dry airÞ Y Oe 2 ¼ Mass fraction of oxygen in the combustion productsðg=gÞ There are three problems with the practical implementation of Equation 27.14. First, oxygen analyzers measure the mole (volume) fraction and not the mass fraction of oxygen in a gas sample. Mole fractions can be converted to mass fractions by multiplying the mole fraction with the ratio between the molar mass of oxygen and the molar mass of the gas sample. The latter is usually close to the molar mass of air (29 g/mol). Second, water vapor is removed from the sample before it passes through a paramagnetic analyzer, so that the resulting mole fraction is on a dry basis. Third, flow meters measure volumetric rather than mass flow rates. The volumetric flow rate in the exhaust duct, normalized to the same pressure and temperature, is usually slightly different
Fig. 27.8 Mass flow rates in oxygen consumption calorimeter
27
Calorimetry
915
from the inflow rate of air because of expansion due to the combustion reactions. Parker [24] and Janssens [25] solved these problems and developed equations for calculating rate of heat release by oxygen consumption for various applications. The equations are a function of the extent of the gas analysis. The oxygen concentration must be measured as a minimum. However, the accuracy can be improved by adding instrumentation for measuring the concentration of other gases. Equations for the two most common configurations of gas analyzers are discussed below. Detailed derivations are not repeated here and can be found in the aforementioned references. Modified equations to address specific circumstances or problems, such as heat release rate measurements during suppression experiments, from fires with significant soot yields, or during experiments conducted in a vitiated (reduced O2) environment, can also be found in the literature [26–28]. Derivation of detailed equations for carbon oxide calorimetry, a technique that is used extensively by FM Global, can also be found in the literature [29, 30]. Carbon oxide calorimetry is discussed in section “Carbon Oxide Calorimetry”.
Only O2 Measured In this case all water vapor (by a chiller and moisture sorbent) and CO2 (by a chemical sorbent) must be removed from the exhaust gas sample stream before O2 is measured. This leads to the assumption that the sample gas consists of only O2 and N2. The resulting equation for calculating heat release rate is Q_ ¼ E
where ϕ ¼ Oxygen depletion factor α ¼ Volumetric expansion factor m_ e ¼ Mass flow rate in the exhaust duct of the calorimeterðg=sÞ MO2 ¼ Molecular mass of oxygenð28 g=molÞ Ma ¼ Molecular mass of the combustion airð29 g=mol for dry airÞ XHa 2 O ¼ Actual mole fraction of water vapor in the combustion air a XCO ¼ Actual mole fraction of carbon dioxide in 2 the combustion air a XAO2 ¼ Measured mole fraction of oxygen in the combustion air c XAO2 ¼ Measured mole fraction of oxygen in the exhaust flow As the composition of the fuel is usually not known, some average value has to be used for α. Complete combustion of carbon in dry air results in α ¼ 1. If the fuel is pure hydrogen, α is equal to 1.21. A commonly-used value for α is therefore 1.105. The average value and standard deviation for the fuels in Table 27.1 is 1.093 0.066. XHa 2 O can be calculated from the relative humidity and temperature in the laboratory. Typically it is of the order of 1–2 % in a a temperature-controlled laboratory.1 XCO in dry 2 2 air is approximately 390 ppm. Note that the symbols for oxygen mole fraction measured in the combustion air (prior to a test) and the exhaust flow include a superscripted A. This is to make a distinction between the actual and measured mole fractions of oxygen, because the latter are for a dry gas sample. Equation 27.15 is expected to be accurate to within 10 %, provided combustion is complete; for example, all carbon is converted to CO2. The error may be larger if CO or soot production is
a ϕ MO a m_ e 2 1XHa 2 O XCO XAO2 2 Ma 1 þ ϕ ðα 1 Þ
ð27:15Þ with a
e
XA þ XA ϕ ¼ O2 e O2 a 1 XAO2 XAO2
ð27:16Þ
For example, air at 20 C, 1013 mbar and a relative humidity of 50 % contains 1.2 % of water vapor by volume. 2 The concentration of carbon dioxide in the atmosphere is measured at the Mauna Loa Observatory in Hawaii. The average concentration measured in 2010 was 390 ppm. The concentration varies annually by about 3–9 ppm, but the annual average has steadily increased by about 74 ppm since 1958, when the measurements were first recorded. 1
916
M. Janssens
considerable, or if a significant amount of combustion products consists of species other than CO2 or H2O (e.g., HCl). The error is partly due to the uncertainty of E and α. If more exact values are available, accuracy can be improved by using those instead of the generic values of 13.1 kJ/g and 1.105.
O2, CO2, and CO Measured In this case, only water vapor is trapped before the exhaust gas sample reaches the analyzers. CO in many cases is negligible. The rate of heat release in those cases can be calculated from Equation 27.15 with the minor modification that a XCO is not included in the expression inside 2 parentheses. In addition, ϕ is slightly different and follows from a e e a XAO2 1 XACO2 XAO2 1 XACO2 e ϕ¼ e e 1 XAO2 XACO2 XAO2 ð27:17Þ where a XACO2
¼ Measured mole fraction of carbon dioxide in the combustion air c XACO2 ¼ Measured mole fraction of carbon dioxide in the exhaust flow Generally, adding CO2 does not greatly improve the accuracy of measuring heat release rate. However, adding a CO2 analyzer eliminates
Fig. 27.9 Effect of ignoring CO on Q_ error
the need for an expensive sorbent to scrub CO2 from the gas sample. If a significant fraction of carbon in the fuel is converted to CO instead of CO2, the equations can be corrected to take incomplete combustion into account. Heat release rate is then calculated from " # e 1 ϕ XACO _ Q ¼ Eϕ ðECO EÞ e 2 XAO2 ð27:18Þ e MO2 m_ e a A 1 XH2 O XO2 1 þ ϕ ðα 1Þ M a
with a Ae Ae Ae Aa XA O2 1 XCO2 XCO XO2 1 XCO2 a ϕ¼ e Ae Ae A 1 XA O2 XCO2 XCO XO2 ð27:19Þ where ECO ¼ Heat release per mass unit of oxygen consumed for COð17:6 MJ=gÞ c XACO ¼ Measured mole fraction of carbon monoxide in the exhaust flow
One might wonder under what conditions the CO correction becomes significant. Figure 27.9 shows the ratio of heat release rate obtained by ignoring CO to the actual heat release rate, as a function of the ratio of measured CO to CO2 mole fractions in the exhaust flow for methane and for a gaseous fuel of composition (CH2O)n. According to Roberts, the molecular formula of
Ratio of measured to actual Q
1.05 CH2O
1.04
CH4 1.03 1.02 1.01 1.00 0.99 0.00
0.05
0.10 Ratio of
0.15 Ae X CO
0.20 to
Ae X C O2
0.25
0.30
27
Calorimetry
917
the latter represents the thermal degradation products of beech wood [31]. For the CO effect examined here, this fuel represents a “worst case” because it contains enough oxygen for combustion of all hydrogen. Methane gives a practical lower limit for the error, because it is the hydrocarbon with the highest hydrogen-tocarbon ratio. There is some experimental evidence that the yield of CO in underventilated fires reaches an upper limit approximately equal to 0.2 kg of CO per kg of fuel, when the equivalence ratio exceeds unity [32]. For the fuels considered here, the limit corresponds to a CO/CO2 mole fraction ratio of 0.27. Figure 27.9 indicates that, even under the worst conditions, the error by ignoring CO generation is less than 5 %.
Carbon Oxide Calorimetry An alternative method for measuring heat release rate is based on the fact that amount of heat released per mass unit of carbon dioxide and carbon monoxide generated is also relatively constant within a category of fuels or polymers (see Table 27.1). This method is particularly useful for oxidizers [33]. Application to the combustion system shown in Fig. 27.8 leads to the following equation for the heat release rate:
e a _ CO _ CO m m ¼ 2 2
0 00 e a e _ _ CO _ CO Q_ ¼ E m m CO2 þ E m 2 0 00 e a e _ a YCO _ e YCO _ e YCO ¼E m m þE m 2 2 ð27:20Þ where E E
0
0
e _ CO m 2 a _ CO m 2 e _ CO m
¼ Heat released per mass unit of carbon dioxide generatedðkJ=gÞ; ¼ Heat released per mass unit of carbon monoxide generatedðkJ=gÞ; ¼ Exhaust flow rate of carbon dioxide ðg=sÞ; ¼ Inflow rate of carbon dioxide from ambient environment ðg=sÞ; ¼ Exhaust flow rate of carbon monoxide ðg=sÞ;
e ¼ Carbon monoxide mass fraction in the YCO 2 exhaust flowðÞ; a YCO ¼ Ambient carbon monoxide mass 2 fraction ðÞ; and e YCO ¼ Carbon monoxide mass fraction in the exhaust flowðÞ:
Khan et al. give values for E0 and E00 of 13.3 kJ/g 11 % and 11.1 kJ/g 18 %, respectively (Chap. 36). Practical implementation of Equation 27.20 faces the same challenges as that of Equation 27.14. The following equations can be used to calculate the generation rates of carbon dioxide and carbon monoxide [34]:
e Aa Aa Ae Ae XA 1 X 1 X X X CO2 O2 CO2 O2 CO e
e
e
A A 1 XA O2 XCO2 XCO
_e MCO2 m 1 XHa 2 O 1 þ ϕð α 1 Þ M a ð27:21Þ
with
e _ CO ¼ m
e Aa Aa XA 1 X X CO O2 CO2 e
e
e
A A 1 XA O2 XCO2 XCO
Practical Considerations The equations presented in the previous sections are rather complex and it is very easy to make mistakes. To illustrate the point, Lattimer and Beitel reviewed 17 different standard test
_e MCO m 1 XHa 2 O 1 þ ϕðα 1Þ Ma
ð27:22Þ
methods for measuring heat release rate based on oxygen consumption calorimetry [35]. They found errors in the equations for 12 of the 17 standards. In total, 22 equations were found to be in error. Because it is difficult to avoid
918
errors in transcribing to a spreadsheet program even with the correct equations, it is essential to do so very carefully and to double-check the results. Improper setup and maintenance of the gas sampling and analysis system is another common cause for errors. The proper sorbent columns have to be installed depending on the configuration of gas analyzers used. It is necessary to use three columns in series when only oxygen is measured. The first column contains a drying agent. The second column contains a sorbent to scrub the CO2 from the gas sample. The third column also contains a drying agent and is necessary to remove water vapor that is generated by the CO2 scrubber. If carbon oxide analyzers are used, a drying column is all that is needed. Silica gel is a commonly used drying agent in chemistry labs. However, it is not suitable for most oxygen consumption calorimetry applications because of the generation of CO2 [36]. Drierite® is commonly used instead of silica gel, but some batches seem to have the same problem. Ascarite® is the most commonly used CO2 scrubbing agent. Finally, the analyzers are calibrated with certified zero and span gases at the start of each testing day and sometimes more than once a day. It is absolutely essential that flows and pressures during these calibrations are the same as during testing.
Factors Affecting Small-Scale Heat Release Measurements This section examines the effects of some calorimeter construction details on quality and accuracy of the measurements. The discussion results in some guidelines for building the “ideal” smallscale calorimeter for a specific application.
Open or Closed Configuration Calorimeters that utilize a measuring technique other than oxygen consumption consist of a closed “box” configuration. Combustion air is
M. Janssens
supplied to one side of the box, and combustion products are removed from the opposite side. Specimen, heater, and ignition device typically are located inside the box. Advantages of a closed configuration are that airflow rate can be measured at the inlet under clean and soot-free conditions, the combustion air can be heated, and the oxygen concentration in the air can be increased (by adding O2) or decreased (by adding N2) from ambient. Disadvantages are thermal lag due to heating or cooling of the enclosure walls and uncontrolled radiation feedback from the enclosure walls to the specimen. To address the first disadvantage, various numerical procedures have been proposed for correcting the temperature signal measured with calorimeters based on the sensible enthalpy rise method [8–12]. These procedures are based on a mathematical model of the calorimeter consisting of two first-order systems in series. The first system has a rather small time constant (between 8 and 30 s for various calorimeters) and is related to the heat capacity of the gases flowing through the calorimeter. The second system has a large time constant (200–930 s for various calorimeters), which is associated with the heat capacity of the calorimeter walls. The correction procedures adjust the output signal for thermal lag, using discrete forward and inverse Laplace transform techniques. In spite of the complex calculations, the resulting correction may not always be accurate due to the crude mathematical model for the calorimeter. A more convenient, and perhaps equally accurate, correction method relies on an electronic compensator as described in ASTM E906 and ASTM E1317. The compensator electronically corrects the output signal of the exhaust thermocouples, based on the negative feedback of a wall temperature signal. The oxygen consumption method also has a time delay, but with properly adjusted sampling flows and oxygen analyzer, this delay consists almost entirely of the transport time for a gas sample from the combustion zone to the analyzer [37]. Because flow rates in the exhaust duct and sampling lines do not change significantly during a test, this delay time is approximately constant.
27
Calorimetry
It can be determined with gas burner calibrations and can be easily addressed by shifting the gas analysis data over the appropriate time interval. To obtain accurate measurements for thin materials that produce a heat release vs. time curve that has the form of a single sharp peak, it is necessary to make corrections for the response time of the oxygen analyzer [12]. An oxygen analyzer is modeled as a first order system and its time constant is obtained from gas burner step response measurements. The second disadvantage can be eliminated only by using blackened water-cooled calorimeter walls. If the walls are allowed to heat or cool freely, they emit radiation, which varies with time. Part of this radiation reaches the specimen surface and enhances the radiant heat flux from the heater in an uncontrolled fashion. Obviously, the need for water-cooled walls makes the apparatus much more complex and costly. Problems with thermal lag and radiation feedback to the specimen can be eliminated by using an open configuration. Solid objects must be water cooled or sufficiently remote from heater and specimen so that they do not interfere with the controlled radiant heat flux to the specimen. A closed configuration can be recommended only for specialized applications, for example, to study the effect of oxygen concentration or temperature of the combustion air on heat release rate and burning behavior.
Type of Heater Heat release rates must be measured at constant heat flux levels over a range that is relevant for the fire scenario of interest. The heat flux can be provided with a gas burner flame in contact with the specimen or with a radiant panel remote from the specimen. Incident heat flux from impinging gas burner flames can be adjusted only over a narrow range. To increase the heat flux from a gas burner, either the flame size has to be increased, or a fuel with higher soot yield has to be used. Usually, these parameters can be adjusted only slightly or not at all. It is very difficult to set and maintain a
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specific heat flux level because a major fraction of the heat transfer is convective. Moreover, the burner gas and combustion products mix with fuel volatiles, which affects burning behavior. In short, impinging flames are not desirable as the external heat source in heat release rate calorimeters. It is much easier to create constant and uniform exposure conditions if the incident heat flux is primarily radiative. Porous gas panels as well as electrical heating elements are used for this purpose. The radiant heat flux can be adjusted by changing the power of the heater or by changing the distance between heater and specimen. If the second method is used, practical upper and lower limits to the range of radiant heat flux levels can be created. If the heater is too close to the specimen, convective heat transfer becomes significant. Therefore, the upper limit corresponds to the minimum distance that has to be maintained in order to ensure predominantly radiative heat transfer. The lower limit is determined by the uniformity of the incident radiant heat flux, which drops with increasing distance between heater and specimen. The exact limits depend on the geometrical configuration, the power of the heater, and the degree of nonuniformity of the incident heat flux profile that is deemed acceptable. Another important aspect is the ability of the heater to maintain the radiant heat flux at a constant level during a test. If the heater is operated at a constant power level, incident radiant heat flux changes during testing. At the start of a test, a cold specimen is inserted. The specimen acts as a heat sink, resulting in a decrease of the heater temperature and consequently a decrease of the incident radiant heat flux. After ignition, the heat released by the specimen results in an increase of the heater temperature and incident radiant heat flux. To maintain incident radiant heat flux during a test, it is therefore necessary to keep the temperature of the heater constant. This is very difficult with a gas panel, but relatively straightforward for electrical heating elements. With the oxygen consumption method, another drawback of using a gas panel is that its products of combustion
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result in an oxygen depletion that is usually much larger than the oxygen consumed for combustion of the specimen. Thus, small fluctuations in panel flow can result in significant error of the measured heat release rate. This “baseline” problem can be avoided by using a separate exhaust system for the heater. It is clear from the preceding discussion that an electrical heater is preferable over a gas panel. Two types of electrical heaters are used: high and low temperature. The former are commonly tungsten filament lamps that operate at temperatures close to 2600 K. According to Wien’s displacement law, peak radiant heat flux from such lamps is at a much shorter wavelength than for real fires, with temperatures in the range of 600–1400 K. Piloted ignition studies on plastics and wood have shown that these materials absorb much less radiation in the visible and near-infrared range than at higher wavelengths [38, 39]. On the basis of these findings, it can be concluded that commercially available low-temperature elements are preferable over high-temperature lamps. Such elements typically operate between 800 and 1200 K, a range that is representative of real fire exposure conditions.
Type of Ignition Pilot Heat release rate tests are usually conducted with an ignition pilot. The use of a pilot reduces the variation in time to sustained flaming between multiple tests conducted under identical test conditions. Because the duration of the preheat period prior to ignition affects burning rate after ignition, use of a pilot also improves repeatability of heat release rate measurements. Furthermore, piloted ignition is used because it is representative of most real fires and conservative in other cases. The ignition pilot in small-scale fire tests consists of a small gas burner flame, a glowing wire, or an electric spark. An impinging flame should not be used because it locally enhances the incident heat flux to the specimen. Another problem with pilot flames is that they are
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sometimes extinguished by fire retardants or halogens in the fuel volatiles. A glowing wire is not an efficient method for igniting fuel volatiles, sometimes leading to poor repeatability. An electric spark remains stable when fire retardants or halogens are present. However, it occupies a small volume, so that the positioning of the spark plug is more critical than with other types of ignition pilots.
Specimen Size The ideal situation would be if small-scale heat release rate data could be used directly to predict burning rate in real-scale fires. Unfortunately, the minimum specimen size that is required to allow for such a straightforward prediction is not practical. As described earlier, the burning rate of a specimen is a direct function of the net heat flux transferred to the fuel. The net flux is equal to the total of external heat flux, flame convection, and flame radiation, minus radiative heat losses from the fuel surface and heat losses (or gains) at the specimen edges. The Russian work on the effect of diameter on pool fire burning rate by Blinov and Khudiakov gives some insight into this problem. A detailed discussion of this work and its implications is given by Drysdale [40]. If the pool diameter is less than 0.03 m, flame convection is laminar and burning rate increases with decreasing diameter. If the pool diameter exceeds 1 m, flame convection is turbulent and burning rate is independent of diameter. There is a transition region between these two limits, with a minimum burning rate for a pool diameter of approximately 0.1 m. This work indicates that specimen size in a heat release rate calorimeter must be at least 1 m for the results to be independent of scale. This is indeed not feasible in practice. The Russian pool fire data also indicate that heat transfer at the edges becomes excessive at diameters below 0.1 m. Therefore, specimen size in small-scale calorimeters should be at least 0.1 m. To predict real-scale burning rates, differences in flame heat transfer, and up to a lesser extent heat transfer at the edges, have to
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Calorimetry
¨ stman and Nussbaum reported be considered. O ignition and heat release data for 13 materials and two specimen sizes [41]. Increase in specimen size from 0.1 m 0.1 m to 0.2 m 0.2 m resulted in a slight reduction of piloted ignition time. Average heat release rate over the first minute after ignition on a per-unit-area basis increased by approximately 12 % at exposure levels exceeding 25 kW/m2. Larger increases were observed at the 25 kW/m2 exposure level and for peak heat release rate. Janssens and Urbas presented a comparison of heat release rate data for nine wood products obtained in the cone and an intermediate-scale calorimeter [42]. A 100-fold increase in specimen size resulted in only a 10 % increase of the heat release rate. This modest effect can be explained by the fact that the heat feedback from the flame is relatively insensitive to specimen area for testing in the vertical orientation, in particular for materials, such as wood, that do not produce very luminous flames. Depending on the specimen size in a smallscale test, there is a limit on the degree of nonuniformity and irregularity of the product being tested, if the test conditions are to be representative of end-use conditions. Therefore, there might be some merit in choosing a specimen size that exceeds the minimum of 0.1 m. However, the main trade-off is that a larger specimen requires a larger and more powerful heater to achieve uniform incident radiant heat flux to the specimen. It should be recognized that, no matter what the specimen size is, there are assemblies and composites for which it is not possible to prepare representative small-scale specimens. Intermediate-scale or full-scale tests are needed to evaluate the fire performance of such assemblies and composites.
Edge Effects An issue that is closely related to specimen size is that of edge effects. These effects have been studied extensively in the cone calorimeter. ASTM and ISO standards of the cone calorimeter prescribe that, except for calibrations with
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polymethylmethacrylate (PMMA), the specimen is to be wrapped with aluminum foil on the sides and bottom. The main purpose of the foil is to eliminate mass transfer along all boundaries except the exposed face of the specimen. Furthermore, the ISO standard requires all tests be conducted in the horizontal orientation with the stainless steel retainer frame. Toal et al. tested several materials with and without foil wrapping, and with and without the retainer frame [43, 44]. They found that the retainer frame reduces peak heat release rate, and lengthens the burning time. This is to be expected because the retainer frame is a relatively large mass of steel that acts as a heat sink, reducing the energy transferred to the specimen. Urbas and Sand were also concerned with the heat sink effect of the retainer frame [45]. They designed an alternative retainer frame, composed of an insulating collar made of medium-density or high-density refractory material. Their conclusion was that the best edge conditions were obtained using the insulating frame with insulation material that most closely resembles the specimen in thermal properties. Researchers at FM Global proposed a similar approach to address edge effects in a small-scale calorimeter [46]. Babrauskas et al. conducted a very extensive study of the effects of specimen edge conditions on heat release rate [47]. The objective of this study was to further examine the issues raised by Toal et al. and by Urbas and Sand, and to develop definitive recommendations. Specimens of 10 materials were tested in the horizontal orientation at 50 kW/m2 using three configurations: without retainer frame, with retainer frame, and with an insulated retainer frame akin to that developed by Urbas and Sand [45]. All specimens were wrapped in aluminum foil. The study concluded that the use of an insulated frame gives heat release rate values that are slightly closer to the expected true values. However, the insulated frame makes the test procedure significantly more complicated, so that it is not recommended for routine testing.
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If the standard retainer frame is used, Babrauskas et al. recommended that heat release rate data be expressed on the basis of an effective exposure area of 0.0081 m2. The standard retainer frame reduces the actual exposed area from 0.1 m 0.1 m to 0.094 m 0.094 m, or from 0.01 to 0.0088 m2. The recommendation by Babrauskas et al. [47] to further reduce the exposed area to an effective value of 0.0081 m2 indicates that the heat sink effect of the retainer frame reduces heat release rate values by approximately 8 %. ¨ stman and Tsantaridis tested 11 products in O the cone calorimeter in the horizontal orientation at 50 kW/m2, with and without the retainer frame [48]. They also found that the use of the retainer frame results in a reduction of heat release rate greater than what can be explained by the reduction of the exposed area. For the average heat release over the first 3 min following ignition, they found an average reduction of 8 %, identical to Babrauskas et al. [47] However, for maximum heat release rate, they found reductions as high as 25 %. It can be concluded from these studies that the specimen holder configuration in a small-scale heat release rate test may have a significant effect on the measurements. This effect should be addressed if the test data are used to predict performance in real fires.
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oxygen. However, specialized studies have been conducted to evaluate the effect of ventilation and vitiation and to determine the ‘Limiting Oxygen Concentration’, which is an important parameter in the design of fire protection systems that rely on a reduction of oxygen concentration in the room [49, 50]. Such studies require a closed configuration.
Other Measurements Heat release rate calorimeters often include additional instrumentation to measure parameters that are important in characterizing the fire performance of materials. Perhaps the most important additional measurement is that of mass loss rate. Most calorimeters can be provided with a load cell to measure specimen mass loss, but this can be very difficult in a closed configuration. Mass loss rate is obtained from numerical differentiation of the mass loss measurements. Smoke meters are added to measure smoke obscuration in the exhaust duct. Both white light and laser light systems are being used. Toxic gas species can be measured in the exhaust duct with additional gas analysis equipment. Such equipment ranges from standard infrared CO and CO2 analyzers to complex online Fourier transform infrared (FTIR) instrumentation. Whether instrumentation can be added depends mainly on the design and construction details of the calorimeter.
Specimen Orientation Products do not necessarily have to be tested in the same orientation as they are used. For practical reasons, the preferred orientation for smallscale testing is horizontal facing upward. The vertical orientation might be preferable for collecting specialized data for research purposes.
Airflow Standard rate of heat release test methods are operated under overventilated conditions. Plenty of excess air is supplied, so that the measurements are not affected by lack of
Commonly Used Small-Scale Calorimeters Ohio State University (OSU) Calorimeter This apparatus, originally designed by Ed Smith at Ohio State University, is one of the most widely used and best-known small-scale calorimeters [3]. The test method was first published as a proposed ASTM standard in 1980. In 1983, it was adopted as ASTM E906. The standard was recently amended to include two configurations of the test apparatus. Configuration A is that which the Federal Aviation
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Calorimetry
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Fig. 27.10 Ohio State University (OSU) calorimeter
10
9
8 ΔT
7
3
6
5 4
1 2 3 4 5
Air supply fan Main flow control By-pass flow control TC cold junctions Air distributor plate
Administration (FAA) uses for assessing aircraft cabin materials at a radiant heat flux of 35 kW/m2. The test procedure in this configuration is also described in the FAA Aircraft Material Fire Test Handbook [51]. Configuration B is the original configuration. Both configurations rely on thermopile measurements. Several laboratories have modified the OSU calorimeter to measure heat release rate based on oxygen consumption.
Thermopile Versions A schematic view of the apparatus is shown in Fig. 27.10. The apparatus consists of an insulated metal box. The conical wall section between the combustion chamber and the stack is hollow. Air flows through this cavity and mixes with the combustion products downstream of the thermocouple hot junctions. However, recovery of the wall heat losses is not fully accomplished. The main features of the OSU apparatus are described below. Measuring technique. Heat release rate is determined by the sensible enthalpy rise method. The temperatures of inflowing air and outflowing gases are measured with a thermopile of three type K thermocouples. The hot junctions are
2 6 7 8 9 10
1
Heating elements Gas pilot Specimen and holder Baffle plate TC hot junctions
located symmetrically along a diagonal of the stack cross section, above the baffle plate. The cold junctions are located below the air distributor plate. An electrical compensator is used to correct the temperature signals for thermal lag. The factor k in Equation 27.12 is obtained from line burner calibration runs. Configuration. Heater and specimen are located inside a box with approximate dimensions of 0.2 m 0.41 m 0.64 m. The side walls of the box are insulated, and the hollow top wall section is cooled with air. Heater. The vertical radiant heat source measures approximately 0.3 m 0.3 m and consists of four silicon carbide heating elements. A steel masking plate is located in front of the elements to improve uniformity of the incident heat flux distribution over the specimen. The maximum incident heat flux to a vertical specimen is approximately 65 kW/m2. Ignition pilot. The optional ignition source is a pilot flame of 2 mL/s methane, premixed with 14 mL/s air. The pilot flame either impinges on
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the specimen at the bottom (point ignition), is located in the gas phase at the top of the specimen (pilot ignition), or is not used. Specimen size and orientation. For testing in the vertical orientation, specimens with an exposed area of 0.15 m 0.15 m are positioned parallel to the heating elements. Specimens can be tested in the horizontal orientation with the aid of an aluminum reflector foil, which reflects the radiation from the heating elements to the specimen. In this case, the maximum radiant heat flux is reduced to 50 kW/m2 and the specimen size is 0.11 m 0.15 m. The use of the reflector plate is awkward and cumbersome, so that testing in the horizontal orientation with the OSU apparatus is not recommended. Airflow. Total airflow rate is 40 L/s, of which only 10 L/s passes through the combustion chamber and the remaining 30 L/s flows through the upper hollow wall section. Nevertheless, the airflow rate through the combustion chamber contains enough oxygen to feed a 36 kW fire. Because the heat release rate from test specimens rarely exceeds 20 kW, burning conditions in the OSU apparatus are always overventilated. The airflow rates are measured accurately with standard orifices. Additional measurements. The ASTM E906 standard does not include a mass loss measurement but has a smoke measuring system with a white light source in the stack. The FAA established a committee in 1978 to examine the factors affecting the ability of aircraft cabin occupants to survive in a postcrash environment. The committee recommended research to evaluate the fire performance of cabin materials and development of a method using radiant heat for testing cabin materials. As a result, the FAA conducted an extensive series of full-scale fire tests and evaluated numerous small-scale tests for their capability to provide results that correlate well with full-scale performance. The OSU apparatus, standardized as ASTM E906, was found to be the most suitable for
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material qualification. Improved flammability standards and requirements for airplane cabin interior materials based on ASTM E906 first went into effect in 1986 [52]. The limits for acceptance were based on heat release rate measured at a radiant heat flux level of 35 kW/m2. Peak heat release rate could not exceed 100 kW/m2, and average heat release rate over the first 2 min following ignition had to be 50 kW/m2 or less. Originally, the test method used by the FAA was identical to ASTM E906. More recently, some significant modifications have been made [11]. The FAA method now uses a thermopile of five thermocouples, a lighter specimen holder, and a modified test procedure to minimize problems associated with thermal lag [52]. The FAA criteria for acceptance were revised in 1990 to 65 kW/m2 for peak heat release rate during the 5 min test and to 32.5 kW/m2 for average heat release rate over the first 2 min following ignition [52].
Oxygen Consumption Versions When oxygen consumption calorimetry became the preferred method for measuring heat release rate, fire research laboratories in the United States, Canada, and Sweden modified their OSU apparatus. These modifications typically consisted of the elimination of the original thermopile, the addition of a gas sampling probe and gas analysis equipment, and some adjustments to the airflow rates [6, 53–55]. The Forest Products Laboratory (FPL) made two additional significant modifications [54]. An auxiliary heat flux meter was added beneath the specimen to monitor incident radiant heat flux during a test. Measurements obtained with this auxiliary meter indicated that the incident radiant heat flux to a burning wood specimen increases significantly during a test. For example, the incident radiant heat flux to a Douglas fir plywood specimen at the end of a 10-min burning period increased by 20 % over the 35 kW/m2 baseline. This is due to the fact that the heater elements in the OSU calorimeter are supplied with constant power and are not temperature controlled, and
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Calorimetry
that the calorimeter walls are allowed to heat up (or cool down) during testing. The fact that exposure conditions in the OSU calorimeter are not constant is a major weakness of the apparatus. It is nearly impossible to remedy this problem. The addition of an auxiliary heat flux meter is highly recommended to record and account for the time-varying exposure conditions. The second modification at FPL was the addition of a load cell to measure specimen mass loss during a test. This was a rather difficult task due to the geometry of the apparatus and the mechanism for inserting specimens. The FPL load cell design seemed to be satisfactory, demonstrating the feasibility of measuring mass loss in the OSU apparatus.
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Configuration. Cone heater, spark igniter, specimen holder, and load cell are located beneath the hood. The standard configuration is open, with free access of air to the combustion zone. Heater. The heater consists of a 5 kW electrical heating element wound inside an insulated stainless steel conical shell. The heater can be oriented horizontally or vertically to perform tests in either orientation. When tests are performed in the horizontal orientation, the specimen is positioned approximately 25 mm below the bottom plate of the cone heater. Flames and products of combustion rise and emerge through a circular opening at the top of the heater. Maximum radiant heat flux to the specimen exceeds 100 kW/m2.
Cone Calorimeter The cone calorimeter was developed at the National Bureau of Standards (NBS) by Dr. Vytenis Babrauskas in the early 1980s [37]. It is presently the most commonly used small-scale calorimeter. The apparatus and test procedure are standardized in the United States as ASTM E1354 and NFPA 271, Standard Method of Test for Heat and Visible Smoke Release Rates for Materials and Products Using an Oxygen Consumption Calorimeter, and internationally as ISO 5660. Standard cone calorimeter specimens are exposed in an open environment with abundant supply of ambient air for combustion. Some laboratories have used a modified version of the standard apparatus to conduct studies in vitiated or oxygen-enriched atmospheres.
Standard Version A schematic view of the apparatus is shown in Fig. 27.11. The main features are summarized below. Measuring technique. Heat release rate is determined by the oxygen consumption method. The gas flow rate in the exhaust duct is calculated from the pressure drop across and temperature at an orifice plate in the duct. A methane burner calibration is performed to determine the orifice constant.
Ignition pilot. An electric spark is used as the ignition pilot at the top of vertical specimens and over the center of horizontal specimens. Specimen size and orientation. Specimen size in both orientations is 0.1 m 0.1 m. The optional retainer frame in the horizontal orientation and the standard specimen holder in the vertical orientation reduce the exposed area to 0.094 m 0.094 m. Airflow. Combustion products and dilution air are extracted through the hood and exhaust duct by a high-temperature fan. The initial flow rate can be adjusted between 10 and 32 L/s. Volumetric flow rate remains relatively constant during testing. Some cone calorimeters include additional instrumentation to optionally control and maintain the mass flow rate through the exhaust duct. Additional measurements. The specimen is mounted on a load cell. Most cone calorimeters include instrumentation for measuring light extinction in the exhaust duct (using a laser light source, described in ASTM E1354 and ISO 5660-2). Instrumentation to measure concentrations of soot, carbon dioxide, carbon monoxide, and other gases is commonly added.
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Orifice plate flowmeter
Exhaust duct
Blower
Hood
Laser smoke meter Gas sampling port
Cone heater
Spark plug
Specimen Specimen holder
Load cell
Vertical orientation
Fig. 27.11 Cone calorimeter
Modified Versions A number of laboratories have used the cone calorimeter to study the effect of reduced or increased oxygen on the burning behavior of materials [28, 49, 56–59]. An enclosure was built around the heater and load cell and a mixture of nitrogen and oxygen, or air, was supplied to create the desired environment.
Fire Propagation Apparatus Factory Mutual Research Corporation (FMRC, currently FM Global Research) developed the fire propagation apparatus (originally referred to as the combustibility apparatus) to measure heat release rate and generation rates of smoke and combustion products [60]. A schematic of the apparatus is shown in Fig. 27.12.
Originally, only convective heat release rate was measured on the basis of enthalpy rise of the exhaust gases. Test results reported since the late 1970s also include total heat release rates calculated from oxygen consumption or carbon dioxide generation. Several industrial laboratories in France, Germany, and the United States constructed the apparatus in the 1980s. Tewarson used the apparatus to determine fire hazard indices [61] and material properties for fire modeling [62]. He also investigated the effect of environmental conditions (such as oxygen concentration in the combustion air) on heat release rate and burning behavior. The results of his extensive research are summarized Chap. 36. The fire propagation apparatus is standardized as ASTM E2058 and has the following main features:
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Calorimetry
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gases through the exhaust duct is determined by measuring pressure drop across a precalibrated orifice. The original apparatus had a vertical exhaust duct. A commercial version with a horizontal duct was recently developed.
Combustion products
Product sample analysis
Collection hood
Quartz tube
Infrared heaters (4)
Test sample
Aluminum support cylinder
Air + oxygen
Sample support (on load cell) Air distribution box
Fig. 27.12 Fire propagation apparatus
Measuring technique: Total heat release rate is determined by the oxygen consumption method. Tewarson also used carbon dioxide generation to calculate heat release rate. However, the amount of energy generated per mass unit of carbon monoxide generated is much more fuel dependent than the amount of energy produced per mass unit of oxygen consumed. Therefore, this technique is not as universally accepted as the oxygen consumption method. Configuration: Tests are conducted in a semiopen environment. The specimen is located inside a segmented quartz tube, 0.66 m in length and 0.17 m in diameter. A mixture of oxygen and nitrogen is supplied at the bottom of the tube. A stainless steel funnel and vertical exhaust duct are located at some distance above the tube. Dilution air is entrained in the area between the tube and the exhaust system. The total flow of
Heater: Four heaters, which are located coaxially outside the quartz tube, are used to generate an incident heat flux to the specimen with a maximum of 65 kW/m2. The electrical heaters operate at high temperatures so that the spectral distribution of the emitted radiation is not representative of that present in most fires. This problem is discussed elsewhere in this chapter. Ignition pilot: The ignition pilot burner consists of a 6.35-mm stainless steel tube. The burner is supplied with a mixture of 60 % ethylene and 40 % air by volume, at a flow rate to create a stable flame length of 10 mm. The flame is located 10 mm above the horizontal specimen surface or 10 mm from the vertical specimen surface. Specimen size and orientation: Horizontal specimens measure 0.1 m 0.1 m or 0.1 m in diameter. ASTM E2058 also describes a procedure for upward flame spread experiments on 0.1 m 0.3 m vertical planar specimens or 0.8m-long cable specimens in an environment of 40 % oxygen in nitrogen. Airflow: Total gas flow rate supplied to the bottom of the quartz tube is 3.3 L/s. Oxygen content of the combustion air can varied between 0 % and 60 %. Oxygen concentrations below ambient are used for simulating ventilation-controlled fires. Oxygen concentrations above ambient are used to increase flame radiation simulating larger fires [63]. Pure nitrogen is used to determine the heat of gasification. Additional measurements: The apparatus includes instrumentation to measure specimen mass loss, smoke obscuration, and concentrations of O2, CO2, and CO in the exhaust flow. An optional hydrocarbon analyzer can be attached as well.
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FAA Microscale Combustion Calorimeter Recently, the U.S. Federal Aviation Administration (FAA) developed the Microscale Combustion Calorimeter (MCC) to assist with the development of fire-resistant polymers for use in commercial passenger aircraft. A schematic of this micro-scale calorimeter is shown in Fig. 27.13. The apparatus is described in ASTM D7309. A milligram-size specimen is heated at a constant rate between 0.2 and 2 K/s. Decomposition can take place in nitrogen (method A) or in a mixture of nitrogen and oxygen (method B). When method A is used, char-forming specimens do not decompose completely and leave a solid residue. In this case the volatiles are mixed with a metered supply of oxygen in the combustor to obtain the heat release rate of the volatiles. When method B is used, the specimen is completely consumed. The temperature of the combustor is set at approximately 900 C to completely oxidize all specimen Fig. 27.13 Fire propagation apparatus
M. Janssens
gases. Oxygen consumption calorimetry with E ¼ 13.1 kJ/g is used to measure heat release rate. The MCC is different from the calorimeters described in the previous three subsections because the primary result is the heat release rate per mass unit of fuel volatiles as a function of time or pyrolysis chamber temperature (as opposed to the heat release rate per unit exposed specimen area as a function of time). The heat release rate per mass unit of fuel volatiles is referred to as the specific heat release rate, Q(t), and is expressed in W/g. A typical result of an MCC test is shown in Fig. 27.14. The following five parameters are calculated when method A is used: 1. The heat release capacity ηc Qmax/β in J/g∙K, where Qmax is the maximum value of Q(t) and β is the heating rate in K/s. 2. The heat release temperature Tmax in K as the pyrolysis chamber temperature at which Q(t) ¼ Qmax. 3. The specific heat release hc in J/g as the area under the Q(t) curve.
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Calorimetry
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Fig. 27.14 Specific heat release rate versus MCC pyrolysis chamber temperature for PMMA
4. The pyrolysis residue Yp mp/mo in g/g, where mp is the residual mass of the specimen at the end of the test. 5. The specific heat of combustion of the specimen gases hc,gas hc/(1Yp) in J/g. For method B only three parameters are calculated: 1. The combustion temperature Tmax in K as the pyrolysis chamber temperature at which the specific heat release rate is a maximum, i.e., QðtÞ ¼ Q0max . 2. The combustion residue Yc mc/mo in g/g, where mc is the residual mass of the specimen at the end of the test. 3. The net calorific value h0c in J/g as the area under the Q(t) curve.
Comparative Studies Between Different Small-Scale Tests A number of comparisons are reported in the literature on how results obtained with different calorimeters for the same material compare. ¨ stman et al. reported on a comparison of heat O release data for 13 building materials obtained with the modified OSU, the cone calorimeter, and an open calorimeter developed by Sensenig at NBS [64]. Agreement was remarkably good with a correlation coefficient exceeding 90 % for
average heat release rate over the first minute following ignition. Babrauskas compared peak heat release rate from various calorimeters for five aircraft wall paneling materials [65]. He found good agreement between the fire propagation apparatus and the cone calorimeter. However, he also found that the peak heat release rate from the OSU apparatus was approximately 50 % of the peak from the cone calorimeter. Whether thermopile or oxygen consumption were employed seemed to have only a minor effect on the results from the OSU apparatus. Unfortunately, correlation of average heat release rate was not reported, so that a compari¨ stman et al. is not possible. son with the work of O Tran compared heat release rate curves for Douglas fir plywood from the cone calorimeter, and the OSU apparatus modified for oxygen consumption [54]. First and second peaks agreed well, but the OSU data exceeded the cone calorimeter data by up to 20 % between the peaks. The increased burning rate can be explained by the enhanced radiant heat flux to the specimen due to temperature rise of the calorimeter walls and heater during a test. Tran tested the same material in the OSU apparatus with the vertical specimen holder from the cone calorimeter and found no effect. Kandola et al. tested several aircraft interior fabrics in the OSU calorimeter according to the
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FAA specification and in the cone calorimeter [66]. They found that the specimens ignited much earlier in the OSU apparatus and that the heat release rates were significantly lower in the cone calorimeter. The heat flux in the cone calorimeter had to be increased to 50 kW/m2 to obtain comparable heat release rates as measured in the OSU calorimeter at 35 kW/m2. Two comparative studies were conducted involving electrical cables. Gandhi et al. measured shorter ignition times and lower heat release rates in the fire propagation apparatus than in the cone calorimeter for communication cables [67]. Carman et al. compared oxygen consumption and thermopile measurements for six different types of cables [68]. Good agreement was obtained between the two measurement techniques under flaming conditions. The thermal combustion properties measured in the MCC are related to flammability characteristics of the material [69–73]. For example, the heat release temperature from method A approximates the surface temperature at ignition. The net calorific value from method B approximates the net heat of combustion measured in an oxygen bomb calorimeter. Heat release data from small-scale calorimeters are always apparatus dependent. Differences in geometry, test conditions, and mounting methods explain discrepancies between the results from different calorimeters. Apparatus-specific factors must be considered and addressed in a comparison between different calorimeters or when the data are used to predict performance in real fire conditions.
Fig. 27.15 Standard calorimeter hood and exhaust duct
Intermediate- and Large-Scale Calorimeters This section covers commonly used intermediate- and large-scale calorimeters. Collection and extraction of the products of combustion generated in these calorimeters are usually accomplished in a specific manner. The standard hood and exhaust duct are described before the main features of different intermediate- and large-scale calorimeters are summarized.
Standard Hood and Exhaust Duct To measure heat release rate in a fire test based on the oxygen consumption technique, it is necessary to collect all combustion products and to measure the oxygen concentration and flow rate of the effluents. A properly designed hood and exhaust duct with the necessary instrumentation are used for this purpose. Various intermediate- and large-scale calorimeters described in subsequent sections use the same standard hood and exhaust duct setup shown in Fig. 27.15. The square opening of the hood is approximately 2.4 m 2.4 m and the bottom of the hood is 2.4–3.0 m above the floor of the laboratory. Skirts can be hung down from the hood to minimize spilling. Baffle plates in the plenum or an orifice plate at the entrance of the exhaust duct are used to provide proper mixing of the exhaust gases.
Gas sampling probe Plenum
Mixing orifice Exhaust duct
Hood
Bidirectional probe and thermocouple
Smoke photometer
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The instrumentation section is located at a distance from the entrance to the exhaust duct of at least 10 times the diameter, that is, 4.0 m for the standard 0.4-m-diameter exhaust duct. The measuring section consists of a combination of a bidirectional probe and thermocouple, a gas sampling probe, and a light extinction measurement system. A straight section of pipe of a length at least six times the diameter is located downstream of the measuring section. The distance between the base of the fire and the bottom of the hood determines the peak heat release rate that can be measured for a burning object located beneath the hood [74]. On the one hand, the hood has to be sufficiently elevated above the fire to avoid flame impingement. Flame impingement has two undesirable effects. First, flames impinging on a relatively cold surface are quenched, which adversely affects completeness of combustion. Second, radiation from hot metal surface enhances the burning rate of an object located beneath the hood above that of a free burn. The maximum heat release rate without flame impingement on the standard hood is approximately 1 MW. This is consistent with the fact that the flame height of a 1 MW fire with an effective diameter of 1.5 m is approximately 2.2 m based on Heskestad’s flame height correlation (see Chap. 13, “Fire Plumes, Flame Height, and Air Entrainment”): L f ¼ 0:235Q_ 1:02D ¼ 0:235ð1000Þ2=5 1:02ð1:5Þ 2:2m 2=5
ð27:23Þ where L f ¼ Flame lengthðmÞ Q_ ¼ Heat release rateðkWÞ D ¼ Effective diameter of the fireðmÞ On the other hand, the hood cannot be located too high above the burning object to avoid spilling. The skirts are helpful in this respect. An ideal exhaust system extracts combustion products at the same rate as the flow rate in the plume when it enters the hood. This results in the
highest and most accurate measurement of oxygen depletion because no additional air above what is entrained in the plume is drawn into the exhaust duct. The plume flow rate at a height of 2.2 m above a fire with an effective diameter of 1.5 m can be estimated from the simple equation developed by Thomas et al. [75] (see Chap. 13): π 2 3=2 D z 4 3:14159 1:52 2:23=2 ¼ 1:08 kg=s ¼ 0:188 4 ð27:24Þ
m_ p ¼ 0:188
where m_ p ¼ Plume flowðkg=sÞ z ¼ Height above the fireðmÞ Assuming a radiative loss fraction of 30 %, which is a typical value for many fuels (see Chap. 36), this corresponds to a volumetric flow rate of 2.8 m3/s at a temperature of 650 C. Intermediate- and large-scale calorimeter test standards that specify the hood and exhaust system described in this section typically require an exhaust fan with a capacity of 3.5 m3/s.
Intermediate-Scale Calorimeter (ICAL) One of the limitations of the cone calorimeter is that only relatively small samples can be evaluated. As a result, products that have joints or layered materials with a thickness exceeding 50 mm can generally not be tested in the cone calorimeter in a representative manner. For those types of products or assemblies, a larger calorimeter, such as the intermediate-scale calorimeter (ICAL) described in ASTM E1623, is required. The ICAL apparatus consists of an array of gas heaters, forming a vertical radiant panel with an approximate height and width of 1.33 m and 1.54 m, respectively (Fig. 27.16). The standard test specimen measures 1 m 1 m and is positioned parallel to the radiant panel. The heat flux to the specimen is preset in the range of 10–60 kW/m2 by adjusting the distance to the panel. Gas flow to the panel is controlled to
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M. Janssens
Fig. 27.16 ICAL apparatus Gas sampling port
Collection hood
Wire igniter Water-cooled supporting frame
Top cap of the specimen holder
Radiant heat units
Specimen
Wire igniter
Weighing platform Trolley
Radiant panel
maintain the temperature to the panel and consequently the heat flux to the specimen during a test. The products of pyrolysis from the specimen are ignited with hot wires located close to, but not in contact with, the specimen at its top and bottom. The specimen is placed in a holder that is put on a load cell to measure mass loss during testing. Panel and specimen are positioned beneath the standard hood described in the previous subsection. Measurements of oxygen concentration, flow rate, and light transmission in the exhaust duct are used to determine the heat release rate and smoke production rate from the specimen as a function of time. Because the combustion products from the radiant panel are also captured in the hood, it is necessary to subtract the corresponding heat release rate or smoke production rate to determine the contribution from the specimen.
Furniture Calorimeter Often it is very difficult to determine the burning behavior of complex objects on the basis of the fire performance of their individual components.
Specimen holder
For example, it is very hard to determine the burning behavior of upholstered furniture on the basis of the fire characteristics of the foam, fabric, and framing materials and to account for the geometry and configuration of the furniture and how it is ignited. It is much more practical to measure the heat release rate and related properties for the complete object. Furniture calorimeters were developed in the 1980s in several laboratories to obtain this kind of data [76, 77]. The first furniture calorimeter test standard was published in 1987 in the Nordic countries as NT Fire 032. A furniture calorimeter consists of a weighing platform that is located on the floor of the laboratory beneath the standard hood (Fig. 27.17). The object is placed on the platform and ignited with the specified ignition source. The products of combustion are collected in the hood and extracted through the exhaust duct. Measurements of oxygen concentration, flow rate, and light transmission in the exhaust duct are used to determine the heat release rate and smoke production rate from the object as a function of time. Furniture calorimeter test standards have been developed in ASTM for chairs (ASTM E1537),
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933
Fig. 27.17 Furniture calorimeter
Gas sampling probe Plenum
Mixing orifice Exhaust duct
Hood
Bidirectional probe and thermocouple
Smoke photometer
Weighing platform
Table 27.3 Ignition sources specified in fire tests for chairs and mattresses Test method ASTM E1537 CAL TB 133 ASTM E1822 ASTM E1590 CAL TB 603 16 CFR 1633
Specimen Single chair Stacked chairs Mattress (set) Mattress (set)
Gas burner ignition source No. Type Heat output 1 Square 19 kW for 80 s 1 Line 18 kW for 80 s 1 Line 18 kW for 180 s 2 Line 19 kW for 70 s Line 10 kW for 50 s
mattresses (ASTM E1590), and stacked chairs (ASTM E1822). The California Bureau of Home Furnishings and Thermal Insulation (CBHFTI) published California Technical Bulletins (CAL TB) 133 and 603. These documents describe fire test procedures to qualify seating furniture and mattresses, respectively, for use in public occupancies in the state of California. Acceptance is primarily based on a peak heat release rate and 10-min total heat release limits of 80 kW and 25 MJ for chairs (CAL TB 133) and 200 kW and 25 MJ for mattresses (CAL TB 603). The primary difference between the different fire test methods for chairs and mattresses is the ignition source, which has been demonstrated to affect heat release rate [78]. The main features of the gas burner ignition source specified in different methods are given in Table 27.3. All mattresses sold in the United States must comply with the heat release requirements
Location of application Horizontal seating surface Bottom chair front edge Front bottom edge Top surface Vertical along side
specified in 16 CFR 1633. The method and requirements are identical to CAL TB 603, except that the 10-min total heat release limit is reduced to 15 MJ. The fire test method for mattresses and mattress/box spring sets described in this document was developed at the National Institute of Standards and Technology (NIST) in a research program sponsored by the Sleep Products Safety Council (SPCS), an affiliate of the International Sleep Product Association (ISPA) [79–81]. The original version of CAL TB 133 specified that the test specimen be located in a corner against the back wall of a 3.7 m 3.0 m 2.4 m room with a 1.0 m 2.1 m open doorway in the front wall. The ignition source consisted of five double sheets of loosely-wadded newspaper inside a chicken wire cage placed on the back of the seat. Acceptance was based primarily on a maximum temperature rise of 111 C just below the ceiling above the chair. Subsequent NIST research resulted in the development of the
934
presently used gas burner as an alternative ignition source [82]. The gas burner flame generates an equivalent thermal insult but is much more repeatable and reproducible than the original ignition source. The NIST research project also resulted in an equivalent heat release rate criterion and demonstrated that the room effects are negligible for heat release rates below 600 kW [83]. Later studies found significant effects at lower heat release rates and proposed a threshold of 460 kW [84]. Because this is still much higher than peak heat release rate limits specified in regulations, all furniture and mattress test standards discussed here permit the use of an open furniture calorimeter configuration as an alternative to the room configuration. In fact, all test standards except 16 CFR 1633 allow two room configurations: the original CAL TB 133 room and a smaller 3.7 m 2.4 m 2.4 m room commonly used for room/ corner testing (see below).
Room/Corner Test Room/corner tests are by far the most frequently conducted large-scale fire experiments throughout the world. This section provides a historical overview of the development of room/corner test protocols and summarizes the resulting test standards in use today.
Historical Overview Much of the work toward the development of a standard room/corner test was performed in the United States in the late 1970s and early 1980s. The need for a standard room fire test and some aspects of its design were discussed by Benjamin in 1977 [85]. Subsequent research in North America to arrive at a standard full-scale test was conducted primarily by Fisher and coworkers at the University of California (UCB) [86] and by Lee at the National Bureau of Standards (NBS) [87]. Considerable seminal research was also performed in the Nordic countries. An extensive project to construct a full-scale room calorimeter was conducted in Sweden [88, 89]. No oxygen
M. Janssens
consumption measurements were made at that time. A heat balance was obtained by comparing the theoretical heat release from combustion of gaseous fuel to the sum of the heat losses. The heat losses consisted of convection through the doorway, conduction through the walls and ceiling, and radiation through the doorway. Heat convection through the doorway was estimated by measuring gas velocity and temperature at many points in the doorway. Heat conduction through the surrounding surfaces was calculated based on total heat flux, radiation, and surface temperature data. Heat loss by radiation through the door was calculated from radiometer measurements. Initially, a series of quasi-steady calibration tests were conducted in an inert room. Three different circular propane gas burners were used with diameters of 0.2, 0.3, and 0.4 m, respectively. Heat balance calculations showed reasonable agreement, with convection losses being dominant. In subsequent tests with surface finishes, a heptane pool fire with a heat release rate of approximately 50 kW was used as the ignition source. Ahonen et al. at the Technical Research Center of Finland (VTT) studied the effects of different gas burner ignition sources on room/corner fire growth [90]. Tests were conducted for each combination of three burner sizes (0.17 m 0.17 m, 0.305 m 0.305 m, and 0.5 m 0.5 m) and three square wave heat release rates (40, 160, and 300 kW). Oxygen consumption calorimetry was used for measuring heat release rate. The burner was placed in a corner in the back of the room. Ceiling and all walls except the front wall were lined with 10-mm-thick particleboard with a density of 720 kg/m3. The following six criteria were used to determine the time to flashover: • Flames emerging through the door (flameover) • Total heat release rate of 1 MW • Total heat flux to the floor of 20 kW/m2 • Specified rate of smoke production • Temperature of 600 C at the geometric center of the room • Total heat flux to the floor of 50 kW/m2
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With the time to flashover defined as the average of the six criteria, the following remarkable results were obtained: • At the 40 kW level, the medium-sized burner resulted in flashover first, followed by the smaller burner, and then the larger burner. • At 160 kW, the largest burner resulted in flashover first, quickly followed by the other two configurations. • At 300 kW, the trend was the same as at 160 kW with an even smaller spread between the three results. The effect of burner size was most significant at the lowest heat release rate, with the mediumsized burner being the most severe. At higher exposure levels, the size of the burner had no significant effect. Radiative and convective heat transfer from the burner flame were shown to depend on burner size and heat release rate and had a significant effect on the performance of the material tested. On the basis of the results, the medium burner size and heat release rate were recommended.
compartments meet specific performance requirements when tested according to NFPA 265, Standard Methods of Fire Tests for Evaluating Room Fire Growth Contribution of Textile Coverings on Full Height Panels and Walls. The principal requirement of these tests is that flashover does not occur. The same codes also require that all other interior wall and ceiling finish materials comply with requirements based on NFPA 286, including a limit on the total smoke released. The Safety Of Life At Sea (SOLAS) convention, promulgated by the International Maritime Organization (IMO), permits the use of combustible bulkhead and ceiling linings on high-speed craft, provided they meet stringent fire performance requirements based on assessment according to ISO 9705. ASTM E2257 is the American version of ISO 9705. The test apparatus and instrumentation described in the NFPA and ISO room/corner test standards are very similar (Fig. 27.18). However, some significant differences exist in terms of specimen configuration and ignition source. The apparatus consists of a room measuring 3.6 m deep by 2.4 m wide by 2.4 m high, with a single ventilation opening (open doorway) measuring approximately 0.8 m wide by 2.0 m high in the front wall. Walls and ceiling are lined for tests according to ISO 9705. For tests according
Room/Corner Test Standards Several standard room/corner test protocols are now available and are specified in codes and regulations for qualifying interior finishes. For example, U.S. model building codes require that textile wall coverings for use in unsprinklered Fig. 27.18 Room/ corner test
Optical density (lamp/photocell) Gas analysis (O2, CO, CO2)
Exhaust gases
Volume flow temperature and differential pressure
Exhaust hood 2.4 m
Gas burner 3.6 m
Doorway 0.8 m × 2.0 m
936
to the NFPA standards, the interior surfaces of all walls (except the front wall) are covered with the test material. NFPA 286 is also suitable for evaluating ceiling finishes (see below). The test material is exposed to a propane burner ignition source, located on the floor in one of the rear corners of the room opposite the doorway. The burner is placed directly against (ISO 9705 and NFPA 286) or at a distance of 50 mm from (NFPA 265) the walls. The ISO burner consists of a steel sandbox measuring 0.17 m 0.17 m 0.145 m, with the top surface 0.145 m above the floor of the room. Propane is supplied to the burner at a specified rate such that a net heat release rate of 100 kW is achieved for the first 10 min of the test, followed by 300 kW for the remaining 10 min (20-min test duration unless terminated when flashover occurs). The NFPA burner consists of a steel sandbox measuring 0.305 m 0.305 m 0.152 m, raised so that the top surface is 0.305 m above the floor of the room. Propane is supplied at a specified rate so that a net heat release rate of 40 kW is achieved for the first 5 min of the test, followed by 150 kW (NFPA 265) or 160 kW (NFPA 286) for the remaining 10 min (15-min test duration unless terminated when flashover occurs). A fundamental difference between NFPA 265 and NFPA 286 is the fact that the flame from the burner alone just touches the ceiling in NFPA 286. This makes it suitable for assessing the fire performance of interior ceiling finish, an application for which NFPA 265 is unsuitable. This effect is partly due to the higher energy release rate of the NFPA 286 burner, but primarily because of the burner being in direct contact with the walls, thereby reducing the area over which the flames can entrain air and increasing the overall flame height. All combustion products emerging from the room through the open doorway are collected in the standard hood. Instrumentation is provided in the exhaust duct for measuring heat release rate based on the oxygen consumed (ISO and NFPA standards) and smoke production rate (ISO 9705 and NFPA 286 only). The room contains a single heat flux meter located in the center of the floor. The NFPA standards also specify that seven
M. Janssens
thermocouples be installed in the upper part of the room and doorway to measure the temperature of hot gases that accumulate beneath the ceiling and exit through the doorway. In addition to quantitative heat release and smoke production rate measurements, time to flashover (if it occurs) is one of the main results of a room/ corner test. Different criteria are commonly used to define flashover; for example, upper layer temperature of 600 C, flames emerging through the doorway, heat flux to the floor of 20 kW/m2, heat release rate of 1 MW, and so forth.
Single Burning Item Test The European reaction-to-fire classification system for construction products except floor coverings (EN 13501) is based primarily on performance in this test. An SBI test in progress is shown in Fig. 27.19. Two specimens of the material to be tested are positioned in a specimen holder frame at a 90 angle to form an open corner section. Both specimens are 1.5 m high. One specimen is 1 m wide and is referred to as the long wing. The other specimen is 0.5 m wide and is referred to as the short wing. During a test,
Fig. 27.19 SBI test in progress (Photo courtesy SwRI.)
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Calorimetry
the specimens are exposed for 20 min to the flame of a triangular-shaped diffusion propane gas burner operating at 30 kW. The specimen holder and primary gas burner are mounted on a trolley that can be moved in and out of an enclosure of 3 m 0.6 m wide, 3 m 0.6 m deep, and 2.4 m 0.1 m high. The enclosure walls consist of noncombustible materials (concrete block, calcium silicate board, etc.) and/or gypsum board, and have windows to allow the operator to observe the test. The mean height and maximum heat flux from the 30 kW burner flame are approximately 0.8 m and 35 kW/m2, respectively [91]. Prior to a test, the specimens are placed in the holder, and the trolley is rolled into the enclosure and positioned under an insulated hood. During a test, the products of combustion are collected in the hood and are extracted through an exhaust duct. Instrumentation is provided in the duct to measure temperature, velocity, gas composition (O2, CO2, and CO), and smoke obscuration. The velocity and gas composition data are used to determine heat release rate on the basis of the oxygen consumption technique. Materials are tested in triplicate. Classification is based primarily on fire growth (FIGRA) and smoke development (SMOGRA) indices that are equal to the peak heat release and smoke production rate, respectively, divided by the time to reach the peak. FIGRA and SMOGRA limits were established based on performance in the ISO 9705 room/corner test as the reference scenario [92].
937
of 15 m3/s. A larger calorimeter and higher fan capacity are needed to handle more severe experimental fires. Cooper presented useful guidelines to address the special challenges associated with the design of an industrial-scale calorimeter [74]. ASTM E2067 is a standard practice for conducting accurate heat release rate measurements at the multimegawatt level. The first industrial-scale calorimeter for fires into the multi-megawatt range was built at Factory Mutual around 1980 [93]. This calorimeter, also referred to as the FM fire products collector, was designed to measure heat and other fire products from test fires up to a size associated with sprinkler activation in commodity warehouse storage and other representative occupancies. Approximately 10 years later, a similar industrial-size calorimeter for heat release rate measurements up to 10 MW was constructed at the National Testing Laboratory (SP) in Sweden [94]. Since then several other laboratories—such as the National Research Council of Canada, the Fire Research Station in the United Kingdom, the Bureau of Alcohol, Tobacco, Firearms and Explosives (ATF) Fire Research Laboratory, the National Institute of Standards and Technology (NIST), Southwest Research Institute and Underwriters Laboratories in the United States—developed the capability of measuring heat release rate from large fires into the megawatt range.
Industrial-Scale Calorimeters
Use and Application of Heat Release Rate Data
Industrial-scale calorimeters consist of a larger version of the hood and exhaust duct shown in Fig. 27.15. To handle fires up to 10 MW in size for a short duration, the hood must be at least 6 m 6 m in size or 6 m in diameter and is typically located 6.5 m or higher above the floor of the laboratory. The fan must be capable of extracting combustion products through a 0.9-m-diameter exhaust duct at a minimum rate
The primary use of heat release rate data is in support of fire hazard assessment of materials and products. Small- and intermediate-scale data can be used in conjunction with mathematical models to predict the performance of materials and products in real fire scenarios. Heat release rates measured in large- and industrial-scale calorimeters can be used directly in support of a fire hazard assessment.
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Small-Scale Calorimeter Data Predictive models that are available for fire hazard assessment on the basis of small- or intermediate-scale heat release rate data vary widely in complexity. The extent of the heat release rate data that are needed varies according to the complexity of the model. Room/corner testing is a widely accepted approach to assess the fire hazard of interior finish materials. The room/corner scenario is used here to illustrate the different types of predictive models and corresponding requirements for input data from small-scale calorimeters. There are three distinct types of room/corner test models: regression models, analytical models, and physics-based models. Regression models express a relationship between a particular room/corner test performance characteristic, for example, the time to flashover, and smallscale fire test data for the same product. Regression models are based on a statistical analysis of room/corner and small-scale test data for a set of products and can be used as a screening tool. Analytical models predict fire growth but do not simulate the room environment. Physics-based models predict how the room environment varies as a function of time and how flames spread over the walls and ceiling of the compartment. There is a strong interaction between regression and physics-based models because the conditions in the room determine the heat that is transferred back to the wall and ceiling surfaces, which affects the flame spread and the heat release and smoke production rate of burning wall and ceiling sections.
Regression Models The least sophisticated models are based on regression analyses. The following equation, ¨ stman et al. based on an analysis obtained by O of test data for 28 materials in the cone calorimeter and according to ISO 9705, serves as a good example of this type of room/corner test modeling [95].
M. Janssens
tfo ¼ 0:0716
1:72 t0:25 ig ρ þ 57:4 0 0 1:30 Q300
ð27:25Þ
where tf0 ¼ Time to flashover (s) tig ¼ Time to ignition in the cone calorimeter at 50 kW/m2 (s) ρ ¼ Density of the material (kg/m3) Q30000 ¼ Total heat released at 50 kW/m2 during 300 s following ignition (MJ/m2) This equation can be used to predict room/ corner test performance on the basis of smallscale data for materials that have not been tested in the room. With this approach the dynamics of the heat release curve are lost entirely. There is no difference in the prediction of full-scale performance for two materials with heat release curves of very different shapes, provided the heat release rate parameter and ignition time used in the correlation are identical. The predictions are valid for one scenario and geometry only. For example, Equation 27.25 cannot be used to predict the time to flashover for the NFPA 265 and NFPA 286 room/corner tests. The main advantage of this approach is that a minimal amount of small-scale testing is needed to obtain the necessary input data.
Analytical Models The approach outlined in the preceding subsection can be improved by using a heat release curve at a single radiant heat flux level. Thus, the dynamic effects of the room fire on the exposure level are ignored while the dynamics of the heat release curve are largely maintained. The radiant heat flux level is chosen so that it is a representative average (over space and time) for the fire scenario that is being modeled [96]. Representative heat flux levels for the room/corner test scenario range from 25 to 50 kW/m2. The single heat release curve is used in combination with a flame spread algorithm to predict heat release rate as a function of time in the room/corner test. The flame spread algorithm can be very simple but needs at least some
27
Calorimetry
939
ignition data for the material. The burning area expands as time proceeds and new sections of the material are ignited. The heat release rate is calculated at discrete time increments, Δt. The flame spread algorithm calculates the expansion of the burning area at every time step. The heat release rate in the room/corner test at a particular time is then obtained by adding the contributions from all incremental areas to the heat release rate from the ignition burner at that time: X Q_ t ðtN Þ ¼ Q_ b ðtN Þ þ Ai Q_ ðtN ti Þ N
00
ð27:26Þ
i¼0
completely consume the material than at higher heat fluxes. To address this problem, heat release rate has to be expressed as a function of a progress variable that is consistent at different radiant heat flux levels. Smith and Green conducted experiments in the OSU calorimeter at different heat flux levels and tested the same material at time-varying heat fluxes [98]. They were able to reconstruct the heat release rate curve measured under dynamic exposure conditions from interpolation between the curves obtained at fixed radiant heat fluxes using total heat release as the progress variable. Mitler used total mass loss as the progress variable [99]. Janssens suggested using char depth as a suitable progress variable for wood [100]. The following modification to Equation 27.26 represents an improved room/corner test model that accounts for the effect of incident heat flux on heat release rate. Total heat release rate is used as the progress variable.
where Q_ t ¼ Total heat release rate in the room=corner testðkWÞ tN ¼ Time after N time increments Δt from the start of the test, equal toNΔtðsÞ Q_ b ¼ Heat release rate from the ignition burnerðkWÞ Ai ¼ Incremental area ignited at time ti ðm2 Þ 00 Q_ ¼ Heat release rate measured in the cone Q_ t ðtN Þ ¼ Q_ b ðtN Þ calorimeterðkW=m2 Þ ti ¼ Time afteritime increments Δt from the start i N 00 h X 00 00 þ Ai Q_ q_ e, i ðtN Þ, Qi ðtN Þ of the test, equal to i ΔtðsÞ i¼0 This method automatically accounts for burnð27:27Þ out. The most widely known room/corner test model of this type was developed by Wickstro¨m where and Go¨ransson [97]. 00 q_ e, i ¼ Incident heat flux to Ai ðkW=m2 Þ 00 Q_ i ¼ Total heat release from Ai ðMJ=m2 Þ
Physics-Based Models
Direct Use of Heat Release Rate Measurements at Multiple Heat Fluxes The modeling approach described in the preceding subsection can be refined by using heat release rate curves obtained at multiple heat fluxes. This makes it possible to account for the fact that the incident heat flux to each incremental area varies with time. The problem, however, is that the heat release rate of an incremental area at a particular time cannot be determined from direct interpolation of the heat release rate curves measured in the calorimeter. This is because it takes more time at lower heat fluxes to
The model calculates the incident heat flux and keeps track of the total heat release rate for each incremental area. A room/corner test model of this type was developed by Smith et al. at Ohio State University [5]. The primary limitations of using this type of model are that (1) it is based on the assumption that the heat flux from the material’s own flame in the small-scale calorimeter is comparable to that in the room/corner test, and (2) Equation 27.27 is assumed to be valid regardless whether the incident heat flux is purely radiative (as in the small-scale calorimeter) or partly convective (as, for example, in areas of the room
940
M. Janssens
where the material is exposed to the flame of the ignition source). These limitations can be addressed, at least in an approximate manner, but not without making the approach much more complex.
Use of Heat Release Properties A more fundamental approach to account for the effects of time-varying heat fluxes on heat release rate is based on two material properties that can be measured in a small-scale calorimeter. These properties are the effective heat of combustion, Δhc,eff, and the heat of gasification, Δhg. Both properties have the units of kJ/g or MJ/kg. The effective heat of combustion is the ratio of heat release rate to mass loss rate measured in a small-scale calorimeter.
during which the heat release rate is at least 80 % of the first peak heat release rate. The third value is equal to the ratio of total heat released and total mass loss over the entire flaming period. The heat of gasification is defined as the net heat flow into the material required to convert one mass unit of solid material to volatiles. The net heat flux into the material can be obtained from an energy balance at the surface of the specimen. Typically, a sample exposed in a small-scale calorimeter is heated by external heaters and by its own flame. Heat is lost from the surface in the form of radiation. A schematic of the heat balance at the surface of a burning specimen in the cone calorimeter is shown in Fig. 27.20. Hence, Δhg is defined as
Δhc, eff
Q_ 00 m_
ð27:28Þ
where 00
Q_ ¼ Heat release rate per unit exposed areaðkW=m2 Þ 00 m_ ¼ Mass loss rate per unit exposed areaðg=m2 sÞ The effective heat of combustion at a particular time t can be calculated by substituting the 00 ˙ 00 at that time in Equavalues for Q_ and m
tion 27.28. A curve of Δhc,eff as a function of time can be determined in this manner. Unfortunately, mass loss rate data are often very noisy and the calculated time-varying heat of combustion values may not have any physical meaning. More meaningful values are obtained by calculating an average Δhc,eff, over a specified time 00 period by substituting average values of Q_ and ˙ 00 over that time period in Equation 27.28. m Dillon et al. proposed three methods to calculate the effective heat of combustion [101]. The first value is equal to the ratio of the first peak heat release rate and mass loss rate at the same time. The second value is obtained as the ratio of the average heat release rate over the peak burning period and the mass loss rate over the same period. The peak burning period is defined as the period around the first peak heat release rate
00
00
00
00
q_ e þ q_ f q_ l q_ Δhg net00 ¼ 00 m_ m_
00
ð27:29Þ
where 00
q_ e ¼ Heat flux to the specimen surface from external sourcesðkW=m2 Þ 00 q_ f ¼ Heat flux to the specimen surface from the flameðkW=m2 Þ 00 q_ l ¼ Heat losses from the exposed surface ðkW=m2 Þ
Cone heater surface
Flame qe⬙
qt⬙
qf⬙
Specimen
Ceramic fiber blanket
Fig. 27.20 Heat balance at the surface of a burning cone calorimeter specimen
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Calorimetry
941 00
00
q_ l q_ f . Tewarson et al. [62] and Petrella [102] have used this technique to obtain average Δhg values for a large number of materials. Tewarson et al. also conducted tests in vitiated O2-N2 00 00 00 00 q_ f ¼ q_ f , c þ q_ f , r ¼ h* Tf T s þ σε f T 4f mixtures and found q_ f to decrease linearly with ð27:30Þ decreasing oxygen concentration. Analysis of these additional experiments made it possible to 00 00 where separate q_ f and q_ l . 00 q_ f , c ¼ Convective fraction of the flame flux Many materials, in particular those that form ðkW=m2 Þ an insulating char layer as they burn, take a long 00 q_ f , r ¼ Radiative fraction of the flame flux time to reach steady burning conditions or may ðkW=m2 Þ never reach steady conditions. Equation 27.29 is h* ¼ Convection coefficient corrected for still valid for such materials, but the heat and blowingðkW=m2 KÞ mass fluxes and resulting Δhg values vary with Tf ¼ Flame temperatureðKÞ time. Tewarson and Petrella have used the Ts ¼ Surface temperatureðKÞ method described in the preceding paragraph to σ ¼ Boltzmann constant 5:67 1011 kW=m2 K4 determine average Δh values for nonsteady g εf ¼ Emissivity of the flame burning materials using average mass loss rates. The flow of combustible volatiles emerging They found that average m ˙ 00 is still an approxithrough the exposed surface of the specimen mately linear function of q_ 00 . However, the avere adversely affects the convective heat transfer age heat of gasification values obtained in this between the flame and the surface. This effect manner may not have any physical meaning. For is referred to as “blowing.” The flame flux in a example, Janssens demonstrated that the values small-scale calorimeter is primarily convective, based on average mass loss rates are too high for in particular in the vertical orientation, and flame wood and suggested a method to determine Δhg absorption of external heater and specimen suras a function of char depth [103]. face radiation can be neglected. Dillon et al. proposed six methods to calculate The heat losses from the surface can be the heat of gasification [101]. The first three expressed as values are derived from Equation 27.29 and are 4 00 equal to the reciprocal of the slope of a linear fit 4 q_ l ¼ σεs T s T 1 ð27:31Þ through data points of peak mass loss rate, average mass loss rate over the peak burning period, where and average mass loss rate over the entire εs ¼ Surface emissivity of the specimen flaming period respectively plotted as a function T1 ¼ Ambient temperature (K) Some materials exhibit nearly steady mass of heat flux. The other three values are equal to loss rates when exposed to a fixed radiant heat the appropriate heat of combustion times the flux. Ts for these materials reaches a steady value reciprocal of the slope of a linear fit through after a short initial transient period and all terms data points of first peak heat release rate, average in Equation 27.29 are approximately constant. heat release rate over the peak burning period, Δhg can then be obtained by measuring steady and average heat release rate over the entire mass loss rates at different radiant heat flux flaming period respectively plotted as a function 00 ˙ 00 as a function of q_ e . of heat flux. levels and by plotting m Physically meaningful nonsteady values for The reciprocal of the slope of a straight line fitted Δh g can be obtained from Equation 27.29, with through the data points is equal to Δhg. The 00 00 intercept of the line with the abscissa is equal to q_ f and q_ l calculated from Equations 27.30 and If the flame is approximated as a homogeneous gray gas volume, the heat flux from the flame can be expressed as follows:
942
27.31, respectively. These calculations require values for h*, εf, Tf, εs, and Ts. All parameters, except Ts, do not vary greatly during a test and can be estimated relatively easily [104]. Ts, however, may change significantly as a function of time. The surface temperature can be measured, but that presents some major challenges. Janssens obtained Ts as a function of time for wood specimens exposed in the cone calorimeter by solving the equation for heat conduction through the char layer using an integral technique. [100] The resulting values for Δhg are consistent with a theoretical analysis [105] and calculated Δhg values based on measured surface temperatures [106]. A drawback of this approach is that thermal properties of the material’s char are needed. The discussion in this subsection is useful in clarifying a common misconception. Often it is believed that materials used in a particular end-use orientation should be tested in that orientation. This is not necessarily correct. Heat release rate is independent of specimen orientation. However, the heat release rate in a calorimeter under otherwise identical conditions is higher in the horizontal than in the vertical orientation. This is because the heat feedback from the flame is much greater in the horizontal orientation. In that orientation, the flame is a relatively large volume of hot gas located above the specimen. The flame is a thin sheet in front of a vertical specimen, leading to a much lower heat feedback. However, neither of these situations is comparable to that in a real fire, where burning areas and flame volumes are much larger and heat flux from the flame is much higher regardless of orientation of the fuel surface. Hence, the best approach is to interpret smallscale measurements in terms of material properties that are independent of the test apparatus. These material properties can then be used to predict full-scale performance using a method that accounts for the effect of the enhanced heat flux from large flames. The preceding reasoning indicates that small-scale testing in the vertical orientation is preferable, because the heat feedback to the flame is smaller and errors of flame
M. Janssens
flux estimates are relatively less important. However, for practical reasons, it is often preferable to run small-scale tests in the horizontal orientation to avoid problems with, for example, melting and dripping of the specimen. The equation to calculate the total heat release rate in a room/corner test based on a model that relies on heat release rate properties has the following form: X Q_ t ðtN Þ ¼ Q_ b ðtN Þ þ Ai N
i¼0
00
q_ net, i ðtN Þ Δhc, eff Δhg ð27:32Þ
00
where q_ net, i is the net heat flux to Ai (kW/m2). A room/corner test model of this type was developed by Quintiere [107].
Intermediate-Scale Calorimeter Data Products that have joints or layered materials with a thickness exceeding 50 mm can generally not be tested in a small-scale calorimeter in a representative manner. The ICAL is suitable to obtain heat release rate data for these products. The ICAL also has some practical advantages over small-scale calorimeters for measuring Δhc,eff and Δhg [106]. The four approaches discussed in the previous section can be used in support of a hazard assessment of such products based on ICAL data.
Furniture Calorimeter Data The primary application of furniture calorimetry is to obtain heat release rate data for input into zone models such as CFAST. [108] Furniture calorimeters are designed to obtain data under free burning conditions. However, the heat release rate of a burning object inside a room might be higher due to heat feedback from the hot upper smoke layer and heated walls and ceiling. Although this effect is not very significant during the early stages of a compartment fire, it can become significant as the fire approaches flashover. Zone models are typically
27
Calorimetry
not capable of accounting for this effect, except for some simple geometries for which the effect of external heat flux on burning rate can be calculated.
Industrial-Scale Calorimeter Data Industrial-scale calorimeters can be used to obtain heat release rate data from large objects in support of the design of passive fire protection of structures. For example, heat release rates from motor vehicles have been measured in several laboratories throughout the world [109–115]. The data obtained in these tests were used to develop guidelines for passive fire protection of structural steel in parking garages. Industrial-scale calorimeters are also used to determine the hazard classification of commodities. The level of active fire protection required to protect a warehouse is based on the hazard classification of the commodity stored in the warehouse. Standard methods for commodity classification have been developed in the United States and Sweden [116]. For example, FM 3995 describes a protocol to determine the hazard class of plastic pallets and other products. The commodity configuration consists of eight pallet loads of products, each measuring 1.1 m 1.1 m 1.1 m. The commodities are placed on a double-row rack segment in a standard 2 2 2 array with each pallet separated by 150 mm. The commodities are ignited at the bottom in the center of the array. Water is applied to the fire by a special applicator located 200 mm above the top surface of the commodity. The water is applied at the time that a sprinkler system located in a warehouse at 3 m above the commodity would activate. The activation time is calculated based on the convective heat release rate measured during the test and a sprinkler activation program akin to DETACT-QS [117]. Tests are performed at three different water application rates in the range of 0.11–0.39 gpm/ft2 (4.5–15.9 mm/min) and the commodity is classified based on the heat release rates measured in the tests. The FM Global commodity classification system in ascending order of hazard is as follows:
943
• Class I: noncombustible products on wood pallets • Class II: Class I products in slatted wooden crates, solid wooden boxes, multiple thickness corrugated cartons, or equivalent combustible packaging material on wood pallets • Class III: packaged or unpackaged wood, paper, natural fiber cloth or products therefrom on wood pallets • Class IV: Class I, II, or III products containing no more than 25 % by volume of expanded plastic or polyurethane or 15 % by weight of unexpanded plastic or polyurethane in ordinary corrugated cartons on wood plastic pallets • Cartoned Group B unexpanded plastics • Cartoned Group A expanded or unexpanded plastics • Idle wood pallets
Uncertainty of Heat Release Rate Measurements The objective of a measurement is to determine the value of the measurand, that is, the physical quantity that needs to be measured. Every measurement is subject to error, no matter how carefully it is conducted. The true value of a measurand is therefore unknowable because it cannot be measured without error. However, it is possible to estimate, with some confidence, the expected limits of error. This estimate, referred to as the uncertainty of the measurement, provides a quantitative indication of its quality. The value of the measurand is generally not obtained from a direct measurement but is determined as a function ( f ) from N input quantities X1, X2, . . ., XN: Y ¼ f ðX 1 ; X 2 ; . . . ; X N Þ
ð27:33Þ
where Y ¼ True value of the measurand f ¼ Functional relationship between measurand and input quantities Xi ¼ True values of the input quantities (i ¼ 1 . . . N)
944
M. Janssens
The input quantities may be categorized as • Quantities whose values and uncertainties are directly determined from single or repeated observation • Quantities whose values and uncertainties are brought into the measurement from external sources such as reference data obtained from handbooks An estimate of the value of the measurand, y, is obtained from Equation 27.34 using input
estimates x1, x2, . . ., xN for the values of the N input quantities: y ¼ f ðx 1 ; x 2 ; . . . ; x N Þ
The standard uncertainty of y is obtained by appropriately combining the standard uncertainties of the input estimates x1, x2. . ., xN. If all input quantities are independent, the combined standard uncertainty of y is given by
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u " #2 uX N N X ∂f uc ð y Þ ¼ t u2 ðxi Þ ½ c i uð x i Þ 2 ∂X i¼1
i xi
where u ¼ Standard uncertainty uc ¼ Combined standard uncertainty ci ¼ Sensitivity coefficients The standard uncertainty of an input estimate xi is obtained from the distribution of possible values of the input quantity Xi. There are two types of evaluations depending on how the distribution of possible values is obtained: • A type A evaluation of standard uncertainty of xi is based on the frequency distribution, which is estimated from a series of n repeated observations xi,k (k ¼ 1 . . . n): rffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffi s2 ðx i Þ 2 uðxi Þ s ðxi Þ ¼ n vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uX n u ðx x Þ2 u i, k i t ¼ k¼1 ð27:36Þ nð n 1Þ
where r(xi, xj) is the estimated correlation coefficient between Xi and Xj. Because the values of the input quantities are not known, the correlation coefficient is
ð27:35Þ
i¼1
• A type B evaluation of standard uncertainty of xi is not based on repeated measurements but on an a priori frequency distribution. In this case, the uncertainty is determined from previous measurements, experience or general knowledge, manufacturer specifications, data provided in calibration certificates, uncertainties assigned to reference data taken from handbooks, and so on. Equation 27.35 is referred to as the law of propagation of uncertainty and is based on a first-order Taylor series approximation of Y ¼ f (X1, X2, . . ., XN). When the nonlinearity of f is significant, higher-order terms must be included. When the input quantities are correlated, Equation 27.35 must be revised to include the covariance terms. The combined standard uncertainty of y is then calculated from
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi N N1 N X X X uc ð y Þ ¼ ½ci uðxi Þ 2 þ 2 ci cj uðxi Þu xj r xi ; xj i¼1
ð27:34Þ
ð27:37Þ
i¼1 j¼iþ1
estimated on the basis of the measured values of the input quantities. The combined standard uncertainty in Equation 27.37 is usually multiplied by a coverage factor to raise the
27
Calorimetry
945
confidence level. A multiplier of 2 is often used, which corresponds to a confidence level of approximately 95 %. Equation 27.37 can be used to calculate the uncertainty of heat release rate measurement based on oxygen consumption calorimetry. For example, Equation 27.15 provides the functional relationship between the measurand (heat release rate) and the input quantities. Assuming the mass flow rate in the exhaust duct is calculated from the differential pressure of and temperature at an orifice plate or bidirectional probe, the output and input quantities are defined as follows: _ Y Q, X1 E, X2 XAO2 , X3 α, X4 C, X5 ΔP, X6 T e e
ð27:38Þ C is the calibration coefficient, which relates the mass flow rate in the exhaust duct to the differential pressure and gas temperature measurements. In a test Q_ is calculated as a function of time based on the input quantities measured at discrete time intervals Δt. The uncertainty of the heat release rate measured at each time interval is estimated from Equation 27.37. Dahlberg used this approach to determine the uncertainty of heat release rate measured in the industrial-size calorimeter at SP and reported values of 7 % and 12 % depending on the use of the CO correction, that is, for Equations 27.18 and 27.15, respectively [118]. Enright and Fleischmann reported an uncertainty of 5 % for the cone calorimeter [119]. These uncertainties are significantly below the precision obtained from interlaboratory trials involving oxygen consumption calorimeters. For example, a cone calorimeter round robin resulted in estimates for the peak heat release rate repeatability and reproducibility of 17 % and 23 %, respectively [120]. The discrepancies can be explained by the fact that the uncertainty analyses did not account for dynamic errors and specimen, operator, and heat flux variations. This is consistent with the calculations performed by Janssens, who accounted for the contribution from specimen variations and heat flux
measurement errors and obtained an uncertainty of 11 % for the peak heat release rate of a glass fiber–reinforced plastic measured in the cone calorimeter at a heat flux of 50 kW/m2 [121].
Summary Heat release rate is the single most important variable in fire hazard assessment. Various test methods have therefore been developed for measuring heat release rate of materials and products under different conditions. This chapter dealt with calorimeters of various sizes and the use and application of heat release measurements. The discussion started with a description of the oxygen bomb calorimeter. The most significant limitation of this test is that it does not provide a quantitative measure of heat generation under realistic fire conditions. The next section described four techniques that have been used to measure heat release rate in fire tests. The sensible enthalpy rise method is the least complicated. The substitution and compensation methods partly address the problem of thermal lag associated with sensible enthalpy rise measurements but require sophisticated control instrumentation. The oxygen consumption method, based on Thornton’s rule, was developed in the late 1970s. It is currently the most popular method for measuring heat release rate in fire tests. The effects of some calorimeter construction details on quality and accuracy of small-scale heat release rate measurements were discussed. Factors examined include configuration (open vs. closed), type of heater, type of ignition pilot, specimen size and orientation, edge effects, and airflow. Four commonly used small-scale calorimeters were briefly described: the Ohio State University calorimeter, the cone calorimeter, the fire propagation apparatus, and the microscale combustion calorimeter. This discussion was followed by a review of studies comparing different small-scale calorimeters. The chapter continued with a description of the hood and exhaust duct that is specified in many intermediate- and large-scale calorimeter standards. This was followed by a description of
946
different calorimeters for measuring the heat release rate from chairs, mattresses, and other objects and from wall and ceiling finishes in a corner configuration. Some historical background was provided for the room/corner test. Industrial-scale calorimeters that can be used to measure multimegawatt heat release rates from large objects and commodities were also briefly discussed. The next section discussed common applications of heat release rate data. Heat release rate data are used primarily in support of fire hazard assessment of materials and products. Small- and intermediate-scale data must be used in conjunction with a mathematical model to predict performance of materials and products in real fire scenarios. General concepts of four types of models were discussed using the room/corner test as an example of a real fire scenario: • Correlations • Models based on heat release rate data obtained at a single heat flux • Models based on heat release rate data obtained at multiple heat fluxes • Models based on heat release rate properties Heat release rates measured in large- and industrial-scale calorimeters can be used directly in support of fire hazard assessment. For example, furniture calorimeter measurements can be used to generate heat release rate curves for input in zone models. Industrial-scale calorimeter data can be used to support the design of passive fire protection for structures or to obtain a hazard classification of a commodity. The chapter concluded with a brief discussion of uncertainty of heat release rate measurements.
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947 Award No. 2010-DN-BX-K221, National Institute of Justice, Washington, DC (2012). 35. B. Lattimer and J. Beitel, “Evaluation of Heat Release Rate Equations Used in Standard Test Methods,” Fire and Materials, 22, pp. 167–173 (1998). 36. V. Babrauskas and P. Thureson, “Short Communication: Drying Agents’ Effects on CO2 Readings,” Fire and Materials, 18, pp. 201–268 (1994). 37. V. Babrauskas, “Development of the Cone Calorimeter—A Bench-Scale Heat Release Rate Apparatus Based on O2 Consumption,” Fire and Materials, 8, pp. 81–95 (1984). 38. J. Hallman, Ignition of Polymers by Radiant Energy, University of Oklahoma, Norman, OK (1971). 39. A. Koohyar, Ignition of Wood by Flame Radiation, University of Oklahoma, Norman, OK (1967). 40. D. Drysdale, An Introduction to Fire Dynamics, 2nd ed., John Wiley and Sons, Chichester, UK (1998). ¨ stman and R. Nussbaum, “Larger Specimens for 41. B. O Determining Rate of Heat Release in the Cone Calorimeter,” Fire and Materials, 10, pp. 151–160 (1986). 42. M. Janssens and J. Urbas, “Comparison of Small and Intermediate Scale Heat Release Rate Data,” in Proceedings of Interflam ‘96, Interscience Communications, London, UK (1996). 43. B. Toal, T. Shields, and G. Silcock, “Observations on the Cone Calorimeter,” Fire and Materials, 14, pp. 73–76 (1989). 44. B. Toal, T. Shields, and G. Silcock, “Suitability and Preparation of Samples for the Cone Calorimeter,” Fire Safety Journal, 16, pp. 85–88 (1990). 45. J. Urbas and H. Sand, “Some Investigations on Ignition and Heat Release of Building Materials Using the Cone Calorimeter,” in Proceedings of Interflam ‘90, Interscience Communications, London, UK (1990). 46. J. deRis (2000). “Sample Holder for Determining Material Properties.,” Fire and Materials, 24, pp. 219-226 (2000). 47. V. Babrauskas, W. Twilley, and W. Parker, “The Effect of Specimen Edge Conditions on Heat Release Rate,” Fire and Materials, 17, pp. 51–63 (1993). ¨ stman and L. Tsantaridis, “Communication: 48. B. O Retainer Frame Effects on Cone Calorimeter Results for Building Products,” Fire and Materials, 17, pp. 43–46 (1993). 49. V. Babrauskas, W. Twilley, M. Janssens, and S. Yusa, “A Cone Calorimeter for Controlled Atmosphere Studies,” Fire and Materials, 16, pp. 37–43 (1992). 50. Y. Xin and M. Khan, “Flammability of Combustible Materials in Reduced Oxygen Environment,” in Proceedings of the 10th Fire and Materials Conference, Interscience Communications, London, England (2007). 51. Aircraft Material Fire Test Handbook, DOT/FAA/ CT-89/15, U.S. Department of Transportation,
948 Federal Aviation Administration, Atlantic City, NJ (1990). 52. In Federal Register, 51, Federal Aviation Administration, Washington, DC, pp. 26206–26221 (1986). 53. J. Blomqvist, “Rate of Heat Release of Building Materials, Experiments with an OSU Apparatus Using Oxygen Consumption,” LUTVDG/(TVBB3017), Lund University, Lund, Sweden (1983). 54. H. Tran, “Modifications to an Ohio State University Apparatus and Comparison with Cone Calorimeter Results,” in HTD, Vol. 141, Proceedings of the AIAA/ASME Thermophysics and Heat Transfer Conference, American Society of Mechanical Engineers, New York (1990). 55. Y. Tsuchiya, “Methods of Determining Heat Release Rate,” Fire Safety Journal, 5, pp. 49–57 (1982). 56. F. Hshieh and R. Buch, “Controlled-Atmosphere Cone Calorimeter Studies of Silicones,” Fire and Materials, 21, pp. 265-272 (1997). 57. J. Leonard, P. Bowditch and V. Dowling, “Development of a Controlled-Atmosphere Cone Calorimeter,” Fire and Materials, 24, pp. 143-150 (2000). 58. C. Gomez, A. Zalkin and M. Janssens, “Using the Cone Calorimeter for Quantifying Toxic Potency,” in Proceedings of Interflam 2010, Interscience Communications, London, England (2010). 59. C. Gomez, M. Janssens and A. Zalkin, “Measuring Yields of Toxic Gases from Materials during Different Stages of Fire Development,” in Proceedings of the 12th Fire and Materials Conference, Interscience Communications, London, England (2011). 60. A. Tewarson, “Heat Release Rates from Burning Plastics,” Journal of Fire and Flammability, 8, pp. 115–130 (1977). 61. A. Tewarson, “Reliable Small-Scale Fire Testing Apparatus,” Modern Plastics, 57, 11, pp. 58–62 (1980). 62. A. Tewarson and R. Pion, “Flammability of Plastics. I. Burning Intensity,” Combustion and Flame, 26, pp. 85–103 (1976). 63. A. Tewarson, J. Lee, and R. Pion, “The Influence of Oxygen Concentration on Fuel Parameters for Fire Modeling,” in Proceedings of the 18th Symposium (International) on Combustion, Combustion Institute, Pittsburgh, PA (1981). ¨ stman, G. Svensson, and J. Blomqvist, “Com64. B. O parison of Three Test Methods for Measuring Rate of Heat Release,” Fire and Materials, 9, pp. 176–184 (1985). 65. V. Babrauskas, “Comparative Rates of Heat Release from Five Different Types of Test Apparatuses,” Journal of Fire Sciences, 4, pp. 148–159 (1986). 66. B. Kandola,, A. Horrocks, K. Padmore, J. Dalton and T. Owen, “Comparison of Cone and OSU Calorimetric Techniques to Assess the Flammability Behaviour of Fabrics Used for Aircraft Interiors,” Fire and Materials, 30, pp. 241-255 (2006). 67. P. Gandhi, L. Caudill, and T. Chapin, “Comparison of Cone Calorimeter Data with FM 3972 for
M. Janssens Communication Cables,” in Proceedings of the 5th International Fire and Materials Conference and Exhibition, Interscience Communications, London, UK (1998). 68. J. Carman, D. Price, G. Milnes, and D. Purser, “Comparison of Heat Release Rates as Measured by Oxygen Depletion and Thermopile Techniques,” in Proceedings of Interflam’99, Interscience Communications, London, UK (1999). 69. R. Lyon, “Heat Release Kinetics,” Fire and Materials, 24, pp. 179-186 (2000). 70. R. Lyon, “Plastics and Rubber,” in Handbook of Building Materials for Fire Protection, (C. Harper, ed.), McGraw-Hill.: New York, NY, pp. 3.1-3.51 (2004). 71. R. Lyon and M. Janssens, “Polymer Flammability” in Encyclopedia of Polymer Science & Engineering (On-line Edition), John Wiley & Sons: New York, NY (2005). 72. R. Lyon, R. Walters and S. Stoliarov, “A Thermal Analysis Method for Measuring Polymer Flammability,” Journal of ASTM International, 3, pp. 1-18 (2006). 73. R. Lyon, R. Walters, N. Safronava and S. Stoliarov, “In A Statistical Model for the Results of Flammability Tests,” in Proceedings of the 11th International Fire and Materials Conference, Interscience Communications Limited, London, England, pp. 141-159 (2009). 74. L. Cooper, “Some Factors in the Design of a Calorimeter Hood and Exhaust,” Journal of Fire Protection Engineering, 6, pp. 99–112 (1994). 75. P.H. Thomas, P.L. Hinkley, C.R. Theobald, and D.L. Simms, Fire Technical Paper No. 7, H.M. Stationary Office, Joint Fire Research Organization, London, UK (1963). 76. V. Babrauskas, J. Lawson, W. Walton, and W. Twilley, “Upholstered Furniture Heat Release Rates Measured with a Furniture Calorimeter,” NBSIR 82-2604, National Bureau of Standards, Gaithersburg, MD (1982). 77. S. Ames and S. Rogers, “Large and Small Scale Fire Calorimetry Assessment of Upholstered Furniture,” in Proceedings of Interflam ‘90, Interscience Communications, London, UK (1990). 78. J, Ezinwa, J. Rigg, D. Torvi and E. Weckman “Effects of Ignition Location on Flame Spread and Heat Release Rates in Furniture Calorimeter Tests of Polyurethane Foams,” in Proceedings of the 11th International Fire and Materials Conference, pp. 645-656 (2009). 79. T. Ohlemiller, “Flammability Tests of Full-Scale Mattresses: Gas Burners versus Burning Bedclothes,” NISTIR 7006, National Institute of Standards and Technology, Gaithersburg, MD (2003). 80. T. Ohlemiller and R. Gann, “Effect of Bed Clothes Modifications on Fire Performance of Bed Assemblies,” NIST Technical Note 1449, National
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Institute of Standards and Technology, Gaithersburg, MD (2003). 81. T. Ohlemiller, T. Shields, A. McLane, and R. Gann, “Flammability Assessment Methodology for Mattresses,” NISTIR 6497, National Institute of Standards and Technology, Gaithersburg, MD (2000). 82. T. Ohlemiller and K. Villa, “An Investigation of the California Technical Bulletin 133 Test, Part II: Characteristics of the Ignition Source and a Comparable Gas Burner,” NBSIR 90-4348, National Bureau of Standards, Gaithersburg, MD (1990). 83. W. Parker, K. Tu, S. Nurbakhsh, and G. Damant, “An Investigation of the California Technical Bulletin 133 Test, Part III: Full Scale Chair Burns,” NBSIR 90-4375, National Bureau of Standards, Gaithersburg, MD (1990). 84. J. Krasny and W. Parker, “Impact of the Room Enclosure on the Peak Heat Release Rates of Upholstered Furniture,” in Proceedings of the Fire and Materials 4th International Conference and Exhibition, Interscience Communications, London, UK (1995). 85. I. Benjamin, “Development of a Room Fire Test,” in Fire Standards and Safety, ASTM STP 614, American Society of Testing and Materials, Philadelphia (1977). 86. F. Fisher and R. Williamson, “Intralaboratory Evaluation of a Room Fire Test Method,” NBS GCR 83-421, National Bureau of Standards, Gaithersburg, MD (1983). 87. C. Lee, “Standard Room Fire Test Development at the National Bureau of Standards,” in Fire Safety: Science and Engineering, ASTM STP 882, American Society of Testing and Materials, Philadelphia, pp. 29–42 (1985). 88. B. Sundstro¨m and U. Wickstro¨m, “Fire: Full Scale Tests,” SP-RAPP, 14, National Testing Institute (SP), Bora˚s, Sweden (1980). 89. B. Sundstro¨m and U. Wickstro¨m, “Fire: Full Scale Tests, Calibration of Test Room,” SP-RAPP, 48, National Testing Institute (SP), Bora˚s, Sweden (1981). 90. A. Ahonen, C. Holmlund, and M. Kokkala, “Effects of Ignition Source in Room Fire Tests,” Fire Science and Technology, pp. 1–13 (1987). 91. J. Zhang, M. Delichatsios and, M. Colobert, “Assessment of Fire Dynamics Simulator for Heat Flux and Flame Heights Predictions from Fires in SBI Tests,” Fire Technology, 46, pp. 291-306 (2010). 92. E. Smith, N. Marshall, K. Shaw, and S. Colwell, “Correlating Large-Scale Fire Performance with the Single Burning Item Test,” in Proceedings of Interflam’01, 9th International Fire Conference, Interscience Communications, London, UK (2001). 93. G. Heskestad, “A Fire Products Collector for Calorimetry into the MW Range,” Technical Report FMRC J.I0C2E1.RA, Factory Mutual Research Corporation, Norwood, MA (1981).
949 94. M. Dahlberg, “The SP Industry Calorimeter—For Rate of Heat Release Rate Measurements up to 10 MW,” SP Report, 43, National Testing Institute (SP), Bora˚s, Sweden (1992). ¨ stman and L. Tsantaridis, “Correlation Between 95. B. O Cone Calorimeter Data and Time to Flashover in the Room Fire Test,” Fire and Materials, 18, pp. 205–209 (1994). 96. V. Babrauskas, “Specimen Heat Fluxes for BenchScale Heat Release Rate Testing,” Fire and Materials, 19, pp. 243–252 (1995). 97. U. Wickstro¨m and U. Go¨ransson, “Full-Scale/ Bench-Scale Correlations of Wall and Ceiling Linings,” Fire and Materials, 16, pp. 15–22 (1992). 98. E. Smith and T. Green, “Release Rate Tests for a Mathematical Model,” in Mathematical Modeling of Fires, ASTM STP 983, American Society of Testing and Materials, Philadelphia (1987). 99. H. Mitler, “Predicting the Spread Rates of Fires on Vertical Surfaces,” in Proceedings of the 23rd Symposium (International) on Combustion, Combustion Institute, Pittsburgh, PA (1991). 100. M. Janssens, “Cone Calorimeter Measurements of the Heat of Gasification of Wood,” in Proceedings of Interflam ‘93, Interscience Communications, London, UK (1993). 101. S. Dillon, W. Kim, and J. Quintiere, “Determination of Properties and the Prediction of the Energy Release Rate of Materials in the ISO 9705 RoomCorner Test,” NIST-GCR-98-753, National Institute of Standards and Technology, Gaithersburg, MD (1998). 102. V. Petrella, “The Mass Burning Rate of Polymers, Wood and Liquids,” Journal of Fire and Flammability, 11, pp. 3–21 (1980). 103. M. Janssens, Thermophysical Properties of Wood and Their Role in Enclosure Fire Growth, University of Ghent, Ghent, Belgium (1991). 104. J. Urbas and W. Parker, “Surface Temperature Measurements on Burning Wood Specimens in the Cone Calorimeter and Effect of Grain Orientation,” Fire and Materials, 17, pp. 205–208 (1993). 105. M. Sibulkin, “Heat of Gasification for Pyrolysis of Charring Materials,” in Proceedings of the 1st International Symposium on Fire Safety Science, International Association for Fire Safety Science, London, UK (1985). 106. J. Urbas, “Non-Dimensional Heat of Gasification Measurements in the Intermediate Scale Rate of Heat Release Apparatus,” Fire and Materials, 17, pp. 119–123 (1993). 107. J. Quintiere, “A Simulation Model for Fire Growth on Materials Subject to a Room-Corner Test,” Fire Safety Journal, 20, pp. 313–339 (1992). 108. R. Peacock, P. Reneke, W. Jones, R. Bukowski, and G. Forney, “A User’s Guide for CFAST: Engineering Tools for Fire Growth and Smoke Transport,” Special Publication 921, National Institute of Standards and Technology, Gaithersburg, MD (2000).
950 109. J. Mangs and O. Keski-Rahkonen, “Characterization of the Fire Behavior of a Burning Passenger Car. Part I: Car Fire Experiments,” Fire Safety Journal, 23, pp. 17–35 (1994). 110. M. Shipp and M. Spearpoint, “Measurements of the Severity of Fires Involving Private Motor Vehicles,” Fire and Materials, 19, pp. 143–151 (1995). 111. C. Joyeux, “Natural Fires in Closed Car Parks,” INC-96/294d-DJ/NB, Centre Technique Industriel de la Construction Me´tallique (CTICM), SaintAubin, France (1997). 112. C. Steinert, “Experimental Investigation of Burning and Fire Jumping Behavior of Automobiles (in German),” VFDB Journal, 49, pp. 163–172 (2000). 113. C. Joyeux, J. Kruppa, L. Cajot, J. Schleich, P. van de Leur, and L. Twilt, “Demonstration of Real Fire Tests in Car Parks and High Buildings,” Centre Technique Industriel de la Construction Me´tallique (CTICM), Saint-Aubin, France (2002). 114. Y. Shintani, N. Kakae, K. Harada, H. Masuda, and W. Takahashi, “Experimental Investigation of Burning Behavior of Automobiles,” in Proceedings of the 6th Asia-Oceania Symposium on Fire Science and Technology, International Association for Fire Safety Science, London, UK (2004). 115. B. Zhao and J. Kruppa, “Structural Behavior of an Open Car Park Under Real Fire Scenarios,” Fire and Materials, 28 (2004). 116. H. Persson, “Commodity Classification—A More Objective and Applicable Methodology,” SP Report, 70, National Testing Institute (SP), Bora˚s, Sweden (1993). 117. D. Evans and D. Stroup, “Methods to Calculate the Response Time of Heat and Smoke Detectors Installed Below Large Unobstructed Ceilings,” NBSIR 85-3167, National Bureau of Standards, Gaithersburg, MD (1985). 118. M. Dahlberg, “Error Analysis for Heat Release Rate Measurements with the SP Industry Calorimeter,” SP Report, 29, National Testing Institute (SP), Bora˚s, Sweden (1994). 119. P. Enright and C. Fleischmann, “Uncertainty of Heat Release Rate Calculation of the ISO 56601—Cone Calorimeter Standard Test Method,” Fire Technology, 35, pp. 153–169 (1999). 120. J. Urbas, “BDMC Interlaboratory Cone Calorimeter Test Program,” Fire and Materials, 26, pp. 29–35 (2002). 121. M. Janssens, “Uncertainty of Fire Test Results,” in Proceedings of Interflam ‘07, Interscience Communications, London, UK (2007).
Codes and Standards 16 CFR 1633, Standard for the Flammability (Open Flame) of Mattresses and Mattress/Foundation Sets,
M. Janssens Consumer Products Safety Commission, Washington, DC (2006). ASTM D3173, Standard Test Method for Moisture in the Analysis Sample of Coal and Coke, ASTM International, West Conshohocken, PA. ASTM D5373, Standard Test Methods for Instrumental Determination of Carbon, Hydrogen, and Nitrogen in Laboratory Samples of Coal, ASTM International, West Conshohocken, PA. ASTM D5865, Standard Test Method for Gross Calorific Value of Coal and Coke, ASTM International, West Conshohocken, PA (2007). ASTM D7309, Standard Test Method for Determining Flammability Characteristics of Plastics and Other Solid Materials Using Microscale Combustion Calorimetry, ASTM International, West Conshohocken, PA (2007). ASTM E906, Standard Test Method for Heat and Visible Smoke Release Rates for Materials and Products, ASTM International, West Conshohocken, PA (2007). ASTM E1317, Standard Test Method for Flammability of Marine Surface Finishes, ASTM International, West Conshohocken, PA (2008). ASTM E1354, Standard Test Method for Heat and Visible Smoke Release Rates for Materials and Products Using an Oxygen Consumption Calorimeter, ASTM International, West Conshohocken, PA (2008). ASTM E1537, Standard Test Method for Fire Testing of Upholstered Furniture, ASTM International, West Conshohocken, PA (2007). ASTM E1590, Standard Test Method for Fire Testing of Mattresses, ASTM International, West Conshohocken, PA (2007). ASTM E1623, Test Method for Determination of Fire and Thermal Parameters of Materials, Products, and Systems Using an Intermediate Scale Calorimeter (ICAL), ASTM International, West Conshohocken, PA (2004). ASTM E1822, Standard Test Method for Fire Testing of Stacked Chairs, ASTM International, West Conshohocken, PA (2007). ASTM E2058, Standard Test Methods for Measurement of Synthetic Polymer Material Flammability Using a Fire Propagation Apparatus, ASTM International, West Conshohocken, PA (2006). ASTM E2067, Standard Practice for Full-Scale Oxygen Consumption Calorimetry Fire Tests, ASTM International, West Conshohocken, PA (2008). ASTM E2257, Standard Test Method for Room Fire Test of Wall and Ceiling Materials and Assemblies, ASTM International, West Conshohocken, PA (2008). CAL TB 133, Flammability Test Procedure for Seating Furniture for Use in Public Occupancies, California Bureau of Home Furnishings and Thermal Insulation, North Highlands, CA (1991). CAL TB 603, Requirements and Test Procedure for Resistance of a Mattress/Box Spring Set to a Large Open-Flame, California Bureau of Home Furnishings and Thermal Insulation, North Highlands, CA (2004).
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EN 13501, Fire Classification of Construction Products and Building Elements—Part 1: Classification Using Test Data from Reaction-to-Fire Tests, European Committee for Standardization (CEN), Brussels, Belgium (2002). EN 13823, Reaction to Fire Tests for Building Products— Building Products Excluding Flooring Exposed to the Thermal Attack of a Single Burning Item, European Committee for Standardization (CEN), Brussels, Belgium (2002). FM 4995, Approval Standard for Commodity Classification of Idle Plastic Pallets, FM Global Research, Norwood, MA (1992). ISO 1716, Reaction to Fire Tests for Building Products— Determination of the Calorific Value, International Organization for Standardization, Geneva, Switzerland (2002). ISO 5660-1, Reaction-to-Fire Tests—Heat Release, Smoke Production and Mass Loss Rate—Part 1: Heat Release Rate (Cone Calorimeter Method), International Organization for Standardization, Geneva, Switzerland (2002). ISO 5660-2, Reaction-to-Fire Tests—Heat Release, Smoke Production and Mass Loss Rate—Part 2: Smoke Production Rate (Dynamic Measurement), International Organization for Standardization, Geneva, Switzerland (2002). ISO 9705, Fire Tests—Reaction-to-Fire—Room Fire Test, International Organization for Standardization, Geneva, Switzerland (1993). NFPA 101®, Life Safety Code®, National Fire Protection Association, Quincy, MA (2006).
951 NFPA 220, Standard on Types of Building Construction, National Fire Protection Association, Quincy, MA (2006). NFPA 259, Standard Test Method for Potential Heat of Building Materials, National Fire Protection Association, Quincy, MA (2003). NFPA 265, Standard Methods of Fire Tests for Evaluating Room Fire Growth Contribution of Textile Coverings on Full Height Panels and Walls, National Fire Protection Association, Quincy, MA (2007). NFPA 271, Standard Method of Test for Heat and Visible Smoke Release Rates for Materials and Products Using an Oxygen Consumption Calorimeter, National Fire Protection Association, Quincy, MA (2004). NFPA 286, Standard Methods of Fire Tests for Evaluating Contribution of Wall and Ceiling Interior Finish to Room Fire Growth, National Fire Protection Association, Quincy, MA (2006). NFPA 5000®, Building Construction and Safety Code®, National Fire Protection Association, Quincy, MA (2006). NT Fire 032, Upholstered Furniture, Burning Behavior— Full-Scale Test, NORDTEST, Helsinki, Finland (1991). Dr. Marc Janssens is a Senior Engineer at Southwest Research Institute in San Antonio, Texas. His research has focused on computer fire modeling, fire hazard and risk assessment, fire test standards development, and the experimental and theoretical evaluation of material flammability with emphasis on heat release calorimetry.
28
The Cone Calorimeter Vytenis Babrauskas
Introduction Chapter 27 describes the history and development of techniques for measuring heat release rate (HRR). This chapter outlines features and details of today’s preferred instrument for measuring bench-scale HRR—the cone calorimeter. Other cone calorimeter measuring functions are 1. Effective heat of combustion 2. Mass loss rate 3. Ignitability 4. Smoke and soot 5. Toxic gases The cone calorimeter is based on the concept of oxygen consumption calorimetry, which is also presented in Chap. 27. This chapter provides both an introduction to and description of cone calorimeter measurement technology. The cone calorimeter has recently assumed a dominant role in bench-scale fire testing of various products; therefore, an emphasis will be placed on the why of various design features. When conducting tests, the cone calorimeter operator needs to consult several other documents. Testing will presumably be in conformance with either ISO 5660 [1] or ASTM E1354 [2]. In addition, the “User’s Guide for the Cone Calorimeter” [3] should be consulted. This chapter does not emphasize the operational aspects documented in these references but
V. Babrauskas (*) Fire Science and Technology Inc.
instead provides the reader with an overall feel for the equipment. Space is not available in this handbook to fully discuss the applications of cone calorimeter data, apart from the review of data given in Chap. 26. Extensive guidance on using cone calorimeter data is given in a textbook on this subject [4]. It also provides example data compilations and information on using cone calorimeter data for predictions of fires.
Summary of Features A schematic view of the cone calorimeter is shown in Fig. 28.1. Figure 28.2 shows a commercial instrument, and Fig. 28.3 identifies some of the major components. The more salient operational features and limits of the apparatus are Specimen size Specimen orientation
Specimen back-face conditions Load cell live load capacity Load cell tare capacity Load cell resolution Ignition Heating flux range Flux uniformity, horizontal Flux uniformity, vertical
M.J. Hurley (ed.), SFPE Handbook of Fire Protection Engineering, DOI 10.1007/978-1-4939-2565-0_28, # Society of Fire Protection Engineers 2016
100 100 mm, thickness of 6–50 mm Horizontal, face up (standard testing) or vertical (reserved for exploratory studies) Very low loss insulating ceramic fibrous material 500 g 3.5 kg 0.005 g Electric spark 0–110 kW · m2 Typically 2 % Typically 7 % (continued) 952
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The Cone Calorimeter
Sensing principle Maximum instantaneous output Normally calibrated range Linearity over 0–12 kW range Noise intrinsic to oxygen meter Noise in HRR measurement, over 0–12 kW range Smoke meter operating range Smoke meter resolution Soot sampler mass fraction range
953
Oxygen consumption, only In excess of 20 kW 0–12 kW 5% 20 ppm O2 2.5 %
1. comparative evaluation of materials; 2. obtaining of thermophysical constants (fire properties) of materials; 3. as input data to fire models or engineering calculation; 4. for regulatory compliance.
Comparative Evaluation of Materials
0–20 m1 (linear) 0.01 m1 0–1 part in 200 (of exhaust gas flow)
Uses of Cone Calorimeter Data Cone calorimeter data are primarily used for four purposes:
Comparative evaluation of materials is the easiest and simplest use of cone calorimeter data. This, in fact, is also where the largest amount of published literature involving cone calorimeter data is found, of which the fire retardants field is a prominent example. There have been hundreds of papers published examining fire retardant formulations with the use of the cone calorimeter. For such studies, modeling or large-scale testing is inappropriate, since the
Laser extinction beam including temperature measurement Temperature and differential pressure measurements taken here Soot sample tube location
Exhaust blower
Exhaust hood Gas samples taken here
Cone heater
Soot collection filter
Spark igniter
Controlled flow rate
Sample
Load cell
Vertical orientation
Fig. 28.1 Schematic view of the cone calorimeter
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Fig. 28.2 A commercial cone calorimeter (Photo courtesy Fire Testing Technology, Ltd.)
Orifice plate, orifice size is 1/2 I.D. of stack
same polymer formulation can be used for a wide array of products. Thus, cone calorimeter data are normally used and a comparative evaluation is made. Most commonly, candidate materials are evaluated simply by comparing their peak HRR values. This approach is not adequate if flame spread in the real-life environment is significant, i.e., if the material is not quickly ignited over its entire face. For taking flame spread into account, albeit in a simplified way, Babrauskas 00 [5] proposed in 1984 that the variable q_ =tig be used, which is the ratio of the HRR value to the ignition time. The ignition time was shown to be correlated to flame spread rate, thus, this hazard parameter increases with both increasing HRR and increasing propensity for rapid flame spread. A reasonable semi-quantitative prediction of the time to flashover was possible using this ratio for various wall lining materials. Petrella [6] later 00 proposed a modified rating system where q_ =tig is plotted on one axis, while total heat released is plotted on the other. Materials of better perfor00 mance have both a low q_ =tig value and a low total heat release. The most refined scheme
Pressure ports Thermocouple (located on stack center line) 685* mm
57 mm* dia. orifice
Gas sample Blower
114 mm dia. duct 140 mm
127 mm Hood
Blower motor
Rubber vibration mounts
530* mm Sample
1625 mm
1680 mm *Indicates a critical dimension
Fig. 28.3 View of major components of the cone calorimeter
686 mm
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The Cone Calorimeter
955
which is still simple is the one put forth in 1991 by Cleary and Quintiere [7]. They introduced a parameter b: 00
b ¼ 0:01q_ avg 1
tig tb
ð28:1Þ
00
where q_ avg ¼ average HRR (kW m2) at a 50 kW m2 irradiance, tig ¼ ignition time (s), and tb ¼ duration of flaming (s). They showed that materials which show b < 0.4 have negligible propensity to spread fire, while those with progressively higher values show increased hazard in full-scale applications. The Cleary/ Quintiere b is not to be confused with Spalding’s B number, sometimes use to characterize hazards of burning liquids.
Obtaining Thermophysical Constants of Materials
Fig. 28.4 The main variables of the ignitability plot
Transformed ignition time (t-0.55)
The HRR of materials cannot be computed from some ostensibly simple material fire properties, but is rather a complex relationship governed by chemical (reaction kinetics), thermal (heat transfer properties), and mechanical (cracking, delamination, etc.) properties. Thus, in general, it is not possible to deduce some underlying material fire properties from HRR data. However, the situation is more amenable for ignition data, where it
is possible to obtain fire properties from cone calorimeter data. This topic is treated at length in the Ignition Handbook [8], but here the most useful computation will be identified. For thermally thick materials, Janssens derived the relationship: 2 !0:55 3 λρC 00 00 5 q_ e ¼ q_ cr 41 þ 0:73 2 ð28:2Þ heff tig According to this, if experimental data are plot00 ted (Fig. 28.4) such that q_ e is put on the x-axis and t0:55 on the y-axis, then the data will fall in a ig 00
straight line, with the x-axis intercept being q_ cr . 00 00 Here q_ e ¼ irradiance ðkWm2 Þ, q_ cr ¼ x-axis intercept, tig ¼ ignition time (s), and λρC is the thermal inertia (kJ2 m4 s1 K2) of the specimen. From such a plot, the value of thermal inertia can be computed, which is an effective fire property of importance in both ignition and flame spread problems.
Input Data for Fire Models or Calculations A number of correlational schemes for making engineering calculations on various types of commodities have been developed which are
Minimum flux
0 0 Critical flux
Irradiance (kW m-2)
956
based on Cone Calorimeter data. These are reviewed in Chap. 26. For more refined models, i.e., zone or CFD models for room fires, the application is more difficult. This is because the HRR is strongly a function of the irradiance. But in most real fires, the irradiance received by any particular locale is a dynamic function of time and is not a constant. Because of this difficulty, it has become more common for modern-day computer codes, e.g., FDS, to adopt a pyrolysis model, rather than using small-scale experimental HRR data as an input. A pyrolysis model effectively is a scheme where the HRR of a small area of material is computed from some sort of input data. But, as discussed above, for realistic materials there generally is no simple series of expression that would be able to predict the HRR, based on the input of a modest collection of constants. Even if the constants can be defined, they must in turn be obtained from experiments, and this is already known to be difficult in the first place. CFD models however may have an option to input small-scale HRR data; typically in that case the HRR at a fixed irradiance is used. Capote et al. [9] illustrated such an approach in modeling train fires with FDS. Aksit et al. [10] described use of cone calorimeter input data for modeling cable tray fires with SOFIE, while Andersson [11] described a more general effort with SOFIE. Tsai et al. [12] described a proprietary CFD model using cone calorimeter data; the model was used solely for calculating ignition behavior of materials. For zone fire models, the most successful example has been the BRANZfire model of Wade [13–15]. Lattimer et al. [16] described a module for CFAST based on cone calorimeter input data. Janssens and Dillon [17] described a simple room fire model based on cone calorimeter data. Cone calorimeter data have also been used in an application simpler than room fires, the prediction of upward flame spread on vertical panels [18–23]. For some models, it is necessary to know the total heat flux incident on the specimen, not just the external heat flux; the total heat flux is comprised of the external heat flux, plus the
V. Babrauskas
flame flux. Hostikka and Axelsson [24] showed an interesting example of CFD modeling by predicting the flame flux in the cone calorimeter.
Regulatory Compliance The New Zealand building code specifies use of the ISO version of the cone calorimeter standard, ISO 5660 [1], for external wall cladding products. The Building Code of Australia uses cone calorimeter testing to assess fire retardant treated wood for use in bushfire-prone areas. The building code of Japan uses cone calorimeter testing extensively, as a primary measure of the fire performance of surface lining materials [25]. In their application, tests are run at 50 kW m2 irradiance for a duration of 5, 10, or 20 min, depending on the classification sought. In each case, a peak HRR value below 200 kW m2 must be found, with the total heat release being less than 8 MJ m2, with the latter being a particularly onerous requirement. Taiwan has also adopted similar provisions. IMO, the International Maritime Organization, which provides the regulations for constructing of sea-going vessels, uses cone calorimeter testing for acceptance of “fire restricting material” for high-speed craft in the case of furniture and related materials.
Operating Principle It is emphasized at this point that the cone calorimeter has been designed to use only oxygen consumption calorimetry as its measurement principle [26]. Other calorimeters that on occasion use oxygen consumption principles, for example, the Factory Mutual Research Corporation (FMRC) flammability apparatus (Chap. 27), sometimes incorporate a sensible enthalpy flow measurement technique to arrive at the convective component of the heat release rate. In the design of the cone calorimeter, such an approach was deemed to be misleading. The implicit assumption behind this type of measurement is that the fraction of the total heat release being
28
The Cone Calorimeter
manifest as the sensible flow enthalpy is a property of the material being tested. Such is not, in fact, the case. The convective fraction is dependent on details of the apparatus design and also on the scale of the specimen [27]. Where high-quality results are required, such as in the cone calorimeter, current-day practice demands that a paramagnetic oxygen analyzer be used. The various manufacturers use measuring schemes that differ in detail, but all rely on the same paramagnetic principle whereby the sensing element is sensitive to the partial pressure of oxygen in the cell. The most significant interferents to this detection principle are NO and NO2, both of which show a strong paramagnetic response, but not as strong as that of oxygen. Interferents are never a problem in fire testing, however, since O2 levels measured are 10–21%, whereas concentrations of NOx are rarely above 100 ppm. Unlike in applications where oxygen levels are monitored as simply one of many indications of fire hazard, in HRR work it is essential that the instrumentation be designed for the highest possible resolution. Thus, both the ASTM and ISO standards specify that the short-term noise + drift of the oxygen analyzer must be less than or equal to 50 ppm O2. The best-grade commercial instruments are able to meet a 20 ppm O2 limit. In addition, the standards provide a significant amount of detail on the layout of the gas sampling system, including desiccation, mass flow control, and bypass flows. All of these aspects have to be in conformance with the specifications for good repeatability and reproducibility performance (see Fig. 28.3) to be achieved. Because the detection principle responds to oxygen partial pressure, there needs to be a compensation for changes in atmospheric pressure, either with a mechanical back-pressure regulator or by measuring the pressure and correcting electrically. Without compensation, there can be significant error in the calculated heat release rate. Carbon dioxide, the other major component expected to be in the oxygen analyzer, causes less than 0.3 % error in the oxy-gen reading. Extensive practice advice on selecting, setting
957
up, and calibrating oxygen analysis systems is given in Twilley and Babrauskas [3] and in Babrauskas and Grayson [4].
The Radiant Heater After establishing the operating principle, the next most important feature is the type of heater. In general, such a heater should be able to achieve adequately high irradiances, have a relatively small convective heating component, present a highly uniform irradiance over the entire exposed face of the specimen, and be designed so as not to change its irradiance when the main voltage varies, when heater element aging occurs, or when the apparatus retains some residual heat from the exposure given to a prior specimen. Range of Heat Fluxes Needed for Testing A room fire burning near its maximum rate can show gas temperatures over 1000 C, producing corresponding irradiances to walls and contents of 150 kW · m2. Testing under such extreme conditions may not be required; nonetheless, if postflashover fires are to be simulated, irradiances of over 75 kW · m2 should be available, and preferably closer to 100 kW · m2. A significant convective component would negate the purpose of having a radiant ignition test. Rather low convective fluxes can be achieved for specimens oriented horizontally, face up, and with the prevailing airflow being upwards. For vertical specimens, orientation is considered, and it becomes evident that a boundary layer will normally be expected to develop that will add some convective component. The convective boundary layer component is not uniform over the height of a specimen; thus it is seen that better uniformity can also be expected under conditions where the convective component is minimized. Choice of Heater Type In a real fire, the ignition source is, in most cases, in the vicinity of a combustible. The radiation spectrum depends on the size of the fire. A very small fire can show a substantial fraction of its radiation at
958
wavelengths characteristic of H2O, CO2, and other combustion products [28]. For larger fires—certainly for room fires reaching a hazardous condition—the radiation from the soot tends to dominate. The result is an approximation to a graybody radiation [29]. For such a graybody radiation the temperature is typically in the vicinity of 1000 C [30]. Experimentally, heater choices for test apparatuses have included gas-fired panels, electric resistance heaters, flames, and high-temperature lamps. Electrical heaters tend to have a near-graybody characteristic and, assuming a dull or oxidized surface condition, a high emissivity. Gas-fired panels derive a substantial portion of their radiation from the ceramic face; thus, while there are discrete molecular wavelength peaks, overall the radiation shows a graybody continuum, typically in the range of 700–1000 C [31]. High-temperature lamps, which have been used by several investigators [28, 32], typically have radiating temperatures of 2200–3000 C. The spectral distribution of such a source—further limited by a translucent enclosure—is much different from one operating at 1000 C. Whether this change in spectral characteristics is important depends on the surface of the material to be ignited. For a material with a radiant absorbance independent of wavelength, this source variation would not matter. Hallman, however, has reported data for a large number of plastics and shows that although there are some specimens with negligible wavelength dependence to their absorbance, the majority shows strong variations [28]. Hallman also measured ignition times of plastics with both a flame source and high-temperature lamps. The effect on ignition times ranges from negligible to more than an order of magnitude, depending on the specimen. For a general-purpose test, flames would probably be the least desirable source of heating. For a bench-scale test, flame size has to be kept small. This means that such flames are optically thin, their emissivity is low, and higher heat fluxes cannot be achieved unless a strong convective component is added. Design Details Once an electrical radiant heater had been decided upon, design details were also
V. Babrauskas
influenced by work at NIST with earlier types of calorimeters. One of the primary requirements of the heater is that it not change the irradiance impressed on the specimen when the specimen ignites. This undesired event is, of course, exactly what happens with several of the older types of calorimeters. The specimen’s flames directly heat nearby ironwork, which, in turn, radiates to the specimen. The heater, which had been viewing a cold specimen prior to ignition, also starts to view a hot flame afterwards. The result is that its efficiency increases drastically, giving a rise to its radiating temperature. Based on these observations, guidelines were formulated so that the specimen must, as much as possible, view only 1. A temperature-controlled heater 2. A water-cooled plate 3. The open-air, ambient-temperature environment Reliance on item 2 increased costs significantly; thus, it was more desirable to use only items 1 and 3. Prior to the development of the cone calorimeter, fire test apparatuses typically controlled the power (or fuel rate) into the heater, but did not maintain it at a fixed temperature. The Conical Shape The cone calorimeter derives its name from the conical shape of the heater (Fig. 28.5). The decision had been made to use an electric resistance heater, running at a realistic maximum temperature of about 950 C, but its material and shape still had to be determined. Based on poor experiences with exposed-wire resistance heaters and with silicon carbide rod–type heaters, the tube heater was chosen. The tube heater consists of a resistive wire element inside a protective tube, swaged over a packing of inorganic insulation. The tube is made of Incoloy™ and can be bent to a desired shape. To determine the best shape, the conical heater used in the ISO 5657 ignitability apparatus [33] was examined. This seemed to be a promising shape. The proper shape had to have a hole in the middle, since otherwise a hot spot would occur at the sample center, where the radiation view factor is the highest. The same
28
The Cone Calorimeter
Fig. 28.5 Cross-sectional view through the cone heater
959 Outer shell Thermocouple
80* mm
Inner shell
65* mm 46* mm 160* mm Spacer block Heating element
Ceramic fiber packing
Cone hinge and mount bracket
*Indicates a critical dimension
heater had to serve in both horizontal and vertical orientations. In the horizontal orientation, it was essential that all the products of combustion flow out the hole in the middle, and not “splash” on the heater coil itself, nor escape from the underside. The original ISO 5657 design proved to be unsuitable in the former respect. It also had problems with durability and assembly. Thus a totally new design was created, which, however, looked superficially similar to the ISO 5657 cone. With the actual cone calorimeter design, the flames from the specimen do not splash on the heater coil. Instead, a sheath of cold air is pulled up, surrounding the flame plume. Thus, there is not a concern that any surface reactions occur on the heater coil. The space between the inner and outer cones is packed with refractory fiber. This arrangement helps keep the outside of the unit cool and also helps bring the heater up to operating temperature rapidly. Emissivity of the Heater The emissivity was characterized by Janssens [34]. The heater coil, once installed and operated a few times, becomes essentially radiatively black. The emissivity itself cannot be directly measured; however, it is possible to compute an approximate view factor, F, for the cone heater. The possibility of measurements is based on a simultaneous determination of the heater surface temperature and the heat flux falling on the heat flux meter, with the meter held in place at the same location
where a specimen is situated. Over the range of fluxes of 10–90 kW · m2, Janssens determined the ε F product to be 0.73, with F being computed as 0.78. Then, solving for ε gives ε ¼ 0.91. Since the temperatures of the heater closely resemble those in room fires, and the emissivity approaches 1.0, this means that the spectral distribution is likely to be very close to that expected from room fires (neglecting the molecular radiation contribution from CO2 and H2O). It is important that the heater element be kept in good repair, in order that expected uniformity be achieved. Aging may cause the coil windings to separate and sag. If this occurs, poorer uniformity has been shown to occur [35]. Convective Fraction of the Heating Flux During the development of the cone calorimeter at NIST, a study was conducted to determine the fraction of the heating flux accounted for by the convective contribution [36]. When measured with respect to a water-cooled heat flux meter, the results showed that, in the horizontal specimen orientation, the convective contribution was immeasurably small. In the vertical orientation, the fraction was typically 8–12 %. Janssens later remeasured the vertical configuration [34] using a more accurately calibrated heat flux meter and found that, even for the vertical orientation, the convective transfer is immeasurably small. Thus, it can be stated that the objective of having a test method where the heating is primarily radiant was successfully
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V. Babrauskas
met. For modeling of test results, however, one may be more interested in the possibility of convective heat transfer to a specimen that is heated, or even burning, not to a calibration meter constrained by its water-cooling jacket at nearroom temperature. Janssens also made some determinations of such actual specimen heating. The direction of the heat transfer was such as to represent a heat loss from the specimen in all cases. A single convective heat transfer coefficient could not be derived, however, since the value was dependent on the irradiance level from the heater. Janssens’s results could be represented by: Irradiance from heater (kWm2) 20 40 60
Convective heat transfer coefficient hc (Wm2K1) 9.0 18.0 27.0
For practical work, Janssens recommended that an average value of hc ¼ 13.5 W · m2K1 should be appropriate for work over the common irradiance range of 20–40 kW · m2. The actual details of this small amount of convective heat transfer are pertinent only to certain specialized studies. For most work, it is entirely adequate to assume that the specimen heating is entirely radiative. Uniformity of the Heating Flux The uniformity of the heating flux over the face of the specimen in the cone calorimeter has been
Orientation of the Heater and Specimen The normal orientation of the specimen should be
Depth of aluminum-foil boat = 50 mm
Measured flux (kW/m2)
Fig. 28.6 Measured flux at various positions below the top surface of a specimen
described [36]. Over the range of irradiances from 25 to 100 kW · m2, the ratio of the flux at the specimen center to average flux varied only from 1.00 to 1.06. The peak deviations from average were typically 2 % in the horizontal orientation and 7 % in the vertical. Deviations are higher in the vertical orientation, since the effect of convective fluxes, due to the boundary layer flow, is more pronounced there. Additional measurements have been made in the specimendepth plane. Control of the surface of the specimen was a special concern to the designers of the ISO apparatus, where a special compressive loading mechanism is provided that attempts to relevel the exposed surface, in case the specimen recedes due to melting. In the cone calorimeter, measurements have been made in the horizontal orientation using a small, 6-mm-diameter Gardon-type heat flux gauge. A flux mapping was obtained starting at the initial surface, and progressing down to the maximum depth of a specimen, which is 50 mm. A normal aluminum foil rectangular specimen wrap was used for these tests, but without any specimen. The results show that, at heating fluxes of both 25 and 50 kW · m2, the deviations over the entire specimen depth are less than 10 %, and can, therefore, be neglected (Fig. 28.6). At the lower depths, reflection from the aluminum foil probably assists in maintaining this uniformity.
50 49 48 47 46 45
25 24 23 22 0
10
20
30
Depth below top (mm)
40
50
28
The Cone Calorimeter
961
Sample (100 mm × 100 mm size)
Chain
Cone hinge and mount bracket
Aluminum foil Low-density ceramic wool
Calibration burner Sample pan Flux meter
13 mm calcium silicate board Sample mount assembly
Load cell
13 mm calcium silicate heat shield
Flux meter mount
Fig. 28.7 Heater in the horizontal (standard) orientation
horizontal, face up, with the heater being parallel, face down. This allows thermoplastics, liquids, and other melting or dripping samples to be successfully tested. Because it was considered desirable to allow testing in a vertical orientation for certain application exploratory studies, provision was made to swing the heater 90 into a vertical orientation. Vertical orientation testing may be preferable when probing the flame regions or measuring specimen surface temperatures is desired. Figures 28.7 and 28.8 show the comparative horizontal and vertical heater orientations, respectively. It is especially emphasized that no standard testing should be specified for the vertical orientation, even for products that are normally used in a vertical orientation. The ASTM standard [2] was amended in 1992 to clarify that the vertical orientation is only for special research studies and not for product testing.
The Shutter The original NIST design for the Cone Calorimeter did not include a shutter. The operator would just quickly drop the specimen holder on top of the mount plate at the top of the load cell. This was satisfactory for most building products and plastics. However, in 1993 researchers at SP (Technical Research Institute of Sweden) found that there were some reproducibility issues when testing upholstered furniture specimens that ignited very quickly. Thus, they designed a shutter (originally described as “heat shield” and later as “radiation shield”) to be interposed between the heater and the specimen surface; this was originally described in a 1996 SP report [37]. The use of a shutter makes it possible to (a) get the load cell to equilibrate before commencing exposure, and (b) provide an nearly step-function initiation of radiant heat flux to the specimen.
962
V. Babrauskas
Spark plug
Vertical sample holder Sample (100 mm × 100 mm) Aluminum foil Latching mechanism
Low-density ceramic wool
Calibration burner
Retaining clip Calcium silicate back-up board
Flux meter Loadcell
Fig. 28.8 Heater in the vertical orientation
However, with the use of a shutter there is potentially a different type of error that is introduced. A shutter will reflect some heat back to the heater, and will also rise in temperature and reradiate heat flux to the heater. Both of these would cause the heater’s temperature to rise. The solution adopted by ASTM [2] and ISO [1] standards was that the shutter should be in place for no longer than 10 s prior to start of test, and that it be either water-cooled with a black coating, or else not water-cooled, but with made of ceramic material or made of reflective metal. The reflective metal option is the least satisfactory, because, while radiation towards the specimen gets eliminated by reflection, the reflection towards the heater does cause its temperature to rise. Thus, the best accuracy is attained with a minimal duration of the shutter’s closure. This change was made in the 1997 edition of ASTM E 1354 and in the second edition (2002) of ISO 5660-1.
Airflow The feasible airflow rate through the system is bound by certain limits. It must not be so fast that
ignition results are improperly affected. It must also not be so slow that products of combustion spill out of the hood. If this were a closed system, one would also be concerned about airflow being so slow that the air/fuel ratio drops into the fuelrich regime. The standard cone calorimeter, however, has been designed for ambient air testing, and this consideration does not apply. Systematic guidance in this area was not available. However, as an example of the effect of airflow, measurements were made at NIST using the OSU apparatus. Specimens of black polymethyl methacrylate (PMMA) were exposed in the horizontal orientation to a heating flux of 35 kW · m2. With an airflow rate of 12 Ls1 through the combustion chamber, the ignition time was 209 s. When the airflow rate was doubled to 24 Ls1, the specimen ignition time increased to 403 s. By contrast, Table 28.1 shows comparative results with the cone calorimeter; it can be seen a flow rate of 24 Ls1 was found to be satisfactory. That flow rate was also about a factor of 2 greater than the minimum at which no spill out of the hood occurs. The exhaust system uses a high-temperature cast-iron blower to exhaust the gases and an
28
The Cone Calorimeter
963
Table 28.1 Effect of exhaust hood airflow on ignition times in the cone calorimetera Material PMMA PMMA PMMA PMMA PMMA PMMA Redwood Redwood Redwood Redwood Redwood Redwood
Thickness (mm) 13 13 13 13 13 13 13 13 13 13 13 13
Orientation Horizontal Horizontal Horizontal Vertical Vertical Vertical Horizontal Horizontal Horizontal Vertical Vertical Vertical
Fan setting No fan 24 Ls 1 41 Ls 1 No fan 24 Ls 1 41 Ls 1 No fan 24 Ls 1 41 Ls 1 No fan 24 Ls 1 41 Ls 1
Ignition timeb (s) 71 76 67 86 84 77 23 24 31 22 27 29
At an irradiance of 35 kW · m2 Typical ignition time scatter was on the order of 10 % (1σ, N ¼ 3)
a
b
(Not to scale) 250 mm A Orifice plate 1.59 mm thick 350 mm
A
*25 mm *25 mm
Section A-A
Section B-B Gas sampling ring probe
Thermocouple 57 mm I.D. hole
75* mm
76 mm
Thermocouple
Hood 57 mm I.D. hole Soot sampler probe 6.35 mm O.D.
Smoke meter purge tubes 7.9 mm O.D. Use an alignment rod when welding tubes to duct to ensure perfect alignment
114 mm
Thermocouple location (rear) 225 mm 111* B mm
Section C-C
685* mm C
Orifice plate
114 mm
Blower
Smoke meter location
B Gas sampling ring probe (sample holes face blower)
C Tube is 0.6 mm thick stainless steel. 114 mm I.D.
Hood
*Indicates a critical dimension
Fig. 28.9 Exhaust duct
orifice plate flowmeter (Fig. 28.9). The orifice plate flowmeter is instrumented with a differential pressure transducer and a thermocouple. For specialized studies, where the entire combustion system is glass enclosed [38], it is possible to go to flow rates below 12 Ls1. With such enclosed systems, accurate measurements can be made down to about 9 Ls1 using the standard orifice plate. For lower flow rates, down to about 5 Ls1, the standard orifice plate is replaced by one with a smaller opening.
Means of Ignition In some cases no external ignition source is desired, and specimen testing is to be done solely on the basis of autoignition. In most cases, however, an external ignition source is desirable. This ignition source should, in general, not impose any additional localized heating flux on the specimen. Apparatus designs have been developed, with impinging pilots that can, in some cases, produce such high localized
964
heat fluxes as to burn a hole through the specimen at the point of impingement, yet not ignite it outside of that region [39]. Applications for such devices tend to be specialized, since the general objective of radiant ignition testing is to produce data that can be analyzed in the context of an assumed one-dimensional heat flow. A design using an impinging pilot has an additional difficulty. Since most of the specimen face is not yet heated to the ignition temperature when ignition first begins in the vicinity of the pilot, no unique ignition time can be determined. Instead, there is a significant time spread between when ignition first occurs at the initial location, to when the final portions of the face have been ignited. The ignitor should reliably ignite a combustible gas mixture in its vicinity. Thus, the location of the ignitor must be chosen so that it is near the place where maximum evolution of pyrolysate gases is expected. Some materials are highly fire-retardant treated, and, when heated, emit vapors that tend to extinguish a pilot flame. The ignitor has to be designed so as not to be extinguished by fire-retardant compounds coming from the specimen, nor by airflows within the test apparatus. The ISO 5657 apparatus was designed with a “dipping” gas pilot, which is periodically thrust for a short while down close to the specimen face, then retracted. This solution, however, introduces an uncertainty into ignition times and provides further complexity. A gas pilot, based on experience, also requires oxygen premix to achieve a flame that is both small and resistant to blowout [40]. With products high in fire retardant, even such precautions are not likely to lead to a reliable pilot; thus, for instance, the ISO 5657 apparatus uses a second pilot to reignite the main pilot. Pilot stability also tends to be crucially dependent on the physical condition of the pilot tube tip, and significant maintenance can be necessary. Finally, if used in a heat release apparatus, a gas pilot can add noise to the baseline of the heat release measurement. Experimental efforts at the National Bureau of Standards (NBS) had success using the NBS-II calorimeter, a more
V. Babrauskas
tractable alternative (i.e., electric spark ignition). This spark plug arrangement for ignition was successful, and so a similar electric pilot was designed for the cone calorimeter. The location of the ignitor should be at the place where the lower flammable limit is expected to first be reached when the specimen begins its pyrolysis. It should, however, not be so close to the specimen surface that minor swelling of the specimen would interfere with the ignition function. In the cone calorimeter, the ignitor locations were chosen so that, when testing in the horizontal orientation, the spark plug gap is located 13 mm above the center of the specimen; in the vertical orientation, the spark plug gap is located at the specimen plane and 5 mm above the top of the specimen holder. The actual spark plug arrangement is shown in Fig. 28.10. The spark plug is provided by a special-purpose 10-kV ignition transformer. The spark plug is moved in and out by remote control, operated by an air motor that rotates the shaft on which the spark plug rests. A reversible lock bar is used to adjust the spark-plug-to-heater distance when changing from the horizontal to the vertical orientation (the spark gap is 13 mm away from the heater baseplate in the horizontal orientation, but 25 mm away in the vertical).
Specimen Area and Thickness Both specimen area and thickness may be expected to have some effect on the ignitability and the heat release rate. The main practical size and thickness limitations come from the fact that the specimens to be tested should exhibit primarily one-dimensional heat transfer. Thus, the configuration should be such that excessive edge effects are not seen. If the specimen thickness is such that it is thermally thick (the heat wave penetration depth being less than the physical depth), then further increases in thickness are not expected to change ignitability results. For thinner specimens, however, there can be expected to be a thickness effect, and the backing or substrate material’s thermophysical properties can be of importance.
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The Cone Calorimeter
965 Spark plug position lock bar
Spark plug arm Spark plug carrier (shown in position for horizontal testing, slide to other stop for vertical testing)
Position of arm when spark plug not in use
Air motor
Fig. 28.10 Spark plug, carrier, and air motor
Specimen Area Janssens [34] studied in some detail the general problem of area effect on ignition. The effect is seen to be smaller when irradiances are high rather than low. The exact magnitude of the effect is also dependent on the specimen’s thermophysical properties. For specimens of area 0.01 m2 or larger, however, his results show an increase in ignition time of only about 10 % over what would be seen with a speci¨ stman men of infinite area. Later, Nussbaum and O [41] studied specimens in an experimental apparatus somewhat similar to the cone calorimeter, but accommodating 200 200 mm specimens. Their comparison of the ignition times of these larger specimens against the standard 100 100 mm ones shows that quadrupling the specimen area decreases the ignition time by about 20 %. For heat release rate, the specimen size affects the measurement, since flame volume is larger over larger specimens; consequently the flame radiation tends to approach a value of higher ¨ stman also examemissivity. Nussbaum and O ined heat release rates from larger specimens; the differences were generally of the same order
of magnitude as the repeatability of the results. Babrauskas, in commenting on these data [42], discussed tests on larger size, horizontal PMMA samples, where each doubling of the specimen’s area increased the heat release rate, per unit area, by about 10 %. The more general treatment of the horizontal specimen, of course, is as a liquid pool. Chapter 26 gives details on the size effect for burning pools. It can be seen that the diameter has to be greater than about 1 m before the specimen area effect becomes negligible. The effect of specimen size for vertical samples was examined at Factory Mutual Research Corporation (FMRC) in a series of experiments on PMMA walls [43, 44]. The FMRC studies showed little size effect for specimen heights up to 200 mm; beyond 200 mm there 00 was approximately a linear dependence of q_ on the height. This was true up to the maximum height tested, that is, 3.56 m. Unlike horizontal pools, the rate of heat release was not leveling off at even these sizes, and estimates suggested that the specimen size would have to be increased by
966
V. Babrauskas
another order of magnitude before a leveling off would be seen. The conclusion from the above studies was that 100 100 mm was a suitable size for bench-scale 00 testing, but that the bench-scale q_ rates will always be somewhat lower than for full-scale fires. Specimen Thickness The cone calorimeter is intended for testing actual commercial products. Thus the specimen thickness should be, as much as possible, the thickness of the finished product. There are limitations at both ends of the scale, however. The instrument is restricted to testing specimens not thicker than 50 mm. For products that in their finished state are greater than 50 mm thick, it can readily be seen that, for almost any realizable combination of thermophysical properties and incident radiant fluxes, a 50 mm specimen is thermally thick, and increasing thickness would not change the ignition times [45, 46]. By making calculations for various densities and heat fluxes, it was found that for particleboard the minimum thickness required to ensure that the specimen is thermally thick can be represented by ‘ ¼ 0:6
ρ 00 q_
ð28:3Þ
where ‘ ¼ Thickness ðmmÞ ρ ¼ Density ðkg m3 Þ 00
q_ ¼ Heat flux ðkW m2 Þ This is probably a reasonable rule of thumb for other materials as well. The proportionality of 00 the required thickness to ρ=q_ is derived from classical heat conduction theory by equating the time for the front surface to reach ignition temperature to the time the rear surface’s temperature begins to rise, assuming that the thermal conductivity is proportional to the density. Numerical calculations were necessary to determine a suitable constant because of the impact of front surface heat losses. For materials that are not thermally thick at the time of ignition, the nature of the backing
material or substrate can influence the measured value of the ignition time. In the cone calorimeter, the substrate is a blanket of refractory ceramic fiber material, having a nominal density of 65 k · gm3. In use, the material assumes a more compacted density of roughly 100 kg · m3. Whenever possible, materials whose thicknesses are less than the minimum suggested in the above formula should be mounted on that substrate material over which they will actually be used. As a practical guide for testing unknown commercial samples, it is desirable to specify that any specimens less than 6 mm thick should always be considered as needing to be tested over their in-use substrate. Fabrics are a special case. Thin fabrics are sometimes used for constructing air-supported structures; these should be tested with an air space in back, simulating the usage conditions. A special holder has been constructed that allows the fabrics to be pulled taut and held above a dead-air space (Fig. 28.11).
Sample Testing Specifications Specimen Orientation and Specimen Holders The specimen holders in Figs. 28.12 and 28.13 show the two specimen holders, respectively. With proper precautions, the horizontal orientation can be used for testing liquids and melting materials, whereas the vertical orientation’s small melt trough can only catch a very small amount of molten material. Also, some specimens, when tested in the vertical orientation, show a tendency to lose physical strength and fall out of the holder, which does not happen in the horizontal orientation. In the vertical orientation, there are several layers of rigid millboard behind the blanket, sufficient in thickness to fill out the depth of the specimen holder. The specimen is wrapped in a single sheet of aluminum foil, covering the sides and bottom. The aluminum foil serves to limit the flow of molten material and prevent it from seeping into the refractory blanket.
28
The Cone Calorimeter
967 2.5
All dimensions in millimeters 18 evenly spaced 90 degree cut teeth
2.5 33 20 Side view Edge frame 111 Sample fabric Tensioning insert
Refractory fiber blanket Horizontal specimen holder
111 Top view
Cross section
Fig. 28.11 Special holder for testing fabrics and similar thin materials
Fig. 28.12 Horizontal orientation specimen holder
106* mm Spot weld, 4 corners
106* A mm
25 mm
59* mm
A
2.4 mm thick
25* mm
30°
8 mm 4 mm Stainless (mill smooth)
59* mm
40 mm
40 mm
Section A-A
*Indicates a critical dimension
Load Cell Many ancillary measurements made in the cone calorimeter (such as yields of various gas species) require the use of a load cell. Transducers
had been tried in various earlier apparatuses, but most suffered because they were not designed for purely single-axis linear motion. That is, if the weight of the specimen was not well balanced, or differential heating stresses occurred, it was
968
V. Babrauskas Section B-B 25
104* 25
2.4 Slot
73* 116 135° 94 58 A
15 2.4
Material: 1.59 mm stainless steel (except base plate)
25
All dimensions in mm (except where noted) *Indicates a critical dimension A
4.8
104* 4.8 mm S.S. base plate
94* B
B 5
10 6 4.8 dia. pins, round off ends, 4 places, press fit
24
13
25.4 25.4 Section A-A
4.8
Fig. 28.13 Vertical orientation specimen holder
likely that a mechanical moment (or torque) would be applied to the device, with the transducer then being prone to jamming. For the cone calorimeter, a commercial-design load cell was found that permits only up-and-down axial motion while being insensitive to torques or forces from other directions. The load cell has to accommodate two differently oriented specimen holders and may need to hold additional fixtures. All of these can have substantial—and different—weights, yet must allow accurate mass determination for low-density specimens. The solution adopted was a weighing system that has a large (3.5 kg)
mechanical tare adjustment range, along with a sensitive weighing range (500 g). A resolution of 0.005 g is readily achievable. Figures 28.7 and 28.8 show, respectively, how the horizontal and vertical orientation specimen holders are accommodated on the load cell. The horizontal holder has a square recess on the bottom and simply is placed straight down. The vertical holder is more conveniently inserted directly toward the heater, correctly locating the specimen by four mounting pins on the bottom. In both cases there is a positive specimen location, and the operator does not have to be concerned with how far to insert the holder.
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The Cone Calorimeter
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Edge Conditions Edge Effects In an apparatus such as the cone calorimeter, it is desired that the small-scale test specimen would behave, as much as is possible, like a correspondingly sized element of the fullscale object. If one is dealing with relatively large, flat, full-scale objects, then heat and mass transfer will occur only in the direction perpendicular to the exposed face. There will be no heat or mass flow along either of the face directions. The guidance to be derived from this conceptual model in designing the bench-scale test environment is clear: there should be a minimum of heat or mass transfer at the specimen edges. The aluminum foil used to wrap the specimen usually serves to minimize any mass transfer that may occur. The heat transfer situation, however, is more complicated. In the vertical specimen orientation, the specimen has to be restrained against falling out; therefore, the vertical specimen holder incorporates a small lip extending 3 mm along the edges. In the horizontal orientation, no special measures need to be taken against falling out. Thus, for many specimens it is satisfactory to simply cover the edges and bottom with aluminum foil, leaving the top exposed in its entirety. Some categories, however, present special problems—specimens that either have a propensity to ignite first along the outside edge or that, when ignited, burn disproportionately vigorously near the edges. Such behavior is often found with wood specimens and with certain composites. This problem is alleviated by using a stainless steel edge frame for the horizontal orientation, which like the vertical holder provides a 3 mm lip around the edge of the specimen face (Fig. 28.14). Specimens showing unrepresentative edge burning can be viewed as having a spurious heat gain along the edges when compared against a hypothetical ideal situation of exactly zero heat loss or gain at the edges. When an edge frame is applied, the opposite situation can tend to result, that is, an observed net heat loss from the specimen [47]. The ideal situation of a specimen prevented from showing unrepresentative increased edge burning but equally not sustaining
94* mm 111* mm
94* mm
54* mm
10-32 tapped hole, 4 places 4 mm 55.5 mm 111* mm Inside dimension (stainless steel, 1.9 mm thick)
*Indicates a critical dimension
Fig. 28.14 Edge frame for the horizontal specimen holder
any losses to an edge frame may be difficult to approach in practice. This is still a topic of active study at several institutions. In some cases, an edge frame is needed for thermostructural reasons. Some specimens, especially certain composites, can show pronounced edge warping and curling when subjected to heat. The burning of such a specimen would be highly nonuniform if its edges were not held down with an edge frame. In many cases, an edge frame is all that is required. In some cases, however, additional measures such as a wire grid (see below) are required. Intumescing Samples Intumescence is a common difficulty with fire test specimens, either before ignition or during the burning. The simplest solution used in the cone calorimeter,
970 Fig. 28.15 Wire grid
V. Babrauskas 10 mm
100 mm 20 mm
10 mm 20 mm 100 mm
Material: Stainless steel, 1.9 mm thick
sufficient in many, but not all, cases, is a wire grid placed on top of the specimen. Figure 28.15 shows a medium-weight grid. To minimize effects on measurements, the grid weight should be the smallest possible consistent with providing adequate mechanical restraint to the tested specimen. Effects on measurements will be negligible if the average grid mass is less than 0.6 kg · m2 of specimen face area. This mass corresponds to quite a thin, small grid and will practically be usable only in occasional cases. Additional guidance is given in the NBS “User’s Guide for the Cone Calorimeter” [3], but testing laboratories will, on occasion, be required to devise their own special schemes for mounting and restraint.
Smoke Measurement One of the most essential ancillary measurements performed with the cone calorimeter is smoke obscuration. Widespread dissatisfaction with older, closed-box types of smoke tests [48, 49]
Sample retaining grid (optional) for use with samples that are expected to intumesce. Material: 2 mm stainless steel rod weld all intersections
caused by the large number of both practical and theoretical difficulties were successfully resolved by developing a flow-through smoke measuring system, using a helium-neon laser as the light source and a sophisticated quasi-dual-beam measuring arrangement. Figure 28.16 shows the overall arrangement of the laser photometer. It is mounted on the exhaust duct at the location shown in Fig. 28.9. A thermocouple is also mounted nearby, since the calculations require a determination of the actual volume flow rate in the duct at the photometer location. The user should consult Geake [49] for details explaining the operation of the laser photometer. Briefly, the light from the laser goes, via two beam splitters, into two detectors. The light reaching the compensation detector is not attenuated by smoke; its signal serves as the reference to cancel out fluctuations in laser output power. The main beam detector measures a signal that is attenuated by the smoke. The optical path is purged by a minute flow of room air through a purge system. The flow is maintained by the pressure differential in the exhaust duct.
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The Cone Calorimeter
Beam splitter
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Purge air orifices
Beam splitter
Filterslot
Optical path 0.11 m Cap Opal glass
Opal glass Filter slot
Ceramic fiber packing
0.5 mW Helium-neon laser
Compensation detector
Main detector
Fig. 28.16 Laser photometer
For certain research purposes, it is advantageous, in addition to obtaining optical smoke obscuration measurement, also to record the gravimetric soot yield by measuring grams of soot evolved per gram of specimen burned. A soot mass sampler is connected to the port indicated in section C-C of Fig. 28.9, and a known mass fraction of the exhaust duct flow is passed through a measuring filter and is weighed before and after the test.
Calibration Equipment Two basic calibrations are needed: (1) the calibration of the temperature controller for the conical heater and (2) the actual heat release rate calibration. The temperature controller is calibrated using a Schmidt-Boelter-type heat flux meter equipped with a locating collar and inserted in place of the specimen, with its face where the specimen face would be located. No specimen holder is used for this operation. Figures 28.7 and 28.8 show the insertion of the heat flux meter. The heat release rate is calibrated with a calibration burner inserted into the same bracket used for the heat flux meter (Fig. 28.17). The calibration burner, however, instead of being inserted facing the heater, is inserted so that the discharge opening faces upward. Calibration is
accomplished by controlling the flow of highpurity methane going to the burner and comparing it to a known value and using the net heat of combustion for pure CH4 as 50 MJ · kg1. The laser photometer is calibrated by neutraldensity glass filters. These are inserted into a filter slot in front of the main beam detector. An auxiliary filter slot is provided in front of the laser. This serves to check the correct balancing of the dual-beam system’s common mode rejection ratio. The NBS “User’s Guide to the Cone Calorimeter” [3] details how calibrations are performed.
Miscellaneous Details Ring Sampler The combustion products flowing through the exhaust system can be heavily laden in soot, which would cause rapid clogging of the oxygen measurement system if precautions were not taken. The most important precaution is the specially designed ring sampler (Fig. 28.18), which is installed in the exhaust duct with the intake holes facing away from the direction of airflow. A number of small holes are used so as to provide a certain degree of smoothing with respect to duct flow turbulence.
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V. Babrauskas 2.1 hole, countersunk for #0 flathead screw, 2 places
16 4.65 28.83
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3.2 square stock, silver soldered around 3 sides
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150 220 Burner main body (brass) Section A-A
Pack burner with ceramic fiber batting
4-40 tapped hole, 8 places Section B-B
Fig. 28.17 Calibration burner
Additional Gas Analyzers Many users of cone calorimeters provide not just an oxygen analyzer but also additional gas analyzers to help determine combustion chemistry and toxicity. CO and CO2 analyzers are simply fitted into the same sampling line serving the oxygen analyzer. Other analyzers, for example, H2O, HCI, and total unburned hydrocarbons, require a completely separate, heated sampling line system. Such a system also needs to have a heated soot filter at the front.
Special Issues with Product Testing The cone calorimeter has been used for studying a very wide range of products and materials. In this section, some items of interest are considered where special care needs to
be exerted in configuring the samples or in testing.
Liquids The HRR of liquids is generally not the quantity of interest to regulators and other individuals charged with enforcing fire safety provisions for liquids. In addition, there is no easy way to scale from bench-scale results to large-scale applications. However, some research studies on liquids using the cone calorimeter have been reported. In such studies, use of a circular dish is generally more convenient than using a square specimen. For example, Hayakawa et al. [50] used a 113 mm diameter dish, while Iwata et al. [51] used a 90 mm dish. Liu et al. [52] conducted a study of liquids in the cone calorimeter, accompanied by water mist extinguishment. A number of other studies [53–57] have been reported.
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All material is stainless steel All dimensions in millimeters (except where noted) A 6.35 5.0 mm hole, 4 places, evenly spaced
2.2 mm hole, 12 places, evenly spaced (12 spaces at 30° each) 114.3 76
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Section A-A A
Fig. 28.18 Ring sampler
Electrical Cables In testing electric cables, pyrolysis gases have a pronounced tendency to flow along the length of the cable interior and burn only at the edges rather than uniformly over the surface. For such specimens, it has often been found useful to coat the cable ends with a sodium silicate cement, such as Insa-Lute Adhesive Cement Paste No. 1, produced by the Sauereisen Cements Co. When the ends are sealed in such a manner, a knife puncture must be made in the face of each piece of cable to avoid pressure buildup and rupture. Even though electrical cables are circular rather than flat, it has been found that they can be successfully tested in the cone calorimeter. Normally, 100 mm long cable sections are cut and placed side by side, filling up the specimen holder. For this to be practical, the diameter
should not be excessive, say less than 15 mm or so. ASTM has issued a standard [58] on the testing of electrical cables with the cone calorimeter. In the ASTM standard, the cables may either be cut into sections, or else the insulation material alone is to be tested as a flat plaque. The latter will generally not be practical, since cable manufacturers do not produce the plastic in this form. The ASTM standard also permits the ends to be sealed, or unsealed, when actual cable sections are tested. Grayson et al. [59] documented the results of the FIPEC research program, where electrical cable testing and modeling was done using a wide array of techniques. A very extensive cone calorimeter testing effort is described in this connection. The FIPEC researchers concluded that the best results are obtained when the ends are sealed, except for very small cables
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( : 0:23 ρ V_ Mechanical ϕ¼
Here, Δh is the heat of combustion, Q_ ¼ m_ f Δh is the peak heat release rate of the fire, ΔhO2 ¼ r Δh is the heat of combustion per unit mass oxygen consumed, A0 is the area of the compartment opening, H0 is the height of the opening, ρ is the density of air, and V_ is the volume flow of air into the compartment due to a ventilation system. The factor 0.23 is the mass fraction of oxygen in air. If ϕ < 1,
K. McGrattan and S. Miles
4.
5.
6.
7.
the compartment is considered “wellventilated” and if ϕ > 1, the compartment is considered “under-ventilated.” In general, under-ventilated fire scenarios are more challenging for the models because the combustion physics are more complicated. Relative Distance Along the Ceiling, rcj =H : This ratio indicates the distance from the fire plume of a sprinkler, smoke detector, etc., relative to the compartment height, H. The maximum ceiling jet temperature, important in determining device activation, has been shown to be a function of this ratio. Relative Distance from the Fire, rrad =D: This ratio indicates whether a “target” is near or far from the fire. In general, it is more challenging to predict the radiative heat flux to objects near the fire. Room Length and Width Relative to the Ceiling Height, L/H and W/H: These ratios are useful mainly when assessing an empirical or zone model because most of the correlations used by these models are limited in terms of compartment aspect ratio. For CFD, extreme values of these ratios might indicate unusual fire behavior. Ceiling Height Relative to the Fire Diameter, H/D∗: This ratio is a non-dimensional measure of the height of the fire plume. D∗ is a length scale that incorporates the heat release rate of the fire:
D ¼
!2=5 Q_ pffiffiffi ρ1 cp T1 g
(32.32)
The larger the ratio H/D∗, the more important the plume becomes in the overall scenario. For empirical and zone models, it indicates whether or not the plume entrainment correlation is appropriate. For CFD, it indicates how “high” the plume actually is, in non-dimensional terms.
Quantifying Model Uncertainty Having determined the appropriateness of the chosen experiments, it is now necessary to quantify the accuracy of the model in predicting the
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Modeling Fires Using Computational Fluid Dynamics (CFD)
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Fig. 32.2 A comparison of measured versus predicted wall temperature. The off-diagonal lines indicate the 2e σ bounds for the experiments (long dash) and the model (short dash)
outcome of these experiments. For each quantity of interest, a summary plot of the results should be constructed like the one shown in Fig. 32.2. The accuracy of the model can be expressed in terms of two statistical parameters. The first, δ, is the bias factor. It indicates the extent to which the model, on average, under or over-predicts the measurements. For example, the bias factor for the data shown in Fig. 32.2 is 1.13. This means that the model over-predicts wall temperatures by 13 %, on average, and this is shown graphically by the dash-dot line. The second statistic is the relative standard deviation of the model, e σ M. This indicates the degree of scatter of the points. Referring again to Fig. 32.2, there are two sets of off-diagonal lines. The first set, shown as long-dashed black lines, indicate the estimated experimental uncertainty. The slopes of these lines are 1 2e σ E , i.e. the 95 % confidence interval for the measurements. In this case, e σ E ¼ 0:07. The second set of off-diagonal lines, shown as short-dashed lines, indicates the model uncertainty. The slopes of these lines are δð1 2 e σ M Þ. In this case, e σ M ¼ 0:2. If the model were as accurate as the measurements against which it is compared, the two sets of off-diagonal lines
would merge and the dash-dot bias line would overlap the solid diagonal line. The extent to which the data scatters outside of the experimental bounds is an indication of the degree of model uncertainty. The derivation of these uncertainty statistics is described in [37], and it is summarized here. First, a few assumptions are made: 1. The experimental measurements are assumed to be unbiased, and their uncertainty is assumed to be normally distributed with a constant relative standard deviation, e σE . 2. The model uncertainty is assumed to be normally distributed about the predicted value divided by a bias factor, δ. The relative standard deviation of the distribution is denoted as e σM . Now, given a set of experimental measurements, Ei, and a corresponding set of model predictions, Mi, compute the following: lnðM=EÞ ¼
n 1X lnðMi =Ei Þ n i¼1
(32.33)
The relative standard deviation of the model, e σ M, can be computed from the following equation:
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e σ 2M þ e σ 2E ¼
K. McGrattan and S. Miles n h i2 1 X lnðMi =Ei Þ lnðM=EÞ n 1 i¼1
(32.34) The bias factor is: e σ 2M e σ 2E δ ¼ exp lnðM=EÞ þ 2 2
(32.35)
For a given model prediction, M, the “true” value of the quantity of interest is assumed to be a normally distributed random variable with a mean μ ¼ M/δ and a standard deviation of σ ¼ e σ M ðM=δÞ. Using these values, the probability of exceeding a critical value, xc, is: 1 xc μ pffiffiffi Pðx > xc Þ ¼ erfc (32.36) 2 σ 2 Note that the complimentary error function is defined as follows: Z 1 2 2 erfcðxÞ ¼ pffiffiffi et dt (32.37) π t It is a standard function in most mathematical or spread sheet programs. As an example of the procedure, suppose that the model whose results are plotted in Fig. 32.2 has predicted that the wall temperature within a compartment would peak at a value of 300 ∘C due to a given design fire. Suppose also that the failure criterion for the wall lining material is 325 ∘C. What is the probability that the wall temperature could reach 325 ∘C? First, it is best to work in terms of temperature rise. The ambient temperature is 20 ∘C; thus, the predicted temperature rise, Δ Tp, is 280 ∘C and the critical temperature rise, Δ Tc, is 305 ∘C. From Eq. 32.36, the probability that the temperature could exceed the critical value is: ! 1 ΔTc ðΔTp =δÞ pffiffiffi PðΔT > ΔTc Þ ¼ erfc 2 e σ M ðΔTp =δÞ 2 ! 1 305 ð280=1:13Þ pffiffiffi ffi 0:12 ¼ erfc 2 0:2 ð280=1:13Þ 2 (32.38)
It must be emphasized that this estimated probability of failure is based only on the model uncertainty. It does not account for parameter uncertainty; that is, the uncertainty in the input parameters.
Applications This section presents examples of how CFD fire models are used in practice. These applications can be divided into three general categories— research, design, and forensic. For research, the models can help explain basic fire phenomena. For design, the models are used to predict the spread of smoke and heat from a hypothetical fire in a real or planned building. For forensics, the models aid in the reconstruction of an actual fire. For a design application, the fire is usually specified; that is, the ignition, growth, and eventual decay of the fire are not predicted by the model but rather specified by the design engineer and reviewed by the code enforcing authority. For a reconstruction, the model is usually used to explain how a small fire grew and spread to cause serious damage or injury. Rarely are fire models of the type described in this chapter used to show how a fire was actually ignited, as the physical mechanism of this event (electrical short, arcing fault, arson, etc.) is usually not included in the model.
Fundamental Fire Dynamics CFD, in particular large eddy simulation, provides a convenient means to study basic fire behavior. The most obvious application is the study of fire plumes; for example, predicting the height of the visible flame, the centerline velocity and temperature, and the pulsation frequency. Heskestad’s empirical flame height correlation (Eq. 32.30) is valid for values of Q_ between 0.1 and 10,000, characterizing intermittent grass fires all the way to oil well blowout fires. Figure 32.3 compares FDS predictions with Heskestad’s correlation. Note that the
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Modeling Fires Using Computational Fluid Dynamics (CFD)
Fig. 32.3 Comparison of FDS predictions of flame height from a 1 m square pan fire for Q* values ranging from 0.1 to 10,000
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Smoke Movement
mechanical smoke exhaust, and pressurization of protected spaces. In routine applications, the design of the smoke control measures may often be achieved by recourse to various guidance publications and empirical correlations [40, 41]. Network airflow and zone fire models are also available to assist in the design process. However, where the building space is large or complex in shape, or where a novel ventilation system is proposed, CFD can be a useful tool. Covered shopping malls, atria in hotels and office buildings, leisure complexes, airport terminals, and large warehouses are just some examples of where CFD is being increasingly employed. Many of the earliest examples of the application of CFD to fire engineering were in smoke movement applications [42, 43]. Simulations were at that time restricted to a few tens of thousands of grid cells. Although this number has increased to hundreds of thousands or even millions of cells, many of the modeling issues remain the same and are discussed later [44].
A significant proportion of fire fatalities can be attributed to the inhalation of smoke particulates and toxic gases. Furthermore, the effects of reduced visibility, high temperature, radiative flux, and oxygen depletion may add to the hazard associated with the smoke generated by an enclosure fire. Means to control the movement of smoke include physical barriers, natural or
Smoke Transport in a Mechanically Ventilated Library In collaboration with Olof Granlund Oy, ANSYS Europe Ltd. conducted a CFD analysis of the movement of smoke generated by a fast-growing fire, with a peak heat release rate of 550 kW, inside a library for which the ventilation system was left running in its normal mode of operation.
simulations were run at three different grid resolutions. A useful way to characterize the grid resolution of a fire simulation is via the ratio D∗/δx, where D∗ (Eq. 32.32) is a measure of the effective fire diameter, based on heat release rate, and δx is the size of a grid cell. In effect, D∗/δx is the number of grid cells spanning the effective fire diameter. The fundamental, or “puffing,” frequency is a quantity that the fire model also ought to predict accurately. Figure 32.4 displays sequential flame images for a single puff from a simulation of a 1 m methane fire experiment conducted at Sandia National Laboratories [38]. The dominant puffing mode shows good agreement with the measured puffing frequency of 1.65 Hz. Higher frequency fluctuations from the simulation exhibit the classic 5/3 scaling of Kolmogorov turbulence [39].
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Fig. 32.4 Snapshots of the flame envelope from a simulation of the Sandia 1 m diameter methane pool fire using 1.5 cm grid resolution. The images span a single “puff”
The building has a pitched, vented glass roof and diffusers at various elevations. ANSYS CFX is a general purpose, commercial CFD model that has a history in fire modeling dating back to the investigation of the 1987 Kings Cross fire in London [45]. Because it is designed to handle virtually any type of geometry, a model like this one can employ a numerical mesh that conforms to the unusual shape of the building. In this case, an unstructured mesh with 3.2 million mesh elements was used. Figure 32.5 shows a contour map of visibility distance after 3 min in a vertical slice through the building.
Smoke Transport in a Historic Landmark CFD fire modeling is commonly used during the renovation of historic buildings. Often at issue is the inclusion or exclusion of a fire protection system (sprinklers, exhaust fans, etc.) that might require a variance from the local building code requirements. For example, as part of an overall effort in modernizing the Rhode Island Statehouse (the rotunda is the fourth largest selfsupporting dome in the world), the LES model FDS was used to model a number of fire
scenarios within the structure. The building supervisors wished to avoid having to disrupt the historical fabric of the rotunda while updating the building’s fire protection systems. The model was used to examine a number of fire scenarios and how they might impact the ability of occupants to evacuate the building. Note in Fig. 32.6 the use of rectangular obstructions to approximate the very complicated geometry of the building—a simple alternative to the more CPU intensive body-fitted coordinate system.
Smoke Transport in a Multistory Residential Building To assist means of escape and fire fighter access in high rise residential buildings it is common practice to provide some form of smoke control to the stairwells, which could take the form of a sophisticated pressurization scheme or a relatively simple natural ventilation provision. There may be cases where smoke protection is required also in the corridors and lobbies at each story, possibly as a compensatory measure for extended travel distances. Another approach, adopted in some parts of the world, is to provide
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Modeling Fires Using Computational Fluid Dynamics (CFD)
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Fig. 32.5 Map of visibility in a vertical plane at time ¼ 3 min for a fire in a library building (Figure courtesy: ANSYS Europe Ltd)
Fig. 32.6 Smoke filling analysis of the Rhode island State capitol (Figure courtesy: Hughes Associates)
mechanical ventilation in the corridor. In the event of a fire in an adjoining apartment smoke is purged from the corridor, while at the same time the ventilation system provides smoke protection to the stairwell by the combined action of pressure differentials and open-door airflows akin to a stair pressurization system. CFD modeling of the air and smoke transport in the corridor and stairwell is often required in support of the design, in particular where the corridors
and lobbies have a more complicated layout or the ventilation inlets and outlets cannot be installed in ideal locations.
Tunnels Historically, smoke control inside tunnels was often considered as an afterthought to design of ventilation for the provision of fresh air. Where natural ventilation was insufficient, mechanical ventilation was designed using network flow
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theory aided in recent years by network models. As a two-layer description is generally not valid within a tunnel environment, fire zone models have been applied to tunnels in only a limited number of cases. CFD, however, is now finding increasing application to fire hazard analysis for road tunnels in particular. In recent years a number of major tunnel fire incidents such as the tragedy in the Mont Blanc tunnel in 1999, resulting in 39 deaths, have highlighted the need to understand better the mechanism of fire development and spread inside tunnels. In particular, heat transfer to the tunnel walls is important to account for correctly as this has a strong influence on the distribution of heat along the tunnel, the degree of stratification that can be expected, and the threat to the integrity of the structure. One area where CFD has been applied successfully is in the analysis of the critical velocity required in a longitudinally ventilated tunnel to control the spread of heat and smoke so that it is forced in the downstream direction, providing safe conditions upstream [46]. Another area currently receiving much attention is the choice of design fire for tunnel fire safety design. In the light of the recent tunnel fire incidents and fullscale fire tests [47], the size of the fire load that can be generated from what were previously considered as nonhazardous cargoes has been revised. Heat release rates well in excess of 100 MW have been measured for heavy-goods vehicles carrying commercial merchandize. CFD was used in the investigation into the Mont Blanc tunnel fire incident in 1999. One of the modeling studies involved the use of the JASMINE fire model to re-construct conditions inside the tunnel during the first 30 min, during which time most of the fatalities would have occurred. Using information available on the ventilation settings and the location of vehicles, the model predicted the transport of smoke and heat along the length of the tunnel. The data were then fed into a model for fractional effective dose to enable an assessment of when and how the fatalities occurred. Subsequent parametric simulations were performed to investigate whether alternative tunnel ventilation measures would have helped on the day of the incident [48].
K. McGrattan and S. Miles
Parking Garages The application of CFD to the analysis and design of smoke control systems in basement car parks may share elements that apply also to road tunnels. Not only is the potential fire source similar, the ventilation strategies and performance criteria may well overlap. Two ventilation strategies that might be considered in a basement car park include dilution (purging by fresh air) and the directional control of smoke by the application of applied air flows. While diluting smoke and vehicle emissions can in principle be achieved by ventilating at a specified air change rate, in many cases additional ventilation provisions will be required in order to ensure an even mixing of fresh air and the elimination of stagnant regions. This is commonly achieved by the strategic location of impulse (jet) fans on the underside of the ceiling, which assist the movement of air from the inlet points to the exhaust locations. CFD may be usefully employed to determine the number and location of these fans. The directional control of smoke in the event of a fire, with the objective of providing a relatively smoke free access to the location of the fire for fire fighting personnel, presents a greater challenge than simply purging smoke from the car park. Here careful design of the ventilation system is required, with the impulse fans operating akin to the case of a longitudinally ventilated tunnel, directing the smoke and heat in a direction away from the approaching personnel.
Fire Investigation CFD is increasingly used to reconstruct actual fires, providing fire service personnel and fire investigators with a better understanding of the events that led to injury, loss of life, or loss of the structure. In any reconstruction, the time line of events provided by the first responders and other eyewitnesses is as crucial as the model input, but it is also invaluable in assessing the results. Rendering the results of the simulation as realistically as possible facilitates the synthesis of
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Modeling Fires Using Computational Fluid Dynamics (CFD)
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Fig. 32.7 Comparison of photographs of the Charleston furniture store fire with a numerical simulation. Figure courtesy of NIST
model simulation with photographic and visual evidence. Most people at the fire scene are certainly not experts in CFD, but they are very experienced with fire. Examples of how CFD has been used in actual fire reconstructions are available [49, 50, 51, 52, 53]. As an example, NIST researchers used the Fire Dynamics Simulator to analyze a fire that occurred on the evening of June 18, 2007, in a furniture store in Charleston, South Carolina [54]. Using evidence collected at the scene and eyewitness accounts, the investigators put together a plausible sequence of events that led to the deaths of nine fire fighters. Figure 32.7 presents a snapshot of the numerical simulation compared to a photograph of the actual fire.
Outdoor Applications and Wind Buoyant windblown plumes have been studied since the early 1960s. A summary of the early work together with a useful bibliography is given by Turner [55]. Most of the models described in these works are integral models, where the profiles of physical quantities in cross-sectional planes perpendicular to the wind direction are assumed, together with simple laws relating entrainment into the plume to macroscopic features used to describe its evolution. The potential shortcomings of these types of models are that they were designed for typical industrial sources, like smokestacks, that are much smaller in terms of energy output than a large fire. The plume from an oil or forest fire will rise higher into the atmosphere, and it is difficult to predict the rise based on empirical
correlations. If the plume rise is not calculated correctly, substantial errors in downwind concentration can result. In the case of smoke-stack emissions, the plume does not rise appreciably high, reducing the uncertainty of the results. Most of the assumptions required by integral models can be removed by taking advantage of the advances in CFD over the past few decades. For example, as part of the process of evaluating the feasibility of using in situ burning as a remediation tool for large oil spills, NIST developed a numerical model, ALOFT (A Large Out-door Fire plume Trajectory), to predict the concentration of smoke and other combustion products downwind of a large fire [56]. The model is simply a variant of the large eddy simulation model FDS, with a simplified plume rise model coupled with a coarsely gridded wind calculation spanning tens of kilometers (Fig. 32.8). This combination of models is not unusual for outdoor application, as the range of length scales spans at least three orders of magnitude.
Virtual Experiments Many codes and standards for fire protection are based upon simple room geometries. For example, the spacing for smoke detectors has historically been based upon smooth, level ceilings with some additional rules for beams, slope, and height. Under those rules a single story room with a 30 m by 30 m smooth ceiling could be protected by a grid of nine smoke detectors, but a ceiling of waffle concrete construction (Fig. 32.9) with structural deep beams 1 m on center, could, under a strict interpretation
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Fig. 32.8 Simulation of smoke from a large oil fire in the Valdez narrows, Alaska (Figure courtesy of NIST)
Fig. 32.9 Simulation of smoke filling under a coffered ceiling (Figure courtesy: Aon Fire Protection Engineering Corp.)
of the guidelines, require 900 detectors, one in each beam pocket. While this is obviously unreasonable, making a change to the building code requires evidence. In lieu of a large number of
costly full-scale experiments, a small set of full-scale experiments was combined with a large set of “virtual” experiments done with CFD [57, 58]. The researchers evaluated the
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Modeling Fires Using Computational Fluid Dynamics (CFD)
appropriateness of the prescriptive provisions and identified ceiling structure parameters, which if altered, would cause significant differences in smoke detection performance as compared to a smooth level ceiling. It had been believed that such beam projections would significantly delay the activation time. The use of CFD modeling showed this expectation to be incorrect and a subsequent full-scale experimental study proved the general findings of the CFD analysis [59]. The final result of the study led to an exception, under some circumstances, to the code requirement of a smoke detector in every beam pocket.
The Role of CFD in the Design Process As discussed elsewhere in this chapter, CFD has an ever increasing role to play in the development of fire safety science, and has an important contribution to make in better understanding the fundamentals such as flame spread and chemical species production where it is being used in parallel with physical experiments. However, it is as a fire engineering design tool that CFD is probably of most relevance to the majority of readers. Here a few words of caution are worth noting. CFD modeling has a useful, and sometimes critical, role in developing safe and robust fire engineering solutions where the control of smoke and heat generated by fire forms part of the fire safety strategy. It allows architectural designs to be adopted that in previous eras would have been difficult to justify, for example in respect to smoke control in large and complicated building atria or where a reduced level of structural fire protection is desired. It should, however, be seen as a contributing component to the overall design process, and not as a “black box” that faithfully provides the correct answers regardless of the inputs and assumptions made. A great deal of care and experience is required in order to sensibly use CFD in support of fire engineering designs, and it should be employed alongside simpler calculation and design methods wherever possible to confirm that the CFD results are comparable to the empirical correlations
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that have traditionally been applied in fire protection engineering. It is as a parametric design tool that CFD is often most gainfully employed, allowing the impact of varying the input and boundary conditions to be examined. For example, how sensitive is the smoke control solution to the design fire size, or how much influence does a change in wind direction have on a natural smoke ventilation strategy? The reader is encouraged to consult the guidance documents available on the best practice use of CFD in the various application areas and to consult the guidance documentation provided with the CFD model being employed. For example, the guidance document prepared by the US Nuclear Regulatory Commission and the Electrical Power Research Institute (EPRI) on fire modeling for nuclear power plants [60] includes useful information on the appropriate role and application of CFD in the fire safety design process, and is relevant also to fire scenarios outside the nuclear field.
Summary Computational fluid dynamics modeling of fire has made tremendous progress over the past few decades as our understanding of fire improves and as computers get ever faster. However, although it appears to many that CFD is the cutting edge of fire protection engineering, many non-modelers are surprised to learn that our ability to reproduce fire phenomena via computer simulation lags our empirical understanding by about 10 years. Indeed, current-generation models address transport phenomena reasonably well, making them useful for many engineering applications. However, they have not yet reached the point of reliably predicting, for large-scale applications, such important phenomena as flame spread, extinction, suppression, and CO and smoke production, all of which demand more detailed chemistry and physics than are currently incorporated in the models. Moving forward will require a new generation of engineers who have expertise in fire physics, mathematics, and computer science to build on
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K. McGrattan and S. Miles
the knowledge possessed by the current generation of modelers. This chapter sets forth the basic elements to lay the foundation of further study for future modelers, and it also provides the current practitioner with a better understanding of the models being used.
κ λ μ μt ρ σ τ
Radiation absorption coefficient Generalized diffusion coefficient Dynamic viscosity Turbulent viscosity (in eddy viscosity turbulence model) Density Stefan-Boltzmann constant Stress tensor
Nomenclature cp Dα f h hc I k m_ 000 α p Pr q q_ 00 q_ 000 R s s Si j Sc t T u ¼ (u, v, w) W x ¼ (x, y, z) Yα
Specific heat Material diffusivity of species α External body force Sensible enthalpy Convective heat transfer coefficient Radiant intensity Thermal conductivity; turbulent kinetic energy Mass production (destruction) rate of species α per unit volume Pressure Prandtl number Heat flux vector Heat release rate per unit area Heat release rate per unit volume Universal gas constant Direction vector Stoichiometric air requirement of the fuel Strain tensor Schmidt number Time Temperature Velocity vector Average molecular weight Position vector Mass fraction of species α
Greek Letters ε
Rate of dissipation of turbulent kinetic energy
Appendix Much of the difficulty in learning and applying computational fluid dynamics is the complexity of the governing equations. In this appendix, some of the common terms found in the mass, momentum, and energy equations are expanded. Many of the variables and operators can be represented as 3 3, 1 3, or 3 1 matrices, and the expansions can be carried out following the rules of linear algebra. For example, the divergence of the flow vector, ∇ u, is a scalar formed by multiplying the 1 3 gradient operator ∇ and the 3 1 vector u. On the other hand, the product of the velocity vectors, u u, is found by multiplying a 3 1 vector by a 1 3 vector: 0 1 1 0 2 u uv uw u B C C B uu ¼ @ v Aðu; v; wÞ ¼ @ vu v2 vw A w wu wv w2 (32.39) Thus, the convection term in the momentum conservation equation can be expanded as follows: 1 0 ρu2 ρuv ρuw C @ @ @ B B ρvu ρv2 ρvw C r ðρuuÞ ¼ A @x @y @z @ 2 ρwu ρwv ρw 0 1T 2 ðρu Þx þ ðρvuÞy þ ðρwuÞz B C B C ¼ B ðρuvÞx þ ðρv2 Þy þ ðρwvÞz C @ A ðρuwÞx þ ðρvwÞy þ ðρw2 Þz (32.40)
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Modeling Fires Using Computational Fluid Dynamics (CFD)
The result is a vector whose components form the convective terms of the three component momentum equation. Note that here the subscripts x, y, and z denote partial derivatives with respect to that particular coordinate direction. The term for the viscosity in the momentum equation, ∇ τ, is deceptively simple. In reality, it is not, and because it constitutes the heart of the debate over turbulence models, some attention must be paid to it. Using customary tensor notation, the viscous stress tensor is defined as @ui @uj 2 τij ¼ μ þ δij r u ; @xj @xi 3 ( (32.41) 1 if i ¼ j δij ¼ 0 if i 6¼ j These expressions assert that the viscous stresses are linearly related to the strains, the very definition of a Newtonian fluid. The proportionality constant, μ, is called the dynamic viscosity of the fluid. The viscous stress tensor can also be represented as a 3 3 matrix: 0
1 0 1 2ux uy þ vx uz þ wx ru 0 0 2@ @ A 2 vy vz þ wy 0 ru 0 A τ ¼ μ vx þ uy 3 wx þ uz wy þ vz 2wz 0 0 ru
(32.42) The dissipation function, ε, is a scalar formed by the dot product of two 3 3 matrices: ε τ ru ¼ μ 2u2x þ 2v2y þ 2w2z 2 þ ðvx þ uy Þ2 þ ðwy þ vz Þ2 þ ðuz þ wx Þ2 ðr uÞ2 3
(32.43)
References 1. P.G. Drazin, editor. Collected Papers of LF Richardson, Volume 1: Meteorology and Numerical Analysis. Cambridge University Press, Cambridge, UK, 1993.
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2. D.A. Anderson, J.C. Tannehill, and R.H. Pletcher. Computational Fluid Mechanics and Heat Transfer. Hemisphere Publishing Corporation, Philadelphia, PA, 1984. 3. J.H. Ferziger and M. Peric. Computational Methods for Fluid Dynamics. Springer-Verlag, Berlin, second edition, 1999. 4. S.V. Patankar. Numerical Heat Transfer and Fluid Flow. Hemisphere Publishing, New York, 1980. 5. R. Peyret and T.D. Taylor. Computational Methods for Fluid Flow. Springer-Verlag, New York, 1983. 6. K. Versteeg and W. Malalasekera. An Introduction to Computational Fluid Dynamics – The Finite Volume Method. Longmann, Essex, UK, 1995. 7. G. Cox. Combustion Fundamentals of Fire, chapter Compartment Fire Modelling. Academic Press, London, 1995. 8. G. Cox. Turbulent closure and the modelling of fire using computational fluid dynamics. Phil. Trans. R. Soc. Lond. A, 356:2835–2854, 1998. 9. V. Novozhilov. Computational Fluid Dynamics Modeling of Compartment Fires. Progress in Energy and Combustion Science, 27:611–666, 2001. 10. S. Olenick and D. Carpenter. An Updated International Survey of Computer Models for Fire and Smoke. Journal of Fire Protection Engineering, 13:87–110, May 2003. 11. R.G. Rehm and H.R. Baum. The Equations of Motion for Thermally-Driven, Buoyant Flows. Journal of Research of the National Bureau of Standards, 83:297–308, 1978. 12. V. Yakhot, S.A. Orszag, S. Thangam, T.B. Gatski, and C.G. Speziale. Development of Turbulence Models for Shear Flows by a Double Expansion Technique. Physics of Fluids A, 4:1510–1520, 1992. 13. D.C. Wilcox. Turbulence Modeling for CFD. DCW Industries, La Can˜ada, CA, third edition, 2006. 14. J. Smagorinsky. General Circulation Experiments with the Primitive Equations. I. The Basic Experiment. Monthly Weather Review, 91(3):99–164, 1963. 15. S.B. Pope. Ten Questions Concerning the Large-Eddy Simulation of Turbulent Flows. New Journal of Physics, 6:1–24, 2004. 16. P.R. Spalart, W.H Jou, M. Stretlets, and S.R. Allmaras. Comments on the Feasibility of LES for Wings and on the Hybrid RANS/LES Approach. In Proceedings of the First AFOSR International Conference on DNS/LES, Louisiana Tech University, 1997. Air Force Office of Aerospace Research. 17. D.B. Spalding. Mixing and Chemical Reaction in Steady State Confined Turbulent Flames. In 13th Symposium (International) on Combusion, pages 649–657, Pittsburgh, PA, 1971. The Combustion Institute. 18. B.F. Magnussen and B.H. Hjertager. On Mathematical Modelling of Turbulent Combustion with Special Emphasis on Soot Formation and Combustion. In 16th
1064 Symposium (International) on Combustion, pages 719–729, Pittsburgh, PA, 1976. The Combustion Institute. 19. S.D. Miles, S. Kumar, and G. Cox. Comparison of ‘Blind Predictions’ of a CFD Model with Experimental Data. In Proceedings of the 6th International Symposium on Fire Safety Science, pages 543–554. International Association of Fire Safety Science, 2000. 20. J. Holen, M. Brostrom, and B.F. Magnussen. Finite Difference Calculation of Pool Fires. In 23rd Symposium (International) on Combustion, pages 1677–1683, Pittsburgh, PA, 1990. The Combustion Institute. 21. N. Peters. Laminar Flamelet Concepts in Turbulent Combustion. In 21st Symposium (International) on Combustion, pages 1231–1250, Pittsburgh, PA, 1986. The Combustion Institute. 22. P.A. Tesner, T.D. Snegirova, and V.G. Knorre. Kinetics of Dispersed Carbon Formation. Combustion and Flame, 17:253–260, 1971. 23. R. Siegel and J.R. Howell. Thermal Radiation and Heat Transfer. Taylor and Francis, New York, fourth edition, 2002. 24. S. Hostikka and K.B. McGrattan. Numerical Modeling of Radiative Heat Transfer in Water Sprays. Fire Safety Journal, 41:76–86, 2006. 25. C. DiBlasi. Modeling and Simulation of Combustion Processes of Charring and Non-Charring Solid Fuels. Progress in Energy and Combustion Science, 19:71–104, 1993. 26. B.E. Launder and D.B. Spalding. The Numerical Computation of Turbulent Flows. Computer Methods in Applied Mechanics and Engineering, 3:269–289, 1974. 27. T. Jin. SFPE Handbook of Fire Protection Engineering, chapter Visibility and Human Behaviour in Fire Smoke. National Fire Protection Association, Quincy, MA, fourth edition, 2008. 28. G.W. Mulholland. SFPE Handbook of Fire Protection Engineering, chapter Smoke Production and Properties. National Fire Protection Association, Quincy, MA, fourth edition, 2008. 29. B.P. Husted, J. Carlsson, and U. Goransonn. Visibility Through Inhomogeneous Smoke Using CFD. In Proceedings of Interflam 2004, pages 697–702, Edinburgh, 2004. 30. G. Heskestad and R.G. Bill. Quantification of Thermal Responsiveness of Automatic Sprinklers Including Conduction Effects. Fire Safety Journal, 14:113–125, 1988. 31. G.M. Makhviladze, J.P. Roberts, O.I. Melikhov, and V.I. Melikhov. Numerical Simulation of Sprinkler Jet-Fire Interaction for Compartment Fires. In Proceedings of the 2nd International Seminar on Fire and Explosion Hazard of Substances and Venting of Deflagrations, pages 485–496, Moscow, August 1997. All-Russian Institute for Fire Proection.
K. McGrattan and S. Miles 32. S. Welch, S. Miles, S. Kumar, T. Lemaire, and A. Chan. FIRESTRUC – Integrating Advanced Three-dimensional Modelling Methodologies for Predicting Thermo-mechanical Behaviour of Steel and Composite Structures Subjected to Natural Fires. In Proceedings of the 9th International Symposium on Fire Safety Science, pages 1315–1326, Karlsruhe, Germany, September 2008. International Association of Fire Safety Science. 33. D.B. Spalding. A Novel Finite Difference Formulation for Differential Expressions Involving Both First and Second Derivatives. International Journal for Numerical Methods in Engineering, 4:551–559, 1972. 34. Society of Fire Protection Engineers, Bethesda, Maryland. Guidelines for Substantiating a Fire Model for a Given Application, 2011. 35. K. Hill, J. Dreisbach, F. Joglar, B. Najafi, K. McGrattan, R. Peacock, and A. Hamins. Verification and Validation of Selected Fire Models for Nuclear Power Plant Applications. NUREG 1824, United States Nuclear Regulatory Commission, Washington, D.C., 2007. 36. G. Heskestad. Luminous Heights of Turbulent Diffusion Flames. Fire Safety Journal, 5:103–108, 1983. 37. K. McGrattan and B. Toman. Quantifying the predictive uncertainty of complex numerical models. Metrologia, 48:173–180, 2011. 38. S. R. Tieszen, T. J. O’Hern, R. W. Schefer, E. J. Weckman, and T. K. Blanchat. Experimental study of the flow field in and around a one meter diameter methane fire. Combustion and Flame, 129:378–391, 2002. 39. Stephen B. Pope. Turbulent Flows. Cambridge University Press, 2000. 40. J.H. Klote and J.A. Milke. Principles of Smoke Management. American Society of Heating, Refrigerating and Air Conditioning Engineers (ASHRAE), Atlanta, GA, 2002. 41. National Fire Protection Association, Quincy, MA. NFPA 92B, Standard for Smoke Management Systems in Malls, Atria and Large Spaces, 2005. 42. K.A. Pericleous, D.R.E. Worthington, and G. Cox. The Field Modelling of Fire in an Air-Supported Structure. In Proceedings of the 2nd International Symposium on Fire Safety Science, pages 871–880, Tokyo, 1988. Hemisphere Publishing Corporation. 43. G. Cox, S. Kumar, P. Cumber, V. Thomson, and A. Porter. Fire Simulation in the Design Evaluation Process: An Exemplification of the Use of a Computer Field Model. In Proceedings of the 5th Interflam Conference, pages 55–66, Canterbury, UK, 1990. 44. S. Kumar and G. Cox. Some Guidance on Correct Use of CFD Models for Fire Applications with Examples. In Proceedings of Interflam 2001, pages 823–834, Edinburgh, 2001. 45. S. Simcox and N.S. Wilkes. Computer Simulation of the Flows of Hot Gases from the Fire at King’s Cross Underground Station. Fire Safety Journal, 18:49–73, 1992.
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46. C.C. Hwang and J.C. Edwards. The Critical Ventilation Velocity in Tunnel Fires – A Computer Simulation. Fire Safety Journal, 40:213–244, 2005. 47. H. Ingason and A. Lo¨nnermark. Heat Release Rates from Heavy Goods Vehicle Trailer Fires in Tunnels. Fire Safety Journal, 40:646–668, 2005. 48. S. Miles and S. Kumar. Computer Modelling to Assess the Benefits of Tunnel Sprinkler and Ventilation Fire Safety Measures. In Proceedings of 5th International Conference on Tunnel Fires, pages 23–32, London, 2004. Tunnel Management International. 49. W.L. Grosshandler, N. Bryner, D. Madrzykowski, and K. Kuntz. Report of the Technical Investigation of The Station Nightclub Fire. NIST NCSTAR 2, National Institute of Standards and Technology, Gaithersburg, MD, 2005. 50. K.B. McGrattan, C. Bouldin, and G.P. Forney. Federal Building and Fire Safety Investigation of the World Trade Center Disaster: Computer Simulation of the Fires in the WTC Towers. NIST NCSTAR 1-5F, National Institute of Standards and Technology, Gaithersburg, MD, 2005. 51. D. Madrzykowski and R.L. Vettori. Simulation of the Dynamics of the Fire at 3146 Cherry Road NE, Washington, D.C., May 30, 1999. NISTIR 6510, National Institute of Standards and Technology, Gaithersburg, MD, 2000. 52. D. Madrzykowski and W.D. Walton. Cook County Administration Building Fire: Heat Release Rate Experiments and FDS Simulations. NIST Special Publication 1021, National Institute of Standards and Technology, Gaithersburg, MD, 2004. 53. A.M. Christensen and D.J. Icove. The Application of NIST’s Fire Dynamics Simulator to the Investigation of Carbon Monoxide Exposure in the Deaths of Three Pittsburgh Fire Fighters. Journal of Forensic Sciences, 49(1):1–4, 2004. 54. N.P. Bryner, S.P. Fuss, B.W. Klein, and A.D. Putorti. Technical Study of the Sofa Super Store Fire - South Carolina, June 18, 2007. NIST Special Publication 1118, National Institute of Standards and Technology, Gaithersburg, MD, 2011.
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55. J.S. Turner. Buoyancy Effects in Fluids. Cambridge University Press, Cambridge, UK, 1973. 56. H.R. Baum, K.B. McGrattan, and R.G. Rehm. Simulation of Smoke Plumes from Large Pool Fires. In Proceedings of the 25th (International) Symposium on Combustion, pages 1463–1469, Pittsburgh, PA, 1994. The Combustion Institute. 57. D.J. O’Connor, E. Cui, M.J. Klaus, C.H. Lee, C. Su, Z. Sun, M. He, Y. Jiang, J. Vythoulkas, and T. Al-Farra. Smoke Detector Performance for Level Ceilings with Deep Beams and Deep Pocket Configurations. Fire Protection Research Foundation report, National Fire Protection Association, Quincy, MA, 2006. 58. C. Mealy, J. Floyd, D. Gottuk, and S. Riahi. Smoke Detector Spacing Requirements for Complex Beamed and Sloped Ceilings. Fire Protection Research Foundation report, National Fire Protection Association, Quincy, MA, 2008. 59. D. Gottuk, C. Mealy, and J. Floyd. Smoke Transport and FDS Validation. In Fire Safety Science – Proceedings of the 9th International Symposium, pages 129–140, Karlsruhe, Germany, September 2008. International Association of Fire Safety Science. 60. D. Stroup and R. Wachowiak. Nuclear Power Plant Fire Modeling Analysis Guidelines. NUREG 1934, United States Nuclear Regulatory Commission, Washington, D.C., 2012. Kevin McGrattan is a mathematician in the Fire Research Division at the National Institute of Standards and Technology in Gaithersburg, Maryland. He is the principal developer of the Fire Dynamics Simulator (FDS) Stewart Miles, qualified originally as a physicist, is currently a practicing fire engineer at International Fire Consultants Ltd. in the UK. Previously he worked in fire research and engineering at the UK Building Research Establishment, where he contributed to the development of the CFD fire model JASMINE
Enclosure Smoke Filling and Fire-Generated Environmental Conditions
33
Frederick W. Mowrer
Introduction Fires in buildings and other structures are distinguished from outdoor fires by the confinement effects associated with enclosure boundaries and by the ventilation effects associated with openings in these boundaries. The confinement of heat and smoke released by a fire in an enclosure gives rise to the evolution of fire-generated environmental conditions that can threaten life safety and cause thermal and nonthermal damage to the structure and its contents. For performance-based building fire safety analysis and design, it is important to be able to calculate the environmental conditions generated by fires in enclosures in order to evaluate the threat levels posed by anticipated fire scenarios. This chapter addresses the enclosure smoke-filling process and the fire-generated environmental conditions that develop within an enclosure during this process. The concept of available safe egress time (ASET) has become a fundamental aspect of performance-based analysis of life safety from fire. In general, life safety from fire is achieved if the required safe egress time (RSET) is shorter than the available safe egress time (i.e., RSET < ASET) for the range of expected fire scenarios. The time it takes to evacuate a space, the RSET, F.W. Mowrer (*) Director of Fire Protection Engineering Programs, California Polytechnic State University, San Luis Obispo, CA, USA
is addressed by Boyce and Gwynne (see Chap. 64) and Gwynne and Rosenbaum (Chap. 59). The available safe egress time is addressed in this chapter in terms of the time it takes for the smoke layer to descend and immerse people located within the fire enclosure and in terms of the hazards associated with firegenerated conditions within the smoke layer. The control volume, or zone modeling, approach presented by Wade (Chap. 29) is used as the basis for the analyses presented here. A number of explicit equations for evaluating the smoke layer interface position and the average conditions within a smoke layer are presented in this chapter for certain idealized fire scenarios. These closed-form equations, sometimes called “hand calculations” because they can be solved without the aid of a computer, are useful for estimating smoke layer interface position and average smoke layer conditions for the range of applications for which these equations are valid. For more detailed analyses and for scenarios where hand calculations are impractical or not valid, use of either a computer-based zone model or a computational fluid dynamics (CFD) model may be warranted to evaluate fire-generated conditions in an enclosure. Such computerbased models will generally be needed to evaluate multiroom fire scenarios and may be preferred to evaluate single room scenarios. The concepts presented here are relevant to the computer-based zone fire models, but the complexities associated with keeping track of multiroom fire scenarios are not addressed.
M.J. Hurley (ed.), SFPE Handbook of Fire Protection Engineering, DOI 10.1007/978-1-4939-2565-0_33, # Society of Fire Protection Engineers 2016
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Computer-based zone models are addressed by Walton, Carpenter, and Wood (see Chap. 31), whereas computer-based CFD models are addressed by McGrattan and Miles (see Chap. 32).
Background The first efforts to characterize the enclosure smoke-filling process and the environmental conditions generated by a fire in a closed room can be traced to the late 1970s and early 1980s. The seminal paper on this topic was published in 1978 by Zukoski [1], who applied thermodynamic control volume concepts to evaluate mass and energy balances within a closed room subjected to a fire. Shortly thereafter, Cooper applied Zukoski’s concepts to develop the available safe egress time (ASET) model [2, 3], a computer-based fire model designed to calculate the evolution of the descending smoke layer interface position and the average temperature and smoke concentration conditions within the smoke layer in response to specified fires. During the early 1980s, Walton [4] converted the original ASET model from FORTRAN to BASIC and simplified the numerical methods used in the model to allow its convenient application on the desktop personal computers that were just then starting to be used in engineering practice; this version of the model was known as ASET-B. Since its original development, various versions of the ASET model have been incorporated into different fire modeling suites, such as FPETOOL [5]. Hurley [6] has compared ASET-B model predictions with large-scale experimental test data. During the early 1990s, Mowrer [7] addressed the evolution of fire and smoke conditions in a closed room as part of the development of the FIVE Methodology [8] (see Chap. 89) for evaluating fire-induced vulnerabilities in commercial nuclear power plants. Subsequently, Milke and Mowrer [9] expanded this analysis for application to smoke management systems in atria and covered malls. This application has been incorporated into the NFPA 92B, Standard
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for Smoke Management Systems in Malls, Atria and Large Spaces [10] and is discussed further by Milke (see Chap. 51). More recently, Mowrer [11] has revisited the enclosure smoke-filling process, recasting its formulation in terms of the volumetric flow rates generally used for ventilation system design. Mowrer [12] has also addressed the role of mechanical ventilation on smoke filling and management in terms of these volumetric flow rates. Matsuyama et al. [13] and Delichatsios [14] have developed closed-form solutions for enclosure smoke filling, whereas Delichatsios [15] has also addressed tenability conditions and filling times for fires in large spaces.
Stages of Enclosure Fires Enclosure fires go through a series of stages that depend on the size and shape of the enclosure, the thermal properties of the boundary materials, the sizes and locations of ventilation pathways through the enclosure boundaries, and the development of the fire. Mowrer [11] has identified the four stages of enclosure fires as • Fire plume/ceiling jet stage • Enclosure smoke filling stage • Preflashover vented stage • Postflashover vented stage
Fire Plume/Ceiling Jet Stage During the first stage of an enclosure fire, the fire plume/ceiling jet stage, air is entrained into the flame region, where it mixes with fuel being released from the fuel surface and burns, typically in a nonpremixed (diffusion) flame. The energy released by the combustion reaction causes the temperature of the combustion products to increase and their density to decrease. Because these combustion products are less dense than the surrounding air, they rise through the surrounding air in a buoyant coherent stream known as the fire plume, as shown in Fig. 33.1. As the buoyant gases rise in the fire plume, additional air is entrained into the fire
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plume, causing the temperature and smoke concentration within the plume to decrease while causing the volume of smoke, which is defined to include the actual combustion products as well as the entrained air, to increase with increasing height above the fire source. Phenomena associated with fire plumes are addressed in more detail by Heskestad (see Chap. 13). When the fire plume impinges on a smooth horizontal ceiling, the buoyant gases turn and spread out radially beneath the ceiling in a
F.W. Mowrer
relatively thin layer known as the ceiling jet, as shown in Fig. 33.1. These gases continue to spread radially beneath the ceiling until they are confined by the enclosing walls of the fire room. The impingement of the plume at the ceiling and the confinement of flow beneath the ceiling constitute the first significant distinction between an enclosure fire and an outdoor fire. Ceiling jets are addressed in more detail by Alpert (see Chap. 14).
Enclosure Smoke-Filling Stage
Fig. 33.1 The fire plume/ceiling jet stage of an enclosure fire
Fig. 33.2 The smokefilling stage of an enclosure fire
Once the ceiling jet reaches the wall boundaries, the smoky gases in the ceiling jet turn downward and begin to accumulate beneath the ceiling, as shown in Fig. 33.2. This begins the second stage of enclosure fires, the smoke-filling stage. During the smoke-filling stage, smoke is injected via the fire plume into the developing smoke layer, where the buoyant smoke accumulates beneath the ceiling. The smoke layer interface descends within the enclosure as a result of continued smoke injection via the plume. If no sizable vents are available in the enclosure boundaries, the smoke layer will continue
33
Enclosure Smoke Filling and Fire-Generated Environmental Conditions
to descend until it reaches either the elevation of the fire source or the floor. Enclosure boundaries in buildings are generally leaky enough to prevent significant pressure increases as a result of the gas expansion associated with enclosure fires. In a closed room, the smoke layer may descend to the level of the fire and act to suppress the fire due to oxygen depletion within the smoke layer, much as a candle flame will extinguish when placed beneath an inverted jar. On the other hand, if a vent is opened, such as a window that breaks from heat-induced stresses or a door that is opened by fire fighters, such a fire may rapidly redevelop due to the influx of fresh air. With an influx of fresh air, a backdraft explosion [16] may occur if sufficient unburned fuel vapors have accumulated within the room.
Preflashover Vented Stage If one or more open wall vents are provided from the fire space, such as a window to the outside or a doorway to an adjacent space, then the smoke will flow from the enclosure into the adjacent space once the smoke layer descends to the level where a wall vent is available, as illustrated in Fig. 33.3. This begins the third stage of
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enclosure fires, the preflashover vented stage. During this stage, the smoke layer will descend to the elevation where the flow of air into the fire room is balanced by the flow of smoke out of the fire room. In many cases, both the inflow of air and the outflow of smoke will be through the same wall vent, as illustrated in Fig. 33.3. Vent flows are addressed in more detail by Tanaka (see Chap. 15).
Postflashover Vented Stage The fourth stage of enclosure fires, the postflashover vented stage, occurs if the fire intensifies to the point where the smoke layer reaches a temperature sufficient to cause the radiant ignition of exposed combustible surfaces within the fire enclosure, as illustrated in Fig. 33.4. Either an average smoke layer temperature of approximately 600 C or an incident heat flux of approximately 20 kW/m [2] at floor level is often used as an indication of the onset of flashover. Methods for estimating the heat release rates necessary to cause flashover and for estimating smoke layer temperatures resulting from pre- and postflashover vented fires are addressed by Walton, Thomas and Ohmiya (see Chap. 30).
Fig. 33.3 The preflashover vented stage of an enclosure fire
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F.W. Mowrer
T ~ 600°C
Fig. 33.4 The postflashover vented stage of an enclosure fire Fig. 33.5 Control volumes and phenomena associated with enclosure smoke filling
ρu, Tu, Vu
zu
Vpl + Vexp
Smoke layer
me , Vexp (Case 2)
mpl Plume
H
mpl , Vpl
zl Qf zf
Phenomena Associated with Modeling of Enclosure Smoke Filling Phenomena associated with the modeling of enclosure smoke filling are described in this section. The basic phenomena associated with this stage of enclosure fires are illustrated in idealized form in Fig. 33.5. A fire located at some arbitrary elevation, zf, above the floor of a room is represented as a point source of heat addition, Q_ f , to the space. A fraction, χl, of the heat released by the fire is lost by heat transfer to the boundaries of the enclosure or to other surfaces within the enclosure, while the remaining fraction, (1 – χl), causes heating and
ρl, Tl, Vl
Lower layer
me , Vexp (Case 1)
expansion of gases within the enclosure. Of the heat released by the fire, a fraction, χr, is radiated away from the combustion zone, while the remaining fraction, χc ¼ 1 – χr, is convected in the buoyant plume that rises from the fire source to the ceiling. The plume entrains surrounding air as it rises through the atmosphere. Combustion products and entrained air are transported along with convected heat to the ceiling, where the plume turns to form a ceiling jet that spreads radially beneath the ceiling. When the ceiling jet reaches the wall boundaries of the enclosure, it is deflected downward. For purposes of modeling enclosure smoke filling, it is common to neglect the ceiling jet altogether and to assume that the
33
Enclosure Smoke Filling and Fire-Generated Environmental Conditions
enclosure begins to fill uniformly with smoke from the ceiling down due to the injection of smoke into the smoke layer via the fire plume. This is the approach taken here. The developing smoke layer is normally treated as a distinct control volume with uniform properties for zone modeling purposes. As a modeling idealization, the upper and lower layer control volumes are assumed to be separated by a distinct thermal discontinuity at the interface between the two layers. This interface is known as the smoke layer interface. The smoke layer descends within the enclosure due to the entrainment of fresh air from the lower layer into the fire plume and, depending on the location of leakage paths from the enclosure to surrounding spaces, the expansion of heated gases in the upper layer. Mechanical ventilation will also influence the development of the smoke layer and the conditions within the smoke layer; it is not included in this discussion of general phenomena, but the influence of mechanical ventilation on the development of the smoke layer and the conditions within the smoke layer is addressed in a subsequent section of this chapter. The expansion of gases within the enclosure due to heat addition pressurizes the enclosure relative to adjacent spaces and forces the flow of gases from the enclosure through available leakage paths. Three different cases are addressed to consider these pressure effects for different leakage flow cases. First, a global analysis is presented where the entire enclosure is treated as a single, fixed control volume assumed Fig. 33.6 Smoke recirculation associated with smoke layer descent to fuel surface
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to have uniform conditions throughout. The primary purpose of this global analysis is to address pressure effects, but this global analysis is also instructive with respect to temperature and smoke concentration effects, providing a basis for comparison of the more detailed smoke layer descent analyses. This global analysis is followed by two smoke layer descent analyses, designated as Cases 1 and 2, that address the descending smoke layer explicitly in terms of upper and lower layer control volumes. Leakage paths are assumed to be at floor level only in Case 1 and at ceiling level only in Case 2, as illustrated in Fig. 33.5. Case 1 is the scenario addressed by the ASET model [2]. As shown in the subsequent analysis of these two cases, the location of leakage paths does not have a large influence on smoke layer development or conditions. Once the smoke layer descends to the elevation of the fire source, the fire source becomes immersed in the smoke layer, and further entrainment of fresh air from the lower layer is assumed to cease. After this time, the fire will entrain and recirculate smoke from within the smoke layer, as illustrated in Fig. 33.6, and the smoke layer will continue to descend due only to gas expansion. Because fresh air is no longer being entrained into the fire, the intensity of the fire will eventually diminish due to oxygen depletion within the smoke layer. As a fire in a closed compartment diminishes due to oxygen depletion, the rate of heat losses to enclosure boundaries will become greater than
zu
me , Vexp (Case 2)
Vexp
H
Smoke layer
ρu, Tu, Vu
zl
Qf zf
ρl, Tl, Vl
Lower layer
me , Vexp (Case 1)
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F.W. Mowrer
the rate of heat addition due to the fire. The smoke will cool and contract as a consequence, causing the fire enclosure to depressurize relative to adjacent spaces. This depressurization will draw air into the enclosure from surrounding spaces, which in turn may allow the fire to reintensify and repressurize the enclosure. This cycle of depressurization and repressurization, sometimes called puffing behavior, can repeat indefinitely and is one of the warning signs of an underventilated fire, which may result in a backdraft if a large ventilation opening is suddenly provided in an enclosure boundary.
Global (One-Zone) Analysis In this section, the entire enclosure gas volume is treated as a fixed control volume, as shown in Fig. 33.7. Zukoski [1] addressed the pressure rise that would occur in both sealed and leaky enclosures by considering this global control volume. In both the sealed and leaky cases, a general energy balance for the enclosure control volume can be written as dU dV ¼ Q_ net þ m_ i hi m_ o ho P dt dt
ð33:1Þ
where U is the total internal energy in the control volume and Q_ net is the net rate of heat addition into the space; it is equal to the difference between the actual heat release rate of the fire,
Q_ f , and the rate of heat loss, Q_ l , to boundaries and other solid surfaces, such as equipment located within the space. Many fire models calculate boundary heat losses explicitly, usually in terms of one-dimensional heat transfer through a slab. For the present discussion, a constant heat loss fraction, χl, is used to represent boundary heat losses, such that Q_ net ¼ Q_ f Q_ l ¼ Q_ f ð1 χ l Þ
ð33:2Þ
This is the approach taken by Cooper [2, 3], who suggests values for χl in the range of 0.6–0.9 for most situations. Cooper suggests that values near the low end of this range are appropriate for spaces with smooth ceilings and large ceiling area to height (A/H2) ratios. Values near the high end of the range would be appropriate for spaces with irregular ceiling shapes, with small ceiling area to height ratios, or where fires are located near walls. Mowrer [7] found that a value of 0.7 for the heat loss fraction provided good agreement with experimental temperature data for a series of fire tests [17] conducted in a room with a floor area of 223 m2, a smooth ceiling, an aspect ratio (A/H2) of 6, and a dimensionless heat release rate, Q*, defined as pffiffiffiffiffiffi _ ρ c p T a gH H 2 Q* Q= a of approximately 1.7 104.
Fig. 33.7 Single control volume and leakage flows used for global analysis
(Sealed case)
H
H – zf
ρg, Tg, V
Qf zf
me , Vexp (Leaky case)
33
Enclosure Smoke Filling and Fire-Generated Environmental Conditions
It should be recognized that temperature predictions are sensitive to the selection of the heat loss fraction when using this approach. Because the heat retained in the gas volume is proportional to (1 – χl), a seemingly small change in the heat loss fraction from 0.9 to 0.8 represents a twofold difference in the net heat addition term.
Sealed Compartment Neglecting fuel vapor addition to the enclosure control volume associated with the fire, the mass flow rates into and out of the enclosure are assumed to be nil for the sealed compartment. The volume of the compartment does not change and the total mass within the compartment remains constant. Assuming ideal gas behavior
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and constant specific heat with properties of air, for the sealed compartment Equation 33.1 reduces to ρV
du dT cv V dP ¼ ρcv V ¼ ¼ Q_ net dt dt R dt
ð33:3Þ
Through manipulation of the ideal gas law, the normalized pressure and temperature rise in a sealed compartment subject to a net change of energy, but without a change in mass or molar quantity, can be expressed as ðt
Q_ net dt
ΔP ΔT Q ¼ net ¼ ¼ o Po T o ρo cv T o V Qo, v
ð33:4Þ
where
Qo, v ð ρo cν T o V Þ ¼ Total internal energy of the control volume Po ¼ Absolute ambient pressure T o ¼ Absolute temperature of the control volume The product of ρocνTo can be treated as a constant with a value of approximately 252 kJ/m3, assuming air properties at standard temperature and pressure. Application of Equation 33.4 to representative building fires demonstrates how quickly typical building boundaries would fail due to overpressurization if the boundaries were in fact hermetically sealed to prevent mass flow through enclosure boundaries. The following example illustrates this point. Pressure changes may be a significant issue for fires in airtight vessels, including submarines and space vehicles, but are not usually significant for typical building spaces, which are leaky by nature.
pressure differential of approximately 1013 Pa (0.01 atm) before failing [18], would this pressure rise be likely to cause window failure?
Example 1 Determine the pressure rise and average temperature increase associated with combustion of 1 L of gasoline within a sealed enclosure with dimensions of 10 m by 10 m by 3 m. Assume a heat loss fraction of 0.90. Assuming ordinary window glass can withstand a
Next, calculate the ambient internal energy level associated with the enclosure gases:
Solution First, estimate the enthalpy of reaction associated with the gasoline: Q f ¼ m f ΔH c ¼ ρ f V f ΔHc ¼ ð760 kg=m3 Þ 103 m3 ð44, 000 kJ=kgÞ ¼ 33, 440 kJ Then, calculate the net heat release associated with the burning of the gasoline: Qnet ¼ Q f ð1 χ l Þ ¼ 33, 440 kJ ð1 0:9Þ ¼ 3344 kJ
Qo, v ¼ ρo cv T o V ¼ 252 kJ=m3 300 m3 ¼ 75, 600 kJ
Next, calculate the dimensionless pressure and temperature changes using Equation 33.4:
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F.W. Mowrer
ΔP ΔT Qnet 3344 kJ ¼ 0:044 ¼ ¼ ¼ Po T o Qo, v 75, 600 kJ Finally, calculate the dimensional pressure and temperature changes: ΔP ¼ 0:044Po ¼ 0:044ð101, 325 PaÞ ¼ 4482Pa ΔT ¼ 0:044T o ¼ 0:044ð293 KÞ ¼ 13 K Thus, the calculated pressure increase is more than four times the specified pressure differential associated with window breakage, despite the following: the fuel source is only 1 L of gasoline, 90% of the heat release is assumed to be lost to the boundaries, the room volume is relatively large at 300 m3, and the average temperature change is only 13 K. The fact that such small fires do not routinely cause overpressure failures of enclosure boundaries can be viewed as de facto evidence that real building enclosures are leaky by nature.
Leaky Compartment For the global analysis of the leaky compartment, the entire enclosure volume is again considered as a fixed control volume, just as it was for the sealed compartment. In this case, the pressure rise in the compartment caused by the release of energy is assumed to force flow out of the enclosure through available leakage paths while at the same time preventing mass flow into the compartment through these same leakage paths. Consequently, for the leaky case, the energy balance expressed by Equation 33.1 reduces to d ðρuV Þ ¼ Q_ net m_ o ho dt
ð33:5Þ
As for the sealed compartment analysis, the lefthand side of Equation 33.5 can be expressed, for an ideal gas, as dðρuV Þ cv V dP ¼ dt R dt
ð33:6Þ
Substituting Equation 33.6 into Equation 33.5 permits the rate of pressure change to be calculated as
ðk 1Þ _ dP R _ Q net m_ o ho Q net m_ o ho ¼ ¼ dt cv V V ð33:7Þ where k cp/cv ( 1.4 for air). Equation 33.7 generally requires numerical solution because the mass outflow term on the right-hand side is a function of the pressure differential between the fire enclosure and surrounding spaces, while the net heat release rate term can vary with time. Zukoski [1] examined the assumption that the rate of pressure change is negligible by comparing the time for the pressure to rise to 86% of its equilibrium value with the time for the smoke layer to descend to the floor. For most scenarios, he found the ratio of these times to be on the order of 102; for relatively large fires or relatively small leakage areas, this ratio was on the order of 101. Based on this analysis, Zukoski concluded that an assumption of quasi-steady pressure would be satisfactory for most fire scenarios. In all the cases considered by Zukoski, the pressure rise was so small that gas density and pressure were virtually unaffected. This quasisteady pressure assumption is employed here. From a practical standpoint, the overall pressure rise relative to atmospheric pressure, ΔP/Po, is generally very small for fires in leaky enclosures, typically on the order of 103 to 105, depending on the heat addition rate and the area of leakage paths. Pressure differences of this magnitude are significant with respect to the flows they cause through leakage paths in the enclosure boundaries, but can be considered as negligible with respect to the energy equation. Consequently, for most enclosure fire scenarios, the pressure can be treated as quasi-steady (i.e., dP/dt ! 0 in Equation 33.7) and the quasi-steady global energy balance for the leaky compartment can then be expressed as Q_ net ¼ m_ o ho ¼ ρe c p T e V_ exp
ð33:8Þ
Equation 33.8 can be rearranged to solve for the volumetric flow rate of gases from a compartment due to expansion. Using air properties with the customary assumptions of constant specific heat, standard atmospheric pressure, and ideal
33
Enclosure Smoke Filling and Fire-Generated Environmental Conditions
gas behavior, this volumetric flow rate caused by expansion can be expressed as Q_ net Q_ net ðkWÞ V_ exp m3 =s ¼ ffi ρe c p T e 353ðkJ=m3 Þ
ð33:9Þ
As illustrated in Figs. 33.5 and 33.6, Equation 33.9 also represents the volumetric expansion rate of the smoke layer. The quasi-steady pressure rise associated with this volumetric expansion rate can be calculated using classical orifice flow theory as discussed by Tanaka (see Chap. 15): sffiffiffiffiffiffiffiffiffi 2ΔP V_ exp ¼ Cd Aleak ve ¼ Cd Aleak ð33:10Þ ρe Equations 33.9 and 33.10 can be combined to solve for the quasi-steady pressure rise, ΔP, within the fire enclosure: !2 1 Q_ net ΔP ¼ ρe ð33:11Þ 2 ρe c p T e Cd Aleak Equation 33.11 can be used to check the assumption that the pressure rise in a compartment fire is negligible relative to the ambient pressure level. Example 2 Calculate the volumetric expansion rate and quasi-steady pressure rise that would be associated with a fire with a heat release rate of 500 kW, a heat loss fraction of 0.7, a discharge coefficient of 0.65, and a leakage area of 0.04 m2. Assume air with a density of 1.20 kg/m3 is being expelled from the fire room. Solution First, calculate the net heat release rate: Q_ net ¼ Q_ f ð1 χ l Þ ¼ ð500 kWÞ ð1 0:7Þ ¼ 150 kW Then, calculate the volumetric expansion rate associated with this net heat release rate: V_ exp
ð150 kWÞ Q_ net ¼ 0:42 m3 =s ¼ ¼ ρe c p T e ð353 kJ=m3 Þ
Finally, calculate the quasi-steady pressure rise associated with this flow rate:
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2 V_ exp 1 ΔP ¼ ρe 2 Cd Aleak 2 ð1:2 kg=m3 Þ 0:42 m3 =s ¼ 2 ð0:65Þ ð0:04 m2 Þ ¼ 157Pa Thus, ΔP 157 Pa O 103 ¼ Po 101, 325 Pa which supports the assumption of negligible effect on the energy equation. Based on measurements of pressure differentials during enclosure fire tests, this is a relatively high pressure differential, suggesting that real enclosures tend to be even more leaky than was assumed for this example.
Temperature Rise The average temperature rise of the fixed control volume associated with a leaky compartment is considered in this subsection. First, the mass balance for the fixed control volume is introduced, recalling that the pressurization of the control volume caused by heat release from the fire is assumed to prevent mass inflow: m_ o ¼
dðρV Þ dρ ¼ V dt dt
ð33:12Þ
Substituting Equation 33.12 into Equation 33.8 yields dρ Q_ net ¼ m_ o ho ¼ c p TV dt
ð33:13Þ
For an ideal gas at constant pressure, the density is related to the temperature as ρ ¼ ρoTo/T. Consequently, the rate of change of density can be related to the rate of temperature change as dρ ρ T o dT ¼ o2 dt T dt
ð33:14Þ
Substituting Equation 33.14 into Equation 33.13 yields dT Qo, p dT Q_ net ¼ ρo c p T o V ¼ Tdt T dt
ð33:15Þ
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F.W. Mowrer
The term Qo,p ( ρocpToV) is analogous to the Qo,v term for the sealed compartment case; this term represents the ambient enthalpy level for a fixed control volume at constant pressure. Assuming that gases within the control volume have the properties of air, the product of ρocpTo can be treated as a constant with a value of approximately 353 kJ/m3 over the temperature range of interest for preflashover enclosure fires. Equation 33.15 can be rearranged and integrated as ðt
Q_ net dt ¼ Qo, p
0
Tðg
dT T
ð33:16Þ
To
The solution to Equation 33.16 can be expressed in terms of the dimensionless average temperature rise in the fixed control volume: ! ΔT Qnet ¼ exp 1 ð33:17Þ To Qo, p
Equation 33.17 permits calculation of an average temperature rise caused by a fire within an enclosure. Equation 33.17 is particularly useful for fire hazard screening purposes, because it allows thermal hazards to be estimated without the need to track conditions in the descending smoke layer by numerical integration. Global temperatures calculated with Equation 33.17 are compared with smoke layer temperatures for Case 1 and Case 2 descending layer scenarios in a subsequent section of this chapter. Example 3 Determine the average global temperature rise in an enclosure with dimensions of 18.3 m by 12.2 m by 6.1 m in response to a fire that grows as a t-squared fire to a heat release rate of 500 kW in 240 s, then burns at a constant heat release rate of 500 kW for another 360 s. Estimate the average temperature rise within the enclosure at 240 s and at 600 s based on this heat release rate history, assuming a constant heat loss fraction of 0.70 and an ambient temperature of 20 C (293 K).
where ðt
control volume as before T o ¼ Absolute ambient temperature
Solution First, calculate the net heat release for the two selected times: ðt ðt Qnet ¼ Q_ net dt ¼ Q_ f ð1 χ l Þdt
The relationship expressed by Equation 33.17 is illustrated in Fig. 33.8.
During the period up to 240 s, the fire heat release rate follows the specified t-squared
Qnet ¼
Q_ net dt ¼ Net energy addition to the
0
o
Fig. 33.8 Average dimensionless temperature rise in a closed room as a function of the dimensionless net energy addition
o
4.0 3.5 3.0
ΔT/To
2.5 2.0 1.5 1.0 0.5 0.0 0.00
0.25
0.50
0.75 Qnet /Qo,p
1.00
1.25
1.50
33
Enclosure Smoke Filling and Fire-Generated Environmental Conditions
growth, and the net heat release during this period is calculated as ! ð 240 500 Qnet ð@240 sÞ ¼ ð1 0:7Þt2 dt 2 ð 240 Þ o ! ! 500 ð240Þ3 ¼ ð0:3Þ 3 ð240Þ2
Qnet ð@600 sÞ ¼ Qnet ð@240 sÞ þ
ΔT Qnet ¼ exp To Qo, p
¼ 66, 000 kJ
Next, the ambient enthalpy level within the enclosure is calculated: Qo, p ¼ ρo c p T o V ¼ 353 kJ=m3 1362 m3 ¼ 480, 746 kJ Then, the average dimensionless temperature rise at each time is calculated as
12, 000 1 ¼ 0:025 at 240 s 480, 746
1 ¼ exp !
500 ð1 0:7Þdt
¼ 12, 000 kJ þ 54, 000 kJ
The net heat release at 600 s is equal to this value plus the net heat release during the period from 240 s to 600 s, when the fire heat release rate is constant: !
ð 600 240
¼ 12, 000 kJ
ΔT Qnet ¼ exp To Qo, p
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66, 000 1 ¼ 0:147 at 600 s 1 ¼ exp 480, 746
Finally, the dimensional temperature changes are calculated at each time as ΔT ¼ 0:025 T o ¼ 0:025 293 K ¼ 7:3 K at 240 s ΔT ¼ 0:147 T o ¼ 0:147 293 K ¼ 43:1 K at 600 s
Note that the ambient enthalpy level has been based on the entire volume of the enclosure, as illustrated in Fig. 33.7, not just on the volume above the fire source, as illustrated in Fig. 33.6. Rather than apply Equation 33.17 based on the entire enclosure volume, it makes sense to consider the fixed control volume defined as the volume between the base of the fire source and the ceiling, as illustrated in Fig. 33.6. Assuming that air entrainment occurs only laterally, this control volume will not have mass inflow across the lower control volume boundary. For this scenario, air entrained into the fire plume is simply recirculated from within the fixed control volume, with some gases forced out of this control volume through its lower face due to expansion. With the smaller control volume defined in this way, the temperature rise expressed by Equation 33.17 will
increase more rapidly for elevated fires than if it is based on the entire enclosure volume, assuming the heat loss fraction does not change significantly for elevated fires. This will produce a more conservative estimate of temperature hazards based on application of Equation 33.17. Example 4 For the previous example, estimate the average temperature rise within the upper layer at the same times (240 s and 600 s) assuming the fire source is located at an elevation of 3.0 m and assuming the same constant heat loss fraction of 0.70. How do these values compare with the results in the previous example? Solution The only difference in this case compared with the previous example is that the size of the control volume has decreased by a factor of two. Therefore, the ambient enthalpy level within the control volume is calculated as Qo, p ¼ ρo c p T o V ¼ 353 kJ=m3 681 m3 ¼ 240, 373 kJ
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F.W. Mowrer
For this case, the average dimensionless temperature rise at each time is calculated as
ΔT Qnet ¼ exp To Qo, p ΔT Qnet ¼ exp To Qo, p
!
!
12, 000 1 ¼ 0:051 at 240 s 1 ¼ exp 240, 373
66, 000 1 ¼ exp 1 ¼ 0:316 at 600 s 240, 373
Finally, the dimensional temperature changes are calculated at each time as ΔT ¼ 0:051 T o ¼ 0:51 293 K ¼ 14:9 K at 240 s ΔT ¼ 0:316 T o ¼ 0:316 293 K ¼ 92:6 K at 600 s
Note that these values for the temperature rise are slightly more than twice the respective values in the previous example. The reason for this is that as the smoke layer heats up, more mass is expelled from the smoke layer, leaving less mass within the smoke layer to absorb additional heat input. That is why the temperature relationship expressed by Equation 33.17 increases exponentially with heat input rather than linearly as in the sealed enclosure case, where the mass within the control volume remains constant.
Concentrations of Smoke and Other Species The conservation of different chemical species (e.g., O2, N2, CO2, CO, H2O, soot) within a control volume can be expressed generally as d ðmY i Þ ¼ ðm_ i Y i, in Þ ðm_ o Y i Þ þ m_ i, gen ð33:18Þ dt Yi is the mass fraction of species i within the control volume. For the fixed control volume shown in Fig. 33.7, it is assumed that mass inflow is precluded by pressurization of the enclosure (i.e., this analysis does not address the “puffing” behavior noted previously), so the first term on the right-hand side of Equation 33.18 is
negligible. Furthermore, the left-hand side of Equation 33.18 can be expanded to dðmY i Þ dY i dm ¼m þ Yi dt dt dt dY i ¼m m_ o Y i dt
ð33:19Þ
The production of a particular species can generally be described in terms of the product of a species yield factor, fi, by the fuel mass loss ˙ f, such that rate, m m_ i, gen ¼ f i m_ f ¼
Q_ f ðΔH c = f i Þ
ð33:20Þ
Equations 33.18, 33.19, and 33.20 can then be combined and simplified to m_ i, gen dY i m_ i, gen ¼ ¼ dt mcv ðρV Þcv ¼
Q_ f ðρV Þcv ðΔH c = f i Þ
ð33:21Þ
Equation 33.21 applies under scenarios where the fire is fuel limited, such that the heat release rate of the fire can be expressed as Q_ f ¼i m_ f ΔH c . The term (ΔHc/fi) in Equation 33.21 represents a “species heat of combustion;” it is the quantity of heat released per unit mass of species i produced (or consumed in the case of oxygen). The species heat of combustion can be estimated based on stoichiometry for products of complete combustion (i.e., CO2 and H2O) or based on experimental yield data for products of incomplete combustion (i.e., CO and soot). Extensive yield data for a range of fuels is provided by Tewarson
33
Enclosure Smoke Filling and Fire-Generated Environmental Conditions
1079
(see Chap. 36). Equation 33.21 can be integrated with appropriate limits to yield ðt Q_ f dt Qf 0 ¼ ðY i Y i, o Þ ¼ ðρV Þcv ðΔHc = f i Þ ðρV Þcv ðΔH c = f i Þ
The volume of the space is calculated as 18.3 m 12.2 m 6.1 m ¼ 1362 m3. Therefore, the heat release per unit volume is calculated at each time as
ð33:22Þ
Q f =V ð@600 sÞ ¼ 220, 000 kJ=1382 m2 ¼ 159:2 kJ=m3
Yi,o is the initial mass fraction of species i in the control volume. For most products of combustion, the initial species mass fraction, Yi,o, is nil. For this case, the species mass concentration can be expressed as Q f =V ρY i ¼ ð33:23Þ ðΔH c = f i Þ
The species heat of combustion is calculated from the given data as
where 3 ρY i ¼ Mass concentration of species iðkgi =m Þ Q f =V ¼ Fire heat release per unit volume of the control volume ðkJ=m3 Þ ðΔH c = f i Þ ¼ Species heat of combustion ðkJ=kgi Þ
Example 5 Assume propylene (C3H6) is the fuel burned in the previous examples. Assume propylene has a heat of combustion of 46.4 MJ/kg of fuel and a soot yield of 0.095 g of soot per g of fuel. Estimate the average mass concentration of soot within the 18.3 m by 12.2 m by 6.1 m enclosure at 240 s and 600 s after ignition of a fire that grows as a t-squared fire to a heat release rate of 500 kW in 240 s, then burns at a constant heat release rate of 500 kW for another 360 s. Solution First, calculate the fire heat released up to the 240 s and 600 s times, respectively: ! ð 240 500 Q f ð@240 sÞ ¼ t2 dt ð240Þ2 o ! ! 500 ð240Þ3 ¼ 3 ð240Þ2 ¼ 40, 000 kJ Q f ð@600 sÞ ¼ Q f ð@240 sÞ þ
ð 600 500 dt 240
¼ 40, 000 kJ þ 180, 000 kJ ¼ 220, 000 kJ
Q f =V ð@240 sÞ ¼ 40, 000 kJ=1382 m2 ¼ 28:9kJ=m3
ΔHc = f i ¼
46:4 MJ=kg f ¼ 488:42 MJ=kgsoot 0:095 kgsoot =kg f
Finally, the soot mass concentration at each time is calculated as ρY soot ð@240 sÞ ¼
28:9 kJ=m3 488:42 103 kJ=kgsoot
¼ 5:92 105 kgsoot =m3 ρY soot ð@600 sÞ ¼
159:2 kJ=m3 488:42 103 kJ=kgsoot
¼ 3:26 104 kgsoot =m3 As discussed in a subsequent subsection, the visibility through smoke can be related directly to the soot mass concentration. For oxygen in air under standard conditions, the initial species mass fraction is Yi,o ¼ 0.233 and the species heat of combustion can be taken as the well-known “oxygen heat of combustion,” for a wide range of representative fuels, with a value of approximately ΔH c = f O2 ¼ 13, 100 kJ=kgO2 , where the negative sign indicates that oxygen is consumed rather than produced in the combustion reaction. For these values, the oxygen mass fraction within the fixed control volume can be estimated as Y O2 ¼ Y O2 , o þ
Qf
ρV ΔH c = f O2 Q f =V ¼ 0:233 ð13; 100Þρ
ð33:24Þ
Example 6 Assume propylene (C3H6) is the fuel burned in the previous examples. Assume propylene has a heat of combustion of 46.4 MJ/kg of
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F.W. Mowrer
fuel and a soot yield of 0.095 g of soot per g of fuel. Estimate the average oxygen mass fraction within the 18.3 m by 12.2 m by 6.1 m enclosure at 240 s and 600 s after ignition of a fire that grows as a t-squared fire to a heat release rate of 500 kW in 240 s, then burns at a constant heat release rate of 500 kW for another 360 s. Solution From the previous example, the fire heat released up to the 240 s and 600 s times is, respectively: ! ð 240 500 Q f ð@240 sÞ ¼ t2 dt ð240Þ2 o ! ! 500 ð240Þ3 ¼ 3 ð240Þ2 ¼ 40, 000 kJ Q f ð@600 sÞ ¼ Q f ð@240 sÞ þ
ð 600 500 dt 240
¼ 40, 000 kJ þ 180, 000 kJ ¼ 220, 000 kJ The volume of the space was calculated as 18.3 m 12.2 m 6.1 m ¼ 1362 m3 and the heat release per unit volume was calculated at each time as Q f =V ð@240 sÞ ¼ 40, 000 kJ=1382m3 ¼ 28:9 kJ=m3 Q f =V ð@600 sÞ ¼ 220, 000 kJ=1382m3 ¼ 159:2 kJ=m3
The oxygen heat of combustion is assumed to be ΔH c = f i ¼ 13, 100 kJ=kgO2 The average temperature in the enclosure was previously calculated at each time to be T ¼ T o þ ΔT ¼ 293 K þ 14:9 K ¼ 307:9 K at 240 s ðso ρ ¼ ρo T o =T ¼ 353=307:9 ¼ 1:15kg=m3 Þ T ¼ T o þ ΔT ¼ 293 K þ 92:6 K ¼ 385:6 K at 600 s ðso ρ ¼ ρo T o =T ¼ 353=385:6 ¼ 0:92kg=m3 Þ
Finally, the oxygen mass fraction at each time is calculated as
Y O2 ð@240 sÞ ¼ 0:233
ð28:9Þ ¼ 0:231 ð13; 100Þ ð1:15Þ
Y O2 ð@240 sÞ ¼ 0:233
ð159:9Þ ¼ 0:220 ð13; 100Þ ð0:92Þ
Thus, for these examples, the oxygen concentration is relatively close to the ambient concentration and consequently would not be expected to have a significant effect on the fire heat release rate. As discussed in the following subsection, however, this is not always the case.
Oxygen Limitations on Heat Release in a Closed Room Fire There is a limit to how much heat can be released by combustion within a closed room because the release of heat is coupled with consumption of a finite amount of oxygen from the air in the enclosure. It is assumed that oxygen does not enter from outside due to pressurization of the compartment, so the fire must eventually die down due to oxygen depletion, much like the familiar candle flame trapped inside an inverted jar. Equation 33.17 will result in nonphysical and incredible temperatures if applied indefinitely because it does not account for the effect of oxygen depletion on limiting heat release within an enclosed space. Mowrer [11] has addressed the issue of oxygen limitations on heat release in unventilated enclosure fires. The heat released by combustion in a room fire is related directly to the oxygen consumed. This relationship can be expressed as " # Qo , p ρo V ΔH c ln 1 þ Q f , lim ¼ χ ð1 χ l Þ Qo, p r air O2 , lim ð 1 xl Þ ð33:25Þ Equation 33.25 can be inserted into Equation 33.17 to yield the limiting temperature rise associated with the oxygen-limited heat release in an enclosure: ΔT g, lim ¼
ΔH c χ O2 , lim ð1 χ l Þ cp r air
ð33:26Þ
33
Enclosure Smoke Filling and Fire-Generated Environmental Conditions
where χ O2 , lim represents the fraction of oxygen that can be consumed before extinction; it is given in general as Y O2o Y O2 , lim χ O2 , lim ¼ Y O2o XO2 o XO2 , lim ¼ ð33:27Þ X O2 o χ O2 , lim is normally evaluated at a limiting extinction value of XO2 or Y O2 . A representative value for XO2 at extinction under normal ambient conditions is approximately 13% for a range of hydrocarbon fuels when the oxygen is diluted with nitrogen (see Chap. 17). For an ambient oxygen mole fraction XO2, 0 of 21%, a representative value for χ O2 , lim would therefore be about 0.4. Example 7 Determine the oxygen-limited average temperature rise in an enclosure fire for heat loss fractions of 0.6 and 0.9, respectively. Assume a value of χ O2 , lim ¼ 0:4. Solution ΔT g, lim ¼
3000ðkJ=kgÞ 0:4 ð1 0:6Þ 1:0ðkJ=kg KÞ
¼ 480 K for χ l ¼ 0:6 ΔT g, lim ¼
3000ðkJ=kgÞ 0:4 ð1 0:9Þ 1:0ðkJ=kg KÞ
¼ 120 K for χ l ¼ 0:9 Although these temperatures are potentially significant from a thermal injury or damage standpoint, they are below the temperature rise of approximately 580 K commonly associated with flashover conditions. This simple analysis suggests the difficulty of attaining flashover conditions in an unventilated, fully enclosed compartment fire. Lower heat loss fractions and higher oxygen consumption fractions would be needed to achieve temperature increases associated with flashover. On the other hand, these calculated global temperature increases might be sufficient to cause the fracture and collapse of ordinary plate glass windows
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[19–21] if present, providing new pathways for the introduction of oxygen to the enclosure and consequent escalation of the fire intensity.
Light Attenuation and Visibility Through Smoke Light attenuation and visibility through smoke can be estimated based on the soot mass concentration within the smoke layer. The light extinction coefficient, K, is directly proportional to the soot mass concentration as K ¼ K m ρY soot
ð33:28Þ
Km is the specific light extinction coefficient. Seader and Einhorn [22] suggested a value of Km ¼ 7600 m2/kg for flaming combustion and Km ¼ 4400 m2/kg for smoke produced by pyrolysis. These values have been widely used for light attenuation and visibility calculations, but more recently Mulholland and Croarkin [23] have suggested a value of Km ¼ 8700 m2/kg for flaming combustion of wood and plastic fuels. Light attenuation within the smoke layer is calculated in accordance with Bougher’s law for monochromatic light: I=I o ¼ eKL
ð33:29Þ
Visibility through smoke is expected to vary inversely with the light extinction coefficient, with this inverse relationship generally expressed as S ¼ C=K
ð33:30Þ
where S ¼ Visibility distance ðmÞ C ¼ Nondimensional constant associated with the object being viewed through the smoke Mulholland [24] suggests a value of C ¼ 8 for light-emitting signs and a value of C ¼ 3 for light-reflecting signs based on the work of Jin (see Chap. 61). These values suggest that lightemitting signs can be observed when the light attenuation is I/Io ¼ e8 ¼ 3.35 104, that is, the transmitted light is much less than 1% of the unattenuated light intensity; whereas
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F.W. Mowrer
light-reflecting signs can be observed when the light attenuation is I/Io ¼ e8 ¼ 0.05, that is, the transmitted light is reduced to 5% of the unattenuated light level. Example 8 Estimate the visibility of a lightreflecting sign through the smoke layer based on the soot mass concentrations determined in a previous example. Solution For this example, the soot mass concentration at each time was calculated to be ρY soot ð@240 sÞ ¼
28:9 kJ=m3 488:42 103 kJ=kgsoot
¼ 5:92 105 kgsoot =m3 ρY soot ð@600 sÞ ¼
159:2 kJ=m3 488:42 103 kJ=kgsoot
¼ 3:26 104 kgsoot =m3 Using these values of soot mass concentration along with the specific light extinction coefficient of 8700 m2/kg suggested by Mulholland and Croarkin, the extinction coefficient is determined to be K ð@240 sÞ ¼ K m ρY soot ¼ ð8700 m2 =kgsoot Þ 5:92 105 kgsoot =m3 ¼ 0:52 m1 K ð@600 sÞ ¼ K m ρY soot ¼ ð8700 m2 =kgsoot Þ 3:26 104 kgsoot =m3 ¼ 2:83 m
1
The visibility distance for a light-reflecting sign is then estimated at each time as S ð@240 sÞ ¼ 3=0:52 m1 ¼ 5:8 m ð19:0 ftÞ S ð@600 sÞ ¼ 3=2:83 m1 ¼ 1:1 m ð3:6 ftÞ This concludes the global analysis of fireinduced conditions in a closed room. In the next section, methods to analyze fire-induced
conditions within the descending smoke layer are addressed. These can then be compared with the global analysis results presented in this section.
Descending Smoke Layer Analysis In this section, the descending smoke layer is treated as a distinct control volume, as illustrated in Fig. 33.5. Two limit cases are addressed based on the location of leakage paths in the enclosure boundaries, following the approach originally taken by Zukoski [1]: • Case 1—Leakage paths near the floor (from the lower layer) • Case 2—Leakage paths near the ceiling (from the upper layer) In Case 1, the expansion of gases in the upper layer pushes fresh air at ambient temperature from the lower layer until the smoke layer descends to the floor. At that point, smoke at the upper layer temperature and composition would be expelled and the analysis would be the same as for Case 0, the global analysis presented in the previous section. The Case 1 scenario is the case addressed by Cooper [2, 3] in the development of the ASET model. In Case 2, the expansion of gases from the compartment is assumed to occur directly from the upper layer. Cooper does not address this scenario, but, as demonstrated by the following analysis, the differences between the two scenarios are minor. Mass balances on the lower layer for the respective cases can be written as Case 1 :
Case 2 :
d ðρV Þl dV l ¼ ρl ¼ m_ pl þ m_ e dt dt ð33:31Þ d ðρV Þl dV l ¼ ρl ¼ m_ pl ð33:32Þ dt dt
These mass balances for the lower layer can be converted to volumetric filling rates for the upper layer by noting that dVu ¼ dVl and by dividing through by the lower layer density, ρl , assumed to remain constant at the ambient air density.
33
Enclosure Smoke Filling and Fire-Generated Environmental Conditions
m_ pl þ m_ e dV u Case 1 : ¼ V_ pl þ V_ exp ¼ dt ρl ð33:33Þ m_ pl dV u ¼ V_ pl ¼ Case 2 : ρl dt
ð33:34Þ
Equations 33.33 and 33.34 show that the volumetric growth rate of the smoke layer is due to both plume entrainment and gas expansion in Case 1 and due to entrainment only in Case 2. This difference occurs because the expanding gases are being expelled directly from the smoke layer rather than the lower layer in Case 2, and consequently gas expansion does not contribute to smoke layer development in Case 2. The rate of smoke layer descent for the two cases derives directly from Equations 33.33 and 33.34 by noting that dVu ¼ Asdzu. For rooms with vertical walls and horizontal ceilings, the horizontal area of the space, As, remains constant with height, assuming no physical obstructions are located within the space. In general, Equation 33.33 must be integrated numerically to determine the smoke layer interface position as a function of time because analytical solutions do not exist for most realistic scenarios. Equation 33.34 does have an analytical solution for the case of a power law fire, where the fire heat release rate is assumed to vary with time as Q_ f ¼ αn tn and axisymmetric plume entrainment [25], where the plume volumetric flow rate varies as 1=3 V_ pl ¼ kv Q_ c z5=3
For these conditions, Equation 33.34 can be rearranged and expressed as ð zu ð dzu kv t ¼ ðαn tn Þ1=3 dt ð33:35Þ 5=3 A s 0 0 ðH zu Þ The solution to Equation 33.35 can be expressed nondimensionally as
3=2 zu 2t ¼1 1þ ðn þ 3ÞτV H
ð33:36Þ
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where V As H ¼ V_ pl, H kv Q_ 1=3 H 5=3 c 2 As =H ¼ kv ðαn tn Þ1=3 =H4=3
τV ¼
ð33:37Þ
τV is a characteristic smoke filling time constant, represented as the volume above the fire source divided by the volumetric entrainment rate evaluated at the ceiling height. Note that this time constant is actually only constant in the case of a steady fire (n ¼ 0). The elevation of the smoke layer interface above the fire source derives directly from Equation 33.36:
3=2 zL zu 2t ¼1 ¼ 1þ ðn þ 3ÞτV H H
ð33:38Þ
The solution represented by Equation 33.38 is shown in Fig. 33.9 for the cases of a steady fire (n ¼ 0) and a t-squared fire (n ¼ 2). This solution is also approximately accurate for Case 1 scenarios where V_ pl V_ exp , such that V_ pl þ V_ exp V_ pl . Qualitatively, Fig. 33.9 illustrates the fact that smoke layer descent is initially very rapid, then slows down and asymptotically approaches the fuel surface. This is because the air entrainment rate for axisymmetric plumes varies with the 5/3 power of the elevation between the fuel surface and the smoke layer interface. As the smoke layer descends, the plume entrains less and less air, causing the descent rate to slow down as shown in Fig. 33.9. The nondimensional representation of smoke layer descent given in Equation 33.38 and shown in Fig. 33.9 is useful to generalize the smoke layer descent analysis, but is not as useful for the computation of specific fire scenarios. This is particularly so for the case of growing t-squared fires because the characteristic time constant given in Equation 33.37 is a function of time for cases other than steady fires (i.e., other than when n ¼ 0). For such computations it is more useful to represent the smoke layer descent in dimensional terms. To calculate the time for the
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F.W. Mowrer
Fig. 33.9 Relative smoke layer interface position as a function of normalized time due to entrainment only in an axisymmetric fire plume
1.0 n=0 n=2
0.9 0.8 0.7
ZL/H
0.6 0.5 0.4 0.3 0.2 0.1 0 0
smoke layer to reach a particular elevation relative to the fuel to ceiling distance (zL/H ) for a t-squared fire, Equation 33.37 is substituted into Equation 33.38 and the resulting equation is solved for t. The result is ( t¼
)1=ð1þn=3Þ ðn þ 3Þ As =H2 H 4=3 zL 2=3 1 1=3 2 H k v αn
ð33:39Þ Similarly, for a t-squared fire, the relative smoke layer elevation can be expressed explicitly as a function of time as "
zL 2kv α1=3 tð5=3Þ ¼ 1 þ n 2 4=3 H 5 As =H H
#3=2 ð33:40Þ
Example 9 For the previous enclosure fire example, determine how long it would take for the smoke layer interface to descend to elevations of 3.0 m and 1.5 m above the floor for the 6.0-m-high enclosure. ( tð3:0 mÞ ¼
2
4
t /τv
6
10
Solution For this example, the enclosure area is As ¼ 18.3 m 12.2 m ¼ 223.3 m2 and the enclosure height above the fire source is H ¼ 6.0 m. The fire grows as a t-squared fire to reach a heat release rate of 500 kW in 240 s, then remains constant at 500 kW for an additional 360 s. Thus, during the growth stage, αn ¼
500 kW ð240 sÞ2
¼ 8:68 103 kW=s2
and n ¼ 2. Assuming an axisymmetric plume, the entrainment coefficient is taken to be kv ¼ 0:064 m4=3 =kW1=3 s For the smoke layer interface elevation of 3.0 m, the relative smoke layer interface elevation is zL 3:0 m ¼ 0:5 ¼ H 6:0 m Substituting these values into Equation 33.39 yields the time for the smoke layer to reach the 3.0 m elevation in the enclosure:
#)1=ð1þ2=3Þ " 2=3 223:3=6:02 6:04=3 2þ3 3:0 1 2 0:064 8:68 103 1=3 6:0
¼ 212 s
8
33
Enclosure Smoke Filling and Fire-Generated Environmental Conditions
Because this time is less than the growth time of 240 s, the smoke layer will descend to the 3.0 m elevation during the growth period. From this analysis, it appears likely that the fire will ( tð1:5 mÞ ¼
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stop growing before the smoke layer descends to the 1.5 m elevation. This can be confirmed by substituting this elevation of 1.5 m into Equation 33.39:
" #)1=ð1þ2=3Þ 223:3=6:02 6:04=3 ð2 þ 3Þ 1:5 2=3 1 1=3 2 6:0 0:064 8:38 103
¼ 375 s
Because the fire stops growing at 240 s, it is necessary to apply Equation 33.40 to determine the smoke layer interface position at the end of the growth period, then use this elevation as the enclosure height H in Equation 33.39 to
determine the additional time needed for the smoke layer interface to reach the 1.5 m elevation as a result of the steady 500 kW fire. Applying Equation 33.40 with a time of 240 s yields
" #3=2 1=3 2ð0:064Þ 8:68 103 240ð1þ2=3Þ zL ð@240 sÞ ¼ 1 þ H ð2 þ 3Þ 223:3=6:02 6:04=3 ¼ 0:44 zL ð@240 sÞ ¼ 0:44 H ¼ 0:44 6:0 ¼ 2:64 m This value then becomes the starting height (i.e., H ) for the steady fire following 240 s: ( tð1:5 mÞ ¼ 240 þ
#)1=ð1þ0=3Þ " 0 þ 3 223:3=2:642 2:644=3 1:5 2=3 1 2 2:64 0:064 ð500Þ1=3
¼ 240 þ 159 ¼ 399 s
In other words, the smoke layer interface reaches the 2.64 m elevation at the end of the 240-s fire growth period, then takes another 159 s to reach the 1.5 m elevation during the ensuing steady fire period.
Conditions in the Descending Smoke Layer The average temperature in the smoke layer is calculated by invoking the ideal gas law relationship for a constant pressure process, ρoTo ¼ ρuTu,
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F.W. Mowrer
and by noting that the average smoke layer density, ρu, is simply the mass of the upper layer divided by the volume of the upper layer. For the two cases, the average temperature of the upper layer is then evaluated as Case 1: 1 0ð t dV u dt B o dt C ρ Tl ρ TlVu C T u ðtÞ ¼ l ¼ l ¼ ρl T l B @ð t dmu A ρu mu dt o dt ðt V_ pl þ V_ exp dt ¼ Tl o ð t V_ pl dt o
ð33:41Þ ðt " mO2 , u Y O2 , u ðtÞ ¼ ¼ mu
Case 2: 0ð t
1 dV u B o dt dtC ρ Tl ρ TlVu C T u ðtÞ ¼ l ¼ l ¼ ρl T l B @ð t dmu A ρu mu dt o dt ðt V_ pl dt ρl T l o ¼ ðt ρl V_ pl ρu V_ exp dt o
ð33:42Þ The mass fraction of oxygen in the smoke layer is calculated for the two cases as Case 1: Q_ f ΔH c =r O2
ρl V_ pl Y O2 , o
o
!# dt ð33:43Þ
mu
Case 2: ðt " mO2 , u Y O 2 , u ðt Þ ¼ ¼ mu
ρl V_ pl Y O2 , o
0
Q_ f ΔH c =r O2
!
ρu V_ exp Y O2 , u
# dt
ð33:44Þ
mu
The mass fractions of different products of combustion in the smoke layer are calculated for the two cases as Case 1: ðt " mi, u Y i, u ðtÞ ¼ ¼ mu
ρl V_ pl Y i, o þ
0
Q_ f ΔH c = f i
!# dt ð33:45Þ
mu
Case 2: ðt " mi, u Y i, u ðtÞ ¼ ¼ mu
0
ρl V_ pl Y i, 0
Q_ f ΔHc = f i mu
!
ρu V_ exp Y i, u
# dt ð33:46Þ
33
Enclosure Smoke Filling and Fire-Generated Environmental Conditions
The denominators in Equations 33.43 through 33.46 are evaluated in the same way as in Equations 33.41 and 33.42, respectively. In general, Equations 33.41 through 33.46 do not have analytical solutions and therefore require numerical integration. Numerical methods are discussed in a subsequent section.
Influence of Mechanical Ventilation on Smoke Layer Conditions The introduction of mechanical ventilation changes the analysis of enclosure smoke filling in a number of ways. As illustrated in Fig. 33.10, with mechanical ventilation, flow may be injected into or extracted from either the upper layer or the lower layer. This will depend on the type of mechanical ventilation system employed, the elevations of injection and extraction vents, and the elevation of the smoke layer interface at a particular time. Smoke layer descent may be either accelerated or retarded relative to the unventilated scenario as a result of mechanical ventilation. Conditions within the smoke layer will also be affected. A quasi-steady smoke layer interface position will develop if the flow rates balance properly. Indeed, the purpose of a dedicated mechanical smoke extraction system is normally to prevent the smoke layer interface position from descending past a certain elevation Fig. 33.10 Mechanical ventilation in a two-layer environment
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within a space, for example, to prevent smoke from reaching the highest elevation of human occupancy.
Global Effects of Mechanical Ventilation Global conditions within a mechanically ventilated enclosure are first considered in terms of a one-zone analysis, as illustrated in Fig. 33.11. This global analysis assumes that conditions throughout the enclosure can be treated as uniform outside the fire-plume/ceiling-jet sublayer as a result of mixing caused by the mechanical ventilation and plume entrainment. One-zone approaches have been used previously to evaluate average fire conditions in mechanically ventilated spaces [7, 26–28]. Volumetric flow rates associated with a fire in a mechanically ventilated enclosure are illustrated in Figs. 33.10 and 33.11. Because the total volume of the enclosure remains essentially constant, the rate at which flow is forced through leakage paths in the boundaries of the enclosure can be expressed as V_ net ¼ V_ in j þ V_ exp V_ ext
ð33:47Þ
V_ net can be either positive or negative, depending on the values for the terms on the right-hand side (RHS) of Equation 33.47. As defined here, V_ net
Vinj
Vext Vnet (Case 2)
Vpl + Vext zext
Vpl zinj
Qf, Vpl, Vexp Vnet (Case 1)
1088 Fig. 33.11 Mechanical ventilation in a one-layer environment
F.W. Mowrer
Vinj
Vext
Vnet
pg , Tg , V
will be positive if flow is forced from the enclosure to surrounding spaces and negative if flow is drawn from surrounding spaces into the enclosure. The injection and extraction rates, V_ in j and _ V ext , will depend on the design of the ventilation system. For present purposes, it is assumed that the user specifies the injection and extraction volumetric flow rates, although it should be recognized that these flow rates may be influenced by fan characteristics and space pressures. Under the quasi-steady pressure conditions assumed here, the volumetric expansion rate of gases can be related directly to the net rate of heat addition resulting from the fire, as shown in Equation 33.9. A global mass balance for the enclosure can be expressed in terms of the volumetric flows across the enclosure boundaries. For situations where V_ net is positive, flow is forced from the enclosure to adjacent spaces through available leakage paths. For this situation, the global mass balance can be expressed as dmgl V_ net > 0 ¼ ρo V_ inj ρgl V_ net þ V_ ext dt ¼ ρo V_ inj ρgl V_ inj þ V_ exp ð33:48aÞ For situations where V_ net is negative, air is drawn into the enclosure through leakage paths and the mass balance becomes
Qf , Vext
dmgl ¼ ρo V_ inj V_ net ρgl V_ ext dt ¼ ρo V_ ext þ V_ exp ρgl V_ ext
V_ net < 0 ð33:48bÞ
For any individual species to be tracked, such as O2, CO2, CO, or soot, a global species balance also depends on the sign of V_ net . This global species balance can be expressed as dmi ¼ ρo Y i, o V_ inj ρgl Y i V_ inj þ V_ exp dt þ m_ i, gen V_ net > 0 ð33:49aÞ dmi ¼ ρo Y i, o V_ ext V_ exp ρgl Y i V_ ext dt þ m_ i, gen V_ net < 0 ð33:49bÞ This global species balance can also be expressed in terms of the mass fraction for each chemical species of interest: dY i 1 _ ¼ ρo V inj ðY io Y i Þ þ m_ i, gen V_ net > 0 mgl dt ð33:50aÞ dY i 1 _ ¼ ρo V ext V_ ext ðY io Y i Þ þ m_ i, gen mgl dt V_ net < 0 ð33:50bÞ
33
Enclosure Smoke Filling and Fire-Generated Environmental Conditions
The generation (or consumption) rate of a ˙ i, gen, can be expressed in terms of the species, m fuel mass loss rate or the fire heat release rate, as shown in Equation 33.20. The global temperature in the enclosure is calculated, assuming ideal gas behavior, constant pressure, and properties of air, as T gl ¼
ρo T o ρo T o V ¼ mgl ρgl
ð33:51Þ
Under quasi-steady conditions, the rate of change of mass in the enclosure goes to zero as the inflow and outflow equilibrate. For an injection-only mechanical system, V_ net will always be positive and the quasi-steady mass balance expressed by Equation 33.48a becomes ρgl V_ inj þ V_ exp ¼ ρo V_ inj ð33:52Þ For this situation, the quasi-steady global temperature can be expressed in dimensionless form as V inj þ V_ exp T gl ρo V_ exp ¼ ¼ ¼1þ ð33:53Þ T o ρgl V_ inj V_ inj Alternatively, the quasi-steady global dimensionless temperature rise above ambient can be expressed simply as the ratio of the expansion flow rate to the injection flow rate: ΔT gl V_ exp ¼ To V_ inj
ð33:54Þ
Example 10 Determine the quasi-steady average global temperature rise in a mechanically ventilated enclosure with dimensions of 18.3 m by 12.2 m by 6.1 m with an air injection rate of ten air changes per hour in response to a fire with a constant heat release rate of 500 kW. Assume a constant heat loss fraction of 0.70 and an ambient temperature of 20 C (293 K). Solution For this example, the volumetric expansion rate, V_ exp , is calculated as in previous examples as
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ð500 kWÞ ð1 0:7Þ Q_ net ¼ V_ exp ¼ ρe c p T e ð353 kJ=m3 Þ ¼ 0:42 m3 =s The volumetric injection rate, V_ inj , is calculated based on the compartment volume and the specified air exchange rate as 10ð18:3 12:2 6:1Þm ¼ 3:78 m3 =s V_ inj ¼ 3600 s 3
The quasi-steady global temperature rise is calculated by applying Equation 33.54: ! V_ exp 0:42 ΔT gl ¼ 293 K To ¼ 3:78 V_ inj ¼ 32:5 K For an extraction only system, the analysis depends on the rate of extraction relative to the expansion rate. If the extraction rate is less than the expansion rate, then the extraction will serve simply to relieve a fraction of the expansion flow, with the remaining fraction forced through available leakage paths. This situation can be treated using the same global analysis as for an unventilated enclosure. There is not a quasisteady solution for this situation. For the situation where the extraction rate is greater than the expansion rate, V_ net will be negative, so air will be drawn into the enclosure through available leakage paths. From Equation 33.48b, the quasi-steady mass balance for this situation is ρgl V_ ext ¼ ρo V_ ext V_ exp
ð33:55Þ
For this situation the temperature ratio is calculated to be T gl ρo V_ ext ¼ ¼ T o ρgl V_ ext V_ exp
ð33:56Þ
The dimensionless temperature rise above ambient for this extraction scenario is
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F.W. Mowrer
ΔT gl V_ exp ¼ _ To V ext V_ exp
ð33:57Þ
Note the similarity between Equations 33.54 and 33.57. The extraction case is analogous to the injection scenario with an effective injection rate equal to the difference between the extraction and expansion rates. This difference is the rate at which air is being drawn into the enclosure when the extraction rate exceeds the expansion rate. Example 11 Determine the quasi-steady average global temperature rise in a mechanically ventilated enclosure with dimensions of 18.3 m by 12.2 m by 6.1 m with an air extraction rate of ten air changes per hour in response to a fire with a constant heat release rate of 500 kW. Assume a constant heat loss fraction of 0.70 and an ambient temperature of 20 C (293 K). Solution This example is the same as the previous example, except that the mechanical ventilation system is extracting smoke at ten changes per hour instead of injecting air at this rate. For this case, the volumetric extraction rate, V_ ext , is the same as the volumetric injection rate from the previous example: 10ð18:3 12:2 6:1Þ m V_ ext ¼ ¼ 3:78 m3 =s 3600 s 3
The quasi-steady global temperature rise is calculated by applying Equation 33.57: " # V_ exp To ΔT gl ¼ V_ ext V_ exp
0:42 ¼ 293 K ¼ 36:6 K ð3:78 0:42Þ The extraction scenario results in a slightly higher average temperature rise than the injection scenario because the airflow rate is lower for the extraction scenario. This assumes that the ventilation rates remain constant and the heat loss fractions remain the same for both scenarios. Scenarios with both injection and extraction can be considered as variations on the injection
only and extraction only analyses. If V_ net is positive, which will occur if V_ inj þ V_ exp is greater than V_ ext , then the global temperature rise can be calculated with Equation 33.52. If V_ net is negative, which will occur if V_ ext is greater than V_ inj þ V_ exp , then the global temperature rise can be calculated with Equation 33.57. Neglecting the injection of fuel into the enclosure, the quasi-steady limits for different species can be evaluated by setting the left-hand side of Equation 33.50a to zero and solving for the mass fraction, Yi: Yi ¼
ρo Y i, o V_ inj þ m_ i, gen ρgl V_ inj þ V_ exp
¼ Y i, o þ
m_ i, gen ρo V_ inj
ð33:58Þ
Example 12 Assume propylene (C3H6) is the fuel burned in the previous mechanically ventilated examples. Assume propylene has a heat of combustion of 46.4 MJ/kg of fuel and a soot yield of 0.095 g of soot per g of fuel. Estimate the quasi-steady average mass concentration of soot within the 18.3 m by 12.2 m by 6.1 m enclosure for a fire that burns at a constant heat release rate of 500 kW, assuming the enclosure is mechanically ventilated with an injection system at ten air changes per hour. Based on this soot mass concentration, estimate the visibility distance for a light-reflecting sign. Solution For this example, the ambient mass fraction of soot is assumed to be zero and the soot mass generation rate is calculated with Equation 33.20 as m_ i, gen ¼ f i m_ f ¼ ¼
Q_ f ðΔH c = f i Þ
500 kW 46, 400 kJ=kg f = 0:095 kgsoot =kg f
¼ 1:02 103 kgsoot =s
Then the soot mass fraction is calculated with Equation 33.58 as
33
Enclosure Smoke Filling and Fire-Generated Environmental Conditions
Y soot ¼ 0 þ
1:02 103 kgsoot =s ð1:20 kg=m3 Þ ð3:78 m3 =sÞ
¼ 2:26 104 kgsoot =kgmix The average soot mass concentration is calculated based on the average temperature and density within the enclosure as 353 ρY soot ¼ kg=m3 ð293 þ 32:5Þ 2:26 104 kgsoot =kg ¼ 2:45 104 kgsoot =m3 Using this value for the soot mass concentration, along with the specific light extinction coefficient of 8700 m2/kg suggested by Mulholland and Croarkin, the extinction coefficient is determined to be K ¼ K m ρY soot
¼ ð8700 m2 =kgsoot Þ 2:45 104 kgsoot =m3 ¼ 2:13 m1
The visibility distance for a light-reflecting sign is then estimated as S ¼ 3=2:13 m1 ¼ 1:4 m ð4:6 ftÞ As a final comment on the global analysis of mechanically ventilated enclosure fires, it is worth noting that V_ net can switch during the course of a fire scenario from negative to positive, for example, for the case of a growing fire where V_ exp increases with time; or from positive to negative, for example, for the case where an extraction system is started at some time after the fire starts. As a consequence, the appropriate equations used to calculate transient and quasisteady conditions may change over the course of a fire scenario.
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Case 1—Leakage paths near the floor (to and from the lower layer) Case 2—Leakage paths near the ceiling (to and from the upper layer) In Case 1, ambient air is expelled from, or drawn into, the enclosure through leakage paths near the floor until the smoke layer descends to the floor. At that point, smoke at the upper layer temperature and composition would be expelled if V_ net were positive. In Case 2, smoke at the upper layer temperature and composition would be expelled from the upper layer through the leakage paths if V_ net were positive, whereas ambient air would be drawn into the smoke layer through these leakage paths if V_ net were negative. The rate of smoke layer descent and conditions within the smoke layer will depend on the elevations of vents and the injection and extraction rates of the ventilation systems. For the present discussion, it is assumed that all injection vents are located at one elevation, zinj, whereas all extraction vents are located at another unique elevation, zext. Multiple elevations for either injection or extraction vents are not addressed. The elevation of the injection vents determines whether air is being injected into the upper layer V_ inj, u or the lower layer V_ inj, l , depending on the current elevation of the smoke layer interface. If the elevation of the injection vents is below the smoke layer interface position, then air is injected into the lower layer; otherwise, it is injected into the upper layer. As the smoke layer interface position moves during a fire scenario, injection can shift between the upper and lower layers. Similarly, the elevation of the extraction vents determines whether smoke is being extracted from the upper layer V_ ext, u or air is being extracted from the lower layer V_ ext, l . For the analysis presented here, it is assumed that no mixing occurs between the upper and lower layers.
Smoke Layer Analysis with Mechanical Ventilation
Floor Leak (Case 1) Analysis
In this section, conditions within the descending smoke layer are addressed in terms of the two limit cases illustrated in Fig. 33.10. These are
The rate of change of the upper layer volume can be expressed in terms of the volumetric flow rates into and out of the smoke layer. For Case 1, it is
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F.W. Mowrer
assumed that there is no leakage from the upper layer until the smoke layer descends to floor level. The rate of change of the smoke layer volume or depth can be expressed as dV u dzu ¼ As ¼ V_ pl þ V_ exp þ V_ inj, u V_ ext, u dt dt ð33:59Þ The last two terms on the right-hand side of Equation 33.59 distinguish the mechanically ventilated Case 1 from the unventilated Case 1. If air is injected into the upper layer, then the rate of smoke layer descent will be faster than for the unventilated case. If smoke is extracted from the upper layer, then the rate of smoke layer descent will be slower than for the unventilated case. The injection or extraction of air from the lower layer does not influence the smoke layer descent rate for the Case 1 scenario. These flows simply affect the net flow rate through the leakage path in the lower layer boundary for this scenario. Provided the upper layer extraction rate is at least large enough to offset the expansion and injection rates, the smoke layer interface will eventually equilibrate at the elevation where a balance is struck between the rates of flow into and out of the smoke layer: V_ ext, u ¼ V_ pl þ V_ exp þ V_ inj, u
ð33:60Þ
Equation 33.60 represents the typical situation for a smoke management system designed according to the exhaust method. For this situation, air is not typically injected into the upper layer because this would require higher extraction rates, so the last term on the right-hand side of Equation 33.60 would normally be zero. The upper layer extraction rate needed to maintain the smoke layer interface at a distance zi above the floor can be determined from Equation 33.60 provided the relationship between plume entrainment, fire intensity, and elevation is known and the fire intensity can be estimated. For the case of an axisymmetric plume, this relationship is normally represented as 5=3 1=3 V_ pl ¼ kv Q_ c zi z f
ð33:61Þ
Based on the Zukoski [25] entrainment correlation, the value for kv will be approximately 0.064 m4/3 s1 kW–1/3. For other plume geometries, such as window plumes, balcony spill plumes, or line plumes, other entrainment rate relationships exist [10]. Further information on plume entrainment is provided by Beyler [29], who prepared a comprehensive review of fire plume and ceiling jet correlations, and by Quintiere and Grove [30], who more recently reviewed the literature on different types of plumes and developed correlations for fire plumes of different geometries. Once the extraction rate needed to maintain the smoke layer interface at an elevation zi above the floor is determined, Equations 33.52 through 33.58 can be used to evaluate the global effects of this extraction rate. These effects will included the makeup air requirements V_ net to balance the design exhaust rate as well as the leakage opening area requirements to prevent excessive pressure drop and flow velocities across the enclosure boundaries. As indicated by Equation 33.47, mechanical injection of air into the lower layer can be used to reduce the makeup air requirements and consequently the pressure drop and flow velocities across openings in the enclosure boundaries. At this point, conditions within the smoke layer are considered. For Case 1, mass conservation for the upper layer can be expressed in terms of the various volumetric flow rates into and out of the smoke layer: dmu ¼ ρl V_ pl þ V_ inj, u ρu V_ ext, u dt
if V 1 > 0 ð33:62aÞ
dmu ¼ ρl V_ pl þ V_ inj, u dt ρu V_ ext, u þ V_ net
if V l ¼ 0 ð33:62bÞ
The additional term in Equation 33.62b compared with Equation 33.62a accounts for the leakage flow from the upper layer that occurs once the upper layer completely fills the enclosure.
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Enclosure Smoke Filling and Fire-Generated Environmental Conditions
Similarly, different species can be tracked in terms of a species balance, which can be expressed for this case as dmi, u ¼ ρl Y i, o V_ pl þ V_ inj, u ρu Y i, u V_ ext, u dt þ m_ i, gen if V l ¼ 0 ð33:63aÞ dmi, u ¼ ρl Y i, o V_ pl þ V_ inj, u if V l > 0 dt ρu Y i, u V_ ext, u þ V_ net þ m_ i, gen ð33:63bÞ Similar to the global analysis, the rate of change of the mass fraction of a species in the upper layer is calculated as 1 _ dY i, u ¼ ρl V pl þ V_ inj, u ðY i, o Y i Þ þ m_ i, gen dt mu ð33:64Þ The generation, or consumption, rate of different species is expressed in terms of a yield factor, fi, as given by Equation 33.20 for the global case. All products generated by the combustion reaction are assumed to enter the upper layer via the fire plume. Finally, the temperature of the upper layer is calculated from the mass and volume of the upper layer as Tu ¼
ρo T o ρo T o V u ¼ ρu mu
ð33:65Þ
This assumes that the upper layer can be treated as an ideal gas at constant pressure with the properties of air. The mass, volume, and species mass fractions in the upper layer change with time in accordance with Equations 33.59, 33.62, and 33.64. Numerical integration is generally necessary to evaluate these differential equations. Once they are evaluated at a particular time, the upper layer temperature at that time can be calculated using Equation 33.65.
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Ceiling Leak (Case 2) Analysis All leakage is assumed to occur from the upper layer for Case 2. The rate of change of the smoke layer volume or depth can be expressed in terms of the upper layer flow terms shown in Fig. 33.10 as dV u dzu ¼ As dt dt _ ¼ V pl þ V_ exp þ V_ inj, u V_ ext, u V_ net
ð33:66Þ
Because V_ net ¼ V_ inj þ V_ exp V_ ext , V_ inj ¼ V_ inj, u þ V_ inj, l , and V ext ¼ V ext, u þ V ext, l , Equation 33.66 can be rewritten as dV u dzu ¼ As ¼ V_ pl þ V_ ext, l V_ inj, l dt dt
ð33:67Þ
The relationship expressed by Equation 33.67 may seem counterintuitive because it shows that, for Case 2, smoke layer descent is affected by injection and extraction in the lower layer but not in the upper layer. Noting that dV u ¼ dV l , an analysis of flow terms can be conducted on the lower layer to reach the same result expressed by Equation 33.67. Alternatively, this result can be explained as follows. Because all leakage flow from the enclosure in Case 2 is assumed to occur via leakage paths from the upper layer, any injection of air into the upper layer will simply be forced through these paths rather than contribute to the descent of the upper layer. Similarly, all expansion is assumed to be forced through these leakage paths from the upper layer rather than contribute to the smoke layer descent, as in the unventilated Case 2 scenario. Finally, extraction from the upper layer will first act to relieve some of the expansion flow from the enclosure. If the extraction rate is less than the combination of the injection and expansion rates, then additional smoky gases will be forced through the leakage paths from the upper layer. On the other hand, if the extraction rate is greater than the combination of the injection and expansion rates, then
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fresh air will be drawn through the leakage paths into the upper layer. Although these factors all influence the composition and temperature of the upper layer, they do not affect the smoke layer descent rate expressed by Equation 33.67. With leakage occurring from the upper layer in Case 2, the injection of air into the lower layer will act to “push” smoke through leakage paths from the upper layer, reducing the rate of smoke layer descent in the process. In contrast, the extraction of air from the lower layer will act to draw the smoke layer down. If the extraction rate is greater than the combination of the injection and expansion rates, air will be drawn into the upper layer through the leakage paths, contributing to the smoke layer descent while at the same time diluting the smoke in the upper layer. For a scenario where there is no injection and the extraction rate is exactly equal to the expansion rate, then the net flow through leakage paths will be nil. In essence, this is the same scenario as the unventilated Case 1, with the expansion flow from the lower layer replaced by extraction from the lower layer at the same rate. In the unventilated Case 1 scenario, expansion contributes to the smoke layer descent just as an equivalent rate of extraction from the lower layer will in the ventilated scenario. Equations 33.66 and 33.67 demonstrate that no amount of extraction from the upper layer will prevent the smoke layer from eventually descending to the elevation of the fire in Case 2 scenarios. Similarly, due to the location of the leakage paths in the upper layer, no amount of injection into the upper layer will affect the rate of smoke layer descent. Such injection or extraction will affect only the composition and temperature of the smoke layer. For Case 2 scenarios, a quasi-steady smoke layer interface position can be achieved only by injecting more air into the lower layer than is extracted from it. The smoke layer will stop descending when the following flow balance is achieved: V_ inj, l ¼ V_ pl þ V_ ext, l
ð33:68Þ
The air injection rate needed to maintain the smoke layer interface at a distance zi above the floor can be determined by Equation 33.68,
provided the extraction rate is known and the relationship between plume entrainment and elevation is known. For the case of an axisymmetric plume, this relationship was given in Equation 33.61. For other plume geometries, other entrainment relationships are available in the literature [10, 29, 30]. The concept of injecting air low in an enclosure while providing ventilation openings high is the basis for the positive pressure ventilation (PPV) technique [31, 32] sometimes employed in fire-fighting operations. This technique is not used as often in building smoke management systems, in part because this technique places the fire enclosure at positive pressure relative to adjacent spaces. Although boundaries adjacent to the smoke layer are assumed to be perfectly tight for the limiting analyses presented here, in reality such boundaries will leak and smoke will be forced from the fire enclosure into adjacent spaces. In contrast, with the exhaust method described in the Case 1 analysis, the extraction of smoke causes the fire enclosure to be at a slightly negative pressure relative to adjacent spaces. Under these conditions, leakage tends to be from the adjacent spaces to the fire enclosure, thus reducing the likelihood and degree of smoke contamination in the adjacent spaces. At this point, conditions within the smoke layer are addressed for the Case 2 scenario. Mass conservation for the upper layer can be expressed in terms of the various volumetric flow rates across the upper layer boundaries: dmu ¼ ρl V_ pl þ V_ inj, u dt ρu V_ ext, u þ V_ net if V_ net > 0 ð33:69aÞ dmu ¼ ρl V_ pl þ V_ inj, u V_ net dt ρu V_ ext, u if V_ net < 0
ð33:69bÞ
Similarly, different species can be tracked in terms of a species balance, expressed as dmi, u ¼ ρl Y i, o V_ pl þ V_ inj, u if V_ net > 0 dt ρu Y i, u V_ ext, u þ V_ net þ m_ i, gen ð33:70aÞ
33
Enclosure Smoke Filling and Fire-Generated Environmental Conditions
dmi, u ¼ ρl Y i, o V_ pl þ V_ inj, u V_ net if V_ net < 0 dt ρu Y i, u V_ ext, u þ m_ i, gen
ð33:70bÞ As for the other cases, these species balances can also be expressed in terms of mass fractions: dY i, u 1 _ ¼ ρl V pl þ V_ inj, u ðY i, o Y i Þ mu dt þ m_ i, gen if V_ net < 0 ð33:71aÞ dY i, u 1 _ ¼ ρl V pl þ V_ inj, u V_ net ðY i, o Y i Þ mu dt þ m_ i, gen if V_ net < 0 ð33:71bÞ Finally, the temperature of the upper layer is calculated from the mass and volume of the upper layer by Equation 33.65. For Case 2, the upper layer volume, mass, and species mass fractions change with time in accordance with Equations 33.67, 33.69a, 33.69b, and 33.71a, 33.71b. Numerical integration is generally necessary to evaluate these differential equations. Once they are evaluated at a particular time, the upper layer temperature at that time is calculated by Equation 33.65.
Numerical Methods for Solving Initial Value Problems In the previous sections of this chapter, the enclosure smoke-filling process has been described in terms of a number of ordinary differential equations to describe the rate of change of volume, mass, and species within the smoke layer. The enclosure smoke filling process is in the class of problems known as initial value problems. This type of problem is also sometimes referred to as a time marching problem, because the objective is to determine the time history of the parameters of interest, given the initial values for these parameters along with equations describing how these parameters
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change with time as a result of specified boundary conditions. As noted previously, the differential equations describing the smoke-filling process can be solved analytically for only a few idealized fire scenarios. For most realistic fire scenarios, these equations must be solved approximately using appropriate numerical methods. Computer models of the smoke-filling process, such as ASET and ASET-B, use a variety of similar numerical methods to develop approximate solutions for the enclosure smoke-filling process. Some of these methods are discussed briefly in this section. For a more comprehensive treatment of numerical methods, readers are referred to texts on this topic (e.g., Ferziger and Peric [33]). Note that most of the equations presented in previous sections are expressed in the form dϕðtÞ ¼ f ½t, ϕðtÞ dt
ð33:72Þ
where ϕ(t) represents the different parameters of interest, such as the smoke layer interface position and the smoke layer temperature and composition. In general, the objective is to predict values for the parameters of interest as a function of time based on the rate of change of the different parameters, dϕ(t)/dt, over each time interval, Δt, being evaluated. Mathematically, this is represented as ð tnþ1 ϕðtnþ1 Þ ¼ ϕðtn Þ þ f ½t, ϕðtÞ dt tn ð33:73Þ ffi ϕðtn Þ þ f ½t, ϕðtÞ Δt The question is how to efficiently and accurately approximate the function, f[t,ϕ(t)] over a time increment, Δt. The simplest approach to solving Equation 33.73 numerically, known as the explicit or forward Euler method, evaluates the derivative function at the current time, tn, that is, f ½t, ϕðtÞ ffi f ½tn , ϕðtn Þ The forward Euler method is known as an explicit method because the value of the parameter at the future time, ϕ(tn+1), is evaluated based
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on the values of parameters evaluated at the current time, tn. For many applications, particularly those in which the function is changing rapidly with time, such an approximation may not be very accurate. This will depend to some extent on the time step selected and the nature of the function being evaluated. The next level of complexity, as well as accuracy, is introduced by methods known as predictor-corrector methods. The simplest of these, known as the improved Euler method or as Heun’s method, uses the explicit Euler method to predict the value of the derivative function; this predicted value is represented as ϕ*(tn+1). This predicted value is then used to estimate the slope of the function at the endpoint. The average slope over the time step is then taken as the average of the slopes evaluated at the beginning and endpoints, that is, at times tn and tn+1. Heun’s method can be expressed mathematically as ϕ*ðtnþ1 Þ ¼ ϕðtn Þ þ f ½tn , ϕðtn Þ Δt 1 ϕðtnþ1 Þ ¼ ϕðtn Þ þ f ½tn , ϕðtn Þ 2 þ f ½tnþ1 , ϕ*ðtnþ1 Þ Δt
ð33:74aÞ
ϕ** tnþ1=2 ¼ ϕðtn Þ þ f tnþ1=2 , ϕ tnþ1=2 Δt=2 ð33:76bÞ ϕ*ðtnþ1 Þ ¼ ϕðtn Þ þ f tnþ1=2 , ϕ** tnþ1=2 Δt
ð33:74bÞ
An iterative form of this predictor-corrector method was used in the development of the ASET-B model [4]. The explicit Euler method and Heun’s method are single point methods because they use information at only the current time step to evaluate conditions at the future time step. Beyond these simple methods, multipoint methods have been developed that use information that has already been computed at previous time steps to fit a polynomial to a number of points. The AdamsBashforth method is an explicit method that uses information at the current time step and the previous two time steps to evaluate the derivative function: Δt 23 f ½tn , ϕðtn Þ 2 16 f ½tn1 , ϕðtn1 Þ þ 5 f ½tn2 , ϕðtn2 Þ
A disadvantage of multipoint methods is that they cannot be started using only data at the initial point because they require data from multiple points prior to the current one. Consequently, other methods must be used to start a calculation. Once started, the advantage of explicit multipoint methods is that they require only one evaluation of the derivative function per time step because the function has already been evaluated at previous time steps. Runge-Kutta methods overcome the difficulties in starting multipoint methods by using additional points between times tn and tn+1 rather than earlier points to evaluate the derivative function. The most popular RungeKutta method is the fourth-order method, which involves multiple evaluations over the time step: ϕ* tn1=2 ¼ ϕðtn Þ þ f ½tn , ϕðtn Þ Δt=2 ð33:76aÞ
ϕðtnþ1 Þ ¼ ϕðtn Þ þ
ð33:75Þ
ð33:76cÞ Δt ϕðtnþ1 Þ ¼ ϕðtn Þ þ f ½tn , ϕðtn Þ 6 þ 2 f tnþ1=2 , ϕ* tnþ1=2 ð33:76dÞ þ 2 f tnþ1=2 , ϕ** tnþ1=2 þ f ½tnþ1 , ϕ*ðtnþ1 Þ The fourth-order Runge-Kutta method was used in the development of the original ASET model [2].
Treatment of Enclosure Smoke Filling in Different Fire Models A number of fire models have been developed over the past three decades to address the enclosure smoke-filling process. The best known of these include the ASET model developed by Cooper [2] during the early 1980s and the ASET-B adaptation of this model developed by Walton [4] during the mid-1980s.
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Enclosure Smoke Filling and Fire-Generated Environmental Conditions
Zone models, such as CFAST, address the enclosure smoke-filling process as a subset of the more general enclosure fire process. Through appropriate specification of vent sizes and locations, users can use these models to address enclosure smoke-filling scenarios. With such vent specifications, the smoke layer will descend within the enclosure until a balance occurs between inflows and outflows. Similar to the more comprehensive zone models, computational fluid dynamics (CFD) models such as the Fire Dynamics Simulator (FDS) address the enclosure smoke-filling process as a subset of the more general enclosure fire process. As with the more comprehensive zone models, users can address enclosure smokefilling scenarios by specifying appropriate vent sizes and locations along with appropriate fire parameters.
Comparisons with Experimental Data The equations describing enclosure smoke filling and conditions presented in the previous sections of this chapter are amenable to solution with spreadsheet templates. A spreadsheet template has been developed [11, 12] based on the explicit Euler numerical method described in a previous section. This spreadsheet template includes calculations and graphs for the global case (Case 0), the floor leak case (Case 1), and the ceiling leak case (Case 2). The parameters calculated in the template include Vul(t) Upper layer volume (m3) zul(t) Smoke layer interface height above the floor (m) mul(t) Upper layer mass (kg) Tul(t) Smoke layer average temperature ( C) Y O2 , ul ðtÞ Smoke layer oxygen mass fraction (kg O2/kg total) These parameters are calculated for both Case 1 and Case 2. The global temperature rise associated with Case 0 is calculated using Equation 33.17, with the net rate of energy addition, Q_ net , calculated using Equation 33.2. For comparison purposes, the smoke layer descent
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rate expressed by Equation 33.38 is identified as the global calculation of smoke layer position (Case 0) in the template. This represents the analytical solution for Case 2 for power law fires, permitting evaluation of the accuracy of the Case 2 numerical solution for smoke layer descent. In the spreadsheet template, the fire is represented as a user-specified power law fire, Q_ f ¼ αn tn , which can be used to represent a wide range of fire growth scenarios, including the commonly used steady (n ¼ 0) and t-squared (n ¼ 2) fire growth rates. The maximum fire size is also specified. The fire grows according to the specified power law relationship until it reaches the maximum fire size and remains constant at the maximum size thereafter. Decay and burnout are not considered in the current implementation of the spreadsheet template. The calculations performed by the spreadsheet template have been compared with experimental data. The first comparison is based on a fire test conducted by Hagglund et al. [34] in a 5.62 m by 5.62 m by 6.15 m high space with a reported steady fire size of 186 kW located 0.2 m above the floor. Q* ¼ 1.6 103 for this scenario, based on a heat release rate of 186 kW, a radiative fraction of 0.35, and a height z ¼ 5.4 m. Karlsson and Quintiere [35] note that for this experiment there was a delay of up to 1 min for the fire to reach its steady value of 186 kW. To evaluate the effect of this delay, the fire was ramped up as a tsquared fire to reach a heat release rate of 186 kW at 60 s (α ¼ 0.052 kW/s2), then maintained at a steady value 186 kW for the rest of the 300 s simulation. Results of this simulation are shown along with experimental data in Fig. 33.12. Figure 33.12 shows that there is little difference between the two numerical cases (Cases 1 and 2) and the analytical solution (Equation 33.38) for the predicted smoke layer descent rates or among the three cases (Cases 0, 1, and 2) for the average smoke layer temperatures. At later times, the smoke layer descends slightly more rapidly for Case 1 than for the other two cases. This is due to the increasingly important role of expansion in Case 1 as the smoke layer
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F.W. Mowrer 70
6
60
5
50
4
40
3
30
2
20
1
10
0
Smoke layer temperature (°C)
Smoke layer height (m)
7
zul Equation 38 zul Case 1 zul Case 2 zul Experimental Tul Equation 16 Tul Case 1 Tul Case 2
0 0
60
120
180
240
300
Time (s)
Fig. 33.12 Experimental and predicted results for smoke filling in a 6 m cube [34]
nears the fuel surface. Cooper [3] has previously noted the increasing importance of expansion as the smoke layer approaches the fuel surface. The smoke layer interface positions for Case 2 and the analytical solution are virtually identical at all times; this serves to verify the accuracy of the numerical solution. The smoke layer temperatures for Cases 1 and 2 are a few degrees Celsius higher than for the global case (Case 0), but for most hazard analysis purposes, these differences are not significant. As a second comparison, an experiment conducted at the Building Research Institute (BRI) in Japan by Yamana and Tanaka [36] is considered. This experiment was conducted in an enclosure with a height of 26.3 m and a plan area of 720 m2 (A/H2 ¼ 1.0). The enclosure was not mechanically ventilated for the experiment considered here. The fire source was a methanol pool with an area of 3.24 m2, estimated to develop a steady heat release rate of approximately 1.3 MW after a 60 s period of initial growth assumed to follow a t-squared profile. Q* ¼ 3.0 103 for this fire, based on the maximum heat release rate of 1.3 MW, a radiative fraction of 0.10 for the methanol pool and a
height of 26.3 m. For the calculations, the heat loss fraction was set to 0.50, a relatively low value. This value was selected on the basis that heat losses due to radiation from the flame would be lower than usual due to the relatively low luminosity of the methanol flame. Results of the comparison with the BRI experiment are shown in Fig. 33.13. For the experimental temperature data, measurements made at an elevation of 16 m above the floor are shown. The experimental smoke layer interface position shown in Fig. 33.13 represents a composite of thermocouple and photometer measurements as well as visual observations reported for this experiment. Figure 33.13 shows generally good agreement between calculated results and measured data for this experiment.
Summary Enclosure smoke filling and smoke layer conditions have been subjects of interest in the fire protection engineering community at least since Zukoski [1] first described the smokefilling process in terms of thermodynamic control
33
Enclosure Smoke Filling and Fire-Generated Environmental Conditions
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30
45 40
Smoke layer height (m)
35 20
30 25
15 20 10
15 10
Smoke layer temperature (°C)
25
zul Equation 28 zul Case 1 zul Case 2 zul Experimental Tul Equation 16 Tul Case 1 Tul Case 2 Tul Experimental
5 5 0
0 0
60
120
180
240
300 360 Time (s)
420
480
540
600
Fig. 33.13 Experimental and predicted smoke-filling results for BRI experiment [36]
volumes and plume flow rates more than 25 years ago. These concepts are now fundamental premises for performance-based consideration of available safe egress time (ASET) [2, 3] and smoke management in large spaces (e.g., NFPA 92B [10]). This chapter reviewed the concepts of enclosure smoke filling first described by Zukoski [1] and addressed extensively by Cooper [2, 3]. It extended these concepts in a number of ways. First, the smoke-filling process was expressed in terms of volumetric flow rates, consistent with the normal practice of ventilation system design. This analysis also showed that the smoke-filling process can be described simply in terms of two distinct volumetric flow processes: plume entrainment and gas expansion. It further showed that the volumetric rate of gas expansion can be treated as a source term that is directly proportional to the net rate of heat addition to a space. The relevant set of ordinary differential equations were shown for describing smoke layer descent, temperature, and composition for both unventilated and mechanically ventilated enclosure fire scenarios. In general, these equations must be solved numerically for
realistic fire scenarios. Appropriate numerical methods were described briefly. A number of example calculations were provided to demonstrate application of the enclosure smoke-filling equations. Such calculations are useful for performing preliminary analyses of enclosure smoke-filling fire scenarios. They can be supplemented by the use of computer-based zone and CFD models described in other chapters.
Nomenclature A cp cv Cd dmO2 h H kv
area (m2) specific heat at constant pressure (kJ/kg · K) specific heat at constant volume (kJ/kg · K) orifice flow coefficient (–) mass of oxygen consumed by combustion (kg) specific enthalpy (kJ/kg) height of space from floor to ceiling (m) volumetric entrainment coefficient (m3/s · kW1/3 · m5/3)
1100
m ˙ m P Po Qf Q_ Q* rair r O2 R t T u U v V V_ Xi Yi z
F.W. Mowrer
mass (kg) mass flow rate (kg/s) pressure (Pa) atmospheric pressure (101,325 Pa) heat released by combustion (kJ) heat release rate (kW) dimensionless heat release rate— _ ρa c p T a pffiffiffiffiffiffi gHH 2 Q= air stoichiometric ratio (kg air/kg fuel) oxygen stoichiometric ratio (kg oxygen/ kg fuel) ideal gas constant of air (287.0 J/kg · K) time (s) temperature (K or C) specific internal energy (kJ/kg) total internal energy (kJ) velocity (m/s) volume (m3) volumetric flow rate (m3/s) mole fraction of species i (ni/ntotal) (molesi/molestotal) mass fraction of species i (mi/mtotal) (kgi/kgtotal) elevation variable (m)
Greek Letters αn χl χ O2 ΔHc ΔT ρ τ
power law fire growth coefficient (kW/sn) heat loss factor Q_ l =Q_ f (–) oxygen consumption fraction (–) fuel heat of combustion (kJ/kg) temperature rise above ambient (K or C) density (kg/m3) time constant (s)
Subscripts atm c e exp ext f g i l net
atmospheric convective exit expansion extraction fire global in, interface loss, lower layer net
o O2 p pl r s tot u, ul v
ambient, reference oxygen constant pressure plume radiative space total upper layer constant volume
References 1. E.E. Zukoski, “Development of a Stratified Ceiling Layer in the Early Stages of a Closed-Room Fire,” Fire and Materials, 2, pp. 54–62 (1978). 2. L.Y. Cooper, “A Mathematical Model for Estimating Available Safe Egress Time from Fires,” Fire and Materials, 6, pp. 135–143 (1982). 3. L.Y. Cooper, “The Development of Hazardous Conditions in Enclosures with Growing Fires,” Combustion Science and Technology, 33, pp. 279–297 (1983). 4. W.D. Walton, “ASET-B: A Room Fire Program for Personal Computers,” Fire Technology, 21, pp. 293–309 (1985). 5. H.E. Nelson, “FPETOOL: Fire Protection Engineering Tools for Hazard Estimation,” NISTIR 4380, National Institute of Standards and Technology, Gaithersburg, MD, General Services Administration, Washington, DC (Oct. 1990). 6. M. Hurley, “ASET-B: Comparison of Model Predictions with Full-Scale Test Data,” Journal of Fire Protection Engineering, 13, 1, pp. 37–65 (2003). 7. F.W. Mowrer, “Methods of Quantitative Fire Hazard Analysis,” TR-100443, Electric Power Research Institute, Palo Alto, CA (May 1992). 8. Professional Loss Control, “Fire Induced Vulnerability Evaluation (FIVE),” TR-100370, Electric Power Research Institute, Palo Alto, CA (Apr. 1992). 9. J.A. Milke and F.W. Mowrer, “A Design Algorithm for Smoke Management Systems in Atria and Covered Malls,” Report No. FP93–04, Department of Fire Protection Engineering, University of Maryland (May 1993). 10. NFPA 92B, Standard for Smoke Management Systems in Malls, Atria, and Large Spaces, National Fire Protection Association, Quincy, MA (2005). 11. F.W. Mowrer, “Enclosure Smoke Filling Revisited,” Fire Safety Journal, 33, pp. 93–114 (1999). 12. F.W. Mowrer, “Enclosure Smoke Filling and Management with Mechanical Ventilation,” Fire Technology, 38, 1, January pp. 33–56 (2002). 13. K. Matsuyama, Y. Misawa, T. Wakamatsu, and K. Hamada, “Closed-Form Equations for Room
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Smoke Filling During an Initial Fire,” Fire Science and Technology, 19, pp. 1–27 (1999). 14. M.A. Delichatsios, “Closed Form Approximate Solutions for Smoke Filling in Enclosures Including the Volume Expansion Term,” Fire Safety Journal, 38, pp. 97–101 (2003). 15. M.A. Delichatsios, “Tenability Conditions and Filling Times for Fires in Large Spaces,” Fire Safety Journal, 24, pp. 643–662 (2004). 16. C.M. Fleischmann and K.B. McGrattan, “Numerical and Experimental Gravity Currents Related to Backdrafts,” Fire Safety Journal, 33, 1, pp. 21–34 (1999). 17. S.P. Nowlen, “Enclosure Environment Characterization Testing for the Base Line Validation of Computer Fire Simulation Codes,” NUREG/CR-4681, SAND86–1296, Sandia National Laboratories, Albuquerque, NM (Mar. 1987). 18. R. Zalosh, “Explosion Protection,” in SFPE Fire Protection Handbook (P.J. DiNenno et al., eds.), National Fire Protection Association, Quincy, MA, pp. 3-402–3-421 (2003). 19. M. Skelly, R. Roby, and C. Beyler, “An Experimental Investigation of Glass Breakage in Compartment Fires,” Journal of Fire Protection Engineering, 3, 1, pp. 25–34 (1991). 20. P.E. Sincaglia and J.R. Barnett, “Development of a Glass Window Fracture Model for Zone-Type Computer Fire Codes,” Journal of Fire Protection Engineering, 8, 3, pp. 101–118 (1997). 21. F.W. Mowrer, “Window Breakage Induced by Exterior Fires,” NIST GCR 98–751, National Institute of Standards and Technology, Gaithersburg, MD (1998). 22. J.D. Seader and I.N. Einhorn, “Some Physical, Chemical, Toxicological, and Physiological Aspects of Fire Smokes,” in 16th Symposium (International) on Combustion, Combustion Institute, Pittsburgh, PA, pp. 1423–1445 (1977). 23. G.W. Muholland and C. Croarkin, “Specific Extinction Coefficient of Flame Generated Smoke,” Fire and Materials, 24, 5, pp. 39–55 (2000). 24. G. W. Mulholland, "Smoke Production and Properties," SFPE Handbook of Fire Protection Engineering, National Fire Protection Association, Quincy, MA, 2008. 25. E.E. Zukoski, T. Kubota, and B. Cetegen, “Entrainment in Fire Plumes,” Fire Safety Journal, 3, pp. 107–121 (1980/1981).
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26. V. Ho, N. Siu, and G. Apostolakis, “COMPBRN III— A Fire Hazard Model for Risk Analysis,” Fire Safety Journal, 13, pp. 137–154 (1988). 27. K.L. Foote, P.J. Pagni, and N.J. Alvares, “Temperature Correlations for Forced-Ventilation Compartment Fires,” Fire Safety Science—Proceedings of the First International Symposium, International Association for Fire Safety Science, London, UK (1986). 28. C. Beyler, “Analysis of Compartment Fires with Overhead Forced Ventilation,” Fire Safety Science— Proceedings of the Third International Symposium, International Association for Fire Safety Science, London, UK (1991). 29. C.L. Beyler, “Fire Plumes and Ceiling Jets,” Fire Safety Journal, 11, 53, pp. 53–75 (1986). 30. J.G. Quintiere and B.S. Grove, “Correlations for Fire Plumes,” NIST GCR 98–744, National Institute of Standards and Technology, Gaithersburg, MD (1998). 31. P.S. Ziesler, F.S. Gunnerson, and S.K. Williams, “Advances in Positive Pressure Ventilation: Live Fire Tests and Laboratory Simulation,” Fire Technology, 30, 2, pp. 269–277 (1994). 32. S. Kerber and W.D. Walton, “Full-Scale Evaluation of Positive Pressure Ventilation In a Fire Fighter Training Building,” NISTIR 7342 National Institute of Standards and Technology, Gaithersburg, MD (2006). 33. J.H. Ferziger and M. Peric, Computational Methods for Fluid Dynamics, 3rd ed., Springer-Verlag, New York (2002). 34. B. Hagglund, R. Jansson, and K. Nireus. “Smoke Filling Experiments in a 6 6 6 Meter Enclosure,” FOA Report C 20585-D6, National Defense Research Establishment, Stockholm, Sweden (1985). 35. B. Karlsson and J. Quintiere, Enclosure Fire Dynamics, CRC Press, Boca Raton, FL (2000). 36. T. Yamana and T. Tanaka, “Smoke Control in Large Scale Spaces (Part 2: Smoke Control Experiments in a Large Scale Space),” Fire Science and Technology, 5, 1, pp. 41–54 (1985).
Frederick W. Mowrer is the Director of Fire Protection Engineering Programs at the California Polytechnic State University in San Luis Obispo, CA. He is also an emeritus faculty member of the Department of Fire Protection Engineering at the University of Maryland. Dr. Mowrer has served as the president of the Society of Fire Protection Engineers and currently serves as the chair of the SFPE Technical Steering Committee.
Methods for Predicting Temperatures in Fire-Exposed Structures
34
Ulf Wickstro¨m
Introduction The fire resistance of structural elements is traditionally determined by standard fire endurance tests. However, there is also a need to be able to predict the response of structures of various designs when exposed to alternative design fire conditions. Accurate and robust analytical methods are then needed. Such methods may also be used for predicting standard tests of, for example, structural elements that cannot be tested due to their size or for extending test results to modified structures. It is necessary when using analytical methods, as well as when interpreting test results and their relations to real fires, to understand the fundamental physics governing the thermal behavior of fire-exposed structures. The focus in this chapter is to meet these needs. The content is based on textbooks on heat transfer theory (e.g., Holman [1] and others) and from various publications in the field of fire safety engineering. Analytical methods for the design of fire resistance of structures have the following three main components: 1. Determining the duration and level of thermal fire exposure 2. Calculating the heat transfer and the internal temperature distribution 3. Estimating the structural response and the load-bearing capacity U. Wickstro¨m (*)
The first step is in general very complex and requires somewhat uncertain assumptions. Most often the fire exposure is assumed according to standardized time-temperature curves, as specified in ISO 834, ASTM E119, or EN 13631. Time-temperature developments determined by fire models or measured at ad hoc tests are seldom applied. The next step is very crucial as the deterioration of material strength depends on the temperature obtained. This chapter focuses on this second step. More information on the first and third steps of an analytical design procedure is outlined elsewhere in this section of the handbook. The temperature calculation methods presented here disregard in general any mechanical failures that may occur that could alter the thermal conditions. Protection systems may, for example, fall off in case of fire exposure and completely change the thermal conditions. Such phenomena must be investigated by full-scale tests and, therefore, new types of structural systems must in general be tested in full scale in standard furnace tests as a basis for type approval and so on. Calculation methods can, however, be used for generalizations or extensions of test results to various dimensions and configurations.
Heat Transfer to Structures Heat is transferred from hot fire gases to structures by convection and radiation. The
M.J. Hurley (ed.), SFPE Handbook of Fire Protection Engineering, DOI 10.1007/978-1-4939-2565-0_34, # Society of Fire Protection Engineers 2016
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34
Methods for Predicting Temperatures in Fire-Exposed Structures qref ⬙
⬙ qinc Incident heat flux
qemi ⬙
Reflected heat flux
qrad ⬙
Surfaceemitted heat flux
Net radiant heat flux
Fig. 34.1 Heat transfer by radiation to a surface, which depends on incident radiation, surface absolute temperature, and surface emissivity
contributions of these two modes of heat transfer are in principal independent and must be treated separately. The convective heat transfer depends on the temperature difference between the target surface and the surrounding gas and the velocity of the gas masses in the vicinity of the exposed surface, whereas the incident heat radiation on a surface originates from surrounding flames and gas masses as well as other surrounding surfaces. 00 Thus, the total heat flux q_ tot to a surface is 00
00
00
q_ tot ¼ q_ rad þ q_ con 00
ð34:1Þ 00
where q_ rad is the net radiation heat flux and q_ con is the heat transfer to the surface by convection. Details of these two contributions to follow.
Radiation 00
The net radiation heat flux q_ rad depends on the 00 incident radiation q_ inc , on the surface emissivity/ absorptivity, and on the fourth power of the absolute temperature Ts of the targeted surface. The heat exchange at a surface is illustrated in Fig. 34.1. Part of the incident radiation is absorbed and 00 the rest q_ re f is reflected. Then the surface emits 00 heat by radiation q_ emi depending on the emissivity and the surface absolute temperature to the fourth power. Thus, the net radiative heat can be written 00
00
q_ rad ¼ αs q_ inc εs σT 4s
ð34:2Þ
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where αs and εs are the target surface absorptivity and emissivity, respectively. In this presentation the surface emissivity and absorptivity are assumed equal according to the Kirchhoff’s identity. Thus, 00 00 q_ rad ¼ εs q_ inc σT 4s ð34:3Þ The incident radiation to a surface is emitted by surrounding gas masses and in case of fire by flames and smoke layers and/or by other surfaces. It depends on the fourth power of the absolute temperature. The emissivity and absorptivity of gas masses and flames increase with depth and become, therefore, in general more important in large-scale fires than in, for example, small-scale experiments. In real fires surfaces are exposed to radiation from a large number of sources (surfaces, flames, gas masses, etc.) of different temperatures and emissivities. The heat fluxes are then in general very complicated to model. A simple summation of the main contributions yields in general a good estimate; that is, X 00 q_ inc ¼ εi Fi σT 4i ð34:4Þ where εi is the emissivity of the ith source, Fi and Ti are the corresponding view factor (see Chap. 4, “Radiation Heat Transfer,” of this handbook) and temperature, respectively. Equation 34.4 may then be inserted in Equation 34.3 to get X 00 q_ rad ¼ εs σ εi Fi T 4i T 4s ð34:5Þ or 00 q_ rad ¼ εs σ T 4r T 4s
ð34:6Þ
where Tr is here termed the black body radiation temperature or just the radiation temperature. Tr is a weighted average identified as X T 4r εi Fi T 4i ð34:7Þ The emissivities as used above are surface properties, in principle independent of the fire conditions.
U. Wickstro¨m
1104
Total Heat Transfer and Adiabatic Surface Temperature
Tg
Ts
Fig. 34.2 Gas velocity profile, with the heat transfer by convection depending on the temperature difference between the adjacent gases and the target surface and on the gas velocity
Convection The heat transferred by convection from adjacent gases to a surface varies a lot depending on adjacent gas velocities and geometries (Fig. 34.2). In most cases it may be written as n 00 q_ con ¼ h T g T s
ð34:8Þ
where h is the convective heat transfer coefficient and Tg is the gas temperature adjacent to the exposed surface. In cases of surfaces heated or cooled by natural or free convection a value of n greater than unity is motivated depending on flow conditions [1]. In fires the heat transfer conditions by convection may vary a lot and the parameters h and n are very hard to determine accurately. However, as radiation heat transfer dominates and the convective conditions are not decisive for the total heat transfer to fire exposed structures, the exponent n is assumed equal to unity for simplicity in most fire engineering cases. Thus, 00 q_ con ¼ h T g T s
ð34:9Þ
The convective heat transfer coefficient h depends mainly on flow conditions in the vicinity of the surface and not so much on the surface or the material properties.
The total heat transfer to a surface may now be obtained by adding the contributions by radiation and convection. Thus, by inserting Equations 34.6 and 34.9 into Equation 34.1, the total heat flux to a surface becomes 00 q_ tot ¼ εs σ T 4r T 4s þ h T g T s ð34:10Þ In most fire engineering design cases the radiation temperature Tr and the gas temperature Tg are assumed equal to a fire temperature Tf. Then the total heat transfer may be calculated as 00 ð34:11Þ q_ tot ¼ εs σ T 4f T 4s þ h T f T s or 00 q_ tot ¼ htot T f T s
ð34:12Þ
where the combined total heat transfer coefficient htot may be identified from Equations 34.11 and 34.12 as H ¼ εs σ T 2f T 2s T f þ T s þ h ð34:13Þ Alternatively the two boundary temperatures in Equation 34.10, Tr and Tg, may be combined to one effective temperature TAST, the adiabatic surface temperature. This temperature is defined as the temperature of a surface of an ideally perfectly insulating material, i.e. a surface which cannot absorb any heat [2]. Thus, TAST is defined by the surface heat balance equation εs σ T 4r T 4AST þ h T g T AST ¼ 0 ð34:14Þ The value of TAST is always between Tr and Tg. Then the total heat transfer may be written as 00 q_ tot ¼ εs σ T 4AST T 4s þ hðT AST T s Þ ð34:15Þ The adiabatic surface temperature TAST can in many cases be measured, and it may be used for calculating heat transfer to fire-exposed surfaces based on practical tests, as discussed later. It can also be obtained from numerical CFD modeling of fires using computer codes like FDS [2, 3].
34
Methods for Predicting Temperatures in Fire-Exposed Structures
Heat Transfer to Fire-Exposed Structures Based on Equations 34.11 and 34.12 the heat transfer to a fire-exposed surface can be calculated for given fire and surface temperatures Tf and Ts. The emissivity εs is a surface property, which can be assumed to equal 0.8 for most building materials except for shiny steel where a lower value may be assumed. The convection coefficient h is not decisive for the temperature development near a fire-exposed surface of a structure as the radiative heat transfer dominates at high temperatures. In Eurocode 1 [4] a value of 25 W/m2 K is recommended at fire-exposed surfaces. The temperature on the nonexposed side of a separating structure will, on the other hand, depend very much on the heat transfer conditions including the convection coefficient. In Eurocode 1 in this case a convective heat transfer coefficient value of 4 W/m2 K is recommended. In many cases, however, a fire-exposed surface will get temperatures very close to the fire temperature (i.e., Tf Ts). This approximation applies for insulation materials with a low density and a low thermal conductivity. It may facilitate calculations considerably and is here applied on calculating temperature in insulated Fig. 34.3 The plate thermometer according to ISO 834 and EN 1363-1 is made of a shielded thermocouple welded to the center of a 0.7-mm-thick Inconel plate, which is insulated on its back side. The exposed front face is 100 mm by 100 mm
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steel structures (as discussed later). Even a normal weight concrete surface will get a temperature of 90 % of the fire temperature after 30 min (as shown in Fig. 34.19, later in the chapter). The heat transfer conditions may be very decisive for the temperature development in a fireexposed bare steel structure (see discussion on unprotected steel structures later in the chapter). They are also very important for the temperature development on the back side of a fire-separating element. This is in particular the case for light weight structures where the thermal insulation properties are decisive rather than the thermal inertia.
Calculating Heat Transfer Using Plate Thermometer Temperatures So-called plate thermometers are used to monitor the temperature in fire resistance furnaces according to the international standard ISO 834 and the European standard EN 1363-1. A plate thermometer (PT) consisting of an Inconel (trade name for a nickel-based superalloy) plate insulated on its back side is shown in Fig. 34.3. A thermocouple fixed to the plate registers its temperature. Figure 34.4 shows plate thermometers Shielded thermocouple Protection tube
10 mm insulation
Thermocouple hot junction
0.7 mm stainless steel
U. Wickstro¨m
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Fig. 34.4 Plate thermometers being mounted around a steel girder for measuring local thermal exposures. Note that the plate thermometers are mounted so that the front
sides of the steel plates are exposed to roughly the same incident radiation as the girder and the back sides are insulated
being mounted at a steel girder with the insulated back side facing the specimen. The front side of the plate thermometer is exposed to approximately the same heating, including radiation conditions, as the specimen. The exposed surface of the plate thermometer is relatively large and, therefore, its sensitivity to convective heat transfer is about the same as that of the specimen surface. The steel plate is thin, only 0.7 mm, and thus responds quickly to temperature changes. As a matter of fact the plate thermometer in a standard fire resistance test measures approximately the temperature of an adiabatic surface (i.e., the temperature of an ideally perfect insulator exposed to the same heating conditions as the specimen surface, as discussed earlier). The plate thermometer was introduced mainly to harmonize fire endurance tests (see Wickstro¨m and Hermodsson [5]), but the measured temperatures are also well suited as input for calculating heat transfer by radiation and convection to fire-exposed surfaces.
As any surface, the plate thermometer surface exchanges heat by radiation and convection. The sum of these equals the transient heat for raising the temperature of the Inconel plate and the backing insulation. Because the plate is thin and does not lose much heat on its back side, this sum is small and can be neglected except for the very first few minutes of a standard test. Thus, the heat balance of the plate can be written as 00 εPT q_ inc σT 4PT þ hPT T g T PT ¼ 0 ð34:16Þ or εPT σ T 4r T 4PT þ hPT T g T PT ¼ 0 ð34:17Þ The index PT refers to plate thermometer. This means the plate thermometer yields the adiabatic temperature of the specimen for a given surface emissivity and a given convective heat transfer coefficient.
34
Methods for Predicting Temperatures in Fire-Exposed Structures
An approximate alternative expression of the 00 net heat transfer q_ tot to a specimen surface can now be obtained in terms of one effective temperature only by deducting Equation 34.17 from Equation 34.10: 00 q_ tot ¼ εs σ T 4PT T 4s þ hðT PT T s Þ ð34:18Þ In other words the adiabatic surface temperature is approximated by the plate thermometer temperature. This rewriting of Equation 34.10 facilitates the calculations in many cases. The 00 error Δq_ introduced can be quantified by a simple algebraic analysis as 00 Δq_ ¼ ðεs εPT Þσ T4r T 4PT þ ðhs hPT Þ T g T PT ð34:19Þ Thus, the error is small when the surface emissivity of the plate thermometer and the specimen are nearly the same and when the convective heat transfer coefficients are nearly the same. Therefore, the surfaces of the plate thermometers are blasted and heat-treated before being used to get an emissivity of about 0.8. It also has a relatively large surface, 100 mm by 100 mm, to obtain a convection heat transfer coefficient similar to a specimen. Because TPT always has a value between Tr and Tg, the error vanishes when these two temperatures are close.
Heat or energy is conducted in solid materials due to temperature gradients. In one dimension in the x-direction the rate of heat transfer or heat flux is expressed according to Fourier’s law as ∂T ∂x
∂ ∂T ∂T k ¼ ρc ∂x ∂x ∂t
ð34:21Þ
where ρ is density, c is specific heat of the material. If the conductivity k is constant, Equation 34.21 may be written as ∂T 2 1 ∂T ¼ ∂2 x α ∂t
ð34:22Þ
where α is the thermal diffusivity defined as α ¼ k/ρc. At the boundaries Fourier’s law applies and may be expressed as 00
q_ x ð0Þ ¼ k
∂T ∂x x¼0
ð34:23Þ
Three types of boundary conditions may occur. 1. Given surface temperature: T(0,t) ¼ Ts 00 2. Given surface heat flux: -k∂T ¼ q_ s ∂x x¼0 3. Given convection and radiation conditions, for
Heat Conduction in Solid Materials
00
structure resulting from conditions imposed on its boundaries. Because these conditions vary with time, the temperature field will be transient or unsteady. It is then governed by the heat diffusion equation, which in one dimension is expressed as
¼ h T f T s þ εσ T 4f T 4s example: k∂T ∂x x¼0
Modeling of Heat Conduction in Materials
q_ x ¼ k
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ð34:20Þ
where k is the thermal conductivity. In fire problems the most usual objective is to determine the temperature distribution in a
All the specified boundary conditions, Ts, qs, and Tf, may vary with time. A special type of heat flux boundary condition is the adiabatic or perfectly insulated surface where qs is equal to zero. The heat diffusion equation can be solved analytically only in some uncomplicated cases (see Chap. 2, “Conduction of Heat in Solids,” of this book). Numerical methods are usually needed as boundary conditions in general are nonlinear and material properties vary with temperature. There are mainly two types of numerical methods, finite difference and finite element methods, depending on how the geometry is approximated and how the temperature field is
U. Wickstro¨m
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Fig. 34.5 The TPS sensor placed between two pieces of a concrete specimen
expressed by a limited number of discrete temperatures. The finite element method is described briefly later for the onedimensional case.
Measurement of Thermal Properties There are a number of techniques to measure thermal properties, each of them suitable for a limited range of materials, depending on thermal properties and temperature level (e.g., see Flynn [6]). However, only a few of the measuring techniques can be used at high temperature levels relevant for fire conditions. They can be divided into steady-state and transient techniques. The steady-state techniques perform the measurements when the material is in complete equilibrium. Disadvantages of these techniques are that it generally takes a long time to reach the required equilibrium and that at low temperature the measurements are influenced by moisture migration. For moist materials like concrete, it is therefore often preferable to determine the apparent conductivity or thermal diffusivity with transient techniques. These techniques perform the measurements during a process of small temperature changes and can be made relatively quickly. The guarded hot plate is the most common steady-state method for building materials with a relatively low thermal conductivity [7]. It is
quite reliable at moderate temperatures up to about 400 C. Because transient thermal processes dominate in fire safety engineering, the thermal diffusivity, a measure of the speed at which temperature is propagating into a material, is the most interesting parameter. It is naturally best measured with transient methods. One of the most interesting techniques is the transient plane source method (TPS). In this method a membrane, TPS sensor, is located between two specimen halves and acts as a heater as well as a temperature detector (Fig. 34.5). By using this technique, thermal diffusivity, thermal conductivity, and volumetric specific heat can be obtained simultaneously for a variety of materials like metals, concrete, mineral wool, and even liquids and films [8].
Finite Element Calculations of Temperature in Fire-Exposed Structures When calculating temperature in fire-exposed structures nonlinearities must in most cases be considered. The boundary conditions are nonlinear varying dramatically with temperature as shown above, and also the thermal properties of most materials vary significantly within the wide temperature span that must be considered in fire safety engineering problems. Therefore, numerical methods must be employed. The most general
34
Methods for Predicting Temperatures in Fire-Exposed Structures
and powerful codes today are based on the so-called finite element method (FEM).
Basic Equations Derived for One-Dimensional Case The basic equations that follow are derived for a simple one-dimensional case as an illustration. The same type of equation may be derived for two and three dimensions. Figure 34.6 shows a wall that has been divided into a number of one-dimensional elements. The temperature between the nodes is assumed to vary linearly along the length. In any element, interior or at the surface, with length L, conductivity k, and a section area A (Fig. 34.7), the heat flow at the nodes can then be calculated as
e
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as T ¼
n o T1 T2
e
and Q ¼
n o Q1 Q2
respectively.
In a similar way an element heat capacity matrix can be defined by lumping the heat capacity of the element in the nodes. Thus, an element heat capacity matrix may be obtained as
ALcp 1 0 e ð34:26Þ c ¼ 0 1 2 When several elements are combined, the global thermal conductivity matrix K can be assembled. In the very simple case of three one-dimensional elements the global heat conduction matrix becomes
q1 ¼ kA=L*ðT 1 T 2 Þ and q2 ¼ kA=L*ðT 1 þ T 2 Þ k, cρ
or in matrix format as e e
qe ¼ k T
ð34:24Þ
1
2
e
where qe is the element node heat flow vector, k e is the element heat conduction matrix, and T is the element node temperature vector. The element heat conduction matrix may then be identified as ( e )
k1, 1 k1e, 2 1 1 e k ¼ ¼ ð kA=L Þ k2e, 1 k2e, 2 1 1 ð34:25Þ and the element nodal temperature and heat flow vectors
T1 q 1
T2 q 2
L, A
Fig. 34.7 A one-dimensional element with local element node numbers 1 and 2, length L, and a section area A. The element is given a thermal conductivity k, a specific heat capacity c, and a density ρ
Fig. 34.6 A wall divided into one-dimensional elements i–1
i
i+1
U. Wickstro¨m
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n 9 o 4 4 0 > > Q ¼ A εσ T T T þ h T i f i i f i > 1 > k21, 2 k2, 2 þ k21, 1 0 = ð34:29Þ 2 3 > k22, 1 k2, 2 þ k31, 1 k1, 2 > > > ; where Ai is the section area of the ith node. The 0 k32, 1 k32, 2 differential equation given in Equation 34.28 can ð34:27Þ be solved numerically by approximating the time derivative as where the superscripts 1–3 denote element numjþ1 j T T bers. The global heat capacity matrix C may be ð34:30Þ T_ ¼ assembled in a similar way as the global conΔt ductivity matrix. Notice that both the thermal j conductivity and the heat capacity matrices are where T is the node temperature vector at time symmetric and dominated by their diagonal step j and Δt is a chosen time increment. Now the elements, and that the global heat capacity heat balance equation in matrix format (Equamatrix assembled from element matrices tion 34.28) can be written as according to Equation 34.26 will have nonzero jþ1 j C T T ð34:31Þ =Δt þ K T ¼ Q elements only in the diagonal. This will have a 8 1 k 1, 1 > > > > 1 < k 2, 1 K¼ > 0 > > > : 0
k11, 2
0
decisive influence on how the global algebraic heat balance equation can be solved as shown below. In global form the heat balance equation may now be written as C T_ þ K T ¼ Q
ð34:28Þ
where T_ is the time derivative of the node temperatures. Each row in this equation system represents the heat balance of a node. For each equation or each node either the temperature or the heat flow given in the corresponding rows in the vectors T and Q, respectively, is known. In principle three options are possible for each equation/row: 1. The node temperature Ti is prescribed. 2. The node heat flow Qi is prescribed. 3. The node heat flow Qi can be calculated as a function of a given gas temperature and the surface temperature. In the first case the corresponding equation vanishes as the unknown quantity is prescribed. The most common case for internal nodes is the second case (i.e., the external flow is zero). A typical boundary condition when calculating temperature in fire-exposed structures is according to the third option. Based on, for example, Equation 34.11, the external heat flow to the ith node becomes
In this differential equation the temperature vector is known at time increment j. The new temperature vector at time j + 1 is obtained either explicitly based on the conditions at time step j as j 1 jþ1 j j T ¼C Q K T Δt þ T ð34:32Þ or implicitly as T
jþ1
1 j j ¼ C=Δt þ K Q þ C T =Δt ð34:33Þ
Combinations of the solution schemes according to Equations 34.32 and 34.33 are also possible. All such schemes require the solution of an equation system containing as many unknowns as there are unknown node temperatures. Most finite element computer codes use such types of implicit solution schemes. They are numerically more stable than the explicit techniques (i.e., longer time increments may be used). The explicit solution according to Equation 34.32 may be very simple when the heat capacity matrix C is diagonal (i.e., it contains only nonzero elements in the diagonal as shown for a one-dimensional element in Equation 34.26). The solution of the equation system
34
Methods for Predicting Temperatures in Fire-Exposed Structures
then becomes trivial because each nodal temperature can be obtained directly/explicitly one at a time. This solution scheme is numerically stable only when the time increment Δt is less than a critical value proportional to the heat capacity over the thermal conductivity of the material times the square of an element length dimension Δx (see Equation 34.34). This requirement applies to all the equations of the entire system. If violated in any of the equations (i.e., at any point of the finite element model), the incremental solution equation will turn unstable. Δtcr
cp ðΔxÞ2 k
ð34:34Þ
A similar condition applies to boundaries of type 3 (e.g., according to Equation 34.29). This means that short time increments are needed for materials with a low density and a high conductivity and when small elements are used. For information on critical time increments, see Sterner and Wickstro¨m [9]. In practice, when calculating temperature in fire-exposed structures, numerical stability is only a problem when modeling sections of thin metal sheets with high thermal conductivity. Then according to Equation 34.34, very short time increments are required. The problem may, however, be avoided by prescribing that nodes close to each other shall have the same temperature. This technique has been applied in the code TASEF [9]. In this code a technique is also developed in which the critical time increment is estimated and thereby acceptable time increments can be calculated automatically at each time step.
Available Computer Codes for Temperature Calculations Several computer codes are commercially available for calculating temperature in fire-exposed structures. In general modern codes are based on the finite element method. Some are specifically developed and optimized for calculating temperature in fire-exposed structures whereas others are more general-purpose codes.
1111
TASEF [10, 11] and SAFIR [12] are examples of programs that have been developed for fire safety problems. They both for temperaturedependent material properties and boundary conditions. TASEF employs a forward difference solving technique, which makes it particularly suitable for problems in which latent heat due to, for example, evaporation of water must be considered. It yields in most cases very short computing times, in particular for problems with a large number of nodes. Both TASEF and SAFIR have provisions for modeling heat transfer by convection and radiation in internal voids. TASEF can be obtained from TASEF Ltd., UK and SAFIR from the University of Lie`ge, Belgium. There are many very advanced generalpurpose finite element computer codes commercially available such as ABAQUS [13], ANSYS [14], ADINA [15], HEATING [See www.oecd-nea.org/tools/abstract/detail/psr-0199/ ] and Comsol [16]. The main advantage of using such codes is that they can be used in combination with structural codes and that they come with advanced graphical user interfaces and postprocessors.
Accuracy of Finite Element Computer Codes At the least the following three steps must be considered when estimating the accuracy of computer codes for numerical temperature calculations: 1. Validity of calculation model 2. Accuracy of material properties 3. Accuracy and reliability of the numerical algorithms of the computer code The first point is, of course, important. For example, the effects of spalling or water migration cannot be accurately predicted with a code based on just heat transfer according to the Fourier heat transfer equation. The second point is also crucial. Errors in material property input will be transmitted into output errors. Methods for measuring material properties at high temperature were briefly discussed earlier.
U. Wickstro¨m
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Finally, the numerical verification of the computer code itself is also important. By definition, verification is the process of determining that a model implementation accurately represents the developer’s conceptual description of the model and the solution to the model [17]. If correctly used, most codes yield results with acceptable accuracy. A scheme to follow including a number of reference cases of various levels of complexity have recently been presented in an SFPE standard [Standard on calculation methods to predict the thermal performance of structural and fire resistive assemblies, please ask Chris Jelenewicz for advice on the status of the standard] partly based on cases earlier suggested by Wickstro¨m and Pa˚lsson [18] and Wickstro¨m [19]. It is mainly developed for finite element codes but it may also be used for codes based on finite difference principles. The first reference example is a linear problem that can be solved analytically. When increasing the number of elements the results should converge to one correct value. Codes yielding results that converge smoothly when increasing the number of elements are generally deemed reliable for the type of problems considered. The scheme suggested employs problems that are relevant for fire safety engineering, including effects of conductivity varying with temperature, latent heat, radiant heat transfer boundary conditions, and combinations of materials, concrete, steel, and mineral wool. For the development of the SFPE standard the computer codes ABAQUS and TASEF were used to obtain solutions which were deemed reliable as these codes use different solutions algorithms.
Calculation of Temperature in Steel Structures Metals in general conduct heat very well. The thermal conductivity of steel is on the order of 30 times higher than the corresponding value for concrete and 100–1000 times higher than that of
insulation products. Therefore, the temperature field in a steel section may in many fire engineering cases be assumed uniform. In particular the temperature across the thickness of a steel sheet will be uniform, whereas the temperature in the plane of the sheet may vary considerably, depending on boundary conditions. The methods presented in Chap. 53, “Analytical Methods for Determining Fire Resistance of Steel Members,” assume uniform steel section temperatures. Then zero- or one-dimensional calculation techniques may often be used. For more general two- and three-dimensional cases, numerical computer codes are needed.
Thermal Properties of Steel The thermal conductivity of carbon steel as a function of steel temperature according to Eurocode 3 [20], is shown in Fig. 34.8. It can also be obtained from Table 34.1. The specific heat capacity is in most cases more important than the conductivity. In many cases it is accurate enough and convenient to assume a constant specific heat capacity. However, for more accurate calculations the variations with temperature as shown in Fig. 34.9 [20] or given in Table 34.2 are recommended in Eurocode 3 [20]. This specific heat capacity varying with temperature yields in general lower calculated temperatures than when a constant value of 500 J/(kg K) is assumed.
Insulated Steel Structures In particular in the case of insulated steel sections the steel temperature over a section may be assumed uniform. Then the surface heat transfer resistance 1/htot is in most cases negligible in comparison with the heat resistance (i.e., the thickness over the conductivity of the insulation di/ki). htot is the combined heat transfer coefficient due to radiation and convection as given in Equation 34.13. The fire-exposed surface temperature is then approximately the same as the
Methods for Predicting Temperatures in Fire-Exposed Structures
Fig. 34.8 Thermal conductivity of steel as a function of the temperature
1113
60 Thermal conductivity (W/m K)
34
50 40 30 20 10 0 0
200
400
600
800
1000
1200
Temperature (°C)
Table 34.1 Thermal conductivity of carbon steel as a function of the temperature [20] Temperature ( C) 20 < Tst < 800 800 < Tst < 1200
Conductivity (W/m K) 54 3.33 102 Tst 27.3
i h ðT s T 0 Þ ¼ T f T 0 1 eðt=τÞ ð34:37Þ where the characteristic response time or time constant τ of the section is identified as τ ¼ cs ρs V s =As ðki =di Þ ¼ ðdi =ki Þðcs ρs Þ=ðAs =V s Þ
fire temperature, and the heat transfer to the steel may under steady-state conditions be approximated as qtot ¼ As ðki =diÞ T f T s ð34:35Þ where As is the fire-exposed area, and Tf and Ts are the fire and steel temperatures, respectively. If the heat capacity of the insulation is negligible in comparison to that of the steel, transient steel temperature can be obtained from the heat balance equation Asðki =diÞ T f T s ¼ cs ρs V s ð∂T s =∂tÞ ð34:36Þ where cs and ρs are the specific heat capacity and density, respectively, of steel and Vs is the volume per unit length of the considered steel section. In case of heavy insulations when the heat capacity of the insulation cannot be neglected, see the following section on heavily insulated steel structures. A very simple solution can be obtained if a constant fire temperature rise and constant material properties are assumed; that is,
ð34:38Þ The relation As/Vs is denoted the section factor or the shape factor that has the dimension one over length. Instructions on how to obtain this factor for various configurations are given in Table 34.3. For a fire temperature Tf arbitrarily varying with time or when the material properties vary with temperature, the steel temperature may be obtained (e.g., from the numerical scheme derived from Equation 34.36) as ΔT s =Δt ¼ T if T si =τ ð34:39Þ T si and Δt are the steel where ΔTs equals T iþ1 s temperature rise and the time increment, respectively. The superscripts i and i + 1 denote the numerical order of the time increments. When the thermal properties vary with temperature, the time constant τ as defined by Equation 34.38 needs to be updated at each time increment. A forward difference solution scheme can be obtained as
U. Wickstro¨m
1114 Fig. 34.9 Specific heat of steel as a function of the temperature [20]
5000 4500 Specific heat (J/kg K)
4000 3500 3000 2500 2000 1500 1000 500 0 0
200
400
600
800
1000
1200
Temperature (°C)
Table 34.2 Specific heat capacity of carbon steel as a function of the temperature [21] Temperature ( C) 20 < Tst < 600 600 < Tst < 735 735 < Tst < 900 900 < Tst < 1200
T iþ1 ¼ Δt=τ T if þ ð1 Δt=τÞ T si s
Specific heat capacity (J/[kg K]) 425 + 7.73 101 Tst 1.69 103 Tst2 + 2.22 106 Tst3 666 + 13,002/(738 Tst) 545 + 17,820/(Tst 731) 650
ð34:40Þ
This forward difference scheme is, however, numerically stable only if Δt τ ¼ ðdi =ki Þðcs ρs Þ=ðAs =V s Þ
ð34:41Þ
This condition must be fulfilled at each time increment. In practice time increments Δt longer than 10 % of that critical value should not be used to ensure accurate results. Heavily Insulated Steel Structures The heat capacity of the insulation normally has an insignificant influence on the steel temperature rise rate. However, it will considerably reduce the steel temperature rise of sections protected with relatively heavy insulation. A simple approximative approach is then to lump a third of the heat capacity of the insulation to the steel [22–24]. Equation 34.39 may then be modified as
ΔT s =Δt ¼ T if T si =½τð1 þ μ=3Þ þ ½expðμ=10Þ 1 ΔT f =Δt
ð34:42Þ
where μ is the relation between the heat capacity of the insulation and the steel, μ ¼ ðAi di ρi ci Þ=ðV s ρs cs Þ
ð34:43Þ
and where ρi and ci are the density and the specific heat capacity of the insulation, respectively. When the material properties vary with temperature, they may be updated at each time increment. The latter term of Equation 34.42 represents a time delay due to the heat capacity of the insulation. ΔTf is the fire temperature rise between two time increments. Notice that when the heat capacity of the insulation is much smaller than that of the steel, μ vanishes and Equation 34.42 becomes identical to Equation 34.39.
34
Methods for Predicting Temperatures in Fire-Exposed Structures
1115
Table 34.3 Section factor As/Vs for steel members insulated by fire protection material [20] Sketch
Description Contour encasement of uniform thickness
Section factor (As/Vs) Steel perimeter Steel cross-sectional area
Hollow encasement of uniform thicknessa
2(b + h) Steel cross-sectional area
Contour encasement of uniform thickness, exposed to fire on three sides
Steel perimeter – b Steel cross-sectional area
Hollow encasement of uniform thickness, exposed to fire on three sidesa
2h + b Steel cross-sectional area
a
The clearance dimensions c1 and c2 should not normally exceed h/4
Equation 34.42 has been adopted by Eurocode 3 [20]. The steel temperature can then be obtained, for example, by a forward difference scheme derived from Equation 34.42 as T iþ1 ¼ T si þ Δt T if T si =½τð1 þ μ=3Þ s ½expðμ=10Þ 1 ΔT f ð34:44Þ As an illustration of the importance of considering the heat capacity of the insulation, a simple example of a steel section is analyzed considering the relative heat capacity μ of the insulation and for comparison neglecting it (i.e., μ ¼ 0). A section factor Ai /Vs As /Vs ¼ 500 m1 and an insulation thickness di ¼ 0.05 m, a conductivity
ki ¼ 0.2 W/m K, and a specific heat capacity ci ¼ 800 Ws/kg are assumed. Calculated steel temperature developments applying Equation 34.44 considering and not considering the heat capacity of the insulation (μ ¼ 0) are shown in Fig. 34.10. For comparison, temperature rises obtained by accurate finite element calculations are shown as well. Notice how well the temperatures calculated by FEM match the temperatures obtained using the scheme according to Equation 34.44 considering the heat capacity of the insulation. On the other hand, the calculated temperature becomes much higher if the heat capacity of the insulation is not considered. In this case the predicted time to reach a steel temperature of 500 C is on the
U. Wickstro¨m
Fig. 34.10 Comparison of calculated steel temperature rise of an insulated steel section when exposed to a standard ISO 834 fire exposure, considering and neglecting the heat capacity of the insulation, respectively
Steel temperature rise (°C)
1116 1000 900 800 700 600 500 400 300 200 100 0 –100
μ as calculated μ neglected TASEF
0
0.5
order of a quarter of an hour shorter when the heat capacity is not considered. Notice also that Equation 34.44 predicts a negative temperature change for the first 5–10 min, which of course is a numerical error embedded in the equation. Insulated Steel Structures Exposed to Parametric Fires Eurocode 3 [20] (EN1991-2-1) has introduced the concept of parametric fires as a convenient way of expressing a set of postflashover design fires. The fire temperature Tf is then expressed as (see Eurocode 1 [4]) T f ¼ 20 þ 1325 1 0:324e0:2t* ð34:45Þ 0:204e1:7t* 0:472e19t* where the modified or scaled time is expressed as t* ¼ Γt
ð34:46Þ
and where Γ is a function of the compartment properties (i.e., sizes of openings and thermal properties of enclosure surfaces). A Γ-value approximately equal to unity yields the ISO 834 standard fire, whereas Γ less than unity yields a more slowly growing fire and Γ greater than unity a faster growing fire. The fire duration depends on the fuel density in the fire compartment (see Eurocode 3 [20]). Below it is demonstrated how these types of design fires can facilitate the calculation and the presentation of temperature in fire-exposed insulated steel sections. The concept of parametric fires can also be used for concrete structures using the technique outlined later in this chapter.
1.0 Time (hr)
1.5
2.0
Table 34.4 Constants in the analytical expression of the parametric fire curve i Bi ( C) βi (h1)
0 1325 0
1 430 0.2
2 270 1.7
3 625 19
When using parametric design fires, the temperature of insulated steel sections can, of course, be obtained by numerical calculations according to Equation 34.40. Then nonlinear phenomena such as temperature-dependent material properties may be considered. However, if the thermal properties are assumed constant and the fire temperature is expressed by exponential terms as in Equation 34.45, then the steel temperature rise as a function of time can be obtained by integration as a closed-form analytic expression [25]. For convenience Equation 34.45 is first written in the form T s ¼ 20 þ
3 X
Bi expðβi t*Þ
ð34:47Þ
i¼0
where the constants Bi and βi are given in Table 34.4. Then the steel temperature can be obtained as a function of the modified fire duration t* and the modified time constant τ* of the steel section as T s 20 ¼
3 X i¼0
Bi ½expðβi t*Þ expðt*=τ*Þ 1 βi τ*
ð34:48Þ
34
Methods for Predicting Temperatures in Fire-Exposed Structures
where τ* ¼ Γτ
ð34:49Þ
The insulated steel section time constant τ is given in Equation 34.38. The relation between the temperature rise as a function of modified time as expressed in Equation 34.48 is also given in the diagram shown in Fig. 34.11 for various modified time constants τ*. The diagram in Fig. 34.11 is particularly easy to use for ISO 834 standard fire exposures when Γ by definition is equal to unity. As an example, consider a steel section with a section factor Ast/Vst ¼ 200 m1 insulated with a 25-mm-thick protection board with a constant thermal conductivity of 0.1 W/(m K). The steel density and specific heat capacity are 7800 kg/m3 and 500 J/(kg K), respectively. The section time constant may then be obtained from Equation 34.38 as τ ¼ 4875 s or 1.35 h. Then if the
1117
section is exposed to standard fire (Γ ¼ 1), a temperature rise of 418 C may be obtained from Equation 34.48 or from Fig. 34.11. If the same section is exposed to a more slowly growing fire with Γ ¼ 0.5, then τ* ¼ Γτ ¼ 0.68 h and the temperature rise after 1 h may be found for a modified time of t* ¼ Γt ¼ 0.5 h to be 363 C. On the other hand, if the section is exposed to a fast-growing fire with Γ ¼ 3.0, then τ* ¼ (3.0) · (1.35) ¼ 4.05 h and t* ¼ (3.0) · (1.0) ¼ 3.0 h, and the steel temperature rise can be obtained from Equation 34.47 or from Fig. 34.11 as 505 C. Notice that the maximum steel temperature for a given fire exposure time increases considerably with an increasing Γ-factor. It must, however, also be kept in mind that the fire duration for a given fuel load is proportional to the inverse of the opening factor included in the Γ-factor. For more information see, for example, Eurocode 1 [4].
Steel temperature 1200
1000
Temperature rise, θ (°C)
Fire temperature 800
t* = 0.2 t* = 0.1
t* = 0.3 t* = 0.5 t* = 0.7
600
t* = 1.0 t* = 1.5 t* = 2.0 t* = 3.0
400
t* = 4.0
200
0
0
0.5
1
1.5
2
2.5
3
Modified time, t* (h)
Fig. 34.11 Temperature of various insulated steel sections exposed to parametric fires in the heating phase as a function of modified time t*. The thermal properties
of the steel sections are expressed in modified time constants τ* [25]
U. Wickstro¨m
1118
Unprotected Steel Structures
Shadow Effects
The temperature of unprotected steel structures is numerically more difficult to calculate as the highly nonlinear heat transfer is decisive for the temperature development of the steel. The total heat transfer qtot may be obtained from Equation 34.11 or Equation 34.12. Then the steel temperature can be obtained from the differential heat balance equation in a similar way as for insulated steel sections (see also Equation 34.36).
When an open section such as an I-section is exposed to fire, the heat transfer by radiation will be partly shadowed (Fig. 34.12). That means the section will only receive as much heat from the fire as if it had the same circumference as a boxed section. Therefore, it is appropriate to replace the area per unit length As with the so-called boxed area A□ in Equations 34.50 and 34.52 as the radiation heat transfer mode dominates at elevated temperature. The boxed area A□ is typically for an I-section 30 % less than the corresponding area As, which means a proportional increase of the section response time τ. Alternatively, a section with a 40 % higher section factor would yield the same temperature if the concept of shadow effects is applied. This means that by considering the shadow effects in the calculations many more open steel sections can be accepted without thermal protection. The principal of shadow effects is particularly important for bare, unprotected steel sections, although the concept can be applied to other types of structures as well.
htot T f T s ¼ cs ρs ðV s =As Þð∂T s =∂tÞ ð34:50Þ where the total heat transfer coefficient htot may be obtained from Equation 34.13. This equation can be solved numerically with a forward difference scheme in a similar way as for insulated sections as T iþ1 ¼ ðΔt=τÞT if þ ð1 Δt=τÞT si s
ð34:51Þ
where the characteristic response time τ of the steel section in this case is defined as τ ¼ cs ρs V s =As htot ¼ ðcs ρs Þ=½htot ðAs =V s Þ ð34:52Þ Notice that the thermal properties of the steel may vary with temperature, and in particular the total heat transfer coefficient htot will increase substantially with the temperature level. It would, therefore, be misleading to call τ a time constant in this case. The stability criterion for the explicit numerical scheme according to Equation 34.51 may then be expressed as Δt τ ¼ ðcs ρs Þ=½htot ðAs =V s Þ
ð34:53Þ
Thus, the critical time increment decreases considerably as htot increases with time and increasing temperature levels. Principles for calculating the section factors for various types of configurations of unprotected steel can be found in Table 34.5 [20].
Example of Steel Temperatures Calculated Using Finite Element Codes The preceding steel temperature calculations assume uniform steel temperatures in the section analyzed as a crude approximation. It leads indeed in general to solutions on the safe side (i.e., the temperatures are overestimated and often overdesigned, leading to unnecessary costs). For more precise analyses numerical calculations are needed employing, for example, finite element computer codes. An example is given below. An encased I-section beam is carrying a concrete slab. It is exposed to standard fire conditions according ISO 834 (Fig. 34.13). Heat transfer conditions according to Equation 34.11 are assumed with ε ¼ 0.8 and h ¼ 25 W/m2 K. The thermal properties of steel and concrete are
34
Methods for Predicting Temperatures in Fire-Exposed Structures
1119
Table 34.5 Section factor As/Vs for unprotected steel members [20] Open section exposed to fire on all sides:
Tube exposed to fire on all sides:
Open section exposed to fire on three sides:
Hollow section (or welded box section of uniform thickness) exposed to fire on all sides:
I-section flange exposed to fire on three sides:
Welded box section exposed to fire on all sides:
(continued)
U. Wickstro¨m
1120 Table 34.5 (continued) Angle exposed to fire on all sides:
I-section with box reinforcement, exposed to fire on all sides:
Flat bar exposed to fire on all sides:
Flat bar exposed to fire on three sides:
Fig. 34.12 Illustration of the shadow effect. The boxed value area per unit length A□ of a steel section represents the area exposed to heating conditions from the fire
a
b
As
I-section exposed to fire from four sides. The surfaces between the flanges will be partly shadowed.
A
The boxed area of the I-section, A , will have a shorter periphery than the original section.
34
Methods for Predicting Temperatures in Fire-Exposed Structures
Fig. 34.13 Encased I-section steel (HE 300B) beam carrying a concrete slab. Slab thickness 160 mm, insulation thickness 30 mm, steel height and width 300 mm, flange thickness 19 mm, and web thickness 11 mm
Concrete
1121
160 mm
19 mm
Steel flange
300 mm
11 mm
Insulation 30 mm
Steel web
300 mm
as given in Eurocodes 2 and 3, respectively, shown above and below. The encasement boards are assumed to have a thermal conductivity (k) of 0.2 W/m K and a volumetric specific heat capacity (cρ) of 40 kJ/m3. The finite element discretization model is shown in Fig. 34.14. Heat transfer inside the void is assumed to be by radiation only with an internal surface emissivity of 0.8. The calculated temperature histories in the steel flanges are shown in Fig. 34.15. For comparison the temperature calculated assuming uniform temperature is also included. Notice that the temperature difference between the minimum and maximum steel temperatures are on the order of 130 C due to uneven heating and steel mass distribution and in particular due to the cooling of the top flange by the concrete slab. A simple approximate calculation can be obtained assuming a uniform steel section temperature, according to the discussion on insulated steel structures, with the section factor calculated as shown in Table 34.3. A time constant τ equal to 6460 s or 1.8 h can then be calculated (Equation 34.38) and a uniform steel temperature after 2 h of about 635 C can be obtained from Fig. 34.10. Notice that this temperature is considerably higher than the average temperature obtained with the much more accurate finite element model.
Calculation of Temperature in Concrete Structures Reinforced concrete structures are sensitive to fire exposure for mainly two reasons. They may spall due to combinations of internal water pressure and high thermal stresses, and they may gradually lose their load-bearing capacity when the reinforcement bars get hot, reaching temperature levels above 400 C. Prestressed steel may even lose strength below that level. In addition the concrete loses both strength and stiffness at elevated temperature. When occurring, spalling usually starts within 30 min of severe fire exposure. Because the spalling phenomenon is very complex and cannot be predicted with simple mathematical temperature models, it will not be further discussed here. Thus, the procedures presented below presume that no spalling occurs that could considerably influence the temperature development. In general, temperatures in fire-exposed structures may be obtained from tabulated values (see, e.g., Eurocode 2 [26]) or by more or less advanced calculations. Below some simple calculation methods are given. For more general situations, finite element calculations are needed.
U. Wickstro¨m
1122
Thermal Properties of Concrete The thermal conductivity of concrete decreases in general with rising temperature. It depends on concrete quality and type of ballast. For design purposes curves as shown in Fig. 34.16 may be used according to Eurocode 2 [26]. For more accurate calculations with alternative concrete qualities more precise material data may be needed, as discussed earlier. The specific heat of dry concrete does not vary much with temperature. However, in reality concrete structures always contain more or less physically bound water. This water will evaporate at temperatures above 100 C and constitute a heat sink as the evaporation consumes a lot of heat. Thus, the specific heat capacity for normal weight concrete according to Eurocode 2 is as shown in Fig. 34.17. The emissivity of concrete surfaces may be assumed to be 0.8 and the convective heat transfer coefficient may, when simulating fully developed fires, be assumed equal to 25 W/m2 K. See, for example, Eurocode 1 [4]. In general the assumed values of these parameters have little influence on calculated temperatures inside concrete structures.
Penetration Depth in Semi-Infinite Structures Fig. 34.14 Finite element discretization used to calculate the temperature development of the steel beam shown in Fig. 34.13 when exposed to a standard fire exposure according to ISO 834 Fig. 34.15 Temperature history of bottom and top flanges, middle and corner points
Concrete is a material with relatively high density and low conductivity. Therefore, it takes a
700
Temperature (°C)
τ* = 1.8 h
Bottom flange middle Top flange middle Bottom flange edge Top flange edge τ* = 1.8 h
600 500 400 300 200 100 0 0
0.5
1.0 Time (hr)
1.5
2.0
Methods for Predicting Temperatures in Fire-Exposed Structures
Fig. 34.16 Upper and lower limits of thermal conductivity as a function of temperature of normal weight concrete according to Eurocode 2 [26]
1123
2.0 1.8 1.6 1.4 λ (W/m K)
34
Upper limit
1.2 1.0 0.8
Lower limit
0.6 0.4 0.2 0.0 0
200
400
600
800
1000
1200
800
1000
1200
θ (°C)
2200
u = 3.0%
2000 1800 1600 Cp (θ) (J/kg/K)
Fig. 34.17 Specific heat capacity of concrete as a function of temperature at three different moisture contents, 0 %, 1.5 %, and 3 %, for siliceous concrete according to Eurocode 2 [26]
u = 1.5%
1400 1200 1000
u = 0%
800 600 400 200 0 0
200
400
600 θ (°C)
long time for heat to penetrate into the structure and raise its temperature, or in other words it takes time before a temperature change at one point is noticeable at another point. Thus, in many cases a concrete structure may then be assumed semi-infinite. For the idealized case of a semi-infinite body at a uniform initial temperature Ti where the surface temperature momentarily is changed to a constant level of Ts, the temperature rise (T Ti) inside the body at a depth x at a time t may be written as a function of the normalized pffiffiffiffiffiffiffiffi group η ¼ x = 2 ðαtÞ where α is an assumed constant thermal diffusivity as defined in Equation 34.22. The relative temperature rise may then be written as
ðT T i Þ ¼ erfcðηÞ ¼ 1 er f ðηÞ ðT s T i Þ
ð34:54Þ
The Gauss complementary error function erfc is shown in Fig. 34.18. Tabulated values of the Gauss error function may be found in textbooks such as Holman [1]. For values of η greater than a value of 1.4 the relative rise is less than 5 %. Thus, depending on accuracy, the temperature penetration depth δ at a given time may be estimated as pffiffiffiffi δ ¼ 2:8 αt ð34:55Þ As an example, the temperature rise can be estimated to penetrate only about 0.11 m into a concrete structure after 1 h, assuming a
U. Wickstro¨m
1124 Complementary error function 1 0.9 0.8 Erfc (x/[2(αt)0.5])
Fig. 34.18 Normalized temperature distribution in a semi-infinite body according to the Gauss complementary error function erfc as in Equation 34.54
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
x/[2(αt)0.5]
1.0 0.9 0.8 0.7
ηs = 1 – 0.062t–0.88
0.6 ηs
Fig. 34.19 Ratio ηs between concrete surface temperature Ts and the fire temperature Tf as a function of time for a normal weight concrete with thermal properties, according to Eurocode 2 [26], exposed to standard fire conditions, according to ISO 834
0.5 0.4 0.3 0.2 0.1 0.0 0.1
conductivity of a 1 W/m K, a density of 2300 kg/ m3, and a specific heat capacity of 1000 J/(kg K). Penetration depth can actually be applied to steel as well. A temperature change at one point of a steel member will not be noticeable beyond a distance corresponding to the penetration depth.
Simple One-Dimensional Calculations With the thermal properties of concrete as given in the earlier discussion on measurement of thermal properties, the temperature can be calculated in structures exposed to fires. In general, numerical procedures such as finite element methods need to be employed. Wickstro¨m [27–29] has, however, shown, based on numerous finite
1 tw (hr)
10
element calculations, that in one-dimensional cases the temperature inside concrete structures exposed to standard fire conditions according to ISO 834 may be obtained from the diagrams shown in Figs. 34.19 and 34.20. These diagrams apply to normal weight concrete with thermal properties, according to Eurocode 2 [26], as shown in the earlier section on measurement of thermal properties. In Wickstro¨m [27–29] it is shown that the same type of diagrams can be used more generally considering both various parametric fires and various material properties. In these references techniques are also presented on how temperatures can be obtained in walls exposed from two sides and in simple two-dimensional cases by superpositioning based on the same
34
Methods for Predicting Temperatures in Fire-Exposed Structures
1125
0.8 0.7
ηx = 0.160 in(t/x2) – 0.70
0.6
ηx
0.5 0.4 50 mm lower limit
0.3
100 mm lower limit
0.2
25 mm upper limit 50 mm upper limit
0.1
100 mm upper limit
0 100
1000
10,000
t/x2 (h/m2)
Fig. 34.20 Ratio ηx between internal concrete temperature Tx and the surface temperature Ts as a function of time divided by depth squared t/x2 for normal weight concrete with thermal properties, according to Eurocode
2 [26], exposed to standard fire conditions, according to ISO 834. Calculations are made assuming the upper and lower limits of the conductivity as shown in Fig. 34.16
simple one-dimensional approximations as outlined below. Thus, the diagram given in Fig. 34.19 shows the ratio ηs between the concrete surface temperature and the standard fire temperature, according to ISO 834, (see Equation 34.63) as a function of time. Ts ηs ¼ ð34:56Þ Tf
to Eurocode 2. Both upper and lower limit values of the conductivity (see Fig. 34.16) are included in the finite element calculations as well as depths of 25, 50, and 100 mm. A straight line is drawn in the logarithmic-linear diagram, which yields approximate temperatures slightly higher than would be obtained with more accurate finite element calculations. The internal concrete temperature may now be written as
The coefficient ηs is in general a function of the pffiffiffiffiffiffiffiffiffiffiffi group time t over thermal inertia ðkρcÞ of the concrete. In Fig. 34.19 normal weight concrete with thermal properties according to Eurocode 2 [26] is assumed. Figure 34.20 shows in turn the ratio between the internal temperature Tx at a depth x and the surface temperature Ts. Thus, Tx ηx ¼ Tw
ð34:57Þ
The coefficient ηx is in principle a function of the Fourier number (i.e., the thermal diffusivity k/ (cρ) of the concrete times the fire duration t over the depth x squared). Results from computer calculations are shown in Fig. 34.20. In these calculations thermal properties of concrete with a water content of 1.5 % are assumed according
T x ¼ ηs ηx T f
ð34:58Þ
The graphs in Figs. 34.19 and 34.20 can be approximated by simple expressions. Thus, ηs ¼ 1 0:062t0:88
ð34:59Þ
ηx ¼ 0:16ln t=x2 0:70
ð34:60Þ
and
respectively, where t is time in hours and x is distance in meters from the surface. Then, in summary, for standard fire exposure according to ISO 834 and normal weight concrete according to Eurocode 2 [26] (see earlier section on thermal properties), a very simple closed-form solution may be obtained for the
U. Wickstro¨m
1126
a
b
Concrete slab fire insulated from below
Concrete cover providing similar thermal protection
Fig. 34.21 Protection of a concrete structure layer with thickness di, which gives an equivalent thermal protection as a concrete layer with thickness dc
temperature at arbitrary times and depths by inserting Equations 34.59 and 34.63 in hours 34.60 into Equation 34.58: 0:88 T x ¼ ð1 0:062t Þ 0:16 lnðt=x2 Þ
ð34:61Þ 0:70 345logð480t þ 1Þ As an illustration, the temperature in a slab of normal weight concrete is calculated at a depth of 4 cm when exposed to an ISO 834 standard fire for 1 h. At first ηs is obtained from Fig. 34.19 to be 0.94 for t ¼ 1 h. Then for t/x2 ¼ 1.0/ (0.04)2 ¼ 625 h/m2, Fig. 34.20 yields ηx ¼ 0.33. As the standard time temperature rise after 1 h is 925 C, the concrete surface temperature rise is obtained from Equation 34.56 as 0.94*925 ¼ 870 C and Equation 34.61 yields the temperature rise at a depth of 4 cm to be Tx ¼ 0.94*0.33*925 C ¼ 287 C. A corresponding accurate finite element calculation yields a temperature rise of Tx ¼ 277 C.
exposed to fire. Some insulation materials undergo chemical transformations requiring a lot of heat (latent heat) to raise the temperature whereas others work just as passive thermal barriers. Only the latter type of insulation systems is further discussed here and the formula given below only applies to this type of inert material. The thermal efficiency of a protection layer is sometimes expressed as the thickness of an additional concrete coverage that would yield the same protection. Wickstro¨m and Hadziselimovic [30] have shown that the same effect is approximately obtained when the thermal resistance of the insulation is the same as that for the concrete (i.e., di/ki ¼ dc/kc where d is thickness and k conductivity, respectively, and the indices i and c stand for insulation and concrete, respectively). Thus, the equivalent concrete layer thickness can be calculated as d c ¼ kc d i =ki
Fire-Insulated Concrete Structures In some applications, it may be advantageous to insulate concrete structure surfaces to prevent them from fast temperature rises. This insulation may either be to avoid spalling or to give the concrete-embedded reinforcement bars additional thermal protection (Fig. 34.21). Behind the protection the temperature of the concrete surface will not rise as quickly as when directly
ð34:62Þ
which indicates that the influence of the specific heat capacity and density of the protecting material is negligible in the case of protecting concrete structures. The thermal inertia of the concrete is totally dominating over the inertia of the insulation. As an example, a 10 mm board of vermiculite with a thermal conductivity of 0.2 W/m K corresponds to a concrete protection layer of 50 mm, assuming the concrete has a conductivity
Methods for Predicting Temperatures in Fire-Exposed Structures
Fig. 34.22 Calculated response of a plate thermometer when exposed to standard fire test conditions, according to ISO 834, Equation 34.63
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1000 800 Temperature (°C)
34
ISO 834 600 400 Plate thermometer 200 0 0
of 1.0 W/m K for the temperature interval considered. This could mean considerable savings in both weight and space for a concrete structure.
Calculation of Temperature in Timber Structures Modeling the thermal behavior of wood is complicated by phenomena such as moisture evaporation and migration, and the formation of char has a decisive influence on the temperature development. Nevertheless, it has been shown that general finite element codes such as SAFIR, TASEF, and COMSOL can be used to predict temperature in fire-exposed cross sections of glued laminated beams [31] provided apparent thermal material properties and appropriate boundary conditions are used. Other specialized numerical codes for timber structures have been developed by Fung [32] and Gammon [33]. More commonly empirical rules are used to estimate the penetration of the charring layer and the loss of strength of timber structures (see, e.g., Eurocode 5 [34]).
Heat Transfer in Fire Resistance Furnaces Nominal time-temperature relations are clearly defined in fire resistance test standards such as ISO 834, EN 1363-1, and ASTM E119. However, furnaces have various characteristics
10
20
30 Time (min)
40
50
60
depending on the difference between the black body radiation temperature Tr (Equation 34.7) and the gas temperature Tg. In addition there is a time delay of the temperature recording due to the thermal inertia of the monitoring thermocouples. Therefore, when theoretically simulating fire resistance tests, it must be considered how the temperature has been measured in the various standards.
Furnaces Controlled According to ISO 834 and EN 1363-1 In ISO 834 and EN 1363-1 the nominal furnace temperature Tf is given as T f ¼ 20 þ 345log10 ð8t þ 1Þ
ð34:63Þ
The furnace temperature shall be monitored with plate thermometers (see ISO 834-1 and EN 13631). The time delay or, in other words, the time constant of the plate thermometers in a furnace test is negligible, which is indicated in Fig. 34.22, where the calculated temperature response of a plate thermometer exposed to uniform furnace temperature according to ISO 834 is shown. The heat transfer is then calculated according to Equation 34.11 assuming the emissivity ε and the convection heat transfer coefficient h equal to 0.9 and 25 W/m2 K, respectively. Notice that the plate thermometer temperature follows the nominal curve very closely except for the first few minutes. Thus, the time delay of the plate thermometer temperature recordings due to inertia in a standard fire test may be neglected
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and the heat transfer to a specimen surface can accurately be calculated according to Equation 34.18. Sometimes it is of interest to know the incident radiation level under a furnace test. This level can be measured directly with heat flux meters, but in the section below it is shown how this radiation level may be obtained from plate thermometer measurements. The incident radiation heat flux qinc may be obtained from Equation 34.16, and plate thermometer temperature recordings given the gas temperature Tg, the emissivity εPT, and the convection heat transfer coefficient hPT of the plate thermometer are known as qinc ¼ σT 4PT hPT T g T PT =εPT ð34:64Þ The latter term in Equation 34.64 is relatively small and may be treated as an error term. For values of the emissivity εPT and the convection heat transfer coefficient hPT equal to 0.8 and 25 W/m2 K, respectively, a temperature level of 1000 K and a gas temperature Tg deviating from the plate thermometer temperature TPT by as much as 50 K yields the latter term of Equation 34.64 to be less than 3 %. At higher temperature levels and at minor deviations between gas and radiation temperatures this error is much smaller and probably seldom greater than must be anticipated when measuring incident radiation directly with heat flux meters.
Furnaces Controlled According to ASTM E119 In the American test standard ASTM E119 the nominal furnace temperature is specified according to the time-temperature relation given in Table 34.6. The standard thermocouple for monitoring the furnace temperature is, however, very thick and, therefore, very slow. According to ASTM E119, it shall have a time constant within the range of from 5.0 to 7.2 min. To eliminate the effects of the time delay the thermocouples may be analyzed as bare steel sections. Thus, by
Table 34.6 Standard Fire Time-Temperature Relation According to ASTM E119 Time (min) 0 5 10 15 30 60
Temperature rise ( C) 0 556 659 718 821 925
Time (min) 90 120 180 240 360
Temperature rise ( C) 986 1029 1090 1133 1193
applying Equation 34.51, the effective fire temperature Tf can be derived from the corresponding thermocouple measurements Ttc as iþ1 i ¼ T iþ1 T iþ1 ð34:65Þ f tc þ τ=Δt T tc T tc The furnace thermocouple time constant, as referred to in the ASTM E119 standard, is rather imprecisely specified as the heat transfer by radiation that is nonlinear and increases by the temperature level raised to the fourth power. More realistic is to assume a time constant of 6 min (in the middle of the range from 5.0 to 7.2 min) at a furnace temperature level of perhaps 1000 K, and then obtain the heat transfer to the thermocouple by calculating the heat transfer according to Equation 34.11 assuming ε and h equal 0.9 and 50 W/m2 K, respectively. Then match a surfaceto-volume ratio obtained from Equations 34.52 and 34.13 to obtain the stipulated time constant. (As a comparison, the corresponding time constant for a plate thermometer at the same temperature level is on the order of 15 s.) Figure 34.23 shows the actual furnace temperature rise in a furnace controlled ideally precisely according to ASTM E119. Notice that the real or effective furnace temperature is much higher than indicated by the slowly responding ASTM type of shielded thermocouples. It must, however, be noted that the above analysis assumes that the furnace radiation and gas temperatures are equal, which is seldom the case. The gas temperature may be higher than the radiation temperature and, therefore, the differences in practice between the ASTM thermocouple and the plate thermometer may be much less, as the
Methods for Predicting Temperatures in Fire-Exposed Structures
Fig. 34.23 Temperatures ASTM E119 and ISO 834 (plate thermometer), respectively, must follow to obtain the effective furnace temperature Tf according to ASTM E119 due to time delay
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1200 1000 Temperature (°C)
34
ASTM thermocouple 800 600 ASTM standard curve 400 Plate thermometer
200 0 0
10
20
30
40
50
60
Time (min)
ASTM thermocouple is more sensitive to convective heat transfer than the plate thermometer. The general observation from this theoretical analysis agrees with the test results reported by Sultan [35]. The difference between the ASTM type of thermocouples and the plate thermometer is insignificant after 10 min.
References 1. J.P. Holman, Heat Transfer, 4th ed., McGraw Hill, New York (1976). 2. U. Wickstro¨m, D. Duthinh, and K.B. McGrattan, “Adiabatic Surface Temperature for Calculating Heat Transfer to Fire Exposed Structures,” Interflam, Interscience Communications, London, UK (2007). 3. K.B. McGrattan, S. Hostikka, J.E. Floyd, H.R. Baum, and R.G. Rehm, Fire Dynamics Simulator (Version 5), Technical Reference Guide, NIST SP 1018–5, National Institute of Standards and Technology, Gaithersburg, MD (2005). 4. EN 1991–1-2, “Eurocode 1: Actions on structures— Part 1–2: General Actions—Actions on Structures Exposed to Fire,” European Committee for Standardization (CEN), Brussels, Belgium (2002). 5. U. Wickstro¨m and T. Hermodsson, T., “Comments on Paper by Kay, Kirby, and Preston, ‘Calculation of the Heating Rate of an Unprotected Steel Member in a Standard Fire Resistance Test’,” Fire Safety Journal, 29, 4, pp. 337–343 (1997). 6. D. Flynn, “Response of High Performance Concrete to Fire Conditions: Review of Thermal Property Data and Measurement Techniques,” NIST GCR 99–767, National Institute of Standards and Technology, Gaithersburg, MD (Mar. 1999). 7. ISO 8302:1991, Thermal insulation -- Determination of steady-state thermal resistance and related properties -- Guarded hot plate apparatus.
8. B. Adl-zarrabi, L. Bostro¨m, and U. Wickstro¨m, “Using the TPS Method for Determining the Thermal Properties of Concrete and Wood at Elevated Temperature,” Fire and Material, 30, pp. 359–369 (2006). 9. E. Sterner and U. Wickstro¨m, “TASEF—Temperature Analysis of Structures Exposed to Fire,” SP Report 1990:05, Swedish National Testing and Research Institute, Bora˚s, Sweden, (1990). 10. U. Wickstro¨m, “TASEF-2—A Computer Program for Temperature Analysis of Structures Exposed to Fire,” Ph.D. Dissertations, Lund Institute of Technology, Department of Structural Mechanics, Report No. 79-2, Lund, Sweden (1979). 11. E. Sterner and U. Wickstro¨m, “TASEF—Temperature Analysis of Structures Exposed to Fire,” SP Report 1990:05, SP Technical Research Institute of Sweden, Bora˚s, Sweden (1990). 12. J.M. Franse´n, V.K.R. Kodur, and J. Mason, “A Computer Program for Analysis of Structures Submitted to Fire,” User’s Manual of SAFIR 2001, University of Liege, Belgium (2000). 13. ABAQUS Standard User’s Manual, volumes I–III, version 6.2, Hibbit, Karlsson and So¨rensen, Inc., Pawtucket, RI (2001). 14. ANSYS, Inc., 275 Technology Drive, Canonsburg, Pennsylvania (http://www.ansys.com). 15. K.J. Bathe, Finite Element Procedures, Prentice Hall, Upper Saddle River, NJ (1996). 16. See website http://www.comsol.com. 17. Guide for Verification and Validation of Computational Fluid Dynamics Simulations, AIAA, Guide G-077–1998, American Institute of Aeronautics and Astronautics, Reston, VA (1998). 18. U. Wickstro¨m and J. Pa˚lsson, “A Scheme for Verification of Computer Codes for Calculating Temperature in Fire Exposed Structures,” SP Report 1999:36, Swedish National Testing and Research Institute, Bora˚s, Sweden (1999). 19. U. Wickstro¨m, “An Evaluation Scheme of Computer Codes for Calculating Temperature in Fire Exposed Structures,” Interflam (1999). 20. EN 1993-1-2, “Eurocode 3: Design of Steel Structures—Part 1–2: General Rules—Structural
1130 Fire Design,” European Committee for Standardization (CEN), Brussels, Belgium (2005). 21. J. Hamann, R. Mu¨ller, R. Rudolphi, R. Schriever, and U. Wickstro¨m, “Anwendung von TemperaturBerechnungsprogrammen auf kritische Referenzbeispiele des Brandschutzes,” Bundesanstalt fu¨r Materialforschung und -pru¨fung, Berlin (1999). 22. U. Wickstro¨m, “Temperature Analysis of HeavilyInsulated Steel Structures Exposed to Fire,” Fire Safety Journal, 5, pp. 281–285 (1985). 23. S.J. Melinek and P.H. Thomas, “Heat Flow to Insulated Steel,” Fire Safety Journal, 12, pp. 1–8 (1987). 24. Z.H. Wang and H.T. Kang, “Sensitivity Study of Time Delay Coefficient of Heat Transfer Formulations for Insulated Steel Members Exposed to Fires,” Fire Safety Journal, 41, pp. 31–38 (2006). 25. U. Wickstro¨m, “Temperature Calculation of Insulated Steel Columns Exposed to Natural Fire,” Fire Safety Journal, 4, pp. 219–225 (1981). 26. EN 1992-1-2, “Eurocode 2: Design of Concrete Structures—Part 1–2: General Rules—Structural Fire Design,” European Committee for Standardization (CEN), Brussels, Belgium (2004). 27. U. Wickstro¨m, “A Very Simple Method for Estimating Temperature in Fire Exposed Concrete Structures”, in Proceedings of New Technology to Reduce Fire Losses & Costs, (S.J. Grayson and D.A. Smith, eds.), Elsevier, New York (1986). 28. U. Wickstro¨m, “Application of the Standard Fire Curve for Expressing Natural Fires for Design Purposes,” Fire Safety: Science and Engineering, ASTM STP 882, American Society of Testing and Materials, Philadelphia, pp. 145–159 (1985). 29. U. Wickstro¨m, “Natural Fires for Design of Steel and Concrete Structures—A Swedish Approach,” International Symposium on Fire Engineering for Building Structures and Safety, the Institute of Engineers, Australia, National Conference Publication No. 89/16, Melbourne (1989).
U. Wickstro¨m 30. U. Wickstro¨m and E. Hadziselimovic, “Equivalent Concrete Layer Thickness of a Fire Protection Insulation Layer Paper,” Fire Sa, Brandteknik, Odense, Denmark (1996). 31. B.L. Badders, J.R. Mehaffey, and L.R. Richardson, “Using Commercial FEA software Packages to Model the Fire Performance of Exposed Glulam Beams,” Fourth International Workshop “Structures in Fire,” Aveiro, Portugal (2006). 32. F.C.W. Fung, “A Computer Program for the Thermal Analysis of the Fire Endurance of Construction Walls,” NBSIR 77.1260, National Bureau of Standards, Washington, DC (1977). 33. B.W. Gammon, “Reliability Analysis of Wood-Frame Wall Assemblies Exposed to Fire,” Ph.D. Dissertation, University of California, Berkeley (1987). 34. EN 1995-1-2, “Eurocode 5, Design of Timber Structures—Part 1–2: General Rules—Structural Fire Design,” European Committee for Standardization (CEN), Brussels, Belgium (2004). 35. M.A. Sultan, “A Comparison of Heat Exposure in Fire Resistance Test Furnaces Controlled by Plate Thermometers and by Shielded Thermocouples,” Interflam 2004, Edinburgh, Scotland, pp. 219–229 (2004).
Professor Ulf Wickstro¨m is teaching heat transfer in fire technology at Lulea˚ University of Technology, Sweden. He is a former head of the Department of Fire research at SP Technical Research Institute of Sweden. Professor Wickstro¨m has a PhD from Lund University of Technology in fire technology and a master of science from the University of California, Berkeley. For his thesis research he developed the computer program TASEF for calculating temperature in fire-exposed concrete and steel structures. His focus of scientific interest is heat transfer analysis of structures exposed to fire, on which he has published several papers.
Fire Load Density
35
Mario Fontana, Jochen Kohler, Katharina Fischer, and Gianluca De Sanctis
Introduction The fire load has a strong influence on the temperature development during a compartment fire. Therefore, the assessment of the fire load as an input to model the time-temperature relationship, is an important task in structural fire design. In combination with the available oxygen and the combustion properties of the material, the fire load density determines the heat release rate HRR of a fire. Figure 35.1 illustrates the qualitative behaviour of the heat release rate as a function of time during a fire. The fire growth phase (including potential flashover), the fully developed state and the decay phase are qualitatively shown for the two burning regimes of fuel (4) or ventilation (3) controlled fires. The area under both curves corresponds to the energy released by the available fire load in the room. The duration of a fire depends on the amount of fire load and the burning regime. For ventilation controlled fires the heat release rate is limited by the available oxygen. In a fuel controlled fire the M. Fontana (*) • G. De Sanctis Institute of Structural Engineering, ETH Zurich, Stefano-Franscini-Platz 5, 8093 Zurich, Switzerland J. Kohler Department of Structural Engineering, Norwegian University of Science and Technology, 7491 Trondheim, Norway K. Fischer Matrisk GmbH, Alte Obfelderstrasse 50, 8910 Affoltern am Albis, Switzerland
maximal heat release rate in the room is achieved and the duration of the fire is usually shorter (1).
Definitions The fire load [MJ] is defined as the quantity of energy which is released by the complete combustion of all combustible material in a fire compartment. The fire load is often subdivided into variable (movable or mobile) and permanent (fixed or immobile) fire load. The net heat of combustion [MJ/kg] is defined as the potential combustion energy per kilogram contained in the material. The fire load density is defined as the fire load per unit floor area [MJ/m2] or per unit volume [MJ/m3]. A fire compartment is defined as the enclosed space, which is separated from adjoining spaces by adequate fire barriers.
Representation of Fire Load Basic Representation The fire load in buildings consists of the energy content of combustible materials, generally comprising furniture, equipment and stored objects and goods (variable fire load) as well as combustible components of the structural elements (permanent fire load) which can burn during a fire. The variable fire load depends
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HRR 4
Fig. 35.1 Illustration of the heat release rate (HRR) development as a function of time during a compartment fire
3
Potential flashover
1
mainly on the occupancy of the room or building, as e.g. residential buildings, hospitals, hotels, stores, storage buildings, industrial facilities, etc. The fire load the also be represented by the fire load density or the distributed fire load by dividing the fire load by the room area. According to CIB W14 [1], the fire load density can be related to the total floor area of the fire compartment [MJ/m2] including aisles and local empty spaces. In some literature [2], the area is related to the total interior area of the surfaces within the compartment including all openings [MJ/m2]. For some building occupancies–especially for storage or industrial buildings–the relation to the volume [MJ/m3] can be more efficient in order to address the effect of storage height on the fire load. The fire load density of a fire compartment containing different combustible materials is defined as: X mi Hi q¼
i
A
ð35:1Þ
mi: the mass of a combustible material i [kg] Hi: heat of combustion or specific energy released from combustion per mass unit of material i [MJ/kg] A: area of fire compartment [m2]
Stochastic Representation The fire load density in a compartment varies in time and in space. In general, it is sufficient to represent the variation in time with a simple time independent random variable q(t,x,y) ¼ q(x,y).
2
time
The variation of the fire load density in space (x,y) can be represented in analogy to the approach proposed in CIB W81 [3] by a stochastic field q(x,y) as: qðx; yÞ ¼ expðLN ðq^ Þ þ V þ Uðx; yÞÞ
ð35:2Þ
where q^ is the overall median fire load density (e.g. specified for a specific occupancy category), V is a zero mean normal distributed variable representing the variation between different structures and different points in time and U(x,y) is a zero mean random field representing the variation within the compartment. The quantities V and U are considered as stochastically independent.
Fire Load Density in Fire Safety Design For localized fire models the spatial distribution of the fire load in space should be taken into account e.g. by the random field in Equation 35.2. Depending on the type and purpose of an analysis, the stochastic representation of the fire load can be simplified. For zone fire models the variability in space can usually be neglected. Then the random variable q can be represented as a simple lognormal distributed random variable with mean value μq and standard deviation σ q. In fire safety design the stochastic representation of the fire load is often simplified. Usually, characteristic values for the fire load are used. These characteristic values are chosen according to the safety format of the corresponding code format. In general, the characteristic values
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Table 35.1 Calculation of characteristic values Distribution type Fractile k-value Characteristic value
Lognormal 80 % 90 % 95 % 0.84 1.28 1.64 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi q qk ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffi exp lnðv2 þ 1Þ k v2 þ 1
Gumbel 80 % 0.72 qk ¼ q þ k σ q
90 % 1.30
95 % 1.87
σ with v ¼ q=q
Fig. 35.2 Overview on the assessment of the fire load
All materials Total fire load Derated fire load Effective fire load
correspond to a specific fractile value of the underlying distribution of q. Fractile values are calculated depending on the distribution type and the mean q and standard deviation σ q of the distributions according to Table 35.1. It is suggested to represent the fire load density as a Lognormal distributed random variable. In some fire safety regulations the Gumbel distribution is prescribed. From a theoretical point of view the Gumbel distribution belongs to the family of extreme value distributions while the fire load is considered as a point in time realization of a random process. However, due to the usually large coefficient of variation of the fire load, it is acceptable to use a Gumbel distribution instead of a Lognormal distribution. Table 35.1 contains information for the use of both distributions.
Assessment of the Fire Load for Fire Safety Design The fire load that is used for design purposes can be assessed as shown in Fig. 35.2: Among all materials only the combustible materials contribute to the potential energy that can be released by
Non-combustibility Protection Incomplete combustion
a fire. The fire load density of these materials can be assessed by Equation 35.1 using their mass and their heat of combustion and is denoted as of the total fire load (Fig. 35.2 second line). A part of total fire load is protected against direct participation in a fire through encapsulation (Fig. 35.2 third line). Derating factors can be used to account for those protected fire loads. The characteristic value that is used for design purposes is usually derived from the probability distribution of the derated fire load. Because the combustion under natural fire conditions is usually incomplete, the effective contribution of the fire load to the energy released during a fire is smaller than the derated fire load (Fig. 35.2 bottom line). The design value of the fire load is related to the effective fire load and is usually calculated by multiplying the characteristic fire load with other factors like partial safety factors (e.g. taking account of the rate of fire occurrence, fire fighting measures etc.). For the design of new buildings the design fire load is estimated based on statistical data of existing buildings with similar occupancies, size and regional tradition. The fire load in an existing compartment or building can be assessed by in situ surveys.
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Estimation of Fire Loads Based on In Situ Surveys The main task in an in situ survey is to identify and to assess the mass and the heat of combustion of all combustible materials and to determine the characteristic fire load for design purposes and can be conducted by different survey methods.
Survey Methods In the literature (e.g. Zalok [4], Culver and Kushner [5]) several fire load survey methods can be identified: – weighing method: direct measurement of weight of the combustible materials – inventory method: indirect estimation of the weight by measuring the dimension and/or the density of the combustible items – questionnaire method: distribution of questionnaires and estimation of the combustible material through photographic selection and inventory tables. Common to all approaches is the attempt to assess the fire load density by the mass of the combustibles and their heat of combustion. The methods differ from each other e.g. in terms of the uncertainties associated with the survey method with the time needed for the survey, with the possibility to verify the results, and with privacy concerns and disruption of business. Based on a study comparing the weighing and the inventory method, Culver and Kushner [5] estimated the relative error to approximately 10 % when using the inventory method instead of the weighing method. The uncertainty in the inventory method is caused mainly by the estimation of the dimensions by the surveyor. On the other hand, also the mass of combustible material estimated based on the weighing method has some inherent uncertainties, e.g. when assessing the individual weights of a composite material. Surveys conducted in the last years constitute that the combination of the inventory and the weighing method leads to results with smallest uncertainties and is therefore considered to be
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the most appropriate fire load survey method, see Zalok [4]. The advantage of the questionnaire method is that surveys can be carried out with relatively little effort and even without physically entering the building.
Assessment of Weight The mass can be directly assessed by weighing the material. In some cases weighing of a material can be complicated because the item is too big for weighing or the item is composed of different materials. In the latter case, weighing of the item without destroying the item is often not possible. In those cases, the weight must be estimated indirectly by assessing the volume and the density of the individual components. As mentioned above the indirect estimation of the mass may lead to an error due to simplification made by the assessment of the volume, especially for irregularly shaped objects. In addition, the actual density of a material can deviate from tabulated or estimated values.
Heat of Combustion The heat of combustion–also known as the calorific value or heating value–is the total amount of heat released when a quantity of a fuel is oxidized completely under standard temperature conditions and (atmospheric) pressure (see also Drysdale [6]). The heat of combustion is related to different units. The most commonly used unit in fire safety engineering is the SI unit [MJ/kg]. For some items values can be established with units like [MJ/m2], [MJ/m3], [MJ/l] or [MJ/piece]. For example the calorific value for a carpet can be defined per square meter [MJ/m2] or for a wooden pallet per piece [MJ/piece]. This can simplify the assessment of the fire load and save time during a survey (see inventory method above). In some (older) surveys the fire load was converted to wood equivalent, e.g. the fire load in [MJ] was converted in kg of wood [kg of wood equivalent] by dividing the fire load by the heat
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of combustion of wood. As the heat of combustion of wood is given by different values in different sources (see e.g. Appendix 3) this may lead to differences among different surveys. The heat of combustion of the material depends on the aggregate state of the reactants and products after combustion. If the reactants and products are in their standard states, the heat of combustion is defined as the gross heat of combustion (or the gross calorific value). Rules how to determine the gross heat of combustion are given in standards e.g. ISO 1716 [7]. The net heat of combustion Hu (or net calorific value) refers to the case where especially water is in vapour state after the combustion. If solid materials are completely dry the gross heat of combustion corresponds to the net heat of combustion. The influence of the moisture content on the net heat of combustion of a material can be considered by accounting the latent heat of evaporation of water as follows [1]: H u ¼ H u0 ð1 0:01 uÞ 0:025 u
ð35:3Þ
Hu: net heat of combustion [MJ/kg] u: the moisture content expressed as mass percentage of dry weight Hu0: the net calorific value of dry materials [MJ/kg] The net heat of combustion of a mixed material H u can be assessed by the mass and the net heat of combustion of the individual components: Hu ¼
n 1 X M i H u, i Mtot i¼1
ð35:4Þ
Mi: mass of the material i [kg] Hu,i: net heat of combustion of material i [MJ/kg] Mtot: total mass of the mixed material [kg] Values for the heat of combustion per kilogram can be found in the literature [1, 8–13] in the form of tabulated data for different materials and items. Data on the heat of combustion for
some products and composites can be found in Appendix 3.
Total Fire Load The total fire load is defined as the sum of the products of the mass and the heat of combustion of all combustible materials in the fire compartment (see Equation 35.1). In general, permanent (or fixed) and variable (or movable) fire load is distinguished. Combustible materials which are part of the structure or the confining elements (e.g. the walls, the floor or the ceiling) contribute to the permanent fire load. Combustible material that is moveable and typically varies in time (e.g. daily, weekly, monthly or during the service life of the building) contributes to the variable fire load. The energy released by the permanent and variable fire loads depends on their reaction to fire or combustibility. For this reason many national standards subdivide the combustibility of building materials (permanent fire load) in different reaction to fire classes. According to the Euroclass system EN 13501 [14], building materials are grouped into seven combustibility classes on the basis of their reaction-to-fire properties (see Table 35.2). All combustible building material and building contents contributing energy to the fire should be accounted for in the fire load assessment. Materials can be neglected if the energy required for pyrolysis is higher than the energy which is released from the material during the combustion. This means that those materials consume more energy than they release under fire exposure. According to Beilicke [8] this applies to materials with homogeneous or quasi-homogeneous properties that have a heat of combustion smaller than 8.5 MJ/kg. If favourable condition for the combustions apply, lower values are possible. Materials (protected and unprotected) that are able to explode under fire exposure, e.g. combustible gases, should be considered separately and are not part of the fire load assessment.
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Table 35.2 Euroclass system for classification of the combustibility of building materials, EN 13501 [14] Performance Class description Non A1 No contribution combustible to fire
Possible test methods ISO 1182 [15] ISO 1716 [7] A2 No significant ISO 1182 [15] contribution to fire ISO 1716 [7] Combustible B Very limited ISO 11925-2 [16] contribution to fire C D E F
Examples of products Products of natural stone, concrete, bricks, ceramic, glass, steel, and many metallic products Products similar to those of class A1, including small amounts of organic compounds
Gypsum boards with different (thin) surface linings Fire retardant wood products Limited ISO 11925-2 [16] Phenolic foam, gypsum boards with different surface contribution to fire linings (thicker than in class B) Contribution to ISO 11925-2 [16] Wood products with thickness about 10 mm and fire density about 400 kg/m3 (depending on end use) Significant ISO 11925-2 [16] Low density fibreboard, plastic based insulation products contribution to fire — Products not tested (no requirements) Incapable of achieving Class E
Derated Fire Load A building material will contribute to a fire depending on its combustibility and its reaction to fire. Non-combustible materials (class A1 and A2 according to EN 13501 [14]–e.g. gypsum boards) and materials with limited reaction to a fire (class B and C) are often used to protect combustible building materials (encapsulation of permanent fire load) and variable fire loads against ignition (e.g. steel containers with combustible content). Whether protected material should be accounted for the fire load assessment should be related to the reliability of the protection under fire exposure. A failure of the protection leads to an ignition of the protected combustible material. Possible reasons include falling off of the protection, cracks or excessive heat transfer. If the combustible material is preheated at the time of ignition its combustibility may be increased. The failure of the protection is assessed considering the exposure of the protection during a fire. Because of the stochastic behaviour of a fire, the failure of the protection is an uncertain event. This uncertainty can be considered by assigning a failure probability to the protection. CIB W14 [1] propose a semi-probabilistic approach to account for protected fire loads by introducing derating factors ψ p,i. These factors
represent the probability for a participation of the protected combustible material in the fire. The derated fire load density q may be written as: X ψ p, i qi, protected ð35:5Þ q ¼ qunprotected þ i
qunprotected fire load density for the unprotected combustible materials [MJ/m2] qi,protected fire load density for the protected combustible material i [MJ/m2] ψ p,i derating factor for the protected combustible material i [-] There is no generally agreed procedure for deriving the derating factor ψ p,i. In an informative annex of the Eurocode 1991-1-2 [17] it is proposed that the protected fire load can be neglected (i.e. ψ p,i ¼ 0) when the largest protected fire load (minimum 10 % of the whole protected fire load) plus the unprotected fire load are not able to ignite the protected fire load. In other cases, the specific value of ψ p,i for a protected material should be assessed individually. For a survey it is important to clarify whether derating factors were used or not. Both the underrated and the derated value of the fire load (especially with regard to the permanent fire load, e.g. encapsulated combustible insulation or structural elements) should be reported, to identify how much combustible material was considered as protected.
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Effective Fire Load
Defining Characteristic and Design Values from In Situ Surveys
The combustion behaviour of a material under real fire exposure depends on the material properties, the surface to volume ratio and the thermal action on the material. Material and geometrical properties, e.g. size, location, etc., will affect the heat release rate (HRR) during a fire and the combustion of the material itself. In most fires there will be no complete combustion of all materials in a room. To consider the incomplete combustion a combustion factor χ can be introduced. The combustion factor χ is defined as the ratio of the effective heat released qeff and the theoretically maximal possible heat released q: χ¼
qeff q
ð35:6Þ
This ratio describes the degree of combustion and has a value between 0 and 1. A combustion factor of 1 means that a complete combustion takes place, while a factor of 0 implies that no combustion of the material takes place. The combustion efficiency depends on the quantity of the material burned and is mainly influenced by the fire exposure of the item (oxygen supply) and the ability of the material to protect itself against thermal actions (e.g. charring of wood). Another important factor which affects the combustion efficiency is the density of storage of the goods, e.g. wood‐wool will burn fast and nearly completely, while a massive block of wood may self-extinguish and only burn partially on its surface. Whether the combustion factor χ is considered in the fire load data of a survey should be stated clearly. However, the fire load under full combustion and under incomplete combustion should be reported to address the range of the maximal potential heat release during a fire. In the context of design this factor is typically used to estimate the design fire load. A general assessment of the combustion factor does not exist yet. EN 1991-1-2 [17] proposes a combustion factor of 0.8 for materials which are mainly composed of cellulosic materials.
It should be noted that the fire load assessed in an in situ survey represents only a momentary situation. Variation of the fire load over time should be considered (e.g. fire load before or after delivering products and daily, weekly, monthly, yearly variations). Fire loads that are supposed to remain unchanged during the service life time of the building should be accounted for their expected value. The fire loads that strongly vary in time should be considered depending on their frequency of occurrence. For design purposes, often a characteristic value of the fire load is used, e.g. an 80 % fractile value. Such a value denotes the fire load that is not exceeded during 80 % of the service time of the building. For fire load surveys involving many buildings within the same occupancy class, the momentary fire load for each building can be assessed. Then, the variation of the fire load in time is characterized by the different momentary situation in the different buildings. The accuracy of predicting the fractile value for the characteristic fire load increases by increasing the number of rooms or buildings that are surveyed. The design value for the fire load depends on the format of the fire safety design codes. It is usually defined as a function of the characteristic value of the fire load and the combustion efficiency. In the design fire load also additional factors can be considered e.g. the occurrence rate of a fire, the fire fighting measures and the required safety level for the structure (see EN 1991-1-2 [17]). It is therefore important to clearly state how design values of the fire load were established.
Fire Load Density for Different Occupancy Classes If an in situ survey is not possible (e.g. during the design phase of a building) the mean and standard deviation of the fire load density can be
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estimated based on data from fire load surveys in buildings within the same occupancy class. Such a statistical approach is especially valuable for common occupancy classes like residential buildings, offices, hotels, schools or hospitals. Choosing an upper fractile (characteristic) value of the statistical distribution, as required by many regulations, allows for future rearrangements as long as the occupancy class remains the same (e.g. different department stores in a shopping mall). In some occupancy classes, e.g. industrial buildings, the variability of the fire load density is very high. Nevertheless, even for industrial buildings information from fire load surveys in rooms of the same occupancy class can be helpful, e.g. for a preliminary analysis in the design phase or for comparison with the fire load estimate obtained by an in-situ survey. Due to the limited available statistical data and the high variability, the fire load density in industrial buildings will be discussed separately from the distributions for the more common situations.
Common Occupancy Classes Due to socioeconomic and cultural characteristics specific to different countries or regions of the world, it is not possible to provide universal estimates for the distribution of the fire load density in different occupancies. For Europe, mean and fractile values have been defined for common occupancy classes in Annex E of EN 1991-1-2 [17]. The annex is informative only; allowing different values to be defined in the national annexes. Outside of Europe, guidance on fire load densities in common occupancy classes can be found in the International Fire Engineering Guidelines [18]. The mean values and standard deviations provided in Table 35.3 have been derived from EN 1991-1-2 [17]. Characteristic values (e.g. an 80 % fractile) can be estimated based on Table 35.1. The Eurocode assumes a Gumbel distributed fire load density, but Table 35.3 can also be applied assuming a Lognormal distribution. Another assumption is that the coefficient
M. Fontana et al. Table 35.3 Mean and standard deviation of the variable fire load density for different occupancy classes according to the EN 1991-1-2 [17] Variable fire load density [MJ/m2] Occupancy Mean Dwelling 780 Hospital (room) 230 Hotel (room) 310 Library 1500 Office 420 Classroom of a school 285 Shopping centre 600 Theatre (cinema) 300 Transport (public space) 100
Standard 234 69 93 450 126 85.5 180 90 30
of variation of the fire load density is equal to 0.3 for all occupancy classes. No permanent fire load is included. The permanent fire load has to be estimated separately based on the methodology described in the in situ survey section above. Combustion factors still have to be applied if incomplete combustion is not treated elsewhere in the fire model. The information on the statistical distribution of the fire load density provided in Table 35.3 is valid for rooms of typical use for each occupancy class; special rooms have to be treated separately. At any rate, tabulated values should be used as a first estimate only. An international overview on fire load surveys conducted before 1986 is given in CIB W14 [1]. However, when referring to older data sources one should bear in mind that today’s furnishing materials and building contents are different to what was observed several decades ago. Therefore, older data may not be used unreflectingly and reference should be made to more recent studies. Since 1986, a number of fire load studies have been conducted in different parts of the world, including Canada [9, 12, 19, 20], India [21, 22], Japan [23, 24], Hong Kong [25, 26], Brazil [27] and Europe [28, 29]. Differences between data collected in different studies can be attributed to the fact that the studies were conducted in different geographical regions and within a time frame of several decades; also that the assumptions and methods
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used for the different surveys can have large effects on the results. Based on the published reports, differences could be identified in the following areas: – Treatment of permanent fire loads: The information published on the composition of the total (permanent and variable) fire loads is not always sufficient for comparison with studies focusing on variable fire loads only. – Fire load units: The fire load is sometimes estimated in terms of “wood equivalent” [kg wood/m2]. The conversion to the “fire load energy density” [MJ/m2] or [Mcal/m2] is ambiguous due to different assumptions for the net calorific value of wood. – Reference area: In some older studies, the total internal surface area of the fire compartment is used as reference area for the fire load. The conversion to fire load per floor area requires assumptions on the geometrical properties of the fire compartment. – Derating factors and combustion efficiency: Some studies use derating factors to account for protected fire loads and/or incomplete combustion while others estimate the full fire loads. – Sampling strategy: The sample of buildings or rooms assessed during the individual studies may be more or less representative for the occupancy group mentioned in the report. – Survey method: The uncertainty of the estimated values depends largely on the
survey method (see discussion in the section on in situ surveys). – Simplifying assumptions: The assumptions made e.g. for assessing the heat of combustion or the weight of the surveyed items can lead to a bias in the values provided by different studies.
Industrial Buildings In occupancy classes with high variability (e.g. industrial buildings), the in situ survey method is preferred. Nevertheless, in this section some tentative values are proposed for several types of industrial buildings. This information may be used for a preliminary analysis or for comparison with the results of an in situ survey. Production and storage rooms are treated separately. Even more than in other occupancy classes, the fire load densities in industrial buildings have to be expected to be changing in time. In 2005, a fire load survey in 95 Swiss industrial and commercial buildings was performed by ETH Zu¨rich. Table 35.4 gives an overview on fire load densities surveyed in production rooms. Details of the survey methodology are described in Ko¨hler et al. [30] (see also Thauvoye et al. [28]). Table 35.4 uses the same occupancy classification as proposed by Klein [31]. Only groups with five or more observations in at least
Table 35.4 Summary of fire load densities observed in Swiss industrial buildings (production rooms) Recorded fire load densities [MJ/m2] Occupancy (production) Wood processing Wood products Wooden furniture Paper, cardboard Paper/cardboard goods Printing shop Polymer processing Goods made of plastics Insulated cables Metal processing Pharmaceutics
Sample size 17 8 9 24 15 9 23 17 6 8 5
Range 80–4923 345–4923 80–1985 201–2674 201–2674 322–2406 68–2779 68–2779 364–1713 81–532 90–3306
Mean 1488 1959 1070 1071 1037 1127 1032 1106 824 246 1006
Standard deviation 1220 1522 731 783 792 813 716 779 496 161 1335
Coefficient of variation 0.82 0.78 0.68 0.73 0.76 0.72 0.69 0.70 0.60 0.66 1.33
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Table 35.5 Summary of fire load densities per room area observed in Swiss industrial buildings (storage rooms)
Occupancy (storage) Wood processing Wood products Wooden furniture Paper, cardboard Polymer goods Metal processing Building materials Pharmaceutics Textiles Sugar goods Special rooms Paint storage Solvent storage Packaging materials
Recorded fire load densities [MJ/m2] Sample size Range 18 1048–39,679 12 1393–39,679 6 1048–13,512 27 1262–48,458 25 755–40,808 6 128–4747 10 166–5734 6 932–26,207 5 380–2754 5 8271–23,572 5 15 8
530–7825 112–27,168 372–6424
two different companies are included. Nevertheless, also for the remaining groups it should be kept in mind that with a coefficient of variation around 0.7, the statistical uncertainty becomes very high if the sample size is small. The fire loads in storage rooms tend to be much higher than in production areas, see Table 35.5. Predicting the fire load density in one specific fire compartment based on data seems to be very difficult because of the high variability within each occupancy group. The fire load density in storage rooms depends not only on the type of materials and goods stored, but also on the storage height and type (e.g. packing density). In the Swiss fire load study, both the gross storage volume (calculated from the total room area and the storage height) and the net storage volume (after subtraction of traffic areas etc.) were recorded. Herein, the fire load in a compartment is referred to the gross storage volume. Based on this fire load survey, values for specific industrial occupancies (production and storage rooms) have been proposed by VKF [11] (available in German, French and Italian) as input data for a Swiss risk evaluation index method. In addition to a range of fire load “suggested values” are proposed derived on the detailed survey protocols of the fire load study
Mean 10,594 12,546 6691 14,602 8545 2024 1554 13,557 1285 13,219 4907 8686 2229
Standard deviation 10,021 11,394 5328 11,378 9041 1761 1678 11,372 928 6461 3095 7995 1995
Coefficient of variation 0.95 0.91 0.80 0.78 1.06 0.87 1.08 0.84 0.72 0.49 0.63 0.92 0.90
summarized in Tables 35.4 and 35.6 and expert judgement. Due to the limited data sample and the large variability of the fire load density in industrial buildings, the estimates could not be defined mathematically, e.g. in terms of characteristic values. The values given in VKF [11] can thus only provide information on the order of magnitude of fire load densities in different industrial production and storage rooms. The older values given in SIA Dok 81 [32] should be interpreted in a similar way. Today these values should be used with care as the data was collected in the 1960s and cannot be assumed to represent well the present situation in buildings. Besides the Swiss survey, fire load data for industrial buildings have also been reported in Germany by Schneider and Max [33] (see also CIB W14 [1]) and Halfkann and Wiese [34] (see also Schneider and Max [35]). Both studies recorded fire load densities that were quantified based on the 1978 (prestandard) version of the German DIN 18230 [36]. With a maximum of 20 observations per occupancy group, the sample size in the fire load study by Schneider and Max [33] is comparable to the Swiss study. A much larger sample of industrial buildings could be observed by Halfkann and Wiese [34]. However, their data is often related to specific fire design projects.
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Table 35.6 Summary of fire load densities per gross storage volume (room area and storage height) observed in Swiss industrial buildings (storage rooms) Recorded fire load densities [MJ/m3] Occupancy (storage) Wood processing Wood products Wooden furniture Paper, cardboard Polymer goods Metal processing Building materials Pharmaceutics Textiles Sugar goods Special rooms Paint storage Solvent storage Packaging materials
Sample size 18 12 6 27 25 6 10 6 5 5 5 15 8
Range 210–6613 696–6613 210–3003 421–6873 326–5056 37–922 37–1220 386–3679 172–542 2298–4911
Mean 1904 2268 1178 2511 2075 433 412 1180 337 3866
Standard deviation 1505 1617 998 1696 1549 396 439 1247 144 982
Coefficient of variation 0.79 0.71 0.85 0.68 0.75 0.91 1.06 1.06 0.43 0.25
265–4347 56–6792 207–1457
2152 2850 616
1517 2114 423
0.70 0.74 0.69
References 1. CIB W14. Design Guide Structural Fire Safety. Fire Safety Journal. 1986;10:76–137. 2. Petterson O, Magnusson SE, Thor J. Fire Engineering Design of Steel Structures. Swedish Institute of Steel Construction; 1976. 3. CIB W81. Actions on Structures - Fire. CIB Report 1993. 4. Zalok E. Validation of Methodologies to Determine Fire Load for Use in Structural Fire Protection. The Fire Protection Research Foundation; 2011. 5. Culver C, Kushner J. A program for survey of fire loads and live loads in office buildings 1975. 6. Drysdale D. An Introduction to Fire Dynamics, 2nd Edition: John Wiley & Sons; 2002. 7. ISO 1716:2010. Reaction to fire tests for products— Determination of the gross heat of combustion (calorific value). International Organization for Standardization. 8. Beilicke G. Zusammenstellung von Heizwerten fu¨r die Brandlastberechnung: Staatsverlag der Deutschen Demokratischen Republik; 1987. 9. Bwalya AC. An Extended Survey of Combustible Contents in Canadian Residential Living Rooms. In: National Research Council Canada, editor. Ottawa, Canada: Institute for Research in Construction; 2004. 10. Krasny JF, Parker WJ, Babrauskas V. Fire behavior of upholstered furniture and mattresses: Noyes Publications; 2001. 11. VKF. Brandschutzerla¨uterung: Bewertung von Brandabschnittsgro¨ssen—Sicherheitsnachweis bei
industriellen und gewerblichen Nutzungen, Berechnungsverfahren. In: Feuerversicherungen VK, editor. 115-03d. Bern, Switzerland 2003. 12. Bwalya AC, Lougheed GD, Kashef A, Saber HH. Survey Results of Combustible Contents and Floor Areas in Multi-Family Dwellings. In: National Research Council Canada, editor. Ottawa, Canada: Institute for Research in Construction; 2008. 13. Di Nenno PJ. SFPE Handbook of Fire Protection Engineering, 3 ed., Quincy, MA, National Fire Protection Association, 2002. 14. EN 13501. Fire classification of construction products and building elements—Part 1: Classification using data from reaction to fire tests. 2010. 15. ISO 1182:2010. Reaction to fire tests for products— Non-combustibility test. International Organization for Standardization. 16. ISO 11925-2:2010. Reaction to fire tests—Ignitability of products subjected to direct impingement of flame—Part 2: Single-flame source test. International Organization for Standardization. 17. EN 1991. Eurocode 1: Actions on structures—Part 1-2: General actions—Actions on structures exposed to fire. 2002. 18. National Research Council Canada, International Code Council (USA), New Zealand. Dept. of Building and Housing, Australian Building Codes Board. International Fire Engineering Guidelines. In: ABCB, editor. Canberra 2005. 19. Hadjisophocleous GV, Chen Z. A Survey of Fire Loads in Elementary Schools and High Schools. Journal of Fire Protection Engineering. 2010;20:55–71.
1142 20. Zalok E, Hadjisophocleous GV, Mehaffey JR. Fire loads in commercial premises. Fire and Materials. 2009;33:63–78. 21. Kumar S, Rao CVSK. Fire Loads in Office Buildings. Journal of Structural Engineering. 1997;123:365–8. 22. Kumar S, Rao CVSK. Fire load in residential buildings. Building and Environment. 1995;30:299–305. 23. Aburano K, Yamanaka H, Ohmiya Y, Suzuki K, Tanaka T, Wakamatsu T. Suvrvey and Analysis on Surface Area of Fire Load. Fire Science and Technology. 1999;19:11–25. 24. Kose S, Motishita Y, Hagiwara I, Tsukagoshi I, Matsunobu S, Kawagoe K. Survey of Movable Fire Load in Japanese Dwellings. Fire Safety Science— Proceedings of the Second International Symposium 1989. 25. Chow WK, Ngan SY, Lui GCH. Movable fire load survey for old residential highrise buildings in Hong Kong. Safety and Security Engineering 2007. p. 215–22. 26. Chow WK. Zone Model Simulation of Fires in Chinese Restaurants in Hong Kong. Journal of Fire Sciences. 1995;13:235–53. 27. Claret AM, Andrade AT. Fire Load Survey of Historic Buildings: A Case Study. Journal of Fire Protection Engineering. 2007;17:103–12. 28. Thauvoye C, Zhao B, Klein J, Fontana M. Fire Load Survey and Statistical Analysis. Proceedings of the Ninth International Symposium on Fire Safety Science. Karlsruhe, Germany. 2008. 29. Korpela K, Keski-Rahkonen O. Fire Loads in Office Buildings. In: Society of Fire Protection Engineers, editor. 3rd International Conference on PerformanceBased Codes and Fire Safety Design Methods. Lund, Sweden 2000. p. 278–86. 30. Ko¨hler J, Klein J, Fontana M. Die Erhebung von Brandlasten in 95 Industrie- und Gewerbebauten. Bauphysik. 2006;28:360–7. 31. Klein J. Zum Verhalten von Tragwerken bei natu¨rlicher Brandeinwirkung unter Beru¨cksichtigung technischer Massnahmen. Zu¨rich: ETH Zu¨rich; 2008. 32. SIA Dok 81. Brandrisikobewertung—Berechnungsverfahren / Evaluation du risque d’incendie— Me´thode de calcul. Schweizerischer Ingenieur- und Architekten-Verein, Brand-Verhu¨tungs-Dienst fu¨r Industrie und Gewerbe, Vereinigung Kantonaler Feuerversicherungen; 1984.
M. Fontana et al. 33. Schneider U, Max U. Brandlasterhebungen in Industrie-Stahlhallen. In: Studiengesellschaft fu¨r Anwendungstechnik von Eisen und Stahl e.V., editor. 1984. 34. Halfkann K-H, Wiese J. Brandlastberechnung im Industriebau—Statistische Auswertung von u¨ber 3000 bearbeiteten Projekten—Einfluss der Neufassung der Norm DIN 18230 (Ausgabe 5/98)— Zuku¨nftige Entwicklung von rechnerischen Verfahren. Erkelenz, Germany: Halfkann + Kirchner Sachversta¨ndigenbu¨ro—Brandschutzingenieure; 1998. p. 34. 35. Schneider U, Max U. Baulicher Brandschutz im Industriebau—Kommentar zur DIN 18230 und Industriebaurichtlinie. 3 ed: Beuth Verlag; 2003. 36. DIN V 18230. Baulicher Brandschutz im Industriebau—Structural fire protection in industrial buildings. Berlin: DIN Deutsches Institut fu¨r Normung; 1987.
Mario Fontana is a professor at ETH Zurich in Switzerland at the Institute of Structural Engineering. His research activity have included structural fire safety, composite, steel and timber structures. Jochen Kohler is a professor in NTNU in Norway in the Department of Structural Engineering. His research activities have included probabilistic design and analysis, of structures, risk analysis, probabilistic modelling, code calibration. Before becoming Prof. at NTNU Prof. Kohler was senior scientist at the Institute of Structural Engineering, ETH Zu¨rich. Katharina Fischer is a consulting engineer at Matrisk GmbH in Switzerland with expertise in risk analysis, probabilistic modelling and code calibration. Before her engagement at Matrisk, she made a PhD at ETH Zu¨rich, focusing on fire risk assessment and societal decisionmaking. Gianluca De Sanctis is a senior researcher at ETH Zurich in Switzerland. His research activities have included quantitative fire risk assessment for rational decision-making, assessment and probabilistic modelling of basic design parameters for fire safety and performance evaluation and optimization of fire safety design provisions.
Combustion Characteristics of Materials and Generation of Fire Products
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Mohammed M. Khan, Archibald Tewarson, and Marcos Chaos
Abbreviations ABS CDG CPVC CR CSP (or CSM) CTFE E-CTFE EPR ETFE EVA FEP FPA GTR IPST OC PAH PAN PC PE PEEK PES PEST
acrylonitrile-butadiene-styrene carbon dioxide generation calorimetry chlorinated polyvinylchloride neoprene or chloroprene rubber chlorosulfonated polyethylene rubber (Hypalon) chlorotrifluoroethylene (Kel-F) ethylene-chlorotrifluoroethylene (Halar) ethylene propylene rubber ethylenetetrafluoroethylene (Tefzel) ethylvinyl acetate fluorinated polyethylenepolypropylene (Teflon) Fire Propagation Apparatus gas temperature rise calorimetry isophthalic polyester oxygen consumption calorimetry polyaromatic hydrocarbons polyacrylonitrile polycarbonate polyethylene polyether ether ketone polyethersulfone polyester
M.M. Khan (*) • M. Chaos FM Global Research, Norwood, MA 02062, USA A. Tewarson Retired from FM Global Research, Norwood, MA 02062, USA
PET PFA PMMA PO POM PP PS PTFE PU PVC PVCl2 PVDF PVEST PVF PVF2 SBR TFE XLPE
polyethyleneterephthalate (Melinex Mylar) perfluoroalkoxy (Teflon) polymethylmethacrylate polyolefin polyoxymethylene polypropylene polystyrene polytetrafluoroethylene (Teflon) polyurethane polyvinylchloride polyvinylidene chloride (Saran) polyvinylidenefluoride (Kynar) polyvinylester polyvinyl fluoride (Tedlar) polyvinylidene fluoride (Kynar Dyflor) styrene-butadiene rubber tetrafluoroethylene (Teflon) cross-linked polyethylene
Introduction Hazards associated with fire are characterized by the generation of calorific energy and products, per unit of time, as a result of the chemical reactions of surfaces and material vapors with oxygen from air. Thermal hazards constitute those scenarios where the release of heat is of major concern. On the other hand, nonthermal hazards are characterized by fire products (smoke, toxic, corrosive, and odorous compounds.) Generation rates of heat and fire products (and their nature) are governed by
M.J. Hurley (ed.), SFPE Handbook of Fire Protection Engineering, DOI 10.1007/978-1-4939-2565-0_36, # Society of Fire Protection Engineers 2016
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(1) fire initiation (ignition); (2) fire propagation rate beyond the ignition zone; (3) fire ventilation; (4) external heat sources; (5) presence or absence of fire suppression/extinguishing agents; and (6) materials: (a) their shapes, sizes, and arrangements; (b) their chemical natures; (c) types of additives mixed in; and (d) presence of other materials. In this handbook most of these areas have been discussed from fundamental as well as applied views. For example, the mechanisms of thermal decomposition of polymers, which govern the generation rates of material vapors, are discussed in Chap. 7, generation rate of heat (or heat release rate) from the viewpoint of thermochemistry is discussed in Chap. 5, Flaming ignition of the mixture of material vapors and air is discussed in Chap. 21, and surface flame spread in Chap. 23. In this chapter emphasis is placed on small scale experiments and how such testing can be used to determine the generation per unit of time of (1) the calorific energy, defined as the heat release rate, and (2) fire products. From these tests, measurements of so-called “fire properties” are made that can be used in models to predict, under a variety of conditions, (1) heat release rate, to assess thermal hazards; and (2) generation rates of fire products, to assess nonthermal hazards. Fire properties are defined herein that help characterize the flammability of a given material and relationships are derived, based on empirical evidence, that elucidate the effect of environmental factors (such as external heat flux and ventilation) on the properties. Also important, and discussed in this chapter, is the connection of these properties to the behavior of large-scale fire phenomena under well ventilated as well as vitiated conditions (i.e., compartment fires.). Lastly, with the advent and quick development of computer modeling as applied to large scale fires, this chapter also discusses the value of small scale testing in determining material flammability parameters specific to such models. Several other chapters in this handbook relate to the subjects discussed here and should be consulted for complete information and context.
M.M. Khan et al.
The chapters are as follows: Chaps. 27, 28, 16, and 24. Physical and combustion properties of selected fuels in air and heats of combustion and related properties of pure substances, plastics, and miscellaneous materials listed in Appendix 3 should be consulted for information that may not be included in this chapter. This chapter presents the applications of the principles discussed in several chapters in this handbook to determine the fire properties of materials. Simple calculations have been included in the chapter to show how the properties can be used for various applications.
Flammability Apparatuses and Measurement Capabilities At the scales of relevance to this chapter, there are mainly three heat release rate apparatuses available: (1) The Ohio State University (OSU) Heat Release Rate Apparatus; (2) FM Global’s Fire Propagation Apparatus (previously known as “Small-Scale Flammability Apparatus”); and (3) NIST’s Cone Calorimeter. These apparatuses are briefly described below. In 1972, gas temperature rise (GTR) calorimetry (details are given in section “Heat Release Rate” of this chapter) was used by the Ohio State University (OSU) to determine heat release rate [1, 2]. The apparatus used is now known as the OSU heat release rate apparatus; it is shown in Fig. 36.1. The OSU apparatus is an ASTM [3] and an FAA [4] standard test apparatus. In GTR calorimetry, it is assumed that almost all the thermal radiation from the flame is transferred to the flowing fire products-air mixture, as the flames are inside an enclosed space and heat loss by conductive heat transfer is negligibly small. Oxygen consumption (OC) calorimetry (details are given in section “Heat Release Rate” of this chapter) has now been adapted to the OSU apparatus [5]. Calorimetry methodologies based on carbon dioxide generation (CDG, details are given in section “Heat Release Rate” of this chapter), OC, and GTR calorimetries were used during the mid-1970s by FM Global Research
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Combustion Characteristics of Materials and Generation of Fire Products
Fig. 36.1 Ohio State University’s (OSU, ASTM E906) heat release rate apparatus [1–4]
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Combustion products exhaust Thermopile
To oxygen analyzer By-pass air Pilot flames
Glowbars (radiant heat source)
Sample Pilot flame
Air distribution plates
(formerly, Factory Mutual Research Corporation—FMRC) to determine chemical, convective, and radiative heat release rates [6–9]. The apparatus used is now known as the Fire Propagation Apparatus (FPA) and is an ASTM [10] and ISO [11] standard; it is shown in Figs. 36.2 and 36.3. Heat release rate from CDG and OC calorimetries in the FPA was originally defined as the “actual heat release rate” until 1986 [9, 12–15]; thereafter, however, it was changed to “chemical heat release rate” to account for the effects of (1) the chemical structures of the materials and additives; (2) fire ventilation; (3) the two dominant modes of heat release, that is, convective and radiative; and (4) the effects of flame extinguishing and suppressing agents. The FPA is a standard test apparatus for electrical cables [16, 17], for wall and ceiling
Air inlet
insulation materials, replacing the 7.6 m (25-ft) corner test (as described in section “Fire Propagation” of this chapter) [18], for clean room materials used in the semiconductor industry [19], and for conveyor belts [20]. In 1982 the National Institute of Standards and Technology (NIST) used OC calorimetry, following the methodology described by Hugget [21]. The apparatus developed to use this methodology, known as the cone calorimeter [22, 23], is shown in Fig. 36.4. The cone calorimeter became an ASTM standard [24] test apparatus in 1990. Details about the cone calorimeter are given in Chap. 28. Sampling ducts have been designed for the FPA and the cone calorimeter to measure the mass generation rates of CO2 and CO and mass consumption rate of oxygen for use in the
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Combustion products
Quartz tube
Product sample analysis
Product sample analysis
Collection hood
Collection hood
Infrared heaters (4)
Aluminum extension cylinder Quartz tube
Sample conveyor belt Infrared heaters (4)
Test sample Aluminum support cylinder
Air + oxygen
Sample support (on load cell) Air distribution box
Fig. 36.2 Fire Propagation Apparatus (FPA) [10, 11] designed by FM Global Research. Sample configuration for ignition, pyrolysis, and combustion tests
calorimetric equations (see section “Heat Release Rate” of this chapter). CDG and OC calorimetries are used in the FPA. In the OSU apparatus and the cone calorimeter, only the OC calorimetry is used. For application of GTR calorimetry, a thermopile located in the flue gas chimney is used in the OSU apparatus, and a thermocouple located in the sampling duct is used in the FPA, where heat losses by conduction are negligibly small. The cone calorimeter has not been designed to use GTR calorimetry. The FPA provides the advantage of determining the radiative heat release rate from the difference between the chemical (determined by CDG or OC) and convective (determined by GTR) heat release rates [25]. Details on sample preparation, sample holders, and measurement procedures are provided for each apparatus [3, 10, 11, 24]. The design features, test conditions, and types of measurements for the three apparatuses are
Aluminum support cylinder
Air + oxygen
Sample support (on load cell) Air distribution box
Fig. 36.3 Fire Propagation Apparatus (FPA) [10, 11] designed by FM Global Research. Sample configuration for fire propagation tests; a conveyor belt sample is shown
listed in Table 36.1. As shown in the table, the Fire Propagation Apparatus measures flammability characteristics of materials under various air flow (ventilation) conditions, in enhanced or reduced oxygen environments, and also has the ability to determine flame extinction by extinguishing agents. Much of the data presented in this chapter takes advantage of all of these capabilities. Figure 36.5 shows an example of typical heat release rate profiles measured in the FPA. These profiles correspond to the chemical heat release rate of polymethylmethacrylate, determined from CDG and OC calorimetries, as well as the convective heat release rate, determined by GTR. The polymethylmethacrylate (PMMA) sample was 100 mm in diameter and 9.53 mm in
36
Combustion Characteristics of Materials and Generation of Fire Products
Fig. 36.4 The cone calorimeter [22–24] designed at the National Institute of Standards and Technology (NIST)
Laser extinction beam including temperature measurement
1147
Temperature and differential pressure measurements taken here
Soot sample tube location Exhaust hood
Exhaust blower Soot collection filter Controlled flow rate
Gas samples taken here
Sample
Cone heater Spark igniter
Load cell
Vertical orientation
thickness. It was exposed to an external heat flux of 50 kW/m2 under co-flowing normal air. The chemical heat release rate profiles from the CDG and OC calorimetries in the FPA are very similar, as expected.
Combustion Characteristics of Materials: Engineering and Modeling Applications Ignition (Fire Initiation) The fundamental ignition principles are described in detail in Chap. 21. These principles suggest that, for fire initiation, a material has to be heated above its critical heat flux (CHF, described below) for ignition. Generally speaking, ignition of a combustible solid, heated by an external source, starts with solid-phase thermal decomposition and evolution of combustible gases from the surface leading to gas-phase combustion, resulting in a sustained diffusion flame.
When a solid material is exposed to an external heat flux, it behaves either as thermally thin or thermally thick, depending on its material properties, dimensions and the magnitude of the incident heat flux. Materials typically behave as thermally thick at high heat fluxes (i.e., at high heating rates); and behave thermally thin at low heat fluxes (i.e., at low heating rates) near their critical heat flux for ignition. A thermally thick material is one having a physical thickness greater than the depth of thermal diffusion at the time of ignition, while the physical thickness of a thermally thin sample is less than the depth of thermal diffusion at ignition. The equation for piloted ignition time of solids under thermally thick conditions may be expressed as [26, 27]: 2 π kρ c p T ig T 0 tigðthickÞ ¼ 4 00 ð36:1Þ 00 2 q_ e χ q_ cr where, tig(thick) is the time to piloted ignition (s); k, ρ and cp are, respectively, thermal conductivity (kW/m/K), density (kg/m3), and specific heat
ASTM E2058 Fire Propagation Apparatusb Co-flow/natural 0–40 0–0.146 Tungsten-quartz 0–110 0.035–0.364 100 100 100 600 Pilot flame 50 Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes
OSUa Co-flow 21 0.49 Electrical resistance elements 0–80 0.04 110 150 150 150 Pilot flame 8 Yes No No Yes Yes No No Yes Yes No No
NA not available a As specified in ASTM E906 [3] and by DOT/FAA [4] b As specified in ASTM E2058 [10] and ISO 12136 [11] c As specified in ASTM E1354 [24]
Design and test conditions Inlet gas flow Oxygen concentration (%) Co-flow gas velocity (m/s) External heaters External heat flux (kW/m2) Exhaust product flow (m3/s) Horizontal sample dimensions (mm) Vertical sample dimensions (mm) Ignition source Heat release rate capacity (kW) Measurements Time to ignition Material gasification rate Fire propagation rate Generation rates of fire products Light obscuration by smoke Smoke yield Effective (chemical) heat of combustion Chemical heat release rate Convective heat release rate Radiative heat release rate Flame extinction _______________________________ Yes Yes No Yes Yes No Yes Yes No No No
Conec Natural 21 NA Electrical coils 0–100 0.012–0.035 100 100 100 100 Spark plug 8
Table 36.1 Design features, test conditions, and types of measurements for the OSU heat release rate apparatus, the Fire Propagation Apparatus, and the NIST Cone Calorimeter
1148 M.M. Khan et al.
Combustion Characteristics of Materials and Generation of Fire Products
Fig. 36.5 Heat release rates determined employing the methodologies described in the text (CDG, OC, and GTR) for a 9.53-mm thick slab of polymethylmethacrylate (PMMA) exposed to an external heat flux of 50 kW/m2 and 0.09 m/s co-flowing normal air in the Fire Propagation Apparatus
1149
10 OC Calorimetry CDG Calorimetry GTR Calorimetry
8 Heat Release Rate (kW)
36
6
4
2
0 0
100
200
300
400
500
600
Time (s)
(kJ/kg/K) of the solid; their product represents the thermal inertia of the solid. Tig and T0 are the surface ignition temperature (K) and ambient 00 00 temperature (K), respectively, q_ e and q_ cr are the incident heat flux (kW/m2) and the critical heat flux for ignition (CHF) (kW/m2), and χ is the average heat loss as a fraction of the critical heat flux and takes into account the fact that heat losses are initially zero and increase as the solid is heated to its ignition temperature. The square root of the term in the numerator of the right hand side of Equation 36.1 is sometimes referred to as the Thermal Response Parameter (TRP) [28]: TRP ¼
π 1=2 kρ c p T ig T 0 4
ð36:2Þ
Under thermally thin conditions for solids of thickness d (m), the time to piloted ignition, tig(thin), is based on the energy required to heat the material to its ignition temperature assuming a uniform temperature throughout the material: tigðthinÞ
ρ c p d T ig T 0 ¼ 00 00 q_ e χ q_ cr
ð36:3Þ
Tig in Equations 36.1 and 36.3 is evaluated here assuming that reradiation heat losses dominate 00 the ignition process so that q_ cr ¼ σ T ig 4 T 0 4
for a black surface, where σ is the StephanBoltzmann constant (kW/m2/K4). The value of χ approximates the effect of heat losses during heat up of the solid. It was recommended [27] that χ ¼ 0.64 for thermally thick conditions assuming surface re-radiation 00 losses close to q_ cr are dominant. After analyzing various materials, and considering both radiant and convective losses Khan et al. [29] proposed a single value of χ ¼ 1.0 for both thermally thin and thermally thick solids. A thermal diffusion time, τth (s), can be defined to demarcate the transition between thermally thick and thermally thin responses as [26, 29]: τth ¼
4ρ c p d2 πk
ð36:4Þ
Using Equations 36.1 and 36.4, the relationship between thermally thick and thin ignition behavior is given by [29]: 1= tigðthinÞ ¼ τth tigðthickÞ 2 π 1=2 1 kρ c p T ig T 0 4ρ c d2 =2 p 4 ¼ 00 00 πk q_ χ q_ cr e ρ c p d T ig T 0 ¼ 00 00 q_ e χ q_ cr ð36:5Þ
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M.M. Khan et al.
A generalized form applicable to both regimes is [29]:
tigðthick=thinÞ
82 38 91=4 2 34 > > > > 00 00 00 00
5 > 5 τth 2 4π > > ; : π kρ c p 2 T ig T 0 kρ c p T ig T 0 4 4
The exponents ¼, 4, and 8 in Equation 36.6 provide a good fit to exact numerical solutions for transition between thermally thin and thick behavior [29]. In Equation 36.6, if tig is less than τth the response of the material becomes thermally thick; whereas, if tig is greater than τth the response becomes thermally thin. Thus τth provides the transition between thermally thin and thermally thick behaviors.
Critical Heat Flux (CHF) The ignition and subsequent burning of a solid sample is sensitive to heat losses from the rear surface of the sample being tested. This heat loss depends on the sample holder and its surrounding environment. Theoretical studies of ignition and pyrolysis in flammability apparatuses show that the construction of the sample holder has a surprisingly large effect on measured parameters, especially for solids having thermally thin behavior near the critical heat flux [30]. This makes flammability measurements apparatus dependent. One naturally wishes to minimize any such heat losses, but to whatever extent such losses remain, they must be made reproducible and quantifiable so that one can correct for their presence. To minimize apparatus dependencies, de Ris and Khan have designed an insulated sample holder [30] that minimizes heat losses from the rear and sides of the sample being heated. The holder ensures that thermal processes remain one-dimensional so as to conform to most theoretical analyses used to interpret data. The critical heat flux may provide a measure of the ignition temperature of a given material if, as stated above, one assumes that all heat losses near the CHF are dominated by radiation; this, again, reinforces the need for a well-insulated
ð36:6Þ
sample. Empirically, the CHF is obtained by collecting piloted ignition data in a flammability apparatus, such as the FPA, over a range of (low) heat fluxes. By plotting the inverse of time to ignition versus heat flux and using Equation 36.3, the intercept of a best-fit line on the heat flux axis corresponds to the CHF. Alternatively, ignition tests may be also performed in search of the heat flux for which no ignition occurs after a specified threshold (e.g., 15 min).
Thermal Response Parameter (TRP) TRP is a very useful parameter for engineering calculations to assess resistance to ignition and fire propagation. For thermally thick materials, the inverse of the square root of time to ignition is expected to be a linear function of the external heat flux away from the CHF value (see Equation 36.1). The inverse of the slope of the line is the TRP (see Equations 36.1 and 36.2). Most commonly used materials behave in a thermally thick manner at practical fire conditions and, thus, satisfy Equation 36.1. This behavior is shown in Fig. 36.6 for polymethylmethacrylate (PMMA) [31]; in Fig. 36.7 for heavy corrugated paper sheets; and in Fig. 36.8 for cone calorimeter data [32]. The TRP value is determined, for example, in the Fire Propagation Apparatus, by (1) measuring the time to ignition for 100 mm 100 mm square or 100-mm diameter and up to 25-mmthick samples at different external heat flux values. The sample surfaces are blackened with a very thin layer of black paint or fine graphite powder to avoid errors due to differences in the radiation absorption characteristics of the materials, and (2) performing a linear regression analysis of the data away from the critical heat
Combustion Characteristics of Materials and Generation of Fire Products
1151
0.35 Natural flow Co-flow; vg = 0.18 m/s Co-flow; vg = 0.18 m/s Co-flow; vg = 0.18 m/s
0.30 0.25 No ignition
Fig. 36.6 Square root of the inverse of time to ignition versus external heat flux for 100-mm 100-mm 25-mm-thick polymethylmethacrylate (PMMA) slab with a blackened surface. Data measured in the Fire Propagation Apparatus [31]
(Time to ignition)–1/2 (s)–1/2
36
0.20 0.15 0.10 0.05
CHF
0.00 0
10
20
30
40
50
60
70
80
90 100
External heat flux (kW/m2)
0.5 0% Coating 10% Coating 15% Coating 20% Coating
0.4
0.3
No ignition
(Time to ignition)–1/2 (s)–1/2
Fig. 36.7 Square root of the inverse of time to ignition versus external heat flux for two 100-mm 100-mm 11-mm-thick sheets of heavy corrugated paper with various levels of fire protection coating. Data measured in the Fire Propagation Apparatus. Lines are linear fits to the data; TRP values derived from the fits are given in Table A.35
0.2
0.1
0.0
0
flux condition, following Equation 36.1, and recording the inverse of the slope of the line. The TRP for a surface may vary depending on whether or not it is blackened. For example, for nonblackened and blackened surfaces of polymethylmethacrylate (PMMA), TRP ¼ 434 and 274 kW · s1/2/m2, respectively [31]. The TRP value for a blackened surface of PMMA is close to the value calculated from the known Tig, k, ρ, and cP values for PMMA [31]. These results highlight the importance of a well-defined
40 60 20 External heat flux (kW/m2)
80
boundary condition, provided by an appropriate high absorptivity surface coating, in ignition tests. Uncoated samples may be subject to other phenomena such as in-depth radiation [33] as well as the spectral characteristics of both sample surface and radiation source [34, 35]. It is for these reasons that standard FPA tests [10, 11] require that samples be coated with high emissivity paint to ensure surface absorption of imposed heat flux. TRP depends on the chemical as well as the physical properties of materials, such as the
1152 0.5 PVEST PVEST—glass Epoxy Epoxy—glass Wood
0.4 (Time to ignition)–1/2 (s)–1/2
Fig. 36.8 Square root of the inverse of time to ignition versus external heat flux for 100-mm 100-mm nonblackened surfaces of 10-mm 11-mm-thick polyvinyl ester (PVEST), 11-mm-thick epoxy, and 6-mm-thick wood (hemlock). Data measured in the cone calorimeter [32]
M.M. Khan et al.
0.3
0.2
0.1
0.0
chemical structure, fire retardants, etc. For example, Fig. 36.9 shows that TRP increases with sample thickness for a composite material (polyester/fiberglass) and increases in the amount of passive fire protection agent used, such as that provided by a surface coating to a heavy corrugated paper sheet (see Fig. 36.7). The TRP response versus thickness shown in Fig. 36.9 is counterintuitive given that TRP is strictly defined for thermally thick materials; this response is a result of the composite material considered and evidences the effect of physical structure and nonhomogeneity of the material. CHF and TRP values for several materials derived from data for time to ignition versus external heat flux are listed in Table A.35. The ranges of CHF and TRP values in Table A.35 are due to differences in the compositions of materials having similar generic natures and differences in the test procedures, such as the use of an insulated sample holder, as described above. Examples of calculated TRP values, using available Tig, k, ρ, and cp data and Equation 36.2, and those measured are listed in Tables A.36 and A.37. The calculated and measured TRP values (TRPcal and TRPmeas, respectively) are plotted in Fig. 36.10. For ordinary polymers that do not contain halogen atoms and do not char significantly, the TRPcal value is only about 17 % lower than the TRPmeas value, but for highly charring, high-temperature, engineered polymers and
0
20
40 60 External heat flux (kW/m2)
80
100
highly halogenated polymers, the TRPcal values are significantly lower than the TRPmeas values. There is strong flame retardation by the fuel vapors of the highly halogenated polymers with a significant reduction in the fuel vapor concentration due to charring. Thus, for the ordinary polymers, thermal arguments to describe the ignition behavior (Equations 36.1 and 36.2) are sufficient, but not for the highly charring, hightemperature, engineered polymers and highly halogenated polymers. The effects of the fuel vapors of the highly charring, high-temperature, engineered polymers and highly halogenated polymers on the ignition behavior can be compensated by performing the ignition experiments under enhanced oxygen concentration and, thus, thermal arguments again can be used to describe the ignition behavior. This is supported by the data reported by Khan and de Ris [36], which are listed in Table 36.2. Example 1 In a fire, newspaper and polypropylene are exposed to a heat flux value of 50 kW/m2. Estimate which material will ignite first, assuming physical conditions to be very similar for both the materials. Solution From Table A.35, for newspaper and polypropylene, CHF ¼ 10 and 15 kW/m2, respectively, and TRP ¼ 108 and 193 kW · s1/2/m2,
Combustion Characteristics of Materials and Generation of Fire Products
Fig. 36.9 Thermal response parameter versus thickness for S-2 polyester/ fiberglass sample and weight percent of surface coating for the heavy corrugated paper (see Fig. 36.7). Data measured in the Fire Propagation Apparatus. w weight %
Thermal response parameter (kW·s2/m2)
36
1153
S–2 Polyester/fiberglass
500
450
400
350
300
0
5
10
15
20
25
30
35
40
45
50
Sample thickness (mm)
Heavy corrugated paper
Thermal response parameter (kW·s2/m2)
800
600
400 TRP = 24.5 w + 181 200
Fig. 36.10 Calculated versus measured values of the thermal response parameter
TRPmeas (kW-s1/2/m2)
0
900 800 700 600 500 400 300 200 100 0
0
5
10 15 20 Surface coating (weight percent)
25
Ordinary High temperature Halogenated
0
100
200
300
400
500
600
TRPcal (kW-s1/2/m2)
respectively. Substituting these values in 00 Equation 36.1 with q_ e ¼ 50 kW/m2, the times to ignition are calculated to be 6 and 24 s for newspaper and polypropylene, respectively. Thus, newspaper will ignite first.
Example 2 Halogenated materials are obtained by replacing hydrogen atoms with halogen atoms in the chemical structures of the materials. For example, a unit in polyethylene (PE) consists of C2H4. If a hydrogen atom (H) is replaced by a
1154
M.M. Khan et al.
Table 36.2 Thermal response parameter values measured in normal air and 40 % oxygen concentration and calculated from physical properties [23, 37] Polymer Ordinary polymers Polymethylmethacrylate (PMMA) Polyoxymethylene (POM) Polypropylene/fire retarded Halogenated polymers Polyvinylchloride (PVC)—rigid Chlorinated PVC (CPVC)—rigid Polyvinylchloride (PVDF)
TRPmeas (kWs1/2/m2) Normal air 40 % oxygen
TRPcal (kWs1/2/m2)
239 252 276
230 260 301
264 269 242
498 435a 447–508
200 230 324
171 280 301
a
Data from Table A.35
chlorine atom (Cl) in a PE unit, it becomes a unit of rigid polyvinylchloride (PVC), that is, C2H3Cl. If two H atoms are replaced by two fluorine atoms (F) in a PE unit, it becomes a unit of Tefzel (ethylene tetrafluorethylene), that is, C2H2F2. If all the hydrogen atoms are replaced by four F atoms in a PE unit, it becomes a unit of Teflon (polytetrafluoroethylene), that is, C2F4. Show how the replacement of hydrogen atoms by the halogen atoms affects the ignitability of the materials. Solution From Table A.35, for PE (high density), PVC (rigid), Tefzel, and Teflon, the CHF values are 15, 15, 27, and 38 kW/m2, respectively, and the TRP values are 321, 406, 356, and 682 kW · s1/2/m2, respectively. In the calculations, it is assumed that these materials are exposed to a uniform heat flux of 60 kW/m2 in a fire under very similar physical conditions. From Equation 36.1, using 00 q_ e ¼ 60 kW/m2, the times to ignition for PE (high density), PVC (rigid), Tefzel, and Teflon are calculated to be 40, 64, 91, and 755 s, respectively. Thus, resistance to ignition increases as the hydrogen atom is replaced by the halogen atom in the chemical structure of PE. The higher the number of hydrogen atoms replaced by the halogen atoms in the structure, the higher the resistance to ignition. When all the hydrogen atoms are replaced by the fluorine atoms, the material becomes highly resistant to ignition.
Fire Propagation The fundamental surface flame spread principles are described in Chap. 23. According to these principles, the fire propagation process, as indicated by surface flame spread, can be explained as follows. As a material is exposed to heat flux from internal and/or external heat sources, a combustible mixture is formed that ignites, and a flame anchors itself on the surface in the ignition zone. As the vapors of the material burn in the flame, they release heat with a certain rate, defined as the chemical heat release rate. Part of the chemical heat release rate is transferred beyond the ignition zone as conductive heat flux through the solid and as convective and radiative heat fluxes from the flame. If the heat flux transferred beyond the ignition zone satisfies CHF, TRP, and gasification requirements of the material, the pyrolysis and flame fronts move beyond the ignition zone, increasing the burning surface area. Consequently, flame height, chemical heat release rate, and heat flux transferred ahead of the pyrolysis front all increase. The pyrolysis and flame fronts move again, and the process repeats itself further increasing the burning area. Fire propagation on the surface continues as long as the heat flux transferred ahead of the pyrolysis front (from the flame or external heat sources) satisfies CHF, TRP, and gasification requirements of the material. The rate of movement of the pyrolysis front is generally used to define the fire propagation rate:
36
Combustion Characteristics of Materials and Generation of Fire Products
Fig. 36.11 Pyrolysis front versus time for downward fire propagation for a 300-mm-long, 100-mmwide, and 25-mm-thick PMMA vertical slab under opposed airflow conditions in the Fire Propagation Apparatus. Airflow velocity ¼ 0.09 m/s. Oxygen mass fraction ¼ 0.334 (Figure is taken from Ref. [31])
1155
400
Xp (mm)
300
200
100
0
0
200
400
600
800
1000
400
500
Time (s)
Fig. 36.12 Pyrolysis front versus time for upward fire propagation for a 600-mmlong, 100-mm-wide, and 25-mm-thick PMMA vertical slab under co-airflow conditions in the Fire Propagation Apparatus. Airflow velocity ¼ 0.09 m/s. Oxygen mass fraction ¼ 0.233 (Figure is taken from Ref. [31])
700 600
Xp (mm)
500 400 300 200 100 0 0
100
200
300
Time (s)
u¼
dX p dt
ð36:7Þ
where u is the fire propagation rate (mm/s or m/s), and Xp is the pyrolysis front length (mm or m). The fire propagation rate can be determined in one of several apparatuses: (1) the LIFT [37] described in Chap. 23; (2) the Fire Propagation Apparatus [10, 11] shown in Fig. 36.3. Examples of the type of data obtained from the FPA are shown in Figs. 36.11, 36.12, 36.13, and 36.14.
In Fig. 36.14, heat release rates increase linearly with time during downward fire propagation, very similar to the pyrolysis front values for the downward fire propagation in Fig. 36.11. The trends of the lines in Figs. 36.11, 36.12, 36.13, and 36.14 represent fire propagation rates. The upward fire propagation rate is much faster than the downward fire propagation rate. For downward fire propagation, linear increases in the pyrolysis front and heat release rates indicate decelerating fire propagation behavior. For upward fire propagation, nonlinear increases
1156 700 600 0.279
0.446 500 Xp (mm)
Fig. 36.13 Pyrolysis front height versus time for upward fire propagation for a 600-mm-long and 25-mm-thick diameter PMMA cylinder under co-airflow conditions in the Fire Propagation Apparatus. Airflow velocity ¼ 0.09 m/s. Numbers inside the frames are the mass fractions of oxygen in air (Figure is taken from Ref. [31])
M.M. Khan et al.
400 300
0.233
200 100 0
0
100
200
300
400
Time (s)
12 Flame spread 0.446
10
Entire surface burning
0.233
6
0.201
•
Qch (kW)
8
0.178 4
2
0
0.233
7 6
Unstable flame
Flame extinction
5 4
•
Qcon (kW)
Fig. 36.14 Chemical (top) and convective (bottom) heat release rate versus time for downward fire propagation, combustion, and flame extinction for a 300-mm-long, 100-mmwide, and 25-mm-thick PMMA vertical slab under opposed airflow conditions in the Fire Propagation Apparatus. Airflow velocity ¼ 0.09 m/s. Numbers inside the frames are the mass fractions of oxygen in air (Figure is taken from Ref. [31])
3 2 1 0 0
200
400
600 800 Time (s)
1000
1200
1400
36
Combustion Characteristics of Materials and Generation of Fire Products
in the pyrolysis front indicate accelerating fire propagation behavior.
Empirical Relationship Between Fire Propagation Rate, Flame Height, Pyrolysis Front, and Heat Release Rate Numerous researchers have found the following relationship between the flame height and pyrolysis front (as discussed in Chap. 13, and reviewed in Refs. [31, 38]): X f ¼ aX np
ð36:8Þ
Flame height (mm)
where Xf ¼ Flame height (m) a ¼ 5.35 n ¼ 0.67–0.80 for steady wall fires [31]. Xp is in m. Fire propagation data for PMMA from the FPA and for electrical cables from several standard tests (ICEA [39], CSA FT-4 [40], and UL-1581 [41]) satisfy Equation 36.8, as shown in Fig. 36.15, with a ¼ 5.32 and n ¼ 0.78. The visual measurement of the pyrolysis front as damage length is used for the acceptance criterion in many of the standard tests for electrical
103
1157
cables. For example, for upward fire propagation in the CSA FT-4, a damage length of less than 60 % of the total length of the cable tray for a 20-min exposure is used as the acceptance criterion. For horizontal fire propagation in the UL-1581 test, a flame length of less than 40 % of the total length of the cable tray is used as the acceptance criterion. The relationship between the flame height and the chemical heat release rate, expressed as the normalized chemical heat release rate (NCHRR), is defined as 0
NCHRR ¼
Q_ ch
3=
ρc p T a g =2 X p2 1
ð36:9Þ
where 0 Q_ ch ¼ Chemical heat release rate per unit width (kW/m) ρ ¼ Density of air (g/m3) cp ¼ Specific heat of air (kJ/g · K) Ta ¼ Ambient temperature (K) g ¼ Acceleration due to gravity (m2/s) Xp is in m.
Cable (ICEA; YO = 0.233) Cable (CSA FT–4; YO = 0.233) Cable (UL–1581; YO = 0.233) PMMA (FMRC–Cylinder 1; YO = 0.233) PMMA (FMRC–Cylinder 2; YO = 0.233) PMMA (FMRC–Slab; YO = 0.233) PMMA (FMRC Cylinder 1; YO = 0.445)
102
101
102
103
Pyrolysis front (mm)
Fig. 36.15 Flame height versus pyrolysis front height for upward fire propagation in normal air. Data are for the vertical fire propagation for electrical cables contained in 2.44-m-long, 310-mm-wide, and 76-mm-deep trays in standard tests for electrical cables (ICEA, CSA FT-4,
and UL-1581) and for 600-mm long PMMA slabs (100-mm-wide and 25-mm-thick) and cylinders (25-mm diameter) in the Fire Propagation Apparatus. Data for fire propagation in an oxygen mass fraction of 0.445 are also included (Figure is taken from Ref. [31])
1158
M.M. Khan et al.
Many researchers have shown that the height ratio of the flame to the pyrolysis front is a function of the heat release rate, such as the following relationship (as discussed in Chap. 13, and reviewed in Refs. [31, 38]): Xf ¼ aðNCHRRÞn Xp
ð36:10Þ
where a and n are constants. This relationship reported in the literature (as reviewed in Ref. [31]) for methane, ethane, and propylene is shown in Fig. 36.16. The data for the upward fire propagation for PMMA [31] and for electrical cables from several standard tests (ICEA [39], CSA FT-4 [40], and UL-1581 [41]) also satisfy this relationship as indicated in Fig. 36.16. In Fig. 36.16, data in the lower left-hand corner are for low-intensity polyvinylchloride (PVC) electrical cable fire propagation in standard tests for cables. These data show that for NCHRR < 0.2, Xf/Xp < 1.5 and n ¼ 1/10. This is a characteristic property of materials for which there is either no fire propagation or limited fire propagation beyond the ignition zone. The data for higher-intensity fire propagation in Fig. 36.16
Flame height/pyrolysis front
102
show that (1) for 0.2 < NCHRR < 5, n ¼ 2/3 and 1.5 < Xf/Xp < 20 (PMMA fire propagation and methane combustion); and (2) for NCHRR > 5, n ¼ 1/2 and Xf /Xp > 20 (ethane and propylene combustion). Thus, the ratio of the flame height to pyrolysis front height is a good indicator of the fire propagation characteristics of the materials. Materials for which flame height is close to the pyrolysis front location during fire propagation can be useful indicators of decelerating fire propagation behavior. Researchers have also developed many correlations between the flame heat flux transferred ahead of the pyrolysis front and heat release rate for downward, upward, and horizontal fire propagation (as discussed in Chap. 23, and reviewed in Refs. [31, 38]). For example, small- and large-scale fire propagation test data suggest that, for thermally thick materials with highly radiating flames, the following semiempirical relationship is satisfied [28]: 1=3 χ rad _ 0 q_ f / Q χ ch ch 00
Cable (UL–1581) Cable (ICEA) Cable (CSA FT–4) Ethane, Propylene Methane PMMA (FMRC)
ð36:11Þ
n = 1/2
101
n = 1/10
n = 2/3
100 10–2
10–1
100
101
102
Normalized chemical heat release rate
Fig. 36.16 Ratio of flame height to pyrolysis front height versus the normalized chemical heat release rate for upward fire propagation in normal air. Data for diffusion flames of methane, ethane, and propylene are from the literature. Data for cables are from standard
tests for electrical cables (ICEA, CSA FT-4, and UL-1581). Data for PMMA are from the Fire Propagation Apparatus for 600-mm-long vertical PMMA slabs (100-mm-wide, 25-mm-thick) and cylinders (25-mmdiameter) [31]
36
Combustion Characteristics of Materials and Generation of Fire Products
1159
00
where q_ f is the flame heat flux transferred ahead of the pyrolysis front (kW/m2) and χ rad is the radiative fraction of the combustion efficiency, χ ch. The fire propagation rate is expressed as [28] 1=3 1= 1 χ rad _ 0 2 u / ð36:12Þ Q TRP χ ch ch On the basis of the discussion above, an emprical parameter termed fire propagation index (FPI) [16, 17, 28, 42–46] has been defined: 1 0 =3
Q_ FPI ¼ 750 ch ð36:13Þ TRP FPI describes the fire propagation behavior of materials under flame-radiating conditions prevalent in large-scale fires. Small- and large-scale fire propagation test data of various materials along with understanding of fire propagation phenomena suggest that the FPI values can be used to classify materials as either propagating (fire propagates rapidly beyond ignition zone) and non-propagating (there is no fire propagation beyond the ignition zone) [28, 31, 43–46]. These FPI-based determinations have been validated by using intermediate-scale parallel panel tests (e.g., [19]) as shown in Figs. 36.17 and 36.18 and described below.
Application of the Fire Propagation Index (FPI) to Classify Materials The FPI values for the upward fire propagation, under flame-radiating conditions, have been determined for numerous materials at reduced scales in the Fire Propagation Apparatus. The highly radiating conditions, representative of large-scale fires, are created in the FPA by burning the materials in an enhanced oxygen environment (0.40 oxygen mass fraction). Two sets of tests are performed: 1. Thermal response parameter test: Ignition tests are performed in the FPA (materials are arranged as in Fig. 36.2), and the TRP value is determined from the time to ignition versus external heat flux as described in the subsection “Thermal Response Parameter (TRP)”. 2. Upward fire propagation test: Fire propagation tests for vertical slabs, sheets, or cables
Fig. 36.17 Nonpropagating fire between two vertical parallel panels of a polymer (FPI < 6) for a test duration of 15 min [19]. The panels are about 0.61 m (2 ft) wide, 2.44 m (8 ft) high, and 25 mm (1 in) thick separated by 0.30 m (1 ft). The ignition source is a 60-kW, 0.30-m-wide, 0.61-m-long, and 0.30-m-high propane sand burner. The tip of the flame from the burner reaches a height of about 0.91 m (3 ft). Marks on the scale are in feet
are performed in the FPA (materials are arranged as in Fig. 36.3). About 300–600mm-long, up to about 100-mm-wide, and up to about 100-mm-thick samples are used. The bottom 120–200 mm of the sample is in the ignition zone, where it is exposed to 50 kW/m2 of external heat flux in the presence of a pilot flame. Beyond the ignition zone, the fire propagates by itself under co-airflow condition with an oxygen mass fraction of 0.40. During upward fire propagation, the chemical heat release rate is measured as a function of time.
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Fig. 36.18 Rapidly propagating fire between two vertical parallel panels of a polymer (FPI > 20) [19]. The panels are about 0.61 m (2 ft) wide, 2.44 m (8 ft) high, and 25 mm (1 in.) thick separated by 0.30 m (1 ft). The ignition source is a 60-kW, 0.30-m-wide, 0.61-m-long, and 0.30-m-high propane sand burner. The tip of the flame from the burner reaches a height of about 0.91 m (3 ft). Marks on the scale are in feet. The photograph was taken a few seconds before flames extended far beyond the top of the panels
M.M. Khan et al.
parallel panel intermediate scale test configuration was first introduced in 1988 [28] to verify the fire propagation behavior of electrical cables based on the fire propagation index (FPI), derived from bench-scale FPA measurements. It consists of two parallel panels of test material, each 0.61 m wide and 4.9 m long facing each other with a separation of about 0.31 m (keeping an aspect ratio of the panel width to the separation distance as 0.5). A 60 kW propane sand burner continuously provides an exposure fire at the base of the two panels. This intermediate scale test scenario contains the essential features of fire phenomena expected at larger scales, most notably enhanced radiant fluxes due to the radiation feedback between the panels. This test configuration provides sufficient size and confinement of flames to yield realistic flame heat transfer to the materials (see Figs. 36.17 and 36.18). The nonpropagating fire condition is satisfied for FPI 10.0 for electrical cables (classified as Group 1) [17] that do not exhibit flame propagation beyond the vicinity of the ignition source in the parallel panel tests. In a recent study [46], plenum rated cables, having FPI values of 7.0, did not exhibit flame propagation in the parallel panel tests. Table 36.3 lists FPI values for selected electrical cables and conveyor belts. Example 3 What type of fire behavior is represented by a 300-mm-wide, 8-m-high, and 25-mm-thick vertical cable array with a TRP value of 95 kW · s1/2/m2 if the peak chemical heat release during upward fire propagation is 50 kW?
The TRP value and the chemical heat release rate so determined are used in Equation 36.13 to calculate the FPI; the maximum (peak) measured chemical heat release rate value is used in the calculation.
Solution Fire propagation behavior is assessed by the FPI value. For the cable material, the chemical heat release rate per unit width, 0 Q_ ¼ 50/0.3 ¼ 167 kW/m. Substituting
Electrical Cables The FM Approval standard for cable fire propagation [17] is used to classify electrical cables, based on their upward fire propagation behavior, under highly flame-radiating conditions (0.40 oxygen mass fraction). A
Conveyor Belts A conveyor belt standard has been developed at FM Global [20]. In this
ch
this value in Equation 36.13, with TRP ¼ 95 kW · s1/2/m2, FPI ¼ 43. The cable material will propagate fire.
36
Combustion Characteristics of Materials and Generation of Fire Products
Table 36.3 Fire propagation index for cables and Conveyor belts, determined in the Fire Propagation Apparatus
Power cables PVC/PVC PE/PVC PVC/PE Silicone/PVC Silicone/XLPO EP/EP XLPE/XLPE XLPE/EVA XLPE/neoprene XLPO/XLPO XLPO, PVF/XLPO EP/CLP EP, FR/none Communications cables PVC/PVC PE/PVC PXLPE/XLPO Si/XLPO EP-FR/none PECI/none ETFE/EVA PVC/PVF FEP/FEP FEP/FEP Conveyor beltsa Styrene-butadiene rubber (SBR) Chloroprene rubber (CR) CR/SBR PVC
Diameter/ thickness (mm)
FPI
4–13 11 34 16 55 10–25 10–12 12–22 15 16–25 14–17 4–19 4–28
11–28 16–23 13 17 6–8 6–8 9–17 8–9 9 8–9 6–8 8–13 9
4 4 22–23 28 28 15 10 5 8 10
36 28 6–9 8 12 18 8 7 4 5 8–11 5 8 4–10
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Example 4 Conveyor belts are made of solid woven or piles of elastomers, such as styrenebutadiene rubber (SBR), polychloroprene rubber (CR), polyvinylchloride (PVC), reinforced with fibers made of polymers, such as nylon. In largescale fire propagation tests in a tunnel, fire on the surface of a CR-based conveyor belt was found to be nonpropagating, whereas for a CR/SBR-based conveyor belt fire was found to be propagating. Small-scale tests showed that the CR- and CR/SBR-based conveyor belts had the following fire properties, respectively: (1) CHF ¼ 20 and 15 kW/m2, (2) TRP ¼ 760 and 400 kW · s1/2/m2, 0 and (3) peak Q_ ¼ 114 and 73 kW/m under ch
highly flame-radiating conditions (0.40 oxygen mass fraction). Show that small-scale test results are consistent with the large-scale fire propagation behaviors of the two conveyor belts, using the criterion that, for nonpropagating fire behavior, the FPI is equal to or less than 7. 0
Solution Substituting the TRP and Q_ ch values in Equation 36.13, the FPI values for the CRand CR/SBR-based conveyor belts are 5 and 8, respectively. Thus, the CR-based conveyor belt is expected to have a nonpropagating fire behavior, whereas the CR/SBR-based conveyor belt is expected to have a propagating fire behavior. The small-scale test results, therefore, are consistent with the large-scale fire propagation behaviors of the two conveyor belts.
a
3–25 mm thick
standard, as with the cable standard [17], TRP and upward fire propagation tests are performed, and Equation 36.13 is used to calculate the FPI. Conveyor belts are classified as propagating or non-propagating. For an approximately 600-mm-long and 100-mm-wide vertical conveyor belt, the data measured in the FPA under highly flame-radiating conditions show that the nonpropagating fire condition is satisfied for FPI 7.0 for belts that show limited fire propagation in the large-scale fire propagation tests [45, 47]. Table 36.3 lists FPI values for selected conveyor belts taken from Refs. [45, 47].
Polymeric Materials For Cleanrooms Microchip devices are manufactured, in bulk, on wafers of semiconducting materials. Wafers are manufactured in several stages: material preparation, crystal growth and wafer preparation, wafer fabrication, and packaging. Wafers are fabricated in cleanrooms where cleanliness is highly controlled in order to limit the number of contaminants to which the wafer is exposed. The stringent requirements of the solid-state devices define levels of cleanliness that far exceed those of almost any other industry. Contamination in a cleanroom is defined as anything that interferes with the production of wafers and/or their performance. The overall cleanroom
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design principle is to build a sealed room that is supplied with clean air, is built with polymeric materials that are noncontaminating, and includes systems to prevent accidental external contamination, interactions of the polymeric materials and wafer cleaning liquids, operator error, and accidental fires. In 1997, FM Global Research introduced a new methodology, identified as the FM Approval Standard 4910 Test Protocol [19], for testing the fire propagation and smoke development behaviors of polymeric materials for use in cleanrooms for the semiconductor industry. For the acceptance of polymeric materials, two criteria need to be satisfied: (1) Fire Propagation Index FPI 6 (m/s1/2)/(kW/m)2/3 and (2) Smoke Development Index SDI 0.4 (g/g) (m/s1/2)/(kW/m)2/3. In the 4910 Test Protocol [19], the Fire Propagation Index (FPI) is formulated from (1) the thermal response parameter (TRP), which relates the time to ignition to the net heat flux, and (2) the chemical heat release rate measured during the upward fire propagation in air having a 40 % oxygen concentration to simulate flame heat transfer at large scale, as described above. SDI is related to the smoke release rate and is obtained by multiplying the FPI value by the smoke yield as shown in Fig. 36.19. The smoke yield is defined as the ratio of the total mass of smoke released per unit mass of burned vapors from the polymeric material (see section “Generation of Fire Products and Smoke Yields” of this
Composites and Fiberglass-Reinforced Materials Composites and fiberglass-reinforced materials are very attractive because of their low weight and high strength characteristics and have found practical applications in a large number of sectors such as in aircrafts, submarines, naval ships, military tanks, public transportation vehicles including automobiles, space vehicles, tote boxes, pallets, chutes, and so forth. Fire propagation, however, is one of the major concerns for
10 Smoke release rate (g/m2·s)
Fig. 36.19 Peak smoke release rate measured in combustion tests in normal air with imposed external heat flux of 50 kW/m2 versus peak FPI values from the propagation tests in 40 % oxygen environments multiplied by the smoke yields from the combustion tests. Tests were performed in the Fire Propagation Apparatus
chapter). The FPI and SDI values for various polymeric materials (including composites) determined from FPA tests are listed in Table 36.4 [19, 43, 44, 48, 49]. It can be noted from Table 36.4 that specialty polymeric materials (highly halogenated thermoplastics and high temperature thermosets) have low FPI and SDI values and several of them satisfy the 4910 test protocol criteria (FPI 6 (m/s1/2)/(kW/m)2/3 and SDI 0.4 (g/g)(m/s1/2)/(kW/m)2/3) for acceptance as cleanroom materials [19]. These polymeric materials have high thermal stability with reduced release of carbon, hydrogen, and halogen atoms, as can be noted from their decomposition temperatures listed in Table 36.5 [50]. Ordinary thermoplastics (such as PE, PP, and PVC) can also be modified such that they behave similarly to the specialty polymeric materials and have low FPI and SDI values to satisfy the 4910 Test Protocol criteria for acceptance as cleanroom materials.
Composites Polymers 1
0.1
0.01 0.001
0.01
0.1
1
FPI x ys (g/g)(m/s1/2)/(kW/m)2/3
10
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Combustion Characteristics of Materials and Generation of Fire Products
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Table 36.4 Fire propagation index and smoke development index for polymeric materials Polymeric material Fire-retarded or unmodified electrical cables Polyvinyl chloride(PVC/polyvinylchloride PVC) Polyethylene (PE)/polyvinyl chloride (PVC) Silicone/polyvinyl chloride (PVC) Modified electrical cables Polyvinylchloride (PVC) High-temperature polyvinylchloride (PVC) Polyethylene (PE)/ethylvinylacetate (EVA) Ordinary polymeric materials Fire-retarded polystyrene (FR-PS) Fire-retarded polybutyleneterephthalate (FR-PBT) Unmodified polymethylmethacrylate (U-PMMA) Unmodified polyoxymethylene (U-POM) Fire-retarded (FR) vinyl ester Unmodified wood slab Unmodified polyethylene (U-PE) Polyethylene with 25 % chlorine Polyethylene with 36 % chlorine Polyethylene with 48 % chlorine Modified polyethylene (M-PE)-1 Modified polyethylene (M-PE)-2 Unmodified polypropylene (U-PP) Fire-retarded polypropylene (FR-PP) Modified polypropylene (M-PP)-1 Modified polypropylene (M-PP)-2 Modified polypropylene (M-PP)-3 Modified polypropylene (M-PP)-4 Modified polypropylene (M-PP)-5 Modified polypropylene (M-PP)-6 Modified polypropylene (M-PP)-7 Modified polypropylene (M-PP)-8 Fire-retarded flexible polyvinylchloride (FR-PVC) Unmodified rigid polyvinylchloride (U-PVC)-1 Unmodified rigid polyvinylchloride (U-PVC)-2 Modified rigid polyvinylchloride (M-PVC)-1 Modified rigid polyvinylchloride (M-PVC)-2 Modified rigid polyvinylchloride (M-PVC)-3 Modified rigid polyvinylchloride (M-PVC)-4 Modified rigid polyvinylchloride (M-PVC)-5 Modified rigid polyvinylchloride (M-PVC)-6 Modified rigid polyvinylchloride (M-PVC)-7 Modified rigid polyvinylchloride (M-PVC)-8 Modified rigid polyvinylchloride (M-PVC)-9 Chlorinated rigid polyvinylchloride (CPVC, Corzan)
FPI (m/s1/2)/ (kW/m)2/3
SDI (g/g)(m/s1/2)/ (kW/m)2/3
36 28 17
4.1 3.8 2.0
8 7 5
1.2 0.69 0.40
34 32 23 15 10 14 30 15 11 8 7 6 31 30 11 7 7 6 5 5 5 4 16 8 7 6 5 4 3 3 2 2 2 1 3
5.60 2.20 1.1 0.03 2.5 0.20 1.4 1.7 1.5 1.9 0.64 0.65 1.7 2.1 3.0 0.95 0.35 0.41 0.40 0.19 0.21 0.19 1.6 0.86 1.2 0.31 0.64 0.15 0.16 0.29 0.11 0.04 0.06 0.03 0.13 (continued)
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Table 36.4 (continued) Polymeric material Highly halogenated specialty polymeric materials Unmodified polyvinylidenefluoride (U-PVDF Kynar)-1 Unmodified polyvinylidenefluoride (U-PVDF)-2 Unmodified ethylenechlorotrifluoroethylene (U-ECTFE, Halar) Unmodified ethylenetetrafluoroethylene (U-ETFE, Tefzel) Unmodified perfluoroalkoxy (U-PFA, Teflon) Unmodified fluorinated ethylene-propylene (U-FEP, Teflon) High-temperature specialty polymeric materials Phenol formaldehyde Polyether ether ketone (PEEK) Melamine Unmodified polycarbonate (U-PC) Modified polycarbonate (M-PC)-1 Modified polycarbonate (M-PC)-2 Unmodified polysulfone (U-POS) Modified polysulfone (M-POS)-1 Modified polysulfone (M-POS)-2 Modified polysulfone (M-POS)-3 Modified polysulfone (M-POS)-4 Modified polyetherimide (M-PEI)-1 Modified polyetherimide (M-PEI)-2 Modified polyetherimide (M-PEI)-3 Unmodified polyphenyleneoxide (U-PPO) Glass fiber–reinforced ordinary polyesters Glass fiber–reinforced fire-retarded polyester (FR-PES)-1 Glass fiber–reinforced fire-retarded polyester (FR-PES)-1 Glass fiber–reinforced fire-retarded polyester (FR-PES)-1 Glass fiber–reinforced modified polyester (M-PES)-1 Glass fiber–reinforced modified polyester (M-PES)-1 Glass fiber–reinforced modified polyester (M-PES)-1 Composites Fire-retarded polyester (30 %)/glass fibers (70 %)-1 Fire-retarded polyester (30 %)/glass fibers (70 %)-2 Unmodified phenolic (16 %)/Kevlar fibers (84 %) Modified phenolic (20 %)/glass fibers (80 %) Fire-retarded epoxy (35 %)/glass fibers (65 %)-1 Fire-retarded epoxy (35 %)/glass fibers (65 %)-2 Fire-retarded epoxy (35 %)/glass fibers (65 %)-3 Modified epoxy (24 %)/glass fibers (76 %)-1 Modified epoxy (29 %)/graphite fibers (71 %) Modified epoxy and phenolic (18 %)/glass fibers (82 %) Modified polyphenylenesulfide (16 %)/glass fibers (84 %) Modified cyanate (27 %)/graphite fibers (73 %) Note: Data taken from Refs. [19, 43, 44, 48, 49]
FPI (m/s1/2)/ (kW/m)2/3
SDI (g/g)(m/s1/2)/ (kW/m)2/3
5 4 4 7 2 3
0.14 0.08 0.15 0.17 0.01 0.01
5 4 7 14 10 7 18 11 11 7 7 6 6 5 9
0.06 0.03 0.24 4.2 4.2 4.0 1.49 1.4 0.32 1.2 0.25 0.24 0.04 0.46 1.6
21 16 14 11 10 9
5.4 7.4 4.0 5.5 5.2 3.1
13 10 8 3 11 10 9 5 5 2 3 4
0.91 0.68 0.33 0.07 2.1 0.94 1.2 0.61 0.54 0.18 0.29 0.41
36
Combustion Characteristics of Materials and Generation of Fire Products
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Table 36.5 Decomposition temperature, char yield, and limiting oxygen index for polymeric materials Polymeric material Polybenzobisoxazole (PBO) Polyparaphenylene Polybenzimidazole (PBI) Polyamideimide (PAI) Polyaramide (Kevlar) Polyetherketoneketone (PEKK) Polyetherketone (PEK) Polytetrafluoroethylene (PTFE) Polyether ether ketone (PEEK) Polyphenylsulfone (PPSF) Polypara(benzoyl)phenylene (PX) Fluorinated cyanate ester Polyphenylenesulfide (PPS) Polyetherimide (PEI) Polypromellitimide (PI) Polycarbonate (PC) Polysulfone (PSF) Polyethylene (PE) Polyamide 6 (PA6)-nylon Polyethyleneterephthalate (PET) Acrylonitrile-butadiene-styrene (ABS) Polyurethane elastomer (PU) Polymethylmethacrylate (PMMA) Polychlorotrifluoroethylene Polyvinylchloride (PVC) Polystyrene (PS) Polyoxymethylene (POM) Polyvinylidenefluoride (PVDF)
Decomposition temperature ( C) 789 652 630 628 628 619 614 612 606 606 602 583 578 575 567 546 537 505 497 474 470 422 398 380 370 364 361 355
Char yield (%) 75 75 70 55 43 62 56 0 50 44 66 44 45 52 70 25 30 0 1 13 0 3 2 0 11 0 0 0
Limiting oxygen index (%) 56 55 42 45 28 40 40 95 35 38 41 40 44 47 37 26 30 18 21 21 18 17 17 95 50 18 15 44
Note: Data are taken from Ref. [50]
composites and fiberglass-reinforced materials; therefore, the FPI concept discussed above for electrical cables and conveyor belts can also be applied to these materials [43, 44]. In the case of composites and fiberglass-reinforced materials the nonpropagating fire condition is satisfied for FPI 6.0, for about 600-mm-long and 100-mmwide vertical composites and fiberglassreinforced materials, under highly flame-radiating conditions (0.4 oxygen mass fraction), very similar to the conveyor belts. Table 36.4 lists FPI values for selected composites and fiberglassreinforced materials [43, 44]. Interior Finish Wall/Ceiling Materials Since 1971, FM Global Research has used the 25-ft
(7.6 m) corner test as a standard test to evaluate the burning characteristics of interior finish wall and ceiling materials [18]. The 25-ft (7.6 m) corner test is performed in a 7.6-m (25-ft)-high, 15.2-m (50-ft)-long and 11.6-m (38-ft)-wide building corner configuration [51, 52]. The materials tested are typically panels with a metal skin over an insulation core material. The materials installed in the corner configuration are subjected to a growing exposure fire (peak heat release rate of about 3 MW) comprised of about 340 kg (750 lb) of 1.2-m (4-ft) 1.2-m (4-ft) wood (oak) pallets stacked 1.5 m (5 ft) high at the base of the corner. The material is considered to have failed the test if within 15 min either (1) fire propagation on the wall or ceiling extends to the limits of the structure,
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Xt ¼ Total available length [11.6-m (38 ft)] in the 25-ft (7.6 m) corner test 00 _ ¼ Convective heat release rate (kW/m2) Q
or (2) flame extends outside the limits of the structure through the ceiling smoke layer. The fire environment within the 25-ft (7.6 m) corner test structure has been characterized through heat flux and temperature measurements [51, 52]. It has been shown that the fire propagation boundary (pyrolysis front) measured by visual damage is very close to the critical heat flux (CHF) boundary for the material, as shown in Fig. 36.20 [52]. This relationship is in agreement with the general understanding of the fire propagation process. Through small- and largescale fire propagation tests for low-density, highly char-forming wall and ceiling insulation materials, a semi-empirical relationship has been developed for fire propagation rate for a 15-min test in the 25-ft (7.6 m) corner test [51, 52].
con
measured in the small-scale test The right-hand side of Equation 36.14 with the convective heat release rate measured (through GTR, see above) for a material exposed to 50 kW/m2 of external heat flux in the Fire Propagation Apparatus is defined as the convective flame spread parameter (FSPc) [51, 52]. Figure 36.21 shows a correlation between the convective flame spread parameter obtained from the FPA and the normalized fire propagation length in the FM Global 25-ft (7.6 m) corner test. Pass/fail regions, as determined from the 25-ft (7.6 m) corner test, are indicated in the figure. Materials for which FSPc 0.39 pass the 25-ft (7.6 m) corner test, and materials for which FSPc 0.47 are judged to be unacceptable (i.e., fail); the region where the FSPc values are greater than 0.39 but less than 0.47 is uncertain [18, 51, 52]. The correlation and pass/fail criterion shown in Fig. 36.21 have been adopted in the
00
X p Q_ con ¼ Xt TRP
ð36:14Þ
where Xp ¼ Average fire propagation length along the eaves (Fig. 36.20) of the 25-ft (7.6 m) corner test (pyrolysis front) measured visually (m)
X5
X5
4
X4
X6 X6
X6
X6
X5
X10
X15
X10 9
X15
X9
X49
X52 X120
X187
100 East wall
X2
X6
X3
97
84
X18
X146
X10 X34
X4 X10
X69
X118 X193
X6
X9
X2 X2
South wall
X3
Visual damage evaluation Critical heat flux boundary
Fig. 36.20 Critical heat flux boundary and visual observations for the extent of fire propagation in the FM Global 25-ft corner test for a product that passes the tests [52]
Combustion Characteristics of Materials and Generation of Fire Products
Fig. 36.21 Normalized fire propagation length measured in the 25-ft corner test versus the convective flame spread parameter obtained from the ASTM E2058 fire propagation apparatus (Figure is taken from Refs. [51, 52])
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1.0 Xp /Xt = 0.82 * FSPc0.25 0.8
0.6 Xp /Xt
36
0.4
0.2
Pass Fail
0.0 0.0
0.2
0.4
0.6
0.8
1.0
FSPc
FM Approval Standard Class No. 4880 for insulated wall or wall and ceiling panels [18]. In this standard, the 25-ft (7.6 m) corner test has been replaced by the Fire Propagation Apparatus tests along with a new intermediate-scale parallel panel test [53], which are a cost-effective alternative and considerably simplify the test protocol. Two sets of tests are performed in the FPA [18, 51, 52]: 1. Thermal response parameter test: Ignition tests are performed using approximately 100-mm 100-mm and up to 100-mm-thick samples. Times to ignition at various external heat flux values are measured to determine the TRP as described earlier. 2. Convective heat release rate test: Combustion tests are performed using about 100-mm 100-mm and up to 100-mm-thick samples. Samples are burned in normal air under an external heat flux exposure of 50 kW/m2. During the test, measurement is made for the convective heat release as a function of time.
Flaming and Nonflaming Phenomena During fire propagation, the surface of the material regresses in a transient fashion with a rate slower than the fire propagation rate [31]. The
surface regression becomes steady after fire propagates throughout the available surfaces. The surface regression continues until all the combustible components of the material are exhausted. During fire propagation and surface regression, the material generates vapors at a transient or steady rate. The generation rate of the material vapors is measured by the mass loss rate. In the presence of a flame and/or external heat flux, the mass loss rate, under steady state, is expressed as [14, 31, 44]: 00
00
m_ ¼
00
00
00
q_ e þ q_ f r þ q_ fc q_ rr ΔH g
ð36:15Þ
where ˙ 00 ¼ Mass loss rate (g/m2 · s) m 00 q_ f r ¼ Flame radiative heat flux transferred to the surface (kW/m2) 00 q_ fc ¼ Flame convective heat flux transferred to the surface (kW/m2) 00 q_ rr ¼ Surface re-radiation loss (kW/m2) ΔHg ¼ Heat of gasification (kJ/g) 00 00 00 total flame heat flux to the surface q_ f ¼ q_ f r þ q_ fc According to Equation 36.15, the generation rate of material vapors is governed by the
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Fig. 36.22 Specific heat of polymethylmethacrylate versus temperature measured by a differential scanning calorimeter at the flammability laboratory of FM Global Research
Specific heat (kJ/g·K) × 103
2.4
2.1
1.8
1.5
1.2
250
300
350
400
450
500
550
600
650
700
Temperature (K)
external and flame heat flux, surface re-radiation loss, and the heat of gasification. Heat of Gasification The heat of gasification for a melting material is expressed as [6] Tðm
ΔH g ¼
Tðv
c p, s dT þ ΔH m þ Ta
c p, l dT þ ΔH v Tm
ð36:16Þ where ΔHg ¼ Heat of gasification (kJ/g) cp,s ¼ Specific heat of solid in kJ/gK cp,l ¼ Specific heat of molten solid in kJ/gK ΔHm ¼ Heat of melting at melting temperature in kJ/g ΔHv ¼ Heat of vaporization at vaporization temperature in kJ/g Ta ¼ Ambient temperature Tm ¼ Melting temperature Tv ¼ Vaporization temperature in K For materials that do not melt, but sublime, decompose, or char, Equation 36.16 is modified accordingly. The heat of gasification can be determined from (1) the parameters on the right-hand side of Equation 36.16, which can be quantified by thermal analysis techniques or calculated from the properties listed in the literature; and (2) nonflaming tests using apparatuses,
such as the OSU heat release rate apparatus, the FPA, or the cone calorimeter. The following are some examples of the techniques: 1. Heats of gasification of polymers from differential scanning calorimetry: Values for cp,s, cp,l, ΔHm, and ΔHv for polymers have been quantified in the FM Global Research Flammability Laboratory [6]. The techniques involve measurement of the specific heat as a function of temperature, such as shown in Fig. 36.22 for polymethylmethacrylate. Further measurements are also made of the heats of melting and vaporization. Some examples of the data measured at FM are listed in Table 36.6. 2. Heat of gasification from literature data for the heats of gasification for various molecular weight hydrocarbons (alkanes): The CRC Handbook of Chemistry and Physics [54] listing for the heats of gasification for liquid and solid hydrocarbons (alkanes) satisfies the following relationship in the molecular weight range of 30–250 g/mol: ΔH g ¼ 0:164 þ 0:0042M 3:72 106 M2 ð36:17Þ where M is the molecular weight of the hydrocarbon (g/mol).
36
Combustion Characteristics of Materials and Generation of Fire Products
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Table 36.6 Surface re-radiation and heats of gasification of various materials Materials Distilled water Hydrocarbons (alkanes) Hexane Heptane Octane Nonane Decane Undecane Dodecane Tridecane Tetradecane Hexadecane Natural materials Filter paper Corrugated paper Wood (Douglas fir) Plywood/FR Particleboard Synthetic materials Epoxy resin Polypropylene Polyethylene (PE) (low density) PE (high density) PE foams PE/25 % chlorine (CI) PE/36 % CI PE/48 % CI Rigid polyvinylchloride (PVC) PVC/plasticizer Plasticized PVC, LOI ¼ 0.20 Plasticized PVC, LOI ¼ 0.25 Plasticized PVC, LOI ¼ 0.30 Plasticized PVC, LOI ¼ 0.35 Rigid PVC, LOI ¼ 0.50 Polyisoprene PVC panel Nylon 6/6 Polyoxymethylene (Delrin) Polymethylmethacrylate (Plexiglas) Polycarbonate Polycarbonate panel Isophthalic polyester Polyvinyl ester Acrylonitrile-butadiene-styrene (ABS) Styrene-butadiene Polystyrene (PS) foams PS (granular)
Surface reradiation (kW/m2) 0.63
Heat of gasification (kJ/g) Flam. App.a Coneb DSCc 2.58 – 2.59
Cald 2.58
0.50 0.63 0.98 1.4 1.8 2.3 2.8 3.0 3.0 3.0
– – – – – – – – – –
– – – – – – – – – –
– – – – – – – – – –
0.50 0.55 0.60 0.64 0.69 0.73 0.77 0.81 0.85 0.92
10 10 10 10 –
3.6 2.2 1.8 1.0 –
– – – – 3.9
– – – – –
– – – – –
– 15 15 15 12 12 12 10 15 10 10 – – – – 10 17 15 13 11 11 16 – – 10 10 10–13 13
– 2.0 1.8 2.3 1.4–1.7 2.1 3.0 3.1 2.5 1.7 2.5 – – – – 2.0 3.1 2.4 2.4 1.6 2.1 2.3 – – 3.2 2.7 1.3–1.9 1.7
2.4 1.4 – 1.9 – – – – 2.3 – 2.4 – 2.1 2.4 2.3 – – – – 1.4 – – 3.4 1.7 2.6 – – 2.2
– 2.0 1.9 2.2 – – – – – — – – – – – – – – 2.4 1.6 – – – – – – – 1.8
– – – – – – – – – – – – – – – – – – – – – – – – – – – – (continued)
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Table 36.6 (continued) Materials Polyurethane (PU) foams Flexible polyurethane (PU) foams Rigid polyurethane (PU) foams Polyisocyanurate foams Phenolic foam Phenolic foam/FR Ethylenetetrafluoroethylene (Tefzel) Fluorinated ethylene propylene (FEP, Teflon) Tetrafluoroethylene (TFE, Teflon) Perfluoroalkoxy (PFA, Teflon) Composite and fiberglass-reinforced materials Polyether ether ketone–30 % fiberglass Polyethersulfone–30 % fiberglass Polyester 1–fiberglass Polyester 2–fiberglass Polyester 3–fiberglass Polyester 4–fiberglass Polyester 5–fiberglass Phenolic fiberglass (thick sheet) Phenolic Kevlar (thick sheet)
Surface reradiation (kW/m2)
Heat of gasification (kJ/g) Flam. App.a Coneb DSCc
Cald
16–19 14–22 14–37 20 20 27 38 48 37
1.2–2.7 1.2–5.3 1.2–6.4 1.6 3.7 0.9 2.4 0.8–1.8 1.0
2.4 5.6 – – – – – – –
1.4 – – – – – – – –
– – – – – – – – –
– – – 10 10 15 10 20 15
– 1.8 – 1.4 6.4 5.1 2.9 7.3 7.8
7.9 – 2.5 – – – – – –
– – – – – – – – –
– – – – – – – – –
a
From the Fire Propagation Apparatus under nonflaming conditions Calculated from the cone calorimeter data reported for the mass loss rate at various external heat flux values in flaming fires [13, 32] c From the flammability laboratory using the differential scanning calorimetry d Calculated from the data reported in the CRC Handbook [54] b
The heats of gasification calculated from Equation 36.17 for various alkanes are listed in Table 36.6. 3. Heat of gasification from literature data for the specific heats and heats of vaporization: Water will be used as an example. The specific heat of liquid water, cp,l, which is assumed constant, is 0.0042 kJ/g-K [55] and the heat of vaporization of water at 373 K is 2.26 kJ/g [54]. Assuming the ambient temperature to be 298 K and the vaporization temperature to be 373 K, the heat of gasification of water from Equation 36.16 is calculated as follows: Tðv
ΔH g ¼
c p, l dT þ ΔHv Ta
¼ c p, l ðT v T a Þ þ ΔHv ¼ 0:0042ð373 298Þ þ 2:26 ¼ 2:58kJ=g
Using differential scanning calorimetry, the heat of gasification of water determined in the FM Global Research Flammability Laboratory is 2.59 kJ/g, which is in excellent agreement with the calculated value. These two values for the heat of gasification of water are listed in Table 36.6. 4. Heat of gasification from nonflaming tests using the Fire Propagation Apparatus: The measurement for the heat of gasification from the nonflaming tests in the ASTM E2058 [10] fire propagation apparatus was introduced in 00 1976 [6]. In the absence of flames, q_ f ¼ 0, and Equation 36.15 simplifies to: 00
00
m_ ¼
00
q_ e q_ rr ΔH g
ð36:18Þ
where mass loss rate is now extrictly a linear function of the external heat flux. Therefore,
36
Combustion Characteristics of Materials and Generation of Fire Products
this equation provides a convenient method to determine the heat of gasification in nonflaming tests, where mass loss rate of the sample is measured at various external heat flux values. The heat of gasification is determined from linear regression analysis of the average steady-state mass loss rate as a function of external heat flux, using Equation 36.18. In the Fire Propagation Apparatus, samples can be exposed to radiant fluxes in 100 % nitrogen atmospheres, allowing the application of this methodology Figure 36.23 shows a plot of the vaporization rate (i.e., mass loss rate), as a function of time, of water in a 0.0072 m2 Pyrex glass dish exposed to 50 kW/m2, measured in the Fire Propagation Apparatus. The figure also includes the predicted mass loss rate using Equation 36.18, where 00 q_ rr ¼ εσ T 4v T 4a
ð36:19Þ
where ε is the emissivity of water (0.95–0.963 in the temperature range 298–373 K), [56] and σ is the Stefan-Boltzmann constant (56.7 1012 kW/m2-K4). For water, Tv ¼ 373 K 00 and Ta ¼ 298 K, and thus q_ rr ¼ 1 kW/m2. 00 From Equation 36.18, using q_ e ¼ 50 kW/m2, 00 q_ rr ¼ 1 kW/m2, and ΔHg ¼ 2.59 kJ/g, ˙ 00 ¼ 19.0 g/m2s. There is excellent agreement m between the measured and predicted values at the steady state in Fig. 36.23.
Heats of gasification determined from mass loss rate as a function of external heat flux at nonflaming conditions in the FPA are listed in Table 36.6 for selected materials. Excellent agreement can be noted between the heats of gasification determined from the FPA data and those obtained from differential scanning calorimetry. Heat of gasification can also be determined from flaming fires if high external heat flux 00 00 00 00 values are used such that q_ e >> q_ f r þ q_ fc q_ rr in Equation 36.15. This method has been used to calculate the heat of gasification from cone calorimeter data using mass loss rates measured in flaming fires reported in the literature [13, 32]. The values calculated from the cone calorimeter data are also listed in Table 36.6 and show a general agreement with the values from the FPA. Example 5 Estimate the ignition temperature of a material with a CHF of 11 kW/m2. Assume its surface emissivity to be unity, ambient temperature to be 20 C, and vaporization temperature to be approximately equal to the ignition temperature. Solution Following the assumption that at the CHF reradiation is the only mode of heat loss, from Equation 36.19,
25 Predicted 20 Vaporization rate (g/m2·s)
Fig. 36.23 Vaporization rate of water versus time measured in the Fire Propagation Apparatus using 99.69 g of water in a Pyrex dish with an area of 0.0072 m2. Water was exposed to an external heat flux of 50 kW/m2
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10
5
0 0
200
400
600 Time (s)
800
1000
1200
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00 q_ rr ¼ CHF ¼ εσ T 4v T 4a 1=4 CHF 4 þ Ta T v ¼ T ig ¼ εσ " #1=4 11kW 2 4 m T ig ¼ þ ð298KÞ 56:7 1012 mkW 2 K4 T ig ¼ 670K Example 6 A material with a surface re-radiation loss of 10 kW/m2 and heat of gasification of 1.8 kJ/g was found to be involved in a fire with an exposed area of 2 m2. The combined flame and external heat flux exposure to the material was estimated to be 70 kW/m2. Estimate the peak mass loss rate at which the material may have been burning in the fire in terms of g/m2 · s and g/s. Solution From Equation 36.15,
ΔHg
kW m2 ¼ 33 g kJ m2 s 1:8 g
ð70 10Þ
The estimated peak mass loss rate of the burning material is 33 g/m2/s, or 33 2 ¼ 67 g/s.
ð36:20Þ
60 Radiative 50
Convective
40
30
10
0
0.507
20
0.427
Flame heat flux (kW/m2)
Fig. 36.24 Flame radiative and convective heat fluxes at various oxygen mass fractions for the steady-state combustion of 100-mm 100-mm square 25-mm-thick slabs of polypropylene in the FPA under co-airflow velocity of 0.09 m/s (Data taken from Ref. [13]). Mass fractions of oxygen are indicated by the numbers inside the frames
00
0.370
m_ ¼
kW m2
0.310
00
0.266
00
q_ e þ q_ f r þ q_ fc ¼ 70 00
00
0.233
00
00
The results from numerous small- and largescale fire tests show that, as the surface area of the material increases, the flame radiative heat flux increases and reaches an asymptotic limit, whereas the flame convective heat flux decreases and becomes much smaller than the flame radiative heat flux at the asymptotic limit in large-scale fires [57]. It is also known that, in small-scale fires of fixed size with buoyant turbulent diffusion flames, as the oxygen mass fraction is increased, the flame radiative heat flux increases and reaches an asymptotic limit comparable to the asymptotic limit in large-scale fires, whereas the flame convective heat flux decreases and becomes much smaller than the flame radiative heat flux [13]. The effect of the mass fraction of oxygen on the flame radiative and convective heat fluxes in small-scale fires is shown in Fig. 36.24 for 100-mm 100-mm square 25-mm-thick slabs of polypropylene. The data were measured in the Fire Propagation Apparatus [13]. The increase in the flame radiative heat flux with increase in the mass fraction of oxygen is due to the increase in the flame temperature and soot formation and decrease in the residence time in the flame [13]. The oxygen mass fraction
0.208
00
00
q_ e þ q_ f r þ q_ fc q_ rr
00
q_ f r þ q_ fc q_ rr m_ ¼ ΔH g 00
0.196
00
00
m_ ¼
Flame Heat Flux For flaming fires, in the absence of external heat flux, from Equation 36.15
36
Combustion Characteristics of Materials and Generation of Fire Products
variation technique to simulate large-scale flameradiative heat flux conditions in small-scale fires is defined as the flame radiation scaling technique [44]. This methodology forms the basis for the approaches described above regarding the flame propagating behavior of materials using the FPI concept. In the flame radiation scaling technique, the flame radiative and convective heat fluxes are determined from (1) mass loss rate measurements at various oxygen mass fractions in the range of 0.12 (close to flame extinction) to about 0.60, under co-airflow conditions; (2) the convective heat transfer coefficient for the FPA, derived from the combustion of methanol; (3) the mass transfer number; and (4) Equation 36.20. In the Fire Propagation Apparatus, the asymptotic limit is reached for oxygen mass fractions in excess of 0.30. At the asymptotic limit, Equation 36.20 can be expressed as 00
00
m_ asy ¼
high molecular weight oligomers, the asymptotic flame heat flux values increase substantially to the range of 49–71 kW/m2, regardless of their chemical structures. The independence of the asymptotic flame heat values from the chemical structures of materials is consistent with the dependence of flame radiation on optical thickness, soot concentration, and flame temperature in large-scale fires. Example 7 Calculate the peak mass loss rate for polypropylene in large-scale fires, burning in the open, with no external heat sources in the surroundings. Solution In the calculation Equation 36.21 will 00 be used. From Table 36.6, q_ rr ¼ 15 kW/m2 and ΔHg ¼ 2.0 kJ/g, and from Table 36.7, 00 q_ f , asy ¼ 67 kW/m2. Using these values in Equation 36.21,
00
q_ f , asy q_ rr ΔHg
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00
ð36:21Þ
where subscript asy represents the asymptotic limit. The asymptotic values for mass loss rate and flame heat flux determined using the flame radiation scaling technique in the FPA are listed in Table 36.7. The measured asymptotic values for mass loss rate reported in the literature and flame heat flux in large-scale fires are also listed in Table 36.7. Flame heat flux values for the largescale fires are derived from the asymptotic values of the mass loss rate and known values of surface re-radiation losses and heats of gasification. The data in Table 36.7 show that asymptotic flame heat flux values, determined in the FPA using the flame radiation scaling technique, are in good agreement with the values measured in large-scale fires. The asymptotic flame heat flux values vary from 22 to 77 kW/m2, depending primarily on the mode of decomposition and gasification rather than on the chemical structures of the materials. For example, for liquids, which vaporize primarily as monomers or as very low molecular weight oligomers, the asymptotic flame heat flux values are in the range of 22–44 kW/m2, regardless of their chemical structures. For polymers, which vaporize as
00
m_ asy ¼ 00
m_ asy ¼
00
q_ f , asy q_ rr ΔH g kW m2 ¼ 26 g kJ m2 s 2:0 g
ð67 15Þ
Example 8 Calculate the peak mass loss rate for polypropylene in large-scale fires burning in the open in the presence of a burning object, which provides 20 kW/m2 of heat flux to the polypropylene surface, in addition to its own flame heat flux of 67 kW/m2. Solution In the calculation, Equation 36.15 will 00 be used with q_ e ¼ 20 kW/m2. From Table 36.6, 00 q_ rr ¼ 15 kW=m2 and ΔHg ¼ 2.0 kJ/g and from 00 Table 36.7, q_ f , asy ¼ 67 kW/m2. Using these values in Equation 36.15, 00
00
00
00
q_ e þ q_ f r þ q_ fc q_ rr m_ ¼ ΔH g 00
kW 00 00 00 q_ e þ q_ f r þ q_ fc ¼ ð67 þ 20Þ 2 m kW ð87 15Þ 2 00 m ¼ 36 g m_ ¼ kJ m2 s 2:0 g
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Table 36.7 Asymptotic values of mass loss rate and flame heat flux 00
00
˙ asy (g/m2/s) m Sa
Material Aliphatic carbon-hydrogen atomsc Polyethylene 26 Polypropylene 24 Heavy fuel oil (2.6–23 m) – Kerosene (30–80 m) – Crude oil (6.5–31 m) – n-Dodecane (0.94 m) – Gasoline (1.5–223 m) – JP-4 (1.0–5.3 m) – JP-5 (0.60–17 m) – n-Heptane (1.2–10 m) 66 n-Hexane (0.75–10 m) – Transformer fluids (2.37 m) 27–30 Aromatic carbon-hydrogen atomsc Polystyrene (0.93 m) 36 Xylene (1.22 m) – Benzene (0.75–6.0 m) – Aliphatic carbon-hydrogen-oxygen atomsc Polyoxymethylene 16 – Polymethylmethacrylate (2.37 m) 28 Methanol (1.2–2.4 m) 20 Acetone (1.52 m) – Aliphatic carbon-hydrogen-oxygen-nitrogen atoms Flexible polyurethane foams 21–27 Rigid polyurethane foams 22–25 Aliphatic carbon-hydrogen-halogen atoms Polyvinylchloride 16 Tefzel (ETFE) 14 Teflon (FEP) 7
Lb
q_ f , asy (kW/m2) Sa
Lb
– – 36 65 56 36 62 67 55 75 77 25–29
61 67 – – – – – – – 32 – 23–25
– – 29 29 44 30 30 40 39 37 37 22–25
34 67 81
75 – –
71 37 44
50 30 25 38
– 57 22 –
– 60 27 24
– –
64–76 49–53
– –
– – –
50 50 52
– – –
Note: Mass loss rates are from the data reported in the literature a Small-scale fires, pool diameter fixed at 0.10 m, flame radiation scaling technique was used in the Fire Propagation Apparatus, YO 0.30 b Large-scale fires in normal air c Numbers in m in parentheses are the pool diameters used in large-scale fires
Pyrolysis and Determination of “ModelSpecific” Material Properties One of the most prevailing observations made with the bench-scale apparatuses discussed in section “Flammability Apparatuses and Measurement Capabilities” of this chapter is the rate of thermal degradation of condensed phase materials under a prescribed heating scenario. This behavior is captured in the tests through the measurement of a mass loss rate (MLR). In the context of this
chapter such behavior is referred to as pyrolysis. Pyrolysis is a complex process that involves a number of coupled physical and chemical phenomena, which include, among many others, phase changes, char formation, water desorption/ migration (e.g., in cellulosic fuels), gas diffusion, gas-solid heat exchange, oxidation, etc. (refer to Chaps. 21 and 23). These processes determine the formation of gradients (thermal, species, etc.) within a given material which control ignition, heat release, and flame propagation in fires.
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Combustion Characteristics of Materials and Generation of Fire Products
There is strong and continued interest in the fire community in the development of predictive fire modeling capabilities for practical largescale fires through the use of new-generation computational fluid dynamics (CFD) tools [58–60]. Such modeling can provide measures to interpret, interpolate, and extrapolate information obtained from limited experimental data as well as providing cost-effective alternatives by reducing the number of large-scale tests necessary to develop fire protection requirements or standards. To reach this objective, physical models for fluid mechanics, gas phase combustion, soot formation and oxidation, radiation, solid phase heat transfer and pyrolysis, and suppression need to be incorporated into an appropriate CFD solver to properly represent the multi-scale, multi-physics phenomena taking place in large-scale fires. Given the mathematical complexity of these CFD tools, it is important that such fire models be verified and validated against experimental data [59, 60]. Of relevance to the present chapter is how bench-scale experiments may contribute to the development of pyrolysis models to be used in the CFD tools described above. Models have become recently available [61–64] which represent the current state of the art of pyrolysis modeling; these are comprehensive models which share similar robust mathematical and numerical frameworks. These models, due to their complexity, require a potentially large number of adjustable input parameters, i.e., material properties. Many applications (e.g., large-scale industrial fires) involve fuels for which such properties are unknown. In certain cases (e.g., [65–67]) detailed property measurements may be performed (via thermogravimetric analyses, TGA, and differential scanning calorimetry, DSC, for example) and successfully used in the comprehensive models. However, experimental venues such as TGA and DSC, although extremely useful in providing fundamental material information, are often not representative of practical applications as they feature relatively slow heating rates and preclude the formation of mass and thermal gradients within the material. Furthermore, properties
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measured in this manner may not be directly used even in the most advanced models since they cannot reflect the true complexity and heterogeneity of the physical processes taking place during pyrolysis. To some degree models must always conceptualize and aggregate complex interactions by the use of only relatively simple mathematical equations. Therefore, in that sense, pyrolysis models cannot use “true” material properties if all the physics are not fully captured. Finally, in the context of large CFD simulations, use of comprehensive and complex models may be computationally prohibitive. On the basis of the above discussion, then, one of the major challenges posed to the end user of CFD pyrolysis models is to make simplifications and approximations to keep the number of parameters manageable and the model computationally efficient while maintaining sufficient model generality and applicability to a given practical scenario. By following this approach the input parameters to the model can be considered “effective” or “model-specific” material properties which are sensitive to the physical processes included in the model. The methodology by which these model-specific properties are obtained is detailed in the following sections.
Optimization The main requirement regarding the performance of CFD pyrolysis models is that they should properly reproduce aspects of the condensedphase material behavior, such as pyrolysis gas (i.e., fuel) generation rates, surface temperatures, etc., which may be critical to the successful performance of the CFD fire simulation. These material response characteristics can in principle be measured via bench-scale tests such as those conducted in the Fire Propagation Apparatus. The model-specific material properties alluded to above are obtained by coupling a simplified pyrolysis model to optimization algorithms and the input parameters (i.e., the material properties) are adjusted in order to obtain the best possible agreement between model outputs and experimental bench-scale pyrolysis data. In the general framework of flammability properties this approach has been seldom used [68, 69]
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Bench-Scale Experiment
True Response
Model
Simulated Response
Parameters
Observed Response Output
True Input
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Time
Optimization
Fig. 36.25 Optimization approach
although it has recently received renewed attention [70–76]. Numerous similar efforts, though, exist in the literature mostly aimed at determining a limited set of thermal properties and for specific applications [77–82]. A schematic of the optimization approach is shown in Fig. 36.25. An experimental process is captured via a numerical model subject to a driving input (e.g., external radiation) and a set of parameters (“material properties”). In the figure, an important distinction is made between the true input to and true response of the experiment and what is actually observed, or measured, in order to represent experimental uncertainty. It is because of this uncertainty that parameters determined through optimization procedures such as the one discussed herein are sensitive to the accuracy of the experimental data used as optimization targets. As can be expected, the optimization problem is complex and highly non-linear. Therefore, local search methods such as direct search [83] and gradient search [84] algorithms are not applicable; however, such methods have been used widely for property estimation [68, 69, 77, 81, 82]. Global methods are needed which can tackle the major complications of high-dimensionality optimization such as local optima, multiple attraction basins, discontinuities, etc. An optimization algorithm with high efficiency and robustness is needed if one is to perform multiobjective and multivariable optimization as little or no a priori knowledge is available of the structure of the model response surface. Furthermore, these qualities allow optimization algorithms to be easily generalized so as to provide consistent performance over a wide range of problems, even if optimization target data are limited. Here, the selected optimization
algorithm is the Shuffled Complex Evolution (SCE) [85]. This is a method that has been mostly applied to hydrological problems [86] but, as will be shown below, it is general and robust enough to show considerably good performance in flammability applications. Chaos et al. [73–75] found SCE to be superior to other global optimization tools, such as genetic algorithms, a finding that has been confirmed by other researchers [87]. A schematic flowchart of the SCE algorithm is shown in Fig. 36.26. Similar to genetic algorithms, SCE is based on a process of natural evolution. A population of s points (i.e., vectors of “material properties” in the present context) is randomly sampled from the feasible parameter space (given the bounds for each parameter) and the value of the objective function to be optimized (e.g., minimization of the sum of squares between model outputs and experimental data) is computed. The points are ranked from smallest to highest objective function value and are then partitioned into p complexes each containing m points (note s ¼ pm) so that the first complex contains every (l – 1)p + 1 ranked point, the second every (l – 1)p + 2 ranked point, etc. where l ¼ 1, 2, . . ., m. Each of these complexes is then allowed to evolve independently according to a competitive complex evolution (CCE) algorithm [85], described below. After the CCE process, all the points in each complex are combined back into a single population, ranked according to their objective function value, and re-partitioned following the procedure above; this effectively “shuffles” the complexes. This procedure is iteratively repeated until specified convergence criteria are met. SCE allows for more extensive (i.e., in different directions) and freer exploration of the feasible space due to the partition of complexes. Shuffling enhances survivability by sharing information about the space gained independently by each complex. The key component of the SCE method is the CCE algorithm which is based on the NelderMead simplex downhill search scheme [83]. In the CCE algorithm q points are randomly selected within each complex according to a
36
Combustion Characteristics of Materials and Generation of Fire Products
1177
Assign triangular probability to each point in complex
σj =
2(m+1−j) m(m+1)
j = 1,... , m
Form a subcomplex by selecting q points (u1, … ,uq) according to σ and sort (f1 < f2 < … < fq) Sample s random points in feasible space, Ψ Compute objective function value, f
Compute centroid g (do not include uq)
g=
1 q −1 ∑u j q − 1 j =1
Sort points (f1 < f2 < … < fs) Reflection step r = 2g - uq Partition into p complexes containing m points Combine complexes
Evolve each complex (CCE algorithm)
r within Ψ ?
No
Generate random point x in hypercube H formed by the q points in subcomplex. Set r = x
Yes Set uq = r and fq = fr
Yes
fr < fq ? No
No
Contraction step c = (g + uq)/2
Convergence satisfied? Yes
fc < fq? STOP
No
Generate random point x in H. Set uq = x and fq = fx
Yes Set uq = c and fq = fc
Sort all points in complex
No, τ = τ +1
τ >= β ? Yes
Fig. 36.26 The Shuffled Complex Evolution algorithm
trapezoidal probability distribution so that the best and worst points in the complex have the highest and lowest chance, respectively, of being chosen. The centroid of the subcomplex formed by the set of q points is calculated without considering the worst point in the subcomplex; then, this worst point is reflected through the centroid. If the new point so computed is better (i.e., its objective function value is improved) than the worst point, the worst point is replaced. Otherwise a point is computed halfway between the centroid and the worst point; if this point is better
than the worst point, the worst point is replaced. In the case that the latter two steps do not generate a better point or if the reflection through the centroid yields a point outside the feasible space, a point is generated randomly which replaces the worst point. This procedure is repeated a specific number of times, β, before the complexes are shuffled as described above. In this manner, each complex evolves independently as a whole. The SCE process is shown graphically in Fig. 36.27 by using a two-dimensional example. A test function was generated (left pane in
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Fig. 36.27 SCE application to a two-dimensional problem
Fig. 36.27) by distorting selected regions of a convex quadratic function so as to introduce local minima with varying regions of attraction, following the methods of Gaviano and Lera [88]. A three-minima function was generated with one global minimum located at (X,Y) ¼ (0.312,0.598). SCE was run with three complexes (denoted by stars, circles, and triangles in Fig. 36.27) consisting of 5 points each (i.e., p ¼ 3, m ¼ 5, s ¼ 15). Note the effect of shuffling in Fig. 36.27. The overall distribution of points from the end of an evolution to the beginning of the next is unchanged; however, the distribution within each complex changes. Also note that some points converge towards the local minimum at (X,Y) ¼ (-0.412,-0.351) in the first two evolutions but shuffling efficiently directs their convergence towards the global minimum.
Application Synthetic Data and Target Selection Foremost, it is important to illustrate the features and limitations of the SCE optimization algorithm when applied to problems of practical interest herein. In order to do this, a simplified
one-dimensional pyrolysis model was used to generate synthetic experimental data for a supposed charring material. One-dimensionality is assumed as this is representative of tests conducted in the Fire Propagation Apparatus or cone calorimeter where the thickness of samples tested is small compared to their diameter and edge effects can be considered negligible. The specific details of the pyrolysis model used are beyond the scope of this chapter, and the reader is referred to [63, 64, 73–75] for further information; only the simplifications made to the model are described here for brevity. The model employs a control volume approach and the governing mass and energy conservation equations are solved numerically using a fully implicit scheme. Only three species are treated: virgin solid, char, and pyrolytic gas and it is assumed that the virgin solid decomposes to char and/or gas through a single heterogeneous nth-order Arrhenius-type reaction. Pyrolysis gas is assumed to be in thermal equilibrium with the solid and to immediately escape once formed. All material properties are assumed to be temperature-independent.
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Combustion Characteristics of Materials and Generation of Fire Products
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Table 36.8 Parameters used to generate synthetic data (Fig. 36.28) and parameters returned by optimization Property Virgin
Char
Arrhenius decomposition
Synthetic Thermal conductivity (W/m/K) 0.10 Density (kg/m3) 500 Heat capacity (J/kg/K) 1500 Emissivity 0.5 Thermal conductivity (W/m/K) 0.25 Density (kg/m3) 100 Heat capacity (J/kg/K) 1000 Emissivity 0.9 Log [pre-exponential factor (s1)] 10 Activation energy (kJ/mol) 150 Reaction order 2 Log [heat of pyrolysis (J/kg)] 5.81
Average deviation (%)
The synthetic dataset consists of mass loss rate and surface temperature data generated for a 5-mm thick material subjected to external radiation levels of 25, 50, and 100 kW/m2. For simplicity, the back boundary of the material was assumed to be perfectly insulated (adiabatic) and a constant convective heat transfer coefficient of 15 W/m2/K was assumed for the front surface. The material properties used in the model to generate the data are listed in Table 36.8. The model-generated curves were modified by adding Gaussian error with standard deviations representative of experimental uncertainty: 100 mg for mass loss and 15 K for temperature measurements [75, 89], In order to obtain mass loss rate, the modified mass loss curve was differentiated using Savitsky-Golay filters [37, 90, 91]. As opposed to previous applications of this methodology [36, 91] in which a fixed filter window size was recommended, the window size of the filter was kept between one and two times the full-width-half-magnitude size of the narrowest transient peak of interest [92] in order to avoid introducing unwanted bias in the derived MLR data. This approach ensured that the magnitude of these peaks was preserved after application of the filter. Figure 36.28 shows plots of the synthetic data prior to and after adding Gaussian error. Also in the figure, the effect of varying the smoothing filter size is shown for the
SCE optimization LB UB Case 1 0.01 1.00 0.04 100 1000 521 500 5000 684 0.0 1.0 0.30 0.01 1.00 0.21 50 500 120 500 5000 5000 0.0 1.0 0.49 6 12 10.7 50 250 160 0 5 1.3 4 7 5.52 57.8
Case 2 0.09 571 1390 0.49 0.30 169 1166 0.99 7.6 119 1.8 5.87 17.1
Case 3 0.10 660 1210 0.59 0.33 260 2071 1.00 8.9 141 1.5 5.85 35.2
Case 4 0.10 510 1470 0.50 0.25 95 1053 0.90 10.0 150 2 5.81 1.2
100 kW/m2 case. Note that by increasing the filter window size by a factor of two the first mass loss rate peak, which is narrower, is “washed out” whereas the second peak is still properly captured. Several optimization runs were preformed by selecting specific subsets of the data shown in Fig. 36.27. This was done in order to test the robustness of the SCE algorithm as it is often the case, especially with complex practical materials, that target experimental data may be limited and/or difficult to measure accurately. An algorithm that can reach the global optimum with the least amount of target data can be extremely useful as it can allow one to limit the target metrics to only those data that can presumably be measured more accurately without considering data with higher uncertainty. Four target data subsets were selected: Case 1—mass loss rate at 50 kW/m2; Case 2—mass loss rate, cumulative mass loss, and surface temperature at 50 kW/m2; Case 3—mass loss rate at 25, 50, and 100 kW/m2; and Case 4— mass loss rate, cumulative mass loss, and surface temperature at 25, 50, and 100 kW/m2. SCE was run subject to the property bounds shown in Table 36.8 and with algorithmic parameters (i.e., p, m, q, and β, see above) selected according to the guidelines of [86]; the population size was 150.
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800
25 kW/m2 5
700
4 600 3 500 2 400
1 0
0
400
600
300 1000
800
50 kW/m2 900
14 12
800
10
700
8
600
6 500 4 400
2 0
0
50
100
150
Surface Temperature (K)
Mass Loss Rate (g/m2/s)
16
200
300 250
200
100 kW/m2 30
1050
25
900
20 750 15 600
10
450
5 0
0
25
50
75
100
300
Time (s)
Fig. 36.28 Synthetic data. Lines show model outputs and symbols denote the model data after Gaussian error was added (see text). The dashed line for mass loss rate at 100 kW/m2 shows the effect of varying the smoothing filter window size from 25 s to 50 s (see text)
The values for the optimized property parameters obtained for each of the four cases are listed in Table 36.8. For the sake of brevity and in lieu of showing plots it is noted that for all cases a near perfect match was obtained against each of the corresponding datasets used for optimization; the R-squared values for all cases were in excess of 0.99. However, regardless of the good agreement obtained, the original
parameters are not recovered in most cases. A clear trend can be observed, nonetheless; the deviation from the original parameters is reduced when more target metrics are added (compare Case 1 to Case 2 and Case 3 to Case 4) and when more heat fluxes are considered for the same target metric (compare Case 1 to Case 3 and Case 2 to Case 4). This trend is an obvious manifestation of how the target data are able to constrain the model and, thus, the optimization algorithm. By considering mass loss rate alone (Case 1 and Case 3) parameters, most notably physical properties such as thermal conductivity and heat capacity, cannot be accurately determined. This is to be expected as these parameters are coupled through the thermal inertia and thermal diffusivity of the material. Introducing temperature as an optimization target improves agreement against these properties and the same can be said about considering additional heat flux levels. It is noted that, in a similar synthetic data exercise as that discussed here, SCE was found to recover the input parameters using datasets consisting of mass loss rate, front and back surface temperatures at two heat flux levels [87]; back surface temperature measurements may present a experimental challenge, however. The discussion above should persuade the reader that the process of obtaining modelspecific properties through optimization will be most successful when considering multiple experimental data (mass loss rate, temperature, etc.) over as wide a range of practical conditions as possible [60]. Furthermore, availability of properties that can be easily measured (e.g., virgin density) will further improve the results by reducing the dimensionality of the problem. Yet, there are cases in the literature (e.g., [76]) where optimization is performed against very limited datasets. As a last word of caution it is reiterated that the “material properties” obtained using the methodology described herein depend on the choice of pyrolysis model as well as the accuracy of the experimental data and are not universally applicable to other models or to scenarios that considerably depart from the experimental conditions used to derive the model-specific properties.
36
Combustion Characteristics of Materials and Generation of Fire Products
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Fig. 36.29 Experimental (symbols) and computed (lines) parallel panel heat release rates for single-wall corrugated cardboard [96]. The experimental configuration is shown on the left panel
FPA Data and Intermediate-Scale Fire Growth Simulations The approach outlined above has been extensively used and applied to the simulation of the vertical spread of fire between parallel panels at an intermediate scale [60, 93–97]. For this application, model-specific properties were determined using the pyrolysis model included in FireFOAM [98, 99], a Large Eddy Simulation (LES) solver. The target data used for optimization were collected in the Fire Propagation Apparatus in inert environments (i.e., 100 % nitrogen); this is a unique feature of the apparatus (see section “Flammability Apparatuses and Measurement Capabilities”) which allows for the decoupling of flame heat flux from the pyrolysis process. Following the recommendations of the previous section, the data consisted of mass loss rates and surface temperatures over heat fluxes spanning the 20–110 kW/m2 range. The model-specific material properties were shown to successfully predict, at least qualitatively, flame propagating and non-propagating behavior of several materials when used in the LES simulation [60]. Further experience with the application of the methodologies described herein has elucidated the importance of properly characterizing boundary conditions in the FPA experiments and the relative
importance of oxidative pyrolysis in certain applications [35, 89, 97]. Considerable progress has been made in the predictive abilities of FireFOAM when compared against flame spread experiments in the parallel panel configuration [97]. An example is shown in Fig. 36.29 where the heat release rate of single-wall corrugated cardboard collected during three separate parallel panel tests (a schematic of the test is also shown in the figure, for more details refer to [93–97] as well as section “Fire Propagation”) is compared against simulations. A considerably good agreement can be observed. This is an encouraging result which confirms that the approach described in this section for the characterization of material flammability is promising and may lead to cost-effective modeling alternatives to large-scale testing.
Heat Release Rate The determination of heat release rate in fires has been influenced by the principles and techniques used for controlled combustion in the heating and power industries. Heat in the flowing combustion products (convective heat) and thermal radiation are used to generate steam, heat a furnace or space, produce mechanical power in internal
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combustion engines or gas turbines, and so forth. Heat is generated by injecting fuel (gas, liquid, or solid) into a hot environment, where it undergoes evaporation, gasification, and thermal decomposition or pyrolysis. Fuel vapors react chemically with oxygen and produce heat and products, such as carbon monoxide (CO), carbon dioxide (CO2), hydrocarbons, water (H2O), and soot and other particulates. The theoretical amount of air required for complete combustion is estimated from an empirical guide [100], which suggests that, for every 10.6 kJ of heat in the fuel burned, 3.4 g of air are required for complete combustion [101]. Equivalently, the heat of combustion per unit mass of molecular oxygen consumed (ΔH0*) is 13.4 kJ/g. Using ΔH0* 13.4 kJ/g to determine the heat release rate in fires from the mass consumption rate of oxygen is discussed in Refs. [14, 21]. This technique forms the basis of oxygen consumption (OC) calorimetry. A combustion process is characterized by its combustion efficiency, χ ch, defined as the fraction of heat of complete combustion released in the chemical reactions, which is the ratio of the chemical heat of combustion to the net heat of complete combustion. The calorific energy generated in chemical reactions leading to complete combustion per unit mass of fuel, with water produced being in the vapor state, is defined as the net heat of complete combustion. The calorific energy generated in chemical reactions leading to varying degrees of
M.M. Khan et al.
incomplete combustion per unit mass of fuel consumed is defined as the chemical heat of combustion. In the heating and power industries, combustion efficiency is determined routinely from the analysis of waste products (flue gas), especially for CO, CO2, and O2, and from the measurements of temperature in the combustion products-air mixture and thermal radiation. For higher combustion efficiency, mass fuel-to-air ratio relative to the stoichiometric fuel-to-air mass ratio or the equivalence ratio is controlled by maintaining the desired primary and secondary airflow. The net heat of complete combustion can be measured in the oxygen bomb calorimeter [102] (see Chap. 27) and is calculated from the standard heats of formation of the materials, CO2, and H2O (the standard heat of formation of O2 in its standard state being zero). In fires, complete combustion is rarely achieved and products of incomplete combustion, such as CO and smoke, are quite common. An example of incomplete combustion is given in Table 36.9, where chemical heat of combustion and combustion efficiency decrease as CO, carbon, and ethylene are formed at the expense of CO2 and H2O with reduced O2 consumption, a typical condition found in ventilation-controlled fires [103]. The upper limit of the combustion efficiency is 1.00, corresponding to complete combustion, and the lower limit is 0.46, corresponding to unstable combustion leading to flame extinction for combustion efficiency 0.40 [103, 104].
Table 36.9 Chemical heat of combustion and combustion efficiency of polymethylmethacrylate Reaction stoichiometry C5H8O2 (g) + 6.0 O2 (g) ¼ 5CO2 (g) + 4H2O (g) C5H8O2 (g) + 5.5 O2 (g) ¼ 4CO2 (g) + 4H2O (g) + CO (g) C5H8O2 (g) + 4.5 O2 (g) ¼ 3CO2 (g) + 4H2O (g) + CO (g) + C (s) C5H8O2 (g) + 3.0 O2 (g) ¼ 2CO2 (g) + 3H2O (g) + CO (g) + C (s) + 0.50 C2H4 (g)
ΔHch (kJ/g)a
χch
24.9
1.00
22.1
0.89
18.2
0.73
11.5
0.46
Standard heat of formation in kJ/mol: PMMA (C5H8O2) (g) ¼ 442.7; O2 (g) ¼ 0; CO2(g) ¼ 393.5; H2O (g) ¼ 241.8; CO (g) ¼ 110.5; C (s) ¼ 0; and C2H4 (g) ¼ +26.2, where g and s stand for gaseous and solid states, respectively a
36
Combustion Characteristics of Materials and Generation of Fire Products
Chemical Heat Release Rate As described in section “Flammability Apparatuses and Measurement Capabilities” of this chapter, chemical heat release rate in bench scale apparatuses such as the Fire Propagation Apparatus and cone calorimeter can be determined from CDG and OC calorimetries. CDG Calorimetry The chemical heat release rate is determined from the following relationships [14, 28, 31, 43, 44, 103, 105]: 00
00
00
Q_ ch ¼ ΔH *CO2 G_ CO2 þ ΔH *CO G_ CO ΔH *CO2 ¼ ΔH*CO ¼
ΔHT ψ CO2
ΔHT ΔHCO ψ CO ψ CO2
ð36:22Þ ð36:23Þ ð36:24Þ
where 00 Q_ ¼ Chemical heat release rate (kW/m2) ch
ΔH *CO2 ¼ Net heat of complete combustion per unit mass of CO2 generated (kJ/g) * ΔHCO ¼ Net heat of complete combustion per unit mass of CO generated (kJ/g) ΔHT ¼ Net heat of complete combustion per unit mass of fuel consumed (kJ/g) ψ CO2 ¼ Stoichiometric yield for the maximum conversion of fuel to CO2 (g/g) ψ CO ¼ Stoichiometric yield for the maximum conversion of fuel to CO (g/g) 00 G_ CO2 ¼ Generation rate of CO2 (g/m2/s) 00 G˙CO ¼ Generation rate of CO (g/m2/s) The values for the net heats of complete combustion per unit mass of fuel consumed and CO2 and CO generated are listed in Table A.38. The values depend on the chemical structures of the materials. With some exceptions, the values remain approximately constant within each generic group of fuels. The average values are also listed in the tables. From the average values, ΔH *CO2 ¼ 13.3 1.5 kJ/g and * ΔHCO ¼ 11.1 2 kJ/g. In CDG calorimetry, the CO correction (which accounts for the heat generated for incomplete combustion) for wellventilated fires is very small because of the small
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amounts of CO generated. The variations of 11 % * values, respecand 18 % in the ΔH*CO2 and ΔHCO tively, would reduce significantly if values for low molecular weight hydrocarbons with small amounts of O, N, and halogen were not used in averaging. For the determination of the chemical heat release rate, generation rates of CO2 and CO are measured and either the actual values (if material composition is known) or the average values of the net heat of complete combustion per unit mass of CO2 and CO generated are used. The measurements for the generation rates of CO2 and CO are described in section “Generation of Fire Products and Smoke Yields” of this chapter. Care must be taken in the application of CDG calorimetry depending on the scenario of interest. For example, in fires where incomplete combustion is ubiquitous and copious amounts of unburned hydrocarbons, soot, and other particulates are generated, the equations above will not yield an accurate measure of heat release rate as corrections for the formation of these species have to be included (much like is done above for CO). One more example is a scenario where a fire is suppressed by water (i.e., a sprinkler) and a large amount water vapor is present in the combustion-product-air mixture. Some correction procedures are available (e.g., [106]) to account for these effects. OC Calorimetry The chemical heat release rate is determined from the following relationships [13, 21–24, 28, 31, 43, 44, 103, 105, 107]: 00
00
Q_ ch ¼ ΔH *O C_ O ΔH *O ¼
ΔH T ψO
ð36:25Þ ð36:26Þ
where ΔHO* ¼ Net heat of complete combustion per unit mass of oxygen consumed (kJ/g) 00 C˙O ¼ Mass consumption rate of oxygen (g/m2/s) ψ O ¼ Stoichiometric oxygen-to-fuel mass ratio (g/g) The values for the net heats of complete combustion per unit mass of oxygen consumed are listed in Table A.38 along with the values for the
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net heats of complete combustion per unit mass of fuel consumed and CO2 and CO generated. The average values of the net heat of complete combustion per unit mass of oxygen consumed are also listed in the tables. The values depend on the chemical structures of the materials. With some exceptions, the values remain approximately constant within each generic group of fuels. From the average values, ΔHO* ¼ 12.8 0.9 kJ/g. The ΔHO* value of 12.8 kJ/g is in good agreement with the value 13.1 0.7 kJ/g reported in Ref. [21]. The variation of 0.9 kJ/g (7 %) would reduce significantly if values for low molecular weight hydrocarbons with small amounts of O, N, and halogen were used in averaging. For the determination of chemical heat release rate, mass consumption rate of oxygen is measured, and either the actual values or the average values of the net heats of complete combustion per unit mass of oxygen consumed are used. The measurement for the consumption rate of oxygen is described in section “Generation of Fire Products and Smoke Yields” of this chapter. As discussed above for CDG calorimetry, in situations where incomplete combustion is prevalent, the equations above will have to be corrected for the formation of products such as soot and unburned hydrocarbons [108, 109]. Furthermore, for materials that have bound oxygen in their chemical structures, oxygen may be released as a product of combustion which will affect the OC methodology [110]. Thus, chemical structure plays an important role in the determination of heat release rate [111].
Convective Heat Release Rate The convective heat release rate is determined from GTR calorimetry, where the following relationship is used [1–3, 13, 14, 28, 31, 44, 103]: _ cp T g T a 00 W ð36:27Þ Q_ con ¼ A where 00 Q_ ¼ Convective heat release rate (kW/m2) con
cP ¼ Specific heat of the combustion product-air mixture at the gas temperature (kJ/g/K) Tg ¼ Gas temperature (K)
M.M. Khan et al.
Ta ¼ Ambient temperature (K) W˙ ¼ Total mass flow rate of the fire product-air mixture (g/s) A ¼ Total exposed surface area of the material (m2) Radiative Heat Release Rate The chemical heat release rate consists of a convective and a radiative component [25]. Some fraction of the chemical heat release rate may be lost as conductive heat. In systems where such conductive heat losses are negligibly small, the radiative heat release rate can be obtained from the difference between the chemical and convective heat release rates [14, 25, 28, 31, 44, 103]: 00
00
00
Q_ rad ¼ Q_ ch Q_ con
ð36:28Þ
00
where Q_ rad is the radiative heat release rate (kW/m2). Energy Released in a Fire The total amount of heat generated as a result of chemical reactions in the combustion of a material is defined as chemical energy. The chemical energy has a convective and a radiative component: Ech ¼ Econ Erad
ð36:29Þ
where Ech ¼ Chemical energy (kJ) Econ ¼ Convective energy (kJ) Erad ¼ Radiative energy (kJ) The chemical energy and its convective and radiative components are calculated by the time integration of the respective heat release rates, expressed here by a numerical summation: Ei ¼ A
n¼tex X
00
Q_ i ðtn ÞΔtn
ð36:30Þ
n¼tig
where Ei ¼ Chemical, convective, or radiative energy (kJ) A ¼ Total surface area of the material burning (m2) tig ¼ Ignition time (s) tex ¼ Flame extinction time (s)
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Combustion Characteristics of Materials and Generation of Fire Products
The total mass of the material lost during combustion can be measured directly from the initial and final mass or calculated by the time integration of the mass loss rate, expressed here by a numerical summation: Wf ¼ A
n¼tex X
00
m_ ðtn ÞΔtn
average chemical heat of combustion determined in the cone calorimeter is defined as the effective heat of combustion [22–24]. Heat Release Parameter (HRP) From Equations 36.15 and 36.32 the amount of energy generated per unit amount of energy absorbed can be expressed as:
ð36:31Þ
n¼tig
where Wf is the total mass of the material lost (g) in the combustion process. Heat release rate can also be expressed as the product of the mass loss rate and the heat of combustion of the material, if it is known a priori: 00
00 Q_ i ¼ ΔH i m_
00
Q_ i ¼
Ei Wf
ð36:32Þ
ð36:33Þ
where ΔH i is the average chemical, convective, or radiative heat of combustion (kJ/g). The
ΔH i 00 00 00 00 q_ e þ q_ f r þ q_ fc q_ rr ð36:34Þ ΔH g
2000 FMRC Average steady-state chemical heat release rate (kW/m2)
Fig. 36.30 Average steady-state chemical heat release rate versus net heat flux for a polystyrene sample. Net heat flux is the sum of the external and flame heat fluxes minus the surface re-radiation
where the ratio ΔHi/ΔHg is defined as the Heat Release Parameter (HRP) and, as the heat release rate itself, has chemical, convective, and radiative components (HRPch, HRPcon, and HRPrad, respectively) [44]. The HRP values are characteristic fire properties of materials but depend on fire ventilation. The chemical HRP is independent of fire size. Experimental data support Equation 36.34, as shown in Figs. 36.30, 36.31, and 36.32, where the average peak or steady-state chemical heat release rates are plotted against the net heat flux. A clear linear relationship between the chemical heat release rate and net heat flux can be discerned. 00 00 00 00 For the condition q_ e >> q_ f r þ q_ fc q_ rr , the average HRP value can be calculated from
where ΔHi is the chemical, convective, or radiative heat of combustion (kJ/g). In turn, the average chemical, convective, or radiative heats of combustion can be calculated from the calorimetry relationships based on Equations 36.22 (or 36.25), 36.27, 36.28, and 36.30 so that: ΔH i ¼
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Cone
1600
1200
800
(HRP)ch = 29
400
0 0
10
20
30
40
50
Net heat flux (kW/m2)
60
70
80
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M.M. Khan et al.
Fig. 36.31 Average steady-state chemical heat release rate versus the net heat flux for a high molecular weight hydrocarbon liquid burning in a 100-mm-diameter dish. The cone calorimeter data were measured at the research laboratory of the Dow-Corning Corporation, Midland, Michigan. Net heat flux is the sum of the external and flame heat fluxes minus the surface re-radiation
2000
Average steady-state chemical heat release rate (kW/m2)
FMRC Cone
1600
1200
800
(HRP)ch = 29
400
0
0
10
20
30
40
50
60
70
Net heat flux (kW/m2)
Fig. 36.32 Peak chemical heat release rate versus the external heat flux for a 100-mm 100-mm 3-mm to 11-mm-thick slab of polyvinyl ester (PVEST), PVEST/ fiberglass, epoxy, epoxy/ fiberglass, and wood (hemlock). Data measured in the cone calorimeter are shown [32]
1200 PVEST PVEST—glass Epoxy Epoxy—glass Wood
Peak chemical heat release rate (kW/m2)
1000
800
600
400
200
0
0
40
20
60
80
100
External heat flux (kW/m2)
the summation of the heat release rate and the external heat flux: n¼tex X
00
Q_ i ðtn ÞΔtn
n¼tig Ei HRP i ¼ ð ¼ n¼tex 00 X 00 A q_ e dt q_ e ðtn ÞΔtn
ð36:35Þ
n¼tig
Incompleteness of Combustion In fires, combustion is never complete. Thus, the chemical heat release rate or the chemical heat of
combustion are less than the heat release rate for complete combustion or the net heat of complete combustion, respectively. The ratio of the chemical heat release rate to the heat release rate for complete combustion or the ratio of the chemical heat of combustion to net heat of complete combustion is defined as combustion efficiency [13, 14, 28, 31, 44, 102]: 00
χ ch
00 Q_ ch m_ ΔH ch ΔH ch ¼ 00 ¼ 00 ¼ ΔH T m_ ΔH T Q_
T
ð36:36Þ
36
Combustion Characteristics of Materials and Generation of Fire Products
where χ ch is the combustion efficiency and 00 Q_ T is the heat release rate for complete combustion (kW/m2). The convective and radiative components of the combustion efficiency are defined in a similar fashion [13, 14, 28, 31, 44, 103]: 00
χ con
00 m_ ΔH con ΔHcon Q_ ¼ con ¼ ¼ 00 00 ΔH T m_ ΔH T Q_
ð36:37Þ
T
00
χ rad ¼
00 Q_ rad m_ ΔH rad ΔH rad ¼ 00 ¼ 00 ΔH T m_ ΔH T Q_
ð36:38Þ
T
where χcon is the convective component of the combustion efficiency and χrad is the radiative component of the combustion efficiency [25]. From the definitions, ΔH ch ¼ ΔH con þ ΔH rad
ð36:39Þ
χ ch ¼ χ con þ χ rad
ð36:40Þ
The chemical, convective, and radiative heat release rates, heats of combustion, and combustion efficiencies depend on the chemical structures of the materials and fire ventilation. The distribution of the chemical heat into convective and radiative components changes with fire size. The larger the fire size, the larger the fraction of the chemical heat distributed into the radiative component. Chemical, convective, and radiative heats of combustion and HRP values for several materials under well-ventilated fire conditions are listed in Tables A.38 and A.39, respectively. Comparisons between the limited data from the OSU apparatus, Fire Propagation Apparatus, and cone calorimeter are satisfactory. Data were taken from Refs. [32, 112–117]. Example 9 Heptane was burned in a 2-m-diameter pan, and measurements were made for the mass loss rate, mass generation rates of CO and CO2, and mass consumption rate of O2. The average values in g/m2/s for the mass loss rate, mass generation rates of CO and CO2, and mass consumption rate of O2 were 66, 9, 181, and 216, respectively. For large-scale fires of
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heptane, the literature values are and χ ch ¼ 0.93, χ con ¼ 0.59, and χ rad ¼ 0.34. The net heat of complete combustion for heptane reported in the literature is 44.6 kJ/g. Calculate the chemical heat release rate and show that it is consistent with the rate based on the literature value of the combustion efficiency. Also calculate the convective and radiative heat release rates. Solution From Table A.38, for heptane, the net heat of complete combustion per unit mass of oxygen consumed is 12.7 kJ/g; the net heat of complete combustion per unit mass of CO2 generated is 14.5 kJ/g; and the net heat of complete combustion per unit mass of CO generated is 12.8 kJ/g. From CDG calorimetry (Equation 36.22), 00
00
00
Q_ ch ¼ ΔH *CO2 G_ CO2 þ ΔH *CO G_ CO 00 kJ g kJ g Q_ ch ¼ 14:5 181 2 þ 12:8 9 2 g m s g m s 00
kW Q_ ch ¼ 2740 2 m
From OC calorimetry (Equation 36.25), 00
00
Q_ ch ¼ ΔH *O C_ O 00 kJ g _ Q ch ¼ 12:7 216 2 g ms 00 kW Q_ ch ¼ 2743 2 m The chemical heat release rate from the CDG and OC calorimetries are in excellent agreement, the average being 2742 kW/m2. The chemical heat of combustion can be obtained from Equation 36.36: χ ch ¼ ΔH ch ΔH ch ΔH ch
ΔHch ΔH T ¼ χ ch ΔH T kJ ¼ ð0:93Þ 44:6 g kJ ¼ 41:5 g
The chemical heat release can now be obtained from the product of the mass loss rate
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M.M. Khan et al.
and chemical heat of combustion, as in Equation 36.32: 00
00 Q_ ch ¼ ΔH ch m_ 00 kJ g _ 66 2 Q ch ¼ 41:5 g m s 00
kW Q_ ch ¼ 2739 2 m Compare this result the averaged value 2742 kW/m2 from the CDG and OC calorimetries. Thus, the chemical heat release determined from the measurements is consistent with the rate obtained from the literature values of the combustion efficiency. Finally, the convective heat release rate can be computed much in the same manner as above. Here, for simplicity, Equations 36.32 and 36.36 are combined to yield the convective heat release rate: 00
00 Q_ con ¼ χ con ΔHT m_ 00
kJ Q_ con ¼ ð0:59Þ 44:6 g 00 kW Q_ con ¼ 1737 2 m
66
g m2 s
(2) polystyrene: 36 27.0 ¼ 972 kW/m2; (3) polyvinylchloride: 16 5.7 ¼ 91 kW/m2; and (4) Teflon: 7 4.1 ¼ 28 kW/m2. Example 11 Heat release rate is the product of the HRP and the net heat flux absorbed by the material, as indicated in Equations 36.34 and 36.35. This concept is used in various models to predict fire propagation and heat release rates, whereas values for the HRP are taken from a handbook such as this handbook, and net heat flux is estimated through correlations. The lower the HRP value for a fixed value of net heat flux, the lower the heat release rate. The values for the surface re-radiation, flame heat flux for large-scale fires, and chemical HRP are listed in Tables 36.6, 36.7, and 36.10, respectively. Calculate the chemical heat release rates expected in large-scale fires of heptane, kerosene, polyethylene, polypropylene, polystyrene, polymethylmethacrylate, polyvinylchloride, and Teflon. Solution The chemical heat release rates are calculated from Equation 36.34: 00
Q_ ch ¼
In a similar fashion, the radiative heat release rate is calculated to be 1001 kW/m2. Example 10 From the flame radiation scaling technique, the asymptotic mass loss rate values in g/m2/s expected in large-scale fires, as listed in Table 36.7, for polyethylene, polystyrene, polyvinylchloride, and Teflon are 26, 36, 16, and 7, respectively. The chemical heats of combustion in kJ/g listed in Table A.38 for these materials are 38.4, 27.0, 5.7, and 4.1, respectively. Estimate the chemical heat release rates expected in large-scale fires of polyethylene, polystyrene, polyvinylchloride, and Teflon. (In this chapter Teflon refers mainly to FEP, except in cases where it is identified otherwise.) Solution The chemical heat release rate is calculated from Equation 36.32. The chemical heat release rates estimated in the large-scale fires are (1) polyethylene: 26 38.4 ¼ 998 kW/m2;
ΔHch 00 00 00 00 q_ e þ q_ f r þ q_ fc q_ rr ΔH g
In this specific example, there is no external heat flux sources. Recognizing that (ΔHch/ΔHg) ¼ HRPch, and setting the asymptotic flame heat 00 00 flux values from 7 to the relationship q_ f r þ q_ fc one obtains: 00 00 00 Q_ ch ¼ HRPch q_ f , asy q_ rr Therefore: heptane: (75)(37 – 1) ¼ 2700 kW/m2 kerosene: (47)(29 – 1) ¼ 1316 kW/m2 polyethylene: (17)(61 – 15) ¼ 782 kW/m2 polypropylene: (19)(67 – 15) ¼ 988 kW/m2 polystyrene: (16)(75 – 13) ¼ 992 kW/m2 polymethylmethacrylate: (15)(57 – 11) ¼ 690 kW/m2 7. polyvinylchloride: (2)(50 – 15) ¼ 70 kW/m2 8. Teflon: (2)(52 – 38) ¼ 28 kW/m2
1. 2. 3. 4. 5. 6.
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Combustion Characteristics of Materials and Generation of Fire Products
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Table 36.10 Chemical and convective heat release parameters Materials
(HRP)ch ASTM E2058 Fire Propagation Apparatus Liquids and gases (hydrocarbons, alkanes) Hexane – Heptane – Octane – Nonane – Decane – Undecane – Dodecane – Tridecane – Kerosene – Hexadecane – Solids (abbreviations/names in the nomenclature) ABS – Acrylic sheet – Epoxy – IPST – Polyamide 21 Polypropylene 19 Polyethylene 17 Polystyrene 16 Polymethylmethacrylate 15 Nylon 12 Polyamide-6 – Filled phenolic foam–50 % inert – Polycarbonate 9 Polyoxymethylene 6 Polyethylene/25 % CI 11 Plasticized-PVC-3, LOI 0.25 – Plasticized-PVC-4, LOI 0.30 – Plasticized-PVC-5, LOI 0.35 – Polyethylene/35 % CI 4 Rigid PVC-1, LOI 0.50 – Rigid PVC-2 2 PVC panel 2 Polyethylene/48 % CI 2 PVEST – ETFE (Tefzel) 6 PFA (Teflon) 5 FEP (Teflon) 2 TFE (Teflon) 2 Wood (hemlock) – Wood (Douglas fir) 7 Wool –
ASTM E1354a
Calb
(HRP)con ASTM E2058 Fire Propagation Apparatus
ASTM E906c
Calb 56 50 46 42 39 36 34 32 17 28
– – – – – – – – – –
83 75 68 64 59 55 52 50 47 44
– – – – – – – – – –
– – – – – – – – – –
14 6 11 6 – – 21 19 14 – 21 1 – – – 5 5 5 – 3 3 – – 13 – – – – 1 – 5
– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –
– – – – – 11 12 6 10 7 – – – 5 5 – – – 2 – 1 – – – – – – – – 5 –
– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –
— – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – (continued)
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M.M. Khan et al.
Table 36.10 (continued) Materials
(HRP)ch (HRP)con ASTM E2058 ASTM E2058 Fire Propagation ASTM Fire Propagation Calb Apparatus E1354a Apparatus Composites and fiberglass-reinforced materials (FGR) (abbreviations/names in the nomenclature) Bismaleimide/graphite/ceramic – 1 – – (CC) Epoxy/FGR – 2 – – Epoxy/graphite 2 – – – Epoxy/graphite/CC 2 – – – Epoxy/graphite/intumescent (IC) 2 – – – IPST/FGR – 1 – – PEEK/FGR – 3 – – PES/FGR – 1 – – PEST-1/FGR 3 – — – PEST-2/FGR 8 – – – PEST-3/FGR 10 – – – PEST-4/FGR 3 – – – PEST-5/FGR 3 – – – PEST-6-FGR 3 – – – Phenol/FGR – 1 – – Phenolic/Kevlar 2 – – – Phenol/graphite 1 – – – PVEST-1/FGR 3 – – – PVEST-1/FGR/CC 3 – – – PVEST-1/FGR/IC 1 – – – PVEST-2/FGR 7 – – – PVEST-3/FGR 2 – – – Aircraft panel materials Epoxy fiberglass 4 4 – 2 Epoxy Kevlar 4 4 – 2 Phenolic Kevlar 5 4 – 2 Phenolic graphite 4 3 – 1 Phenolic fiberglass 4 3 – 2 Polycarbonate panel 9 – – – Foams Polystyrene GM53 20 – – 6 GM49 19 – – 8 GM51 18 – – 9 Flexible polyurethane GM 21 7 – – 3 GM 23 9 – – 5 GM 25 14 – – 6 GM 27 9 – – 4 Phenolic – 1 – – Electrical cables (abbreviations/names in the nomenclature) PVC/PVC-1 (Group 3) 15 – – – PE/PVC (Group 3) 19 – – –
ASTM E906c
Calb
–
–
– – – – – – – – – – – – – – – – – – – – –
– – – – – – – – – – – – – – – – – – – – –
1 2 – – 1 –
– – – – – –
– – –
– – –
3 6 4 2 –
– – – – –
– –
– – (continued)
36
Combustion Characteristics of Materials and Generation of Fire Products
1191
Table 36.10 (continued) Materials
PP, PEST/PVC (Group 3) PVC/PVC-2 (Group 3) Chlorinated PE (Group 2) PVC/PVC-3 (Group 2) EPR/PVC (Group 2) PVC/EPR (Group 2) XLPE/XLPE (Group 2) EPR/hypalon-1 (Group 2) EPR/hypalon-2 (Group 2) EPR/hypalon-3 (Group 1) EPR/hypalon-4 (Group 1) EPR/EPR-1 (Group 1) EPR/EPR-2 (Group 1) EPR/EPR-3 (Group 1) XLPE-EVA-1 (Group 1) XLPE-EVA-2 (Group 1) ETFA (Group 1) PVC/PVF2 (Group 1) FEP/FEP-1 (Group 1) FEP/FEP-2 (Group 2)
(HRP)ch ASTM E2058 Fire Propagation Apparatus 11 14 5 4 6 4 6 6 4 3 3 3 3 2 3 3 3 1 2 2
ASTM E1354a – – – – – – – – – – – – – – – – – – – –
Calb – – – – – – – – – – – – – – – – – – – –
(HRP)con ASTM E2058 Fire Propagation Apparatus – – – – – – – – – – – – – – – – – – – –
ASTM E906c – – – – – – – – – – – – – – – – – – – –
Calb – – – – – – – – – – – – – – – – – – – –
a
Calculated from the data reported in Refs. [32, 113] Calculated from the data in Refs. [112, 114] c From Ref. [115] b
The example shows the importance of the chemical HRP, flame heat flux, and surface re-radiation. Heat Release Rate and Fire Ventilation For the most part, fire hazards are due to fires occurring in enclosed spaces. In early stages, a building fire is well ventilated and is easy to control and extinguish. However, if the fire is allowed to grow, especially with limited enclosure ventilation and large material surface area, it becomes a ventilation-controlled fire and can lead to flashover, a very dangerous condition. In ventilationcontrolled fires, the chemical reactions between oxygen from air and products of incomplete combustion from the decomposed and gasified material (e.g., smoke, CO, hydrocarbons, and other intermediate products) remain incomplete and heat release rate decreases [103]. In ventilation-controlled fires, heat release rate depends on the air supply rate and the mass
loss rate, in addition to other factors. For ventilation-controlled fires, the effects of mass flow rate of air and fuel mass loss rate are characterized, most commonly, by the local equivalence ratio: 00
Φ¼
Sm_ A m_ air
ð36:41Þ
where Φ ¼ Equivalence ratio S ¼ Stoichiometric air-to-fuel mass ratio (g/g) ˙ 00 ¼ Mass loss rate (g/m2 · s) m A ¼ Exposed area of the burning material (m2) ˙ air ¼ Mass flow rate of air (g/s) m Generalized-state relationships between mass fractions of major species (O2, fuel, CO2, H2O, CO, and H2) and temperature as functions of local equivalence ratios for hydrocarbon-air diffusion flames are available [118]. The relationships suggest that the generation
1192
M.M. Khan et al.
efficiencies of CO, fuel vapors, water, CO2, and H and the consumption efficiency of O2 are in approximate thermodynamic equilibrium for well-ventilated combustion but deviate from equilibrium for ventilation-controlled combustion. This concept has been used for fires of polymeric materials [103]. In the tests, chemical and convective heat release rates, mass loss rate, and generation rates of fire products were measured for various equivalence ratios in the Fire Propagation Apparatus (Fig. 36.2) and in the Fire Research Institute’s (FRI) 0.022 m3 enclosure in Tokyo, Japan [103]. The combustion efficiency and its convective component were found to decrease as fires become fuel rich, due to an increase in the equivalence ratio. The ratio of the combustion efficiency and its convective component or chemical and convective heats of combustion for ventilationcontrolled to well-ventilated combustion is expressed as [103] ζ ch
ðχ Þ ðΔHch =ΔH T Þvc ðΔH ch Þvc ¼ ch vc ¼ ¼ ðχ ch Þwv ðΔH ch =ΔH T Þwv ðΔH ch Þwv ð36:42Þ
ζ con
ðχ Þ ðΔHcon =ΔH T Þvc ðΔHcon Þvc ¼ con vc ¼ ¼ ðχ con Þwv ðΔH con =ΔHT Þwv ðΔH con Þwv
where ζ ch is the ratio of the combustion efficiency for ventilation-controlled (vc) combustion to that for well-ventilated (wv) combustion; similarly, ζ con is the ratio of the convective component of the combustion efficiency for ventilation-controlled combustion to that for well-ventilated combustion. These ratios can be represented by the ratio of the chemical or convective heats of combustion for ventilationcontrolled to well-ventilated combustion. The experimental data for the ratios of the chemical and convective heats of combustion for ventilation-controlled to well-ventilated fires at various equivalence ratios are shown in Figs. 36.33 and 36.34. The data and measurement details are described in Ref. [103]. The data for the polymers indicated in the figures satisfy the following general empirical correlations, regardless of their chemical structures: ðΔHch Þvc ¼1 ðΔH ch Þwv
ðΔH con Þvc ¼1 ðΔH con Þwv
0:97 # Φ 1:2 2:15
" exp
" exp
ð36:43Þ
Φ 1:38
2:8 #
ð36:45Þ
1.4 1.2
Wood PMMA Nylon PE PP PS
ζch = 1 – 0.97 / exp(2.5φ–1.2)
1.0 (ΔHch)vc /(ΔHch)wv
Fig. 36.33 Ratio of ventilation-controlled to well-ventilated chemical heat of combustion versus equivalence ratio (Data are taken from Ref. [103]). Subscript vc represents ventilation-controlled fires, and subscript wv represents well-ventilated fires
1:0
ð36:44Þ
0.8 0.6
Nonflaming
0.4 0.2 0.0 10–1
100
101 Equivalence ratio
102
Combustion Characteristics of Materials and Generation of Fire Products
Fig. 36.34 Ratio of the ventilation-controlled to well-ventilated convective heat of combustion versus the equivalence ratio (Data are taken from Ref. [103]). Subscript vc represents ventilation-controlled fires, and subscript wv represents well-ventilated fires
1193
1.4 1.2
Wood PMMA Nylon PE PP PS
ζcon = 1 – 1.0 / exp(2.5φ–2.8)
1.0 (ΔHcon)vc /(ΔHcon)wv
36
0.8 0.6
Nonflaming
0.4 0.2 0.0 10–1
100
101
Equivalence ratio
The effects of ventilation on the chemical and convective heats of combustion are reflected by the magnitudes of the expressions within the parentheses on the right-hand sides of Equations 36.44 and 36.45. For a well-ventilated fire, Φ 1.0, (ΔHch)vc ¼ (ΔHch)wv, and (ΔHcon)vc ¼ (ΔHcon)wv. As a fire changes from well ventilated to ventilation controlled, the equivalence ratio increases and the magnitudes of the expressions within the parentheses on the right-hand sides of Equations 36.44 and 36.45 increase. Thus, with increasing equivalence ratio, the chemical and convective heats of combustion decrease. The decrease in the convective heat of combustion is higher than that for the chemical heat of combustion because the coefficients for the equivalence ratios are different. The correlation suggests that a higher fraction of the chemical heat of combustion is expected to be converted to the radiative heat of combustion as fires change from well ventilated to ventilation controlled. This is in general agreement with observations for ventilation-controlled fires in buildings. Equations 36.44 and 36.45 can be used in models for the assessment of the ventilationcontrolled fire behavior of materials, using chemical and convective heats of combustion for wellventilated fires such as from Table A.39.
Example 12 Calculate the chemical heats of combustion at equivalence ratios of 1, 2, and 3 for red oak, polyethylene, polystyrene, and nylon using Equation 36.44 and data from Table A.39 for well-ventilated fires. Solution
Material Red oak Polyethylene Polystyrene Nylon
Chemical heats of combustion (kJ/g) Φ 1.0 Φ ¼ 1.0 Φ ¼ 2.0 Φ ¼ 3.0 12.4 11.4 8.3 6.2 38.4 35.3 25.9 19.3 27.0 24.9 18.2 13.6 27.1 24.9 18.2 13.6
Generation of Fire Products and Smoke Yields Chemical compounds (smoke, toxic, corrosive, and odorous compounds) are the main contributors to nonthermal hazards and, thus, the assessments of their chemical natures and generation rates are of critical importance for the protection of life and property. In fires, compounds are generated as a result of gasification and decomposition of materials involved in the fire and burning of the species in the gas phase with air in the form of a diffusion flame. In general, generation of fire products and
1194
consumption of oxygen in diffusion flames occur in two zones [103]. 1. Reduction zone. In this zone, the material melts, decomposes, gasifies, and/or generates species that react to form smoke, CO, hydrocarbons, and other intermediate products. Very little oxygen is consumed in this region. The extent of conversion of the material to smoke, CO, hydrocarbons, and other products depends on the chemical nature of the material. 2. Oxidation zone. In this zone, the reduction zone products (smoke, CO, hydrocarbons, and other intermediates) react with varying degrees of efficiency with the oxygen from air and generate chemical heat and varying amounts of products of complete combustion, such as CO2 and H2O. The lower the reaction efficiency, the higher the amounts of reduction zone products emitted from a fire. The reaction efficiency of the reduction zone products with oxygen depends on the concentrations of the products relative to the oxygen concentration, temperature, and mixing of the products and air. For example, in laminar diffusion flames, smoke is emitted when the temperature of the oxidation zone falls below about 1300 K. The hot ceiling layer in a building fire may be considered in terms of oxidation and reduction zone products. In building fires with plenty of ventilation, the concentrations of the reduction zone products are higher in the central region of the ceiling layer, whereas the concentrations of the oxidation zone products are higher closer to the room opening. As the air supply rate, or oxygen concentration available to the fire, decreases due to restrictions in the ventilation, the ceiling layer expands and starts occupying a greater room volume accompanied with an increase in the concentrations of reduction zone products. Under these conditions, large amounts of reduction zone products are released within the building increasing the nonthermal hazard. The generation rate of a fire product is directly proportional to the mass loss rate, the proportionality constant being defined as the yield of the product (e.g., [9, 112]):
M.M. Khan et al. 00
00 G_ j ¼ y j m_
ð36:46Þ
00 where G˙j is the mass generation rate of product j (g/m2/s), and yj is the yield of product j (g/g). The total mass of the product generated is obtained by the summation of the generation rate:
Wj ¼ A
n¼t f X
00
G_ j ðtn ÞΔtn
ð36:47Þ
n¼t0
where Wj ¼ Total mass of product j generated from the flaming and/or nonflaming processes involving the material (g) t0 ¼ Time when the sample is exposed to heat(s) tf ¼ Time when there is no more product formation From Equations 36.31, 36.46, and 36.47, the average value of the yield of product j is yj ¼
Wj Wf
ð36:48Þ
Similarly, the mass consumption rate of oxygen is also directly proportional to the mass loss rate (e.g., [9, 112]): 00
00 C_ O ¼ cO m_
ð36:49Þ
00
Where C˙O is the mass consumption rate of oxygen (g/m2/s), and cO is the mass of oxygen consumed per unit mass of fuel (g/g). In the bench-scale apparatuses described in this chapter, the mass generation rates of fire products and mass consumption rate of oxygen are determined by measuring the volume fractions of the products and oxygen and the total volumetric or mass flow rate of the fire products-air mixture (e.g., [10, 11, 28, 31]): 00
G_ j ¼
f j V_ ρ j ρj ¼ f j W_ A ρg A
!
f V_ ρ ρO C_ O ¼ O O ¼ f O W_ A ρg A 00
where
ð36:50Þ ! ð36:51Þ
36
Combustion Characteristics of Materials and Generation of Fire Products
1195
EXHAUST SYSTEM AIR VELOCITY PORT VERTICAL ACROSS DUCT
736.0
300
300
1.575 mm WALL, S.S. TUBING, 152 mm O.D.
76 30
260
413
GAS SAMPLE PORT HORIZONTAL ACROSS DUCT
TEST SECTION DUCT
MIXING DUCT 50
304
457
BLOWER
ORIFICE PLATE (1.6 mm THK, THERMOCOUPLE PORT 91.5 mm ORIFICE DIA.) AT THIS POSITION
LASER SMOKE MEASURING SYSTEM
INTAKE FUNNEL 610
IR HEATING SYSTEM & SPECIMEN AREA OF FPA
40
INSTRUMENTATION CART 1451
MAIN VIEW
ALL DIMENSIONS IN MM UNLESS NOTED
Fig. 36.35 Schematic of the commercial version [119] of the Fire Propagation Apparatus showing locations where measurements are made for product concentration, optical transmission, particulate concentration, and corrosion
fj ¼ Volume fraction of product j fO ¼ Volume fraction of oxygen V_ ¼ Total volumetric flow rate of the fire productair mixture (m3/s) W˙ ¼ Total mass flow rate of the fire product-air mixture (g/s) ρj ¼ Density of product j at the temperature of the fire product-air mixture (g/m3) ρg ¼ Density of the hot fire product-air mixture (g/m3) ρO ¼ Density of oxygen at the temperature of the fire product-air mixture (g/m3) A ¼ Total area of the material burning (m2) For volume fraction measurements, sampling ducts are used where fire products and air are well
mixed, such as in the Fire Propagation Apparatuses (Figs. 36.2, 36.3, and 36.35) and in the cone calorimeter (Fig. 36.4). Figure 36.35 shows the measurement locations in the sampling duct of a commercial version [119] of the Fire Propagation Apparatus. The volume fractions are measured by various types of instruments; for example, in the Fire Propagation Apparatus, they are measured continuously by (1) commercial non-dispersive infrared analyzers for CO and CO2; (2) a highsensitivity commercial paramagnetic analyzer for oxygen; (3) a commercial flame ionization analyzer for the mixture of low molecular weight gaseous hydrocarbons; and (4) by a laser (wavelength: 0.6328 μm) smoke measuring system.
1196
M.M. Khan et al.
The optical density at the measurement location in the sampling duct is determined from the following equation: D¼
lnðI 0 =I Þ l
ð36:52Þ
where, D is the optical density (m1) at a laser wavelength of 0.6328 μm; I/I0 is the fraction of monochromatic light transmitted through smoke; and l is the optical path length (m). The volume fraction of smoke fs is obtained from the following expression [120]: fs ¼
Dλ 106 Ω
ð36:53Þ
where, λ is the wavelength of the light source (μm) and Ω is the coefficient of smoke extinction taken as 7 [120]. The mass generation rate (kg/m2/s) of smoke is given by: 00 f V_ ρ G_ s ¼ s s ¼ A
Dλ 106 ρs V_ ð36:54Þ A 7
Incorporating the value of smoke density, ρs ¼ 1.1 106 g/m3, as determined in Ref. [120] and the laser wavelength of 0.6328 μm in Equation 36.54 then gives the following result: _ 00 2 DV _ G s ¼ 9:944 10 A
ð36:55Þ
Equation 36.55 can then be used along with Equations 36.31, 36.47, and 36.48 to calculate the average smoke yield, ys , for a given material. The average value of smoke yield, can also be obtained from the average mass-specific extinction area [24, 121], τ (m2/g), at the same laser wavelength of 0.6328 μm: τ¼
ð n¼t 1 _ 1 Xf _ VDdt ¼ V ðtn ÞDðtn ÞΔtn Wf W f n¼t0 ð36:56Þ
The average smoke yield is, in this case, calculated from the following expression: ys ¼ 9:944 102 τ
ð36:57Þ
The average data for the yields of CO, CO2, mixture of gaseous hydrocarbons, and smoke for well-ventilated fires are listed in Table A.39. Example 13 For a fiberglass-reinforced material, the following data were measured for combustion in normal air at an external heat flux value of 50 kW/m2: Total mass of the sample lost (g) Total mass generated (g) CO CO2 Hydrocarbons Smoke Total energy generated (kJ)
229 0.478 290 0.378 6.31 3221
Calculate the average yields of CO, CO2, hydrocarbons, and smoke and the average chemical heat of combustion. Solution The average yields are calculated from Equation 36.48, and the average chemical heats of combustion are calculated from Equation 36.33. Average yields (g/g) CO CO2 Hydrocarbons Smoke Average chemical heats of combustion (kJ/g)
0.0021 1.27 0.002 0.028 14.1
Example 14 A circular sample of polystyrene, about 0.007 m2 in area and 25 mm in thickness, was burned in normal air in the presence of external heat flux. In the test, measurements were made for the mass loss rate and light obscuration by smoke in the sampling duct with an optical path length of 0.149 m. The total volumetric flow rate of the mixture of fire products and air through the sampling duct was 0.311 m3/s, and the wavelength of light source used was 0.6328 μm. At the steady-state combustion of polystyrene, the measured mass loss rate was 33 g/m2/s with smoke obscuring 83.5 % of the light. Calculate the yield of smoke from the data using a value of 1.1 106 g/m3 for the density of smoke.
36
Combustion Characteristics of Materials and Generation of Fire Products
Solution The tion 36.52 is D¼
optical
density
from
Equa-
lnðI 0 =I Þ lnð1=0:835Þ ¼ ¼ 1:21 m1 l 0:149
The smoke generation rate from Equation 36.55 is 00 g DV_ G_ s ¼ 9:944 102 2 m A 3 2 1 m3 1:21 0:311 00 g6 m s 7 7 G_ s ¼ 9:944 102 2 6 5 m 4 0:007 m2 00 g G_ s ¼ 5:35 2 m s
The smoke yield from Equation 36.46 is 00
00 G_ s ¼ ys m_
g 00 G_ s 5:35m2 s ys ¼ 00 ¼ g m_ 33 2 m s ys ¼ 0:162
Efficiencies of Oxygen Mass Consumption and Mass Generation of Products A chemical reaction between oxygen (air) and a fuel monomer of a material can be expressed as X F þ νO O2 þ νN N2 ¼ νN N2 þ ν ji J i
ΨO ¼ Stoichiometric oxygen-to-fuel mass ratio for the maximum possible conversion of the fuel monomer to products MO ¼ Molecular weight of oxygen (32 g/mol) Mf ¼ Molecular weight of the fuel monomer of the material (g/mol) Mf is calculated from its elemental composition which may be determined from microanalytical techniques. The stoichiometric yield for the maximum possible conversion of the fuel monomer of the material to a product is expressed as Ψj¼
00
00 C_ stoich, O ¼ Ψ O m_
ð36:58Þ where F ¼ Fuel monomer of a material νO ¼ Stoichiometric coefficient for oxygen νN ¼ Stoichiometric coefficient for nitrogen v ji ¼ Stoichiometric coefficients for the maximum possible conversion of the fuel monomer to products Ji The stoichiometric mass oxygen-to-fuel ratio for the maximum possible conversion of the fuel monomer is expressed as
where
νO M O Mf
ν jM j Mf
ð36:59Þ
ð36:60Þ
where Ψj is the stoichiometric yield for the maximum possible conversion of the fuel monomer of the material to product j, and Mj is the molecular weight of product (g/mol). The stoichiometric yields for some selected materials, calculated from the elemental composition data from the flammability laboratory, are listed in Table 36.11 for fuel monomer conversion to CO, CO2, hydrocarbons, smoke, HCl, and HF. The yields provide an insight into the nature of products and the amounts of products expected to be generated in flaming and nonflaming processes, when expressed as the stoichiometric oxygen mass consumption rate and stoichiometric mass generation rates of products:
i
ΨO ¼
1197
00
00 G_ stoich, j ¼ Ψ j m_ 00
00
ð36:61Þ ð36:62Þ
where C_ stoich, O and G_ stoich, j are the stoichiometric oxygen mass consumption rate and stoichiometric mass generation rate of product j for the maximum possible conversion of the fuel monomer to the product, respectively (g/m2/s). In fires, due to incompleteness of combustion as discussed above, the actual oxygen mass consumption rate and the mass generation rates of products may be significantly less than the stoichiometric rates. The ratio of the actual oxygen mass consumption rate to stoichiometric rates is
1198
M.M. Khan et al.
Table 36.11 Stoichiometric yields of major productsa Material Formula ΨO Ψ CO2 ΨCO Carbon-hydrogen atoms in the structure PE CH2 3.43 3.14 2.00 PP CH2 3.43 3.14 2.00 PS CH 3.08 3.38 2.15 Expanded polystyrene GM47 CH1.1 3.10 3.36 2.14 GM49 CH1.1 3.10 3.36 2.14 GM51 CH 3.08 3.38 2.15 GM53 CH1.1 3.10 3.36 2.14 Carbon-hydrogen-oxygen-nitrogen atoms in the structure POM CH2O 1.07 1.47 0.933 PMMA CH1.6O0.40 1.92 2.20 1.40 Nylon CH1.8O0.17 N0.17 2.61 2.32 1.48 Wood (pine) CH1.7O0.83 1.21 1.67 1.06 Wood (oak) CH1.7O0.72 N0.001 1.35 1.74 1.11 Wood (Douglas fir) CH1.7O0.74 N0.002 1.32 1.72 1.10 Polyester CH1.4O0.22 2.35 2.60 1.65 Epoxy CH1.3O0.20 2.38 2.67 1.70 Polycarbonate CH0.88O0.19 2.26 2.76 1.76 PET CH0.80O0.40 1.67 2.29 1.46 Phenolic foam CH1.1O0.24 2.18 2.60 1.65 PAN CHN0.33 2.87 2.50 1.59 Flexible polyurethane foams GM21 CH1.8O0.30 N0.05 2.24 2.28 1.45 GM23 CH1.8O0.35 N0.06 2.11 2.17 1.38 GM25 CH1.7O0.32 N0.07 2.16 2.22 1.41 GM27 CH1.7O0.30 N0.08 2.21 2.24 1.43 Rigid polyurethane foams GM29 CH1.1O0.23 N0.10 2.22 2.42 1.54 GM31 CH1.2O0.22 N0.10 2.28 2.43 1.55 GM37 CH1.2O0.20 N0.08 2.34 2.51 1.60 Rigid polyisocyanurate foams GM41 CH1.0O0.19 N0.11 2.30 2.50 1.59 GM43 CH0.93O0.20 N0.11 2.25 2.49 1.58 Carbon-hydrogen-oxygen-silicone atoms in the structure Silicone-1b CH1.3O0.25Si0.18 1.98 1.97 1.25 Silicone-2c CH1.5O0.30Si0.26 1.86 1.72 1.09 Silicone-3d CH3O0.50Si0.50 1.73 1.19 0.757 Carbon-hydrogen-oxygen-chlorine-fluorine atoms in the structure Fluoropolymers PVF (Tedlar) CH1.5 F0.50 1.74 1.91 1.22 PVF2 (Kynar) CHF 1.00 1.38 0.875 ETFE (Tefzel) CH1.0 F0.99 1.01 1.38 0.880 E-CTFE (Halar) CHF0.75CI0.25 0.889 1.22 0.778 PFA (Teflon) CF1.7O0.01 0.716 1.00 0.630 FEP (Teflon) CF1.8 0.693 0.952 0.606 TFE (Teflon) CF2 0.640 0.880 0.560 CTFE (Kel-F) CF1.5CI0.50 0.552 0.759 0.483
Ψs
Ψhc
ΨHCI
ΨHF
0.857 0.857 0.923
1.00 1.00 1.00
0 0 0
0 0 0
0.916 0.916 0.923 0.916
1.00 1.00 1.00 1.00
0 0 0 0
0 0 0 0
0.400 0.600 0.634 0.444 0.476 0.469 0.709 0.727 0.754 0.625 0.708 0.681
0.467 0.680 0.731 0.506 0.543 0.536 0.792 0.806 0.872 0.667 0.773 0.681
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0.622 0.593 0.606 0.612
0.715 0.682 0.692 0.698
0 0 0 0
0 0 0 0
0.660 0.662 0.685
0.721 0.729 0.753
0 0 0
0 0 0
0.683 0.679
0.740 0.732
0 0
0 0
0.537 0.469 0.324
0.595 0.528 0.405
0 0 0
0 0 0
0.522 0.375 0.377 0.333 0.270 0.260 0.240 0.207
0.587 0.406 0.409 0.361 0 0 0 0
0 0.435 0 0.594 0 0.622 0.257 0.417 0 0.765 0 0.779 0 0.800 0.310 0.517 (continued)
36
Combustion Characteristics of Materials and Generation of Fire Products
1199
Table 36.11 (continued) Material Chloropolymers PE-25 % CI PE-36 % CI Neoprene PE-42 % CI PE-48 % CI PVC PVCI2
Formula
ΨO
Ψ CO2
ΨCO
Ψs
Ψhc
ΨHCI
ΨHF
CH1.9CI0.13 CH1.8CI0.22 CH1.25CI0.25 CH1.8CI0.29 CH1.7CI0.36 CH1.5CI0.50 CHCI
2.56 2.16 1.91 1.94 1.73 1.42 0.833
2.38 2.05 2.00 1.84 1.67 1.42 0.917
1.52 1.30 1.27 1.17 1.06 0.903 0.583
0.650 0.558 0.546 0.501 0.456 0.387 0.250
0.753 0.642 0.602 0.576 0.521 0.436 0.271
0.254 0.368 0.409 0.424 0.493 0.581 0.750
0 0 0 0 0 0 0
a
Calculated from the data for the elemental compositions of the materials; subscript hc is total gaseous hydrocarbons; s is soot b ηSiO2 ¼ 0.483 c ηSiO2 ¼ 0.610 d ηSiO2 ¼ 0.811
thus defined as the efficiency of oxygen mass consumption or product mass generation (e.g., [103]): 00
ηO ¼
C_ actual, O 00
C_ stoich, O
00
cO m_ cO ¼ 00 ¼ ΨO Ψ O m_
00
ηj ¼
C_ actual, j 00
C_ stoich, j
¼
y j m_
00
Ψ j m_
00
¼
yj Ψj
ð36:63Þ
ð36:64Þ
Where ηO is the efficiency of oxygen mass consumption and ηj is the generation efficiency of product j. Example 15 A material is made up of carbon, hydrogen, and oxygen. The weight of the material is distributed as follows: 54 % as carbon, 6 % as hydrogen, and 40 % as oxygen. Calculate the chemical formula of the fuel monomer of the material. Solution From the atomic weights and the weight percent of the atoms, the numbers of atoms are as follows: carbon (C): 54/12 ¼ 4.5; hydrogen (H): 6/1 ¼ 6.0; and oxygen (O): 40/16 ¼ 2.5. Thus, the chemical formula of the fuel monomer of the material is C4.5H6.0O2.5 or, dividing by 4.5, CH1.33O0.56. Example 16 For the material in Example 15, calculate the stoichiometric oxygen-to-fuel mass
ratio, stoichiometric air-to-fuel mass ratio, and stoichiometric yields for maximum possible conversion of the fuel monomer of the material to CO, CO2, hydrocarbons, water, and smoke. Assume smoke to be pure carbon, and hydrocarbons as having the same carbon-atomto-hydrogen-atom ratio as the original fuel monomer. Solution 1. For stoichiometric yields of CO2 and water and the stoichiometric oxygen- and air-tofuel mass ratio for the maximum possible conversion of the fuel monomer of the material to CO2 and H2O, the following expression is used: CH1:33 O0:56 þ 1:06 O2 ¼ CO2 þ 0:67 H2 O The molecular weight of the fuel monomer of the material is 1 12 + 1.33 1 + 0.56 16 ¼ 22.3 g/mol, the molecular weight of oxygen is 32 g/mol, the molecular weight of CO2 is 44 g/mol, and the molecular weight of H2O is 18 g/mol. Thus, from Equation 36.59: 44 ¼ 1:97 22:3 0:67 18 Ψ H2 O ¼ ¼ 0:54 22:3 1:06 32 ¼ 1:52 ΨO ¼ 22:3 The stoichiometric air-to-fuel mass ratio can be obtained by dividing ΨO by 0.233 (i.e., the Ψ CO2 ¼
1200
M.M. Khan et al.
mass fraction of oxygen in air); that is, 1.52/ 0.233 ¼ 6.52. 2. For stoichiometric yields of CO, hydrocarbons, and smoke for the maximum possible conversion of the fuel monomer of the material to these products, different chemical reactions have to be written, as follows: For CO, CH1:33 O0:56 þ z O2 ¼ CO þ xðHOÞ Ψ CO ¼ 28=22:3 ¼ 1:26 For hydrocarbons (same H/C ratio as fuel monomer), CH1:33 O0:56 þ z O2 ¼ CH1:33 þ xðHOÞ Ψ hc ¼ 13:3=22:3 ¼ 0:60 For smoke (i.e., pure carbon), CH1:33 O0:56 þ z O2 ¼ C þ xðHOÞ Ψ s ¼ 12=22:3 ¼ 0:54 Example 17 For the material in Examples 15 and 16, the generation efficiencies of CO2, CO, hydrocarbons, and smoke are 0.90, 0.004, 0.002, and 0.036, respectively. The heat of gasification is 1.63 kJ/g, the surface re-radiation loss is 11 kW/m2, and the predicted asymptotic flame heat flux value for large-scale fires is 60 kW/m2. Calculate the yields and asymptotic values for the generation rates of CO2, CO, hydrocarbons, and smoke expected in large-scale fires. Solution 1. Yields from Equations 36.63 and 36.64 and data from Example 16: yCO2 ¼ ηCO2 Ψ CO2 ¼ 0:90 1:97 ¼ 1:77 g=g yCO ¼ ηCO Ψ CO ¼ 0:004 1:26 ¼ 0:005 g=g yhc ¼ ηhc Ψ hc ¼ 0:002 0:60 ¼ 0:001 g=g ys ¼ ηs Ψ s ¼ 0:036 0:54 ¼ 0:019 g=g 2. Asymptotic values for the mass loss rate from Equation 36.15: 00
00
m_ ¼
00
q_ f , asy q_ rr ΔH g
¼
60 11 g ¼ 30 2 1:63 m s
3. Asymptotic values for the mass generation rates of products from Equation 36.46 and the above data: 00
00 G_ CO2 ¼ yCO2 m_ ¼ 1:77 30 ¼ 53 g=m2 =s 00
00 G_ CO ¼ yCO m_ ¼ 0:005 30 ¼ 0:159 g=m2 =s 00
00 G_ hc ¼ yhc m_ ¼ 0:001 30 ¼ 0:036 g=m2 =s 00
00 G_ hc ¼ yhc m_ ¼ 0:019 30 ¼ 0:584 g=m2 =s
Generation Rates of Fire Products and Fire Ventilation Effects As discussed previously, the effects of decreasing fire ventilation, as characterized by the increase in the local equivalence ratio, are reflected by an increase in the generation rates of the reduction zone products (smoke, CO, hydrocarbons, and others). For example, for flaming wood crib enclosure fires, as the equivalence ratio increases, the combustion efficiency decreases, flames become unstable, and the generation efficiency of CO reaches its peak for the equivalence ratio between about 2.5 and 4.0 [103]. Ventilation-controlled building fires are generally characterized by two layers: (1) a vitiated ceiling layer, identified as upper layer, and (2) an uncontaminated layer below, identified as lower layer. Incorporation of these two layers is the classical two-zone modeling of fires in enclosed spaces. Under many conditions, the depth of the upper layer occupies a significant fraction of the volume of the enclosed space. Eventually, the interface between the upper layer and the lower layer positions itself so that it is very close to the floor, very little oxygen is available for combustion, and most of the fuel is converted to the reduction zone products, that is, smoke, CO, hydrocarbons, and others. Ventilation-controlled large- and smallenclosure and laboratory-scale fires and fires in the vitiated upper layer under experimental hoods have been studied in detail and reviewed [103, 122–125]. The results from these types of fires are very similar. Detailed studies [103] performed for the generation rates of fire products for various fire ventilation conditions
36
Combustion Characteristics of Materials and Generation of Fire Products
Fig. 36.36 Ratio of the mass of oxygen consumed per unit mass of the fuel for ventilation-controlled to well-ventilated fires (Data are taken from Ref. [103]). Subscript vc represents ventilation-controlled fires, and subscript wv represents well-ventilated fires
1201
ζσ = 1 – 0.97 / exp(2.5φ–1.2)
Wood PMMA Nylon PE PP PS
(co)vc /(co)wv
100
Nonflaming
10–1
10–1
in the Fire Propagation Apparatus and in the Fire Research Institute’s (FRI) enclosure, show that with an increase in the equivalence ratio (1) generation efficiencies of oxidation zone products, such as CO2, and reactant consumption efficiency (i.e., oxygen) decrease, and (2) generation efficiencies of the reduction zone products, such as smoke, CO, and hydrocarbons increase. Generalized correlations have been established between the generation efficiencies and the equivalence ratio for the oxidation and reduction zone products. The changes in the consumption or generation efficiencies of the products are expressed as ratios of the efficiencies for the ventilation-controlled (vc) to well-ventilated (wv) fires: Reactants (oxygen) ζO ¼
ðηO Þvc ðcO =ΨO Þvc ðcO Þvc ¼ ¼ ðηO Þwv ðcO =ΨO Þwv ðcO Þwv
ð36:65Þ
Oxidation zone products (carbon dioxide, water, etc.) y =Ψ yj j j ηj vc ¼ vc ζ oxid ¼ vc ¼ ηj wv yj =Ψ j yj wv
wv
ð36:66Þ
100 101 Equivalence ratio
102
where ζ oxid is the oxidation zone product generation efficiency ratio. Reduction zone products (smoke, carbon monoxide, hydrocarbons, etc.) yj =Ψ j yj ηj vc vc ¼ vc ð36:67Þ ζ red ¼ ¼ ηj wv yj =Ψ j yj wv
wv
where ζ red is the reduction zone product generation efficiency ratio. The relationships between the ratios of the mass of oxygen consumed per unit mass of fuel, the yields of the products for the ventilationcontrolled to well-ventilated fires, and the equivalence ratio are shown in Figs. 36.36, 36.37, 36.38, 36.39, and 36.40. The ratios for oxygen and CO2 (an oxidation zone product) do not depend on the chemical structures of the materials, whereas the ratios for the reduction zone products do depend on the chemical structures of the materials. Oxygen and CO2 The relationships for oxygen consumed and carbon dioxide generated are shown in Figs. 36.36 and 36.37, respectively. The relationships are very similar to the relationships for the chemical and convective
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Fig. 36.37 Ratio of the mass of carbon dioxide generated per unit mass of the fuel for ventilationcontrolled to wellventilated fires (Data are taken from Ref. [103]). Subscript vc represents ventilation-controlled fires, and subscript wv represents well-ventilated fires
ζco2 = 1 – 1.0 / exp(2.5φ–1.2)
Wood PMMA Nylon PE PP PS
(yco2)vc /(yco2)wv
100
Nonflaming
10–1
10–1
100
101
102
Equivalence ratio
Fig. 36.38 Ratio of the mass of carbon monoxide generated per unit mass of the fuel for ventilationcontrolled to wellventilated fires (Data are taken from Ref. [103]). Subscript vc represents ventilation-controlled fires, and subscript wv represents well-ventilated fires
(yco)vc /(yco)wv
102 Wood PMMA Nylon PE PP PS 101
Nonflaming
100 100
101
102
Equivalence ratio
heats of combustion ratios (Equations 36.44 and 36.45), as expected: ðcO Þvc 0:97 h i ¼1 1:2 ðcO Þwv exp Φ
ð36:68Þ
2:14
yCO2
yCO2
vc ¼ 1 wv
exp
0:97 h i Φ 1:2 2:15
ð36:69Þ
Carbon Monoxide The relationship between the ratio of the CO yields for ventilationcontrolled to well-ventilated fires and the equivalence ratio is shown in Fig. 36.38. The data suggest the following relationship [103]: ð yCO Þvc α ¼1þ ð yCO Þwv exp 2:5Φξ
ð36:70Þ
Combustion Characteristics of Materials and Generation of Fire Products
Fig. 36.39 Ratio of the mass of hydrocarbons generated per unit mass of the fuel for ventilationcontrolled to wellventilated fires (Data are taken from Ref. [103]). Subscript vc represents ventilation-controlled fires, and subscript wv represents well-ventilated fires
1203
103 Wood PMMA Nylon PE PP PS
102 (yhc)vc /(yhc)wv
36
Nonflaming 101
100
100
101 Equivalence ratio
3.0 2.8
Wood PMMA Nylon PE PP PS
2.6 2.4 (ys)vc /(ys)wv
Fig. 36.40 Ratio of the mass of smoke generated per unit mass of the fuel for ventilation-controlled to well-ventilated fires (Data are taken from Ref. [103]). Subscript vc represents ventilation-controlled fires, and subscript wv represents well-ventilated fires
2.2 2.0
Nonflaming
1.8 1.6 1.4 1.2 1.0
100
101
Equivalence ratio
where α and ξ are the correlation coefficients, which depend on the chemical structures of the materials. The values for the correlation coefficients for CO are listed in Table 36.12. The increase in the ratio of the carbon monoxide yields for the ventilation-controlled to well-ventilated fires with the equivalence ratio is due to the preferential conversion of the fuel carbon atoms to CO. The experimental data show
the following order for the preferential conversion: wood (C-H-O aliphatic structure) > PMMA (C-H-O aliphatic structure) > nylon (C-H-O-N aliphatic structure) > PE (C-H aliphatic linear unsaturated structure) > PP (C-H aliphatic branched unsaturated structure) > PS (C-H aromatic structure). A similar trend is found for the liquid and gaseous fuels, such as shown in Table 36.13 [103]. The presence of O
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and N atoms in the fuels with aliphatic C-H structure appears to enhance preferential fuel carbon atom conversion to CO. Hydrocarbons The relationship between the ratio of the hydrocarbon yields for ventilationcontrolled to well-ventilated fires and the equivalence ratio is shown in Fig. 36.39. The data suggest the following relationship [103]: ð yhc Þvc α ¼1þ ð yhc Þwv exp 5:0Φξ
ð36:71Þ
The correlation coefficient values for hydrocarbons are listed in Table 36.12. The numerator in the second term on the right-hand side of Equation 36.71 is 10–40 times that of CO, whereas the denominator is twice that for CO. This relationship suggests that there is a significantly higher preferential fuel conversion Table 36.12 Correlation coefficients to account for the effects of ventilation on the generation rates of CO, hydrocarbons, and smoke
Material PS PP PE Nylon PMMA Wood PVC
CO α 2 10 26 36 43 44 7
β 1.44 1.39 1.39 1.36 1.33 1.30 0.42
Hydrocarbons Smoke ξ α β ξ α β 2.5 25 2.45 1.8 2.8 2.02 2.8 220 1.90 2.5 2.2 2.50 2.8 220 1.90 2.5 2.2 2.50 3.0 1200 1.65 3.2 1.7 3.14 3.2 1800 1.58 3.5 1.6 4.61 3.5 200 2.33 1.9 2.5 2.15 8.0 25 0.42 1.8 0.38 2.02
ξ 1.3 1.0 1.0 0.8 0.6 1.2 8.0
to hydrocarbons than to CO, as the equivalence ratio increases. The order for the preferential fuel conversion to hydrocarbons is very similar to CO, except for wood; that is, PMMA > nylon > PE ¼ PP > wood > PS. The exception for wood may be due to the char-forming tendency of the fuel, which lowers the C-to-H ratio in the gas phase. Smoke The relationship between the ratio of the smoke yields for ventilation-controlled to wellventilated fires and the equivalence ratio is shown in Fig. 36.40. The data suggest the following relationship: [103] ð ys Þvc α ¼1þ ð ys Þwv exp 2:5Φξ
ð36:72Þ
The correlation coefficient values for smoke are listed in Table 36.12. The values of the correlation coefficients in the second term on the right-hand side of Equation 36.72 suggest that, with increasing equivalence ratio, the preferential fuel conversion to smoke is lower than it is to hydrocarbons and CO. Also, the order for the preferential conversion of the fuel carbon atom to smoke is opposite to the order for the conversion to CO and hydrocarbons, except for wood. The order is PS > wood > PE ¼ PP > nylon > PMMA, suggesting that the order is probably due to a decrease in the preference for the reactions between OH and CO compared to the reactions between OH and soot.
Table 36.13 Carbon monoxide generation efficiency for ventilation-controlled and well-ventilated combustiona
Fuel Methane Propane Propylene Hexane Methanol Ethanol Isopropanol Acetone a
Well-ventilated (wv)b Φ < 0.05 0.001 0.001 0.004 0.002 0.001 0.001 0.002 0.002
Table taken from Ref. [103] Data taken in the Fire Propagation Apparatus c Nonflaming b
Ventilation-controlled (vc) Φ 4.0 Beyler [123] Beyler [124] 0.10 – – 0.12 0.10 – 0.10 0.52c 0.27 1.00c 0.18 0.66c 0.21 – 0.21 0.63c
(yCO)vc/(yCO)wv 100 120 25 50 (260c) 270 (1000c) 180 (660c) 105 105 (315c)
36
Combustion Characteristics of Materials and Generation of Fire Products
Other Reduction Zone Products Since the sum of the generation efficiencies of all the products for a material cannot exceed unity, the generation efficiency of products other than CO, CO2, hydrocarbons, and smoke is ηother ¼ 1 ηCO þ ηCO2 þ ηhc þ ηs ð36:73Þ where ηother is the generation efficiency of products other than CO, CO2, hydrocarbons, and smoke. The generation efficiency of other products can be calculated from Equations 36.68, 36.69, 36.70, 36.71 and 36.72 using correlation coefficients from Table 36.12. The generation efficiency values for other products calculated in this fashion for various equivalence ratios are shown in Fig. 36.41. The figure shows that, for equivalence ratios greater than 4, where fires are nonflaming, about 10–60% of fuel carbon is converted to products other than CO, CO2, soot, and hydrocarbons. The order for the preferential conversion of fuel carbon to other products in the nonflaming zone is PS (C-H aromatic structure) < PE & PP (C-H aliphatic structure) < wood (C-H-O aliphatic structure) < nylon (C-H-O-N aliphatic structure) < PMMA (C-H-O aliphatic structure). It thus appears that, in nonflaming environments,
fuels with C-H structures are converted mainly to CO, smoke, and hydrocarbons, rather than to other products, whereas fuels with C-H-O and C-H-O-N structures are converted mainly to products other than CO, CO2, smoke, and hydrocarbons. Some of the products include formaldehyde (HCHO) and hydrogen cyanide (HCN) [103]. Generation Efficiencies of Formaldehyde, Hydrogen Cyanide, and Nitrogen Dioxide The experimental data for the generation efficiencies of formaldehyde, hydrogen cyanide, and nitrogen dioxide versus the equivalence ratio are shown in Figs. 36.42 and 36.43. Formaldehyde is generated in the pyrolysis of wood (C-H-O structure). It is attacked rapidly by oxygen (O) and hydroxyl (OH) radicals in the flame, if unlimited supply of oxygen is available. Thus, only traces of formaldehyde are found in well-ventilated fires. The generation efficiency of formaldehyde, however, increases with the equivalence ratio, indicating reduced concentrations of O and OH radicals and gas temperature due to lack of oxygen available for combustion. In fires, hydrogen cyanide is formed in the reduction zone from materials with hydrogen
0.8 Nonflaming Generation efficiency of other products
Fig. 36.41 Generation efficiency of products other than CO, CO2, hydrocarbons, and smoke versus the equivalence ratio
1205
PMMA
0.6
Nylon Wood 0.4
PE & PP 0.2 PS 0.0 10 0–2
10–1
100
101
Equivalence ratio
102
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Fig. 36.42 Generation efficiency of formaldehyde generated from wood versus the equivalence ratio
Generation efficiency of formaldehyde
Nonflaming
10–3
10–4
100
101 Equivalence ratio
Fig. 36.43 Generation efficiencies of hydrogen cyanide and nitrogen dioxide generated from nylon versus the equivalence ratio
10–1
Generation efficiency
Nonflaming
10–2
10–3
HCN NO2 10–4 100
101 Equivalence ratio
and nitrogen atoms in the structure, such as nylon (C-H-O-N structure). Nitrogen dioxide (NO2), on the other hand, is formed in the oxidation zone, as a result of the oxidation of hydrogen cyanide. The data in Fig. 36.40 show that the generation efficiency of hydrogen cyanide increases and the generation efficiency of NO2 decreases with the equivalence ratio. This observation supports that O and OH radical concentrations decrease with increase in the equivalence ratio. The decrease in
the generation efficiency of hydrogen cyanide in nonflaming environments suggests a decrease in the fuel mass transfer rate. Relationship Between the Generation Efficiencies of CO2 and CO The relationship between the generation efficiencies of CO2 and CO is shown in Fig. 36.44, where the data are taken from Ref. [103]. CO is generated in the reduction zone of the flame as a result of the
Combustion Characteristics of Materials and Generation of Fire Products
Fig. 36.44 Relationship between the generation efficiencies of CO2 and CO (Data taken from Ref. [103])
1207
0.30 Chemical structure
CO generation efficiency
Methanol
0.20
CH4, C3H6, C3H8, C6H14
36
Fuel Ethanol
PMMA
Wood
Nylon
PP
0.10
PE PS Air
0.00 0.0
oxidative pyrolysis of the fuel, and is oxidized to CO2 in the oxidation zone of the flame. The generation efficiency of CO2 is independent of the chemical structure of the fuel (Fig. 36.37), whereas the generation efficiency of CO depends on the chemical structure of the fuel (Fig. 36.38). In Fig. 36.44, the curves represent approximate predictions based on the correlation coefficients from Table 36.12 and Equations 36.69 and 36.70. The relationship between the generation efficiencies of CO2 and CO is quite complex. The boundary of the shaded region marked air in Fig. 36.44 is drawn using the data for the wellventilated combustion for equivalence ratios less than 0.05. The boundary of the air region may be considered as equivalent to the lower flammability limit. No flaming combustion is expected to occur in this region, as the fuel-air mixture is below the lower flammability limit; however, nonflaming processes, generally identified as smoldering, may continue. The boundary of the shaded region marked fuel is drawn using the data for the ventilation-controlled combustion for equivalence ratio of 4.0, and may be considered as equivalent to the upper flammability limit. In the fuel region, no flaming combustion is expected to occur, as the fuel-air mixture is
0.2
0.4 0.6 CO2 generation efficiency
0.8
1.0
above the upper flammability limit; however, nonflaming processes may continue. The shaded region marked chemical structure and drawn to the right of the methanol curve is an imaginary region as it is not expected to exist, because there are no stable carbon-containing fuel structures below the formaldehyde with a structure of HCHO. For the stable fuels with C-H-O structures, formaldehyde (HCHO) and methanol (CH3OH) have the lowest molecular weights (30 and 32, respectively). Thus, data for HCHO and CH3OH probably would be comparable. The curves in Fig. 36.44 show that, in flaming combustion, with increase in the equivalence ratio, the preference for fuel carbon atom conversion to CO, relative to the conversion to CO2, follows this order: methanol (C-H-O structure) > ethanol (C-H-O structure) > wood (C-H-O structure) > PMMA (C-H-O structure) > nylon (C-H-O-N structure) > PP (C-H aliphatic unsaturated branched structure) (CH4, C3H6, C3H8, C6H14) PE (C-H aliphatic unsaturated linear structure) > PS (C-H aromatic unsaturated structure). Thus, for fires in enclosed spaces, generation of higher amounts of CO relative to CO2 at high local equivalence ratios is expected for fuels with C-H-O structures compared to the
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M.M. Khan et al.
fuels with C-H structures. The reason for higher amounts of CO relative to CO2 for fuels with C-H-O structures is that CO is easily generated in fuel pyrolysis, but is oxidized only partially to CO2 due to limited amounts of oxidant available. Relationship Between the Generation Efficiencies of CO and Smoke The relationship between the generation efficiencies of CO and smoke is shown in Fig. 36.45, where data are taken from Ref. [103]. CO and smoke are both generated in the reduction zone of the flame as a result of the oxidative pyrolysis of the fuel, and their generation efficiencies depend on the chemical structure of the fuel (Figs. 36.38 and 36.40). In Fig. 36.45, the curves represent approximate predictions based on the correlation coefficients from Table 36.11 and Equations 36.70 and 36.72. The relationship in Fig. 36.45 is quite complicated. The boundary of the shaded region marked air is drawn using the data for the well-ventilated combustion for equivalence ratios less than 0.05. The boundary of the shaded region marked fuel is drawn using the data for the ventilationcontrolled combustion for equivalence ratio of 4.0. The boundary for the region marked air may be considered as equivalent to the lower flammability limit, and the boundary for the region marked fuel may be considered as equivalent to the upper flammability limit.
Generalized Relationships to Calculate Chemical, Convective, and Radiative Heats of Combustion and Yields of Products at Various Equivalence Ratios Equations 36.44, 36.45, and 36.68, 36.69, 36.70, 36.71, and 36.72 can be generalized as follows: 9 > > =
8 > >
> > > ; : exp Φβ
ð36:74Þ
PS Fuel
Air PP
Smoke generation efficiency
Fig. 36.45 Relationship between the generation efficiencies of CO and smoke (Data taken from Ref. [103])
In Fig. 36.45, the order for the preference for fuel carbon atom conversion to smoke relative to conversion to CO is wood (C-H-O structure) < PMMA (C-H-O structure) < nylon (C-H-O-N structure) < PP (C-H aliphatic unsaturated branched structure) PE (C-H aliphatic unsaturated linear structure) < PS (C-H aromatic structure). The generation efficiency of smoke for PS, which is a polymer with aromatic C-H structure, is the highest. The generation efficiency of smoke for wood, which is a polymer with aliphatic C-H-O structure, is the lowest.
Nylon & PE
10–1
PMMA Wood
10–2
10–3 10–3
10–2
10–1
CO generation efficiency
100
36
Combustion Characteristics of Materials and Generation of Fire Products
where fp ¼ Fire property α, β, and ξ ¼ Correlation coefficients characteristic of the chemical structures of the polymers subscript 1 ¼ Infinite amount of air (i.e., well ventilated conditions) It is noted that this relationship is applicable under turbulent flame conditions where a given fire property remains constant (i.e., it is not a function of flow conditions). Fire properties to consider include heat of combustion (or combustion efficiency) and yields (or generation efficiencies) of products. Three conditions can be identified: (1) for Φ β, fp ¼ fp1(1 + α); (2) for Φ β, fp ¼ fp1; and (3) Φ β, fp fp1(1 + α/2.7). Thus, the parameter α is associated primarily with the magnitude of the fire properties in nonflaming processes (high Φ values). The parameter β is associated with the fire properties in the transition region between fires with an infinite amount of air and fires with a very restricted amount of air. The parameter ξ is associated with the range of Φ values for the transition region. A high value of α is indicative of a strong effect of ventilation on the fire and its properties and vice versa. High values of β and ξ are indicative of rapid change from flaming to nonflaming conditions by a small change in the equivalence ratio, such as for the highly fire-retarded or halogenated materials for which flaming combustion in normal air itself is unstable. Chemical Heat of Combustion Versus Equivalence Ratio for Nonhalogenated Compounds From Equation 36.74, 8
polyethylene, polypropylene, and polyethylene foams (ϕ ¼ 0.27 to 0.25) > polystyrene (ϕ ¼ 0.21) > polyurethane, polystyrene, and polyisocyanurate foams and chlorinated polyethylenes (ϕ ¼ 0.09 to 0.19). As expected from the firepoint theory [150, 151], the reactivity of the vapors in the gas phase follows the kinetic parameter. The combustion efficiency and product generation efficiencies follow the reactivity of the vapors in the gas phase, such as shown in Fig. 36.53 for the combustion efficiency. The lower the value of the kinetic parameter (Equation 36.94), the lower the reactivity of the material vapors, which is reflected in the (1) reduced values of the combustion efficiency (Equations 36.36, 36.37 and 36.38), (2) reduced values of the generation efficiencies
(Equation 36.66) of the oxidation zone products (such as CO2), and (3) increased values of the generation efficiencies (Equation 36.67) of the reduction zone products (such as smoke, CO, and hydrocarbons). Flame extinction can also be expressed in terms of the critical heat release rate: 00
00 Q_ cr, i ¼ ΔH i m_ cr
ð36:95Þ
00
where Q_ cr, i is the critical heat release rate (chemical, convective, or radiative in kW/m2), and ΔHI is the heat of combustion (chemical, convective, and radiative in kJ/g). Table 36.16 lists the critical chemical, convective, and radiative heat release rates for flame extinction, where critical mass loss rate values are taken from Table 36.15 and heats of combustion from Table A.39. The data in Table 36.16 suggest that the critical heat release rate for flame extinction is weakly dependent on the chemical nature of the material, contrary to the critical mass loss rate. The critical heat release rates thus can be averaged, which are 100 7, 53 9, and 47 10 kW/m2 for the chemical, convective, and radiative heat release rates, respectively. For materials with highly reactive vapors, such as polyethylene, large amounts of extinguishing agent are needed to reduce the heat release rate to the critical value. For materials with highly
1.0
Combustion efficiency
Fig. 36.53 Combustion efficiency versus kinetic parameter for flame extinction versus. Data were measured in the Fire Propagation Apparatus
1221
0.8
0.6
0.4
0.0 0.0
0.1
0.2
0.3
Kinetic parameter
0.4
0.5
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M.M. Khan et al.
Table 36.16 Critical chemical, convective, and radiative heat release rates for flame extinction Critical heat release rate (kW/m2) Chemical Convective (65) 50 77 53 96 55 104 61 88 51 95 48 108 44 101 48 102 44 96 10 51 6
Material Polyoxymethylene Polymethylmethacrylate Polyethylene Polypropylene Polyethylene foams Chlorinated polyethylenes Polystyrenes Polyurethane foams (flexible) Polyurethane foams (rigid) Average
Radiative (14) 24 42 43 38 47 64 53 58 46 12
Note: Critical mass loss rates from Table 36.15, and heats of combustion from Table A.39
nonreactive vapors, such as Teflon, it is difficult to reach the critical heat release rate values unless high external heat flux is applied. The energy balance at the surface as the flame extinction condition is reached can be represented by modifying Equations 36.15 and 36.34 [156] 00
00
m_ ¼
00
00
00
ΦΔH T m_ cr þ q_ e q_ rr q_ agent ΔH g
ð36:96Þ
00 ΔHi 00 00 00 00 ΦΔH T m_ cr þ q_ e q_ rr q_ agent Q_ i ¼ ΔH g ð36:97Þ where 00 q_ e ¼ External heat flux (kW/m2) 00 q_ rr ¼ Surface re-radiation loss (kW/m2) 00 q_ agent ¼ Heat flux removed from the surface or from the flame by the agent as the flame extinction condition is reached (kW/m2) ΔHi ¼ Chemical, convective, or radiative heat of combustion (kJ/g) ΔHg ¼ Heat of gasification (kJ/g) ΔHi/ΔHg is defined as the heat release parameter (HRP) (see section “Heat Release Rate” of this chapter).
Flame Extinction by the Processes in the Gas Phase The process of flame extinction by gaseous, powdered, and foaming agents and by an increase in
the local equivalence ratio is predominantly a gas-phase process and, thus, is different from the process of flame extinction by water, which occurs predominantly in the solid phase at the surface of the material. The kinetic parameter for flame extinction defined in Equation 36.94, however, is still applicable [156]: 1 þ Δc p ðT ad T a Þ þ ΔH D Φ0 κY j, ex Y O ΔH *O Φ¼ 1 Y j, ex ð36:98Þ where ϕ ¼ Kinetic parameter in the presence of the extinguishing agent ϕ0 ¼ Kinetic parameter in the absence of the extinguishing agent κ ¼ Ratio between the kinetic parameters at the flame temperature and at the adiabatic flame temperature Yj,ex ¼ Mass fraction of the extinguishing agent Δcp ¼ Difference between the heat capacities of the extinguishing agent and the fire products (kJ/g/K) Tad ¼ Adiabatic flame temperature at the stoichiometric limit (K) Ta ¼ Initial temperature of the reactants (K) ΔHD ¼ Heat of dissociation (kJ/g) Equation 36.98 shows that the addition of an extinguishing agent reduces the kinetic parameter from its normal value and includes the effects of four flame extinction mechanisms
36
Combustion Characteristics of Materials and Generation of Fire Products
[156]: (1) dilution, effects are included in the κYj,ex term; (2) added thermal capacity, effects are included in Δcp; (3) chemical inhibition, effects are included through Tad; and (4) kinetic chain breaking and endothermic dissociation through ΔcP and ΔHD terms. From Equation 36.96, in the presence of an extinguishing agent that works in the gas phase, 00
00
m_ ¼
00
00
φΔH T m_ cr þ q_ e q_ rr ΔH g
ð36:99Þ
For fixed values of external heat flux, the addition of an extinguishing agent reduces the normal value of the kinetic parameter by one or more of the four mechanisms expressed by Equation 36.98; the mass loss rate decreases and approaches the critical value at which the flame is extinguished. Increasing the external heat flux would increase the mass loss rate, and further addition of the extinguishing agent would be needed to reduce the mass loss to its critical value and to reestablish the flame extinction condition. Continued increases in the extinguishing agent for increasing external heat flux will result in the denominator of Equation 36.98 to approach zero, at which point it would represent a nonflaming condition. For a fixed airflow rate, as is generally the case in enclosure fires where the extinguishing agent working in the gas phase is used, an increase in the mass loss rate due to increasing external heat flux results in an increase in the equivalence ratio, defined in Equation 36.41. As the equivalence ratio increases and approaches values of 4.0 and higher, the combustion efficiency approaches values less than or equal to 0.40 (see Fig. 36.33), flames are extinguished, and nonflaming conditions become important [103, 104]. Thus, the upper limit for the application of the extinguishing agent working in the gas phase is dictated by the equivalence ratio 4.0 and/or the combustion efficiency 0.40. Under nonflaming conditions, an increase in the external heat flux increases the generation rate of the fuel vapors and the reduction-zone products.
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Flame Extinction by Reduced Mass Fraction of Oxygen Flame extinction by reduced mass fraction of oxygen can be the result of (1) dilution and heat capacity effects due to the addition of inert gases, such as N2 and CO2; and (2) chemical effects due to the retardation of chemical reactions and reduction in the flame heat flux to the surface, especially the radiative component. Theoretical and experimental analyses have been performed for flame extinction by reduced oxygen mass fractions. For example, for polymethylmethacrylate (PMMA), an oxygen mass fraction value of 0.180 is predicted for flame extinction [157] compared to the experimental values of 0.181 for a 70-mm-wide, 190-mm-high, and 19-mm-thick vertical PMMA slab [158] and 0.178 for a 100-mm-wide, 25-mmthick, and 300- and 610-mm-high vertical slabs of PMMA, and 25-mm-diameter and 610-mm-high vertical cylinder of PMMA [31]. The critical values of the chemical, convective, and radiative heat release for PMMA are 106, 73, and 33 kW/m2 [31], respectively, showing a trend similar to one reported in Table 36.16. At oxygen mass fractions equal to or less than 0.201, flames are unstable and faint blue in color [31]. The effect external heat flux on flame extinction due to reduced oxygen mass fraction has been examined for buoyant turbulent diffusion flames [159]. For example, for rectangular and circular horizontal PMMA slabs, 0.06–0.10 m2 in area and 0.03–0.05 m in thickness, exposed to external heat flux values of 0, 40, 60, and 65 kW/m2, flame extinction is found at oxygen mass fractions of 0.178, 0.145, 0.134, and 0.128, respectively [6]. The data support Equation 36.99 and show that, for buoyant turbulent diffusion flames, flaming can occur up to relatively low oxygen mass fraction values. The only condition is that, in the gas phase, the reactant-oxidizer mixture is within the flammability limit. The effect of reduced oxygen mass fraction on flame extinction of materials in a threedimensional arrangement, where flame heat flux is enhanced, has been examined. Figure 36.54 shows an example where chemical heat release
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M.M. Khan et al.
Chemical heat release rate (kW)
15
0.233
12
9 0.190 6 0.167 3
0
0
50
100
150
200
250
300
Time (s)
Fig. 36.54 Chemical heat release rate versus time for 50-mm empty corrugated paper boxes in a 2 2 2 arrangement (two boxes along the length two boxes along the width two layers, for a total of eight boxes
separated by about 12 mm). Measurements were made in the Fire Propagation Apparatus with no external heat flux under co-flow conditions and at various oxygen mass fractions, which are indicated in the figure
rates at oxygen mass fractions of 0.233, 0.190, and 0.167 versus time are shown for the combustion of 50-mm cubes of empty corrugated paper boxes in a 2 2 2 arrangement. The weight of each box is about 13 g (839 g/m2). The measurements were taken in the Fire Propagation Apparatus. In Fig. 36.54, at an oxygen mass fraction of 0.167, the flame is close to the extinction condition, only 10.5 % of the initial weight of the boxes is consumed, which is equivalent to consumption of a single box with a surface area of about 0.0155 m2. The peak chemical heat release rate close to flame extinction, in Fig. 36.54, is about 1.5 kW or 97 kW/m2, using a surface area of 0.0155 m2. This value is in excellent agreement with the average value in Table 36.16, derived from the critical mass loss rates for ignition. The data in Fig. 36.54 for the threedimensional arrangement of the corrugated boxes thus support the firepoint theory [150, 151], independent of the critical heat release rate for flame extinction from the geometrical arrangement and surface areas of the materials, and Equations 36.98 and 36.99 as originally formulated in Ref. [156].
Definitions Chemical heat of combustion
Convective heat of combustion Heat of gasification Heat release parameter Kinetic parameter for flame extinction Net heat of complete combustion
calorific energy generated in chemical reactions leading to varying degrees of incomplete combustion per unit fuel mass consumed calorific energy carried away from the flame by the fire products-air mixture per unit fuel mass consumed energy absorbed to vaporize a unit mass of fuel originally at ambient temperature calorific energy generated per unit amount of calorific energy by the fuel maximum fraction of combustion energy that the flame reactions may lose to the sample surface by convection without flame extinction calorific energy generated in chemical complete reactions leading to combustion, with water as a gas, per unit fuel mass consumed
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Combustion Characteristics of Materials and Generation of Fire Products
Radiative heat of combustion
calorific energy emitted as thermal radiation from the flame per unit fuel mass consumed
ΔHT ΔHv ΔH*CO
Nomenclature
ΔH *CO2 * ΔHO
A aj bj Bcr CHF 00 C˙O 00 C˙stoich,O
cO cP ΔcP
D Ei fj fp FPI FSPc 00 G˙j 00 G˙stoich,j
ΔHi ΔHD ΔHg ΔHg,con ΔHm
total exposed surface area of the material (m2) mass coefficient for the product yield (g/g) molar coefficient for the product yield (g/mol) critical mass transfer number critical heat flux (kW/m2) mass consumption rate of oxygen (g/m2/s) stoichiometric mass consumption rate of oxygen (g/m2/s) mass of oxygen consumed per unit mass of fuel (g/g) specific heat (kJ/g/K) difference between the heat capacities of the extinguishing agent and the fire products (kJ/g/K) optical density (1/m) total amount of heat generated in the combustion of a material (kJ) volume fraction of a product fire property Fire Propagation Index convective flame spread parameter mass generation rate of product j (g/m2/s) stoichiometric mass generation rate of product j (g/m2/s) heat of combustion per unit mass of fuel vaporized (kJ/g) heat of dissociation (kJ/g) heat of gasification at ambient temperature (kJ/g) flame convective energy transfer to the fuel per unit mass of fuel gasified (kJ/g) heat of melting at the melting temperature (kJ/g)
HRP hi I/I0 j k Lsp l ˙ 00 m M mi ˙ air m 00 q_ e 00
q_ f 00 Q_ i 0
Q_ i S t tf t0 T ΔTig TRP u V_ W˙
1225
net heat of complete combustion per unit of fuel vaporized (kJ/g) heat of vaporization at the vaporization temperature (kJ/g) net heat of complete combustion per unit mass of CO generated (kJ/g) net heat of complete combustion per unit mass of CO2 generated (kJ/g) net heat of complete combustion per unit mass of oxygen consumed (kJ/g) heat release parameter mass coefficient for the heat of combustion (kJ/g) fraction of light transmitted through smoke fire product thermal conductivity (kW/m/K) smoke point (m) optical path length (m) mass loss rate (g/m2/s) molecular weight (g/mol) molar coefficient for the heat of combustion (kJ/mol) mass flow rate of air (g/s) external heat flux (kW/m2) flame heat flux (kW/m2) heat release rate per unit sample surface area (kW/m2) heat release rate per unit sample width (kW/m) stoichiometric mass air-to-fuel ratio (g/g) time (s) time at which there is no more vapor formation (s) time at which the sample is exposed to heat (s) temperature (K) ignition temperature above ambient (K) thermal response parameter (kWs1/2/ m2) fire propagation rate (mm/s or m/s) total volumetric flow rate of fire product-air mixture (m3/s) total mass flow rate of the fire productair mixture (g/s)
1226
Wf Wj
Xf Xp Xt yj Yj,ex YO
M.M. Khan et al.
total mass of the material lost in the flaming and nonflaming process (g) total mass of product j generated in the flaming and nonflaming process (g) flame height (m or mm) pyrolysis front (m or mm) total length available for fire propagation (m or mm) yield of product j mass fraction of extinguishing agent mass fraction of oxygen
Greek Letters α β ϕ ξ Φ χ ch χ con χ rad ηj κ λ σ τ ρ νj νO Ψj ΨO ζ ζ oxid ζ red
correlation coefficient (nonflaming fire) correlation coefficient (transition region) kinetic parameter for flame extinction correlation coefficient (transition region) equivalence ratio combustion efficiency convective component of the combustion efficiency radiative component of the combustion efficiency generation efficiency ratio between the kinetic parameters for the flame temperature and adiabatic flame temperature wavelength of light (μm) Stefan-Boltzmann constant (56.7 1012 kW/m2/K4) average specific extinction area (m2/g) density (g/m3) stoichiometric coefficient of product j stoichiometric coefficient of oxygen stoichiometric yield for the maximum conversion of fuel to product j stoichiometric mass oxygen-to-fuel ratio (g/g) ratio of fire properties for ventilationcontrolled to well-ventilated combustion oxidation zone product generation efficiency ratio reduction zone product generation efficiency ratio
Subscripts a ad asy ch con cr e ex f fc fr g g,con i ig j n 0 oxid rad red stoich
rr s vc wv 1
air or ambient adiabatic asymptotic chemical convective critical external extinguishment flame or fuel flame convective flame radiative gas flame convective energy for fuel gasification chemical, convective, radiative ignition fire product net initial oxidation zone of a flame radiation reduction zone of a flame stoichiometric for the maximum possible conversion of fuel monomer to a product surface re-radiation surface, smoke ventilation-controlled fire well-ventilated fire infinite amount of air
Superscripts . 0 00
per unit time (s1) per unit width (m1) per unit area (m2)
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1230 Bounds. SIAM J Optim 6:418–445. doi:10.1137/ S1052623494240456 85. Duan Q, Gupta VK, Sorooshian S (1993) Shuffled Complex Evolution Approach for Effective and Efficient Global Minimization. J Optim Theory Appl 76:501–521. doi:10.1007/BF00939380 86. Duan Q, Sorooshian S, Gupta VK (1994) Optimal Use of the SCE-UA Global Optimization Method for Calibrating Watershed Models. J Hydrol 158:265–284. doi:10.1016/0022-1694(94)90057-4 87. Lautenberger C, Ferna´ndez-Pello C (2011) Optimization Algorithms for Material Pyrolysis Property Estimation. Fire Saf Sci 10:751–764. doi:10.3801/ IAFSS.FSS.10-751 88. Gaviano M, Lera D (1998) Test Functions with Variable Attraction Regions for Global Optimization Problems. J Glob Optim 13:207–223. doi:10.1023/ A:1008225728209 89. Chaos M, Khan MM, Dorofeev SB (2012) Pyrolysis of Corrugated Cardboard in Inert and Oxidative Environments. Proc Combust Inst 34. doi:10.1016/ j.proci.2012.06.031 90. Savitzky A, Golay MJE (1964) Smoothing and Differentiation of Data by Simplified Least Squares Procedures. Anal Chem 36:1627–1639. doi:10. 1021/ac60214a047 91. Staggs JEJ (2005) Savitzky-Golay Smoothing and Numerical Differentiation of Cone Calorimeter Mass Data. Fire Saf J 40:493–505. doi:10.1016/j. firesaf.2005.05.002. 92. Bromba MUA, Ziegler H (1981) Application Hints for Savitzky-Golay Digital Smoothing Filters. Anal Chem 53:1583–1586. doi:10.1021/ac00234a011 93. Krishnamoorthy N, Chaos M, Khan MM, Chatterjee P, Wang Y, Dorofeev SB (2010) Experimental and Numerical Study of Flame Spread in Parallel Panel Geometry. Proceedings of the 6th International Seminar on Fire and Explosion Hazards, Leeds, UK, paper 155. doi:10.3850/978981-08-7724-8_03-07 94. Krishnamoorthy N, Chaos M, Khan MM, Chatterjee P, Wang Y, Dorofeev SB (2010) Application of Bench-Scale Material Flammability Data to Model Flame Spread in Medium-Scale Parallel Panel Test. Proceedings of the 12th International Fire Science and Engineering Conference, Interflam2010, Nottingham UK, pp. 709–720. 95. Chaos M, Khan MM, Krishnamoorthy N, Chatterjee P, Wang Y, Dorofeev SB (2011) Experiments and Modeling Of Single- and TripleWall Corrugated Cardboard: Effective Material Properties and Fire Behavior. Proceedings of the 12th International Conference on Fire and Materials, San Francisco, CA, pp. 625–636. 96. Krishnamoorthy N, Chaos M, Khan MM, Chatterjee P, Wang Y, Dorofeev SB (2011) Numerical Modeling of Flame Spread over Corrugated Cardboard on Vertical Parallel Panels. Proceedings of the 7th US National Technical Meeting of the Combustion Institute, Atlanta, GA, Paper 1 F16.
M.M. Khan et al. 97. Chaos M, Wang Y, Dorofeev SB (2012) CFD Modeling of Flame Spread over Corrugated Cardboard Panels. Proceedings of the International Congress on Fire and Computer Modeling, Oct. 18–19, 2012, Universidad de Cantabria, Spain. 98. Wang Y, Chatterjee P, de Ris JL (2011) Large Eddy Simulation of Fire Plumes. Proc Combust Inst 33:2473–2480. doi:10.1016/j.proci.2010.07.031 99. http://www.fmglobal.com/modeling. Accessed August 2015. 100. Thornton WM (1917) The Relation of Oxygen to the Heat of Combustion of Organic Compounds. Philos Mag Ser 6 33:196–203. doi:10.1080/ 14786440208635627 101. Macrae JC (1966) An Introduction to the Study of Fuel. Elsevier Publishing Company, London, UK. 102. ASTM D4809-13 (2013) Standard Test Method for Heat of Combustion of Liquid Hydrocarbon Fuels by Bomb Calorimeter (Precision Method). ASTM International, West Conshohocken, PA. doi:10.1520/ D4809-13, www.astm.org. 103. Tewarson A, Jiang FH, Morikawa T (1993) Ventilation-Controlled Combustion of Polymers. Combust Flame 95:151–169. doi:10.1016/00102180(93)90058-B 104. Tewarson A, Khan MM (1993) Extinguishment of Diffusion Flames of Polymeric Materials by Halon 1301. J Fire Sci 11:407–420. doi:10.1177/ 073490419301100503 105. Costa C, Treand G, Moineault F, Gustin J-L (1999) Assessment of the Thermal and Toxic Effects of Chemical and Pesticide Pool Fires Based on Experimental Data Obtained Using the Tewarson Apparatus. Process Saf Environ Prot 77:154–164. doi:10. 1205/095758299529974 106. Brohez S, Delvosalle C (2009) Carbon Dioxide Generation Calorimetry - Errors Induced by the Simplifying Assumptions in the Standard Test Methods. Fire Mater 33:89–97. doi:10.1002/fam.988 107. Tewarson A, Marlair G (2004) Liquids and Chemicals. In: Harper CA (ed) Handbook of Building Materials for Fire Protection. McGraw-Hill, New York, pp. 8.1–8.43. 108. Brohez S, Delvosalle C, Marlair G, Tewarson A. (2000) The Measurement of Heat Release from Oxygen Consumption in Sooty Fires. J Fire Sci 18:327–353. doi:10.1177/ 073490410001800501 109. Brohez, S (2005) Uncertainty Analysis of Heat Release Rate Measurement from Oxygen Consumption Calorimetry. Fire Mater 29:383–394. doi:10. 1002/fam.895 110. Biteau H, Fuentes A, Marlair G, Brohez S, Torero JL (2009) Ability of the Fire Propagation Apparatus to Characterise the Heat Release Rate of Energetic Materials. J Hazard Mater 166:916–924. doi:10. 1016/j.jhazmat.2008.11.100 111. Biteau H, Steinhaus T, Schemel C, Simeoni A, Marlair G, Bal N, Torero JL (2008) Calculation Methods for the Heat Release Rate of Materials of
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Combustion Characteristics of Materials and Generation of Fire Products
Unknown Composition. Fire Saf Sci 9:1165–1176. doi:10.3801/IAFSS.FSS.9-1165 112. Tewarson A (1986) Prediction of Fire Properties of Materials Part 1: Aliphatic and Aromatic Hydrocarbons and Related Polymers. Technical Report NBS-GCR-86-521, National Institute of Standards and Technology, Gaithersburg, MD. 113. Hirschler MM (1987) Fire Hazard and Toxic Potency of the Smoke from Burning Materials. J Fire Sci 5:289–307. doi:10.1177/073490418700500501 114. Tewarson A (1988) Smoke Point Height and Fire Properties of Materials. Technical Report NBS-GCR-88-555, National Institute of Standards and Technology, Gaithersburg, MD. 115. Tewarson A, Zalosh RG (1989) Flammability Testing of Aircraft Cabin Materials, Paper 33 in AGARD Conference Proceedings No. 467 - Aircraft Fire Safety; Propulsion and Energetics Panel 73rd Symposium, Sintra, Portugal, May 22–26, 1989. 116. Tsantarides L, Ostman B (1989) Smoke, Gas, and Heat Release Data for Building Products in the Cone Calorimeter. Technical Report I 8903013, Swedish Institute for Wood Technology Research, Stockholm, Sweden. 117. Khan MM (1992) Characterization of Liquid Fuel Spray Fires. In: Cho P, Quintiere J (eds) Heat and Mass Transfer in Fire and Combustion Systems, American Society of Mechanical Engineers, New York, NY. 118. Sivathanu YR, Faeth GM (1990) Generalized State Relationships for Scalar Properties in Nonpremixed Hydrocarbon/Air Flames. Combust Flame 82:211–230. doi:10.1016/0010-2180(90)90099-D 119. Khan MM, Bill RG Jr (2003) Comparison of Flammability Measurements in Vertical and Horizontal Exhaust Duct in the ASTM E-2058 Fire Propagation Apparatus. Fire Mater 27:253–266. doi:10.1002/ fam.830 120. Newman JS, Steciak J (1987) Characterization of Particulates from Diffusion Flames. Combust Flame 67:55–64. doi:10.1016/0010-2180(87)90013-7 121. Mulholland GW, Choi MY (1998) Measurement of the Mass Specific Extinction Coefficient for Acetylene and Ethene Smoke Using the Large Agglomerate Optics Facility. Proc Combust Inst 27:1515–1522. doi:10.1016/S0082-0784(98)80559-6 122. Drysdale D (1985) An Introduction to Fire Dynamics. Wiley, New York, NY, pp. 278–400. 123. Beyler CL (1986) Major Species Production by Diffusion Flames in a Two-Layer Compartment Fire Environment. Fire Saf J 10:47–56. doi:10.1016/ 0379-7112(86)90031-7 124. Beyler CL (1991) Analysis of Compartment Fires with Overhead Forced Ventilation. Fire Saf Sci 3:291–300. doi:10.3801/IAFSS.FSS.3-291 125. Morehart JH, Zukoski EE, Kubota T (1991) Characteristics of Large Diffusion Flames Burning in a Vitiated Atmosphere. Fire Saf Sci 3:575–583. doi:10.3801/IAFSS.FSS.3-575
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126. Tewarson A, Chu F, Jiang FH (1994) Combustion of Halogenated Polymers. Fire Saf Sci 4:563–574. doi:10.3801/IAFSS.FSS.4-563 127. ASTM D1322-08 (2008) Standard Test Method for Smoke Point of Kerosine and Aviation Turbine Fuel, ASTM International, West Conshohocken, PA. doi:10.1520/D1322-08, www. astm.org. 128. Haynes BS, Wagner HGg (1981) Soot Formation. Prog Energy Combust Sci 7:229–273. doi:10.1016/ 0360-1285(81)90001-0 129. Kent JH, Wagner HGg (1984) Why Do Diffusion Flames Emit Soot. Combust Sci Technol 41:245–269. doi:10.1080/00102208408923834 130. Olson DB, Pickens JC, Gill RJ (1985) The Effects of Molecular Structure on Soot Formation, II. Diffusion Flames. Combust Flame 62:43–60. doi:10.1016/ 0010-2180(85)90092-6 131. Markstein GH (1985) Relationship between Smokepoint and Radiant Emission from Buoyant Turbulent and Laminar Diffusion Flames. Proc Combust Inst 20:1055–1061. doi:10.1016/S00820784(85)80595-6 132. Kent JH (1986) A Quantitative Relationship Between Soot Yield and Smoke Point Measurements. Combust Flame 63:349–358. doi:10.1016/0010-2180(86)90004-0 133. Kent JH (1987) Turbulent Diffusion Flame Sooting Relationship to Smoke-Point Tests. Combust Flame 67:223–233. doi:10.1016/0010-2180(87) 90098-8 134. Glassman I (1989) Soot Formation in Combustion Processes. Proc Combust Inst 22:295–311. doi:10. 1016/S0082-0784(89)80036-0 135. Markstein GH (1989) Correlations for Smoke Points and Radiant Emission of Laminar Hydrocarbon Diffusion Flames. Proc Combust Inst 22:363–370. doi:10.1016/S0082-0784(89)80042-6 ¨ L (1989) Influence of Hydrocarbon Fuel 136. Gu¨lder O Structure Constitution and Flame Temperature on Soot Formation in Laminar Diffusion Flames. Combust Flame 78:179–194. doi:10.1016/0010-2180(89) 90124-7 137. Shivathanu YR, Faeth GM (1990) Soot Volume Fractions in the Overfire Region of Turbulent Diffusion Flames. Combust Flame 81:133–149. doi:10. 1016/0010-2180(90)90060-5 € ¨ , Sivathanu YR, Faeth GM (1991) Carbon 138. Ko¨ylu¨ UO Monoxide and Soot Emissions from Buoyant Turbulent Diffusion Flames. Fire Saf Sci 3:625–634. doi:10.3801/IAFSS.FSS.3-625 € ¨ , Faeth GM (1991) Carbon Monoxide and 139. Ko¨ylu¨ UO Soot Emissions from Liquid-Fueled Buoyant Turbulent Diffusion Flames. Combust Flame 87:61–76. doi:10.1016/0010-2180(91)90027-9 140. Orloff L, de Ris JL, Delichatsios MA (1992) Radiation from Buoyant Turbulent Diffusion Flames. Combust Sci Technol 84:177–186. doi:10.1080/ 00102209208951852
1232 ¨ L (1992) Soot Formation in Laminar Diffu141. Gu¨lder O sion Flames at Elevated Temperatures. Combust Flame 88:75–82. doi:10.1016/0010-2180(92)90008-D € ¨ , Faeth GM (1992) Structure of Overfire 142. Ko¨ylu¨ UO Soot in Buoyant Turbulent Diffusion Flames at Long Residence Times. Combust Flame 89:140–156. doi:10.1016/0010-2180(92)90024-J 143. de Ris JL, Cheng X (1994) The Role of Smoke-point in Material Flammability Testing. Fire Saf Sci 4:301–312. doi:10.3801/IAFSS.FSS.4-301 144. Linteris GT, Rafferty JP (2008) Flame Size, Heat Release, and Smoke Points in Materials Flammability. Fire Saf J 43:442–450. doi:10.1016/j.firesaf. 2007.11.006 145. Tran MK, Dunn-Rankin D, Pham TK (2012) Characterizing Sooting Propensity in Biofuel-Diesel Flames. Combust Flame 159:2181–2191. doi:10. 1016/j.combustflame.2012.01.008 146. Lautenberger CW, de Ris JL, Dembsey NA, Barnett JR, Baum HR (2005) A Simplified Model for Soot Formation and Oxidation in CFD Simulation of Non-Premixed Hydrocarbon Flames. Fire Saf J 40:141–176. doi:10.1016/j.firesaf.2004.10.002 147. Chatterjee P, de Ris JL, Wang Y, Dorofeev SB (2011) A Model for Soot Radiation in Buoyant Diffusion Flames. Proc Combust Inst 33:2665–2671. doi:10.1016/j.proci.2010.06.112 148. Madorsky SL (1964) Thermal Degradation of Organic Polymers. Interscience Publishers, John Wiley & Sons, Inc., New York, NY, p. 192. 149. Tewarson A, Khan MM (1991) The Role of Active and Passive Fire Protection Techniques in Fire Control, Suppression and Extinguishment. Fire Saf Sci 3:1007–1017. doi:10.3801/IAFSS.FSS.3-1007 150. Rasbash DJ (1976) A Flame Extinction Criterion for Fire Spread. Combust Flame 26:411–412. doi:10. 1016/0010-2180(76)90095-X 151. Rasbash DJ (1986) The Extinction of Fire with Plain Water: A Review. Fire Saf Sci 1:1145–1163. doi:10. 3801/IAFSS.FSS.1-1145 152. Spalding DB (1960) A Standard Formulation of the Steady Convective Mass Transfer Problem. Int J
M.M. Khan et al. Heat Mass Transf 1:192–207. doi:10.1016/00179310(60)90022-3 153. Heskestad G (1980) The Role of Water in Suppression of Fire: A Review. J Fire Flammabl 11:254–262. 154. Magee RS, Reitz RD (1975) Extinguishment of Radiation Augmented Plastic Fires by Water Sprays. Proc Combust Inst 15:337–347. doi:10.1016/S00820784(75)80309-2 155. Thomson HE, Drysdale DD (1989) Critical Mass Flowrate at the Firepoint of Plastics. Fire Saf Sci 2:67–76. doi:10.3801/IAFSS.FSS.2-67 156. Beyler C (1992) A Unified Model of Fire Suppression. J Fire Prot Eng 4:5–16. doi:10.1177/ 104239159200400102 157. Kodama H, Miyasaka K, Ferna´ndez-Pello AC (1987) Extinction and Stabilization of a Diffusion Flame on a Flat Combustible Surface with Emphasis on Thermal Controlling Mechanisms. Combust Sci Technol 54:37–50. doi:10.1080/00102208708947042 158. Kulkarni AK, Sibulkin M (1982) Burning Rate Measurements on Vertical Fuel Surfaces. Combust Flame 44:185–186. doi:10.1016/0010-2180(82) 90072-4 159. Xin Y, Khan MM (2007) Flammability of Combustible Materials in Reduced Oxygen Environment. Fire Saf J 42:536–547. doi:10.1016/j.firesaf.2007. 04.003
Mohammed M. Khan is a Senior Lead Research Scientist (retired) (in place of Senior Research Specialist). He has more than 30 years of flammability research experience. He is recognized for his work on ignition, flame spread, and material flammability characterization. Archibald Tewarson retired from FM Global. His major specialization is in chemical aspects of fires. Marcos Chaos is a Senior Lead Research Scientist at the Research Division of FM Global. He has specialized in pyrolysis modeling and optimization algorithms as well as experimental aspects of flammability testing.
Performance-Based Design
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Morgan J. Hurley and Eric R. Rosenbaum
Introduction The SFPE Engineering Guide to PerformanceBased Fire Protection [1] defines performancebased design as “an engineering approach to fire protection design based on (1) agreed upon fire safety goals and objectives, (2) deterministic and/or probabilistic analysis of fire scenarios, and (3) quantitative assessment of design alternatives against the fire safety goals and objectives using accepted engineering tools, methodologies, and performance criteria.” This definition identifies three key attributes of performance-based design. The first is a description of the desired level of fire safety in a building (or other structure) in the event of a fire. The second attribute includes definition of the “design basis” of the building. The “design basis” is an identification of the types of fires, occupant characteristics, and building characteristics for which the fire safety systems in the building are intended to provide protection. In the vernacular of performance-based design, these fires are referred to as “design fire scenarios.” The third element involves an engineering analysis of proposed design strategies to determine whether or not they provide the intended level of safety in the event of the design fire scenarios.
M.J. Hurley (*) • E.R. Rosenbaum
The purpose of this chapter is to provide an overview of performance-based design and to serve as insight into how other chapters in this handbook can be used as resources. In most cases, utilizing performance-based design goes beyond code application to analysis of how a building and its occupants will be affected by fire. This generally requires consideration of the science of fire and human physiology and psychology. That is why performancebased design potentially utilizes many sections of the SFPE Handbook of Fire Protection Engineering.
Types of Performance For performance-based design, Nelson [2] identifies the following four types of “performance” that may be evaluated.
Component Performance Component performance identifies the intended performance in fire of individual building systems or components, such as doors, structural framing, or individual protection systems such as detection. In component performance analysis, individual components and systems are designed in isolation without considering how their performance may impact, or be impacted by, the performance of other systems or components. Any
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system or component that meets the stated performance would be considered to be acceptable. An example of a component-performancebased approach would be a structural element that is designed to achieve a 1-h fire resistance rating when exposed to the “standard” fire. In this case, the intended performance would involve maximum acceptable point and average temperatures, and the design fire scenario would be the standard time-temperature curve. Although building codes typically require this performance to be achieved through fire testing, calculation methods are available as well [3]. Any assembly that achieves the intended performance when exposed to the design fire scenario would be acceptable. Another example would be an individual sprinkler used in a sprinkler system. Sprinkler design standards and component standards might require a maximum actuation temperature and thermal response characteristics. Any sprinkler that meets the performance identified would be acceptable. It is noteworthy that the codes and standards that govern fire-resistant structural elements and sprinklers contain specific requirements that are not performance based, such as limitations on the types of materials that can be used in fireresistant assemblies and sprinklers.
Environmental Performance Environmental performance involves identification of the maximum permissible fire conditions within a building or portion thereof. The specification of environmental conditions could involve temperature, heat flux, or products of combustion. Environmental performance approaches identify conditions that are tolerable if a fire were to occur. It is not possible to include fire prevention strategies within an environmental performance approach. An example of an environmental performance approach would be a requirement that the smoke layer within an atrium not descend below a given elevation above the highest occupied level. Any design that would achieve this criterion would be acceptable, and the performance requirement
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does not specify or limit how this can be achieved.
Threat Potential Performance Threat potential performance involves identification of the maximum acceptable threat to life, property, business continuity, or the natural environment. Unlike environmental performance requirements, which involve statements of maximum acceptable conditions in the environment surrounding items that are desired to be protected from fire, threat potential performance involves a statement of the maximum tolerable conditions of the item or items being protected. An example of a threat potential performance requirement would be a fractional effective incapacitation dose (see Chap. 63). Another example would be an identification of the maximum permissible temperature of an object. As with environmental performance requirements, threat potential performance requirements do not specify or limit how the conditions can be achieved.
Risk Potential Performance In risk potential performance, the summation of the products of probabilities of occurrence of fire events and their consequences are specified. An example of a risk potential performance requirement would be that the average permissible property loss in a facility resulting from fire must not exceed an average of $10,000 in value per year. When applying this type of approach, a designer would evaluate all possible fire events and their potential consequences. This can be expressed mathematically as [1]: X X Risk ¼ Riski ¼ ðLossi Pi Þ where Riski ¼ Risk associated with scenario i Lossi ¼ Loss associated with scenario i Pi ¼ Frequency of scenario i occurring Nelson [2] also identifies the typical “prescriptive” approach, which he defines as
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Performance-Based Design
“specification.” “Specification” involves strict definition of dimensions, construction methods, and other features. An example of “specification” would be some of the requirements in NFPA 101®, Life Safety Code®, [4] applicable to stairway construction. NFPA 101 identifies specific dimensional requirements for stairs and handrails.
History of Performance-Based Fire Protection Design Early (pre-1900s) fire protection requirements largely fit into the category of “specification,” with such requirements including the permissible materials from which building exteriors could be constructed or the minimum acceptable spacing between buildings. However, most modern building and fire code requirements have some element of performance associated with them. Performance-based approaches for designing building fire protection can be traced to the early 1970s, when the goal-oriented approach to building fire safety was developed by the U.S. General Services Administration [5]. Other major developments in performance-based design include the following: • Publication of the performance-based British Regulations in 1985 • Publication in 1988 of the first edition of the SFPE Handbook of Fire Protection Engineering • Publication of the performance-based New Zealand building code in 1992 and the New Zealand Fire Engineering Design Guide in 1994 • Publication of the Performance Building Code of Australia and the Australian Fire Engineering Guidelines in 1995 • Publication of the Performance Requirements for Fire Safety and Technical Guide for Verification by Calculation by the Nordic Committee on Building Regulations in 1995 • Publication of the performance option in the NFPA 101, Life Safety Code, in 2000
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• Publication of the SFPE Engineering Guide to Performance-Based Fire Protection Analysis and Design of Buildings in 2000 • Publication of the Japanese performancebased Building Standard Law in 2000 • Publication of the ICC Performance Code for Buildings and Facilities in 2001 • Publication of the performance option in the NFPA 5000®, Building Construction and Safety Code®, in 2003 The foregoing documents represent only the formalization of performance-based design. Performance-based design has long been practiced through the use of “equivalency” or “alternate methods and materials” clauses found in most, if not all, prescriptive codes and standards. These clauses permit the use of approaches or materials not specifically recognized in the code provided that the approach or material can be demonstrated to provide at least an equivalent level of safety as that achieved by compliance with the code or standard. However, “equivalency” or “alternate methods and materials” clauses typically do not provide any detail as to how an equivalent level of safety can be achieved. Therefore, the approaches used by individual designers or regulatory officials were frequently developed on an ad hoc basis, with approaches varying among designers and among regulatory officials. The effect of the documents identified in the preceding text was to standardize the practice of performance-based design. The development of performance-based design has followed an evolution in the quantitative understanding of fire. Before fire science was well understood, proven technologies would be codified into regulations. Similarly, as major fires occurred, and the causes and contributing factors of those fires were identified, codes and standards were modified to prevent similar major fires from occurring in the future. Specification codes have the following two disadvantages: • They potentially only protect against events of a type that have occurred in the past. Major
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fires are low-probability, high-consequence events. Because of their stochastic nature, some types of rare events have not yet occurred. • They potentially stifle innovation. By specifying certain types of methods and materials, it can be difficult to introduce new methods and materials into the marketplace. As the science of fire has become better understood, performance-based fire protection design has become possible. Other engineering disciplines have evolved in a similar manner—as the underlying science has become better understood, their design approaches have become more performance based.
Advantages and Disadvantages of Performance-Based Design Performance-based design offers a number of advantages and disadvantages over specification-based prescriptive design. As the design approach used moves from specification based toward risk based, these advantages and disadvantages are magnified.
Advantages One advantage of performance-based design is that it allows the designer to address the unique features and uses of a building. For example, the stores in a shopping mall might have an identical occupancy classification under prescriptive building and fire codes and, hence, require similar fire protection strategies. However, the stores could contain significantly different fire hazards. Some could contain flammable liquids, whereas others might contain few or no combustible items at all. A corollary to this advantage is increased cost-effectiveness of performancebased designs. Another advantage is that performance-based design promotes a better understanding of how a building would perform in the event of a fire. Compliance with prescriptive codes and standards
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is intended to result in a building that is “safe” from fire. However, what constitutes “safe” is generally not defined. Similarly, the types of fires against which the building is intended to achieve fire safety are not identified. Although most common fire scenarios would likely result in acceptable performance, the low-frequency scenarios that are not envisioned may not. Two fire scenarios can be used to illustrate this. Carelessly discarded smoking materials would likely be within the design basis for a code that is intended to apply to a high-rise residential building. However, a gasoline tank truck that accidentally crashes into the building’s lobby likely is not. Within these two extremes is a large range of possible events. A corollary to this advantage is that increased thought and engineering rigor are brought to solving fire protection problems.
Disadvantages A disadvantage of performance-based design is that it requires more expertise to apply and review than does prescriptive-based design. Generally, application of prescriptive codes only requires the selection of building features and systems that fit within the code’s requirements. Verification of the acceptability of a prescriptivebased design is equally straightforward. Performance-based design can take more time to conduct and review than prescriptive-based design. Another disadvantage of performance-based design is that it can be more sensitive to change than prescriptive-based design. Changes in use of a building or portion thereof can result in unacceptable performance in the event of a fire if the effect of the change on fire safety is not contemplated in the design. With prescriptive-based designs, changes in use may be acceptable if the portion modified stays within the original occupancy or hazard classification. This is not to say that prescriptive designs are completely tolerant to changes; even if a modification remains with the original occupancy
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classification, some types of changes could result in the modification not being compliant with prescriptive codes. For example, movement of walls during tenant renovations in an office building could result in the sprinkler system no longer being in compliance with governing codes and standards. If a building is designed according to a performance basis, then some changes in use may result in increased vulnerability in the event of a fire. The process that is identified in the subsequent section provides methods of overcoming the limitations.
framework, for performance-based design. This process is identified in the flowchart in Fig. 37.1. The process is intended to be flexible, so that it can be tailored to the individual requirements of individual performance-based design projects. This flowchart identifies the steps that are involved in performance-based design without specifying which methods or models should be used to perform specific calculations relating to the development or evaluation of an individual design.
Defining the Project Scope
Process of Performance-Based Design [1] The SFPE Engineering Guide to PerformanceBased Fire Protection [1] provides a process, or
The performance-based design process identified in the SFPE Engineering Guide to PerformanceBased Fire Protection begins with developing the project scope. (Defining the project scope is Step 1 in the process section later in the chapter.)
Define project scope
Identify goals
Define objectives Design brief Develop performance criteria
Develop fire scenarios and design fires
Develop trial design(s)
Evaluate trial design(s)
Modify design or objectives
No
Selected design meets performance criteria Yes Select final design
Prepare design documents
Fig. 37.1 Performance-based design process [1]
Performancebased design report Plans and specifications, operations and maintenance manuals
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Project scopes for performance-based designs are frequently not highly different than project scopes for prescriptive-based designs, although unique features may be identified that might be difficult or impossible to achieve through compliance with prescriptive-based codes. The project scope identifies the portions of a building or facility that will be considered by the design, the desired features of the design, the intended characteristics of the building, and the regulations that are applicable to the design. The scope also includes identification of the project stakeholders—those that have an interest in the success of the design. Stakeholders may include building owners or their representatives, regulatory authorities, insurance providers, building tenants, fire officials, or other parties. From the scope, a clear understanding can be gained of the needs of the project.
Identifying Goals Once the scope is identified, the next steps involve the definition of goals and objectives for the design project. (Identifying goals is Step 2 in the process section later in the chapter.) The SFPE Engineering Guide to Performance-Based Fire Protection defines goals as the “desired overall fire safety outcome expressed in qualitative terms.” Goals are intended to be stated in broad terms that can easily be understood by people who do not have engineering expertise. The purpose of identifying goals is to facilitate understanding and agreement on how the building is intended to perform in the event of a fire. Laypeople would likely not be able to understand the significance of keeping the upper-layer temperature below a certain temperature, but they could understand what it means to provide for life safety in the event of a fire. The SFPE Engineering Guide to Performance-Based Fire Protection identifies four fundamental goals for fire safety: life safety, property protection, mission continuity, and environmental protection. Although these types of statements are entirely qualitative in nature,
M.J. Hurley and E.R. Rosenbaum
they point the direction of the design process. For example, an unattended, fully automated warehouse may have property protection and mission continuity as its primary design goals. A hotel would likely have life safety as its primary fire safety goal. Goals can come from a variety of sources. Some codes identify goals. For example, NFPA 101 specifies the following fire safety goal [5]: 4.1.1 Fire. A goal of this Code is to provide an environment for the occupants that is reasonably safe from fire by the following means: (1) Protection of occupants not intimate with the initial fire development (2) Improvement of the survivability of occupants intimate with the initial fire development 4.1.2 Comparable Emergencies. An additional goal is to provide life safety during emergencies that can be mitigated using methods comparable to those used in case of fire. 4.1.3 Crowd Movement. An additional goal is to provide for reasonably safe emergency crowd movement and, where required, reasonably safe nonemergency crowd movement. NFPA 5000 [6] provides the following goals: 4.1.1 Goals. The primary goals of this Code are safety, health, building usability, and public welfare, including property protection as it relates to the primary goals. NFPA 5000 specifies more goals than NFPA 101 does, which is due to the fact that NFPA 5000 has a broader scope than NFPA 101. NFPA 101 addresses only life safety, whereas NFPA 5000 addresses many additional aspects of building safety. The ICC Performance Code for Buildings and Facilities [7] identifies goals that are similar to those contained in NFPA 5000. Designs that comply with the prescriptive option of NFPA 101 or NFPA 5000 are “deemed” to comply with the goals specified by those codes. Similarly, designs that comply with the ICC family of codes are deemed to comply with the goals of the ICC Performance Code for Buildings and Facilities. However, designers
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who prepare performance-based designs would have to demonstrate that they achieve the goals of the applicable code. In some cases, project stakeholders may specify their own goals. See the section on “Application of Performance-Based Design” later in this chapter. As qualitative statements, goals are insufficient by which to judge the adequacy of a design. Therefore, they will have to be quantified as measurable values. The next two steps of the process outlined in the SFPE Engineering Guide to Performance-Based Fire Protection are intended to facilitate translating these broad statements into specific numerical criteria that can be predicted using engineering methods.
Defining Objectives The next step in this process is the development of objectives. (Defining objectives is Step 3 in the process section later in the chapter.) The SFPE Engineering Guide to PerformanceBased Fire Protection identifies two types of objectives: stakeholder objectives and design objectives. Stakeholder objectives provide greater detail of maximum allowable levels of damage than goals do. Stakeholder objectives might be expressed in terms of maximum allowable levels of injury, damage to property, damage to critical equipment, or length of loss of operations. Stakeholder objectives facilitate agreement among the stakeholders of the maximum level of damage that would be tolerable if a fire were to occur. After the stakeholder objectives have been developed, the SFPE Engineering Guide to Performance-Based Fire Protection recommends developing design objectives. Design objectives focus on the items that are intended to be protected from fire and describe the maximum or minimum acceptable fire conditions necessary to achieve the stakeholder objectives. As with goals, stakeholder objectives could be specified by a performance-based code. For
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example, NFPA 101 [5] provides the following objectives: 4.2.1 Occupant Protection. A structure shall be designed, constructed, and maintained to protect occupants who are not intimate with the initial fire development for the time needed to evacuate, relocate, or defend in place. 4.2.2 Structural Integrity. Structural integrity shall be maintained for the time needed to evacuate, relocate, or defend in place occupants who are not intimate with the initial fire development. 4.2.3 Systems Effectiveness. Systems utilized to achieve the goals of Section 4.1 shall be effective in mitigating the hazard or condition for which they are being used, shall be reliable, shall be maintained to the level at which they were designed to operate, and shall remain operational. NFPA 5000 provides additional objectives resulting from the additional goals of the code. If they are not specified by a code, stakeholder objectives will need to be developed by the engineer in consultation with project stakeholders based on the goals. In most cases, design objectives would be developed by an engineer based on the goals and stakeholder objectives agreed to by the stakeholders.
Developing Performance Criteria Performance criteria are threshold values that, if exceeded, indicate that unacceptable damage has occurred. (Developing performance criteria is Step 4 in the process section later in the chapter.) Although design objectives provide more detail than the goals or stakeholder objectives, they are not sufficiently detailed for the evaluation of trial designs. Performance criteria might include temperatures of materials, gas temperatures, smoke concentration or obscuration levels, carboxyhemoglobin levels, or radiant heat flux levels. Performance criteria should be predictable with engineering tools such as fire models.
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Table 37.1 Examples fire protection goals, stakeholder objectives, design objectives, and performance criteria [1] Fire protection goal Minimize fire-related injuries and prevent undue loss of life Minimize fire-related damage to the building and its contents
Minimize undue loss of operations and business-related revenue due to fire-related damage
Stakeholder objective No loss of life outside of the room or compartment of fire origin No significant thermal damage outside of the room or compartment of fire origin No downtime exceeding 8 h
Limit environmental impacts of No water contamination by fire and fire protection measures fire suppression water runoff
The SFPE Engineering Guide to Performance-Based Fire Protection divides the types of performance criteria that may need to be developed into two categories: life safety criteria and non–life safety criteria. Life safety criteria address the survivability of people exposed to fire or fire products. The values selected as performance criteria might vary depending on the physical and mental conditions of building occupants and length of exposure. Performance criteria may need to be developed in the areas of thermal effects to people (e.g., exposure to high gas temperatures or thermal radiation), toxicity of fire products, or visibility through smoke. Non–life safety criteria may need to be developed to assess the achievement of goals relative to property protection, mission continuity, or environmental protection. Performance criteria relative to these goals may relate to thermal effects, such as ignition, melting, or charring; fire spread, smoke damage, fire boundary damage, structural integrity, damage to exposed items, or damage to the environment. Given that performance criteria can vary widely depending on the specific design situation, the SFPE Engineering Guide to Performance-Based Fire Protection does not provide specific performance criteria. Rather, the guide identifies a number of reference sources that can be used to assist with the
Design objective Prevent flashover in the room of fire origin
Performance criteria Upper-layer temperature not greater than 200 C Minimize the likelihood of fire Upper-layer spread beyond the room of fire temperature not origin greater than 200 C Limit the smoke exposure to less than would result in unacceptable damage to the target
HCl not greater than 5 ppm Particulate not greater than 0.5 g/m3 Provide a suitable means for Impoundment capturing fire protection water capacity at least 1.20 runoff times the design discharge
development of design-specific performance criteria. Table 37.1 contains examples of goals, objectives, and performance criteria. Some performance-based codes provide performance criteria. NFPA 101 [5] provides the following performance criterion: 5.2.2 Performance Criterion. Any occupant who is not intimate with ignition shall not be exposed to instantaneous or cumulative untenable conditions. Since “instantaneous or cumulative untenable conditions” is not defined, this performance criterion is more akin to an objective. However, additional specificity can be found in the annex of NFPA 101. The options outlined in the annex deal with prevention of incapacitation from smoke or prevention of exposure to smoke. In many cases, the engineer will need to develop performance criteria from the goals and objectives. To develop performance criteria, the engineer will need to understand the mechanism of harm to the object being protected. Chapter 63 addresses the mechanisms of harm to people in detail.
Developing Fire Scenarios A second input needed to evaluate whether a trial design is acceptable is the design fire scenario, which describes the conditions of exposure, such
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as types of fires and building and occupant conditions for which a design is intended to provide protection. (Developing fire scenarios is Step 5 in the process section later in the chapter.) The SFPE Engineering Guide to Performance-Based Fire Protection suggests a two-step process for identifying design fire scenarios. The first step is considering all possible fire scenarios that could occur in the building or portion of the building that is within the scope of the design. The second step is to reduce the population of possible fire scenarios to a manageable set of design fire scenarios. Both fire scenarios and design fire scenarios comprise three sets of characteristics: building characteristics, occupant characteristics, and fire characteristics. Building characteristics describe the physical features, contents, and ambient environment within the building. They can affect the evacuation of occupants, growth and spread of fire, and the movement of combustion products. Occupant characteristics determine the ability of building occupants to respond and evacuate during a fire emergency and the potential impact a fire will have on the occupants. Fire characteristics describe the history of a fire scenario, including first item ignited, fire growth, flashover, full development, and decay and extinction. The SFPE Engineering Guide to Performance-Based Fire Protection identifies a number of methods that can be used to identify possible scenarios, including the following: • Failure modes and effects analysis, where the different types of failures that could occur are studied, and the effects of those failures are analyzed. • Failure analysis, where potential causes of failures are identified and the expected system performance is investigated. • “What if” analysis, where expert opinion is used to consider possible events and the consequences of those events. • Historical data, manuals, and checklists, where past events in a building or a similar building are studied to consider whether similar events could occur in the building that is
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being designed or modified. Manuals and checklists can be studied to consider warnings, cautions, or operational sequences that could lead to a fire if not followed. • Statistical data of fires across broad classifications of buildings. • Other analysis methods such as hazards and operability studies, preliminary hazard analysis, fault tree analysis, event tree analysis, cause-consequence analysis, and reliability analysis. Given the large number of possible fire scenarios for a given performance-based design project, it is usually necessary to reduce the possible fire scenario population to a manageable number of design fire scenarios for evaluating trial designs. If the design is being done on a deterministic basis, this can be accomplished in part by excluding scenarios that are highly unlikely to occur or that would result in an acceptable outcome regardless of the trial design strategy that is used. However, for a fire scenario to be excluded from further analysis because it is considered too unlikely, all stakeholders must recognize and accept that if the scenario were to occur, an unacceptable outcome may result. Another method of reducing the number of fire scenarios is to select bounding scenarios, where if the performance criteria can be achieved in these scenarios, it can be safely assumed that they would be achieved in the scenarios that are not specifically considered. For risk-based analyses, it would only be acceptable to exclude a fire scenario from further reconsideration if it could be established that no design could handle the scenario. Scenarios can be grouped into clusters of like scenarios according to common defining characteristics (e.g., all fires that start in a single room) [8]. When scenarios are clustered, the scenario cluster will be analyzed as a single, aggregate scenario. The probability that will be used for analysis will be the sum of the probabilities of all of the scenarios in the cluster. The consequence that will be used is an average of the consequences of the scenarios in the cluster.
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Some performance-based codes provide fire scenarios. Even when such a code is applicable to a design, the fire protection engineer should work with project stakeholders to determine if there are other scenarios that should be considered. For example, NFPA 101 [5] and NFPA 5000 [7] specify fire scenarios that must be addressed for performance-based designs. These fire scenarios include elements of fire characteristics, building characteristics, and occupant characteristics. However, these elements are not defined explicitly for all of the scenarios. The New Zealand building code [9] provides a verification method that includes fire scenarios in a similar manner as NFPA 101, but also provides information needed to quantify design fire scenarios. The Japanese building code also provides quantitative design fire scenarios. The ICC Performance Code for Buildings and Facilities [8] provides general classifications of fire events.
Developing Trial Designs Trial designs are fire protection strategies that are intended to achieve the goals of the project. (Developing trial designs is Step 6 in the process section later in the chapter.) To be considered acceptable, trial designs much achieve each of the performance criteria when subjected to the design fire scenarios. The SFPE Engineering Guide to Performance-Based Fire Protection groups the types of methods that might be used in trial designs into six subsystems. Attributes from one or more subsystems would be used in a trial design. The six subsystems identified in the guide are the following: • Fire initiation and development, where methods are used to reduce the likelihood that ignition would occur or reduce the rate of fire development if a fire were to occur. • Spread, control, and management of smoke, where smoke hazards are reduced by limiting smoke production, controlling smoke movement, or reducing the amount of smoke after it has been produced.
M.J. Hurley and E.R. Rosenbaum
• Fire detection and notification, where the presence of a fire would be detected for purposes of notifying building occupants or first responders, or to activate a fire suppression system. • Fire suppression, including automatic or manual systems. • Occupant behavior and egress, where the travel to a place of safety prior to the onset of untenable conditions is facilitated. • Passive fire protection, including limiting fire spread though construction or preventing premature collapse of all or part of a structure. When developing trial designs, the engineer should refer back to the goals of the analysis and decide what types of strategies would best achieve those goals. NFPA 550, Guide to the Fire Safety Concepts Tree [10], can assist with the development of trial design strategies. The top branches of the tree may closely align with the objectives of the design. In these cases, the protection methods that are identified below the objectives that align with the design goals could be used as trial designs. Trial design strategies involve the same types of building components and systems that would generally be included in a prescriptive design. In fact, compliant prescriptive system designs may be appropriate as part of a trial design strategy. However, in some cases, augmented performance may be needed beyond that which would be achieved by a prescriptive-compliant system.
Fire Protection Engineering Design Brief The preceding steps constitute the qualitative portion of the design, and agreement of all stakeholders should be attained prior to proceeding to the quantitative analysis. A mechanism that is suggested by the SFPE Engineering Guide to Performance-Based Fire Protection for achieving this agreement is a fire protection engineering design brief. Evaluating and formally documenting performance-based designs can require extensive effort, and if fundamental aspects of the design change after detailed evaluation, significant
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rework may be required. For example, if a design is completed and evaluated based on achieving life safety goals, and after the design is evaluated property protection goals are identified, then effort previously expended may be wasted. Similarly, if project stakeholders insist on certain types of design strategies being used, then these should be identified before other types of design strategies are developed and evaluated. The purpose of the fire protection engineering design brief is to facilitate agreement on the qualitative portions of the design prior to conducting detailed engineering analysis. The contents of the fire protection engineering design brief will typically include the project scope, goals, objectives and performance criteria, design fire scenarios, and trial design strategies proposed for consideration. The form of the fire protection engineering design brief is intended to be flexible, based on the needs of the project and the relationship of the engineer performing the design to other stakeholders. In some cases, a verbal agreement may be sufficient. In other cases, formal documentation, such as minutes of a meeting or a document that is submitted for formal review and approval, may be prudent. Once the design team and stakeholders have agreed on the approach that is proposed for the performance-based design, the detailed analysis work begins. This includes quantification of the design fire scenarios, evaluation of trial designs, and development of project documentation.
Quantifying Design Fire Scenarios After the design fire scenarios have been agreed upon by the stakeholders, they need to be quantified. (Quantifying design fire scenarios is Step 7 in the process section later in the chapter.) The building characteristics, occupant characteristics, and fire characteristics will need to be quantified as necessary to adequately evaluate the trial designs. The SFPE Engineering Guide to PerformanceBased Fire Protection identifies several types of characteristics. These characteristics are intended to include a listing of any item that might need to
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be quantified. However, for most design situations, it will not be necessary to quantify all of the characteristics. Quantifying Building Characteristics Building characteristics describe the physical features, contents, and internal and external environments of the building. Building characteristics can affect the evacuation of occupants, the growth and spread of fire, and the movement of combustion products. The SFPE Engineering Guide to Performance-Based Fire Protection identifies the following building characteristics that may need to be quantified: • Architectural features, such as compartment geometry, interior finish, construction materials, and openings • Structural components, including any protection characteristics • Fire load • Egress components • Fire protection systems • Building services, such as ventilation equipment • Building operational characteristics • Fire-fighting response characteristics • Environmental factors (interior and exterior temperatures, wind speeds, etc.) Occupant Characteristics For any design in which life safety or occupant response is considered, it will be necessary to consider the occupant characteristics. The SFPE Engineering Guide to Human Behavior in Fire [11] identifies the following fundamental occupant characteristics that could influence the response of building occupants to a fire: • Population (number and density) • Alone or with others • Familiarity with the building • Distribution and activities • Alertness • Physical and cognitive ability • Social affiliation • Role and responsibility • Location • Commitment • Focal point
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• • • •
Occupant condition Gender Culture Age Occupant characteristics provide information as to how people might respond when subjected to fire cues, where fire cues include seeing fire or smoke, smelling smoke, hearing a fire alarm audible signal, or other cues. This includes actions people may take as well as physical effects of fire products. Design Fire Curves Fire characteristics will typically be quantified as design fire curves, which provide a history of the size of a fire as a function of time. Typically, the “size” of a fire is measured in terms of heat release rate. Figure 37.2 shows an example of a design fire curve. The SFPE Engineering Guide to Performance-Based Fire Protection divides design fire curves into five stages. Depending on the scope of the design, it may not be necessary to quantify each stage of the design fire curve. For example, it may only be necessary to quantify the growth stage for evaluation of a detection system. Similarly, evaluation of structural integrity may only require quantification of the fully developed stage. The guide provides suggestions on how to quantify each stage of the design fire curve. For most designs, ignition will be assumed to occur. Typically, the design team will consider different first items ignited. If information is
known about an item and an energy source, it is possible to predict whether the item will ignite. After an item ignites, the fire might grow in size. The rate at which a fire grows is a function of the first item ignited and the location of the item within a compartment. As the fire grows, additional items may be ignited and the fire may spread outside of an enclosure. Flashover occurs when all combustible items within an enclosure ignite. Compartment geometry, compartment ventilation, fire heat release rate, and the thermal properties of the enclosure influence whether and when flashover occurs in a compartment. If there is no intervention, a fire may reach a maximum size, which is a function of either the amount of fuel in the compartment or the amount of available ventilation. The fully developed stage of the fire is typically used to determine radiation through openings, failure of the structure, fire spread to other enclosures, or failure of compartmentation. Fires will decay and eventually burn out. Decay can occur due to depletion of fuel, lack of ventilation, or suppression. When developing design fire curves, it is important to realize that design fires need not be exact or should not be presented as precise predictions of what will happen in a fire. Design fires are meant to be a representation of anticipated fires. Current modeling technology and data make it unnecessary and impractical to create exact predictions of how a potential fire will burn.
Evaluating Trial Designs Heat release rate
Fully developed
Ignition
Growth
Decay
Flashover
Time
Fig. 37.2 Sample design fire curve
Evaluation is the process of determining if a trial design meets all of the performance criteria in each of the design fire scenarios. (Evaluating trial designs is Step 8 in the process section later in the chapter.) The SFPE Engineering Guide to Performance-Based Fire Protection states that the level, or detail, of an evaluation is a function of factors such as the complexity of geometry, level of subsystem interaction, and the margin between evaluation output and the performance
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criteria. In some cases, a relatively simple evaluation may be appropriate, whereas in others, an in-depth evaluation would be required. The levels of evaluation identified in the guide are (1) subsystem, (2) system, and (3) whole building.
the performance criteria have been achieved. Additionally, uncertainty is always present in any design or analysis.
Subsystem A subsystem performance evaluation typically consists of a simple comparative analysis in which the performance of a design that involves a single component or subsystem (e.g., egress, detection, suppression, fire resistance, etc.) is compared to the performance of a similar component or subsystem. This type of analysis is frequently employed when using the equivalency provision in a prescriptive code. For an alternate design strategy to be acceptable, it must provide equal or greater performance than that which is required by the code or standard.
Following completion of the evaluation and selection of the final design, thorough documentation of the design process should be prepared. This documentation serves three primary purposes: (1) to present the design and underlying analysis such that it can be reviewed and understood by project stakeholders, such as regulatory officials; (2) to communicate the design to the tradespeople who will implement it; and (3) to serve as a record of the design in the event that it is modified in the future or if forensic analysis is required following a fire. The SFPE Engineering Guide to Performance-Based Fire Protection provides detailed descriptions of the types of documentation that should be prepared by the design team. This material includes the documentation associated with the fire protection engineering design brief (discussed previously), a performance-based design report, specifications and drawings, and operations and maintenance manuals. The guide suggests that a detailed performance-based design report should be prepared that describes the quantitative portions of the design and evaluation. Every model or calculation method that was used should be identified, including the basis for selection of the model or calculation method. Similarly, any input data for the model or calculation method should be documented, including the source of the input data and the rationale of why the data are appropriate for the situation being modeled. All fire protection analyses have some uncertainty associated with them. This uncertainty may come from limited ranges of applicability of a model or simplifications within models or calculation methods, applicability of data sources to the scenarios modeled, limitations of scientific understanding, or other sources. The design should include methods of compensating
System A system performance evaluation might consist of a comparison to prescriptive requirements or an analysis based on specific performance requirements. A system performance evaluation is used when more than one fire protection system or feature is involved. It is more complex than a subsystem evaluation because the analysis must account for the interaction between various subsystems. Whole Building In a building performance analysis, all subsystems used in the protection strategy and their interactions are considered. A performance-based design that analyzes total building fire safety can provide more comprehensive solutions than subsystem or system performance analysis because the entire building-firetarget (where “targets” are the items being protected, such as people, property, etc.) interaction is evaluated. The “levels of performance” describe the complexity of a design, whereas the types of performance identified by Nelson [2] in the Introduction describe approaches that a code or standard could use to state desired fire performance. Typically, engineering tools such as fire models will be used to evaluate trial designs. The tools that are selected must provide information that can be used to determine whether or not
Documenting the Design Process
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for this uncertainty, and how this was accomplished should be documented. As with prescriptive designs, performancebased designs use specifications and drawings to communicate to tradespeople how to implement the design. However, master specifications may not be applicable to performance-based designs without significant editing. Similarly, any features of a design that differ from typical prescriptive designs should be clearly identified on drawings. One feature of documentation of performancebased designs that differs significantly from prescriptive-based designs is the operations and maintenance manual. The operations and maintenance manual communicates to facility managers the limitations that are placed on the design. These limitations stem from decisions made during the design process. For example, heat release rates used as input data place a limitation on the use of a space. Any furnishings placed within a space that could have higher heat release rates than the heat release rates used during fire modeling could result in greater consequences than the model predicted. The operations and maintenance manual should be written in a format that can be easily understood by people who are not fire safety professionals, since most building owners and facility managers will not have this type of background.
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As an example, the requirements for atrium smoke control systems in prescriptive codes are typically performance based.
Use with Prescriptive-Based Regulations Prescriptive-based regulations provide requirements for broad classifications of buildings. These requirements are generally stated in terms of fixed values, such as maximum travel distances, minimum ratings of boundaries, and minimum features of required systems (e.g., detection, alarm, suppression, and ventilation). In addition, most prescriptive-based regulations contain a clause that permits the use of alternative means to meet the intent of the prescribed provisions. This provides an opportunity for a performance-based design approach. Through performance-based design, it can be demonstrated whether or not a design is satisfactory and complies with the implicit or explicit intent of the applicable regulation. When applying performance-based design in this manner, the scope of the design is equivalency with the prescriptive provision(s) for which equivalency is sought. The “intent,” or performance achieved by compliance with the prescriptive code provision(s), is identified to provide the goals and objectives for the design.
Application of Performance-Based Design
Use with Performance-Based Regulations
Performance-based design can be applied in one of three situations: with prescriptive regulations, with performance-based regulations, and as a stand-alone design methodology [1]. It is noteworthy that many codes are not wholly performance based or prescriptive; many codes contain a mixture of performance-based and prescriptive requirements. For example, a performance-based code may contain a “deemed to satisfy” prescriptive option. Similarly, a prescriptive code may contain some performance-based requirements.
Performance-based codes and standards provide goals, objectives, and performance criteria for buildings or other structures that fall within the scope of the code or standard. Performancebased codes generally either provide specific fire scenarios that must be addressed or information that is intended to identify the types of fire scenarios that must be addressed. Performancebased codes may also provide additional administrative provisions, such as review or documentation requirements.
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Use as a Stand-Alone Methodology In some cases, a building owner or insurer may have additional fire safety goals beyond the minimum requirements of applicable prescriptive codes and standards. In these cases, additional or complementary fire safety goals and objectives might be identified, thus requiring additional fire protection engineering analysis and design. For example, property protection and continuity of operations might be goals of a building owner or insurer, and these goals might not be fully addressed in applicable regulations. The performance-based design process can be used to identify and address these additional goals.
Hazard Versus Risk In performance-based design, all scenarios must be considered in some manner. There are two ways that can be used to consider the universe of possible scenarios: risk based and deterministic.
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any scenario that is expected to occur more frequently than a threshold frequency would be analyzed. If the probability of system failure is found to be below the established threshold, this scenario would not be addressed and it would be concluded the system being considered could be used without redundancy. Conversely, if the probability of system failure is found to be above the established threshold, then the scenario in which the system fails would be analyzed, and it would likely be concluded that both must be installed. Deterministic analysis does not provide a complete evaluation of the fire safety in buildings. Although the probabilities of failure were considered, and the consequences determined by evaluation, probabilities and consequences were considered separately on a pass/fail basis. Risk assessments differ from traditional, hazard-based assessments in that frequencies or probabilities of fires and the reliability of fire protection systems are explicitly addressed and used to weight the expected consequences. Hazard-based assessments evaluate the consequences given a set of conditions (e.g., a fire starts and sprinklers activate).
Risk-Based and Deterministic Analyses Event Trees Risk-based analysis looks at the big picture of all of the possible scenarios—the consequences of each scenario are analyzed; however, these consequences are weighted by the probability of the event occurring. If the sum of the products of the probability of the scenarios occurring and the consequences of the scenarios (e.g., value of property lost, deaths or injuries, length of business interruption, etc.) are below some threshold value, then the design is considered acceptable. In deterministic analysis, scenarios that are expected to occur with a frequency above a threshold value are analyzed to determine their consequences. If the consequences of those scenarios are within the design objectives, then the design is considered to be acceptable. Although deterministic analyses are typically used in performance-based fire protection, it may be difficult to use deterministic analysis to judge the superiority of one type of system against another, particularly when the systems protect against fires differently. In deterministic analysis,
Event trees can be used to illustrate the possible courses of action of a fire following ignition. An event tree is a graphical means of identifying all possible outcomes following an initiating event [12]. Event trees are often used to analyze complex situations with several possible scenarios or where several fire or life safety systems are in place or are being considered [13]. Event trees are constructed by identifying an initiation event (the start of a fire) and branching out with the subsequent events that could occur. Possible successes and failures following an initiating event are identified on branches of an event tree. The branches follow a temporal sequence, based on which items would be expected to occur soonest following the fire start. For an event tree to be complete, all possible events should be identified. Figure 37.3 shows an example of an event tree for the possible course of action for a fire that starts in a room [14].
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Occupant successfully extinguishes fire
Smoke detector Ignition activates
t=0
t=t1; fire develops to a stage where smoke is detected
Fire Sprinkler compartment successfully barrier contains suppresses fire fire
t=t2; t2>t1; t=t3; t3>t2; fire assuming occupant may develop to needs to be alerted a higher heat by the detector release rate if prior to fighting not extinguished by the occupant the fire
Yes
P(a)
P(c) No 1-P(b)
Consequence
t=t4; t4>t3; fire may develop toward flashover if not suppressed by sprinklers P(a)P(b)
Fire extinguished: low fatality/injury expected
P(a)[1-P(b)]P(c)
Consequence determined by simulations
Yes P(d)
P(a)[1-P(b)][1-P(c)]P(d)
Consequence determined by simulations
No
P(a)[1-P(b)][1-P(c)][1-P(d)]
Consequence determined by simulations
[1-P(a)]P(b*)
Fire extinguished; low fatality/injury expected
[1-P(a)][1-P(b*)]P(c)
Consequence determined by simulations
Yes P(d)
[1-P(a)][1-P(b*)][1-P(c)]P(d)
Consequence determined by simulations
No 1-P(d)
[1-P(a)][1-P(b*)][1-P(c)][1-P(d)]
Consequence determined by simulations
Yes P(b) Yes
Scenario probability
No 1-P(c) 1-P(d) Yes P(b*) Yes P(c)
No 1-P(a) No 1-P(b*)
No 1-P(c)
Fig. 37.3 Example of an event tree [14]
Following the ignition event in Fig. 37.3, the smoke detector that protects the room could either activate or not activate. Similarly, the room occupant could either successfully extinguish the fire or not. If the occupant does not extinguish the fire, the sprinkler that is installed in the room could either control the fire or not. Finally, if the sprinkler is not successful, the room compartmentation could either contain the fire or the fire could spread beyond the room of origin. Detector operation, occupant extinguishment, sprinkler activation, and barrier containment are all subsequent events that could occur (or not occur) following the initial fire initiation event. From the single ignition event in the room, there are eight possible scenarios that could result. Each scenario occurs with a different probability that can be determined by multiplying the probabilities along each branch of the tree leading to an outcome. If the probabilities of the mitigation strategies being successful are high, then the overall probability that the fire will not be controlled or contained within the room of origin is low.
There would likely be a number of event trees that could be prepared for the room shown in Fig. 37.3. Figure 37.3 illustrates the possible scenarios that could occur following a specific ignition event, for example, a carelessly discarded cigarette. There are likely many other ignition events that could occur in this room, and each would have its own event tree associated with it. In some cases, the event tree for other ignition events might be identical or similar to Fig. 37.3. Identical would mean that the same possible subsequent events could occur with the same probabilities. Similar would mean that the same subsequent events could occur, but with different probabilities. However, for other ignition scenarios, the event trees might be much different. If Fig. 37.3 illustrates the possible scenarios that could occur if smoking materials are carelessly discarded in a wastebasket, then other fire initiation events that start in the wastebasket might have similar or identical event trees. However, if the fire ignition event is a Christmas tree fire, then the event tree for this event would likely be much different—the occupant might
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not be capable of extinguishing the fire, and the probability of success of the other mitigation methods would likely be different. Additionally, the room in Fig. 37.3 would likely be located within a larger building, meaning that the event tree could be expanded to include other events that could occur if the fire is not contained within the room of origin. Event trees might be prepared to evaluate different fire protection strategies. If so, one or more event trees could be developed for each strategy. Each scenario that is a terminus on the righthand side of an event tree represents a series of events that could occur. Each series of events occurs with a different probability, and the probabilities of some scenarios occurring are higher than others.
Model Use in Performance-Based Design Fire models take a variety of forms. The simplest are algebraic models, which are mathematical equations used to estimate the value of one or more variables as a function of space and/or time. More complex are zone or lumped parameter models, which simplify the behavior of a system by making the approximation that a particular volume or region is homogeneous, uniform, or well-mixed. The most complex are computational fluid dynamics (CFD) models, which are also known as field models. CFD models provide a method for calculating the fluid flow through a volume using numerical solutions of the governing equations for conservation of total mass, chemical species, momentum and energy. The use of fire models has flourished over the last few decades. Models are used to simulate fire phenomena to determine if a proposed design strategy is acceptable, to test hypotheses developed during fire investigations, or to simulate tests as part of fire research. Each of these applications has potential impacts on public health, safety or welfare, so it is incumbent on model users to make sure that they can have confidence in model results. The American Society of Testing and Materials (ASTM) published a guide for evaluating fire models in 1990. The Guide is identified as ASTM E-1355. These guidelines
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provide an approach to evaluating models that consists of defining the model and the scenarios for the evaluation, verification of the appropriateness and the theoretical basis of the model, verifying the mathematical and numerical robustness of the model, and quantifying the uncertainty and accuracy of model results. The ASTM guidelines are useful where someone wishes to evaluate a model for a broad range of applications. However, the methodology requires a level of effort that is prohibitive for specific, individual project applications. For example, the Society of Fire Protection Engineers evaluated DETACT-QS using the ASTM E-1355 methodology. DETACT-QS is one of the simplest fire models that have been published (it has under 200 lines of code); the evaluation required over a person-year of effort, and the report is 140 pages in length. The standard of care that is applied to the use of model predictions is that the model should either be accepted by the relevant professional community or the user should demonstrate that the model is acceptable. Only a few models have been formally evaluated using the ASTM E-1355 process—including DETACT-QS and five models that were evaluated for application in nuclear power plants [15] (Fire Dynamics Tools, Fire Induced Vulnerability Evaluation, CFAST, MAGIC and FDS.) In 2003, 168 fire models were identified [16], and several more have been published since then. Additionally, the published evaluations do not address every possible application of the models that were evaluated, so in most cases it will fall to the person who uses a model to show that the model is appropriate for the intended use. In 2011, the Society of Fire Protection Engineers published the Guide to Substantiating a Fire Model for a Given Application to provide a framework for determining if a fire model is suitable for use for a specific fire protection application. The Guide to Substantiating a Fire Model for a Given Application provides a five step process for determining the suitability of a fire model. These steps include defining the problem, selecting a candidate model, verifying and validating the model, determining the impact of uncertainty and user effects on the model results,
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Fig. 37.4 Fire model selection flow chart
Start
Define Problem
Perform Analysis
Select Candidate Model
Determine Uncertainty & User Effects
Y N Can Problem Be Redefined?
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N
Candidate Exist?
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Using Computer Model Will Require Model Development
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Confirm Basis for Selection
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Analysis Suitable?
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and finally, documenting of the model evaluation. This process is illustrated in Fig. 37.4. Any of these steps may require repetition. If a candidate model is determined to be unsuitable, then another candidate may be selected for evaluation. If no suitable candidate models exist for a given application, then there are several options. These options include: 1. Reevaluate the application to determine if the problem being solved can be reposed to allow the use of another model. 2. Develop, verify, and validate either a new model or a modified version of an existing model. 3. Use an alternate method that does not use a fire model—such as fire testing.
Definition of the Problem of Interest The first step described in the Guide to Substantiating a Fire Model for a Given Application is to define the problem of interest. The problem of interest should be clearly defined by identifying the relevant phenomena and key
physics, collecting available information and determining the analysis objectives. Commonly encountered key physics in fire modeling generally relate to thermodynamics, fluid dynamics, heat transfer, combustion, or material response. Identification of relevant phenomena and key physics requires knowledge of the details of the problem of interest as well as the underlying chemical and physical processes involved. The appropriate level of knowledge is required to prevent users from treating a fire model as a black-box tool, which can result in using a fire model beyond the scope of its capability. Defining the problem of interest encompasses several elements. First, the geometry needs to be established. The geometry includes the spatial domain and the objects involved within the spatial domain. For a room or a facility such as a warehouse or office building, the spatial domain is often defined by the physical boundaries like walls, ceilings and floors. For open domain problems, e.g. outdoor pool fires of flammable liquids, a sufficiently large domain should be selected to avoid significant impact along the
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boundaries. Detailed geometries should be provided for fuels, building structures, protection devices and other important objects in the spatial domain; however, some specific details may depend upon the type of model utilized. Next, Guide to Substantiating a Fire Model for a Given Application recommends establishing a timeline. The timeline for the problem of interest includes the duration of the problem and the sequence of events. The problem of interest can be either transient, steadystate, or at a specific point along the timeline. Events should be included in the information collection process unless they are deemed unimportant to the problem of interest. Examples of events are ignition, closing or opening of doors and windows, actuation of sprinklers or smoke exhaust fans, and collapse of furniture and building structures. Some events will occur at specific points on the timeline, while others will be modeled. A list of materials relevant to the problem of interest should be generated and relevant material properties should be assigned to each material. The incorporation of specific material properties may depend upon the type of model used in the analysis. The most important properties for most fire problems are often whether the material is combustible and the products of combustion. Other relevant material properties may include, but are not limited to, viscosity, specific heat, heat of combustion, thermal conductivity, heat of gasification and heat of vaporization. The initial and boundary conditions should be established. This type of information is often needed to start numerical simulations in time and space, respectively. Examples of initial conditions are room temperature and door and window status, while examples for boundary conditions are openings that allow free air passage or an air conditioner on the ceiling blowing at an established flow rate. Lastly, the analysis objectives should be established. Analysis objectives define what the modeler hopes to achieve by using the fire model. The most important objective related to the use of a fire model is a list of quantities that should be determined to address the problem of interest.
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Select a Candidate Model The next step identified in the Guide to Substantiating a Fire Model for a Given Application is to select a candidate model. A wide variety of models are available for predicting a range of fire phenomena. A number of factors should be considered before selecting a particular model for a problem, including computational resources, time limitations, required level of accuracy, and most importantly, whether or not the governing equations and assumptions in the model are appropriate for the problem of interest. The guide recommends three major considerations for selecting a candidate model: determining the available model inputs, identifying the desired model outputs, and determining the available resources. Determining the available model inputs requires the model user to identify the inputs that are available for a given problem and to identify the inputs that are not available but must be acquired before proceeding with an analysis. To perform this analysis of available data, it is often helpful to list each relevant input, along with its value (or range of values) and an indication of any uncertainty that may be involved in the measurement of that input value. In addition to the known input variables, there may be unknown inputs that can be estimated through use of past research or engineering judgment; these inputs should also be listed, along with appropriate references or assumptions that were used to obtain a value. In some cases, not all of the input data required by a model will be available. In such cases, the guide recommends three possible options: • Perform preliminary calculations aimed at identifying the value of that specific variable. • Make a reasonable assumption as to the range of values that the input could have and then perform a sensitivity analysis to determine the effect on the model results of changing that variable. • Conduct experiments to obtain a value for the input.
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After analyzing the available model inputs, but before proceeding with the selection of a fire model, it is important to define the accuracy that is required in the final model output. The acceptable level of resolution of the model output values will vary depending on the problem. It is up to the user of the fire model to determine how much detail is required to appropriately address a problem and to convey this decision to those who will review or make use of the results of the simulations. When evaluating potential candidate fire models, some consideration should be given to the sensitivity of the desired output values to both the available input variables and to the type of model that is chosen. While this is not always a formal process, it is something that should be taken into account. There is often more than one model available that may provide a sufficiently accurate solution to a problem. In such cases, model selection can be based upon the resources that are available to run the model. While a CFD model may provide benefits, such as the ability to more exactly represent the geometry of a space and better visualization tools than a zone model, it may not always provide a more accurate solution to a problem. If time constraints and lack of computer resources prohibit a thorough sensitivity analysis using CFD, then for some problems it might be more appropriate to use a zone model or algebraic model in order to more thoroughly address uncertainty. The guide suggests developing a resourcing plan that follows the following steps before starting large fire modeling projects: 1. Determine the number of simulations needed to address any sources of uncertainty. 2. Determine the amount of time required to run a simulation on the available computational resources. 3. Determine whether or not several simulations can be run simultaneously. 4. Determine the available time before the project must be completed. After following the steps noted above, the user should make a decision as to whether a candidate model is appropriate for the given
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problem. The modeler might select an algebraic model, a zone or lumped parameter model, or a computational fluid dynamics model.
Verification and Validation Prior to using a model for a particular problem, the model user needs to determine if the model is capable of generating a useful result. The formal process by which this is demonstrated is verification and validation (V&V). Model verification serves two purposes. First, it ensures that the mathematical equations have been properly implemented. Second, it ensures that the model user understands the assumptions of the model. Verification ensures that the model is working as designed, i.e., that the equations are being properly solved. It essentially is a check of the mathematics. The Guide to Substantiating a Fire Model for a Given Application suggests that, at a minimum, model users should read the model documentation that describes efforts made by the developers to verify the model. Then, the user should supplement the work performed by the developers to better address the specific application under consideration. The guide suggests a number of exercises that the model user can perform to supplement the verification efforts of the developers: • Verify the basic functionality of the model— This typically involves creating simple test cases and comparing the model results to known analytical solutions. • Verify consistency of input parameters—The user should address the appropriateness of input values, especially as they are used collectively. • Verify that the input parameters are appropriately used—This generally involves studying the model documentation and diagnostic output. • Verify the range of validity for input parameter values—Some values of the input parameters are only valid within a certain range. The model user should confirm that the input values are consistent with the underlying physical assumptions or experimental conditions.
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• Verify consistency of results—In short, this involves demonstrating that the results make sense. Verification ensures that the model is working as designed; that the equations are being properly solved. It essentially is a check of the mathematics. Validation is a check of the physics, i.e., whether the equations are an appropriate description of the fire scenario. Most often, validation takes the form of comparisons with experimental test data. Validation does not mean that a model makes perfect predictions, only that the predictions are good enough for its intended use. The meaning of “good enough” is up to the model user, and to say a model has been validated only means that an end user has decided that the model is sufficiently accurate for a particular application. The Guide to Substantiating a Fire Model for a Given Application suggests the following procedure for validating a model for a given application:
Select Experiments The guide provides the following considerations for selecting experiments that will be used as the basis for model validation: • Relevance to the application. The organizations that perform model validation usually have a particular application in mind, which limits the scope, scale and measurements. • Comprehensive documentation. The experimental results should be available and fully documented, or not needed, otherwise implies or interested modelers cannot replicate what was done in the validation study or attempt to do their own validation study. • Experimental uncertainty. There are two major forms of experimental uncertainty to consider in a validation study. The most obvious is the measurement uncertainty. This is the uncertainty of the measurement of the quantity under consideration. The second form of uncertainty is the model uncertainty, which reflects the uncertainty in the model predictions that are due to the uncertainty of
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the physical parameters that are input into the model. The uncertainty in the input parameters needs to be propagated through the model to ascertain its impact on the final prediction.
Choose a Metric to Quantify Accuracy Measurements can vary in space and time. Comparisons with model predictions can be based on extreme values, like peak temperatures, or spatial or temporal averages. The decision to use a particular metric is made by the organization doing the validation study based on the particular use of the model. Usually, it is convenient to express these comparative values in terms of a relative difference. Report Results The Guide to Substantiating a Fire Model for a Given Application recommends that the validation report provide sufficient detail about the experiments and the model inputs such that an interested reader could repeat the calculations. Specifically, the guide recommends providing the following information: • Person or organization responsible for the validation study • References to model documentation and reports of experimental measurements • Description of the fire scenarios that the experiments were designed to address • Quantification of the model accuracy • Conclusion, including limitations of the model and its potential for extension for other fire scenarios Typically, model validation involves a large amount of data—both in terms of model predictions and experimental measurements— and it can be difficult to succinctly display the results of the study. If all the experimental measurements can be quantified by the same total uncertainty, then a simple graph can be made to summarize the validation exercise. The graphs can indicate the experimental uncertainty in the experimental data. If the model predictions lie within the band defined by the experimental uncertainty, then it cannot be said that the model
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predictions differ significantly from the measured data. If the model predictions lie outside the uncertainty interval, this does not necessarily mean that the model is unsuitable. In such cases, the trend in the model’s predictive ability needs to be evaluated in the context of the intended use.
User Effects Once the verification and validation have been conducted, the next step identified in the Guide to Substantiating a Fire Model for a Given Application is to focus on the uncertainty that arises in model predictions due to the use of a predictive model. Possible sources of uncertainty include definition of the model space or computational domain, simplifying assumptions (in the application of the model), and the choice of input parameters. The result is a propagation of “error” or uncertainty through the model that should be understood, at minimum, at a qualitative level, but preferably, quantitatively.
Input Uncertainty In addition to uncertainty that exists within the model, the input data can introduce uncertainty into the model calculation. Predictive models require a description of the model space, often a simplified representation of the actual physical space. The choice of the model extents is a function of the model type and the available computational resources. Choice of the model domain and how boundary conditions—the physical conditions at the model boundaries—are defined can impact the analysis outcome. The resolution of the model can also affect the analysis outcome. The analysis outcome should be independent of the definition of the domain or the grid resolution. Input data, often based on assumed values or experimental data, is subject to many sources of uncertainty, including uncertainty in theory (for deriving the parameter) and measurement. Such uncertainty in input imposes a limit on the
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confidence in model output. It is important to understand the limitations of the input values and of the means by which they were derived in order to quantify or estimate the uncertainty or possible range of the property value. Variation in one or a combination of input parameters may substantially alter the model outcome. Treatment of uncertainty in the assumptions and input that define a problem is an important component of analysis that the modeler should address.
Implications for the Design Process The Guide to Substantiating a Fire Model for a Given Application suggests several methods of dealing with uncertainty introduced through the use of models. • Performance Criteria. Fire models are often used as part of a design process in which the results are evaluated against threshold performance criteria. The conclusions that may be drawn from an analysis are limited by the predictive accuracy of the model as well as the potential uncertainty in the input parameters. Performance criteria thresholds should account for limitations in the models and input. • Safety Factors. Safety factors and margins of safety are used to provide a buffer to allow for uncertainty in the design process. A safety factor is a multiplier of a prediction for reference against a threshold or criterion. Safety margins are additive, not multiplicative. • Sensitivity Analysis. A sensitivity analysis determines the relationships between the uncertainty in the input variables and the uncertainty in the resultant output. A sensitivity analysis provides information regarding how the uncertainty in the output of a model can be apportioned to different sources of variation in the input of a model. Sensitivity analysis allows the identification of those parameters that are most important to the outcome. It does not necessarily provide information regarding the value that should be used, but it can show the impact of using different values.
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• Parametric Analysis. In a parametric analysis, a special form of a sensitivity analysis, detailed information of the effect of a certain input variable on model output is examined by systematically varying the input value of that variable, while holding others constant. A parametric analysis may be useful if detailed information regarding the potential variation of the input variable is unknown. • Bounding. Bounding is a form of sensitivity study that evaluates the consequences of the extremes of possible values of an uncertain input quantity. If the outcome values at both extreme ends of the range of the uncertain input are acceptable relative to some criteria, further sensitivity analysis may be avoided. Bounding can be applied to not only input parameters but also selections for boundary conditions. • Differential Analysis. For some models or systems, it is possible to solve directly for the partial derivative of the predicted values with respect to each of the input variables. The set of partial derivatives measures the sensitivity of the solution with respect to changes in the input parameters. A differential analysis has the advantages of being very quick and requiring very few resources to implement. • Power Dependence. Less formal than differential analysis, power dependence assesses the proportionality or power-dependence of a model target output to an input parameter. By examining the relationship of model outcome to input, the user will be able to identify the relative importance of the input. As a result, the user may be able to focus on refining the estimate for a “more” important input variable, while accepting perhaps a higher variability in a “less” important variable.
Documentation Finally, the results of the evaluation should be documented so that they can be understood by people who wish to understand how it was
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determined that the model is appropriate for its intended use.
SFPE Handbook Use in the Step-byStep Process of Performance-Based Design Publication of the first edition of the SFPE Handbook of Fire Protection Engineering in 1988 was one of the key events that supported the development of performance-based fire protection designs. Earlier in this chapter, the following steps in the performance-based design process as outlined in the SFPE Engineering Guide to Performance-Based Fire Protection were identified: Step 1—Defining project scope Step 2—Identifying goals Step 3—Defining objectives Step 4—Developing performance criteria Step 5—Developing fire scenarios Step 6—Developing trial designs Step 7—Quantifying design fire curves Step 8—Evaluating trial designs Step 9—Documenting design process Chapters within this edition of the SFPE Handbook of Fire Protection Engineering can be used to support design development and evaluation. This section identifies typical applications of the information contained in the SFPE Handbook of Fire Protection Engineering in the performance-based design process. Step 1—Defining Project Scope The project scope is generally defined as part of discussions between the engineer and the project stakeholders. One of the aspects that is determined to be part of the project scope is how the analysis will be conducted. Chapter 72 provides an overview of fire risk analysis that can be referenced when determining if the project will be done on a deterministic or a risk basis and, if the project will be done on a risk basis, the techniques that will be used. Where risk assessments are to be used, Chap. 82 addresses fire risk index methods. Chapter 75 addresses the general subject of
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building fire risk analysis. Specific applications of fire risk assessment can be found in the following chapters: Chaps. 83, 89, 90, and 85. Step 2—Identifying Goals The project goals are generally stated by or inferred from applicable codes and standards or through discussions between the engineer and other stakeholders. Step 3—Defining Objectives Since they represent a refinement of the amount of loss that is tolerable, objectives are typically developed by the engineer through discussions with the project stakeholders. Step 4—Developing Performance Criteria Performance criteria are quantitative values that are used to determine whether or not a trial design achieves the project goals and objectives. Developing performance criteria requires understanding the mechanism(s) of harm of the items that the design will protect from fire. When people are to be protected from fire, performance criteria generally involve one or more of the following: • Prevention of incapacitation by fire or smoke • Prevention of thermal damage • Providing sufficient visibility such that people can navigate means of egress Chapter 63 provides information that can be used to set performance criteria associated with prevention of incapacitation by fire products. Additionally, Chap. 63, provides information that can be used to set performance criteria associated with thermal damage from heat exposure. Several researchers have published suggested maximum values of limiting extinction coefficients or optical densities that could be used as performance criteria associated with maintaining visibility. For more information, see the following chapters: Chaps. 24, 61, and 63. However, these limiting values have embedded within them desired minimum visibility distances, and hence, these values should only be used when the geometry of interest correlates with the minimum visibility distances embedded
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within the limiting extinction coefficients or optical densities. In some cases, avoidance of exposure to smoke altogether (either by keeping the smoke layer above a defined elevation or keeping smoke from entering a space) may be selected as a performance criterion. When things other than people are protected, performance criteria may take one or more of the following forms: • Prevention of ignition • Prevention or minimization of flame spread • Maintenance of fire barrier integrity or structural stability • Avoidance of nonthermal damage due to exposure to smoke Prevention of ignition of solid items is typically accomplished by keeping the incident radiant flux to a combustible object below a minimum value, typically the minimum heat 00 flux for ignition ( q_ min ) or the critical heat flux 00 for ignition ( q_ crit ), depending on how it is measured. In some cases, values might be expressed as the minimum temperature at ignition. Values for a variety of fuels can be found in Appendix 3. The mechanism of ignition of solid fuels is described in Chap. 21. For prevention of ignition of liquid fuels, performance criteria would typically involve keeping the liquid below its flashpoint. The flashpoint is not a fundamental material property and will vary depending on the test method used to measure it. More information and flashpoints for a variety of fuels can be found in Chap. 18. For gases, performance criteria generally relate to keeping a gas/air mixture outside of its flammable range, which is discussed in more detail in Chap. 17. This chapter on flammability limits also contains flammability data for several gases. Flame spread is a process of continuous ignition, as the flame front progresses from portions that are burning to unburned material. This is discussed in Chap. 23. Performance criteria related to maintenance of barrier integrity is generally limited to specific
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Fig. 37.5 Process for identifying design fire scenarios
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Possible fire scenarios
Design fire scenarios
Fire characteristics
Design fire curves
Building characteristics
Building characteristics
Occupant characteristics
Occupant characteristics
assemblies. Chapter 55 provides information for gypsum board on wood studs. Chapter 54 discusses concrete assemblies. In many cases, the methodologies in the chapters referenced are limited to the standard time-temperature exposure. Information related to structural integrity can also be found in Chap. 55, and Chap. 54, for wood and concrete structural materials, respectively. Steel assemblies are addressed in Chap. 53. Performance criteria associated with exposure of items to smoke can be developed using Chap. 36. Step 5—Developing Fire Scenarios A performance-based design requires the evaluation of fire safety based on various design fire scenarios. The SFPE Engineering Guide to Performance-Based Fire Protection provides a two-step process for identifying design fire scenarios. As depicted in Fig. 37.5, the first step is considering all possible fire scenarios that could occur in the building or portion of the building that is within the scope of the design. The second step is to reduce the population of possible fire scenarios into a manageable set of design fire scenarios. The design fire scenarios will be used to evaluate trial designs. Fire scenarios are comprised of three elements: building characteristics, occupant characteristics and fire characteristics. Building characteristics are determined either by surveying an existing building, reviewing architectural design plans, or as part of a trial design strategy. Chapter 38 discusses fire scenarios. Fire load is frequently considered as part of a fire
Evaluate trial designs
Develop trial designs
scenario, and this topic is addressed in Chap. 35. Chapter 57 provides information on occupant characteristics that can be used when developing fire scenarios. Step 6—Developing Trial Designs Several chapters in this Handbook relate to the design and evaluation of trial designs. When developing a trial design, an initial design is usually created. The initial design would be evaluated, and if it achieved the performance criteria when tested using the design fire scenarios, it would be considered acceptable. However, if the design did not achieve the performance criteria, it could either be eliminated or refined and revaluated. In this sense, the process of design development and evaluation can be iterative. Several chapters can be used in both the development and evaluation of trial designs. These chapters generally do not articulate what must be done for strictly code-compliant designs but rather provide methods and engineering calculations that can be used to support system designs. Chapter 39 provides a broad overview of the considerations involved with selecting a fire safety system as a trial design approach. System activation is addressed in Chap. 49. Chapter 40 provides calculation methods for the design of heat detection systems, smoke detection systems, and radiant energy detection systems. That chapter also provides methodologies for designing fire alarm audibility. Approaches for developing occupant egress strategies are presented in Chap. 56.
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For automatic sprinkler systems, Chap. 41, can be used to support the design of water supplies. Chapter 42 provides information relating to hydraulic calculations and also provides calculation methods relative to hanging and bracing and to sprinkler performance. Water mist systems, which are water-based systems that utilize very small droplets, are covered in Chap. 46. Foam systems are addressed in Chaps. 47 and 48. The former provides a basic description of foam agents and foam extinguishment. This chapter also discusses aviation fire protection considerations, foam water sprinkler systems, and environmental considerations associated with fire-fighting foams. Chapter 48, provides calculation methods associated with foam system design. Clean agents are addressed in Chaps. 43 and 44. Chapter 43 would generally be used in the evaluation or modification of existing halon systems, since they are rarely used in new construction. Chapter 44 provides an overview of the halon replacements that are available and information that can be used in the design of halon replacement systems. Chapter 36 also provides information associated with fire control, suppression, and extinguishment. Chapter 45 addresses carbon dioxide system design. Fundamental information relative to systems that employ fluids can be found in Chap. 1. Several chapters provide information that is generally used in fire resistance design. Fire resistance design is comprised of three steps: determination of the thermal boundary conditions to the structure or portion thereof, determination of the heating of the structure that results from the thermal boundary conditions, and determination of the structural response of the structure at elevated temperature. Chapter 53 provides an introduction to structural fire protection design. Chapter 30 provides methods for calculating the fire exposures that could be used in fire resistance design. These fire exposures form the thermal boundary conditions. Chapter 34 discusses heat transfer to the structure. Chapter 52 provides an overview of structural systems and frame effects. Chapters 53, 54,
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and 55 cover the design of fire resistance of steel members, concrete members, and timber members, respectively. Chapters 54 and 55 address fire barrier design to a limited extent for concrete and timberframed assemblies, respectively. Smoke control is addressed in two chapters. Chapter 50 provides an overview, methodologies, and calculation methods for smoke control systems. Chapter 51 focuses on smoke management systems in covered malls, atria, and other similar large spaces. Step 7—Quantifying Design Fire Curves The design fire curve consists of many elements, including ignition, fire growth, fully developed burning, and decay. For information on ignition, consult the SFPE Engineering Guide to Piloted Ignition of Solid Materials Under Radiant Exposure [17], Chaps. 18 and 21. There are a number of ways the fire curve can be produced, including testing (large and small scale) and correlations as well as analytical approaches. Information on flame spread and the effect on fire growth rates is provided in Chaps. 23 and 25. Chapter 65 provides information associated with liquid fuel fires. This chapter addresses determination of pool size, growth rate of pool fires, and fire size. In many evaluations, one of the most critical tasks is estimating the size or heat release rate of a fire. The heat release rate that is estimated affects several other calculations that are used in the evaluation. Chapter 26 provides methodologies for estimating heat release rates and a tremendous amount of heat release rate data for a variety of commodities. In some cases, heat release rate data from small-scale test methods will be used in estimations of heat release rates. Chapters 27 and 28 provide overviews of bench-scale methods. Compilations of fire data for many forms of fuel, including furniture and storage materials, can be found in Chaps. 26, 36, and 40. The information specifies material burning characteristics, fire growth curves, fire growth rates, and/or maximum heat release rates as well as other information that will assist in
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estimates of design fires. Chapter 65, can also be used to calculate fully developed fire sizes for pool fires. Fire is a dynamic phenomenon influenced by changes in air, fuel, and heat. Modification of any of these factors can increase or decrease the size of the fire. Chapter 16 discusses these effects. Step 8—Evaluating Trial Designs The evaluation of trial designs will usually involve performing fire dynamics calculations and hazard calculations. Several chapters address these types of calculations. Calculations involving fire plumes (temperature, velocity, and mass entrainment), flame heights, and ceiling jets are included in Chaps. 13 and 14. These types of calculations are typically used in the analysis of detection systems and smoke control systems. Chapter 15 addresses the flows through vents, where vents are any type of opening. These types of calculations are used in modeling the movement of smoke from or into enclosures, such as smoke flows through doorways. Chapter 61 addresses visibility and human behavior in smoke. The calculation methods in this chapter would be used in any design in which people movement through smoke is contemplated. Equations and graphs are provided for estimating the effect of smoke on visibility and on the reduction on movement speed that could occur in smoky environments. Chapter 58 provides an overview of behavioral response to fire and smoke. Chapters 64 and 59 provide methodologies and calculation methods for estimating evacuation times. Evacuation times consist of two components: the time for people to determine that there is a need to evacuate and the time necessary to move through building egress components. Evacuation models are addressed in Chap. 60. In cases in which people may be exposed to smoke, it may be necessary to estimate the concentrations of combustion products. Chapter 16 identifies means of performing these analyses, and Chap. 24 provides additional information. The impact of the combustion products on people can be determined using the
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methodologies in Chap. 63. The information in Chap. 16, and in Chap. 24, is also useful in cases in which it is desired to consider the effect of constituents as part of a smoke detection analysis. If an analysis involved determining whether or not an item will ignite, Chap. 17, 18, and 21, provide methods of determining if and when gases, liquids, and solids will ignite, respectively. Spontaneous combustion (self-heating that leads to combustion) is discussed in Chap. 20. Chapter 19 covers smoldering combustion, including propagation of smolder through media and transition from smoldering combustion to flaming combustion. Chapter 23 addresses the spread of flaming combustion along the surface of solids and liquids. The heat flux from local fires can be determined using Chap. 25. This type of analysis is typically performed in determinations of the heat flux from a local fire to part of a structure or to a fire barrier. This type of analysis could also be performed in calculations involving the ignition of items from exposure to a localized fire. Chapter 66 presents methods of performing hazard calculations associated with large hydrocarbon pool fires. Fire modeling is frequently used in the evaluation of trial designs. Chapter 36 and Appendix 3 provide a tremendous amount of data that can be used in fire modeling. Chapter 29 provides an overview of compartment fire modeling techniques. Chapter 30 provides closed-form equations that can be used for estimating compartment fire temperatures. Chapter 31 provides a discussion of zone modeling, and Chap. 32, addresses CFD, or field models. Smoke filling of enclosures is discussed in Chap. 33, these types of calculations are frequently employed in cases where it is desired to keep a smoke layer above a critical elevation. A broad overview of computer modeling can also be found in Chap. 80. For designs in which protection from explosions is an objective (either prevention, suppression, or response), Chaps. 69 and 70, provide methods and data that can be used.
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Once the engineering calculations have been completed, a decision must be made as to whether or not a design is acceptable. For most cases, acceptability will be judged by seeing if the results of the analyses do not exceed the performance criteria. Chapter 77 provides information where more complex decision analysis is needed. Most fire protection strategies used will have a reliability that is less than 100 %, and the effects of imperfect reliability should be addressed. Chapter 74 addresses the subject of reliability. Uncertainty will be introduced in many of the steps of the process. Chapter 76 provides several uncertainty analysis techniques. Almost all analyses will require data of some sort as input into calculations or models. In some cases, the needed data will be readily available. However, in others, it will be difficult to find. Chapter 78 provides an overview of data types, sources, and issues associated with data. In some cases, it will be desirable to measure all fire consequences using a single metric. Chapter 79 discusses measuring fire consequences in economic terms. Engineering economics, which are frequently considered in design decisions, are summarized in Chap. 81. Step 9—Documenting Design Process All aspects of the design are generally documented. Documentation is provided as a way for stakeholders, regulatory officials, and tradespeople to review, understand, and be able to implement the design. Documentation also serves as a record in case modification or analysis following a fire is required in the future.
Summary Performance-based design, while drawing increased attention recently, has been evolving over the last several decades. The SFPE Engineering Guide to Performance-Based Fire
M.J. Hurley and E.R. Rosenbaum
Protection [1] provides a process for conducting performance-based designs. Information in the SFPE Handbook of Fire Protection Engineering can be used to support engineering designs and calculations associated with developing and evaluating performance-based designs.
References 1. SFPE Engineering Guide to Performance-Based Fire Protection, National Fire Protection Association, Quincy, MA (2006). 2. H. Nelson, “Performance-Based Fire Safety,” in Proceedings: 1996 International Conference on Performance-Based Codes and Fire Safety Design Methods, Society of Fire Protection Engineers, Bethesda, MD (1996). 3. ASCE/SFPE 29-05, Standard Calculation Methods for Structural Fire Protection, American Society of Civil Engineers, Reston, VA (2005). 4. NFPA 101®, Life Safety Code®, National Fire Protection Association, Quincy, MA (2012). 5. R. Custer and B. Meacham, Introduction to Performance-Based Fire Safety, National Fire Protection Association, Quincy, MA (1997). 6. NFPA 5000®, Building Construction and Safety Code®, National Fire Protection Association, Quincy, MA (2012). 7. ICC Performance Code® for Buildings and Facilities, International Code Council, Falls Church, VA (2012). 8. Engineering Guide—Fire Risk Assessment, Society of Fire Protection Engineers, Bethesda, MD (2006). 9. Verification Method: Framework for Fire Safety Design Fire New Zealand Building Code Clauses C1-C6 Protection from Fire, Department of Building and Housing, Wellington, New Zealand, 2012. 10. NFPA 550, Guide to the Fire Safety Concepts Tree, National Fire Protection Association, Quincy, MA (2012). 11. Engineering Guide—Human Behavior in Fire, Society of Fire Protection Engineers, Bethesda, MD (2003). 12. J. Watts and J. Hall, “Introduction to Fire Risk Analysis,” SFPE Handbook of Fire Protection Engineering, Springer, New York (2015). 13. B. Meacham, “Building Fire Risk Analysis,” SFPE Handbook of Fire Protection Engineering, Springer, New York (2015). 14. M. Hui, “How Can a Fire Risk Approach Be Applied to Develop a Balanced Fire Protection Strategy,” Fire Protection Engineering, 30, pp. 12–21 (Spring 2006).
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15. NUREG-1824 and EPRI 1011999, “Verification and Validation of Selected Fire Models for Nuclear Power Plant Applications,” Vols. 1-7, U.S. Nuclear Regulatory Commission, Washington, DC and Electric Power Research Institute, Palo Alto, CA, 2007. 16. Olenick, S., and Carpenter, D., “An Updated International Survey of Computer Models for Fire and Smoke,” Journal of Fire Protection Engineering, 13 (2), 2003, p. 87–110. 17. Engineering Guide—Piloted Ignition of Solid Materials Under Radiant Exposure, Society of Fire Protection Engineers, Bethesda, MD (2002).
1261 Morgan J. Hurley is a project director with Aon Fire Protection Engineering. He is also adjunct faculty at the University of Maryland and California Polytechnic University. He holds bachelor’s and master’s degrees in fire protection engineering from the University of Maryland and is a licensed professional engineer. Eric R. Rosenbaum is the director of architectural and engineering services for JENSEN HUGHES, Inc. Mr. Rosenbaum is the chair of the Society of Fire Protection Engineers Task Group on Performance-Based Analysis and Design.
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Fire Scenarios George V. Hadjisophocleous and Jim R. Mehaffey
Introduction The engineering approach to fire safety design requires the selection and evaluation of fire scenarios that may occur in a building. Each fire scenario represents a unique combination of events and circumstances that influence the outcome of a fire in a building, including the impact of fire safety measures. The SFPE Engineering Guide to Performance-Based Fire Protection [1] refers to fire scenarios as “a set of conditions that defines the development of fire and the spread of combustion products throughout a building or part of a building.” It is obvious that the total number of fire scenarios that may occur in a building can be very large; hence it is not possible to analyze each scenario separately. To reduce the number of scenarios to a manageable number, it is necessary to follow a scenario identification and selection process in a systematic fashion to ensure that the outcome of the engineering analysis is credible and acceptable to all stakeholders. The scenario identification and selection process can be performed by considering both the expected frequency of occurrence of each scenario and its expected consequences. This must be done so that the selected fire scenarios yield a fire
G.V. Hadjisophocleous (*) Carlton University J.R. Mehaffey CHM Fire Consultants
protection design that provides acceptable levels of safety for the building occupants and property. The SFPE Engineering Guide [1], the International Fire Engineering Guidelines [2], and other publications that provide guidance on the design process clearly indicate that the task of identifying and selecting fire scenarios is an integral part of the design process. Figure 38.1 is a section of the performance-based design process described in the SFPE Engineering Guide. The figure shows that developing fire scenarios follows the tasks of defining the project scope, goals, and objectives, and developing performance criteria. Project scope, goals, and objectives inform the scenario identification and selection process. The project scope identifies whether the design is for a new building or an existing building, specific building components for the whole or part of a building, or repairs to the whole or part of a building. The fundamental fire safety goals for a building can be to • Provide life safety for building occupants and emergency responders • Protect property • Provide for continuity of operations • Limit the environmental impact of the fire • Protect the heritage and cultural value of the property. Although the fire safety goals are expressed in general terms, the fire safety objectives delineate more specific ways of attaining these goals. Quantifiable performance criteria can then be chosen to provide the basis for assessing whether fire protection designs achieve these objectives.
M.J. Hurley (ed.), SFPE Handbook of Fire Protection Engineering, DOI 10.1007/978-1-4939-2565-0_38, # Society of Fire Protection Engineers 2016
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Define project scope
Identify goals
Define objectives
Develop performance criteria
Develop fire scenarios
To ensure that the design will satisfy the above goals/objectives, the selected fire scenarios should be such that they challenge the proposed fire protection designs. Details on these steps can be found in the SFPE Engineering Guide [1]. A useful approach to the process of identifying and selecting fire scenarios has been developed by the International Organization for Standardization (ISO) [3], and it is summarized in Table 38.1.
Development of Fire Scenarios Before one can identify potential fire scenarios, a significant amount of information about the project must be assembled. The types of information that may be required are described in this chapter.
Develop trial designs
Building Characteristics Evaluate trial designs
Fig. 38.1 Performance-based design process [1]
Building characteristics need to be well documented, as they have a profound impact on potential fire scenarios. The physical layout of
Table 38.1 Steps used for identifying and selecting fire scenarios Steps of ISO/TS 16733 1. Location of fire
Comments Characterize the space in which fire begins as well as the specific location within the space 2. Type of fire Characterize the ignition, initial intensity, and growth of potential fires 3. Potential fire hazards Identify fire scenarios that could arise from fire hazards associated with the intended use of the property or the design 4. Systems impacting on fire Identify the fire safety systems and features that are likely to have a significant impact on the course of the fire or development of untenable conditions. Characterize the initial status of each system or feature 5. Occupant response Identify actions that people take that can have significant impact, favorable or otherwise, on the course of the fire or the movement of smoke 6. Event tree Construct an event tree that represents alternative event sequences from fire ignition to outcome associated with fire scenarios 7. Consideration of Estimate the probability of occurrence of each event using available data and/or probability engineering judgment 8. Consideration of Estimate the consequence of each scenario using available loss data and/or engineering consequence judgment 9. Risk ranking Rank the scenarios in order of relative risk. The relative risk can be evaluated by multiplying the consequence (step 8) by the probability of occurrence (step 7) of the scenario 10. Final selection and For each fire safety objective, select the highest ranked fire scenarios for quantitative documentation analysis. Selected scenarios should represent the major portion of the cumulative risk (sum of the risk of all scenarios)
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the building and the choice of building materials affect fire growth and severity within the compartment of fire origin. The building layout also plays major roles in fire and smoke spread through the building, occupant evacuation, and fire fighter access. The detail required to describe building characteristics depends on the nature and complexity of the engineering analysis to be undertaken. Not all of the characteristics discussed below need to be quantified for every project. The proposed layout and construction of compartments of interest, as well as interconnections among them, must be known. The information required could include • Number of stories above and below grade • Physical dimensions of compartments • Construction materials and design of all building assemblies (walls, floors, etc.) • Flammability and thermal properties of interior finish (density, thermal conductivity, specific heat, etc.) • Location and dimensions of potential openings that could provide ventilation to the fire (doors, windows, areas of low fire resistance, etc.) • Interconnections among compartments. Other features of the construction of the building need to be considered as well, such as • Location, dimensions, and properties of structural components (materials, thermal properties, mechanical properties, anticipated loads, etc.) • Location and size of fire compartments (spaces enclosed by fire-resistant assemblies) • Location and nature of concealed spaces • Description of the proposed egress routes. The nature and properties of proposed building services must be determined. This could include HVAC, electrical distribution, and plumbing systems as well as fire protection equipment related to automatic or manual fire suppression, smoke control, and fire detection. Plans for use of firestopping materials and dampers for such systems must also be considered.
G.V. Hadjisophocleous and J.R. Mehaffey
Where the potential for fire spread to neighboring buildings is an issue, the location of the building on the site in relation to site boundaries must be determined. The properties of the exterior walls must also be known including their fire-resistant capabilities, the flammability of their claddings, and the size and nature of unprotected openings.
Fuel Loads The combustible contents of a building can play a more significant role in fire development and severity than building products. It is therefore necessary to estimate the quantity of fuel in each compartment of interest as well as the types of fuel that may be present. The quantity of fuel (combustible contents) is commonly expressed as a fuel load density; that is, fuel load per unit floor area in MJ/m2. Statistical data derived from surveys are available for many occupancy types [4]. When a severe but credible representation of the quantity of fuel is desired, it is advisable to choose the 80th or even 95th percentile in the distribution of fuel load densities. Although the fire load density concept implicitly assumes a uniform distribution of combustibles in compartments, it should be recognized that the actual distribution of combustibles may need to be addressed in some buildings.
Types of Combustibles Different types of combustibles burn at different rates and exhibit different yields of various products of combustion as they burn. Characterizing the fuel in terms of the fuel load density, that is, in terms of its energy content, is often not sufficient. It can be important to know how much of the fuel is cellulosic, how much is plastic, how much is combustible liquid, and so forth. Some recent surveys provide such detailed data for selected occupancy types [5, 6].
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Often the contents of a compartment come in the form of specific fuel packages. For example, an upholstered chair may be constructed of several combustible materials arranged in a unique configuration. It is challenging to model the burning of such a chair based on the flammability characteristics of each component. A simpler and reliable alternative is to rely on experimental data available in the literature [7–9].
Functions in Building For many occupancy types, statistics are available to draw conclusions concerning likely sources of ignition and first items ignited. Statistics may also indicate which combinations of ignition sources and first item ignited lead to the most serious fire losses [10]. To supplement such statistics, an assessment of potential ignition sources and vulnerable combustibles can be undertaken for the proposed building layout and activities. This may be particularly important in an industrial building where several different manufacturing processes may be carried out, raw materials may be stored, finished products may be warehoused, and office space may be provided for staff. Although statistical data may not be available for the specific functions, the owner, operator, and perhaps even the insurance provider can be very helpful in identifying potential ignition sources and vulnerable combustibles.
Passive Fire Protection Systems To inhibit fire spread through a building, it can be subdivided into fire compartments enclosed by fire-resistant assemblies. Commonly referred to as compartmentalization, this is a passive fire protection strategy. Although wall and floor/ceiling assemblies can be designed to be sufficiently fire resistant to meet the objectives of the design, the challenge is often to ensure connections between fire compartments are also sufficiently fire resistant.
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Details and the statuses of closures intended to protect connections between fire compartments and to ensure the integrity of fire compartments in the event of fire must be determined. Doors can often be assumed to be closed and can be chosen to be sufficiently fire resistant; for example, doors between an apartment and a public corridor. In some occupancies or locations, fireresistant doors may be held open for operational reasons and must be prompted to close in the event of fire. Detection systems can cut the current to electromagnetic “hold-open” devices and the doors will close. Thus the passive fire protection strategy is ensured by an automatic fire protection system. Similarly, ducts connecting fire compartments may need to be protected by dampers that operate by the use of fusible links or by other means. Although most passive fire protection systems can be assumed to be very reliable, one must be confident that the design (resistance) of the system is adequate for the risk and that the system will not be compromised by modification (planned or accidental) through the years.
Detection and Suppression Systems In the analysis of an existing building, the type (smoke detection, heat detection, UV/IR) of an automatic detection system must be documented. The location of detectors and their response time index (RTI) and activation temperatures (if appropriate) also must be noted [11]. The type of alarm notification, the location of alarm devices, and their acoustical performance should be noted. Of course, in the design of a new building the same information is required for the proposed (or trial) detection system(s). Similarly, whether in an analysis of an existing building or in the design of a new building, the characteristics of automatic suppression systems must be documented. Information such as the types and locations of discharge devices is required. The activation characteristics (RTI and activation temperature) as well as the agent discharge density and distribution must be known [12].
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Estimates of the reliability of detection and suppression should be made. Independently, one might also need to consider whether the anticipated fire development is such that these devices cannot be activated.
Occupant Load and Characteristics Life safety is a common fire safety objective. Many of the variables affecting occupant behavior are either qualitative or difficult to quantify [13–15]. Nonetheless, whether the fire safety strategy involves evacuation or provision of safe areas of refuge, the following “occupant factors” must be considered: • Occupant load (number and distribution of occupants) • Familiarity with the building • Alertness (sleeping or awake) • Physical and mental ability.
Actions Taken by Occupants The actions that occupants take can have significant impact, favorable or otherwise, on the course of the fire or the movement of smoke and should be considered. Depending on the nature of the building, trained staff or a wellequipped in-house fire brigade can have a profound influence on a fire in the early stages of development. In many facilities, fire wardens may play a significant role in assisting with evacuation. On the other hand, poorly trained staff or casual visitors could leave key doors open, allowing for rapid fire development and smoke transport. Any of these effects could introduce new potential fire scenarios.
Actions Taken by the Fire Department A decision can be taken to ignore the beneficial actions taken by the fire department despite the fact that these actions can have a dramatic impact on fire spread within and between buildings. Whether fire department actions are explicitly
G.V. Hadjisophocleous and J.R. Mehaffey
modeled or not, the location, capability (types of equipment, training, etc.), and response time of the fire department need to be determined [16, 17]. The method of and hence inherent delay in alerting the fire department must be noted. The access of fire fighting appliances to the site and the access of fire fighters to the building must also be noted.
Identification of Potential Fire Scenarios Having collected the data described in the preceding sections, it is now important to identify potential fire scenarios. One way to proceed is to follow the first five steps in the ISO methodology outlined in Table 38.1. Step 1—Location of Fire The most likely locations for fire may often be determined by the review of statistics or from the assessment of potential ignition sources and vulnerable combustibles. Identification of the most adverse or challenging locations for fire normally entails the use of engineering judgment. ISO/TS 16733 provides guidance on selecting challenging locations for fire [3]. Where life safety is the primary objective, Chap. 5 of NFPA 101®, Life Safety Code®, identifies eight “required” design fire scenarios [18]. Most of these scenarios identify what are considered to be challenging locations. As a minimum, the engineer should give consideration to modeling fires in the following locations: • Fires in or its spread to “rooms” with a large number of occupants or vulnerable property • Fires that render part(s) of the means of egress unusable • Fires that commence within building assemblies and remain undetected while they grow in intensity (e.g., within concealed spaces, sandwich panels, etc.) • Localized fires and/or postflashover fires that could challenge the structure and compartmentation in the building • Fire locations that are challenging for proposed active measures (e.g., fires that are
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shielded from sprinkler sprays, fires at floor level in the center of a space that generate large volumes of smoke that must be exhausted, etc.) Step 2—Type of Fire At this point in the analysis, the type of fire refers to a qualitative description of the ignition, initial intensity, and growth of a fire. Much insight can often be gained from perusing statistics. For a given occupancy, one may be able to identify the most common ignition sources and the associated first item(s) ignited. One may also identify those combinations of ignition sources and associated first item(s) ignited that cause the largest percentage of deaths, the largest property losses, the largest percentage of fires that spread beyond the room (or compartment) of fire origin, and so forth [10]. Often Step 1 and Step 2 can be combined. Cooking fires take place on stoves in kitchens, and specific industrial fires take place at certain stages in the manufacturing process associated with specific equipment. Step 3—Potential Fire Hazards Statistics give information of past and current fire problems but may not shed light on problems in the future as new designs, products, or hazards are introduced. It is therefore important to employ engineering judgment to identify potential fires that may not be identified by reviewing statistics. For some occupancy types, for example, industrial buildings, the assessment of potential ignition sources and vulnerable combustibles undertaken in the section “Functions in Building” of this chapter may suggest types of fires that must be considered. Step 4—Systems Affecting Fire The fire safety systems that are proposed for the building or facility, and that are likely to have a significant impact on fire development and the generation of untenable conditions, should be identified. For each system, consider the possibilities that it is operational and that it is not operational (due to routine maintenance, degradation over the years, etc.).
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Passive systems that may play an important role are • Fire separations such as walls and floors (ratings, penetrations, etc.) • Closures in fire separations (fire doors, dampers, etc.) • Structural members (rating, status of protection, etc.) • Protection of means of egress. Active systems that may play an important role are • Suppression systems (sprinklers, CO2, etc.) • Smoke management systems (mechanical, natural venting, etc.) • Fire detection systems (smoke, heat, etc.) • Hold-open devices. Step 5—Occupant Response Identify actions that people could take that can have significant impact, favorable or otherwise, on the course of the fire or the movement of smoke. Actions of occupants might also impact significantly on evacuation choices. It may also be possible to consider the impact that in-house fire brigades or municipal fire fighters could have, particularly early in fire development while occupants are still evacuating. This may entail search and rescue efforts as well as suppression and smoke venting.
Selection of Design Fire Scenarios In principle, all of the fire scenarios identified above should be used to evaluate trial fire protection designs. Such an approach is used by fire risk assessment models such as FiRECAM [19], which is applicable to typical apartment and office buildings. An example of the scenarios used by FiRECAM is described in Appendix 1 at the end of the chapter. In practice, it is not possible to evaluate all possible fire scenarios due to the large number for a given performancebased project. It is therefore necessary to filter possible fire scenarios to reduce their numbers to manageable levels. The selected scenarios are known as the design fire scenarios. The scenario
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screening process is done using engineering judgment and a variety of deterministic and probabilistic tools such as event trees or qualitative analysis and risk ranking. Steps 6–10 of Table 38.1 can be followed to screen and select fire scenarios for quantitative analysis.
Event Trees Step 6 of Table 38.1 deals with event trees, which are a useful tool for identifying and screening fire scenarios. An event tree can be constructed to explicitly display the possible states and alternative event sequences from ignition to burnout or extinguishment for each identified fire scenario. Some of the factors to be considered include the activation (or not) of detection and suppression systems, the presence of occupants in the fire area, the success of manual fire fighting, and fire department response and actions. In addition, factors such as the attainment of flashover, the status (open or closed) of fire doors in the compartment of fire origin, and the status (awake, asleep, infirm, etc.) of occupants of the building can also be considered. An example of an event tree is shown in Fig. 38.2 for fire scenarios starting at a specified location. The frequency of fire of a specific type
Fire type and location
Manual suppression
Automatic suppression
starting at this location, P1, is an important factor that will influence the selection of design fire scenarios. Following ignition is the event “manual suppression,” which has a conditional probability of success P1,1 and of failure P1,2 (equal to 1 – P1,1). The tree then considers the event “automatic suppression,” with probability of success P1,2,1 and of failure P1,2,2 (1 – P1,2,1). As can be seen from Fig. 38.2, the paths with successful events are not expanded for subsequent events, as these events will not have an impact on the final outcome of these paths. The tree considers two additional events, “venting effective” and “barriers effective,” in a similar manner. For each of the resulting paths, a path probability can be computed using the product of the probabilities of events found along that path. PS11 ¼ P1 P1, 1 PS12 ¼ P1 P1, 2 P1, 2, 1 PS13 ¼ P1 P1, 2 P1, 2, 2 P1, 2, 2, 1 PS14 ¼ P1 P1, 2 P1, 2, 2 P1, 2, 2, 2 P1, 2, 2, 2, 1 PS15 ¼ P1 P1, 2 P1, 2, 2 P1, 2, 2, 2 P1, 2, 2, 2, 2 For each path, the consequences in terms of life safety or property damage may be roughly estimated and placed in the last column of Fig. 38.2. Knowledge of the probabilities and
Venting effective
Barriers effective
Yes P1,1
Fire scenario
Consequence
S11
C11
PS11
Fire 1
Yes
S12
P1
P1,2,1
PS12
No
Yes
P1,2
P1,2,2,1
S13
C13
PS13
No
Yes
S14
P1,2,2
P1,2,2,2,1
PS14
No
No
S15
P1,2,2,2
P1,2,2,2,2
PS15
Fig. 38.2 Event tree for a given fire type occurring in a given location
C12
C14
C15
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consequence of each fire scenario (each path) can then be used to decide which scenarios should be considered as the design fire scenarios for more detailed analysis.
Frequency Calculation Step 7 of Table 38.1 deals with the probability of occurrence of scenarios. Each fire scenario has a frequency of occurrence, which is the product of the frequency that this fire type occurs at a given location, P1, and the probabilities of the occurrence of the different events associated with that scenario. In other words, it is the probability of the branch representing the fire scenario. Values required in determining fire scenario frequencies include the frequency that this fire type occurs at a given location; the reliability and effectiveness values of the active fire protection systems such as detection and alarm systems, suppression systems, and smoke control systems; as well the probability of failure of passive fire protection systems such as walls, floors, and rated doors. Data for estimating these values can be found from statistical databases, from expert judgment, and from mathematical models that may themselves include event and fault trees analysis.
Statistics and Historical Information Statistical databases of past fire incidents contain data that could be analyzed to determine the most likely areas of ignition, item first ignited, and fuel source, as well as the probability of fire reaching various stages of severity and spreading to areas beyond the compartment of fire origin. Data can be found for various occupancies and can be used to determine frequency of ignition and the availability of active systems and their probability of activation and effectiveness [10].
Consideration of Consequence In this step of the scenario selection process, Step 8 of Table 38.1, the expected consequences of
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each scenario or cluster of scenarios are estimated using available loss data and/or engineering judgment. This is a preliminary estimate of consequence for scenario screening purposes only using a risk-ranking matrix, as discussed below. A more detailed consequence analysis is done for each of the selected (design) fire scenarios as part of the quantitative engineering assessment.
Risk Ranking Risk ranking, which is Step 9 in Table 38.1, is a useful method for screening scenarios because it allows comparison of scenarios based on both their frequencies and their consequences. Risk ranking can be used to perform either a quantitative or a qualitative analysis. For a quantitative screening process, the probabilities and consequences of each potential scenario must be estimated and then the risk computed as the probability times the consequence. Design fire scenarios are chosen as those that represent the greatest risk. Two examples of how to select scenarios using this technique are provided in the annexes of ISO/TS 16733. To perform a qualitative analysis, the identified scenarios can be grouped based on their expected consequences in order to implement a “risk binning” method. The SFPE Engineering Guide [1] suggests four consequence levels: negligible, low, moderate, and high. Consequences can reflect threat to life, property damage, downtime, environmental damage, and so on. Separate risk matrices can be developed for each type of consequence. A description of the impact on occupants of the four consequence levels is as follows: Negligible: Negligible injuries Low: Minor injuries, no permanent disabilities Moderate: Serious injuries, permanent disabilities, hospitalization required High: Sudden fatalities, acute injuries, immediately life-threatening situations, permanent disabilities.
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In terms of the impact on property and operations the four groups are described as follows: Negligible: Minimum damage to building, minimal operational downtime Low: Damage less than a specified dollar value $YY, reparable damage to building, significant operational downtime, no impact on surroundings Moderate: Damage greater than $YY and less than a specified dollar value $XX million, major equipment destroyed, minor impact on surroundings High: Damage greater than $XX million, building destroyed, surrounding property damaged. Following the estimation of the consequences of the various scenarios, the risk binning method requires an estimate of the frequency level of each of the scenarios. In a similar fashion to the evaluation of the consequences, the frequencies
Fig. 38.3 Risk-ranking matrix (Adapted from SFPE Design Guide [1])
Frequency
can be determined using a qualitative or a quantitative approach. The SFPE Engineering Guide [1] suggests the following levels of frequencies: • Anticipated, expected: incidents that might occur several times during the lifetime of the building f > 1 102 =yr • Unlikely: events that are not anticipated to occur during the lifetime of the facility 1 104 =yr < f 1 102 =yr • Extremely unlikely: events that will probably not occur during the life cycle of the building 1 106 =yr < f 1 104 =yr • Beyond extremely unlikely: all other incidents f 1 10;6 =yr . With these scales a risk-ranking matrix is constructed, as shown in Fig. 38.3. Once the risk matrix has been constructed, scenarios with high or moderate risk can be selected as the design fire scenarios for further analysis.
Beyond extremely unlikely
Consequence f ≤10–6yr –1
High
Moderate
10
Low
Negligible
Extremely unlikely
Unlikely
Anticipated
10–4 ≥ f > 10–5yr –1
10–2 ≥ f > 10–4yr –1
f > 10–2yr –1
7
4
1
8
5
2
9
6
3
11
12
Key High Risk
Moderate Risk
Low Risk
Negligible risk
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Scenario Selection In Step 10 of Table 38.1, the selection of fire scenarios for quantitative analysis is done and documented. These are the highest ranked scenarios for each fire safety objective. Documentation should include a clear scenario description that includes the design fire associated with each selected scenario and the condition of the active and passive fire protection systems.
Quantifying Design Fire Scenarios The process of quantifying the selected design fire scenarios is the essence of a fire protection engineering analysis. This process involves the quantification of the fire and smoke characteristics from ignition to outcome (referred to as the design fires) and their impact on property and building occupants (the consequences). In addition, it may involve the quantification of the frequencies of the various scenarios that can assist in selecting appropriate cost-effective designs. Although this process is very broad, it covers all aspects of fire safety engineering and utilizes computer models and other tools in the analysis. In the following sections, some guidelines are provided to assist fire protection engineers.
Design Fires Following identification of the design fire scenarios, it is necessary to describe the assumed characteristics of the fire on which the scenario quantification will be based. These assumed fire characteristics are referred to as the “design fire.” This section provides guidance on characterization of design fires in terms of time-dependent heat release rates. In principle, a design fire may progress from an incipient phase to a growth phase to a fully developed phase and finally to a decay phase. Depending on the nature of the fire safety engineering assessment, one may not need to model every phase of the fire.
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Modeling Preflashover Fire Growth The preflashover growth phase could consist of a smoldering and/or flaming stage. As smoldering produces heat at a slow rate, it is not considered here, but some models, such as FiRECAM [19], do address this phenomenon. For preflashover fires or fires that remain localized, the rate of heat release as discussed in this section, as well as the location of the fire, forms the fundamental description of the design fire. Rate of Heat Release Modeling preflashover fire growth involves estimating the rate of heat _ of the fire as a function of time. release, Q, Several methods are available for the purpose. The first method is the generic t2 model. When combustible items of varying composition are present, it is often not practical to attempt to model early fire growth by identifying the first item ignited and modeling fire spread from the first item to involve an increasing quantity of fuel. In such cases, it is more appropriate to use a generic fire growth curve that represents the general types of combustible material in the enclosure. Fires that do not involve flammable liquids or gases often grow relatively slowly at the outset. As the fire grows, the rate of growth accelerates. Such fires often grow proportionately to the square of the time. Q_ ¼ ðt=t1000 Þ2 ðkWÞ
ð38:1Þ
where t ¼ time (s) t1000 ¼ time (s) to reach a heat release rate of 1000 kW (1 MW) Analyses of the results of fire tests and real fires have provided a basis for estimating t1000. Four fire growth rates, appropriate for design, are identified in Table 38.2. Each of these fire growth rates is characterized by a specific value of t1000 as depicted in the table. Table 38.2 also identifies examples of fuel configurations known to fit into each of the four fire growth categories. Another method is the experimental data method. If it is possible to identify the first item likely to be ignited, the initial rate of fire growth can be determined from test data. Results from
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G.V. Hadjisophocleous and J.R. Mehaffey
of heat release of the first item ignited has been determined from specific data or models, an analysis should be performed to ascertain whether the fire is likely to spread to neighboring items. This can be accomplished by considering the radiant heat transfer from flames to adjacent fuel items. The radiant flux incident on the adjacent packages should be compared with critical levels for the relevant materials to determine whether secondary ignition (fire spread) is likely. As the fire spreads from item to item, fire modeling can be used to estimate fire growth curves representative of the cumulative heat release rate due to the burning of multiple fuel packages. This should be considered an approximation since the nature and strength of the ignition source could differ from the ignition source used in the specific fire tests where the fire growth curves for the adjacent items were measured. When modeling the preflashover growth phase as a t2 fire (Equation 38.1), it should kept in mind that the fire may not be able to grow without limit. There may be a maximum rate of heat release that can be realized. If so, the heat release rate could be modeled employing Equation 38.1 until the maximum rate is reached and Table 38.2 Categories of t 2 fires then assumed to level off at the maximum value. Growth rate t1000 (s) Typical real fires This is depicted in Fig. 38.4, where, in the growth Slow 600 Densely packed wood products phase, the fire grows as t2, but levels off at a Medium 300 Solid wood furniture (desks) steady-burning rate. Several examples of this Individual furniture items with type of behavior follow. small amounts of plastic At the point in time when sprinklers activate, Fast 150 High stacked wood pallets if shielding of combustibles from the water spray Cartons on pallets Some upholstered furniture can be expected, it might be advisable to assume Ultrafast 75 Upholstered furniture that sprinklers prevent the fire from growing but High stacked plastic materials do not suppress it. In such cases one could Thin wood furniture (wardrobes) assume the heat release rate remains at the level
calorimeter or large-scale tests may be used, provided the limitations are considered. Most information on burning rates for single items has been collected from items burning in a large enclosure. These data will be appropriate for the early stages of fire in large enclosures, but if the fire grows large or if it takes place in a small enclosure, the free-burning rate must be adjusted to account for • Radiative feedback from the hot smoky layer or from enclosure surfaces • Restriction of fire by an inadequate supply of oxygen. Based on such large-scale tests, analytical models have been developed [20] to predict the rate of heat release when the burning item is a wooden crib, wooden pallets, or liquid (or thermoplastic) pool fires. Data are also available for a number of other products [7, 9, 20]. Another method is by calculations from first principles. In some circumstances, where the relative orientation and spacing of fuel packages are well known, it is possible to undertake calculations from first principles. Once the rate
Fig. 38.4 Depiction of the three phases of fire: growth, steady burning, and decay
Steady burning •
Q
Growth
Decay
Time
tD
tF
38
Fire Scenarios
1273
when sprinklers activated. For many scenarios, the activation of sprinklers will cause the heat release rate to drop; however, for some shielded fires, the heat release rate may continue to rise even after sprinklers activate. In the absence of sprinkler activation, the amount, type, and configuration of burning items that can become involved in fire may also impose an upper limit on the rate of heat release. The maximum heat release rate then would be given by the maximum free-burning value. The available ventilation can also impose an upper limit on the rate of heat release in the absence of sprinkler activation. If the available ventilation is restricted, the fire may not even reach flashover. Many computer models automatically account for the possibility of ventilation control. If hand calculations are to be undertaken and there is only one principal opening, the maximum rate of heat release can be predicted as pffiffiffiffi Q_ ¼ 1400A H ðkWÞ
ð38:2Þ
Where A is the area of the opening in m2 and H the height of the opening in m. Modeling Postflashover Fires The discussion above does not account for the possibility of flashover. Flashover can be considered to occur when the • Temperature of the hot gas layer under the ceiling reaches 500 C • Heat flux at the floor (or the level of combustibles) reaches 20 kW m2. These criteria can be used along with two-zone fire models to predict whether or when flashover is expected to occur in an enclosure. Simple analytical models are also available to predict whether flashover is likely [21]. If flashover occurs, Fig. 38.4 would still apply, but the steady-burning rate would now be defined by the postflashover value predicted below. Following flashover, the rate of heat release increases rapidly until it reaches the maximum value for the enclosure. The rate of consumption of fuel is approximately constant and is limited
by the quantity and nature of the fuel or by the available ventilation. The rate of consumption for both fuel-bed-controlled and ventilationcontrolled regimes should be calculated and the lesser value taken as representing the fully developed fire. To simplify design, the growth period between flashover and the maximum heat release rate is usually ignored, and it is assumed that the rate of heat release instantaneously increases to the steady-state level after flashover. As with preflashover fires, the maximum rate of heat release for ventilation-controlled fires can, in general, be predicted employing Equation 38.2. With fuel-bed-controlled fire, the combustibles are able to burn freely. The rate of heat release is limited by the amount, type, and configuration of the burning items. Modeling the Decay Phase of the Fire The decay phase of the fire commences at time tD, which can be defined as the time when about 70–80% of the design fire load has been consumed. In the decay phase it can be assumed that the heat release rate exhibits a linear decrease with time.
Quantifying the Fire and Its Impacts The process of quantifying the fire and its impacts on life safety and property for each fire scenario, also known as hazard analysis, involves calculations of all the subsystems of the fire safety system. Subsystems include fire initiation development and spread, smoke movement, activation of detection and suppression systems, impact on structure, occupant response and evacuation, and fire department intervention. These calculations may involve simple correlations such as plume calculations or the use of complex mathematical models such as computational fluid dynamics (CFD) models. The following sections consider each subsystem and discuss the various calculation approaches that may be used. The purpose is to provide guidance on the available calculation methods and refer the reader to the appropriate sources for more detailed analysis.
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Smoke Movement Smoke movement from the compartment of fire origin to other areas in the building is the main cause of deaths and injuries in building fires. In addition to the life safety impacts of smoke due to toxic gases and high temperature, smoke spread may decrease visibility in the building causing disorientation, reducing traveling speeds, and rendering exits routes untenable, thereby preventing occupants from evacuating safely. The conditions in a building during a fire in terms of temperature, concentration of toxic gases, and visibility can be determined using a number of available computer models. In general, these models fall into three broad categories: network models, two-zone models, and computational fluid dynamics (CFD), or field, models. Network models, such as CONTAMW [22], can be used for large highrise multicompartment buildings with hundreds or even thousands of compartments. Two-zone models, such as CFAST [23], can be used for buildings with a small number of compartments of typically small size in which the two-zone concept is valid. CFD models, such as the Fire Dynamics Simulator [24], are used for buildings with large compartments and complex geometries where a more detailed spatial resolution is required. Criteria can be used to determine the impact of smoke conditions on occupants and can be related to the level of the hot layer in compartments or the dosage of toxic gases received by occupants. Details of how to determine impacts of smoke on life safety can be found in Purser [25]. Detection and Suppression Systems Detection and suppression systems may have a significant impact on the outcome of a fire. Detection systems may activate smoke management systems, initiate the activation of suppression systems, and trigger alarm systems. Early warning to building occupants of the fire may lead to its extinguishment if the fire it is still in the early stages of development and will initiate building evacuation. Activation of suppression systems will affect fire development leading to its control or extinguishment. In fire scenarios that consider
G.V. Hadjisophocleous and J.R. Mehaffey
the impact of detection or suppression systems, it is necessary to predict the activation time of these systems. The prediction of the activation time depends on the type of system, the rate of growth of the fire, and the location of the fire in relation to the detector. In the case where computer models such as CFAST or FDS are used to predict fire development, the activation time can be predicted by these models. Simple calculations can also be done to predict detection times by following the procedures outlined in Schifiliti et al. [26] or by using simple computer models such as DETACT [27]. The effect of the activation of suppression systems such as sprinklers on the fire depends on the fire size at the time of activation, whether the fire is shielded so that the suppression agents do not reach it, and the spray density of the agent. If the system has no effect, then we can assume that the fire will continue to grow as if the system were not present. In the case when the suppression system controls the fire, we can assume that the fire will continue to burn at the same intensity as at the time of activation. In the case of fire extinguishment by the suppression system, the equation derived by Madrzykowski and Vittori [28] can be used to predict the heat release rate after activation time. QðtÞ ¼ Qact e0:023Δt where Q(t) ¼ Heat release rate at time t (kW) Qact ¼ Heat release rate at activation time (kW) Δt ¼ Time after sprinkler activation (s) t ¼ Time (s) Impact on Structure The fire impact on structures can be used not only to estimate consequences based on structural damage but also to determine fire spread from the compartment of fire to other compartments in the building as a result of failure of compartment barriers to contain the fire. Typically fire attack on structures for most buildings begins after flashover has occurred. The duration of the attack depends on fire duration, which is a function of the total fire
38
Fire Scenarios
1275
load in the compartment and the postflashover heat release rate. In certain instances, the structure may be subjected to direct flame impingement; hence it would be necessary to include this in the calculations. Direct flame impingement may cause greater damages to the structure due to the fact that flame temperatures are higher than hot layer temperatures. Occupant Response and Evacuation Occupant response to a fire depends on the warnings received by the occupants during fire development. These in turn depend on the relative location of the occupants to the fire and the availability and operation of fire detection and alarm systems. The earliest occupants can respond to a fire is by receiving fire cues at their location such as seeing the fire, smelling smoke, and hearing fire noises. As not all occupants receive and respond to the various warnings at the same time, an event tree can be constructed, as shown in Fig. 38.5, that considers the types of warnings and response to such warnings. The three different warnings occur at
Fire starts
Occupant response I
different times as shown in the figure. The response of occupants to the fire cues is denoted as “Occupant response I” in Fig. 38.5 and occurs at time t(I). If a fire detection and alarm system is available, it will detect the fire and warn occupants at a later time. The response to the alarm signals is denoted as “Occupant response II” in the figure and occurs at t(II). Occupants that responded to the various warnings would notify other occupants in the buildings. The response to these warnings is denoted as “Occupant response III” and occurs at t(III). The probability associated with each response type depends on the probability of receiving the warning and the probability that occupants will respond to that warning. PðIÞ ¼ PðcuesÞ PðrespÞ where P(I) ¼ Probability of response at time t(I) P(cues, I) ¼ Probability of cues at time t(I) P(resp, I) ¼ Probability of response to cues For example, if the probability of smoke detector activation given a fire is 0.7 and the
Occupant response II
Occupant response III
Occupant response
Yes
Response I
P0,1
P0,1
Design fire
Yes
Response II
P
P0,2,1
P0,2
No
Yes
Response III
P0,2
P0,2,2,1
P0,3
No
No response
P0,2,2,2
P0,4
No P0,2,2
t (I)
t (II)
t (III)
Fire cues
Fire alarm
Warning from others
Fig. 38.5 Event tree for occupant response
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probability that occupants will respond to the alarm issued by the smoke detector is 0.8, the probability of responding to this warning is 0.7 0.8 ¼ 0.56. As these probabilities may be different for occupants in the compartment of fire and for occupants in remote compartments, event trees may be constructed for different groups of occupants. Occupants who respond to the various warnings will commence evacuation. The time required for evacuation depends on the location of occupants in the building, the number of occupants, and the number of available egress routes. The total time required for evacuation can be computed using te ¼ tw þ tr þ td þ tm where te ¼ Evacuation time (s) tw ¼ Time of receiving warning (s) tr ¼ Time to respond to warning (s) td ¼ Delay time, preparing to evacuate (s) tm ¼ Movement time (s) Fire Department Intervention Fire department intervention will have a significant impact on the outcome of the fire and the response and evacuation of occupants. This impact, however, is considered as a additional safety feature, and it is usually not explicitly considered in the design calculations.
Consequence Analysis The consequence of a particular design fire scenario can be determined from information on the fire, its heat and smoke production rates, and fire spread and smoke movement from the location of the fire to other locations. The outcome of the consequence analysis includes injuries and fatalities and property damages to both the building and its contents, as well as damages to the environment and losses resulting from business interruption. Injuries and Fatalities Injuries and fatalities are caused by the inhalation of toxic products of combustion, exposure to thermal radiation, or
direct contact with flames. The impact of a fire scenario on life safety can be determined by tenability analysis. This analysis involves not only calculations of fire development and spread and smoke movement but also an occupant response and evacuation analysis that determines the location of occupants at different times during the fire scenario and the effect of the exposure on occupants. Criteria for determining the effect of the exposure can be found in Purser [25]. Damages to Building and Contents Property damage is a result of exposure to thermal loads, exposure to soot, and corrosive gases. In addition, water damage should be considered as water is the most common fire-extinguishing agent. Thermal loads that include both radiation heat fluxes and convective heat fluxes can be computed from the available information on fire development and spread. Similarly, damage from smoke can be estimated using information on smoke movement and concentration of toxic gases in the building. The level of damage to contents depends to a great extent on the sensitivity of contents to heat, smoke, and water. Information on thermal damages for many materials obtained from results of standard tests can be used to determine threshold damage levels. Business Interruption Losses from business interruption refer to loss of income as a result of the fire. These losses can be estimated based on expected downtimes caused by the fire. An exact estimate of this may not be easily determined, however, good estimates can be determined. For example, total damage to process equipment may require its replacement. Knowledge of the time for the manufacture, delivery, and installation of this equipment is necessary in estimating downtimes. Environmental Damage Damage to the environment can be a result of the release of toxic products of combustion or contaminated runoff water. The potential for damage is great especially when dealing with chemical process plants that store significant amounts of chemicals,
38
Fire Scenarios
the release of which into surface or groundwater reservoirs may have a great impact on aquatic life and the health of people using these resources. Deposition of toxic products of combustion on vegetables and other vulnerable plants and animals may also cause large damages. Example An example that demonstrates the use of the described methodology for identifying and selecting fire scenarios for a multi-use building is included in Appendix 2 at the end of the chapter.
Summary The development of fire scenarios is an integral part of the performance-based fire protection design process. The process of identifying and quantifying fire scenarios is described in this chapter. This process requires knowledge of building characteristics, fuel loads and types of combustibles, functions of building, passive and active fire protection systems, and occupant load characteristics. Based on this information all potential fire scenarios can be identified, the number of which may be too large for further analysis. To reduce the number of the identified fire scenarios to those that merit further analysis a selection process is described that involves the use of event trees and other tools to estimate the frequency and consequence of the identified scenarios. Information on the frequency and consequence of the identified scenarios can then be put into a risk-ranking matrix that facilitates the selection of scenarios. The selected fire scenarios can then be quantified using engineering analysis to determine fire severity and impact on occupants and property, as well downtime and impact on environment.
Appendix 1: Fire Scenarios in Risk Model FiRECAM FiRECAM™ is a fire risk and cost assessment model developed by the National Research Council of Canada [19, 29]. As a result of
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simplifying assumptions made, the model is applicable to apartment and office buildings. FiRECAM calculates the expected risk to life and fire cost expectation based on a hazard analysis of a number of scenarios. These scenarios and their probability of occurrence are hard coded in the model. The approach employed in FiRECAM is to consider only three generic fire types that represent the three distinct types of fires that may occur. They are (1) smoldering fires where only smoke is generated, (2) nonflashover flaming fires where a small amount of heat and smoke is generated, and (3) flashover fires where a significant amount of heat and smoke is generated with a potential for fire spread to other parts of the building. The design fires can occur on each floor of the building, and each fire could happen with the apartment door open or closed. In addition, scenarios are considered with occupants being awake or asleep, and suppression systems being effective in extinguishing the fire or not. Within each fire scenario analysis, the times of occupant response and evacuation are based on analysis of the impact of fire detection systems, alarm systems, and other possible perceptions that occupants may receive during the fire. The probabilities of these three fire types, for both apartment and office buildings, were obtained for Australia, the United States, and Canada [30]. They were obtained based on independent analyses of fire statistics in these three countries. The definition of fire type is based on the severity of the fire when it was observed and recorded by the fire fighters on their arrival. Obviously, small fires can develop into fully developed, postflashover fires if they are given enough time and the right conditions. For risk assessment purposes, however, the fire conditions at the time of fire department arrival are the appropriate ones to use. They represent the fire conditions that the occupants are exposed to prior to fire department extinguishment and rescue operations. In the event of no fire department response, then the eventual conditions of the fire at extinguishment, either by itself or by occupant intervention, are the ones to be used.
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Table 38.3 Probabilities of fire types for apartment buildings Type of fire Smoldering fire Nonflashover fire Flashover fire
Australia (%) 24.5 60.0
United States (%) 18.7 63.0
Canada (%) 19.1 62.6
15.5
18.3
18.3
The reason why fires can develop into different types with different probabilities is because they are governed by a number of random parameters that cannot be predicted, such as the type of ignition source, the point of ignition, and the arrangement of the combustibles. Table 38.3 shows the probabilities of the three fire types, after ignition, for apartment buildings. It is interesting to note that the probabilities are quite similar among the three countries, even though there is no reason that these numbers should be the same due to climatic and cultural differences. Table 38.3 also clearly demonstrates the importance of considering all fire types. For example, flashover fires, which can pose significant hazards to the occupants, have a relatively low probability of occurrence; whereas nonflashover and smoldering fires, which pose lower hazards to the occupants, have a higher probability of occurrence.
Design Fires In addition to the random parameters, described in the previous section, that govern the type of fire that can develop, the condition of the door to the compartment of fire origin is another random parameter that also affects the fire growth. The fire type and the door condition can be combined to create six design fires that allow all the random parameters that govern fire growth to be easily considered. These six design fires are (1) smoldering fire with the fire compartment entrance door open, (2) smoldering fire with the fire compartment entrance door closed, (3) flaming nonflashover fire with the fire compartment entrance door open, (4) flaming nonflashover fire with the fire compartment entrance door
closed, (5) flashover fire with the fire compartment entrance door open, and (6) flashover fire with the fire compartment entrance door closed. The probability of each of these design fires is the product of the probability of the fire type (Table 38.3) and the probability of the door to the compartment of fire origin being open or closed. The probability of the door being open or closed can be estimated based on experience. For example, the entrance door to an apartment unit can be assumed to be mostly closed (for security and privacy reasons), whereas the entrance door to an office room can be assumed to be mostly open (to allow work interaction). The scenarios used in FiRECAM are shown in Fig. 38.6, which demonstrates the various parameters used that may impact fire development and smoke movement as well as occupant response. The model does not attempt to decrease the number of scenarios, although it is evident from the results that some scenarios such as the smoldering scenarios and flaming nonflashover scenarios contribute less to the overall risk to life. Important scenarios, as identified by the model, are the flashover scenarios with door open and sprinklers nonfunctioning.
Appendix 2: Example Demonstrating Selection of Fire Scenarios Example The fire protection team is in the process of performing a performance-based design for a complex building with multiple occupancies, including a parking garage on the four floors below grade and shopping areas on the first four floors, which are interconnected through an atrium and a 20 story hotel tower. The complex is fully sprinklered with a central alarm and voice communication, and the atrium has a smoke exhaust system. Solution The ten steps identified in Table 38.1 are followed for the solution of this example. Step 1—Location of Fire A brainstorming session has identified the following fire locations to be considered in the analysis:
38
Fire Scenarios
Fire ignition
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Type of fire
Door open
Season
Floor
Occupants awake
Sprinklers
Fire scenario
Yes
S1
No
S2
Yes
S3
No
S4
Yes
Floor 1
No
Summer
No
Floor 2
Winter Flashover P1
Spring/fall Yes
Ignition Nonflashover P2 Smoldering P3
Fig. 38.6 Event tree showing fire scenarios in FiRECAM
• • • •
Fire in a hotel room Fire in the underground parking garage Fire in the atrium Fire in the restaurant of the hotel adjacent to the hotel lobby • Fires in stores of the commercial area Step 2—Type of Fire The type of fire that may start at each location depends on the type of combustibles, fuel load, and ignition sources. Hotel Room One type of fire that may be expected in a hotel room are those that start with a cigarette thrown into a garbage container that ignites curtains and then spreads to a couch and bed. Another type of fire may start in a garbage can but then ignites the wood cabinet with a TV and clothing items in the drawers. Fire development for these two fires may be different, although after flashover both fires may have similar characteristics. Underground Parking Garage The type of fire expected in an underground garage is one
that involves a car and then spreads to adjacent cars. Atrium In the atrium area, the expected fire could be a fire of a Christmas tree that is placed there during the holidays or a fire involving couches and tables located there. Restaurant In the case of restaurants, the fire may start in the kitchen area or it may start in the sitting area. These two types of fire are different. Commercial Area Fire in this area could potentially start in any store. This may result in different types of fires depending on the combustible materials and fire loads in each store as well the size and ventilation characteristics. Examples of different fires in stores are fires in clothing stores, bookstores, and shoe stores. A survey of commercial stores done in 2004 has identified a number of different types of fires that should be considered for commercial areas [5, 6]. Due to space limitations and to avoid repetition, only the fires in the hotel room, the parking
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garage, and the atrium are considered in the remainder of the example. Step 3—Potential Fire Hazards For this type of occupancy, no special hazards are anticipated. However, the authorities having jurisdiction may request consideration of arson or hazards as a result of functions or events that may be held in the atrium space. This could include exhibitions and displays of goods and merchandise. Step 4—Systems Affecting Fire The building is fully sprinklered with central alarm with voice communication. In addition, the atrium and the parking garage have smoke management systems. The effects of these systems should be considered. Step 5—Occupant Response Consideration is given here to the response of the occupants to the various warnings and their likelihood to extinguish the fire. For this example, a probability of response and effectiveness in extinguishing the fire is assigned as 0.3 for all fire scenarios. Step 6—Event Tree For each fire location, an event tree is constructed so that the different fire scenarios can be identified. Figure 38.7 shows the event tree for fire starting in a hotel room. As the figure shows, four scenarios are associated with this Fire location
Manual suppression
fire type. The probability of occurrence of this fire type could be obtained from statistics. For this example, however, it is assumed that the probability of fire starting at the three locations is the same. Probabilities for each of the events shown in the tree can also be obtained from statistical data; however, because this is a qualitative analysis, expert judgment can be used. Figure 38.8 shows the event tree for the fire starting in the parking garage. This tree considers the events of manual suppression, sprinkler activation and effective control of the fire, effective smoke ventilation, and barriers that are effective in containing the fire. The fire in this location results in six fire scenarios. Figure 38.9 shows the event tree for the atrium fire. It considers the same events as the parking garage fire, so it results in six scenarios. (Although it is possible that sprinklers operate but venting does not, for brevity, this potential scenario is not considered here.) Step 7—Consideration of Probability The probabilities of the various events shown in the event trees produced in Step 6 can be determined from statistical data and other sources. However, because at this stage of the process the analysis is qualitative, expert
Automatic suppression
Barriers effective
Fire scenario
Yes
S11
P1,1
PS11
Hotel room
Yes
S12
P1
P1,2,1
PS12
No
Yes
S13
P1,2
P1,2,2,1
PS13
No P1,2,2
Fig. 38.7 Event tree for hotel room fire
No
S14
P1,2,2,2
PS14
38
Fire Scenarios
Fire location
1281
Manual suppression
Automatic suppression
Venting effective
Barriers effective
Fire scenario
Yes
S21
P2,1
PS21
Parking garage
Yes
S22
P2
P2,2,1
PS22
No
Yes
S23
P2,2
P2,2,2,1,1
PS23
Yes P2,2,2,1 No P2,2,2 No
No
S24
P2,2,2,1,2
PS24
Yes
S25
P2,2,2,2,1
PS25
P2,2,2,2
No
S26
P2,2,2,2,2
PS26
Fig. 38.8 Event tree for parking garage fire
Fire location
Manual suppression
Automatic suppression
Venting effective
Barriers effective
Fire scenario
Yes
S31
P3,1
PS31
Atrium
Yes
S32
P3
P3,2,1
PS32
No
Yes
S33
P3,2
P3,2,2,1,1
PS33
Yes P3,2,2,1 No P3,2,2 No P3,2,2,2
No
S34
P3,2,2,1,2
PS34
Yes
S35
P3,2,2,2,1
PS35
No
S36
P3,2,2,2,2
PS36
Fig. 38.9 Event tree for atrium fire
judgment can be used for the initial screening of the fire scenarios. For this example, the probabilities of each of the events will be described in qualitative terms and then converted to probability values to facilitate
the calculation of the scenario probabilities. For this, the descriptions and values shown in Table 38.4 are used. The very high value of 0.95 corresponds to the probability of effectiveness of sprinkler
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systems in hotel rooms, whereas the value of 0.7 is associated with the probability of smoke detector activation. Using these values, the probabilities of the events of the event trees are assigned and the scenario probabilities are calculated, as shown in Figs. 38.10, 38.11, and 38.12. Step 8—Consideration of Consequence In this step, a qualitative evaluation of the consequence of each of the scenarios is performed. This evaluation is done using engineering judgment based on the type of fire, the location of the fire, and the effectiveness of the active fire protection systems. This evaluation considers the impact of the fire on both property as well as life safety. To facilitate this assessment, Table 38.5 shows the different consequence
Table 38.4 Values descriptions
associated
Quantitative description Very low Low Moderate High Very high
Fire location
with
probability
Associated value 0.05 0.3 0.5 0.7 0.95
Manual suppression
Automatic suppression
levels that are chosen for this example. The level is determined by considering both the property losses and the occupant impact. For example, the consequence level of a scenario with $30,000 in losses and serious injuries is “high.” Based on the levels shown in Table 38.5 and considering the fire type, fire location, and effectiveness of the active fire protection systems, the consequences of the scenarios in the three event trees are determined as shown in Figs. 38.13, 38.14, and 38.15. Step 9—Risk Ranking Figure 38.16 presents the risk-ranking matrix developed based on the results of Steps 7 and 8. The matrix has six levels of probabilities of occurrence, from extremely low to very high, and five levels of consequence estimates. The levels for the probabilities of scenario occurrence for this example have been set as shown in Table 38.6. The three levels of shaded areas in Fig. 38.16 represent areas of different risk levels, with the darker area representing high risk and the lighter area representing low risk. The white areas represent very low-risk scenarios.
Barriers effective
Yes
Fire scenario
Scenario probability
S11
0.3
S12
0.665
S13
0.0245
S14
0.0105
0.3 Hotel room
Yes
Low
0.95 No
Yes
0.7
0.7 No 0.05 No 0.3
Fig. 38.10 Probabilities of scenarios for hotel room fire
38
Fire Scenarios
Fire location
1283
Manual suppression
Automatic suppression
Venting effective
Barriers effective
Yes
Fire scenario
Scenario probability
S21
0.3
S22
0.49
S23
0.103
S24
0.044
S25
0.044
S26
0.019
Fire scenario
Scenario probability
0.3 Parking garage
Yes
P2
0.7 Yes
No 0.7
Yes 0.7
0.7 No 0.3
No 0.3
Yes No 0.3
0.7 No 0.3
Fig. 38.11 Probabilities of scenarios for parking garage fire
Fire location
Manual suppression
Automatic suppression
Venting effective
Barriers effective
Yes
S21
0.3
S22
0.49
S23
0.103
S24
0.044
S25
0.044
S26
0.019
0.3 Atrium
Yes
P3
0.7 No
Yes
0.7
0.7
Yes 0.7
No 0.3
No 0.3
Yes No 0.3
0.7 No 0.3
Fig. 38.12 Probabilities of scenarios for atrium fire
Table 38.5 Consequence levels and associated loss estimates Qualitative description Very low Low Moderate High Very high Extremely high
Associated loss estimate Property losses ($1000) 0–5 5–20 20–100 100–1000 1000–10,000 >10,000
Occupant impact No deaths or injuries No deaths or injuries No deaths, minor injuries No deaths, serious injuries Small number of deaths and injuries Multiple deaths and injuries
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Fire location
G.V. Hadjisophocleous and J.R. Mehaffey
Manual suppression
Automatic suppression
Barriers effective
Fire scenario
Scenario consequence
S11
Very low
S12
Low
Yes
S13
Moderate
No
S14
Extremely high
Yes
Hotel room
Yes
No
No
Fig. 38.13 Consequence of hotel room fire scenarios
Fire location
Manual suppression
Automatic suppression
Venting effective
Barriers effective
Fire scenario
Scenario consequence
S21
Low
S22
Low
Yes
S23
Very high
No
S24
Extremely high
Yes
S25
Very high
No
S26
Extremely high
Yes
Yes
Parking garage
No Yes
No
No
Fig. 38.14 Consequence of parking garage fire scenarios
As shown in Fig. 38.16, no scenario falls in a high-risk area. Scenarios S23 and S24 are moderate-risk scenarios and should be considered for quantitative analysis. Scenarios S25, S33, and S34 are low-risk scenarios that can
also be considered further. In addition, Scenario S14, although it falls into a very low-risk area, may be considered for further analysis, as it is a scenario in a different section of the building with different fire protection
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Fire Scenarios
Fire location
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Manual suppression
Automatic suppression
Venting effective
Fire scenario
Scenario consequence
S31
Low
S32
Moderate
Yes
S33
High
No
S34
Very high
Yes
S35
High
No
S36
Extremely high
High
Very high
Barriers effective
Yes
Atrium
Yes
No Yes
No
No
Fig. 38.15 Consequence of atrium fire scenarios
Probability of scenario occurrence Consequence
Extremely low
Extremely high
S26, S36, S14
Very low
Moderate
S24
Very high High Moderate
Low
S25 S26
S23
S35
S33
S13
Low
S32 S21
Very low
S22
S12
S11, S31
Fig. 38.16 Risk-ranking matrix of identified scenarios Table 38.6 Scenario probability values used for riskranking matrix Probability level Extremely low Very low Low Moderate High Very high
Scenario probability 0.0–0.02 0.02–0.04 0.04–0.1 0.1–0.3 0.0–0.5 0.5–1.0
systems and different impacts, and it has an extremely high consequence. All other scenarios do not require further analysis and can be dropped.
Step 10—Final Selection and Documentation The final selection of the design fire scenarios is done in this step, and the fire scenarios are documented in detail. As indicated in Step 9, scenarios S14, S23, S24, S25, S33, and S34 should be considered for further analysis. To facilitate the quantitative analysis, Table 38.7 describes the characteristics of these scenarios. The quantitative analysis of these scenarios should consider both the impact of the fires on life safety and property. The procedure outlined in the section “Development of Fire Scenarios” in this chapter can be followed for the analysis.
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Table 38.7 Description of design fire scenarios Scenario ID Location Design fire Description S14 Hotel Fire involving curtains Fire started in a garbage container and spread to the curtain and room and mattress mattress. Nobody was in the room of fire origin. The sprinkler system did not activate because the water supply was turned off for repairs. The fire spread from the room door to the corridor of the hotel. For life safety calculations, assume that occupants were asleep when the fire started S23 Parking Vehicle fire Fire started in a vehicle parked in the parking garage. The sprinkler garage systems activated but could not control the fire. The exhaust ventilation system operated, and it was effective in removing smoke from the parking garage to the outside. The barriers were effective in containing the fire on the floor of fire origin S24 Parking Vehicle fire Fire started in a vehicle parked in the parking garage. The sprinkler garage systems activated but could not control the fire. The exhaust ventilation system operated, but it was not effective in removing smoke from the parking garage to the outside. The barriers failed to contain the fire on the floor of fire origin S25 Parking Vehicle fire Fire started in a vehicle parked in the parking garage. The sprinkler garage systems activated but could not control the fire. The exhaust ventilation system operated, but it was not effective in removing smoke from the parking garage to the outside. The barriers were effective in containing the fire on the floor of fire origin S33 Atrium Christmas tree fire Fire started involving a Christmas tree and stage at the center of the atrium. The sprinklers failed to control the fire. The smoke management system was effective in maintaining smoke levels to the design level, and the fire was contained in the atrium S34 Atrium Christmas tree fire Fire started involving a Christmas tree and stage at the center of the atrium. The sprinklers failed to control the fire. The smoke management system was not effective in maintaining smoke levels to the design level; however, the fire was contained in the atrium
References 1. Society of Fire Protection Engineers, SFPE Engineering Guide to Performance-Based Fire Protection, 2nd ed., Society of Fire Protection Engineers and National Fire Protection Association, Quincy, MA (2007). 2. ICC, International Fire Engineering Guidelines, International Code Council, Washington, DC (2005). 3. ISO/TS 16733, Fire Safety Engineering—Selection of Design Fire Scenarios and Design Fires, International Organization for Standardization, Geneva, Switzerland (2006). 4. A.H. Buchanan, Fire Engineering Design Guide, Centre of Advanced Engineering, University of Canterbury, New Zealand (2001). 5. G. Hadjisophocleous and E. Zalok, “A Survey of Fire Loads in Commercial Premises,” 4th International Seminar on Fire and Explosion Hazards, Londonberry, Northern Ireland (2003).
6. G. Hadjisophocleous and E. Zalok, “Development of Design Fires for Commercial Buildings,” Fire Safety Engineering: Issues and Solutions, FSE International Conference 2004, Sydney, Australia (2004). 7. V. Babrauskas, J.R. Lawson, W.D. Walton, and W.H. Twilley, “Upholstered Furniture Heat Release Rates Measured with a Furniture Calorimeter,” NBSIR 82–2604, National Institute of Standards and Technology, Washington, DC (1982). 8. M. Janssens, “Calorimetry,” in SFPE Handbook of Fire Protection Engineering, 3rd ed. (P.J. DiNenno et al., eds.), National Fire Protection Association, Quincy, MA, pp. 3-38–3-62 (2002). 9. CBUF, Fire Safety of Upholstered Furniture—The Final Report on the CBUF Research Programme (B. Sundstrom, ed.), Interscience Communications Ltd., London (1996). 10. J.R. Hall and M.J. Aherns, “Data for Engineering Analysis,” in SFPE Handbook of Fire Protection Engineering, 3rd ed. (P.J. DiNenno et al., eds.),
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National Fire Protection Association, Quincy, MA, pp. 5-65–5-78 (2002). 11. R.P. Schifiliti, B.J. Meacham, and L.P. Custer, “Design of Detection Systems,” in SFPE Handbook of Fire Protection Engineering, 3rd ed. (P.J. DiNenno et al., eds.), National Fire Protection Association, Quincy, MA, pp. 4-1–4-43 (2002). 12. ISO/TR 13387–7, Fire Safety Engineering—Part 7: Detection, Activation and Suppression, International Organization for Standardization, Geneva, Switzerland (1999). 13. J. Bryan, “Behavioral Response to Fire and Smoke,” in SFPE Handbook of Fire Protection Engineering, 3rd ed. (P.J. DiNenno et al., eds.), National Fire Protection Association, Quincy, MA, pp. 3-315–3-341 (2002). 14. G. Proulx, “Movement of People: The Evacuation Timing,” in SFPE Handbook of Fire Protection Engineering, 3rd ed. (P.J. DiNenno et al., eds.), National Fire Protection Association, Quincy, MA, pp. 3-347–3-366 (2002). 15. H.E. Nelson and F.W. Mowrer, “Emergency Movement,” in SFPE Handbook of Fire Protection Engineering, 3rd ed. (P.J. DiNenno et al., eds.), National Fire Protection Association, Quincy, MA, pp. 3-367–3-380 (2002). 16. R. Marchant, K. Nabeel, and S. Wise, “Development and Application of the Fire Brigade Intervention Model,” Fire Technology, 37, pp. 263–278 (2001). 17. N. Be´nichou, A. Kashef, and G. Hadjisophocleous, “Fire Department Response Model (FDRM) and Fire Department Effectiveness Model (FDEM) Theory Report,” Internal Report No. 842, Institute for Research in Construction, National Research Council of Canada, Ottawa (2002). 18. NFPA 101®, Life Safety Code®, National Fire Protection Association, Quincy, MA, 2006 edition. 19. D. Yung, G.V. Hadjisophocleous, and G. Proulx, “Modelling Concepts for the Risk-Cost Assessment Model FiRECAM and Its Application to a Canadian Government Office Building,” Proceedings of the Fifth International Symposium on Fire Safety Science, Melbourne, Australia, p. 619 (1997). 20. V. Babrauskas, “Heat Release Rates,” in SFPE Handbook of Fire Protection Engineering, 3rd ed. (P.J. DiNenno et al., eds.), National Fire Protection Association, Quincy, MA, pp. 3-1–3-37 (2002). 21. W.D. Walton, P.H. Thomas and Ohmiya, “Estimating Temperatures in Compartment Fires,” in SFPE Handbook of Fire Protection Engineering, 5tf ed. (M. J. Hurley et al., eds.), Springer, (2015). 22. G.N. Walton, CONTAMW96 User Manual, NISTIR 6056, National Institute of Standards and Technology, Gaithersburg, MD (1997). 23. W.W. Jones, “A Multi-Compartment Model for the Spread of Fire, Smoke and Toxic Gases,” Fire Safety Journal, 9, 55 (1985).
1287 24. K.B. McGrattan, G.P. Forney, F.E. Floyd, S. Hostikka, and K. Prasad, Fire Dynamics Simulator (Version 3)—User Guide, NISTIR 6784, National Institute of Standards and Technology, Gaithersburg, MD (2002). 25. D.A. Purser, “Toxicity Assessment of Combustion Products,” in SFPE Handbook of Fire Protection Engineering, 3rd ed. (P.J. DiNenno et al., eds.), National Fire Protection Association, Quincy, MA, pp. 2-83–2-171 (2002). 26. R.P. Schifiliti, B.J. Meacham, and R.L.P. Custer, “Design of Detection Systems,” in SFPE Handbook of Fire Protection Engineering, 3rd ed. (P.J. DiNenno et al., eds.), National Fire Protection Association, Quincy, MA, pp. 4-1–4-43 (2002). 27. D.D. Evans and D.W. Stroup, “Methods to Calculate the Response Time of Heat and Smoke Detectors Installed Below Large Unobstructed Ceilings,” NBSIR 85–3 167, Building and Fire Research Laboratory, U.S. Department of Commerce, Gaithersburg, MD (1985). 28. D. Madrzykowski and R. Vittori, “A Sprinkler Fire Suppression Algorithm,” Journal of Fire Protection Engineering, 4, pp. 151–164 (1992). 29. G.V. Hadjisophocleous and D.T. Yung, “Parametric Study of the NRCC Fire Risk-Cost Assessment Model for Apartment and Office Buildings,” Fourth International Symposium on Fire Safety Science, Ottawa, Canada, pp. 829–840 (1994). 30. J. Gaskin and D. Yung, “Canadian and U.S.A. Fire Statistics for Use in the Risk-Cost Assessment Model,” IRC Internal Report No. 637, National Research Council of Canada, Ottawa, (Jan. 1993).
George V. Hadjisophocleous is a professor at Carleton University and holder of the Industrial Research Chair in Fire Safety Engineering and President of CHM Fire Consultants Ltd. Prior to moving to Carleton University, he was a senior research officer and group leader at the Fire Risk Management Program of the National Research Council of Canada. He holds a PhD in Mechanical Engineering from the University of New Brunswick and he is the author of over 150 publications in the areas of fire research, fire risk assessment, performance-based codes, and CFD modeling. His research areas include fire risk analysis and fire and smoke movement modeling using CFD and zone models. Dr. Hadjisophocleous is a Fellow of SFPE and member of NFPA, IAFSS, ASHRAE, and CIB W14 and a Registered Professional Engineer in the Provinces of Ontario and British Columbia. Jim R. Mehaffey From 1980 to 1987, Dr. Jim R. Mehaffey was a research scientist at the National Research Council where he developed models to predict the growth and severity of building fires. From 1988 to
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2009, he was a research scientist with FPInnovations (Forintek) where he modeled the performance of woodframe assemblies exposed to fire. From 1993 to 1997, he was seconded to the University of British Columbia where he was director and associate professor in UBC’s Fire Protection Engineering Program. He is currently an
G.V. Hadjisophocleous and J.R. Mehaffey
adjunct professor in the Department of Civil and Environmental Engineering at Carleton University and a Principal with CHMfire Consultants. He holds a PhD in physics from the University of Toronto and is the author of over 80 scientific publications.
Engineering Considerations for Fire Protection System Selection
39
Milosh Puchovsky and Craig Hofmeister
Introduction A fundamental responsibility of an engineer is the design of systems that satisfy the overall goals and objectives for a given facility. When it comes to fire and life safety, the fire protection engineer (FPE) is called upon to design those systems deemed necessary to meet the performance objectives for the project. However, before specific protection systems can be designed, decisions must be made regarding what systems are most appropriate and necessary in light of the fire events of concern, and the overall outcomes to be achieved at the conclusion of these events. While FPE’s may not always make the final decision about system type, their decision making approach, input and recommendations are vital to the overall success of the enterprise. Ideally, the ultimate choice about system type is given the proper priority, is well informed, and is made well before any system design work or construction commences. Furthermore, such a decision needs to fit into the overall fire safety strategy, which addresses the fire related concerns specific to site conditions, operations and personnel in question. When considering a specific fire fighting agent and accompanying system, numerous questions that impact the selection arise. The more obvious M. Puchovsky (*) Department of Fire Protection Engineering, Worcester Polytechnic Institute, Worcester, MA, USA C. Hofmeister (registered in NC and GA), The Fire Consultants, Inc.,
pertains to the agent’s effectiveness and compatibility with the types of fuels and fires events, i.e., can the agent extinguish, suppress or control the fire in the time period needed. However, other considerations must also be dealt with. For instance, can the agent be discharged on electrically energized components? Can a fire be detected and an agent discharged in the timeframe necessary to be effective? Does agent discharge sound frequency affect electronic and computer equipment performance? Will the discharged agent leave a residue or otherwise impact the equipment or contents it is intended to protect? Is the agent chemically and physically compatible with the fuel, e.g. physical reaction of water on tissue paper, or chemical reaction of discharge on metal fires involving aluminum or magnesium? Does the agent decompose in the presence of the fire or heat and do such agent decomposition products have an affect on the components to be protected? Can the agent be discharged in an occupied area and/or are there health or environmental concerns associated with the agent? Should the agent once discharged be reclaimed or otherwise contained? What are the costs for the overall system including those associated with necessary maintenance activities? How quickly can the agent supply be replenished? Has the fire protection system operation been sufficiently coordinated with facility operations and other equipment? If multiple systems are utilized to protect specific areas or hazards, how are the systems interconnected to operate effectively? Does system operation
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require specialized training of building staff and emergency responders? As should be appreciated, the above only presents a partial list of possible considerations that require attention. Additionally, the necessary comprehensive approach in addressing fire protection and life safety can at times be met with resistance due to cost and other factors. Some owners view fire protection systems as a cost without a direct return on investment, unless they have experienced a previous fire event or truly understand the associated risks. Similarly, some design team members might view fire protection as a required inconvenience and do not want to spend time or effort beyond the simplest path to meet minimum code requirements. Therefore it is important to open lines of communication with the stakeholders early in the process and discuss the importance and benefits of developing the most appropriate protection schemes. A generic prescribed approach for selecting the most effective system does not exist within a regulatory document or general application guides. Neither does any comprehensive guidance exist that facilitates the decision as to why one type of agent or system should be chosen over another. The responsible FPE typically needs to develop their own approach that guides and influences their final recommendations. This chapter puts forth, in a single reference, a collection of topics and other information pertaining to various types of fire fighting agents and their associated systems that can impact a FPE’s approach and final recommendations about selecting a specific type of fire protection system. The material presented here should not be interpreted as a formalized step-by-step procedure, but rather an assembly of information that can underpin an FPE’s decision-making process. Further to this point, the order of subjects presented is not intended to represent the only sequence in which they can be considered.
Structuring the Decision Making Process A comprehensive and coordinated decision making process is the basis for selecting the
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appropriate fire protection system(s) for a given application. The FPE needs to possess a thorough knowledge of the facilities under consideration and the limitations and uses of the various types of fire protection systems he or she might consider as part of the overall fire protection package. As noted above, it often falls upon the individual FPE to develop his or her own approach for selecting and recommending the most appropriate system to meet the overall objectives. While approaches may differ, the key concepts are relatively typical regardless of the application. Information from applicable building, fire and safety regulations and relevant system design and installation standards as well as from other sources such as system manufacturer materials, listing protocols and fire tests is essential in developing an effective approach. Ideally, a comprehensive fire risk assessment should serve as the basis for structuring any application guide or method for recommending a specific fire protection system. As a minimum the decision process should be at least risk-informed. A fire risk assessment is a process used to characterize the risk associated with fire for specific scenarios. Both the probability of the scenarios occurring, and their potential consequences are addressed. Within the context of the risk assessment, fire protection systems largely serve to mitigate or moderate the consequences. However, fire protection systems could also be used to decrease the likelihood of an undesirable event from occurring, i.e. inerting an atmosphere before an ignition source occurs. In undertaking a fire risk assessment, the level of acceptable fire risk needs to be sufficiently considered and articulated, i.e. the desired outcome or consequence at the conclusion of a fire event or scenario. The fire risk assessment will help crystalize the overall intent and purpose of any fire protection system, and how it fits into the overall fire safety strategy, i.e. will the system be used to protect the overall facility or just specific areas or operations. Preferably, the fire protection systems need to be linked to the overall goals and objectives of not only the building owners, but also all key stakeholders involved with the project.
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Certain fire protection standards specifically call out the use of fire risk assessments. For example, NFPA 75, Standard for the Fire Protection of Information Technology Equipment, indicates that a fire risk analysis can be used to determine the construction, fire protection and fire detection requirements for information technology equipment, information technology rooms, and information technology areas [1]. NFPA 75 identifies factors such as the effect of loss of function of information technology equipment on life safety, e.g. process controls; life safety functions controlled by particular equipment; threat of fire from burning equipment to occupants and other property; and economic impact from loss of function, loss of records or loss of physical assets, among others that need to be considered to determine the level of acceptable fire risk. Numerous resources on fire risk assessments including several chapters in this Handbook, the SFPE Engineering Guide to Fire Risk Assessment [2], and NFPA 551, Guide for the Evaluation of Fire Risk Assessments [3] are available to the FPE in this regard. Another resource available for structuring the decision making process is NFPA 550, Guide to the Fire Safety Concepts Tree. The “Tree” can be used to develop and analyze the potential impact of fire safety strategies, and help identify gaps or areas of redundancy. The logic of the “Tree” is directed toward the achievement of specified fire safety objectives that need to be sufficiently articulated. Strategies for achieving the objectives are divided into two general categories: “Prevention of Fire Ignition” and ”Managing Fire Impact”. Active fire protection systems can be employed to address both categories: preventing a fire from starting, e.g., inerting the atmosphere once a certain concentration of flammable vapors of a particular fuel are detected, and by managing the impact of the fire once ignition has occurred, e.g., suppressing or controlling the fire, and/or safeguarding exposure concerns. The Guide can be used to protect the entire facility or just specific areas or operations [4]. The decision methodology or structure of the analysis can be similar to other types of fire protection engineering analysis such as
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performance-based design or a particular calculation methodology. The structure of such analyses as outlined in documents including the SFPE Performance-Based Design Guide or the SFPE Guide to Substantiating a Fire Model as Appropriate for a Given Application can provide good reference for a coordinated decision making process.
Considering Stakeholders Concerns It is important that the various stakeholders are involved in the decision making process leading to the selection of the appropriate fire protection system. Each stakeholder may not provide direct guidance or information to the FPE, but it is important that the FPE have an understanding of the goals and objectives of each stakeholder or their perspective. Typically, the stakeholders will include representatives from the owner, facility operators, tenants, insurer(s), other members of the design team, and the authorities having jurisdiction, but may also include others depending on the facility type and use. See the SFPE Performance-Based Design Guide for more specific information on the role of stakeholders in a coordinated decision making process. The active participation of each of the individual stakeholder categories may vary from project to project but the FPE should consider the viewpoint for each category in the decision making process. The individual viewpoints may vary significantly and the FPE should consider and address each as it relates to the overall fire safety objectives and the expected role of fire protection system(s). Some stakeholders may view fire protection systems as a cost without a direct return and would therefore want to minimize the process. Other stakeholders may have experienced a previous fire event or have specific operational or business interruption goals that make them more sensitive to the impact of a fire event. Ideally, the different viewpoints can be discussed in a meeting or conference and the general impact of each viewpoint on the systems purpose can be addressed.
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As an example, a large multi-tenant data center design would likely have a variety of stakeholders and viewpoints as it relates to the fire protection systems performance for the facility. The owner may have specific goals related to facility and space flexibility, cost, and potential liability, the facility operators and tenants may have specific goals related to equipment protection and business continuity, the insurer may have specific goals related to structure and maximum loss, the design team may have specific goals related to sustainable design and energy usage, and the authorities having jurisdiction may have specific goals related to not only code compliance but also the operations and safety of responding emergency personnel safety. The FPE is then responsible for understanding, considering and integrating the individual stakeholders concerns and objectives in the decision making process, and addressing each in the establishment of system performance criteria and in the selection of the most appropriate fire protection system(s). Given that many projects and applications will include a variety of viewpoints from the relevant stakeholders, good communication and documentation throughout the process is critical. Ideally, the FPE is leading, organizing, and taking responsibility for the process to ensure that all stakeholder concerns are addressed and sufficiently satisfied, and each stakeholder subsequently understands the reasoning for the final decisions.
Understanding the Facility’s Intended Purpose and Operation Any building project and commercial enterprise is a significant investment and undertaken with specific design and end-use goals and outcomes in mind. Once built, the structure serves the purposes and needs of its owners. The building and its associated systems enable the operations of the overall enterprise contained within, i.e. provide a workplace, facilitate heath care services, support manufacturing processes, shelter people and assets, etc.
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Before any fire safety concerns can be properly addressed, the fire protection engineer must possess a functional understanding of the facility operations, their purpose and what the owners expect from their investment. The detail of the facility and operational review may vary but should include features including the site configuration, geographical location and climate; building construction and materials; equipment and/or industrial/manufacturing processes; storage configuration and commodities; presence and categories of hazardous materials; utilities location and configuration; occupancy/occupant loading, occupant locations and responsibilities; and overall building operations. Additionally, seasonal variances should also be reviewed and considered. Do manufacturing or processing operations ramp up due to market conditions? Is there an increase in occupants, including temporary occupants less familiar with their surroundings at different times of the year? Is there a different procedure or an increase in storage at a specific time of the year? Is weather or an accumulation of snow an additional consideration? Are seasonal decorations a notable fire load that needs to be considered, etc? Regardless of the facility type, the operational conditions can vary significantly and therefore it is important that the review and analysis are specific to the subject facility and not a “typical” facility type. As an example, if the facility is a wood working operation, the details of the site layout and building construction should be reviewed as a baseline; however, the FPE should also invest the time to gain sufficient knowledge about the associated workflow, processes, storage configuration, equipment, materials, operation and configuration, and occupant loading and locations. The operations in each wood working facility will differ to some degree and therefore it is important the FPE understand the specific operation and configuration of the subject facility, such as the type of wood species processed, raw material delivery and storage, cutting, drying, veneer preparation, panel manufacturing, milling, laminating, sanding, finishing, final product storage and distribution, and wood waste management. Further, does the facility have additional
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Engineering Considerations for Fire Protection System Selection
operation shifts or modified hours at different times of the year or during periods of equipment maintenance or outage? Do the materials or storage methods/configuration change for peak or slow operational periods? Are there peak times for raw material or hazardous material delivery? Are there weather or other environmental considerations for the specific facility location? The full appreciation of the facility, its key processes and configuration, and the operational considerations provides the background to identify and properly understand potential hazards and fire scenarios.
Characterizing How Fire Can Impact the Facility and Its Operations: Defining Fire Hazards and Scenarios Once the make-up and purpose of the facility is properly understood, the potential fires that could affect its occupants, operations, and contents can be addressed. An important step is to conduct a general hazard assessment to define potential fire events or scenarios. After reviewing the details of the construction and operation as outlined above, a review of potential fire hazards can be conducted specific to the facility and its operations. In general, the hazard assessment should be conducted without considering any protection systems, as the ultimate intent is to identify the most appropriate system to eliminate, mitigate or manage the associated fire hazards. The assessment should consider fire hazards associated with the processes contained within, with specific attention given to the likely range of combustible contents, fuel loads and ignition sources. Potential hazards associated with normal and abnormal operational functions need to be considered, i.e. various failure modes of process equipment and their effects should be investigated. Overall, the assessment would include a review of potential fire scenarios pertaining to the contents and equipment located within the facility; normal processes and operations; and events resulting from malfunctioning equipment. General fire scenarios should consider all
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combustible materials and fuel loading locations, and would likely involve building construction materials, storage and packaging materials, furniture and equipment, and other transient items such as trash, decorations, and normal use items. The operations related scenarios would involve a thorough review of potential fire hazards associated with the various aspects of the process housed within the facility and would consider the production or release of dusts, ignitable liquids, flammable gases, etc. Failure scenarios should include a review of reasonable potential events as a result of a single failure of a piece of equipment, process, or even in some cases a malicious event such as arson or security concern. For example, a fire hazard assessment for a laboratory facility may consider scenarios involving the ignition of general combustibles such as a trash receptacle, a furniture grouping, a computer station, material storage, etc. Operational related scenarios for the laboratory may consider an ignitable liquid spill due to a dropped container or liquid transfer operation, a bench fire resulting from an experiment or noncompatible materials, etc. Failure scenarios may consider a flammable gas line and/or fitting leak, a ruptured flammable liquid container, failure of a critical ventilation fan, etc. The depth and detail of the hazard assessment is often related to the complexity of the facility use and operation, its range and type of occupants, the value of its contents, and the magnitude of potential loss. As an example, the assessment for a small office building would likely focus more on general combustible scenarios while the assessment for a manufacturing and production facility would include a wider range of operational and failure scenarios. The assessment may also need to consider the potential for outside influences, which may range from exposure from a fire event in an adjacent structure to a wildland fire to a terrorist event. However, regardless of the scenario type, the hazard assessment should include a review of fuel and oxidizer arrangements, ignition sources, and environmental conditions, as well as, the degree to which the outcome of the scenario could impact occupant life safety,
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property, operations, responding emergency personnel safety, etc. The assessment should also consider the timelines for the development and impact of potential fire scenarios. For instance does the scenario involve a smoldering fire that would provide a longer time frame for detection and active protection measures or does the scenario involve an explosive hazard which would result in a very limited time frame for detection and active measures? Further, does the scenario involve isolated combustibles or does it include adjacent fuel sources that can result in accelerated fire spread, significantly increasing the potential for severe consequences? In the laboratory example, a trash receptacle fire may have a relatively slow growth rate; however, if the fire is not initially controlled, fire spread to other items such as flammable liquids may significantly increase the fire growth rate, size, and severity. Scenarios can be represented as a function of fire effect such as fire size and time, i.e. the fire is expected to become larger as time from ignition increases. The details of the developed scenarios should include a complete timeline to better define the potential outcomes. In general, if the scenario is terminated earlier along its potential timeline, less damage would result. The development of fire scenarios is a wellestablished technique for FPE’s and is often used in the design process. However, it should also be employed when deciding on which type of fire protection system to use. Fire scenarios are typically developed to encompass a range of events that often include smaller more likely scenarios with limited potential consequences to larger less likely scenarios that could result in significant consequences. In the laboratory example previously discussed, a small trash receptacle fire scenario may have a higher likelihood of occurrence but also may have a lesser potential for severe consequences, while a flammable gas line leak scenario may have a lower likelihood of occurrence but may have much higher potential for severe consequences. The resulting time frame for the development of these two scenarios is also quite different.
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Describing the Desired Outcomes and Consequences If a Fire Should Occur: Defining Overall Fire Safety Goals The description of the range and likelihood of specific fire scenarios in combination with the established goals of the stakeholders helps outline the necessary protection scheme. It is important to recognize that the establishment of the potential fire scenarios and their outcomes articulates how and what could go wrong in a particular facility if the scenario is allowed to run its full course. The degree to which a particular scenario runs its course is dependent, in part, upon the overall risk tolerance of the stakeholders, i.e. their fire safety goals, and the recommended fire protection system(s). In other words, a fire protection system should be selected to ensure that the fire scenario is terminated at some specific point along its timeline. This termination point should align with and represent the goals and desired outcomes of the stakeholders. The review of the potential hazards and the development of the fire scenarios and timelines, along with the establishment of stakeholder goals, facilitate the quantification of specific performance objectives for the fire protection systems. An initial stakeholder viewpoint may be to prevent all potential fire scenarios and, therefore, eliminate any potential detrimental consequences. Realistically however, the associated costs and/or operational tradeoffs might make such a strategy unattainable. Further, some fire outcomes are the result of a combination of a long string of unlikely events that sometimes cannot be reasonably accounted for ahead of time. Therefore it is important that the developed fire scenarios encompass a range of reasonably expected fuel loads, ignition sources and events that adequately capture the relevant and agreed upon concerns. As discussed above, each of the stakeholders is likely to also have distinct objectives and concerns based upon their responsibilities, perspective and experience. Some of these objectives and concerns may be in general alignment such as those pertaining to occupant safety
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and structural protection and which are generally addressed by applicable building and fire regulations. However there may also be differences among some of the stakeholders concerns and objectives such as those relating to preservation of historic fabric and culturally significant items, business continuity and protection of physical assets such as equipment, finished product or raw materials. Even when stakeholders are in general agreement about their respective concerns and objectives, the best means by which to address them can be a topic of debate. In any event, the overall goals and objectives need to be assimilated and quantified as performance criteria for the fire protection systems in light of the relevant hazards and fire scenarios for the facility under consideration. For instance, typical objectives such as the assurance of life safety for occupants not intimate with initial fire growth, isolation of a fire to the room or area of origin, or limiting business interruption to a specific length of time need to be expressed as measurable and quantifiable performance criteria that can be associated with fire protection system performance. This process might involve an iterative approach in which initial objectives and performance criteria are assessed and refined.
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Target maximum fire size and growth rate, factors not explicitly described in building regulations and most design standards, will help inform the decision as to whether extinguishment, suppression or control of the fire is needed; and by when how soon after ignition fire signatures must be detected and system activation is to be initiated; and what quantity and flow of agent will be needed. The type of fuel including its location and orientation, ignition source, enclosing construction, if any, availability of oxygen and ventilation, greatly influence a fire’s growth and heat release rate and need to be addressed when considering the previously discussed fire scenarios. With respect to the various types of systems that can be used, some systems are more appropriate for fire suppression after a relatively short period of agent discharge followed by a longer time period in which the concentration of agent is held in the vicinity or room of the fire. Other systems are better suited for fire control in which the agent is directly applied to the burning and adjacent surfaces for an extended period of time. For many of these systems a supplemental detection system may be necessary to activate and control discharge. Such detection systems and devices need to be integrated into the overall fire safety strategy, and selected and designed so that they initiate fire protection system discharge within the time period necessary to achieve the overall fire safety goals and objectives.
Articulating Goals and Objectives Ideally, the objectives necessary to achieve the stated goals will be quantified in some manner and translated into performance criteria, i.e. expressed as a maximum permitted fire size or a specific concentration of products of combustion that can be achieved within some time period. In other words, how big a fire and for what duration can the owner or other stakeholder (s) tolerate and still achieve the life safety or property protection goals? From a fire protection engineering perspective, especially through the application of performance-based design approaches, the fire can be quantified in terms of heat release rate as a function of time, i.e. a timeline as was previously discussed.
Associating Fire Event Outcomes with Building and Fire Regulations Governmental building, fire and safety regulations are typically applicable to most new facility and renovation projects and must be adhered to. One of the principle needs and goals of the stakeholders is identification of and compliance with the relevant regulations. Failing to comply with the applicable rules can prevent occupancy, delaying or interrupting the use of the facility, and significantly impacting the overall return on investment for the facility. The intent of most regulations is to establish the minimum requirements for safeguarding
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public health, safety, and general welfare. The key term here being “minimum”, and most regulations are based upon establishing the minimum level of safety for building occupants and responding emergency personnel with limited application to property protection, business interruption, and similar related fire protection goals. So the following questions need to be addressed. Do the minimum requirements of the applicable regulations align with the expected outcomes of the stakeholders, and the intended operations of the enterprise? Has it been determined that the “minimum” requirements provide the desired level of life safety, property protection, continuity of business operations or preservation of cultural resources should a fire occur? They might, but has this decision been given proper priority and consideration, and have the overall fire safety goals and objectives of the operation been adequately articulated? As previously noted, building regulations have traditionally only addressed property protection to the extent necessary for occupant and fire fighter safety. How might this realization impact the overall implementation of the fire protection strategy during not only the design and construction process but throughout the life of the building and its operations? Conversely, how does any modification to the fire protection strategy account for specific goals such as business continuity or equipment protection, and how does this compare to the baseline applicable code requirements and subsequently the basic goal of occupant and fire fighter safety? A typical example is the use of a special total flooding or local application suppression system for a critical computer room. Oftentimes the building owner, operator, or designer may have a goal to use the special suppression system in place of otherwise required sprinkler protection for the room. Most building codes allow the installation of a special suppression system to protect the room and/or specific equipment; however, a sprinkler system is often still required to protect the building and in turn the occupants throughout the remainder of the building. The combination of systems must then be integrated to ensure proper operation and coordination.
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It is worthy to note that while model codes and standards serve as the basis for building regulations in various locations, many jurisdictions and governmental agencies amend the various adopted versions of the model regulations, or enact bylaws that override one or more rules of the adopted model codes and standards. Thus, a uniform level of safety from fire is not necessarily prescribed nor implemented. The FPE must be aware of this and clearly identify the applicable rules of the jurisdiction in which the facility is located.
Addressing Property Protection, Business Continuity and Historic Preservation Goals Depending upon the facility or operation under consideration, certain fire protection codes and standards do indeed address fire safety beyond life safety, and include provisions for property protection, business continuity and historic preservation. However, these codes and standards are not necessarily mandated and referenced by the applicable building, fire and safety regulations. The FPE needs to be aware of these other documents and how they could possibly impact the overall project, and serve to satisfy the overall fire protection goals of the stakeholders. An example of one such document is NFPA 76, Standard for the Fire Protection of Telecommunications Facilities, which has three identified goals. As noted in its purpose, NFPA 76 establishes a minimum level of fire protection in telecommunications facilities to: (1) provide a minimum level of life safety for occupants; (2) protect the telecommunications equipment; and (3) preserve service continuity of the equipment. Another example is NFPA 914, Code for Fire Protection of Historic Structures. This code addresses ongoing operations, renovation, and restoration of historic structures, and acknowledges the need to preserve historically significant and character-defining building features. Additionally, the code provides provisions for the continuity of
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Engineering Considerations for Fire Protection System Selection
operations of historic structures. The code covers those construction, protection, operational, and occupancy features that are necessary to minimize danger to life, structures, and historic fabric from the effects of fire, including smoke, heat, and fumes. These types of reference documents can provide valuable information for developing the specific protection scheme including the need for specific types of fire fighting systems, however, as noted above the FPE must be cognizant of the integration and coordination of the different protection goals, and provisions of the applicable regulations.
Insurance Company Objectives The FPE also needs to understand and address any specific insurance company requirements. Insurance loss control and underwriting recommendations often serve to address property protection and business continuity concerns and can have specific requirements for operations or processes deemed too hazardous or with significant loss potential. For example, one insurance company’s guidelines state that typically, special protection systems are recommended where the potential property damage and business interruption from fire for a particular process or occupancy is considered unacceptably high. It is further stated that the above protection rationale applies whether automatic sprinklers are provided as backup protection or not. Occasionally, a special protection system may be acceptable as sole protection without backup sprinkler protection to achieve an acceptable loss potential [5]. Considering the above, the owner’s desired level of fire protection for the facility needs to be considered and gauged with that of any applicable insurance interests and recommendations. The degree of property protection recommended by the insurance company is normally based upon the policy purchased and the overall philosophy of the insurer, not necessarily the long-term objectives and needs of the building owner and other stakeholders. The degree to which the
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insurance company policy is based on the expected fire events and desired outcomes specific to the facility in question requires prudent consideration.
Identifying Candidate Fire Fighting Agents Various types of fire fighting and/or inerting agents are available for achieving specific fire safety goals and objectives under certain scenarios. A brief overview of such agents follows. The agents can take the form of liquids, solids and gases, with the physical form of some agents changing as they flow from the storage container through a piping network and discharge nozzle, and are delivered to the fire area. Each agent, whether water, an aqueous solution, gas, or chemical powder, possesses certain characteristics and limitations. A proper understanding of the various agents, their means of fighting the fire, diluting vapor concentrations, associated system operations and corresponding system design principles is essential in making the correct decision about which type of agent and system to recommend. When considering fire-fighting agents, the following qualities should be investigated as noted by Friedman [6]. 1. Flammability 2. Heat of vaporization 3. Boiling point with respect to the pyrolysis temperatures of solid fuels under consideration 4. Ability to be transported through distribution networks at expected ambient temperatures 5. Toxicity 6. Formation and effect of decomposition products 7. Potential to cause property damage 8. Ability to conduct electricity Other factors associated with the agent also come into play and deserve appropriate consideration. These include but are not limited to: 1. Environmental concerns and/or limitations. 2. Cost 3. Availability 4. Storage requirements
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5. Means of generating the necessary system flow and pressure 6. Ease of reaching the combustion zone 7. Ability to achieve and maintain design discharge concentrations 8. Effect of discharge sound frequency on protected equipment 9. Overall clean up 10. Containment once discharged 11. Compatibility with other agents, fuels and surrounding equipment, 12. Corrosive effects with respect to system piping and components,
Water Water, the most common fire-fighting agent, is generally low in cost and normally readily available. It possesses many of the qualities noted above that make it uniquely desirable. Its heat of vaporization is relatively high, allowing for the greater absorption of energy from the fire. Water possesses a rather ideal boiling point because it is well above most ambient room temperatures and well below the decomposition temperature of most solid combustibles. It is also considered nontoxic. The two most common means of applying water are: (1) manually through a hose nozzle, and (2) through an automatic sprinkler system. The practical aspects of fire protection hydraulics and automatic sprinkler system design calculations are addressed elsewhere in this handbook. Water as a fire fighting agent can take the form of a solid stream when discharged from a firefighter’s nozzle, a range of relatively course droplets when discharged from an automatic sprinkler or water spray nozzle, as finely divided droplets when discharge from a water mist nozzle, or as a fog when discharged from a fog generating device. Depending upon the form in which it is applied, water may extinguish a fire by a combination of mechanisms—cooling the solid or liquid combustible; diluting watersoluble flammable liquids; cooling the flame itself; generating steam that prevents oxygen access; and as fog, blocking radiative heat
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transfer. Although all of these mechanisms may contribute to extinguishment, probably the most important is cooling a gasifying or vaporizing combustible [7]. Most fuels, whether liquid or solid, need to gasify in order for combustion to occur. There are situations, however, where water might not be the best fire-fighting agent for the application in question. Water freezes below 32 F (0 C), and does conduct electricity. It can irreversibly damage some items, although, in certain cases, it is possible to salvage wet items. When applied in bulk or in sprays consisting of large droplets, water can have limited positive effect on ignitable liquid fires, especially for those liquids such as hydrocarbons that are insoluble and float on water. Water is also not compatible with certain hot metals, where it can yield hydrogen, and certain chemicals. The application of water to some substances such as food-stuffs and pharmaceuticals can also initiate undesirable reactions. In some cases, excessive corrosion concerns for system piping exist with water. While this can be a function of the water supply and type of system and its installation, it warrants proper attention. It is possible to improve the properties of water by using additives. For example, introducing antifreeze such as ethylene glycol or glycerin can lower the freezing point of water. However, at certain concentrations and discharge pressures the solution of antifreeze and water can become flammable [8]. Restrictions have been placed on the use of antifreeze with sprinkler systems. The use of dry-pipe or pre-action systems provides a potential alternative to using antifreeze additives where cold temperatures are a concern. However, there is a water delivery time delay with some of these systems that needs to be considered. Other additives are intended to improve other qualities of water as a fire-fighting agent. For instance NFPA 18A, Standard on Water Additives for Fire Control and Vapor Mitigation, notes that water additives might provide enhanced cooling, emulsification, foaming and insulating characteristics of water [9].
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Engineering Considerations for Fire Protection System Selection
Other additives, referred to “wetting agents” can reduce the surface tension of water and improve water’s ability to penetrate porous materials and spread across surfaces [10]. A recent Fire Protection Research Foundation Project has been initiated to provide a comprehensive evaluation of water additives used for fire control and vapor mitigation, with the intent to clarify the fire protection benefit of using water with additives for fire suppression versus water without additives [11]. As noted in the report, “various water additives are available in today’s marketplace that claim to provide advantageous performance characteristics for fire control and vapor mitigation. Of particular interest are additives that report to provide superior fire suppression capabilities through emulsification or encapsulation. However, a scientific assessment of these various additives is lacking, and the fire protection community would benefit from an evaluation of the various available water additives for fire control and vapor mitigation”. Emulsification can be described as a forced mixture of two or more liquids that are normally immiscible. From a fire protection standpoint, the two liquids could be a hydrocarbon and water, with or without additives. The water is applied to the surface of the hydrocarbon with some energy so that the two liquids are agitated together and the water is dispersed within in the hydrocarbon, in the vicinity of its surface, in the form of droplets which in some cases appear as a froth. This solution of dispersed droplets within the hydrocarbon is referred to as an emulsion. The presence of the emulsion serves to cool the hydrocarbon surface mitigating the release of flammable vapors, thus rendering the hydrocarbon less flammable or more benign [12]. In some cases, depending upon the agents used, usually not just plain water, the emulsion hardens forming a crust. This process is referred to as saponification. The fire protection qualities of water might also be improved for specific applications without the use of additives. Misting systems have received attention especially since the initiation of the phase-out of halons in the late 1980s. Mist systems typically deliver water in finely divided droplets so that some drops remain suspended in
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the air entrained with the spray and fire plume, and others fall due to gravity. Water mist system standards such as NFPA 750, Standard on Water Mist Fire Protection, set limits on the size of water droplets produced. For some applications, water mist serves to control or extinguish fire by various mechanisms. The mist droplets evaporating near the combustion zone, can remove heat, either at the surface of the combustible potentially reducing pyrolysis or vapor generation, or within the flame, reducing the flame temperature. The mist droplets evaporating in the hot environment might do so before reaching the combustion zone, generating steam, which could displace air and dilute the oxygen concentration. Before they evaporate, the mist droplets might block the radiative heat transfer from the flame to the combustible fuel. Various system designs utilizing a range of operating pressures, droplet sizes, and discharge nozzles have been developed and are discussed elsewhere in this Handbook. The limits and specific applications of mist systems need to be confirmed with system manufacturers and third party testing organizations.
Aqueous Foams Fire-fighting foam consists of a mass of bubbles formed by various methods from aqueous solutions consisting of specially formulated foaming agents and water. Some foams are intended to be gently applied to the surface of ignitable liquids, and float on the liquid surface, creating an air-excluding, cooling, continuous layer of vapor-sealing, water-bearing material that can terminate or prevent combustion. Other foams expand rapidly and are intended for use as large volumes of wet gas cells for inundating spaces and filling cavities. Yet other foams are thick, pasty and viscous, and when applied through a nozzle form a tough heat-resistant blanket covering three-dimensional burning areas and vertical surfaces. Foam concentrates can also be added to sprinkler and water spray systems to aid in the control of certain types of ignitable liquid and storage commodity fires. It needs to be noted that as foam systems are
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largely water-based, many of the concerns associated with water and fuel interactions previously discussed also apply. Fire-fighting foams are usually formulated by mechanical means in which a certain percentage of foam concentrate is added to a flow of water to form a foam solution. Air is then induced into the foam solution by various means such as foam generators or discharge nozzles, and the foam solution is created and applied. Different types of foam concentrates exist and are intended for certain types of applications and fuels. Foam concentrate types are described as: (1) protein, which contain natural protein polymers; (2) flouroprotein, which in addition to the natural protein polymers contains surface-active agents; (3) aqueous filmforming, which consists entirely of synthetic materials; (4) alcohol-resistant types; (5) high-expansion foams; and (6) Class A foams. A further description of the foams produced by these concentrates, and the various methods for applying them are addressed in other chapters of this Handbook. It needs to be recognized that foam breaks down because it is a rather unstable air-water emulsion. The water content is vaporized when exposed to heat and flame. In the case of liquid surface fires, the foam should be applied at a sufficient rate and volume to compensate for this loss, and to provide an additional amount to ensure that a residual foam layer remains over the extinguished portion of the fuel. Sufficient quantities of foam concentrate and water need to be available to form and sustain a cohesive foam blanket of some depth over the entire anticipated burning surface for some time period. Failing to do so can result in only partial extinguishment, allowing the fire to reach its original intensity after the foam supply has been depleted. In addition to foam breakdown by heat, physical or mechanical forces can also break down the foam concentrate. As an example, certain chemical vapors or fluids can destroy foam quickly and where certain other extinguishing agents are used in conjunction with foam, severe breakdown of the foam can occur. Turbulent air or violently convective combustion gases can divert light foam from its intended area of application.
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As with some other agents, consideration of foam needs to extend beyond the fire fighting characteristics. The growing awareness of environmental issues in many parts of the world has focused on the potential adverse impact of foam solution discharge. Primary areas of concern pertain to toxicity, biodegradability, persistence, treatability in wastewater treatment plants, and nutrient loading when foam solutions reach natural or domestic water systems. While the release of foam solutions into the environment can occur with fire suppression system discharge, all manufacturers are required to address foam retention, clean-up and disposal procedures in Material Safety Data Sheets (MSDS). Therefore, fire fighting foams should be used in a responsible manner to limit the associated environmental concerns associated with their use [13].
Inert Gases and Carbon Dioxide Inert gases serve to extinguish fires or prevent ignition by displacing the combustion air in the vicinity of the reaction zone and diluting the concentration of oxygen below that necessary for combustion, typically below 12 %. Inert gases can also have an effect on increasing the heat capacity of the atmosphere supporting the flame. Application of an inert gas in sufficient quantity can extinguish the flame over a liquid or solid. Upon their release, inert gases leave no residue and therefore no clean up of agent after a fire incident is needed. Additionally, inert gases do not form potentially harmful decomposition products when subject to high temperatures. Another potential advantage of inert gases is their suitability for suppressing fires in the presence of physical barriers or obstructions. Inert gases in the context of this chapter pertain to the agent’s affect on the combustion chemical reaction, i.e. rendering it chemically inactive due largely to the displacement of oxygen. Depending upon the specific design standard or regulation applied, different definitions of the term inert gas might be employed. Inert gases for fire protection use consist largely of carbon dioxide, nitrogen and certain
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Engineering Considerations for Fire Protection System Selection
formulations of inert gas mixtures classified as clean agents. Note that carbon dioxide is not considered a clean agent because of its toxic effects. In this instance, carbon dioxide is not inert with respect to human physiology. Quantity and unit cost are usually the driving factors when considering a specific inert gas agent. Certain agents are more efficient on a volume and weight basis due to their heat capacity. The use of inert gases becomes problematic in occupied areas necessitating additional safeguards, as the premise is to reduce oxygen concentrations below that necessary to support combustion, which is typically below the level required to sustain human life. However certain inert gas mixtures have been approved and shown safe for occupied spaces [14]. Depending upon the fuel and the type of inert gas used, specific concentrations of inert gas are to be achieved and maintained near the reaction zone for a period of time. This time duration is referred to as hold time. In sufficient quantity, an inert gas will prevent the combustion of most fuels with the exception of certain metals or unstable chemicals such as pyrotechnics, solid rocket propellants, etc. Inert gases generally have limited affect on fuels that contain or liberate oxygen during combustion such as nitrates for the former and conjugated ketones for the latter. Deep-seated fires of ordinary cellulosic fuels also require prudent consideration, as extinguished surface fires can be re-ignited. Inerting concentrations can be achieved and maintained due to the presence of an enclosure around the anticipated combustion zone. In this case, successful extinguishment is tied to the integrity and ventilation aspects of the enclosure in which the agent is discharged. Inerting concentrations can also be maintained by continuously saturating the combustion zone with the inert gas for some specified period of time. If the necessary concentration of inert gas cannot be maintained and dissipates before the fire is completely extinguished and the reaction zone does not cool, remaining glowing embers or hot surfaces could reignite any lingering flammable vapors. Depending upon the value of the equipment or contents to be protected, providing a
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reserve supply of agent or a redundant system serves to minimize the associated risk. Minimum design concentrations for specific inert gases are fuel dependent, but the lowest referenced concentration for most is about 34 %. Even at these minimum design concentrations, the oxygen level in the vicinity of the agent discharge will be reduced to levels that are generally hazardous to exposed humans with some exceptions. In the case of carbon dioxide, an additional serious physiological effect will occur at concentrations much lower than that necessary to extinguish a fire [15]. Minimum design concentrations must be confirmed with design standards and system manufacturer’s data. See Chap. 44 and Chap. 45 for more discussion on inerting agents.
Halocarbon Clean Agents Clean agents were developed in response to the Montreal Protocol, which called for the phaseout of the production of chlorofluorocarbon agents (halons) in the late 1980s. With respect to fire protection, Halon 1301 and Halon 1211 were the most notable agents affected. Clean agents are generally described as electrically non-conducting fire extinguishing agents that vaporize readily and leave no residue. They are subject to specific evaluation with regard to their hazards to personnel and their potential effect on the environment, specifically Ozone Depletion Potential (ODP) and Global Warming Potential (GWP) [14]. Depending upon the agent, they are stored under high pressure as a liquid or a gas, and are utilized in their gaseous state when released from their storage containers. Clean agent halon replacements fall into two broad categories: (1) halocarbon compounds and (2) inert gas mixtures. Halocarbon clean agents include compounds containing carbon, hydrogen, bromine, chlorine, fluorine, and iodine. They extinguish fires by a combination of chemical and physical mechanisms depending on the compound. Chemical suppression mechanisms of certain compounds are similar to Halon 1301 in that the bromine and iodine species scavenge flame
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radicals and interrupt the chemical combustion chain reaction. However, such compounds of clean agents are not widely used. Most halocarbon compounds suppress fires primarily by extracting heat from the flame reaction zone, reducing the flame temperature below that necessary to sustain combustion. Halocarbon agents also decompose which further absorbs energy from the combustion reaction. As noted in Chap. 44, decomposition products of halocarbons merit consideration. Oxygen depletion by halocarbons also plays a role in reducing flame temperature and extinguishing the fire, similar to the effect that inert gases have. The lack of significant chemical reaction inhibition in the flame zone by most halocarbon compounds results in reduced performance on a volumetric basis and requires higher extinguishing concentrations relative to Halon 1301. Halocarbon agents can be considered for applications similar to those intended for carbon dioxide and other inert gases. One potential advantage of halocarbons over inert gases is that halocarbons are effective in lower volumetric concentrations so that sufficient oxygen necessary to support human life remains in area of discharge. As with inert gases, a certain concentration of the halocarbon needs to be maintained in the vicinity of the combustion reaction zone. The potential drawbacks to using halocarbons relate to their potential toxicity, and the toxicity and corrosive nature of potential decomposition products during a fire. In general, halocarbon agents are not appropriate for use on certain burning metals such as, but not limited to, aluminum, magnesium, iron, chromium, cobalt, copper, nickel and the alkali metals. These fuels reduce the extinguishing agent to liberate halogenated acids, metal salts, organometallic compounds and metal carbonyls, all of which can pose consequential hazards to both occupants and property. Therefore, in addition to a halocarbon’s fire extinguishing characteristics, consideration also needs to be given to the agent’s impact on safety to exposed personnel, its decomposition products and its environmental impact.
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Dry Chemicals A dry chemical is a finely divided powdered material that has been specially treated to be water repellent and capable of being fluidized and free-flowing so that it can be discharged through piping under expellant gas pressure. Dry chemicals are sodium bicarbonate, potassium or mono-ammonium phosphate-based, and certain agents are more effective than others on specific types of fires. For example, potassiumbased dry chemicals are not generally recommended for the extinguishment of fires involving ordinary, Class A, combustibles [16]. Once discharged, dry chemical will settle on and coat surrounding surfaces and objects. It is generally understood that dry chemicals act to suppress the flame of a fire by chemical mechanism that stops the chain reaction taking place in the flame combustion. It is presumed that the dry chemical interacts with the flame to form volatile species that react with hydrogen atoms or hydroxyl radicals similar in some ways to the effect of halon. Dry chemicals also discourage combustion by absorbing heat, by blocking radiative energy transfer, and in the case of mono-ammonium phosphate, by forming a surface coating [7]. Dry chemicals have been used to effectively protect hazards involving flammable and combustible liquids and gases, combustible solids, electrical hazards, such as oil-cooled transformers and circuit breakers, textile operations subject to flash surface fires, and ordinary combustibles such as wood, paper and cloth [17]. Surface coating by dry chemical can be especially effective on elevated objects and vertical surfaces. In cases where other agents would run-down vertical surfaces, dry chemical is more likely to adhere to surfaces, and provide a coating and insulation of the object. Upon discharge, dry chemical residue will remain on surrounding objects and potential corrosion and staining concerns exist. Prompt cleanup will minimize these concerns. Certain dry chemicals can corrode metals such as steel, cast iron, and aluminum among others. In most
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Engineering Considerations for Fire Protection System Selection
cases, dry chemical agents can be readily removed from surfaces by wiping, vacuuming or washing exposed surfaces. Consideration of environmental restrictions is prudent if dry chemical residue is washed away into bodies of water or wastewater systems. Some dry chemicals will require scraping and washing if the exposed surfaces were hot when the chemical was applied. Health affects of dry chemicals also warrant attention. While dry chemicals are considered non-toxic from a physiological perspective, they are finely divided powders and can produce irritation affects when discharged, especially in enclosed areas. Discharge can reduce visibility, and cause breathing difficulty and irritation to the eyes. Suitable safeguards should be provided to ensure prompt evacuation of any exposed occupants during discharge [16]. While there are specific types of dry chemicals based on certain chemical compounds, they are produced by different manufacturers. As such, dry chemicals produced by different manufacturers are usually not identical in all characteristics, and each manufacturer develops equipment for use with a specific dry chemical. System design principles applicable to the products of one manufacturer are not applicable to the products of another manufacturer.
Wet Chemicals A wet chemical fire-fighting agent consists of organic or inorganic potassium-based salts or both, mixed with water to form an alkaline solution capable of being discharged through piping or tubing when pressurized by an expellant gas. The primary use of wet chemical agents is for the protection of fires in cooking oils and fats [18]. Upon discharge, the wet chemical results in a vapor-suppressing foam-like substance that rapidly spreads across the fuel known as saponification. The wet chemical application extinguishes and secures the flame by forming a barrier between the liquid fuel and the
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surrounding air. The barrier prevents oxygen from reaching the combustion reaction zone, and mitigates the release of flammable vapors from the fuel surface. The cooling affect of the wet chemical also lowers the temperature of the oil or fat further decreasing the release of ignitable vapors. Wet chemicals are usually discharged in the form a fine spray. As such some of the agent can settle on surrounding surfaces and can have a corrosive effect on electrical components and cooking equipment. As with dry chemicals, prompt clean-up will minimize staining or corrosion. Similar to dry chemicals, wet chemicals produced by various manufacturers are usually not identical in all characteristics, and each manufacturer develops equipment for use with a specific wet chemical. Therefore, system design principles applicable to the products of one manufacturer are not applicable to the products of another manufacturer.
Aerosols Aerosols are a relatively new type of fire fighting agent first appearing in the marketplace in the mid 1990s. Two types of aerosol agents exist: condensed aerosols and dispersed aerosols. Condensed aerosols are described as an extinguishing medium consisting of finely divided solid particles, generally less than 10 microns in diameter, and a gaseous matter, generated by a combustion process of a solid aerosol-forming compound. Dispersed aerosols are described as an extinguishing medium consisting of finely divided solid particles, generally less than 10 microns in diameter, already resident inside a pressurized agent storage container, suspended in a halocarbon or inert gas [19]. At the time of the writing of this chapter, dispersed aerosol systems are not commercially available. Fixed condensed aerosol extinguishing system units include condensed aerosol generators with mounting brackets, actuating mechanisms,
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and other accessory equipment (as applicable). Condensed aerosol generators are normally non-pressurized devices incorporating an aerosol-forming compound consisting of a mixture of oxidant(s) and combustible component(s) that, when pyrotechnically actuated, produces an aerosol extinguishing agent of gaseous matter and finely divided solid particles that flow through a cooling mechanism within the device prior to exiting through discharge port(s) and into the protected space. The primary mechanism of fire extinguishment by condensed aerosols is reported to be the interruption of the chemical combustion chain reaction taking place in the flame, similar to the affects of halon and dry chemicals. Some cooling near the combustion zone also occurs due to heat absorption by the aerosol particles. For total flooding applications, the hazard is surrounded by a fixed enclosure to enable the required aerosol extinguishing agent concentration to be achieved and maintained for the required hold time to effectively extinguish the fire within the enclosure. Aerosol-generating extinguishing system units, when assembled into a system with one or more condensed aerosol generators, are designed for automatic and manual actuation. Aerosol-generating automatic extinguisher units are self-contained units designed for automatic thermal actuation and do not have a manual means of actuation. The extinguisher units are also limited to a single protected enclosure. The use of condensed aerosol agents might present hazards to personnel. The discharge of aerosol extinguishing systems to extinguish a fire could create a hazard to personnel from the natural form of the aerosol or from certain products of aerosol generation, including combustion products and trace gases from condensed aerosols. Acid by-products, such as hydrofluoric acid, can also be formed and present a hazard to exposed personnel. Unnecessary exposure of personnel to either the natural agent or the decomposition products should be avoided. Potential hazards associated with noise, turbulence, reduced visibility, cold temperature, toxicity, thermal hazards and irritation to persons
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in the protected spaced and other areas where the aerosol agent can migrate should to be evaluated [19].
Code Mandated Fire Protection Systems Building regulations mandate active fire protection systems, largely automatic sprinkler systems, based upon the occupancy types associated with the building, the size and location of the fire area, and the expected occupant load. For instance the International Building Code (IBC) requires automatic sprinkler systems in Group A-2 occupancies, e.g. restaurants, where one of the following conditions exist: i) the fire area exceeds 5000 sq ft; ii) the fire area has an occupant load of 100 or more; or iii) the fire area is located on a floor other than the level of exit discharge. Similar requirements are found in NFPA 5000, Building Construction and Safety Code, and NFPA 101, Life Safety Code. Additionally, model codes require sprinkler systems for certain types of buildings regardless of the occupancy type. For example, sprinkler systems are required for all high-rise buildings. The basis for mandating such fire protection systems is largely based on the premise that the building owner is obligated to provide a safe environment for the building occupants, or the public at large. In general, building regulations do not force a building owner to protect his or her own property. Fire regulations typically have more specific occupancy related requirements that can include specific requirements for special fire protection systems. As an example, the International Fire Code (IFC) contains requirements for the application of foam systems for flammable and combustible liquid storage tank protection for certain configurations. However, similar to building regulations, the detail of such requirements are typically limited and based upon the goal of occupant and emergency personnel safety. Building regulations also allow for “Alternative Automatic Fire-Extinguishing Systems” or “Other Automatic Extinguishing Equipment”,
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Engineering Considerations for Fire Protection System Selection
but provide limited direction on when such systems are needed, or should be considered. Although, the terms “Alternative” and “Other” with respect to fire protection systems are not specifically defined, it is often interpreted that such systems are used to protect against “special hazards”. Harrington [20] describes special hazards as a fuel array that for one or more reasons cannot be effectively protected by standard spray sprinkler systems. Numerous alternatives to standard spray sprinkler systems have been developed to protect special hazards, each having certain characteristics uniquely suited to effectively protect specific aspects of certain special hazards. Special hazard fire protection systems employ various types of agents including water as previously described. The term “special protection system” is also sometimes used to describe these systems. Depending upon the model code, these “Alternative” or “other” systems are identified as wet chemical, dry chemical, foam, carbon dioxide, halon, clean-agent, water spray, foam-water, and water mist. Reference is normally made to the associated NFPA standards for the specific type of system under consideration for relevant design, installation and related provisions, i.e. NFPA 2001, Standard for Clean Agent Fire Extinguishing Systems, or NFPA 17, Standard on Dry Chemical Extinguishing Systems. It needs to be recognized that when a building or fire regulation references an “alternative” or “other” system it is usually done so in the context of providing life safety for building occupants, usually as an alternative to the requirement for installing an automatic sprinkler system. It needs to be further recognized that although building and fire regulations typically mandate the installation of sprinkler systems for life safety, sprinkler systems were initially invented and developed for property protection and business continuity concerns and they continue to serve this purpose for various types of commercial, residential and industrial applications. For instance, the provisions of NFPA 13 pertaining to the protection of storage facilities were developed specific to property protection goals. However, certain types of systems have
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been developed and are intended primarily to enhance life safety, e.g., residential sprinkler systems.
Facility Specific Standards In addition to regulatory provisions found in applicable building and fire codes, other fire protection related documents specific to certain types of facilities and operations exist and might provide some insight as to the type of fire protection system to be used. Examples of such documents include NFPA 34, Standard for Dipping, Coating, and Printing Processes Using Flammable or Combustible Liquids; NFPA 45, Standard for Laboratories Using Chemicals; NFPA 76, Standard for the Fire Protection for Telecommunications Facilities; and NFPA 409, Standard on Aircraft Hangers among others. The FPE needs to confirm whether or not these facility specific standards are mandated by the jurisdiction in which the facility is located or if any governmental regulations come into play. A summary of the relevant provisions of NFPA 34, NFPA 76 and NFPA 409 pertaining to fire protection systems follows. NFPA 34 specifically states that processes are to be protected with any of the following approved automatic fire protection systems: (1) a water spray extinguishing system especially on liquids having flash points above 60 C (140 F); (2) a foam extinguishing system; (3) a carbon dioxide system; (4) a dry chemical extinguishing system; and (5) a gaseous clean agent extinguishing system. It is further noted that fixed, automatic carbon dioxide systems historically have been provided to protect: (a) Flexograph presses and rotogravure presses using Class I and Class II inks, with CO2 nozzles arranged to protect printing heads, ink reservoirs, and other areas likely to contain flammable liquid-based inks; and (b) presses using flammable liquid-based inks having shielded spaces where automatic sprinkler installation is impractical. Additional considerations for CO2 systems include providing a connected reserve supply for high-pressure carbon dioxide systems, and
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sufficient agent for two complete discharge cycles for low-pressure carbon dioxide systems. It is further noted that if a foam extinguishing system is used, hoods and ducts are to be protected by other approved fire protection systems. NFPA 34 also allows for the use of standard automatic sprinkler system protection for certain components of the associated coating, dipping and printing processes. These components specifically include tanks containing liquids having flash points above 93 C (200 F) and their associated process hazards, and tanks equipped with covers arranged to close automatically in the event of fire. NFPA 45 requires, and assumes as a baseline, that all laboratory units be provided with full automatic sprinkler protection, and provides guidance on the hazard classification dependent upon the laboratory unit classification. The standard also recognizes that other types of special hazard extinguishing systems and non-water automatic extinguishing systems may be used and provides reference to the appropriate design standards, but provides no specific design criteria. In the standard’s purpose section, it states that “This standard is designed to control hazards and protect personnel from the toxic, corrosive, or other harmful effects of chemicals to which personnel might be exposed as a result of fire or explosion [21]. ” Given the types of hazards that may be present in a laboratory, the protection scheme must include a comprehensive fire protection strategy to ensure that the utilized system does not result in unintended consequences, i.e. the use of a standard sprinkler system for a laboratory with notable and/or exposed quantities of water reactive chemicals, or the use of a fire protection system that may produce a hazardous atmosphere as part of the extinguishing process. NFPA 45 provides guidance on the fire protection systems as noted above, and also provides guidance on construction, ventilation, chemical storage, handling, and disposal, chemical container sizes, and laboratory operations to result in a coordinated protection approach. It is the FPE’s responsibility to understand the various
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requirements and controls to review the impact on the fire protection system decision making process. As part of its fire protection provisions, NFPA 76 makes reference to several types of automatic fire suppression systems, but does not specifically mandate their use. Some commentary is provided on when a particular type of system could be used. For instance, NFPA 76 notes that automatic or manual fire suppression equipment should be considered as an element in the overall fire protection plan for a telecommunications facility. However, the standard seems to caution on the use of such suppression systems, as it states that telecommunications facilities have experienced an excellent fire loss record due to the high standards of construction, compartmentation of hazards, and high quality of telecommunications equipment, mostly without the use of automatic extinguishing systems. The standard notes that automatic suppression should be considered when other fire protection elements cannot be employed. Furthermore, the potential impact of the suppression agent on energized telecommunications equipment requires thorough evaluation as accidental discharge of agents can cause damage to equipment or otherwise harm personnel. The standard also states that fire suppression agents are not to cause severe damage to the telecommunications equipment, and those agents containing dry chemicals or corrosive wet chemicals in fixed systems should not be used in any area containing telecommunications equipment. NFPA 76 states that wet pipe, dry pipe, and pre-action systems are acceptable for use in the protection of technical support, administrative and building service areas, and support areas of telecommunications facilities, but they are not recommended for the power area, main distributing frame (MDF) areas, signal processing area, and standby power areas. The need to introduce water piping into telecommunications power areas, MDF areas, or signal-processing areas needs thorough evaluation, as water is a risk to telecommunications signal-processing equipment and, by extension, to public safety. The use of special sprinkler configurations, such
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Engineering Considerations for Fire Protection System Selection
as double-interlock pre-action systems, can minimize the risk of inadvertent water discharge. With regard to aircraft hangers, NFPA 409 states that the protection of aircraft storage and servicing areas of Group II aircraft hangars is be with any one of the following systems: (1) foam-water deluge systems with or without air-aspirating discharge devices; (2) a combination of automatic sprinkler protection and an automatic, low-level, low-expansion foam system; (3) a combination of automatic sprinkler protection and an automatic, high-expansion foam system; or (4) a closed-head foam-water sprinkler system. As can be observed, the four referenced facility standards noted above that pertain to four very different types of facilities and hazards, make no clear recommendation on the type of fire protection system to be used, or whether fire control, suppression or extinguishment are intended. However, even in the absence of a stated fire protection goal, the selection of a specific fire protection system will usually imply the overall objective of fire suppression or fire control. Naturally, any decision needs to be coordinated with the overall outcomes to be achieved for the expected fire scenarios. Rather than providing specific recommendations, each facility standard provides options on the types of systems that could be used, and in some cases includes additional commentary or precautionary statements about the use of the various types of fire suppression systems. Specifically, NFPA 34 cautions about the flash points of liquid fuels, the position and location of certain types of discharge nozzles, the need for reserve supply of fire fighting agent and the limitation of certain types of systems. NFPA 76 cautions about accidental system discharge, the affect of agent discharge on equipment, and the corrosive affects of certain types of agents. NFPA 409 identifies four different types of systems for a specific type of aircraft hangar. NFPA 484 specifically cautions against the use of automatic sprinkler protection where certain types of metals are produced or handled. It should be obvious that in many cases, the stakeholders and the FPE cannot rely solely on the on the facility standards or the
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applicable building and fire regulations for a prescriptive mandate on the most appropriate type of system to be used.
Insurance Company Guidelines Some insurance companies issue guidelines that address the use of special hazard or special protection systems. One company notes that such systems are used to extinguish or control fires in easily ignitable, fast-burning substances such as flammable liquids, some gases and chemicals. It is further stated that the systems can also be used to protect ordinary combustibles in certain high-value occupancies especially susceptible to damage and in certain high-piled storage occupancies. The quick action of these systems can keep production downtime at a minimum [5]. Insurance company recommendations for application of special protection systems include dip tanks, drainboards, flow coaters, engine test rooms, foil mills, electronic computer installations, storage tanks of flammable liquid or liquefied gas, fur vaults, oil-filled transformers, rotating electrical equipment, aircraft hangars, rubber tire storage, and chemical processing equipment. In certain cases, recommendations for specific types of systems for specific applications are identified. In other cases, options are provided. Depending upon the insurance company, special protection systems might only be considered a supplement to automatic sprinkler systems, and not a substitute for them. Sprinkler systems are usually designed to operate for longer periods of time than most special protection systems, and can be restored to service more quickly. Special protection systems are more complex than conventional sprinkler systems, and consequently subject to more electrical and mechanical failure modes. Reflash or reignition potential is also a concern, especially for total flooding systems and certain types of extinguishing agents. However, sprinkler systems are usually designed for fire control over a longer period of time, where as special protection systems are usually designed for suppression or extinguishment in a much shorter time frame.
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Fire Protection System Reference Standards As previously noted, standards addressing certain types of fire protection systems are referenced by building and fire regulations and specific facility standards. These system reference standards, especially those promulgated by NFPA, are generally intended for use by those responsible for purchasing, designing, installing, testing, inspecting, approving, listing, operating, and maintaining such systems, and contain various information in this regard. System reference standards usually make it clear that it is not within their purview to identify where such systems are required to be used, e.g. NFPA 11, Standard for Low-, Medium-, and High-Expansion Foam, specifically states that it is not the intent of this standard to specify where foam protection is required. However, such system reference standards might include some information about the fire hazards and conditions under which the systems could be used. For example, NFPA 12, Standard on Carbon Dioxide Systems, includes Annex B, Examples of Hazard Protection, in which five applications of Carbon Dioxide Systems are specifically identified. These applications include (1) Commercial/ Industrial Food Processing Deep-Fat (Hot Oil) Cookers; (2) Restaurant Range Hoods, Connected Ducts, and Associated Equipment, (3) Newspaper Printing and Rotogravure Presses; (4) Open-Top Pits and (5) Below Raised Floors. Another example includes NFPA 2001, which provides advisory annex language indicating that clean agent fire extinguishing systems are useful within certain limits for extinguishing fires in specific hazards or equipment, and in occupancies where an electrically non-conductive medium is essential or desirable, or where cleanup of other media presents a problem. Such total flooding clean agent systems are used primarily to protect hazards that are enclosed or equipment that in itself includes an enclosure to contain the agent. A list of typical hazards that could be suitable for protection by clean agent systems is provided and includes (1) electrical and electronic hazards,
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(2) subfloors and other concealed spaces, (3) flammable and combustible liquids and gases, (4) high-value assets, and (5) telecommunications facilities. NFPA 2001 also states that clean agent systems could be used for explosion prevention and suppression where flammable materials collect in confined areas. Again, the standard does not explicitly prescribe where such systems are to be used but rather provides some commentary about their potential application. Even when a system reference standard does not explicitly identify the application of such a system, the standards might include design and installation requirements that address the types of hazards or fuels for which the fire protection agent and system could be used and oftentimes includes reference data such as fuel specific extinguishing and/or inerting concentrations. Referring again to NFPA 12, provisions about the design of carbon dioxide systems for specific hazards are provided and can be applied once a decision has been made to install a carbon dioxide system. Specifically, CO2 design concentrations for certain fuels such as acetone, gasoline and propane among others are identified. Other reference standards do not directly identify the hazards they are intended to protect, but rather tie the appropriateness of the system to specific listing and testing requirements. For example, NFPA 750, Standard on Water Mist Fire Protection Systems, states that water mist protection systems are to be designed and installed for the specific hazards and protection objectives specified in the listing. An Annex note in NFPA 750 includes a list of fire test protocols and the associated listing organizations. It should be obvious that the FPE needs to be sufficiently familiar with the application and limits of the listing protocols, as well as the design and installation manual for each type of water mist system that might be under consideration. More discussion on listing protocols is discussed below. It is important to recognize that with many of these “alternative” or “other” systems, not just water mist systems, a generic design approach such as for automatic sprinkler systems as outlined in NFPA 13, Standard for the
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Engineering Considerations for Fire Protection System Selection
Installation of Sprinkler Systems, does not exist. Many of these “alternative” systems are of a proprietary nature and the design and installation provisions are specific to the manufacturer of each type of system. For a given hazard, the design, installation and operational details of one manufacturer’s water mist system is likely to be significantly different from that of another manufacturer. It is worth noting, that even with sprinkler systems more specialized devices are entering the marketplace.
Manufacturer’s Literature It should not be concluded, that the only applications appropriate for a certain type of special hazard system are those identified in a particular system reference standard or a specific facility document. System and component manufacturer literature typically includes information on the possible applications of such systems. However, any claims on system appropriateness for specific hazards needs to be verified by the FPE. The question is how? If a system manufacturer’s literature state that its system is appropriate for use in addressing specific fire scenarios, it is reasonable to expect that the system manufacturer possesses specific fire test data and, therefore, more detailed and comprehensive information about such system performance and the verification of such performance. This information, which can take the form of test reports and other evaluation protocols, should be requested by the FPE and examined during the system selection process. Key considerations in the examination of such information include the degree to which evaluation protocols, acceptance criteria, overall hazard dimensions, etc. correlate with those of the desired outcomes and identified hazards of the specific facility and operation in question. Simply relying on the manufacturer’s marketing information should not be considered adequate justification by the FPE that the system is appropriate for the specific scenarios under consideration. More discussion of listing protocols and system testing is provided in the next section.
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Listing Protocols The majority of fire protection systems and their components, including special hazard systems, are associated with some type of listing requirements. A generally accepted definition of the term “listed” means equipment, materials, or services included in a list published by an organization that is acceptable to the authority having jurisdiction and concerned with evaluation of products or services, that maintains periodic inspection of production of listed equipment or materials or periodic evaluation of services, and whose listing states that either the equipment, material, or service meets appropriate designated standards or has been tested and found suitable for a specified purpose [22]. When a fire protection system or its components are “listed” as noted above, it is understood that such equipment has been evaluated for a specified purpose, and that such evaluation has been done in accordance with appropriate standards or has been otherwise tested and found suitable. Therefore an examination of listing protocols will provide some insight as to the appropriateness and applicability of a certain system for a specific hazard. Here again, the FPE needs to confirm that the information presented in the listing protocols correlates with that of the facility operation in question, the fire hazards to be protected against and the desired outcomes. Listing organizations usually contain on-line databases and other recourses that FPE’s and others can use to verify if a particular manufacturer’s system or equipment has been evaluated and “listed” by the organization. However, the fact that a system or piece of equipment is listed does not serve as validation that the system or equipment is appropriate for the given situation or application. As noted above, the listing protocols and evaluation reports should be further examined. Even within a given listing organization, the evaluation and testing protocols for the various types of fire protection systems and equipment differ. Depending upon the system and equipment, attributes about their associated performance vary.
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Listing organizations might provide some detail about the application or intended use of the system. Referring to Factory Mutual Global (FM) Approvals on-line guide [23] with respect to CO2 systems, it notes that carbon dioxide discharge falls into two broad categories, total flooding and local application. The approvals guide further states that total flooding systems are intended to protect enclosed special hazards such as rooms or spaces involving flammable liquids or containing electrical equipment, records, furs, or other storage where a fire would be extinguished. Local application systems are intended to protect flammable liquids in unenclosed special hazards such as dip tanks and drain boards by discharging carbon dioxide directly on the burning material. Further information might be found in the listing organization’s published listing protocol. For instance, FM Approvals Standard 5420 on Carbon Dioxide Extinguishing Systems [24] includes specific fire tests for carbon dioxide extinguishing systems for the protection of wet benches and similar processing equipment. Additional criteria pertain to other performance characteristics such as those associated with salt fog corrosion, thermal shock and areas of coverage among others. In some cases, system reference standards refer directly to any associated listing protocols for information about system application. As previously noted, NFPA 750, requires that water mist protection systems be designed and installed for the specific hazards and protection objectives specified in the listing. NFPA 750 goes on to state that the characteristics of the specific application, e.g. compartment variables and hazard classification, are to be consistent with the listing of the system. Furthermore, an evaluation of the compartment geometry, fire hazard, and system variables are to be performed to ensure that the system design and installation are consistent with the system listing. As such, the listing of water mist fire protection systems are to be based on a comprehensive evaluation designed to include fire test protocols, system components, and the contents of the manufacturer’s design and installation manual.
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While the following concepts are paraphrased from NFPA 750, they are pertinent to any fire protection system for which no generalized application guide and design method are readily available. Listings about system performance should be obtained through full-scale fire tests and thorough system component evaluations conducted by recognized laboratories to demonstrate that performance objectives can be met. Where full-scale assessments are not possible or practical, an extrapolation and assessment of available data and information might be appropriate. However, the setting of practical limits of any extrapolated data needs to be well informed with good intuitive reasoning applied. Where fire tests are employed as part of a listing protocol, they should reflect, to the extent possible, the intended conditions under which the special hazard system is expected to operate. It needs to be verified that the fire tests are sufficiently and appropriately challenging so that the performance of the system can be adequately assessed. It also needs to be confirmed that any performance objectives outlined in a listing protocol are consistent with those of the intended application of the system. New potential applications of fire protection systems can occur. In these cases, existing listing protocols might not necessarily address the intended application of the system. Ad hoc test procedures for such applications could be developed and completed. Where ad-hoc tests protocols are developed, they should adequately address the associated concerns and be: (1) based on an evaluation of the fire hazard, the compartment and space conditions where the fire hazard is located, and the performance objectives for the system; and (2) developed, executed, and interpreted by recognized fire testing professionals acceptable to the stakeholders. Only those ad-hoc test protocols developed in such a manner should be recognized. Listing evaluations typically consist of an approval report describing the results of the fire testing and component evaluations, and are associated with the manufacturer’s design, installation, maintenance and operations manual. For special hazard systems, nozzle characteristics;
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Engineering Considerations for Fire Protection System Selection
spacing between nozzles; distances from ceilings, walls, or obstructions; minimum operating pressures; and agent supply requirements, among other criteria are all usually documented in the listing report. Again, where the listing protocols for such system component performance cannot be correlated with the intended outcomes and scenarios under consideration, it is incumbent on the responsible FPE to make appropriate assessments.
Long Term System Performance When deciding on those fire protection systems that best serve the intended fire and life safety purposes, the long-term effectiveness, reliability and performance of the systems should be incorporated into the decision making process. Once the systems are commissioned, the occupancy certificate is issued and the building is in operation, the design team moves on. It is now the owner’s responsibility to keep the building and the respective fire and life safety systems in proper working order. The applicable fire code, which normally applies to existing buildings, will address the need to maintain an appropriate level of safety. As previously noted, most regulations primarily address life safety rather than property protection. Nonetheless, any provision promulgating effective system performance should be translated and implemented into an effective inspection, testing and maintenance program for the installed fire and life safety systems. Details of this program should be incorporated into the early stages of the system selection and design process, as it will have a distinct impact on the building’s overall operational costs. Most design and installation standards contain some information about the necessary inspection, testing and maintenance activities. For instance NFPA 2001 includes a chapter entitled Inspection, Testing, Maintenance and Training. However, these provisions can be generic in nature. When it comes to specific
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types of proprietary or pre-engineered systems, the design, installation and operation manual furnished by the system manufacturer should be obtained and evaluated before any system is selected. While these manuals tend to be tailored for each individual system installed, sample manuals for the types of applications under consideration can be requested and made available. Designing the system to facilitate the work of inspection, testing and maintenance personnel, as well as contemplating the availability of replacement parts and system supplies should also receive proper priority. Designing the system to best facilitate testing and maintenance activities is not necessarily a provision mandated by the applicable design and installation standard, but doing so will help ensure more costeffective long-term performance of the system. Additionally, if replacement parts and supplies are not readily available but are needed, the resulting disabled or impaired system means that life safety and the owner’s investment are unduly compromised. While not within the scope of routine inspection and maintenance, consideration of future building expansion and anticipated changes in building operations also deserve attention. Can the fire protection system once installed be expanded or otherwise modified to address the related change in fire hazard, or will an entirely new replacement system be necessary?
Concluding Remarks In the absence of any standardized generic application guides for the selection of fire protection systems, validating one’s choice is not always a straightforward matter. Providing the appropriate systems will often require more than just code consulting and compliance with the applicable regulations. As has been discussed, building and fire regulations are often not likely to give much guidance on the selection and use of systems other than sprinkler systems for life safety
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concerns. Where other types of systems are permitted in place of, or in combination with sprinkler systems, or needed for other purposes, limited guidance is provided with regard to the conditions under which such so called special hazard systems could be used, and the reasons why such systems should be used. A comprehensive fire and life safety strategy needs to be developed and implemented with the overall long-term goals of the stakeholders clearly articulated, agreed upon and properly documented. A competent fire safety analysis and assessment will facilitate the overall strategy, identify if the applicable regulations adequately serve the fire and life safety needs over the expected lifespan of the facility, and more effectively address any gaps in protection. Specific attention needs to be given to any property protection, business continuity and historic preservation goals that might not be sufficiently addressed by the prescribed solutions embodied in applicable building and fire regulations. The FPE needs to be knowledgeable and well versed with the application and limitations of the different types of fire protection systems that could be used to satisfy the overall fire and life safety goals and objectives. This requires not only an unbiased in-depth grasp of the applicable rules, regulations, available technologies, design principles and testing protocols, but also a sufficient understanding of the operations for the planned building and the associated fire and life safety risks. Information about the appropriateness of the proposed system, especially if it is a special hazard system, typically needs to be obtained from a combination of building and fire regulations; stakeholder viewpoints; system design, installation and testing standards; insurance company recommendations; listing protocols and evaluations; manufacturer’s information and in certain cases the completion of calculations. In the end, the FPE needs to confirm that all applicable regulations are complied with, and that the proposed system will satisfy the goals and objectives of the stakeholders under the conditions specified, i.e. validation that the expected
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outcomes can be achieved for the fire scenarios to be considered. Naturally, the right choice is predicated on the assumption that the recommended system is properly designed, installed, and maintained.
References 1. NFPA 75, Standard for the Fire Protection of Information Technology Equipment, National Fire Protection Association, Quincy, MA, 2011. 2. Engineering Guide to Fire Risk Assessment, Society of Fire Protection Engineers, Bethesda, MD, 2006. 3. NFPA 551, Guide for the Evaluation of Fire Risk Assessments, National Fire Protection Association, Quincy, MA, 2010. 4. Watts, J. “Systems Approach to Fire-Safe Building Design,” Fire Protection Handbook, 20th Edition, National Fire Protection Association, Quincy, MA: 2008. 5. FM Global Property Loss Prevention Data Sheet 4-0, Special Protection Systems, Factory Mutual Insurance Company, Johnston, RI, 2002. 6. Friedman, R., “Fire Fighting Procedures,” Principles of Fire Protection Chemistry and Physics, 3rd Edition, Jones and Bartlett, Sudbury, MA, 2009. 7. Yu, H.Z. & Newman, J.S., “Theory of Fire Extinguishment,” Fire Protection Handbook, 20th edition, National Fire Protection Association, Quincy, MA, 2008. 8. Updated NFPA Alert Regarding Antifreeeze – April 5, 2011, National Fire Protection Association, Quincy, MA. 9. NFPA 18A, Standard on Water Additives for Fire Control and Vapor Mitigation, National Fire Protection Association, Quincy, MA, 2011. 10. NFPA 18, Standard on Wetting Agents, National Fire Protection Association, Quincy, MA, 2011. 11. Scheffey, J.L, Forssell, E.W. & Childs, J.T., Evaluation of Water Additives for Fire Control and Vapor Mitigation, Phase 1, Final Report, Fire Protection Research Foundation, Quincy, MA, June 2013. 12. Frank, J.A., “Characteristics and Hazards of Water and Water Additives for Fire Suppression,” Fire Protection Handbook, 20th Edition, National Fire Protection Association, Quincy, MA, 2008. 13. NFPA 11, Standard for Low-, Medium-, and HighExpansion Foam, National Fire Protection Association, Quincy, MA, 2010. 14. NFPA 2001, Standard on Clean Agent Fire Extinguishing Systems, National Fire Protection Association, Quincy, MA, 2012. 15. NFPA 12, Standard on Carbon Dioxide Extinguishing Systems, National Fire Protection Association, Quincy, MA, 2011.
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16. NFPA 17, Standard for Dry Chemical Extinguishing Systems, National Fire Protection Association, Quincy, MA, 2013. 17. Hague, D.R., Fire Protection Systems for Special Hazards, National Fire Protection Association, Quincy, MA, 2004. 18. NFPA 17A, Standard for Wet Chemical Extinguishing Systems, National Fire Protection Association, Quincy, MA, 2013. 19. NFPA 2010, Standard for Fixed Aerosol FireExtinguishing Systems, National Fire Protection Association, Quincy, 2010. 20. Harrington, J. “Application of Gaseous Agents to Special Hazards Fire Protection,” Fire Protection Handbook, 20th edition, National Fire Protection Association, Quincy, MA 2008. 21. NFPA 45, Standard on Fire Protection for Laboratories Using Chemicals, National Fire Protection Association, Quincy, MA 2011. 22. “NFPA Glossary of Terms,” National Fire Protection Association, Quincy, MA 2013.
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23. FM Approvals Guide, http://www.approvalguide.com (Accessed August 2013) 24. Approval Standard for Carbon Dioxide Systems, Class Number 5420, FM Approvals, Norwood, MA, 2007. Milosh Puchovsky P.E., FSFPE is Professor of Practice in the Department of Fire Protection Engineering at Worcester Polytechnic Institute in Worcester, MA, USA, where his efforts focus on the application, design, installation and maintenance of active and passive fire protection systems. His e-mail is [email protected]. Craig Hofmeister P.E., FSFPE, LEED AP is a Principle at the fire protection engineering firm The Fire Consultants, Inc., where he consults on a variety of project types including fire protection systems design and review, code compliance, and performance-based design/ alternate design analysis. His e-mail is [email protected].
Design of Detection Systems
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Robert P. Schifiliti, Richard L.P. Custer, and Brian J. Meacham
Introduction Fire detection and alarm systems are recognized as key features of a building’s fire prevention and protection strategy. This chapter presents a systematic technique to be used by fire protection engineers in the design and analysis of detection and alarm systems. The majority of discussion is directed toward systems used in buildings. However, many of the techniques and procedures also apply to systems used to protect planes, ships, outside storage yards, and other nonbuilding environments. Scientific research on fire growth and the movement of smoke and heat within buildings provides fire protection engineers with information and tools that are useful in the design of fire detection systems. Also, studies of sound production and transmission allow communication systems to be engineered, thus eliminating the uncertainty in locating fire alarm sounders. All of this information allows engineers and designers to design systems that meet specific, identifiable goals.
R.P. Schifiliti (*) Schifiliti Associates, Inc., Fire Protection Engineers, 297MA 01867, USA R.L.P. Custer Associates, Inc. Fire Protection Engineers, P.O. Box 297 Reading, MA 01867, USA B.J. Meacham Fire Protection Engineering and Architectural Engineering, Worcester Polytechnic Institute, 50 Prescott Street, MA 01609, Worcester
Previous chapters in this handbook introduced and discussed a series of concepts and tools for use by fire protection engineers. This chapter shows how some of these tools can be used collectively to design and evaluate detection and alarm systems.
A Note About Precision When solving multiple equations with numerous variables from many sources, it is often easy to overlook the importance of precision and confidence in the final answer. This acknowledgment is particularly true since engineers have progressed from slide rulers to calculators to computers in a relatively short span of time. Most calculations in this chapter have been done using a computer—most often with a simple spreadsheet. The generally accepted practice for these types of tools is to round off only the final answer to the correct number of significant digits. The standard and most widely taught rule for rounding is to round off using the same number of significant digits as the least precisely known number used in the calculation. An alternate rule suggests using one more significant figure than suggested by the standard rule. It has been shown that the alternate rule is more accurate and does not lead to loss of data as does the standard rule [1, 2]. The alternate rule for rounding has been used in this chapter. For more information or to refresh your knowledge of precision, rounding, and significant figures, consult the references or
M.J. Hurley (ed.), SFPE Handbook of Fire Protection Engineering, DOI 10.1007/978-1-4939-2565-0_40, # Society of Fire Protection Engineers 2016
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Design of Detection Systems
a standard text on engineering and scientific measurements.
Overview of Design and Analysis To design a fire detection and alarm system, it is first necessary to establish the system’s goals. These goals are established by model codes, the property owner, risk manager, insurance carriers, and/or the authority having jurisdiction. Ultimately, the goals of the system can be put in the following four basic categories: 1. Life safety 2. Property protection 3. Business protection 4. Environmental concerns Some designers include heritage conservation in the list of goals. However, the protection of historic property is really another form of property and mission protection, although the methodology and extent for protection may vary. When designing for life safety, it is necessary to provide early warning of a fire condition. The fire detection and alarm system must provide a warning early enough to allow complete evacuation of the danger zone before conditions become untenable. The fire detectors or fire alarm system may be used to activate other fire protection systems, such as special extinguishing systems and smoke control systems, that are used to help maintain a safe environment during a fire. In some situations, the life safety mission of a detection system is enhanced by providing information to occupants. This situation is often the case in stay-in-place or defend-in-place strategies or partial evacuation/relocation strategies. The detection system is used to provide information about the location and extent of the fire. Instructions are then given to the target audience. Property protection goals are principally economic. The objective is to limit damage to the building structure and contents. Maximum acceptable losses are established by the property owner or risk manager. The goal of the system is to detect a fire soon enough to allow manual or automatic extinguishment before the fire exceeds acceptable damage levels. Goals for the protection of a mission or business are determined in a manner similar to that
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used in property protection. Here fire damages are limited to prevent undesirable effects on the business or mission. Some items that need to be considered are the effects of loss of raw or finished goods, loss of key operations and processes, and loss of business to competitors during downtime. Other concerns include the availability and lead time for obtaining replacement parts. If the equipment to be protected is no longer available or requires several months for replacement, the ability to stay in business during and after an extended period of downtime may be jeopardized. Protection of the environment is also a fire protection concern. Two examples are (1) toxicity of products of combustion and (2) contamination by fire protection runoff water. Should large quantities of contaminants be expected from a large fire, the goal of the system may well be to detect a fire and initiate appropriate response prior to reaching a predetermined mass loss from burning materials or quantity of fire suppression agent discharged. Once the overall goals have been set, specific performance and design objectives for a performance-based design can be established [3–5]. Performance-based fire protection design requires that specific performance objectives, rather than generic prescriptive requirements, be met. A typical prescriptive requirement would be to provide a smoke detector for every 84 m2 (900 ft2) or 9-m (30-ft) spacing. In prescriptive design, speed of detection and the fire size at detection for such an installation are not known or considered explicitly. In addition, if some action must be taken in response to the alarm in order to control the fire, the expected damage is also unknown. Implementation of a fire safety performance objective requires that the objective be stated first by the client in terms of acceptable loss. The client loss objectives must then be (1) expressed in engineering terms that can be quantified using fire dynamics, and (2) related to design fires, design fire environments, and the performance characteristics of fire suppression equipment. For example, the client loss objective may be to prevent damage to essential electronic equipment in the compartment of origin. To meet this objective, one must first define what damage is. This
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R.P. Schifiliti et al.
damage could be expressed in terms of the thickness of the smoke layer. Other criteria, such as temperature or concentration of corrosive combustion products, or a combination of criteria, could also be used. Based on a study of the likelihood of ignition and fire growth scenarios, a design fire needs to be established. The design fire is characterized _ at any moment in by its heat release rate, Q, time; its growth rate, dq/dt; a combustion product rate, dcp/dt, such as smoke particulate, toxic or corrosive species, and so forth; and production rate, dp/dt. The design fire may be determined by (1) a combination of small- and largescale testing specific to the application or (2) analysis of data taken from studies reported in the literature. For a given fire safety design objective, there will be a point, Q_ do , on the design fire curve where the energy and product release rates will produce conditions representative of the design objective. Given that there will be delays in detecting the fire, notifying the occupants, accomplishing evacuation, or initiating suppression actions, the fire will need to be detected at some time in advance of Q_ do . In order to account for these delays, a critical fire size, Q_ cr , can be defined as the point on the design fire curve at which the fire must be detected in order to meet Fig. 40.1 Design fire curve
the design objectives for a given spacing or radial distance from the fire. There are two types of delays that influence the size of the fire at detection: (1) those that are variable and (2) those that are fixed. Variable delays represent transport lag and are related to radial distance of the detector from the fire, ceiling height, and the convective heat release rate of the fire. Fixed delays are associated with system characteristics, such as alarm verification time. Adding the fixed delays to Q_ cr defines another point on the design fire curve: Q_ i or the ideal fire; that is, the fire that would be detected with no transport delay. The design fire, Q_ do , has been defined as the fire size (in terms of peak heat release and given growth rate history) that corresponds to the maximum acceptable loss fire, and the critical fire, Q_ cr , as the maximum fire size at time of detection that allows actions to be taken to limit the continually growing fire to the design fire limit. The time needed to take the limiting actions is the response lag. The total system response time, then, is the amount of time required between the critical fire and the design fire for all the actions to take place before Q_ do is reached, and is the sum of the fixed and variable delays and the response lag. The various design and evaluation points on a design fire curve are shown in Fig. 40.1.
1400
1200
Heat release (kW)
1000
Notes: · Qdo = Heat release design objective · Qi = Heat release ideal · Qcr = Heat release critical · Q do
800 Transport and detection lag
600 · Qi
400 200 0
Response lag
· Q cr
2
4
6 Time (min)
8
10
12
40
Design of Detection Systems
For example, if the design fire is determined to be 1500 kW and manual suppression will be employed, the critical fire can be selected at a moment in time that permits detection, notification, and response before the 1500 kW fire size is reached. If the total system response time is estimated to be 3 min, the critical fire would be at the size determined at 3 min prior to reaching 1500 kW using the estimated fire growth rate. Expressing fire size or fire load as an energy release and growth rate may be thought of in the same way that structural engineers use earthquake zone maps to design for potential earthquakes. Electrical engineers might compare fire loads to fault currents used in designing overcurrent protection devices. At the present time, design fire, critical fire, and total system response time requirements are not established by any building codes. It is the job of the design engineer to work with the building owner and local code officials to establish the performance requirements for a given system application. Once the goals of a system have been established, several probable fire scenarios should be outlined. The occupancy of the building and the expected fuels should be analyzed to establish an expected fire growth rate and an expected maximum heat release rate. Fire loss reports and fire test data can be used to help estimate heat release rates and the production of smoke and fire gases. It is important that different fire scenarios be evaluated to establish how the system design or response might change as a result of varying fire conditions. Several possible fire scenarios should be outlined using the techniques presented elsewhere in this handbook. When designing a system, select the most likely fire scenario as the basis of the design. Once the design requirements for spacing and detector type are established, the system’s response can be analyzed using the other possible fire scenarios. If the alternate fire scenarios cause the design not to meet the established goals, design changes can be made and retested, if warranted.
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The several fire scenarios used when analyzing a system will produce upper and lower bounds or a range of system performance characteristics. The fire scenarios selected should include best- and worst-case fires as well as several likely scenarios for the particular building characteristics and occupancy. For the purposes of design or analysis, detection and alarm systems have three basic elements: detection, processing, and signaling. The first, detection, is that part of the system that senses fire. The second element involves the processing of signals from the detection portion of the system. Finally, the processing section of the system activates the signaling portion in order to alert occupants and perform other auxiliary signaling operations. Auxiliary functions may include smoke control, elevator capture, fire department signaling, and door closing. This chapter focuses on the detection and signaling elements of a fire alarm system. Engineering methods for the design and analysis of heat detector response are presented along with several examples. A method to calculate the audibility of fire alarm sounders is also presented. The selection of a system’s control panel and the design of auxiliary functions is beyond the scope of this chapter.
Detection To design the detection portion of a fire alarm system, it is necessary to determine where fire detectors should be placed in order to respond within the goals established for the system. Several different detector types might respond to the expected fire, so it may be necessary to develop several candidate system designs, using various combinations of detector types in order to optimize the system’s performance and cost. A fire signature [6] is some measurable or sensible phenomenon present during combustion. Table 40.1 is a cross-reference of fire signatures and commercially available detector types. The table shows the predominant fire signature to which the detector responds.
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R.P. Schifiliti et al.
Table 40.1 Fire signatures and commercially available detectors Electromagnetic radiation wave length 1700–2900 angstroms X
Fire signature/ detector type Ultraviolet detector Infrared detector — Submicron particle detector Wilson cloud — chamber Infrared particle — detector Smoke detector Photoelectric — Ionization — Photo beam — Rate-of-rise heat — detector Rate — anticipation heat detector Fixed — temperature heat detector
Electromagnetic radiation (thermal) 6500–8500 —
Invisible products of combustion less than 0.1 μm —
Visible smoke and products of combustion more than 0.1 μm —
Rapid change in High temperature temperature — —
X
—
—
—
—
—
X
—
—
—
—
—
—
—
—
— — — —
— X — —
X — X —
— — — X
— — — —
—
—
—
—
X
—
—
—
—
X
Heat Detection This section discusses an engineering method for determining the placement of heat detectors on a large flat ceiling. The present practice in designing fire detection systems using heat detectors is to space the detectors at intervals equal to spacings established by tests at Underwriters Laboratories Inc. Listed spacings are determined in full-scale fire tests [7]. In the Underwriters Laboratories Inc. (UL) test, a burning pan of 190-proof denatured alcohol is located in the center of a test room. Sprinkler heads having a 160 F (71 C) rated operating temperature are located on the ceiling in a square array having 10 ft (3 m) sides. The fire is in the center of the square. The distance between the fire and the ceiling is varied so that the 160 F (71 C) sprinkler head being used operates in approximately 2 min.
As shown in Fig. 40.2, detectors of the type being tested are located at the corners of squares having 20, 30, 40, and 50 ft (6.1, 9.1, 12.2, and 15.2 m) sides. The spacing of the last detector to operate prior to a sprinkler head operating becomes the detector’s listed spacing. A similar test procedure is employed by Factory Mutual Research Corporation (FMRC) to arrive at an approved detector spacing. Most codes require that detectors be spaced at intervals equal to the UL or FMRC spacing. NFPA 72®, National Fire Alarm Code® [8], 2007 edition, requires that the installed spacing be less than the listed spacing to compensate for high ceilings, beams, and air movement. High ceilings mean that the fire plume will entrain more ambient air as it rises. This condition has the effect of cooling the gases and reducing the concentration of fire products. Beams, joists, walls, or sloped ceilings alter the flow of combustion products. This situation can serve to restrict or enhance the operation of a fire
40
Design of Detection Systems
1319
detector. For instance, consider the case where a fire detector is located on a ceiling between two parallel beams and a fire occurs at floor level between the beams. If the distance between the beams is small compared to the horizontal
50 ft (15.2 m) 40 ft (12.2 m) 30 ft (9.1 m) 20 ft (6.1 m) 10 ft (3.0 m)
H
H
H
H H
H H
H S
S F
S
S
H
H
H H H
H
H = Heat detector S = Sprinkler F = Fire
Fig. 40.2 Detector test layout Fig. 40.3 Detector spacing
distance from the fire to the detector, the beams will act as a channel directing the flow of hot gas to the detector, thus speeding operation. NFPA 72 allows detector spacing to be increased beyond the listed spacing in areas, such as corridors, with narrow walls to confine the smoke and heat produced by the fire. Systems can be designed using this type of code approach; however, this approach will not permit quantitative assessment of detector response or measure the ability of a given system design to meet specific design goals relating to fire size, allowable damage, or hazard. The best possible location for a heat detector is directly over the fire. If there are specific hazards to be protected, the design should include detectors directly overhead or inside of the hazard. In areas without specific hazards, detectors should be spaced evenly across the ceiling. When detectors are evenly spaced, as shown in Fig. 40.3, the point that is farthest from any detector will be in the middle of four detectors. The spacing between detectors is S ¼ 21=2 r
H H
ð40:1Þ
For a given detector, the problem is to determine the maximum distance the detector can be located from the fire and still respond within the S — 2
S — 2
S
S = r ÷ 0.7
S
r = 0.7 × S
S
S
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R.P. Schifiliti et al. · qcond
· qconv
· qrad
· · · · qtotal = qcond + qconv + qrad
Fig. 40.4 Heat transfer to a ceiling-mounted detector
design goals of the system. This determination requires a method for predicting detector response, based on fire size and growth rate, ceiling height, and detector characteristics. Fire plume and ceiling-jet models can be used to estimate the temperature and velocity of fire gases flowing past a detector. The heat transfer can be calculated, and the response of the detector can be modeled. Figure 40.4 describes the heat transfer taking place between a heat detector and its environment. The total heat transfer rate to the unit, q_ ltotal , can be expressed by the relationship q_ total ¼ q_ cond þ q_ conv þ q_ rad ðkW or Btu=sÞ ð40:2Þ where q_ cond ¼ Conduction q_ conv ¼ Convection q_ rad ¼ Radiation heat transfer rates During the initial stage of fire growth, radiation heat transfer can be neglected. Also, the elements of most commercially available heat detectors are thermally isolated from the remainder of the unit. In these cases, it can be assumed that the heat lost from the heat-sensitive element by conduction to other parts of the detector, and to the ceiling by conduction, is negligible in comparison to the convection heat transfer taking place. This exclusion leaves a net rate of heat transfer to the detector equal to q_ conv . The convective heat transfer rate to the detector is described by q_ ¼ qconv ¼ hA T g T d ðkW or Btu=sÞ ð40:3Þ
where h ¼ Convective heat transfer coefficient in kW/(m2 C) or Btu/(sft2 F) A ¼ Area being heated Td ¼ Detector temperature Tg ¼ Temperature of the gas heating the detector Treating the detector element as a lumped mass, m (kg or lbm), the change in its temperature is found by dT d q_ ¼ deg=s dt mc
ð40:4Þ
where c is the specific heat of the element being heated and has units of kJ/(kg C) or Btu/(lbm F) and q_ is the heat transfer rate. This equation leads to the following relationship for the change in temperature of the detector with respect to time: dT d hA T g T d ð40:5Þ ¼ mc dt Heskestad and Smith [9] have proposed use of a time constant, τ, to describe the convective heat transfer to a particular detector element: mc τ¼ s ð40:6Þ hA dT d T g T d ¼ ð40:7Þ dt τ Note that is a function of the mass, area, and specific heat of the particular detector element being studied. For a given fire-gas temperature and velocity and a particular detector design, an increase in mass increases τ. A larger τ results in slower heating of the element. The convective heat transfer coefficient, h, is a function of the velocity of the gases flowing past the detector element and the shape of the detector element. For a given detector, if the gas velocity is constant, h is constant. It has been shown [10] that the convective heat transfer coefficient for spheres, cylinders, and other objects similar to a sprinkler or heat detector element is approximately proportional to the square root of the Reynolds number, Re: Re ¼
ud v
ð40:8Þ
40
Design of Detection Systems
1321
where u ¼ Gas velocity d ¼ Diameter of a cylinder or sphere exposed to convective heating v ¼ Kinematic viscosity of the gas For a given detector, this equation means that h and, hence, τ, is approximately proportional to the square root of the velocity of the gases passing the detector. This relationship can be expressed as a characteristic response time index, RTI, for a given detector: 1=2
τu1=2 ’ τ0 u0
¼ RTI
ð40:9Þ
Thus, if τ0 is measured in the laboratory at some reference velocity u0, this expression is used to determine the τ at any other gas velocity, u, for that detector. The product, τ1/2, is the response time index, RTI. The use of RTI as a heat transfer function is a simplification. The determination of RTI assumes that τ (and, therefore, h) is proportional to the square root of the gas velocity, regardless of the magnitude of the velocity. The flow of gases past irregularly shaped objects such as detectors and sprinklers is very complex. Even the flow past cylinders is too complex to use a simple relationship for the heat transfer coefficient (i.e., constant RTI). Hollman showed that the heat transfer coefficient (and, therefore, τ) is actually proportional to the Reynolds number raised to a fractional power, n, that varies from 0.330 to 0.805 depending on the value of the Reynolds number [10]. For values of Re between 40 and 4000, which is probably the range for most fire detection scenarios, the value of n is given as 0.466. This value is close to 0.5 (square root), but may explain some of the variation found in the experimental determination of τ and RTI. Plunge tests performed on a variety of heat detectors by Bissell [11] show variations in τ and RTI, whereas other tests produced reasonable results for a variety of test parameters. It is possible that further analysis may show that an RTI based on n ¼ 0.5 is reasonable and that the potential errors are insignificant in the context of fire and detector modeling. On the contrary, it may be found that some other value for n produces better results.
The exponent n may vary over ranges of Reynolds numbers less than those reported by Hollman. Some detector geometries are aerodynamically designed to channel fire gases to the detector element. The ability to affect the gas flow is a function of both the flow velocity and whether the flow is turbulent or laminar. These effects introduce additional variables that complicate the determination of a heat transfer function. An added source of error in heat transfer modeling is that the temperature-sensing element of a heat detector is never completely isolated from the detector body. This setup results in conductive heat loss that may not be accounted for when using only one time constant. Kokkala has shown that for some detectors as much as 10 % of the heat gained by convection is lost by conduction to the detector body [12]. A two-time-constant approach, similar to the C parameter used in modeling the response of sprinkler heads, is suggested by Kokkala. In a plunge test, the velocity may be high enough so that the conduction heat loss is negligible when compared to the heat gain by convection. In actual fire conditions, this conduction heat loss may contribute to the variation in RTI as it is currently used. The magnitude of the potential error resulting from the assumption that RTI is constant has not been investigated. Future research and analysis should also consider the possibility that it might be best to test and report several discrete values for τ (hence, h) [13]. An example is using a plunge test to find τ at three different velocities. The slow, medium, and fast velocities should be representative of the range of possible fire-gas velocities. A continuous curve of τ versus u for every model detector would be ideal. However, the economic feasibility of testing must be considered. At the present time, heat detectors are tested in ovens to determine their operating temperatures and are tested in full-scale fire tests to determine their listed spacing (relative sensitivity). A single oven could be used to test for operating temperature and τ at several different velocities as discussed above. This type of
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testing would be more repeatable (precise), have a lower environmental impact, and give results that can be directly used by engineers in performance-based analysis and design. The test data could be used to calculate a listed spacing comparable to that determined in the present fullscale test so that current code-based design methods could continue to be used. The remainder of the calculations in this chapter will be made using RTI as a heat transfer function. The user will readily see how other functions, when available, can be incorporated into the equations to effect other solutions. Heskestad and Smith [9] developed a test apparatus at Factory Mutual Research Corporation to determine the RTI of sprinkler heads. In the test, called a plunge test, the sprinkler head is suddenly lowered into the flow of a hot gas. The temperature and velocity of the gas are known and are constant during the test. The equation for the change in the detector temperature is then dT d 1 ¼ Tg Td ð40:10Þ τ dt Since the gas temperature is constant during the test, the solution to this equation is ti h ð40:11Þ T d T g ¼ T g T a 1 exp τ where Ta is the ambient, or initial, temperature of the sprinkler or detector at time t ¼ 0. Td is the temperature of the detector at time t. Rearranging the equation gives τ¼
t ln T g T a = T g T d
ð40:12Þ
By measuring the response time, tr, of the unit in the plunge test, this equation can be used to calculate τ0 at the test velocity u0. This calculation is done by substituting the response temperature and time for Td and t. The sensitivity of the detector or sprinkler can then be expressed as τo ðat u0 Þ ¼
t ðsÞ ln T g T a = T g T r
ð40:13Þ
In terms of the response time index, this equation becomes 1=2
RTI ¼
t r u0 ln T g T a = T g T r
ð40:14Þ
The RTI has units of m1/2s1/2 or ft1/2s1/2. A plunge test can be used to determine the RTI for a heat detector or a sprinkler. Knowing the RTI, the change in temperature of similar units can be calculated for any history of fire gases flowing past it. The form of the heat transfer equation is dT d u1=2 T g T d ¼ RTI dt
ð40:15Þ
This equation is used to calculate the temperature of a fixed-temperature heat detector or sprinkler exposed to fire gases. The equation can be used to determine the time at which the unit reaches its operating temperature. The use of a lumped mass model may not hold for rate-of-rise heat detectors and ratecompensated heat detectors. The heat transferred to a fixed-temperature heat detector either heats a sensing element until it melts, or it heats two dissimilar metals of a snap disk. In each case, the element itself is exposed to the hot gases. This result is not true for rate-of-rise heat detectors or rate-compensated heat detectors. Most commercial rate-of-rise heat detectors operate when the expansion of air in a chamber exceeds the rate at which the air can escape through a small vent hole. For this type of detector, it is also necessary to model heat transfer from the detector body to the air in its chamber. Then the expansion of the air and its escape through a vent hole must be accounted for. The response time index determined in a plunge test may not be constant as fire-gas velocities or temperatures vary. Hence, RTI is only an approximation of how the detector responds. Also, it has been hypothesized, but not tested, that rate-ofrise detectors may be modeled by simply comparing the rate of change of gas temperature to their rated response threshold [13]. This hypothesis may be true since their rated response in
40
Design of Detection Systems
degrees per minute or degrees per second is actually the measured rate of gas temperature change in the test apparatus. Thus, it would be expected that if the velocity of the fire gases was on the same order of magnitude as in the test, the rate of change of gas temperature would be the measure for detector response. A rate-compensated detector consists of a metallic shell surrounding two bowed metal struts. There are electrical contacts on the struts. The struts and shell expand at different rates as the detector is heated. When heated fast, the outer shell expands and causes the bowed struts to straighten and close the contacts, signaling an alarm. This condition usually occurs at temperatures below the rated operating temperature. However, if the unit is heated more slowly, the difference between the expansion rates of the inner and outer parts is such that the contacts close at or near the unit’s rated temperature. For rates of temperature rise up to approximately 22 C/min (40 F/min), rate-compensated detectors tend to respond when the surrounding gas temperature reaches the unit’s rated operating temperature [14]. Obviously, the rate-compensated type of heat detector cannot be treated as a lumped mass when calculating its response to a fire. However, at rates of temperature rise less than approximately 22 C/min (40 F/min), they can be modeled by simply assuming that they respond when the surrounding gas temperature reaches their operating temperature. From the discussion above, it is evident that the response of fixed-temperature heat detectors can be modeled. It is necessary to know the temperature at which the detector is rated to operate. For rate-of-rise heat detectors, it is necessary to know the rate of change in the detector’s temperature at which it will alarm. The RTI or τ0 and u0 for the detector are also needed. In order to calculate the response of a heat detector, it is necessary to know the temperature and velocity of the gases flowing past it. Some fire plume models or ceiling-jet models may give functional relationships for temperature and velocity that can be substituted into the heat
1323
transfer equation and integrated. Other models may not be suitable for an analytical solution. In this case, the fire model should be used to produce data on time-versus-temperature and time-versus-gas velocities. These data can then be used to numerically solve the detector heat transfer equation. Most fire and ceiling-jet models do not model the temperature and velocity profile as a function of distance from the ceiling. This lapse introduces error and uncertainty in the results. Marrion [15] showed that maximum temperature and velocity occurs between 1 and 3 in. (25 and 76 mm) below the ceiling for small (5- to 7-in. [127- to 178-mm] diameter) gasoline pan fires with a ceiling clearance of about 14 ft (4.3 m). Others have reported maximums at a distance down from the ceiling of approximately one-tenth the distance from the fuel to the ceiling. Alpert [16] reports ceiling-jet thickness to be approximately 5–12 % of the ceiling to fuel distance. Users are cautioned when modeling detector mechanisms that are not within this range. When the responses of multiple detectors or sprinklers are modeled, no provisions are made to account for sprinkler spray cooling of the room and, therefore, the activation of additional elements (beyond the first) may be inaccurately predicted. For more information on this topic the reader is referred to the references for works by Cooper [17], Delichatsios and Alpert [18], and Heskestad [19].
Heat Detection: Steady-State Fires Alpert [16] presented the following series of equations to calculate temperature and velocity of fire gases in a ceiling jet as a function of heat release rate and position for steady-state fires: h
2=3 i _ 5:38 Q=r
h
H
Tg Ta ¼ ¼
_ 4:74 Q=r
where r/H > 0.18, and
H
C
2=3 i
F
1324
Tg Ta ¼
R.P. Schifiliti et al.
h i 2=3 16:9Q_ H 5=3
C¼
h i 2=3 14:9Q_
H 5=3
ΔT d ¼ T d T a F
where r/H 0.18, and 1=3 1=3 0:20Q_ H1=2 0:25Q_ H1=2 u¼ m=s ¼ ft=s r 5=6 r 5=6 where r/H > 0.15, and Q_ u ¼ 0:95 H
!1=3
Q_ m=s ¼ 1:2 H
tu1=2 ¼ T g T a 1 exp C RTI
The response of heat detectors to fires with ceiling jets having a near constant gas temperature and velocity can be modeled using the above equations.
!1=3 ft=s
where r/H 0.15. In the above series of equations, Tg ¼ Maximum, near ceiling, fire-gas temperature in C or F Ta ¼ Ambient temperature in C or F Q_ ¼ Total heat release rate of the fire in kW or BTU/min r ¼ Radial distance from the axis of the fire plume in m or ft H ¼ Height above the origin of the fire in m or ft u ¼ Maximum, near ceiling, fire-gas velocity in m/s or ft/s This model assumes that the temperature and velocity of the fire gases at a point away from the source are related to the instantaneous heat release rate of the fire. This assumption neglects the time required for transport of the fire gases from the source to the detector. Also, because the correlations are based on the total heat release rate rather than only the convective heat release rate, errors will be introduced when the convective fraction differs from that in the tests used to develop the correlations. For a constant gas temperature and constant gas velocity, the basic heat transfer equation can be solved: Tg Td dT d ¼ dt τ ðt 1 T g T d dt dT d ¼ 0τ ti h C ΔT d ¼ T d T a T g T a 1 exp τ ð40:7Þ or, substituting the equation for RTI
Heat Detection, Growing Fires, and Quasi-Steady-State Modeling A growing fire can be modeled by assuming the fire to be composed of a series of increasing steady heat release rates. This model is referred to as quasi-steady-state modeling. The first step is to break the heat release rate curve into a series of small time intervals. For each interval, use the average heat release rate for that interval to calculate the fire-gas temperature and velocity. Then, starting at ambient temperature, calculate the change and resulting temperature of the detector at the end of the first interval. Using that new detector temperature at the start of the next interval, use the next gas temperature and velocity to calculate the detector temperature at the end of the interval. Continue until you have reached the time of interest or until the detector temperature exceeds its operating temperature. Example 1 A stack of wood pallets is burning under a flat ceiling that is 6 m high. Table 40.2, showing heat release rates, is given below. The ambient temperature is 20 C. What would be the temperature of a ceiling-mounted heat detector having an RTI of 55 m1/2 s1/2 after a 180-s exposure if it were located 6 m from the center of the plume? Solution The detector is located in the developed ceiling jet. The first step is to calculate the change in temperature and the velocity for each heat release rate in the table. For the period 0 to 10 s, the heat release rate is given as 5 kW. The change in temperature and the velocity of the ceiling jet at the detector are
40
Design of Detection Systems
1325
"
Table 40.2 Example 1: heat release rates Δt 0 10 20 30 40 50 60 70 80 90
Q_ 0 5 19 42 75 117 169 230 300 380
2
_ 45:38 Q r Tg Ta ¼
Q_ 469 567 675 792 919 1055 1200 1355 1519
Δt 100 110 120 130 140 150 160 170 180
!2=3 3 5
H " 2=3 # 5 5:38 6
C
¼ 0:794 C 6 T g, 1 ¼ 20:794 C 1=3 0:20Q_ H 1=2 m=s u¼ r 5=6 h i 0:20ð5Þ1=3 ð6Þ1=2 ¼ 0:188 m=s u1 ¼ 65=6
T g, 1 T a ¼
Next calculate the change in detector temperature ΔTd as a result of that exposure by assuming the temperature and velocity to be steady over short intervals; 1 T g T d u =2 T g T d dT d ¼ ¼ dt τ RTI 1 = un 2 T g, n T d:n1 ΔT d ¼ T d, n T d, n1 ¼ Δt C RTI " 1= # u 2 T g, n T d, n1 T d, n ¼ Δt þ T d, n1 C RTI
Initially, the detector is not exposed to hot gases and is at ambient temperature. For the first step or interval, the detector is exposed and the resulting detector temperature at the end of the interval (Td,1) is calculated:
T d, 1
T d, 1
# 1 u =2 T g, 1 T d, 0 Δt þ T d, 0 C ¼ RTI " # 1 = ð0:188Þ 2 ð20:794 20Þ 10 þ 20 ¼ 50 ¼ 20:063 C
To simplify the process, set up a table or a spreadsheet, as shown in Table 40.3, to complete the calculations. Rounding to two significant digits is done last. After 180 s of exposure, the detector temperature is approximately 46 C. If the detector were rated at 57 C, it would not have responded.
Heat Detection: Potential Errors: Steady-State and Quasi-Steady-State Modeling There are many sources of potential error in these calculations. These include uncertainty in the operating temperature, uncertainty in the ambient temperature, and inaccuracies in the fire-gas temperature and velocity correlations. Because the magnitude of these potential errors is unknown or unreported, a tolerance or confidence interval for the answer cannot be estimated. In addition, it has been assumed that use of the ceiling-jet model is valid for the previous example. The model assumes an infinite ceiling for the ceiling jet to flow outward without encountering walls and developing a layer. In the example, the velocity of the ceiling jet for each interval can be used to estimate the approximate position of the leading edge of the ceiling jet. If the ceiling jet is a sufficient size to have reached the bounding walls or draft curtains in a space, a layer will begin to develop. This analysis can be used as a test to determine if additional error is possible because limitations of the model have been exceeded. Evans and Stroup [20] published a computer program called DETACT-QS, which uses Alpert’s equations to calculate the response of heat detectors. That program requires the
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Table 40.3 Example 1: spreadsheet calculations Step, n 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
t
Q
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180
0 5 19 42 75 117 169 230 300 380 469 567 675 792 919 1055 1200 1355 1519
ΔTg 0 0.794 1.934 3.281 4.830 6.496 8.301 10.194 12.170 14.247 16.393 18.603 20.896 23.246 25.669 28.143 30.666 33.252 35.884
Tg — 20.794 21.934 23.281 24.830 26.496 28.301 30.194 32.170 34.247 36.393 38.603 40.896 43.246 45.669 48.143 50.666 53.252 55.884
ΔTd 0 0.063 0.184 0.341 0.525 0.718 0.918 1.112 1.297 1.476 1.641 1.792 1.935 2.063 2.183 2.289 2.385 2.474 2.554
u 0 0.188 0.294 0.383 0.464 0.538 0.609 0.674 0.737 0.797 0.855 0.911 0.965 1.018 1.070 1.120 1.170 1.218 1.265
Td 20 20.063 20.247 20.588 21.114 21.832 22.749 23.861 25.158 26.633 28.274 30.066 32.001 34.064 36.247 38.536 40.921 43.396 45.950
following input: ceiling height, H; ambient temperature, Ta; distance from fire axis to detector, r; detector response or activation temperature, Tr; and detector response time index (RTI). The user must also input history of time versus heat release rate for the fire. The program uses the quasi-steady-state method demonstrated above to calculate the detector response.
NFPA 72, Appendix B, uses a constant called the fire growth time, tg, in lieu of α to describe the fire intensity. The fire growth time is defined as the time at which a power-law fire would reach a heat release rate of 1055 kW (1000 Btu/s). In terms of tg, the power-law equation becomes ! 1055 p _ Q¼ t kW t2g
Heat Detection: Power-Law Fires
The nondimensional functional relationships given by Heskestad and Delichatsios [21] for temperature and velocity of fire gases in a ceiling jet are
Heskestad and Delichatsios [8] presented functional relationships for modeling the temperature and velocity of fires whose heat release rates grow according to the power-law relationship: Q_ ¼ αt p kW where α ¼ Constant for a particular fuel describing the growth of the fire (kW/s2) t ¼ Time (s) p ¼ Positive exponent Q_ ¼ Heat release rate (kW)
u∗p ¼
u A1=ð3þ pÞ α1=ð3þ pÞ H ð p1Þ=ð3þ pÞ
r u∗p ¼ f t∗p0 H
ΔT ∗p ¼
ð40:16Þ
ΔT 2=ð3þ pÞ
A ðT a r ΔT ∗p ¼ g t∗p0 H
=gÞα2=ð3þ pÞ Hð5 pÞ=ð3þ pÞ ð40:17Þ
40
Design of Detection Systems
1327
where
This relationship may also be expressed as A¼
t*p ¼
g C p T a ρo
ð40:18Þ
t
ð40:19Þ
A1=ð3þ pÞ α1ð3þ pÞ H 4=ð3þ pÞ
34=3 2 t∗ t∗ 2 2 f 5 ΔT *2 ¼ 4 D where
All variables are described in this chapter’s nomenclature section. For p ¼ 2 power-law fires, the above nondimensional equations reduce to the following: u∗ 2 ¼ ΔT ∗ 2 ¼
A
t∗ 2 ¼
u A1=5 α1=5 H1=5
2=5
ΔT ðT a =gÞα2=5 H3=5
t A1=5 α1=5 H 4=5
Heskestad and Delichatsios [21] presented correlations to the functional relationships for fires whose release rates vary according to the power-law equation, with p ¼ 2. These fires are referred to as t2 fires. It has been shown [22, 23] that the p ¼ 2 power-law fire growth model can be used to model the heat release rate of a wide range of fuels. The original correlations were used in several publications and popular calculation programs for ceiling-jet and heat-detector modeling, including the first two editions of this handbook [8, 9, 20, 23–26]. Subsequently Heskestad and Delichatsios found that an incorrect value for the heat of combustion of wood resulted in the correlations being in error. All examples in this chapter that use these correlations have been updated or replaced. The corrected data correlations are as follows: [27] r t∗ ¼ 0:861 1 þ 2f H t2f* is the nondimensional time at which the heat front reaches the detector. When t2* < t2f*, the heat front has not reached the detector position. Therefore, ΔT2* ¼ 0. For t2* < t2f*, 2 4 ΔT ∗ 2f ¼
∗ t∗ 2 t2 f
ð0:146 þ 0:242r=H Þ
34=3 5
r H r 0:63
D ¼ 0:146 þ 0:242
u∗ 2 ¼ 0:59 ∗ 1=2 H ΔT 2
The above correlations assume that the convective heat release rate is approximately 75 % of the total heat release rate. When the convective fraction differs from 75 %, the following equations are more useful forms and are used with the nondimensional equations for ΔT2* and u2* by first multiplying α by the convective fraction X: [2] αc ¼ Xα kW=s2 r t∗ 2 f ¼ 0:813 1 þ H
ð40:20Þ
When t2* < t2f* ΔT2* ¼ 0 For t2* t2f*, 2 4 ΔT ∗ 2 ¼
t*2 t∗ 2f
34=3
ð0:126 þ 0:210r=H Þ
5
ð40:21Þ
This may also be expressed as 34=3 2 t*2 t∗ 2f 4 5 ΔT ∗ 2 ¼ D where D ¼ 0:126 þ 0:210
r H
r 0:63 u∗ 2 ¼ 0:59 1:2 H ΔT ∗ 2
ð40:22Þ
ð40:23Þ
Beyler found that these correlations for temperature and velocity could be substituted into the heat transfer equation and integrated [28].
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Beyler’s analytical solution was published in Fire Technology [29] and is repeated here. The analytical solution for the instantaneous rate of change of detector temperature is γ dT d ðtÞ 4 ΔT ∗1=4 ð1 e Þ ¼ ΔT 2 dt 3 ΔT ∗ t=t∗ 2 2 D
ð40:24Þ
The analytical solution for change in detector temperature is ΔT d ¼ T d ðtÞ T d ð0Þ
ΔT ð1 eγ Þ * ¼ ΔT 2 1 γ ΔT *2
ð40:25Þ
where 3 γ¼ 4
rffiffiffiffiffiffisffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ∗ u u∗ ΔT 2 t 2 ∗ 1=2 ∗ D u∗ t RTI 2 ΔT 2 2 ð40:26Þ
and as previously defined, D ¼ 0:126 þ 0:210
r H
ð40:22Þ
In a design situation, the objective is to determine the spacing of detectors required to respond to a specific fire scenario. The detector must respond when the fire reaches a certain threshold heat release rate or in a specified amount of time. Time and heat release rate are interchanged using the fire growth model. The steps in solving this type of problem using the p ¼ 2 power-law model are outlined below and are discussed in more detail in the examples following this section. The referenced equation numbers assume that the correlations used are the ones for a variable convective fraction. The procedure would be the same if using the correlations for the fixed, 75 % convective fractions except that α is not multiplied by the convective fraction when used in the equations. For design problems, 1. Determine the environmental conditions of the area being considered. (a) ambient temperature, Ta (convert to absolute temperature) (b) ceiling height or height above fuel, H
2. Estimate the fire growth characteristic α or tg for the fuel expected to be burning. If tg is used, calculate the corresponding α. Multiply α by the convective fraction to get αc before using in the equations. 3. Establish the goals of the system: required response time tr or maximum permitted threshold heat release rate Q_ T . 4. Select the detector type to be used. For fixedtemperature units, this choice establishes the detector response temperature Tr and its RTI, or τ0 and u0. 5. Make a first estimate of the distance, r, from the fire to the detector necessary to meet the system goals. 6. Assume that the fire starts obeying the power-law model at time t ¼ 0. 7. Set the initial temperature of the detector and its surroundings at ambient temperature. 8. Using Equation 40.20, calculate the nondimensional time, t2f*, at which the initial heat front reaches the detector. 9. Calculate the factor A defined in Equation 40.18. 10. If the equations for a variable convective fraction are used, multiply α by the convective fraction X to get αc and use result that with the required response time in Equation 40.19 to calculate the corresponding value of t*2. 11. If t2* is greater than t2f*, continue with Step 12. If not, try a new detector position, r, closer to the fire and return to Step 8. 12. Calculate the ratio u/u*2 using Equation 40.16. 13. Calculate the ratio ΔT/ΔT2* using Equation 40.17. 14. Use Equation 40.21 to calculate ΔT2*. 15. Equation 40.23 is used to calculate the ratio u2*/(ΔT2*)1/2. 16. Use Equations 40.22 and 40.26 to calculate D and Y. 17. Equation 40.25 can now be used to calculate the resulting temperature of the detector. 18. If the temperature of the detector is below its operating temperature, this procedure must be repeated using a smaller r. If the
40
Design of Detection Systems
temperature of the detector exceeds its operating temperature, a larger r can be used. 19. Repeat this procedure until the detector temperature is about equal to its operating temperature. The required spacing of detectors is then S ¼ 141r. This same procedure is used to estimate the response of rate-of-rise heat detectors. The difference is that in Step 17, Equation 40.24 is used to calculate rate of change of the detector temperature. This result is then compared to the rate at which the detector is designed to respond. The discussion and procedure so far has centered around the solution of a design problem. The question asked was, How far apart must detectors of a specific design be spaced to respond within specific goals to a certain set of environmental conditions and a specific fire scenario? The second type of problem that must be addressed is the analysis of an existing system or the analysis of a proposed design. Here the spacing of detectors or sprinklers is known. The engineer must still estimate the burning characteristics of the fuel and the environmental conditions of the space being analyzed. The equations can then be solved in a reverse fashion to determine the rate of heat release or the time to detector response. The technique is as follows: 1. Determine the environmental conditions of the area being considered. (a) ambient temperature, Ta (convert to absolute temperature) (b) ceiling height or height above fuel, H 2. Estimate the fire growth characteristic α or tg for the fuel expected to be burning. If tg is used, calculate the corresponding α. Multiply α by the convective fraction to get αc before using in the equations. 3. Determine the spacing of the existing detectors or sprinklers. The protection radius pffiffiffi is then r ¼ S= 2. 4. Determine the detector’s rated response temperature and its RTI, or τ0 and u0. 5. Make a first estimate of the response time of the detector or estimate the heat release rate at detector response and calculate the
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corresponding response time using the power-law equation. 6. Assume that the fire starts obeying the power-law model at time t ¼ 0. 7. Set the initial temperature of the detector and its surroundings at ambient temperature. 8. Using Equation 40.20, calculate the nondi* mensional time, t2f , at which the initial heat front reaches the detector. 9. Calculate the factor A defined in Equation 40.18. 10. Use the estimated response time along with Equation 40.19 to calculate the corresponding value of t2*. * 11. If t2* is greater than t2f , continue with Step 12. If not, try a longer estimated response time or a larger estimated heat release rate and return to Step 8. 12. Calculate the ratio u/u2* using Equation 40.16. 13. Calculate the ratio ΔT/ΔT2* using Equation 40.17. 14. Use Equation 40.21 to calculate ΔT2*. 15. Equation 40.23 is used to calculate the ratio u2*/(ΔT2*)1/2. 16. Use Equations 40.22 and 40.26 to calculate D and Y. 17. Equation 40.25 can now be used to calculate the resulting temperature of the detector. 18. If the temperature of the detector is below its operating temperature, this procedure must be repeated using a longer estimated response time. If the temperature of the detector exceeds its operating temperature, a smaller tr can be used. 19. Repeat this procedure until the detector temperature is about equal to its operating temperature. The resulting response time, tr, can be used to calculate either the total heat release rate or the convective heat release rate at response using the power-law equation. As in the design problem, this technique can be used to estimate the response of existing systems of rate-of-rise heat detectors. The difference is that in Step 4 the set point or rate of temperature rise at which the detector will
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respond must be determined from the manufacturer’s data. In Step 17, Equation 40.24 is used to determine the rate at which the temperature of the detector is changing.
Heat Detection: Potential Errors: Power-Law Fire Modeling When the exact conditions of velocity and temperature of fire gases flowing past a detector are not known, errors are introduced in the design and analysis of fire detector response. Graphs in Heskestad and Delichatsios’s report show the errors in calculated fire-gas temperatures and velocities [22]. An exact treatment of these errors is beyond the scope of this chapter, though some discussion is warranted. Plots of actual data and calculated data show that errors in ΔT2* can be as much as 50 %, though generally there appears to be much better agreement [22, 23]. The maximum errors occur at r/H values of about 0.37. All other plots of actual and calculated data, for various r/H, show much smaller errors. In terms of the actual change in temperature over ambient, the maximum errors are on the order of 5–10 C. The larger errors occur with faster fires and lower ceilings. At r/H ¼ 0.37, the errors are conservative when the equations are used in a design problem. That is, the equations predicted lower temperatures. Plots of data for other values of r/ H indicate that the equations predict slightly higher temperatures.
Errors in fire-gas velocities are related to the errors in temperatures. The equations show that the velocity of the fire gases is proportional to the square root of the change in temperature of the fire gases [22]. In terms of heat transfer to a detector, the detector’s change in temperature is proportional to the change in gas temperature and the square root of the fire-gas velocity. Hence, the expected errors bear the same relationships. Based on the discussion above, errors in predicted temperatures and velocities of fire gases will be greatest for fast fires and low ceilings. Sample calculations simulating these conditions show errors in calculated detector spacings on the order of plus or minus 1 m, or less [23]. Similar to Alpert’s steady-state model, the power-law ceiling-jet model assumes a flat infinite ceiling. If the leading edge of the ceiling jet has passed the detector position and not reached a wall or other obstruction, then the model is within its stated parameters. The nondimensional time that the heat front reaches some position, r/H, * is given by the equation for t2f . The corresponding nondimensional time at response is given by the equation for t2*. Setting these equal to each other and solving for r at t ¼ tr gives the radial distance from the fire to the leading edge of the heat front. Using the equations for a userentered convective fraction, r t∗ 0:813 1 þ 2f H and
t∗ 2 ¼
tr 1=5 1=5 4=5 A αc H
∗ t∗ 2 f ¼ t2 r tr 0:813 1 þ ¼ 1=5 1=5 H A αc H 4=5 nh i o 1=5 r¼ tr = ¼ A1=5 αc H 4=5 =0:813 1 H r ¼ t∗ 2 =0:813 1 H
40
Design of Detection Systems
Selection of Data for Design and Analysis In order to calculate the required spacing of heat detectors or sprinklers to respond to a given fire, the following information is required: 1. System goals: desired fire size (heat release rate) at response or time to detector response from the start of open flaming 2. Fire growth constant α or tg 3. Ambient temperature 4. Height above the fuel or ceiling height In addition to the above, the heat capacity of air at constant pressure, Cp, the density of air, ρ, and the gravitational constant, g, are used in the calculations. It is also necessary to know the characteristics of the detector for which the spacing calculations are being made. Specifically, the response temperature and the RTI of the detector must be known. Establishing system goals is not within the scope of this chapter. However, it should be pointed out that, no matter what the goals are, they must be expressed in terms of heat release rate or time to detector response. The system’s goals may actually be to limit damages to some dollar value, provide adequate escape time, or limit the production of toxic gases. In order to calculate required detector spacing using this system, these goals would have to be translated. For instance, as the fire grows, at what time or heat release rate must the detector respond so that the fire department can be summoned and extinguish the fire before damage levels are exceeded or conditions become untenable due to toxic gases? Table 40.4 is a list of furniture calorimeter tests done at the National Bureau of Standards [16, 24]. The tests provide a database of heat release rate, particulate production, and radiation from a variety of common furnishings. The table provides the corresponding α or tg for the calorimeter tests [23]. The virtual time data in the table is the approximate time at which the heat release rate in the test began to follow the p ¼ 2 power-law model ( Q_ ¼ αt2 kW ). Prior to this time, the behavior of the fire cannot be predicted
1331
with this model. Figure 40.5 shows some test data along with a power-law curve superimposed. The data in Table 40.4 can be used to select α or tg for use in spacing calculations. However, in many cases the data in this table will not match the scenario being studied. If the heat release rate versus time history can be obtained or approximated for the expected fuel, the α or tg can be calculated using curve-fitting techniques [23]. In most cases, since the exact fuel that will be involved in a fire cannot be known, the rigorous calculation of α is not warranted. Engineering judgment can be used to select α or tg that approximates the severity of the fire. The data in Table 40.4 suggest a range of 50–500 s for tg. Only a few rapidly developing fires had a tg below 50 s. Three slow fires had values above 500 s for tg. Table 40.4 also lists the maximum heat release rate reached during the power-law growth. The heat release rate model Q_ ¼ αt2 does not predict when a fuel package stops following the model or when the fuel is depleted. This task is an important point often missed by many designers. A simple test is to calculate the mass of fuel consumed from t ¼ 0 to the time of interest. For p ¼ 2 power-law fire growth rate, the total energy consumed is ðt ðt E¼ αt2 kJ Q_ ¼ t¼0
E¼
t¼0
αt3 kJ 3
Knowing the heat of combustion, Hc, for the fuel permits calculation of the mass of fuel necessary to release a given amount of energy in the time period: E ¼ mH c kJ E g or kg ðdepending on the units for Hc Þ m¼ Hc When doing a design or analysis, try several different fire growth rates to determine the effect of their variance on the calculations. In some
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Table 40.4 Summary of NBS calorimeter tests
Test no. Test 15 Test 18 Test 19 Test 19 Test 21 Test 21 Test 21 Test 22 Test 23 Test 24 Test 25 Test 26 Test 27 Test 28 Test 29 Test 29 Test 30 Test 31 Test 37 Test 38 Test 39 Test 40 Test 41 Test 42 Test 42 Test 43 Test 44 Test 45 Test 46 Test 47 Test 48 Test 49 Test 50 Test 51 Test 52 Test 53 Test 54 Test 55 Test 56 Test 57 Test 61 Test 62 Test 64 Test 66 Test 67 Test 67
Description Metal wardrobe 41.4 kg (total) Chair F33 (trial loveseat) 39.2 kg Chair F21 28.15 kg (initial stage of fire growth) Chair F21 28.15 kg (later stage of fire growth) Metal wardrobe 40.8 kg (total) (average growth) Metal wardrobe 40.8 kg (total) (later growth) Metal wardrobe 40.8 kg (total) (initial growth) Chair F24 28.3 kg Chair F23 31.2 kg Chair F22 31.9 kg Chair F26 19.2 kg Chair F27 29.0 kg Chair F29 14.0 kg Chair F28 29.2 kg Chair F25 27.8 kg (later stage of fire growth) Chair F25 27.8 kg (initial stage of fire growth) Chair F30 25.2 kg Chair F31 (loveseat) 39.6 kg Chair F31 (loveseat) 40.40 kg Chair F32 (sofa) 51.5 kg 1 /2-in. Plywood wardrobe w/ fabrics 68.8 kg 1 /2-in. Plywood wardrobe w/ fabrics 68.32 kg 1 /8-in. Plywood wardrobe w/ fabrics 36.0 kg 1 /8-in. Ply. wardrobe w/ fire-ret. (int. fin. initial) 1 /8-in. Ply. wardrobe w/ fire-ret. (int. fin. later) Repeat of 1/2-in. Plywood wardrobe 67.62 kg 1 /8-in. Ply. wardrobe w/ F-R., latex paint 37.26 kg Chair F21 28.34 kg (large hood) Chair F21 28.34 kg Chair adj. back metal frame, foam cush. 20.8 kg Easychair CO7 11.52 kg Easychair 15.68 kg (F-34) Chair metal frame minimum cushion 16.52 kg Chair molded fiberglass no cushion 5.28 kg Molded plastic patient chair 11.26 kg Chair metal frame w/ padded seat and back 15.5 kg Loveseat metal frame w/ foam cushions 27.26 kg Group chair metal frame w/ foam cushion 6.08 kg Chair wood frame w/ latex foam cushions 11.2 kg Loveseat wood frame w/ foam cushions 54.60 kg Wardrobe 3/4-in. particleboard 120.33 kg Bookcase plywood w/ aluminum frame 30.39 kg Easychair molded flexible urethane frame 15.98 kg Easychair 23.02 kg Mattress and boxspring 62.36 kg (later fire growth) Mattress and boxspring 62.36 kg (initial fire growth)
Maximum Virtual heat release Fire growth time (s) (tg) α (kW/s2) time (s) rate (kW) 50 0.4220 10 750 400 0.0066 140 950 175 0.0344 110 350 50 0.4220 190 2000 250 0.0169 10 250 120 0.0733 60 250 100 0.1055 30 140 350 0.0086 400 700 400 0.0066 100 700 2000 0.0003 150 300 200 0.0264 90 800 200 0.0264 360 900 100 0.1055 70 1850 425 0.0058 90 700 60 0.2931 175 700 100 0.1055 100 2000 60 0.2931 70 950 60 0.2931 145 2600 80 0.1648 100 2750 100 0.1055 50 3000 35 0.8612 20 3250 35 0.8612 40 3500 40 0.6594 40 6000 70 0.2153 50 2000 30 1.1722 100 5000 30 1.1722 50 3000 90 0.1302 30 2900 100 0.1055 120 2100 45 0.5210 130 2600 170 0.0365 30 250 175 0.0344 90 950 200 0.0264 50 200 200 0.0264 120 3000 120 0.0733 20 35 275 0.0140 2090 700 350 0.0086 50 280 500 0.0042 210 300 Never exceeded 50 kW heat release rate 500 0.0042 50 85 350 0.0086 500 1000 150 0.0469 0 1200 65 0.2497 40 25 1000 0.0011 750 450 75 0.1876 3700 600 350 0.0086 400 500 1100 0.0009 90 400
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Design of Detection Systems
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2 1.9
Rate of heat release (kW) (thousands)
1.8 1.7
Test data
1.6
Best fit
1.5
p = 2 power-law curve
1.4 1.3 1.2 1.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0
40
80
120
160
200
Time (s)
Fig. 40.5 Test 27 chair
cases, the effect will be minimal. In other cases, this type of sensitivity analysis will show that a more thorough analysis of the possible fuels and fire scenarios is warranted. The selection of an ambient temperature can have a measurable effect on the calculations. The calculations assume that the detector or sprinkler starts out at the same temperature as the ambient air when the fire starts. Hence, if a temperature of 20 C is assumed for the spacing calculations and the actual temperature at the time of the fire is 10 C, the system’s goals will not be met. For design calculations to be conservative, the lowest expected ambient temperature should be used. The relationships presented by Heskestad and Delichatsios [21] are correlated to fire test data using the ceiling height above the fuel surface for H. If this height varies, the larger value of H will produce more conservative results in the calculations for detector spacing or response. The most conservative results are obtained when the floor-to-ceiling height is used, since this height is the maximum vertical distance from fuel to detector.
The values for Cp, ρ0, and g should be 1.040 kJ/(kgK), 1.1 kg/m3, and 9.81 m/s2, respectively. Slight variations in these constants have negligible effects on the calculations. As previously mentioned, the design or analysis calculations are done for a particular detector or sprinkler. Therefore, it is necessary to know the unit’s operating temperature. The response time index or τ0 and u0 are also needed. Operating temperature is obtained from manufacturer’s data. The detector’s sensitivity is best determined by conducting a plunge test [9]. In the absence of plunge test data, a detector’s UL-listed spacing can be used as a measure of detector sensitivity. Heskestad and Delichatsios analyzed UL test data and calculated time constants, τ0, for various combinations of UL-listed spacing and detector operating temperature [22]. The Appendix Subcommittee of NFPA 72 expanded the table to include a larger selection of detectors [8]. That table is reproduced here as Table 40.5.
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Table 40.5 Time constants for any listed detector t0 (s)a Listed spacing (ft) 10 15 20 25 30 40 50 70
UL ( F) 128 400 250 165 124 95 71 59 36
135 330 190 135 100 80 57 44 24
145 262 156 105 78 61 41 30 9
160 195 110 70 48 36 18
170 160 89 52 32 22
196 97 45 17
FMRC all temp. 195 110 79 48 36
Reproduced from NFPA 72 (1993, Appendix B [8]) These time constants are based on an analysis of the Underwriters Laboratories Inc. and Factory Mutual Research Corporation listing test procedures Plunge test results performed on the detector to be used will give a more accurate time constant a At a reference velocity of 5 ft/s
Heat Detection Design and Analysis Examples Using the Power-Law Fire Model Analysis and design problems will be used to show how fire protection engineers can use the techniques presented in this chapter. The examples show the sensitivity of these techniques to changes in variables and input parameters. A design problem is first worked by hand to solve the equations presented earlier in the section on heat detection. The remaining examples were worked using a spreadsheet written to solve the equations. Example 2 A fire detection system is being designed for an unsprinklered manufacturing building. The area being considered has a large, flat ceiling 5.0 m high. Ambient temperature is normally 20 C, but on weekends it is cut back to 10 C. It will be assumed that the fire scenario involves the ignition of a stack of wood pallets. The pallets are stacked 1.5 m (5 ft) high. Fire tests [8] show that this type of fire follows the p ¼ 2 power-law equation with a tg of approximately 150 s. The corresponding α can be calculated: Q_ ¼ αt2 kW α¼
1055 1055 ¼ ¼ 0:047 kW=s2 t2g 1502
The goal is to detect the fire before it reaches a total heat release rate of 2500 kW. Fixedtemperature heat detectors will be used. The detectors have a 57 C (135 F) operating temperature and a UL-listed spacing of 30 ft. From Table 40.5 the time constant is found to be 80 s. This time constant is referenced to a gas velocity of 1.5 m/s and can be used with Equation 40.9 to calculate the detector’s RTI. First, use the power-law equation to calculate the time that the fire would reach a total heat release rate of 2500 kW: Q_ ¼ αt2 kW rffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffi 2500 Q_ ¼ t¼ ¼ 231 s 0:047 α The RTI is calculated using Equation 40.9 and a reference velocity, u0, of 1.5 m/s (5 ft/s): 1=2
RTI ¼ τ0 u0
pffiffiffiffiffiffiffi ¼ 80 1:5 ¼ 98 m1=2 s1=2
As described previously in Step 5 for design of a proposed system, it is necessary to make a first guess at the required detector spacing. In this case, try using r ¼ 6.0 m. Use Equation 40.20 to calculate the nondimensional time, t2f*, at which the initial heat front reaches the detector. Use the distance from the top of the fuel package to the ceiling for H.
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Design of Detection Systems
1335
r t∗ ¼ 0:813 1 þ 2f H 6:0 ∗ t2 f ¼ 0:813 1 þ ¼ 2:207 3:5 Next, Equation 40.18 is used to calculate A. Note that in this equation the ambient temperature, Ta, must be expressed as an absolute temperature. In this case add 273 to C to get K (Kelvin). A¼
The nondimensional time corresponding to the required response time is now calculated. However, first we must calculate αc. Assuming a convective fraction of 70 %: αc ¼ Xα ¼ 0:70ð0:047Þ ¼ 0:033 kW=s2
t∗ 2 ¼
ΔT ΔT ∗ 2 ΔT ΔT ∗ 2
u
2=5 ðT a =gÞαc H 3=5 T a 2=5 3=5 ¼ A2=5 αc H g 2=5 283 ¼ ð0:030Þ ð0:033Þ2=5 ð3:5Þ3=5 9:81 A
2=5
¼ 0:855 The nondimensional change in gas temperature is now calculated:
g C p T a ρo
9:81 ¼ 0:030 A¼ 1:040ð10 þ 273Þ1:1
t∗ 2 ¼
ΔT ∗ 2 ¼
t
ð0:030Þ1:5 ð0:033Þ1=5 ð3:5Þ4=5
ΔT ∗ 2
ð21:256 2:207Þ ¼ 0:486
4=3 ¼ 133:142
Next, the ratio u2*/(ΔT2*)1/2 is calculated:
1=5 A1=5 αc H 4=5
231
6:0 D ¼ 0:126 þ 0:210 ¼ 0:486 3:5 34=3 2 ∗ t∗ 2 t2 f 4 5 ΔT ∗ 2 ¼ D
¼ 21:256
Since t*2 f > t*2 , we know that the heat front has passed the detector location. Next, the ratio of the velocity to the nondimensional velocity is calculated: u u∗ 2 ¼ 1=5 1=5 1=5 A αc H u 1=5 ¼ A1=5 αc H 1=5 u∗ 2 u ¼ ð0:030Þ1=5 ð0:033Þ1=5 ð3:5Þ1=5 ¼ 0:322 u∗ 2 The ratio of the change in gas temperature to the nondimensional gas temperature is calculated:
r 0:63 u∗ 2 ¼ 0:59 1=2 H ΔT ∗ 2 0:63 u∗ 6:0 2 ¼ 0:59 ¼ 0:420 ∗ 1=2 3:5 ΔT 2
Y is now calculated: ffi rffiffiffiffiffiffisffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u u∗ ΔT ∗ t 2 2 ∗ D 1=2 RTI u∗ t ð ΔT Þ 2 2 2 p ffiffiffiffiffiffiffiffiffiffiffi p ffiffiffiffiffiffiffiffiffiffiffi 3 133:142 231 0:322 0:420 ϒ¼ ð0:486Þ 4 98 21:256 3 ϒ¼ 4
¼ 1:979
The resulting temperature of the detector at t ¼ 231 s, Td(t), can now be calculated. Assume that the temperature of the detector at the start of the fire, Td(0), is the same as ambient temperature, Ta.
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ΔT d ¼ T d ðtÞ T d ð0Þ
ΔT 1 eϒ ∗ ¼ ΔT 2 1 ΔT ∗ ϒ 2 ΔT d ¼ T d ðtÞ T d ð0Þ
1 e1:979 ¼ 0:855ð133:142Þ 1 1:979
ΔT d ¼ T d ðtÞ T d ð0Þ ¼ 64:264 T d ðtÞ ¼ ΔT d ¼ T d ð0Þ ¼ 64:264 þ 10 ¼ 74:264 ¼ 74 C After 231 s, when the heat release rate has reached 2500 kW, the detector located 6 m from the fire axis has reached an approximate temperature of 74 C. Note that the answer has been rounded to two significant digits, one more than the least precision of any of the variables. This rule is the alternate rule for rounding as discussed in the introduction of this chapter. The detector actuation temperature is 57 C. This result indicates that the detector has responded before the fire has reached 2500 kW. Since the calculated temperature is higher than the actuation temperature, a larger r can be tried. The calculations should be repeated until the calculated detector temperature is approximately equal to the actuation temperature. For this example the answer converges on a radial distance of approximately 7.4 m. The spacing between detectors is pffiffiffi pffiffiffi S ¼ r 2 ¼ 7:4 2 ¼ 10:5 m Example 3 This example will show how an existing heat detection system or a proposed design can be analyzed to determine its response time or fire size at response. The scenario used in Example 2 will be repeated, except that the manufacturing building has an existing system of heat detectors, which are spaced evenly on the ceiling at 15.0-m intervals. The detector characteristics are the same as above. The actuation temperature is 57 C and the RTI is 98 m1/2 · s1/2. The ceiling height is 5 m, and the height of the pallets is 1.5 m. Ambient temperature is 10 C. α is 0.047 kW/s2 (tg ¼ 150 s) and αc is 0.033 kW/s2.
The maximum radial distance from the fire axis to a detector is calculated first, using Equation 40.5. pffiffiffi S¼r 2m S 15:0 r ¼ pffiffiffi ¼ pffiffiffi ¼ 10:6 m 2 2 The next step in the analysis is to estimate the response time of the detector or the fire size at response. In the design above, the fire grew to about 2500 kW in 231 s when the detector at a distance of 7 m responded. The radial distance in this example is larger and should result in a slower response and larger fire size at response. A first guess at response time might be 6 min or 360 s. The fire size (total heat release rate) at 360 s is Q_ ¼ αt2 kW Q_ ¼ 0:047ð360Þ2 ¼ 6091 kW The remaining calculations for the resulting detector temperature are similar to those in Example 2. Rather than show the detail, a spreadsheet was used to complete the calculations. The resulting detector temperature at 360 s was calculated to be approximately 84 C. This result indicates that the detector response time is less than the estimated 6 min. Therefore, a smaller response must be tried. If the calculated temperature were lower than the actuation temperature, a larger t would be tried. The calculations are repeated until the calculated detector temperature is approximately equal to the actuation temperature. In this case, the response time converges at 295 s. This result corresponds to a fire size at response of 4070 kW. It is at this time and heat release rate that the detector temperature reaches its actuation temperature of 57 C. This example assumes that the fire continues to follow the power-law relationship through the burning period. If there is not enough fuel available, it is possible for the heat release rate curve to flatten out before reaching 4070 kW. These calculations do not predict when this development will happen. These calculations also do
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Design of Detection Systems
1337
not predict how the detector temperature changes after the fire stops following the power-law relationship. It may be that sufficient heat continues to be released and the detector eventually responds. It is also possible for the fire gases to cool sufficiently to preclude detector actuation unless additional fuel becomes involved in the fire. Comparing Example 2 with Example 3 shows how detector spacing affects response time. A difference in spacing of 4.4 m (15–10.6 m) results in a difference of approximately 64 s in the detector response time. Because the fire is accelerating according to the p ¼ 2 power-law relationship, the resulting difference in fire size at response is 1570 kW. Example 4 A warehouse is used to store sofas and other furniture. The sofas are similar to one tested by the National Bureau of Standards in their furniture calorimeter [30]. Burning characteristics are assumed to be similar to the sofa used in Test 38: [23, 30] α ¼ 0.1055 kW/s2, tg ¼ 100 s; peak heat release rate ¼ 3000 kW. The sofas are stored one or two high. Assume a convective fraction of 65 %. The building has a flat roof and ceiling. The distance from the floor to the ceiling is 4.6 m. When the sofas are stacked two high, the distance from the top of the fuel package to the ceiling is 2.4 m. Ambient temperature in the warehouse is kept above 10 C (Fig. 40.6). Fig. 40.6 Example 4: warehouse
Based on maximum allowable property loss goals established by the owner, it is desirable to detect a fire and notify the fire department prior to a second fuel package becoming involved. The original NBS report [30] contains data on radiation measured during Test 38. This information can be used along with other techniques presented in this handbook to determine when a second item might ignite. For instance, it might be determined that furniture across a 2-m aisle might ignite when the fire reaches a total heat release rate of 3000 kW. The objective would then be to detect the fire soon enough so that the fire can be extinguished or controlled before the fire reaches a total of 3000 kW. In this example, it is assumed that the fire must be detected when it reaches a total heat release rate of about 2000 kW. The fire detection system will consist of fixedtemperature heat detectors connected to a control panel that is, in turn, connected to the local fire department. The detector to be used has a fixed-temperature rating of 57 C and an RTI of 42 m1/2 s1/2. The problem is determining the spacing of detectors required to detect this fire. When the computer program runs, the user is prompted for all of the above information. In this example, the data are fixed except for the distance from the ceiling to the flame origin. If the distance between the top of the fuel and the ceiling (2.4 m) is used, the calculations indicate that the
Roof T∞ = 50°F 10°C
2.4 m (8 ft)
4.6 m (15 ft)
3.7 m (12 ft)
2.1 m (7 ft)
Floor
Warehouse
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R.P. Schifiliti et al.
detectors must be spaced 7.3 m apart to respond when the fire reaches a heat output of 2000 kW. For a worst-case analysis, the distance from the floor to the ceiling (4.6 m) is used. This distance results in a required detector spacing of 5.9 m. A more realistic worst-case scenario would be when the sofas are not stacked two high. With one sofa on the floor, the distance from the fuel to the ceiling would be about 3.7 m. The required detector spacing would then be 6.5 m. These results are summarized in Table 40.6. This table clearly shows the relationship between ceiling height and detector response. The greater the distance from the fire to the ceiling, the closer the detectors must be spaced to respond within the goals of the system. Designs based on the floor-to-ceiling distance are conservative and representative of a worst-case condition. More realistic designs are based on the most probable or the greatest expected vertical clearance between fuel and detector. Example 5 For the same conditions in Example 4, if the detector spacing is fixed at 10.3 m (r ¼ 7.3 m), how does the ceiling height affect the response time of the system? Using the spreadsheet, the results, after rounding, are summarized in Table 40.7. Example 6 This example will show how to select a detector type to economically meet the system’s goals. The fire scenario and goals used Table 40.6 Example 4: ceiling height or height above fuel versus detector spacing Ceiling height, H (m) 2.4 3.7 4.6
Required spacing, S (m) 10.3 9.2 8.4
Table 40.7 Example 5: ceiling height or height above fuel versus response time Ceiling height, H (m) 2.4 3.7 4.6
Required spacing, tr (s) 140 150 160
in Examples 4 and 5 will be used: H ¼ 2.4 m; Ta ¼ 10 C; RTI ¼ 42 m1/2 s1/2; X ¼ 65 %, tg ¼ 100 s. In Example 4, it was found that heat detectors with a fixed temperature rating of 57 C and an RTI of 42 m1/2 s1/2 must be spaced 10.3 m apart to meet the system’s goals—a response at 2000 kW. Here, the spacing of rate-of-rise heat detectors will be estimated. The detector to be used is rated to respond when its temperature increases at a rate of 11 C minutes or more. The detector’s RTI will be assumed to be the same as the detector in Example 4. The calculation procedure is the same as for fixed temperature detectors except that, in the last step, the equation for the rate of temperature change is used: ϒ dT d ðtÞ 4 ΔT ∗1=4 1 e ¼ ΔT 2 dt 3 ΔT ∗ t=t∗ 2 2 D Solving the equations, it is found that the rateof-rise heat detectors can be spaced up to 25 m apart and respond at approximately 2000 kW total heat release rate. If the total area of the warehouse is 5000 m2, approximately 48 fixed-temperature heat detectors would be required to meet the established goals. The same goals can be met with approximately eight rate-of-rise heat detectors. Additional detectors might be required due to obstructing beams or walls. It should also be pointed out that the use of m2 for calculating the required number of units is only an estimate. The detector does not cover an area that is 625 m2 (25 m 25 m). It is covering a circular area having a radius no more than about 17.7 m. That is, all points on the ceiling must be within the protection radius of a detector for the calculations to be valid. If one used a “rated area” for a detector rather than a radial measurement, it could be concluded that a single detector in this example could cover a space that was 125 m long if it were only 5 m wide. By trying different detector types or detectors with higher sensitivities, project goals might be met with a fewer number of detectors. The scenario in this example shows that, to detect the
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Design of Detection Systems
1339
same fire, a much greater number of fixedtemperature heat detectors than rate-of-rise heat detectors is required. This conclusion is not always the case. Many fires will develop slowly and cause high ceiling temperatures without ever exceeding the rate of temperature rise necessary to actuate a rate-of-rise heat detector. As a backup, most commercially available rate-of-rise heat detectors have a fixed-temperature element also. The rate-of-rise element and the fixedtemperature element should be considered separately when designing or analyzing a system. Example 7 In this example, a combination fixedtemperature and rate-of-rise heat detector will be analyzed and the response of the two elements will be compared. For an installed spacing of 10.0 m (r ¼ 0.707 m), the effect of fire growth rate on response time will be shown. The following conditions from Examples 4, 5, and 6 will be repeated: H ¼ 2.4 m; Ta ¼ 10 C; RTI ¼ 42 m1/2 s1/2; X ¼ 65 %. The fixed-temperature element response threshold is Tr ¼ 57 C, and the rate-ofrise threshold is dTr/dt ¼ 11 C/min. The results are shown in Table 40.8 and Fig. 40.7. For fire growth times up to tg ¼ 509 s, the rate-of-rise element responds faster. For fires that grow slower (increasing tg), the fixedtemperature element will respond faster. For larger installed spacings, such as the 25 m spacing calculated in the previous example for the spacing of the rate-of-rise detector, the crossover point occurs sooner. The results for a 25 m spacing are shown in Table 40.9 and Fig. 40.8. For fire growth times up to tg ¼ 228 s, the rateof-rise element responds faster. For fires that Table 40.8 Response time as a function of fire growth time, tg tg 50 100 200 300 400 500 509 600
Response time, tr (s) Fixed temperature 85 135 219 297 373 447 454 521
Rate of rise 31 53 98 155 241 426 454 835
grow slower (increasing tg), the fixedtemperature element will respond faster. Example 8 In this example, the effects of fire growth rate on detector spacing will be examined. The scenario used in Examples 4 through 7 will be used again. The following conditions from these examples will be repeated: H ¼ 2.4 m; Ta ¼ 10 C; RTI ¼ 42 m1/2 s1/2; X ¼ 65 %. The fixed-temperature element response threshold is Tr ¼ 57 C and the rate-of-rise threshold is dTr/dt ¼ 11 C/min. In Examples 4, 5, and 6, the rate of fire growth followed the power-law equation with an α of 0.1055 kW/s2 or tg ¼ 100 s. Calculations were done for several values of tg. The results are summarized in Table 40.10 and Fig. 40.9. For fixed-temperature detectors, if the fire grows at a faster rate (smaller tg), a smaller spacing is required to meet the system’s goals. If the fire grows at a slower rate, a larger detector spacing is allowed. This relationship clearly shows the effects of thermal lag on detector response. At slow rates of growth, the detector is immersed in the hot fire gases and, despite thermal lag, has time to absorb the heat before the fire reaches the maximum permissible heat release rate. The effects of thermal lag are less important at slow rates of fire growth. The rate-of-rise detector also experiences thermal lag. However, the curve peaks at approximately tg ¼ 110 m1/2 s1/2 and S ¼ 25 m. For the rate-of-rise detector, as the fire growth rate slows (larger tg), thermal lag decreases as it did for the fixed-temperature detector. However, as the rate of fire growth slows, so does the rate of change of the detector’s temperature. For this particular detector and fire scenario, at fire growth times greater than about 110 s, the detector spacing must be reduced so that the threshold rate of change of the detector temperature is reached before the maximum permissible heat release rate is reached. Example 9 In this example a detector is exposed to the ceiling jet for a fire with tg ¼ 150 s and a 75 % convective fraction. Ambient temperature is 10 C. The ceiling is 4 m high, and the detector is located at a radial distance of 5 m from the fire.
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R.P. Schifiliti et al. Example 4a
Fig. 40.7 Response time as a function of fire growth time, tg
900
Response time, tr (s)
800
Fixed temperature Rate of rise
700 600 500 400 300 200 100 0 0
200
400
600
800
Fire growth time, tg (s)
Table 40.9 Response time as a function of fire growth time, tg tg 50 100 200 228 300
Response time, tr (s) Fixed temperature 168 269 448 497 619
Rate of rise 77 140 355 497 1330
The RTI of the detector is 50. Plot the detector temperature and the fire-gas temperature at the detector location for t up to 240 s. The detector remains at ambient temperature until the ceiling jet first reaches the detector position. At what time does the ceiling jet first reach the detector? This result is found by setting t*2 f ¼ t*2 and solving for t. First, αc is calculated: t2g
1055 ¼ 0:047 kW=s2 1055 1502 αc ¼ Xα ¼ 0:75ð0:047Þ ¼ 0:035 kW=s2 α ¼
¼
∗ t∗ 2 f ¼ t2 r t 0:813 1 þ ¼ 1=5 H A1=5 αc H4=5 r 1=5 ¼ A1=5 αc H 4=5 s t ¼ 0:813 1 þ H 5 t ¼ 0:813 1 þ 4 1=5 ¼ 0:030 0:0351=5 44=5
¼ 21:86 ¼ 22 s
The heat front reaches the detector at about 22 s, and heating begins. Prior to this point, the detector and gas temperature surrounding the detector are at ambient temperature. The method to calculate the detector temperature is the same as in previous examples. To calculate the change in ceiling-jet gas temperature, combine the following equations and solve to ΔT: ΔT *2 ¼
ΔT A
2=5
ðT a =gÞαc H3=5 2=5
and ∗ t∗ 2 22 f
2 4 ΔT ∗ 2 ¼
ð0:126 þ 0:210r=H Þ
ΔT ¼ A
2=5
2 4
34=3 5
T a 2=5 3=5 αc H g ∗ t∗ 2 22 f
ð0:126 þ 0:210r=H Þ
34=3 5
A spreadsheet solution is shown Table 40.11 and graphed in Fig. 40.10.
in
Example 10 A sprinkler system is being installed in a large exhibition hall. The building has a flat roof deck supported by open space frame trusses. The distance from the underside
40
Design of Detection Systems
1341 Example 7
Fig. 40.8 Response time as a function of fire growth time, tg
1400 Fixed temperature Rate of rise
Response time, tr (s)
1200 1000 800 600 400 200 0 0
100
200
300
400
Fire growth time, tg (s)
Table 40.10 Required detector spacing as a function of fire growth time, tg tg 50 75 100 110 120 150 200 300 400 500 600
Required spacing (m) Fixed temperature 7.2 9 10 11 11 12 14 15 16 17 18
Rate of rise 23 24 25 25 24 24 22 18 14 12 10
Example 8
Fig. 40.9 Required detector spacing as a function of fire growth time, tg Detector spacing, S (m)
30 Fixed temperature
25
Rate of rise
20 15 10 5 0 0
200
400 Fire growth time, tg (s)
600
800
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R.P. Schifiliti et al.
of the roof deck to the floor is 12 m. Ambient temperatures do not usually fall below 5 C. Three different designs for the sprinkler system have been proposed. All three are designed to provide the same water density over a
Table 40.11 Example 9: ceiling jet and detector temperature as a function of time t (s) 22 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240
Td (s) 10 10 10 11 13 15 18 21 25 30 35 40 46 52 59 66 73 81 88 96 104 112 120
Tg (s) 10 12 15 19 24 29 34 39 45 51 58 64 71 78 85 93 100 108 116 124 132 140 148
specified area. Each proposal uses a sprinkler with a temperature rating of 74 C and an RTI of 110 m1/2 s1/2. The only difference among the three systems is the spacing of the sprinklers and the branch lines that feed them. The first proposal uses a square array with a spacing of 3.0 m. The second and third proposals are based on square array spacings of 3.7 m and 4.6 m, respectively. What effect will the three different spacings have on the size of the fire when the system responds? Assume two different fire scenarios. In the first, the fire grows at a moderate rate with tg ¼ 200 s. The second fire scenario has a slower fire growth rate with tg ¼ 500 s. For both, assume a convective fraction of 75 %. Results of the calculations are shown in Table 40.12 after rounding. The calculations show an increase of about 25 % in the fire size at response when the spacing is increased 50 % from 3.0 to 4.6 m. The increased spacing may result in a lower system cost. However, closer spacings mean that the sprinkler system will probably respond sooner. The fire protection engineer can use this type of analysis to assist in choosing a system that best meets the project’s overall goals. Example 11 A fire impacting elevator machinery can result in passengers or fire fighters being carried to a fire floor or being trapped between floors. Elevator safety codes generally do not require any sprinkler protection or detection at Example 9
Fig. 40.10 Example 9: ceiling jet and detector temperature as a function of time
160
Temperature (°C)
140
Gas temperature Detector temperature
120 100 80 60 40 20 0 0
100
200 Time (s)
300
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Design of Detection Systems
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Table 40.12 Example 10: effects of sprinkler spacing on fire size at response and time to response tg ¼ 200 s S (m) 3.0 3.7 4.6
tr (s) 350 370 400
Table 40.13 Example 11: sprinkler and heat detector response to different fire growth rates
tg ¼ 200 s Q_ T ðkWÞ 3300 3600 4100
tr (s) 800 840 890
Q_ ðkWÞ 2700 3000 3400
the top of shafts since the fuel load is typically insufficient to actuate a sprinkler or affect persons in the cars. Smoke detection is used in elevator lobbies and machine rooms to recall elevators to a safe level when smoke threatens the elevator shaft. The presence of sprinklers in the elevator machine room presents another risk: the possibility of water discharge on energized controllers and motors and on the elevator brakes. To reduce this risk, in addition to smoke detection, heat detectors may be used to ensure that equipment is de-energized on or prior to the discharge of water. To accomplish this task, some codes may require a heat detector with a lower temperature rating and a lower RTI within 0.61 m of every sprinkler in an elevator machine room. Are these requirements sufficient to assure response before the sprinkler to a range of possible fire scenarios? Solution For this example, use an ambient temperature of 15 C and a ceiling height or clearance of 4 m. Assume the actuation temperature of the sprinklers is 74 C and the actuation temperature of the heat detectors is 57 C. The RTI of the sprinklers is 110 m1/2 s1/2, and the RTI of the detectors is 42 m1/2 s1/2. Spacing of the sprinklers is 3.0 m. Calculate the response of the sprinkler and the heat detector to a fast fire, tg ¼ 50 s, and a slow fire, tg ¼ 600 s. Assume a 75 % convective fraction. A sprinkler spacing of 3.0 m results in a worst-case radial distance of 2.12 m. The heat detector could be an additional 0.61 m beyond at r ¼ 2.73 m. The results of the calculations are summarized in Table 40.13. These calculations show that the heat detector will respond before the sprinkler. Depending on the actual conditions, additional
Sprinkler Heat detector
Response time (s) tg ¼ 50 s 65 50
tg ¼ 600 s 370 300
calculations should be tried for different fire scenarios and for changes in other variables such as RTI, ambient temperature, ceiling clearance, and so forth.
Smoke Detection In order to determine whether or not a smoke detector will respond to a given Q_ cr , a large number of factors must be evaluated. These include smoke aerosol characteristics, aerosol transport, detector aerodynamics, and sensor response. Smoke aerosol characteristics at the point of generation are a function of the fuel composition, the combustion state (smoldering or flaming), and the degree of vitiation of the combustion air. The characteristics considered include particle size and distribution, particle number or concentration at various sizes, composition, color, and refractive index. Given the dynamic nature of fire growth and spread and fuels involved, ventilation conditions will change over time, thus affecting the smoke produced. Transport considerations include (1) changes to the aerosol characteristics that occur with time and distance from the source and (2) transport time. Changes in the aerosol largely relate to the particle size and concentration and result from the processes of sedimentation, agglomeration, and coagulation. Transport time is a function of the characteristics of the travel path from the source to the detector, which include ceiling height and configuration (sloped, beamed, etc.), intervening barriers such as doors, and buoyancy effects such as layering and thermal inversions. Once smoke reaches the detector, other factors become important, namely the
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aerodynamic characteristics of the detector and the type of sensor. The aerodynamics of the detector relate to the ease with which smoke can pass through the detector housing and enter the sensor. In addition, the location of the entry portion of the housing relative to the velocity profile of the detector normal to the plane of the ceiling is also a factor. Finally, different sensing modes (e.g., ionization or photoelectric) will respond differently, depending on the characteristics of the transported aerosol. Within the family of photoelectric devices, there will be variations depending on the wavelengths of light and the scattering angles employed. Also, algorithms used to sample and weight the sensor’s response are introduced by the manufacturer and affect the detector’s response. Standard practice for the design of smoke detection systems is much the same as that for heat detection systems. Recommended spacing criteria are established based on detector response to a specific parameter, such as the optical density within an enclosure. A variety of smoke tests are used to verify that the detector responds between defined upper and lower activation thresholds and within required response times to a range of different types of smoke. This information translates into recommended spacing criteria intended to ensure that the detector responds within defined parameters. In some cases, the recommended spacing can be increased, or must be decreased, depending on factors such as compartment configuration and air flow velocity [8]. In applications where estimating the response of a detector is not critical, the recommended spacing criteria provide sufficient information for the design of a basic smoke detection system. If the design requires detector response within a certain time frame, optical density, specified heat release rate, or temperature rise, then additional analysis may be required. In this case, information concerning the expected fuel, fire growth, sensor, and compartment characteristics is required. The following examples show various performance-based approaches to evaluating smoke detector response.
R.P. Schifiliti et al.
Modeling Smoke Detector Response: General The response of smoke detectors to fire conditions is not easily modeled. The response characteristics of smoke detectors vary widely compared with thermal detectors. In addition, less is known about the production and transport of smoke in the early stages of a fire. Natural and forced air currents have a larger effect on the movement of smoke at the time of interest (very early in the fire) than they do on the stronger thermal currents required to alarm heat detectors. A comparison of how smoke detectors operate with the smoke measurement methods most often employed and reported by researchers shows that smoke measurements do not generally include the factors that we need to model smoke detector response [13]. Thus, there is a gap between the data generated by fire researchers and the data needed to model smoke detector response. For example, fire researchers most often measure and report data on heat release rate, temperature and velocity of fire gases, and the optical density or obscuration per unit distance of the smoke at various locations. Of these, only optical density and obscuration relate to smoke. Although called obscuration, it is more accurately called attenuation since the light beam may be absorbed, reflected, or refracted by the smoke. These are calculated as follows: Percent obscuration, O:
I O ¼ 100 I I0
Percent obscuration per unit distance, Ou "
1=I # I Ou ¼ 100 1 I0 Optical density, D I0 I D ¼ log10 ¼ log10 I0 I Optical density per unit distance, Du (m1)
40
Design of Detection Systems
D 1 I0 I Du ¼ ¼ log10 m1 ¼ log10 l l I0 I where I0 is the initial intensity of a light beam reaching a photocell, I is the intensity of the light beam in the presence of smoke, and l is the distance between the source and the photocell. Optical density and obscuration are useful data for evaluating visibility. However, the only commercially available smoke detector that operates by sensing the attenuation of a light beam is the projected-beam-type smoke detector. Further, these measurements are sensitive to the wavelength of light used. Thus, to be valuable for estimating the response of a projected-beam smoke detector, the data must be measured and reported using the same wavelength as the light source used by the detector. The two most common types of smoke detectors are ionization type and photoelectric type. Neither type operates using light attenuation. Without a correlation between the optical density data and the response characteristics of a particular detector, accurate modeling is not possible. In addition, detectors often use complex response algorithms rather than simple threshold or rate-of-change response levels. The algorithms are used to reduce false and nuisance alarms and to enhance fire signature matching. These algorithms vary from detector to detector and are generally not published by the manufacturers. Thus, even if correlations between optical density and the response of scattering- and ionizationtype smoke detectors were available, the actual response of each model is affected by the signal sampling algorithm. Nevertheless, there are methods that can be used to grossly estimate smoke detector response. These estimation methods may not provide accurate prediction of time to detector response because the potential errors in the estimation methods are not generally known and the response algorithms for a particular detector are not known. Without knowledge of the accuracy of the models and the potential errors, these estimation methods should not be used to compare detector response to other model
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calculations such as egress time calculations or time to untenability. Estimation methods are best used to compare changes in the response of a particular detector as a result of changes in spacing or location, while holding all other variables constant. In addition to these estimation methods, actual fire tests with detectors present may provide information to compare smoke detector response to other factors such as egress time, structural response, heat release rate, and so forth. Product performance tests may be sources of data. Although the actual response may not be reported in manufacturer’s literature, the minimum and maximum permissible performance imposed by the test standard provides ranges of possible response.
Modeling Smoke Detector Response: Light Obscuration Smoke Detectors For projected-beam-type detectors, fire or smoke models that calculate the optical density per unit length, Du, in a space or the total optical density in the path of the detector, D, may be used to determine when the detector would respond. Manufacturer specifications will typically indicate at what levels of total obscuration or total optical density the detectors respond. Projectedbeam smoke detectors generally have adjustable response thresholds. Many fire models estimate the unit optical density, Du, in a uniform upper layer or volume. This method is referred to as zone modeling. The optical density over the entire length of the beam is then determined by multiplying Du by the path length, l. The path length is the distance between the source and receiver or the projected-beam smoke detector. This method assumes homogenous distribution of smoke throughout the path, an assumption that may not be valid. Another method to model the response of projected-beam obscuration-type detectors is to calculate the unit optical density, Du, at several discrete points or in several discrete segments between the source and the receiver of the projected-beam smoke detector. This approach
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is a form of field modeling. The optical density per unit length is then multiplied by the length of that particular segment. The total optical density of the path is then the sum of all of the densities for the individual segments.
Modeling Smoke Detector Response: Light Scattering (Photoelectric) Smoke Detectors The amount of light scattered by smoke is very complex and is related to factors such as the particle number density and size distribution, refractive index, the wavelength of the light source, and the angle between the source and the receiver. Some of these variables can be described by the manufacturer for a particular detector. Some require information about the smoke produced by the fuel and its transport to the detector location. Information about smoke properties related to light scattering is presently limited to a few types of fuels and is not readily available to practicing fire protection engineers. In addition, the data may not be in a useable format. For instance, the data must match the wavelength of the light source used in the detector being modeled. Scattering data at other wavelengths introduces errors and uncertainties. Meacham has shown that it is possible to model the response of light-scattering detectors using information about smoke properties obtained by small-scale testing of various fuels [31, 32]. However, the recommended test methods have not been further developed, tested, or incorporated into fire test programs. At the present time, there are no practical methods available to directly model the response of light-scattering-type detectors. However, obscuration or optical density modeling, as discussed above for obscuration-type detectors, can be used in a limited way to estimate scattering-type smoke detector response. A scattering-type detector responds at different optical densities for different types of smoke. For example, a scattering-type smoke detector that responds at an optical density of
R.P. Schifiliti et al.
.029 m1 (2.0 %/ft obscuration) to smoke produced by a smoldering gray cotton lamp wick may not respond until an optical density of 0.15 m1 (10 %/ft) is reached for smoke from a kerosene fire. At the response threshold, both types of smoke are scattering the same amount of light to the receiver of the scattering photoelectric smoke detector. There are many factors involved in this effect. One is that the darker smoke from the kerosene fire does not reflect as much light as the lighter colored smoke from the lamp wick. Another way to understand the differing response of a scattering-type detector to two types of smoke is to consider the amount of light being scattered when both smoke samples have the same optical density. Both samples of smoke equally block our vision of the light reflected by an object. One type of smoke may be composed of large, highly reflective smoke particles that cause the incident light to scatter in many directions. Thus, it reduces the amount of light in the forward direction. The other type of smoke may consist of a smaller number of larger particles that absorb light more readily than they reflect it. Though they have equal optical densities, one is more likely to scatter light and set off a scattering-type detector. In order to model the response of a scatteringtype detector using obscuration or optical density, it is necessary to know the optical density required for a particular type of smoke to alarm a particular model detector. For example, many manufacturers label their smoke detectors with a unit optical density, Du, or unit obscuration, Ou, based on a calibration test that is part of UL standard number 268 [33]. That number indicates the unit optical density required for that detector to respond to smoke having very specific characteristics. The optical density required to alarm a particular detector as quoted by the manufacturer is just one value for a given particle size distribution, concentration, color, and so on used in the laboratory calibration test of that model detector. If the smoke and conditions are similar to that used in the test of the detector, the specified alarm threshold can be used in calculations.
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It is not sufficient to have data for a particular fuel and detector combination. It is known that smoke changes as it moves away from a fire [34]. There may be changes in the number, size, shape, and velocity of the particles. The optical density at response to any smoke signature other than the laboratory calibration test will be different and will vary with different fuels and burning modes. Threshold response data to various fuels for a particular detector are not readily available. Some manufacturers may provide data if available and when requested. Product performance and safety tests as well as fire tests with detectors present are useful sources of limiting performance data. Product standards typically test detectors in rooms with specified fuels and smoke buildup rates and velocities. The detectors must respond at certain levels or within certain time limits. Although the exact performance data may not be made available, the test limits are useful for estimating the range of possible detector response. Geiman and Gottuk [35] have provided further guidance on selecting general optical density (OD) at alarm thresholds. This guidance was developed from data collected from full-scale tests conducted by the U.S. Navy [36, 37], the Fire Research Station [38], and the Indiana Dunes Tests [39] using a wide variety of ion and photoelectric smoke detectors with smoldering and flaming fires. Table 40.14 presents the arithmetic means of the cumulative 20, 50, and 80 % of the OD at alarm thresholds for each combination of detector and fire type. The data represent nominal sensitivity values ranging from 0.0071 to 0.0288 OD/m (0.5–2 %/ft) for ionization detectors and from 0.0071 to 0.0508
OD/m (0.5–3.5 %/ft) for photoelectric detectors. These ranges capture most alarm settings for which the detectors will be used in practice. Geiman and Gottuk also investigated using the “nominal” detector sensitivity, that determined by a standard laboratory test such as UL. They determined that using the nominal sensitivity as the alarm threshold provides extremely poor results. They found the majority of the 20 % OD alarm thresholds were greater than the nominal sensitivity levels of the detectors indicating that premature detector response was predicted. Except for ionization detectors with flaming fires, using the nominal sensitivity of the detector as the alarm threshold with OD/m data would only have been approximately 21 % effective at signifying an actual alarm based on the data studied. The use of the nominal detector sensitivity as an alarm threshold will generally result in predicting alarms before they actually occur. However, their results suggested that typical responses (i.e., 50 %) of ionization detectors with flaming fires could be reasonably predicted using the nominal sensitivity. The Geiman and Gottuk work evaluated the use of an alarm threshold of 0.14 OD/m (9.4 %/ft) for modeling. This OD/m value represents the upper bound in the UL smoke detector tests [40, 41] and was compared to the optical density measurements at the time of alarm for all cases in the test data set. They found that, using the nominal detector sensitivity, the alarm threshold of 0.14 OD/m provided a much higher level of certainty that a detector will have alarmed. At a measured smoke optical density of 0.14 OD/m in the tests, 91 % of the ionization detectors alarmed for flaming fires and
Table 40.14 Average OD alarm thresholds for all test series and nominal detector sensitivities OD alarm threshold (%) 20 50 80
Fire type Flaming fires Smoldering fires Flaming fires Smoldering fires Flaming fires Smoldering fires
Source: Geiman and Gottuk [35, p. 204]
Ionization detectors (OD/m) 0.007 0.004 0.045 0.028 0.021 0.005 0.113 0.048 0.072 0.027 0.176 0.052
Photoelectric detectors (OD/m) 0.031 0.016 0.032 0.016 0.063 0.029 0.059 0.019 0.106 0.039 0.110 0.034
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65 % for smoldering fires. Similarly, 86 % of the photoelectric detectors alarmed for flaming fires and 85 % for smoldering fires at a measured smoke optical density of 0.14 OD/m. For all but one case, over 75 % of the photoelectric detectors alarmed for both flaming and smoldering fires. According to Geiman and Gottuk [35], an alarm threshold of 0.14 OD/m provides a relatively high level of confidence in predicting detector alarms. However, that value is not necessarily optimized or narrowly defined. For example, many detectors alarmed at OD/m values less than 0.14 OD/m. The use of this alarm threshold will lead to estimated alarm response times that are potentially longer than would actually occur [35].
To use the method proposed by Newman it is necessary to know what change in detector chamber signal, ΔI, will cause a detector or system to alarm. Although manufacturers do not presently provide these data, they may be persuaded to do so in the future. Newman’s work was done using a small-scale apparatus and three ionization smoke detectors. A wider range of tests, including some full-scale testing, is needed to verify this method. Presently, the only way to model ionization detector response is to use the optical density estimations as discussed for scattering-type photoelectric smoke detectors.
Modeling Smoke Detector Response: Ionization Smoke Detectors
In addition to smoke characteristics and the detector’s operating mechanism, the ability to get the smoke into the chamber affects the response of the unit. For spot-type photoelectricand ionization-type smoke detectors, entry resistance is caused by bug screens, chamber design, and the detector’s aerodynamic characteristics. In a scenario where the optical density at the detector location is increasing with time, the optical density inside the detector chamber will always be less than that outside the detector chamber. Similarly, if a detector is placed in a smoke stream having a constant optical density, there will be a time delay before the optical density inside the chamber approaches that outside the detector. As with heat transfer to heat detectors, smoke entry resistance can be characterized by a detector time constant, τ:
The signal produced by the chamber of an ionization detector has been shown to be proportional to the product of the number of particles and their diameter [42–45]. The exact signal produced by an ionization smoke detector is given by a more complex equation in the literature and requires an additional number called the chamber constant. The chamber constant varies with each different model of detector. Given the quantity and size distribution of smoke particles and the chamber constant (from the manufacturer), it is possible to model the ionization smoke detector. Unfortunately, there are no fire models that provide the required detector model input. In addition, manufacturer specifications do not presently include chamber constants. Newman modified the chamber theory to account for ionization detector sensitivity to the small electrical charge carried by some fire aerosols [46]. Newman also developed a method to model ionization smoke detector sensitivity as a function of the soot yielded by a particular fuel. Using his method, the change in a detector’s signal, ΔI, can be related to the optical density of smoke measured at a particular wavelength, Duλ.
Modeling Smoke Detector Response: Entry Resistance
dDui 1 ¼ ðDu Dui Þs1 m1 τ dt where Dui ðm1 Þ ¼ Optical density per unit length inside the detector chamber Du ðm1 Þ ¼ Optical density per unit length outside the detector τ ¼ Detector time constant ðsÞ
If the time constant and the rate of change of optical density outside the detector are constant,
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then this equation can be solved. Further, substituting Dur for the optical density outside the detector at response and Duo for the optical density required inside the detector to produce response yields the following: [47, 48] dDu Dur ¼ Duo þ τ dt
1 dDu 1 exp Dur m1 τ dt Heskestad proposed that the time constant could be represented by the following: L τ¼ s u where L is the detector’s characteristic length and u is the velocity of the ceiling jet flowing past the detector. The characteristic length is thought to be a property of the detector that is independent of the smoke and ceiling-jet properties. It is interpreted as the distance the smoke would travel at the velocity u before the optical density inside the detector reaches the value outside of the detector. Combining the equations, L dDu Dur ¼ Duo þ u dt
u dDu 1 exp Dur m1 L dt The exponential term is small compared to the rest of the equation, allowing the equation to be
simplified [47]. Simplification of the equation is not necessary when calculations are made using a computer. However, the simplified form clearly shows the effect of entry resistance: dDu 1 Dur ¼ Duo þ τ m dt or L dDu Dur ¼ Duo þ m1 u dt This form of the entry resistance equation clearly shows that when the optical density outside a detector is increasing with time, the optical density inside the detector will lag behind if there is any entry resistance. Heskestad and, later, Bjorkman et al. [49] have plotted test data to determine the L number for a variety of smoke detectors. Additional work has been done by Marrion and by Oldweiler to study the effects of detector position and gas velocity on the L number [15, 50]. Bjorkman et al., Marrion, and Oldweiler all observed variations in L that may be attributed to a dependence on velocity. Marrion’s and Oldweiler’s data also imply that there may also be a dependence on the characteristics of the smoke. Table 40.15 below summarizes the results from the works cited above. Examination of the data and analysis work cited above shows that more work needs to be done to study the effects of low velocities
Table 40.15 Range of characteristic length (L) numbers Researcher Heskestad [47] Bjorkman et al. [49] Marrion [15] Oldweiler [50] a
Ionization detector L (m) 1.8 3.2 0.2b Not tested 4.0–9.5g 4.3–14.2h
Scattering detector L (m) 15a 5.3 2.7c 7.2,d 11.0–13.0e 18.4f Not tested
Older style detector with more elaborate labyrinth L determined by best fit for three test velocities c L based on a single test velocity and a limited number of tests (complete equation used) d Low L number at low test velocity e Range of L for several fuels and detector positions f L increased by adding “fence” to further restrict smoke entry g Range of L for a variety of velocities using simplified equation for entry resistance h Range of L for a variety of velocities using simplified equation for entry resistance b
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and smoke characteristics on detector entry characteristics. The sharp increase in L at lower velocities appears to indicate that entry resistance may be related to smoke particle size. It is also possible that L is a function of the smoke momentum at low velocities. Thus, the time lag would be inversely proportional to the velocity squared. Engineers can use L as a measure of entry resistance and the resulting time lag. However, in scenarios where the ceiling-jet velocity is low, there will be greater uncertainty in the results. Without validation of L as a measure of lag time, manufacturers and test laboratories are not measuring or reporting L in their literature. Nevertheless, the range of L numbers reported in Table 40.15 can be used to estimate possible errors in detector response time.
Smoke Detection Calculation Examples Example 12 The smoke level measured outside of a detector at the time of response in a laboratory calibration test is listed on manufacturers’ specifications as the optical density or obscuration required to alarm the unit. Because of entry resistance, the smoke level inside the detector will be less. The specified response is for a particular type of smoke and is measured in a laboratory test apparatus. An example of one calibration test is the gray smoke test listed in the UL 268 smoke detector test standard [33]. In the test, the smoke detector response threshold must not exceed 0.0581 m1 (4.0 %/ft). Velocity in the test chamber is 9.8 m/min. The test starts with clear air. A smoldering cotton lamp wick is used to increase the optical density in the test chamber. The rate of increase of optical density in the chamber must fall within the following limits: 3:7 103
dDu 5:3 103 m1 min1 dt
What is the range of optical density inside of the detector at the time of response (Duo) if the detector has an L of 3 m? What would it be if the detector had an L of 14 m?
Solution For L¼3 m dt ¼ 3.7 103 m1 · min1,
and
dDu/
L dDu m1 u dt L dDu ¼ Dur m1 u dt
Dur ¼ Duo þ Duo
Duo ¼ 0:0581
3 3:7 103 ¼ 0:057 m1 9:8
For L¼3 m 103 m1 · min1, Duo ¼ 0:0581
and
dDu/dt ¼ 3.7
14 3:7 103 ¼ 0:053 m1 9:8
For L ¼ 14 m 103 m1 · min1, Duo ¼ 0:0581
dDu/dt ¼ 3.7
3 5:3 103 ¼ 0:056 m1 9:8
For L ¼ 14 m 103 m1 · min1, Duo ¼ 0:0581
and
and
dDu/dt ¼ 5.3
14 5:3 103 ¼ 0:051 m1 9:8
These calculations indicate that the actual quantity of this particular type of smoke required to alarm the detector varies from 0.051 to 0.057 m1 or from 3.5 to 3.9 %/ft. Smoke Production and Characteristics The fuel characteristics of primary concern for smoke detection are (1) material and (2) mode of combustion. These two parameters are important for determining pertinent features of expected products of combustion, such as particle size, distribution, concentration, and refractive index. The importance of these features with regard to smoke detection are well documented [6, 31, 32] and are discussed by Mulholland [34] Assuming a well-mixed smoke-filled volume, data on smoke characteristics for given fuels can provide an estimation of detector response. Example 13 The design objective is to detect the smoke from a flaming 200 g (0.5 lb)
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polyurethane pillow in less than 2 min. The pillow is located in a 36 m2 room with a ceiling height of 2.5 m (8 ft). Assume that the pillow is burning at a steady rate of 50 g/min. Can the design objective be met? What assumptions are required? Solution The total mass loss at 2 min is 100 g. Given this information, the optical density in the room can be calculated from the relationship [34]: Dm M Du ¼ Vc
ð40:27Þ 2
where Dm (mass optical density [m /g]) can be taken from Mulholland [34] as 0.22 m2/g. Du ¼
ð0:22 m2 =gÞ ð100 gÞ ¼ 0:244 m1 ð36 m2 Þ ð2:5 mÞ
Assuming the detector will respond at the UL upper sensitivity limit of 0.14 m1 (black smoke) [33], it can be assumed that the detector will respond within 2 min. This approach is simplified, however, and assumes that the smoke is confined to the room, is well mixed, can reach the ceiling level, and can enter the detector.
Dm ¼
Du V 2 m =g Δm
Du ¼
ΔmDm 1 m V
Du ¼
350ð0:22Þ ¼ 0:002 m1 37, 500
Knowing Du and assuming the path length of the beam to be 75 m, the ratio of light reaching the receiver of the unit can be calculated: I I0
¼ 10Du I
I I0
¼ 100:002ð75Þ ¼ 0:708
Next, the percent obscuration caused by the smoke is calculated: I O 100 1 I0 O ¼ 100ð1 0:708Þ ¼ 29:2 Thus, a projected-beam smoke detector would have to be set to respond at about 30 % total obscuration or less to meet the design objective.
Example 14 Polyurethane mattresses are stored in a room that is 50 m 75 m 10 m high. A goal has been set to detect a flaming fire before approximately 350 g of fuel has been consumed. Using a projected beam smoke detector with sensitivity settings that can vary from 20 % to 70 % total obscuration in 10 % increments, what is the minimum sensitivity setting for response to this fire? Assume the smoke is mixed evenly throughout the space.
Discussion Related to the Use of Dm The previous two examples used the mass optical density, Dm, to calculate the expected optical density, Du, in a space when a certain mass of fuel was consumed. Dm data are typically measured in smallscale tests due to the need for accurate measurements of mass loss and optical density. The use of Dm from small-scale tests to calculate the resulting Du in a large-scale scenario introduces error. Some comparisons show qualitative correlation. However, it has been reported that the correlation breaks down with complex fires [34].
Solution The mass optical density, Dm, for a flaming polyurethane mattress is given in this handbook on page 2–298 as 0.22 m2/g. The volume of the room is 37,500 m3. From the equation for mass optical density, calculate the resulting unit optical density in the room when 350 g of fuel is consumed:
Stratification In the context of this chapter, smoke dilution refers to a reduction in the quantity of smoke available for detection at the location of the detector. This dilution can occur either through natural convection (entrainment in the plume or the ceiling jet) or by effects of a heating or ventilation system. In many cases, forced
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ventilation systems with high exchange rates cause the most concern. In the early stages of fire development, when smoke production rate is small and the plume is weak, smoke can easily be drawn out of the room and away from area smoke detectors. In addition, high velocity air flows out of supply and into return vents creating defined patterns of air movement within a room. Such flows can either keep smoke away from detectors that are located outside of these paths, or, in some cases, inhibit smoke from entering a detector located directly in the air flow path. Although there currently are no quantitative methods for estimating either smoke dilution or air flow effects on smoke detector siting, these factors must be considered qualitatively. It should be clear, however, that the air flow effects become larger as the required fire size at detection, Q_ cr , gets smaller. If the application warrants, it may be useful to obtain velocity profiles of the air movement within a room or to perform small-scale smoke tests under various conditions to aid in the smoke detector placement analysis. The potential for smoke stratification is another concern in the detection of low-energy fires and fires in rooms or volumes with very high ceilings. Stratification occurs when the temperature within the plume equals that of the surrounding air, and there is insufficient thermal energy from the fire to force the smoke higher. Once this point of equilibrium is reached, the smoke layer will maintain its height above the fire, regardless of the ceiling height, until additional energy is provided. Unlike the effects of air flow on smoke dilution, stratification effects can be calculated using the relationship [51] q_ conv > 0:352H 5=2 T 3=2 s
ð40:28Þ
where q_ conv ¼ Convective heat release rate in W H ¼ Distance from the top of the fuel package (base of the fire) to the ceiling level in m Ts ¼ Difference in ambient gas temperature in C between the fuel location and ceiling level
This same relationship can also be found in NFPA 92B, Standard for Smoke Management Systems in Malls, Atria, and Large Areas, 2005 edition [52]. A more through treatment of stratification can be found in Chapter 2-1 of this handbook. Example 15 The design objective is to detect the pyrolysis of overheated PVC cable insulation in a 7-m (23-ft) high, 100 m2 (1076 ft2) room. The room is air conditioned with a temperature differential of 10 C (18 F) between the base of the switch equipment and the ceiling. The proposed design has smoke detectors mounted at the ceiling level. Assuming the critical fire size is 1000 W, will there be sufficient thermal energy to force the smoke to the ceiling level? Solution In this case, one can rearrange Equation 40.28 and solve for H: !2=5 q_ conv H< 0:352T 3=2 s where Q_ cr ¼ 1000 W, and Ts ¼ 10 C (18 F). This result indicates that the highest level of smoke rise is estimated to be 6 m (20 ft). As a result, the design objective may not be achieved by the proposed design. This approach is also valid for evaluating the effects of stratification in a high-ceiling room where a larger fire might be expected. However, the effects of heating and air conditioning systems and warm or cold walls are not considered. Example 16 The design objective is to detect the flaming combustion of a chair located in the lobby of an office building in order to initiate smoke management functions. The lobby is located at the lowest level of a 20-m (64-ft) high atrium. The atrium has offices on three sides and a glass facade to the outside on the other. The atrium is air conditioned with a temperature differential of 20 C (36 F) between the lobby and the ceiling level. The proposed design is for smoke detectors to be mounted at the ceiling level. Is there sufficient thermal energy to force the smoke to the ceiling level? Solution First, a value for Q_ cr must be selected for the burning chair. From an analysis of the
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Design of Detection Systems
chair and a review of published heat release data, it is determined that the chair most closely resembles the metal frame chair with padded seat used in Test 53 of the NIST furniture heat release rate tests [8]. This chair had a maximum heat release rate of 280 kW, which can be used as q_ conv (or in this case Q_ cr , the critical fire) in Equation 40.28. Equation 40.28 can then be rearranged to solve for H: 2=5 H < Q_ cr = 0:352T 3=2 s where Q_ cr ¼ 280,000 W and Ts ¼ 20 C (36 F). In this case, the highest point of smoke rise is estimated to be 38 m (125 ft). Thus, the smoke would be expected to reach the ceiling-mounted detector. It should be noted that air flow concerns were not considered in Examples 10, 11, and 12. In some cases, a system supplying air at a low level and exhausting at an upper level may actually help transport the smoke to the upper levels of a room, where in other cases it may serve to inhibit smoke movement. It should also be noted that, simply because the smoke reaches the level of the detector, there is no guarantee that it can enter the sensor chamber. Velocity Analog Spot-type smoke detectors, whether commercial or residential, or ionizationor light-scattering type, all require smoke to enter the detection chamber in order to be sensed. This requirement is another factor that must be considered when attempting to estimate smoke detector response. Smoke entry into the detector can be affected in several ways, for example, due to insect screens, chamber configuration, and proximity of the detector to the ceiling. As previously discussed in this chapter, Heskestad [53] introduced the concept of smoke detector lag to explain the difference between the optical density outside (Dur) and inside (Duo) of a detector at the time of activation. Although studies of this relationship have provided useful information concerning smoke detector lag [15, 48], the difficulty in quantifying L for different detectors and relating it to siting requirements
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has limited its usefulness. In its stead, the concept of critical velocity (uc) has been introduced [4, 54]. Critical velocity, in this context, refers to the lowest gas velocity required for smoke entry into the sensor chamber at a level to sound an alarm at a given threshold. Experimental work has shown this requirement to be in the range of 0.15 m/s for the detectors tested in one study [54]. When velocities fell below this value, the smoke level outside the detector at the time a specified analog output level was reached rose dramatically compared to levels when the velocity was above the critical value. This figure can be useful for design and evaluation purposes, as it is close to the low-velocity value (0.16 m/s) at which a detector must respond in the UL smoke detector sensitivity chamber in order to be listed [33]. Thus, the location of a velocity of 0.16 m/s in the ceiling jet for a given fire and ceiling height can be considered as a first approximation design radius for detector siting purposes. It should be noted that the ceiling-jet velocity correlations assume a horizontal, smooth ceiling. A detailed discussion of ceiling-jet flows by Alpert is presented in Chap. 14, “Ceiling Jet Flows.” The critical velocity approach can be illustrated with a simplified example. Example 17 The new owners of a hotel have established a fire detection design objective that the smoke detection system in the grand ballroom must be able to detect a 50 kW fire. The ballroom is 50 m (160 ft) long by 30 m (96 ft) wide with a 7.1-m (23-ft) high smooth ceiling. The existing smoke detectors are installed at a listed spacing of 10 m on center and have a critical velocity of 0.15 m/s. Assuming the fire starts at a point equally spaced between the existing smoke detectors, will the velocity of the ceiling jet from a 50 kW fire be sufficient to force smoke into the detection chamber? Assume there will be no ventilation system effects. Solution The stated design objective is to detect a 50 kW fire. Because it is not stated whether the fire is steady state or growing, this solution will assume a steady-state fire of 50 kW. This
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assumption allows the use of Alpert’s [16] velocity correlations for a steady-state fire. Alpert provides two equations that can be used: one for r/H ¼ 0.15, and the other for r/H > 0.15. This correlation is generally considered to be valid when r/H is between 0.15 and 2.1. Therefore, the ratio r/H must be determined first. In addition, the fire source should be at a distance of at least 1.8 times the ceiling height from the nearest enclosure wall. The installed spacing is 10 m (32 ft) on center. Using the relationship S ¼ 21/2r, the radial distance is found to be approximately 7.1 m (23 ft). Given that H is also 7.1 m (23 ft), the ratio r/H is found to be 1.0. This value is greater than 0.15; thus, the following equation can be used: 0:195Q_ H 1=2 r 5=6 1=3
u¼
By entering the values of Q_ ¼ 50 kW, H ¼ 7.1 m (23 ft), and r ¼ 7.1 m (23 ft), a velocity of 0.37 m/s is calculated. This indicates that, for a steady-state 50 kW fire, there will be sufficient velocity to force smoke into the detectors at their existing locations. However, if the 50 kW fire as stated is the design fire, Q_ do , and it was determined that the critical fire, Q_ cr , was only 5 kW, the resulting velocity using the steady-state correlation at 5 kW would be 0.17 m/s—very close to the critical velocity of 0.16 m/s. Furthermore, with a relatively small fire and a relatively high ceiling, stratification is likely to be a factor and should be considered. Assuming the room is air conditioned, with a temperature differential of 10 C from the top of the fuel package to the ceiling level, the smoke from a 5 kW fire would stratify at a level of about 7.3 m (23.4 ft)—very close to the ceiling height of 7.1 m (23 ft). Given probable dilution of smoke and errors in approximations, it could be considered unlikely that a 5 kW fire would be detected under the defined conditions. In addition to illustrating how the concept of critical velocity can be used for the design of smoke detection systems, it clearly points out the need to adequately define performance and
design objectives, and to select correlations that fit those objectives. First, the objectives should be stated in terms of both the design fire and the critical fire. A 50 kW design fire is significantly different from a 50 kW critical fire, and the design for one may not meet the requirements for the other. Second, care should be taken in selecting a ceiling-jet velocity correlation that most closely fits the design objectives. Unless the hazard analysis indicates that the maximum fire size of Q_ do will be 50 kW, it may be better to apply a ceiling-jet velocity correlation, based on a growing fire. In this case, the fire growth rate must also be estimated as part of the evaluation. The following example shows the importance of these factors by using the same ballroom as described in Example 17, and provides more specific performance and design parameters. Example 18 After additional consultation, the owners of the hotel described in Example 17 have modified their objectives as follows: assuming that a fire will begin in a chair, the smoke detection system for the grand ballroom must be able to detect the fire and initiate an internal response before it spreads beyond the chair of origin. The typical fuel load within the room consists of metal-framed chairs with padded seats and backs and plywood tables with cotton tablecloths. The response time from when the alarm signal is indicated at the annunciator until the first staff member arrives is estimated to be 60 s. The delay time from detector activation until alarm initiation, as measured at the sensor, is 10 s. Because of the potential for nuisance alarms, the detection system employs an alarm verification feature that has a minimum delay time of 15 s and a maximum delay time of 60 s. The existing smoke detectors are installed at a UL-listed spacing of 10 m on center and have a critical velocity of 0.15 m/s. Assuming the fire starts at a point equally spaced between the existing smoke detectors, and there are no ventilation system effects, can the existing smoke detection system be expected to meet the design objectives?
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Design of Detection Systems
Solution The complete solution to a problem like this one may require several steps; for example, determination of the design fire, determination of the critical fire, estimation of ceiling jet velocity at Q_ cr , estimation of smoke production or optical density, and analysis of possible stratification effects. In all cases, however, determination of the design fire and the critical fire is essential. Given that the goal is to detect the fire while in the chair of origin, a first step might be to estimate the fire size within the chair that could ignite the cotton tablecloth. From analysis of the chair and a review of published heat release data, it is determined that the chair most closely resembles the metal frame chair with padded seat and back used in Test 53 of the NIST furniture heat release rate tests [8]. This chair had a maximum heat release rate of 280 kW; a fire growth rate of 0.0086 kW/s2; a growth time, tg, of 350 s; and a virtual start time, tv, of 50 s. Assuming that the fire would likely grow up the seatback of the chair and that the seatback is located approximately 0.5 m from the tablecloth, an estimate of the energy output required for ignition of the tablecloth can be made. In this case, using the radiant ignition routine in FIREFORM [55] and assuming the fuel is easy to ignite (ignition flux of 10 kW/m2) with a separation distance of 0.5 m, it is estimated that the tablecloth will ignite when the total energy output from the burning chair reaches 139 kW. These parameters define the design fire. The next step is to calculate the time for the design fire to reach the threshold limit of 139 kW. Using the relationship Q_ ¼ αt2, a time of 118 s (about 2 min) is calculated. This calculation is growth time of the fire after it begins to follow an exponential growth rate until the design fire size is reached. Given that the fire would probably start as smoldering combustion, the actual growth time could be considerably larger (1 to 2 h possible). The critical fire size can then be estimated by subtracting the various response times and estimating the heat release rate at that moment
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in time. In this regard, reasonable time delays should be used based on the information provided. The focus should be on obtaining the “most reasonable” worst-case delay for the situation. From the problem statement, this delay is estimated based on the response times given, using the following equation: tresponse ¼ ttransport þ tverify þ tsystem þ tstaff where ttransport ¼ Smoke transport time (unknown) tverify ¼ Verification time (60 s maximum) tsystem ¼ System response time (10 s) tstaff ¼ Staff response time (60 s) Momentarily ignoring the smoke transport time and assuming prompt staff response, the result is a maximum detection system response time of 130 s. However, in an actual fire situation, the smoke detector verification time should be at its minimum of 15 s, and not at its maximum of 60 s. Making this assumption, the total response time (still ignoring smoke transport time) is 85 s. This result is less than the 127 s time to ignition of the tablecloth and is used to help define the critical fire size (Q_ cr ). Here, the 85 s is subtracted from the 127 s (that defines the design fire), and the relationship Q_ ¼ αt2 is used to calculate the heat release rate at that moment in time. The result is a heat release rate of 15 kW. Assuming no smoke transport time, this result would be the critical fire size at which detection must occur in order to detect the fire and cause the required response before the design fire size is reached. The next step is to factor in a lag due to the smoke transport time. In order to account for smoke transport lag, Brozovsky [54] suggests a safety factor that is equivalent to a heat release rate that is 80 % of the maximum fire size at the time of detection. This factor would result in a critical fire size of 12 kW and a corresponding response time of 37 s. These values can then be used to determine if the ceiling-jet velocity will exceed 0.16 m/s. Although several simplifications have been made, this example outlines a methodology for
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estimating the potential for detector response, given the concepts of design fire and critical fire. In addition, the cross-checking utilized points out the importance of understanding the limitations and boundary conditions of correlations and empirical relationships (i.e., simply because one condition can be met, it does not automatically mean that all others will be met as well, and the complete scenario should be considered). Engineering of smoke detection, especially for low-energy fires, can be a difficult task, and the application of any method for this purpose should include clear statements of all assumptions made. Temperature Approximation Method for Modeling Smoke Detection The temperature approximation theory is another method used to estimate the optical density produced by flaming fires. The theory hypothesizes that the mass concentration of smoke particles at a point is proportional to the change in temperature due to the fire (at that point) [56]. The following assumptions are necessary: 1. Particle size distribution is constant in space and time. 2. Mass generation rate is proportional to mass burning rate. 3. There is no heat transfer between particles or between the particles and the confining surfaces. 4. The smoke does not continue to react as it travels. Heskestad then hypothesized that the ratio of optical density to temperature rise would be a constant for a particular fuel and burning mode (flaming, smoldering, vertical combustion, horizontal combustion, etc.). There are actually three parts to this hypothesis. The first is that each fuel and burning mode results in a unique optical density required to alarm a particular model and type of detector. This aspect was discussed previously regarding photoelectric, ionization, and projected-beam smoke detectors. This phenomenon is regularly observed, explained by theory, and accepted by the scientific and engineering community.
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The second part of the hypothesis is that for each fuel and burning mode the optical density at a point is proportional to the mass concentration of particles: Du / C The final part of the hypothesis is that, for each fuel and burning mode, the mass concentration of particles is proportional to the change in temperature at a point: C / ΔT Combining these proportionalities, optical density is proportional to the change in gas temperature for a given fuel and combustion mode: Du / ΔT Therefore, the ratio of optical density to temperature rise is constant for a given fuel: Du ¼ Constant ΔT g This hypothesis assumes that the only way to move the smoke particles from the source to the detector at the ceiling is by buoyant forces. Heskestad and Delichatsios examined experimental data for obscuration and temperature rise at various locations on a ceiling for different fuels. They concluded that while the data showed some variation in time at different radial positions relative to the fire source, the ratio could be approximated as a constant. Table 40.16 lists the ratios recommended by Heskestad and Delichatsios for various fuels. Examining the original data, the last column has been added to show the range of values for each fuel. Averages have also been calculated and listed in the last row of the table for reference. Others experiments have resulted in data that differ from that of Heskestad and Delichatsios. Bjorkman et al. reported values for polyurethane that are approximately one half that reported by Heskestad and Delichatsios [49]. The data produced by Heskestad and Delichatsios show the ratio of optical density to temperature rise was
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Table 40.16 Ratios recommended by Heskestad and Delichatsios for various fuels Material Wood Cotton Paper Polyurethane Polyester PVC Foam rubber PU Average
Du/ΔT (1/m C) 1.2 103 5.9 104/1.2 103 1.8 103 2.4 102 1.8 102 3.0 102/5.9 102 7.7 102 2.4 102
not constant. The authors concluded that the variation was the result of slowly changing characteristics of the smoke particles as they left the flaming source and traveled in the plume and ceiling jet. Nevertheless, they concluded that a constant value could be used as a rough approximation to allow engineers to model optical density produced by a fire. Although it has not yet been done, it is possible to examine their original data and place error bars on the values recommended in Table 40.16. A fire model can be used to calculate the temperature rise at a smoke detector location or in a layer. Then, using the ratios reported by researchers, the optical density at that location as a function of time can be approximated. Discussion Related to the Use of fire Models for Heat and smoke Detector Modeling Some computer fire models or sets of computational tools include routines for calculating heat or smoke detector response. It is important for users to understand the underlying detector models being used so that limitations and potential errors can be understood. For heat detection, most computational tools use a lumped mass model as described in this chapter. However, for smoke detection some use a temperature rise model, and some use a mass optical density or specific extinction area model. The specific extinction area is similar to the mass optical density except that it is based on calculations using the natural log, e, rather than log10. Most do not include entry resistance modeling. Some permit the use of fuel-specific parameters for smoke yield and mass optical density. Others use preset values.
Range of values 8.9 104 to 3.2 3.0 104 to 1.8 Data not available 1.2 102 to 3.2 Data not available 5.9 103 to 5.9 Data not available 3.0 104 to 7.7
103 103 102 102 102
Radiant Energy Detection During the combustion process, electromagnetic radiation is emitted over a broad range of the spectrum. Currently, however, fire detection devices operate only in one of three bands: ultraviolet (UV), visible, or infrared (IR), where the wavelengths are defined within the following ranges: [8] Ultraviolet Visible Infrared
0.1–0.35 μm 0.35–0.75 μm 0.75–220 μm
Selection of a specific sensor type for fire detection is based on a number of factors, including fuel characteristics, fire growth rate, ambient conditions, resulting control or extinguishing functions, and environmental conditions in the detection area. More specifically, it includes evaluation of the radiant energy absorption of the atmosphere, presence of nonfire-related radiation sources; the electromagnetic energy of the spark, ember, or fire to be detected, the distance from the fire source to the sensor; and characteristics of the sensor. These factors are important for several reasons. First, a radiation sensor is primarily a line-of-sight device, and must “see” the fire source. If there are other radiation sources in the area, or if atmospheric conditions are such that a large fraction of the radiation may be absorbed in the atmosphere, the type, location, and spacing of the sensors may be affected. In addition, the sensors react to specific wavelengths, and the fuel must emit radiation in
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the sensors’ bandwidth. For example, an infrared detection device with a single sensor tuned to 4.3 μm (the CO2 emission peak) cannot be expected to detect a noncarbon-based fire. Furthermore, the sensor must be able to respond reliably within the required time, especially when activating an explosion suppression system or similar fast-response extinguishing or control system. Once the background information has been determined, the detection system can be designed. Standard practice for the design of radiant energy detection devices is based on application of generalized fire size versus distance curves that are derived using the inverse square law: [8] S¼
kPexpζd d2
where S ¼ Radiant power reaching the detector (W) k ¼ Proportionality constant for the detector P ¼ Radiant power emitted by the fire ζ ¼ The extinction coefficient of air d ¼ The distance between the fire and the detector This relationship is used to produce sensor response information for specific fuels. By then plotting the normalized fire size versus the normalized distance, the resulting curve defines the maximum distance at which the tested sensor can be expected to consistently detect a fire of a defined size (usually provided in m2). By testing a sensor using various fuels, a family of curves can be developed to assist in system design. These curves (sometimes given in tabular form) are usually provided by the sensor manufacturer. Before applying the distance obtained from such a curve, one must also consider the sensor’s field of view. Because the radiation sensor is a line-of-sight device, the sensitivity of the device to a defined fire size decreases as the fire location is moved off the optical axis of the device. This result means that a fire of X m2, which is detectable at a distance Y m on axis from the sensor, may not be detectable at the same distance Y m if it is located 30 off axis. Limitations of viewing angles are also provided by manufacturers.
Ambient conditions should also be considered as part of the evaluation and design process. Factors such as humidity and dust can affect the absorption of radiation in the atmosphere, thus limiting the amount of radiation reaching the sensor for a given fire size. Similarly, temperature can affect the relative sensitivity of a sensor. As the ambient temperature increases, the relative sensitivity can decrease. Even if the decrease is small, it can affect the response of the sensor to the expected fire.
Radiation Detection Example Example 19 The design objective is to detect a 1.0 m2 (11 ft2) pool fire of JP4 aircraft fuel in a large hangar in order to activate a fixed suppression system. The hangar dimensions are 50 m (160 ft) by 80 m (257 ft) with a 20 m (64 ft) ceiling height. The ambient temperature at the ceiling level varies between 15 C (59 F) and 60 C (140 F), depending on time of day and season. The humidity also varies by season, with relative humidity of 90 % possible. What steps should be taken during system design? Solution The first step should be selection of a detection device. Because the hazard is carbon based, IR detection at 4.3 μm is suitable. Also, because IR detectors generally provide a larger surveillance area per device than UV detectors, they could be more cost effective than UV detection in this case. One should then determine possible sources of interfering radiation and select a device that is resistant to these extraneous sources. Such resistance to false response can be obtained by filtering, use of multiple sensors (e.g., two- or three-channel detector), or a combination. The next step is to review the manufacturer’s data to determine mounting criteria based on the size of the critical fire [1.0 m2 (11 ft2)]. Generally, this step begins with the fire size versus distance curve or table. If only a curve is provided, one must then determine the mounting height and lateral distance limits of the detector. Lateral distances are important as related to the sensors’ field of view.
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20 m
80 m
Fig. 40.11 IR detector layout for an aircraft hangar
Given this information, a device layout design can be made. This design should consider all possible obstructions, and result in all parts of the hangar being monitored. One such design is illustrated in Fig. 40.11. As part of the layout, one should consider the possible effects of reduced device sensitivity due to angular displacement, temperature, and humidity. Because manufacturers’ criteria vary on these parameters, typical values are used in this solution to illustrate their effects. For example, the proposed layout has devices utilizing a field of view of 45 . Assuming the nominal sensitivity is such that a 1.0 m2 (11 ft2) fire can be detected at 40 m (128 ft), and there is a reduction in sensitivity of 30 % due to angular displacement, the distance at which a 1.0 m2 (11 ft2) fire can be detected at 45 is reduced to 28 m (90 ft). If the manufacturers’ data indicate a further reduction in sensitivity for temperature, for example 3 % at 50 C (122 F) the distance is reduced to about 26.8 m (86 ft). If there are further reductions due to humidity, for example a 3% reduction at 90% relative humidity, the resulting detection distance at 45 is about 25.6 m (82 ft). In this example, the viewing distance at 45 is a maximum of 20 m (64 ft), and the design can be considered valid. Had the sensitivity decreased such that the distance dropped below 20 m (64 ft), an alternative layout or different devices must be used. In all cases, the manufacturers’ literature should be consulted to determine all
pertinent increases or reductions in detector sensitivity due to fuel, distance, angular displacement, and environmental conditions.
Designing Fire Alarm Audibility In most cases, the purpose of a fire detection and alarm system is to alert the occupants of a building that an emergency exists and to initiate evacuation. In situations such as high-rise or industrial buildings, it may be desirable to provide the occupants with more information, such as the nature and location of the fire. In either case, the purpose of the system is defeated if the signal is not heard and understood by the occupants. This section demonstrates a method for fire protection engineers to estimate the relative effectiveness and cost of various fire alarm alerting systems during the design process. In the past, the selection and location of fire alarm devices has been based on experience and engineering judgment. The use of this simplified methodology can save thousands of dollars in retrofit costs required to correct deficiencies in an alarm system. The transmission of sound from a source to a target is a function of many factors, such as humidity; air viscosity and temperature; the frequency of the signal; the location of the source relative to the target; the construction of walls, floors, and ceilings; and the furnishings in the
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area. Architectural Acoustics [57] contains a good discussion of these and many other factors affecting sound transmission and loss. Sound power and sound pressure levels are expressed in decibels (dB) relative to a reference. It is assumed that the reader is familiar with this system of measurement. Throughout this chapter sound power level (SWL or LW) in decibels is referenced to 1012 W. Sound pressure level (SPL or LP) in decibels is referenced to 2 105 Pa. This discussion also assumes that the reader is familiar with the concept of A-weighting. The purpose of A-weighting is to adjust sound pressure level measurements to correspond as closely as possible to the way humans perceive the loudness of the many different frequencies we hear. For instance, a 1000 Hz signal at an SPL of 20 dB would be clearly audible. A 100 Hz signal at the same SPL would not be heard. A-weighting allows a single number to describe the SPL produced by a signal containing frequencies between 20 and 20,000 Hz. The weighting of the various frequencies is established by an internationally accepted A-weighting curve [58]. Typical fire alerting systems consist of a combination of audible and visual signals activated by fire detection systems. The audible devices are usually horns, bells, chimes, or speakers. The visual indicators are usually strobe lights, incandescent lamps, or, occasionally, revolving beacons. In residential occupancies, fire alerting systems should be capable of awakening a sleeping person and informing him or her that a fire emergency exists. Several studies have been done to establish the sound pressure level required to achieve this goal [59, 60]. These studies suggest an SPL between 55 and 70 dBA will awaken a college-age person with normal hearing. The minimum required SPL is also a function of the background noise or signal-tonoise ratio. These levels establish the SPL required to alert or be audible. They do not address the problem of how the person will perceive the sound or react to it. Until recently, fire codes did not set forth the SPL that a fire alarm system must produce within a building. NFPA 72 [8] requires signals to be
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15 dBA above ambient in areas where people may be sleeping. British standards require fire alarm signals to produce a sound pressure level of 65 dBA or 5 dBA above ambient noise in areas where occupants are not sleeping [61]. A sound pressure level of 75 dBA at the head of the bed is required in occupancies where people may be sleeping. The audible design requirements listed above and the remaining discussion and examples in this section all use dBA as a measure of audibility. However, it should be pointed out that for a sound to be perceived as audible, it need only penetrate or be greater than the background noise level at one particular frequency bandwidth. For example, certain facilities such as manufacturing plants may have a background noise level in excess of 85 dBA. An installed fire alarm may produce only 75 dBA at a certain location. Nevertheless, occupants will hear and respond to the fire alarm system. Why? The reason is because the background noise that contributes to the 85 dBA is mostly low frequency sound and the fire alarm is mostly high and midrange frequencies. Figure 40.12 illustrates this concept. Like two picket fences, one behind the other, only one picket or octave band must be taller for us to perceive the presence of the second fence or signal. More discussion on this approach can be found in the National Fire Alarm Code. While the balance of this section uses dBA, the procedure and methods apply equally well to work done in a single frequency band. Visual signals are located to assist people in deciphering potentially confusing alarm signals. The visual signals also help alert occupants in high background noise environments. Butler et al. [58] have described a method to estimate sound pressure levels at some location remote from the sound source. Formulas presented in their study are analogous to standard sound attenuation formulas found in other references [59, 62]. They have been simplified by replacing complex terms with constants for which they have provided tables of data (see Tables 40.17, 40.18, 40.19, 40.20, 40.21, 40.22, 40.23, 40.24, 40.25, 40.26, 40.27, 40.28, 40.29, and 40.30). The equations and data presented in
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Noise Alarm
90 80 70
dBA
60 50 40 30 20 10 0 31.5
63
125
250
500
1000
2000
4000
8000
16,000
Frequency band (Hz)
Fig. 40.12 Penetration of noise by alarm
Table 40.17 Adjustment for mounting position of sounder (C1) Sounder position Wall/ceiling mounted (more than 1 m from any other major surface) Wall/ceiling mounted (closer than 1 m to one other major surface)
Table 40.18 Adjustment for distance (C2) with distance from source (m) Distance from source (m) 1 2 3 6 12 15 20 25 30 40 50 60 80 100
C2 11 17 21 27 33 35 37 39 41 43 45 47 49 51
their study provide a straightforward method for analyzing proposed designs. The same equations and data can be used to determine the power requirement and maximum allowable spacing of signaling devices required to achieve a specified
C1 +5 +7
sound pressure level. The technique presented in their study is suitable for acoustically simple buildings only and may not be suitable on their own for voice alarm systems. Complex building arrangements and materials may require a more rigorous analysis using other methodologies which are beyond the scope of this chapter. In assessing signaling system design, one may have to consider estimating required sound levels for devices located within a space, external to the space, or in combination. With respect to the sound at a point within an enclosed space, one may need to consider direct and reverberant components [58]. The direct component is a function of the sound pressure level (SWL or LW) and distance from the source. The reverberant component is affected by the characteristics and contents of the enclosure, including type and quantity of finishes and furnishings, with acoustically soft materials absorbing sound waves and acoustically hard materials reflecting them. In large open spaces, such as open plan offices or ballrooms, it has been found for sound power
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Table 40.19 Adjustment for number of directions of sound propagation (C3) C3 0 3 5
Number of directions Single direction (e.g., positioned at one end of a corridor) Two-directional (e.g., positioned in the length of a corridor) Three-directional (e.g., positioned at a T junction of corridors)
Table 40.20 Adjustment based on the finishes in the corridor (C4) Surface finishes Hard (e.g., walls and ceiling with solid surfaces and terrazzo floor) Medium (e.g., acoustic ceiling, plastered solid walls with 5 % coverage of soft surfaces and floor of composite tiles) Soft (e.g., acoustic ceiling, plastered solid walls with 5 % coverage of soft surfaces and carpets on felt on concrete floor)
Table 40.21 Adjustment for distance from source to midpoint of the partition (C5) C5
Distance from source (m) 1 3 6 10 12 15 20 30 50
0 4 8 10 11 12 14 15 17
Table 40.22 Addition of two sound pressure levels Difference between the two levels (dB to be added) 0 1 2 3 4 5 6 7 8 or more
Add to the higher level (dB) 3 2 2 2 2 1 1 1 0
assessment of nonvoice signals, the reverberant component has little contribution and can be effectively ignored (note: this does not apply to voice signals where intelligibility is a concern and reverberation does play a role). For basic analysis of the situation where the alarm
C4 0 8 9
Table 40.23 Factor for area of partition between sounder and receiver (C6) Partition area (m2) 2 4 8 10 15 20 30 50 80 100 200
C6 +3 +6 +9 +10 +11.5 +13 +15 +17 +19 +20 +23
Table 40.24 Adjustment for frequency of maximum output of sounders (C7) Frequency of sounder (Hz) 500 1000 2000 4000
C7 0 3 5 9
sounding device is located within the enclosed space, the sound pressure level needed at a defined point from the source can be determined by the following relationship: LP ¼ LW þ C1 þ C2 dBA where C1 is a function of the mounting position of the sounder and C2 is a function of the distance
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Table 40.25 Second reduction indices (dB) for a selection of typical structures (100–3150 Hz frequency range) Building element Walls and partitions 1. 100-mm-dense concrete with or without plaster 2. 150-mm “no fines” concrete with 12-mm plaster on both faces 3. 115-mm brickwork with 12-mm plaster on both faces 4. 115-mm brickwork unplastered 5. 300-mm lightweight concrete precast blocks with well-grouted joints 6. 75-mm clinker blockwork with 12-mm plaster on both faces 7. 50-mm-dense concrete 8. 25.4-mm plasterboard (two layers) separated by timber studding (75 mm) and mineral fiber blanket 9. 200-mm lightweight concrete precast blocks with well-grouted joints 10. 150-mm lightweight concrete precast blocks with well-grouted joints 11. 50-mm clinker blocks with 12-mm plaster on both faces 12. 63-mm hollow clay blocks with 12-mm plaster on both faces 13. 9.5-mm plasterboard (two layers) separated by timber studding (75-mm with 12-mm) with plaster on both faces 14. 6-mm plywood/hardboard (two layers) separated by timber studding (50- and 50-mm) mineral fiber blanket 15. 19-mm chipboard on a supporting frame 16. 0.8-mm sheet steel 17. 21-mm tongued and grooved softwood boards tightly clamped on a support frame 18. 3.2-mm hardboard (two layers) separated by 44-mm polystyrene core Doors 19. Flush panel, hollow core, hung with one large air gap 20. Flush panel, hollow core, hung with edge sealing 21. Solid hardwood, hung with edge sealing Windows 22. Single glass in heavy frame 23. Double-glazed 9-mm panes in separate frames 50-mm cavity 24. Double-glazed 6-mm panes in separate frames 100-mm cavity 25. Double-glazed 6-mm and 9-mm panes in separate frames 200-mm cavity, absorbent blanket in reveals
from the sounder to the point of concern. The values for C1 and C2 are given in Tables 40.17 and 40.18. If the space of concern is large enough that the receiver (e.g., person in the room) can receive alarm signals (noise, sound) from more than one source, the combined noise level should be estimated. The combined noise level is not the arithmetic sum of the individual sound pressure levels (dBA); rather, it will be a level that corresponds to the arithmetic addition of the individual sound powers in watts. For the purpose of this methodology, the combined noise
Weight of partition (kg/m2)
Average attenuation (dB)
250 250 250 195 190 115 120 —
45 45 45 42 42 40 40 40
122 93 — — —
40 37 35 35 35
—
30
— — —
25 25 20
—
20
9 9 28
14 20 26
15 62 112 215
24 34 38 58
level at a particular receiver position can be estimated by first estimating the noise level from each sounder in the space (ignoring the existence of the other sounders) and then combining the noise level based on the difference in sound pressure levels using the values in Table 40.22. For example, if an estimated sound pressure level from one device is 65 dBA and is 63 dBA from another, the resulting total sound pressure level will be 67 dBA (from Table 40.22, the difference in noise level between the two sounders is 2 dBA, so 2 dBA is added to the higher sound pressure level value).
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Table 40.26 Average sound reduction indices (dB) of partitions incorporating a door of 26 dB attenuation (i.e., heavy door with edge sealing) (100–3150 Hz frequency range) Door representing percentage of total area of partition (%) 100 50 25 10 5
Sound reduction index of partition without glazing 25 dB 30 dB 35 dB 40 dB 26 26 26 26 25 27 28 28 25 28 30 31 25 28 32 34 25 28 33 36
45 dB 26 28 31 35 38
50 dB 26 28 31 35 38
Table 40.27 Average sound reduction indices (dB) of partitions incorporating a door of 14 dB attenuation (i.e., one with large air gaps) (100–3150 Hz frequency range) Door representing percentage of total area of partition (%) 100 50 25 10 5
Sound reduction index of partition without glazing 25 dB 30 dB 35 dB 40 dB 14 14 14 14 16 16 16 16 19 19 19 19 21 23 23 23 23 25 26 26
45 dB 14 17 20 23 26
50 dB 14 17 20 23 26
Table 40.28 Average sound reduction indices (dB) of partitions incorporating a door of 20 dB attenuation (i.e., light door with edge sealing) (100–3150 Hz frequency range) Door representing percentage of total area of partition (%) 100 50 25 10 5
Sound reduction index of partition without glazing 25 dB 30 dB 35 dB 40 dB 20 20 20 20 21 22 22 22 23 24 25 25 24 27 28 29 24 28 30 32
45 dB 20 22 25 29 32
50 dB 20 23 26 29 32
Table 40.29 Combined sound reduction indices for combination of standard doors and glazing (100–3150 Hz frequency range) Sound reduction index for standard size door (1.54 m2) Area of (24 dB) glazing (m2) 1 2 4 6 8 10 12 16 20
14 dB 20 dB Insulation values for combined door and glazing 16 21 17 22 18 22 19 23 20 23 20 23 21 23 21 23 22 23
26 dB 25 25 24 24 24 24 24 24 24
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Table 40.30 Average sound reduction indices for a partition whose surface is a combination of glass, door, and wall partition (100–3150 Hz frequency range) Sound reduction value of partition without glazing or door 30 dB Door + glazing as percentage of total partition area 5 10 20 30 50 75 100
35 dB
40 dB
45 dB
Insulation value of combined door and glazing (dB) (from Table 40.29) 15 20 25 15 20 25 15 20 25 15 26 28 30 28 31 33 28 32 36 28 24 27 29 24 29 32 25 30 34 25 22 25 28 21 26 31 22 27 32 22 20 24 28 20 25 29 20 25 30 20 18 23 27 18 23 28 18 23 28 18 16 21 26 16 21 26 16 21 26 16 15 20 25 15 20 15 15 20 25 15
For sounders located outside of the space of concern, one needs to consider additional factors, particularly if the arrangement is from a corridor to another space, such as an office, a hospital suite, or a hotel guest room. If the sounder is located in a corridor, for example, there may be directional considerations for the sounder, and consideration must also be given to the distance from the sounder to the partition separating the corridor and space of concern, in addition to the acoustical characteristics of the corridor. One then needs to consider the attenuation of the sound through the partition and the distance to the receiver. These factors are addressed in more detail in the following examples. To demonstrate how signaling systems can be designed and analyzed, two scenarios will be considered. Both scenarios are based on a typical dormitory or office layout. The building has long corridors with rooms of equal size on each side. Each room is approximately 5 m wide by 6 m deep. The walls consist of two layers of Sheetrock (total of 25.4 mm thick) separated by wood studs. The wall cavities contain 75-mm-thick mineral fiber insulation. The floors are concrete with carpeting. The ceiling is 3 m high and consists of acoustical tiles. The room doors are solid core with good edge seals. The alerting systems will be designed to achieve a 75 dBA sound pressure level at the farthest point in the rooms. In the first scenario, wall-mounted fire alarm speaker/light combinations are spaced equally in
20 33 30 27 25 23 21 20
25 37 35 32 30 28 26 25
the corridor with a nonvoice alarm signal being transmitted. Calculations determine the maximum allowable spacing of the speakers in order to achieve the design goal of 75 dBA in the rooms. In the second scenario, speakers are placed in each room as well as in the corridor. Calculations determine the size of the speaker and the power needed to drive that speaker to achieve the design goal of 75 dB. Calculations are also presented to determine the required spacing of speakers in the corridor to achieve a sound level of 65 dB. Unless otherwise noted, the following formulas and data are from Butler, Bowyer, and Kew [58]. Scenario A In this scenario, the fire alerting system, or sounder, will consist of wall-mounted speaker/light combinations in the corridors only. LW is the sound power level of a horn, bell, speaker, or any sounder (dBA referenced to 1012 W). LW ¼ L þ 20 log10 r þ 11 dB where L is the manufacturer’s stated output in dBA at a distance r meters. A typical compression driver-type fire alarm speaker powered at 2 W has an L equal to 94 dBA at 3.05 m [63]. Therefore, LW ¼ 94 þ 20 log10 ð3:05Þ þ 11 LW ¼ 115 dB
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LP1 is the sound pressure level (dBA referenced to 2 105 Pa) produced outside of a room wall from one speaker. LP1 ¼ LW þ C3 þ C4 þ C5 where C3 ¼ Correction for the number of directions that the sounder propagates C4 ¼ Correction for the characteristics of the corridor walls, ceiling, and floor C5 ¼ Function of the distance from the sounder to the center of the bedroom wall From Table 40.19 [58] C3 is 3 dB, because the speaker propagates in two directions along the corridor; from Table 40.20 is C4 is 9 dB, because the floor and ceiling are acoustically soft; and C5 is unknown since the required spacing of the corridor speakers has not yet been determined. Table 40.21 provides C5 values for determined distances. A worst-case condition exists for a room located farthest from a speaker. In this situation the room is located equally between two speakers. Since each unit propagates sound to the room, the sound pressure level outside of the room is higher than if there were only one speaker. The sound pressure level is not double that for a single speaker. For equally spaced sounders, Table 40.22 indicates to add 3 dB to the level expected from a single unit. Therefore, LP1 ¼ 115 3 9 þ C5 þ 3 LP1 ¼ 106 þ C5 LP2 is the sound pressure level at the farthest point in a room. To achieve the established goals, LP2 must be 75 dBA. In this situation, with the speaker located outside of the occupied space, LP2 ¼ LP1 R þ C2 þ C6 þ C7 þ 11 dBA where R ¼ Average sound reduction index for the wall C2 ¼ Function of the distance from the wall to the point of interest C6 ¼ Function of the area of the room wall (see Table 40.23) C7 ¼ Function of the frequency of the sound reaching the wall (see Table 40.24)
In this case, from data presented by Butler, Bowyer, and Kew [58], the sound reduction index R for the wall is about 40 dB (see Table 40.25). This value is based on incident sound in the range of 100–3150 Hz. Sound attenuation through the door is about 26 dB (see Table 40.25). The average sound reduction index, R, for the combined door and wall is 34 dB, if the door is 10 % of the area (see Table 40.26). C2 is found to be 27 dB, because there are 6.5 m from the center of the wall to the corner of the room (see Table 40.26). Since the wall is 15 m2, C6 is +11.5 dB (see Table 40.23). If it is assumed that the sound reaching the wall is at a maximum at a frequency of 2000 Hz, C7 ¼ 15 dB (see Table 40.24). Therefore, LP2 ¼ ð106 þ C5 Þ 34 27 þ 11:5 5 þ 11 dBA LP2 ¼ 62:5 þ C5 dBA
If there were no loss of sound pressure level between the speaker and the room wall due to distance, C5 would be zero and LP2 would be 62.5 dBA. This result shows that even if the two speakers were right outside the room, the goal of 75 dBA in the room would not be met. In fact, the resultant noise level in the room would be slightly less than the 65 dBA required by British standards [61] to alert nonsleeping persons. The sound level of 62.5 dBA would exceed the 55 dBA reported by Nober et al. [32] to alert sleeping college-age persons in a quiet ambient setting. To meet the goal of 75 dBA in the room, either the sound system or the environment would have to be changed. Fire alarm speakers are normally available with multiple power taps such as 4, 2, 1, 1/2, and 1/4 W. A single unit may allow choice of two or three different power levels, which allows balancing of the system after installation. If a 4-W power input were used, this would be a doubling of the 2 W originally tried in the previous calculation. Because decibels are logarithmic, a doubling of power results in a change of 3 dB in LW (10 log10 2 ¼ 3).This action alone would not be sufficient to meet the 75-dBA goal. In addition, the higher sound pressure level
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in the immediate vicinity of the speaker might be discomforting. If the fire alarm system were also used for voice communication, a speaker tapped at 4 W in a small corridor might sound very distorted and be unintelligible. It is also possible to change the sound pressure level in dBA by changing the frequency of the source. In general, the higher the frequency, the higher the attenuation as the sound waves pass through a wall. Hence, a lower frequency would increase the sound pressure level in the room. In the calculations above, it was assumed that the predominant frequency of the source was 2000 Hz. This frequency resulted in a C7 of 5 dBA. According to Table 40.24, if this frequency were 500 Hz, C7 would be 0 dBA. This adjustment would increase the SPL in the room by 5 dBA. Changes could be made to the building design that would make it possible to meet the design goal. For instance, the use of a lighter-weight door or one without good edge sealing could increase sound transmission to the room by as much as 12 dBA (see Tables 40.27, 40.28, 40.29, and 40.30). However, changes such as this one would tend to defeat other goals such as fire resistance and resistance to smoke spread. If the floor and ceiling were hard surfaces without carpeting or tiles, C4 could be increased from 9 to 0 dBA (Table 40.31). Changes such as this would probably be resisted for reasons other than fire safety. The only remaining alternative is to provide speakers in each of the rooms. Scenario B In this case, a speaker in each room powered at only 1/4 W will be tried in addition to
the speaker in the corridor. The building use is a dormitory space. The problem, then, is to select a speaker with a sound power output that can meet the goal of 75 dB at the pillow. L ¼ ? r ¼ at 305 m (3.05 m is a commonly used reference point). LW ¼ L þ 20 log10 r þ 11 dB LW ¼ L þ 20 log10 ð3:05Þ þ 11 dB LW ¼ L þ 21dB LP2 is the sound level at the bed. In this case, with the speaker in the occupied space, LP2 ¼ LW þ C1 þ C2 dBA where C1 is a correction for how close the sounder is to an adjacent surface, and C2 is a correction for the distance from the speaker to the bed. In this case, the speaker is on the wall and close to the ceiling. Therefore [58], C1 is +7 dB, and C2 is 27 dB (approximately 6.5 m from the speaker to the bed) (see Tables 40.17 and 40.18). Therefore, LP2 ¼ ðL þ 21Þ þ 7 27 dBA LP2 ¼ L þ 1 dBA To get LP2 ¼ 75 dBA, L must be at least 74 dBA. The smallest and least expensive fire alarm speaker available is a 4-in. paper cone speaker. A typical speaker of this size and type, powered at 1/4 W, has an L equal to 75 dB at 3.05 m [64]. This speaker would meet the design goal in the room, without even
Table 40.31 Average sound reduction indices (dB) of partitions incorporating single glazing (100–3150 Hz frequency range) Percentage of glazing (24 dB) (%) 100 75 50 33 25 10 5 2½ —
25 dB 24 24 24 25 25 25 25 25 25
30 dB 24 25 26 27 27 29 29 30 30
35 dB 24 25 27 28 29 31 33 34 35
40 dB 24 25 27 29 30 33 35 37 40
45 dB 24 25 27 29 30 34 36 39 45
50 dB 24 25 27 29 30 35 37 40 50
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considering any sound contribution from corridor-mounted speakers. For the corridor speakers in Scenario B, LP1 is the sound pressure level at a point farthest from a speaker. LP1 ¼ LW þ C3 þ C4 þ C5 dBA where C3 and C4 are the same as in Scenario A (3 and 9 dB, respectively). C5 is a function of the spacing, which is to be determined. If a single corridor speaker tapped at only 1/4 W is used, with an L of 85 dB at 3.05 m [63], LW ¼ L þ 20 log10 r þ 11 dB LW ¼ 85 þ 20 log10 ð3:05Þ þ 11 dB LW ¼ 106 dB LP1 ¼ 106 3 9 þ C5 dBA LP1 ¼ 94 þ C5 The goal is to maintain a 65 dBA sound pressure level in the corridors (LP1). Therefore, C5 must be 29 dBA or more for LP1 to be 65 dBA or higher. From Table 40.20 [58], it is found that distance of 50 m between source and target in the corridor could be exceeded and still meet the 65 dBA goal. Earlier in this section it was noted that designing for alarm audibility alone is not always sufficient, especially when voice alarm signals are involved. This is because speech is not Talker
Microphone
Mixer
necessarily intelligible simply because it is audible: adding more sound level to speech that has been blurred by reverberation, echoes, or distortion does not make it more intelligible [65]. A sufficiently loud but overly reverberant speech signal can be almost completely unintelligible. There are many examples of this in airports, train stations, and other large spaces, particularly those with hard acoustical surfaces. When considering intelligibility, there are a variety of factors which are important, starting with the person who is speaking, the mode and features of the transmission system, the characteristics of the space wherein the signal is received, and the listener. This is illustrated in Fig. 40.13. For fire alarm signaling system design, major facility use concerns include the characteristics of the space and the intended occupant population. The population matters from the perspective of understanding the message (e.g., language and abilities). The space matters from the perspective of how the signal, once introduced into the space, may become distorted or otherwise affected such that intelligibility is diminished. Factors that can corrupt the integrity of a voice signal on its path from talker to listener are summarized below [65]. • Speech-signal-to-noise ratio. Noise has the effect of masking or obscuring the voice signal. Remarkably, we are able to tolerate a great deal of noise before intelligibility
Amplifier
Room
Listener
Noise, reverberation, echoes
Language, hearing
A
Language, speed, articulation Assumed normal
Bandwidth, distortion
Bandwidth, distortion
Bandwidth, distortion
Intelligibility measurements
Fig. 40.13 Talker-to-listener transmission path [65]
Assumed normal
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Design of Detection Systems
diminishes appreciably, but once it begins to diminish, it diminishes rapidly. • Reverberation. Most are familiar with how difficult it can be to understand speech in a reverberant environment such as a cathedral or gymnasium. Reverberation is made up of sound reflections that have the effect of smearing or blurring speech, making it less clear and distinct and therefore more difficult to understand. • Echoes. If echoes arrive much later in time than the first arrival of sound, they can harm intelligibility. In continuous speech, the echo from a previously uttered syllable masks or obscures the sound of subsequent syllables, making speech more difficult to understand. The time delay and level of the echo are key variables in determining the impact of echoes on intelligibility. • Distortion. If one of the electrical or electroacoustical components in the sound system is distorting, it is generating a form of noise that masks the original speech signal. Severe amplifier clipping, for example, can make an otherwise perfect speech signal at the input to the amplifier more difficult to understand at the output. To accurately account for the effect of the above factors, they must be measured in at least octave-band resolution; a single broadband measurement is insufficient and more than octaveband resolution is almost always unjustified. Various documents exist for guiding the measurement of intelligibility [66–69], and appropriate instrumentation is available for obtaining the speech transmission index (STI) and other acoustical data necessary for better siting speakers for emergency voice communication. Descriptions of how to collect and use these data can be found in the literature (e.g., Woycheese [70]).
Cost Analysis Scenario A For comparison purposes, assume that sufficient changes could be made to the building and alarm system to allow speakers to be mounted in the corridor only at a spacing of
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3 m. A typical dormitory with about 30 bedrooms per floor requires approximately 24 speakers per floor in the corridors. In a building with seven floors, this requirement amounts to 168 speakers. At 2 W per speaker, the result would be 336 W. This setup requires three 125 W power amplifiers at an installed cost of about $3500.00 each. This amount does not include other fixed costs, such as control equipment and detectors, that are the same for each of the scenarios. Assume each corridor unit to be a speaker/ light combination. The average installed cost, including backbox, wiring back to a control panel on the first level, and conduit, would total to about $250.00 per unit. The total cost is then TOTAL ¼ ð3 $3500:00Þ þ ð168 $250:00Þ TOTAL ¼ $52, 500 Scenario B In this case, there are thirty 4-in. paper cone speakers per floor at an average cost of $200.00, installed. Assume a total of four speaker/light units per floor in the corridors. The calculations show that the system goals are met with only one or two units in the corridors. However, the halls may be split by smoke doors or they may be irregular in shape. Also, system reliability is increased by using more than one unit. Each bedroom speaker and corridor speaker is powered at 1/4 W. For seven floors, this setup gives a total power requirement of 59.5 W. Therefore, one 60 W amplifier, at a unit cost of $1500.00, is needed. The total cost is then TOTAL ¼ ð3 $1500:00Þ þ ð7 30 $200:00Þ þ ð7 4 $250:00Þ TOTAL ¼ $50, 500:00
The estimates show the relative costs of the different scenarios, not the actual costs. The real costs of the systems are affected by factors such as whether the building is new or existing. If existing, the price is affected by the extent of other renovations. Also, the estimates do not reflect the cost of other parts of the system. The balance of the system includes such items as
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smoke and heat detectors, equipment for elevator capture, and air handler controls. The relative costs of the two systems in Scenarios A and B under “Cost Analysis” differ by only about 4 %. In a building of this size and type, such a small margin cannot be considered significant enough to conclude that one system is more economical than the other. The small difference in the costs of the two systems is due to the additional cost of amplifiers needed to power the system that has only corridor units. The total number of units (corridor + room) in Scenario B is 70 more than in Scenario A. The reduced power requirement offsets the added cost of their installation. Scenario A has a higher equipment cost but a lower installation cost than Scenario B. This result means that the relative costs of the two systems will be slightly sensitive to the type of equipment used and the cost of installation labor. By changing the figures used in the cost estimates, it can be shown that the variance is only a few percent and probably not significant. If the building were four stories or less in height, the difference in relative cost rises to about 5 %. Again, this amount is not considered to be a significant difference. By increasing the size of the building to 12 stories, Scenario B becomes significantly less expensive than Scenario A. Above this height, the combined use of room and corridor units becomes increasingly economically attractive. Changing the size of each floor has about the same effect as changing the height of the building. Therefore, increasing the floor area makes Scenario B more viable. A reduction in floor area and building height does not make the corridor-only system attractive, unless the building is only a few stories in height. Then a voice system is probably not needed. From an economics standpoint, a corridor-only horn/light system is probably best, since the cost of these units is generally less than that of speakers. Again, this conclusion assumes that sufficient changes could be made to the building design to increase the level of sound penetrating the corridor walls.
R.P. Schifiliti et al.
Obviously, if the sound loss from the corridor to the individual rooms is less, Scenario A starts to look better. This situation has the effect of raising the height above which Scenario B becomes significantly less expensive. However, changing construction features to reduce sound loss may reduce the passive fire resistance of the structure below an acceptable level as well as decrease the privacy level. There are other factors to consider when choosing between different systems. In Scenario A, the quantity of speakers in the corridors and the high power levels driving each speaker (2 W each) can cause sound distortion. Voice messages may not be intelligible in the bedrooms even though there is enough sound to wake a sleeping occupant. Also, the high sound levels (106 dBA plus) in the corridors approach uncomfortable levels. It is clear from the discussions above that a system with room speakers in conjunction with corridor units is the most desirable case. That system has the added advantage of eliminating most of the uncertainties in the design of the system. It is easier and more accurate to calculate sound levels at a point in the same room as the sound source than it is to estimate sound losses through composite walls. This cost-benefit analysis shows that a fire alarm alerting system with units in each office or bedroom can be installed at about the same cost or less than a corridor-only system. In addition, there is a higher confidence level that the system with the sounders in each room will perform its intended function: to awaken and alert sleeping occupants.
Designing Fire Alarm Visibility Visual alarm notification is an important part of a fire alarm system. This visual aspect is especially important in cases where the ambient noise level is high, building occupants may be sleeping, or building occupants or their visitors may have hearing impairments. In these cases, it should be expected that the visual alarm will be required to alert occupants and initiate evacuation or
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Design of Detection Systems
1371
relocation. As such, one first needs to determine a suitable intensity required to obtain this function. In many cases, a suitable intensity can be obtained from regulatory documents, such as building codes, fire codes, or the Americans with Disabilities Act. These references typically give a required appliance intensity and a maximum size space that can be covered by an appliance with that intensity. If additional guidance is needed, reference can be made to appropriate documentation on alerting of persons by visual means [71]. It is also possible that a reference may cite a required level of illumination to alert someone. This requirement should not be confused with the intensity of the lamp providing the signal. The two are related by the inverse square law where E is the illumination (lumens per unit area), I is the intensity of the light source (candela), and d is the on-axis distance between the light source and the point where the illumination is measured (Fig. 40.14). E¼
I d2
In cases where flashing signals are required, the source strength or output is cited as effective intensity. Effective intensity is used to equate the perceived brightness of a flashing light to that of a steady light. It can be calculated using the relationship [64],
Fig. 40.14 Relationship between intensity of lamp and level of illumination required to alert someone
ð t2
I dt
Ie ¼
t1
ða þ t2 t1 Þ
ð40:29Þ
where Ie ¼ Effective intensity I ¼ Instantaneous intensity t1 ¼ The time (s) of the beginning of that part of the flash where I exceeds Ie t2 ¼ The time (s) of the ending of that part of the flash where I exceeds Ie In the United States, the value of 0.2 is usually used for the constant a. This relationship is shown graphically in Fig. 40.15. There are two ways to use light as a notification method. The first is direct viewing where the person must be “see” the appliance in their direct or peripheral vision. The second is indirect viewing where the person is alerted by light reflected off of adjacent surfaces. Equation 40.29 is referred to as the BlondelRey equation and was adopted as a product metric in the early 1990s. This allowed different light sources to be evaluated as being equivalent. The research by Blondel and Rey was published in 1912 and is based on direct viewing of a flashing light in a dark environment [72]. Equation 40.29 has worked as a metric to compare two light sources that use the same technology and that have similar pulse durations and pulse shapes.
E=
Ι d2
I = Intensity of source (1 cd or 12.57 lumens) E = Illumination (1 lumen/ft2 or 1 footcandle [1 lumen/m2 or 1 lux or 0.0926 footcandle]) d = Distance from source to object (ft or m)
1372 Fig. 40.15 Peak versus effective intensity (Source: R.P. Schifiliti Associates, Inc., Reading, MA)
R.P. Schifiliti et al. Intensity in candela (cd)
Short-duration pulse, high peak
Long-duration pulse, low peak
10% of peak
10% of peak
10% of peak
Time duration
Until recently, all lights used for occupant notification in the fire alarm industry have been based on Xenon flash tubes. These strobe lights all have pulse durations less than 1 millisecond (ms) and have the similarly shaped response curves. Recent research has indicated that Equation 40.29 it is not suitable for comparing the detection of indirect flashing lights or for comparing different light technologies, such as Xenon strobes versus LED lights that have rectangular pulse curves [73]. Additional research is being done to define a new metric that allows different technologies to be compared and that is well correlated to actual indirect alerting effectiveness. The examples that follow are valid only for strobe lights that use Xenon flash tube technology. If the duration of the flash is less than 1 millisecond, Equation 40.29 can be further simplified to [64] ð I e ¼ 5 I dt where the integration is performed over the complete flash cycle. As part of a test program to determine signaling applications for the hearing impaired, UL determined that an illumination of 0.398 lm/m2 (0.037 lm/ft2) as viewed on axis from a single flashing light source located in the center of one
wall of a 6.1 m by 6.1 m (20 ft by 20 ft) room was the minimum required by their objective. It was also determined that, by increasing the “square” dimensions in increments of 3 m (10 ft) in both directions (length and width), the minimum illumination value of 0.398 lm/m2 could be used to extrapolate the required signal intensity as the room size increased. For example, if the room size were increased to 12.2 m by 12.2 m (40 ft by 40 ft), the effective intensity, cd eff, of the flashing strobe signal could be determined using the inverse square law and solving for I: E¼
I ; therefore d2
I ¼ Ed 2 ¼ ð0:398 lumens=m2 Þ ð12:2 m2 Þ ¼ 59:2 candela Thus, one signal rated at 60 cd eff would be sufficient for the space. Using the same approach, but smaller squares, one would also find that two signals rated at 30 cd eff, or four signals rated at 15 cd eff each, would also be applicable. Designers should check with the authority having jurisdiction or the current edition of NFPA 72 regarding the use of multiple flashing lights.
40
Design of Detection Systems
Example 20 The design objective is to evaluate the visual alarm notification system installed in a large open space for suitability in providing signals for the hearing impaired. The space is 21 m (70 ft) by 37 m (120 ft), with a 6.5 m (20 ft) ceiling height. The notification appliances are located 2 m (6.5 ft) above floor level and are spaced as shown in Fig. 40.16. The signals are rated at 45 cd eff each. Is the required illumination of 0.398 lm/m2 currently provided? Solution The first step is to section off the space into blocks that are anticipated to be covered for each signal. In this case, the result is six blocks, each 12.2 m (40 ft) long by 10.5 m (34 ft) wide. This step is illustrated in Fig. 40.17. Given these dimensions, one could calculate the illumination at point A, where E¼
45 cd ¼ 0:41 lumens=m2 ð10:5 m2 Þ
21 m
37 m
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This illumination is greater than the minimum required of 0.398 lm/m2. However, application of this method requires the blocks of coverage by a signal to be square with the lateral distance (90 ) being equal to one-half the coverage distance on-axis. In this case, the lateral distance is 12.2 m (40 ft), and this is the figure that should be used to calculate the illumination throughout the entire block. In doing this, one finds that the illumination provided is E¼
45 cd eff ¼ 0:29 lumens=m2 ð10:5 m2 Þ
which is below the minimum required 0.398 lm/m2. This outcome results in areas of the space not having the required illumination. This outcome is illustrated in Fig. 40.18. To determine what intensity is required for the signals in order to provide the required 0.398 lm/m2, the inverse square law can be applied using the value d ¼ 12.3 m. This application results in a required incident intensity of 60 cd eff for each existing signal location. By applying this method of dividing spaces into squares and applying the inverse square law, the intensity of signals and their required spacing can be calculated for spaces of any shape and size. Trade-offs can be made between the number of signals and the intensity of signals to best fit the application (e.g., one signal of 60 cd eff Luminosity below required level
Fig. 40.16 Notification appliance (~) locations
A
10.5 m
12.2 m
Fig. 40.17 Sections for anticipated signal (~) coverage
Fig. 40.18 Diagram of subadequate luminosity intensity
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versus four properly spaced signals of 15 cd eff each). In cases where a minimum required illumination at all points in a space is specified (as opposed to the minimum effective intensity on-axis within a square), the illumination can be calculated using the inverse square law, the cosine law, and the cosine cubed law. In this case, the inverse square law provides the illumination on-axis, application of the cosine law provides the illumination at a perpendicular surface within the same plane as the signal, and application of the cosine cubed law provides the illumination at parallel surfaces within the same plane as the signal. With this information, it should be possible to calculate visual fire alarm signals for most situations. In all cases, a value for the required effective intensity at some point within the room is required. If not provided at the beginning of the design process, one should determine an effective intensity based on the specific application and the condition of the occupants being alerted.
H ΔHc Hf Lp LW m p q_ q_ cond q_ conv q_ rad q_ total _ Q _ Q cr _ Q do _ Q i _ Q p _ Q T r
Nomenclature α A A c Cp d D Δt ΔT ΔTd ΔTp f g g hc
*
Fire intensity coefficient (Btu/s3 or kW/s2) Area (m2 or ft2) g/(CpTaρ0) [m4/(s2kJ) or ft4/(s2Btu)] Specific heat of detector element [Btu/(lbmR) or kJ/(kgK)] Specific heat of air [Btu/(lbmR) or kJ/(kgK)] Diameter of sphere or cylinder (m or ft) Nondimensional change in gas temperature Change in time (s) Increase above ambient in temperature of gas surrounding a detector ( C or F) Increase above ambient in temperature of adetector ( C or F) Change in reduced gas temperature Functional relationship Functional relationship Gravitational constant (m/s2 or ft/s2) Convective heat transfer coefficient [kW/(m2 C) or Btu/(ft2s F)]
ρ0 Re RTI S t tc
tr tv t2f t2f* tp* T Ta Td Tg Ts
Ceiling height or height above fire (m or ft) Heat of combustion (kJ/mol) Heat of formation (kJ/mol) Sound pressure level Sound power level Mass (lbm or kg) Positive exponent Heat release rate (Btu/s or kW) Heat transferred by conduction (Btu/s or kW) Heat transferred by convection (Btu/s or kW) Heat transferred by radiation (Btu/s or kW) Total heat transfer (Btu/s or kW) Heat release rate (Btu/s or kW) Critical heat release rate Design heat release rate Ideal heat release rate Predicted heat release rate (Btu/s or kW) Threshold heat release rate at response (Btu/s or kW) Radial distance from fire plume axis (m or ft) Density of ambient air (kg/m3 or lb/ft3) Reynolds number Response time index (m1/2s1/2 or ft1/2s1/2) Spacing of detectors or sprinkler heads (m or ft) Time (s) Critical time—time at which fire would reach a heat release rate of 1000 Btu/s (1055 kW) (s) Response time (s) Virtual time of origin (s) Arrival time of heat front (for p ¼ 2 power-law fire) at a point r/H (s) Reduced arrival time of heat front (for p ¼ 2 power-law fire) at a point r/H (s) Reduced time Temperature ( C or F) Ambient temperature ( C or F) Detector temperature ( C or F) Temperature of fire gases ( C or F) Rated operating temperature of a detector or sprinkler ( C or F)
40
U u u0 up* v x Y τ τ0
Design of Detection Systems
Velocity (m/s) Instantaneous velocity of fire gases (m/s or ft/s) Velocity at which τ0 was measured (m/s or ft/s) Reduced gas velocity Kinematic viscosity (m2/s or ft2/s) Vectorial observation point (m or ft) Defined in Equation 40.26 Detector time constant—mc/(hA) (s) Measured at reference velocity u0 (s)
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1375 12. M. Kokkala, “Thermal Properties of Heat Detectors and Sprinklers,” Nordtest Brand Symposium, Boras, Sweden (1986). 13. R.P. Schifiliti and W.E. Pucci, “Fire Detection Modeling: State of the Art,” The Fire Detection Institute, Bloomfield, CT (1996). 14. “Discussion of a New Principle in Fire Detection, Rate Compensation,” Fenwal, Inc., Ashland, MA (1951). 15. C. E. Marrion, “Lag Time Modeling and Effects of Ceiling Jet Velocity on the Placement of Optical Smoke Detectors,” Master’s Thesis, Worcester Polytechnic Institute, Center for Firesafety Studies, Worcester, MA (1989). 16. R. Alpert, Fire Technology, 8, p. 3 (1972). 17. L.Y. Cooper, “Interaction of an Isolated Sprinkler and a Two Layer Compartment Fire Environment,” National Institute of Standards and Technology, Gaithersburg, MD (1991). 18. M. Delichatsios and R. L. Alpert, “Calculated Interaction of Water Droplet Sprays with Fire Plumes in Compartments,” NBS-GCR 86-520, Center for Fire Research, National Bureau of Standards, Washington, DC (1986). 19. G. Heskestad, “Sprinkler/Hot Layer Interaction,” NIST-GCR 91-590, National Institute of Standards and Technology, Gaithersburg, MD (1991). 20. D.D. Evans and D.W. Stroup, “Methods to Calculate the Response Time of Heat and Smoke Detectors Installed Below Large Unobstructed Ceilings,” NBSIR 85-3167, National Bureau of Standards, Gaithersburg, MD (1985). 21. G. Heskestad and M.A. Delichatsios, “The Initial Convective Flow in Fire,” 17th Symposium on Combustion, Combustion Institute, Pittsburgh, PA (1978). 22. G. Heskestad and M.A. Delichatsios, “Environments of Fire Detectors—Phase I: Effect of Fire Size, Ceiling Height, and Material,” Volume I: “Measurements” (NBS-GCR-77-86), (1977), Volume II: “Analysis” (NBS-GCR-77-95), National Technical Information Service (NTIS), Springfield, VA (1977). 23. R.P. Schifiliti, “Use of Fire Plume Theory in the Design and Analysis of Fire Detector and Sprinkler Response,” Master’s Thesis, Worcester Polytechnic Institute, Center for Firesafety Studies, Worcester, MA (1986). 24. D.W. Stroup, D.D. Evans, and P. Martin, NBS Special Publication 712, National Bureau of Standards, Gaithersburg, MD (1986). 25. SFPE Handbook of Fire Protection Engineering, National Fire Protection Association, Quincy, MA (1988 and 1995). 26. NFPA 72®, National Fire Alarm Code®, National Fire Protection Association, Quincy, MA, 1984 through 1996 editions. 27. G. Heskestad and M. Delichatsios, “Update: The Initial Convective Flow in Fire,” Fire Safety Journal, 15, pp. 471–475 (1989).
1376 28. C. Beyler, personal communication (1985). 29. C. Beyler, “A Design Method for Flaming Fire Detection,” Fire Technology, 20, 4, pp. 9–16 (1984). 30. J.R. Lawson, W.D. Walton, and W.H. Twilley, NBSIR 83-2787, National Bureau of Standards, Washington, DC (1983). 31. B.J. Meacham, “Characterization of Smoke from Burning Materials for the Evaluation of Light Scattering-Type Smoke Detector Response,” Master’s Thesis, Worcester Polytechnic Institute, Center for Firesafety Studies, Worcester, MA (1991). 32. B.J. Meacham and V. Motevalli, “Characterization of Smoke from Smoldering Combustion for the Evaluation of Light Scattering-Type Smoke Detector Response,” Journal of Fire Protection Engineering, SFPE, 4, 1, p. 17 (1992). 33. UL 268, Standard for Safety Smoke Detectors for Fire Protective Signaling Systems, Underwriters Laboratories, Inc., Northbrook, IL (1989). 34. G. Mulholland, “Smoke Production and Properties,” SFPE Handbook of Fire Protection Engineering, 4th ed., National Fire Protection Association, Quincy, MA, (2008). 35. J. Geiman and D.T. Gottuk, “Alarm Thresholds for Smoke Detector Modeling,” Fire Safety Science— Proceedings of the Seventh International Symposium, International Association for Fire Safety Science, Worcester, MA, pp. 197–208 (2003). 36. D.T. Gottuk, S.A. Hill, C.F. Schemel, B.D. Strehlen, S.L. Rose-Phersson, R.E. Shaffer, P.A. Tatem, and F.W. Williams, “Identification of Fire Signatures for Shipboard Multicriteria Fire Detection Systems,” Naval Research Laboratory, Memorandum Report, 6180-99-8386, Washington, DC, June 18, 1999. 37. H.W. Carhart, T.A. Toomey, and F.W. Williams, “The Ex-USS SHADWELL Full-Scale Fire Research and Test Ship,” NRL Memorandum Report 6074, revised January 20, 1988, reissued 1992. 38. M.J. Spearpoint and J.N. Smithies, “Practical Comparison of Domestic Smoke Alarm Sensitivity Standards,” Fire Research Station, Home Office Fire Research and Development Group, FRDG Publication No. 4.97 (1997). 39. R.W. Bukowski, T.E. Waterman, and W.J. Christian, “Detector Sensitivity and Siting Requirements for Dwellings,” Final Technical Report, IITRI Project J6340, Contract No. 4-36092, NBS-GCR-75-51, National Bureau of Standards, Gaithersburg, MD (1975). 40. UL 217, Standards for Single and Multiple Station Smoke Alarms, Underwriters Laboratories Inc., Northbrook, IL (1999). 41. UL 268, Standard for Smkie Detectors for Fire Protective Signaling Systems, Northbrook, IL (1996). 42. J. Hoseman, “Uber Verfahren zur Bestimmung der Korngrossenverteilung Hokkonzentrierter Polydispersionen von MiePartikeln,” Ph.D. Thesis, Aachen, Germany (1970). 43. C.D. Litton, “A Mathematical Model for Ionization Type Smoke Detectors and the Reduced Source
R.P. Schifiliti et al. Approximation,” Fire Technology, 13, 4, pp. 266–281 (1977). 44. R.W. Bukowski and G.W. Mulholland, “Smoke Detector Design and Smoke Properties,” TN 973, U.S. Department of Commerce, National Bureau of Standards, Washington, DC (1978). 45. C. Helsper, H. Fissan, J. Muggli, and A. Scheidweiler, “Verification of Ionization Chamber Theory,” Fire Technology, 19, 1, p. 14 (1983). 46. J. Newman, “Modified Theory for the Characterization of Ionization Smoke Detectors,” in Fire Safety Science—Proceedings of the Fourth International Symposium, International Association for Fire Safety Science, Ottawa, Ontario (1994). 47. G. Heskestad, “Generalized Characteristics of Smoke Entry and Response for Products-of-Combustion Detectors,” in Proceedings, 7th International Conference on Problems of Automatic Fire Detection, Rheinish-Westfalischen Technischen Hochschule, Aachen, Germany (1975). 48. M. Kokkala et al., “Measurements of the Characteristic Lengths of Smoke Detectors,” Fire Technology, 28, 2, p. 99 (1992). 49. J. Bjorkman, O. Huttunen, and M. Kokkala, “Paloilmaisimien toimintaa kuvaavat laskentamallit (Calculation Models for Fire Detector Response),” Research Notes 1036, Technical Research Center of Finland (1989). 50. A. Oldweiler, “Investigation of the Smoke Detector L Number in the UL Smoke Box,” Master’s Thesis, Worcester Polytechnic Institute, Worcester, MA (1995). 51. M.A. Delichatsios, “Categorization of Cable Flammability, Detection of Smoldering, and Flaming Cable Fires,” Interim Report, Factory Mutual Research Corporation, Norwood, MA (1980). 52. NFPA 92B, Guide for Smoke Management Systems in Malls, Atria, and Large Areas, National Fire Protection Association, Quincy, MA (2005). 53. G. Heskestad, FMRC Serial Number 21017, Factory Mutual Research Corp., Norwood, MA (1974). 54. E.L. Brozovsky, “A Preliminary Approach to Siting Smoke Detectors Based on Design Fire Size and Detector Aerosol Entry Lag Time,” Master’s Thesis, Worcester Polytechnic Institute, Center for Firesafety Studies, Worcester, MA (1991). 55. S. Deal, “Technical Reference Guide for FPEtool Version 3.2,” NISTIR 5486, National Institute for Standards and Technology, Gaithersburg, MD (1994). 56. G. Heskestad and M.A. Delichatsios, “Environments of Fire Detectors, Phase I: Effects of Fire Size, Ceiling Heights, and Material,” Volume II, Analysis Technical Report Serial Number 11427, RC-T-11, Factory Mutual Research Corp., Norwood, MA (1977). 57. K.B. Ginn, Architectural Acoustics, Bruel and Kjaer (1978). 58. H. Butler, A. Bowyer, and J. Kew, “Locating Fire Alarm Sounders for Audibility,” Building Services Research and Information Association, Bracknell, UK (1981).
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59. E.H. Nober, H. Pierce, A. Well, and C.C. Johnson, NBS-GCR-83-284, National Bureau of Standards, Washington, DC (1980). 60. M.J. Kahn, “Detection Times to Fire-Related Stimuli by Sleeping Subjects,” NBS-GCR-83-435, National Bureau of Standards, Washington, DC (1983). 61. British Standard Code of Practice CP3, British Standards Institution, London (1972). 62. C. Davis and D. Davis, Sound System Engineering, Howard H. Sams and Co., Inc., Indianapolis, IN (1975). 63. Product Catalog, Fire Control Instruments, Newton, MA (1986). 64. “Nomenclature and Definitions for Illuminating Engineering,” IES RP-16-1987, Illuminating Society of North America, New York (1987). 65. K. Jacobs, Understanding Speech Intelligibility and the Fire Alarm Code, presented at the NFPA Congress, Anaheim, CA, copyright Bose corporation (2001). 66. Accredited Standards Committee S3 (Bioacoustics), “Method for Measuring the Intelligibility of Speech over Communications Systems,” ANSI S3.2, Acoustical Society of America, Melville, NY (1995). 67. International Organization for Standardization, “Acoustics—The Construction and Calibration of Speech Intelligibility Tests,” ISO TR 4870, Geneva, Switzerland (1991). 68. International Electrotechnical Commission, “Sound Systems for Emergency Purposes,” IEC 60849, 2nd ed., IEC, Geneva, Switzerland (1998). 69. International Electrotechnical Commission, “Sound System Equipment—Part 16: Objective Rating of Speech Intelligibility by Speech Transmission Index,” IEC-60268-16, 3rd ed., IEC, Geneva, Switzerland (2003). 70. J.P. Woycheese, “Speech Intelligibility Measurements in an Office Building,” Journal of Fire Protection Engineering, 17, 4, pp. 245–269 (2007).
1377 71. UL 1971, Standard for Safety Signaling Devices for the Hearing Impaired, Underwriters Laboratories, Inc., Northbrook, IL (1992). 72. A. Blondel, and J. Rey, “The perception of lights of short duration at their range limits”. Transactions of the Illuminating Engineering Society, 7, 625–662 (1912). 73. J.D. Bullough, N.P. Skinner, and Y. Zhu, “Parameters for Indirect Viewing of Visual Signals Used in Emergency Notification” The Fire Protection Research Foundation, Quincy, MA, September 2013.
Further Readings V. Babrauskas, J.R. Lawson, W.D. Walton, and W.H. Twilley, NBSIR 82-2604, National Bureau of Standards, Washington, DC (1982).
Robert P. Schifiliti is a fire protection consultant specializing in fire detection and alarm systems design and analysis. Located in Reading, Massachusetts, he is a licensed Fire Protection Engineer and holds a Master of Science degree in Fire Protection Engineering from Worcester Polytechnic Institute. Mr. Schifiliti is a fellow of the Society of Fire Protection Engineers. Richard L.P Custer is senior fire consultant for Arup Fire located in Massachusetts. Mr. Custer is a fellow of the Society of Fire Protection Engineers. Brian J. Meacham is an associate professor in the Department of Fire Protection Engineering at Worcester Polytechnic Institute (WPI) in the United States. He is a licensed Professional Engineer, a Chartered Engineer, and a fellow of the Society of Fire Protection Engineers.
41
Hydraulics Kenneth E. Isman
Introduction
Physical Properties of Fluids
Hydraulics may be regarded as the application of knowledge about how liquids behave in static and flowing conditions to solve practical fluid related problems. It is generally held to describe the behavior and effects of water in motion in both closed conduits and open channels. In the field of fire protection we are concerned primarily with the closed conduit flow regime. In this chapter we will restrict our discussion to the behavior and properties of water flowing in pipes as the phenomenon of paramount interest, although other fluids such as antifreezes at room temperature and foam/water solutions are similar enough to water that the discussion will be applicable to them as well. Additionally some of the principles presented here also apply to system designs utilizing other fluids such as foam concentrate or antifreeze at low temperatures.
The solution of any flow problem requires a basic knowledge of the physical properties of the fluid being considered. A brief description of the most basic properties follows.
Density The density of a fluid (ρ) is the mass of the fluid (m) per unit volume (V) as shown in the equation below: m ρ¼ V Density is expressed in SI units as kg/m3 and in English, or U.S. customary, units as slugs/ft3 (or lbf · s2/ft4). The density of water at 4 C (~40 F) is 1000 kg/m3 (1.94 lbf · s2/ft4).
Specific Weight
A significant portion of this chapter was written by John J. Titus. Editorial and technical updates were incorporated and additional information on pumps and water supplies have been provided for this edition. K.E. Isman (*)
The specific weight of a fluid (γ) is the representation of the force exerted by gravity on a unit volume of the fluid. The specific weight can also be calculated by multiplying the density of a fluid (ρ) by the gravitational constant (g) as shown below: γ ¼ ρg Specific weight takes on units of weight per unit volume, which in SI units would be kN/m3 and in
M.J. Hurley (ed.), SFPE Handbook of Fire Protection Engineering, DOI 10.1007/978-1-4939-2565-0_41, # Society of Fire Protection Engineers 2016
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English customary units would be lb/ft3. At 4 C, the specific weight of water is 9.81 kN/m3 (62.4 lb/ft3) [1].
Specific Gravity (Relative Density) Specific gravity (SG) is the ratio of a liquid’s density (ρ) or specific weight (γ) to that of water (ρwater or γwater) as shown by the following formulas: ρ γ SG ¼ or SG ¼ ρwater γ water Where the specific gravity of a fluid is greater than 1.0, it means that the fluid is heavier than water. Where the specific gravity of a fluid is less than 1.0, it means that the fluid is lighter than water. If the fluid is also not miscible with water, it will float or settle on top of the water creating a defined interface.
Viscosity The term viscosity refers to a proportionality constant in the equation relating cross-sectional velocity variations (or rate of fluid deformation) to shear stresses developed in the fluid flow. (See the subsection of this chapter titled “Fluid Flow Energy Loss Equations” to see how viscosity is used.) Viscosity can be considered a measure of a fluid’s resistance to deformation or shear or, alternatively, its readiness to flow when acted upon by an external force. In engineering analyses it is useful to think of viscosity as a momentum diffusivity term. Viscosity is commonly expressed in one of two forms: absolute (or dynamic) viscosity (μ), which is the proportionality constant referred to above, or kinematic viscosity (ν), which is related to the absolute viscosity divided by the density (ρ) as follows: v¼
μ ρ
Note that the kinematic viscosity is expressed with the Greek letter “nu”, which looks like a
“v”, but is not a “vee”. This means that the kinematic viscosity often gets mixed up with the velocity. Engineers must understand and distinguish the meanings of the variables in the equations that they use. For this reason, some engineers use the Greek letter kappa (κ) for kinematic viscosity. A wide variety of units is used to express absolute (or dynamic) viscosity, depending not only on U.S. customary or SI formulations but also on older English and metric conventions as well as on the type of instrument used to measure this fluid property. In S.I. units, absolute (or dynamic) viscosity is measured in kilograms per meter-seconds (kg/(m-sec)). In customary English units, absolute or dynamic viscosity is measured in pounds per foot-seconds (lb/(ft-sec)). A unit based on the c.g.s. (centimeter, gram, second) convention of the old metric system has gained wide favor in the representation of absolute (or dynamic) viscosity. This unit, called the poise, has dimensions of dyne · seconds per square centimeter or grams per centimeter · second. The centipoise, which equals 0.01 P, is the form of preference for many engineers because the viscosity of water at 20 C (68 F) is very close to one centipoise. One centipoises is equal to 6.72 104 lb/(ft-sec). For kinematic viscosity, there is also a wide variety of units used. In the S.I. system, the units of kinematic viscosity are square meters per second (m2/s) and in the customary English system the units are square feet per second (ft2/s). Another unit has also gained favor in the engineering community called the centistoke (named after George Gabriel Stokes, a late nineteenth century English mathematician and physicist). One centistoke is equal to 0.000001 m2/s or 0.0000107639 ft2/s.
Fluid Pressure Pressure is a force per unit area that arises when a fluid is subjected to a compressive stress. Units may be newtons/m2, lb/ft2, lb/in.2, or any similar equivalent of force over area. Pascal’s law states that the pressure in a fluid at rest is the same in all directions, a condition different from that for a
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The term (z2–z1) may be called a static pressure head, which can be expressed in units of length such as feet, inches, or meters of water. A simplified form of Equation 41.3 is often written
z (ρ + dρ) dx dy
ρ ¼ γh dz
ρg (dx dy dz ) x dy dx y
p (dy dx )
Fig. 41.1 Notation for basic eq. of fluid statics
stressed solid where the stress on a plane depends upon the orientation of that plane. For an infinitesimal fluid element in a larger static body of fluid, a free body diagram of the vertical forces can be drawn as shown in Fig. 41.1. The pressure difference ½ð p þ d pÞ p is due only to the weight of the fluid element. Since the weight of the element is given by mg ¼ ρg dz dA, a summing of forces in the vertical direction gives: d p dA ¼ ρg dz dA d p ¼ ρgdz
ð41:1aÞ ð41:1bÞ
In integral form, Equation 41.1b becomes ð2 ð2 dp ¼ dz ¼ ðz2 z1 Þ ð41:2Þ 1 ρg 1 where the path endpoints 1 and 2 refer to different elevation levels. To integrate Equation 41.2, it is necessary to establish a functional relation between the pressure p and the product of the density times the gravitational constant (ρg). Where density varies with pressure, the fluid is considered compressible, and the functional relation may be complex. For fluids that may be considered incompressible, such as water, ρ is a constant at any specified temperature. Equation 41.2 then becomes p2 p1 ¼ ρgðz2 z1 Þ
ð41:3Þ
ð41:4Þ
where h is height (elevation) of the column of liquid above a reference surface (i.e., (z2–z1). For water at 60 F (15.6 C), γ is taken to equal 62.4 lb/ft3 (16.02 kg/m3). The pressure corresponding to a head of h feet, then, is 0.433 h lb/in.2 (psi), or approximately 3 kPa per meter elevation. The head corresponding to a pressure of 1 psi (0.07 bar) is, inversely, 2.3 ft (0.7 m). Note that Equation 41.4 is valid only for a homogeneous, noncompressible fluid at rest, and that regardless of the shape of the container, points in the same horizontal plane experience the same pressure. The vertical distance h is termed the head of a fluid. A pressure due only to the weight of a column of fluid is called a static pressure and can be measured by a standard Bourdon-type gauge (see Fig. 41.4). Such a measure is generally referred to as gauge pressure. The term absolute pressure takes into account the pressure exerted by the atmosphere as well, which at sea level is approximately 14.7 psi (1 bar), equivalent to a 33.9 ft (10.3 m) column of water. A pressure less than atmospheric is called a vacuum pressure, a perfect vacuum being zero absolute pressure. Since most fluid properties of interest are not significantly affected by small changes in atmospheric pressure, most fluids calculations are in terms of gauge pressure, although this fact is not often indicated in standard calculation nomenclature. When they are explicitly identified, gauge pressure is denoted by the term psig and absolute pressure by psia. If not stated otherwise, psi may be taken to designate gauge pressure.
Pressure Measuring Devices Manometer Tube Pressure measurement in a manometer tube is obtained by measuring the vertical displacement of a relatively heavy fluid (usually mercury),
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1381
p h=— γ X Y B
C A Z
A
A⬘
Fig. 41.3 Piezometer Elliptical cross section
which will rise a smaller vertical distance than water in proportion to the ratio of its specific weight to that of water. Depending on the actual arrangement of the manometer tubing, a gauge equation can be written to solve for the pressure head. For the manometer shown in Fig. 41.2, the gauge equation is written by proceeding from the open end through the tube to point A0 , adding terms when descending a column and subtracting when ascending. Using mercury as the manometer fluid, we can write ð y þ zÞγHg zγHg xγ þ ðx þ zÞγ ¼ pA ð41:5Þ
Combining terms, generalizing the result, and expressing in terms of feet of water (head), PA ¼ ys þ z γ
Spring
Hairspring
Fig. 41.2 Manometer
ð41:6Þ
where s is the specific gravity of the manometer fluid.
Sector
Pinion
Adjustable link
30
20 10
0
Movement plate
Dial
Stem
Fig. 41.4 Standard Bourdon gauge
from a container enclosing a fluid under pressure (Fig. 41.3). Through the relation among pressure, height, and specific weight, the height to which the fluid rises in the tube represents the pressure of the contained fluid. While useful for some laboratory work, piezometer tubes are not generally feasible in practical applications.
Bourdon Gauge Piezometer Tube Literally a pressure measuring tube, a piezometer consists essentially of a narrow tube rising
The standard pressure measuring device used in a wide variety of fluid pressure measurement applications is the Bourdon gauge (Fig. 41.4).
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The gauge contains a curved tube of elliptical cross section that undergoes a change in curvature with change in pressure. A dial hand, connected to the inner tube through a linkage system, indicates gauge pressure on a numerical dial face. Bourdon gauges are factory calibrated and reasonably accurate instruments if not damaged by pressure surge or impact force. A field reading, unless known to be correct, cannot be assumed to be accurate and should be checked by independent means.
Fluid Dynamics While the study of fluids in a static condition (at rest) yields some interesting information, it is the study of fluids in motion that is the most relevant to the fire protection engineer. Water, the most common fluid for fire protection needs to be available at the location of the fire, and therefore, needs to be moved from its source of supply though a series of conduits, typically pipes and hoses. The study of fluids in motion is called Fluid Dynamics.
Forces on Submerged Plane Areas due to Fluid Pressure Conservation Laws in Fluid Flows It is sometimes of interest to determine the magnitude of the resultant force on a submerged area and the location of the center of pressure where the resultant force can be assumed to act. Consider the following example of a tank that has a plate in a vertical wall (Fig. 41.5). The magnitude of the resultant force can be determined from FR ¼ γhc A
Fig. 41.5 Tank with a plate in a vertical wall
ð41:7Þ
Fluid flow may be characterized as uniform or nonuniform, steady or unsteady, compressible or incompressible, laminar or turbulent, rotational or irrotational, and one-, two-, or threedimensional or some combination thereof. Real flows may be modeled as approximations of ideal flows when real properties do not depart significantly from the ideal characteristics defined by these terms. For example, uniform flow occurs when the average velocity of a fluid does not change in either magnitude or direction anywhere along the flow path. Thus, liquid flow in a constant head pipeline of unchanging diameter is considered uniform flow. Steady flow, on the other hand, is determined with reference to a stationary point in the flow path. For steady flow to occur, the velocity of flow at that point must remain constant with time. This condition implies that the fluid density, the pressure head, and the volume rate of flow also are invariant with time. Thus, liquid flow in a constant head pipeline of varying diameter may be considered steady, nonuniform flow. It is important to note that a flow may be considered uniform (no change in magnitude or direction of the velocity) in a curved pipeline as long as the reference direction of the velocity vector is taken in the direction of the flow. We can then say that the velocity of the fluid does not change direction with respect to its enclosing boundaries.
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We can also consider this flow one-dimensional whenever it is permissible to say that velocities or accelerations normal to the general direction of the flow are negligible. Clearly, real flow in a real-world structure has three dimensions, but a one-dimensional analysis is highly desirable as it represents a considerable mathematical simplification. Fortunately, a very large number of practical engineering flow problems involving water can be modeled as one-dimensional, steady flow problems, particularly many pipeline flows. In such cases it is possible to apply basic physical principles of conservation of mass and conservation of energy in the direction of flow to obtain the energy balance at any point in the flow. In fire flow hydraulics, it is common practice to introduce additional simplifying assumptions, such as the requirements that the fluid be incompressible and that flow properties be invariant with temperature and pressure. It then follows directly that with no flow additions or subtractions, the volumetric flow rate at any point in a fluid stream must be a constant. This statement of mass conservation, known as the equation of continuity, can be expressed mathematically as ρ1 A1 v1 ¼ ρ2 A2 v2 ¼ Constant
ð41:9Þ
If the fluid is considered incompressible, as is the case with water, the density will not change with respect to the fluid at different locations in the flow, so Equation 41.9 becomes A1 v1 ¼ A2 v2 ¼ Constant ¼ Q
ð41:9aÞ
By applying the principal of conservation of energy to a flowing fluid, an expression can be derived that gives the theoretical net energy balance of the fluid at any point along its flow path. This is known as the Bernoulli equation, which can be written as: p1 v21 p v2 þ þ z1 ¼ 2 þ 2 þ z2 γ 2g γ 2g
ð41:10Þ
In Equation 41.10, p1, v1, and z1 represent the pressure, velocity, and elevation (above a given data plane) of the fluid at one location in the flow stream while p2, v2, and z2 represent the pressure,
velocity, and elevation of the same fluid at a second point in the same flow stream. In this form, units are feet (or meters) of fluid. Each term thus represents a fluid head with the addition of the three terms representing the total head (or energy) of the fluid at any point. Multiplying each term by the specific weight, γ, converts the equation to units of pressure. Changes in internal energy of the fluid are ignored and are assumed to be negligible. The form of Equation 41.10 suggests that the flow of liquid (or transport of fluid energy) results from three principal causes: pressure difference, gravity, and inertia. Equation 41.10 expresses an ideal condition fulfilled by the three components of head corresponding to these three causes. The assumption of incompressibility (i.e., constant density) requires that the product of the velocity of flow and the cross-sectional area of the flow of any conserved portion of the stream be constant; the ideal flow streamlines, therefore, converge as the velocity increases and diverge as the velocity decreases. If it could be assumed that the total Bernoulli head were, indeed, constant or, equivalently, if it were possible to obtain total head simply as a function of the coordinates of the moving fluid element, then many hydrokinetic problems could be solved theoretically by mathematically manipulating and extrapolating the Bernoulli equation. Unfortunately, this is not the case. Other energy transfers are possible, and these require use of a more general form of the equation. In addition to the pressure, velocity, and position (elevation) energies possessed by the fluid at sections 1 and 2, energy may be added to the fluid (work done on the fluid by a pump), lost by the fluid (through friction), or extracted from the fluid (work done by the fluid). Therefore, we write the Bernoulli energy conservation expression in the more general form: p1 v21 þ þ z 1 þ hA hL hE γ 2g ð41:10aÞ p2 v22 þ þ z2 ¼ γ 2g In Equation 41.10a, the value of hA represents the energy being added to the fluid, hL represents the
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energy lost from the fluid due to friction loss, and hE represents the energy taken from the fluid. An example of how the Bernoulli equation can be used to solve a simple water flow problem follows as Example 1. Example 1 Water flows from a reservoir through a pipeline as shown in the following diagram. The flow is considered frictionless and discharges freely at point C. A
hC ¼ 0 þ
v2 þ0 2g
Since the total energy at one point in the flow is equal to the total energy at another point, we know that hC is also equal to hA and hB, which are 150 ft. Using this knowledge, we can solve the equation for “v” as follows: v2 2g v2 ¼ ð150Þ2g ¼ ð150Þ2ð32:2Þ ¼ 9, 660 150 ¼
v ¼ 98:3 150⬘ (45.7 m)
or, in SI unit equivalents,
B C
(a) What is the total head (total specific energy) at point A? (b) What is the total head (total specific energy) at point B? (c) What is the discharge velocity at point C? Solution (a) At A, both the velocity and gauge pressures are considered to be zero. Assuming that the plane at the middle of the discharge outlet at C is the reference data place, by Bernoulli, then, the total head would be written as: hA ¼ 0 þ 0 þ 150 ft ¼ 150 ft or, in SI unit equivalents, hA ¼ 0 þ 0 þ 45:7 m ¼ 45:7 m (b) At B, the fluid has a nonzero velocity head and is under hydrostatic pressure. As long as we consider the flow frictionless, the total head is constant. Therefore, hB ¼ hA ¼ 150 ft ð45:7 mÞ (c) At C, the pressure head is again zero, since the discharge is at atmospheric pressure and the discharge of the water is at the reference data elevation, so it is also zero. Once more by Bernoulli,
v2 ¼ 2ð9:81Þ ð45:7Þ v ¼ 29:9 m=s Note that we could calculate the actual values of the pressure and velocity heads at point B if we had more information about the system. For example, we could determine the flow at the discharge point (C), if we knew the area and type of discharge opening (see section “Free Discharge at an Opening”). This determination is simply an application of the continuity equation. Knowing the pipeline diameter at point B allows us to apply continuity constraints once again to calculate vB from which the velocity head may be determined. The pressure head at B is simply a function of the weight of the vertical column of water. The components of the Bernoulli equation may be expressed graphically in terms of energy levels existing at any points in the flow regime. In Fig. 41.6 a simple system representing a realistic flow is shown. Water flows from a reservoir (with presumed constant surface elevation) to atmosphere. The flow is accompanied by losses of energy represented by hL. The losses may occur in many places such as at valves, bends, and sudden changes in pipe diameter. Generally, the most important loss is that due to friction between the moving fluid and the pipe wall. Since there are always energy losses in real flows, the total energy of the system decreases in the direction of flow. Graphically, the linear curve in Fig. 41.6 connecting all points
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1385 Head loss due to entrance conditions Head loss due to sudden expansion
2
V4 –— 2g
2
V3 –— 2g
Head loss due to sudden contraction
p —3 γ
Energ y gradie nt
p —4 γ
Z1
Σ(ΔhL )
HT 2
Hydra uli gradie c nt
V5 –— 2g
2
p —5 γ
Z3
V6 –— 2g
Z4 Z6
Z5
Fig. 41.6 Realistic flow characteristics
represents the total energy in the piping system and is referred to as the energy gradient (EG). It must always decrease in the direction of flow unless energy is added to the system such as by a pump. The hydraulic gradient (HG) connects the points representing the sum of static pressure and elevation energies (i.e., the heights to which water in piezometer tubes would rise in a flow path). Note that the hydraulic gradient may increase in the direction of flow if velocity head is converted to pressure head at a given point in the system (such as at an increase in pipe diameter). Thus, the relationship between the energy and hydraulic gradients can be written as EG ¼ HG þ
v2 2g
ð41:11Þ
General Considerations for Fluid Energy Losses in Pipe Flows Energy losses in fluids due to friction in piping are of key importance in fire protection engineering. Losses due to friction are due to shear stresses set up within a moving fluid in a conduit by an imposed pressure gradient. Flow driven by the pressure force is restrained by drag forces acting at the conduit wall. To better visualize
this phenomenon, it is useful to introduce the concept of the boundary layer. For many fluids, such as air or water, motion through a stationary conduit or pipe is characterized in most practical situations by a nearly constant velocity cross section everywhere except in a very thin layer near the wall of the pipe. This layer may be as little as 0.1 mm thick, but may vary significantly with the nature of the fluid, the velocity of flow, and the surface roughness of the conduit. We may visualize boundary layer flow in terms of a velocity profile (Fig. 41.7). Theories developed primarily by Prandtl [2, 3] hold that a very thin (molecular) layer of fluid sticks to the conduit wall. The tendency of the next fluid layer to move due to an imposed force creates a shearing stress, τ, between the layers. If the boundary is thought of as many thin fluid plates (lamina) sliding on each other, then we can expect the velocities of these lamina to increase with distance y from the wall until, at the edge of the boundary layer, the local velocity reaches the freestream velocity of the fluid. The factor relating the velocity profile to the developed stress in the fluid is termed the fluid viscosity. The relationship was expressed mathematically by Newton as τ¼μ
du dy
ð41:12Þ
1386
K.E. Isman
a
y
Parabolic curve
u (y ) Velocity profile
umax v
du dy du τ = μ −−− dy
b v
0
umax
No slip at wall
Fig. 41.7 Velocity profile
The smaller the value of fluid viscosity, the thinner the boundary layer will be. The first layer of fluid sticks or adheres to the surface of the conduit while lamina above it successively slide on each other, exerting drag forces that, for most fluids, are proportional to the viscosity (so-called Newtonian fluids). The rate of change of the velocity between successive lamina is a measure of the unit shearing force between them. A curve joining the tips of velocity vectors plotted for the different lamina in the boundary layer is called a velocity profile. Laminar (smooth, streamline) flow (Fig. 41.8a) is characterized by a parabolic velocity profile with maximum velocity attained at the theoretical centerline of the flow. Turbulent flow, by contrast, is rough (nonstreamline) flow (Fig. 41.8b), characterized by an essentially uniform average velocity across the flow section, with only a very thin boundary layer close to the wall where viscous forces predominate. The velocities associated with laminar flows are generally so low that they are not representative of typical velocities in fire protection systems. Most flows of interest are turbulent, and the use of an approximated uniform or average velocity in calculating kinetic energy and velocity pressures does not introduce notable errors. In those situations where relatively large velocity heads are involved (such as where a pump adds a large amount of energy), a correction factor may be used to relate the actual average kinetic energy to
Fig. 41.8 Laminar (a) and turbulent (b) pipe flow velocity profiles for the same volume
the kinetic energy calculated using average velocity. From continuity considerations, ð ð 3 KE ¼ ρu dA ¼ αρ v3 dA ð41:13Þ A
A
where KE ¼ True kinetic energy of the flow v ¼ Average velocity of flow α ¼ Kinetic energy correction factor For incompressible fluids, α can be represented by the following: ð 1 u3 α¼ dA ð41:14Þ A A v The value of α is approximately 1.1 for most turbulent flow problems. However, since the velocity head in most water distribution fire protection piping systems is relatively small, this correction factor is usually ignored. While the development of boundary layer theory and the theory of viscous forces has led to an improved theoretical understanding of the mechanics of pipe flows, most flows of interest in fire protection cannot be fully analyzed from theoretical considerations alone. Fire protection flows are almost always turbulent flows. Despite a great expenditure of effort to develop a general predictive theory of turbulent flow phenomena, a fully descriptive theory does not yet exist.
41
Hydraulics
1387
While it is postulated that head losses arise because of friction between the fluid and the pipe wall, there is an additional head loss contribution due to turbulence within the flowing fluid. In turbulent flows the rate of head loss, unfortunately, is not simply a function of fluid velocity but depends also on pipe wall roughness. The determination of head loss is further complicated by the changing interaction among these variables at different flow velocities, interior pipe surface roughness and actual pipe sizes. Within the last century, however, a large body of empirical flow data has been collected, analyzed, and reproduced by several investigators. The major features and limits of applicability of the more important results are presented in the following paragraphs.
Fluid Flow Energy Loss Equations Chezy Equation Theoretical development of the physical relationships describing pipe flows dates from about the middle of the nineteenth century, when Chezy postulated a fundamental proportionality between volumetric flow and pipe size based on the continuity equation. His formula is commonly given as πD2 πD2 Cpffiffiffiffiffiffi Q¼ DS v¼ 4 4 2 and may also be written as 2 8Q S¼ D5 πC
ð41:15Þ
ð41:16Þ
where D and S are pipe diameter and slope of the energy gradient, respectively. The factor, C, is a proportionality factor incorporating a significant degree of physical uncertainty. Since, by definition hL S¼ L the equation can be rewritten as an expression for pipe flow head loss as a function of pipe diameter and discharge as follows:
hL ¼
8 2L 2 Q πC D5
ð41:17Þ
Use of the Chezy equation was limited by uncertainties relating to evaluations of the Cfactor, which is not, in fact, a constant for a given size conduit or wall condition as was originally thought.
Darcy-Weisbach Friction Loss A theoretically more satisfying approach was taken by Darcy, Weisbach, and others. Their formula, which bears the names of the two primary investigators, is generally written as: hL ¼ f
L v2 D 2g
ð41:18Þ
It postulates a basic proportionality between head loss and the kinetic energy of the flow, as well as to pipe length and diameter. The proportionality factor f, known as the friction factor, became the subject of extensive theoretical and experimental investigation. The value of f for laminar flow can be shown theoretically to be a simple linear function of the Reynolds number, Re, where: Re ¼
De vρ μ
The term De is the equivalent flow diameter, which is the actual inside diameter of a circular pipe. The equivalent diameter, De, can be found from the hydraulic radius, rh, which is defined as the area in flow divided by the wetted perimeter. The wetted perimeter does not include the free fluid surface. De ¼ 4r h For Re less than about 2000 (corresponding to low velocity flows or fluids of high viscosity) the relation is f ¼
64 Re
ð41:19Þ
In turbulent flows (higher Reynolds numbers) the roughness of the pipe walls becomes a much more significant factor, and a simple expression to determine f is unavailable.
1388
K.E. Isman
roughness values that correspond to new pipe should not be used. To be consistent with fire protection standards, values for aged pipe should be used. Also shown in Table 41.1 are a number of recommended roughness values that should be considered for aged pipe in fire protection system calculations. Moody plotted various solutions for the friction factor (f) using different Reynolds numbers and relative roughness of pipes on a graph. The resulting Moody diagram (Fig. 41.10) is widely used today in conjunction with the DarcyWeisbach equation to compute friction losses for water flowing in pipe. Figure 41.11 presents relative roughness values for use with the Moody diagram over a wide range of conditions. Other diagrams have been developed for use with the Darcy-Weisbach equation [6, 7] when parameters other than hL are sought. Essentially, the alternative graphical formulations employ a rearrangement of variables to facilitate solving for some other unknown variables such as Q or D. Both experimental and theoretical investigations have yielded uncertain results in
A systematic investigation of the actual characteristics of piping inner wall surfaces was first performed by Nikuradse in 1933. To simulate varying degrees of roughness in commercial pipes due to corrosion or surface finish, Nikuradse glued sand grains of known sizes to the inside walls of test pipes. The resulting logarithmic plot of friction factor versus Re is shown in Fig. 41.9. Although the tests are from Nikuradse, the plot is called Stanton’s diagram in recognition of his earlier (1914) elucidation of the relation between friction factor and Reynolds number. Note that at sufficiently high Re, the friction factor depends almost entirely on pipe roughness and is essentially independent of Re. In these plots the roughness parameter is expressed as the ratio of the root mean square grain diameter to the pipe diameter. The resulting ratio is termed the relative roughness and is represented mathematically as ε/D. Typical values for the roughness (ε) of new commercial pipes are shown in Table 41.1. However, fire protection engineers are expected to build safety factors into their calculations, so the use of pipe
0.10 0.09 0.08 0.07
D = 4.82 cm
D = 2.412 cm
1 ∈ = ——– —– 30 D
0.06 D = 4.87 cm
0.05
D = 9.64 cm
1 ∈ —– = ——– D 61.2
D = 2.434 cm
0.04 hL f = ——— L v2 —— D 2g 0.03
D = 9.8 cm
1 ∈ = ——– —– 120 D
D = 9.92 cm
1 ∈ —– = ——– D 252 1 ∈ = ——– —– 504 D
D = 2.434 cm D = 2.474 cm D = 9.94 cm
0.02
1 ∈ —– = ——– D 1014
D = 4.94 cm D = 9.94 cm
0.01
103
104
105 vDρ R = —— μ
Fig. 41.9 Nikuradse’s sand-roughened-pipe tests
106
41
Hydraulics
1389
Table 41.1 Values of absolute roughness of commercial pipes Type of pipe or tubing New clean pipe [4] Asphalted cast iron Brass and copper Concrete Cast iron Galvanized iron Wrought iron Steel Riveted steel Wood stave Aged pipe [5] Steel, dry system Steel, wet system Plastic Copper
ε in ft 106 Range
Design
Probable maximum variation of f from design (%)
400 5 1000–10,000 850 500 150 150 3000–30,000 600–3000
400 5 4000 850 500 150 150 6000 2000
5 to +5 5 to +5 35 to +50 10 to +15 0 to +10 5 to +10 5 to +10 25 to +75 35 to +20
1250 333 7 7
Notes: For ε values in meters, multiply the above numbers by 0.3048 For ε values in inches, multiply the above numbers by 12
64 Laminar flow f = — R 0.1 0.09
Laminar flow
Critical zone
Transition zone
0.08
Complete turbulence, rough pipes 0.05 0.04
0.07 0.06
0.03 0.02
0.01 0.008 0.006
Rcr 0.03
∈
0.015 0.04
0.004 0.025
0.002
0.02
0.015
0.01 0.009 0.008
Riveted steel Concrete Wood stove Cast iron Galvanized iron Asphalted cast iron Commercial steel or wrought iron Drawn tubing
∈ (ft)
0.001 0.0008 0.0006 0.0004
∈ (mm)
0.003–0.03 0.001–0.01 0.0006–0.03 0.00085 0.0005 0.0004
0.9–9.0 0.3–3.0 0.18–0.9 0.25 0.15 0.12
0.00015 0.000005
0.046 0.0015
Relative roughness — D
hL Friction factor f = ————— (Lv 2/D2g)
0.05
0.0002 0.0001 Smooth pipes
0.000,001 0.000,005
0.000,05
0.000,01 7 9 103 2(103) 3 4 5 6 7 9 104 2(104) 3 4 5 6 7 9 105 2(105) 3 4 5 6 7 9106 2(106) 3 4 5 67 9 107 2(107) 3 4 5 67 9 108 vD Reynolds number R = —– v
Fig. 41.10 Moody diagram
the region known as the critical zone, wherein the flow changes from laminar to turbulent. Uncertainty may be expected since the transition point is difficult to define precisely and, in
fact, varies over a considerable range of Re depending upon the direction of the transition (i.e., flow going from laminar to turbulent or from turbulent to laminar) and the local
1390
K.E. Isman
25
Pipe diameter D (mm) 200 500 1000 1250
100
50
2500
5000
.05 .04
.07 .06
.03
.05
.02 Riveted steel
.04
e =
.01 .008
0.
Concrete
03
.035
= ft 9
=
Wood stave
m m
e
.006 .005
01 0.
.03
ft
.004
= 3 m
=
m
e
.003
= ft
ph
ca
26 0.
d
=
te
ft
al
.018
st n
e
m
m m m m 3 15 0. 0. = = ft ft 1 m 05 00 m 00 0. 5 0. = 04 = e 0. e = m n ft m iro 15 d .12 00 m ize 0 = n 0. m = va ft 4 e al n G 000 iro 0. ht =
iro
.016
er al
ci ee
st
.014
ug
ro
rw
lo
.0002
ƒ for wholly rough pipes
m
5 08 00 0. m m
18
As om
.0003
.02
=
0.
∈
m
e
= C
Relative roughness — D
9
n
ft
.0008
0.
ro
06
ti
00
as
0.
C
=
.001
.0006 .0005 .0004
.025
3 00 0.
e
.002
.0001 .000,08
n w ra D
.000,06 .000,05 .000,04
tu bi ng
.000,03
.012
.01
e = 0.
.009
5 00 0, 00
.000,02
ft =
15 00 0.
.008 m
m
.000,01 .000,008 .000,006 .000,005
1
2
3
4 5 6
8 10
20
30 40 50 60 80 100
200
300
Pipe diameter D (inches)
Fig. 41.11 Relative roughness chart
conditions affecting flow stability. As a practical consideration, however, this uncertainty is of little importance in fire protection, since most real flows of interest fall well into the turbulent range.
Colebrook developed an empirical transition function for the region between smooth flow and complete turbulence. Flow in this region is sometimes referred to as hydraulically smooth or turbulent smooth. The equation has been presented
41
Hydraulics
1391
in various forms, the following expression being commonly used: 1 ε=D 2:51 pffiffiffi ¼ 0:86 ln þ pffiffiffi 3:7 Re f f
ð41:20Þ
An alternate and equivalent expression is 2 ε 9:35 þ pffiffiffi f ¼ 1:14 2 log ð41:20aÞ D Re f This relation forms the primary basis for the Moody diagram. VonKarman used boundary layer theory to derive an expression characterizing the friction factor for fully turbulent flow within roughwalled pipes. The final numerical form of the equation 1 D pffiffiffi ¼ 1:4 þ 2 log ε f
ð41:21Þ
was adjusted to agree more closely with Nikuradse’s experimental results. As pipe roughness decreases, this expression approaches Colebrook’s equation. The Darcy-Weisbach equation and the Reynolds number calculation both force the engineer to utilize variables in unusual units. Typically, engineers deal with flow in gallons per minutes instead of cubic feet per minute or velocity in feet per second. Similarly, the diameter of the pipe is typically in inches and not in feet. The formulas for the Darcy-Weisbach equation and the Reynolds number can be rewritten in terms of variables that are much more commonly used (ΔP is friction loss in psi, Q is flow in gpm, d is the internal diameter of the pipe in inches, and μ is the viscosity in centipoises) as follows: lρQ2 ΔP ¼ 0:000216 f 5 d
50:6Qρ Re ¼ dμ
Hazen-Williams Friction Loss While the Darcy-Weisbach method of friction loss calculation yields sufficiently accurate results for a broad range of flow conditions, it can be difficult to use because of the associated variables that need to be determined. The density
and viscosity of a fluid are not always known at every temperature at which the fluids are going to be used. In addition, since the friction factor cannot be solved for directly, it needs to be obtained from the Moody diagram, which introduces some potential error into the use of the technique because the engineer can arrive at some widely different friction factors based on very small changes in how the curves on the Moody diagram are interpreted. A much more straight forward calculation technique was developed by Hazen and Williams (two civil engineers affiliated with the University of Michigan) around the turn of the nineteenth to the twentieth Century. Due to its simplicity, this technique has become one of the most widely used flow-energy loss relations. The empirically based Hazen-Williams formula was developed from observations of a very large number of pipeline flows. The Hazen-Williams equation was originally written in the form V ¼ 0:113CD0:63 S0:54
ð41:22Þ
where V is the average velocity in feet per second, S is the slope of the energy gradient—that is, the loss of energy per unit length of the pipe— and D is the actual internal pipe diameter in inches. The coefficient C is a friction factor introduced as a constant to represent the roughness of the pipe walls. Table 41.2 presents a representative list of C coefficients for various piping materials. Note that the value of C can vary significantly with the piping material, the age of the pipe, and the corrosive qualities of the water. The Hazen-Williams formula is also encountered in the form Q ¼ 0:285CD2:63 S0:54
ð41:22aÞ
where Q is volumetric flow rate in gpm and D is in inches. Yet another form, also in the same units for Q and D, is widely used in automatic sprinkler system design. It is arranged to solve for the pressure drop in psi per linear foot of pipe: p¼
4:52Q1:85 C1:85 D4:87
ð41:22bÞ
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K.E. Isman
Table 41.2 Values of C in Hazen-Williams formulaa C values for certain pipe diameters 2.5 cm 7.6 cm 15.2 cm 30.5 cm (1 in.) (3 in.) (6 in.) (12 in.) — 121 125 130 — 129 133 138
61 cm 122 cm Type of pipe (24 in.) (48 in.) Uncoated cast iron—smooth and new 132 134 Coated cast iron—smooth and new 140 141 30 years old Trend 1—slight attack — 100 106 112 117 120 Trend 2—moderate attack — 83 90 97 102 107 Trend 3—appreciable attack — 59 70 78 83 89 Trend 4—severe attack — 41 50 58 66 73 60 years old Trend 1—slight attack — 90 97 102 107 112 Trend 2—moderate attack — 69 79 85 92 96 Trend 3—appreciable attack — 49 58 66 72 78 Trend 4—severe attack — 30 39 48 56 62 100 years old Trend 1—slight attack — 81 89 95 100 104 Trend 2—moderate attack — 61 70 78 83 89 Trend 3—appreciable attack — 40 49 57 64 71 Trend 4—severe attack — 21 30 39 46 51 Miscellaneous Newly scraped mains — 109 116 121 125 127 Newly brushed mains — 97 104 108 112 115 Coated spun iron—smooth and new — 137 142 145 148 148 Old—take as coated cast iron of same age Galvanized iron—smooth and new 120 129 133 — — — Wrought iron—smooth and new 129 137 142 — — — Coated steel—smooth and new 129 137 142 145 148 148 Uncoated steel—smooth and new 134 142 145 147 150 150 Coated asbestos-cement—clean — 142 149 150 152 Uncoated asbestos-cement—clean — 142 145 147 150 Spun cement-lined and spun bitumen-lined—clean — 147 149 150 152 153 Smooth pipe (including lead, brass, copper, 140 147 149 150 152 153 polythene, and smooth PVC)—clean PVC wavy—clean 134 142 145 147 150 150 Concrete—Scobey Class 1—Cs ¼ 0.27; clean — 69 79 84 90 95 Class 2—Cs ¼ 0.31; clean — 95 102 106 110 113 Class 3—Cs ¼ 0.345; clean — 109 116 121 125 127 Class 4—Cs ¼ 0.37; clean — 121 125 130 132 134 Best—Cs ¼ 040; clean — 129 133 138 140 141 Tate relined pipes—clean — 109 116 121 125 127 Prestressed concrete pipes—clean — — — 147 150 150 a The above table has been compiled from an examination of 372 records. It is emphasized that the Hazen-Williams formula is not suitable for the coefficient C values appreciably below 100, but the values in the above table are approximately correct at a velocity of 0.9 m/s (3 ft/s) For other velocities the following approximate corrections should be applied to the values of C in the table above [8] Values of C at 0.9 m/s
Velocities below 0.9 m/s for each halving Rehalving of velocity relative to 0.9 m/s
Velocities above 0.9 m/s for each doubling Redoubling of velocity relative to 0.9 m/s (continued)
41
Hydraulics
1393
Table 41.2 (continued) Values of C at 0.9 m/s C below 100 C from 100 to 130 C from 130 to 140 C above 140
Velocities below 0.9 m/s for each halving Rehalving of velocity relative to 0.9 m/s Add 5 % to C Add 3 % to C Add 1 % to C Subtract 1 % from C
In SI units, p¼
6:05Q1:85 105 C1:85 D4:87
ð41:22cÞ
where the units of Q are L/min, D is in mm, and p is in bars per meter of pipe. Many manufacturers of fire protection equipment, many fire underwriters, and others have published Hazen-Williams-based pipe friction loss data (usually in tabular format) over applicable ranges of pipe sizes, flow rates, and C-factors. A useful calculation aid in a more compact format is the Hazen-Williams nomograph (Fig. 41.12), which is reproduced here in its generalized form. The Hazen-Williams formula is most appropriate for water flow at or around 60 F (15.6 C), as it does not contain any factors relating to the physical properties of the fluid. The formula gives acceptable results in practice with a judicious choice of the C-factor. Fundamentally, the C-factor is a proportionality constant and, as such, its true value depends as much upon the values chosen for the associated exponent in the accompanying formula as it does upon actual pipe roughness. The suggested values are the result of curve-fitting exercises and cannot be expected to accurately and evenly represent flow parameter relationships across the full range of observed flow velocities. Allowing fpr the desirability of retaining constant exponent values for D and S (i.e., a presumed theoretically stable correlation among all flow parameters in the equation), the value of C for any given flow scenario becomes a narrowly bounded variable that reflects the pipe roughness. Although, as in the Chezy formula, C is not actually a constant,
Velocities above 0.9 m/s for each doubling Redoubling of velocity relative to 0.9 m/s Subtract 5 % from C Subtract 3 % from C Subtract 1 % from C Add 1 % to C
for practical use it is assigned a constant value for a given presumed roughness. Unfortunately, as Table 41.2 shows, the Hazen-Williams equation is a much better model of smooth pipe flow than of rough pipe flow. As long as the flow velocity is close to that at which C was measured and as long as the pipe roughness is not excessive, the Hazen-Williams relation can be expected to give reliable results. It has been noted, however, that in rough pipes head loss varies with flow (and velocity) to the power of 2 rather than the power of 1.85 characteristic of smooth pipes [9]. This observation introduces a significant element of uncertainty into the hydraulic analysis of rough pipe with higher velocity flows. Example 2 Water at 50 F (10 C) flows through 4 in. (102 mm) Schedule 40 welded steel pipe at a rate of 500 gpm (1892.7 l/m). Compare the friction head losses calculated by the DarcyWeisbach and Hazen-Williams equations for flow through 100 ft of pipe. Solution Basic Data: For 50 F water, kinematic viscosity, ν ¼ 1:41 105 ft2 =s Pipe flow area ¼ 0.0884 ft2 ε ¼ 0.0002 (very close to new pipe) Pipe inside diameter ¼ 0.3355 ft ¼ 4.026 in. Using the Darcy approach, we first determine the Reynolds number (Re), and then we determine the relative roughness of the pipe as a ratio of the roughness to the diameter (ε/D). After obtaining these values, we enter the Moody diagram (Fig. 41.10) to get the friction factor (f). In order to get the Reynolds number, we need the velocity associated with the flow:
1394
K.E. Isman D
V
C
H 500 400
40,000 0.3
300
30,000
60 54 48
6,000 5,000
42
4,000
36 30
800
24 20 18 16 14 12 10 8
0.7
60 50 40
0.8
30
0.9 1
20
2
3
4
600 500 400 300
5 6 5
6
4 3
8 9 10
2½ 2 100
50 100 150 200
0.10
0.01
6 5 4 3 2
1 0.8
0.001
0.6 0.5 0.4 0.3 0.2
7 3½
200
10 8
20
1.5 Diameter of pipe, in inches, D
1,000
Flow, in gallons per minute, Q
3,000
0.6
Loss of head, in feet per 1,000 ft
72
8,000
100 80
Velocity, in feet per second, V
10,000
0.5
Hazen-Williams coefficient, C
Turning line
96 84
2,000
200
0.4
20,000
0.1 0.08
0.0001
0.06 0.05 0.04 0.03
15 1½
0.02
80 20 60 50
1 25
Fig. 41.12 Nomograph for solution of the Hazen-Williams formula
0.01 0.008 0.006 0.005
0.00001
Hydraulic slope
Q
41
Hydraulics
1395
Flow quantity ¼ Q ¼ 500 g pm 1:1140 cfs ð31:54 L=sÞ Q 1:1140 Velocity ¼ v ¼ ¼ A 0:0884 ¼ 12:60 fps ð3:8 m=sÞ Re ¼
Dv 0:3355ð12:60Þ ¼ ¼ 3:0 105 ν 1:41 105 ε 0:0002 ¼ ¼ 0:0006 D 0:3355
From the Moody friction chart, f ¼ 0.0188. From Equation 41.18, hL ¼
0:0188ð100Þ ð12:60Þ2 ¼ 13:8 ft 2ð0:3355Þ ð32:2Þ
¼ 5:98 psi ð0:41barÞ For the Hazen-Williams approach (Equation 41.22b) a C-factor for the pipe needs to be selected. Since the Darcy-Weisbach method used an ε value associated with new pipe, it would make sense to use a C-factor for new pipe in order to make an accurate comparison. As Table 41.2 shows, new steel pipe has C-factors between 134 and 150. If we assume C ¼ 140, Δp ¼
Minor Losses Flows through pipe fittings, valves, or other pipeline fixtures generate additional turbulence and, therefore, additional energy losses. These losses, although termed minor, can be rather significant fractions of the total energy loss. In particular, losses due to pipeline obstructions such as swing-type check valves and certain types of flow meters are equivalent to adding many feet (or meters) of piping to the system. Thus, in some instances minor losses may have to be considered major, particularly in systems where there are many fittings, valves, or other appurtenances. Empirical methods are used to determine these losses for a range of flow or obstruction geometries. One common method is to define a minor loss coefficient to express head loss as a function of velocity head. Thus,
4:52ð100Þ ð500Þ1:85 ð140Þ1:85 ð4:026Þ4:87
Δ p ¼ 5:40 psi ð0:37 barÞ The Hazen-Williams formula comes within 10 % of the value obtained using the DarcyWeisbach equation, with significantly less effort. This is considered to be within the range of acceptable values in an engineering exercise involving fire protection system piping. Note that the system design and installation standards such as NFPA 13 do not allow the use of C-factors for new pipe for this very reason. Using a C-factor of 100, to simulate the aged pipe associated with dry-pipe systems and solve directly for pressure drop in psi per 100 ft we would obtain: Δp ¼
Note that the friction loss with the aged pipe is nearly twice what would have been predicted with the use of the value for new pipe. Accuracy in using Hazen-Williams clearly depends on a careful choice of C-factor. The Darcy-Weisbach result does not seem to be so sensitive to choice of roughness.
4:52ð100Þ ð500Þ1:85 ð100Þ1:85 ð4:026Þ4:87
¼ 10:06 psi ð0:69 barÞ
hL ¼ k
v2 2g
ð41:23Þ
where k is a dimensionless loss coefficient. It is sometimes convenient to express such losses in terms of equivalent length of straight pipe, or as pipe diameters that produce the same head loss. Thus, by Darcy-Weisbach, L k ¼ D f
ð41:24Þ
Table 41.3 shows local loss coefficients for a number of fittings and flow patterns. Wherever possible, manufacturers’ data should be used, particularly for valves because of the wide variety of designs for the same generic valve type. Such data are often published in the form of flow coefficient or Cv values, which may be used in the equation
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K.E. Isman
Table 41.3 Local loss coefficients Use the equation hL = kv 2/2g unless otherwise indicated. Energy loss EL equals hv head loss in feet. 1
Perpendicular square entrance: k = 0.50 if edge is sharp
v
2
Perpendicular rounded entrance:
d
R
3
R/d =
0.50
0.1
0.2
0.3
0.4
k=
0.25
0.17
0.08
0.05
0.04
Perpendicular re-entrant entrance: k = 0.8
Additional loss due to skewed entrance: k = 0.505 + 0.303 sin α + 0.226 sin2 α
4 α
5
Suction pipe in sump with conical mouthpiece:
D Q
5.6Q v2 EL = D + ———–— – —– √2gD 1.5 2g
D
Without mouthpiece:
4D 0.75D
4Q v2 EL = 0.53 D + ———–— – —– √2gD 1.5 2g Width of sump shown: 3.5D
v
6
(After I. Vágás)
Strainer bucket: k = 10 with foot value k = 5.5 without foot value
(By Agroskin) 7
Standard tee, entrance to minor line: k = 1.8 v
8
Sudden expansion: v1
v2
9
(
)
(
)
Sudden contraction:
d D v1
2 v1 v 2 2 v 21 v 22 EL = 1 – –— —— or EL = –—2 – 1 —— v1 2g v 2g
v2
(d/D ) 2 = 0.01 k = 0.5
0.1
0.2
0.4
0.6
0.8
0.5
0.42
0.33
0.25
0.15
Diffusor:
10 v1
α
v2
EL = k (v 12 – v 22)/2g α ° = 20
40
60
80
k =
0.28
0.32
0.35
0.20
(continued)
41
Hydraulics
1397
Table 41.3 (continued) 11
Confusor: EL = k(v12 – v22)/2g α d
D v1
v2
α° = k for D = 3d D = 1.5d
12
6
10
20
40
60
80
100
120
140
0.12 0.12
0.16 0.16
0.39 0.39
0.80 0.96
1.0 1.22
1.06 1.16
1.04 1.10
1.04 1.06
1.04 1.04
Sharp elbow: k = 67.6 × 10–6(α°)2.17 α (By Gibson)
13
Bends: k = [0.13 + 1.85(r /R )3.5] α °/180°
r
α°
R
(By Hinds) 14
Close return bend: k = 2.2
15
Gate valve: e
e /D =
D
k =
0
1/4
3/8
1/2
5/8
3/4
7/8
0.15
0.26
0.81
2.06
5.52
17.0
97.8
16
Global value: k = 10 when fully open
17
Rotary valve:
α°
α° = 5
10
20
30
40
50
60
70
80
k =
0.29
1.56
5.47
17.3
52.6
206
485
¥
0.05
(By Agroskin) 18
Check valves: Swing type k = 2.5 when fully open Ball type k = 70.0 Lift type k = 12.0
19
Angle valve: k = 5.0 if fully open
20
Segment gate in rectangular conduit:
ϕ0
1 k = 0.3 + 1.3 — n
2
[( )]
v
ϕ
where n = ϕ/ϕ 0 = the rate of opening with respect to the central angle
21
(By Abelyev)
Sluice gate in rectangular conduit: H
h
2 1 k = 0.3 + 1.9 — n –n
[( ) ]
v
where n = h/H
Q ¼ Cv
pffiffiffiffiffi hL
ð41:25Þ
Cv is determined from the relation Cv ¼ πD2
rffiffiffiffiffi g 8k
ð41:26Þ
(By Burkov)
which results directly from a combination of the continuity equation with the equations above. Use the equation hL ¼ kv2 =2g unless otherwise indicated. Energy loss EL equals hv head loss in feet.
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K.E. Isman
Table 41.4 Typical equivalent lengths of schedule 40 straight pipe for screwed steel fittings and valves for any fluid in turbulent flow Equivalent length Pipe size (ft) 1 in. (25.4 mm) 5.2 2.7 1.3 3.2 6.6 5.2 29.0 0.84 17.0 11.0 0.29
Fitting type Regular 90 elbow Long radius 90 elbow Regular 45 elbow Tee, flow through line (run) Tee, flow through stem 180 return bend Globe valve Gate valve Angle valve Swing check valve Coupling or union
Example 3 Table 41.4 lists a number of equivalent lengths of standard Schedule 40 pipe for screwed steel fittings and valves. 7⬘
2 in. (50.8 mm) 8.5 3.6 2.7 7.7 12.0 8.5 54.0 1.5 18.0 19.0 0.45
4 in. (101.6 mm) 13.0 4.6 5.5 17.0 21.0 13.0 110.0 2.5 18.0 38.0 0.65
Using the table determine the equivalent length of the 2-in.-diameter pipe network shown below.
10⬘
15⬘
Source
Sink
GV CV
5⬘
5⬘
Solution The line comprises 19:0 ft ð5:7 mÞ
1 check valve
3 8:5 ¼ 25:5 ft ð7:7 mÞ 7:7 ft ð2:4 mÞ
3 90 standard elbows 1 tee ðflow through runÞ 1 tee ðflow through branch or stemÞ 1 gate valve 1 straight pipe
12:0 ft ð3:7 mÞ 1:5 ft ð0:5 mÞ 42:0 ft ð12:8 mÞ Le ¼ 107:7 ft ð32:8 mÞ
The Darcy equation for determining friction losses through the network would then have the form hL ¼
f Le v2 2Dg
Alternately, the loss coefficient approach may be used, where hL ¼ k
v2 2g
41
Hydraulics
1399
This method must be used to find entrance and exit losses. For this example, however, we either refer to manufacturer’s data for valve and fitting Cv values or calculate k from the relation k¼
f Le D
Energy Losses in Pipe Networks Flow networks can consist of pipes arranged in series, parallel, or combinations or multiples thereof. In any case, an evaluation of friction losses for the flows is based on energy conservation principles applied to the flow junction points. Methods of solution depend on the particular piping configuration. In general, however, they involve establishing a sufficient number of simultaneous equations or employing a friction loss formula where the friction coefficient depends only on the roughness of the pipe (e.g., Darcy-Weisbach or Hazen-Williams). Pipes in Series When two pipes of different sizes or roughnesses are connected in series (Fig. 41.13a), head loss for a given discharge, or discharge for a given head loss, may be calculated by applying the energy equation between the bounding points, taking into account all losses in the interval. Thus, head losses are cumulative. Fig. 41.13 Energy losses in pipe network: (a) pipes in series, (b) pipes in parallel
Series pipes may be treated as a single pipe of constant diameter to simplify the calculation of friction losses. The approach involves determining an equivalent length of a constant diameter pipe which has the same friction loss and discharge characteristics as the actual series pipe system. Minor losses due to valves and fittings are also included. Referring again to Example 3, we note that application of the continuity equation to the solution allows the head loss to be expressed in terms of only one pipe size. The lost head in equivalent feet of 6-in. pipe is then given in Darcy-Weisbach form by Le v2 hL ¼ f 2g D Le can be obtained if f is known. Exact hydraulic equivalence in the velocity head terms depends upon f being a constant over the range of velocities applicable to the problem. In fact, f is not a constant over wide ranges of velocity. Since it varies only slightly with Reynolds number, however, solutions are sufficiently accurate. Pipes in Parallel Two or more pipes connected as in Fig. 41.13b, so that flow is first divided among the pipes and is then rejoined, comprise a parallel pipe system. Flows in pipes arranged in parallel are also determined by application of energy conservation principles—specifically, energy losses through all pipes connecting
a (1)
(2)
A•
b
(3) •B
(1)
(2) A•
•B (3)
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K.E. Isman
common junction points must be equal. Each leg of the parallel network is treated as a series piping system and converted to a single equivalent length pipe. The friction losses through the equivalent length parallel pipes are then considered equal and the respective flows determined by proportional distribution. For a given Q, an outline of the procedure is as follows: 1. Express each branch of the parallel system as an equivalent length of a single pipe size, including all minor losses between the bounding junction points. 0 2. Assume a discharge Q1 through pipe branch 1. 0 3. Solve for hL, using Q1 . 0 0 4. Using hL, find Q2 and Q3 for the remaining branches. 5. Knowing the proportional distribution of flow 0 0 0 among the legs, Q1 , Q2 , and Q3 are adjusted so that their sum equals the known Q; thus, 0
0
0
Q Q Q Q1 ¼ X1 0 Q Q2 ¼ X2 0 Q Q3 ¼ X3 0 Q Q Q Q ð41:27Þ 6. hL1 , hL2 , and hL3 are computed for the values of Q1, Q2, and Q3 as a check for correctness. For judicious choice of assumed discharges, solutions are obtained rapidly that agree within a few percent, well within the range of accuracy of the assumed friction factors. In the case where the head loss is known between points A and B, Q for each branch is found simply by solution of the equation for pipe discharge. The discharges are added to obtain the total flow through the system. Compound Piping Networks Energy loss calculations in compound piping configurations or networks employ the same basic physical principles as for single pipes. That is, conservation of energy and conservation of mass (continuity) must be satisfied throughout the network. In particular, at each pipe junction X Q ¼ Q1 þ Q2 þ þ Qn ¼ 0 ð41:28Þ and around each closed loop or circuit
X
hL ¼ hL 1 þ hL 2 þ þ hL n ¼ 0
ð41:29Þ
The general solution procedure involves setting up a sufficient number of independent equations of these two types and solving simultaneously for the unknowns. For complicated networks, straightforward algebraic solution is clearly impractical. A very widely used relaxation method for systematic solution of large networks was developed by Hardy Cross in 1928. The method is well suited for solution by hand and is readily adaptable for machine computation. We have seen that loss of head in a pipe may be represented generally by an equation of the form hL ¼ KQn (where, for the Hazen-Williams formula, n ¼ 1.85). For any single pipe in a network, we may write Q ¼ Q0 þ Δ
ð41:30Þ
where Q ¼ Corrected flow Q0 ¼ Assumed flow Δ ¼ Flow correction The problem, so stated, reduces to finding Q to a desired degree of accuracy by successive evaluations of Δ based on updated estimates of Q0. We solve for Δ as follows: hL ¼ KQn ¼ K ðQ0 þ ΔÞn
¼ K Q0n þ nQn1 0 Δ þ
ð41:31Þ
If Δ is small relative to Q0, the higher-order terms in the expansion may be neglected. Since, for any circuit, ΣhL ¼ 0, we may write X
KQn ¼ 0 ¼
X
KQ0n þ KnQn1 0 Δ
ð41:32Þ to a good approximation. Solving for Δ we have X X hL 0 KQ0n Δ¼ X ¼ X
n1 n KQ0 n hL 0 =Q0
ð41:33Þ
The overall formulation is made algebraically consistent by designating clockwise flows positive and counterclockwise flows negative.
41
Hydraulics
The calculation procedure is controlled by the requirement that the algebraic sum of all assumed flows must equal zero at each pipe junction. The originally assumed flows are repeatedly and cyclically corrected until the Δ values are negligible, indicating that a hydraulic balance has been reached. Note that pipes common to two circuits are corrected twice in each cycle, once for each circuit. For a system where total head loss is known, flows can be balanced by correcting assumed head losses instead of flows. Several other methods exist for determining flows and head losses in compound pipe networks. Many can be performed manually, although computer analysis is desirable and necessary for the more complex methods, particularly those involving unsteady flow. For a review of alternative methods, the reader is referred to Stephenson [10] and Walski [9].
Flow Measurement and Discharge Flow Measuring Devices This section deals primarily with the basic principles of operation of some flow measuring devices in common use and, in particular, with the pitot tube and the pipeline differential flow meters that have been standardized by the ASME (American Society of Mechanical Engineers): namely, the Venturi, the flow nozzle, and the square-edge thin-plate concentric orifice. In general, an incompressible fluid of density ρ, viscosity μ, flows with average velocity v through a metering element of diameter d. The metering element is located in a horizontal metering tube of roughness ε and diameter D. The flow through the element produces a pressure differential Δp sensed by pressure taps located a distance L apart. It can be shown by dimensional analysis that the fundamental parameters involved in fluid metering, namely L, ε, v, ρ, μ, d, D, and Δp, yield relational solutions conventionally formulated as follows:
1401
dρv ¼ Red μ
Metering element Reynolds number
L D
Tap location ratio
d ¼β D ε D
Beta ratio
Relative roughness
v pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ K 2gΔ p=ρ
Flow coefficient
ðpressure coefficientÞ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Since v ¼ K 2gΔ p=ρ, the continuity equation allows the volumetric flow rate measured by the meter to be expressed as pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Q ¼ KAd 2gΔ p=γ ð41:34Þ where Ad is the flow area of the metering element. Typically, flow meter calculations are based on the idealized flow of a one-dimensional, frictionless, incompressible fluid in a horizontal metering tube. Real conditions require corrections to the ideal formulation. Conventional corrections for the effects of variations from ideal geometry and flow velocity profile are achieved through the use of modification factors. Thus, in Equation 41.34 above, K includes pressure and flow modifications which are conventionally defined as K ¼ CE
ð41:35Þ
where C is the coefficient of discharge defined as the ratio of actual flow rate to ideal flow rate and 1 E ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffi 1 β4 where E is known as the velocity of approach factor, since it accounts for the one-dimensional kinetic energy at the inlet tap. The general volumetric flow metering equation is then given as, sffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffi 2gΔ p 2gΔ p Q ¼ KAd ¼ CEAd ð41:36Þ γ γ
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K.E. Isman
Fig. 41.14 Venturi tube
Chambers
D O
D = Large-orifice diameter d = Small-orifice diameter O = Chamber opening
d O
Inlet cone
Throat
Divergent cone
Convergent entrance
Table 41.5 ASME coefficients for venturi tubes Type of inlet cone Machined Rough welded sheet metal Rough cast
Re2 Minimum —
Maximum 1,000,000
Value of C 0.995
Tolerance (%) 1.00
500,000 —
2,000,000 —
0.985 0.984
1.50 0.70
Venturi Flow Meter Figure 41.14 shows a schematically typical Venturi-type flow tube. The divergent cone section reduces the overall pressure loss of the meter. Pressure is sensed through a series of holes in the inlet cone and throat. These holes lead to an annular chamber, and the two chambers are connected to a pressure differential sensor such as a U-tube manometer. Standardized discharge coefficients, C, as reported by ASME are given in Table 41.5. Venturi tubes must be individually calibrated to obtain coefficients outside range identified in the table. Determination of volumetric flow rate is a simple calculation employing the general flow metering formula—Equation 41.36—where C is obtained from Table 41.5 based on Red, and E is calculated directly from the beta ratio. ASME Flow Nozzle This nozzle is depicted in Fig. 41.15. The pressure differential is sensed by either throat taps or appropriately located pipe wall taps. Coefficients of discharge for ASME flow nozzles may be accurately computed from the following equation:
C ¼ 0:9975 0:00653
106 Red
a ð41:37Þ
where 1 for Red < 106 2 1 a ¼ for Red < 106 5 a¼
Volumetric flow rates are calculated in the same manner as for the Venturi tube. ASME Orifice Meters Fluid flowing through a thin, square-edged orifice plate experiences a contraction of the flow stream some distance downstream from the orifice. The minimum cross sectional area of flow is called the vena contracta and its location is a function of the beta ratio. Figure 41.16 shows the relative pressure difference due to the presence of the orifice plate and the location of the vena contracta with respect to beta. By inspection of Fig. 41.16 it is clear that the actual location of the pressure taps is critical. Three distinct arrangements for tap locations are specified by the ASME for
41
Hydraulics
1403
accurately measuring the pressure differential. These types of tap arrangements are called the flange, vena contracta, and the 1D and ½D. Each has certain advantages and disadvantages and affects the value of the discharge coefficient. Discharge coefficients for orifice metering plates may be calculated from the equation C ¼ Co þ
ΔC Reda
ð41:38Þ
Throat taps 1 —D 2
D
D
d
where Co and α are obtained from Table 41.6. Since the jet contraction downstream of the orifice can amount to nearly half of the orifice area, orifice discharge coefficients are in the order of 0.6 compared to the near-unity coefficients obtained with Venturi tubes and flow nozzles. Pitot Tube A pitot tube is a device designed to sense stagnation or total pressure for the determination of velocity and volumetric flow rate. A number of commercial devices are available, some of which include a static pressure tap, that are designed for insertion into a water main under pressure through a standard pipe tap or corporation cock. The installed pitot tube measures velocity at a point in the fluid. Conventional practice assumes that the conversion of kinetic energy to flow work in the tube is frictionless. Thus, applying the energy equation to the generalized pitot tube diagram (Fig. 41.17) we obtain u2s u2i p p0 þ s ¼0 2g ρ0 g where us ¼ Stagnation point velocity ui ¼ Ideal streamtube velocity ps ¼ Stagnation pressure p0 ¼ Static pressure
1 —D 2
D Pipe wall taps
Fig. 41.15 ASME flow nozzle
D
ð41:39Þ
dc
d
Vena contracta 0
Percent pressure difference
50
100
1
0
1
2
Pipe diameters
Fig. 41.16 Relative pressure changes due to flow through an orifice
3
1
1404
K.E. Isman
Table 41.6 Values of Co, DC, and a for use in Equation 41.38 D ¼ 2 in. ¼ 50 mm β Co ΔC Flange taps α ¼ 1 0.20 0.5972 127 0.30 0.5978 144 0.40 0.6014 181 0.50 0.6050 260 0.60 0.6078 392 0.70 0.6068 573 Vena contracta taps α ¼ ½ 0.20 0.5938 1.61 0.30 0.5939 1.78 0.40 0.5970 2.01 0.50 0.5994 2.29 0.60 0.6042 2.68 0.70 0.6069 3.34 1D and ½D taps α ¼ ½ 0.20 0.5909 2.03 0.30 0.5915 2.02 0.40 0.5936 2.17 0.50 0.5979 2.40 0.60 0.6036 2.67 0.70 0.6078 3.19
D ¼ 4 in. ¼ 100 mm Co ΔC
D ¼ 8 in. ¼ 200 mm Co ΔC
D ¼ 16 in. ¼ 400 mm Co ΔC
0.5946 0.5977 0.6005 0.6034 0.6055 0.6030
0.5951 0.5978 0.6002 0.6026 0.6040 0.6006
0.5955 0.5980 0.6001 0.6022 0.6032 0.5991
200 209 256 386 622 953
327 307 362 584 1015 1637
551 457 514 903 1710 2898
0.5928 0.5934 0.5954 0.5992 0.6041 0.6068
1.61 1.78 2.01 2.29 2.68 3.37
0.5925 0.5933 0.5953 0.5992 0.6041 0.6067
1.61 1.78 2.01 2.29 2.69 3.44
0.5924 0.5932 0.5953 0.5991 0.6041 0.6068
1.61 1.78 2.01 2.29 2.70 3.57
0.5922 0.5930 0.5951 0.5978 0.6040 0.6072
1.41 1.50 1.72 1.99 2.31 2.98
0.5936 0.5944 0.5963 0.5999 0.6044 0.6068
1.10 1.24 1.49 1.79 2.12 3.07
0.5948 0.5956 0.5974 0.6007 0.6048 0.6064
0.94 1.12 1.38 1.69 2.11 3.51
a ps
u
d um
p0
Δp/p
Fig. 41.17 Pitot tube study
Since, by definition us ¼ 0, solving for ui we obtain sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffi 2gð ps p0 Þ 2gΔ p ui ¼ ¼ γ0 γ0
ð41:40Þ
Typically, a pipe coefficient, Cp, which is independent of the geometry of the velocity profile, is defined as Cp ¼
Average velocity Centerline velocity
41
Hydraulics
1405
For typical velocity profiles, Cp, varies from about 0.75 to 0.97 but usually lies within a narrower range of about 0.80–0.90. Knowing the centerline velocity, the flow can be obtained simply by Q ¼ C p AvCL
ð41:41Þ
In situations where pipe velocity profiles are unknown, and therefore average velocities are not available, it may be necessary to obtain velocity measurements at many individual points. Given n velocities, the flow is then Q¼
n X
ð41:42Þ
vi Ai
i¼1
where vi ¼ Velocity at the ith point Ai ¼ Area of annular ring of flow cross section for which velocity vi is accurate Detailed procedures for obtaining accurate pitot traverses are available in the literature along with suggestions for assessing the reliability of water audits, C-factor tests, and so forth, based on pitot gauge measurements [6, 9]. See the next section for a discussion of discharge measurements using pitot tubes.
Free Discharge at an Opening Flow discharging to the atmosphere from a tank, hydrant, nozzle, or open conduit is affected by the area and shape of the opening. The total energy of the fluid is converted into kinetic energy at the orifice according to an appropriate form of the Bernoulli equation. In the most general case of a closed pressurized tank, v20 p ¼ z1 þ 1 2g ρ
ð41:43Þ
p1 1=2 v0 ¼ 2g z1 þ ρ
ð41:44Þ
Accounting for losses at the point of discharge, pffiffiffiffiffiffiffiffi v0 ¼ Cv 2gh ð41:45Þ where Cv, the coefficient of velocity, is determined from the coefficients of discharge and contraction Cv ¼
Cd Cc
Commonly used values of orifice coefficients for water are given in Table 41.7. The orifice discharge can then be expressed as
Table 41.7 Orifice coefficients for water
Flow
A
B
C
D
E
F
G
Illustration
Description
Cd
Cc
A B C D E F G Not shown
Sharp-edged Round-edged Short tube (fluid separates from walls) Short tube (no separation) Short tube with rounded entrance Reentrant tube, length less than one-half of pipe diameter Reentrant tube, length 2–3 pipe diameters Smooth, well-tapered nozzle
0.62 0.98 0.61 0.82 0.97 0.54 0.72 0.98
0.63 1.00 1.00 1.00 0.99 0.55 1.00 0.99
Cv
0.98 0.98 0.61 0.82 0.98 0.99 0.72 0.99
1406
K.E. Isman
Qo ¼ Cd A0
pffiffiffiffiffiffiffiffi 2gh
ð41:46Þ
and the head loss due to turbulence at the orifice as 2 1 v hL ¼ ð41:47Þ 1 0 2g C2v where
1 C2v
For the orifice:
πD2 ¼ 3:14 ft2 0:29 m2 4 Cd ¼ 0:62 ðsharp‐edged orificeÞ
Ao ¼
For the tank:
πD2 ¼ 176:7 ft2 16:4 m2 4 50ð144Þ ¼ 125:38 ft ð38:2 mÞ h0 ¼ 10 þ 62:4 50ð144Þ h1 ¼ 0 þ ¼ 115:38 ft ð35:2 mÞ 62:4 At ¼
1 ¼ Minor loss K-factor
For the general case of a tank of varying crosssectional area being replenished with inflow, Q_ IN , the time to empty from height z1 to z2 is given by ð z2 At dz t¼ ð41:48Þ pffiffiffiffiffiffiffiffi _ IN z1 cd Ao 2gh Q where At is expressed as a function of z. For a tank of constant cross section this simplifies to pffiffiffiffi pffiffiffiffi
2At z1 z2 pffiffiffiffiffi t¼ ð41:49Þ Cd Ao 2g Example 4 A 15-ft-diameter tank discharges water at 50 F through a 2-in.-diameter sharpedged orifice. If the initial water depth in the tank is 10 ft and the tank is continuously pressurized to 50 psig, how long will it take to empty the tank? 50 psi
10⬘ – 0
2⬙-diameter orifice
15⬘ diameter
Solution At 50 F (10 C),
γ ¼ 62:4 lbm=ft3 16:02 kgm=m3
The total pressure head on the discharging fluid results from both an elevation and a static pressure head. Therefore, h i 2At ðz0 ¼ p0 =γÞ1=2 ðz1 þ p1 =γÞ1=2 pffiffiffiffiffi t¼ Cd Ao 2g t ¼ 10:4 s Discharge stream coordinates are given by sffiffiffiffiffi 2y pffiffiffiffiffi x ¼ v0 t ¼ v0 ð41:50aÞ ¼ 2Cv zy g y¼
gt2 2
ð41:50bÞ
For the simpler case of a hydrant discharging to atmosphere, the flow can be determined by an appropriate form of Equation 41.36, pffiffiffiffi Q ¼ 29:8 D2 Cd p ð41:51Þ where Q ¼ Discharge (gpm) D ¼ Outlet diameter (in.) p ¼ Pressure detected by pitot gauge (psi) Cd ¼ Coefficient based on hydrant outlet geometry (usually taken to be 0.90 for full flow across a standard 2½-in. outlet) In the absence of a pitot gauge, hydrant flows may be estimated by observing the trajectory of the discharge stream. The horizontal component of the velocity does not change appreciably over time, thus allowing calculation of the velocity
41
Hydraulics
1407
Fig. 41.18 Determining discharge by the trajectory method
Vena contracta
y
x
based on the height of the outlet and the distance traveled by the stream. Figure 41.18 presents the basic parameters. The velocity determined in this manner is at the vena contracta and is given by x v ¼ pffiffiffiffiffiffiffiffiffiffi 2y=g
ð41:52Þ
The discharge is simply the product of this velocity and the area of the vena contracta. The method is relatively inaccurate due to the obvious difficulty of measuring the required area and the distance x. It is a useful bounding guide, however, in the absence of precision measuring devices.
Water Hammer Water hammer in a pipeline is caused by a sudden stoppage of flow and is characterized by loud noise and vibration.1 The kinetic energy from the interrupted flow is transferred to the walls of the enclosing pipe or equipment. Associated pressures, or shock waves, can be severe enough to damage the pipe network and attached equipment. Density changes due to pressure are assumed zero for nearly all hydraulic calculations, as water is considered incompressible for practical purposes even though it is about 100 times more
1 This discussion is patterned after the theory of water hammer as developed by N. J. Zhukovsky and as presented in Andrew L. Simon’s Practical Hydraulics, 2nd ed. [6].
compressible than steel. When shock waves arise in confined water, however, the compressibility of water becomes very significant, and water’s elastic properties must be taken into account. The primary property of interest is the bulk modulus of elasticity, E, which is defined as the ratio of pressure change to the corresponding change of volume as determined by compression tests on volumes. (The bulk modulus is analogous to Young’s modulus in solid mechanics, which is the ratio of linear stresses to linear strains as determined by tension tests.) The formula expressing the relationship between pressure and volume is Δ p ¼ E
ΔV V0
ð41:53Þ
where the minus sign indicates that a positive change in pressure produces a decrease in volume. A modulus of compressibility, K, is also defined as the inverse of E. Under normal conditions, water confined and flowing under pressure in a pipeline exerts pressure on the pipe walls according to the pressureenergy term of the energy equation. Any change in discharge within the system (due to valve closure, pump stoppage, etc.) results in a change of flow momentum. By virtue of the impulsemomentum relation, the momentum change will cause an impulse force to be created. This force in a pipeline is commonly referred to as water hammer. The theory of water hammer, as developed by Zhukovsky, can be briefly illustrated as follows: a valve in a pipeline is closed instantaneously;
1408
K.E. Isman
the fluid impacts the closed gate and is decelerated to zero velocity, thereby creating a pressure shock. By Newton, pressure shocks in fluids of infinite extent travel at a velocity given by sffiffiffiffiffiffiffi KE c* ¼ ð41:54Þ ρ where c* is called the celerity (velocity) of the shock wave, KE is the kinetic energy of the fluid, and ρ is the fluid density. The pipe, however, also posses certain elastic properties. Therefore, if the fluid in the pipe is subject to a sudden force, the force will be transmitted to the pipe and associated equipment and fittings. Depending upon the magnitude of the force, the pipe and fittings will resist the force as they remain rigid, expand and compress, based upon the associated limits of elasticity of the pipe and fitting materials, or fail via a rupture. The modulus of elasticity, Ec, of a system composed of fluid and pipe may be determined from the equation 1 1 D ¼ þ Ec E E p w
ð41:55Þ
where D ¼ Pipe diameter w ¼ Thickness of the pipe wall Ep ¼ Modulus of elasticity of the pipe material Table 41.8 gives the modulus of elasticity for common pipe materials. The celerity of a shock
wave in a pipe system of finite extent can then be computed from c 1 ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffi c* 1 þ ED= E w
ð41:56Þ
p
which is plotted in Fig. 41.19. The graph indicates the considerable influence of pipe rigidity on the velocity of the shock. The shock waves that travel upstream and downstream from the valve closure eventually reach points in the system that correspond to large stationary energy stores (e.g., reservoirs) or other sudden closure points, which may vary in their ability to absorb or reflect the shock wave. If the shock is absorbed into a larger energy field it will disappear, and it will do so in a certain amount of time as indicated by Equation 41.57, t¼
L c
ð41:57Þ
where L is the distance from the energy reservoir to the shock wave point of origin. At the instant of shock absorption the compressed fluid, that is no longer balanced, begins to flow backward, creating a relief pressure shock that travels back to the valve. The time period T that the initial shock or impulse pressure acts on the valve is, therefore, the time required for the pressure wave to travel away from and back to the valve. T can be determined as follows:
Table 41.8 Modulus of elasticity Ep of various pipe materials Pipe material Lead Lucite (at 73 F) Rubber (vulcanized) Aluminum Glass (silica) Brass, bronze Copper Cast iron, gray Cast iron, malleable Steel
Ep (psi) 0.045 106 0.4 106 2 106 10 106 10 106 13 106 14 106 16 106 23 106 28 106
(lb/ft2) 6.48 106 57.6 106 288 106 1440 106 1440 106 1872 106 2016 106 2304 106 3312 106 4023 106
(kg/m2) 31.64 106 281.23 106 1406 106 7030 106 7030 106 8489 106 9842 106 11,249 106 16,170 106 19,685 106
41
Hydraulics
1409
10
10
1.0
1.0
E D —— Ep w
0.1 1.0
p ¼ p0 p*
100
100
0.1 c — c*
0.1 0.01
T ¼ 2t ¼
2L c
ð41:58Þ
At time T, all the fluid is moving backward at some velocity v. Since the valve is closed, there is no supply for this flow. A negative pressure shock is created at the valve. The shock travels to and back from the reservoir, as the flow is reversed. Such oscillations of pressure and periodic flow reversals persist until the kinetic energy is dissipated by friction. The process described will occur both upstream and downstream from the point of origin, though the initial shock will be positive upstream and negative downstream and the periodicities would not likely be equal. The theoretical magnitude of the pressure shock at instantaneous valve closure can be determined directly from p* ¼ ρcΔv
In actuality, the time of closure of a valve is not zero but some finite time period which we may call Tc. The water hammer pressure increases gradually with the rate of closure of the valve. Depending on whether Tc is smaller or larger than T, we distinguish between quick and slow closure. For Tc less than T, the shock pressure will attain its maximum value p*. (In this sense, quick closure is equivalent to instantaneous closure.) For Tc greater than T, maximum pressure will be somewhat less than p* and may be calculated by the Allievi formula 0 1 sffiffiffiffiffiffi 2 N N p ¼ p0 @ þ þ NA ð41:61Þ 2 4 in which
Fig. 41.19 Celerity of pressure waves in pipes, c equals celerity in elastic pipe; c* equals celerity in fluid of infinite extent
ð41:59Þ
and the pressure will oscillate in the pipe within the range
ð41:60Þ
N¼
Lvρ p0 T c
2 ð41:61aÞ
In general the calculation of water hammer pressure rises, regardless of method, will tend to underestimate the actual values. Real systems will tend to experience superimposition of positive or negative pressure waves due to complex piping configurations. Discontinuities introduced by a variety of auxiliary valving and metering equipment complicate the analysis considerably. Other methods are available for analyzing water hammer effects on systems that may not be reasonably handled by the above idealized method [11]. Since water hammer can be extremely detrimental, often resulting in complete loss of the system, it is desirable to perform an analysis wherever such effects are of concern. Control over the development of damaging shock waves is achieved through use of slow-closing valves, pressure relief valves, or shock-absorbing devices.
Water Supplies An adequate supply of water is essential to any water-based fire protection system. Water can be provided from a number of sources: public
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mains, private mains, elevated tanks, ground level tanks, pressure tanks, ponds, rivers, or oceans. Each of these sources has its advantages and disadvantages. Public mains, private mains, elevated tanks, and pressure tanks are typically associated with a positive pressure, that in certain cases can be sufficient to supply the flow and pressure demands for the water-based fire protection system for some specified period of time. In other cases, a means of providing supplemental pressure, such as through a fire pump, or augmenting the quantity of water is needed. Ground level tanks, ponds, rivers, or oceans are typically not associated with a positive pressure capable of forcing the water through a pipe network. This, however, is dependent upon the relative elevation of the water supply with respect the fire protection system. These water supplies usually need to be served by a fire pump.
Water Mains Water mains can be either public or private. The only real difference between the two is ownership. Public mains are owned and operated by municipalities or public utilities that serve the citizens of a particular community. Generally any tax-paying entity in the associated community has a right to access to the mains, albeit through a fee. Private mains are generally owned and operated by a single property owner or cooperative group that makes the water available for their own use. Before deciding whether a water main (public or private) can be used as a water supply for a fire protection system, two questions need to be addressed. The first pertains to whether or not the water supply is “reliable”. There are no universal measurements or criteria to determine whether or not a water supply is “reliable”. This is a judgment to be made by the stakeholders of a given project after evaluating the availability of waterflow while considering the length and frequency of any potential disruption of service. Factors to consider in this regard are associated with the means of supplying and ensuring
K.E. Isman
pressure for the mains including the reliance on pumps, availability of power supply for any electrically motor driven pumps, fuel supplies and condition of any diesel engine driven pumps, use of elevated tanks and the overall condition and maintenance of the water mains. The second question pertains to the adequacy of the supply. In other words, can the supply provide the necessary flow and pressure to meet the demand of the fire protection system? Testing of the water supply along with detailed hydraulic calculations are undertaken to assess if the main can meet the demand of the fire protection system. In assessing water supplies, the system demand in terms of flow, pressure and duration are needed. As exact system layouts and designs are not usually finalized until the later stages of a project, a series of assessments might need to be made during the design process, and possibly even during the installation phase of the project. Engineers can use an estimating technique to facilitate the process. The simplest technique for estimating the flow demand for the system is to first determine the number of sprinklers that are expected to operate should a fire occur. The number of sprinklers can be determined from design and installation standards based upon the occupancy, commodity or fire hazard under consideration. Additional factors also need to be considered including the type of sprinkler used, its spacing, and required discharge density or discharge pressure. From this basic information, the minimum flow from each sprinkler can be determined. The minimum estimated total flow (Qd) needed for the sprinkler system will then be the number of sprinklers (N) multiplied by the minimum flow necessary from each sprinkler (q) multiplied by an “overage factor” (O) as indicated in Equation 41.62. The overage factor is an approximation of the added pressure that needs to be introduced into the system to overcome the pressure losses associated with waterflow through the system. It accounts for the extra flow that occurs at sprinklers closer to the water supply due to the fact that higher pressures are expected closer to the water supply and this condition will produce a greater flow
41
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discharge. Average “overage factors” are about 15 %, but consideration needs to be given to relative pipe sizes, piping arrangements, i.e. tree, looped or gridded, and piping elevation changes. Qd ¼ N q O
ð41:62Þ
The estimation of the required system pressure will involve consideration of two pressure components. As previously noted, the water supply needs to possess sufficient pressure to overcome friction and other losses, and elevation changes while meeting the demand of the fire protection system. To estimate the pressure demand for a sprinkler system (Pd), add an estimate of the total friction loss in the system (Pf) to an estimate of the pressure due to elevation (Pe) to the pressure needed by the most demanding sprinkler (Ps). P d ¼ P f þ Pe þ Ps
ð41:63Þ
To determine Pf an estimate of the average friction loss per foot from the main to the most remote sprinkler is needed. A value sometimes used is 0.15 psi/ft. However, smaller pipes in tree systems would have larger friction losses and larger pipes in looped and gridded systems would have smaller friction losses. The above formulas can be used to generate a rough “ball-park” approximation of the system demand when assessing an available water supply. Any early estimates would need to be confirmed by the completion of more detailed hydraulic calculations usually completed with the aid of a computer. The following example illustrates the estimation technique. Example 5 Estimate the demand of a sprinkler system utilizing 12 ESFR (K25.2) sprinklers requiring a discharge pressure of 25 psi. (each discharging at least 126 gpm) where The sprinklers are located 40 ft above the elevation where the water supply was measured. The piping system will be installed in a gridded arrangement under the flat roof of the building. The total pipe length from the water supply to the most
remote sprinkler is about 400 ft. This includes equivalent lengths for pipe fittings and valves. Solution The minimum flow demand for each sprinkler is 126 gpm (25.2 (25)1/2)). The flow demand can be estimated by multiplying the number of sprinklers in the design area (12 for ESFR’s) times the minimum flow per sprinkler (126 gpm) times an overage factor. Given the flat roof and the gridded piping arrangement, the overage factor is likely to be less than the average of 15 %. However, as a conservative estimate a value of 15 % is used. The flow demand is estimated to be 1739 gpm (12 126 1.15). The friction loss that is likely to occur in the system can be estimated by first estimating the average friction loss per linear foot for waterflow through the system. Given that the piping is going to be gridded, the average friction loss is likely to be less than 0.15 gpm per ft. However, as conservative estimate, the value of 15 gpm/ft will be used. The friction loss associated with water flowing from the main to the most remote sprinkler can be estimated at 60 psi (0.15 gpm/ ft 400 ft). The change in elevation will be responsible for another 17 psi (0.433 psi/ft 40 ft ¼ 17 psi). The hydraulically most remote sprinkler requires a minimum of 25 psi to operate properly. The pressure demand can then be estimated as 102 psi (60 + 17 + 25). The demand for this sprinkler system can be estimated at 1739 gpm at 102 psi. To determine whether a the main can sufficiently meet the demand of a fire protection system, some analysis of the water supply needs to take place. One way to analyze the water supply is to conduct a water flow test in close proximity to the project and apply appropriate safety factors to account for daily and seasonal fluctuations that might occur. Another way to analyze the water supply without physical testing is to use existing data about the main and a computer model to determine the flow and pressure available at any location along the main. Certain models might account for daily and seasonal fluctuations in water usage, so additional adjustments would not be necessary.
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Whether the information is obtained from a specific flow test or a computer model, the engineer is looking for at least two data points: a static pressure (pressure when no water is flowing out of the main) and a residual pressure at a known flow out of the main. These points can be plotted to characterize the water supply over a range of flows and pressures. The relationship between flow and pressure is exponential (to the 1.85 power). Therefore, the water supply curve can be drawn as a line if the associated graph is scaled to log-1.85 as shown in Fig. 41.20. The figure shows four different flow scales. Other scales can be created by picking one of the scales and multiplying the number on it by a consistent factor. The correct or applicable flow scale needs to be clearly indicated. Example 6 illustrates the graphing technique. Example 6 A proposed sprinkler system for a specific building is estimated to have a flow demand of 750 gpm. The main that will serve
Fig. 41.20 Log-1.85 graph paper
K.E. Isman
as the sprinkler system supply has recently been tested. The test locations are relatively close to the effected building. Test results, which have been adjusted for reasonable worse-case daily and seasonal fluctuations, are a static pressure of 50 psi and a residual pressure of 35 psi at 1600 gpm. Plot the water supply curve and determine what pressure is available at a flow of 750 gpm. Solution The water supply curve is plotted as shown on Fig. 41.21. The “X” on the curve is approximately at the location of 750 gpm, showing that the pressure at this flow would be about 46 psi, but it is difficult to tell exactly which pressure is associated with the flow due to the inaccuracies involved in reading numbers on graphs, especially when one of the axes is not linear. Rather than representing the water supply as a graph, the water supply can also be expressed as a function of the flow as shown in Equation 41.64
41
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Fig. 41.21 Water supply graph for Example 6
where P is the pressure that you want to know at some flow (Q), PS is the static pressure from the test, PR is the residual pressure from the test and QR is the residual flow from the test. 1:85 Q þ PS ð41:64Þ P ¼ ð PR PS Þ QR Equation 41.64 can be used to develop an equation for a given water supply. For example, the water supply in Example 6 can be represented as follows: 1:85 P ¼ ð35 50Þ 1, Q600 þ 50 ! Q1:85 ð41:65Þ P ¼ 15 þ 50 ð1; 600Þ1:85 5
P ¼ 50 1:77 10 Q
calculated by inserting 750 into Equation 41.65 as Q and solving for P as follows: P ¼ 50 1:77 105 ð750Þ1:85 P ¼ 50 3:7 ¼ 46:3 When evaluating a water supply, it is sometimes advantageous to determine the flow that will be available at a certain pressure. In these cases, Equation 41.64 can be solved for Q and rewritten as shown in Equation 41.66. P PS 0:54 Q¼ QR ð41:66Þ PR PS
Elevated Tanks
1:85
Equation 41.65 represents the water supply in Example 6. The pressure at 750 gpm can be
There are at least four basic situations, as noted below, where a tank or some other stored body of water such as a pond, reservoir, river or ocean
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might be considered as the water supply for a fire protection system: 1. Where a public or private main is not available. 2. Where a public or private main is available, but does not produce sufficient flow for the fire protection system. 3. Where a public or private main is available and sufficient, but a redundant supply is desired improve overall reliability of the fire protection system. 4. Where a public or private main is available and sufficient, but a redundant supply is required such as in active seismic zones. Once it has been determined that a tank or other body of water is needed, an elevated tank might be considered. The advantage of an elevated tank is that it is inherently associated with potential energy without the need for any pumps or supplemental pressurization. The amount of energy is function of the height of the tank. As discussed earlier in this chapter, water will develop 0.433 psi for every foot that it raised above some datum plane, i.e. the base of a sprinkler riser. As a further example, if a tank is elevated so that its bottom discharge flange is 150 ft above the location where the water from the tank will be used (such as the outlet of a hydrant), the water in the tank will posses a static pressure head of 65 psi (150 ft 0.433 psi/ft). Of course, friction losses associated with waterflow need to be considered in determining the available pressure at the hydrant. The further from the tank the hydrant is located, the greater the friction losses and less of a residual pressure would be available at a hydrant. While some elevated tanks are actually built some distance above the ground, other elevated tanks are built at ground level but located on hilltops at higher elevations that the building and systems they are intended to serve. Similarly, tanks can be located un upper floors of tall buildings where the water is used for fire protection systems on lower floors. There are situations when it is necessary to determine the maximum flow that can be generated from an elevated tank. To accomplish this, an energy balance needs to be established by
K.E. Isman
equating the energy gained from gravity to the energy lost due to friction and flow effects. Using the Hazen-Williams friction loss method of calculation, Equation 41.67 can be set up with PE representing the energy gained from elevation and L representing the length of pipe between the tank and the location where the water will be used for fire protection: PE ¼
4:52LQ1:85 C1:85 d4:87
ð41:67Þ
PE is equal to 0.433 multiplied by the height of the elevation of the tank (H in feet). Equation 41.67 can be rewritten and solved for Q so that the flow can be determined as shown in Equation 41.68. Q¼
0:28CH 0:54 d2:63 L0:54
ð41:68Þ
Example 7 A tank is going to be installed at the top of a hill to serve an industrial park located at the base of the hill. The bottom of the tank is estimated to be 200 ft above the point of connection to the water main in the industrial park served by the elevated tank. It is further estimated that the pipe from the tank to the center of the industrial park will be 500 ft in length including equivalent lengths for fittings and valves. What is the maximum fire flow that would be available at the center of the industrial park if the pipe material is lined ductile iron (Hazen-Williams C-factor of 140) with an actual inside diameter of 8.27 in.? Note that no other pressure producing devices, such as pumps, will be used. Solution Using Equation 41.68, the maximum flow that could develop from this tank on the hill is 6186 gpm, calculated as follows: Q¼ ¼
0:28CH 0:54 d 2:63 L0:54 0:28ð140Þ ð200Þ0:54 ð8:27Þ2:63 ð500Þ0:54
¼ 6, 186
The duration for which the above flow can be maintained will depend upon the size of the tank. The above solution assumes that the flow is
41
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1415
taking place at a pressure of about 86 psi (200 ft 0.433 psi/ft) not including friction losses. As the tank drains, the flow and available pressure will decrease until they both reach a value of zero once the tank is drained. Many public utilities and operators of water mains require that pressures within the main not drop below a certain value, typically 20 psi. Some private operates might allow lower pressures. Equation 41.69 is a variation of Equation 41.68 with PM representing the minimum pressure that needs to be maintained in the piping system: Q¼
Cd2:63 ½ð0:433HÞ PM 0:54 2:26L0:54
ð41:69Þ
Example 8 For the situation is Example 7, what is the available fire flow if the plan is to keep a minimum pressure of 20 psi in the main? Solution Q¼ ¼
Cd 2:63 ½ð0:433H Þ PM 0:54 2:26L0:54 ð140Þ ð8:27Þ2:63 ½ð0:433ð200ÞÞ 200:54 2:26ð500Þ
0:54
¼ 5, 399 As the solution above shows, for the situation described in Example 7, the available fire flow drops from 6186 to 5399 gpm when the decision is made to maintain a minimum of 20 psi in the mains. While elevated tanks inherently posses some amount of potential energy so that water can be discharged from them, the adequacy of the elevated tank with respect to any associated fire protection systems still needs to be properly accessed to ensure that the elevated tank can meet the flow and pressure demands of the fire protection system.
Pumps and Tanks For tanks that are not elevated, a supplemental means of adding pressure is needed to provide and maintain the proper water flow rate from the
tank into the fire protection system. Depending upon the size of the tank, a fire pump usually serves this purpose. Fire pumps serve to increase the pressure in a given fluid system, thereby increasing the flow rate. While fire pumps can increase the flow rate, they cannot increase the capacity of a water supply, i.e. they cannot create water. If a given water supply consisting of a public main cannot produce the necessary flow anywhere along its representative water supply curve or can only produce the necessary flow at a point below the pressure permitted by the water utility, i.e. at less than 20 psi, a fire pump on it own will not solve the problem. A pump and a tank will likely be needed. Brief details on selecting fire pumps and designing a fire protection system with a fire pump are included later in this chapter. More detailed information on fire pumps is available from a number of sources including the text Pumps for Fire Protection Systems..
Pumps and Other Stored/Static Water Sources As previously stated, other relatively static water sources such as ponds, reservoirs, rivers, lakes and even oceans can be used for fire protection. From a hydraulic design perspective, these sources are very similar to tanks. However, these water sources also challenge the engineer with additional considerations for corrosion protection and concerns for sediment and other particulate in the water being deposited in the fire protection system. Typically, screens and strainers are used to minimize the amount of sediment and other debris from entering the system. Cleaning of these screens is critical to good performance of such systems. In addition, it is also common to use upright sprinklers on such systems, so that sediment does not accumulate on the sprinkler orifice, or pendent sprinklers on return bends. A return bend is a pipe that is connected to the top of a branch line with an elbow, a lateral piece of pipe, and then another elbow to a drop in order to feed a pendent
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K.E. Isman
Fig. 41.22 Vertical shaft turbine pump taking suction from a reservoir
sprinkler. In this manner, sediment in the water is more likely to settle at the bottom of the branch line rather than at the sprinkler. When a pump takes suction from a static source such as a pond or reservoir, that is located below the pump, vertical shaft turbine type pumps, as shown in Fig. 41.22, is typically used. In some cases, a pipe arrangement can be used to feed a pit with water from the pond or reservoir, and a fire pump is then arranged with the pit. In situations where a pipe is used to feed the wet pit as shown in Fig. 41.22, it is necessary to ensure that the pump will receive a sufficient amount of water to continuously operate at maximum flow, which is typically defined as 150 % of the rated pump flow. A calculation needs to be completed to ensure that the maximum flow will occur between the reservoir and the pit. Equation 41.68 can be used to determine whether the flow will be acceptable. Example 9 For a situation where a 1500 gpm rated vertical shaft turbine pump is installed similar to Fig. 41.22 with the pipe at least 10 ft under the lowest expected water level in the reservoir and a 50 ft long lined ductile iron pipe with an internal diameter of 8.27 in. used to feed the wet pit, will the maximum flow needed for the pump (1500 1.5 ¼ 2250 gpm) be achieved for this arrangement? Solution Using Equation 41.68, the maximum flow that can be achieved with this arrangement
is 4255 gpm (as shown below), which well exceeds the requirement for the pump of 2250 gpm. This arrangement would be acceptable (assuming that the friction loss for the strainer was accounted for in the 50 ft of pipe through an equivalent length assumption). Q¼ ¼
0:28CH 0:54 d 2:63 L0:54 0:28ð140Þ ð10Þ0:54 ð8:27Þ2:63 ð50Þ0:54
¼ 4, 255
Pumps Pump Operating Characteristics Pumps are mechanical devices that convert electrical or mechanical energy into hydraulic energy (net pressure). There are many types of pumps— for example, reciprocating, rotary, jet, ram, centrifugal—with each type name referring to the different means by which the pump increases the energy of the liquid. The most common type of pump used for fire protection is the centrifugal pump due to its simplicity and reliability. However, for some applications such as high pressure water mist systems and foam concentrate pumps, centrifugal pumps are not ideal and rotary gear or other types of positive displacement pumps are used. For centrifugal pumps, the impeller (the rotating component) imparts energy to the water
41
Hydraulics
1417
using centrifugal force. Vanes within the impeller improve the efficiency to which energy is transferred. Centrifugal pumps may be divided into several categories. Turbine or radial flow centrifugal pumps force water outward at right angles to the rotating axis. Mixed flow pumps force water in both radial and axial directions. Propeller pumps move water in the axial direction only. Any of these types may be single or multistage with the stage number referring to the number of impellers on the pump’s rotating shaft. For example, a two-stage pump has two impellers on the same shaft whereas a fourstage pump would have four impellers on the same shaft. The orientation of the shaft may be vertical or horizontal. The following discussion, while broadly applicable, is directed mainly to centrifugal pumps. Figure 41.23 illustrates several of the terms commonly used to describe pump performance
conditions. In general, pumping of liquids requires that the pressure at any point in the intake line be greater than the vapor pressure of the liquid to avoid the loss of prime (water entering the pump due to its own pressure head) and the highly destructive phenomenon known as cavitation. The pressure gradient that causes a liquid to move through the intake line to the pump impeller is termed the net positive suction head (NPSH). In pump selection, it is essential to determine that the available NPSH of the water supply exceeds the required NPSH for the pump under consideration so that prime is provided. Required NPSH depends upon many factors relating to pump geometry and construction and intake system operating conditions, but it is defined simply as the difference between net suction head and vapor pressure at a given flow, or the energy needed to fill the pump on the intake side and overcome intake system head
Net discharge head
Losses
Total head
Atmospheric pressure
Total static head
Atmospheric pressure Losses
Static discharge head Static suction head
Net suction head
Pump centerline
Fig. 41.23 Pump head definitions
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K.E. Isman
losses. If the net suction head is less than the vapor pressure of the incoming water, the water will form small vapor bubbles or cavities within the pump. Where the small vapor bubbles formed in the low-pressure region collapse violently upon entering regions of high pressure, they cause localized stress concentrations and vibrations, ultimately leading to mechanical failure of the pump. This phenomenon is referred to as cavitation. The required net positive suction head (NPSHreq) for any pump can be obtained from the manufacturer. The available net positive suction head (NPSHav) must be calculated for each system. Because the total energy of a system is constant, the available NPSH may be determined at any point in the system. The general expression at the pump centerline follows from Bernoulli as
pgauge þ patm pv p NPSHav ¼ þ z hL ρg ρg ð41:70Þ where hL ¼ Friction head loss in intake system piping (in feet of water) pvp ¼ Vapor pressure (0.256 psia for water at 20 C) Knowing the pressure and pipe friction loss terms, the pump can be set at a height, z, which will ensure that NPSHav is greater than NPSHreq. Where a free surface exists on the intake side (such as at the surface of an intake reservoir) and the velocity at a point on the surface is negligible, the above expression simplifies to
patm pv p NPSHav ¼ z hL þ ρg
ð41:71Þ
For pumps of relatively low heads and large discharge capacities (common in fire protection applications) the available NPSH may be less than zero (hL is large). These pumps should be installed well below the reservoir water level to eliminate the possibility of cavitation. For this reason and also to avoid accidental loss of prime,
authorities having jurisdiction generally require positive suction installation. In such instances the pump should be of the vertical shaft type so that the pump impellors sit in the water supply and the pump driver is installed at an elevation above any possible flood level. The useful work done by a pump is the product of the weight of the liquid pumped and the head developed by the pump. The work per unit time in this context is the hydraulic horsepower, commonly called the water horsepower (WHP). For discharge, Q, in gpm, total dynamic head, h, in feet, and specific weight, γ, for water at 20 C (68 F), WHP ¼
Qh 3, 960
ð41:72Þ
The power required to actually drive the pump is the brake horsepower (BHP). The difference between water horsepower and brake horsepower is the power lost within the pump due to mechanical and hydraulic friction. The ratio of WHP to BHP is the pump efficiency, ηp. Similarly, the ratio of BHP to electrical or engine horsepower (EHP) is the motor efficiency, ηm . The overall efficiency is, then, the pump efficiency multiplied by the motor efficiency:
WHP BHP η ¼ η p ðηm Þ ¼ BHP EHP
ð41:73Þ
Although WHP should be calculated using the specific weight of the fluid at known conditions of temperature and pressure, the variation for water is very small; it should be noted that pump motor and engine sizes are chosen from standard available sizes in any case. The interrelations of head, capacity, power, and efficiency for a given pump are known as the characteristics of the pump. They can be expressed graphically in the form of pump characteristic curves. Figure 41.24 shows a standard plot of the several variables at constant impeller speed (N ). Note that the point of maximum operating efficiency on the head-capacity curve corresponds to the maximum value of the efficiency curve. The actual operating point of the
Hydraulics
1419
Fig. 41.24 Centrifugal pump characteristics
N = 1760 RPM
180
90 80
Feet total head-H
160 H-Q
140 120
60
η-Q
100
70
P-Q
80
Point of maximum efficiency
60 40 20 0
50 40 30
BHP-P % efficiency-η
41
20 10
0
2
4
6
8
10 12 14 16 18 20 22
0
Capacity, Q, in 100 gpm
Pump Selection 300
System head curve Operating point
200
Head-characteristic curve
h
100
1000
2000 Q
Fig. 41.25 Graphical determination of operating point
pump, however, depends on the system demand (or system head) curve. The system head loss for any flow rate is the sum of the system friction head loss at that rate plus the total static head to be overcome in the system. Figure 41.25 illustrates the relationship. Recall from Fig. 41.23 that the total static head is the difference in elevation between the discharge level and the suction level. System friction losses may be determined by calculations methods given in previous sections.
Economical pump selection for fire protection applications requires consideration of the following factors: 1. The maximum discharge rate required under the most demanding design conditions 2. The total head-capacity relation (characteristic curve) 3. The suction head—in particular, the net positive suction head available 4. Pump speed and power source requirements 5. Pump spatial and environmental requirements 6. The maximum allowable system head downstream of the pump discharge The usual design condition is that a system will be given or will be chosen from a very limited range of possibilities, and the proper pump must be selected. As shown in Fig. 41.25, when the system demand curve and the pump headcapacity curve are superimposed, their intersection will determine the operating point of the pump. This point also locates the efficiency and, therefore, the power requirements. It is often economically desirable to select a pump such that its operating point is at or near its peak efficiency. In many fire protection applications, however, a pump may be called upon to operate very infrequently. Power consumption may, therefore, not be a significant factor relative to initial cost. Common practice in fire protection applications
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K.E. Isman
is to select a pump to operate at 150 % of rated capacity at 65 % of rated head (see NFPA 208)— that is, an operating point farther out along the characteristic curve. A pump is chosen such that its operating point so defined meets or exceeds the system demand curve at that point. If the pump is to be used as a booster to increase supply main pressure, it must be confirmed that when selecting a pump having a maximum discharge head at zero flow (also known as churn head), which, when added to the maximum water main’s supply head, does not exceed the maximum allowable working pressure on the system. The maximum allowable working pressure typical for many components in fire sprinkler systems is 175 psig [12], although higher rated components are available.
Centrifugal Pump Affinity Relations The abstract concept of pump specific speed has been developed to simplify the description of pump performance characteristics. It consolidates the discharge, head, and speed (rpm) at optimum performance into a single number. For a single stage, single suction pump, specific speed may be calculated from Ns ¼
NQ1=2 H 3=4
ð41:74Þ
where Q (in gpm) is taken at pump rpm, N, and total dynamic head, H. The specific speed of a pump is not actually a speed for that pump in any physical sense; it is defined as the speed in revolutions per minute at which a homologous (geometrically similar) pump would run if constructed to deliver 1 gpm against 1 ft total head at its peak efficiency. For pump impeller designs of identical proportions but different sizes, the specific speed is a constant performance index. That is, the performance of any impeller can be predicted from knowledge of the performance of any other geometrically similar impeller. Changing the impeller diameter results in changes in discharge, total head, and delivered power. These changes occur according to the follow relations:
3 D 1 n1 D 2 n2
ð41:75aÞ
2 2 D1 n1 D2 n2
ð41:75bÞ
1=2 2 H1 D1 H2 D2
ð41:75cÞ
5 D1 ρ1 n31 D2 ρ2 n32
ð41:75dÞ
N 1 D1 ¼ N 2 D2
ð41:76Þ
Q1 ¼ Q2 H1 ¼ H2 Q1 ¼ Q2
BHP1 ¼ BHP2 Since
a change in motor speed only will yield similar results. That is, a change in impeller size has the same effect on pump performance as a change in speed provided, of course, that there is no marked change in operating efficiency. Example 10 A 6 in. (152.4 mm) pump operating at 1770 rpm discharges 1500 gpm (5678 l/m) of water at 40 F against a 120 ft (36.6 m) head. (a) What discharge capacity and total head can be expected from a homologous 8 in. (203 mm) pump operating at 1170 rpm? (b) If the pumps operate at an overall 80 % efficiency, what is the 8 in. (203 mm) pump power requirement? Solution (a) From Equation 41.75b, " # 82 ð1; 170Þ2 H2 ¼ ð120Þ ¼ 93:2 ft ð28:4 mÞ ð6Þ2 ð1; 170Þ2 From Equation 41.75a, " # 83 ð1; 170Þ ð1; 500Þ Q2 ¼ ð6Þ3 ð1; 170Þ ¼ 2, 350 g pm ð8, 895:5 L=mÞ (b) From Equation 41.72, WHP ¼
2, 350ð93:2Þ ¼ 55:3 HP 3, 960
41
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pumps may be combined to provide the necessary output. For example, when discharge is too little, pumps may be installed in parallel, sharing the same suction and inlet conditions. Figure 41.26 illustrates the principle. If a pump provides sufficient discharge but too little head, a second pump may be installed in series, the output of the first pump being fed directly into the suction of the second pump. Figure 41.27 depicts the
Therefore, BHP ¼
55:3 ¼ 69:1 HP 0:8
The motor chosen would be the next highest standard horsepower rating. If more discharge or more head is required than a single pump can provide, two or more Fig. 41.26 Two pumps combined in parallel
H Pump A Combined in parallel
Pump B
System curve
QA
0
Fig. 41.27 Two pumps combined in series
QB
B
Operating points
A
A+B
Q
H
System curve
HB
Combined in series
HA Pump A Pump B 0
Operating points
B
A
A+B
Q
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K.E. Isman
series arrangement. A variety of compound arrangements are possible, depending on details of actual supply and demand, with economics being the prime arbiter.
Nomenclature A C c D d E f G H h hc hL I K k L l m N p Q Re S s u V v z α
area proportionality constant or flow coefficient, Hazen-Williams C-factor celerity of a shock wave pipe diameter element diameter velocity of approach factor, bulk modulus of elasticity Darcy-Weisbach friction loss factor gravitational acceleration constant, 9.8 m/s2 head of water head height of centroid head loss moment of inertia proportionality constant or flow coefficient proportionality constant or flow coefficient length of conduit (in friction loss equations) length or distance mass pump rpm pressure volumetric discharge rate Reynolds number slope of energy gradient specific gravity stream velocity at a given point in flow cross section volume average stream velocity height above a reference datum (potential head) kinetic energy correction factor
β γ Δ ε η μ ν ρ τ
beta ratio specific weight increment pipe wall absolute roughness efficiency absolute (dynamic) viscosity kinematic viscosity density fluid shear stress
References 1. H.E. Hickey, Hydraulics for Fire Protection, National Fire Protection Association, Quincy, MA (1980). 2. R.P. Benedict, Fundamentals of Pipe Flow, WileyInterscience, New York (1980). 3. V.L. Streeter and E.G. Wylie, Fluid Mechanics, McGraw-Hill, New York (1979). 4. Pipe Friction Manual, 3rd ed. Hydraulic Institute (1961). 5. Isman, K. “Darcy Weisbach Friction Loss”, Sprinkler Quarterly, National Fire Sprinkler Association, Winter 2001, pp 27–30. 6. A.L. Simon, Practical Hydraulics, John Wiley & Sons, New York (1981). 7. F.M. White, Fluid Mechanics, McGraw-Hill, New York (1986). 8. Journal AWWA, 73, 5 (1981), by permission. Copyright # 1981, The American Water Works Association. 9. T.M. Walski, Analysis of Water Distribution Systems, Van Nostrand Reinhold, New York (1984). 10. D. Stephenson, Pipeflow Analysis, Elsevier, Amsterdam (1984). 11. NFPA 20, Installation of Centrifugal Fire Pumps, National Fire Protection Association, Quincy, MA (2013). 12. NFPA 13, Installation of Sprinkler Systems, National Fire Protection Association, Quincy, MA (2013).
Kenneth E. Isman has been a Clinical Professor in Fire Protection Engineering at the University of Maryland since 2014. Prior to that, he worked for 28 years for the National Fire Sprinkler Association where he established an expertise in pumps, hydraulics, water supplies, and the design and installation of fire sprinkler systems and other water-based fire protection systems.
Automatic Sprinkler System Calculations
42
Russell P. Fleming
Introduction Applications Where Water Is Appropriate Water is the most commonly used fire fighting agent, mainly due to the fact that it is widely available and inexpensive. It also has very desirable fire extinguishing characteristics such as a high specific heat and high latent heat of vaporization. A single gallon of water can absorb 9280 Btus (2586.5 kJ) of heat as it increases from a 70 F (21 C) room temperature to become steam at 212 F (100 C). Water is not without limits as an extinguishing agent, however, and is considered inappropriate for the protection of certain water reactive materials. In some cases, the application of water can exacerbate the production of heat, flammable or toxic gases, or cause an explosive reaction. The quantities and arrangement of such products must be considered, however, because the sufficient application of water can overcome the combustion reaction in some cases. Another drawback of water is that it is more dense than most liquid hydrocarbon fuels, and immiscible with these liquids as well. Therefore, water will not effectively cover the burning liquid hydrocarbons, nor will it mix with them and dilute the volatile concentrations to the point where they will no longer sustain combustion. R.P. Fleming (*)
Instead, the hydrocarbons will float on top of the water, continuing to burn. In certain cases, the application of water could spread unconfined ignitable liquids and the associated fire. However, water additives such as foam concentrates can be added to the water discharge to produce foams that will float on the hydrocarbon surfaces to provide an effective cover and smother the fire. Applying water in a fine mist has also been successful for certain types of fires involving ignitable liquids. Other types of additives and discharge methods are also available to improve the effectiveness of water for specific applications. Even when water from sprinklers will not suppress the fire, its cooling ability can protect structural elements of a building by controlling the fire until it can be extinguished by other means.
Types of Sprinkler Systems For the majority of applications, automatic sprinkler systems are considered to be the most effective and economical way to apply water to control, suppress, or extinguish a fire. There are four basic types of sprinkler systems: 1. A wet pipe system is by far the simplest and most common type of sprinkler system. It consists of a network of piping containing water under pressure. Automatic sprinklers activated by internal heat responsive elements are connected to the piping such that each
M.J. Hurley (ed.), SFPE Handbook of Fire Protection Engineering, DOI 10.1007/978-1-4939-2565-0_42, # Society of Fire Protection Engineers 2016
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sprinkler protects an assigned horizontal building area, usually a floor area. The application of heat to any sprinkler will cause that single sprinkler to operate, permitting water to discharge over its area of protection. 2. A dry pipe system is similar to a wet system, except that water is held back from the piping network by a special dry pipe valve. The valve is kept closed by air or nitrogen pressure maintained in the system piping. The operation of one or more sprinklers will allow the air pressure to escape, causing operation of the dry valve, which then permits water to flow into the piping network to control or suppress the fire. Dry systems are used where the water in the piping would be subject to freezing. 3. A deluge system is one that does not use automatic sprinklers, but rather open sprinklers. A special deluge valve holds back the water from the piping, and is activated by a separate fire detection system. When activated, the deluge valve admits water to the piping network, and water flows simultaneously from all of the sprinklers comprising the system. Deluge systems are used for protection against rapidly spreading, high heat release fires. 4. A preaction system is similar to a deluge system except that automatic sprinklers rather than open sprinklers are used. A small amount of air pressure is usually maintained in the piping network to ensure that the system is air tight. As with a deluge system, a separate detection system is used to activate a deluge valve, admitting water into the piping network. However, because automatic sprinklers are used, the water is only discharged from activated sprinklers, i.e. those that were fused by heat from the fire. Some special arrangements of preaction systems permit variations on detection system interaction with sprinkler operation. Preaction systems are generally used where there is special concern for accidental discharge of water, as in data processing computer rooms or flash freeze warehouses.
R.P. Fleming
These four basic types of systems differ in terms of the most fundamental aspect of how the water is discharged into the fire area. There are other variations of sprinkler system arrangements, classified according to the hazard they protect (such as residential, in-rack, or exposure protection); additives to the system (such as antifreeze or foam concentrate); or special connections to the system (such as multipurpose piping). However, all sprinkler systems can still be categorized as one of the basic four types.
Applicable Standards Various sprinkler system design and installation standards are in use around the world. NFPA 13, Standard for the Installation of Sprinkler Systems (hereafter referred to as NFPA 13), is the most widely used, and is referenced by most building and life safety codes in the United States and Canada [1]. This standard, in turn, references other NFPA standards for design and installation requirements relating to water supply or interconnection with other systems. These standards include NFPA 14, Standard for the Installation of Standpipe and Hose Systems, NFPA 20, Standard for the Installation of Stationary Pumps for Fire Protection, and NFPA 22, Standard for Water Tanks for Private Fire Protection. For protection of warehouse storage, NFPA 13 traditionally referenced special storage standards that contained sprinkler system design criteria, including NFPA 231, Standard for General Storage Materials, NFPA 231C, Standard for Rack Storage of Materials, NFPA 231D, Standard for Storage of Rubber Tires, and NFPA 231F, Standard for Storage of Roll Paper. However, beginning with the 1999 edition of NFPA 13 these standards were all merged into NFPA 13 to produce a consolidated sprinkler system design and installation standard. Other standards contain design and installation criteria for specific types of facilities or water-based systems, including NFPA 13D, Standard for the Installation of Sprinkler Systems in One- and Two-Family Dwellings and
42
Automatic Sprinkler System Calculations
Manufactured Homes, NFPA 15, Standard for Water Spray Fixed Systems for Fire Protection, NFPA 16, Standard for the Installation of FoamWater Sprinkler and Foam-Water Spray Systems, NFPA 30, Flammable and Combustible Liquids Code, NFPA 30B, Code for the Manufacture and Storage of Aerosol Products, and NFPA 409, Standard on Aircraft Hangars. The European standard addressing sprinkler system design and installation is EN 12845— Fixed Firefighting Systems, Automatic Sprinkler Systems, Design, Installation and Maintenance. The standard was first published in 2004, but is the successor to European insurance standards that in turn were based on sprinkler design and installation rules originally published by the Fire Offices Committee of the United Kingdom. Insurance companies may also develop and enforce their own standards for their customers. For example, FM Global has developed Property Loss Prevention Data Sheet 2-0, Installation Guidelines for Automatic Sprinklers. In Europe, may insurers reference the use of CEA 4001sprinkler systems: planning and installation. In some cases insurance companies or other authorities might modify the provisions or a given standard such as NFPA 13. While this chapter addresses the calculations and engineering considerations associated with the general design of sprinkler systems, the reader needs to confirm the applicable rules and regulations in effect for the particular project under consideration.
Trends in Sprinkler System Development Since the 1970s, there have been a number of new developments in a technology with more than a century of performance history. Hydraulic calculations allowed system designers to take advantage of strong water supplies in order to use smaller pipe sizes. More aesthetically pleasing sprinklers entered the marketplace to appeal to architects and owners as sprinkler system installation spread from factories and warehouses to public spaces and private homes.
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New types of piping offered options. Fast response sprinklers enhanced safety to life while reducing design areas and water supplies based on fewer sprinklers expected to open during a fire event. Larger sprinkler orifice sizes were developed to better address the hazards of high challenge industrial and storage fires. Almost all of these developments were aimed at equal or better fire protection at less cost, made possible through improved allocation of resources. The more efficient use of resources remains a challenge today, with a great deal of focus on sustainability. Because fire sprinklers systems utilize water for periodic testing as well as fire suppression, conservation will increase in importance, and the potential impact of reduced available water supplies on sprinkler system performance will need to be monitored [2]. Proposed environmental solutions such as the use of gray water supplies must be evaluated for their potential to reduce the long-term performance and reliability of fire sprinkler systems. For this reason, NFPA 13 requires that any source of recycled or reclaimed water and its proposed treatment process be analyzed before being made available to the sprinkler system, with a specific concern for compatibility with system components.
Limits of Calculation in an Empirical Design Process Engineering calculations are best performed in areas where an understanding exists as to relationships between parameters. This is not the case with the technology of automatic sprinkler systems. Calculation methods are widely used with regard to only one aspect of sprinkler systems: water flow through piping. There are only very rudimentary calculation methods available with regard to the most fundamental aspect of sprinkler systems, that is, the ability of water spray to suppress fires. The reason that calculation methods are not used is simply the complexity of the mechanisms by which water suppresses fires. Water-based fire suppression has to this point not been thoroughly
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characterized to permit application of mathematical modeling techniques. As a result, the fire suppression aspects of sprinkler system design are empirical at best. Some, but not all, of the current sprinkler system design criteria are based on full-scale testing, including the criteria originally developed for NFPA 231C, NFPA 13D, and parts of NFPA 13, such as the provisions pertaining to the use of CMSA (control mode specific application) and ESFR (early suppression fast response) sprinklers. Most of the protection criteria of NFPA 13 and other sprinkler system design standards, however, are the result of the evolution and application of experienced judgment and intuitive reasoning. In the 1970s, the capabilities of pipe schedule systems, which had demonstrated a hundred years of satisfactory performance, were codified into a system of density/ area curves [3]. This permitted the introduction of hydraulic calculations to what had become a cookbook-type method of designing sprinkler systems. Hydraulic calculations allowed system designers to take advantage of strong water supplies to produce more economical systems. It also permitted the determination of specific flows and pressures available at various points of the system, opening the door to the development and use of new types of sprinklers. The number of different types of sprinklers available in the global marketplace has increased dramatically in the past few decades, and the fire protection engineer needs to be knowledgeable with regard to the variety of fire sprinkler products. Even where design criteria were developed on the basis of full-scale testing, the number and sequence of operating sprinklers has been found to be variable. Some of this variability is due to the variability in fire growth itself and prevailing air currents within a building, but there are also observed phenomena such as “sprinkler skipping,” in which a sprinkler will operate substantially prior to a nearby sprinkler that is closer to the fire plume. Generally associated with high challenge fire scenarios, skipping has been attributed to water drop impingement from nearby operating sprinklers [4], and there is evidence that steps can be taken to shield a
R.P. Fleming
sprinkler’s heat sensing element from such impingement [5]. Because of this history, the calculation methods available to the fire protection engineer in standard sprinkler system design are only ancillary to the true function of a sprinkler system. The sections that follow in this chapter address hydraulic calculations of flow through piping, simple calculations commonly performed in determining water supply requirements, and optional calculations that may be performed with regard to hanging and bracing of system piping. The final section of this chapter deals with the performance of a system relative to a fire, and the material contained therein is totally outside the realm of standard practice. This material is not sufficiently complete to permit a full design approach, but only isolated bits of total system performance. The technical reference guide to the current version of the Fire Dynamics Simulator (FDS), a computational fluid dynamics model that has become the most popular tool in fire protection engineering, includes the statement that “simulating the effects of a sprinkler spray involves a number of elements beyond just activation: computing the droplet trajectories and tracking the water as it drips onto the burning surface” [6]. Efforts are underway to develop a mathematical model of sprinkler spray discharge based on first principles [7], with the hope of ultimately being able to model the impact of a fire sprinkler system on a fire.
Hydraulic Calculations Density-Based Sprinkler Demand Occupancy hazard classification, or commodity classification in the case of protecting storage, is the most critical aspect of the sprinkler system design process. If the hazard or commodity class is underestimated, it is possible for fire to overpower the sprinklers, conceivably resulting in a large loss of property or life. Hazard classification is not an area in which calculation methods are presently in use, however. The proper classification of hazard requires experienced judgment
42
Automatic Sprinkler System Calculations
1427
and familiarity with relevant design and installation standards, and an understanding of sprinkler system performance. Commodity classification is also not possible by means of calculation, but intermediate scale fire testing is sometimes used as the basis of classifying a specific product. Once the hazard or commodity classification is determined and a sprinkler spacing and piping layout has been proposed in conformance with the requirements of the applicable standard, the system designer can initiate a series of calculations to demonstrate that the delivery of a prescribed rate of water application will be accomplished for the maximum number of sprinklers that might be reasonably expected to operate. This number of sprinklers, which must be supplied regardless of the location of the fire within the building, is the basis of the concept of the remote design area. The designer needs to demonstrate that the shape and location of the sprinkler arrangement in the design area will be adequately supplied with water in the event of a fire. Adequacy of water relates to flow, pressure and quantity of water available through the sprinklers expected to operate in response to the fire. Prior to locating the design area, there is the question of how many sprinklers are to be Fig. 42.1 Sample density/ area curve
included in the expected maximum simultaneous flow area. This question is primarily addressed by the occupancy hazard classification, but the designer also has some freedom to decide this matter. For example, in the 2013 edition of NFPA 13, Figure 11.2.3.1.1 contains density/area curves from which the designer can select a design area and density appropriate for the occupancy hazard classification. Any point on or to the right of the curve in the figure is acceptable. The designer may select a high density over a small area, or a low density over a large area. In either event, the fire is expected to be controlled by the sprinklers within that design area, without opening any additional sprinklers. For the protection of storage, similar curves or individual density/area specifications can be found in Chaps. 12, 13, 14, 15, 16, 17, 18, 19, 20, and 21. Chapter 22 of NFPA 13 (2013) contains some sprinkler design density/area specifications or hazard classifications from other NFPA codes and standards relating to the protection of specific occupancies. Example 1 Using the sample density/area curve shown in Fig. 42.1, many different design criteria could be selected, ranging from a density of
5000 4500
Area (ft2)
4000 3500 3000 2500 2000 1500 .05
.10
.15 Density
.20 (gpm/ft2)
.25
.30
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R.P. Fleming
0.1 gpm/ft2 (3.7 mm/min) over 5000 ft2 (500 m2) to 0.17 gpm/ft2 (6.9 mm/min) over 1500 ft2 (139 m2). Either of these two points, or any point to the right of the curve (such as 0.16 gpm/ft2 [6.5 mm/min] over 3000 ft2 [276 m2]) would be considered acceptable. A selection of 0.15 gpm/ft2 (6.1 mm/min) over 2400 ft2 (221 m2) is indicated. Water is provided only for the number of sprinklers in the design area, since no water is needed for the sprinklers that are not expected to open. The design area will be located in the hydraulically most demanding portion of the system. The actual number of sprinklers in the design area depends, of course, on the spacing of the individual sprinklers. NFPA 13 requires that the design area be divided by the maximum sprinkler spacing used, and that any fractional result be rounded up to the next whole sprinkler, as illustrated below. Example 2 Based on the point selected from the sample density/area curve above and the proposed maximum spacing of sprinklers, the number of sprinklers to be included in the design area can be determined. If sprinklers are spaced at 12 15 ft (3.66 4.57 m) so as to each protect an area of 180 ft2 (16.72 m2), the design area of 2400 ft2 (221 m2) would include. 2, 400 ¼ 13:33 ¼ 14 sprinklers 180 The remote design area is required to have a rectangular shape, with the long side of the rectangle parallel to the branch lines. The length of the long side of the design area needs to be determined to calculate the number of sprinklers to be included on each branch line in the design area. This length is normally determined by multiplying the square root of the design area by a factor of 1.2 in accordance with the rules of NFPA 13. Again, any fractional result is rounded to the next whole sprinkler as indicated below. Note that other standards or design methods may use multiplication factors other than 1.2. The higher the factor, the more conservative the design, since it requires more
water to be available through individual branch lines. Example 3 If the 14 sprinklers from Example 2 were spaced 12 ft (3.66 m) along the branch lines and the branch lines were spaced 15 ft (4.57 m) apart, the number of sprinklers along the length of the branch lines in the design area would be 1:2ð2; 400Þ1=2 1:2ð49Þ ¼ 4:9 ¼ 5 sprinklers ¼ 12 12 If the sprinklers were spaced 15 ft (4.57 m) along the branch lines with the branch lines spaced 12 ft (3.66 m) apart, the design area rectangle would include only 4 sprinklers along its length. NFPA 13 (2013) contains some exceptions to this method of locating a remote design area and determining the number of sprinklers to be supplied. Chapters 11 and 12 of the standard include special adjustments to the design area based on factors such as the use of a dry system, the use of quick response sprinklers under flat smooth ceilings of limited height, and the existence of nonsprinklered combustible concealed spaces within the building. These chapters also contain rules for the use of a room design method, which can reduce the number of sprinklers expected to operate in a highly compartmented occupancy. Also, beginning in 1985, the standard adopted a four sprinkler design area for dwelling units and their adjacent corridors when residential sprinklers are installed in accordance with their listing requirements. Listing requirements are specific to the applicable standard but normally pertain to the independent laboratory evaluation of performance of a product, system or service, in this case a residential sprinkler. A step-by-step hydraulic calculation procedure is usually applied. For example, see Chapter 23 of the 2013 edition of NFPA 13. The starting point is the most remote sprinkler in the design area. For tree systems, in which each sprinkler is supplied from only one
42
Automatic Sprinkler System Calculations
direction, the most remote sprinkler is generally the end sprinkler on the farthest branch line from the system riser. This sprinkler, and all others in the design area, must be provided with a sufficient flow of water to meet the density appropriate for the point selected on the density/area curve. Where a sprinkler protects an irregular area, NFPA 13 prescribes that the area of coverage for the sprinkler must be based on the largest sides of its coverage. In other words, the area which a sprinkler protects for calculation purposes is equal to Area of coverage ¼ S L where S is twice the larger of the distances to the next sprinkler (or wall for an end sprinkler) in both the upstream and downstream directions, and L is twice the larger of the distances to adjacent branch lines (or wall in the case of the last branch line) on either side. This reflects the need to flow more water with increasing distance from the sprinkler, since increased flow tends to expand the effective spray umbrella of the sprinkler. The minimum flow from a sprinkler must be the product of the area of coverage multiplied by the minimum required density Q ¼ Area of coverage Density Most of the special listed sprinklers and residential sprinklers have a minimum flow requirement associated with their listings, which is often based on the spacing at which they are used. These minimum flow considerations override the minimum flow based on the density/area method. Example 4 If a standard spray sprinkler protects an area extending to 7 ft (2.1 m) on the north side (half the distance to the next branch line), 5 ft (1.5 m) on the south side (to a wall), 6 ft (1.8 m) on the west side (half the distance to the next sprinkler on the branch line), and 4 ft (1.2 m) on the east side (to a wall), the minimum flow required for the sprinkler to achieve the density requirement selected in Example 1 can be found
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by completing two steps. The first step involves determining the area of coverage. In this case: S L ¼ 2ð6 ftÞ 2ð7 ftÞ ¼ 12 ft 14 ft ¼ 168 ft2 ð15:6 m2 Þ The second step involves multiplying this coverage area by the required density: Q ¼ A ρ ¼ 168 ft2 0:15 gpm=ft2 ¼ 25:2 gpm ð95:4 L=minÞ
Pressure Requirements of the Most Remote Sprinkler When flow through a sprinkler orifice takes place, the energy of the water changes from the potential energy of pressure to the kinetic energy of flow. A formula can be derived from the basic energy equations to determine how much water will flow through an orifice based on the water pressure inside the piping at the orifice: Q ¼ 29:83cd d 2 P1=2 This formula contains a factor, cd, which is a discharge coefficient characteristic of the sprinkler orifice that is determined by laboratory testing. For sprinklers, the product listing organizations determine the orifice discharge coefficient for each particular model of sprinkler. To simplify matters, all physical factors of the sprinkler orifice are lumped into what is experimentally determined as the K-factor of a sprinkler, such that Q ¼ K P1=2 where K has units of gpm/(psi)1/2 [L/min/(bar)1/2]. Since the required minimum flow at the most remote sprinkler is known, determined by either the density/area method or the special sprinkler listing, the minimum pressure needed at the most remote sprinkler can easily be calculated. Since Q ¼ KðPÞ1=2 then P ¼ ðQ=KÞ2 Many sprinklers require a minimum operating pressure of 7 psi (0.48 bar) to ensure proper spray pattern development.
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Example 5 The pressure required at the sprinkler in Example 4 can be determined using the above formula once a specific sprinkler is selected. The K-factor for any sprinkler needs to be confirmed with the manufacturer and listing organization. For the purposes of this example, a K-factor of 5.6 is assumed, since this is a common value for what are considered standard ½-inch orifice sprinklers. P¼
2 Q 25:2 2 ¼ ¼ 20:2 psið1:4 barÞ K 5:6
Once the minimum pressure at the most remote sprinkler is determined, the hydraulic calculation method proceeds backward toward the source of water supply. If the sprinkler spacing is regular, it can be assumed that all other sprinklers within the design area will be flowing at least as much water, and the minimum density is assured. If sprinkler spacing is irregular due to walls and obstruction, or sprinklers with different K-factors are used, it must be verified that each sprinkler is provided with sufficient flow. As the calculations proceed toward the system riser and water supply, the minimum pressure requirements increase, because additional pressures are needed to overcome losses associated with elevation changes, pipe friction, and turbulence caused by fittings, so that the minimum design densities for all sprinklers in the design area are maintained. The determination of the friction and elevation losses are discussed below, with their values added to the total pressure requirements. It should be noted that each sprinkler closer to the source of supply will show a successively greater flow rate, since a higher total pressure is available at that point in the system piping. This effect on the total water demand is termed hydraulic increase, and is the reason why the total water demand of a system is not simply equal to the product of the minimum density and the design area. When calculations are complete, the sprinkler system demand will be known, stated in the form of a specific flow at a specific pressure. A hose demand is also sometimes added to the sprinkler system demand.
The total quantity of water will be determined based upon the duration of required flow that will be specified by applicable standards.
Pressure Losses Through Piping, Fittings, and Valves Friction losses resulting from water flow through piping can be estimated by several engineering approaches, but the most common is the HazenWilliams method. This approach is based on the formula developed empirically by Hazen and Williams: p¼
4:52Q185 C1:85 d4:87
where p ¼ Friction loss per ft of pipe in psi Q ¼ Flow rate in gpm d ¼ Internal pipe diameter in in. C ¼ Hazen-Williams coefficient The choice of C is critical to the accuracy of the friction loss determination, and is therefore normally stipulated by design standards. C values for various types of pipe materials are shown in Fig. 42.1. The values assigned for use are intended to simulate the expected interior roughness of aged pipe (Table 42.1). Rather than make the Hazen-Williams calculation for each section of piping, it has become standard practice, when doing hand calculations, to use a friction loss table, which contains all values of p for various values of Q and various pipe sizes. In many cases the tables are based on Table 42.1 C values for pipes Type of pipe Steel pipe—dry and preaction systems Steel pipe—wet and deluge systems Galvanized steel pipe—dry and preaction systems Galvanized steel pipe—wet and deluge systems Cement lined cast or ductile iron Copper tube Plastic (listed)
Assigned C factor 100 120 100 120 140 150 150
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Automatic Sprinkler System Calculations
the use of Schedule 40 steel pipe for wet systems. The use of other pipe schedules, pipe materials, or system types may require the use of multiplying factors. Most commercially available sprinkler system hydraulic calculation programs have these values programmed into the software. Once the value of friction loss per foot is determined using either the previous equation or friction loss tables, the total friction loss through a section of pipe is found by multiplying p by the length of pipe, L. Since some standards use p to designate loss per foot, total friction loss in a length of pipe can be designated by pf, where pf ¼ p L In the analysis of complex piping arrangements, it is sometimes convenient to lump the values of all factors in the HazenWilliams equation (except flow) for a given length of pipe into a constant, K, identified as a friction loss coefficient. To avoid confusion with the nozzle coefficient K, this coefficient can be identified as FLC, friction loss coefficient. ðL 4:52Þ FLC ¼ 1:85 4:87 C d The value of pf is therefore equal to p f ¼ FLC Q1:85 Example 6 If the most remote sprinkler on a branch line requires a minimum flow of 25.2 gpm (92.1 L/min) for a minimum pressure of 20.2 psi (1.4 bar) as shown in Examples 4 and 5, and the second sprinkler on the line is connected by a 12 ft (3.6 m) length of 1 in. (25.4 mm) Schedule 40 steel pipe, with both sprinklers mounted directly in fittings on the pipe (no drops or sprigs), the minimum pressure required at the second sprinkler can be found by determining the friction loss caused by a flow of 25.2 gpm (92.1 L/min) through the piping to the end sprinkler. Typically, pressure losses associated with straight-through fittings can be ignored in the calculation process if there is no change in flow direction. Also, the fitting directly attached to each sprinkler is generally ignored, since K-factors of sprinklers are determined with such a fitting in place.
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Using the Hazen-Williams equation with values of 25.2 for Q, 120 for C, and 1.049 for d (the inside diameter of Schedule 40 steel 1 in. pipe) results in a value of p ¼ 0.20 psi (0.012 bar) per foot of pipe. Multiplying by the 12 ft (3.6 m) length results in a total friction loss of pf ¼ 2.4 psi (0.17 bar). The total pressure required at the second sprinkler on the line is therefore 20.2 psi + 2.4 psi ¼ 22.6 psi (1.6 bar). This will result in a flow from the second sprinkler of Q ¼ K(P)1/2 ¼ 26.6 gpm (100.7 L/min). Minor losses through fittings and valves are not friction losses but energy losses, caused by turbulence in the water flow, which increase as the velocity of flow increases. Nevertheless, it has become standard practice to simplify calculation of such losses through the use of “equivalent lengths,” which are added to the actual pipe length in determining the pipe friction loss. NFPA 13 contains a table of equivalent pipe lengths for this purpose (Table 42.2). As an example, if a 2 in. (50.8 mm) 90-degree long turn elbow is assigned an equivalent length of 3 ft (0.914 m), this means that the energy loss associated with turbulence through the elbow is expected to approximate the energy loss to friction through 3 ft of 2 in. pipe (0.914 m of 50.8 mm pipe). As with the friction loss tables, the equivalent pipe length chart is based on the use of steel pipe with a C-factor of 120, and the use of other piping materials requires multiplying factors. The equivalent pipe length for pipes having C values other then 120 should be adjusted using the following multiplication factors: 0.713 for a C value of 100; 1.16 for a C value of 130; 1.33 for a C value of 140; 1.51 for a C value of 150. Example 7 If the 12 ft (3.6 m) length of 1 in. (25.4 mm) pipe in Example 6 had contained four elbows so as to avoid a building column, the pressure loss from those elbows could be approximated by adding an equivalent length of pipe to the friction loss calculation. Table 42.2 gives a value of 2 ft (0.610 m) as the appropriate equivalent length for standard elbows in 1 in. (25.4 mm) Schedule 40 steel pipe. For four elbows, the equivalent fitting length would be 8 ft (2.4 m). Added to the actual pipe length of
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R.P. Fleming
Table 42.2 Equivalent pipe length chart (for C ¼ 120) Fittings and valves 45 elbow 90 standard elbow 90 long turn elbow Tee or cross (flow turned 90 ) Butterfly valve Gate valve Swing checka
Fittings and valves expressed in equivalent feet of pipe ¾ in. 1 in. 1¼ in. 1½ in. 2 in. 2½ in. 3 in. 3½ in. 4 in. 5 in. 6 in 1 1 1 2 2 3 3 3 4 5 7 2 2 3 4 5 6 7 8 10 12 14 1 2 2 2 3 4 5 5 6 8 9 3 5 6 8 10 12 15 17 20 25 30
8 in. 9 18 13 35
10 in. 11 22 16 50
12 in. 13 27 18 60
— — —
12 4 45
19 5 55
21 6 65
— — 5
— — 7
— — 9
6 1 11
7 1 14
10 1 16
— 1 19
12 2 22
9 2 27
10 3 32
For SI units: 1 ft ¼ 0.3048 m Due to the variations in design of swing check valves, the pipe equivalents indicated in the above chart are to be considered average
a
12 ft (3.6 m), the total equivalent length would be 20 ft (6 m). This results in a new value of pf ¼ 20 ft 0.20 psi/ft ¼ 4.0 psi (0.28 bar). The total pressure at the second sprinkler would then be equal to 20.2 psi + 4.0 psi ¼ 24.2 psi (1.67 bar). The total flow from the second sprinkler in this case would be Q ¼ K(P)1/2 ¼ 27.5 gpm (100.4 L/min). Some types of standard valves, such as swing check valves, are included in Table 42.2, the equivalent pipe length chart. Equivalent lengths for pressure losses through system alarm, dry, and deluge valves are determined by the approval laboratories at the time of product listing.
Use of Velocity Pressures The value of pressure, P, in the sprinkler orifice flow formula can be considered either the total pressure, Pt, or the normal pressure, Pn, since design standards typically permit the use of velocity pressures at the discretion of the designer. Total pressure, normal pressure, and velocity pressure, Pv, have the following relationship: P n ¼ Pt P v Total pressure is the counterpart of total energy or total head, and can be considered the pressure that would act against an orifice if all of the energy of the water in the pipe at that point were focused toward flow out of the orifice. This
is the case where there is no flow past the orifice in the piping. Where flow does take place in the piping past an orifice, however, normal pressure is the portion of the total pressure acting perpendicular to the direction of flow in the piping, and therefore acting in the direction of flow through the orifice. The amount by which normal pressure is less than total pressure is velocity pressure, which is acting in the direction of flow in the piping. Velocity pressure corresponds to velocity energy, which is the energy of motion. There is no factor in the above expression for elevation head, because the flow from an orifice can be considered to take place in a datum plane. When velocity pressures are used in calculations, it is recognized that some of the energy of the water is in the form of velocity head, which is not acting normal to the pipe walls (where it would help push water out the orifice), but rather in the downstream direction. Thus, for every sprinkler (except the end sprinkler on a line), slightly less flow takes place than what would be calculated from the use of the formula Q ¼ K(Pt)1/2 (Fig. 42.2). Design standards typically permit the velocity pressure effects to be ignored, however, since they are usually rather minor for most sprinkler system configurations. Additionally, ignoring the effects of velocity pressure tends to produce a more conservative design in that the calculated system demand (flow and pressure) increase when velocity pressures are not taken into account.
42
Automatic Sprinkler System Calculations
1433
Fig. 42.2 Velocity and normal pressures in piping
PR gauges
N
T
V
N
Flow
Pipe
If velocity pressures are considered, normal pressure rather than total pressure is used when determining flow through any sprinkler except the end sprinkler on a branch line, and through any branch line except the end branch line on a cross main. The velocity pressure, Pv, which is subtracted from the total pressure in order to determine the normal pressure, is determined as Pv ¼
v2 0:433 psi=ft ð0:098 bar=mÞ 2g
or Pv ¼ 0:001123Q2 =d 4 where Q is the upstream flow through the piping to an orifice (or branch line) in gpm and d is the actual internal diameter of the upstream pipe in inches. Because design standards typically mandate the use of the upstream flow, an iterative approach to determining the velocity pressure is necessary. The upstream flow cannot be determined unless the flow from the sprinkler (or branch line) in question is known. Since the flow from the sprinkler (or branch line) is affected by the velocity pressure resulting from the upstream flow, an estimate of the upstream flow is needed to start the iteration. Example 8 If the pipe on the upstream side of the second sprinkler in Example 6 were 3 in. Schedule 40 steel pipe with an inside diameter of 1.38 in. (35 mm), the flow from the second sprinkler would be considered to be 26.6 gpm (100.2 L/min) as determined at the end of
Example 6, if velocity pressures were not included. If velocity pressures were to be considered, an upstream flow would first be assumed. Since the end sprinkler had a minimum flow of 25.2 gpm (95.2 L/min) and the upstream flow would consist of the combined flow rates of the two sprinklers, an estimate of 52 gpm (196.8 L/min) appears reasonable. Substituting this flow and the pipe diameter into the equation for velocity pressure gives Pv ¼ ¼
0:001123Q2 d4 0:001123ð52Þ2
ð1:38Þ4 ¼ 0:8 psi ð0:06 barÞ This means that the actual pressure acting on the orifice of the second sprinkler is equal to Pn ¼ Pt Pv ¼ 22:6 psi 0:8 psi ¼ 21:8 psi ð1:50 barÞ This would result in a flow from the second sprinkler of Q ¼ KðPÞ1=2 ¼ 26:1 gpm ð98:7 L=minÞ Combining this flow with the known flow from the end sprinkler results in a total upstream flow of 51.3 gpm (194.2 L/min). To determine if the initial guess was close enough, determine the velocity pressure that would result from an upstream flow of 51.3 gpm (194.2 L/min).
1434
This calculation also results in a velocity pressure of 0.8 psi (0.06 bar), and the process is therefore complete. It can be seen that the second sprinkler apparently flows 0.5 gpm (1.9 L/min) less than the estimated flow due to velocity pressures.
Elevation Losses Variation of pressure within a fluid at rest is related to the density or unit (specific) weight of the fluid. The unit weight of a fluid is equal to its density multiplied by the acceleration of gravity. The unit weight of water is 62.4 lbs/ft3 (1000 kg/m3). This means that one cubic foot of water at rest weighs 62.4 lbs (1000 kg). The cubic foot of water, or any other water column one foot high, thus results in a static pressure at its base of 62.4 lbs/ft2 (304.66 kg/m2). Divided by 144 in.2 per ft2 (1.020 104 kg/m2 bar), this results in a pressure of 0.433 lb per in.2 per ft (0.099 bar/m) of water column. A column of water 10 ft (3.048 m) high similarly exerts a pressure of 10 ft 62.4 lbs/ft2 1 ft2/144 in.2 ¼ 4.33 psi (3.048 m 999.5 kg/m2 1.020 104 kg/m2 bar ¼ 0.299 bar). The static pressure at the top of both columns of water is equal to zero (gauge pressure), or atmospheric pressure. On this basis, additional pressure must be available within a sprinkler system water supply to overcome the pressure loss associated with elevation, i.e. when water flow is acting against the force of gravity. This pressure is equal to 0.433 psi/ft (0.099 bar/m) of elevation of the sprinklers above the level where the water supply information is known. Sometimes the additional pressure needed to overcome elevation is added at the point where the elevation change takes place within the system. If significant elevation changes take place within a portion of the system that is likely to be considered as a representative flowing orifice (such as a single branch line along a cross main that is equivalent to other lines in the remote design area), then it is considered more accurate to wait until calculations have been completed, and simply add an elevation pressure increase to
R.P. Fleming
account for the total height of the highest sprinklers above the supply point. Example 9 The pressure that must be added to a system supply to compensate for the fact that the sprinklers are located 120 ft (36.6 m) above the supply can be found by multiplying the total elevation difference by 0.433 psi/ft (0.099 bar/m). 120 ft 0:433 psi=ft ¼ 52 psi ð3:62 barÞ
Loops and Grids Hydraulic calculations become more complicated when piping is configured in loops or grids, such that water feeding any given sprinkler or branch line can be supplied through more than one route. A number of computer programs that can quickly complete the repetitive calculations have therefore been developed specifically for fire protection systems, and are being marketed commercially. Determining the flow split that takes place in the various parts of any loop or grid is accomplished by applying the basic principles of conservation of mass and conservation of energy. For a single loop, it should be recognized that the energy loss across each of the two legs from one end of the system to the other must be equal. Otherwise, a circulation would take place within the loop itself. Also, mass is conserved by the fact that the sum of the two individual flows through the paths is equal to the total flow into (and out of) the loop (Fig. 42.3). Applying the Hazen-Williams formula to each leg of the loop p f ¼ L1
4:52Q1:85 4:52Q1:85 1 2 ¼ L 2 4:87 1:85 C1:85 C1:85 1 d1 2 d2
Substituting the term FLC for all terms except Q, p f ¼ FLC1 Q1:85 ¼ FLC2 Q1:85 1 2 This simplifies to become 1:85 Q1 FLC2 ¼ Q2 FLC1
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Automatic Sprinkler System Calculations
1435
Fig. 42.3 Example of a simple loop configuration
pf Q1 Q
Q Q2
Since Q1 and Q2 combine to create a total flow of Q, the flow through one leg can be determined as Q1 ¼ h
2.
Q ðFLC1 =FLC2 Þ0:54 þ 1
i
For the simplest of looped systems, i.e. a single loop, hand calculations are not complex. Furthermore, sometimes a seemingly complex piping system can be simplified by substituting an “equivalent pipe” for two or more pipes in series or in parallel. For pipes in series FLCe ¼ FLC1 þ FLC2 þ FLC3 þ . . .
3.
4.
5.
For pipes in parallel
1 FLCe
0:54
¼
1 FLC1
0:54
þ
1 FLC2
0:54 þ
For gridded systems, which involve flow through multiple loops, computers are generally used since it becomes necessary to solve a system of nonlinear equations. When hand calculations are performed, the Hardy Cross [8] method of balancing heads is generally employed. This method involves assuming a flow distribution within the piping network, then iterating, i.e. applying successive corrective flows until differences in pressure losses through the various routes are nearly equal. The Hardy Cross solution procedure applied to sprinkler system piping is as follows: 1. Identify all loop circuits and the significant parameters associated with each line of the loop, such as pipe length, diameter, and Hazen-Williams coefficient. Reduce the number of individual pipes where possible
6.
7.
by finding the equivalent pipe for pipes in series or parallel. Evaluate each parameter in the proper units. Minor losses through fittings should be converted to equivalent pipe lengths. A value of all parameters except flow for each pipe section should be calculated (FLC). Assume a reasonable distribution of flows that satisfies continuity, proceeding loop by loop. Compute the pressure (or head) loss due to friction, pf, in each pipe using the FLC in the Hazen-Williams formula. Sum the friction losses around each loop with due regard to flow direction, i.e. assume clockwise flow positive and counter-clockwise flow as negative. Flows are correct when the sum of the losses, dpf, is as small as desirable, typically 0.5 psi (0.03 bar). If the sum of the losses is not sufficiently small for each loop, divide each pipe’s friction loss by the presumed flow for the pipe, pf/Q. Calculate a correction flow for each loop as dQ ¼
d p f P 1:85 p f =Q
8. Add the correction flow values to each pipe in the loop as required, thereby increasing or decreasing the earlier assumed flows. For cases where a single pipe is in two loops, the algebraic difference between the two values of dQ must be applied as the correction to the assumed flow. 9. With a new set of assumed flows, repeat steps 4–7 until the values of dpf are sufficiently small.
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R.P. Fleming
10. As a final check, calculate the pressure loss by any route from the initial to the final junction. A second calculation along another route should give the same value of pressure loss within the range of accuracy expected, again typically 0.5 psi (0.03 bar). Design standards typically require that pressures be shown to balance within 0.5 psi (0.03 bar) at hydraulic junction points. The designer, with or without the use of a computer program, must continue to make successive guesses as to how much flow takes place in each section of pipe until the pressure loss from the design area back to the source of supply is approximately the same (within 0.5 psi [0.03 bar]) regardless of the path chosen. Example 10 For the small two-loop grid shown in Fig. 42.4, the total flow in and out is 100 gpm (378.5 L/min). It is necessary to determine the flow taking place through each pipe section. The system has already been simplified by finding the equivalent pipe for all pipes in series and in parallel. The following values of FLC have been calculated:
2
4
Pipe 1 FLC Pipe 2 FLC Pipe 3 FLC Pipe 4 FLC Pipe 5 FLC
0.001 0.002 0.003 0.001 0.004
Recall that FLC pertains to the length, internal diameter, and Hazen-Williams C-factor for each pipe segment. Under step 3 of the Hardy Cross procedure, flows that would satisfy conservation of mass are estimated as shown in Fig. 42.5. Steps 4–9 are then carried out in a tabular approach as shown in Table 42.3. As the difference between dpf for loop 1 and loop 2 is greater than 0.5 psi (0.03 bar), at least another iteration is necessary to balance flows. Using the calculated flow estimates from the first iteration, another set of calculations is completed as shown in Table 42.4. Revised flows after the first iteration are shown in Fig. 42.6. With regard to the flow in pipe #3, which is common to both loops, the first iteration indicates that the estimated flow should be reversed. For loop 1, the flow calculates to 11.4 gpm but was estimated to be +5 gpm. 60
100 gpm
100 gpm
¼ ¼ ¼ ¼ ¼
Loop 2
Loop 1 Loop 1 3
40
Loop 2
+
5
55
100 gpm
100 gpm 1
+
45
5
Original flow assumptions
Simplified system
Fig. 42.5 Original flow assumptions Fig. 42.4 Simplified system, pipe in series
Table 42.3 First iteration Loop 1
Pipe 1 2 3
Q 40 60 5
FLC 0.001 0.002 0.003
pf 0.92 3.90 0.06
2
3 4 5
5 55 45
0.003 0.001 0.004
0.06 1.66 4.58
dpf
¼3.04
¼ 2.98
( pf/Q) 0.023 0.065 0.012 0.100 0.012 0.030 0.102 0.144
dQ ¼ d p f =1:85 Σ p f =Q dQ ¼ 16.4
dQ ¼ 11.2
Q + dQ 56.4 +43.6 11.4 +6.2 +66.2 +33.8
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Automatic Sprinkler System Calculations
1437
Table 42.4 Second iteration Loop 1
Pipe 1 2 3
Q 56.4 43.6 22.6
FLC 0.001 0.002 0.003
pf 1.74 2.16 0.96
dpf
¼ 0.54 2
3 4 5
22.6 66.2 33.8
0.003 0.001 0.004
0.96 2.34 2.69 ¼0.61
43.6
100 gpm
56.4
66.2 22.6 100 gpm 33.8
Fig. 42.6 Corrected flows after first iteration
dQ ¼ d p f =1:85 Σ p f =Q
dQ ¼ 2.4
Q + dQ 54.0 +46.0 20.2 +20.5 +64.1 +35.9
dQ ¼ 2.1
pressure losses around both loops are balanced within 0.5 psi. Therefore, the flow split assumed after two iterations can be accepted. As a final check, step 10 of the above procedure calls for a calculation of the total pressure loss through two different routes, requiring that they balance within 0.5 psi (0.03 bar): Water flow route through pipes 1 and 5: FLC1 ðQ1 Þ1:85 þ FLC2 ðQ2 Þ1:85 ¼ 0:001ð54:0Þ1:85 þ 0:004ð35:9Þ1:85 ¼ 1:6 þ 3:0 ¼ 4:6 psi ð0:32 barÞ
46.0
100 gpm
( pf/Q) 0.031 0.050 0.042 0.123 0.042 0.035 0.080 0.157
54.0
64.1
Water flow route through pipes 2 and 4:
18.1 100 gpm 35.9
Fig. 42.7 Corrected flows after second iteration
For loop 2, the flow calculates +6.2 gpm but was estimated to be 5 gpm. As indicated in step 8, where a pipe segment is common to another loop, the algebraic difference between the two values of dQ is to be applied as the correction to the assumed flow. In other words, the flow correction for the common pipe is the net effect of the corrections for both loops. For pipe #3, the algebraic difference in dQ for loops 1 and 2 is 27.6 gpm (16.4 gpm + 11.2 gpm). This results is a corrected flow for pipe #3 of 5–27.6 ¼ 22.6 gpm for loop 1 and +22.6 for loop 2. After completion of the second iteration, the difference in dpf between loops 1 and 2 is still too large, so a third iteration is needed. The flows after the second iteration are shown in Fig. 42.7. The third iteration calculations, as shown in Table 42.5, indicate that the In starting the
0:002ð46:0Þ1:85 þ 0:001ð64:1Þ1:85 ¼ 2:4 þ 2:2 ¼ 4:6 psi ð0:32 barÞ This is acceptable. Note that this example required less than three full iterations to achieve a successful solution, i.e. correctly balanced flow, despite the fact that the initial flow assumption called for reverse flow in pipe #3. The initial assumption was for a clockwise flow of 5 gpm (18.9 L/min) in pipe 3, but the final solution shows a counterclockwise flow of 18.1 gpm (68.5 L/min).
Water Supply Calculations Determination of Available Supply Curve Depending upon the location of the sprinkler system, public or private water main networks might be available to serve as the water supply
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R.P. Fleming
Table 42.5 Third iteration Loop 1
Pipe 1 2 3
Q 54.0 46.0 18.1
FLC 0.001 0.002 0.003
pf 1.60 2.38 0.64
2
3 4 5
18.1 64.1 35.9
0.003 0.001 0.004
0.64 2.20 3.01
dpf
(pf/Q)
dQ ¼ d p f =1:85 Σ p f =Q
Q + dQ
¼0.14
¼ 0.17
100 Pressure (psi)
for the system. For instance, the municipal underground water mains of many large cities in North America are permitted to be used for fire protection purposes. Flow testing of public or private water supply mains permits an evaluation of the strength of the available water supply in terms of both quantity of flow and available pressures. The strength of a water supply is the key to whether it will adequately serve a sprinkler system. Each test of a water supply must provide at least two pieces of information—a static pressure and a residual pressure at a known flow. The static pressure is sometimes referred to as the “no flow” condition, as no water is being discharged from the main in the vicinity of the test. However, it must be recognized that rarely is any public water supply network in a true no flow condition. This condition is intended represent a situation where the fire protection system is not creating an additional flow demand beyond that which is ordinarily placed on the system. The residual pressure reading is taken with an additional flow being taken from the system, preferably a flow that approximates the likely maximum system demand. Between the two (or more) points, a representation of the water supply (termed a water supply curve) can be made. For the most part, this water supply curve is a fingerprint of the system supply and piping arrangements, since the static pressure tends to represent the effect of elevated tanks and operating pumps in the system, and the drop to the residual pressure represents the friction and minor losses through the piping network that result from the increased flow during the test.
90
60
450
1000 Flow (gpm)
Fig. 42.8 Pressure available from 450 gpm flow water supply
The static pressure is read directly from a gauge attached to a hydrant. The residual pressure is read from the same gauge while a flow reading is taken from another hydrant, preferably downstream. A pitot tube is usually used in combination with observed characteristics of the nozzle through which flow is taken in order to determine the amount of flow. Figure 42.8 is an example of a plot of water supply information. The static pressure is plotted along the y-axis, reflecting a given pressure under zero or no-flow conditions. The residual pressure at the measured flow is also plotted, and a straight line is drawn between these two points. Note that the x-axis is not linear, but rather shows flow as a function of the 1.85 power. This corresponds to the exponent for flow in the Hazen-Williams equation. Using this semiexponential graph paper demonstrates that the residual pressure effect is the result of friction loss through the system, and permits the water supply curve to be plotted as a straight line.
42
Automatic Sprinkler System Calculations
Since the drop in residual pressure is proportional to flow to the 1.85 power, the available pressure at any flow can be read directly from the water supply curve. For adequate design, the system demand point, including hose stream allowance, should lie below the water supply curve. Example 11 If a water supply is determined by test to have a static pressure of 100 psi (6.9 bar) and a residual pressure of 80 psi (5.5 bar) at a flow of 1000 gpm (3785 L/min), the pressure available at a flow of 450 gpm (1703 L/min) can be approximated by plotting the two known data points on the hydraulic graph paper as shown in Fig. 42.8. At a flow of 450 gpm (1703 L/min), a pressure of 90 psi (6.2 bar) is indicated.
Pump Selection and Testing Specific requirements for pumps used in sprinkler systems are normally contained in separate design and installation standards such as NFPA 20. Fire pumps provide a means of making up for pressure deficiencies where an adequate volume of water is available at a suitable net positive suction pressure. Plumbing codes or municipal water supply regulations sometimes set a minimum allowable net positive suction pressure of 10–20 psi (0.69–1.38 bar) for water taken from public mains. If insufficient water is available at such pressures from such sources, then it becomes necessary to use a stored water supply. Listed centrifugal fire pumps are available with either diesel or electric drivers, and with capacities ranging from 25 to 5000 gpm (95–18,927 L/min), although fire pumps are most commonly found with capacities ranging from 250 to 2500 gpm (946–9463 L/min) in increments of 250 up to 1500 gpm (946 up to 5678 L/min) and 500 gpm (1893 L/min) increments beyond that point. Each pump is specified with a rated flow and rated pressure. Rated pressures vary extensively, since manufacturers can control this feature with small changes to impeller design.
1439
Pump affinity laws govern the relationship between impeller diameter, D, pump speed, N, flow, Q, pressure head, H, and brake horsepower, bhp. The first set of affinity laws assumes a constant impeller diameter. Q1 N 1 ¼ Q2 N 2
H 1 N 21 ¼ H 2 N 22
bh p1 N 31 ¼ bh p2 N 32
These affinity laws are commonly used when correcting the output of a pump to its rated speed, such as during a fire pump acceptance test when the installed pump is not operating precisely at its rated speed. The second set of the affinity laws assumes constant speed with change in impeller diameter, D. Q1 D1 ¼ Q2 D2
H 1 D21 ¼ H 2 D22
bh p1 D31 ¼ bh p2 D32
Pumps are selected to fit the system demands on the basis of three key points relative to their rated flow and rated pressure (Fig. 42.9). Fire pump standards such as NFPA 20 specify that centrifugal fire pumps meet these three points as noted below, and the listing laboratories verify this and establish pump performance curves for each pump. 1. A minimum of 100 % of rated pressure at 100 % of rated flow 2. A minimum of 65 % of rated pressure at 150 % of rated flow (overload) 3. A maximum of 140 % of rated pressure at 0 % of rated flow (churn) While each fire pump has its individual performance curve, a pump specifier knows the basic performance characteristics of a pump even before the performance curve is available, since it must meet the three points described above. It is usually possible to have more than one option when choosing pumps, since the designer is not limited to using a specific point on the pump performance curve. There are limits to flexibility in pump selection, however. For example, it is not permitted to install a pump in a situation where it would be expected to operate with a flow exceeding 150 % of rated capacity, since the performance is not a
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R.P. Fleming
Fig. 42.9 Pump performance curve
140
Percent of total rated head
120
Rated capacity
100
Total rated head
80 60 40 20
0
50
100
150
200
Percent of rated capacity
known factor, and indeed available pressure is usually quick to drop off beyond this point. NFPA 20 has traditionally provided guidance on what part of the pump curve to use. A centrifugal fire pump should be selected in the range of operation from 90 % to 150 % of its rated capacity. The performance of the pump when applied at capacities over 140 % of rated capacity may be adversely affected by the suction conditions, but if suction conditions can be properly assured, the pump can operate at any point on its characteristic curve from shutoff to 150 % of its rated capacity. Application of the pump at capacities less than 90 % of the rated capacity is not recommended. Where specific pump performance curve is not available, the adequacy of a pump can be determined on the basis of the required performance points. For design capacities below the rated capacity, the rated pressure should be used. For design capacities between 100 % and 150 % of rated capacity, the pressure used should be found by the relationship made apparent by similar triangles. 0
0:35P P 0:65P ¼ 0 0:5Q 1:5Q Q where P and Q are the rated pressure and capacity, and P0 is the minimum available pressure at capacity, Q0 , where Q < Q0 < 1.5Q.
Example 12 A pump is to be selected to meet a demand of 600 gpm (2271 L/min) at 85 psi (5.86 bar). To determine whether a pump rated for 500 gpm (1893 L/min) at 100 psi (6.90 bar) would be able to meet this point without having an actual pump performance curve to work from, the above formula can be applied, with P ¼ 100, Q ¼ 500, and Q0 ¼ 600. Inserting these values gives 0 P ð0:65Þ ð100Þ ð0:35Þ ð100Þ ¼ ð0:5Þ ð500Þ ½ð1:5Þ ð500 Þ 600 0 P 65 35 ¼ 250 ð750 600Þ 0 P ¼ 65 þ 21 ¼ 86 psi ð5:93 barÞ Since the value of P0 so calculated is greater than the 85 psi (5.86 bar) required, the pump will be able to meet the demand point.
Tank Sizing Tank selection and sizing are relatively straightforward compared to fire pump selection. The most basic question is whether to use a standalone elevated storage (gravity) tank, or a pressure tank, or a suction tank in combination with a fire pump. Standards such as NFPA 22 describe the types of tanks in terms of suitable
42
Automatic Sprinkler System Calculations
construction materials, and provide design and installation requirements. From a calculation standpoint, tanks must be sized to provide the minimum durations specified by NFPA 13 or other applicable standards for the system design. Required pressures must still be available when the tanks are nearly depleted of their water supplies. Durations are based on consideration of the full hydraulic demand (i.e., all sprinklers flowing in the design area). This is a conservative assumption for an automatic sprinkler system, due to the fact that the design area itself is considered to include some conservatism, with the additional understanding that sprinkler operations take place incrementally. Because of this conservatism, it is not necessary that the duration also be provided for a hydraulically less demanding design area, which would be a design area closer to the tank. Minimum durations are generally based on hazard classification, with shorter minimum durations allowed for systems with remote alarm service to a constantly attended location. If the tank is intended to provide the needed supply without the use of a fire pump, the energy, i.e. pressure for the sprinkler system must be available due to the height of the bottom of a gravity tank or the air pressure held within a pressure tank. An important factor in gravity tank calculations is the requirement that the pressure available from elevation (calculated using 0.433 psi per foot [0.099 bar/m]) must be determined using the lowest expected level of water in the tank. This is normally the point at which the tank would be considered empty. In sizing pressure tanks, the percentage of air in the tanks must be controlled so as to ensure that the last remaining quantity of water leaving the tank will be flowing at an adequate pressure. While a common rule of thumb has been that one-third of the tank’s volume consist of air at a minimum pressure of 75 psi (5.17 bar), this rule does not hold true for systems with high pressure demands or where the tank is located a considerable distance below the level of the highest sprinkler.
1441
For pipe schedule systems, two formulas have traditionally been used, based on whether the tank is located above the level of the highest sprinkler or some distance below. For the tank above the highest sprinkler P¼
30 15 A
For the tank below the highest sprinkler 30 0:434H P¼ 15 þ A A where A ¼ Proportion of air in the tank P ¼ Air pressure carried in the tank in psi H ¼ Height of the highest sprinkler above the tank bottom in ft It can be seen that these formulas are based simply on the need to provide a minimum pressure of 15 psi (1.03 bar) to the system at the level of the highest sprinkler, and an assumption of 15 psi (1.03 bar) atmospheric pressure. Using the same approximation for atmospheric pressure, a more generalized formula has come into use for hydraulically designed systems: Pi ¼
P f þ 15 15 A
where Pi ¼ Tank air pressure to be used Pf ¼ System pressure required per hydraulic calculations A ¼ Proportion of air in the tank Example 13 A pressure tank is to be used to provide a 30 min water supply to a system with a hydraulically calculated demand of 140 gpm (530 L/min) at a pressure of 118 psi (8.14 bar). Due to nearby component pressure ratings, it is important that air pressure in the tank not exceed 175 psi (12.0 bar). To determine the minimum size tank that can be used, it is important not only to consider the total amount of water needed, but also the amount of air necessary to keep the pressures within the stated limits of 118 and 175 psi.
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R.P. Fleming
The above equation for hydraulically designed systems can be used to solve for A. P f þ 15 Pi ¼ 15 A If P f þ 15 A¼ ðPi þ 15Þ ð118 þ 15Þ 133 ¼ ¼ 0:70 A¼ ð175 þ 15Þ 190 then This means that the tank will need to be 70 % air if the air pressure in the tank is to be kept to 175 psi (12.0 bar). The minimum water supply required is 30 min 140 gpm ¼ 4200 gal (15,898 L). Thus, the minimum tank volume will be such that 4200 gal (15,898 L) can be held in the remaining 30 % of volume. 0:3V ¼ 4, 200 gal 4, 200 V¼ ¼ 14, 000 gal tank ð53, 000 LÞ 0:3
Hanging and Bracing Methods Hangers and Hanger Supports Sprinkler design standards such as NFPA 13 contain a great deal of specific guidance relative to hanger spacing and sizing based on pipe sizes. It should be recognized that performance-based approaches are also often permitted. Different criteria can exist for individual hangers and their connection to the supporting building structure. For example, NFPA 13 considers any hanger and installation method is acceptable if certified by a registered professional engineer to meet the following criteria: 1. Hangers are capable of supporting five times the weight of the water-filled pipe plus 250 lb (114 kg) at each point of piping support. 2. Points of support are sufficient to support the sprinkler system.
3. Spacing between hangers does not exceed the limits within the standard for the various types of piping materials. 4. Ferrous materials are used for hanger components. 5. Detailed calculations are submitted when required by the reviewing authority. The building structure itself must be capable of supporting the weight of the water-filled pipe plus 250 lbs (114 kg) applied at the point of hanging. The 250 lb (114 kg) weight is intended to represent the extra loading that would occur if a relatively heavy individual were to hang on the piping.
Trapeze Hangers Trapeze hangers are used where structural members are not located, so as to provide direct support of sprinkler lines or mains. This can occur when sprinkler lines or mains run parallel to structural members such as joists or trusses. Because they are considered part of the support structure, the criteria within NFPA 13 call for the hangers to support the weight of 15 ft (5 m) of water-filled pipe plus 250 lbs (114 kg) applied at the point of hanging. An allowable bending stress of 15 ksi (103 MPa) is used for steel members. Two tables are provided in the standard, one of which presents required section moduli based on the span of the trapeze and the size and type of pipe to be supported, and the other of which presents the available section moduli of standard pipes and angles typically used as trapeze hangers. In using the tables, the standard allows the effective span of the trapeze hanger to be reduced if the load is not at the midpoint of the span. The equivalent length of trapeze is determined from the formula L¼
4ab ð a þ bÞ
where L is the equivalent length, a is the distance from one support to the load, and b is the distance from the other support to the load.
42
Automatic Sprinkler System Calculations
Example 14 A trapeze hanger is required for a main running parallel to two beams spaced 10 ft (3.048 m) apart. If the main is located 1 ft 6 in. (0.457 m) from one of the beams, the equivalent span of trapeze hanger required can be determined by using the formula L¼
4ð1:5 ftÞ ð8:5 ftÞ ¼ 5:1 ftð1:554 mÞ ð1:5 ft þ 8:5 ftÞ
Earthquake Braces Protection for sprinkler systems in earthquake areas is provided in several ways. Flexibility and clearances are added to the system where necessary to avoid the development of stresses that could rupture the piping. Too much flexibility could also be dangerous, however, since the momentum of the unrestrained piping during shaking could result in breakage of the piping under its own weight or on collision with other building components. Therefore, lateral and longitudinal bracing is required for all mains and lateral bracing is required for branch lines exceeding 2 in. (50 mm) in diameter. Smaller branch lines are required to be restrained against movement, which involves a less rigorous means of holding the piping in place. Calculating loads for earthquake braces is based on the assumption that the normal hangers provided to the system are generally capable of handling vertical forces. However, the upward vertical component of strong horizontal forces must be addressed where braces are insufficiently angled from the horizontal. Traditionally, horizontal forces were conservatively approximated by a constant acceleration equal to one-half that of gravity. ah ¼ 0:5g Due to advances in earthquake engineering, more specific mapping of expected earthquake accelerations is now available. Current codes call for the design of mechanical building systems to be based on maximum short-period (0.2 s) accelerations expected for the 500 year earthquake. NFPA 13 (2013) contains a seismic
1443
coefficient table that allows a simplified method by which these accelerations can be converted to the horizontal seismic load for braces using the formula F pw ¼ C p W p where Fpw is the force acting on the brace, Cp is the seismic coefficient selected in the table on the basis of short period response, and Wp is 1.15 times the weight of water-filled piping supported by the brace. Table 42.6 contains some of the NFPA 13 seismic coefficients based on short period accelerations, where the horizontal accelerations Ss are expressed relative to gravity. The seismic coefficients are based on the assumption of fairly soft soil and other conservative assumptions. Since the braces can be called on to act in both tension and compression, it is necessary not only to size the brace member to handle the expected force applied by the weight of the pipe in its zone of influence, but also to avoid a member that could fail as a long column under buckling. The ability of the brace to resist buckling is determined through an application of Euler’s formula. Tables provide loads based on maximum slenderness ratios of 100, 200, and 300. The 300 value corresponds to the maximum slenderness ratio generally used under steel construction codes for secondary framing members. This is expressed as
Table 42.6 Seismic coefficient table Ss 0.33 or less 0.50 0.75 0.95 1.00 1.25 1.50 2.00 2.40 3.00 Source: NFPA 13, Table 9.3.5.9.3 (2013)
Cp 0.35 0.40 0.42 0.50 0.51 0.58 0.70 0.93 1.12 1.40
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R.P. Fleming
ℓ 300 r where ℓ is the length of the brace and r is the least radius of gyration for the brace. The least radius of gyration for some common shapes is as follows: pipe r¼
r 20 þ r 2i 2
1=2
rod r¼
r 2
flat r ¼ 0:29h Special care must be taken in the design of earthquake braces so that the load applied to any brace does not exceed the capability of the fasteners of that brace to the piping system or the building structure, and that the braces are attached only to structural members capable of supporting the expected loads.
Performance Calculations Sprinkler Response as a Detector Automatic sprinklers serve a dual function as both heat detectors and water distribution devices. As such, the response of sprinklers can be estimated using the same methods as for response of heat detectors (see Chap. 40). Care should be taken, however, that these calculations are used within their limitations. Factors pertaining to sprinkler orientation, air flow deflection, radiation effects, heat of fusion of solder links, and convection within glass bulbs are all considered to introduce minor errors into the calculation process. Heat conduction to the sprinkler frame and distance of the sensing mechanism below the ceiling have been demonstrated to be significant factors affecting response, but are ignored in some computer
models. Efforts have been made to quantify the prediction capability of the models, including DETACT-QS and the more recent Fire Dynamics Simulator (FDS) [9]. Modeling of sprinkler response can be useful, particularly when used on a comparative basis. Beginning with the 1991 edition, an exception within NFPA 13 permitted variations from the rules on clearance between sprinklers and ceilings “. . .provided the use of tests or calculations demonstrate comparable sensitivity and performance.” Example 15 Nonmetallic piping extending 15 in. (0.38 m) below the concrete ceiling of a 10-ft (3.048 m) high basement 100 ft by 100 ft (30.48 30.48 m) in size makes it difficult to place standard upright sprinklers within the 12 in. (0.30 m) required by NFPA 13 for unobstructed construction. Using the LAVENT [10] computer model, and assuming RTI values of 400 ft1/2 s1/2 (221 m1/2 s1/2) for standard sprinklers and 100 ft1/2 s1/2 (55 m1/2 s1/2) for quickresponse sprinklers, it can be demonstrated that the comparable level of sensitivity can be maintained at a distance of 18 in. (0.457 m) below the ceiling. Temperature rating is assumed to be 165 F, and maximum lateral distance to a sprinkler is 8.2 ft (2.50 m) (10 ft 13 ft [3.048 m 3.962 m] spacing). Assuming the default fire (empty wood pallets stored 5 ft [1.52 m] high), for example, the time of actuation for the standard sprinkler is calculated to be 200 s, as compared to 172 s for the quick-response sprinkler. Since the noncombustible construction minimizes concern relative to the fire control performance for the structure, the sprinklers can be located below the piping obstructions.
Dry System Water Delivery Time Total water delivery time consists of two parts. The first part is the trip time taken for the system air pressure to bleed down to the point where the system dry valve opens to admit water to the piping. The second part is the transit time for
42
Automatic Sprinkler System Calculations
the water to flow through the piping from the dry valve to the open sprinkler. In other words Water delivery time ¼ Trip time þ Transit time where water delivery time commences with the opening of the first sprinkler. Sprinkler standards such as NFPA 13 have traditionally not contained a maximum water delivery time requirement if system volume is limited, generally to no more than 750 gal (2839 L). Larger systems were permitted only if water flow from a remote inspector’s test connection took place within 60 s. As such, the rule of thumb for dry system operation is that no more than a 60-s water delivery time should be tolerated, and that systems should be divided into smaller systems if necessary to achieve this 1-min response. Beginning with the 2007 edition of NFPA 13, the 60-s water delivery time was mandated for dry pipe systems protecting dwelling unit portions of any building. Dry system response is simulated in field testing by the opening of an inspector’s test connection. The inspector’s test connection is required to be at the most remote point of the system from the dry valve, and is required to have an orifice opening of a size simulating the smallest orifice sprinkler installed on the system. The water delivery time of the system is recorded as part of the dry pipe valve trip test that is conducted using the inspector’s test connection. However, it is not a realistic indication of actual water delivery time for two reasons: 1. The first sprinkler to open on the system is likely to be closer to the system dry valve, reducing water transit time. 2. If additional sprinklers open, the trip time will be reduced since additional orifices are able to expel air. Water transit time may also be reduced since it is easier to expel the air ahead of the incoming water. FM Global researchers have shown [11] that it is possible to calculate system trip time using the relation VT pa0 t ¼ 0:0352 ln 1=2 pa An T 0
1445
where t ¼ Time (s) VT ¼ Dry volume of sprinkler system (ft3) T0 ¼ Air temperature ( R) An ¼ Flow area of open sprinklers (ft2) pa0 ¼ Initial air pressure (absolute) pa ¼ Trip pressure (absolute) Calculating water transit time is more difficult, but may be accomplished using mathematical models. FM Global researchers developed the first such model in the 1970s. In 2003 a dry system water delivery model was introduced to the commercial marketplace [12], following the incorporation of acceptance criteria into the 2002 edition of NFPA 13. A literature review conducted in 2007, intended to develop data to assist in the evaluation of the traditional 60-s water delivery requirement of NFPA 13, observed that “the water delivery time limit of 60 s has some, but not overwhelming data to support requiring or not requiring a time limitation for small systems” [13].
Droplet Size, Penetration and Motion For geometrically similar sprinklers, the median droplet diameter in the sprinkler spray has been found to be inversely proportional to the 1/3 power of water pressure and directly proportional to the 2/3 power of sprinkler orifice diameter such that dm /
D2=3 D2 / 2=3 1=3 p Q
where dm ¼ Mean droplet diameter D ¼ Orifice diameter P ¼ Pressure Q ¼ Rate of water flow The relationship of droplet size production to pressure and orifice diameter has been confirmed using high-magnification shadow imaging [14]. A sprinkler “penetration ratio” has likewise been observed to be proportional to the median droplet diameter, which is needed for fire plume penetration when the sprinkler spray is in the
1446
R.P. Fleming
gravity mode [15]. However, fire plumes can also be penetrated by water sprays using a momentum mode. Fire plume penetration is considered essential to the early suppression of the fire by automatic sprinklers, as compared to fire control, in which the spread of the fire is stopped and the impact mitigated. Total droplet surface area has been found to be proportional to the total water discharge rate divided by the median droplet diameter As /
Q dm
where As is the total droplet surface area. Combining these relationships, it can be seen that 1=3 As / Q3 pD2 When a droplet with an initial velocity vector of U is driven into a rising fire plume, the one-dimensional representation of its motion has been represented as [16] CD ρg ðU þ V Þ2 m1 dU ¼ m1 g dt 2S f where U ¼ Velocity of the water droplet V ¼ Velocity of the fire plume m ¼ Mass of the droplet ρg ¼ Density of the gas g ¼ Acceleration of gravity CD ¼ Coefficient of drag Sf ¼ Frontal surface area of the droplet The first term on the right side of the equation represents the force of gravity, while the second term represents the force of drag caused by gas resistance. The drag coefficient for particle motion has been found empirically to be a function of the Reynolds number (Re) as [17] CD ¼ 18:5 Re0:6 for Re < 600 CD ¼ 0:44 for Re > 600 Mathematical modeling comparing the drag force of a sprinkler spray to the buoyancy of a smoke layer in the vicinity of sprinklers, validated by full scale experiments, has been
used recently to address the long-standing question of the value of automatic smoke vents in sprinklered buildings. The modeling indicated that increases in sprinkler operating pressure eventually lead to ineffective smoke venting, and that the area of smoke venting has very little influence on smoke flow once sprinkler operation causes a loss in smoke flow efficiency [18].
Spray Density and Cooling The heat absorption rate of a sprinkler spray is expected to depend on the total surface area of the water droplets, As, and the temperature of the ceiling gas layer in excess of the droplet temperature, T. With water temperature close to ambient temperature, T can be considered excess gas temperature above ambient. Chow [19] has developed a model for estimating the evaporation heat loss due to a sprinkler water spray in a smoke layer. Sample calculations indicate that evaporation heat loss is only significant for droplet diameters less than 0.5 mm. For the droplet velocities and smoke layer depths analyzed, it was found that the heat loss to evaporation would be small (10–25 %), compared to the heat loss from convective cooling of the droplets. FM Global researchers [20] have developed empirical correlations for the heat absorption rate of sprinkler spray in room fires, as well as convective heat loss through the room opening, such that Q_ ¼ Q_ cool þ Q_ c þ Q_ l where Q_ ¼ Total heat release rate of the fire Q_ cool ¼ Heat absorption rate of the sprinkler spray Q_ c ¼ Convective heat loss rate through the room opening _ Q l ¼ Sum of the heat loss rate to the walls and ceiling, Q_ s , the heat loss rate to the floor, Q_ f , and the radiative heat loss rate through the opening, Q_ r
42
Automatic Sprinkler System Calculations
"
Test data indicated that Q_ cool =Q_ ¼ 0:000039Λ3 0:003Λ2 þ 0:082Λ For
0 < Λ 33= min kW
1=2
m
5=4
where Λ is a correlation factor incorporating heat losses to the room boundaries and through openings as well as to account for water droplet surface area. 1=2 3 2 1=3 Λ ¼ AH 1=2 Q_ l W PD for P¼
p ð17:2 kPaÞ
1447
and
D¼
d 0:0111 m
where A ¼ Area of the room opening (m) H ¼ Height of the room opening (m) P ¼ Water pressure at the sprinkler (bar) d ¼ Sprinkler nozzle diameter (m) W ¼ Water discharge (L/min) The above correlations apply to room geometry with length-to-width ratio of 1.2–2 and opening size of 1.70–2.97 m2.
Suppression by Sprinkler Sprays In 1993, researchers at the National Institute of Standards and Technology (NIST) developed a “zeroth order” model of the effectiveness of sprinklers in reducing the heat release rate of furnishing fires [21]. Based on measurements of wood crib fire suppression with pendant spray sprinklers, the model was described as conservative. The model assumed that all fuels have the same degree of resistance to suppression as a wood crib, despite the fact that tests have shown furnishings with large burning surface areas can be extinguished easily compared to the deep-seated fires encountered with wood cribs. The recommended equation, which relates to fire suppression for a 610-mm-high crib, has also been checked for validity with 305 mm crib results. The equation is
ðt tact Þ Q_ ðt tact Þ ¼ Q_ ðtact Þexp 00 1:85 3:0 w_
#
where Q_ ¼ Heat release rate (kW) t ¼ Any time following tact of the sprinklers (s) 00 W_ ¼ Spray density (mm/s) The NIST researchers claimed the equation was appropriate for use where the fuel is not shielded from the water spray, and the application density is at least 0.07 mm/s (4.2 mm/min [0.1 gpm/ft2]). The method does not account for variations in spray densities or suppression capabilities of individual sprinklers. The model must be used with caution, since it was developed on the basis of fully involved cribs. It does not consider the possibility that the fire could continue to grow in intensity following initial sprinkler discharge, and, for that reason, should be restricted to use in light hazard applications. Sprinklers are assumed to operate within a room of a light hazard occupancy when the total heat release rate of the fire is 500 kW. The significance of an initial application rate of 0.3 gpm/ft2 (0.205 mm/s) as compared to the minimum design density of 0.1 gpm/ft2 (0.07 mm/s) can be evaluated by the expected fire size after 30 s. With the minimum density of 0.07 mm/s (0.1 gpm/ft2), the fire size is conservatively estimated as 465 kW after 30 s. With the higher density of 0.205 mm/s (0.3 gpm/ft2), the fire size is expected to be reduced to 293 kW after 30 s. Corresponding values after 60 s are 432 and 172 kW, respectively. More recent efforts to model suppression by automatic sprinklers have taken place as part of the NIST’s development of the Fire Dynamics Simulator (FDS) computational fluid dynamics model. Within that model, simulating the effects of a sprinkler spray involves predicting activation, computing droplet trajectories, and tracking water as it drips onto the burning fuel. In order to compute droplet trajectories, the initial size and velocity of each droplet must be estimated, a process that is one of the limiting factors in the use of the model for practical applications. As stated earlier, efforts have been under way to
1448
R.P. Fleming
develop atomization models for integration with FDS to better characterize the formation and distribution of droplets from the impact of a water stream on a sprinkler deflector [22, 23]. The effect of droplets on burning surfaces is another area in which additional work is needed. When dealing with liquid droplets hitting a solid surface, the current Version 5 of FDS assigns a random horizontal direction and moves at a fixed velocity on the order of 0.5 m/s until it reaches the edge, at which point it is assumed to drop down at the same velocity. While on the surface, the droplet is assumed to contribute to the formation of a surface film of water that participates in heat transfer. If the surface is burning, assumptions need to be made about the extent to which the water reduces the pyrolysis rate of the fuel. Most of the available correlations are based on fires involving rack storage of standard commodities in corrugated cartons. Work at Factory Mutual [24] has led to the following expression: Q_ ¼ Q_ o ekðttoÞ where Q_ o is the total heat release at the time of water application to and k is a fuel-dependent constant, which in turn is dependent on the rate of water application.
Nomenclature C FLC Q Q_ _ 00 W Cp K
coefficient of friction friction loss coefficient flow (gpm) heat release rate (kW) spray density (mm/s) seismic coefficient fuel-dependent constant
References 1. NFPA Codes and Standards, National Fire Protection Association, Quincy, MA (2013). 2. Thomas, R., “Water Conservation and Sustainable Use in Fire Suppression Systems,” SUPDET 2009
Suppression & Detection Conference, Fire Protection Research Foundation (2009). 3. Palenske, G. and O’Connor, D., “Single Point Design Criteria vs. Traditional Density-Area Curves,” Fire Protection Research Foundation, (2007). 4. Croce, P., Hill, J., and Xin, Y., “An Investigation into the Causative Mechanism of Sprinkler Skipping,” Journal of Fire Protection Engineering, Vol. 15, No. 2 (2005). 5. Ditch, B., de Ris, J., and Yu, H.Z., “Development and Experimental Evaluation of a Sprinkler Resistant to Skipping,” SUPDET Suppression and Detection Conference, Fire Protection Research Foundation (2009). 6. K. McGrattan, S. Hostikka, J. Floyd, H. Baum, and E. Rehm, “Fire Dynamics Simulator (Version 5) Technical Reference Guide,” NIST Special Publication 1018–5, National Institute of Standards and Technology, Gaithersburg, MD (2007). 7. A. Marshall, “Unraveling Fire Suppression Sprays,” International Association of Fire Safety Science, College Park, MD, (2011). 8. H. Cross, Analysis of Flow in Networks of Conduits or Conductors, University of Illinois Engineering Experiment Station, Urbana, IL (1936). 9. M. J. Hurley and A. Munguia, “Analysis of Prediction Capability of FDS for Response of Thermal Detectors,” Journal of Fire Protection Engineering, Vol. 20, No. 2 (2010) 10. W.D. Davis and L.Y. Cooper, “Estimating the Environment and Response of Sprinkler Links in Compartment Fires with Draft Curtains and Fusible-Link Actuated Ceiling Vents, Part 2: User Guide for the Computer Code LAVENT,” NISTIR/89-4122, National Institute of Standards and Technology, Gaithersburg, MD (1989). 11. G. Heskested and H. Kung, FMRC Serial No. 15918, Factory Mutual Research Corp., Norwood, MA (1973). 12. Golinveaux, J., “Taking the Guesswork out of the Numerous Variables That Impact the Water Delivery Time of Dry-Pipe Sprinkler Systems,” NFPA Journal, March/April (2004). 13. O’Connor, D., Pennel, G., Cohn, B., Cul, E., Sun, Z., and Gummersail, M., “Review of NFPA 13 Dry System Water Delivery Provisions,” Fire Protection Research Foundation, (2007). 14. M. Avila, H. Boham, Z. Magnone, R. Winsten, C. Yueshan, and N. Dembsey, “Droplet Characterization Using Direct Imaging Techniques,” SupDet Conference March 8, 2012, Fire Protection Research Foundation, (2012). 15. C. Yao, C., “Overview Of Sprinkler Technology Research,” Fire Safety Science 5: 93–110.doi:10. 3801/IAFSS.FSS.5-93, (1997) 16. C. Yao and A.S. Kalelkar, “Effect of Drop Size on Sprinkler Performance,” Fire Technology, 6, 4 (1970). 17. C.L. Beyler, “The Interaction of Fire and Sprinklers,” NBS GCR 77–105, National Bureau of Standards, Washington, DC (1977).
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Automatic Sprinkler System Calculations
18. K.Y. Li, M. J. Spearpoint, J. Ji, R. Huo, Y.Z. Li and L. H. Hu, “A Mathematical Model of the Drag Component of a Sprinkler Spray Adjacent to Horizontal Smoke Vents,” Journal of Fire Protection Engineering, Vol. 20, No. 1 (2010) 19. W.K. Chow, “On the Evaporation Effect of a Sprinkler Water Spray,” Fire Technology, pp. 364–373 (1989). 20. H.Z. You, H.C. Kung, and Z. Han, “Spray Cooling in Room Fires,” NBS GCR 86–515, National Bureau of Standards, Washington, DC (1986). 21. D.D. Evans, “Sprinkler Fire Suppression Algorithm for HAZARD,” NISTIR 5254, National Institute of Standards and Technology, Gaithersburg, MD (1993). 22. D. Wu, D. Guillemin, and A.W. Marshall, “A Modeling Basis for Predicting the Initial Sprinkler Spray,” Fire Safety Journal, 42, pp. 283–294 (2007). 23. Tabaddor, M., Dubriel, D., Troolin, D., and Hart, P., “Complex Spray Pattern Measurements for Fire
1449 Sprinkler Modeling,” SUPDET Suppression, Detection and Signaling Conference, Fire Protection Research Foundation, (2011). 24. H.Z. Yu, J.L. Lee and H. C. Kung, “Suppression of Rack-Storage Fires by Water,” Fire Safety Science— Proceedings of the Fourth International Symposium, pp. 901–912, International Association for Fire Safety Science (1994). Russell P. Fleming is Managing Director of the International Fire Sprinkler Association, Patterson, New York. Mr. Fleming has served as a member of 20 different NFPA technical committees, including 30 years as a member of the Committee on Automatic Sprinklers. He is a past president of SFPE, past chair of the Standards Council and past member of the Board of Directors of NFPA.
Halon Design Calculations
43
Casey C. Grant
Introduction Fire protection systems using halogenated extinguishing agents provide a classic example of a fire protection technology with a comprehensive evolutionary lifespan. These systems are a relatively recent innovation in fire protection, but, despite this, they already face extinction. As of January 1, 1994, the production of fire protection halons in most countries ceased, based on international treaties. The phase-out of halon agent production has obviously created significant limitations on the proliferation of this technology. Yet despite this phase-out numerous systems still exist today based on agent reserves. Although global production of fire protection halons essentially ceased on January 1, 1994, this technology continues to linger. Accordingly, a need remains to address the modification and maintenance of existing systems, and new essential systems that will use recycled surplus stock of halon. The stratospheric ozone layer depletion issue is a problem confronting the global community unlike any other. Late in 1987, the United States and 24 other countries (including the European Economic Community) signed the Montreal Protocol to protect stratospheric ozone [1]. Originally, the protocol restricted the consumption of ozonedepleting chlorofluorocarbons (CFCs) to 50% of C.C. Grant (*) Executive Director of the Fire Protection Research Foundation
the 1986 use levels by 1998, and halon production was to be frozen in 1993 at 1986 production levels. But the November 1992 Copenhagen revision to the Montre´al Protocol accelerated this, such that all production of the chemicals ceased worldwide as of January 1, 1994. The Montreal Protocol is based on unprecedented trade restrictions and is the first time nations of the world have joined forces to address an environmental threat in advance of fully established effects. The trade restrictions concern nations not participating in the agreement (the nonsignatories). Within 1 year of the agreement taking effect, each party shall ban the import of the bulk chemicals from the nonsignatory nations. About 4 years after the effective date of the agreement, imports of products containing the identified chemicals from nonsignatory nations are banned. Within 5 years, products made with the chemicals (but not containing them) are banned or restricted. This is truly significant since many products, including many electronic components, are currently manufactured using some of these chemicals.
Characteristics of Halon Background, Definition, and Classifications of Halon Compounds Although there are a variety of methods available for applying halogenated agents, the most common is the total flooding system. The most
M.J. Hurley (ed.), SFPE Handbook of Fire Protection Engineering, DOI 10.1007/978-1-4939-2565-0_43, # Society of Fire Protection Engineers 2016
1450
43
Halon Design Calculations
popular halogenated agent is Halon 1301, with its superior fire extinguishing characteristics and low toxicity. Halogenated extinguishing agents are hydrocarbons in which one or more hydrogen atoms have been replaced by atoms from the halogen series: fluorine, chlorine, bromine, or iodine. This substitution confers flame extinguishing properties to many of the resulting compounds that made them ideal for certain fire protection applications. The halogenated extinguishing agents are currently known simply as halons, and are described by a nomenclature that indicates the chemical composition of the materials without the use of chemical names. This simplified system was proposed by James Malcolm at the U.S. Army Corps of Engineers Laboratory in 1950 and avoids the use of possibly confusing names [2]. The United Kingdom and parts of Europe have been known to use the initial capital “alphabet” system, that is, bromotrifluoromethane (Halon 1301) is BTM and bromochlorodifluoromethane (Halon 1211) is BCF. The number definition for the chemical composition of Halon 1301, perhaps the most widely recognized halogenated extinguishing agent, is 1 (carbon), 3 (fluorine), 0 (chlorine), 1 (bromine), and 0 (iodine). By definition, the first digit of the number represents the number of carbon atoms in the compound molecule; the second digit, the number of fluorine atoms; the third digit, the number of chlorine atoms; the fourth digit, the number of bromine atoms; and the fifth digit, if any, the number of iodine atoms. Trailing zeros in this system are not expressed. Figure 43.1 graphically demonstrates this concept by illustrating Halon 1301 in comparison to methane. There are three halogen elements commonly found in halon extinguishing agents used for fire protection: fluorine (F), chlorine (Cl), and bromine (Br). Compounds containing combinations of fluorine, chlorine, and bromine can possess varying degrees of extinguishing effectiveness, chemical and thermal stability, toxicity, and volatility. In general, the relevant properties of these three halogen elements are characterized as shown in Table 43.1.
1451 Halogenated hydrocarbon (Halon 1301)
Methane H
H
C
F
H
F
C
F
Br
H
Fig. 43.1 Molecular composition of methane and Halon 1301 Table 43.1 Contributing characteristics of fluorine, chlorine, and bromine Stability to compound Toxicity Boiling point Thermal stability Fire extinguishing Effectiveness
Fluorine Enhances Reduces Reduces Enhances —
Chlorine — Enhances Enhances Reduces Enhances
Bromine — Enhances Enhances Reduces Enhances
Due to the many chemical combinations available, the characteristics of halogenated fire extinguishing agents differ widely. It is generally agreed that the agents most widely used for fire protection applications are Halon 1301, Halon 1211, Halon 1011, and Halon 2402. Also somewhat common is Halon 122, which has been used as a test gas because of its economic advantages. However, because of its widespread use as a test agent, many individuals have wrongly assumed that Halon 122 is an effective fire extinguishing agent. Table 43.2 illustrates the halogenated hydrocarbons most likely to be used today.
History The earliest halogenated fire extinguishing agent known to be used for industrialized fire protection was carbon tetrachloride (Halon 104) [3]. First becoming available as early as 1907, it was most widely used in handpump portable extinguishers and was popular due to its low electrical conductivity and lack of residue
1452
C.C. Grant
following application. Also referred to as “pyrene” extinguisher fluid, Halon 104 caused a number of accidental deaths and serious injuries due to its toxicity, and eventually its use was halted during the 1950s. Methyl bromide (Halon 1001) gained popularity after it was discovered in the late 1920s to be a more effective extinguishing agent than carbon tetrachloride. Due to its high toxicity, it was never used in portable extinguishers even though it was used extensively in British and German aircraft and ships during World War II. Interestingly, methyl bromide possesses a narrow flammability range between 13.5 % and 14.5 % in air, though above and below this range it is an efficient fire extinguishant. Germany developed bromochloromethane (Halon 1011) in the late 1930s to replace methyl bromide, but it failed to enjoy widespread use until after World War II [4].
Table 43.2 Halons commonly used for fire protection Chemical name Methyl bromide Methyl iodide Bromochloromethane Dibromodifluoromethane Bromochlorodifluoromethane Dichlorodifluoromethane* Bromotrifluoromethane Carbon tetrachloride Dibromotetrafluoroethane
Formula Halon number CH3Br 1001 CH3I 10001 CH2BrCl 1011 CF2Br2 1202 CF2BrCl 1211 CF2Cl2 122 CF3Br 1301 CCl4 104 C2F4Br2 2402
*A previously popular test gas without substantial fire extinguishing properties
Thus, prior to World War II, three halogenated fire extinguishing agents were available: Halon 104, Halon 1001, and Halon 1011. Yet because of their inherently high toxic nature, these agents slowly disappeared from typical system applications. By the mid-1960s Halon 104 and Halon 1001 were no longer being used, and Halon 1011 was only in limited use for specialized explosion suppression applications. Figure 43.2 represents a chronology chart that indicates the usage of these early halons as well as the halons more commonly used today. Joint research was undertaken in 1947 by the U.S. Army Chemical Center and the Purdue Research Foundation to evaluate the fire suppression effectiveness and toxicity of the large number of available agents [2]. After testing more than 60 new agents, 4 were selected for further study: dibromodifluoromethane (Halon 1202), bromochlorodifluoromethane (Halon 1211), bromotrifluoromethane (Halon 1301), and dibromotetrafluoromethane (Halon 2402). Further testing revealed that Halon 1202 was the most effective yet also most toxic, while Halon 1301 was the second most effective and least toxic. As a result of this testing, the use of halon to provide fire protection for modern technology took on new dimensions. Halon 1202 was used by the U.S. Air Force for military aircraft engine protection while the Federal Aviation Administration (FAA) selected Halon 1301 for a similar application in commercial aircraft engine nacelles [5]. Portable extinguishers using Halon 1301 were implemented by the U.S. Army. The use of total flooding systems Halon 1011
Halon 1001 Halon 104 1900
1910
1920
1930
1940
1950
1960
1970
Halon 1301 Halon 1211 Halon 2402 Halon 1202
Fig. 43.2 Time span usage of selected halons
1980
1990
2000
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Halon Design Calculations
originated in 1963, and in the following 5 years several total flooding systems were installed based on carbon dioxide system technology. In 1966, attention began to focus on the use of Halon 1301 for the protection of electronic data processing equipment. That year, the NFPA organized a Technical Committee (NFPA 12A) to standardize the design, installation, maintenance, and use of halon systems. Their resulting work was officially adopted by the NFPA membership as a standard in 1968 [6]. Subsequent recognition that there were differences among the halon agents made it apparent that separate standards would be necessary. The initial halon standard, NFPA 12A, Standard for Halon 1301 Fire Extinguishing Systems (hereinafter referred to as NFPA 12A), focused on the use of Halon 1301 due to its high desirability and growing popularity [7]. Work on an additional standard, NFPA 12B, Standard on Halon 1211 Fire Extinguishing Systems, concerning the use of Halon 1211, was started in 1969 and was officially adopted by the NFPA as a standard in 1972 [8]. A tentative standard on the use of Halon 2402 (NFPA 12CT) was developed, but was never officially adopted [9]. Another NFPA committee directly concerned with the use of halon is the NFPA Committee on Electronic Computer/Data Processing Equipment (NFPA 75, Standard for the Protection of Information Technology Equipment) [10]. Even though this standard was adopted in 1961, the use of halon was not considered until after 1972, when extensive testing by several major companies demonstrated that the use of Halon 1301 was suitable for protecting electronic computer and data processing equipment [11]. Halon 1301 eventually became the most widely used extinguishing agent for this purpose in the United States and throughout much of the world. However, certain areas of Europe have preferred Halon 1211 and 2402. In anticipation of the worldwide production phase-out of fire protection halons, which eventually settled at January 1, 1994, a new committee was established during 1992 within the NFPA codes- and standards-making system designated
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as the Technical Committee on Alternative Protection Options to Halon, and later renamed the Technical Committee on Halon Alternative Protection Options. The committee’s first document is NFPA 2001, Standard on Clean Agent Fire Extinguishing Systems, which addresses the design, installation, maintenance, and operation of total-flooding fire extinguishing systems that use halon replacement agents [12].
Halon 1301 Attributes and Limitations Of all the halogenated extinguishing agents used in fire protection, Halon 1301 was by a wide margin the most commonly used. The primary use of this agent is for the protection of electrical and electronic equipment, flammable liquids and gases, and surface-burning flammable solids such as thermoplastics. Areas normally or frequently occupied, air and ground vehicle engines, and other areas where rapid extinguishment is important or where damage to equipment or materials or cleanup after use must be minimized were also ideally protected by this agent. However, Halon 1301 was not a panacea, and it is appropriate to recognize its limitations as well as its attributes. The benefits of Halon 1301 are: fast chemical suppression, penetrating vapor, clean (no residue), noncorrosive, compact storage volumes, nonconductive, and colorless (no obscuration). There are also limitations to using Halon 1301: it has minimal extinguishing effectiveness on reactive metals and rapid oxidizers, it may have unfavorable side effects on deep-seated Class A fires, the agent is expensive, and it is potentially harmful to the environment. Obviously, the most significant limitation is the detrimental effect that the halons have on the earth’s stratospheric ozone layer. Because Halon 1301 inhibits the chain reaction of the combustion process, it chemically suppresses the fire very quickly, unlike other extinguishing agents that work by removing the fire’s heat or displacing oxygen or air in close proximity to the combustion zone. Stored as a liquid under pressure and released at normal room temperature as a vapor, Halon 1301 gets
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into blocked and baffled spaces readily and leaves no corrosive or abrasive residue after use. A high liquid density permits compact storage containers, which on a comparative weight basis, makes Halon 1301 approximately 2.5 times more effective as an extinguishing agent than carbon dioxide. Since it is virtually free of electrical conductivity, Halon 1301 is highly suitable for electrical fires. Halon 1301 is a colorless vapor when discharged into a hazard volume, though it sometimes temporarily clouds the volume due to the chilling of any moisture in the air. But of all its attributes, the most attractive is that of people compatibility; unlike other extinguishing agents, Halon 1301 is essentially nontoxic in the concentrations usually required for fire suppression. There are several types of flammable materials on which Halon 1301 is ineffective and not recommended. Reactive metals such as potassium, Nak eutectic alloy, magnesium, sodium, titanium, and zirconium burn so intensely that they overpower the agent’s extinguishing abilities [5]. Included with these are the metal hydrides such as lithium hydride, and petroleum solvents such as butyl-lithium. Autothermal decomposers and fuels that contain their own oxidizing agent will also burn freely in the presence of halon agents. These latter substances, such as gunpowder, rocket propellants, and cellulose nitrate, have an oxidizer physically too close to the fuel, and the agent cannot penetrate the fire zone fast enough. Halon is also not effective in preventing the combustion or reaction of chemicals capable of autothermal decomposition such as hydrazine or organic peroxides. Even though Halon 1301 is effective with certain surface-burning flammable solids such as thermoplastics, deep-seated Class A fires typically require relatively high agent concentrations for long soaking periods. When exposed to deep-seated fires for long periods of time, Halon 1301 may decompose into toxic and corrosive products of decomposition. Therefore, it is important that the agent be dispersed while the fire is small. The expense necessary to purchase, install, and maintain a properly functioning Halon 1301 system for more specific Class A
C.C. Grant
hazards is often not economically justified. Halon 1301 fire suppression systems are usually not associated with everyday commodities, but instead are found in applications pertaining to highly valued risks.
Properties Physical Properties On the average, Halon 1301 requires 10% less agent on a gas-volume basis than does Halon 1211 to extinguish any given fuel [2]. However, both agents are approximately 2.5 times more effective on a weight-of-agent basis than carbon dioxide. Halon 1301 is a gas at 70 F (21 C) with a vapor pressure of 199 psig. Although this pressure would adequately expel the material, it decreases rapidly to 56 psig (4 bar) at 0 F (18 C) and to 17.2 psig (1.2 bar) at 40 F (40 C). Therefore, it is necessary to increase the container pressure with dry nitrogen either to 360 or 600 psig (25 or 41 bar) at 70 F (21 C), ensuring adequate performance at all temperatures. Figure 43.3 demonstrates the temperature-pressure profile for Halon 1301 and Halon 1301 superpressurized with dry nitrogen. Halon 1301 is normally stored in a pressure vessel as a liquid before it is released to occupy the hazard volume as a vapor. With a boiling point of 72 C (58 C), it is approximately 1.5 times more dense than water in its liquid phase and approximately 5 times heavier than air in its vapor phase. Thus, Halon 1301 vapor will typically escape through openings in the low portions of a totally flooded volume. Other physical properties are shown in Table 43.3. Traditionally, there were three distinct elements assumed for combustion: heat, fuel, and oxygen. Known as the fire triangle, this theory had to be modified as halons became more widely used and better understood. Typical fire extinguishment involves either removing the fuel from the fire, limiting oxygen to the fire (smothering), or removing the heat (quenching). The halons do not extinguish fire in any of these ways, but instead break up the uninhibited chain reaction of the combustion process. The tetrahedron of the fire, as it is called, is shown in Fig. 43.4.
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Halon Design Calculations
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Fig. 43.3 Temperaturepressure relationship for pure Halon
70
1500
60 1400 50 lb/ft 3 )
1300
ity (
1200
Fill d
50
900 800 700 600
F 0° t7 a ig ps
500
0 60
400
F 0° t7 a g psi 360 01 13 n o al eH Pur
300 200 100 0 –40 –20
0
20
40
60
Fill den sit
y (lb /ft 3)
1000 Pressure (psig)
60
ens
1100
70
Critical point 560.2 psig 152.6°F
80 100 120 140 160 180
Temperature (°F)
Table 43.3 Selected physical properties of Halon 1301
Temperature
72.0 F 270.4 F 1.57 5.14 98.0 lb/ft3 7.49 lb/ft3 (standard) 152.6 F 575 PSIA
Fuel
Boiling point Freezing point Specific gravity of liquid (@70 F) Specific gravity of vapor (@70 F) Liquid density @70 F Vapor density @70 F Critical temperature Critical pressure
The extinguishing mechanism of the halogenated agents is not completely understood, yet there is definitely a chemical reaction that interferes with the combustion process. The halogen atoms act by removing the active chemical species involved in the flame chain reaction. While all the halogens are active in this way, bromine is much more effective than chlorine or fluorine. With Halon 1301 (54% by weight
Oxygen
Uninhibited chain reaction of combustion process
Fig. 43.4 The tetrahedron of fire
bromine), it is the bromine radical that acts as the inhibitor in extinguishing the fire. Yet the fluorine in the molecule also serves a specific task since it is the fluorine that gives the agent thermal stability and keeps Halon 1301 from decomposing until approximately 900 F (480 C) [13].
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Ordinary
Flammable
Electrical
Combustible
A
B
C
D
combustibles
liquids
equipment
metals
Fig. 43.5 The four classes of fire
Extinguishing Effectiveness As shown in Fig. 43.5, the four types of fire are ordinary combustibles (Class A), flammable liquids and gases (Class B), electrical (Class C), and reactive metals (Class D) [5]. It was previously mentioned that Halon 1301 is ineffective on Class D fires and is not as desirable as other agents in extinguishing deep-seated Class A fires. The effectiveness of Halon 1301 on Class A fires is not as predictable as with other classes of fire. It depends to a large extent upon the burning material, its configuration, and how early in the combustion cycle the agent is applied. Most plastics behave as flammable liquids and can be extinguished rapidly and completely with 4–6% concentrations of Halon 1301 [14]. Other materials, particularly cellulosic products, can in certain forms develop deepseated fires in addition to flaming combustion. The flaming portion of such fires can be extinguished with low 4–6% Halon 1301 concentrations, but the glowing deep-seated portion of the fire may continue under some circumstances. Even so, the deep-seated fire can be controlled since its rate of burning and consequent heat release will be reduced. Considerably higher concentrations (18–30%) of Halon 1301 are required to achieve complete extinguishment, but these levels are seldom economical to apply and their application may result in unwanted products of decomposition. However, the concept of controlling deep-seated fires with halogenated agents has been accepted in the respective NFPA standards [14]. It is Class B and Class C fires for which halon is particularly well suited. The most common applications involve Class C electrical hazards, with the increase in popularity of Halon 1301 keeping well in stride with the development of high technology. Typically, electrical and
electronic equipment are protected with a concentration of 5% Halon 1301 by volume, though a significantly lower concentration will suitably extinguish a potential fire [15]. The concentrations necessary to extinguish Class B fires have been the subject of much testing with results that vary widely. The effectiveness of halogenated agents on flammable liquid and vapor fires is quite dramatic, especially in total flooding systems. Rapid and complete extinguishment is obtainable with low concentrations of the agent [14]. To be effective, the fire must be contained (such as inside a room or chamber) so that the agent can react with it; Halon 1301 applied to large exterior running pool fires dissipates into the atmosphere without penetrating the flame zone. Corrosive Effects of Undecomposed Halons Unlike Halon 1301 and Halon 1211, the early nonfluorinated halogenated agents had significant corrosive problems. Laboratory tests by DuPont in a 44-month exposure period with aluminum, magnesium, steel, stainless steel, titanium, and brass exposed to undecomposed Halon 1301 support the fact that this agent will not corrode these metals, which may all commonly be used in fixed fire extinguishing systems. [13] This is not surprising from a chemical standpoint because the presence of the fluorine atom in a molecule generally reduces its chemical reactivity and corrosive properties and increases its stability. The presence of free water in systems containing Halon 1301 should be avoided. Free water is defined as the presence of a separate water phase in the liquid halon. When present in a small quantity, free water can provide a site for concentrating acid impurities into a corrosive liquid [16]. Free water should not be confused with dissolved water, which is not a problem in a Halon 1301 system. Halon 1301 is inert toward most elastometers and plastics. In general, rigid plastics that are normally unaffected include polytetrafluorethylene, nylon, and acetal copolymers. Most of the commonly used plastics undergo little, if any, swelling in the presence of Halon 1301, with the
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Halon Design Calculations
exception of ethyl cellulose and possibly cellulose acetate/butyrate. Elastomers are particularly suitable when exposed to Halon 1301 for extended periods of time with the notable exception of silicone rubber [13]. Halons decomposed at high temperatures during suppression produce halogen acids such as HF and HBr and free halons that can be corrosive.
Toxicity General Toxic Properties The relative safety of Halon 1301 has been established through more than 30 years of medical research involving both humans and test animals. No significant adverse health effects have been reported from the proper use of Halon 1301 as a fire extinguishant since its original introduction into the marketplace [14]. Early studies by the U.S. Army Chemical Center on Halon 1301 determined the approximate lethal concentration for a 15 min exposure to be 83% by volume [2]. Animals exposed to concentrations below lethal levels exhibit two distinct types of toxic effects. Concentrations greater than 10% by volume produce cardiovascular effects such as decreased heart rate, hypotension, and occasional cardiac arrythmias [17]. Concentrations of Halon 1301 greater than 30% by volume result in central nervous system changes including convulsions, tremors, lethargy, and unconsciousness. Effects are considered transitory and disappear after exposure [18]. Human exposure to concentrations of Halon 1301 greater than 10% by volume have shown indications of pronounced dizziness and a reduction in physical and mental dexterity [19]. With concentrations between 7% and 10% by volume, subjects experienced tingling of the extremities and dizziness, indicating mild anesthesia. Exposure to Halon 1301 concentrations less than 7% by volume have little effect, with the exception of a deepening in the tone of voice caused by a higher density in the medium between the vocal chords. The effects at all levels of concentration disappear quickly after removal from the exposure. Testing of Halon 1301 for potential
1457 Table 43.4 Permitted exposure time for Halon 1301 Concentration (percent by volume) Normally occupied areas 0–7 % 7–10 % Above 10 % Normally unoccupied areas 0–7 % 7–10 % 10–15 % Above 15 %
Permitted time of exposure 15 min 1 min Not permitted 15 min 1 min 30 s Prevent exposure
teratogenic (i.e., altering the normal process of fetal development) and mutagenic (a carcinogen in humans) effects has indicated that no serious problems exist. [5] Most fire protection applications today have a design concentration of 5% by volume, thus the question of toxicity is usually not a serious concern. Exposure limitations for Halon 1301 (indicated by NFPA 12A) are summarized in Table 43.4 [14]. In addition to possible toxic effects, liquid Halon 1301 (including the spray in the immediate proximity of a discharge) may freeze the skin on contact and cause frostbite. However, direct contact is necessary for this to occur and is unlikely, since with engineered Halon 1301 fire extinguishing systems the discharge nozzles are typically distant from all occupants.
Products of Decomposition Consideration of the life safety of Halon 1301 must also include the effects of breakdown products which have a relatively higher toxicity than the agent itself. Upon exposure to flames or hot surfaces above approximately 900 F (480 C), Halon 1301 decomposes to form primarily hydrogen bromide (HBr) and hydrogen fluoride (HF) [20]. Trace quantities of bromine (Br2), carbonyl fluoride (COF2), and carbonyl bromide (COBr2) have been observed, but the quantities are generally too small to be of concern. Although small amounts of carbonyl halides (COF2 and COBr2) were reported in early tests, more recent studies have failed to confirm the
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Table 43.5 Predominant Halon 1301 decomposition products Compound Hydrogen fluoride Hydrogen bromide Bromine Carbonyl fluoride Carbonyl bromine
ALC* for 15 min exposure ppm by volume in air 2500 4750 550 1500 —
Formula HF HBr Br2 COF2 COBr2
* = acute lethal exposure Table 43.6 Selected physical properties of typical halogenated fire extinguishing agents Halon number 104 1001 1011 1202 1211 1301 2402
Type of agent Liquid Liquid Liquid Liquid Liquefied gas Liquefied gas Liquid
Approximate boiling point ( F) 170 40 151 76 25 72 117
presence of these compounds. Table 43.5 summarizes the predominant products of decomposition for Halon 1301 [21]. The primary toxic effect of the decomposition products is irritation. Even in concentrations of only a few parts per million, the decomposition products have characteristically sharp, acrid odors. This characteristic provides a built-in warning system since the irritation becomes severe well in advance of truly hazardous levels. In addition, the odor also serves as a warning that carbon monoxide and other potentially toxic products of combustion may be present. Prompt detection and rapid extinguishment of a fire will produce the safest postextinguishment atmosphere.
Approximate freezing point ( F) 8 135 124 223 257 270 167
Specific gravity of liquid (@70 F) 1.59 1.73 1.93 2.28 1.83 1.57 2.17
(besides low toxicity) is the ability of the agent to vaporize and penetrate all portions of the hazard volume. Table 43.6 shows that Halon 1301 has the lowest boiling point and Halon 1211 has the second lowest. With the discharge of a halon system at ambient temperature, Halon 1301 flashes to a vapor almost instantaneously, while Halon 1211 tends to pool momentarily. Agents with boiling points exceeding the temperature of the hazard volume will stay liquid until heated by the fire itself. These high boiling point halogenated agents have two distinct attributes: they can be projected in a liquid stream and they have a quenching effect in addition to breaking the uninhibited chain reaction. Thus, portable extinguishers generally use Halon 1301 as a propellant for other halon agents.
Other Halons Physical Properties The predominant halogenated agent still in existence today for total flooding fire extinguishing systems is Halon 1301, though some areas of Europe have utilized Halon 1211 for this purpose. One reason for this use of Halon 1301
Toxicity One of the primary reasons that Halon 1301 is the most preferred of the halogenated agents is its relatively low toxicity, as discussed earlier. Table 43.7 compares the approximate lethal concentration of both the natural and decomposed vapors for a variety of fire extinguishing halon
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Halon Design Calculations
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Table 43.7 Approximate lethal concentrations (ppm) for 15 min exposure to vapors of various fire extinguishing agents Formula CCl4 CH3Br CH2ClBr CF2Br2 CF2ClBr CF3Br C2F4Br2 CO2
Halon number 104 1001 1011 1202 1211 1301 2402 —
Natural vapor 28,000 5900 65,000 54,000 324,000 832,000 126,000 658,000
Decomposed vapor 300 9600 4000 1850 7650 14,000 1600 658,000
Table 43.8 Necessary control measures for computer room fire stage sequence Fire stage 1. Pre-ignition 2. Initial pyrolysis 3. Incipient 4. Preflashover 5. Postflashover
Control Good housekeeping practices, control combustible furnishings and interior finish Smoke detection system Portable fire extinguishers, Halon 1301 automatic suppression system Automatic sprinklers Fire walls, compartmentalization
agents and carbon dioxide (CO2). For sake of comparison, carbon dioxide is included with this list of halon agents. As a natural vapor, Halon 1301 is the least toxic halogenated agent. Carbon dioxide may appear to compare favorably with Halon 1301, yet high concentrations of carbon dioxide are necessary for fire extinguishment, which also makes the hazard volume lethal to human occupants.
Halon in the Fire Protection Spectrum Halogenated agent extinguishing systems are only one segment of the total fire protection spectrum. Good engineering judgment is necessary when trying to determine the applicability of halon and whether it should be used instead of, or in addition to, other fire protection measures. It must be clearly understood that halogenated agent extinguishing systems are not the panacea for all fire hazards, yet they do offer a safe method to extinguish certain fires in their very early stages. Thus, these systems have been
Serious danger concern
Occupants and business interruption Occupants and contents Occupants and structure Surrounding structures
commonly applied to situations where even the smallest fire is absolutely unthinkable. As an example, total computer room fire protection might involve several different control measures addressing different possible fire conditions. Table 43.8 illustrates this concept, based on the different stages of a growing fire. The table is not a rigid description of the fire protection requirements of every computer room, but instead an example of how total fire protection is the overall objective when approaching a design situation. An important factor of developing halogenated agent extinguishing systems is the interaction of all concerned individuals. To design, install, maintain, and operate a halon system requires a cooperative effort from a number of different groups. As shown in Fig. 43.6, these individuals include the end users, consultants, manufacturers, installers, insurance representatives, and other selected authorities. Representatives from all these groups work together to develop and enhance model codes, which provide guidance and understanding for proper halon system usage.
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Equipment approval agency
Model codes (NFPA, ISO, BSI, etc.)
Special interest groups
Agent manufacturer
Equipment manufacturer
Installer
Insurance broker
Insurance company Authority having jurisdiction
Engineering
Consultant
End user
Fig. 43.6 Typical interrelationship of halon fire protection interests
System Configurations Detection The three primary parts of every halogenated agent extinguishing system are detection, control panel, and agent delivery. Since there is no single type of detector that offers the ultimate for every application, consideration must be given to the best detection made for the types of combustibles and combustion that are likely to occur in the protected area and the required response time (see the section on design of detection). Photoelectric and ionization smoke detectors have different response characteristics to fires, depending on the situation, and can be susceptible to certain types of false or unwanted alarms. Thermal detectors, although more reliable, react more slowly to fire conditions. In certain
applications, speed is critical and optical detectors would be required. To optimize the speed and reliability of detection systems, it is important to use two different types of detectors on two separate detection loops within the hazard area. This method is referred to as cross-zone detection. Each detection loop functions independently to provide both added reliability and a comforting degree of redundancy [22].
Control Panels Features As its name implies, the control panel is the device that controls system operation and allows the system to function as designed. When a control panel protects more than one area, each individual area is referred to as a zone of
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Halon Design Calculations
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Table 43.9 Typical control unit features Initiating circuit Signaling circuit Release circuit
Halon zone Two cross-zone detection circuits Multiple signaling sequence One circuit
Fire alarm zone One circuit for detection Multiple signaling sequence None
Table 43.10 Modes of control panel operation Unpowered condition Normal condition Alarm condition: Prealarm Prerelease Release Postrelease Trouble condition
protection. Each zone of every halon control panel has three different types of circuits: initiating, signaling, and release. A fire alarm zone and halon zone are compared in Table 43.9 to illustrate the differences between these circuit types. It is unusual for a single halon control panel to protect more than five zones at once due to the high number of circuits required. Fire alarm control panels, on the other hand, may have dozens of individual zones. Initiating circuits provide the input into the panel and support automatic detectors, manual pull stations, and other initiating devices. Automatic detectors are normally cross-zoned, which implies two separate detection circuits. One circuit is required for prealarm and both circuits are necessary for halon release. The signaling circuits, sometimes referred to as bell or auxiliary circuits, are used for audible/visual alarms and other auxiliary functions. The release circuits allow the halon to release from the containers and are sometimes referred to as firing, solenoid, initiator, dump, or halon circuits.
Modes of Operation At any time, a halon control panel and the halon system could be in one of four modes of operation; as shown in Table 43.10 these include unpowered, normal, alarm, and trouble
Off On One detector activates. Two cross-zoned detectors activate. Time delay starts. Time delay ends or manual pull station activates. Halon is released. Halon has been released. Failure or disruption of field wiring. Insufficient power input.
condition. The alarm condition is further definable with prealarm, prerelease, release, and postrelease conditions. Typical systems utilizing cross-zoning detection activate, when required, into prealarm and/or release condition, but this often becomes more complicated with time delays, abort switches, and other auxiliary functions. Unless otherwise specified, manual pull stations activate all alarm conditions, override abort switches, if present, and immediately release the halon. These different alarm conditions provide a convenient mechanism for sequential operation of audible/visual signaling, equipment shutdown, fire service notification, and other auxiliary functions.
Control Panel Economics Large-scale projects with multiple halon zones in a single facility are not uncommon. For example, in the past entire data processing centers and telecommunications buildings were protected throughout with Halon 1301 systems. To protect a large building with many halon zones, it may appear that the most effective way of configuring the system is by using a single large control panel with the capacity for all required halon zones. This is not true, since there is a limitation to the number of halon zones that any one halon panel can effectively manage. Figure 43.7 illustrates an
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Maintenance control Equipment room Equip. room
Detection
Second floor Carrier room
Essoc room Detection
Legend Equip. room
Frame room
Halon panel Detection
First floor
Fig. 43.7 The network concept of control panel interface for a typical halon application
alternative method, where the individual halon zones of a large building each have their own halon panel wired to give an alarm or trouble signal to a central fire alarm panel. A typical halon zone required an average of 12 wires to support all the necessary system functions. Thus, the cost of running multiple wires and large conduit instead of only two wires (for interpanel communication) often offsets the cost of smaller, more numerous panels located near the halon zones. This configuration offers flexibility for future consolidations or additions, which are common for hightechnology facilities. Aesthetics are enhanced at the master control location, and system operation is simplified. Installation checkout and servicing is easier when the halon control panel is within the hazard area. Finally, the overall system is more reliable due to less wiring, lack of design complexity, simplified maintenance, and multisource dependence.
Agent Delivery In addition to the control panel and detection, the other primary part of every halogenated agent
extinguishing system is agent delivery. The agent delivery includes the discharge nozzles, agent storage container(s), release mechanism, and associated piping. As shown in Table 43.11, three methods of agent delivery exist: (1) central storage, (2) modular, and (3) shared supply. Central storage has the container(s) centrally located, with the agent piped accordingly. This method is popular due to its similarity with carbon dioxide system technology (which helped develop early systems), along with usually having the lowest initial cost. Modular systems use smaller containers strategically located throughout the hazard area, with minimal piping. The high reliability of modular systems is based on lack of dependency on piping integrity, negligible piping calculations, total system supervision, multisource dependence, and the inherent ability to be heat actuated regardless of catastrophic system failure. Modular systems are simple to design, are relatively easy to install, and have a high degree of future flexibility. Systems utilizing shared supply are essentially central storage systems with a container(s) shared by more than one hazard volume. Even though fewer containers are used, directional valves and extensive piping do not often allow shared
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Table 43.11 Comparison of different methods of agent delivery Hardware cost Installation cost Design simplicity Installation simplicity Operation and maintenance simplicity Reliability Future flexibility
Central storage Moderate Moderate Difficult Difficult Medium Moderate Low
supply systems to be cost effective. Adding to its unpopularity are its design and installation complexity, low reliability, and impaired future flexibility. When a shared supply halon system activates for one hazard, the remaining hazards become unprotected until the system is completely recharged.
Modular High Low Simple Medium Medium High High
Shared supply Moderate Moderate Difficult Difficult Medium Low Low
Halon System
Fire Alarm System
• 1 control unit
• 1 control unit
• 1–5 zones
• 1–100 zones
• ~12 wires per zone
• ~4 wires per zone
Halon Zone
Fire Alarm Zone
• Volume of halon zone coverage
• Area of detection zone coverage
• Release circuit equals halon zone
• Detection circuit equals fire alarm zone
Design Concepts and Methodology
Fig. 43.8 Halon/fire alarm differences
Definitions and Terminology
A halon zone usually equates to an area of halon coverage functioning on a single release circuit, while the zones in a fire alarm system typically are each detection circuit. As an example, one halon zone could be a single computer room, whereas a fire alarm zone could be the entire floor of a building. A halon system also has much fewer (though more comprehensive) zones than a fire alarm system.
Halogenated agent extinguishing systems are typically classified as either total flooding or local application systems. A total flooding system is designed to develop and maintain a concentration of halon that will extinguish fires in combustible materials located in an enclosed space. Local application systems are designed to apply the agent directly to a fire that may occur in an area or space that is not immediately enclosed. In addition to these, there are specialized applications, which may include combination total flooding/local application or partial flooding. The vast majority of existing halon systems today are the total flooding type using Halon 1301. The definitions of halon system and halon zone are often confusing. This is especially true to individuals closely associated with the fire alarm industry, since fire alarm terminology is similar. Figure 43.8 defines the basic features of a halon system and halon zone and offers a comparison with each respective fire alarm counterpart.
Halon Design Guidelines The design process necessary for total flooding systems is easily quantified. The procedure can be separated into five definable steps: (1) hazard identification, (2) determination of agent quantity, (3) specification of operating requirements, (4) determination of hardware requirements, and (5) generation of postdesign information. The initial step is to provide a definition of the hazard. This includes determining the fuels involved, the dimensions and configuration of the enclosure, the maximum and minimum net volumes, the status of occupancy, the expected
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hazard area temperature range, and possible unclosable openings. Based on this information, the minimum design concentration can be established. Next, the agent quantity is determined based upon the design concentration, the volume, minimum expected temperature, leakage due to ventilation or unclosable openings, and altitude above sea level. Usually, the gross volume is used to calculate the agent quantity to allow for extra agent to replace that lost through normal building leakage. However, agent concentrations must conform with the applicable toxicity criteria with respect to the minimum net volume and maximum temperature. The operating specifications are then required if they have not already been established. These will indicate how the system is to operate, the modes of operation, the type of agent delivery, and so forth. When these are known, the necessary hardware requirements must be obtained and the design of the system completed. The final step is to generate the postdesign information necessary for others to install, test, operate, and maintain the system. Postdesign information should contain all design calculations (including hydraulic calculations), complete blueprint drawings, and detailed information describing the testing, operation, and maintenance of the system.
Local Application and Special Systems Local application systems were typically installed to extinguish fires involving flammable liquids, gases, and surface burning solids. Such systems are designed to apply the agent directly Fig. 43.9 Local application system
Control panel
to a fire that may occur in an area or space not immediately enclosed. They must be designed to deliver halon agent to the hazard being protected in such a manner that the agent will cover all burning surfaces during discharge of the system. Because of its lower volatility, Halon 1211 may be better suited than other forms of halon for local application systems. The lower volatility, plus a high liquid density, permits the agent to be sprayed as a liquid and thus propelled into the fire zone to a greater extent than is possible with other vaporized agents. Examples of areas protected by local application are spray booths, dip and quench tanks, oil-filled electric transformers, printing presses, heavy construction equipment, and vapor vents. An example of a local application system is shown in Fig. 43.9. Traditionally, NFPA standards have not set a minimum limit on the discharge time for a local application design. The rate of discharge and the amount of agent required for a given application must be determined by experimentation and evaluation. The most critical components of these systems are the discharge nozzles; the discharge velocity and rate must be sufficient to penetrate the flames and produce extinguishment but not be so great as to cause splashing or spreading of fuel and thus increase the fire hazard. The minimum design discharge quantity should not be less than 1.5 times the minimum quantity required for extinguishment at any selected design rate [21]. Also of critical importance are type and location of detectors. As with other types of gaseous suppression systems, local application systems have been designed according to the rate-by-volume Discharge nozzle (4)
Detector (2)
Halon 1301 storage containers
Protection object
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Halon Design Calculations
1465
method or the rate-by-area method. The rate-byarea method determines nozzle discharge rates based on the exposed surface area of the hazard being protected. This method is less popular than the rate-by-volume method, which requires discharge rates sufficient to fill (within the discharge time) a volume whose imaginary boundaries extend a limited distance from the protected hazard. This method is favored since it performs similarly to total flooding systems. Important factors to be considered in the design of a local application system are the rate of agent flow, the distance and area limitations of the nozzles, the quantity of agent required, the agent distribution system, and the placement of detectors. Unlike total flooding systems, only the liquid portion of the discharge is effective for local application systems. The computed quantity of agent needed for local application must be increased to compensate for the residual vapor in the storage container at the end of liquid flow. An additional 25% storage capacity is required in the absence of an enclosure that would prevent gas dissipation. Systems should also compensate for any agent vaporized in the pipe lines due to heat absorption from the piping. The heat transfer is important when the piping is at a higher temperature than the agent. The following equation determines the amount of agent increase necessary to compensate for this effect: [14] 2πkL T p T a ðtÞ Wx ¼ 3600hðlnr o =r i Þ
ð43:1Þ
where Wx ¼ Amount of agent increase, kg (lb) k ¼ Thermal conductivity of the piping, W/m · K (Btu · t/h · ft2 · F) L ¼ Linear length of the piping, m (ft) Tp ¼ Pipe temperature, C ( F) Ta ¼ Agent temperature, C ( F) t ¼ System discharge time h ¼ Heat of vaporization of the agent at Ta, kJ/kg (Btu/lb) ro ¼ Outside pipe radius, mm (in.) ri ¼ Inside pipe radius, mm (in.) Specialized systems using a variety of agents are in wide use throughout the world to protect
hazards such as aircraft engine nacelles, military vehicles, emergency generator motors, earth moving equipment, and racing cars. The characteristic common to all these systems is that they can only be applied to the specific hazard for which they were designed and tested. One unusual concept used to protect aircraft flight simulator areas is known as partial flooding, where only the volume containing the simulator equipment receives the total flooding concentration, and not the expansive open areas above it. A design concentration of 7% is recommended to achieve a 5% concentration in the hazard area and should provide for a minimum agent height level relative to the agent concentration of approximately 1.5 m (5 ft) above the highest part of the hazard. The placement of the nozzle is critical and should be designed to direct agent discharge approximately 30 below the horizontal plane. As shown in Fig. 43.10, the savings associated with partial flooding systems can be substantial, especially in areas with very high ceilings [20].
Agent Requirements: Total Flooding Design Concentrations: Solid Fuels Flammable solids may be classified as those that do not develop deep-seated fires and those that do. Class A combustible solids that develop deep-seated fires do so after exposure to flaming combustion for a certain length of time, which varies with the material. Some materials may begin as deep seated through internal heating such as spontaneous ignition. With respect to Halon 1301 total flooding systems, a fire is considered deep seated if a 5% concentration will not extinguish the fire within 10 min after agent discharge [14]. Materials that do not become deep seated undergo surface combustion only and may be treated much the same as those in a flammable liquid fire. The presence of Halon 1301 in the vicinity of a deep-seated fire will extinguish the flame and reduce the rate of burning, yet the quantity of agent required for complete extinguishment of
1466
C.C. Grant
Fig. 43.10 Agent reduction associated with partial flooding systems
.7
hp Partial flood height = ht Total height
.6
.5
.4
.3
.2
.1
0
20
40
60
80
100
Percent reduction in agent requirement hp % = 1 – 1.43 — ht
all embers is difficult to assess. Often it is impractical to maintain an adequate concentration of Halon 1301 for a sufficient time to ensure the complete extinguishment of a deep-seated fire. Factors affecting this concentration include: 1. Nature of fuel 2. Time during which it has been burning 3. Availability of oxygen within the enclosure 4. Ratio of burning surface area to the volume of the enclosure 5. Geometric characteristics of the fuel 6. Fuel distribution within the enclosure Table 43.12 illustrates the extinguishing concentrations of selected flammable solid fires as indicated by six different halon industry groups [23]. Even where the fire has inadvertently become deep seated, application of a low Halon 1301 concentration has two benefits. First, all flaming combustion is halted, preventing rapid spread of the fire to adjacent fuels. Second, the rate of combustion is drastically reduced. These two characteristics justify the ability of Halon 1301 to control, if not extinguish, deep-seated fires. However, Halon 1301 systems that are
specifically designed to extinguish deep-seated fires are seldom economical to apply and may not be as effective in these fires as other types of extinguishing systems.
Design Concentrations: Liquid and Gas Fires There are two general types of flammable liquid or gas fires. First, a flammable or explosive mixture of vapors exists that must be prevented from burning; and second, fuel is burning that must be extinguished. Associated with each of these conditions is a minimum level of Halon 1301 extinguishing concentration, respectively known as inerting and flame extinguishment. When determining the halon design concentration, proper consideration must be given to the quantity and type of fuel involved, the conditions under which it normally exists in the hazard, and any special conditions of the hazard itself. If certain hazards have explosion potential either before or following a fire due to the presence of volatile, gaseous, or atomized fuel, then special
43
Halon Design Calculations
1467
Table 43.12 Extinguishing concentrations of selected flammable solid fires Halon 1301 concentration (percent by volume) Factory mutual Fenwal Ansul DuPont Safety first Underwriter labs Surface fires Polyvinyl chloride Polystyrene Polyethylene Stacked computer printout Polyester computer tape Wood crib 30 pcs. 3/400 7/8 00 Wood crib 24 pcs. 200 200 1800 Wood crib 1A 50 pcs. 200 200 1800 Excelsior loose on floor Shredded paper loose on floor Polyurethane foam Cotton lint Crumpled paper Wood pallets—stack of 10 Deep-seated fires Shredded paper in wire basket Polyester computer tape loose in open wire basket Charcoal Parallel wood blocks Glazed fox fur
— — — — — 3 — — — — — — 3 3
2.0 3 3 — 5 — — — — — — — 6 —
— — — 5.1 — — — — — — — — — —
2.6 — — — — — — — — — 3 — — —
3.8 — — — 3.8 — 3.8 3.8 3.8 3.8 3.8 3.8 3.8 —
— — — — — — — 3.88 6.0 — — — — —
— —
— 10
— —
— —
20 —
18.0 —
13 20 —
— — —
— — —
— — —
— — 6.5
— — —
consideration should be given to vapor detection and explosion suppression measures. As its name implies, the flame extinguishment concentration assumes that the given fuel is burning and that Halon 1301 injected into the air surrounding the fuel at the stated concentration will extinguish the fire [14]. Design concentrations for flame extinguishment are given in Table 43.13. These concentrations are not considered effective with premixed flames or explosive mixtures of fuel vapor in air, but instead apply to diffusion flames, where the flames emanate from pure fuel vapor, and oxygen suffuses into the flame zone from the outside. If the possibility of a subsequent reflash or explosion exists, then the flame extinguishing concentration is not sufficient. NFPA 12A [14] defines these conditions as “when both: 1. The quantity of fuel permitted in the enclosure is sufficient to develop a concentration equal
to or greater than one-half of the lower flammable limit throughout the enclosure, and 2. The volatility of the fuel before the fire is sufficient to reach the lower flammable limit in air (maximum ambient temperature or fuel temperature exceeds the closed cup flash point temperature) or the system response is not rapid enough to detect and extinguish the fire before the volatility of the fuel is increased to a dangerous level as a result of the fire.” Most fuels exhibit about a 30–40% higher concentration for inerting than for flame extinguishment. The minimum inerting concentration suppresses the propagation of the flame front at the “flammability peak” or stoichiometric fuel/ air composition and inerts the enclosure so that any fuel/air mixture will not burn. The higher inerting concentration is often considered safer to use even if the flame extinguishment concentration is feasible, yet the sacrifices include
1468
C.C. Grant
Table 43.13 Design extinguishment Fuel Acetone Benzene Ethanol Ethylene Methane n-Heptane Propane
concentration
for
flame
Minimum design concentration (percent by volume) 5.0 5.0 5.0 8.2 5.0 5.0 5.2
Table 43.14 Halon 1301 design concentrations for inerting Fuel Acetone Benzene Ethanol Ethylene Hydrogen Methane n-Heptane Propane
Minimum concentration (percent by volume) 7.6 5.0 11.1 13.2 31.4 7.7 6.9 6.7
Note: Includes a safety factor of 10% added to experimental values
higher system cost and higher concentrations to which personnel may be exposed (Table 43.14). It is possible to calculate whether the flame extinguishing concentration is acceptable by determining if the fuel present in the hazard will permit attainment of the one-half lower flammable limit of the fuel. The equation to determine the maximum allowable fuel loading (MFL) for flame extinguishment concentrations is MFL ¼
ðK c ÞðLFLÞðMWÞ T
ð43:2Þ
where MFL ¼ Maximum allowable fuel loading, kg/m3 (lb/ft3) Kc ¼ Conversion factor, 0.06093 (0.00685) LFL ¼ Lower flammable limit of fuel in air, percent volume MW ¼ Molecular weight of fuel
T ¼ Temperature, K (R) This can be compared with the actual fuel loading (FL), which is calculated by FL ¼
ðVFÞðW h2 O ÞðSGÞ V
ð43:3Þ
where FL ¼ Fuel loading, kg/m3 (lb/ft3) VF ¼ Volumetric quantity of fuel, m3 (ft3) Wh2 C ¼ Specific weight of water, 997.9 kg/m3 (62.3 lb/ft3) SG ¼ Specific gravity of fuel V ¼ Volume of enclosure, m3 (ft3) If the fuel loading, FL, exceeds the maximum allowable fuel loading, MFL, then the inerting concentration for the particular fuel should be used. Most applications involve a variety of fuels within a single enclosure. If the sum of the actual fuel loadings, FL, is greater than any single maximum allowable fuel loading, MFL, then the most stringent inerting concentration is recommended. If it is determined that a flame extinguishment concentration is sufficient, the value for the fuel requiring the greatest concentration is most applicable.
Calculation of Agent Quantity The calculations necessary for determining the Halon 1301 total flooding quantity are dependent on temperature, volume of the enclosure, agent concentration, altitude with respect to sea level, and losses due to ventilation and leakage. Most applications are based on a static volume enclosure with all openings sealed and all ventilation systems shut down prior to discharge. This simplifies the calculation significantly. Often the ventilation system does not shut down but instead is dampered to allow recirculating air (without makeup air) to continue cooling sensitive electronic equipment and promote the mixing of halon and air. Total flooding quantities are still based on a static volume for these applications. However, in this instance, it may be necessary to include the volume of the ventilation ductwork in addition to the volume of the
43
Halon Design Calculations
1469
Table 43.15 Correction factors for altitudes Altitude Feet 3000 4000 5000 6000 7000 8000 9000 10,000 11,000 12,000 13,000 14,000 15,000
Meters 914 1219 1524 1829 2134 2438 2743 3048 3353 3658 3962 4267 4572
Correction factor 0.90 0.86 0.83 0.80 0.77 0.74 0.71 0.69 0.66 0.64 0.61 0.59 0.56
enclosure. The equation to determine the Halon 1301 total flooding quantity is W¼
ðV ÞðCÞðAc Þ Sð100 CÞ
ð43:4Þ
where W ¼ Weight of Halon 1301 required, kg (lb) C ¼ Halon 1301 concentration, percent by volume Ac ¼ Altitude correction factor (Table 43.15) S ¼ Specific vapor volume based on temperature, m3/kg (ft3/lb) S ¼ 0.14781 + 0.000567 T; T ¼ temperature C S ¼ 2.2062 + 0.005046 T; T ¼ temperature F
Application Rate Discharge Time and Soaking Period When designing a Halon 1301 total flooding system, it is important to determine the system discharge time and soaking period. As indicated in NFPA 12A, “the agent shall be completed in a nominal 10 s or as otherwise required by the authority having jurisdiction.” [14] The reasons for a rapid discharge time include keeping unwanted products of decomposition to a minimum and achieving complete
dispersal of agent throughout the enclosure. Sometimes a much faster application rate is required due to the possibility of a fast spreading fire; yet, discharge times longer than 10 s are sometimes necessary for areas such as museums requiring that turbulence be kept to a minimum, or areas with unavoidably difficult piping configurations. The soaking time is another important requirement for a Halon 1301 total flooding system. This is especially true for deep-seated fire or fires that may reflash. The most common application today for total flooding systems is the protection of valuable electronic equipment. Fires in these applications are almost always extinguished within a few seconds by the Halon 1301 agent, yet a 10-min soaking period is usually required. This estimated time period allows responsible individuals to arrive at the scene to take follow-up action. It is important to remember that halogenated agent extinguishing systems in most cases have only a single chance to control an unwanted fire.
Effects of Ventilation When Halon 1301 is discharged into a total flooding enclosure that is ventilated, some agent will be lost with the ventilating air. Assuming that ventilation must continue during and after discharge, a greater amount of agent is required to develop a given concentration. Also, to maintain the concentration at a given level requires continuous agent discharge for the duration of the soaking period. If an enclosure initially contains pure air, the Halon 1301 discharge rate required to develop a given concentration for agent at any given time after the start of discharge is [14] R¼
ðCÞðEÞ ðSÞð100 CÞ½1 eðEt1 =V Þ
ð43:5Þ
where R ¼ Halon 1301 discharge rate, kg/s (lb/s) E ¼ Ventilation rate, m3/s (ft3/s) t1 ¼ Discharge time, s e ¼ Natural logarithm base, 2.71828
C.C. Grant
After the agent discharge is stopped, the decay of the agent concentration with respect to time is [14] C ¼ C0 eðEt2 =V Þ
ð43:7Þ
where C0 ¼ Agent concentration at end of discharge, percent volume t2 ¼ Time after stopping discharge, s
Compensation for Leakage Occasionally a Halon 1301 total flooding system is designed for an enclosure that has openings that cannot be closed. An example may be a conveyor belt penetrating an enclosure wall, yet even these openings can sometimes be closed using inflatable seals. Halon 1301 discharged into an enclosure for total flooding will result in an air/agent mixture that has a higher specific gravity than the air surrounding the enclosure. Therefore, any openings in the lower portions of the enclosure will allow the heavier air/agent mixture to flow out and the lighter outside air to flow in. Fresh air entering the enclosure will collect toward the top, forming an interface between the air/agent mixture and fresh air. As the leakage proceeds, the interface will descend toward the bottom of the enclosure. The space above the interface will be completely unprotected, whereas the lower space will essentially contain the original extinguishing concentration. There are two methods of compensating for unclosable openings: initial overdose and extended discharge. The initial overdose method provides for an adequate overdose of Halon 1301 to ensure a pre-established minimum of agent at the end of the desired soaking period. Mechanical mixing is required within the enclosure to prevent stratification of agent concentration and a descending interface. Also, caution must be used to prevent personnel exposure to the high initial
06
40
0. 00
ð43:6Þ
G
50 Initial Halon 1301 concentration (% by volume)
ðCÞðEÞ R¼ ðSÞð100 CÞ
0.005 0.004 0.003 0.002 5 0.002 0.001 8 0.00 0.0 16 014 0.0 012 0.0 01
The Halon 1301 discharge rate necessary to maintain a given concentration of agent is [14]
=0 .00 08
1470
30
5
00
0.0
20
4
00
15
0.0
10
0.0
3
00
025
8
0.00
6 5 4 3
2
0
20
40 60 80 Soaking time (min)
100
120
Fig. 43.11 Initial amount of Halon 1301 to produce a 5% residual concentration in enclosures equipped for mechanical mixing
concentrations. The necessary initial concentration depends upon the extended protection time required, the opening height, the opening width, and the volume of the enclosure. Referring to Fig. 43.11, the equation used to determine the initial concentration for a final concentration of 5% is [14] 1=2 ðK ÞðW o Þ 2gc H 3 G¼ 3V
ð43:8Þ
where G ¼ Geometric constant K ¼ Orifice discharge coefficient, 0.66 Wo ¼ Opening width, m (ft) gc ¼ Acceleration due to gravity, 9.81 m/s2 (32.2 ft/s2) H ¼ Opening height, m (ft) The other method used to compensate for unclosable openings is extended discharge. This involves at least two separate piping systems: one to achieve the initial agent concentration, and the other to provide a continuous addition
Halon Design Calculations
1471
of Halon 1301 at a rate which will compensate for leakage out of the enclosure during the soaking period. The agent must be discharged in such a way that uniform mixing of agent and air is obtained. This mixing is often difficult due to the extremely low flow rates being discharged over the entire soaking period, occasionally resulting in small nozzles freezing due to air moisture. Based on the design concentration and opening height, Fig. 43.12 can be used to determine the Halon 1301 makeup rate per unit opening width. Assuming the design concentration of Halon 1301 is established in the enclosure initially, the time required for the interface to reach halfway down the enclosure height can be calculated. Referring to Fig. 43.13, the geometric constant previously calculated for initial overdose is used to find the soaking time based on the initial design concentration.
Flow Calculations Piping Theory The overall objective of designing a Halon 1301 piping system is to properly disperse the required concentration of Halon 1301 throughout the hazard volume within the specified time period. Systems must be engineered to operate quickly and effectively. The discharge time (usually a nominal 10 s as indicated by NFPA 12A) is a critical system constraint and is measured as the interval between the first appearance of liquid at the nozzle and the time when the discharge becomes predominantly gaseous [14]. The hydraulic calculations are considered to be the most difficult part of the entire design process, and are almost always calculated with the aid of computer programs due to the tedious nature of manual calculations.
4.0
5.0 4.0
3.0
3.0
Halon 1301 discharge rate (lb/s/ft of opening width)
2.0
3.0) 10 ( 4) 8 (2.
1.0 0.8
2.0
.8)
6 (1
0.6 0.5 0.4
1.0 0.8 0.6 0.5 0.4
.2)
4 (1
0.3
0.3
0.2
0.6)
2( 0.1 0.08 0.06 0.05 0.04 0.0.3
O
n pe
in g
h
ht, e ig
0.02
ft (
0.2
m)
0.1 0.08
)
.3 1 (0
0.5
0.06 0.05 0.04 5)
Halon 1301 discharge rate (kg/s/m of opening width)
43
0.03
(0.1
0.02 0.01
2
4
6
8 10 12 14 16 Halon 1301 concentration (% by volume)
18
20
22
24
Fig. 43.12 Extended discharge rate of Halon 1301 to maintain constant concentrations in enclosures with openings
1472
C.C. Grant
40 30 20
G =
10
4 00 0.0 005 0.0
6 5
0.001
8
25 00 3 0.0 000 0.
02 00 0.
15
0.002
Initial Halon 1301 concentration (% by volume)
50
4 3 2 0
20
40 60 80 Soaking time (min)
100
120
Fig. 43.13 Time required for interface between effluxing Halon 1301/air mixtures and influxing air to descend to center of enclosures not equipped for mixing
Pipe
Discharge nozzle
Agent storage container
Fig. 43.14 Primary components of a Halon 1301 piping system
As illustrated in Fig. 43.14, the primary components of a Halon 1301 piping system are the agent storage container, the discharge nozzle, and the pipe. Often, more than one nozzle is required, complicating the calculations significantly. An attempt should always be made to keep the piping system simple and if possible, balanced. A balanced system has the actual and equivalent pipe lengths from container to each nozzle within 10% of each other and has equal design flow rates at each nozzle [14].
As with sprinkler systems or other systems involving fluid flow, the methodology for solving Halon 1301 piping calculations involves seeking terminal characteristics based on property changes encountered due to the movement of the fluid. The system hydraulics are controlled by the selection of the orifice area at the discharge nozzle. This orifice area is calculated from the nozzle pressure, which is based on the starting pressure in the container and pressure losses in the pipe. Because the flow of Halon 1301 is nonsteady and has a change in phase from liquid to vapor, the calculations become highly complex. To simplify calculations, the average discharge conditions are determined so that they might reasonably represent the entire discharge time span. This timeindependent model is based on the moment in time when half the liquid phase of the agent has left the nozzle. All the calculations for a 10 s discharge condition shown in Fig. 43.15 would be solved at the mid-discharge condition (5 s). Hence, the critical characteristics that vary with discharge, such as the storage container pressure and the pressure-density relationship in the pipeline, are replaced with average time-independent values [24]. By the time half of the liquid agent is out of the nozzle, the original pressure in the storage container has dropped considerably. To calculate the mid-discharge storage container pressure, the percent of agent still within the pipe must be determined. Also, the initial drop in pressure immediately after the start of discharge is nonlinear. As seen in Fig. 43.16, the pressure recovery is due to the nitrogen vigorously boiling out of the halon/nitrogen mixture within the storage container. Unlike water-based fluid flow, the pressure drop occurring when Halon 1301 flows through a pipe is nonlinear and is dependent on the pipeline agent density, not the distance traveled. The pipeline flow is two phase, with a mixture of liquid and vapor agent. As the agent travels in the pipe, the pressure and density decrease, which increases the velocity and the amount of halon vapor. Interestingly, the evolution of the nitrogen from the halon/nitrogen mixture in the storage container causes the halon to drop in
43
Halon Design Calculations
Fig. 43.15 Summary of Halon 1301 discharge conditions based on a 10 s discharge
1473
A Predischarge condition
B Initial discharge condition (time = 0 s)
C Mid-discharge condition (time = 5 s)
D Final discharge condition (time = 10 s)
temperature and become more dense. This phenomenon fortunately is not a factor in the calculations since a time-independent model is being used. The increase in density at any one
location over the entire time span should not be confused with the decrease in density that occurs when the agent flows from one location to another.
C.C. Grant
Pressure (bar [psig])
1474 26.89 (390) 24.82 (360) 22.75 (330) 20.69 (300) 18.62 (270) 16.55 (240) 14.48 (210) 12.41 (180) 10.34 (150) 8.27 (120) 6.21 (90) 4.14 (60) 2.07 (30)
Pressure recovery Container pressure
Nozzle pressure
End of liquid
1
0
1
2
–psig = –kPa
3
4
5
6
7
Time (s)
Fig. 43.16 Pressure profile during system discharge
Guidelines and Limitations Unrealistic distribution networks often fail to perform to specifications and are difficult if not impossible to predict from a calculation standpoint. As the piping system becomes more unrealistic, the calculations become more unreliable. To aid in the development of accurate calculations, certain fundamental limitations are necessary to ensure proper system design. These limitations are especially important with respect to computer programs since these programs have a tendency to be operated abusively with high expectations. Summarized below are the design constraints for Halon 1301 hydraulic calculations [25]. 1. Good design practice 2. Discharge time 10 s 3. Favorable system temperature 4. Initial container pressure ¼ 2482.2 kPa (360 psig) or 4137.0 kPa (600 psig) 5. Initial container fill density 1121.4 kg/m3 (70 lb/ft3) 6. Percent in pipe maximum value
7. Turbulent flow minimum value 8. Nozzle pressure minimum value 9. Actual nozzle area percentage of feed pipe area 10. Actual nozzle area ¼ calculated nozzle 5% Good design practice includes such items as favoring balanced systems, keeping the degree of flow/split imbalance below a maximum value, avoiding vertically installed tees, and avoiding nozzles on different floor levels which may separate the halon gas/vapor mixture. The values for some of the constraints are determined by the individuals developing computer programs that are verified by approval agencies through testing.
Calculation Procedure The piping calculations comprise four steps: 1. Determining the necessary input data 2. Calculating the average storage container pressure
43
Halon Design Calculations
1475
3. Calculating the nozzle pressure at each nozzle 4. Calculating the nozzle orifice areas Pipeline calculations are performed for each segment of pipe having both a constant flow rate and a uniform pipe diameter; thus the piping network is divided into sections called junctions. Each discharge nozzle is also identified. The forms necessary for the input data, pressure calculations, and nozzle calculations are contained in Figs. 43.17 and 43.18. Assuming the appropriate input data are known, the average storage container pressure is determined from Fig. 43.19 based on the percent agent in pipe, which itself is determined by [14]
System Halon weight Container fill density Discharge time
B
lb lb C
D
Form I: System summary
lb lb F
G
N5: N6: H
lb lb I
W
Elevation change h
Junction pressure P (starting of from Form II)
Inputs
Junction number
Nozzle number
Flow rate Q
Pipe type
Pipe diameter D
ð43:9Þ
Once the average storage container pressure is known, Figs. 43.18 and 43.20 and Equations 43.10 through 43.22 can be used to determine the nozzle orifice areas for a 360 psig system. Usually the calculations are based on a 10 s discharge time, though this is sometimes changed
N3: N4: E
K1 W i =V p þ K2
where Wi ¼ Initial charge weight of Halon 1301, lb Vp ¼ Internal pipe volume, ft3 (Table 43.16) K1 and K2 ¼ Constants (Table 43.17)
lb lb/ft3 s
N1: N2: A
% in pipe ¼
X
Y
Outputs
Actual pipe length L
Fig. 43.17 Halon 1301 piping calculation summary form
Fittings, equivalent length L
Total length L
Density at orifice r (Fig. 4-6.20)
Orifice area F (Eq. 22)
1476
C.C. Grant
Form II: Pressure calculations
J
K
L
M
N
O
P
Q
Initial pressure Elevation
Junction pressure
Density r (Fig. 4-6.20)
R
S
T
U
V
2nd Y factor Y2 (Eq. 20)
Final junction pressure P (Table 4-6.19, Eq. 21)
Final pressure Pipe size factors Corrected starting pressure P0
Pressure Pe (Eq. 10)
A (Eq. 11)
B (Eq. 12)
1st Y factor Y1 (Table 4-6.19, Eq.13)
1st Z factor Z1 (Eqs. 14–17)
Temporary Y factor Yt (Eq. 18)
Temporary pressure Pt 2nd Z factor (Table Z2 4-6.19, (Eqs.14–17) Eq.19)
Fig. 43.18 Halon 1301 pressure calculation summary form
slightly to produce flow rates in accordance with Table 43.18. Turbulent pipeline flow can also be achieved by using smaller pipe sizes. Pipe diameters that are too small result in unacceptably high pressure losses; therefore, care must be used in pipe size selection. It is important to recognize that approximations have been made for Y and Z factors and nozzle coefficients. The calculation procedure presented here is only intended to demonstrate the current methodology and not to provide a rigorous solution. The necessary equations are [14, 26]
Average Storage Cylinder Pressure vs. Percent of the Agent Supply Needed to Fill the Pipeline 500 60 0p
Mid-discharge storage pressure (psig)
450
sig , 40
psi g, 5 0 lb /ft 3 60 0p sig ,6 0 lb/f 3 60 t 0p sig ,7 0 lb /ft 3
350
300
360 psig, 40 lb /ft 3 360 p 360 sig, 50 psig lb/ft 3 , 60 lb/ft 3 360 psig , 70 lb/ft 3
250
200
150
lb/f 3 t
60 0
400
0
10
20
30
40
50
Pe ¼
60
70
80
rLe 144
ð43:10Þ
where Pe ¼ Elevation pressure, psig r ¼ Agent density, lb/ft3 Le ¼ Pipe elevation length, ft
Percent of agent to fill pipeline
Fig. 43.19 Mid-discharge storage container pressure
A ¼ 1:013D5:25
ð43:11Þ
43
Halon Design Calculations
1477
Table 43.16 Internal volume of steel pipe Nominal pipe diameter (in.) 1/4 3/8 1/2 3/4 1 11/4 11/2 2 21/2 3 31/2 4
Schedule 40 inside diameter (in.) 0.364 0.493 0.622 0.824 1.049 1.380 1.610 2.067 2.469 3.068 3.548 4.026
Schedule 80 inside diameter (in.) 0.302 0.423 0.546 0.742 0.957 1.278 1.500 1.939 2.323 2.900 3.364 3.826
ft3/ft 0.0007 0.0013 0.0021 0.0037 0.0060 0.0104 0.0141 0.0233 0.0332 0.0513 0.0687 0.0884
ft3/ft 0.0005 0.0010 0.0016 0.0030 0.0050 0.0089 0.0123 0.0205 0.0294 0.0459 0.0617 0.0798
Table 43.17 Constants to determine percent of agent in piping Filling density 70 60 50 40 70 60 50 40
Fig. 43.20 Pipeline density/pressure relationship for a 360 psig system
K1 7180 7250 7320 7390 6730 6770 6810 6850
100
K2 46 40 34 28 52 46 40 34
60 50 40
90
ns ity
80
60 50
lb /ft 3 f i ll in g
Density (lb/ft3)
de
70
70
Storage (psig) 600 600 600 600 360 360 360 360
40 30 20 10 0 100 120 140 160 180 200 220 240 260 280 300 320 Pipeline pressure (psig)
1478
C.C. Grant Table 43.18 Minimum design flow rates to achieve turbulent pipeline flow Nominal pipe diameter (in.) 1/8 1/4 3/8 1/2 3/4 1 11/4 11/2 2 21/2 3 4 5 6
Schedule 40 minimum flow rate (lb/s) 0.20 0.34 0.68 1.0 2.0 3.4 5.8 8.4 13 19.5 33 58 95 127
Schedule 80 minimum flow rate (lb/s) 0.11 0.24 0.48 0.79 1.9 2.8 4.8 7.5 13 17 26 48 81 109
Table 43.19 Constant for Y factor/pressure equations P storage (psig) 360 360 360 360
Fill density (lb/ft3) 70 60 50 40
a 3.571 4.018 3.125 3.720
7:97 D4
Y1 ¼
a 3 b 2 p þ p þ cP0 þ d 3 0 2 0
ð43:12Þ
4 4 4 4
b 0.6971 0.6913 0.6238 0.6187
c 63.50 64.01 56.90 55.55
d 5921 6333 7386 8120
for 60 lb=ft3 fill density
Z ¼ 0:96412 0:01051ðP 175Þ
for 50 lb=ft3 for 40 lb=ft3
ð43:16Þ Z ¼ 0:95900 0:01008ðP 180Þ
fill density ð43:17Þ
ð43:13Þ where Z ¼ Z factor P ¼ Pressure, psig
where Y1 ¼ First Y factor P0 ¼ Junction starting pressure, psig a, b, c, and d ¼ Constants (Table 43.19) Z ¼ 1:01790 0:01179ðP 160Þ
ð43:15Þ
where B ¼ Pipe size factor
10 10 10 10
Z ¼ 0:96913 0:01098ðP 170Þ
where A ¼ Pipe size factor D ¼ Actual pipe diameter, in. B¼
2 Q YT ¼ Y1 þ L A
for 70 lb=ft3 fill density
ð43:14Þ
where YT ¼ Temporary Y factor Q ¼ Flow rate, lb/s
ð43:18Þ
43
Halon Design Calculations
1479
P3T
3b 2 3c 3 3d þ P þ PT ¼ YT 2a T a a a ð43:19Þ
where PT ¼ Temporary pressure, psig Y 2 ¼ Y T þ BðZ2 Z 1 ÞQ2
ð43:20Þ
where Y2 ¼ Second Y factor 3b 2 3c 3 3d 3 P þ P þ P¼ Y2 2a a a a ð43:21Þ h i F ¼ 1:5Q 1= f ðr pÞ1=2
ð43:22Þ
where F ¼ Nozzle orifice area, in.2 f ¼ Nozzle coefficient (approximately 0.7)
Information can be recorded entirely on system drawings or in both a written manual and system drawings.
System Manual 1. Design Data (a) Functional and operational description (b) Halon 1301 weight calculations (c) Hydraulic piping calculations (d) Special considerations 2. Installation, Maintenance, and Inspection Instructions
As-Built System Drawings 1. Floor Plan Layout (a) Suitable dimensions (b) Equipment locations (c) Special installation details 2. Electrical Schematic 3. Equipment Identification 4. Special Notes
Inspection and Acceptance
Postdesign Considerations Postdesign considerations are divided into two categories: system documentation and inspection/acceptance practices. Good halon system design is not complete until full documentation is provided for installation, acceptance, and eventual end user operation. Proper documentation is especially important to prevent the inadvertent discharge of a halon system for other than a fire, since replacement of the halon agent could be very difficult with future availability being dependent on recycled stock.
System Documentation System documentation should include the items listed below. This material is necessary for others to install, test, operate, and maintain the system.
After installation, each system should be inspected and tested by technicians trained by the equipment manufacturer covering the items listed below: 1. Test system wiring for proper connection, continuity, and resistance to ground. 2. Check system control unit in accordance with factory recommended procedures. 3. Calibrate and test each detector in accordance with factory recommended procedures. 4. Test each releasing circuit for proper resistance by means of a current-limiting meter. 5. Test the operation of all ancillary devices such as alarms, dampers, magnetic closers, and so on. 6. Obtain a certificate of inspection signed and dated by the installing contractor and the authority having jurisdiction. An installation checklist is often used, which expands on the above items in complete detail [27]. These checklists are available from agent
1480
and equipment manufacturers, installers, insurance groups, and consultants. When accepting a newly installed halon system, it is important to determine compliance with design specifications. In previous years, a full discharge test was required to provide unquestionable evidence of performance, yet this could be a costly and sometimes unnecessary burden carried by the end user. End users with multiple systems would often prove system acceptance based on the performance characteristics of their other systems. The primary reason for discharge test failure, when it was performed, was because the hazard enclosure would not hold the design concentration over the entire soaking period [28]. Checking the enclosure for possible halon leakage points has always been difficult and is the only questionable part of the acceptance/inspection procedure. A method referred to as the enclosure integrity test has proved to be very effective for this problem, and validates the integrity of the protected enclosure [14]. This technique shows much promise and has potential for substantially enhancing the reliability of proper system operation. The most effective use of fan pressurization techniques for these types of applications is for leakage path indication [29]. This involves pressurizing or depressurizing the enclosure with the fan pressurization apparatus and using an indicating device, such as a smoke pencil or acoustic sensor, to determine leakage paths. The installers’ visual inspection of the enclosure now becomes very effective since even the smallest cracks can be located. Due to low cost and simplicity, a smoke source is usually the most desirable method for locating leaks, but an excellent alternative is the use of a directional acoustic sensor that can be selectively aimed at different sound sources [30]. Highly sensitive acoustic sensors are available that can detect air as it flows through an opening and are sensitive enough to clearly hear a human eye blink [31]. Openings can also be effectively detected by placing an acoustic source on the other side of the barrier and searching for acoustic transmission. Another method is to use an infrared
C.C. Grant
scanning device if temperature differences across the boundary are sufficient [32]. These techniques are not quantitative, but they are effective, inexpensive, and easily performed.
Environmental Considerations Scientific evidence indicates that fire protection Halon 1301 is one of several man-made substances adversely affecting the earth’s ozone layer [33]. Ozone exists naturally as a thin layer of gas in the stratosphere that blocks the sun’s harmful ultraviolet rays and thus is vital to life on earth. Several adverse environmental and direct health effects are linked to ozone layer depletion, and its preservation is of paramount concern to mankind. It’s believed that Halon 1301 (and other chlorofluorocarbons) chemically destroy ozone when emitted into the atmosphere. Earlier, the phase-out of full system discharge tests that were used to verify enclosure integrity received special attention since they accounted for a proportionately large percentage of fire protection halon emissions. Fortunately, the amount of fire protection Halon 1301 released for actual fires is relatively small. Testing a system by performing a full discharge test allows the release of Halon 1301, which on a cumulative basis may be potentially harmful to the environment and depletes relatively precious stocks of halon agent that should be dedicated to suppressing fires. The release of Halon 1301 should be minimized. With regard to ozone layer depletion, halons used for fire protection are different than halons used for other industrial applications [34]. Fire protection halons are unique because of their essential mission to prevent the loss of life, minimize the loss of irreplaceable property, assure the continuity of vital operations, and reduce the amount of fire by-products polluting the atmosphere. Efforts have been made to minimize the release of fire protection halons for noncritical tasks such as training, testing, and research. It is assumed that existing halon systems will remain in existence for an undetermined time into the
43
Halon Design Calculations
future, despite the present worldwide restriction on their production.
1481
R ri ro S
Nomenclature a A Ac b B c C C0 d D e E f F FL gc G h H k K Kc L Le LFL MFL MW P P0 Pe PT Q r
constant (see Table 43.19) pipe size factor altitude correction factor (see Table 43.15) constant (see Table 43.19) pipe size factor constant (see Table 43.19) Halon 1301 concentration, percent by volume agent concentration at end of discharge, percent by volume constant (see Table 43.19) actual pipe diameter, in. natural logarithm base, 2.71828 ventilation rate, m3/s (ft/s) nozzle coefficient (approximately 0.7) nozzle orifice area, in [2]. fuel loading, kg/m3 (1b/ft3) acceleration due to gravity, 9.81 m/s2 (32.2 ft/s2) geometric constant heat of vaporization of the agent at Ta, kJ/kg (Btu/lb) opening height, m (ft) thermal conductivity of the piping, W/m · K (Btu · t/h · ft2 · f) orifice discharge coefficient, 0.66 conversion factor, 0.06093 (0.00685) linear length of piping, m (ft) pipe elevation length, ft lower flammable limit of fuel in air, percent volume maximum allowable fuel loading, kg/m3 (lb/ft3) molecular weight of fuel pressure, psig junction starting pressure, psig elevation pressure, psig temporary pressure, psig flow rate, lb/s agent density, lb/ft3
SG t T t1 t2 Ta Tp V VF Vp Wx Wh2 O W Wo Wi Y1 Y2 YT Z
Halon 1301 discharge rate, kg/s (lb/s) inside pipe radius, mm (in.) outside pipe radius, mm (in.) specific vapor volume of Halon 1301 based on temperature, m3/kg (ft3/lb) specific gravity of fuel system discharge time temperature, K (R) discharge time, s time after stopping discharge, s agent temperature, C (F) pipe temperature, C (F) enclosure volume, m3 (ft3) volumetric quantity of fuel, m3 (ft3) internal pipe volume, ft3 (see Table 43.16) amount of agent increase, kg (lb) specific weight of water, 997.9 kg/m3 (62.3 lb/ft3) weight of Halon 1301 required, kg (lb) opening width, m (ft) initial charge weight of Halon 1301, lb first Y factor second Y factor temporary Y factor factor
References 1. C.C. Grant, “Fire Protection Halons and the Environment: An Update Symposium,” Fire Technology, 24, p. 1 (1988). 2. “The Halogenated Extinguishing Agents,” NFPA Quarterly, 48, 8, Part 3 (1954). 3. D. Wharry and R. Hirst, Fire Technology: Chemistry and Combustion, Institute of Fire Engineers, Leicester, England (1974). 4. R. Strasiak, “The Development of Bromochloromethane (CB),” WADC Technical Report 53–279, Wright Air Development Center, Dayton, OH (1954). 5. Fire Protection Handbook, 17th ed., National Fire Protection Association, Quincy, MA (1991). 6. NFPA 12A-T, Standard on Halogenated Fire Extinguishing Agent Systems, National Fire Protection Association, Quincy, MA (1968). 7. NFPA 12A, Standard on Halon 1301 Fire Extinguishing Systems, National Fire Protection Association, Quincy, MA (1992).
1482 8. NFPA 12B, Standard on Halon 1211 Fire Extinguishing Systems, National Fire Protection Association, Quincy, MA (1990). 9. NFPA 12C-T, Tentative Standard on Halon 2402 Fire Extinguishing Systems, National Fire Protection Association, Quincy, MA (1983). 10. NFPA 75, Standard for the Protection of Electronic Computer/Data Processing Equipment, National Fire Protection Association, Quincy, MA (1992). 11. C. Ford, Halon 1301 Computer Fire Test Program— Interim Report, DuPont Co., Wilmington, DE (1972). 12. NFPA 2001, Standard on Clean Agent Fire Extinguishing Systems, National Fire Protection Association, Quincy, MA (1994). 13. “DuPont Halon 1301 Fire Extinguishant,” Technical Bulletin B-29E, DuPont Co., Wilmington, DE. 14. NFPA 12A, Standard on Halon 1301 Fire Extinguishing Systems, National Fire Protection Association, Quincy, MA (2004). 15. Evaluation of Telephone Frame Fire Protection, GTE/Fenwal, Holliston, MA (1970). 16. “Handling and Transferring ‘Freon’ FE 1301 Fire Extinguishing Agent,” Technical Bulletin FE-2, DuPont Co., Wilmington, DE (1969). 17. D.G. Clark, The Toxicity of Bromotrifluoromethane (FE 1301) in Animals and Man, Ind. Hyg. Res. Lab., Imperial Chemical Industries, Alderley Park, Cheshire, England (1970). 18. R.D. Stewart, P.E. Newton, A. Wu, C. Hake, and N.D. Krivanek, Human Exposure to Halon 1301, Medical College of Wisconsin, Milwaukee, unpublished (1978). 19. The Hine Laboratories, Inc., Clinical Toxicologic Studies on Freon Fe-1301, Report No. 1, San Francisco, CA, unpublished report (1968). 20. J.L. Bryan, Fire Suppression and Detection Systems, Macmillan, New York (1982). 21. N. Sax, Dangerous Properties of Industrial Materials, Section 12, 2nd ed., Reinhold, New York (1963). 22. G.J. Grabowski, Fire Detection and Actuation Devices for Halon Extinguishing System, An Appraisal of Halogenated Fire Extinguishing Agents, National Academy of Sciences, Washington, DC (1972). 23. C. Ford, “Extinguishment of Surface and Deep-Seated Fires with Halon 1301,” Symposium of an Appraisal
C.C. Grant of Halogenated Fire Extinguishing Agents, National Academy of Sciences, Washington, DC (1972). 24. H.V. Williamson, Halon 1301 Flow Calculations— An Analysis of a Series of Tests Conducted by FEMA at the Fenwal Test Site, Chemetron Corp., Hanover, PA (1975). 25. C.C. Grant, “Computer-Aided Halon 1301 Piping Calculations,” Fire Safety Journal, 9, 2, pp. 171–179 (1985). 26. Flow in Pipes—Pyroforane Halon 1301, Produits Chimiques Ugine Kuhlmann, Corbevoie, France. 27. J.J. Brenneman and M. Charney, “Testing a Total Flooding Halon 1301 System in a Computer Installation,” Fire Journal, 68, p. 6 (1974). 28. S.A. Chines, “Halon System Discharge Testing—An Authority Having Jurisdiction Point of View,” Seminar Paper for Fire Protection Halons and the Environment, NFPA Annual Meeting, Cincinnati (1987). 29. C.C. Grant, “Controlling Fire Protection Halon Emissions,” Fire Technology, 24, p. 1 (1988). 30. D.N. Keast, and H.S. Pei, “The Use of Sound to Locate Infiltration Openings in Buildings,” Proceedings of the ASHRAE-DOE Conference on the Thermal Performance of the Exterior Envelope of Buildings, Orlando, FL, p. 85 (1979). 31. Ultraprobe 2000 Data Sheet (acoustic sensor), UE Systems, Elmsford, NY (2000). 32. A.K. Blomsterberg, and D.T. Harrje, “Approaches to Evaluation of Air Infiltration Energy Losses in Buildings,” in ASHRAE Transactions, Vol. 85, Pt. 2, p. 797 (1979). 33. S.O. Andersen, “Halons and the Stratospheric Ozone Issue,” Fire Journal, p. 56 (May/June 1987). 34. G. Taylor, “Achieving the Best Use of Halons,” Fire Journal, 81, 3, p. 69 (1987). Casey C. Grant is Executive Director at the Fire Protection Research Foundation and was previously secretary of the NFPA Standards Council. He is a former member of the NFPA Technical Committee on Halogenated Fire Extinguishing Agent Systems and was previously supervisor of systems design engineering at Fenwal Incorporated.
Clean Agent Total Flooding Fire Extinguishing Systems
44
Philip J. DiNenno and Eric W. Forssell
Introduction Total flooding clean agents and systems were developed in response to the regulation of Halon 1301 under the Montreal Protocol and its amendments, which culminated in the phase-out of production of halons in the developed countries on December 31, 1993. This regulation engendered tremendous research and development efforts across the world in a search for replacements and alternatives. Since that time, on the order of 15 total flooding clean agent alternatives to Halon 1301 have been commercialized and development continues on others. In addition to clean total flooding gaseous alternatives, new technologies, such as water mist and fine solid particulate, are being introduced. This chapter focuses on total flooding clean agent halon replacements. Table 44.1 is a summary of common halocarbon and inert gas extinguishing agents developed to date. The most widely used commercialized total flooding agents include HFC-227ea, HFC-125, FK-5-1-12 and all of the inert gases. Perfluorocarbons (PFC) and Hydrochlorofluorocarbons (HCFC) agents are essentially no longer used due to environmental regulations. The best performing replacement agent in terms of effectiveness per unit mass is the Trifluoroiodide P.J. DiNenno • E.W. Forssell (*) Jensen Hughes (Formerly Hughes Associates, Inc.), 3610 Commerce Drive, Suite 817, Baltimore, MD 21227
but concerns regarding toxicity precluded that agent from widespread commercialization and adoption. The table gives the chemical name; trade name; American Society of Heating, Refrigerating, and Air Conditioning Engineers, Inc. (ASHRAE) designation (for halocarbons); and the chemical formula.
Characteristics of Clean Agents Clean fire suppression agents are generally defined as electrically nonconducting fire extinguishants that vaporize readily and leave no residue [1]. They are subject to specific evaluation with regard to their hazards to personnel and their effect on the environment. Depending upon the agent, they are stored under high pressure as a liquid or a gas, and are utilized in their gaseous state when released from their storage containers. Clean agent halon replacements fall into two broad categories: (1) halocarbon compounds and (2) inert gases and mixtures. Halocarbon clean agents include compounds containing carbon, hydrogen, bromine, chlorine, fluorine, and iodine. They are grouped into five categories: (1) hydrobromofluorocarbons (HBFC), (2) hydrofluorocarbons (HFC), (3) hydrochlorofluorocarbons (HCFC), (4) perfluorocarbons (FC or PFC), and (5) fluoroiodocarbons (FIC) and Fluoroketones (FK). The recent introduction of Fluoroketones has enabled the use of halocarbon agents with near zero global warming potential in normally occupied areas.
M.J. Hurley (ed.), SFPE Handbook of Fire Protection Engineering, DOI 10.1007/978-1-4939-2565-0_44, # Society of Fire Protection Engineers 2016
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P.J. DiNenno and E.W. Forssell
Table 44.1 Commercialized halon replacement nomenclature Chemical name Heptafluoropropane Trifluoromethane Chlorotetrafluoroethane Pentafluoroethane Dodecaflouro-2-methylpentan-3-one Hexaflouropropane Triflouroiodide N2/Ar/CO2
Trade name FM-200 FE-13 FE-24 FE-25 Novec 12330 FE-36 Triodide Inergen
ASHRAE designation HFC-227ea HFC-23 HCFC-124 HFC-125 FK-5-1-12mmy2 HFC-236fa FIC-13I1 IG-541
N2/Ar
Argonite
IG-55
Argon Nitrogen
Argon Nitrogen
IG-01 IG–100
Although the characteristics of halocarbon clean agents vary widely, they share several of the following common attributes: 1. All are electrically nonconductive, 2. All are clean agents; that is, they vaporize readily and leave no residue, 3. All are liquefied gases or display analogous behavior (e.g., compressible liquid), 4. All can be stored and discharged from typical Halon 1301 hardware (with the possible exception of HFC-23, which more closely resembles 600 psig [40 bar] superpressurized halon systems), 5. All (except HFC-23) use nitrogen superpressurization in most applications for discharge purposes, 6. All are less efficient fire extinguishants than Halon 1301 in terms of storage volume and agent weight. The use of most of these agents requires increased storage capacity. 7. All are total flooding gases after discharge. Many require additional care relative to nozzle design and mixing, 8. All produce more decomposition products (primary HF) than Halon 1301, given similar fire type, fire size, and discharge time, 9. All halocarbon agents except FK-5-1-12mmy2 and FIC-13I1 have substantial greenhouse warming characteristics; FK-5-1-12mmy2, a
Chemical formula CF3CHFCF3 CHF3 CHClFCF3 CHF2CF3 CF3CF2C(O)(CF(CF3))2 CF3CH2CF3 CF3I N2 (52 %) Ar (40 %) CO2 (8 %) N2 (50 %) Ar (50 %) Ar (100 %) N2
Fluoroketone, has a near zero global warming potential, 10. All of the halocarbon agents have a near zero ozone depletion potential, (ODP) and, 11. All halocarbon agents must be evaluated with respect to health and safety concerns, which are primarily related to cardiac sensitization, as discussed later in this chapter. Inert gas clean agents include nitrogen and argon and blends of these. One inert gas replacement has a small fraction of carbon dioxide. Carbon dioxide is not an inert gas because it is physiologically active and toxic at low concentrations. However, the approximately 8 % of carbon dioxide used as a component of IG-541 is not considered to pose a safety concern in terms of toxicity. Inert gas clean agents share the following common attributes: 1. All are electrically nonconductive. 2. All are clean agents; that is they leave no residue. 3. All are stored as compressed gases utilizing low capacity high pressure cylinders, 4. All are less efficient fire extinguishants than Halon 1301 in terms of storage volume and agent weight. Storage volumes are much greater than Halon 1301 or the halocarbon clean agents due to the need for high pressure cylinders,
44
Clean Agent Total Flooding Fire Extinguishing Systems
1485
Table 44.2 Comparisons of systems in 500–5000 m3 range of volumes [2] Percentage additional weight when compared to a Halon 1301 system Halon 1301 CO2 FE-13 FM-200 Novec 1230 Weight comparison 0 150 200 50 50 500 m3 1000 m3 0 163 188 38 50 3000 m3 0 200 219 48 71 5000 m3 0 186 211 36 58 Footprint comparison 500 m3 0 84 105 20 20 1000 m3 0 82 94 20 20 3000 m3 0 118 122 19 43 5000 m3 0 99 107 6 19 Percentage cost comparison 500 m3 0 108 315 202 259 1000 m3 0 140 406 267 368 3000 m3 0 200 553 351 513 5000 m3 0 204 585 361 515
5. Inert gases do not produce more decomposition products, 6. Inert gas agents have zero global warming potentials, 7. All of the halocarbon agents have a zero ozone depletion potentials, and, 8. All inert gas agents must be evaluated with respect to health and safety concerns, which are primarily related to oxygen depletion, as discussed later in this chapter. Wickham [2] has provided comparative values for cost and footprint of potential halon, replacement systems for use in marine applications. These comparisons are given for weight, footprint, and cost in Table 44.2. Note that all clean agents require at least 50 % more agent by weight than halon as a consequence of the elimination of bromine in the compounds and subsequent level of catalytic recombination of flame radicals. These data should be taken as representative values, as there are variations among hardware manufacturers. The storage volume equivalent does not translate directly to a required area or volume for storage cylinders. The relative footprint of these storage volume equivalents will vary with the volume of the space protected and the maximum storage cylinder size offered by a manufacturer for a particular gas.
Inergen
Water mist
400 450 529 497
625 613 671 522
327 365 459 404
1119 889 1030 636
277 330 449 460
1032 723 478 376
Extinguishing Mechanisms Halocarbon clean agents extinguish fires by a combination of chemical and physical mechanisms depending on the compound. Chemical suppression mechanisms of HBFC and FIC compounds are similar to Halon 1301; that is, the Br and I species scavenge flame radicals, thereby interrupting the chemical chain reaction. FIC-13I1 is the only HBFC or FIC compound listed in Table 44.1. Other replacement compounds suppress fires primarily by extracting heat from the flame reaction zone, thereby reducing the flame temperature below that which is necessary to maintain sufficiently high reaction rates by a combination of heat of vaporization, heat capacity, and the energy absorbed by the decomposition of the agent. Oxygen depletion also plays a role in reducing flame temperature. The energy absorbed in decomposing the agent by breaking fluorine and chlorine bonds is quite important, particularly with respect to decomposition production formation. There is undoubtedly some degree of “chemical” suppression action in flame radical combustion with halogens, but it is considered to be of minor importance since it is not catalytic (e.g., one F radical combines with one H flame radical).
1486
P.J. DiNenno and E.W. Forssell
a
b 85
28-31 25 50
635 4 5
235
3
1
2
All dimensions in mm
Fig. 44.1 Schematic of cup burner apparatus [3]
The lack of significant chemical reaction inhibition in the flame zone by HCFC, HFC, and FC compounds results in higher extinguishing concentrations relative to Halon 1301. The relative importance of the energy sink represented by breaking halogen species bonds results in higher levels of agent decomposition relative to Halon 1301. Inert gas clean agents act by reducing the flame temperature below thresholds necessary to maintain combustion reactions. This condition is created by reducing the oxygen concentration and by raising the heat capacity of the atmosphere supporting the flame. The addition of a sufficient quantity of inert gas to reduce the oxygen concentration below 12 % (in air) will extinguish flaming fires. The agent concentration required is also a function of the heat capacity of the inert gas added. Hence, there are differences in minimum extinguishing concentration between inert gases.
Flammable Gas and Liquid Extinguishing Concentration Flame suppression effectiveness of total flooding clean agents has been evaluated in a number of ways. The predominant small-scale test method
for establishing flame extinguishing concentrations for liquid and gaseous fuels is the cup burner or variations thereof. Figure 44.1 is a schematic of the cup burner apparatus as specified in ISO 14520 [3]. A small laminar flame is established above a “cup” of fuel surrounded by a cylindrical chimney. An air-agent mixture flows up the chimney surrounding the flame. The minimum concentration of agent (in air) at which the flame is extinguished is the minimum extinguishing concentration (MEC). There are many variations of the basic device as used by different laboratories. These variations include cup and chimney diameter, different mixing and measuring methods, chimney height, and agent-air mixture velocity past the flame [3]. Since about 2005, cup burner devices and test procedures have been standardized to the point where very little variation is seen between devices and laboratories. Users are cautioned that older data may not have been obtained using the standardized apparatus and procedures. The current n-heptane cup burner extinguishing values using the more recent standardized device are given Table 44.3. In addition, the validity and utility of the cup burner test apparatus has been verified in part by a theoretical model of the flame extinction process [4].
44
Clean Agent Total Flooding Fire Extinguishing Systems
1487
Table 44.3 n-Heptane cup burner extinguishing values from various investigators Reference NFPA 2001[1]
Halon 1301 ~3.2
FK-5-1-12 4.5
HFC-125 8.7
HFC 227ea 6.7
IG-541 31
IG-55 35
From NFPA 2001[1] Table 44.4 Agent fraction in the oxidizer stream at extinction of n-heptane cup burner flames [5] Agent type Inert
Nitrogen containing Silicon containing Sodium containing Hydrofluorocarbons
Fluorocarbons
Chlorine containing
Bromine containing
Iodine containing
Agent N2 CO2 He Ar NF3 SiF4 NaHCO3 (10–20 μm) CF3H CF2H2 CF2H2/C2HF5 CH2FCF3 CHF2CF3 CF3CH2CF3 C3HF7 CF4 C2F6 C3F6 C3F8 c-C4F8 C4F10 CHF2Cl CHCl2F CH3CF2Cl CF2 ¼ CHCl CF2 ¼ CFCl CHFClCF3 CF3Br CF2Br2 CH2BrCF3 CH2 ¼ CHBr CF2 ¼ CFBr CF2 ¼ CHBr CF3l
Mass percent 31 32 6.0 38
Volume percent 32 23 31 41
a
a
36 3.0 25
13
c
c
30 29 29 27 28 37 30 29 30 32 32 28 32
15 10 8.7 6.5 6.2 16 8.1 7.3 6.3 6.3 5.3 12 11
c
c
c
c
31 26 14 16 17
10 7.0 3.1 2.6 3.5
c
c
27 24 18
6.3 6.0 3.2
b
12
a
Acted as an oxidizer, promoted flame stability Solid powder not expressed in volume percent c Agent observed to be flammable b
The cup burner concentration for IG-541 is 31 % as given in Table 44.3. This result is in contrast to concentrations of 32, 41, and 23 % by volume measured by the National Institute of Standards and Technology (NIST) for nitrogen, argon, and carbon dioxide, the components of
Inergen. NIST has conducted investigations on a wide range of halon replacement chemicals for aviation use. In order to give a wider perspective on the type and range of chemicals being evaluated for fire suppression use, Table 44.4 is included. The table gives cup burner n-heptane
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P.J. DiNenno and E.W. Forssell
Table 44.5 Cup burner minimum extinguishing concentrations [5–9] Fuel Acetone Acetonitrile AV gas n-Butanol n-Butyl acetate Cyclopentanone Diesel no. 2 Ethanol Ethyl acetate Ethylene glycol Gasoline (unleaded) n-Heptane Hydraulic fluid JP-4 JP-5 Methane Methanol Methyl ethyl ketone Methyl isobutyl ketone Morpholine Propane i-Propanol Pyrrolidine Tetrahydrofuran Toluene Turbo hydraulic oil 2380 Xylene
Cup burner extinguishment concentration (Vol %) HFC-227eab FC-3-1-10 HFC-23 5.5a 6.8e 3.7e 6.7e 7.1e 6.6e 6.7e 6.7e 8.1e 6.8a e 5.6 7.8e 6.5e 6.0b 5.2c 12.0c c d 5.8–6.6 5.0 12.6d b b 5.8 4.3–4.5 6.6e 6.0b 4.8b c 6.6 6.2e 10.0e 9.4a e 6.7 6.6e 7.3e 6.3e 6.0b e 7.3 7.0e 7.2e 5.8e 5.1e 5.3e
HCFC Blend A
N2
12.6d
32b 22–26b 27b
32.5b
a
From Ferreira et al. [9] From Hamins et al. [5] c From Sheinson et al. [7] d From Moore et al. [8] e From Robin [6] b
flame extinction data for a wide range of potential halon replacements. Table 44.5 presents cup burner MEC for a range of fuels and agents taken from various sources [5–9]. Where multiple values of the MEC were found, they are given. The nitrogen data are presented as representative inert gas values. Argon/N2 blend MEC values would be higher. These data were not all developed using the standardized cup burner device. These data should not be used for design purposes without
ensuring that the concentrations are consistent with system manufacturer requirements and third-party approvals. Table 44.6 presents cup burner and full-scale data from VdS [10]. Table 44.7 is a compilation of “best values” of cup burner data from a range of sources compiled by Tapscott [11]. In addition to the cup burner apparatus, researchers at NIST have utilized an opposedflow diffusion flame (OFDF) apparatus to rank clean agents (halon replacements) for fire
44
Clean Agent Total Flooding Fire Extinguishing Systems
1489
Table 44.6 Inert gas extinguishing concentration data from VdS [10] ISO cup burner
Extinguishant gas Fuel Acetone CO2 Diethyl ether Ethanol n-Heptane n-Hexane Methanol n-Pentane Toluol Polypropylene Polyethylene Wood crib Argon Acetone Diethyl ether Ethanol n-Heptane n-Hexane Methanol n-Pentane Toluol Polypropylene Polyethylene Wood crib Inergen Acetone Diethyl ether Ethanol n-Heptane n-Hexane Methanol n-Pentane Toluol Polypropylene Polyethylene Wood crib Nitrogen Acetone Diethyl ether Ethanol n-Heptane n-Hexane Methanol n-Pentane Toluol Polypropylene Polyethylene Wood crib a
Fuel unheated (percent by volume gas) 18.7 – 20.8 19.6 20.4 27.5 – 15.9
Room fire Fuel heated (percent by volume gas) 19.4 23.0 23.0 21.1 21.3 28.5 21.6 16.7
VdS large cup burner (percent by volume gas) 21.4
Extinguished (percent by volume gasa)
Not extinguished (percent by volume gasa)
23.3
24.1
23.1
26.8
24.4
40.8
38.7
30.7
29.0
28.1
26.6
36.6
33.8
28.6
27.7
31.3
21.5 20.8 37.8 – 41.4 40.9 40.0 52.2 – 32.7
38.8 44.8 44.1 41.4 41.5 55.6 41.7 35.5
43.7
45.0 54.5
40.6 37.8 29.4 – 32.8 33.0 31.6 41.1 – 25.7
31.7 35.7 35.5 33.8 34.8 43.8 32.9 28.1
35.9
37.2 47.3
35.8 31.3 28.5 – 32.1 30.9 30.6 38.5 – 22.2
29.9 33.8 34.5 32.3 32.6 41.2 32.4 28.0
Calculated on the basis volume of discharge extinguishant
33.2
35.6 44.8
34.7 30.8
Ethyl acetate Ethylene glycol Exxon Turbo Oil Gasoline (unleaded) Heptane (commercial) n-Heptane
n-Decane Diesel Diesel no. 2 Diethyl ether n-Dodecane Ethanol
Acetonitrile Aviation gas, 100 octane, low lead Benzene n-Butanol n-Butyl acetate Carbon disulfide Cyclohexane
Fuel 70 % isopropanol in water 80 % methanol/ 20 % n-heptane Acetone
9.9 (1)
6.7 0.3 8.9 (3)* (1)
6.5 0.2 (1) 6.6 0.0 (5)
IG-55 26 (1)
35 3.7 (2)
30 (1) 30 (1) 16 (1) 26 (1)
30 (1)
26 (1)
33 (1) 36 (1) 49 (1) 32 (1)
29 0.90 31 (1) (3) 16 (1) 30 (1) 26 (1)
IG-541
34 (1) 36 (1) 33 (1) 35 2.7 35 3.3 (3) (2)
34 (1)
31(1)
29 (1)
IG-100
12.6 0.5 32 (1) (2) 13.0 0.2 6.3 0.4 42 1.4 33 1.6 31.2 (5) (3) (3)* (3) (3)
37 (1)*
7.5 (1)
9.7 (1)*
41 (1) 35 (1)* 31 (1)*
16.0 0.0 (2)
27 (1)* 45 (1)
10.6 (1)* 11.1 (1)*
8.9 (1)
8.5 0.2 (2)
33 (1)* 32 (1)*
38 (1)
IG-01
36 (1)*
10.6 (1)
HFC 236fa
10.1 0.3 (2)*
4.8 (1)
6.8 0.1 (2)*
8.3 (1)*
HFC 125 HFC 227ea HFC-23
36 (1)*
6.8 (1)*
HCFC 124
12.2 (1)* 9.8 (1)*
10.0 0.7 (2)* 7.0 (1)* 11.4 0.1 (2)*
FIC HCFC 13I1 Blend A
3.4 0.0 5.4 0.1 (3) 3.2 (2) (1)
3.2 (1)
3.7 (1) 4.3 0.0 6.9 0.0 (2) (2)
3.9 (1)
3.4 (1)
5.2 (1)
5.8 (1)*
2.4 (1)
FC-3-1-10
Halon 1301
Table 44.7 “Best values” of cup burner concentrations (vol %) [11]
1490 P.J. DiNenno and E.W. Forssell
8.0 (1)
7.8 (1)
3.8 (1)
*Not determined with standard cup burner apparatus
2.3 0.0 3.6 0.0 (2) (2) 2.3 (1) 5.4
3.4 (1)
5.0 (1)
3.4 (1)
8.7 (1)*
6.8 (1)
12.6 (1)* 10.6 (1)* 10.1 (1)* 12.0 (1)*
13.7 (1)* 12.4 (1)*
9.4 (1)*
13.7 (1)* 17 (1)
9.0 (1)* 10.1 (1)* 9.7 (1)
9.8 (1)* 10.6 (1)*
20 (1)*
11.0 0.1 (2)*
6.9 (1)*
12.5 (1)
11.3 (1)
4.8 0.3 (4) 6.6 (1)
9.7 0.0 (2) 12.8 (1)
10.2 0.4 19 (1) (3)
6.4 (1)
5.9 (1) 7.2 0.2 (1)
8.0 (1)*
26 (1)*
33 (1)
40 (1)*
34 (1)*
38 (1)*
35 (1)* 52 (1)
32 (1)* 32 (1)*
35 (1)*
26 (1)*
40 (1)
31 (1)
28 (1)
31 0.4 (2)
25 2.0 25 0.5 (3) (2) 27 (1) 28 (1) 33 (1)
34 (1) 30 (1)*
41 3.5 41 (1) (2)
30 (1)
31 (1)
24 (1)
26 (1)
31 (1) 32 (1)
34 (1)
32 (1)
25 (1) 39 (1)
26 (1)
28 (1)
29 (1)
21 (1)
29 (1)
Clean Agent Total Flooding Fire Extinguishing Systems
Xylene
Transformer oil n-Undecane
Toluene
Methyl isobutyl ketone Morpholine Natural gas Nitromethane n-Octane n-Pentane Propane n-Propanol Pyrrolidine Tetrahydrofuran
Jet A/JP-5 JP-4 JP-8 Kerosene Methane Methanol
Hydraulic oil (Mobil Fluid 350) Hydrogen Isobutanol Isooctane Isopropanol
n-Hexane
44 1491
1492
P.J. DiNenno and E.W. Forssell
extinguishing effectiveness. The OFDF burner is commonly used for combustion research. It has many advantages as a research tool for fundamental combustion studies. Its primary advantage is in its ability to relate the results to fundamental predictions of flame structure and conditions at flame extinction. The oxidizer (and suppressant) stream is forced down onto the fuel surface, exhaust gases are drawn down through an annulus or jacket around the fuel cup, and a flat flame is established. Water cooling is provided for the fuel cup and exhaust gas. The OFDF burner can vary the turbulence intensity or strain rate of the flame. For most applications of clean agent fire suppression, the strain rate is not a major concern, but in specialized applications, such as engine nacelles with high fuel and oxidizer flow rates or in highpressure spray or jet fires, the strain rate will substantially impact the minimum condition for extinguishment. Figure 44.2 is a sample plot showing the variation of the mole fraction of extinguishing agent versus the strain rate at extinction for n-heptane fuels for a range of suppressants. For typical natural fires, the strain rate is approximately 25 s1. At high strain rates, the flame is extinguished at lower agent concentrations. Figure 44.3 shows the relationship between MEC for the cup burner and OFDF apparatus.
Fig. 44.2 Mole fraction of various suppressants as a function of strain rate at extinction for n-heptane [5]
As expected, the cup burner concentration is quite similar to the OFDF concentration at a low strain rate (25 s1), typical of natural fires. In all cases, the MEC of agent is much lower for high strain rate flames, which further reinforces the value of the cup burner and OFDF apparatus for evaluation of minimum extinguishing concentration. The reduction in extinguishing concentration as a function of the velocity of the agent/air mixture across the flame has important ramifications in the evaluation of extinguishment results when the velocity of the agent/air mixture at the flame is not well controlled. This often gives rise to erroneous and misleadingly low extinguishing concentrations obtained from fullscale room test results. When in doubt the higher extinguishing concentration obtained by smallscale tests at low strain rates should be used. This is particularly important because at near flame extinction conditions there is a very strong dependence of extinguishing concentration and velocity of the agent/air mixture. The practical implications of this fact are discussed later in this chapter under design concentrations.
Solid Fuel Extinguishing Concentrations Extinguishing concentrations for Class A fuels were traditionally developed using wood cribs as
0.40 XCF3Br XFC 31–10 XFC 218 XFC c318 XHFC 227 XHFC 236 XHCFC 124
XInhibitor
0.30
0.20
XHFC 125 XHFC 134a XFC 116 XHCFC 22 XHFC 32/125 XN 2
0.10
0.00 0
50
100
150
200
Strain rate at extinction (s–1)
250
300
Clean Agent Total Flooding Fire Extinguishing Systems
Fig. 44.3 Comparison of n-heptane extinction results for the cup burner and OFDF apparatus at two strain rates [5]
1493
35 Cup burner Volume percent of agent in oxidizer
44
Counterflow (a = 25 s−1)
30
Counterflow (a = 180 s−1) 25 20 15 10 5
N2
HFC-32/125
HCFC-22
FC-116
HFC-134a
HFC-125
HCFC-124
HFC-236
HFC-227
FC-318
FC-218
FC-31-10
1301
0
N-Ext N-Ext 660
72.6 m3 14.5 m3
PMMA-Blk PMMA-Clr Polypropylene ABS Pine
Extinguishment time (s)
600 540 480 420 360 300 240 180 120 60 0 4.5
5.0
5.5
6.0
6.5
7.0
7.5
Agent concentration (vol %)
Fig. 44.4 Typical Class A extinguishment results for HFC-227ea
part of the equipment listing/approval process. Further, the minimum Class A extinguishing concentration used for design purposes was required to be greater than or equal to the minimum extinguishing concentration (MEC) for heptane. Additional tests utilizing plastic sheet
arrays of polymethylmethacrylate (PMMA), acrylonitrile-butadiene-sytrene (ABS), and polypropylene (PP) have been required [12, 13]. Typical results are shown in Fig. 44.4 for two different room sizes. The results of these tests indicate that for extinguishment times exceeding
1494
3 min, the extinguishing concentrations for these materials are below the heptane cup burner value and in general above the concentration required to cause extinguishment of the wood crib fires. The plastic sheet array fires therefore determine the Class A concentration requirements for these agents. Note that the most recent addition of NFPA 2001[1], imposes a minimum Class A design concentration equal to that of the minimum extinguishing concentration for n-heptane as determined with the cup burner apparatus. Table 44.8 gives extinguishment and design concentration values for clean agents, using both NFPA 2001, Standard on Clean Agent Fire Extinguishing Systems, and the related UL third-party approval protocols and ISO 14520 installation standard. The extinguishing concentration values designated as test results in the table vary between NFPA 2001 and ISO 14520, primarily due to the slight differences in the test protocols, particularly for Class A solid fuel surface fires. There are differences between some equipment manufacturers for the same agent, which indicates a significant problem with the validity of the test result, in that the extinguishing concentrations should be independent of the system delivery hardware used. To the extent that there are hardware dependencies, the actual extinguishing concentration is, at best, equal to the higher value. Test differences between NFPA 2001 and ISO 14520, particularly for Class A fuels, indicate that the NFPA minimum extinguishing concentrations are artificially low for most agents. This is in part due to efforts by system manufacturers to reduce the minimum extinguishing concentration for Class A fuels with regards to the NFPA 2001 Standard and UL Approval Standards. For example, the HFC-227ea minimum extinguishing concentration for Class A fuels was reduced from 5.8 % to 5.2 % between 1996 and 2010. At a minimum, the ISO test values for minimum extinguishing concentration should be used. Additional discussion of the design concentration values in the table is presented later in this chapter.
P.J. DiNenno and E.W. Forssell
Energized Electrical Equipment Extinguishing Concentrations Clean agent systems are widely used in electronic equipment areas where fires involving electrically energized cables and equipment are encountered. Extinguishment tests involving PMMA heated externally with Nichrome wire indicated that agent concentrations substantially higher than those typical for plastic fuels were required. For example, minimum extinguishing concentrations of 9.5, 9, 20, and 56.1 % were required for FC-3-1-10, HFC-227ea, HFC-23, and IG-541 respectively at the highest applied energy level (192 W applied to wrapped 7.5 5.0 0.6 cm (3 2 0.25 in. block of PMMA). The increase in required concentration was a direct function of the energy applied, consistent with the heat absorption extinguishing mechanism utilized by these agents. Note that increased fire size does not require an increase in agent concentration as the heat flux to the fuel surface does not vary significantly with fire size. Linteris [14] at NIST obtained similar results that showed that minimum extinguishing concentrations may easily double when even small amounts of external heating are applied, using the Radiant Enhanced Extinguishment Device (REED). For example the minimum extinguishing concentration of Nitrogen more than doubled with the addition of relatively small external heat flux from results reported by Factory Mutual. Additional data from NIST on HFC-23 showed an increase in required extinguishing concentration of 350 %. These data are summarized in Fig. 44.5. Additional data using the same device for the range of current clean agents shows similar results [15]. Extinguishment tests on actual wire and cable materials were reported by McKenna et al. [16]. Three types of tests were conducted: ohmic heating, conductive heating, and printed wiring board arcing. The ohmic heating tests involved deliberate electrical overheating of the conductor. The electrical current applied was just below what would result in melting and breaking the conductor. These results are summarized in
Trade name FM-200, FE-227
FE-25
NAF-S-125 FE-13
Novec-1230
Inergen Argonite Argon Nitrogen
Agent HFC-227ea
HFC-125
HFC-23
FK-5-1-12
IG-541 IG-55 IG-01 IG-100
A B
Equipment manufacturer A B C D E F A B ~ C A B 4.5 4.5 28.9
12.9
8.7 8.7
5.9 5.9 37.6
11.3 11.3 18 16.8
28.5
3.5
6.7
6.7
5.2 5.4
34.2
4.2
8.0 18
8.0
6.2 6.5
4.5 31.7 36.5 39.2 33.6
12.6
9.3
6.9
5.9 41.2 47.5 51.0 43.7
16.4
12.1
9.0
Class B Test Design
Design 8.7 8.7 8.7 8.7 8.7 8.6
ISO 14520
Class B Test 6.7 6.7 6.7 6.7 6.7 6.6
Class A Test Design
UL (NFPA 2001)
5.6 39.1 45.1 48.4 41.5
15.6
11.5
8.5
Class A Min (95 % of Class B)
Table 44.8 Summary of the Class a and Class B extinguishing concentrations for various agents and equipment manufacturers
4.1 (3.4 WdCrib) 30.7 (28.2 WdCrib) 31 (28.7 WdCrib) 32.2 (30.7 WdCrib) 31.0 (30 WdCrib)
12.5 (10.5 WdCrib)
6.7
8.6 (6.7 WdCrib)
6.1 (4.9 WdCrib)
Test
5.3 36.5 40.3 41.9 40.3
16.3
8.7
11.2
7.9
Design
44 Clean Agent Total Flooding Fire Extinguishing Systems 1495
1496
P.J. DiNenno and E.W. Forssell
70
Agent Volume Fraction (%)
60
N2
50 40 CF3H 30 20 FMRC FPA REED, NIST
10
REED, 3M 0 0
60 20 40 External Heat Flux / kW/m2
Fig. 44.5 Effect of external applied energy on extinguishment concentration (Linteris [14])
Table 44.9 for HFC-227-ea. This limited testing with low energy single and small cable bundles indicated that for HFC-227ea a concentration of between 6.5 % and 6.8 % was necessary to extinguish small cable bundles or arrays with PVC/PE or PE insulation. These values exceed the minimum Class A extinguishing concentration for HFC-227ea of between 5.2 % and 5.4 % and the design concentration of 6.2–6.5 %, which is supposed to embody a 20 % safety factor. This dangerous situation has arisen, in part, because the Class A extinguishing concentration for HFC-227ea has been reduced from 5.8 % to 5.2% over time. This further illustrates the weakness of the test method used to determine Class A minimum extinguishing concentrations. A situation now exists in which small energized electrical fires would not be extinguished at either the minimum extinguishing concentration or the design concentration. These same fires would have been expected to be extinguished at the design concentration in 1996. This is due, in part, to poor experimental design of full scale tests where the effects of agent/air velocity at the flame were not sufficiently controlled and erroneous low minimum extinguishing concentrations were obtained.
The 6.5–6.8 % concentration required to extinguish all the test fires in Table 44.9 should be viewed as minimum extinguishing concentration with respect to these fires. A design concentration, suitable for use in actual installations, would incorporate an appropriate safety factor (20–30 % similar to Class A or B applications). This would imply a design concentration between 8.2 % and 8.8 % which would correspond to an approximate 50–60 % increase over the minimum Class A extinguishing concentration for HFC-227ea. Linteris [14] also included a comprehensive review of suppression of energized electrical equipment and discussed the relevance and weaknesses of various ad hoc electrical equipment tests including those described above. The conclusion of this work is that the current guidance on minimum extinguishing concentrations for energized electrical equipment is inadequate, and insufficient data is available to definitively prescribe these concentrations. It is clear that theoretical and experimental results indicate that substantially higher concentrations than those currently used, are necessary. These very limited results on small electrically energized conductors are not applicable to large-diameter, high-voltage, and high-powerrated cables, particularly in cable bundles and arrays. Such cables in these arrays have historically required much higher extinguishing concentrations than Class A surface values. For example, Sandia Laboratories and the Nuclear Regulatory Commission required design concentrations of 40 % for carbon dioxide and 6 % for Halon 1301 for such periods of at least 30 min. NFPA 12, Standard on Carbon Dioxide Extinguishing Systems, requires a CO2 design concentration of >40 % for energized electrical equipment. These values represent increases of at least 20 % (for Halon 1301) over the Class A design value. As indicated in previous discussions, the Class A design value for the Halon 1301 is in the range of 80 % higher than HFC-125 when compared to a common baseline. ISO 14520 [3], recognizing the more challenging nature of energized electrical fires,
44
Clean Agent Total Flooding Fire Extinguishing Systems
1497
Table 44.9 Summary of ohmic heating tests with HFC-227ea [16]
Test EEE035 EEE036 EEE046 EEE049 EEE037 EEE038 EEE039 EEE054 EEE055 EEE040 EEE047 EEE050 EEE053 EEE041 EEE043 EEE044 EEE056 EEE059 EEE062 EEE068 EEE069 EEE071 EEE075 EEE079 EEE076 EEE077 EEE078 EEE058 EEE061 EEE065 EEE066 EEE067 EEE057 EEE060 EEE064 EEE031 EEE033 EEE048 EEE029 EEE030 EEE028 EEE026
Current Sample (A) 8 AWG XLPE, 5 wire bundle, center wire 350 energized 350 350 350 350 350 350 350 350 350 12 AWG SJTW-A, 6 cable bundle, 4 of 600 18 conductors energized 600 600 600 600 600 8 AWG PVC, 7 cable bundle, center wire 325 energized 325 325 18 AWG chrome PVC, over PE, 4 cable 350 bundle, 12 conductors energized 350 350 350 350 350 350 350 350 350 350 350 350 16 AWG neoprene over rubber, 9 of 500 12, conductors energized 500 500 18 AWG PE, 4 parallel wire array, all 475 wires energized 475 475 475 475 475 475
Orientation Horizontal Horizontal Horizontal Horizontal Horizontal
Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal
Ignition source Pilot Pilot Pilot Pilot Pilot Pilot Pilot Pilot Pilot Pilot Pilot Pilot Pilot Pilot Pilot Pilot Pilot Pilot Pilot Pilot Pilot Pilot Pilot Pilot Pilot Pilot Pilot Pilot Pilot Pilot Pilot Pilot Pilot Pilot Pilot Self-ignited Self-ignited Self-ignited Self-ignited Self-ignited Self-ignited Self-ignited
% C3HF7 (FM 200) 5.8 5.8 5.8 5.8 5.8 5.8 5.8 5.8 5.8 5.0 5.8 5.8 5.8 5.5 5.5 5.0 5.8 5.8 5.8 6.8 6.8 6.5 6.5 6.5 6.2 6.2 6.2 5.8 5.8 5.8 5.8 5.8 5.8 5.8 5.8 6.8 6.8 6.8 6.5 6.5 5.8 5.7
Time to extinguish (s) 9 9 10 13 13 8 8 10 10 11 11 11 9 9 8 11 12 10 13 12 13 15 11 16 DNE 15 DNE 12 DNE 10 11 DNE 3 6 6 14 14 14 DNE DNE DNE DNE
1498
provides additional guidance for applications involving energized electrical equipment: It is recognized that the wood crib and polymeric sheet Class A fire tests may not adequately indicate extinguishing concentrations suitable for the protection of certain plastic fuel hazards (e.g., electrical and electronic type hazards involving grouped power or data cables such as computer and control room under-floor voids, telecommunication facilities, etc.) An extinguishing concentration not less than that determined in accordance with 7.5.1.3 (wood crib and plastic sheet array fire tests), or not less than 95% of that determined from the heptane fire test described in C.6.2 (heptane pan fire test), whichever is the greater, should be used under certain conditions. These conditions may include: 1. Cable bundles greater than 100 mm in diameter; 2. Cable trays with a fill density greater than 20% of the tray cross-section; 3. Horizontal or vertical stacks of cable trays (closer than 250 mm); 4. Equipment energized during the extinguishment period where the collective power consumption exceeds 5 kW.
Given the uncertainty apparent in the NFPA 2001 Class A and energized electrical equipment values for minimum extinguishing concentrations, designers should consider using ISO 14520 as the basis of any total flooding clean agent system design. Section “Design Concentrations” provides additional guidance and discussion on this topic.
Explosion Inerting One of the most important application areas of total flooding fire suppressants is explosion inertion. The inerting concentration of an agent is the concentration required to prevent unacceptable pressure increases in a premixed fuelair-agent mixture subjected to an ignition source. Inertion concentrations are typically measured in small laboratory-scale spheres with an electric spark initiator. The measured inerting concentration of an agent is dependent on the details of the test apparatus used, particularly the ignition source strength and “allowable” pressure rise. The allowable pressure rise is a surrogate measurement of the distance the flame front travels inside
P.J. DiNenno and E.W. Forssell Table 44.10 Explosion inerting concentrations, smallscale inertion sphere [6, 17–19] Inerting concentration (vol %) of fuel Propane Methane i-Butane Pentane 10.3a ~7.8b – – b 9.5 HFC-227ea 12.0b 8.0b 11.3a 11.6c c 11.6 HFC-23 20.2a 20.2a – – b 19.8 14.0b IG-541 49.0d 43.0d – – b HCFC Blend A 18.0 13.3b – –
Agent FC-3-1-10
a
From Senecal [17] From Heinonen [19] c From Robin [6] d From Tamanini [18] b
the constant-volume sphere prior to suppression. Inerting concentration is not appropriate for use in explosion suppression either deflagrations or detonations. Small-scale sphere data are used to develop flammability diagrams for various fuel-oxidizeragent concentrations. Chapter 17, which addresses flammability limits, gives an excellent introduction to the subject. There is a wealth of data in the combustion literature on flammability limits of a variety of fuels in the presence of an atmosphere of inert gases, such as nitrogen and argon. Table 44.10 provides inerting concentration data for several agents and fuels taken from small scale inertion spheres [17–19]. There are some substantial differences in results. Heinonen [20] has identified both ignition source type and strength as important variables with differences of 40 % for Halon 1301 inerting concentrations reported. Large scale inertion results have been presented by Moore [21]. While the small to large scale agreement is reasonable, there are scale effects.
Explosion Suppression Explosion suppression systems employ rapid delivery of agent following very early detection of an ignition. Such systems employ significantly
44
Clean Agent Total Flooding Fire Extinguishing Systems
higher agent quantities (than flame suppression or inertion) delivered at higher rates. The total agent delivery time is on the order of 100 ms. Explosion suppression systems must be specifically designed for a particular application. There are no generic design requirements or standards currently available for such systems. Senecal [22] and Senecal et al. [23] report on explosion suppression testing in occupied armored fighting vehicles and aerosol filling rooms. Results were obtained on premixed fuel droplet (aerosol) sprays. In contrast to flame suppression or inerting, suppression of a deflagration or detonation requires significantly more agent. The tests employed 20 kg of HFC-227ea, FC-3-1-10, and HFC-236fa, and 10 kg of water in an 80 m3 test room to suppress a 90 g propane release in a simulated aerosol filling station. Suppression of the propane-air deflagration was achieved, and the maximum flame front extension was approximately 1.22 m. Suppression tests of heated diesel fuel droplet cloud deflagrations were also conducted in simulated armored fighting vehicle crew compartments. Table 44.11 summarizes typical data for flame suppression, inertion, and deflagration suppression concentrations. Note these values are for comparison purposes only. They should not be used in any way for design purposes. Suppression of detonations requires substantially higher agent concentrations than for deflagrations. An excellent discussion on this topic is given in Hamins et al. [5].
1499
Toxicity A major factor in the use of a clean agent fire suppressant in a normally occupied space is toxicity. Although all halocarbon agents are tested for long-term health hazards, the primary endpoint is acute or short-term exposure. The primary acute toxicity effects of the halocarbon agents described in this chapter are anesthesia and cardiac sensitization. For inert gases, the primary physiological concern is reduced oxygen concentration. Halocarbon Agents Cardiac sensitization is the primary short-term toxicity problem for fire suppression applications involving halocarbon agents. Cardiac sensitization is an increased potential for cardiac arrhythmia with exposure to the agent in conjunction with the hormone epinephrine or adrenalin. Cardiac arrhythmia is a condition in which the heart beats with an irregular or abnormal rhythm and in an extreme case, can lead to a heart attack. Epinephrine is produced naturally by the body with increased production rates when the body is under stress. Epinephrine can cause arrhythmia on its own at high concentrations. Cardiac sensitization reduces the epinephrine concentration associated with the onset of cardiac arrhythmia when exposed to the agent. The two toxicity endpoints used to describe cardio-toxicity and allowable exposure levels are (1) no observed adverse effect level (NOAEL) and (2) the lowest observed adverse effect level
Table 44.11 Comparison of concentrations for flame extinguishment, inertion, and deflagration suppression [1, 22] Volume (%) Agent Halon 1301 FC-3-1-10 HFC-227ea HFC-23 IG-541
Typical value flame suppression 3 5.5 5.8 12 29
Inerting concentration in propane 6–7 10.3 ~12 20.2 49.0
Diesel fuel droplet deflagration suppression 12 8 11 – –
1500
P.J. DiNenno and E.W. Forssell
(LOAEL). The NOAEL is the highest concentration of an agent at which no “marked” or adverse effect occurred. The LOAEL is the lowest concentration of an agent at which an adverse effect was measured. The procedures used to evaluate cardiac sensitization vary somewhat. The basic approach involves a stepped method that includes the intravenous dosing of male beagle hounds with epinephrine for 5 min. Continuous inhalation exposure to the agent at a specific concentration follows for 5 min. Following this inhalation exposure, the hound is dosed again with epinephrine and monitored for another 5 min to determine the effect of the agent and epinephrine. The protocol is performed at higher doses until an effect occurs. Effects are monitored by electrocardiograph (EKG) measurements. An adverse effect is generally considered to be the appearance of five or more arrhythmias or ventricular fibrillation. The data from these tests are evaluated by medical experts, and the appropriate NOAEL and LOAEL values are reported by the United States Environmental Protection Agency (EPA) under the Significant New Alternatives Policy (SNAP) program. There is no direct correlation between the experimental results from hounds to humans. It is generally accepted, due to the combination of the high doses of epinephrine in the tests and the similarity in cardiovascular function between
hounds and humans, that the results can be applied to humans. For most of the listed halocarbon agents, the concentration where adverse effects are observed is higher than the design concentration required for use in fire suppression. The exceptions to this are FIC-13I1 (CF3I) and HFC-125 (C2HF5). The concentration where cardiac sensitization effects are noted (LOAEL) for FIC-13I1 is 0.4 % by volume [1] while its minimum design concentration for Class B hazards is 4.2 % by volume. For HFC-125, the concentration where cardiac sensitization effects are noted is 10 % by volume which is exceeded by the minimum design concentration for Class B hazards of 11.3 % by volume, however, for Class A hazards, the minimum design concentration is 8.7 % by volume which is less than the LOAEL. In addition to the short-term chronic exposure limits of interest in fire suppression system design, the EPA evaluates longer-term inhalation data for these compounds. One procedure used to evaluate longer-term effects involves the exposure of a concentration of the halocarbon agent to a population of rats for a period of 4-h. The measure LC50 is the concentration of the halocarbon agent lethal to 50 % of the rat population during the 4-h exposure. This is also referred to as the approximate lethal concentration (ALC). Table 44.12 summarizes NOAEL, LOAEL, and
Table 44.12 Toxicity data for halocarbon clean agent fire suppressants [1] Agent FIC-1311 FK-5-1-12 HCFC Blend A HCFC-124 HFC-125 HFC-227ea HFC-23 HFC-236fa HFC Blend B
Trade name Triodide Novec 1230 NAFS-III FE-24 FE-25 FM-200 FE-13 FE-36 Halotron II
LC50 and ALC (%) >12.8 >10 64 23-29 >70 >80 >65 >45.7 56.7a
NOAEL (%) 0.2 10 10 1 7.5 9 30 10 5.0a
LOAEL (%) 0.4 >10 >10 2.5 10.0 10.5 >30 15 7.5a
Notes (1) LC50 is the concentration lethal to 50% of a rat population during a 4-h exposure. The ALC is the approximate lethal concentration (2) The cardiac sensitization levels are based on the observance or non-observance of serious heart arrhythmias in a dog. The usual protocol is a 5 min exposure followed by a challenge with epinephrine (3) High concentration values are determined with the addition of oxygen to prevent asphyxiation a These values are for the largest component of the blend, HFC Blend B (HFC-134A)
44
Clean Agent Total Flooding Fire Extinguishing Systems
1501
Table 44.13 Exposure limits derived from PBPK modeling for HFC-227ea and HFC-125 [1] HFC-227ea concentration % V/V 9.0 9.5 10.0 10.5 11.0 11.5 12.0
ppm 90,000 95,000 100,000 105,000 110,000 115,000 120,000
HFC-125 concentration Human exposure time (min) 5.00 5.00 5.00 5.00 1.13 0.60 0.49
LC50 values. Note that the LC50 values greatly exceed the NOAEL and typical fireextinguishing concentrations. Because the arrhythmia potential is measured in dogs, a means of providing improved human relevance has been established. Physiologically based pharmacokinetic modeling (PBPK) for evaluation of acute exposure to halocarbon agents has been used to establish alternative exposure limits for halogenated agents [1]. PBPK modeling utilizing a computerized tool attempts to account for the time-dependent uptake rate of halocarbons in the body and establishes exposure limits based on the rate of uptake [24–28]. The limits are based on the concentration of agent and the time at which the concentration of agent in the blood equals that of the LOAEL. Typical PBPK results for safe exposure times for HFC227ea and HFC-125 are given in Table 44.13. Note that exposure above the NOAEL limits and up to the LOAEL is permitted. These limits were derived and supported by the EPA, which has the primary regulatory authority for health and toxicity associated with halon replacements. The use of the PBPK approach partially accounts for the differences between laboratory animal tests and humans. The laboratory results form the basis of the endpoints (NOAEL, LOAEL) and are still
% V/V 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5
ppm 75,000 80,000 85,000 90,000 95,000 100,000 105,000 110,000 115,000 120,000 125,000 130,000 135,000
Human exposure time (min) 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 1.67 0.59 0.54 0.49
conservative due to the nature of epinephrine dosage used during the animal tests [29]. Where PBPK modeling data do not exist, the use of halocarbon agents in occupied areas is subject to the constraint that the design concentration must be less than the NOAEL. Although it is recommended that all systems employ predischarge alarms and that personnel evacuate prior to system actuation, it is understood that inadvertent discharges and short-term exposures will occur, hence, the limitation. It is expected that emergency exposures for up to several minutes at or below the NOAEL are reasonably safe. In no case should systems be designed or installed where intentional exposure of any duration is anticipated. It has been proposed by the EPA that agents be permitted for use at concentrations up to the LOAEL where evacuation will occur in less than 60 s. This proposal has not been integrated into design standards to date due to the uncertainty of accidental exposure conditions. Based on the limitation that the design concentration must be below the NOAEL, it can be seen from Table 44.12 that three agents are acceptable for use in normally occupied areas for flame extinguishant purposes: HFC-227ea, HFC-23, and FK-5-1-12. Inert Gas Agents Inert gas agents are, in effect, physiologically inert. The primary physiological
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problem with these agents is the reduced oxygen concentration caused by the high agent design concentrations. One inert gas blend employs a low concentration of CO2 (which is not physiologically inert) in order to counter the effects of the reduced oxygen concentration. The mechanism of this effect is discussed in EBRDC Report 10.30.92 [30]. Current limitations on exposure limits for inert gases are as follows: for gas concentrations up to 43 % (a residual oxygen concentration of 12 %), exposure time is limited to 5 min. For agent concentrations between 43 % and 52 % (12 % and 10 % residual oxygen concentration), the exposure time is limited to 3 min. For concentrations greater than 52 %, exposure time is limited to 30 s. There is strong indication that small concentrations of CO2 added to inert gases (such as IG-541) substantially reduce hypoxic effects and improve human performance at low oxygen levels. Regulatory authorities have not yet differentiated between such agents and other inert gases or blends [30].
Environmental Factors Two main environmental impacts need to be considered with respect to halocarbon extinguishing agents: (1) ozone depletion and (2) global warming [1]. Another environmental factor, atmospheric lifetime, can be considered in the discussion of each of these environmental impacts. It is also a “stand-alone” environmental concern that needs to be addressed. International, national, state, and local governments currently regulate halocarbon fire-fighting agents based on their effect on ozone depletion. However, the EPA also takes into account atmospheric lifetimes and global warming potentials in the implementation of its SNAP program under Section 612 of the Clean Air Act in the United States, as amended in 1990. Although no specific national environmental regulations cover global warming and atmospheric lifetimes, the consideration of these issues in the EPA’s implementation of existing regulations makes these issues of concern.
P.J. DiNenno and E.W. Forssell
Ozone Depletion Ozone (O3) is a naturally occurring gas that is found in the atmosphere. Most naturally occurring ozone is created by the reaction of O2 with ultraviolet (UV) light coming from the sun. O2 þ UV O þ O O þ O2 O3 The UV light causes this reaction to occur. Ozone is also created in nature when the high energy output from lightning initiates a similar reaction. Ozone is also formed by a number of manufactured sources, mainly as a result of air pollution. When carbon monoxide, methane, and other hydrocarbons meet nitrogen oxide (e.g., from car exhaust) and ordinary sunlight, ozone is produced. It is also produced by laser printers and electric motors and is responsible for the pungent odor often associated with the devices. Man-made ozone is often called “smog” and is a considerable health risk. Halons, HCFCs, and other halocarbons containing chlorine or bromine have been shown to cause the destruction of stratospheric ozone. The characterization of stratospheric ozone destruction is not a measure of the exact amount of ozone destroyed. Instead, it is the relative amount of ozone destroyed as compared with an arbitrary standard. The standard chosen is trichlorofluoromethane, CFC-11, a compound of chlorine, fluorine and carbon, which has been assigned an ozone depletion potential (ODP) of 1. ODP of all other halocarbons relates to their relative effect on the destruction of ozone as compared with CFC-11. Halon 1301 has an ODP of 12, meaning it will destroy 12 times as much ozone as CFC-11 on a pound-for-pound (kilogram-for-kilogram) basis. A compound having an ODP of 0.1 would have 10 % of the relative ozone-depleting effects of CFC-11. All ODP values are based on mass (weight) and not on moles (numbers of molecules). The only remaining nonzero ozone-depleting fire-extinguishing gases are HCFC compounds, none of which are widely used for total flooding system applications. All HCFCs are subject to
44
Clean Agent Total Flooding Fire Extinguishing Systems
some degree of environmental regulation in most parts of the world.
Atmospheric Lifetimes When one thinks of a chemical species lifetime, the term half-life is often used. This usage is most common in the nuclear field when calculations are made to determine how long it takes a species to decay to half its original concentration. Atmospheric lifetime values used in the determination of ozone depletion and global warming potentials are not half-lives. They are 1/e lifetimes, sometimes called e-folding lifetimes. It has been determined that greenhouse gases break down in the atmosphere according to the following equation: C ¼ Co ekt where: C ¼ Concentration at time t Co ¼ Initial concentration at time t k ¼ An experimentally determined rate constant ðunits ¼ 1=timeÞ A mathematical manipulation can be made to express this equation as a function of more readily quantifiable terms and is accomplished by defining the atmospheric lifetime, L, as an e-folding lifetime, or the time it takes for the ratio of C:Co to be equal to 1/e (e is the base of the natural logarithm system and has a numerical value of approximately 2.718). The resulting equation is as follows: C ¼ Co et=L Although the term half-life is most commonly used when describing the decay of a species concentration, the use of the e-folding lifetime allows for quantification of concentration in terms of a compound’s atmospheric life-time, as previously shown. A half-life refers to the time it takes for half a given amount of compound to be broken down in the atmosphere; thus, the ratio C: Co is equal to ½. Using an e-folding lifetime, the ratio is equal to 1/e or 0.368. After one lifetime, the concentration will be equal to 0.368 times its original value. After two lifetimes, the
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concentration will be 0.135 or (0.368)2 times its original value. After three lifetimes, the concentration will be 0.0498 or (0.368)3 times its original value, and so on. An important factor when using the preceding equation to solve for concentration as a function of time is that, no matter what value is used for time, the concentration never equals zero. Some portion will always exist in the atmosphere. When the atmospheric life-time is small, the concentration over hundreds of years may become negligible. When the atmospheric lifetime is very large, on the order of tens of thousands of years, the concentration in the atmosphere may not be negligible. The environmental concern is one of “what if.” The halons were believed to be “safe” for many years after their release into the atmosphere began. It was not until many years later that they were linked to ozone depletion. There is a concern that these halocarbons, or other compounds, may cause other environmental impacts that are yet unknown. If the atmosphere is filled with these chemicals and they exist in appreciable amounts for hundreds, thousands, and millions of years, what then? Might the damage we do to our environment be more than humans can cope with? Nature can probably overcome this impact, but it may take tens of millions of years. This is a short time frame for nature but not for man. Current implementation of the EPA SNAP program places restrictions on perfluorocarbons that have very large or “outlying” atmospheric lifetimes as compared with the rest of the halocarbons. This restriction is not based on any known or anticipated environmental problem. It is a response to the “what if” concerns raised previously.
Global Warming Potential The most important global environmental issue is currently climate change. A basic understanding about the earth’s climate and atmosphere is needed to understand what global warming potential (GWP) is and how to attempt its measurement. Estimates of the average temperature of earth’s atmosphere have been made, assuming two theoretical conditions. The first assumes no
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atmosphere at all, and the second assumes an atmosphere made up solely of N2 and O2 (normally representing 99 % of our atmosphere). In both cases, models have predicted that earth’s surface would be some 91 F (33 C) cooler than it is. The temperature difference is believed to be a direct result of the very small amounts of trace gases, water vapor, and CO2. These act very much like the glass on a greenhouse that lets the sunlight in but helps to prevent the heat from escaping, hence, the terms greenhouse effect and greenhouse gases. A greenhouse gas is defined as any gas that absorbs infrared (IR) radiation. Climate change and global warming are not synonymous. Climate change includes cooling and warming of the atmosphere. Global warming only deals with the aspects of climate change that result in warming of the atmosphere. It is estimated that about one-third of the total solar radiation is reflected off earth’s atmosphere. Most of the remaining two-thirds passes through the atmosphere and is absorbed by the earth’s surface, causing it to warm [31]. The earth cools itself by releasing heat, or IR. In order for a balance to be maintained, the solar radiation coming in must equal the radiation going out. If more radiation entered the atmosphere than left, the earth would be constantly getting warmer. The opposite would be true if more radiation left the earth than came in; that is, the earth would be constantly getting cooler. To estimate the amount of global warming expected from a release of a particular greenhouse gas, a scale was developed by the International Panel on Climate Change (IPCC), based on the idea of radiative forcing. This scale is called the global warming potential (GWP) and relates to positive radiative forcing that will cause the atmosphere to heat up. The GWP is the cumulative amount of radiative forcing between the present and some future time caused by a unit mass (weight) of a compound, as compared with the same unit mass (weight) of an arbitrary standard. Carbon dioxide, CO2, is the most common reference, and 20-year, 100-year, and 500-year time periods, or horizons, are the most common time references cited in the literature. The choice
P.J. DiNenno and E.W. Forssell
of time horizons is a policy issue and not a technical one. Since the GWP is a cumulative effect, summed year by year over a given time horizon, the quantity present in the atmosphere must be known year by year over that horizon. The atmospheric lifetime is used to perform these calculations. GWPs are also affected by the specific IR-absorbing capabilities of the chemical. Analogous to ODPs, GWPs are not exact numbers showing the precise effect on global warming. A 100-year horizon GWP of 6200 for Halon 1301 means that 1 lb (0.454 kg) of Halon 1301 will cause as much global warming as 6200 lb (2812 kg) of CO2. A 500-year horizon GWP for methylene chloride of 0.3 means that 1 lb (0.454 kg) of methylene chloride will cause the same warming as 0.3 lb (0.14 kg) of CO2. GWPs are used to determine the future global warming contribution of a substance over a given time by multiplying the weight of the greenhouse gas by a specific time-horizon-GWP. The resultant number can be compared with others to decide which will have the least (or greatest) impact over that time horizon. Emitting a large quantity of a small GWP greenhouse gas may cause less global warming than a small release of a very large GWP greenhouse gas over a certain time horizon. Different time horizons may lead to different results.
Environmental Regulation of Halon Replacements The evaluation of clean agent fire suppressants includes a consideration of environmental factors. International, national, and local government regulations control the use of any alternatives in this regard. As described above, a key environmental consideration is ODP. All chemicals with a nonzero ODP are subject to phaseout under the Montreal Protocol and its amendments. Table 44.14 summarizes environmental impact data for halocarbon agents. Note that FC and HFC compounds have zero ODP. As also discussed above other environmental factors important in a regulatory context are GWP and atmospheric lifetime. The evaluation of GWP is an extremely complex issue, and
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Clean Agent Total Flooding Fire Extinguishing Systems
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Table 44.14 Environmental factors for halocarbon clean agents [31] Designation Halon 1301 HFC-227ea HFC-23 HFC-125 FK-5-1-12 Inert gas
ODP 12.000 0.000 0.000 0.000 0.000 0.000
GWP (100 years) 7030 2900 14,310 3450 1 0
currently none of these compounds are regulated on that basis in the United States. Long atmospheric lifetime, a measure of the persistence of a chemical in the atmosphere, is of concern not only as it relates to GWP but also due to the uncertainty of the effects of chemicals for long time periods in the atmosphere. The EPA currently has use restrictions on FC-3-1-10 based primarily on its long atmospheric lifetime. These restrictions permit the use of this chemical in applications where no other alternative is technically feasible. There is regulation of HFCs and PFCs for fire protection use in many parts of the world. There are few blanket prohibitions of HFCs for fire protection use, but regulation relating to minimizing emissions on the basis of global warming currently exists in Europe. As consensus grows at the magnitude and threat posed by global climate change, one would reasonably expect increased regulation worldwide on HFC fire suppressants. Note that some of the inert gases have no GWP impact and that the FK-51-12, a halogenated agent, has a GWP of 1; therefore, low climate change impact fire suppression gases currently exist. This agent possesses many of the advantages of a halogenated agent but with an environmental impact similar to inert gases. It is also important to bear in mind that the total usage relative to total global production of these gases for fire suppression uses is quite low and perhaps more importantly the emissions of these gases relative to other uses is very low. Hence the overall impact of fire suppression agents to climate change can be expected to be minimal if not negligible. The Halon Alternative Research Commission (HARC) estimates that
Atmospheric lifetime (years) 65 34.2 270 29 0.038 NA
fire protection use of all halocarbons contributes less than .01 % of the impact of all greenhouse gas emissions [32].
Thermophysical Properties Tables 44.15 and 44.16 give thermophysical properties of clean agent replacements from NFPA 2001 for halocarbon and inert gases. Additional thermophysical and transport property data can be found in Robin [6] for FM-200 and Yang and Bruel [33] for a range of halocarbon alternatives. Isometric diagrams for halocarbon agents HFC-227ea, pressurized at 360 and 600 psig at 70 F with nitrogen, and HFC-23 are given in Figs. 44.6, 44.7, and 44.8, respectively. Note that HFC-23 is not pressurized with nitrogen. Figure 44.9 gives the pressure-temperature relationship for inert gases IG-541, IG-55, and IG-01, pressurized to 2175 psig, at 70 F. This display is the pressure-temperature relationship for an ideal gas.
Clean Agent System Design Once an agent has been selected for a specific application, the general discussion on clean agent system design presented in Chapter 43, should be reviewed. Many of the design principles for clean agent systems have been adapted from those principles used for halon systems. The basic process is outlined below: 1. Determine the design concentration. 2. Determine the total agent quantity. 3. Establish the maximum discharge time.
Specific heat, vapor at constant pressure (1 atm) and 25 C Heat of vaporization at boiling point Thermal conductivity of liquid at 25 C Viscosity, liquid at 25 C Relative dielectric strength at 1 atm at 734 mm Hg, 25 C (N 2 ¼ 1.0) Solubility of water in agent
Physical property Molecular weight Boiling point at 760 mmHg Freezing point Critical temperature Critical pressure Critical volume Critical density Specific heat, liquid at 25 C
FIC-1311 195.91 22.5 110 122 4041 225 871 0.592 0.3618 112.4 0.07 0.196 1.41 1.0062 % by weight
Units NA C C C kPa cc/mole kg/m3 kJ/kg C kJ/kg kJ/kg W/m C Centipoise NA ppm
0.12 % by 0.11 % by 700 at weight weight 25 C
165.9 0.0684 0.257 1.55
0.742
HFC HCFC-124 136.5 12.0 198.9 122.6 3620 243 560 1.153
50 %) higher than that measured using the FTIR. Since the HCFC blend contains an HF “scrubber,” it is postulated that treatment of the grab sample with a basic solution, as required for the ISE measurements, caused formation of additional HF by reentry with F loosely bound up by reaction with the scrubber. Hence, the FTIR data presented for HCFC Blend A represent a significantly lower quantity of HF than would actually be expected if the product were hydrolyzed. The effect of long discharge times or delayed extinguishing times is shown in Fig. 44.12 [43]. The variation between the HFC/HCFC alternatives and Halon 1301, relative to HF production, is approximately the same as that shown in Fig. 44.11 for different fire sizes. Although other thermal decomposition products have been identified in some cases, it appears that HF is the primary thermal
Clean Agent Total Flooding Fire Extinguishing Systems
Fig. 44.12 Maximum HF concentration resulting from extinguishment of 4.0-kW heptane fires [43]
6000 HF concentration (ppm)
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1.2 m3 Halon 1301 C3HF7 C4F10 CHF3 C3F8 C2HF5 NAF-S-III
5000 4000 3000 2000 1000 0
0
5
10
15
20
25
30
35
Total discharge time (s)
Table 44.19 Potential human health effects of hydrogen fluoride in healthy individuals [1] Exposure time 2 min
5 min
10 min
Hydrogen fluoride (ppm) 200 200 200
Reaction Slight eye and nasal irritation Mild eye and upper respiratory tract irritation Moderate eye and upper respiratory tract irritation, slight skin irritation Moderate irritation of all body surfaces, increasing concentration may impair escape Mild eye and nasal irritation Increasing eye and nasal irritation, slight skin irritation Moderate irritation of skin, eyes, and respiratory tract Definite irritation of tissue surfaces, will impair escape at increased concentrations Definite eye, skin, and upper respiratory tract irritation Moderate irritation of all body surfaces Moderate irritation of all body surfaces, escape-impairing effects likely Escape-impairing effects will occur, increasing concentrations can be lethal without medical intervention
decomposition product of interest relative to human safety and equipment damage. HF, like HCl, is an irritant gas, detectable at very low concentrations. For HF there are very large differences between the approximate lethal concentration (ALC) and human detection and severe sensory irritant thresholds (approximately 2 and 3 orders of magnitude, respectively). The fire size necessary to generate short-term lethal concentrations of HF in an enclosure (on the order of >1000 ppm) can, in some cases, pose a greater hazard to personnel in the
protected space during a discharge in a fire incident, due to the fire and its effects, than the secondary impact of agent thermal decomposition products. This effect, however, should be verified for a particular application under a range of fire scenarios, using engineering methods discussed by Hanauska [46] and Hanauska et al. [47]. The production of HF and other agent decomposition products forms a potential hazard for occupants. Table 44.19 [1] summarizes potential health effects in healthy individuals. Note that
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exposures above 200 ppm may begin to impair escape, particularly at exposure times exceeding 5 min. Emergency Response Planning Guidelines (ERPG) values, developed by the American Industrial Hygiene Association, for 10 min exposures, are as follows: ERPG-2, a level at which mitigating steps such as evacuation should be taken is 50 ppm, and ERPG-3, the maximum nonlethal exposure concentration for 10 min is 170 ppm. The ERPG values are in contrast to an analysis by Meldrum [48] which indicates that a dose of 12,000 ppm/min has 1 % lethality in exposed animals. Additional health-effect and risk-assessment data are given in Dalby [49], Machle and Kitzmiller [50], Machle et al. [51], and Brock [52]. The impact of thermal decomposition products on electronics equipment is another area of concern. There is not sufficient data at present to predict the effects of a given HF exposure scenario on all electronics equipment. Several evaluations of the impact of HF on electronics equipment have been performed relative to the thermal decomposition of Halon 1301, where decomposition products include HF and HBr. One of the more notable was a NASA study where the shuttle orbital electronics were exposed to 700, 7000, and 70,000 ppm HF and HBr [53]. In these tests, exposures up to 700 ppm HF and HBr caused no failures. At 7000 ppm, severe corrosion was noted; there were some operating failures at this level. Dumayas exposed IBM-PC-compatible multifunction boards to environments produced by a range of fire sizes as part of an evaluation program on halon alternatives [54]. He found no loss of function of these boards following a 15-min exposure to postfire extinguishment atmosphere up to 5000 ppm HF, with unconditioned samples stored at ambient humidity and temperature conditions for up to 30 days. Forssell et al. [55], exposed multifunction boards for 30 min in the postfire extinguishment environment; no failures were reported up to 90 days post-test. HF concentrations up to 550 ppm were evaluated. Although no generic rule or statement can be made at present, it appears that short-term
P.J. DiNenno and E.W. Forssell
damage (95 %) of the agent has already been delivered through the nozzles. The importance of the pipe filling and nozzle run-out with these alternatives is relatively more critical with low vapor pressure alternatives due to (1) the inability of the agent to deliver significant pressure to the system by boiling and (2) the
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Clean Agent Total Flooding Fire Extinguishing Systems
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Nozzle
Nozzle Valve Agent vapor / N2
Pressure decrease
Agent vapor / N2 (dissolved)
N2, agent vapor released Density decreased
Cylinder
Fig. 44.14 Initial conditions
Fig. 44.15 Valve open, pipe filling
higher fluid densities that occur in the piping relative to Halon 1301. Figures 44.14, 44.15, 44.16 and 44.17 illustrate the stages of the agent discharge network.
44.19 depict the dispersed-bubble and bubbleflow regimes, respectively.
Flow Regime If the flow velocity of the agent in the piping is not high enough, the flow may separate into two distinct phases within the piping [60]. This phase separation causes rather unpredictable fluid behavior at tee splits and makes evaluating pressure drop in the piping system more challenging. Therefore, minimum flow rates that ensure a homogeneous mixture of liquid agent and vapor-nitrogen bubbles must be maintained. Various flow regimes are illustrated in Figs. 44.18 and 44.19 for horizontal and vertical pipe, respectively. One of the objectives of approval testing of flow calculation procedures is to ensure that homogeneous flow regimes are maintained in the piping throughout the clean agent discharge process. Figures 44.18 and
Flow Division at Tees For a single-component (agent only, i.e. no dissolved nitrogen), singlephase flow condition, the flow split at a tee junction can be determined by the flow rate of the nozzles downstream of the tee. For two-phase fluids, flow distribution at the tees is sensitive to four physical conditions: (i) the velocity of the fluid flow along each branch of the tee, (ii) the orientation of the tee, (iii) the pressure at the tee, and (iv) the phase distribution of the fluid (gas or liquid) entering the tee. The primary cause of preferential flow splits at tees is the inertia of the liquid versus vapor-gas phase. This condition is most readily envisioned for side-flow tees where one branch of the flow is required to turn 90 . Gas-vapor bubbles with lower momentum relative to the liquid agent will make this change of direction more readily.
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Fig. 44.16 Quasi-steady flow, liquid throughout network
P.J. DiNenno and E.W. Forssell
Fig. 44.17 Cylinder liquid runout
Fig. 44.18 Horizontal pipe flow regimes [60] Stratified smooth
Stratified
Stratified wavy
Elongated bubble
Intermittent
Slug
Annular/annular-mist
Annular
Wavy annular Dispersed bubble Dispersing bubble
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Clean Agent Total Flooding Fire Extinguishing Systems
Bubble
Slug
Churn
Annular
Fig. 44.19 Vertical pipe flow regimes [60]
Fig. 44.20 Bullhead-teeflow split corrections for Halon 1301 [61]
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This change results in relatively less mass flow down the side-flow branch at approximately the same volumetric flow rate or velocity. For bullhead tees, the same phenomenon occurs, except that it is more subtle and involves velocity differences through each branch of the tee. For evenly split (50%/50%) flows, the velocity is identical in both directions, resulting in no flow split correction; as the split becomes greater the velocity differences are greater, and inertial effects of the gas-vapor portion of the fluid relative to the liquid portion cause significant redistribution of mass through each branch of the tee. The dependence was understood for Halon 1301 and described in detail by Williamson [61]. Similar processes occur in all two-phase flows including air-water, steam- water, and refrigerant flows. In the context of clean agent system design calculations, this flow distribution is dealt with using empirical factors that redistribute the flow relative to the pure pressuredriven flow distribution that would occur without preferential phase distribution at tees. Figures 44.20 and 44.21 illustrate these correction factors for Halon 1301 flows in bullhead and side-flow tees, respectively [61]. All of the
130
Percent of calculated flow
Bullhead tee
120
110
100
90
0
20
40
60
Branch flow in percent
80
100
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P.J. DiNenno and E.W. Forssell
Fig. 44.21 Side- and through tee-flow split corrections for Halon 1301 [61]
Through flow in percent 100 130
80
60
Percent of calculated flow
Through tee
40
20
0
Through tee
120 Side tee Through 110
100 Side
90
0
halocarbon agent flow predictions require similar treatment. Side-flow tees and bullhead tees require independent empirical correction factors. One of the most important limitations to any flow calculation procedure is the maximum flow split allowed for each type of tee. For a bullhead tee, as one moves farther away from 50%/50% splits, the correction factor becomes greater, and at some point usually in the range of 80%/20%, it becomes so large that the prediction becomes unreliable. For side-allowable flow splits, ranges between 75%/25% and 90%/ 10% are typical. This correction of flow splits at tees is one reason that final approval of engineered system designs should be constrained to calculation methods that have undergone testing within the range of the flow splits required. Pressure Drop due to Friction Loss The pressure drop caused by friction in the pipeline is calculated differently for two-phase fluids. The presence of agent vapor and gas affects the pressure drop per unit length of pipe. There are numerous methods for dealing with two-phase fluid pressure drop [62, 63]. Those typically used for fire suppression agent calculations involve either (1) correcting the pressure drop
20
40 60 Side flow in percent
80
100
estimated for single-phase fluid as a function of liquid to vapor-gas volume fraction or (2) empirical correlations of the pressure drop to average fluid density. Figure 44.22 illustrates the dependence of pressure drop on liquid volume fraction. In all cases for purposes of design of fire protection systems, the pressure drop is calculated on the basis of a homogeneous flow assumption where changes in the liquid fraction are seen as density changes in the homogeneous fluid. Testing and Approval of Design Methods The approval or listing of a two-phase flow calculation procedure is part of the overall approval necessary for engineered systems. Since some aspects of two-phase flow calculations are empirically based (e.g., flow regime, pressure drop, and flow splits) and all calculation procedures have some bounds on their validity, testing is performed to verify the predictions and establish the limits of the calculation procedure. These calculation procedure limitations are crucial in helping to ensure overall adequacy of system designs. One of the most rigorous approval procedures used in verifying design calculation methods for clean agent systems are outlined in UL 2127, Inert Gas Clean Agent Extinguishing System Unit [12] and in UL 2166, Halocarbon Clean
Clean Agent Total Flooding Fire Extinguishing Systems
Fig. 44.22 Pressure drop versus liquid volume fraction [62]
Two-phase pressure drop, single-phase water pressure drop
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103 8 6 4 Lockhart and Martinelli
2 102 8 6 4 2
14.7 psi 100 psi 1000:1500;2000 psi Martinelli–Nelson
101 8 6 4 2 100
2
4
6 8 10–2
2
4
6 8 10–1 2
4
6 8 100
Liquid volume fraction
Agent Extinguishing System Units [13]. Design method limitations are described by the following 10 parameters: 1. Percentage of agent in piping (maximum) 2. Minimum and maximum discharge times 3. Minimum pipeline flow rates 4. Variance of piping volume to each nozzle 5. Maximum variance of nozzle pressures within a piping arrangement 6. Maximum ratio of nozzle diameter to inlet pipe diameter 7. Arrangement most likely to exhibit vapor time-imbalance condition at nozzle 8. All types of tee splits, including through tees, bullhead tees, and so forth 9. Minimum and maximum container fill density 10. Minimum and maximum flow split for each type of tee. These parameters are related to the important attributes of the agent discharge process previously discussed. Full-scale testing is performed to evaluate the performance of the design
method. The limits on flow calculation method performance are as follows: 1. Actual versus predicted discharge time 1 s for halocarbon agents and 10 s for inert gas agents 2. Actual versus predicted nozzle pressure 10 % 3. Actual versus predicted mass flow through a nozzle, 10 % The flow calculation method testing is performed with the specific manufacturer’s hardware to ensure that the flow through the hardware is modeled correctly. Several generic flow calculation routines have been developed [43, 64–67]. Of these, two are directed at single-nozzle systems with very short discharge times [66] or relatively simple balanced networks [65]. It is not recommended that any generic calculation procedure be used for final design purposes unless the procedure has been tested with the specific hardware to be installed, and system performance is within the limitations derived by testing.
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In order to preserve a 10 s discharge time, the mass flow rate of these clean agents must be higher than Halon 1301. The increased density of some of the clean agents in the piping, caused by lower vapor pressures and nitrogen solubility differences, may result in high enough mass flow rates to retrofit existing Halon 1301 systems. Although agent cylinders and nozzles will require replacement, it is possible to preserve the existing Halon 1301 pipe network. Preservation often requires the use of lower fill density cylinders to increase the average system pressure throughout the discharge time. Any retrofit using existing Halon 1301 piping must be prudently evaluated with respect to hydraulic performance, with particular attention given to preserving the minimum required nozzle pressures and flow divisions at tees.
Nozzle Area Coverage and Height Limitations One of the most important requirements of a gaseous total flooding fire suppression system is the ability of the system to deliver a uniform concentration of agent throughout the protected enclosure within the discharge period. The nozzle design and minimum nozzle discharge pressure are critical in ensuring this distribution of agent. The performance of the nozzle is evaluated by full-scale testing, such as through UL 2127 [12] and UL 2166 [13]. The basic testing performed to evaluate nozzles is as follows: 1. Establish minimum nozzle pressure and maximum nozzle height by ensuring extinguishment of heptane fires located throughout a space with a height equal to the maximum allowable, at the minimum allowable nozzle pressure. 2. Establish maximum nozzle coverage area by extinguishing tests in a plenum at the minimum height (generally less than 0.5 m) at the maximum nozzle coverage area (on the order
P.J. DiNenno and E.W. Forssell
of 100 m2) and minimum nozzle operating pressure. There are substantial differences among hardware manufacturers relative to minimum nozzle pressure, maximum ceiling height, and maximum average cover- age. All nozzle anticipated orientations should be evaluated. In general, maximum nozzle heights are on the order of 4–5 m, nozzle area coverage on the order of 90–100 m2, and minimum nozzle pressure between 3 and 6 bar. It is critical to ensure that the nozzle spacing, height, and minimum pressure limits are not exceeded for a particular manufacturer’s hardware in a specific design. The flow, mixing, and distribution of an agent from a nozzle into an enclosure can be predicted theoretically for relatively simple nozzle designs using sophisticated computer models [65]. Further development of such methods for complex nozzle designs and compartment geometries could eventually form the basis of a design procedure. At present, however, the primary means of ensuring adequate nozzle performance is the hardware approval process and real-scale testing. Since many of the halocarbon agents have lower vapor pressures than Halon 1301, there is often a much higher percentage of liquid at the nozzle. This liquid makes the task of vaporizing and mixing the agent in the compartment more difficult. In general, nozzle designs used for Halon 1301 systems are not adequate for the halocarbon replacement agents. Due to the increased liquid fraction at the nozzle, it is critical to ensure that no unenclosed openings exist along the trajectory of the nozzle orifices. Increased liquid fraction may result in significant preferential loss of agent through these openings. This condition further emphasizes the need for third-party approval testing and listing of nozzle performance. In any retrofit situation including those of other types of clean agent systems and Halon 1301 systems, the nozzles will need to be replaced even if the piping is adequately sized to deliver proper agent flow rates.
3
N10S44
2 1
–2 –3 60
65
70
75
80
Total discharge
–1
Liquid runout
0
Discharge start
Fig. 44.23 Pressure measured in 28 m3 enclosure during HFC-227ea (C3F7H) discharge, with nominal 15 s discharge time and 5 cm pan of n-heptane [43]
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85
90
95
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6 –0.7 100
Pressure (kPa)
Clean Agent Total Flooding Fire Extinguishing Systems
Pressure (iwc)
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Time (s)
Compartment Pressurization The rapid discharge of agent into a compartment will cause rapid changes in the compartment pressure. Depending on the agent and rate of discharge, the initial pressure change may be negative. Figure 44.23 is a plot of compartment pressure versus time for the discharge of HFC-227ea into a 28 m3 room with a 360 cm2 (56 in.2) leakage area [43]. Immediately after discharge, the pressure in the compartment drops below ambient to a minimum of 0.3 kPa; at approximately 1.5 s after discharge, the pressure then begins to increase to a maximum of approximately 0.14 kPa after nozzle liquid run-out. Similar results were obtained for FC-3-1-10. HFC-23 discharge exhibited much higher compartment overpressurization, without the marked initial negative pressure. The maximum overpressure for HFC-227ea and FC-3-1-10 discharge was similar to that of Halon 1301. As the halocarbon agent is discharged into the space, it vaporizes rapidly, cooling the compartment and lowering the pressure. As the agent-air mixture gains heat from the walls or other objects in the space, the pressure recovers and, as additional agent is added, the pressure increases over ambient as mass is added to the compartment.
The expected maximum and minimum compartment pressure during discharge will be a function of the following: 1. Thermodynamic state of the agent at the nozzle 2. Nozzle design 3. Compartment volume and wall surface area 4. Size of fire 5. Initial conditions in space 6. Leakage area from compartment 7. Agent flow rate For inert gases, significant compartment overpressurization can occur during discharge unless adequate free vent area is provided. Calculation of required open area for venting is a part of the design manual for inert gas systems as for IG-541 systems [68]. No generalized design procedure for calculating under/overpressurization has been established. Forssell and DiNenno [43] have developed a procedure for estimating the compartment pressure as a function of agent, agent flow rate, agent thermodynamic state at the nozzle, compartment volume, and surface area and leakage area. However, the method has not been sufficiently tested for general application. The Fire Suppression System Association, FSSA, has developed a guide for estimating the pressure relief vent areas for preventing damage to enclosures during the discharge of clean agent
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systems [69]. The guide is based on empirical correlations developed during a experimental research program.
Agent Hold Time and Leakage Traditionally, total flooding gas systems were required to maintain a minimum concentration for a specified time period (10–20 min) after discharge. The minimum required hold time was based on the following: 1. Soak time required for deep-seated Class A fuels 2. Response time of emergency personnel 3. Prevention of re-flash of the fire due to the presence of hot surfaces, electrical energy and other reignition sources, particularly with flammable and combustible liquid applications. The absolute minimum hold time requirement is 10 min. The variables described above will vary between installations, and there is no significant database on the performance of these agents on deep-seated fires other than wood cribs. The designer will be required to specify the minimum soak time consistent with the requirements of the hazard being protected. The ability of a compartment to maintain adequate agent concentrations is a function of the leakage of the compartment. Historically, this was done with Halon 1301 through the use of discharge tests. Discharge testing for this purpose was rendered unnecessary by the introduction of door fan pressurization leakage tests. The only difference between alternative agents and Halon 1301 in this regard is the density of the agent-air mixture, which is the driving force for leakage in quiescent environments. The mixture density can be estimated as follows [1]: C ρ ð100 CÞ ρm ¼ V d þ a 100 100 where: ρm¼ Clean agent-air mixture density (kg/m3) ρa¼ Air density (1.202 kg/m3) C ¼ Clean agent concentration (%)
P.J. DiNenno and E.W. Forssell
Vd ¼ Agent vapor density (kg/m3) Agent vapor densities are given below: FC‐3‐10 HBFC‐22B1 HCFC‐Blend A HFC‐124 HFC‐125 HFC‐227ea HFC‐23 IG‐541 Halon 1301
9:85 kg=m3 0:615 lb=ft3 5:54 kg=m3 0:346 lb=ft3 3:84 kg=m3 0:240 lb=ft3 5:83 kg=m3 0:364 lb=ft3 5:06 kg=m3 0:316 lb=ft3 7:26 kg=m3 0:453 lb=ft3 2:915 kg=m3 0:182 lb=ft3 1:43 kg=m3 0:089 lb=ft3 6:283 kg=m3 0:392 lb=ft3
All agents, except inert gases, have higher mixture densities than Halon 1301 at 5 % when used at their design concentrations requiring slightly more leak-tight enclosures to maintain the same hold time. There are several methods available to estimate the hold time of gaseous agent mixtures based on leakage measured by the door fan pressurization method. The first method, initially developed by DiNenno and Forssell [70] and Grant [71], modeled the leakage of a gas-air mixture from a compartment as a two-layer system with a uniform gas-air mixture below a sharp interface and air above the interface. In this idealization, the gas-air mixture leaks out of the bottom of the room and the inter-face descends with time much like a draining bathtub. This method is standardized in NFPA 2001. The interface is modeled as remaining well defined throughout its descent. Spreading of the interface due to diffusion and localized mixing is ignored. Another idealized case treated by DiNenno and Forssell [70] is the case of a uniform mixture of gas and air across the height of the room in which the uniform concentration decays with time as air leaks in and gas-air mixture leaks out. This case is the so-called “uniform mixing” case. Dewsbury and Whitely [72, 73] also proposed a treatment of a widely spreading interface. In this idealization there are two “zones” in a compartment. At the ceiling, the agent concentration is assumed to be zero and over time a zone where the agent concentration increases from zero at the ceiling to the initial agent concentration at the interface boundary exists. This so-called
44
Clean Agent Total Flooding Fire Extinguishing Systems
spreading interface increases in depth as the agent-air mixture leaves from the bottom of the room. This method is embodied in ISO 14520 and is more conservative than the other methods. Additional refinements to the spreading interface modeling approach have been proposed by Hetrick et al. [74]. A key difference between this wide interface case and the sharp interface case is that the position within the spreading interface, where the agent concentration falls below 70 % or 80 % of the design concentration, is defined to be the position in the room above which the agent concentration is inadequate. In the sharp interface case this position would occur when the agent concentration is 50 % of the initial value (assuming a non-sharp interface actually occurred). Consequently, the allowable leakage will be significantly less than that permitted using the sharp interface model in NFPA 2001. The full-scale data obtained by Dewsbury and Whitely [72, 73] and Klocke [75] for inert gas mixtures indicate widely spreading interfaces are typical. Additional refinements relying much more on empirical data on interface spread and refinements in the estimation of leakage area were added to the provisions of NFPA 2001. All of these leakage area measurement methods and leakage calculation estimates are approximate since the precise size and location of the leakage paths are never know. Based on a range of full-scale idealized experiments it appears that the hold time or retention calculations are likely conservative.
Summary A range of inert gas and halocarbon total flooding clean agents are available. The use of an agent must be consistent with applicable environmental and toxicity regulations. The selection of an agent is driven by its fire performance characteristics, agent and system space and weight concerns, toxicity (particularly for use in occupied areas), and the availability of approved system hardware.
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The design of clean agent systems must be thoroughly completed in accordance with thirdparty listing and approval limitations on the agent, distribution hardware, and hydraulic calculation procedure. Given the specialized knowledge associated with these types of fire protection systems, particular care in the design, installation, inspection, testing, and maintenance of these systems is warranted. It is important to recognize that fire protection standards, such as NFPA 2001, form the minimum requirements for these clean agent technologies. In the case of all clean agents, system designs are much less robust than those for Halon 1301 systems. Of particular concern is the application of inadequate or unjustified design concentrations particularly where energized electrical equipment is used or deep-seated fires are a concern. Designers and users are encouraged to investigate the means by which the design concentrations are established and consult the ISO 14520 standard for more conservative design concentration requirements.
References 1. NFPA 2001, Standard on Clean Agent Fire Extinguishing Systems, National Fire Protection Association, Quincy, MA (2012). 2. R.T. Wickham, “Review of the Use of Carbon Dioxide Total Flooding Fire Extinguishing Systems,” Wickham Associates prepared for US EPA, August 8, 2003. 3. ISO 14520-1, “Gaseous Fire Extinguish Systems – Physical Properties and System Design, Part 1: General Requirements,” International Standards Organization, 2006. 4. A. Liu and M. Colket, “Modeling Cup-burner Minimum Extinguishing Concentration of Halogenated Agents,” Proceedings of 2010 Suppression, Detection and Signaling Research and Applications Symposium, February 16–19, 2012, National Fire Protection Research Foundation, Quincy, MA, (2010). 5. A. Hamins, G. Gmurczyk, W. Grosshandler, R. Rehwoldt, I. Vazquez, and T. Cleary, “Flame Suppression Effectiveness,” in Evaluation of Alternative In-Flight Fire Suppressants for Full-Scale Testing in Simulated Aircraft Engine Nacelles and Dry Bays, NIST SP 861, National Institute of Standards and Technology, Gaithersburg, MD (1994). 6. M.L. Robin, “Properties and Performance of FM-200™,” in Proceedings of the Halon Options
1528 Technical Working Conference 1994, New Mexico Engineering Research Institute, Albuquerque, NM, pp. 531–542 (1994). 7. R. Sheinson, H. Eaton, B. Black, R. Brown, H. Burchell, A. Maranghides, C. Mitchell, G. Salmon, and W., “Halon 1301 Total Flooding Fire Testing, Intermediate Scale,” in Proceedings of the Halon Options Technical Working Conference 1994, New Mexico Engineering Research Institute, Albuquerque, NM, pp. 43–53 (1994). 8. T.A. Moore, D. Dierdorf, and S. Skaggs, “Intermediate Scale (645 ft3) Fire Suppression Evaluation of NFPA 2001 Agents,” in Proceedings of the Halon Options Technical Working Conference 1993, New Mexico Engineering Research Institute, Albuquerque, NM, pp. 115–127 (1993). 9. M.J. Ferreira, C. Hanauska, and M. Pike., “Thermal Decomposition Product Results Utilizing PFC-410,” in Proceedings of the Halon Options Technical Working Conference 1992, New Mexico Engineering Research Institute, Albuquerque, NM (1992). 10. “Extinguishing Behavior of Inert Gases,” Final Report, VdS, Cologne, Germany (1998). 11. R.E. Tapscott, “Best Values of Cup Burner Extinguishing Concentration,” in Proceedings of the Halon Technical Options Technical Working Conference 1999, New Mexico Engineering Research Institute, Albuquerque, NM, pp. 27–29 (1999). 12. UL 2127, Inert Gas Clean Agent Extinguishing System Units, Underwriters Laboratories Inc., Northbrook, IL (1999). 13. UL 2166, Halocarbon Clean Agent Extinguishing System Units, Underwriters Laboratories Inc., Northbrook, IL (1999). 14. Linteris, G “Clean Agent Suppression of Energized Electrical Equipment Fires,” NIST Technical Note 1622 NIST, Gaithersburg, MD (2009). 15. R. Patel and P. Rivers, “Performance Based Guidance in Specifying Clean Extinguishing Agent Protection Against Energy Augmented Data Center Fire Conditions,” Proceedings of 2012 Suppression, Detection and Signaling Research and Applications Symposium, March 5–8, 2012, National Fire Protection Research Foundation, Quincy, MA (2012). 16. L.A. McKenna, D. Gottuk, P. DiNenno; A. Kline, and S. Mehta, “Extinguishment Tests of Continuously Energized Class C Fires,” in Halon Options Technical Working Conference 1998, New Mexico Engineering Research Institute, Albuquerque, NM (1998). 17. J.A. Senecal, “Agent Inerting Concentrations for Fuel-Air Systems,” CRC Technical Note No. 361, Fenwal Safety Systems (1992). 18. F. Tamanini, Determination of Inerting Requirements for Methane/Air and Propane/Air Mixtures by an Ansul Inerting Mixture of Argon, Carbon Dioxide, and Nitrogen, Factory Mutual Research Corp., Norwood, MA (1992).
P.J. DiNenno and E.W. Forssell 19. E. Heinonen, “Laboratory-Scale Inertion Results,” Halon Substitutes Program Review (1993). 20. E.W. Heinonen, “The Effect of Ignition Source and Strength on Sphere Inertion Results,” in Proceedings of the Halon Options Technical Working Conference 1993, Albuquerque, NM, pp. 565–576 (1993). 21. T.A. Moore, “Large-Scale Inertion Evaluation of NFPA 2001 Agents,” in Proceedings of the 1993 International CFC and Halon Alternatives Conference, Washington, DC (1993). 22. J.A. Senecal, “Explosion Protection in Occupied Spaces: The Status of Suppression and Inertion Using Halon and Its Descendants,” in Proceedings of the 1993 International CFC and Halon Alternatives Conference, Washington, DC, pp. 767–772 (1993). 23. J.A. Senecal, D.N. Ball, and A. Chattaway, “Explosion Suppression in Occupied Spaces,” in Proceedings of the Halon Options Technical Working Conference 1994, Albuquerque, NM, pp. 79–86 (1994). 24. A. Vinegar and G.W. Jepson, “Cardiac Sensitization Thresholds of Halon Replacement Chemicals Predicted in Humans by Physiologically-Based Pharmacokinetic Modeling,” Risk Analysis, 16, 4 (1996). 25. A. Vinegar, G.W. Jepson, and J.H. Overton, “PBPK Modeling of Short Term (0 to 5 min) Human Inhalation Exposures to Halogenated Hydrocarbons,” Inhalation Toxicology, 10, pp. 411–429 (1998). 26. A. Vinegar, Performance of Monte Carlo Simulations of Exposure to HFC-227ea, ManTech Environmental Technology, Inc., Dayton, OH (1999). 27. A. Vinegar, G.W. Jepson, M. Cisneros, R. Rubenstein, and W.J. Brock, “Setting Safe Exposure Limits for Halon Replacement Chemicals Using Physiologically Based Pharmacokinetic Modeling,” Inhalation Toxicology, 12, 8, pp. 751–763 (2000). 28. A. Vinegar and G. Jepson, “Pharmacokinetic Modeling for Determining Egress from Exposure to Halon Replacement Chemicals,” in Proceedings of Halon Options Technical Working Conference 1998, New Mexico Engineering Research Institute, Albuquerque, NM (1998). 29. A. Vinegar and G. Jepson, “Epinephrine Challenge for Cardiac Sensitization Testing versus Endogenous Epinephrine,” in Proceedings of the Halon Technical Working Conference 1999 New Mexico Engineering Research Institute, Albuquerque, NM (1999). 30. “Research Basis for Improvement of Human Tolerance to Hypoxic Atmospheres in Fire Prevention and Extinguishment,” EBRDC Report 10.30.92, Environmental Biomedical Research Data Center, Institute for Environmental Medicine, University of Pennsylvania, Philadelphia, PA (1992). 31. David de Jager, Martin Manning, Lambert Kuijpers, Stephen O. Andersen, Paul Ashford, Paul Atkins, Nick Campbell, Denis Clodic, Sukumar Devotta, Dave Godwin, Jochen Harnisch, Malcolm Ko,
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Suzanne Kocchi, Sasha Madronich, Bert Metz, Leo Meyer, Jose Roberto Moreira, John Owens, Roberto Peixoto, Jose Pons, John Pyle, Sally Rand, Rajendra Shende, Theodore Shepard, Stephen Sicars, Susan Solomon, Guus Velders, Dan Verdonik, Robert Wickham, Ashley Woodcock, Paul Wright, and Masaaki Yamabe, “Technical Summary,” Safeguarding the Ozone Layer and the Global Climate System: Issues Related to Hydrofluorocarbons and Perfluorocarbons, IPCC/TEAP Special Report, United Nations Environment Programme (2005). 32. Halon Alternatives Research Corporation (HARC) (2007), “Report of the HFC Emissions Estimating Program, 2002–2005 Data Collection,” HARC, Arlington, VA, November 2007. 33. J.C. Yang and B.D. Bruel, “Thermophysical Properties of Alternative Agents,” in Evaluation of Alternative In-Flight Fire Suppressants for FullScale Testing in Simulated Aircraft Engine Nacelles and Dry Bays, NIST SP 861, National Institute of Standards and Technology, Gaithersburg, MD (1994). 34. P.J. DiNenno, “Direct Halon Replacement Agents and Systems” in Fire Protection Handbook, Nineteenth edition, National Fire Protection Association, Quincy, MA (2003). 35. NFPA 12A, Standard on Halon 1301 Fire Extinguishing Systems, National Fire Protection Association, Quincy, MA (2009). 36. NFPA 12, Standard on Carbon Dioxide Extinguishing Systems, National Fire Protection Association, Quincy, MA (2011). 37. J.C. Brockway, “Recent Findings on Thermal Decomposition Products of Clean Extinguishing Agents,” 3 M Report presented to NFPA 2001 Committee, Ft. Lauderdale, FL (1994). 38. I. Schlosser, “Reliability and Efficacy of Gas Extinguishing Systems,” in Proceedings of Conference on Fire Extinguishing Systems, VdS, Cologne, Germany (1998). 39. Halon Alternatives, A Report on the Fire Extinguishing Performance Characteristics of Some Gaseous Alternatives to Halon 1301, LPR6: July 1996, Loss Prevention Council, Hertfordshire, UK (1996). 40. ISO 14520–1, Gaseous Fire Extinguish Systems— Physical Properties and System Design, Part 1: General Requirements, International Standards Organization (2000). 41. C. Hanauska and P. DiNenno, “The Adequacy of Guidance on Agent Concentrations for Gaseous Fire Extinguishing Systems,” Proceedings of Suppression and Detection Research Applications- A Technical Working Conference, Orlando FL, Feb 24–27, 2009, National Fire Protection Research Foundation, Quincy, MA (2009). 42. G.G. Back, C.L. Beyler, P.J. DiNenno, and M. Peatross, “Draft Report: Full-Scale Machinery Space Testing of Gaseous Halon Alternatives,” USCG R&D Center, Groton, CT (1994).
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43. E.W. Forssell and P.J. DiNenno, “Evaluation of Alternative Agents for Use in Total Flooding Fire Protection Systems,” Contract NAS 10–1181, National Aeronautics and Space Administration, John F. Kennedy Space Center, FL (1994). 44. P.J. DiNenno, E. Forssell, M. Peatross, J. Wong, and M. Maynard, “Thermal Decomposition Testing of Halon Alternatives,” in Proceedings of the Halon Alternatives Technical Working Conference 1993, New Mexico Engineering Research Institute, Albuquerque, NM (1993). 45. D.S. Dierdorf, T. Moore, and S. Skaggs, “Decomposition Product Analysis During Intermediate Scale (645 ft3) Testing of NFPA 2001 Agents,” in Proceedings of the Halon Alternatives Technical Working Conference 1993, New Mexico Engineering Research Institute, Albuquerque, NM (1993). 46. C.P. Hanauska, “Hazard Assessment of HFC Decomposition Products,” presented at the 1994 International CFC and Halon Alternatives Conference, Washington, DC (1994). 47. C.P. Hanauska, E. Forssell, and P. DiNenno, “Hazard Assessment of Thermal De- composition Products of Halon Alternatives,” in Proceedings of the Halon Alternatives Technical Working Conference 1993, New Mexico Engineering Research Institute, Albuquerque, NM (1993). 48. M. Meldrum, Toxicology of Substances in Relation to Major Hazards: Hydrogen Fluoride, Health and Safety Executive (HSE) Information Centre, Sheffield, England (1993). 49. W. Dalby, Evaluation of the Toxicity of Hydrogen Fluoride at Short Exposure Times, Stonybrook Laboratories, Inc., Pennington, NJ, sponsored by the Petroleum Environmental Research Forum (PERF), PERF Project 92–90 (1996). 50. W. Machle and K.R. Kitzmiller, “The Effects of the Inhalation of Hydrogen Fluoride, II, The Response Following Exposure to Low Concentrations,” Journal of Industrial Hygiene and Toxicology, 17, pp. 223–229 (1935). 51. W. Machle, F. Tharnann, K.R. Kitzmiller, and J. Cholak, “The Effects of Inhalation of Hydrogen Fluoride, I, The Response Following Exposure to High Concentrations,” Journal of Industrial Hygiene and Toxicology, 16, pp. 129–145 (1934). 52. W.J. Brock, “Hydrogen Fluoride: How Toxic Is Toxic? (A Hazard and Risk Analysis),” in Proceedings of the Halon Options Technical Working Conference 1999, New Mexico Engineering Research Institute, Albuquerque, NM, pp. 27–29 (1999). 53. M.D. Pedley, “Corrosion of Typical Orbiter Electronic Components Exposed to Halon 1301 Pyrolysis Products,” NASA TR-339-001, National Aeronautics and Space Administration, 1995. 54. W.A. Dumayas, “Effect of HF Exposure on PC Multifunction Cards,” Senior Research Project, University of Maryland, College Park (1992).
1530 55. E.W. Forssell et al., “Draft Report: Performance of FM-200 on Typical Class A Computer Room Fuel Packages,” Hughes Associates, Inc., Columbia, MD (1994). 56. “Fire Suppressants Impact on Hard Disks,” The Availability Digest, 2011. Earlier article, “WestHost Fire-Suppression Test Fiasco-An Update,” The Availability Digest, (2010). 57. Siemens, “Potential Problems with computer hard disks when fire extinguishing systems are released,” Siemens Switzerland Ltd. (2010). 58. Ansul, “Impact of System Discharge/Alarm on Sensitive Hard Drives,” Bulletin 5651, (2010). 59. Ansul, Bulletin 5688, “Study of System Discharge/ Alarm on Sensitive Hard Disc Drives-Update,” (2010). 60. D. Barnea and Y. Taitel, “Flow Pattern Transition in Two-Phase Gas-liquid Flows,” in Encyclopedia of Fluid Mechanics, Vol. 3 (N.P. Cheremisinoff, ed.), Gulf Publishing Company, Houston, TX (1986). 61. H.V. Williamson, “Halon 1301 Flow in Pipelines,” Fire Technology, 13, 1, pp. 18–32 (1976). 62. D. Chisholm, “Predicting Two-Phase Flow Pressure Drop,” in Encyclopedia of Fluid Mechanics, Vol. 3 (N.P. Cheremisinoff, ed.), Gulf Publishing Company, Houston, TX (1986). 63. Y.Y. Hsu and R.W. Graham, Transport Processes in Boiling and Two-Phase Systems, Hemisphere Publishing Corporation, Washington, DC (1976). 64. P.J. DiNenno, E. Forssell, M. Ferreira, C. Hanauska, and B. Johnson, “Modeling the Flow Properties and Discharges of Halon Replacement Agents,” in Proceedings of the Halon Options Technical Working Conference 1994, New Mexico, Engineering Research Institute, Albuquerque, NM, (1994). 65. E.B. Bird, H. D. Giesecke, J.A. Hillaert, T.J. Friderichs, and R.S. Sheinson,, “Development of Computer Model to Predict the Transient Discharge Characteristics of Halon Alternatives,” in Proceedings of the Halon Options Technical Working Conference 1994, New Mexico, Engineering Research Institute, Albuquerque, NM, (1994). 66. T.G. Cleary, W. Grosshandler, and J. Wang, “Flow of Alternative Agents in Piping,” in Proceedings of the Halon Options Technical Working Conference 1994, New Mexico Engineering Research Institute, Albuquerque, NM (1994). 67. W.M. Pitts, J. Yang, G. Gmurczyk, L. Cooper, W. Grosshandler, W. Cleveland, and C. Presser, “Fluid Dynamics of Agent Discharge,” in Evaluation
P.J. DiNenno and E.W. Forssell of Alternative In-Flight Fire Suppressants for FullScale Testing in Simulated Aircraft Engine Nacelles and Dry Bays, (W. Grosshandler, R. Gann, and W. Pitts., eds.), NIST SP 861, National Institute of Standards and Technology, Gaithersburg, MD (1994). 68. Ansul Co., Inergen System Design Installation and Maintenance Manual, Ansul Co., Marinette, WI (1994). 69. FSSA, Guide to Estimating Enclosure Pressure and Pressure Relief Vent Area for Applications Using Clean Agent Fire Extinguishing Systems, First Edition, Fire Suppression Systems Association, Baltimore, MD, April 2008. 70. P.J. DiNenno and E.W. Forssell, “Evaluation of the Door Fan Pressurization Leakage Test Method Applied to Halon 1301 Total Flooding Systems,” Journal of Fire Protection Engineering, 1, 4, pp. 131–140 (1989). 71. C.C. Grant (ed.), “Enclosure Integrity Procedure for Halon 1301 Total Flooding Fire Suppression Systems,” National Fire Protection Research Foundation, Quincy, MA, revision 1.0 (1989). 72. J. Dewsbury and R.A. Whitely, “Review of Fan Integrity Testing and Hold Time Standards,” Fire Technology, 36, 4, pp. 249–265 (2000). 73. J. Dewsbury and R.A. Whitely, “Extensions of Hold Time Standards,” Fire Technology, 36, 4, pp. 266–278 (2000). 74. T.M. Hetrick, A.S. Rangwala, and P.E. Rivers, “Development and Validation of a Modified Hold Time Model for Total Flooding Fire Suppression,” Proceedings of Suppression and Detection Research Applications – A Technical Working Conference, Orlando FL, Feb 24–27, 2009, National Fire Protection Research Foundation, Quincy, MA (2009). 75. M. Klocke, “Door Fan Test,” in Proceedings of Conference on Fire Extinguishing Systems, VdS, Cologne, Germany (1998).
Philip J. DiNenno was the president of Hughes Associates, Inc., a fire protection engineering research and development firm. He was actively involved in the testing and development of halon replacement chemicals and alternate fire suppression technologies. Ericis Forsell, PE a Senior Engineer with Jensen Hughes (formerly Hughes Associates, Inc) He has over 25 years experience with design and application research with clean agent systems.
Carbon Dioxide Systems
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Jeff Harrington and Joseph A. Senecal
Introduction Carbon dioxide (CO2) fire extinguishing systems have been in use continuously since the early 1900s. The National Fire Protection Association (NFPA) first published its design standard on carbon dioxide extinguishing systems in 1929. Since this time, carbon dioxide extinguishing systems have gained wide acceptance around the world, and have successfully protected fire hazards in a large variety of configurations and locales, including in land-based industrial environments, and on ships and mobile drilling platforms at sea. Carbon dioxide is electrically non-conductive and, when used at concentrations recommended in design standards, extinguishes fires relatively quickly leaving no residue. The health risk associated with carbon dioxide extinguishing systems is notable. Carbon dioxide is lethal at the minimum design concentrations (vol.%) required by the various design standards over relatively short durations of exposure. Death occurs from a severe reduction of oxygen in the blood due to hypercapnia. During the long history of carbon dioxide use in fire extinguishing systems, numerous fatal accidents have occurred, especially during the maintenance and testing of
J. Harrington, P.E., FSFPE (*) Harrington Group, Inc., 2400 Meadowbrook Parkway, Suite 250, Duluth 30096, GA J.A. Senecal Kidde-Fenwal, Inc., 400 Main Street, Ashland 01721, MA
the systems. However, the risk of exposure to carbon dioxide resulting from CO2 system discharge can be effectively managed. This chapter provides useful information about the design and safe use of carbon dioxide in fire extinguishing systems to protect industrial and marine fire hazards. There are numerous design standards currently in use. No attempt is made to duplicate all of the information contained in those standards. The intention is to supplement and clarify some of the critical concepts these standards address.
Range of System Configurations Carbon dioxide fire extinguishing systems are most commonly arranged in either of two configurations: total flooding or local application. The appropriate configuration choice is dependent on the nature of the hazard being protected. In both cases, a stationary, connected supply of carbon dioxide is attached to a fixed network of pipes and discharge nozzles that deliver carbon dioxide to the hazard location and discharge it within, on, or about the protected volume, surface, or area in a manner designed to accomplish fire extinguishment or suppression. Either system configuration can be designed to operate automatically and manually, or manually-only. Carbon dioxide is also used in manual hose applications. The most common configuration consists of a stationary, connected supply of
M.J. Hurley (ed.), SFPE Handbook of Fire Protection Engineering, DOI 10.1007/978-1-4939-2565-0_45, # Society of Fire Protection Engineers 2016
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carbon dioxide attached to a fixed network of pipes and manual hose stations. Carbon dioxide can also be configured with a fixed pipe network known as a standpipe system, which does not have a stationary, connected supply of carbon dioxide attached to it. The carbon dioxide supply is a mobile supply on a cart or truck designed to be towed or driven to the scene and quick-connected to the standpipe system for delivery to the protected hazard.
Total Flooding A total flooding system discharges carbon dioxide into an enclosure that surrounds the hazard. For example, the enclosure may be the walls, floor and ceiling that form a room, which houses electrical switchgear, flammable liquids storage, or paper archival records. Carbon dioxide is discharged into the enclosure in such a manner that promotes mixing of the enclosure atmosphere, achieving a relatively uniform pre-determined concentration of carbon dioxide throughout the enclosure to achieve extinguishment or suppression of the fire. No matter where the fire is located within the enclosure, it will be extinguished or suppressed by a total flooding system.
Local Application A local application system discharges carbon dioxide directly onto a hazard that is not surrounded by an enclosure. Two design approaches are used as determined by the spatial orientation of the hazard. Relatively flat, two dimensional hazards where the fire will be of the surface type are protected by rate-by-area local application systems. Three dimensional hazards where the fire will be of the surface type are protected by rate-by-volume local application systems.
Extended Discharge Duration Extending the duration of carbon dioxide discharge is a strategy that can be incorporated into the design of both total flooding and local
J. Harrington and J.A. Senecal
application systems where the initial discharge of agent cannot be retained about the hazard long enough to ensure fire extinguishment. This approach is important when the nature of the environment surrounding the hazard allows excessive dissipation of the initial carbon dioxide discharge.
Hand Hose Line System—Fixed Supply A fixed-supply manual hose system discharges significantly more carbon dioxide through the hand-held hose and nozzle than a hand portable or wheeled carbon dioxide fire extinguisher unit. Each manual hose station consists of a length of hose attached to the fixed pipe network equipped with a discharge nozzle [1]. The hose and attached nozzle are commonly stored on a hose reel or a rack. This system of manual hose stations is used to supplement fixed total flooding or local application systems, or as the sole form of protection for a hazard where fixed total flooding or local application system are deemed unsuitable.
Standpipe System—Mobile Supply Such a system can be arranged as a total flooding or local application system, and manual hose stations may or may not be employed. The carbon dioxide supply is typically not attached to the pipe network, but is transported to the site using a trailer or truck and attached to the standpipe system using a quick-connect coupling. A mobile supply arrangement can also be used as a non-connected reserve to supplement a connected supply.
Range of Applications Carbon dioxide has been in use since the early 1900s to protect a wide variety of special fire hazards. One study reports that approximately 20 % of all fire protection applications are considered special hazards, where the use of an automatic sprinkler system is not the best
45
Carbon Dioxide Systems
solution, and about 20 % of the protected special hazards are protected by carbon dioxide systems [2]. Between the 1920s and 1960s, carbon dioxide was the only gaseous fire extinguishing agent commercially available. In the late 1960s, halon 1301 was commercialized and grew in popularity as the preferred gaseous agent for total flooding applications where human exposure was probable, such as in normally occupied spaces. There was a corresponding reduction in the use of carbon dioxide systems for these types of applications. Halons were found to be potent depleters of stratospheric ozone and were targeted for a phased reduction in production and import by the US Clean Air Act, as amended in 1990. Subsequent rulemaking by the EPA established January 1, 1994 as the date to complete this phase-out [3]. Since the halon phase-out, the decline in the use of carbon dioxide in fire extinguishing systems reversed in some use sectors, most notably the marine sector [4].
Classification of Fire Hazards One system used to classify various fire hazards is found in NFPA 10, Standard for Portable Fire Extinguishers [5]. Fire hazards are grouped into five distinct classes, shown in Table 45.1. Class A Fires and Type of Burning Fires in ordinary combustible materials, such as wood, cloth, paper, rubber, and many plastics are Class A fires. Class A fuel arrays may burn with a predominant surface flame and negligible smoldering combustion. This type of fire is often referred to as a Class A surface fire. Materials
1533
made of plastic or rubber often produce Class A surface fires. A surface flame propagates in the gas phase in close proximity to the fuel surface, but not actually in contact with it [6]. Heat from the flame vaporizes the solid or liquid fuel just ahead of the flame front. The flame then ignites the vaporized fuel at the lower limit flammability of the vapor mixture, and the flame advances. The spreading flame vaporizes more solid or liquid fuel and the process continues. Surfacetype flame spread can also occur in liquid-fuel fires (Class B). In Class A fuel arrays that are comprised of cellulosic material in fibrous or particulate form, smoldering may be the predominant form of combustion, either in the absence of any surface flaming, or after the surface flaming has subsided. Wood, pressed fiber insulation board, corrugated paper board, paper, and natural textile fabrics are examples of cellulosic materials or products that will produce significant smoldering combustion. Smoldering is a form of combustion without flame that occurs in fuel that is comprised of finely divided fibers or particles that have a relatively large surface area to mass ratio [7]. Smoldering combustion is commonly referred to as deep-seated combustion. The fuel aggregate must be permeable allowing oxygen transport to the combustion reaction zone below the surface of the fuel. The fuel aggregate must also be dense enough to form an effective insulation layer that slows down heat losses from the reaction zone. Smoldering combustion can occur only in solid fuels. Class C Fires Fires that involve energized electrical equipment are Class C fires. Examples of Class C fire hazards include telecommunication switches, satellite uplink transmitters, data
Table 45.1 Fire classification and fuel Fire classification Class A Class B Class C Class D Class K
Fuel Ordinary combustible materials, such as wood, cloth, paper, rubber, and many plastics Flammable liquids, combustible liquids, petroleum greases, tars, oils, oil-based paints, solvents, lacquers, alcohols, and flammable gases Energized electrical equipment Combustible metals, such as magnesium, titanium, zirconium, sodium, lithium, and potassium Combustible cooking media (vegetable or animal oils and fats)
1534
processing equipment, and industrial process control rooms. When a fire in such hazards results in a planned interruption of power to the equipment, the fire classification is immediately converted from a Class C to a Class. A-type hazard. The polymeric materials used in electric cable insulation and printed circuit boards are inherently Class A materials. When these materials burn, the flame is predominantly a surface burning phenomenon. Class C hazards with combustibles in dense configurations can promote smoldering combustion due to restricted air circulation combined with a relatively large fuel surface area.
Carbon Dioxide Suitability Carbon dioxide is effective in extinguishing fires in Class A, Class B, Class C, and Class K fire hazards. Where surface type burning is expected, carbon dioxide in both total flooding and local application configurations is effective. For smoldering type combustion, only total flooding should be used because the design concentration of carbon dioxide must be maintained for at least 20 min. Carbon dioxide is not suitable as an extinguishant for Class D fire hazards [8]. Carbon dioxide is not effective in extinguishing fires involving combustible metals (e.g., aluminum, magnesium, titanium, zirconium), alkali metals (e.g., lithium, potassium, cesium), and metal hydrides [9]. Use of carbon dioxide to extinguish fires in these materials is ineffective, and in some cases can accelerate the fire, making it more severe [10]. Carbon dioxide is also not suitable as an extinguishant for materials that contain and release oxygen when they burn, such as cellulose nitrate [8].
Industrial Applications Carbon dioxide extinguishing systems can be designed and configured to effectively protect a wide range and variety of fire hazards. The types of applications that are suitably
J. Harrington and J.A. Senecal
protected by carbon dioxide systems are virtually limitless. A single document listing all possible industrial applications may not exist. Numerous documents were reviewed that contain authoritative information about common carbon dioxide system applications [1, 2, 8, 11–14]. The following list, which is not all exhaustive, was compiled from the information contained in these documents. • Battery storage rooms • Cable trays • Cargo areas (aircraft) • Coal storage silos • Computer room subfloor spaces • Control rooms, industrial process • Dip tanks • Dryers • Dust collectors • Electrical cabinets • Electrical rooms (motor control, switchgear, transformers) • Flammable liquid/gas storage rooms and lockers • Industrial fryers (fryers, cookers, roasters) • Lube oil pits • Mixing tanks • Ovens • Paint spray booths • Particle board chippers • Printing presses • Quench tanks • Records storage rooms • Rolling mills • Transformers (high voltage) • Turbine generators • Vehicle parking areas • Wave solder machines • Wet chemistry benches
Marine Applications Carbon dioxide fire extinguishing systems are used extensively in a wide range of marine applications, including cargo, passenger and tank vessels, as well as mobile offshore drilling units. These marine environments contain a myriad of fire hazards which are required by the applicable governing regulations to be protected
45
Carbon Dioxide Systems
by fixed fire extinguishing systems. Carbon dioxide fire extinguishing systems are identified by these regulations as acceptable for many types of marine fire hazards. Marine vessels involved in international commerce are regulated by Safety of Life at Sea (SOLAS), 1974, as amended, and promulgated by the International Maritime Organization (IMO). Fire protection requirements are included in Chapter II-2 of that document which is titled Fire Protection, Fire Detection, and Fire Extinction [15, 16]. Marine vessels are subject to the rules and regulations of the flag administration under which they are registered, and in addition, for commercial vessels, the vessel’s classification society [12]. United States-flagged commercial vessels fall under the jurisdiction of the United States Coast Guard, Department of Homeland Security (USCG). The fire safety regulations enforced by the USCG are contained within the Code of Federal Regulations (CFR) under Title 46, Shipping [15, 17]. American Bureau of Shipping (ABS) is the second largest classification society in the world based upon tonnage [18]. Based in Houston, TX, ABS is the classification society generally used by U.S. manufactured and flagged vessels [12]. ABS publishes rules for constructing vessels of various types and contain detailed requirements covering the application and design criteria for fixed gas fire extinguishing systems, including carbon dioxide. For example see Rules for Building and Classing Steel Vessels, Jan. 1, 2013, Part 4, Chap. 7 [19]. Carbon dioxide fire extinguishing systems are commonly used in total flooding configurations to protect marine vessel fire hazards in the following locations: 1. Cargo Holds 2. Cargo Pump Spaces 3. Electrical Spaces (e.g., electrical propulsion, power generation, power distribution) 4. Machinery Spaces (e.g., engines, pumps, oil-filling stations, heating-ventilating-air condition equipment)
1535
5. Paint and Flammable Liquid Storage Lockers 6. Vehicle Spaces (e.g., automobiles, other selfpropelled vehicles)
Characteristics of Carbon Dioxide Carbon dioxide, which depending upon its physical form and chemical make-up, may also be referred to as carbon anhydride, carbonic acid gas, carbonic anhydride and dry ice. Carbon dioxide has certain characteristics that make it well suited for use as a fire extinguishing agent both in manual firefighting equipment and automatic fire protection systems. It is a gas at atmospheric pressure and the full range of ambient temperatures likely to be encountered when there is a need to suppress a fire. Carbon dioxide does not leave a residue, will not chemically react with the fire, or with objects in the environment being protected, and is electrically nonconductive. Most fires will be extinguished when carbon dioxide is supplied in sufficient quantity to the flame zone. These and other favorable characteristics of carbon dioxide are shown in the following list: 1. Gaseous form at atmospheric pressure and expected range of ambient temperatures 2. Is an effective fire extinguishant 3. Does not leave a residue 4. Is not corrosive or otherwise reactive 5. Is electrically non-conductive 6. Its own vapor pressure provides sufficient discharge force 7. It is widely available 8. It is relatively inexpensive Carbon dioxide also has certain detrimental characteristics that must be carefully accounted for in system design to effectively mitigate them. These include: 1. Is lethal at fire extinguishing concentrations 2. Discharge can create conditions leading to electrostatic charging 3. Discharge can create high sound pressure levels 4. Discharge can create disruptive turbulence
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J. Harrington and J.A. Senecal
5. Discharge can create harmful changes within an enclosure
pressure
Fire Extinguishing Mechanisms The discharge of carbon dioxide into air results in two effects: (1) a decrease in oxygen concentration, and (2) an increase in the heat capacity per mol of available oxygen. Understanding the latter point is central to understanding how gaseous agents contribute to flame extinction. The combustion of oxygen and ordinary carbonaceous fuels releases heat at the rate of approximately 406 kJ per mol of oxygen consumed. In the adiabatic case (no heat loss), that heat must be absorbed by the combustion product gases resulting in a rise in temperature. The stoichiometric combustion of a hydrocarbon fuel and air results in an adiabatic flame temperature of about 2400 K. As the concentration of carbon dioxide added to air increases, the flame temperature decreases because the total thermal mass per unit mass of oxygen for the gas mixture increases. 1 X m i C pi mO2
ð45:1Þ
The result is a lower flame temperature. Combustion reaction rates are very sensitive to temperature, decreasing exponentially with decreasing temperature. When the concentration of carbon dioxide in air is sufficiently high, the combustion temperature becomes depressed to the point where the rate of heat release falls below the rate of heat loss to the surroundings and the flame is extinguished (in simple cases) or suppressed (in complex geometries). For example, the flame above heptane burning in the cup-burner apparatus is extinguished when the concentration of carbon dioxide added to the air flowing past the “cup” reaches about 21 vol. % [20]. Carbon dioxide is often called an “efficient” extinguishing gas. One reason for this claim lies in the fact that compared with other extinguishing gases such as nitrogen and argon,
Table 45.2 Agent gas heat capacity and minimum extinguishing capacity Agent Gas IG-01 IG-55 IG-541 IG-100 CO2
Composition Argon 50/50 N2/Ar 52/40/8 N2/Ar/CO2 Nitrogen Carbon dioxide
Cp (298 K) J/mol-K 20.8 24.6 26.1 28.5 37.5
MEC vol.% 42.5 36.4 34.3 31.9 20.9
carbon dioxide has a much larger heat capacity so less of it is required to extinguish a flame. One study reported the relationship between extinguishing agent gas heat capacity and minimum extinguishing concentration (MEC) for n-heptane in the cup-burner test as shown in Table 45.2 [21]. The data in Fig. 45.1 illustrates that the extinguishing effectiveness of inert gas agents is an inverse function of their heat capacity.
Thermo-physical Properties Carbon dioxide for fire extinguishing systems is stored either as a liquefied compressed gas, usually in U.S. DOT 3AA1800 high-pressure steel cylinders, or as a refrigerated liquid in insulated tanks maintained at approximately 0 2 F. The amount of carbon dioxide that can be safely stored in a container of a given type and size depends on the vapor pressure and densities of the liquid and gas phases. The thermo-physical properties of carbon dioxide are indicated in Table 45.3. While carbon dioxide is a gas at normal ambient conditions, 21 C (70 F) and 101.3 kPa (14.7 psia), it can assume any of the three usual physical forms—as a liquid, gas, or solid— depending on the prevailing pressure and temperature. The thermodynamic properties (vapor pressure, density, enthalpy, entropy, heat capacity, and heat of vaporization) and physical properties (viscosity and thermal conductivity) also vary widely with temperature as indicated in Tables 45.4 and 45.5.
45
Carbon Dioxide Systems
1537
Relationship of MEC to Heat Capacity
Fig. 45.1 Relationship of MEC to heat capacity
MEC, vol%
45 40 35 30
MEC= 885 (1/Cp)
25 20 15 10 5 0 0.00
0.01
0.02
0.03
0.04
0.05
0.06
(1/Cp), mol-K/J
Table 45.3 Reference properties of carbon dioxide [22] Chemical name Synonyms CAS Registry No.a Chemical formula Property Molecular weight Vapor pressure at 2 F (16.7 C) Specific gravity of gas at 70 F (21.1 C) and 1 atm Solid to gas expansion ratio at 70 F (21.1 C) and 1 atm Gas density at 70 F (21.1 C) and 1 atm Density of solid (dry ice) at 109.3 F (78.5 C) Sublimation temperature at 1 atm Critical temperature Critical pressure Critical density Triple point Latent heat of vaporization at 16.7 C, 2.18 Mpa Latent heat of fusion at 518 kPa; at 93.8 C Latent heat of sublimation at 78.5 C, 101.3 kPa Specific heat at constant pressure, CP, gas at 25 C Specific heat at constant volume, CV, gas at 25 C Ratio of gas specific heats, CP/CV, at 15 C Solubility in water at 20 C Viscosity of saturated liquid at 16.7 C
Carbon dioxide Carbon anhydride; carbonic acid gas; carbonic anhydride; dry ice 124-38-9 CO2 S.I. units 44.01 g/mol 2181.4 kPa 1.522 0.5457 m3/kg 1.833 kg/m3 1563 kg/m3 78.5 C 31.1 C 7381.8 kPa 468 kg/m3 56.6 C at 518 kPa 276.8 kJ/kg 547 kJ/kg 571.0 kJ/kg 0.850 kJ/kg- C 0.657 kJ/kg- C 1.304 0.90 vol/vol 0.000119 kg/m-s
a
CAS numbers are unique numerical identifiers assigned by the Chemical Abstracts Service to every chemical described in the open scientific literature
The Shomate equations, shown below, and the appropriate coefficients as indicated in Table 45.6, can be used to calculate the heat capacity, molar enthalpy, and molar entropy at
specific temperatures. See Table 45.7 for a tabulation of these values for a range of temperatures [24]. The Shomate equation coefficients given in Table 45.6 are for calculations in S.I. units.
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Table 45.4 Saturation properties of carbon dioxide [23] Temp. K 218 220 222 224 226 228 230 232 234 236 238 240 242 244 246 248 250 252 254 256 258 260 262 264 266 268 270 272 274 276 278 280 282 284 286 288 290 292 294 296 298 300 302 304
Pressure Mpa 0.5504 0.5991 0.6510 0.7062 0.7648 0.8270 0.8929 0.9626 1.0363 1.1141 1.1961 1.2825 1.3734 1.4690 1.5693 1.6746 1.7850 1.9007 2.0217 2.1483 2.2806 2.4188 2.5630 2.7134 2.8701 3.0334 3.2033 3.3802 3.5642 3.7555 3.9542 4.1607 4.3752 4.5978 4.8289 5.0688 5.3177 5.5761 5.8443 6.1227 6.4121 6.7131 7.0268 7.3555
Density, liquid kg/m3 1173 1166 1159 1151 1144 1136 1129 1121 1113 1105 1097 1089 1081 1072 1064 1055 1046 1037 1028 1018 1009 999 989 979 968 957 946 934 922 910 897 884 870 855 839 823 805 785 764 740 713 679 634 530
Density, vapor kg/m3 14.58 15.82 17.13 18.53 20.02 21.60 23.27 25.05 26.94 28.93 31.05 33.30 35.67 38.18 40.85 43.66 46.65 49.80 53.14 56.68 60.44 64.42 68.64 73.12 77.89 82.97 88.37 94.15 100.33 106.95 114.07 121.74 130.05 139.09 148.98 159.87 171.96 185.55 201.06 219.14 240.90 268.58 308.15 406.42
Enthalpy, liquid kJ/kg 82.80 86.73 90.67 94.62 98.59 102.57 106.57 110.59 114.62 118.67 122.74 126.84 130.96 135.10 139.27 143.48 147.71 151.98 156.28 160.62 165.01 169.44 173.92 178.45 183.04 187.69 192.41 197.21 202.08 207.05 212.12 217.30 222.61 228.06 233.70 239.54 245.63 252.01 258.80 266.10 274.14 283.37 295.02 318.36
Enthalpy, vapor kJ/kg 430.9 431.6 432.3 432.9 433.5 434.1 434.6 435.1 435.5 435.9 436.2 436.5 436.7 436.9 437.0 437.1 437.0 437.0 436.8 436.6 436.3 435.9 435.4 434.9 434.2 433.4 432.6 431.5 430.4 429.1 427.6 425.9 424.1 421.9 419.6 416.9 413.7 410.2 406.0 401.0 394.9 387.1 375.7 347.9
Heat of vaporization kJ/kg 348.1 344.9 341.6 338.3 334.9 331.5 328.0 324.5 320.9 317.2 313.5 309.7 305.8 301.8 297.7 293.6 289.3 285.0 280.5 276.0 271.3 266.5 261.5 256.4 251.2 245.8 240.1 234.3 228.3 222.0 215.5 208.7 201.5 193.9 185.9 177.3 168.1 158.2 147.2 134.9 120.8 103.7 80.7 29.6
45
Carbon Dioxide Systems
1539
Table 45.5 Specific heat, thermal conductivity, viscosity [23] Temp. K 220 225 230 235 240 245 250 255 260 265 270 275 280 285 290 295 300
Cp, liquid J/kg-K 1962 1977 1997 2021 2051 2087 2132 2187 2255 2342 2454 2603 2814 3133 3676 4794 8698
Thermal cond., liquid W/m-K 0.1762 0.1697 0.1633 0.1570 0.1508 0.1446 0.1385 0.1324 0.1264 0.1203 0.1143 0.1082 0.1020 0.0958 0.0895 0.0836 0.0806
Viscosity, liquid uPa-s 242.0 222.2 204.2 187.9 173.0 159.3 146.7 135.1 124.4 114.4 105.0 96.2 87.7 79.5 71.4 62.9 53.1
Table 45.6 Shomate equation coefficients for carbon dioxide Temperature range, K A B C D E F G H MW
298–1200 24.99735 55.18696 33.69137 7.948387 0.136638 403.6075 228.2431 393.5224 0.044
1200–6000 58.16639 2.720074 0.492289 0.038844 6.447293 425.9186 263.6125 393.5224 kg/mol
C p ¼ A þ B*t þ C*t2 þ D*t3 þ E=t2 ð45:2Þ
H H 298:15 ¼ A*t þ B*t =2
Cv, vapor J/kg-K 639 654 670 687 705 725 746 769 794 822 852 885 923 969 1026 1106 1248
Thermal cond., vapor W/m-K 0.01130 0.01175 0.01222 0.01274 0.01330 0.01392 0.01461 0.01540 0.01631 0.01738 0.01869 0.02033 0.02247 0.02542 0.02982 0.03722 0.05369
Viscosity, vapor uPa-s 11.14 11.41 11.69 11.98 12.27 12.58 12.90 13.25 13.61 14.02 14.47 14.99 15.60 16.36 17.36 18.79 21.31
S ¼ standard entropy (J/mol-K) t ¼ temperature (K)/1000 Carbon dioxide is soluble in water to an extent that depends on pressure and temperature as shown in Fig. 45.2 below [26]. The dissolution of CO2 in water (this may be sea water, or the saline water in geological formations) involves a number of chemical reactions between gaseous and dissolved carbon dioxide (CO2), carbonic acid (H2CO3), bicarbonate ions (HCO3) and carbonate ions (CO32) which can be represented as follows: CO2ðgÞ ↔CO2ðaqÞ
ð45:5Þ
CO2ðaqÞ þ H2 O↔H 2 CO3ðaqÞ
ð45:6Þ
H 2 CO3ðaqÞ ↔Hþ aq þ HCO3ðaqÞ
ð45:7Þ
2 þ HCO 3ðaqÞ ↔H aq þ CO3ðaqÞ
ð45:8Þ
2
þ C*t3 =3 þ D*t4 =4 E=t þ F H ð45:3Þ S ¼ A*lnðtÞ þ B*t þ C*t2 =2 þ D*t3 =3 E= 2*t2 þ G where Cp ¼ heat capacity (J/mol-K) H ¼ standard enthalpy (kJ/mol)
ð45:4Þ
Addition of CO2 to water initially leads to an increase in the amount of dissolved CO2. The dissolved CO2 reacts with water to form carbonic acid. Carbonic acid dissociates to form bicarbonate ions, which can further dissociate into carbonate ions. The net effect of dissolving
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J. Harrington and J.A. Senecal
Table 45.7 Properties of superheated carbon dioxide at 101.3 kPa Temp
Heat capacity
Enthalpy
Entropy
Temp
Heat capacity
Enthalpy
Entropy
T C 4 1 2 4 7 10 13 16 18 21 24 27 29 32 35 38 41 43 46 49 52
CP kJ/kg-K 0.81 0.81 0.82 0.82 0.82 0.83 0.83 0.83 0.84 0.84 0.84 0.85 0.85 0.85 0.85 0.86 0.86 0.86 0.87 0.87 0.87
H kJ/kg 8.97 8.97 8.96 8.96 8.96 8.96 8.95 8.95 8.95 8.95 8.95 8.94 8.94 8.94 8.94 8.93 8.93 8.93 8.93 8.92 8.92
S kJ/kg-K 4.75 4.76 4.76 4.77 4.78 4.79 4.80 4.80 4.81 4.82 4.83 4.84 4.84 4.85 4.86 4.86 4.87 4.88 4.88 4.89 4.90
T C 54 57 60 63 66 68 71 74 77 79 82 85 88 91 93 96 99 102 104 107 110
CP kJ/kg-K 0.87 0.88 0.88 0.88 0.89 0.89 0.89 0.89 0.90 0.90 0.90 0.90 0.91 0.91 0.91 0.91 0.92 0.92 0.92 0.92 0.93
H kJ/kg 8.92 8.92 8.92 8.91 8.91 8.91 8.91 8.90 8.90 8.90 8.89 8.89 8.89 8.89 8.88 8.88 8.88 8.88 8.88 8.87 8.87
S kJ/kg-K 4.90 4.91 4.92 4.92 4.93 4.94 4.94 4.95 4.96 4.97 4.97 4.98 4.98 4.99 4.99 5.00 5.01 5.02 5.02 5.03 5.03
Values of the above can be computed for temperatures up to 1600 K, in metric units on a mole basis, using the Shomate equation
anthropogenic CO2 in water is the removal of carbonate ions and production of bicarbonate ions, with a lowering in pH. Data on the compatibility of carbon dioxide with specific materials is indicated in Table 45.8 [27]. Although the information has been compiled from what are considered reliable sources (International Standards: Compatibility of cylinder and valve materials with gas content; Part 1: ISO 11114-1 (Jul 1998), Part 2: ISO 111142 (Mar 2001), the data should be used with a sufficient degree of prudence. No raw data such as that presented in Table 45.8 can address all scenarios and conditions of concentration, temperature, humidity, impurities and aeration. It is therefore recommended that the data in Table 45.8 be used to initially choose possible materials with a more extensive investigation and testing carried out under the specific anticipated conditions of use. The collected data
mainly concern high-pressure applications at ambient temperature and the safety aspect of material compatibility.
Health and Safety Carbon dioxide is usually described as an asphyxiant gas. However, exposure to atmospheres that contain high concentrations of carbon dioxide result in a condition called hypercapnia (also called hypercarbia). Hypercapnia, is a condition whereby there is too much carbon dioxide in the blood [28]. In severe hypercapnia, generally where the ambient partial pressure of carbon dioxide exceeds approximately 10 kPa, or 10 vol. % at sea level, the symptomatology progresses, over a period of several minutes, to disorientation, panic, hyperventilation, convulsions, unconsciousness, and, eventually, death [29].
45
Carbon Dioxide Systems
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Fig. 45.2 Solubility of carbon dioxide in water [25]
8 700 ATMOSPHERE 600
7
500 400 300
200 2 CO
5
150
R PO vA
100
EQ B LI UI
CO2 solubility (LBCO2/100 LB of H2O)
6
R IU
4
3
M
LI NE
75
50 45 40 35 30 25 20
2
15 10 5
1
1
0
0
10
20
Death will occur because of a lack of oxygen in the blood, leading to complete organ failure as the oxygen has been overtaken by the carbon dioxide. In some cases, victims who have been exposed to very high levels of carbon dioxide in the atmosphere have been known to die almost immediately of asphyxiation, as the carbon dioxide serves to displace, or push out, the oxygen in the air [30]. Treating hypercapnia is best achieved by removing a victim from the exposure to carbon dioxide and providing high concentrations of oxygen. If the exposure was at mild to moderate levels (6–9 kPa), the patient should recover fully. If the exposure was at levels higher than 10 kPa, the patient may suffer from permanent damage of the central nervous system. The acute physiological effects of exposure to atmospheres containing carbon dioxide depend on the carbon dioxide concentration and the
30
40
70 50 60 Temperature (°C)
80
90
100 110
120
duration of exposure. The effects of exposure have been reported in several sources. Table 45.9 summarizes the effects of exposure to carbon dioxide as reported in three different sources. Protection standards have been developed for workers who may be exposed to carbon dioxide. (Table 45.10 shows exposure limits as noted in U.S. standards but similar limits are understood to apply in standards of other countries). A carbon dioxide fire extinguishing system discharges carbon dioxide in sufficient quantity to produce a lethal concentration in a localized or confined atmosphere. Total flooding type systems are required to achieve a minimum design concentration of 34 vol.% [33]. For many fire hazards, the design concentration is required to be substantially higher than 34 vol. %. As indicated in Table 45.9, a carbon dioxide concentration in the range of 17–30 vol.% is lethal to humans within only 1 min of exposure.
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Table 45.8 Material compatibility of carbon dioxide [27] Material Metals Aluminium Brass Copper Ferritic steels (e.g. carbon steels) Stainless steel Plastics Polytetrafluoroethylene (PTFE) Polychlorotrifluoroethylene (PCTFE) Vinylidene polyfluoride (PVDF) (KYNAR™) Polyamide (PA) (NYLON™) Polypropylene (PP) Elastomers Buthyl (isobutene – isoprene) rubber (IIR) Nitrile rubber (NBR) Chloroprene (CR) Chlorofluorocarbons (FKM) (VITON™) Silicon (Q) Ethylene – Propylene (EPDM) Lubricants Hydrocarbon based lubricant Fluorocarbon based lubricant
All properly designed total flooding carbon dioxide fire extinguishing systems, therefore, have the potential to be lethal. In fact there have been numerous incidents with carbon dioxide fire extinguishing systems that have resulted in fatalities and serious injuries. One study by the U.S. Environmental Protection Agency (EPA) reported that between 1975 and 1999, 72 deaths and 145 injuries occurred as a result of 51 incidents involving carbon dioxide fire extinguishing systems [2]. This study also reported on incidents that occurred prior to 1975. Table 45.11, which is reproduced from the EPA study, shows data on deaths and injuries categorized by time frame, geographical region, and military/non-military installations.
Compatibility Satisfactory Satisfactory Satisfactory Satisfactory but risk of corrosion in presence of CO and/or moisture. cold brittleness Satisfactory Satisfactory Satisfactory Satisfactory Satisfactory Satisfactory Non recommended, significant swelling Non recommended, significant swelling and significant loss of mass by extraction or chemical reaction Non recommended, significant swelling and significant loss of mass by extraction or chemical reaction Non recommended, significant swelling and significant loss of mass by extraction or chemical reaction Acceptable but strong rate of permeation Acceptable but important swelling and significant loss of mass by extraction or chemical reaction Satisfactory Satisfactory
The EPA study included a comprehensive data search and analysis of incidents involving carbon dioxide fire extinguishing systems. The search included governmental, public, and private document archives internationally. Many details about each reported incident were collected and presented in the study. All of the 13 military incidents reported were marine-related. Only 11 of the 49 nonmilitary incidents reported were marine-related. The remaining incidents occurred in a variety of land-based facilities noted below: • Data processing centers • Nuclear power plants • Pilot training centers • Airplanes • Bus garages
7–10
6
1–2 min 14.15–45.28 m3 gross volume >45.28–127.35 m3 gross volume >127.35–1415 m3 gross volume >1415 m3 gross volume Propulsion machineryinternational voyage Cargo spaces Vehicle spaces Electrical equipment spaces 500–1600 ft3 gross volume >1600–4500 ft3 gross volume >4500–50,000 ft3 gross volume >50,000 ft3 gross volume Propulsion machineryinternational voyage Cargo spaces Vehicle spaces Electrical equipment spaces 19 L (5 gal) fuel Vehicle storage 19 L (5 gal) fuel
NFPA 12 [38] 85 % of design concentration (DC) in 2 min No discharge rate given 85 % of design concentration (DC) in 2 min 2/3 of design concentration (DC) in 10 min
U.S. Coast Guard, DHS [17] 85 % of mFD in first 2 min
SOLAS (FSS) [36] 85 % of mFD in first 2 min
Specific rate not required 100 % of mFD in first 2 mina
No discharge rate given No discharge rate given
No discharge rate given N/Ab
N/Aa
No discharge rate given
N/Ab
ABS [37] 85 % of mFD in first 2 min
a
Requirements are not based upon quantity of fuel in vehicles Carbon dioxide systems are not allowed in these spaces
b
29.5 vol.%. The USCG requirement for a space of this size (see Table 45.20) is to use a flooding factor of 0.80 kg/m3 (0.05 lb/ft3) giving a required quantity of 400 kg (883 lb) which would result in a concentration of 36.1 vol.% per Equation 45.9. All referenced marine carbon dioxide system design standards require a flooding factor (FF) be applied to the protected volume (VP) to determine the quantity of carbon dioxide for one or more hazard types (refer to Equation 45.11). SOLAS does not require adjustments to the base design quantity of carbon dioxide calculated using Equations 45.23 or 45.9 [44]. ABS requires an additional quantity of carbon dioxide equal to that lost through “non-tight” cargo space hatch covers [45] but provides no guidance to calculate this quantity.
Discharge Rate Marine total flooding carbon dioxide system discharge rate requirements are dependent on both the specific type of hazard being protected and the governing standard. Table 45.21 illustrates this point by summarizing the discharge rates found in the four referenced standards.
Enclosure Venting for Pressure Control for Total Flooding Systems Carbon dioxide enters a nozzle as a mixture of cold liquid and vapor and exits as a mixture of
vapor and solid-phase “dry ice” or “CO2-snow.” Sublimation (vaporization) of the solid carbon dioxide and exchange of the cold vapor with the air in a room results in a temperature reduction. The net effect on the pressure in a tightly sealed room depends on the storage condition of the carbon dioxide (high-pressure or refrigerated low-pressure), total quantity of gas discharged, the size of the protected volume, and its initial temperature. In most cases the enclosure pressure will rise upon carbon dioxide discharge. It is possible, however, under unusual circumstances for the enclosure pressure to decrease. Discharge of a large quantity of cold carbon dioxide into a tightly sealed room can result in a pressure decrease. Where such conditions are possible it is recommended that an energy balance evaluation be completed for the enclosure air and the quantity, and storage enthalpy of the carbon dioxide discharged, to determine if there is a risk of pressure decrease. The pressure rise in an enclosure due to carbon dioxide discharge is capable of causing damage to the enclosure construction due to characteristics common to many system installations. The risk of enclosure damage can be greatly reduced by designing and installing a means of pressure relief. Enclosure construction, including walls, ceilings and floors, are commonly not tightly sealed. Such enclosures contain numerous locations where pressure would be relieved to
45
Carbon Dioxide Systems
1567
some degree. The aggregate effect of such leakage locations is often referred to as “normal leakage” or “average leakage”. Normal leakage should not be relied upon to provide adequate pressure venting to prevent unsafe pressure rise resulting from carbon dioxide discharge. The size of the minimum pressure relief area required is based on the maximum flow rate of carbon dioxide and is calculated using Equation 45.24 [46]. AV ¼
239 w pffiffiffi P
ð45:24Þ
Where: AV ¼ vent area, mm2 w ¼ carbon dioxide flow rate, kg/min P ¼ allowable enclosure pressure limit, kPa The pressure relief (vent) area can be provided by passive (e.g. barometric dampers) or actuated vents (motor-controlled louvers that are opened before the onset of carbon dioxide discharge). Where a minimum concentration of carbon dioxide must be maintained in a room for a specific hold time, vents must be located at the highest point in an otherwise tightly closed room and should be arranged to close after discharge ceases. Assessment of the allowable pressure limit for an enclosure is often a challenge. Table 45.22 indicates approximate pressure limits for three general types of construction. In the absence of a structural analysis of an enclosure, the user should consider discounting the values in Table 45.22 to provide a safety margin for the design. Pressure Relief Example What size pressure relief vent is necessary to protect the enclosure described in the total-flooding example given above? Assume the pressure limit is 0.6 kPa (0.09 psi), half of the rated strength for light building construction. The design rate of discharge is 560 kg/min (1,234.6 lb/min). Light building construction has a rated strength of 1.2 kPa (0.17 psi) as shown in Table 45.22. For this example the design pressure limit is half of the rated value,
Table 45.22 Allowable pressure for average enclosures [47] Construction type Light building Normal building
P, kPa 1.2 2.4
Vault building
4.8
Note Venting sash remains open Venting sash designed to open freely
or (½) (1.2 kPa) ¼ 0.6 kPa (0.09 psi). Using half of the rated value in this manner is a choice of the designer to incorporate a design safety margin. Using Equation 45.24, the required vent area is: AV ¼
239 560 pffiffiffiffiffiffiffi ¼ 172, 787 mm2 ¼ 0:173 m2 0:6
Local Application Systems A total-flooding system discharges carbon dioxide throughout an entire enclosed volume so that the atmosphere can no longer support combustion. By contrast, a local application system projects carbon dioxide directly onto or in close proximity to a defined surface-fire hazard (flammable gases, liquids, or shallow solids) and maintains an extinguishing atmosphere on or about a precisely define geometric space, but only during the discharge period. Local application systems are designed by either of two methods: rate-by-area or rate-by-volume. Local application systems are used where the fire hazard is either not confined within an enclosure or the defining enclosure is too large to protect by total flooding in a practical manner. Protected hazards may by completely indoors, partly sheltered, or completely outdoors. The discharge of carbon dioxide must be so arranged that extinguishment of the target fire is not impaired by air currents or wind. A local application system must be designed to protect the entirety of the hazard which must be sufficiently separated from other hazards so as not to pose a risk of fire spread outside of the protected space. The definition of the protected hazard must include the principal process space or equipment as well as locations or items that can be wetted by splashing, leaking, dripping, or
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condensing flammable liquids and associated items or materials such as coated objects, drain boards, hood, or ducts that could serve to propagate a fire into or out of the primary protected space. A series of hazards that expose each other to fire propagation can be can be divided and protected as subgroups or sections with the approval of the local authority having jurisdiction. The basic design quantity of carbon dioxide required is determined by rate of liquid discharge to protect a defined area or volume times the liquid discharge time. The basic design quantity must be increased based upon consideration of the following factors: high-pressure storage supply; carbon dioxide vaporization in distribution pipe system.
High-Pressure Storage Supply Where carbon dioxide is supplied from highpressure storage containers the basic carbon dioxide quantity shall be increased by 40 %, i.e. multiplied by a liquid efficiency factor of 1.4, as these containers discharge only about 70–75 % of their contents as liquid which is deemed, in local application, to be the effective part of the discharge. Vaporization in Pipe System Some carbon dioxide is vaporized in the pipe system at the start of discharge. The basic quantity of carbon dioxide must be augmented by the amount so vaporized which can be estimated as follows: mCO2:V
mP CP ðT 1 T 2 Þ ¼ ΔH V
ð45:25Þ
where CP ¼ specific heat of steel pipe, approximately 0.46 kJ/kg-K ΔHV ¼ latent heat of vaporization of liquid CO2 (149 kJ/kg for high-pressure storage and 279 kJ/kg for low-pressure storage) mCO2,V ¼ mass of CO2 evaporated in the pipe, kg mP ¼ mass of pipe system, kg T1 ¼ initial pipe temperature, C
T2 ¼ average temperature of liquid CO2 flowing in pipe, taken as 16 C for high-pressure storage and 21 C for low-pressure storage Assuming that T1 ¼ 20 C and average values of T2 C, the amount of CO2 vaporized in a pipe system will be approximately: mCO2, V ¼ 0:012mP
high‐pressure storage ð45:26Þ
mCO2, V ¼ 0:0678 mP
ð45:27Þ
The total rate of discharge of a local-application system will be the sum of the individual discharge rate of all nozzles or other dispensing points in a system. The number of nozzles for a local application system is determined as described under Nozzle coverage, in the Rateby-Area and Rate-by-Volume methods sections below. Where part of a hazard is to be protected by total flooding and part by local application the following guidance applies: The total-flooding design concentration must be achieved not later than the end of discharge for the local-application portion of the system. The discharge rate for the total-flooding part shall be computed by dividing the quantity required for total flooding by the factor 1.4 and by the time of the local application discharge in minutes. Use the following equation: wTF ¼
mTF 1:4 tLA
ð45:28Þ
where wTF flow rate into total-flood part, kg/s mTF total quantity of CO2 for the total-flood part, kg tLA discharge time for local-application part, s The duration of liquid discharge for computing the basic carbon dioxide quantity for a localapplication system, or the local-application portion of a combined system, shall be at least 30 s. Where a liquid fuel has an auto-ignition temperature below its boiling point (e.g., cooking oils, paraffin waxes) the minimum discharge time shall be 3 min. Longer discharge times should
45
Carbon Dioxide Systems
1569
Table 45.23 Example nozzle coverage values Coated surface Area, m2 1.29 1.51 1.72 1.95 2.16 2.36
Side of square, m 1.14 1.22 1.31 1.39 1.46 1.53
Nozzlea Height, m 0.75 1.00 1.25 1.50 1.75 2.00
Flow rate, kg/min 16.99 21.69 27.20 32.57 37.80 42.99
Liquid surface Area, m2 0.92 1.08 1.22 1.38 1.53 1.68
Side of square, m 0.96 1.03 1.11 1.17 1.23 1.29
a
Refer to manufacturer’s values for actual specific nozzles
be considered to compensate for hazard conditions that may require more time for them to be rendered ineffective as re-ignition sources. For example, additional time may be required to cool hot liquids or heated surfaces to at least 35 C (95 F) below the autoignition temperature of exposed flammable liquids or gases. In such cases an engineering analysis may be required to estimate cooling times.
Rate-by-Area Method The rate-by-area method is used where the fire hazard is primarily characterized by flat surfaces or low-level objects. System designs are based on use of nozzles having approved area coverage based on location and height above the protected surface. Since each nozzle used in the rate-byarea or rate-by-volume method is used to protect a specific portion of a hazard, the flow rate through each nozzle must be within its listed and approved limits. For each over-head nozzle, its discharge rate is based only on its location and distance from the hazard. The approved discharge rate is determined by testing to establish the design flow rate at which a nozzle should be used for the height at which it is installed above a liquid surface. The carbon dioxide system manufacturer’s manual will contain nozzle tables for each type of nozzle approved for use in local application extinguishing systems. Typically, each table will list a range of nozzle mounting heights. Table 45.23 shows typical format and coverage values for one nozzle type. For each height there will be a corresponding CO2 flow rate, the maximum coverage area and “side-of-square” for
liquid-surface and coated-surface fire hazards. “Side-of-square” is the width of a square corresponding to the allowed area coverage and represents the maximum distance between nozzles, or between rows of nozzles. Table 45.23 (illustrative only) shows how manufacturer’s nozzle coverage data would typically be tabulated. A system protecting multiple hazards can be designed to incorporate both local-application and total-flooding protection. The rate of discharge for the total-flooding portion shall be as described under Rate of discharge in the preceding total flooding section. The discharge rate for a tank-side nozzle is based on its projection of CO2 required to cover a protected surface. The approved discharge rate is determined by test. Fire tests are conducted to develop curves relating the maximum and minimum flow rates at which a nozzle can be used to the area of fire that the nozzle is capable of extinguishing, with additional limitations regarding maximum width of hazard and spacing requirements between nozzles and to the nearest corner of a hazard. The rate-by-area method is used to protect fire hazards characterized predominantly by flat surfaces or low-level objects associated with horizontal surfaces. Examples include vats, drip trays, dip tanks, coated rollers or surfaces where liquid drains off and where the area of localized liquid pooling is less than 10 % of the protected area. The maximum area covered by a nozzle is based on its projection distance and maximum rated discharge rate. The shape of area covered by a nozzle is deemed to be square.
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Where the area to be protected consists of coated surfaces, and where there is not a heavy accumulation of combustible residue, it is permissible to increase the maximum area coverage of a nozzle by 40 %. Where a local application nozzle is used to project carbon dioxide across the face of an opening the maximum area coverage of the nozzle may be increased by 20 % over its rated value. Where flammable liquids having depth are to be protected, a freeboard of at least 152 mm (6 in.) must be provided unless otherwise noted in the approved rating of a nozzle. The number of nozzles used in an application shall be sufficient to cover the entire hazard area. Tank-side and linear nozzles shall be located within their approved spacing and discharge rate limits. Overhead nozzles must be mounted centered over and perpendicular to the covered hazard area. The nozzle height used to determine the flow rate is based on the distance from the nozzle face to the aiming point. Nozzles may be installed in non-overhead locations. In such cases nozzles need may be aimed at an angle of 45 –90 (perpendicular) with respect to the plane of the hazard surface provided that the following conditions are met: • The distance to the nozzle is measured to an aiming point at the near side of the protected area. • The design area coverage for each nozzle is reduced from its approved rated value by an “aiming factor.” See Table 45.24. • The design nozzle area coverage is calculated as the product of the width of the protected area times the aiming factor. The flow path from a nozzle to its protected hazard area must be unobstructed. Where an Table 45.24 Nozzle aiming factors [48] Nozzle discharge anglea 45 –60 60 –75 75 –90 90 a
Aiming factorb 0.25 0.25–0.375 0.375–0.50 0.50
From plane of hazard surface Fractional amount of nozzle area coverage
b
object protects above the protected surface, nozzles shall be arranged to cover the object with an extinguishing atmosphere. The effects of air currents in the protected area shall be compensated for by adjusting nozzle locations or extending the area of coverage beyond the perimeter of the hazard. To summarize, the quantity of carbon dioxide required for a rate-by-area system can be calculated as follows (assuming initial pipe temperature of 20 C, and average temperature of carbon dioxide liquid flowing in pipe system of 16 C for high pressure systems and 21 C for low pressure systems): High‐pressure storage : " # X mD ¼ 1:4 tD ni wi þ 0:012mP
ð45:29Þ
i
Low‐pressure storage : " # X ni wi þ 0:127mP m D ¼ tD
ð45:30Þ
i
where ni ¼ number of nozzles with flow rate wi wi ¼ flow rate i, kg/min tD ¼ liquid discharge time, at least 0.5 min mP ¼ mass of pipe, kg Example—Local Application Rate-by-Area Method Consider a quench tank measuring 5 m 3 m with a 0.15 m free board as shown in Fig. 45.8. The fuel is quench oil. Nozzle heights are limited to 0.6–1.8 m above the liquid. Describe a high-pressure CO2 system using 45.4 kg capacity cylinders, number type and arrangement of nozzle to protect the quench tank and a spillage perimeter that extends 0.6 m on all sides. Assume 30 s discharge time and a pipe system with a mass of 300 kg. Hazard dimensions: length ¼ 5 þ 0:6 þ 0:6 ¼ 6:2 m ; width ¼ 3 þ 0:6 þ 0:6 ¼ 4:2 m ; area ¼ ð6:2Þð4:2Þ ¼ 26:0 m2 . Nozzle height: initially select 1.5 m (this dimension is a design choice)
45
Carbon Dioxide Systems
Fig. 45.8 3 m 5 m quench tank
Fig. 45.9 Nozzle arrangement over quench tank hazard
Consult example nozzle table: Flow rate ¼ 32.57 kg/min; side-of-square ¼ 1.17 m No. nozzle rows parallel to length ¼ 4.2/ 1.17 ¼ 3.6; round up to 4 No. nozzle rows parallel to width ¼ 6.2/ 1.17 ¼ 5.3; round up to 6 Total number nozzles ¼ 4 6 ¼ 24 CO2 liquid flow rate ¼ 24 32.57 ¼ 781.7 kg/min Quantity of CO2: (a) Basic design quantity ¼ rate of discharge x discharge time highpressure efficiency factor ¼ 781.7 0.5 1.4 ¼ 547.2 kg; (b) Quantity to compensate for pipe-cooling: (0.012 kg CO2/kg-pipe) (300 kg) ¼ 3.6 kg. Total CO2 requirement ¼ 561 kg. The number of cylinders ¼ 561/45.4 ¼ 12.1, round up to 13 cylinders. The nozzles can be arranged in four rows of six nozzles each centered over the hazard as illustrated in Fig. 45.9.
1571
Rate-by-Volume Method The rate-by-volume method is used where the fire hazard consists of three-dimensional irregularly shaped objects that cannot be reasonable represented as a simple equivalent surface. The total rate of discharge is based on the gross volume of a virtual hazard enclosure that extends at least 0.6 m beyond the lateral and vertical dimensions of the actual hazard, unless an actual wall or ceiling is closer, and which includes areas of possible spillage, splashing, or leakage. The smallest dimension of the virtual hazard is to be no less than 1.2 m. The floor beneath the virtual volume should be a uniformly closed surface and, if not, special provisions are required to account for openings. If the protected volume is subject to winds or drafts, the virtual hazard volume shall be increased to compensate for losses on the windward sides. The total discharge rate for the basic system shall be equal to 16 kg/min · m3 of virtual volume. The discharge rate may be reduced by as much as 12 kg/min · m3 in proportion to the fraction of the perimeter of the virtual volume that consists of permanent and continuous walls that extend at least 0.6 m above the hazard, and provided that the walls are not actually part of the protected hazard. See Fig. 45.10. The number of nozzles used to cover the entire protected hazard volume is based on the total discharge rate as determined by the assumed volume. Nozzles are located and aimed so as to promote retention of the discharged carbon dioxide within and throughout the virtual hazard volume to the extent possible and to compensate for the effects of air currents, winds, or forced drafts. The design discharge rates through individual nozzles shall be determined on the basis of location or projection distance in accordance with their approved use for surface fires. The extinguishing system is to be designed for automatic operation except where the authorities having jurisdiction permit manual operation. The fire detection system should be designed to initiate discharge promptly after ignition to prevent excessive heating of materials within the hazard.
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Flow Rate with Partial Perimeter Walls 16
Flow Rate, kg/m3-min
14 12 10 8 6 4 0
10
20
30
40
50
60
70
80
90
100
Fraction of Perimeter With Walls
Fig. 45.10 Carbon dioxide flow rate with partial perimeter walls
The carbon dioxide supply should be located as close as practicable to the hazard while not exposing the equipment to a prospective fire. The pipeline should be as short and direct as practicable to minimize the time from cylinder actuation to the onset of carbon dioxide discharge into the protected space. Nozzles shall be used within their approved performance limits (flow rate, range, area coverage), and positioned and aimed in accordance with the system design requirements as previously described. Example—Rate-by-Volume Method Consider protection of a diesel fuel pumping skid having an equipment arrangement with a footprint measuring 3 m by 4 m and an overall height of 3 m as illustrated in Fig. 45.11. The equipment is located on a solid floor and in a corner where two walls meet at 90 . The ceiling height is 5 m. The equipment is positioned so that each edge of the skid 1 m from a wall. The equipment is not enclosed on the other two sides. Determine the design quantity of carbon dioxide to be delivered from high-pressure storage for a rate-by-volume system assuming a virtual volume that includes
the 1 m distance between the equipment and the two walls and a 0.6 m distances above the equipment and beyond the two unenclosed sides. Neglect the amount required to compensate for pipe cooling. The sketch below depicts (a) two confining walls; (b) the equipment volume surrounded by (c) the virtual design volume in dashed lines. The size of the protected volume is L W H ¼ (4 + 0.6 + 1) (3 + 0.6 + 1) (3 + 0.6) ¼ 92.7 m3. The protected perimeter is (2) [(4 + 0.6 + 1) + (3 + 0.6 + 1)] ¼ 20.4 m. One-half of the protected perimeter, 10.2 m, consists of permanent and impermeable walls. As such, the basic discharge per unit volume can be reduced from 16 kg/min-m3 by the amount (½) (12 kg/min-m3) ¼ 6 kg/min-m3. Thus, the design rate of liquid CO2 discharge is (92.7 m3) ([16 – 6] kg/min-m3) ¼ 927 kg/min. The duration of liquid discharge is 30 s. The total design quantity of CO2 ¼ rate of discharge discharge time high-pressure efficiency factor ¼ 927 0.5 1.4 ¼ 649 kg. The number of 45.4 kg high-pressure CO2 cylinders is 649/45.4 ¼ 14.3, rounded up to 15 cylinders.
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Carbon Dioxide Systems
1573
Fig. 45.11 Representation of three-dimensional hazard including virtual boundaries
0.6
3
1 4 0.6
1 3 0.6
The design challenge, therefore, is to deter-
Carbon Dioxide Hydraulic Calculations mine the effective average pressure at each nozzle during discharge. Commercial computer to Estimate Nozzle Pressure Pipeline Pressure Loss due to Flow A carbon dioxide fire extinguishing system is designed to discharge a certain quantity of carbon dioxide through one or more nozzles within a specified time period as determined by a total flooding or local application system design approach. Each nozzle in a system is selected based on its design flow rate at the average anticipated discharge pressure. The flow rate of carbon dioxide through a nozzle, QNOZ, is calculated as the product of the mass flow rate per unit of orifice area of the nozzle, i.e. the orifice mass flux, G, times the equivalent nozzle orifice area, ANOZ as indicated in Equation 45.31. QNOZ ¼ G ANOZ
ð45:31Þ
The equivalent orifice area of a given manufacturer’s nozzle is determined through testing. The carbon dioxide orifice mass flux, G, varies depending on the average fluid density which, in turn, depends on the pressure at the discharge outlet. Values of G are tabulated as a function of pressure in Table 45.25.
programs are available for facilitating the design and layout of carbon dioxide pipe distribution systems. These programs calculate pressures at key nodes of a pipe network, optimize the pipesize, nozzle sizes, and determine the mass of liquid and vapor discharged at each nozzle. Flow calculation routines are usually based on, or are at least benchmarked against, the method described in NFPA 12, Annex C. The same method is also documented in ISO 6183 [35]. The following describes how to use the NFPA 12 carbon dioxide flow equation to calculate pressure loss in a pipeline and select nozzle sizes. As noted previously, carbon dioxide is stored as a liquefied compressed gas in either refrigerated low-pressure tanks, maintained at about 18 C (0 F), or in high-pressure cylinders stored at ambient temperatures. Upon discharge, carbon dioxide flows into a pipe system that terminates at one or more nozzles. The average pressure at any point in the pipe system is governed by conservation equations of momentum and energy. The momentum equation relates pressure changes to changes in fluid
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Table 45.25 Discharge rate per unit of orifice area Low-pressure storage Orifice G, pressure, psi lb/min-in.2 300 4220 290 2900 280 2375 270 2050 260 1825 250 1655 240 1525 230 1410 220 1305 210 1210 200 1125 190 1048 180 977 170 912 160 852 150 795
Orifice pressure, Pa 2068 1999 1931 1862 1793 1724 1655 1586 1517 1448 1379 1310 1241 1172 1103 1034
G, kg/min-mm2 2.970 2.041 1.671 1.443 1.284 1.165 1.073 0.992 0.918 0.851 0.792 0.737 0.688 0.642 0.600 0.559
High-pressure storage Orifice G, pressure, psi lb/min-in.2 750 4630 725 3845 700 3415 675 3090 650 2835 625 2615 600 2425 575 2260 550 2115 525 1985 500 1860 475 1740 450 1620 425 1510 400 1400 375 1290 350 1180 325 1080 300 980
Orifice pressure, Pa 5171 4999 4826 4654 4481 4309 4137 3964 3792 3620 3447 3275 3103 2930 2758 2586 2413 2241 2068
G, kg/min-mm2 3.258 2.706 2.403 2.174 1.995 1.840 1.706 1.590 1.488 1.397 1.309 1.224 1.140 1.063 0.985 0.908 0.830 0.760 0.690
This table combines the data presented in Tables 4.7.5.2.1 and 4.7.5.3.1 from NFPA 12 [34]
density and friction loss along the pipe network. The energy equation accounts for heat exchange between carbon dioxide and the pipe system, particularly during initial flow when the pipe system is cooled to the fluid temperature. Vapor-liquid equilibrium is assumed to prevail everywhere in the pipe system. The momentum equation is presented as: dx d p þ d ρu2 þ 1=2 ρu2 f ¼ 0 D
ð45:32Þ
Here p is pressure, u is velocity, ρ is density, x is distance, D is the internal pipe diameter, and f is the Darcy-Weisbach friction factor. The first term on the left is the pressure change over distance dx; the second term accounts for pressure change due to variations in the fluid density and velocity (e.g. acceleration as liquid vaporizes); and the third term accounts for pressure loss due to friction effects with the pipe wall. The friction factor is a non-linear function of the degree of turbulence in the flow,
characterized by the Reynolds number, Re, which is equal to ρDu/μ, where μ is viscosity, and on the surface roughness, ε, of the pipe [49]. At very high Reynolds numbers the value of f is insensitive to changes in u, ρ, and μ. In this flow regime f is effectively a function of ε and D only. The applicable friction factor relations are assumed to apply during system discharge for three common types of pipe used in carbon dioxide systems: Uncoated steel pipe Galvanized pipe Drawn tubing
f ¼ 0:0227 D0:25 f ¼ 0:032 D0:35 f ¼ 0:011 D0:117
where D is in inches. The solution of Equation 45.32 over a defined pipe length, L, yields the following governing flow equations for each type of pipe: Uncoated steel pipe
Q2 ¼
3647 YD5:25 L þ 8:08D1:25 Z ð45:33aÞ
45
Carbon Dioxide Systems
Galvanized pipe
1575
Q2 ¼
Drawn tubing Q2 ¼
2586 YD5:35 L þ 5:72D1:35 Z ð45:33bÞ
7524 YD5:117 L þ 16:66D1:117 Z ð45:33cÞ
Where Q is mass flow rate (lb/min), D is inside pipe diameter (in), and L is the equivalent pipe length (ft). Values of Y and Z are non-linear functions of pressure and density defined as follows: ðP Y ¼ ρdP
ð45:34Þ
Po
ðρ Z¼ ρo
dρ ρ
ð45:35Þ
The values of Y and Z are functions of pressure that depend on the storage method of the carbon dioxide supply which is either as a refrigerated low-vapor pressure liquid or as an ambienttemperature high-vapor pressure liquid. Values of pressure (averaged over the period of discharge) along a pipe system are determined by solving Equations 45.34 and 45.35 for Y and Z and then looking up the corresponding value of pressure in Tables 45.26 and 45.27.1 In practice a pipe network is evaluated in sections. A section may be as small as a single pipe fitting or length of pipe, or may consist of multiple lengths of pipe and fittings so long as the pipe diameter is constant. The equivalent length, L, of a section of a pipe system is the sum of the lengths of the included pipe sections and all fittings or flow devices such as valves. Values of equivalent length of manufacturer-supplied components (cylinder discharge valves, check valves, etc.) are determined by testing. Corrections to pressure are made to account for
1
Tables 45.26 and 45.27 are expanded versions, in 1 psi pressure increments, of Tables C.1 (a) and C.1 (b) from NFPA 12 [34].
changes in pipe elevation. Values of pipe diameters, equivalent length of standard pipe fittings, and elevation pressure correction factors are indicated in the Tables 45.28, 45.29, 45.30 and 45.31.
Nozzle Selection A manufacturer’s nozzle is characterized by an “equivalent single orifice area” regardless of the actual number of orifices it contains. The standard “Orifice Code No.” is equal to the diameter, in increments of 1/32 in., of the equivalent single orifice. • Orifice Codes 1 to 9.5 are in size increments of 0.5 • Orifice Codes 10 to 64 are in size increments of 1 For example, a nozzle having an equivalent single orifice area of 0.0431 in.2 has an equivalent diameter of 15/64 in., or 7.5/32 in., therefore the Orifice Code No. is 7.5. In a design application where a calculated orifice size falls between two standard sizes, choose the nearest size unless the applicable flow rate requirement is a minimum value, in which case choose the next larger size.
Estimation of Nozzle Pressure The choice of nozzle depends on the estimated value of average pressure at the nozzle. Commercially available computer programs are able to perform the associated calculations to determine average nozzle pressures for complex piping arrangement. While somewhat tedious, the associated calculations can be performed by hand or with the use of a spreadsheet. The procedure for performing hand or spreadsheet calculations is described below. Calculation of pressure along a pipe network is carried out by solving Equation 45.33 in a stepwise manner, i.e. node-to-node. Here, a node is any component junction and includes: cylinder siphon tube entrance, cylinder valve exit, flexhose to valve, flex-hose to manifold tee, tee to
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Table 45.26 Y and Z factors vs. P for 300 psi systems P, psi 300 299 298 297 296 295 294 293 292 291 290 289 288 287 286 285 284 283 282 281 280 279 278 277 276 275 274 273 272 271 270 269 268 267 266 265 264 263 262 261 260
Z 0.000 0.014 0.027 0.041 0.054 0.068 0.081 0.095 0.108 0.122 0.135 0.148 0.161 0.174 0.187 0.200 0.212 0.225 0.238 0.251 0.264 0.276 0.289 0.301 0.313 0.326 0.338 0.350 0.362 0.375 0.387 0.399 0.411 0.422 0.434 0.446 0.458 0.470 0.481 0.493 0.505
Y 0 63 126 187 248 308 367 426 483 540 596 652 706 760 814 866 918 969 1020 1070 1119 1168 1216 1263 1310 1357 1402 1448 1492 1536 1580 1623 1666 1708 1749 1790 1831 1871 1911 1950 1989
P, psi 260 259 258 257 256 255 254 253 252 251 250 249 248 247 246 245 244 243 242 241 240 239 238 237 236 235 234 233 232 231 230 229 228 227 226 225 224 223 222 221 220
Z 0.505 0.517 0.528 0.540 0.551 0.563 0.574 0.586 0.597 0.609 0.620 0.631 0.642 0.654 0.665 0.676 0.687 0.698 0.710 0.721 0.732 0.743 0.754 0.765 0.776 0.787 0.797 0.808 0.819 0.830 0.841 0.852 0.863 0.874 0.885 0.896 0.906 0.917 0.928 0.939 0.950
Y 1989 2027 2065 2102 2139 2176 2212 2248 2283 2318 2352 2386 2420 2454 2487 2519 2552 2583 2615 2646 2677 2708 2738 2768 2797 2826 2855 2884 2912 2940 2968 2995 3022 3049 3075 3102 3128 3153 3179 3204 3228
P, psi 220 219 218 217 216 215 214 213 212 211 210 209 208 207 206 205 204 203 202 201 200 199 198 197 196 195 194 193 192 191 190 189 188 187 186 185 184 183 182 181 180
Z 0.950 0.961 0.971 0.982 0.993 1.004 1.014 1.025 1.036 1.046 1.057 1.068 1.079 1.089 1.100 1.111 1.122 1.133 1.143 1.154 1.165 1.176 1.187 1.198 1.209 1.220 1.230 1.241 1.252 1.263 1.274 1.285 1.296 1.307 1.318 1.329 1.340 1.351 1.362 1.373 1.384
Y 3228 3253 3277 3301 3325 3349 3372 3395 3418 3440 3462 3485 3506 3528 3549 3570 3591 3612 3632 3653 3673 3692 3712 3731 3750 3769 3788 3807 3825 3843 3861 3879 3896 3914 3931 3948 3965 3981 3998 4014 4030
P, psi 180 179 178 177 176 175 174 173 172 171 170 169 168 167 166 165 164 163 162 161 160 159 158 157 156 155 154 153 152 151 150
Z 1.384 1.395 1.407 1.418 1.429 1.441 1.452 1.463 1.474 1.486 1.497 1.509 1.520 1.532 1.543 1.555 1.566 1.578 1.589 1.601 1.612 1.624 1.636 1.648 1.660 1.672 1.683 1.695 1.707 1.719 1.731
Y 4030 4046 4062 4077 4093 4108 4123 4138 4152 4167 4181 4196 4210 4223 4237 4251 4264 4277 4291 4303 4316 4329 4341 4354 4366 4378 4390 4402 4413 4425 4436
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Table 45.27 Y and Z factors vs. P for 750 psi systems P, psi 750 749 748 747 746 745 744 743 742 741 740 739 738 737 736 735 734 733 732 731 730 729 728 727 726 725 724 723 722 721 720 719 718 717 716 715 714 713 712 711 710 709 708 707 706 705 704 703
Z 0 0.004 0.008 0.011 0.015 0.019 0.023 0.027 0.030 0.034 0.038 0.042 0.045 0.049 0.053 0.057 0.060 0.064 0.068 0.071 0.075 0.079 0.082 0.086 0.089 0.093 0.096 0.100 0.103 0.107 0.11 0.113 0.117 0.120 0.123 0.127 0.130 0.133 0.136 0.140 0.143 0.146 0.149 0.152 0.155 0.159 0.162 0.165
Y 0 51 101 151 201 251 300 350 399 448 497 545 594 642 690 738 786 833 881 928 975 1022 1068 1115 1161 1208 1254 1299 1345 1391 1436 1481 1527 1572 1616 1661 1706 1750 1794 1838 1882 1926 1970 2013 2057 2100 2143 2186
P, psi 690 689 688 687 686 685 684 683 682 681 680 679 678 677 676 675 674 673 672 671 670 669 668 667 666 665 664 663 662 661 660 659 658 657 656 655 654 653 652 651 650 649 648 647 646 645 644 643
Z 0.205 0.208 0.211 0.214 0.217 0.220 0.223 0.226 0.229 0.232 0.235 0.238 0.241 0.244 0.247 0.250 0.253 0.256 0.259 0.262 0.265 0.268 0.271 0.274 0.277 0.281 0.284 0.287 0.290 0.293 0.296 0.299 0.302 0.305 0.308 0.312 0.315 0.318 0.321 0.324 0.327 0.330 0.334 0.337 0.340 0.344 0.347 0.350
Y 2733 2774 2815 2856 2897 2937 2978 3018 3059 3099 3139 3179 3219 3259 3298 3338 3377 3416 3455 3494 3533 3572 3611 3649 3688 3726 3764 3802 3840 3878 3916 3953 3991 4028 4065 4102 4139 4176 4213 4250 4286 4323 4359 4395 4431 4467 4503 4539
P, psi 630 629 628 627 626 625 624 623 622 621 620 619 618 617 616 615 614 613 612 611 610 609 608 607 606 605 604 603 602 601 600 599 598 597 596 595 594 593 592 591 590 589 588 587 586 585 584 583
Z 0.393 0.396 0.400 0.403 0.407 0.410 0.413 0.417 0.420 0.424 0.427 0.431 0.434 0.438 0.441 0.445 0.448 0.452 0.455 0.459 0.462 0.466 0.469 0.473 0.476 0.480 0.484 0.487 0.491 0.494 0.498 0.502 0.505 0.509 0.513 0.517 0.520 0.524 0.528 0.531 0.535 0.539 0.542 0.546 0.550 0.554 0.557 0.561
Y 4993 5027 5061 5095 5129 5162 5196 5229 5263 5296 5329 5362 5395 5427 5460 5493 5525 5557 5589 5621 5653 5685 5717 5749 5780 5811 5843 5874 5905 5936 5967 5997 6028 6058 6089 6119 6149 6179 6209 6239 6268 6298 6328 6357 6386 6415 6444 6473
P, psi 570 569 568 567 566 565 564 563 562 561 560 559 558 557 556 555 554 553 552 551 550 549 548 547 546 545 544 543 542 541 540 539 538 537 536 535 534 533 532 531 530 529 528 527 526 525 524 523
Z Y 0.609 6840 0.613 6868 0.616 6895 0.620 6922 0.624 6949 0.628 6976 0.631 7003 0.635 7030 0.639 7057 0.642 7084 0.646 7110 0.650 7137 0.653 7163 0.657 7190 0.661 7216 0.665 7242 0.668 7268 0.672 7294 0.676 7320 0.679 7345 0.683 7371 0.687 7396 0.690 7422 0.694 7447 0.697 7472 0.701 7498 0.705 7523 0.708 7548 0.712 7572 0.715 7597 0.719 7622 0.723 7647 0.726 7671 0.730 7696 0.734 7720 0.738 7744 0.741 7768 0.745 7792 0.749 7816 0.752 7840 0.756 7864 0.760 7888 0.763 7911 0.767 7935 0.770 7958 0.774 7982 0.778 8005 0.781 8028 (continued)
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Table 45.27 (continued) P, psi 702 701 700 699 698 697 696 695 694 693 692 691 690 510 509 508 507 506 505 504 503 502 501 500 499 498 497 496 495 494 493 492 491 490 489 488 487 486 485 484 483 482 481 480 479 478 477 476
Z 0.168 0.171 0.174 0.177 0.180 0.183 0.186 0.190 0.193 0.196 0.199 0.202 0.205 0.827 0.831 0.834 0.838 0.841 0.845 0.849 0.852 0.856 0.859 0.863 0.867 0.870 0.874 0.877 0.881 0.884 0.888 0.891 0.895 0.898 0.902 0.905 0.909 0.912 0.916 0.919 0.923 0.926 0.930 0.933 0.936 0.940 0.943 0.947
Y 2229 2271 2314 2357 2399 2441 2483 2525 2567 2608 2650 2691 2733 8323 8345 8367 8389 8411 8433 8454 8476 8497 8519 8540 8562 8583 8604 8625 8646 8667 8688 8709 8730 8750 8771 8791 8812 8832 8852 8873 8893 8913 8933 8953 8973 8993 9012 9032
P, psi 642 641 640 639 638 637 636 635 634 633 632 631 630 450 449 448 447 446 445 444 443 442 441 440 439 438 437 436 435 434 433 432 431 430 429 428 427 426 425 424 423 422 421 420 419 418 417 416
Z 0.353 0.357 0.36 0.363 0.367 0.370 0.373 0.377 0.380 0.383 0.386 0.390 0.393 1.038 1.042 1.045 1.049 1.052 1.056 1.059 1.063 1.066 1.070 1.073 1.077 1.080 1.084 1.087 1.091 1.095 1.098 1.102 1.105 1.109 1.113 1.116 1.120 1.124 1.128 1.131 1.135 1.139 1.142 1.146 1.150 1.154 1.157 1.161
Y 4575 4610 4645 4681 4716 4751 4786 4821 4855 4890 4924 4959 4993 9520 9538 9556 9574 9592 9609 9627 9644 9662 9680 9697 9714 9731 9748 9765 9782 9799 9816 9833 9850 9866 9883 9900 9916 9933 9949 9966 9982 9998 10,014 10,030 10,046 10,062 10,078 10,094
P, psi 582 581 580 579 578 577 576 575 574 573 572 571 570 390 389 388 387 386 385 384 383 382 381 380 379 378 377 376 375 374 373 372 371 370 369 368 367 366 365 364 363 362 361 360 359 358 357 356
Z 0.565 0.568 0.572 0.576 0.579 0.583 0.587 0.591 0.594 0.598 0.602 0.605 0.609 1.262 1.266 1.270 1.274 1.278 1.282 1.286 1.290 1.294 1.298 1.302 1.306 1.310 1.315 1.319 1.323 1.327 1.331 1.336 1.340 1.344 1.348 1.352 1.357 1.361 1.365 1.369 1.373 1.378 1.382 1.386 1.390 1.395 1.399 1.403
Y 6502 6531 6560 6588 6616 6645 6673 6701 6729 6757 6785 6812 6840 10,486 10,501 10,515 10,529 10,543 10,557 10,571 10,585 10,599 10,613 10,627 10,641 10,654 10,668 10,681 10,695 10,708 10,722 10,735 10,749 10,762 10,775 10,788 10,801 10,814 10,827 10,840 10,853 10,866 10,878 10,891 10,904 10,916 10,929 10,941
P, psi 522 521 520 519 518 517 516 515 514 513 512 511 510 330 329 328 327 326 325 324 323 322 321 320 319 318 317 316 315 314 313 312 311 310 309 308 307 306 305 304 303 302 301 300
Z 0.785 0.788 0.792 0.796 0.799 0.803 0.806 0.810 0.813 0.817 0.820 0.824 0.827 1.518 1.523 1.527 1.532 1.536 1.541 1.546 1.550 1.555 1.559 1.564 1.569 1.573 1.578 1.582 1.587 1.592 1.596 1.601 1.605 1.61 1.615 1.619 1.624 1.629 1.634 1.638 1.643 1.648 1.652 1.657
Y 8052 8075 8098 8120 8143 8166 8189 8211 8234 8256 8278 8301 8323 11,247 11,258 11,269 11,280 11,291 11,302 11,313 11,323 11,334 11,345 11,356 11,366 11,377 11,387 11,398 11,408 11,418 11,428 11,439 11,449 11,459 11,469 11,469 11,479 11,499 11,509 11,519 11,529 11,539 11,548 11,558
(continued)
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Table 45.27 (continued) P, psi 475 474 473 472 471 470 469 468 467 466 465 464 463 462 461 460 459 458 457 456 455 454 453 452 451 450
Z 0.950 0.953 0.957 0.960 0.964 0.967 0.971 0.974 0.978 0.981 0.985 0.988 0.992 0.995 0.999 1.002 1.006 1.009 1.013 1.016 1.020 1.024 1.027 1.031 1.034 1.038
Y 9052 9071 9091 9110 9129 9149 9168 9187 9206 9225 9244 9263 9282 9301 9319 9338 9356 9375 9393 9412 9430 9448 9466 9484 9502 9520
P, psi 415 414 413 412 411 410 409 408 407 406 405 404 403 402 401 400 399 398 397 396 395 394 393 392 391 390
Z 1.165 1.169 1.173 1.176 1.180 1.184 1.188 1.192 1.195 1.199 1.203 1.207 1.211 1.214 1.218 1.222 1.226 1.230 1.234 1.238 1.242 1.246 1.250 1.254 1.258 1.262
Y 10,110 10,126 10,141 10,157 10,173 10,188 10,204 10,219 10,234 10,250 10,265 10,280 10,295 10,310 10,325 10,340 10,355 10,370 10,385 10,399 10,414 10,429 10,443 10,458 10,472 10,486
pipe, pipe to elbow, pipe to nozzle, etc. Pressure change calculations can be performed at each node or for a pipe segment between several nodes involving the same pipe diameter. The procedure uses a variant of Equation 45.33 as follows: L aY 2 þ c Z ¼ 0 Dd Q D
ð45:36Þ
ðbd=Þ=2
The constants a, b, c and d for the different types of pipe are shown in the Table 45.32. For uncoated steel pipe (sometimes called “black” pipe), Equation 45.36 becomes L 3647 Y 2 þ 8:08Z ¼ 0 D1:25 D D
2
ð45:37Þ
P, psi 355 354 353 352 351 350 349 348 347 346 345 344 343 342 341 340 339 338 337 336 335 334 333 332 331 330
Z 1.408 1.412 1.416 1.420 1.425 1.429 1.433 1.438 1.442 1.447 1.451 1.455 1.460 1.464 1.469 1.473 1.478 1.482 1.487 1.491 1.496 1.500 1.505 1.509 1.514 1.518
Y 10,954 10,966 10,978 10,991 11,003 11,015 11,027 11,039 11,051 11,063 11,075 11,087 11,099 11,110 11,122 11,134 11,145 11,157 11,168 11,180 11,191 11,202 11,214 11,225 11,236 11,247
P, psi
Z
Y
In a given pipe section the total equivalent length, L, the flow rate Q, and diameter, D, are known. The terms Y and Z are functions of pressure (tabulated in Tables 45.26 and 45.27). The end-of-segment pressure, P, having Y and Z values that make the left-hand side (LHS) of Equation 45.37 equal to zero is the solution. The hand or spreadsheet calculation procedure can be performed as follows: 1. Create a sketch of the required pipe system layout showing the carbon dioxide supply (one or more high-pressure cylinders or a low-pressure tank), discharge manifold, pipe type, size and length, elevation changes, fittings (elbows, tees, check valves, etc.). Label all the nodes at which pressure will be calculated as illustrated in Fig. 45.12.
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Table 45.28 Size data for ANSI steel pipe Nominal size, in. 1/4 3/8 1/2 3/4 1/4 3/8 1/2 3/4 1 1–1/4 1–1/2 2 2–1/2 3 4 5 6 7 8
Pipe schedule 40 40 40 40 80 80 80 80 80 80 80 80 80 80 80 80 80 80 80
D, in. 0.364 0.493 0.622 0.824 0.302 0.423 0.546 0.742 0.957 1.278 1.500 1.939 2.323 2.900 3.826 4.813 5.761 6.625 7.625
D1.25 0.2827 0.4131 0.5524 0.7851 0.2239 0.3411 0.4693 0.6887 0.9465 1.3588 1.6600 2.2881 2.8679 3.7844 5.3510 7.1289 8.9253 10.6288 12.6707
D2 0.1325 0.2430 0.3869 0.6790 0.0912 0.1789 0.2981 0.5506 0.9158 1.6333 2.2500 3.7597 5.3963 8.4100 14.6383 23.1650 33.1891 43.8906 58.1406
2. Set up a table to capture data for each pipe segment as indicated in Table 45.33. 3. Determine the equivalent length, L, between nodes. This is the sum of (1) actual pipe length, (2) equivalent length of fittings in the flow path,2 and (3) the equivalent length of the pipe system upstream of the section being evaluated. “Up-stream” equivalent length is calculated as follows: L¼
a YDb c Dd Z Q2
ð45:38Þ
Where the values of D and Q are for the pipe segment being evaluated and the values of Y and Z are those of the exit end of the previous pipe segment. Values of a, b, and c are indicated in Table 45.32. The remaining steps indicate how the values for D, Q, Y and Z are determined.
2 The equivalent lengths of the custom components (cylinder valve, hose, check valves) must be obtained from the manufacturer.
4. Specify the quantity of carbon dioxide liquid to be discharged from each nozzle. For highpressure cylinders, the total carbon dioxide supply is 140 % of the required liquid quantity. 5. Specify the required liquid discharge time in accordance with the requirements of the design approach and applicable standard.. 6. The flow rate, Q, in a pipe segment is the liquid quantity passing through the pipe segment divided by the discharge time. 7. Enter data for pipe system components (D, L, fitting equivalent lengths), and segment flow rates, Q. 8. Segment inlet pressure. For first segment use the supply pressure (750 or 300 psi). Otherwise use exit pressure from prior segment. 9. Segment exit pressure, Y, and Z are determined by determining values of Y and Z that satisfy Equation 45.36. Approaches using trial-and-error and spreadsheet methods are described. (a) Calculation by trial-and-error approach. Guess a pressure, P, then look up the corresponding values of Y and Z in Table 45.26 and 45.27. Calculate the value of the left-hand side (LHS) of Equation 45.36. If the result is greater than zero then make a second guess at a lower pressure. If the result is less than zero then make a second guess at a higher pressure. (b) Spreadsheet calculation approach. (i) Prepare lookup table 1. Copy, in columns 2, 3, and 4 the table of P, Y, and Z to an area of spread sheet. 2. In column 1 enter Equation 45.36 (in form for pipe type) with reference to the values of Q, D, and L for the segment and to values of Y and Z in col. 3 and 4. Copy equation to each cell in column 1 for this table. 3. The calculated values in column 1, the “residue,” decrease progressively from the 750 psi row (or 300 psi row) from positive to negative numbers.
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Carbon Dioxide Systems
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Table 45.29 Equivalent length of threaded pipe fittings Pipe size, in. 3/8 ½ ¾ 1 1¼ 1½ 2 2½ 3 4 5 6
Std 45 elbow 0.6 0.8 1.0 1.3 1.7 2.0 2.6 3.1 3.8 5.0 6.3 7.6
Std 90 elbow 1.3 1.7 2.2 2.8 3.7 4.3 5.5 6.6 8.2 10.7 13.4 16.2
90 long radius elbow and thru tee 0.8 1.0 1.4 1.8 2.3 2.7 3.5 4.1 5.1 6.7 8.4 10.1
Side tee 2.7 3.4 4.5 5.7 7.5 8.7 11.2 13.4 16.6 21.8 27.4 32.8
Gate valve and union coupling 0.3 0.4 0.5 0.6 0.8 0.9 1.2 1.4 1.8 2.4 3.0 3.5
Side tee 1.6 2.1 2.8 3.5 4.6 5.4 6.9 8.2 10.2 13.4 16.8 20.2
Gate valve and union coupling 0.3 0.4 0.5 0.6 0.8 0.9 1.2 1.4 1.8 2.4 3.0 3.5
Table 45.30 Equivalent length of welded pipe fittings Pipe size, in. 3/8 ½ ¾ 1 1¼ 1½ 2 2½ 3 4 5 6
Std 45 elbow 0.2 0.3 0.4 0.5 0.7 0.8 1.0 1.2 1.8 2.0 2.5 3.0
Std 90 elbow 0.7 0.8 1.1 1.4 1.8 2.1 2.8 3.3 4.1 5.4 6.7 8.1
90 Long-radius elbow and thru tee 0.5 0.7 0.9 1.1 1.5 1.7 2.2 2.7 3.3 4.4 5.5 6.6
Table 45.31 Pressure correction factors for pipe elevation changes 300 psi systems Average line pressure, psi 300 280 260 240 220 200 180 160 140
Elevation pressure correction, psi/ft 0.443 0.343 0.265 0.207 0.167 0.134 0.107 0.085 0.067
750 psi systems Average line pressure, Psi 750 700 650 600 550 500 450 400 350 300
Elevation pressure correction, psi/ft 0.352 0.300 0.255 0.215 0.177 0.150 0.125 0.105 0.085 0.070
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4. By inspection, identify the table row and P value where the residue changes from positive to negative. Interpolate to find the exact value of P where the residue is zero. This is the solution for the given pipe segment. (ii) Set up spreadsheet table. Referring to example below: 1. Col. 1–9. Pipe segment data. 2. Col. 10–12. Segment equivalent length. 3. Col. 13. Segment inlet pressure. 4. Col. 14. Segment exit pressure due to flow (not elevationcorrected). Determined from the Lookup Table described above. 5. Col. 15. Calculate pressure correction to account for elevation change.
Table 45.32 Pipe flow pressure constants Pipe type Uncoated steel Galvanized Drawn tubing
a 3647 2586 7524
Fig. 45.12 High pressure, 2-nozzle, balanced CO2 system
b 5.25 5.35 5.117
c 8.08 5.72 16.66
d 1.25 1.35 1.117
6. Col. 16. Calculate exit pressure (Col. 14 + Col. 15). 7. Col 17–18. Lookup segment exit values of Y and Z, needed calculate the Upstream Equivalent Length in next pipe segment. While rather complex, the procedures strictly follow the NFPA 12 method and yield results as accurate as the overall method allows. Example Consider a system that is required to discharge 71.4 lb of carbon dioxide liquid from each of two nozzles in the balanced pipe system shown in the figure. The carbon dioxide supply is two 100 lb high-pressure cylinders. The required quantity of carbon dioxide is 2 71.4 140 % ¼ 200 lb. The carbon dioxide supply is two 100 lb high-pressure cylinders. The liquid discharge time is 30 s. This example shows the design input and calculation results for a balanced two-nozzle high-pressure carbon dioxide system. Use the pipe segment sizes shown in Table 45.33. Nozzle Selection In this example, nozzle pressure at Nodes 8 and 10 is 554.7 psi. The corresponding mass flux, G, interpolated from
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Carbon Dioxide Systems
1583
Table 45.33 Seven-segment calculation—cylinder and every pipe section Segment nodes
Flow
Segment parts description
Elev.
1 2 3 4 5 6 7 Inlet Exit Q, lb/min Segment partsa Pipe size, in. Pipe Sch Pipe ID, in. 1 2 142.8 VH 1/2 40 0.622 1/2 40 0.622 2 3 142.8 ST; 1/200 P 3 4 285.6 TT; 3/400 P 3/4 40 0.824 4 5 285.6 EL; 3/400 P 3/4 40 0.824 5 6 285.6 EL; 3/400 P 3/4 40 0.824 6 7 142.8 ST; 1/200 P 1/2 40 0.622 7 8 142.8 EL; 1/200 P 1/2 40 0.622 6 9 142.8 See 6–7 9 10 142.8 See 7–8 a Parts: VH cylinder valve & hose, ST side tee, TT thru-tee, EL elbow, P pipe Segment nodes 1
2
Equivalent flow length
10 Fitting Inlet Exit equiv L, ft 1 2 30 2 3 3.4 3 4 1.4 4 5 2.2 5 6 2.2 6 7 3.4 7 8 1.7
11 Up-stream Eq. Len, ft 0 31.2 38.7 43.1 59.2 84.2 101.6
12 Total equiv L, ft 30.0 35.6 43.1 57.3 91.4 101.6 104.3
8 Pipe L, ft 0 1 3 12 30 14 1
9 Elev chng, dh, ft 6.28 0 0 12 0 0 1
Inlet P
PFlow
Elevation
Segment exit P, Y, Z
13 Inlet P, psi 750 703.7 696.5 689.7 663.8 604.2 561.8
14 Unadjusted exit P, psi 705.6 696.5 689.7 667.0 604.2 561.8 554.5
15 ΔP due to elev. psi 1.92 0.00 0.00 3.23 0.00 0.00 0.18
16 Exit P, psi 703.7 696.5 689.7 663.8 604.2 561.8 554.7
Table 45.25, is 2142 lb/in.2-min. The required flow rate is 142.8 lb/min. A nozzle having an equivalent area of (142.8 lb/min)/(2142 lb/in.2min) ¼ 0.0667 in.2 is required. The corresponding equivalent orifice diameter is 0.291 (9.32-32nd) inch for which the nearest Nozzle Orifice Code is 9.5. The preceding calculation shows how each of the seven segments of the example carbon dioxide pipe system contributes to the determination of the nozzle pressure. Shown below is an abbreviated, if slightly less accurate, calculation can be used for estimating purposes. The three-row Table 45.34 shows how the calculation can be performed by combining pipe segments of the same diameter. The nozzle pressure in the abbreviated calculation is
17 Exit Y 2156 2462 2745 3772 5837 7062 7250
18 Exit Z 0.163 0.185 0.206 0.284 0.483 0.639 0.666
566.1 psi as compared to 554.7 psi in the more detailed calculation. The pressure difference of 1.4 psi arises from the difference in reference pressure (663.8 psi vs. 605.5 psi) used to calculate the pressure loss in the 12 ft riser, Nodes 4–5. Nozzle Selection In this example, nozzle pressure at Nodes 8 and 10 is 556.1 psi. The corresponding mass flux, G, interpolated from Table 45.25, is 2150 lb/in.2-min. The required flow rate is 142.8 lb/min. A nozzle having an equivalent area of (142.8 lb/min)/(2150 lb/in.2min) ¼ 0.0664 in.2 is required. The corresponding equivalent orifice diameter is 0.291 (9.30-32nd) inch for which the nearest Nozzle Orifice Code is 9.5.
3
4
5.8 5.2
12 1
0.622
40
15
45
0.824
40
Fittings 10 Fitting equiv L, ft 33.4
Elev.
9 Elev Pipe Pipe Pipe L, chng, dh, Sch ID, in. ft ft 40 0.622 1 6.28
8
7
6
Segment parts description
5 Pipe Q, Segment size, Inlet Exit lb/min parts in. 1 3 142.8 V, H, ST, 1/2 P 3 6 285.6 TT, 2EL, 3/4 P 6 8 142.8 ST, EL, 1/2 P
Flow
1
2
Segment nodes
Table 45.34 Three-segment calculation—constant pipe diameter
83.6
38.7 103.8
89.5
12 Total equiv L, ft 34.4
Equiv length 11 Upstream Eq L, ft 0
Inlet P
605.5
696.5
13 Segm’t inlet P, psi 750
605.5
608.4
0.18
2.64
556.1
605.5
7213 0.660
5796 0.478
18 ΔP due to Exit P, Exit Exit elevation, psi psi Y Z 1.87 696.5 2462 0.185
17
Segment exit P, Y, Z 16
Unadjusted exit P, psi 698.4
Elevation 15
PFlow 14
1584 J. Harrington and J.A. Senecal
45
Carbon Dioxide Systems
References 1. Kidde Fire Systems (2007) Engineered carbon dioxide (CO2) fire suppression systems: design, installation, operation and maintenance manual 190 [3–76] 2. US Environmental Protection Agency Office of Air and Radiation, Stratospheric Protection Division (2000) Carbon dioxide as a fire suppressant: examining the risks: SPA430-R-00-002 3. US Environmental Protection Agency (1998), Federal register, rules and regulations: 40 CFR part 82, final rule 4810–7, vol 63, no 43 4. Wickham RT (2003) Review of the use of carbon dioxide total flooding fire extinguishing systems 5. National Fire Protection Association (2010) NFPA 10 standard for portable fire extinguishers 6. Quintiere J (2012) Surface flame spread. In: SFPE fire protection handbook, 3rd edn 7. Ohlemiler TJ (2008) Smoldering combustion. In: SFPE fire protection handbook, 3rd edn 8. Wysocki TJ (2008) Carbon dioxide and application systems. In: NFPA fire protection handbook, 20th edn, vol 2 9. National Fire Protection Association (2012) NFPA 484 standard for combustible metals 10. Christman (2008) NFPA fire protection handbook, 20th edn, vol 2 11. Ansul (2001) Carbon dioxide systems: components, design, installation, recharge, and maintenance manual 12. Fire Suppression Systems Association (2011) FSSA design guide for use with carbon dioxide total flooding applications, 1st edn 13. Fire Suppression Systems Association (2005) FSSA design guidelines for carbon dioxide local application rate-by-volume 14. Fire Suppression Systems Association (2010) FSSA Design guidelines for carbon dioxide local application systems rate-by-area 15. Eberly, R (2008) Marine Vessels. In: NFPA fire protection handbook, 20th edn, vol 2 16. International Maritime Organization (2007) SOLAS, chapter II-2-Construction - fire protection, fire detection and fire extinction 17. CFR Title 46 Shipping, Chapter 1, Part 76.15-Carbon Dioxide Extinguishing Systems, Details, U.S. Coast Guard, Department of Homeland Security 18. American Bureau of Shipping (2012) Annual review 2011 19. American Bureau of Shipping (2013) Rules for building and classing steel vessels. In: Annual review 2011 20. National Fire Protection Association (2006) NFPA cup-burner inter laboratory study: rev 1 21. Senecal J (2005) Flame extinguishing in the cup-burner by inert gas. Fire Safety Journal 40: 579–591
1585 22. Compressed Gas Association (2009) CGA-G-6 – 2009 Carbon dioxide, 7th edn 23. NIST Chem WebBook, October, 2013. http:// webbook.nist.gov/cgi/fluid.cgi?Action ¼ Data&Wide ¼ on&ID ¼ C124389&Type ¼ SatP&Digits ¼ 5& THigh ¼ 304&TLow ¼ 218&TInc ¼ 1&RefState ¼ DEF&TUnit ¼ K&PUnit ¼ MPa&DUnit ¼ mol% 2Fl&HUnit ¼ kJ%2Fmol&WUnit ¼ m%2Fs&Vis Unit ¼ uPa*s&STUnit ¼ N%2Fm 24. National Institute of Standards and Technology (2011) Carbon dioxide. NIST chemistry web book http://webbook.nist.gov/cgi/cbook.cgi?Formula ¼ co2 &NoIon ¼ on&Units ¼ SI&cTG ¼ on&cTC ¼ on& cTP ¼ onAccessed on 5 September 2013 25. Kohl AL, Nielsen RB (2005) Gas purification, 5th edn. Gulf Publishing Company, Houston 26. Bachu S, Freund P, Gupta M, Simbeck D, Thambimuthu K (2005) Annex I: properties of CO2 and carbon-based fuels. In IPCC special report on carbon dioxide capture and storage. Cambridge University Press, New York 27. Gas encyclopedia. Air Liquide. http://encyclopedia. airliquide.com/Encyclopedia.asp?GasID ¼ 26 Accessed 5 September 2013 28. Hypercapnia. Wikipedia. http://en.wikipedia.org/ wiki/Carbon_dioxide_poisoning Accessed on 5 September 2013 29. Documentation for immediately dangerous to life or health concentrations (IDLHs): carbon dioxide. Centers for Disease Control and Prevention. http:// www.cdc.gov/niosh/idlh/124389.html Accessed on 5 September 2013 30. Sanders A How does carbon dioxide poisoning kill a human. Ehow. http://www.ehow.com/how-does_469 5252_carbon-dioxide-poisoning-kill-human_.html Accessed on 5 September 2013 31. Air Products (1993) Safetygram-18: carbon dioxide. Air Products. http://www.airproducts.com/en/com pany/Sustainability/environment-health-and-safety/~/ media/Files/PDF/company/safetygram-18.pdf Accessed on 5 September 2013 32. Rice SA (2004) Human health risk assessment of CO2: survivors of acute high-level exposure and populations sensitive to prolonged low-level exposure, Third Annual Conference on Carbon Sequestration, Alexandria, VA 33. National Fire Protection Association (2011) Total flooding systems: flammable materials. In: NFPA 12 standard on carbon dioxide extinguishing systems 34. National Fire Protection Association (2011) NFPA 12 standard on carbon dioxide extinguishing systems 35. International Organization for Standardization (2009) ISO 6183 - Fire protection equipment-carbon dioxide extinguishing systems for use on premises-design and installation 36. International Maritime Organization (2007) SOLAS FSS Code - International code for fire safety systems
1586 37. American Bureau of Shipping (2005) Guidance notes on fire-fighting systems 38. National Fire Protection Association (2011) Marine systems. In: NFPA 12 standard on carbon dioxide extinguishing systems 39. National Fire Protection Association (2011) Annex d total flooding systems. In: NFPA 12 standard on carbon dioxide extinguishing systems 40. National Fire Protection Association (2011) Figure e.1b, calculated CO2 loss rate. In: NFPA 12 standard on carbon dioxide extinguishing systems 41. National Fire Protection Association (2011) Table 5.4.2.1, flooding factors for specific hazards. In: NFPA 12 standard on carbon dioxide extinguishing systems 42. National Fire Protection Association (2011) Table a.5.5.3(a) extended discharge protection for enclosed recirculating rotating electrical equipment. In: NFPA 12 standard on carbon dioxide extinguishing systems 43. National Fire Protection Association (2011) Table a.5.5.3(b) extended discharge protection for enclosed recirculating rotating electrical equipment. In: NFPA 12 standard on carbon dioxide extinguishing systems 44. International Maritime Organization (2007) Section 2.2.1. In: International code for fire safety systems (FSS) 45. American Bureau of Shipping (2005) Section 3.2.1. In: Guidance notes on fire-fighting systems 46. National Fire Protection Association (2011) Venting consideration. In: NFPA 12 standard on carbon dioxide extinguishing systems 47. National Fire Protection Association (2011) Table a.5.6.2 strength and allowable pressures for average enclosures. In: NFPA 12 standard on carbon dioxide extinguishing systems 48. National Fire Protection Association (2011) Table 6.4.4.3.2 aiming factors for angular placement of nozzles. In: NFPA 12 standard on carbon dioxide extinguishing systems 49. Crane Co (2013) Technical paper no 410, flow of fluids through valves, fittings, and pipe
Jeffrey L. Harrington, P.E., FSFPE, is a registered fire protection engineer and has been actively working since 1977 in fire protection engineering, property loss control, and code consulting. He is the President and Founder of Harrington Group, Inc., one of the oldest and largest firms
J. Harrington and J.A. Senecal headquartered in the Southeast dedicated solely to fire protection engineering consulting. Mr. Harrington has served in a leadership capacity on several National Fire Protection Association (NFPA) technical committees, including the Technical Committee on Gaseous Fire Extinguishing Systems (GFE-AAA), which is responsible for three separate NFPA standards: NFPA 12, Carbon Dioxide Extinguishing Systems; NFPA 12A, Halon 1301 Fire Extinguishing Systems, and NFPA 2001, Clean Agent Fire Extinguishing Systems. Additionally, Mr. Harrington is the first Chair of the NFPA Hybrid (Water and Inert Gas) Fire Extinguishing Systems Technical Committee (HYBAAA). Mr. Harrington is a frequent author and lecturer on an array of fire protection engineering topics and is a nationally recognized expert, having received numerous awards for his contributions to the fire protection engineering industry. He is also a leader in activities with the Society of Fire Protection Engineers (SFPE), both locally and internationally He has been an SFPE Fellow since 2006. Joseph A. Senecal has, since 1987, been an employee of Kidde-Fenwal, Inc., a Buildings & Industrial Systems company of United Technologies Corp. He has a Ph.D. in Chemical Engineering, an MBA, and is a Registered Professional Chemical Engineer. During his KiddeFenwal career he has been deeply involved in advancing the technology of special-hazard fire and explosion protection systems including product development, materials flammability testing, process hazards consulting, national and international standards development, and trade association representation with a particular interest in gaseous fire extinguishing systems. He is a charter member of the NFPA standard 2001 committee and has continued to serve actively on the since-merged NFPA “GFE” committee (NFPA 2001, 12, and 12a). In 2008 Joe was appointed to Senior Fellow (for UTC Fire & Security, since merged with UTC’s Carrier and Otis divisions). Joe is one of only a few recipients of both the U.S. EPA’s Stratospheric Ozone Protection Award (2004) and the Climate Protection Award (2009). Joe has presented or published over 50 articles related to fire and explosion protection technology. He is an inventor on five issued patents and on four current patent applications. His reading preferences include biographies of persons of scientific note, history, and character-rich fiction.
Water Mist Fire Suppression Systems
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Jack R. Mawhinney and Gerard G. Back III
Introduction This chapter addresses the engineering of fixed fire suppression systems that discharge water mist. The term water mist, as currently understood in the fire protection field, relates to fine water sprays with no drops larger than 1.0 mm, or 1000 μm (micrometers or microns) [1, 2]. Such sprays are not true mists, however. A mist in the scientific sense consists of drops somewhere on a continuum between aerosol (particles with diameter approximately 5 μm) and fog (droplet diameters ranging between 10 and 100 μm). Particles less than 20 μm in diameter take a long time to settle out and, hence, create what is recognized in both literature and science as a “mist.” A water mist as intended for fire protection purposes is a fine water spray consisting of a range of droplet sizes, many of which are in the range of true mist particles and some of which are considerably larger. Water mist nozzles produce sprays that have a higher fraction of very fine droplets, in the range of mist, than is typical of standard sprinklers or water spray nozzles. Fire suppression research performed in the past 60 years typically referred to “fine water sprays” or “finely divided water sprays” as the subject of study. Remarkable success at cooling and extinguishing diffusion flames was documented using fine water sprays with mean diameters less than 0.3 mm J.R. Mawhinney (*) • G.G. Back III Jensen Hughes, 3610 Commerce Drive, Arbutus, MD 21227
(300 μm) [3, 4]. Researchers in the 1950s confirmed the expected improvement in the efficiency of heat absorption due to the increase in surface area available for heat transfer as a spray is divided into smaller and smaller particle sizes. Also, as particles become smaller they settle out less quickly (remain suspended), providing more time for heat absorption and evaporation to take place. More heat is absorbed per unit of mass as the particle size decreases. Thus, it was understood that increasing the fraction of very fine water droplets contained in a water spray could reduce the amount of water needed for fire suppression, or in other words, improve the efficiency of application. The term water mist was adopted by the National Fire Protection Association (NFPA) Technical Committee on Water Mist Fire Suppression systems in the early 1990s as part of the renewed interest in efficient use of water in fire suppression systems. This term distinguishes the technology of NFPA 750, Standard on Water Mist Fire Protection Systems, 2010 edition, from that of NFPA 15, Standard for Water Spray Fixed Systems for Fire Protecting, 2012 Edition [5], and NFPA 13, Standard for the Installation of Sprinkler Systems, 2013 Edition [6]. A more thorough discussion of drop size distribution as a significant spray characteristic is presented later in this chapter. For technical and economic reasons, the knowledge about the advantages of using fine water sprays for fire suppression did not result in an immediate movement to finer sprays for fire protection. Technical concerns included the
M.J. Hurley (ed.), SFPE Handbook of Fire Protection Engineering, DOI 10.1007/978-1-4939-2565-0_46, # Society of Fire Protection Engineers 2016
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negative effects of increasing operating pressures to improve atomization, the potential plugging of small orifices with corrosion products, and doubts about the long-term maintainability of equipment. Economic concerns related to the fact that there were less expensive alternatives: either standard sprinklers or the halogenated hydrocarbons—gaseous agents (halons) such as Halon 1301—could be used. So long as water was an inexpensive resource and halons were available to handle a broad range of special hazards, finer water sprays did not offer enough of a suppression advantage to justify their widespread use. Three events happened in the 1980s that changed the economic background and revitalized interest in using fine water sprays for fixed fire suppression systems. These were the following: 1. The aviation industry’s response to the Manchester air crash in 1984 2. The 1987 signing of the Montreal Protocol, an agreement to phase out the use and manufacture of ozone-depleting substances (halons), and 3. An International Maritime Organization (IMO) ruling that required the installation of marine sprinklers on all existing and new passenger ships capable of carrying more than 35 passengers The Manchester, England, plane crash in 1984 [7] initiated an international effort to develop a fixed water spray system for passenger compartments on aircraft. The SAVE program, as it was called, was funded by the Civil Aviation Authority in England; the Federal Aviation Administration (FAA) in the United States; Transport Canada; and by the major builders of aircraft, such as Boeing and Airbus. The objective of the program was to increase the time available for evacuation of an aircraft passenger compartment exposed to a ground pool fuel fire after a crash landing. Tests were conducted utilizing water spray to prolong the tenability of the space to allow more time for safe evacuation of passengers. The SAVE program set welldefined performance objectives relating to occupant tenability [8]. The design was constrained
J.R. Mawhinney and G.G. Back III
by the need to minimize the weight of the system including the stored quantity of fire fighting agent. The choice of a fine water spray to maximize the effectiveness of a small quantity of water was a natural outcome of the work. A water mist system that exceeded all of the performance objectives was accomplished. The system extended tenability for 7 min, within the weight and volume constraints, using approximately 10 L of water. The SAVE study demonstrated that a fine water mist system using a limited supply of water could be custom designed to meet very specific objectives, within the constraints of the industry. The aviation industry regulatory authorities, however, did not make such systems mandatory on aircraft, on the basis that the cost per life saved was unacceptably high [7]. Nevertheless, international awareness of the SAVE research, which was focused on improving the heat absorption qualities of a water spray using a minimum application rate of water, for the purpose of achieving a specific performance objective, meant that the idea of “fine water sprays” was readily picked up by other researchers working on a larger issue that emerged at the same time, that is, the search for an alternative for gaseous fire-extinguishing agents. The second key event that spurred interest in fine water spray fire suppression systems was the 1987 signing of the Montreal Protocol, an international agreement to reduce the manufacture and use of ozone-depleting substances [9]. Widely used halogenated fire suppression gases were discovered to be ozone-depleting substances. The threat of a phase-out of halon fire-extinguishing agents motivated the release of funds for research into alternative fire suppression agents, water among them. Water at least was not likely to be phased out in the future as an environmentally harmful substance. The highlevel research into halon alternatives provided a windfall of improved scientific understanding of the physical and chemical nature of combustion and extinguishment processes. Advances in measurement of suppression phenomena, understanding of fire dynamics, and computer modeling of complex fire scenarios were
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applicable to the engineering design of innovative fire suppression systems. The loss of halons as a class of extinguishing agents forced the re-examination of old assumptions about the unsuitability of water for certain types of fires, such as Class B fires in machinery compartments. With improved atomization and reduced flow rates, water could be used where the traditional default had been to use the gaseous clean-agent suppressants. Fine water spray fire suppression systems began to look viable from both performance and economic perspectives as an alternative to gaseous fire suppressants for a number of applications. A third congruent event that propelled the use of fine water sprays into the realm of practical fire suppression systems was a move by the International Maritime Organization (IMO) to mandate the installation of sprinkler systems on passenger ships. This very influential rulemaking body involves the interests of marine shipping societies, marine regulatory authorities (coast guards), and shipping companies worldwide. This regulatory action came about as a result of several large life-loss fires on-board Scandinavian passenger ferries that occurred in the 1980s [10]. In response, the International Maritime Organization mandated the installation of marine sprinklers on all ships capable of carrying 35 or more passengers to come into effect in 1995. Marine architects view marine sprinklers as a negative feature in terms of weight, space, and effects on vessel stability. Adding weight to the upper levels of a ship creates potential stability problems, particularly when sprinklers are retrofitted to an existing ship that was not designed to support the additional weight. There were strong economic and technical incentives to develop a system equivalent to sprinklers that would satisfy the intent of the IMO ruling but use less water and weigh less than traditional marine sprinkler systems. Fine water spray fire suppression systems promised to deliver just that. Research was conducted to develop performance criteria for fine water spray systems that could be impartially evaluated as equivalent to sprinklers installed on Solas II-2/ 12 [11–13]. The Scandinavian countries Sweden,
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Norway, and Finland performed development testing that laid the foundation for fire test protocols for marine machinery rooms and for accommodations and public spaces on passenger ships. The Swedish National Testing and Research Institute (SP) in Bora˚s, Sweden; SINTEF, the Norwegian fire research institute in Trondheim, Norway; and VTT Building Technology research facility in Espoo, Finland, were the key centers of development for water mist fire testing. Manufacturers interested in developing water mist nozzles participated in the development of the tests. The test results were discussed, modified, and eventually accepted as consensus test protocols at meetings of the IMO fire protection subcommittees. The availability of substantial funding to support research for halon alternatives and the creation of a worldwide market for alternatives to marine sprinklers were the two most important factors that changed the economic viability of using fine water sprays for fire suppression systems. Now there was financial incentive to support the cost of overcoming the engineering challenges involved. As a result of the two distinct origins of renewed interest, there are two basic domains of application for water mist systems. One area of application is as a replacement for gaseous fire suppressants such as Halon 1301. Thus, in applications involving Class B flammable liquid fuels—or where clean agents were used because of concern about water damage—water mist is viewed as a halon system alternative. For applications where the water mist systems are installed for Class A fuels (ordinary cellulosic combustibles), a water mist system is viewed as potential alternative to sprinkler systems. Water mist systems are not intended to be designed on a “rote” or prescriptive basis. As of 2014, it is becoming evident that water mist systems should be recognized foremost for the opportunity they provide to take a performance based design approach to managing challenging fire hazards. Water mist technology relies on an advanced fire protection engineering understanding of the fire hazard and the fire dynamics that need to be managed. The performance that is
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claimed must be verified by conducting fire tests designed by experienced, commercially neutral engineers and testing laboratories. Water mist sytsems present an opportunity for importing types of equipment into fire protection from nontraditional fire protection equipment manufacturers.
Fundamentals of Water Mist Systems The following review of the fundamentals of water mist system design covers mechanisms of extinguishment and suppression and spray characteristics.
Mechanisms of Fire Extinguishment and Suppression Excellent discussions of the extinguishing mechanisms of water mist from an engineering perspective can be found in Braidech et al. [3], Rasbash et al. [4], and Mawhinney et al. [14] An understanding of the mechanisms of extinguishment associated with water mist (then called “finely divided water spray”) was articulated approximately 50 years ago [3, 4]. Braidech and Rasbash both concluded that fires were extinguished by dilution of the air (oxygen) with water vapor (steam), resulting from evaporation of water droplets in the area local to the flame. They also concluded that the cooling effects of the water may contribute to the extinguishment of flames. Mawhinney et al. [14] describe five mechanisms associated with extinguishment of hydrocarbon fires. They are the following: • Gas phase cooling; • Oxygen depletion and flammable vapor dilution; • Wetting and cooling of the fuel surface; • Radiation attenuation; and, • Kinetic effects The extinguishing mechanisms apply to extinguishment of Class B liquid fuel fires as well as Class A solid fuels, although with different importance of one mechanism over another.
J.R. Mawhinney and G.G. Back III
Typically, all mechanisms are involved to some degree in the extinguishment process.
Gas Phase Cooling Gas phase cooling refers to the removal of heat from the combustion zone due to evaporation of water. The cooling efficacy of water mist is due to the fact that the water is broken up into many fine droplets, which enhances the evaporation rate. The more water that evaporates, the greater the amount of heat that is extracted from the combustion zone, thus reducing the temperature of the flame and hot gases. If the flame temperature is reduced below the critical value necessary to sustain combustion (limiting adiabatic flame temperature), the flame will be extinguished. The limiting adiabatic flame temperature for diffusion flames is approximately 1600 K (1326 C) [15]. The cooling of the flame also reduces the radiation (thermal feedback) to the fuel surface, thus reducing the pyrolysis or gasification rate of the fuel. Scientific work involving the extinguishment of methane-air counterflow flames has been conducted that has shown that water mist/vapor is more effective on a mass basis than Halon 1301, if it can be delivered at near 100 % efficiency [16, 17]. The reality is that in full-scale compartment fire suppression, the efficiency of application of water is very much less than 100 %. Various attempts have been made to establish a design relationship between the fire size and amount of water needed to extinguish the fire by gas phase cooling. Wighus [18] defined the term spray heat absorption ratio (SHAR), which relates the rate at which heat is absorbed by evaporation of a given mass of water (Qw), to the rate at which heat is given off by the fire (Qf). SHAR ¼
Qw Qf
ð46:1Þ
Wighus’s experiments showed that, for optimized application of mist to an unconfined propane flame, the heat absorption rate in the water needs to be only a fraction of the heat release rate of the fire, as low as 0.3 under optimum conditions. SHAR values in the range of
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0.6 were noted for more realistic machinery space conditions, where small flames can persist in shielded areas to cause reignition. (In the absence of reignition sources, only enough heat has to be absorbed from the flame to drop the temperature to the limiting adiabatic flame temperature: it is not necessary to drop the temperature of the compartment or the fuel to ambient.) On the surface, it seems promising to use a calculation of the amount of water that must be evaporated to extinguish a fire of a certain heat release rate as a design parameter. In real systems, however, the efficiency of delivery of water mist into flame, hence the rate of evaporation of the droplets in the flame zone, is almost unpredictable and certainly uncontrollable over the range of conditions encountered in fire events. The SHAR relationship nonetheless may be useful in a hydrocarbon extinguishment submodel for use in a computational fluid dynamics (CFD) approach to mist system design [19–21]. Andersson et al. [22] present the concept of the required extinguishing medium portion (REMP). This is the ratio of the mass application 0 rate of extinguishing agent required (me) to the 0 mass rate of fuel consumed (mg). The REMP parameter is similar to the SHAR in that a certain mass of water must be evaporated to extract enough heat to extinguish the flame. 0
m REMP ¼ 0e mg
ð46:2Þ
For propane flames, Andersson et al. [22] measured that the mass application rate of water needed to extinguish a propane flame under laboratory mixing conditions was between 1.2 and 2.2 times the mass burning rate of propane gas. They indicate that this range of REMP values corresponds to a water content volume concentration of 100–200 g/m3—that is, the mass of water mist suspended in a unit volume of air. Note that both the SHAR and REMP values were measured under conditions of ideal interaction of flame and mist: the mist was discharged downward into the upward rising plume. The velocity vectors of mist and flame were opposite,
resulting in the maximum degree of turbulent mixing in the collision zone. The mass flow rate of mist estimated from the REMP values should represent the minimum mass application rate. The mist mass flow rate values for real systems could be expected to be higher to account for inefficiency in delivery of mist to the flame and variability in the directional aspects of interaction. The REMP parameter suggests that the mass application rate of extinguishing agent would have to be set for the largest expected mass burning rate of fuel. This assumption does not take into account the simultaneous action of other extinguishing mechanisms, however. As will be discussed shortly, for fires in enclosures, it has been observed that larger fires can be extinguished using less water than smaller fires due to the increased efficiency of evaporation attributed to heat confinement in the enclosure and other phenomena. Thus, one would expect the REMP values to go in opposite directions for enclosed fires versus unenclosed fires, indicating that the REMP value is not uniquely a function of the mass rate of fuel consumed. As was suggested for the SHAR parameter, the REMP parameter is potentially useful in a computer submodel of extinguishment of spray or pool hydrocarbon flame [20]. Today, more complex physical models for evaporation and cooling of hot gases by water sprays are embedded in computational fluid dynamics (CFD) models as will be discussed later in this chapter. The accuracy of the CFD models remains limited by the difficulty of accurately modeling the sprays produced by the different types of water mist nozzles. Furthermore, the ability to model extinguishment of different types of fuels by cooling, wetting and oxygen displacement on principles of physics or chemistry, is limited. The concepts of SHAR and REMP remain conceptually useful for illustrating the principle that not all of the water mass discharged contributes effectively to fire extinguishment. A number of researchers have sought to estimate a critical extinguishing concentration (in g/m3) of water mist surrounding a diffusion flame. A number of international laboratories are
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able to measure volume concentrations in g/m3 of mist at various points in a spray, using a phaseDoppler particle size anemometer. Experimental values range from 100 to 200 g/m3 [21–24] although values as low as 50 g/m3 have successfully extinguished heptane flames [25]. Newer technology, referred to as “nanomist,” generates clouds of suspended ultrafine water droplets with a suspended mass concentration as high as 240 g/ m3, using an ultrasonic transducer assembly and a process technology for aerosolization, extraction, and transport of mist. This technology is likely to be limited by cost to relatively smallscale applications [26–28]. Although the REMP concept appears to be a promising possibility for a universal design parameter, it is difficult to make practical use of this value for selecting spray characteristics or nozzle spacing. It is possible to calculate nominal total mass discharge per unit volume values for nozzles discharging into a compartment. On the macroscale of a machinery space, however, it is extremely difficult to predict or control volume concentrations at the point of interaction with flame. There are many randomizing events that alter the local concentrations of water mist at the point of extinguishment.
Oxygen Depletion and Flammable Vapor Dilution These mechanisms can occur on either a localized or compartmental scale. On the localized scale, as the water droplets are converted to the vapor phase, the volume occupied by the water mist droplets increases over three orders of magnitude. If the vaporization of the water occurs in the flame, the volumetric expansion can disrupt the entrainment of air (oxygen) into the flame. On a compartmental scale, the production of steam resulting from mist interactions with the flame, hot gases, and/or hot surfaces can significantly reduce the oxygen concentration in the space [29]. The oxygen available for combustion is a function of the size of the fire, the compartment volume, and the ventilation conditions in the compartment. As the size of the fire increases, the average temperature in the space increases, and the
J.R. Mawhinney and G.G. Back III
oxygen concentration decreases due to consumption of the oxygen by the fire and dilution of the oxygen by water vapor. If the combined effects of oxygen depletion due to the fire and dilution by water vapor can reduce the oxygen concentration below the critical value necessary to sustain combustion (i.e., the limiting oxygen concentration [LOC]), the fire will be extinguished [29]. The LOC for most hydrocarbon fuels is approximately 13 % [15].
Wetting and Cooling of the Fuel Surface Wetting/cooling of the fuel surface will be, in many cases, the dominant extinguishment mechanism for fuels that do not produce combustible mixtures of vapor above the fuel surface at ambient temperatures (i.e., solid fuels and liquid fuels with flashpoints above normal ambient temperatures). Wetting/cooling of the fuel surface reduces the pyrolysis or gasification rate of the fuel. If the vapor-air mixture above the fuel surface is reduced below the lower flammability limit (LFL) of the fuel, the flame will be extinguished. Radiation Attenuation and Kinetic Effects Water mist and water vapor measurably reduce radiant heat flux to objects near the fire, which assists in preventing fire spread to unburned fuel. Within the combustion zone, radiation attenuation is the result of gas phase cooling and the increase in water vapor concentration between the fuel and the flame. Lowering the flame temperature reduces the radiation feedback to the fuel surface. Also, water vapor in the air above the fuel surfaces acts as a graybody radiator that absorbs radiant energy and reradiates it to the fuel surface at a reduced intensity [19]. Kinetic effects may contribute either to flame intensification or to extinction. Flame intensification has been measured [14] as a flare-up of a flame on first contact with mist. Possibly the turbulence and entrainment associated with the rapid evaporation at the flame surface accelerate the burning rate. Ho [30], who studied the phenomenon in high-flashpoint oils, noted that most of the intensification is due to spray-induced oil splattering, which increased with increasing
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Water Mist Fire Suppression Systems
Weber number as well as increased oil temperature. He noted that the heat release rate is enhanced by a factor from 2.12 to 5.55 compared to the heat release rate of free burning cooking oil. Kinetic effects may also be involved in flame suppression, the result of both gas phase cooling and oxygen depletion/dilution. When a diluent (in this case water vapor and recycled, vitiated combustion gases) is added to the combustion reaction, combined with flame cooling, it is hypothesized that reaction rates at the molecular level are significantly different from stoichiometric conditions.
Enclosure Effects, Turbulent Mixing, and Cycling The importance of enclosure effects is described by Mawhinney, Dlugogorski, and Kim [14] and by Liu, Kim, and Su [31]. Enclosure effects maximize the benefits of oxygen depletion and dilution. The hot, vitiated gases collecting in the upper layer of an enclosure are cooled rapidly by the first contact with the water mist. Vitiated gases plus water vapor are forced down by the spray to the seat of the fire and contribute to extinguishment through oxygen depletion. Depending on the temperature and depth of the hot layer, the rapid cooling results in an instantaneous volume reduction, creating a negative pressure that can suck in the windows or walls of a tight enclosure. If the enclosure had reached flashover temperatures before mist activation, assuming that water could flow through the pipes and mist could be introduced, it is hard to say which phenomenon would dominate, the expansion due to steam generation or contraction due to cooling. At least one manufacturer has investigated a means of allowing an initially small injection of spray to initiate cooling, followed by a gradual increase in flow. Such an approach was described as taking the “shock” out of the introduction of mist to the hot enclosure. With reasonably early detection and activation, an automatically activated system will release in the first few minutes of a fire in an enclosure before the upper layer becomes too hot and deep. With systems that are manually activated, some thought should be given to the expected
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effect on introduction of the water mist into a very hot compartment. The author’s experience has shown that the rapid cooling of a deep hot layer (by water mist) in a closed compartment can create a sudden negative pressure pulse strong enough to pull in the walls of the enclosure. The experience is contrary to the often cited but unfounded fear of “steam explosion,” that is, a strong positive pressure forcing hot gases out of the compartment. Some manufacturers have noticed that turning the spray off momentarily and then on again can speed up extinguishment in enclosures. The benefits of pulsing, that is, the on-off action of water sprays, also described as cycling, are well described in Liu et al. [31] and Liu and Kim [32]. Liu et al. [31] showed that pulsing the injection of water mist into an enclosure resulted in more rapid extinguishment, with less total water usage, than continuous application of mist. It was noted that the compartment temperature rose as the fire regrew during the first off-stage, allowing for more evaporation of lingering fine mist. The resurgent fire further reduced the oxygen concentration in the enclosure. The next injection of spray further cooled and mixed the oxygendepleted gases. In this manner, cycling appeared to lead to greater net evaporation and oxygen reduction than with steady injection. Liu et al. [31] attributed the improvement of the efficacy of water mist in fire suppression using cycling discharges to the faster depletion rate of oxygen in the compartment and the recurrent turbulent mixing created by cycling discharge. In some systems cycling was used to avoid too rapid cooling of the simulated turbine casing in the FM Global test protocol [33]. That protocol includes a test to ensure that cooling of the turbine casing will not result in damage to the turbine blades. By having spray on for only 50 % of the time, not only was the cooling test passed but also the volume of stored water needed for 10 min of protection was significantly reduced. The manufacturer’s design criteria, therefore, incorporated the cycling as an essential element of system performance. Although the repeated off-stages in the cycle had been acceptable for
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purposes of passing the FM Global test protocol, the author notes that cycling may not always be acceptable in installations where the equipment cannot tolerate re-exposure to flame during an extended off cycle. Furthermore, the apparent benefit is likely to be very dependent on the volume of the compartment.
Explosion Hazard Mitigation with Water Mist A number of studies have been done to assess the potential for water mists to mitigate explosion hazards. The interest originates with several plausible hypotheses, such as: (a) that a deflagration flame front in a pre-mixed combustible vapor, moving through a cloud of finely atomized water droplets would be quenched as it encountered sufficiently small water droplets; (b) that the energy of a detonation shock wave moving through a field of water droplets would be “stripped” by the break-up of spherical water drops; and, (c) that the ignition energy required to ignite a vapor/air mixture would be increased by the presence of the water mist. A review of experimental work performed over the last three decades reveals that there is mixed opinion about “whether application of water spray will quell or invigorate an explosion [34].” In some experiments, the peak Fig. 46.1 Reduction in explosion chamber overpressure due to presence of water mist [36]
overpressure was reduced, although it occurred sooner than if the mist had not been present. In other tests, the peak overpressure was increased by the water mist, presumably due to increased turbulence and stretching of the flame front. Unfortunately, there were major differences in spray characteristics involved in the various experimental programs, so the data are inconclusive. Analytical work supports the idea that benefits of using water mist to mitigate explosions are substantial, provided attention is paid to the details of application [35–38]. Butz et al. [36] investigated the use of water sprays to reduce explosion overpressures from a stoichiometric mixture of hydrogen gas and air released in a test chamber. The test scenario involved creating a mixture of hydrogen and air in a closed chamber, injecting a water spray, and then igniting the mixture. The tests demonstrated that ignition required higher spark energy than without the mist, and the overpressure generated by the deflagration was reduced by about 15 % (Fig. 46.1). Figure 46.1 shows a pressure reduction from 35 to 30 psia “with mist.” Butz also measured a significant temperature reduction of the passing flame front, which could reduce the risk of burn injury to personnel who might be exposed to the flash inside a compartment.
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The U.S. Naval Research Laboratory examined the potential for water mist fire suppression systems to perform dual service in suppressing peacetime fires and mitigating blast effects in wartime scenarios [37, 38]. A survey of the use of water (bulk, sprays, mists, etc.) as an agent for blast mitigation was conducted [37]. That survey showed that there are several ways in which the use of water sprays can mitigate the effects of an explosion. It may (1) break up larger droplets into finer mist, (2) directly lead to an attenuation of the shock waves produced, (3) reduce the intensity of secondary shock and pressure waves, (4) slow down or quench the chemical reactions taking place behind the shock waves, and (5) dilute the concentration of explosive gases in the enclosure and, hence, prevent a secondary gas explosion or fire. Studies by Kailasanath and Schwer concluded that water mists will reduce the propagation rate of shock waves. In general, finer droplets increase the attenuation rate. The reduction in propagation rate does not necessarily lead to a reduction in the peak overpressure, however, because the peak overpressure occurs at some distance behind the shock front. In addition, the interaction differs for a shock wave or a flame front.
Fig. 46.2 Blast overpressures measured in an enclosure with no open side, with and without water mist, from Selby and Burgan [39]
2.5
British Gas (BG) conducted a study aimed at improving the oil industry’s confidence in its safety systems with respect to hydrocarbon fires and explosions [39]. A similar study was undertaken at the Christian Mikelson Institute in Norway. In contrast to the results recorded by Butz, the oil industry studies showed that water spray increased the overpressure caused by ignition of a methane-air mixture in a fully enclosed compartment (Fig. 46.2). However, in an open compartment (one wall removed) from the test compartment, a reduction in the overpressure was recorded (Fig. 46.3), but it was a much greater reduction than the 15 % measured by Butz. Both studies also pointed out the role that turbulence plays in accelerating the flame front. Piping clutter and the injection of large drop water sprays increase turbulence in the gas-air mixture and thereby contribute to worsening the deflagration. There were significant differences in the spray characteristics of the nozzles used in Butz’s tests and those used in the BG tests. BG tests used a water deluge nozzle typically used on offshore platforms, which produces spray much coarser than what we now define as water mist. It is believed that subsequent work by Kailasanath and Schwer [38] for example, more accurately
Test with water sprays
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Fig. 46.3 Blast overpressure reduction due to the application of water mist in an enclosure with one open side, from Selby and Burgan [39]
Test without water sprays
Overpressure (bag)
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reflects the interaction of blast waves with smaller droplets typical of water mist. The editors of the BG industry report concluded that more work is needed with focus on working with sprays with finer drop size distributions. During preparation of the first edition of NFPA 750 (1996), a task group of the committee prepared a review of the literature on fine water spray suppression systems. As part of that work, Robert Zalosh of Worcester Polytechnic Institute (WPI) prepared a review of studies on the use of fine water sprays to mitigate explosion hazards [40]. Several relevant conclusions based on his review are summarized as follows: • In an unconfined environment, highmomentum water spray can entrain air into a gas cloud and dilute it below the lower flammable limit. • Water vapor can slightly narrow the flammability limits for a gas, and it can dilute the gas-air mixture below the flammability limit. At higher temperatures, higher concentrations of water vapor are possible than at lower temperatures, so warm mist is likely to be more effective than cool mist.
• In near-limit gas-air mixtures, the spray/mist can have either a mitigating effect or an exacerbating effect on flame speeds and pressures depending on the turbulence produced by the spray and the characteristic drop size. The mitigating effect has occurred only with gas concentrations only slightly above the lower flammable limit. • In the case of a very high flame speed with an accompanying shock wave, the spray/mist can reduce deflagration pressures and possibly extinguish the flame because the shock wave breaks up the drops into a micromist with a characteristic drop size on the order of approximately 1 μm. These tiny drops can evaporate in a sufficiently short time interval to absorb a significant fraction of the combustion energy released during the deflagration. • The exacerbating effect that occurs in some situations is due to the turbulence produced by the water spray causing the flame speed to increase and/or causing a larger fraction of the flammable gas to burn. • Generally, drops do not vaporize rapidly enough to absorb the combustion energy
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Water Mist Fire Suppression Systems
before the deflagration is complete, unless they are very small (i.e., on the order of 1 μm). • More widespread use of water spray systems for deflagration control will depend on the viability of generating a micromist with sufficiently small drop sizes, which will require water mist systems that are different from those being developed commercially for fire suppression applications.
Spray Characteristics Measuring and understanding the characteristics of sprays produced by different nozzles are prerequisites for understanding differences in performance. To fully characterize a spray requires information about the following elements: • Drop size distribution (DSD); • Cone angle; • Velocity of the discharge jet(s); • Mass flow rate; and, • Spray momentum (product of velocity and mass). These spray characteristics, which are discussed in more detail below, potentially determine nozzle location and spacing as well as ceiling height limitations.
Drop Size Distribution Water mist is made up of finely divided water drops of different sizes. Some of the drops may be falling under gravitational force, while other smaller drops may be “floating” in the air entrained with the spray. The drop size distribution of the spray is not yet used explicitly as a parameter in the design of a water mist system. Effective practical application awaits the results of further research. Nevertheless, the drop size distribution of a water spray clearly relates to overall system performance, as it impacts the rate of mist evaporation, how discharge is affected by obstructions, and the momentum of the spray relative to the buoyancy of the fire plume. If the differences in drop size distributions of water sprays are not quantified and understood, an explanation of the differences
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in performance between different manufacturers’ nozzles might not be attainable. When using computer models to approximate the dynamics of suppression with water mist, a quantitative estimation of the drop size characteristics of the mist discharge is essential. The term drop size distribution refers to the range of drop sizes contained in a representative sample of a mist discharge. There is a distribution of small and large drops, which varies with location in the discharge as a function of time. For a continuous discharge, the distribution of drop sizes changes with distance from the source as drops collide, evaporate, or hit surfaces and fall out. For a short burst of discharge, the distribution measured at a point in space changes with time as the larger droplets pass through quickly, leaving increasingly finer drops, which take more time to settle. There are a number of ways to present data about drop size distributions of sprays [31, 32]. It is customary in some fields to refer to the size of particles in a spray by a single drop size parameter, such as a Sauter mean diameter (SMD) or volumetric median diameter (VMD). Such singlepoint parameters reveal little about the range of drop sizes in a spray, however. It is important to know the fraction contained in larger drop sizes and the fraction contained in much smaller drop sizes during a given discharge to understand the mist’s performance as a fire suppressant. NFPA 750 has adopted the curve of cumulative percent volume versus diameter to represent the distribution of drop sizes in a water mist. Reasons for this choice are that the cumulative percent volume plot visually reveals the range of sizes, and the volume distribution converts readily to mass distribution, which is the most relevant term for analyzing heat transfer and evaporation rates using computer modeling. The range of drop sizes can be fully described by characteristic parameters such as Dv0.90 and Dv0.50. The Dv0.90 is the drop diameter at which 90 % of the volume of a sample of the spray is contained in drops of that diameter or smaller. Similarly, Dv0.50 is the volumetric mean drop diameter; that is, 50 % of the volume of the spray is contained in drops less than that diameter.
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Spray Cone Angle Commercially available nozzles typically produce either 90 or 102 spray cones. Other cone angles are possible but not available as Listed nozzles. Typically the sprays are solid cones, not hollow cone sprays. Spray Velocity Velocity is a vector quantity—it has both direction and magnitude. The directions of individual jets define the shape of the spray cone. The magnitude of the jet velocity is the velocity at which water emerges from a small orifice and begins to atomize. There is also a transfer of the velocity of the individual water particles to the surrounding air (through drag effects). In a multijet nozzle, the drag effect of adjacent spray jets pulls surrounding air into the spray cone, adding to the mass flux of the spray cone. It is the combined velocity of the water droplets from all the jets and the air entrained in the flow that contributes to the spray momentum, which dictates the overall impact of the spray on a fire plume. Discharge Rate The mass discharge rate of a nozzle is a function of water pressure and the total area of the orifice (s). Ideally the discharge rate per nozzle could be designed around the SHAR or REMP values— theoretical minimum application rates relative to the amount of heat to be absorbed. In reality, discharge rates vary for different manufacturers for the same fire test scenario. Spray Momentum Momentum is calculated as mass times velocity. The combination of the mass of water droplets plus the mass of entrained air, multiplied by the velocity of mist particles plus entrained air, constitutes the momentum of a water spray. In general, for a constant mass discharge rate, increasing spray velocity increases the air entrainment rate, which contributes to the spray momentum. Like velocity, momentum has both magnitude and direction—and its direction relative to the fire plume or fuel source has a bearing on its effectiveness. Where the spray direction is opposed to the fire plume direction there is
J.R. Mawhinney and G.G. Back III
penetration of the flame by the water mist, and any water vapor created in the flame may be carried to the seat of the fire. In contrast, codirectional flows may not create the turbulent flame-mist mixing needed to enhance evaporation and cooling, and the water vapor formed will be carried away from the fuel surface rather than pushed down to it. Studies to evaluate the relative benefits of using high-velocity or low-velocity water mist nozzles must include this directional component of the momentum factor, not only the magnitude of jet velocities. Also, since the entrained air forms a significant proportion of the mass flow rate, it contributes to the momentum of the overall spray cone. Two nozzles with similar initial jet velocities and mass flow rate could have very different degrees of air entrainment—hence, the spray momentum for each could differ significantly. As control over the directional aspects of spray application can be a design choice, spray velocity and spray momentum represent potential first-principles design parameters.
Measurement of Drop Size Distributions An annex of NFPA 750 describes a methodology for obtaining a statistically meaningful measurement of the drop size distribution of a water spray. Listing organizations typically measure the drop size distribution of a nozzle as part of the component approval process. A phaseDoppler anemometer may be used to measure the drop sizes passing through a small volume of space within the spray cone. The drop size distribution in a spray is not the same at all locations in the spray cone. A single reading taken at one location is not representative of the average drop size in the spray. It is standard practice to take a set of readings and combine them into a statistically representative value [41, 42]. For the purpose of being able to compare water mist sprays, NFPA 750 prescribes the measurement of drop size distribution with the spray cone axis vertically downward over an imaginary plane through the spray cone a distance of 1 m below the nozzle. This distance is usually sufficient so that the atomization process is complete and the average droplet velocity has
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Water Mist Fire Suppression Systems Nozzle (Q, P )
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Z=0 Z = 0.3 m
Z = 1.0 m –R3, –R2, –R1
+R1, +R2, +R3
Cone diameter, D D3 D4
D2
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Drop size measurement ±R1 = 0.204 * D ±R2 = 0.354 * D ±R3 = 0.456 * D
Fig. 46.4 Locations within spray cones for measurement of flux density distribution and drop size distribution. The positions shown are the centroids of segments of equal area [42]
slowed to approximately the velocity of the entrained air. Figure 46.4 illustrates a setup in which spot readings were taken at 24 locations in the spray, measured on a plane 1 m below the nozzles. The positions for taking a measurement represent the midpoint of sectors of equal area in the circular cross section of a spray cone. A grid of collector pans is used to collect the flux density at each of the measurement locations. It is assumed that the drop size distributions measured in areas of high flux density are more representative of the overall distribution than measurements taken in areas of low flux density. Thus, Equation 46.3 is used to calculate a weighted average drop size distribution curve, weighted according to the flux density measurements at each location.
X R j , i Ai V i i X Rk ð Ai V i Þ
ð46:3Þ
i
where Rk ¼ Weighted cumulative volume percent readings for sizes equal to and less than dupper Rj,i ¼ Cumulative volume percent readings for sizes equal to and less than dupper at location i Ai ¼ Area centered at location i in which the size distribution is represented by Rk Vi ¼ Water flux density measured at location i The NFPA 750 annex method was used to obtain weighted average cumulative percent volume drop size distribution (DSD) curves for four commercially available water mist nozzles. Figure 46.5 compares the weighted cumulative percent volume DSD curves for the four nozzles investigated [43, 44]. Nozzles A and B were low-pressure single-fluid nozzles; nozzles C and D were high-pressure single-fluid nozzles. It is interesting to note that even the coarsest spray measured (A) had at least 50 % of its volume contained in drop sizes smaller than 300 μm. Spray B shows approximately 80 % of its volume (mass) in drop sizes smaller than 300 μm. However, nozzle B discharged at a rate of 5 l/min (¼5 kg/min) whereas nozzle A discharged at a higher rate of 12 kg/min. Therefore, nozzle A, the apparently “coarser” spray, generated about 6 kg/min of drop sizes below 300 μm, whereas nozzle B, the apparently “finer” spray, produced only 4 kg/min of sub-300 m droplets. In terms of potential for heat extraction by rapid evaporation of the smallest droplets, one cannot conclude that one spray is “better” than another on the basis of drop size distribution alone. Factors such as mass flow rate, cone angle, air entrainment, and spray velocity also influence the mixing of mist with fire gases in the compartment.
Spray Velocity Laboratories involved in measurement of water spray characteristics for research or approvals may use a phase-Doppler anemometer (PDA) instrument to measure drop size distributions and
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Weighted average cumulative % volume drop size distributions 100 90
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80 Cumulative volume (%)
Fig. 46.5 Comparison of statistically weighted cumulative percent volume versus drop size distribution plots for two low-pressure (A and B) and two high-pressure (C and D) water mist nozzles
J.R. Mawhinney and G.G. Back III
70 60 50 40
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drop velocity, including speed and direction. The PDA may be mounted on a movable structure of vertical and horizontal beams, which can be raised or lowered relative to the position of a nozzle. The PDA measurement focuses two laser beams on a small volume of space and is able to count the number of particles of different sizes at a point inside the spray volume. It determines at least one component of the velocity, using the principle of the Doppler shift that occurs depending on the velocity of the object relative to the viewer. By moving the laser source to different positions around the spray cone, a map of drop size particle size, mass density, and velocity can be constructed. As part of the same study referred to for the drop size distributions shown in Fig. 46.5, measurements of vertical-downward velocity profiles were taken for two of the nozzles [43, 44]. The velocity was measured by placing a vane-type anemometer horizontally in the spray cone at different locations and at two different distances below the nozzle. The anemometer measured the velocity of the entrained air plus water drops normal to the plane of the anemometer vanes. Individual drops hitting the rotating vane either accelerated or decelerated the vane. It was estimated that the effects of
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individual water drops on the vane speed approximately canceled out, so that the velocity of the entrained air dominated the measurement. The measured velocity was probably less than the velocity of the fastest-moving drops but close to the average velocity of the entrained air. Figure 46.6 compares the downward velocity profiles measured 0.3 m and 1.0 m below a highpressure (C) and a low-pressure (A) nozzle. These data provide a qualitative means of understanding the difference between how a highpressure and a low-pressure water mist nozzle might interact with the fire plume. At this time it is not possible to formulate invariable relationships between spray drop size distributions, spray velocity, and the suppression efficiencies of different water mist nozzles. There are many interacting factors involved in suppression, such as enclosure effects and fuel properties. There are, therefore, many possible combinations of spray characteristics and local conditions that will effectively control or extinguish fires. Computational fluid dynamics (CFD) field models present a fruitful means of studying the relative importance of specific spray characteristics. However, it is necessary to measure the physical characteristics of water mist
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18 C, 0.3, D1 C, 0.3, D4 A, 0.3 m A, 0.3 m, D4
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Fig. 46.6 Downward spray velocity profiles, measured 0.3 m and 1.0 m below a high-pressure (C) and a low-pressure (A) water mist nozzle
sprays as they are needed as input parameters for the field models.
Additives and Health Concerns In the early 1990s concerns were raised that inhalation of very fine water droplets could cause persons to drown. Various studies were conducted to review the literature on the subject of inhalation of aerosol sized particles into the lungs. Examination of drop size distribution measurements revealed that even the finest water mist sprays do not contain a significant mass of water in drop sizes small enough to be inhaled, and the limited fraction of aerosol-sized particles that could be inhaled are removed as they move through the bronchial tract before reaching the lungs. Consensus was reached that inhalation of “pure” water could be dismissed as a health concern [45]. The use of potentially toxic additives to the water mist, however, was considered to be a potential health concern. Low concentrations of additives, such as alkali salts and the surfactants in AFFF solution, improve the extinguishment capabilities of water mist [46, 47]. In Class B fires, the surfactant spreads over the liquid pool surface, blocks the
generation of fuel vapors, and helps extinguish small flames in hidden corners. Extinguishing the small flames helps break the extinctionreignition cycles that prolong the extinguishment of obstructed pool fires. For enclosed systems, the addition of inert gas (nitrogen) to the spray has been demonstrated to enhance extinguishment by aiding in oxygen depletion [48]. Antifreeze and biocides to prevent algae growth are also potential water mist additives. The use of additives introduces concern about possible negative effects on human health. The U.S. Environmental Protection Agency (EPA) permits the use of water mist as a halon alternative in occupied spaces only when potable water or normal seawater is used [49]. This permission was based on the response of a panel of toxicity experts convened under the Halon Alternatives Research Corporation (HARC) to question the possible adverse health effects of water mist. The report concluded that even the smallest drop sizes in water mist are not present in sufficient quantities to harm humans if breathed into the lungs, provided the water is of potable quality. The report Water Mist Fire Suppression Systems Health Hazard Evaluation (1995) was generated by the Halon Alternatives Research
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Corporation (HARC) [45]. Members of the NFPA 750 technical committee provided input to the panel of health experts. The report provided data for discussion of concerns over water mist and additives to the water. The report included a section entitled “Toxicity Profile— Water Mist Spray with Additives” that was prepared for the Army Program Executive Office, Armored Systems Modernization group, by the Toxicology Division, U.S. Army Environmental Hygiene Agency. The US Army study summarized the available toxicity data on water mist and six potential additives. It identified additives that are the least toxic: • Propylene and ethylene glycol (antifreeze)— acceptable; • Potassium acetate and calcium chloride (antifreeze plus fire retardant)—acceptable with reservation; and, • Potassium iodide and lithium chloride— potentially hazardous to humans. Since the US Army study was done in the mid-1990s, the fire protection engineering community has become aware that propylene and ethylene glycol antifreeze solutions in excess of 50 % may cause a flash fire deflagration if finely atomized and discharged into an ignition source. If the phenomenon has been observed with sprinkler sprays, it is inadvisable to use such antifreeze solutions in water mist systems, where the fraction of spray that is in very fine droplets is much higher. The army toxicity report does not address the matter of how much additive may be present. Is a product safe at 1 % but unsafe at 5 %? Some antifreeze concentrations may be as high as 30–50 % by weight. The concentrations of biocide needed for bacteria control may be below the harmful threshold for humans. One must distinguish between chronic, or long-term, exposure, and short-term, low-probability exposure that would be less harmful than the exposure to the fire combustion products. At the present time there are no simple answers to such questions. There are concerns with storage of water in cylinders for water mist systems for crew compartments in military vehicles. The concerns range from toxicology of chemical additives used
J.R. Mawhinney and G.G. Back III
as antifreeze agents or fire retardants, to bacteriological growth in untreated stored water. The U.S. Environmental Protection Agency (EPA) states that only “pure” (i.e., potable) water or natural seawater can be used without question for water mist systems in occupied spaces. If additives are considered, the onus is on the proponent to prove that there is no toxicological risk. Dr. Martial Pabon, of DuPont de Nemours, France, presented an example of a toxicological study of the effect of a fluorosurfactant additive (2 % Forafac) to water mist at the 2005 conference of the International Water Mist Association [50]. Working with G. LeFort and Dr. Andre´ Marshall at the University of Maryland, it was proven that the additive did not alter the atomization process and that the additive improved the extinction capability of the water mist and prevented reignition of a hydrocarbon pool fire [50, 51]. A toxicological study was carried out at Haskell Laboratory by J. Stader and T. Kegelman. This study was based on the “OECD Guideline for the Testing of Chemicals, Section 4: Health Effects, Acute Inhalation Toxicology, Number 403” (1981) [52]. The conclusion of the toxicity study was that “according to the guide for the labeling of dangerous substances published in the Official Journal of the European Communities (EEC Directive 93/21), 2 % (of the Forafac additive) to the water mist is not classifiable (LC50 > 5 mg/L).” Addressing health concerns involves not only studying the effect of chemical additives, but also the bacterial content of the water. Heating and air conditioning engineers in the United States have noted that Legionella bacteria can be spread to humans by inhalation of fine sprays that may carry the bacteria [53]. In 1976, an unnamed bacterium caused 34 deaths and 221 people at a Legionnaire’s convention in Philadelphia to become sick with symptoms of pneumonia. At the time of its discovery and naming as “Legionella,” it was thought that the bacteria were not present in fresh potable water, but only in stored water associated with the building cooling systems. Experience with worldwide outbreaks since then, however, has shown that Legionella bacteria can be present in
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potable water systems, particularly in the hot water plumbing systems, and can be spread through any systems involving atomization of water. Legionella bacteria thrive in water between 20 C and 48 C (68 F and 108 F) [53]. Precautions against bacterial growth are also recommended to prevent plugging of the control valves and nozzles by algae growth. Water mist systems often utilize water storage tanks as part of the design. Some marine water mist systems utilize water reservoirs or break tanks. Although in principle only clean potable water goes into the tanks, conditions may change over time, particularly when the tanks are placed in warm machinery rooms. Filtration removes particulates but not bacteria present in the source water. The American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE) produced a guideline with recommendations for controlling the development of Legionella in stored water systems [54]. Careful annual maintenance and cleaning are recommended. It notes that during the release of fire water in a fire emergency, fire department personnel wear breathing apparatus, and non-fire-fighting personnel will exit the fire area. However, appropriate precautions should be taken when testing the fire protection system. Some water mist systems have been designed to provide a high level of cleanliness in the water supply [55]. The system water is circulated continuously between a reservoir and the system piping. An ultraviolet treatment chamber kills bacteria and filters remove particulates on a continuous basis. Pressure loss across the filters can be monitored to indicate when the filters have reduced flow capacity. High-cleanliness water supply precautions are a solution for any applications where there is concern about maintaining the quality of the water, either for health or functional reasons.
Fire Suppression Modeling The major difficulties with water mist systems are those associated with a standardized approach to their engineering design. The
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problems arise from the need to generate, distribute, and maintain an adequate concentration of the proper size drops throughout the compartment or fire area for the necessary time period while accounting for the effects of gravity and water deposition on surfaces, which deplete the overall concentration of mist. There is currently no theoretical basis for considering these parameters in the design process. System design parameters are normally extrapolated from largescale test data on a case-by-case basis for specific applications. This approach is not necessarily cost effective for water mist system manufacturers and poses difficulties for standards-making and regulating authorities. There has been at least one significant effort at developing and applying physical scaling rules (i.e. Froude number scaling) to water mist system design applications [56]. Although the study showed some applicability, the overall approach is significantly limited. Over the years, an empirical understanding of how water mist systems extinguish a fire has been bounded. The degree of understanding however is still not yet at the stage where water mist systems can be designed from first principles, although some progress continues to be made. The progress that is currently being made is through the application, development and validation of CFD algorithms for specific applications. Now that water mist technology has been fielded for over 15 years, the trends have shifted from basic/fundamental research to the assessment of specific applications. A basic understanding of the mechanisms of extinguishment associated with water mist was developed over 45 years ago [3, 4]. Braidech and Rasbash both concluded that fires were extinguished by dilution of the air (oxygen) with water vapor (steam), resulting from evaporation of water droplets in the area local to the flame. They also concluded that the cooling effects of the water with respect to the flame and the fuel might contribute to the extinguishment process. Research conducted to date has not altered this understanding. Recent research has, however, identified the primary mechanism(s) associated with extinguishment for a given set
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of conditions as well as some additional less predominant extinguishment mechanisms [14]. The mechanisms of extinguishment can be broken down into two basic groups—direct and indirect flame interaction. Direct flame interaction includes gas phase cooling and localized oxygen depletion, and indirect effects include global oxygen depletion and surface wetting/ cooling effects. Direct flame interaction encompasses a broad range of both chemical and thermodynamic relations associated with the release and distribution of energy during the combustion process. Extinguishment by direct flame interaction (primarily gas phase cooling) is basically the removal of energy from the flame and hot gases. As the energy is removed from the flame, the temperature of the flame is reduced. If the flame temperature is reduced below the critical value necessary to sustain combustion (limiting adiabatic flame temperature), the flame will be extinguished. The limiting adiabatic flame temperature for a number of hydrocarbon fuels is on the order of 1600 K (1326 C) [15]. Recent investigations have bounded some of the parameters associated with direct flame interaction [20, 22, 57]. Numerous research programs have focused on identifying the critical mist concentrations needed to extinguish diffusion flames [17, 58–62] and to extinguish hydrocarbon pool fires [22, 63–67]. Other research agencies have studied the effects of water vapor as an inerting gas [68, 69], as well as the attenuation of radiation to the fuel surface provided by the mist [70–72]. The difficulty in predicting extinguishment by direct effects is associated with being able to predict and/or measure the amount of mist reaching the fire. The ability of mist to diffuse into all areas in the space in the same manner as the gaseous agents is significantly limited for the range of drop sizes produced by current commercially available hardware [63, 73]. Recent studies have shown that the concentration of mist decreases by more than a factor of two after traveling less than a meter horizontally away from the spray pattern of a nozzle. To compensate for this limitation, the higher performance
J.R. Mawhinney and G.G. Back III
water mist systems rely on high-velocity sprays to mix the mist throughout the compartment (i.e., to create turbulent conditions in the space). The fire size (heat release rate) and fire location are also variables that need to be considered. The fire tends to alter the mist conditions in the compartment by changing the drop size distribution (vaporization and condensation) and affecting the flow patterns throughout the space due to the plume and ceiling jets. Additional research has bounded the effects of oxygen depletion and dilution (indirect effects) on extinguishment [18, 74–76]. The production of steam resulting from mist interactions with the flame, hot gases, and/or hot surfaces can significantly reduce the oxygen concentration in the space. The oxygen available for combustion on a compartmental scale is a function of the size of the fire, the compartment volume, and the ventilation conditions in the compartment. As the size of the fire increases, the average temperature in the space increases, and the oxygen concentration decreases due to both the consumption of the oxygen by the fire and dilution of the oxygen by water vapor (steam). If the combined effects of oxygen depletion and dilution can reduce the oxygen concentration below the critical value necessary to sustain combustion (limiting oxygen concentration [LOC]), the fire will be extinguished. The LOC for most hydrocarbon fuels is on the order of 13 % [77]. Fuel surface effects can be the predominant extinguishment mechanism for fuels that do not produce combustible mixtures of vapor above the fuel surface at ambient temperatures, that is, solid fuels and liquid fuels with high flashpoints (i.e., diesel 60 C). Wetting/cooling of the fuel surface reduces the pyrolysis rate of the fuel. If the vapor-air mixture above the fuel surface is reduced below the lower flammability limit (LFL), the flame will be extinguished. The ability to predict extinguishment based on surface cooling has also been investigated in numerous experimental programs [78–82]. This information includes both Class A materials as well as high-flashpoint hydrocarbon pool fires. Typically, a combination of mechanisms is involved to some degree in the extinguishment
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process. In order to accurately predict the conditions required for extinguishment, the combustion chemistry, combined with thermodynamics and fluid dynamics, needs to be covered in detail. These complex relations are best analyzed using computational models that are based on first principles. The current mathematical models used to predict suppression of fires by water mist systems cover the range of approaches from zone fire modeling to computation fluid dynamics (CFD), which are often referred to as field models. A zone model calculates the fire environment by dividing each compartment into one or two homogeneous zones. The energy balance and conservation of mass equations are solved based on a control volume dictated by the boundaries of the compartment for a singlezone model or by the zonal boundaries for a two-zone model. The input requirements for zone models vary depending on the model and the desired output. The compartment geometry and opening dimensions are needed to define the space and the surroundings. The thermal properties of the compartment boundaries are needed to estimate the heat loss through the walls, ceiling, and floor. The fire size must be entered, though the model may modify the heat release rate as the oxygen concentration in the compartment is reduced by the fire. Some zone models account for effects of mechanical ventilation, which means that the fan flow rate and the location of the vent inlets and outlets are required as input to the model. CFD models divide the control volume into a large number of small three-dimensional cells and calculate the fire environment within the control volume by numerically solving the conservation equations (mass, energy, momentum, diffusion, species, etc.) within each cell. Solving these equations is accomplished by using finite difference, finite element, or boundary element methods. The results are three-dimensional in nature and are very refined when compared to a zone-type model. The enormous number of computations performed during these modeling exercises is very time consuming and requires powerful computational equipment.
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Like zone models, CFD models require a description of the compartment geometry and the openings within the compartment as input. Depending on the sophistication of the extinguishment/fire model, the fire heat release rate may also need to be specified. Heat losses to the compartment boundaries are calculated using the thermal properties of the bounding materials. CFD models have the capabilities to simulate the conditions that occur within complex compartment geometries as well as unenclosed fires since these models are not strictly limited to compartment fire scenarios.
Zone Models Zone fire suppression models for water mist have been developed by Back et al. [83], Li and Chow [84], Forssell et al. [85], Vaari [86], and Wighus and Brandt [87]. All five models assume a single zone and vary in sophistication from steady-state predictions to transient computations.
Quasi-Steady-State Zone Models Two quasi-steady-state models have been developed to predict the effectiveness of water mist systems for extinguishing hydrocarbon fuel fires in machinery space applications. The model developed Wighus and Brandt [86] addresses only pool fires whereas the model developed by Back et al. [83] was developed for both pools and spray fires. Both models were developed for obstructed fires where extinguishment primarily occurs as a result of a reduction in oxygen concentration (consumption and dilution) and neglects the effects of the interaction of mist with the flame. Consequently, the predictions made by these models serve as the limiting case where obstructions prevent direct spray interactions with the fire. The models are based on conservation of energy and mass and require the following input parameters: fire size, compartment geometry, vent area, and water flow rate. The steadystate compartment temperatures and oxygen
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J.R. Mawhinney and G.G. Back III
concentrations predicted by these models are used to determine the smallest fire (critical fire size) that will sufficiently reduce the oxygen concentration to below the LOC of the fuel. The energy balance used in these two zone models can be expressed by the following equation: Q_ Fire ¼ Q_ Boundary þ Q_ Vent þ Q_ Vapor þ Q_ Water ð46:4Þ where ¼ Heat release rate of the fire Q_ Fire Q_ Boundary ¼ Energy lost through the walls, ceiling, Q_ Vent Q_ Vapor Q_ Water
and floor ¼ Energy lost out of the vent opening ¼ Heat absorbed by evaporation
¼ Energy absorbed by the mist The following assumptions were made to simplify the calculation: • Combustion is complete and takes place entirely within the confines of the compartment • The heat release rate of the fire is a constant (steady state). • The temperature is uniform within the compartment at all times (after discharge), and the gases exhausted are assumed to be at the compartment temperature. • The exhaust gases and the gases contained in the compartment are assumed to be saturated with water vapor. • A single surface heat transfer coefficient is used for the entire inner surface of the compartment. • The heat transfer through the compartment boundaries is unidimensional; that is, corners and edges are ignored and the boundaries are assumed to be infinite slabs. • Mist droplets are assumed to be heated to the compartment gas temperature. The individual components of Equation 46.4 are calculated as follows: the heat release rate of the fire is an input parameter and is calculated based on the known constant fuel spray or mass burning rate of the fire and the heat of combustion of the fuel. The heat lost through the
boundaries of the compartment is determined using an overall heat transfer coefficient developed for preflashover fires. The energy losses by vent gas flow are based on the temperature of the exhaust gases and the exhaust rate determined from a vent flow correlation applicable to wellstirred compartment environments. The heat lost by evaporation is based on achieving the equilibrium vapor pressure (assuming saturation), the vent flow rate, and the heat of vaporization. The heat absorbed by the water is determined from the water mist application rate, assuming all the mist is heated to the compartment temperature. The computational exercise begins by solving the energy balance to predict the steady-state compartment temperatures in the space and the mass flow rate of air/gases through the vent opening. Once the steady-state temperatures and the mass flow rates are known, the steady-state oxygen concentration is then calculated by first determining the amount of oxygen consumed by the fire and then diluting the remaining oxygen with water vapor until the gases are saturated. The steady-state oxygen concentrations are then used to predict the critical fire size for the selected compartment configuration and water mist system flow rate. In this context, the critical fire size is defined as the smallest fire that will reduce the oxygen concentration below the LOC of the fuel. The approach used to predict the time of extinguishment varies between the two models. For the model developed by Back, the extinguishment times are predicted using a coupled energy and mass-transfer correlation. The mass transfer is implicit in the following equation, whereas the energy/temperature dependence is embedded in the volumetric flow rate and predicted steady-state oxygen concentration terms. Assuming that steady-state conditions occur quickly and that the extinguishment of these fires becomes related to the time required to dilute the gases in the compartment, the extinguishment times can be approximated using the following equation: ΔCO2 ðtÞ ¼ ΔCO2 ðssÞ 1 eν_ t=ν
ð46:5Þ
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Water Mist Fire Suppression Systems
where CO2 ðtÞ ¼ Oxygen concentration (percent by volume) in the compartment at time t CO2 ðssÞ ¼ Predicted steady-state oxygen concentration v ¼ Volume of the compartment ν_ ¼ Volumetric flow rate of air/gas through the compartment The extinguishment times are determined by setting CO2 ðtÞ equal to the LOC of the fuel (14 % is typically used during this calculation) and solving Equation 46.5 for t. This approach is a first-order approximation and is best suited to predict the extinguishment times of large fires and loses accuracy as the fire size approaches the critical value. For the model developed by Wighus and Brandt, the extinguishment times are predicted by iterating through the equations in 0.05-s time steps. The primary outputs of the model are the steady-state compartment temperature and the extinguishment times for a range of fire sizes for a specific compartment configuration and water mist discharge rate. The predictions made by these models compared favorably to the results of four full-scale machinery space investigations conducted for the U.S. Coast Guard. For the range of compartment sizes (100–3000 m3) and ventilation conditions (closed compartment, naturally ventilated [1.25–5.7 m5/2 ventilation factors], and forced ventilation [25 m3/min]) included in these investigations, the models were able to accurately predict the steady-state compartment temperatures and oxygen concentrations that occurred during the test. In many cases, the larger fires were extinguished before steadystate conditions were reached. This result was also predicted by these models. The models were also able to accurately predict the smallest fire (critical fire size) that could be extinguished due to a reduction in oxygen concentration in the space. Both models were able to accurately predict the extinguishment times for a wide range of fire sizes but lost accuracy as the fire approached the critical value.
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Although these models show promise for predicting the steady-state temperatures and oxygen concentrations in an enclosure for a given set of parameters and provide reasonably accurate fire extinguishment time predictions, more sophisticated models are required to accurately predict the transient conditions that occur in a compartment during the discharge of a water mist system. The analysis of these transient conditions significantly increases the complexity of the computations.
Transient Zone Models Three transient zone models that predict the effectiveness of water mist systems to extinguish hydrocarbon fires have also been developed [84–86]. The models developed by Vaari [85] and Li and Chow [83] are very similar and use the same basic set of equations as described above for the quasi-steady state zone models. The model developed by Forssell et al. [85] is similar in some respects but different in others. With respect to similarities, all three models solve the conservation of mass and energy equations as a function of time for a given set of conditions. The conservation of mass equations used in the quasi-steady-state models have been replaced by conservation of species. The mass/volumetric flow rate of air through the vent is determined using an orifice flow correlation and the pressure in the compartment similar to the quasi-steady-state models. The compartment pressure is calculated from the density and gas temperature in the compartment using the equation of state for an ideal gas. New mist concentration, droplet evaporation, and extinguishment algorithms have also been developed. The models are different with respect to how they handle boundary losses, drop evaporation, and predict extinguishment. The models developed by Vaari and Li and Chow neglect all energy losses to the boundaries, whereas the model developed by Forssell et al. includes a lumped mass boundary heat loss algorithm similar to the quasi-steady-state models.
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The evaporation algorithms differ significantly among the models. The algorithm developed by Vaari is fairly detailed, as compared to the simplified versions developed by Li and Chow and Forssell et al. In the algorithm developed by Vaari, it is assumed that the heat transfer between the gas and liquid phases is infinitely fast, making the two phases identical temperatures. As a result, all of the heat absorbed by the drop is utilized in the evaporation process. The algorithm includes drop concentration and drop size subroutines that include drop agglomeration and terminal velocity predictions. Using the Clausius-Clapeyron equation to calculate the vapor pressure near the drop surface, the mass transfer number (B) for a single drop is determined. This mass transfer number is then used to determine the evaporation rate for a single drop, which in turn is applied to the entire spray. The algorithm developed by Li and Chow uses a similar approach that has been significantly simplified. In the algorithm developed by Forssell et al., the evaporation model incorporates a correlation constant that represents the combination of the mass transfer number (B) and the surface area–to-volume ratio of the droplet. Rather than including a set of subroutines based on spray characteristics of the nozzle/system that may or may not be available in the public domain, Forssell et al. chose a single empirically fitted correlation constant. The extinguishment algorithms are also somewhat different among the models. In the algorithms developed by Vaari and Li and Chow, extinguishment is predicted based on a calculated flame temperature determined based on an energy balance conducted in the flame. For this calculation, a limiting flame temperature must be selected (typical values are on the order of 1550 K). This energy balance calculates the temperature of the gases in the flame region by taking into account the species concentrations in the combustion process as well as the mist entrained into the flame. In order to estimate the amount of water droplets entrained into the flame, a simple mist concentration algorithm was developed based on mist discharge rate, terminal drop velocity, and compartment height.
J.R. Mawhinney and G.G. Back III
Forssell et al. selected a critical oxygen concentration (14 %) to predict extinguishment, similar to the quasi-steady-state models, which is basically equivalent to the previous approach with the exception that the entrainment of mist into the flame is not included in the computation. All three transient models provide as output the gas (species) concentrations and temperature histories in a compartment for a given set of input parameters (e.g., compartment configuration, ventilation condition, and fire scenario). Transient models provide the capability to study scenarios that never achieve steady-state conditions and that cannot be represented by the steady-state computations. Two examples of these are growing fires (fires with varying heat release rates) and variable flow rate water mist systems. The transient models include more sophisticated evaporation algorithms, which, in theory, should allow them to predict extinguishment more accurately than the steady-state models. The limitations are associated with the single-zone approximation and the need for experimental data to define the unknown parameters used in the model (namely, the spray characteristics of the system). The singlezone approximation may cause the model to fail if the space is not well mixed or the fire is allowed to burn for a significant duration prior to mist system activation. None of the three transient zone models has been thoroughly validated. However, the limited validation performed by Vaari shows promise with respect to the accuracy of these models.
CFD Models (Field Models) CFD models are much more sophisticated than the previously described zone models and show promise for handling the complex physical and chemical relations that occur. As stated previously, CFD models divide the computational domain into a large number of small threedimensional cells and solve the conservation equations (Navier-Stokes) in each cell simultaneously. CFD models can provide detailed information on the mass/energy transfer between the
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fire and the water mist and on the distribution of water vapor and mist concentration throughout the compartment. Like zone models, CFD models require a description of the compartment geometry and the openings within the compartment as input. Compartment contents and boundary materials must also be specified. The model is run for a specific set of conditions (compartment configuration, fire scenario, and water mist system). The outputs are very detailed in nature and consist of data files containing information pertaining to the conditions (temperature, velocity, mist concentration, gas/species concentrations, etc.) for each element and time step in the computation. This detailed information allows a graphical/ visual representation of the conditions in the compartment during selected time intervals. For example, color contour temperature images and velocity fields represented by small arrows, with the magnitude of the velocity indicated by the length of the arrow, are typical outputs for CFD modeling runs. These outputs allow the visualization of the conditions that occur in the compartment during a specific scenario. Some of the CFD models currently in use include ALOFT-FT [88], CFX [89], FDS [90], FIRE [91], FLUENT [92], JASMINE [93], KAMELEON [94], KOBRA-3D [95], MEFE [96], PHOENICS [97], RMFIRE [98], SMARTFIRE (sometimes referred to as FIREDASS) [99], SOFIE [100], SPLASH [101], STAR-CD [102], and UNDSAFE [103], but only a limited number of them have been used to characterize water mist applications. Many of these CFD models contain variants of the K-Epsilon submodel required to handle the turbulent conditions produced in this application. K-Epsilon submodels are two additional differential or algebraic equations (where K is turbulence energy and Epsilon is its dissipation rate) that relate turbulent stresses and fluxes to the flow field. The limitations for applying CFD modeling to water mist applications include the following three general areas: the inability to accurately model the spray characteristics of the nozzle/ system discharge, the inability to accurately
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predict drop transport and flow around obstructions, and the lack of knowledge/ algorithms to accurately predict extinguishment. The ability of CFD models to accurately predict water sprays needs additional research/ development and validation. The difficulty with drop transport is associated with linking the liquid water droplets to the gas phase domain and demonstrating the influence of one on the other. Detailed extinguishment algorithms must include an energy balance conducted in the flame and at the fuel surface during the entire combustion process. The approximation of the combustion process must take into account the following species concentrations: fuel vapor, water vapor, oxygen, nitrogen, combustion gases, and water mist concentration. In most cases, the fuel vapor concentration is driven by the radiation from the flame back to the fuel surface and must be solved simultaneously. Although progress continues to be made in all three areas, more work still needs to be done. The ability of Fire Dynamics Simulator (FDS), Version 4, to reproduce a measured flux distribution map was recently assessed for two multiple-orifice–high-pressure water mist nozzles at two operating pressures [104]. During the study, several flux density distributions were measured under identical conditions in order to achieve an average value. Experimental data were used to define the drop size distribution, the initial drop velocity, and the directional geometry of the nozzle orifices. The cumulative volume fraction curve was reproduced using a Rosin-Rammler/log-normal distribution equation. The study showed that the current nozzle characterization technique used in FDS that employs sectors on the surface of a sphere as source points, input as a single line in the input file, was problematic and required a new approach. Acceptable agreement was achieved by characterizing each orifice in the multiport nozzle as a single solid cone spray with a separate line of parameters in the input file. The results again showed that accuracy of the modeled distribution is very sensitive to the resolution of the computational grid. It was concluded that if high-resolution predictions of
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flux distributions are the goal, the numerical nozzle characterization requires some trial-anderror adjustments of values such as spray cone angle, spray direction, and initial drop velocity. Other recent studies have arrived at the same conclusions [105–107]. Based on these studies, it appears that fine computational grids (i.e. small cell sizes) may be required to accurately predict mist discharge characteristics in the region local to the nozzle. This may prove to be a significant limitation depending on the size of the protected space being modeled and the required resolution of the predictions. The manner in which the spray characteristics of the nozzle affect drop transport and the transport phenomenon in general also needs additional research. Recent research has focused on both the flow of water droplets through cluttered environments [108–112] and on the effects of fire plumes and ceiling jets on the water droplets [113–119]. However, the problem lies more on a fundamental level. Drop transport and tracking are currently being performed using either Eulerian or Lagrangian formulations [120, 121]. A Eulerian formulation uses a fixed grid and assumes the drops pass through (drops and gases travel at different velocities), whereas the Lagrangian formulation considers the droplets and gases to be a single homogeneous mixture. Research has been conducted using both formulations but the information found throughout the literature is very inconclusive regarding the choice of the appropriate method [122]. The appropriate formulation may depend on the spray characteristics of the nozzle as well as on the application. For example, the transport of larger drops may be better predicted using a Eulerian formulation whereas smaller drops may be better predicted using a Lagrangian tracking model. To make matters more complicated, a specific technique may work better closer to the nozzle (near field) and lose accuracy in the far field. Additional research is needed. With respect to extinguishment algorithms, the physics and computational issues associated with numerical modeling of fire suppression have been identified [123–125]. Studies found throughout the literature typically focus on
J.R. Mawhinney and G.G. Back III
specific fire types and scenarios. The National Institute of Standards and Technology (NIST) and the Naval Research Laboratory (NRL) have both recently developed algorithms to predict suppression of opposed flow diffusion flames [126, 127]. A recent study validated the accuracy of these algorithms [128]. Limited research has also been conducted on premixed flames [129]. On a larger scale, extinguishment algorithms have also been developed for pool fires [130–134], spray fires [135] and solid fuels [136–141]. Although these advances are promising, there is still the need to develop an all-encompassing extinguishment algorithm capable of handling a variety of fuel types and configurations to be used with CFD modeling. With respect to the general use of CFD models to simulate the conditions during a specific application, CFD models are currently being used to evaluate full-scale test results, to assess the effects that the application and system design parameters have on the capabilities of the system (i.e., to conduct a sensitivity analysis on the system and application), to extrapolate results/ capabilities to conditions outside the bounds of the approval test, and to bound the capabilities of a system in an application where there is little or no empirical data. Most of this information is proprietary with only a limited amount available to the public. A limited number of general studies using CFD models for full-scale fire suppression research have been carried out by Hadjisophocleous [108, 142]. The research includes the extinguishment of liquid pool fires in both open and closed compartments and fire suppression in an aircraft cabin. The modeling was performed using the CFD model TASCFLOW with the water spray transport handled using a Lagrangian tracking model. During the initial study [108], water mist system parameters (the number of nozzles, nozzle locations, spray characteristics, and discharge rate) were systematically varied to determine their effect on the extinguishment process. The predicted results showed reasonably good agreement with corresponding experimental data. Recently, a sensitivity analysis on how drop size affects extinguishment was conducted using FDS
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[125]. As expected, the results of the study were inconclusive due to the number of potential variables associated with the fuel and fire type, and the extinguishment process. Studies have also been conducted using the CFD model FDS to augment full-scale fire suppression research programs [143–145]. The research includes the extinguishment of liquid pool fires in both open and closed compartments. In both cases, the water spray transport was handled using a Eulerian tracking model. During the latter study, both sprinkling and water mist systems were included in the study. The predicted results showed reasonably good agreement with corresponding experimental data. A study was also conducted to assess the capability of the CFD model CFX to predict the suppression of hydrocarbon pool fires in an unobstructed enclosure [146]. The modeling work included a sensitivity study that looked at a number of parameters and compared the predictions to empirical data collected in a 96 m3 enclosure. The results showed that the accuracy of the predictions was highly dependent on the grid/ mesh resolution (finer resolutions produced more accurate results). This was also observed during at least three previous studies conducted with FDS [104, 145, 147]. Over the past few years, a significant amount of research has been conducted with the focus of quantifying the hazard associated with vehicle tunnels. This research includes full scale hazard quantification testing, standards development, mitigation system development and testing, modeling and validation testing [148, 149]. In a paper written by Mawhinney and Trelles [148], large scale fire tests conducted in a tunnel test facility in San Pedro de Anes, Spain were modeled using FDS. The objective was to show that the CFD simulations could be, at minimum, partially validated by demonstrating a reasonable degree of agreement with the conditions measured during the tests. The level of agreement between the fire suppression tests results and the simulated conditions was deemed to be adequate to establish confidence in applying the model to examine the conditions that would occur during an unsuppressed fire
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(i.e. the free-burn, baseline hazard conditions, which were not tested due to cost and potential damage to the tunnel). In a paper written by Nilsen and Log, the results of large scale tunnel fire tests were simulated using three different models ranging in complexity from spread sheet level calculations to CDF modeling predictions using the CFD model SOLVENT [150] The results showed good agreement across the board for smaller fires but the larger fires were better simulated using CFD. Although there were deviations in the results for the larger fires, the paper concluded that all three models were acceptable tools for assessing baseline tunnel fire hazards. The U.S. Navy has been investigating the concept of using water mist to reduce the blast overpressures produced during a weapon hit by activating the ship-board water mist system just prior to weapon impact. A series of tests were conducted to validate the concept. The results of the tests were later successfully modeled using FDS [151, 152]. To increase the accuracy of the predictions, an algorithm was developed to predict droplet breakup caused by the initial pressure wave produced by the blast. The results obtained using CFD modeling demonstrate its potential for analyzing the complex physical and chemical phenomena of fire suppression by water mist. The primary use of CFD modeling has been to extend the understanding of the relationships between the water mist system design parameters and fire suppression (i.e., CFD modeling has been successfully used to extrapolate large-scale test results and to conduct sensitivity analyses on specific water mist system design parameters). CFD modeling not only has the potential to augment the test and evaluation process as currently being used but also shows promise for approving specific water mist system designs for actual applications in the future. The potential for CFD modeling as a research and design tool is now recognized. CFD modeling is currently being used as a research tool at NRC Canada, NRL, NIST, SP, SINTEF, and at numerous universities.
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Modeling Summary An empirical understanding of how water mist systems extinguish a fire is continuing to emerge. Although progress continues to be made, the degree of understanding is not yet at the stage where water mist systems can be designed from first principles. In order to accurately predict the conditions required for extinguishment, the combustion chemistry, combined with thermodynamics and fluid dynamics, needs to be covered in detail. These complex relations are best analyzed using computational models. The current mathematical models used to predict suppression of fires by water mist systems cover the range of approaches from zone fire modeling to computational fluid dynamics (CFD), which are often referred to as field models. Five zone models (two steady-state and three transient) have been developed to predict the effectiveness of water mist systems against hydrocarbon fuel fires (both spray and pan fires). The models appear to make reasonably accurate first-order approximations of the extinguishment of a range of fire sizes for a given compartment configuration and set of mist system parameters/characteristics. The strength of the zone models is their ability to bound the capabilities of a water mist system for a given application. The limitation of these zone models is associated with a general lack of detail incorporated in the computation. As a result, these zone models may lose accuracy when applied to complex configurations (geometries). CFD modeling has been shown to be a promising tool for analyzing the complex physical and chemical phenomena of fire suppression by water mist. The strength of the CFD models is their ability to expand the understanding of how the application and system design parameters affect the performance of the system. The graphical/visual nature of the output can illustrate the physical phenomena occurring during the event. The limitations are associated with the high labor costs required to develop a fine computational grid for a large-scale application and the associated long computer run-times to perform
J.R. Mawhinney and G.G. Back III
the simulation. Applying CFD modeling to a specific application can be an iterative process and requires a certain level of expertise. Additional research is required to further develop and validate techniques to model the spray characteristics of the nozzle/system, formulations to accurately predict drop transport, and an all-encompassing extinguishment algorithm capable of handling a variety of fuel types and configurations. Only limited progress has been made in these areas over the past few years due to the application specific nature of the latest research and the limited amount of validation test data. In any case, modeling still has the potential not only to augment the test and evaluation process but also to aid in approving specific designs for actual applications in the future.
Approval Testing of Equipment Creating and delivering water mist as an effective fire suppression agent requires different types of hardware than traditional fire sprinkler equipment. The first decade of water mist development saw the introduction of innovative ideas and hardware from non-fire related industries, such as positive displacement pumps from the hydraulics (machinery) field, and the use of compressed gas as an energy source. By the end of the 1990s there were several distinct types of water mist systems on the world market: low pressure systems operating within the pressure range of conventional fire pumps and sprinkler system fittings; intermediate pressure systems requiring slightly higher pressure than conventional sprinkler systems, and high pressure systems operating at pressures much higher than conventional sprinkler systems. Some systems combined water and compressed gas as the driving force. The types of nozzles differed greatly among manufacturers, as they attempted to develop and patent atomization methods and customized valves and control equipment. Hardware, such as positive displacement pumps and pneumatically-released deluge valves, came
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from industrial markets where UL Listings or FM Approvals were not common. Therefore, the only effective way to establish that a particular water mist system design based on non-listed hardware can meet performance objectives for a given application is to conduct specialized component evaluations and fire tests. Consequently, water mist approval protocols have been developed and adopted as a means to allow the introduction of non-traditional equipment to the fire protection industry. Fire test protocols are designed to match or simulate a specific hazard. Water mist systems that meet performance criteria appropriate for that application, which are specified in a consensus test protocol, receive the approval of the approval or listing agency. Table 46.1 shows a list of formalized fire test protocols produced by approval entities recognized in North America and Europe, and that are widely accepted globally. Ideally, test protocols should test the limits of performance of systems against a realistic range of conditions, including worst-case scenarios, and establish measurable performance objectives that meet the needs of a broad range of potential end users and stakeholders. For marine applications, consensus test protocols have been developed through the International Maritime Organization (IMO). The IMO test protocols encompass machinery room fire hazards (Class B fuels) and accommodation (sleeping rooms) and public spaces on ships (Class A fuels), where water mist systems are installed in place of marine sprinkler systems. For land-based industrial applications, the IMO test protocols have been adopted and modified by FM Global for turbine enclosures, machinery spaces, and pump rooms where liquid fuel fire hazards exist (see Table 46.1). FM Global has also developed test protocols for light and ordinary hazard classifications as referenced in traditional sprinkler system design, and wet benches in clean room environments. UL has also adopted and modified the IMO marine test protocols for machinery spaces, marine accommodation spaces, and land based ordinary and light hazard occupancy classifications.
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Annex C of NFPA 750 [2] describes a number of formalized fire test protocols in detail. Note that the criteria for deciding what constitutes acceptable performance is often decided with a specific situation in mind. Successful performance may not mean extinguishment of the fire in all cases. For example, the IMO test protocols for accommodation spaces and public spaces on ships require that the fire only be controlled for a period of 10 min with a limit to the fire spread during that time period. At the end of 10 min, the fire is manually extinguished and the percentage of burned to unburned fuel is calculated. Fire damage to the test materials must be within certain limits. The fire continues to burn throughout the 10 min discharge, and when the water mist system is shut off, the fire may re-kindle. The IMO machinery space protocol, however, requires extinguishment of all fires within 15 min. To achieve extinguishment, the system designers are permitted to utilize combinations of total flooding ceiling nozzles and screening nozzles over the ventilation opening, as well as the addition of surfactants to the water supply for obstructed bilge areas. The existence of a listing under one of the formalized test protocols does not eliminate the need for experienced judgment in applying the criteria and results of the listing evaluation to a specific application of a water mist system. It is important to confirm that the application sufficiently correlates with the conditions of the listing, and that the performance criteria used to judge pass or fail in the test protocol are consistent with the end user’s needs.
Development of Additional Fire Test Protocols The formalized fire test protocols presented in Table 46.1 do not include all potential applications for water mist systems. Where there is no existing standardized fire test protocol for an application where water mist could provide important advantages, an ad-hoc hazard-specific test protocol often needs to be developed and implemented. One possible difference between
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Table 46.1 Fire test protocols for water mist fire protection systems as of September 2012 Agency Water mist fire test protocol 1. International Maritime IMO Res. A800 (19): Revised Guidelines for Approval of Sprinkler Systems Equivalent to Organization (IMO) That Referred to in SOLAS Regulations II-2, Chap. 12 [153, 154] Appendix 1, “Component Manufacturing Standards for Water Mist Nozzles” Appendix 2, “Fire Test Procedures for Equivalent Sprinkler Systems in Accommodation, Public Space and Service Areas on Passenger Ships,” December 1995 IMO MSC/Circular 668: Alternative Arrangements for Halon Fire Extinguishing Systems in Machinery Spaces and Pump Rooms [155] Appendix A: “Component Manufacturing Standards of Equivalent Water-Based Fire Extinguishing Systems,” 1994 Appendix B: “Interim Test Method for Fire Testing Equivalent Water-Based Fire Extinguishing Systems for Machinery Spaces of Category A and Cargo Pump Rooms,” 1994 As amended in MSC/Circ. 728: “Amendments to the Test Method for Equivalent WaterBased Fire-Extinguishing Systems for Machinery Spaces of Category A and Cargo PumpRooms contained in MSC/Circ. 668, Annex B,” June 1996 MSC/Circ. 913: “Guidelines for the Approval of Fixed Water-Based Local Application FireFighting Systems for use in Category A Machinery Spaces,” June 4, 1999 [156] MSC/Circ. 1165, “Revised Guidelines for the Approval of Equivalent Water-Based FireExtinguishing Systems for Machinery Spaces and Cargo Pump-Rooms,” 10 June 2005 [157] 2. FM Global Research FM Global, Approval Standard for Water Mist Systems, Class Number 5560, 2009 [158] Corporation (formerly (a) Appendix A, B, C: Fire Tests for Water Mist Systems for the Protection of Machinery FMRC) Norwood, Spaces, Special Hazard Machinery Spaces, Combustion Turbines with Volumes up to, MA, USA and including, 2825 ft3 (80 m3) (respectively) (b) Appendices D, E, and F: Fire Tests for Water Mist Systems for the Protection of Machinery Spaces, Special Hazard Machinery Spaces, Combustion Turbines with Volumes up to and including 9175 ft3 (260 m3) (respectively) (c) Appendix G: Fire Tests for Water Mist Systems for the Protection of Machinery Spaces and Special Hazard Machinery Spaces with Volumes Exceeding 9175 ft3 (260 m3) (d) Appendix H: Fire Tests for Water Mist Systems for the Protection of Combustion Turbines with Volumes Exceeding 9175 ft3 (260 m3) (e) Appendix I: Fire Tests for Water Mist Systems for the Protection of Light Hazard Occupancies (f) Appendix J: Fire Tests for Water Mist Systems for the Protection of Wet Benches and Other Similar Processing Equipment (g) Appendix K: Fires Tests for Water Mist Systems for the Protection of Local Applications (h) Appendix L: Fire Tests for Water Mist Systems for the Protection of Industrial Oil Cookers (i) Appendix M: Fire Tests for Water Mist Systems for the Protection of Computer Room Subfloors (j) Appendix N: Other Occupancies Which FM Global Has an Interest in Protecting with Water Mist Systems 3. Underwriters ANSI / UL 2167, Proposed First Edition of the Standard for Water Mist Nozzles for Fire Laboratories Inc. Protection (UL) Northbrook, IL Service, June 1998 [159] Machinery Spaces Passenger Cabin Fire Tests Passenger Cabins Greater Than 12 m2 Public Space Fire Tests Residential Area Fire Tests Light Hazard Area Fire Tests Ordinary Hazard I and II Tests Nozzle Construction Design, Marking, and Performance Requirements (continued)
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Table 46.1 (continued) Agency 4. Verband der Schadenversichen e. V. (VdS) Cologne, Germany
Water mist fire test protocol VdS 2498 Guidelines for Water Extinguishing Systems Requirements and Test Methods for Fine Spray Nozzles, August 1996 [160] Fine Spray Nozzles for Cable Conduits Fine Spray Nozzles for Engine Test Cell VdS Safety Concept for Road Tunnels: VdS 3502—Leaflet on Fire Protection in Road Tunnels, VdS-Draft 16.10.2006 VdS 2562en, “Guidelines for Extinguishing Systems, Procedure for the Approval of New Extinguishing Techniques”, 1998-xx (01); VdS Schadenverhu¨tung GmbH, Cologne, Germany [161]
an ad hoc test program and a formalized test protocol conducted by a listing organization is the range of expertise and opinions involved in identifying failure conditions and criteria for judging acceptability of the equipment or system being evaluated. Worldwide, many ad hoc water mist test programs have taken place and continue to be undertaken. Examples include local application systems [25], high-voltage cable tunnels [162], railway tunnels [163, 164], heritage properties [165], libraries and archival storage on fixed shelving [166, 167], electronic equipment rooms [168], computer room underfloor areas [48], aircraft cargo bays [169], and outdoor transformers [170]. Water mist standards, such as NFPA 750, provide guidance on what to include and how to develop a meaningful protocol for a specific hazard. Key factors to consider in the development of such a protocol include the following: • The test protocols are to be based on a fire protection engineering evaluation of the fire hazard, the compartment conditions, and the performance objectives for the system. • The test protocols are to be developed, carried out, and interpreted by recognized fire testing laboratories. Specific to the fire test scenario of the ad-hoc protocol, the following factors should be considered: 1. Simulate the compartment conditions and fuel type and geometry (volume, height, width, and elevation of ventilation and exhaust openings). 2. Provide capability to vary the ventilation conditions to determine sensitivity of the performance to ventilation factors. 3. Select the fuel arrangement that simulates the expected combustibility and fire growth rate.
This may require conducting a review of the end users’ facilities to establish a realistic fuel geometry. Obtain enough fuel packages to do repeatable tests. 4. Establish meaningful and measurable performance objectives appropriate for the risk. 5. Develop an experiment plan to test the range of parameters for the water mist system design: nozzle selection, cone angle, K-factor, operating pressure (hence, flow rate), nozzle locations, spacing, and orientation. Formalized listing protocols such as VdS 2562 [161], which is referenced in Table 46.1, describes a methodical approach to the approval of new extinguishing techniques similar in principle to that described in NFPA 750. Test protocols developed in the above manner for ad hoc testing may eventually become formalized protocols and the basis of a listing. All details of the test must be accurately documented so that the test can be repeated (by others) in the future. The full listing process culminates in the following outputs: • A report showing the results of the fire tests; • A report summarizing the results of the component evaluations intended to verify the functionality, durability, corrosion, and environmental resistance of the key components; and, • A design and installation manual explaining the correct application, installation, and maintenance of the specific equipment. The nozzle characteristics; spacing between nozzles and maximum distances from walls, ceilings, or obstructions; minimum operating pressures; and water supply requirements are all documented in the manual.
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Water Mist Systems in Tunnels One of the most active areas involving the development and application of water mist systems has been for highway road tunnels. Until recently, the European and North American standards [171–175] pertaining to fire safety in highway tunnels were opposed to the use of active water-based fire suppression systems in tunnels. To give an example, Annex D of the 2004 edition of NFPA 502, Standard for Road Tunnels, Bridges, and Other Limited Access Highways [171], listed the objections to the use of water-based suppression systems long believed to be unassailable truths by the tunnel fire safety community. The information in NFPA 502-2004 echoed the European equivalent standards, PIARC-1999, “Fire and Smoke Control in Road Tunnels [173].” These documents included statements such as “water spray will cause explosions in petrol”; “vaporized steam can hurt people”; and “visibility is reduced due to de-stratification of the smoke layer.” Appendix 4 of NFPA 502-2004 went on to recommend that sprinklers definitely not be installed in tunnels, except possibly for tunnels involving dangerous or hazardous cargo, but even for that risk the advice was to carefully consider the advantages and disadvantages of such systems. After a series of serious highway and rail tunnel fires that occurred between 1995 and 2005, which resulted in a large number of casualties and financial losses totaling in the billions of dollars [176], road tunnel authorities have reconsidered their reluctance to use active water-based fire suppression systems in tunnels. NFPA 502-2004 and PIARC-1999 represented a different understanding of the fuel loads involved and suppression processes available, and the overall risks. Some of the conditions described the standards might be valid for a fleeting moment in a developing fire scenario, but they neither take into account the rapidity with which fire may progress from incipient to “uncontrollable”, nor do they consider the catastrophic scale of the consequences of an unmitigated fire in a highway tunnel. When one considers that
J.R. Mawhinney and G.G. Back III
uncontrolled fire in the Mont Blanc tunnel burned for more than 50 h, involved hundreds of vehicles over a 500 m length of tunnel, caused catastrophic damage to the tunnel structure that cost billions in repair costs and lost revenue, and 39 fatalities [176], the concern about de-stratification of the smoke layer during the first 5 min of a fire is put into perspective. Conventional practice for fire protection in highway and railway tunnels has been to rely on ventilation to mitigate the hazard associated with fire in a tunnel by attempting to control the flow of smoke. Refractive coverings are applied to concrete and other structural elements to protect against severe time-temperature exposures [176]. To aid in the design of such safety measures, NFPA 502 provides guidance on the expected fire size for different types of vehicles, or which “time-temperature” curve and duration to use for structural protection. For design of tunnel ventilation systems and determination of the critical velocity needed to control smoke conditions, NFPA 502-2004 indicated that a “bus” results in a heat release rate (HRR) of 20 MW; and a heavy goods vehicle (HGV) fire could achieve 20–30 MW [171]. These designfire sizes were shown to be significant underestimates of the probable size of fires in large vehicles as a result of full-scale fire testing carried out in the Runehamar test tunnel in Norway. The Runehamar tunnel was instrumented to measure heat release rate during the fires [177, 178]. Results reported by Ingason and Lo¨nnermark indicated that HGV’s carrying standard household furniture could create fires of 150–200 MW in a tunnel fire scenario [178, 179]. This new information suggested that tunnel ventilation systems and structural fire protection based on a grossly underestimated fire size of 20–30 MW fires could prove inadequate in the event of a HGV fire in an existing tunnel. As a result of the Runehamar tests, NFPA-502 2008 Edition [172] and PIARC-2008 [174] now indicate much larger estimated heat release rates are to be used in the design of tunnel safety systems. These influential documents have also removed the language discouraging the use of fixed fire fighting systems. Many tunnel
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structural engineers now recognize that installation of fixed fire fighting systems should be (re)considered for existing tunnels as a means to reduce fire severity so that existing ventilation systems and structural protection can survive a foreseeable fire [180]. Since 1997, a number of fire test programs have been carried out in Europe to determine design criteria for water mist systems for tunnels [181–183]. Fire tests carried out in 2003 and in 2005 in the Hagerbach test facility in Switzerland [181] involved the burning of standard passenger cars arranged to simulate an accident involving three vehicles surrounded by stationary vehicles. The tunnel outlet was instrumented to permit measurement of heat release rate of the fires. The ventilation air velocity was initially 6 m/s, but after ignition the wind velocity dropped to 3 m/s over a 2-min period. The reduction simulated the reduced piston effect as vehicles in the tunnel come to a stop on encountering the accident. Fire in the group of three vehicles typically achieved 15 MW in 7 or 8 min, then rapidly grew to 30–35 MW as the first fuel tanks ruptured. Fuel from the ruptured fuel tanks flowed downslope in the tunnel but was easily extinguished by the water mist system, primarily due to the water mist cooling the fuel as it spread into a thin layer on the roadway. Once the water mist system was activated, the fire in the three vehicles first involved was controlled to 5–7 MW, which gradually diminished as fuel
inside the vehicles was consumed. The fire did not spread to adjacent vehicles. In cases where flames impinged on target vehicles about 1 m away, fire did not become established in the interiors even when the windows were breeched by heat, as illustrated in the photographs in Fig. 46.7. When the windows fell out, water mist entered the passenger compartment and soaked the plastic and fabric surfaces. Fire was limited to the three vehicles initially involved in the simulated accident. Although fire did not propagate to the adjacent vehicles, conditions inside the vehicles shown in Fig. 46.7 photographs (a) and (b) would not have been “tenable.” Claims have been made by some proponents of water mist systems that water mist provides a “scrubbing” benefit that may improve visibility and create “breathable” conditions in tunnel fires [184, 185]. If we understand tenability to be a function of temperature, soot concentrations affecting visibility, the toxicity of combustion gases such as carbon monoxide, and the duration of exposure, it is primarily the temperature component that is mitigated by the water mist. A fraction of the carbon soot may be washed out of the smoke and some of the soluble gases may be absorbed by water, but not to the extent necessary to render the environment tenable [186]. This dangerous overstatement of the effect of water mist on smoke has been disproven repeatedly in fullscale fire tests.
Fig. 46.7 Photographs showing the benefit of a water mist system in preventing fire propagation to adjacent vehicles in a passenger car tunnel [181]. With three
vehicles fully involved in fire, fire did not propagate into adjacent vehicles because of the wetting and cooling effects of the water mist
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Fire tests conducted in the San Pedro de Anes test facility near Oviedo in Spain in 2006 confirmed the satisfactory performance of water mist systems in mitigating fire in HGV’s [182]. The fuel package consisted of European wood pallets stacked 2.5 m high, 2.5 m wide, and up to 14 m long on a platform, simulating a fully loaded trailer of a heavy goods transport vehicle. There was enough fuel in the fuel array to support a fire of 70 MW or larger if unsuppressed. The water mist system was typically activated when the fires were between 15 and 20 MW and growing. Over a total of 11 tests, the water mist system prevented the fires from growing to their full potential—reducing the peak heat release rates to 50–60 % of their maximum potential. At a distance of less than 10 m downwind of a fire with a sustained heat release rate (HRR) in the range of 20 MW, ceiling temperatures were less than 100 C. Except in a small zone of flame impingement immediately over the fuel array, gas temperatures were too low to be a threat to the tunnel lining. Fire did not spread to targets located 5 m away from the vehicle [182]. Furthermore, the reduced temperature of the combustion gases made it possible for an air velocity of less than 2 m/s to overcome the backlayering of the smoke and heat [187]. In spite of the fact that there was a sustained 20 MW fire in the tunnel, due to the cooling provided by the mist engulfing the flames, the thermal impact on the tunnel was nothing like what would occur with an uncontrolled 20 MW fire. The very large simulated HGV fires used in current testing are highly dynamic and rather unpredictable. Large variations in local temperature conditions may occur from one test to the next, under apparently similar conditions. In spite of some unpredictability of spot temperature readings in the near-field of the fire, the water mist consistently reduced the combustion gas temperatures to below the threshold for ignition of targets or thermal damage to concrete, within 5–10 m from the fuel array. It is important to avoid setting performance criteria based on single point measurements, such as a maximum temperature at a particular distance from the fire or elevation in the tunnel. Judgments about
J.R. Mawhinney and G.G. Back III
adequacy of the fire protection system should reflect the overall ability of the mist system to reduce fire severity [187]. The performance evaluation of a fixed fire protection system should recognize the macro-benefits of cooling and preventing fire propagation to surrounding vehicles, thus protecting the structural elements from catastrophic thermal damage. The benefits should not be viewed as limited to property protection, however. Sprinkler systems are installed in industrial buildings ostensibly for property protection objectives, yet it is widely recognized that there are very few multiple life loss fire events in sprinklered buildings including those that are industrial in nature [188]. This is because the sprinkler system provides a degree of fire control or fire suppression within the time period necessary for occupants to escape, and can prevent the fire from escalating into a lifethreatening event. The same logic should apply to fixed fire fighting systems in tunnels: preventing a fire from escalating to uncontrollable intensity reduces the risk to life of persons trying to escape the fire as well as to fire fighters attempting to approach and suppress the fire. Water mist systems in tunnels are typically open nozzle, deluge-type systems divided into approximately 30 m long zones controlled by a deluge valve. The water supply is designed so that three zones can be activated simultaneously. It is intended that a fire detection system will locate the fire source accurately and automatically activate the water mist system in the zone where the fire is located, plus one zone upstream and one zone downstream. Very seldom do the fire test protocols for water mist systems include testing the ability of the detection system to reliably locate the source of the fire within a given timeframe. In principle, the efficacy of the detection system should be evaluated as part of the performance testing of the system. There are many difficulties inherent in pinpointing the source of heat, smoke or flame in the dynamic, turbulent and dirty environment typical of roadway tunnels. There is some debate about what the fire size could be when the water mist system is activated in a real roadway tunnel fire scenario. The fire
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size will likely depend on the sensitivity of the detection system and the administrative policy regarding manual activation of the suppression system. It is this author’s opinion that activating the water mist system will be beneficial at any stage, although it is obviously preferable to do so before damage to critical infrastructure occurs. The most important performance requirement of the detection system is to locate the fire so that the correct water mist zones may be activated. The benefits of the water mist system can be fully realized even if applied when the fire has reached 15 or 20 MW. HGV fires are likely to reach such intensity within 5–10 min. With 20–25 m long water mist zones and an appropriately designed and coordinated detection and releasing strategy, the fire should not activate any more than the three zones allowed for in the hydraulic design of the water supply. It should be relatively straightforward for any detection technology to detect and accurately locate a fire as large as 15 MW in a tunnel. There may be advantages in being able to detect smaller fires in order to initiate emergency response in a tunnel, such as traffic control and dispatch of emergency personnel, but there is little advantage in imposing an unnecessary requirement to detect very small fires on the detection system controlling release of the water mist system. Any gain in ability to detect smaller fires is likely to be at the cost of reduced reliability in determining the location. A research project to evaluate fire detection technologies for highway tunnels, coordinated by the National Fire Protection Research Foundation and the National Research Council, Canada, was completed in 2007. A part of the study included monitoring four trial detection technologies over a 10-month period in the Lincoln Tunnel between New Jersey and Manhattan, NY. Detection technologies for the study were selected based only on the willingness of the manufacturers to fund their own participation in the study. One optical flame detector, two video imaging detection systems, and an air sampling detection system were evaluated. One finding of the study was that the systems were prone to generating “nuisance” alarms, or their overall reliability in being able to detect the fire source
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was adversely affected by the grime and other effluent that is characteristic of roadway tunnel environments. At the end of 10 months all of the systems were tested in a fire demonstration. Test fires were approximately 1–2 MW maximum HRR and were ignited inside a passenger van with windows. The two video imaging systems did not detect any of the demonstration fires, whereas the optical detection and the air aspirating systems detected most but not all of the test fires [189]. The NFPRF study did not include any linear heat detection, which is widely specified for tunnel fire detection in Europe and Japan. Linear detection is resistant to the grimy conditions of the tunnel environment. However its ability to accurately locate the fire at high ventilation air velocities can be questioned. It should further be noted that the tunnel fire testing that has been conducted in Europe has focused on the hazard presented by HGV fires, which can reach a HRR in excess of a 20 MW relatively quickly. The detection tests based on 1–2 MW fires are perhaps pertinent to fires in passenger automobiles, which do not typically result in catastrophic damage to tunnels. More research is needed on selection and evaluation of appropriate fire detection technologies to integrate with water mist systems. However, most highway tunnels that are candidates for installation of fixed fire protection systems are equipped with closed circuit television monitors, control room and trained operators. Where CCTV monitors are present, manual activation of the water mist system by a tunnel operator can be an acceptable alternative to automatic detection.
Engineering Details of Water Mist Systems Types of Water Mist Systems Requirements to conduct performance-based testing of water mist systems result in an assessment of the fire fighting capabilities of the system, and promote the evaluation of new types of hardware and assemblies. This testing has
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increased the rate of introduction of new equipment and fire control concepts to the generally conservative field of fire protection systems design. Hardware borrowed from non-fire industries (such as positive displacement pumps from the petroleum industry and hydraulics field), and from gaseous fire protection system hardware, can be component tested and receive the equivalent of an assembly approved for fire protection as part of the process of satisfying the testing protocol. Positive displacement pressure pumps, pressure regulating or unloading valves, compressed gas driven equipment, pneumatic and hydraulically actuated deluge valves, high pressure valves, piping and tubing, as well as tube bending and piping support methods not previously employed in fire protection systems are now available. Fire protection engineers need to understand the associated hardware in order to design, specify, test and commission new types of systems. A few of the engineering design and evaluation concepts that have been introduced as a result of water mist system research and development are described below. Water mist systems can be categorized based on several distinguishing factors. The four most important from a systems engineering perspective are (a) the mode of application of the mist, (b) method of spray generation (c) the pressure regime, and (d) the means of providing the necessary system flow and pressure. There are several subcategories of systems, each with its own specific technical features, such as single-fluid and twin-fluid systems, and constant pressure versus decaying pressure discharges. The mode of application refers to how the system is intended to develop and deploy the mist within a given space or environment, and includes total compartment application (TCA); local application (LA), and zoned application (ZA) systems. With regard to pressure regimes, water mist systems distinguish among Low, Intermediate and High Pressure systems. The means of providing the necessary flow and pressure distinguish between the general categories of pumps either electric or gas driven, or some arrangement of compressed gas cylinders. The latter category can be further divided into systems
J.R. Mawhinney and G.G. Back III
that operate at a constant pressure, similar to a pumped system, versus those that have a declining pressure.
Mode of Application Water mist systems can perform well in enclosed compartments where the confinement of heat, water vapor and the oxygen depletion caused by the fire can contribute to the extinguishment of even shielded fires. However, it is not the case that water mist systems only work well in enclosed compartments. They also provide fire control benefits in the open air, and in large, wellventilated spaces such as tunnels. If the compartment is very large relative to the size of the fire, enclosure effects are diminished, and more attention must be paid to projecting water mist to the seat of the fire and wetting or cooling the flame and the surrounding fuels and surfaces. TCA systems consist of open nozzles distributed throughout the compartment according to the manufacturer’s spacing rules. Water is discharged from all open nozzles on opening of a control valve in the same manner as a deluge sprinkler or water spray system. TCA systems benefit from enclosure effects (capture of heat, confinement of water vapor, and recirculation of oxygen-depleted gases) to varying degrees, depending on the size of the compartment. However, TCA water mist systems can accomplish extinguishment with fairly large openings in the compartment, which is not the case with gaseous total-flooding agents [73]. On the other hand, it is not enough to inject a fixed quantity of mist into a compartment, close the door, and expect the fire to go out immediately. The amount of time needed to extinguish a fire varies according to the compartment volume and the size of fire [83]. Water mist must be injected continuously for a sufficient length of time to bring about control, and the fire must generate enough heat to convert water droplets into water vapor and sustain a relatively high water vapor concentration. The extinguishment time of a hydrocarbon fire can be predicted approximately on the basis of a ratio of HRR to volume
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(MW/m3) ratio, and it has been expressed that there will be a fire size that is too small to be extinguishable [83]. It is generally intended that TCA water mist systems be activated automatically by a fire detection and releasing system. In some marine or military applications, however, manual activation of the system is permitted. Some caution should be observed in the design of a system intended to be manually released. If there is a long delay in activation, the combustion gas layer in the compartment may become quite hot and deep. The empty piping may become so hot that water will boil explosively when water is introduced, potentially rupturing some types of piping systems. If the piping survives, the sudden introduction of water mist into a hot gas layer may result in a very rapid cooling, which creates a strong negative pressure in the compartment. In some experimental work a negative pressure spike of minus 1700 Pascal was measured, which resulted in violent damage to the walls of the test structure [46]. The total water discharged by a TCA system in a large space must be considered. Water mist systems require much less water than sprinkler deluge systems, but they still discharge water which must be collected and treated. On Alaska’s North Slope, machinery modules up to 1500 m3 in volume, may be protected by TCA water mist systems. State of Alaska environmental regulations require that all of the water discharged in the enclosure must be captured and removed to a waste-water treatment facility. The water cannot be simply drained into the natural environment. The retention and removal of runoff from a total compartment application system must be considered as part of the design of the system. TCA systems may be designed for a range of objectives. The IMO machinery space systems are required in the IMO test protocol to completely extinguish most test fires in a specified period of time (15 min). On the other extreme, TCA systems have been installed in Norwegian historic wood stave churches to achieve flashover suppression [43, 165, 167] at much lower flow rates. For flashover suppression a fine mist is injected into the upper portion of the
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compartment to cool the fire gases and reduce thermal feedback to the objects in the compartment, which prevents flashover from occurring. The amount of water that strikes the art on the walls is minimized. Extinguishment of the source fire is achieved by installing nozzles at floor level that discharge water spray at a much higher rate than the ceiling nozzles, without damaging the treasured wall paintings. The lower nozzles are local application nozzles that work in concert with the total compartment system. LA systems are designed to discharge directly on an object or hazard in an enclosed, partially enclosed, or open area. Since there will be no confinement of heat, water vapor, or vitiated gases, extinguishment will depend largely on gas phase cooling or wetting of the fuel. To achieve extinguishment requires projection of mist to all areas in which fire can persist. Local application systems do not necessarily need to be designed to achieve extinguishment. The discharged water mist can act as a screen to block radiant heat transfer, mitigating fire spread or limiting damage to surrounding materials. Local application systems are considered necessary compliments to a TCA system in some machinery room systems on ships [157] and in industrial process buildings. The compartment ceiling may be so high that low level equipment must be surrounded with local application mist nozzles to facilitate fire control. Local application systems may be installed around specific hazards such as diesel engines, flammable liquid or vapor compressors, or large turbines in an open floor area [190]. The IMO prepared IMO MSC/Circ. 913 test protocol for fixed water-based local application systems for marine machinery spaces [156]. FM 5560, FM Global’s water mist testing standard, has test protocols for local application water mist systems for industrial food processing burners, deep-fat fryers, outdoor transformers, flammable liquid storage racks, and other special equipment [158]. VdS in Germany has test protocols for local application systems for engine test cells and electric cable tunnels (see Table 46.1) [176].
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As discussed for TCA systems, choice of fire detection and system activation strategy for local application systems is an important part of the design of the system. Some systems are intended to be manually activated, whereas others incorporate special detection equipment for automatic activation. The detection system, release, and delivery equipment must be matched to the conditions dictated by the hazard. ZA systems are designed to protect hazards in a portion of an enclosure, eliminating the need to flood the entire compartment. The concept intends that multiple zones surrounding the fire location will be activated, such that the fire area will be totally engulfed by mist in a manner similar to a deluge system. The incentive for zoning a system is to reduce the overall water flow requirement to a fraction of that required for total compartment flooding. Recent testing conducted to develop water mist systems for highway tunnels has confirmed the satisfactory fire control performance of zoned water mist systems [181–183]. The water mist system is divided into zones up to 32 m long, each controlled by a local deluge valve. The water supply and pumping capacity are designed to support the activation of three complete zones: the zone in which the fire is located and one zone upstream and one zone downstream. Clearly it is essential that there be either a fixed fire detection system that is suitably precise to correctly locate the fire, or a CCTV system monitored by trained operators with authority to activate the system manually. Experience with thermally activated sprinklers or nozzles in tunnels has shown that heat from a fire will travel along the ceiling and open sprinklers or nozzles faster than can be controlled by the resulting water discharge. The risk is that more sprinklers may be opened than can be supported by the water supply. For this reason, zoned deluge water mist systems are preferred because the water supply can be designed to supply a fixed, pre-determined number of nozzles, an attractive option for protecting tunnels [183]. It is essential of course that the zones that are opened completely envelope the source of the fire. Thermally activated nozzles
J.R. Mawhinney and G.G. Back III
(automatic nozzles) have been used in conjunction with a ZA system, to further reduce the amount of water required by the water mist system. Every second nozzle on a line is thermally activated and covered by a protective cap, with an open mist nozzle inbetween. Three zones of nozzle lines are activated by the detection system as for a normal zoned deluge system. There is enough water mist distributed to prevent “runaway” activation of the thermally activated nozzles as hot gases flow along the tunnel prior to activation of the mist system. Once detected and located by a separate detection system normally used in the tunnel, the appropriate zones are activated. The protective caps in the activated zones are released by water pressure, exposing the thermal elements. Then in the hottest areas directly surrounding the fire, the thermally activated nozzles activate and effectively double the mist application rate over the fire. This patented concept has been tested by Marioff Corporation and shown to be as effective at controlling temperatures as the full deluge system, with approximately 60 % of the water discharge rate. The proper performance of a zoned application water mist system depends critically on the performance of the detection system. Testing of the ability of the detection system to determine the fire location and actuate the correct zone should be made part of the approval test protocol for such systems. Automatic Sprinkler Alternative Water Mist Systems are a fourth category of mode of application, which is that of a water mist system with closed, thermally activated (automatic) nozzles installed throughout a building in the same manner as a conventional sprinkler system. IMO has long accepted water mist systems with automatic nozzles as equivalent to marine sprinkler systems. Such systems are installed throughout accommodation and public spaces on most passenger ships. It is not surprising that there is interest in providing similar systems in landbased applications. In a number of jurisdictions in Europe, water mist systems have been installed in hotels and office buildings in lieu of conventional sprinkler systems. The concept is
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now recognized by the NFPA 750 committee. A new definition has been approved for publication in NFPA 750, 2013 Edition, which defines an “Occupancy Protection System” as “a water mist system utilizing automatic water mist nozzles installed throughout a building or portion of a building and intended to control, suppress or extinguish a fire.” The question that remains to be explored is whether the building and fire regulations, which provide substantial trade-offs in building construction requirements in recognition of the benefits of automatic sprinklers, will apply those benefits to water mist systems designed and installed as an automatic sprinkler system alternative. At the present time (2012) water mist systems do not have as broad a range of approval tests as conventional sprinklers. Generic prescriptive design and installation criteria, and standardized listing evaluations exist for conventional sprinkler systems for light hazard to extra hazard applications. Such is not the case for water mist systems, which rely upon manufacturer specific design and installation criteria, and performancebased listing criteria for light and ordinary hazards (OH1 and OH2),. However, efforts are underway to expand testing of water mist systems against as many hazard scenarios in buildings as for sprinkler systems, so that the benefits associated with conventional sprinkler systems can be extended to water mist systems. Pre-engineered versus engineered systems. A pre-engineered water mist system is one that has been developed for a hazard of a limited size and consistent features defining the compartment. For example, a water mist system may be tested in a test structure of a certain volume to represent a turbine or diesel engine enclosure, with specific ceiling height, obstructions, ventilation openings, and fire scenarios. The detection time and the size of fire on detection will be largely predictable. The number of nozzles, their locations, the amount of stored water required for the required duration of flow, and the diameters and maximum lengths of pipe or tubing are all determined by the test protocol. The installer need only match the nozzle spacing
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and stay within the limits specified for pipe diameter and length of run to install the system properly. No engineering calculations are required to ensure that nozzle pressures are adequate or that flow rates and water storage volume are sufficient for the hazard. Pre-engineered should not be taken to mean fool-proof or “no engineering required.” Pre-engineered water mist systems are sometimes improperly installed and maintained. In the international off-shore oil industry, for example, pre-engineered water mist systems are widely used to protect small turbine enclosures. The nature of the contracting environment is such that installers of the fire protection systems often work for a general piping contractor that is approved to work in the particular oil field, as opposed to a fire protection specialist familiar with the intricacies of the water mist system. Errors that can occur and have occurred, are many. The volume of the enclosure may be outside the limits of the pre-engineered system listing. Nozzles may be improperly placed or oriented; tubing diameters and lengths may be incorrect; the water storage unit may be located too far from the hazard, and specialty pneumatic releasing valves may be improperly set up. The interlocks to accomplish automatic release of the water mist and shut down the fuel pumps and ventilation may not be complete and may never have been tested. The inspecting engineers from the production sector do not have the experience necessary to inspect the systems and identify the faults. Annual maintenance may be performed by personnel unfamiliar with the system hardware, so that the installation faults never get corrected. It is not surprising that fires have occurred in which the pre-engineered system failed to operate. Engineered systems, on the other hand, are designed in the same manner as traditional sprinkler or water spray system, based on criteria in the manufacturer’s design, installation, operation and maintenance manual. The designer applies nozzle spacing rules, pipe or tubing and water flow requirements to a variety of compartment sizes and fire hazards. The pump or compressed gas supply is dimensioned to be able to satisfy
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the calculated flow and pressure requirements. An engineer must perform hydraulic calculations to confirm that minimum nozzle pressures and system flow rates are achieved. Problems such as those listed above may still occur during installation, but an engineered system is likely to receive a higher level of construction supervision, acceptance testing and maintenance, than a pre-engineered system.
Methods of Spray Generation There are numerous ways to generate atomized sprays [41]. Water mist system equipment manufacturers have staked out and filed patent applications for their preferred means of mist generation. Research in the spray and atomization literature discusses exotic technologies such as electrostatic sprays, nebulizers, and ultrasonic devices [27]. However, not all atomization processes are practical for fire protection systems. Some techniques are only suitable for mass flows of milligram/second with projection distances measured in millimeters, whereas sprays suitable for water mist fire suppression systems must have mass flow rates in the kilogram/second, with projection distances measured in meters. Suitable nozzle types include multi-orifice pressure jet nozzles, impingement nozzles, and twin-fluid nozzles. Mass flow rates are typically measured in the range of 0.033–0.667 kg/s (2–40 L/min). Cone diameters and projection distances are typically measured in meters. The atomization process must be sustained for tens of minutes in most cases. This section will highlight some of the engineering features of interest associated with different methods of generating water mist. Twin-fluid nozzles. Twin-fluid water mist nozzles involve combining two independent streams of fluid, one of water and one of compressed gas, at a nozzle to generate finely atomized spray. By combining the energy stored in the compressed gas with a water stream, finely atomized sprays can be produced at relatively low water pressure. Twin-fluid nozzles generally have separate piping networks for water and compressed gas,
J.R. Mawhinney and G.G. Back III
which join at the nozzle. They provide a high degree of adjustability between the balance of liquid and gaseous streams—hence, they can be tuned to maximize the quality of the spray. On the small-scale twin-fluid nozzles provide excellent control and versatility in spray production. On the larger scale necessary for general fire protection, practical limits to their applicability are encountered. Designing the piping systems for both liquids involves trying to balance the airto-liquid mass ratio (ALR) (ratio of the mass flow rate of air to the mass flow rate of water) at each nozzle throughout the discharge. Twin-fluid nozzles can utilize larger orifices than pressure jet nozzles, and are therefore somewhat less vulnerable to plugging. On the negative side, twinfluid nozzle systems require storage and delivery of media with distinctly different engineering characteristics. Calculations must be done for both compressible and incompressible fluids in two distribution systems. A suggested approach to balancing the distribution of atomizing medium with the water flow is provided in Mawhinney [191]. The NFPA 750, 2013 Edition expands the definition of twin-fluid system to include those that combine both the water and the compressed gas in one piping system. One manufacturer has produced a reciprocating pump driven by compressed nitrogen that discharges water and nitrogen into the piping system. The friction losses in the distribution piping cannot be calculated using either incompressible liquid flow equations (normal hydraulics) or compressible flow equations. Nor is the mix a “two-phase flow” because the mix consists of two fluids, not two phases of the same fluid. The engineering of such systems, including the dimensioning of piping, confirmation of end nozzle pressures, and ensuring balanced discharge through nozzles close to the source and those far from the source, not to mention comparable discharge duration of both water and compressed gas supplies, depends almost entirely on empirical data. Single-fluid nozzles discharge water only. Most water mist systems utilize single-fluid nozzles. The water is ejected through one or
46
Water Mist Fire Suppression Systems
1625
more orifices and either disintegrates into mist due to velocity differences between the water jet and the surrounding air (pressure jet nozzles) or disintegrates into small particles on impact against an impingement surface such as a deflector plate (impingement nozzles). A more in-depth discussion of the physical mechanisms involved in atomization can be found in Lefebvre [41] and of common water mist nozzles, in Mawhinney [191]. Manufacturers of nozzles for industrial applications have catalogs filled with different nozzle designs, delivery rates, and cone shapes. They have been manufacturing a wide range of nozzles for many years. It is surprising, therefore, how much money and effort have gone into the custom design of nozzles for water mist systems by fire protection specialists. The water mist system manufacturers have developed their preferred nozzle design through in-house research and development. Some off-the-shelf commercial nozzles have been successfully applied in water mist systems, but have required customized selection of individual orifice sizes [23, 33].
spray, so that 30 cm away from the discharge orifice, the mist temperature may be 35 C or less [193]. The flashing process does not require a nozzle—simply an open orifice—and it results in a rapid distribution of mist plus fog throughout the protected space. The condensed fog is similar in particle size to NanoMist, that is, an order of magnitude finer than can be achieved by mechanical generation of spray. The phenomenon is very dynamic and allows for the rapid distribution of “fog” and water vapor throughout a space. Fullscale fire suppression tests carried out by Mawhinney et al. [193] determined that the ultrafine mist was not more effective than other mists at extinguishing pool fires in enclosures. It was suggested, however, that its success in dust explosion mitigation may be due to the high mass fraction of very small (~20 μm), closely spaced droplets, suggested by Zalosh [40] to be a prerequisite for explosion mitigation with water mist. Further experimental work is required to validate its potential for vapor-air explosion mitigation [194].
Mist generation by flashing of superheated water. Evidence that water mist with sufficiently small drop sizes may quell a dust explosion is found in work conducted at the Irish agricultural research facility involving dusts of dried milk products [192–194]. The mist-generating method involves the flashing of superheated water released from a self-pressurized container [195]. Water is superheated to 175 C in a closed container up to 70 L (18.5 gal) in volume. As steam tables indicate, this puts the closed container at a pressure of approximately 10 bar (145 psig). When released to atmospheric pressure through a fast-opening valve, a percentage of the water flashes directly to vapor phase and then condenses into fog-sized particles (600 C, σ yT ¼
340 0:34T σ y0 T 240
690 0:69T E0 ET ¼ T 53:5
ð53:5; 53:6Þ
For any temperature of interest, αT ¼ ð0:04T þ 12Þ 106
ð53:7Þ
where σyT ¼ Yield strength at temperature T (MPa) (psi) σy0 ¼ Yield strength at 20 C (68 F) (MPa) (psi) 593 (1100) ET ¼ Modulus of elasticity at temperature 538 (1000) T (MPa) (psi) 649 (1200) E0 ¼ Modulus of elasticity at 20 C (68 F) a Maximum temperature cited refers to the maximum tem(MPa) (psi) perature rise above initial conditions αT ¼ Coefficient of thermal expansion at temperature T (m/m C) T ¼ Steel temperature ( C) 8 Alternatively, values of the yield and tensile ð0 T < 650 CÞ 0:51T þ 420 > > > > strength and modulus of elasticity at elevated > > > < 8:65T þ 4870 ð650 C < T 725 CÞ temperature are included in Appendix 4 of the cs ¼ AISC Specification [19], and BSI 5950 [20]. In > > 10:9T þ 9340 ð725 C < T 800 CÞ > > addition to the changes in material properties that > > > : occur at elevated temperatures, the crystalline 578 ð800 C < T Þ½J=kg:K structure of steel also changes, as noted in Fig. 53.3 [21]. However, for the low-carbon ρ ¼ 7860 kg=m3 steels typically used in building construction, ð53:2Þ significant changes in crystalline structure begin to occur only at temperatures in excess of 650 C The influence of temperature on the mechani- (1200 F) [22], above the endpoint temperature cal properties of A36 steel is presented in noted in the standard test. Fig. 53.2. At 538 C (1000 F) the yield strength Creep, the time-dependent deformation of a is approximately 60 % of the value at normal material, may be significant in structural steel at room temperature. temperatures in excess of 460 C (860 F) [23]. Mathematical expressions describing the The rate of creep increases approximately relationship of the yield strength, modulus of 300 times for ASTM A36 structural steel when elasticity, and coefficient of thermal expansion the steel temperature is increased from 460 to on temperature are [8, 17, 18] 520 C (860–968 F). In-depth discussions of 593 (1100)
1914
J.A. Milke
Fig. 53.2 Temperature effects on properties of ASTM A36 steel [13, 16] Proportion of property at ambient temperature
1.0
0.8
0.6
0.4 Modulus of elasticity Yield strength
0.2
0
0
100
200
300
400
500
600
700
Temperature (°C)
creep have been prepared by Harmathy [24, 25]. Because of the complexity in addressing creep explicitly, given its dependence on the stress level, rate of heating, and other factors, often creep is included implicitly in the mechanical properties to simplify the fire resistance calculations [16, 23]. One exception to this approach was in the NIST study of the collapse of the North and South Towers of the World Trade Center. In their study, Gross and McAllister proposed that creep was a significant factor that led to the collapse of the towers [26].
Methods of Protection The basic intent of the various methods of protection is to reduce the rate of heat transfer to the structural steel. This is accomplished by using insulation, concrete filling, membranes, flame shielding, and heat sinks.
Insulation Insulation of the steel is achieved by surrounding the steel with materials that preferably have the following characteristics [27]: 1. Noncombustibility and the added attribute of not producing smoke or toxic gases when subjected to elevated temperatures 2. Thermal protective capability when subjected to elevated temperatures
3. Product reliability giving positive assurance of consistent uniform protection characteristics 4. Availability in a form that permits efficient and uniform application 5. Sufficient bond strength and durability to prevent either dislodgement or surface damage during normal construction operations 6. Resistance to weathering or erosion resulting from atmospheric conditions In addition to the insulating qualities of the protection materials, chemical reactions may occur in the insulation, further reducing the rate of heat transfer. The chemical reactions include calcination, ablation, intumescence, thermal hydrogeneration, and sublimation. Insulating methods include the use of board products, spray-applied materials, and concrete encasement. A brief review of each method is presented below. Board Products Four types of board products are commonly used to protect structural steel: gypsum board, fiber-reinforced calcium silicate board, vermiculite-sodium silicate board, and mineral fiber board. In each case, the means of attachment of the boards surrounding the steel is a critical parameter affecting the performance of the assembly. Two commonly used methods of attachment of gypsum wallboard with and without steel covers are illustrated in Fig. 53.4. Detailed descriptions of the attachment mechanisms for the other board products are
53
Analytical Methods for Determining Fire Resistance of Steel Members
1915
Steel part °C 1600 1536 1500
°F
Carbon content in atomic percent 0
2.3
3.6
4.5
6.6
2912
A 1493C
2732
H
1400 1392
2552
1300
2372
Yellowish white
1200
2192
Light yellow
1146°C 1100
2012
1000
1832
Yellow
Light yellowish red Reddish yellow
911 900
1652
800
1472
Light cherry red Cherry red
(K) 1292
Dark cherry red
700
Very reddish yellow Light red
Dark red 600
1112
500
932
400
752
Brown red Dark brown
300
572
200
392
100
212
0
0
0.5
0.8
1
1.5
2
Gray Black gray Light blue Dark blue Violet Red Yellowish brown Strong yellow Very pale yellow
32
Carbon content in weight percent 0
5
10
15
20
25
30
Cementite content in weight percent
Fig. 53.3 Influence of elevated temperatures versus carbon content in steel [21]
provided elsewhere [29, 30]. Also, board products can be used in wall assemblies to provide an envelope around steel trusses.
Spray-Applied Materials Several types of spray-applied materials are commonly used. These include cementitious plasters, mineral
1916
J.A. Milke
A
A
1 2 3
1 2 3
A
A
No. 8 × 12 in. sheet steel screws. Spaced 12 in. (0.3 m) O.C.
5/8 in. (16 mm)
3/8 in. (9 mm)
/ in. (9 mm) 38
/ in. min. (8 mm)
3/4 in. (19 mm)
5 16
Snap-lock
Pittsburg seam
Lap
Corner Joint Details (A)
1
1
2 7
4 7
A
1 Layer = 5/8 in. (16 mm) or 1/2 in. (13 mm)
B
2 Layers = 11/4 in. (32 mm) or 1 in. (25 mm)
1
1
6 5
2
3
4 7
3
2
3
4
2
3
5 4
C
3 Layers = 17/8 in. (48 mm) or 11/2 in. (38 mm)
7
C
4 Layers = 21/2 in. (64 mm) or 2 in. (50 mm)
Fig. 53.4 Attachment mechanisms of gypsum wallboard to steel columns [29]
fibers, magnesium oxychloride cements, and intumescents. Sufficient data have been obtained to characterize spray-applied cementitious and mineral fiber materials for the purpose of estimating the fire endurance of structural steel protected with these materials. An illustration of
a steel column protected by a spray-applied material is presented in Fig. 53.5. Concrete Encasement Concrete encasement of steel members to surround and insulate the steel is illustrated in Fig. 53.6. As indicated in
53
a
Analytical Methods for Determining Fire Resistance of Steel Members
b
1917
Concrete Filling Concrete filling of hollow steel members can also be used to provide a fire-resistant assembly. The concrete may be plain concrete or reinforced concrete [31, 32].
Membrane
Fig. 53.5 (a) Sprayed insulation; (b) metal lath and plaster encasement [27]
Suspended ceiling assemblies are used as membranes to protect structural steel in floor and roof assemblies. The ceiling panels and tiles comprising the ceiling assembly may consist of gypsum, perlite, vermiculite, or mineral fibers. Gypsum wallboard and other board products also fall into this category of protection. The membrane method of protection is illustrated in Fig. 53.8. Heat transfer to the structural steel is reduced due to the air space above the membrane and the insulating characteristics of the membrane. Also, membranes help prevent the direct impingement of flame on the structural steel.
Flame Shield Flame shields are intended to reduce the incident radiant heat flux on the steel by preventing direct flame impingement. The effectiveness of flame shields to protect exposed spandrel beams was first examined by Seigel [2, 33]. In this instance, 14-gauge sheet steel was used as the flame shield. Fig. 53.6 Steel column with concrete encasement [27]
Heat Sinks Fig. 53.6, the concrete is cast to fill in all re-entrant spaces. Alternatively, concrete column covers may be used, as illustrated in Fig. 53.7. The concrete is assumed to act only to thermally protect the steel. Some empirical correlations implicitly account for the load-bearing capacity of the concrete and possible steel-concrete composite action.
The heat sink approach delays the heating of steel by absorbing heat transferred through the steel. The heat sink approach usually involves liquid or concrete filling of the interior of hollow steel members (tubular and pipe sections). Liquid filling can be used to provide a sufficient level of protection for the columns, without any externally applied coating. The liquid used for
1918
J.A. Milke
a
b
c
h
h2
h2
L
L2
d
L
h
L
h1
bf
h1
Fig. 53.7 Concrete-protected structural steel columns. (a) Square shape protection with a uniform thickness of concrete cover on all sides; (b) rectangular shape with varying thickness of concrete cover; and (c) encasement having all re-entrant spaces filled with concrete
a 8 J2 joists 24⬙ (610 mm) O.C.
Damper protected with 1/16⬙ (1.6 mm) asbestos paper both sides & held open with 160F fusible link
24-gage galvanized steel Air duct 18⬙ w. × 6⬙ dp. × 5⬘–0⬙ lg. (457 mm × 152 mm × 1.5 m)
12 SWG hanger wire
1-1/2⬙ (38 mm) C.R. channel 4⬘ (1.2 m) O.C.
Duct support 1-1/2⬙ (38 mm) C.R. channel
12 ⬙ (305 mm)
3/4⬙ × 12⬙ × 12⬙ (19 mm × 305 mm × 305 mm) K & R Fire-rated mineral tile
12 ⬙ × 24 ⬙ (305 mm × 610 mm) air diffuser
Concealed Z runner 12⬙ (0.3 m) O.C.
Border channel 1-3/8⬙ (35 mm) high with 3/4⬙ (19 mm) flanges
b 2-1/2⬙ (63.5 mm)
A
4-1/2⬙ (114 mm)
1/2⬙ (12.7 mm)
1-1/2⬙ A (38 mm) 12⬙ (0.3 m)
7/8⬙ (22 mm)
1/2⬙ (12 mm)
1/2⬙ (13 mm) Section A–A
7/8⬙ (22 mm)
7/8⬙ (22 mm)
Fig. 53.8 Membrane method of protection [27]. (a) Cross-section of a floor-ceiling system with conventional sheet steel fusible-link damper for protecting typical ceiling outlets in galvanized sheet ducts; (b) sprayed contact fireproofing applied directly to the underside of formed-steel decking and to a supporting steel beam
protection is an aqueous solution. Additives are provided primarily for antifreeze, corrosion protection, and biological reasons.
A diagram of a typical design for a liquidfilled column fire protection system is presented in Fig. 53.9. The components of this system
53
Analytical Methods for Determining Fire Resistance of Steel Members
Fig. 53.9 Schematic layout of a typical piping arrangement used in a liquid-filled column fire protection system [33]
1919
Open vent Zone water storage tank
Pipe loop at top of zone
Solid diaphragm between zones
May be interior or exterior
Pipe loop at bottom of zone
include the hollow structural steel columns, piping to connect the columns, a water storage tank, and associated valves. The system operates on the principle that heat incident on the column is removed by circulation of the liquid. If sufficient heat is delivered to the liquid, boiling can be expected, which enhances the efficiency of the heat removal process. In many tests with liquid filling, steel temperatures have been observed to be well below those required for failure, as long as the column remains full of the liquid. Another heat sink approach consists of filling the interior of hollow steel columns with concrete. If the concrete is reinforced, load transfer from the steel to the concrete can be expected as the steel weakens with increasing temperature. Calculation methods to determine the fire
resistance of concrete-filled steel columns are available [11, 13].
Empirically Derived Correlations Numerous easy-to-use, empirically derived correlations are available to calculate the fire resistance of steel columns, beams, and trusses. The correlations are based on data from performing the standard test numerous times on variations of a particular assembly. Curve-fitting techniques are used to establish the various correlations. In some cases, a best-fit line has been drawn for the data points, whereas in other cases, lines were placed to provide conservative estimates of the fire endurance by connecting the two lowest points [34].
1920
Steel Columns The correlations to estimate the fire endurance of unprotected and protected steel columns are given in Table 53.3. Present in each of the equations is W/D for wide-flange sections and A/P for hollow sections. The W/D and A/P ratios are comparable. The W/D ratio is the weight per lineal foot to the heated perimeter of the steel at the protection interface (or the perimeter of the steel if unprotected). The A/P ratio is the crosssectional area divided by the heated perimeter. Essentially, the W/D ratio relates to the product of the density of the steel and the A/P ratio. The relevance of the W/D and A/P ratios was first noted by Lie and Stanzak [35]. W/D ratios for commonly used wide-flange and tubular shapes for columns and beams are available elsewhere [29, 36–38]. The two factors in the W/D ratio that affect the rate of heat transfer to the steel (and consequently the rise in temperature of the steel) are (1) shape of the fire protection system, D, and (2) steel mass per unit of length, W. The parameter that characterizes the shape of the fire protection system is D, the heated perimeter expressed in inches, which is defined as the inside perimeter of the steel at the fire protection material interface. Figure 53.10 illustrates the method for determining D in four typical cases. As indicated in the figure, the heated perimeter depends on the dimensions of the column and also on the profile of the protection system. Two different commonly used profiles are (1) contour profile, where all surfaces of the steel column are in contact with the protection material; and (2) box profile, where a rectangular box of protection material is built around the column. A large value of W refers to a column with a large weight per lineal foot. A given amount of energy will raise the temperature of the massive column to a lesser degree than that of a light column. Less surface area is available for heat transfer if the heated perimeter, D, is small, thereby inhibiting the temperature rise in the steel. The greater the W/D ratio, the greater the inherent fire resistance of the assembly is.
J.A. Milke
Because steel elements with larger W/D ratios are inherently more fire resistant, substituting shapes with greater W/D ratios for shapes identified in the listed designs in the UL Fire Resistance Directory [3] is permitted while maintaining the same thickness of protection. However, such substitution yields inefficient designs, because shapes with large W/D ratios actually require less fire protection material than shapes with small W/D ratios for the same level of fire resistance. The equation for gypsum wallboard protection is nonlinear. The weight of the gypsum wallboard is included because the heat capacity of gypsum has a considerable impact on the fire resistance of the assembly. The thickness of wallboard required to achieve a particular level of fire resistance as a function of the W/D ratio of the column is presented in Fig. 53.10. Based on an elementary heat transfer analysis for spray-applied fire protection materials, Stanzak and Lie conducted a parametric analysis that resulted in correlations of the following form to estimate the thickness of material required to achieve a particular level of fire resistance [29, 30]: R ¼ ðC1 W=D þ C2 Þh
ð53:8Þ
where R ¼ Fire endurance (min., note: the version in the UL Directory expresses the equation with R in hour.) W ¼ Steel weight per lineal foot (lb/ft) D ¼ Heated perimeter of the steel at the insulation interface (in.) h ¼ Thickness of insulation (in.) The constants C1 and C2 need to be determined for each protection material. The constants take into account the thermal conductivity and heat capacity of the insulation material. Constants for some materials are included in listings in the UL Fire Resistance Directory [3]. Considering the equation for the concrete cover column protection method (see Table 53.3), R0 is the fire endurance of the assembly if the concrete has no moisture content. However, because the fire resistance of concrete cover
53
Analytical Methods for Determining Fire Resistance of Steel Members
1921
Table 53.3 Empirical equations for steel columns [22, 28–30] Member/protection Column/unprotected
Column/gypsum wallboard
Solution
Symbols R ¼ 10:3ðW=DÞ , for W=D < 10 R ¼ fire endurance time (min) R ¼ 8:3ðW=DÞ0:8 , for W=D 10 W ¼ weight of steel section per linear foot (lb/ft) (for critical temperature of 1000 F) D ¼ heated perimeter (in.) 0 0:75 h ¼ thickness of protection (in.) hW =D R ¼ 130 W0 ¼ weight of steel section and gypsum 2 wallboard (lb/ft) where 50hD W0 ¼ W þ 144 C1 and C2 ¼ constants for specific protection R ¼ ½C1 ðW=DÞ þ C2 h material 0:7
Column/spray-applied materials and some board products—wide flange shapes Column/spray-applied R ¼ C1 AP h þ C2 materials and some board products—hollow sections
Column/concrete cover or encased
C1 and C2 ¼ constants for specific protection material The A/P ratio of a circular pipe is determined by tð d tÞ A=Ppipe ¼ d where d ¼ outer diameter of the pipe (in.) t ¼ wall thickness of the pipe (in.) The A/P ratio of a rectangular or square tube is determined by tða þ b 2tÞ A=Ptube ¼ aþb where a ¼ outer width of the tube (in.) b ¼ outer length of the tube (in.) t ¼ wall thickness of the tube (in.) R ¼ R0 ð1 þ 0:03mÞ R0 ¼ fire endurance at zero moisture content of where concrete (min) ! m ¼ equilibrium moisture content of concrete h1:6 R0 ¼ 0:17ðW=D Þ0:7 þ 0:28 0:2 (% by volume) kc ( 0:8 ) bf ¼ width of flange (in.) H 1 þ 26 d ¼ depth of section (in.) ρc cc hðL þ hÞ kc ¼ thermal conductivity of concrete at ambient temperature (Btu/hr·ft· F) H ¼ thermal capacity of steel section at ambient H is temperature (¼0.11 W Btu/ft·F). If encased, c cc defined as: H ¼ 0:11W þ ρ144 b f d As cc ¼ specific heat of concrete at ambient temperature (Btu/lb· F) L ¼ inside dimension of one side of square concrete box protection (in.) If encased, L ¼ (bf + d )/2 As ¼ cross-sectional area of steel column (in.2)
over steel columns is known to increase by approximately 3 % for each 1 % of moisture, R0 is multiplied by the (1 + 0.03m) factor where m is the equilibrium moisture content of concrete. The parameters h and L noted in the equation are shown in Fig. 53.7. If the protection
thickness or column dimensions are not the same in the vertical and horizontal directions, average values are used for h and L. The heat capacity of the concrete must be accounted for in the determination of H if all re-entrant spaces are filled (see Fig. 53.7).
1922
J.A. Milke
Fig. 53.10 Heated perimeter for steel columns [29]
c
b
b
a
a
D = 2(a + b)
D = 4a + 2b – 2c
b
b
a D = 4b
D = 2(a + b)
If specific data on the concrete’s thermal properties are not available, values given in Table 53.4 may be used. Typical densities for normal-weight and lightweight concrete are 145 and 110 lb/ft3 (2320 and 1760 kg/m3). Also, the typical equilibrium moisture content (by volume) for normal-weight concrete is 4 % and lightweight concrete is 5 %. Many of the equations cited in Table 53.3 are limited to a range of shapes or protection thicknesses. Before applying any equation from this table, users should consult the original reference and confirm that the equation is being applied properly. Example 1 Determine the thickness of sprayapplied cementitious material to obtain a 2-h fire endurance when applied to a W 12 106 column. Solution From UL X772, the applicable equation is
R ¼ ð1:05 W=D þ 0:6Þh
ð53:9Þ
Solving for h, h¼
R 1:05 W=D þ 0:6
ð53:10Þ
where R¼2h W/D ¼ 1.44 lb/ft·in. (0.0844 kg/m2) for a W 12 106 with contour profile protection Substituting, h¼
2 ¼ 0:95 in: 1:05 1:44 þ 0:6
ð53:11Þ
ð24:1mmÞ Example 2 Determine the fire endurance of a W 8 28 column encased in lightweight concrete (density of 110 lb/ft3 [176.2 kg/m3]) with all re-entrant spaces filled. The concrete cover thickness is 1.25 in. (31.8 mm).
53
Analytical Methods for Determining Fire Resistance of Steel Members
1923
Table 53.4 Thermal properties of concrete at 70 F
Thermal conductivity (k)a Specific heat (c)b
Normal-weight Concrete 0.95 Btu/hft F (1.64 W/m K) 0.20 Btu/lb F (835 J/kg K)
Solution From Table 53.3, the appropriate equation is R ¼ R0 ð1 þ 0:03mÞ
kc ¼ 0:35 Btu=hr ft Fð0:605 W=m:KÞ cc ¼ 0:20 Btu=lb Fð836 J=kg:KÞ
ð53:12Þ
ρc ¼ 100 lb=ft3 1600 kg=m3
where R0 ¼ 10ðW=DÞ0:7 þ 17 h1:6 =kc0:2 n ð53:13Þ 1 þ 26½H=ρc cc hðL þ hÞ0:8
Referring to Fig. 53.7, h2¼h1¼h¼1.25 in. (31.8 mm) bf ¼ 6.535 in. (166.0 mm) d ¼ 8.060 in. (204.7 mm) W/D ¼ 0.67 lb/ftin. (39.3 kg/m2) (contour profile) A ¼ 8.25 in.2 (0.0053 m2) From Table 53.4,
1:251:6 R0 ¼ 0:17ð0:67Þ0:7 þ 0:28 0:350:2
(
Structural Lightweight concrete 0.35 Btu/hft F (0.61 W/m K) 0.20 Btu/lb F (835 J/kg K)
L¼
1 b f þ d ¼ 7:30 in: ð185mmÞ 2 ρc c c b f D As 144 110 0:20 ¼ 0:11 28 þ 144 ð6:535 8:060 8:25Þ
ð53:14Þ
H ¼ 0:11W þ
ð53:15Þ
¼ 9:87in:ð251mmÞ
9:87 1 þ 26 110 0:2 1:25ð7:30 þ 1:25Þ
0:8 ) ¼ 1:63 hr: ð53:16Þ
Assuming a moisture content of 5 % for lightweight concrete, R ¼ 1:63ð1 þ 0:03 5Þ ¼ 1:87 hours ð53:17Þ
Steel Beams As in the case of columns, the W/D ratio is an important parameter affecting the fire resistance of a beam. Beams with larger W/D ratios may be substituted for beams with lesser W/D ratios for an equivalent rating with no change in the protection thickness. However, as with columns, designs resulting from the direct substitution of larger beams without reducing the protection thickness may be inefficient.
In 1984, an empirically derived correlation was developed to calculate the required thickness of spray-applied material protection [37]. Correlations of the form for steel columns are not possible, given the deck’s role as a heat sink. Thus, the thickness of protection for steel beams is determined based on the following scaling relationship: h1 ¼
W 2 =D2 þ 0:6 h2 W 1 =D1 þ 0:6
ð53:18Þ
where h ¼ Thickness of spray-applied fire protection (in.) W ¼ Weight of steel beam (lb/ft)
1924
J.A. Milke
D ¼ Heated perimeter of the steel beam (in.) (Fig. 53.11) and where the subscripts 1 ¼ Substitute beam and required protection thickness 2 ¼ The beam and protection thickness specified in the referenced tested design or tested assembly Limitations of this equation are noted as follows: 1. W/D 0.37 lb/ft-in (0.0217 kg/m2) 2. h 3/8 in. (9.5 mm) 3. The unrestrained beam rating in the referenced tested design or tested assembly ¼ at least 1 h It should be noted that the above equation pertains only to the determination of the protection thickness for a beam in a floor or roof assembly. All other features of the assembly, including the protection thickness for the deck, must remain unaltered. Example 3 Calculate the thickness of sprayapplied fire protection required to provide a 2-h fire endurance for a W 12 16 beam to be substituted for a W 8 17 beam requiring 1.44 in. (36.6 mm) of protection for the same rating.
Fig. 53.11 Heated perimeter for steel beams [36]
Solution The beam substitution correlation, presented as Equation 53.18, is used. h1 ¼
W 2 =D2 þ 0:6 h2 W 1 =D1 þ 0:6
ð53:19Þ
Where W2/D2 ¼ 0.54 lb/ft in. (0.070 kg/m2) for W8X17 W1/D1 ¼ 0.45 lb/ft in. (0.058 kg/m2) for W12X16 h2 ¼ 1.44 in. (36.6 mm) h1 ¼
0:54 þ 0:6 1:44 ¼ 1:6 in:, 0:45 þ 0:6
ð53:20Þ 0:070 þ 0:036 h1 ¼ 36:6 ¼ 40:6mm 0:053 þ 0:036
Steel Trusses There are three types of trusses used in buildings: transfer, staggered, and interstitial trusses. Because of the inherent features of each type of truss, some fire protection systems are more appropriate than others [39]. A load-transfer truss (Fig. 53.12) supports loads from more than one floor. The loads may be suspended from a transfer truss, or the transfer
a
b
tw
d
d
bf
bf
D = 3bf + 2d – 2tw
D = 2d + bf
Contour protection
Box protection
53
Analytical Methods for Determining Fire Resistance of Steel Members
Fig. 53.12 Vierendell truss providing support from above and below [39]
1925 Roof 17 16
Truss
15 14 13
Suspended
12 11 Interior columns omitted 10 9 8 7 6 5
Supported
4 3 2 Grade
Existing
New caisson
truss can be used to eliminate columns on lower floors. A staggered truss is illustrated in Fig. 53.13. Generally, staggered trusses are used in residential occupancy buildings. Staggered trusses carry loads from two floors. Interstitial trusses are used to create deep floor/ceiling concealed spaces containing mechanical and electrical equipment, as shown in Fig. 53.14. Interstitial trusses support only those loads from the equipment enclosure and the floor above. Interstitial trusses are typically used in health care facilities with heavy mechanical equipment needs. Three methods of fire protection are often used for trusses: membrane, envelope, and individual element protection. Some fire protection methods are more appropriate than others for the specific truss types. The fire protection methods
Existing subway structure
New caisson
typically used for each truss type are indicated in Table 53.5. Membrane protection is accomplished through the use of a fire-resistant ceiling assembly. Design parameters for such an assembly can be determined from listings of fire-rated designs [3, 39]. No empirical correlations are available to assess the design of membrane protection systems. The envelope means of protection is illustrated in Fig. 53.15. The truss is enclosed in layers of a board product, with the number of layers determined by the required fire endurance. Some practical rules of thumb based on test results are noted in Table 53.6. Individual element protection is generally accomplished using a spray-applied material. Because critical truss elements perform structurally as columns, that is, in tension or compression (as opposed to bending), the applicable equations
1926 Fig. 53.13 A typical truss and positionings in a staggered truss system [39]
J.A. Milke A
B
B
Truss
A Truss framing plan
Section A–A Truss Truss
Truss
Section B–B
Fig. 53.14 Hospital interstitial truss system [39]
53
Analytical Methods for Determining Fire Resistance of Steel Members
Table 53.5 Typical fire protection methods for steel trusses Truss type Transfer Staggered Interstitial
Fire protection method Membrane Envelope — X — X X X
Individual element X X X
1927
Table 53.6 Practical guidelines for thickness of gypsum wallboard for steel truss envelope protection [39] Fire Endurance (h) 1 2 3
Gypsum X 5 00 /8 (16 mm) 11 00 /4 (32 mm) —
Wallboard Type 5 00 /8 (16 mm) — 11/200 (38 mm)
Top chord of truss Gusset plate
Secondary truss members
Cont-horizontal steel stud at mid-height
Third layer may be placed horizontally
Steel studs
Tape joints
Gusset plate Bottom chord of truss
Required number of layers of fire-resistant gypsum wallboard
Fig. 53.15 Staggered truss protection with envelope protection [39]
for determining the thickness of spray-applied material for columns is used. In order to use these equations, the W/D ratio must be calculated for each element. Unlike columns and beams, the ratio may not be readily available. The diagrams in Fig. 53.16 are provided for assistance in calculating the heated perimeter.
Heat Transfer Analyses Heat transfer analyses are applied to determine the time period required to heat structural
members to a specified critical temperature or to provide temperature data as input to the structural analysis of the heated member. The time required to heat the member to a specified critical temperature is often defined as the fire endurance time of the member. The critical temperature of a structural member can be determined by referring to the temperature endpoint criteria cited in ASTM E119 [1] or by a structural assessment, as is discussed later in this chapter. The available types of heat transfer analyses can be grouped into the following categories:
1928
J.A. Milke
member is at a uniform temperature. The equation for temperature rise during a short time period, Δt, is [23]
d tw
d
ΔT s ¼
bf
bf
D = 3bf + 2d – 2tw
D = bf + 2d
tw
d
b
t
bf
c
D = 4bf + 2d – 2tw
a
D = 4a + 2b + 2c
d
tw
a
bf
D = 8bf + 2d + 2a – 4tw
d
a
bf
D = 4bf + 2d + 2a
Fig. 53.16 Heated perimeter for steel truss shapes [39]
1. Numerical methods 2. Graphical solutions 3. Computer-based analyses
α T f T s Δt cs ðW=DÞ
where ΔTs ¼ Temperature rise in steel ( F) ( C) α ¼ Heat transfer coefficient from exposure to steel member (Btu/ft2·s·R) (W/m2·K) D ¼ Heated perimeter (ft) (m) (see Fig. 53.16) cs ¼ Steel specific heat (Btu/lb· F)/(J/kg· C) W ¼ Steel weight per lineal foot (lb/ft)/(kg/m) Tf ¼ Fire temperature (R) (K) Ts ¼ Steel temperature (R) (K) Δt ¼ Time step (s) where α¼αr+αc αr¼ radiative heat transfer coefficient c ε αr ¼ T f2Tf s T 4f T 4s αc¼ convective heat transfer coefficient αc¼ 9.8 104–1.2 103 Btu/ft2-s-R (20–25 W/m2K) where C1 ¼ 4:76 1013 Btu=s ft2 R4 ð5:67 108 W=m2 K4 Þ and εf, the effective emissivity, can be evaluated from Table 53.7. The quasi-steady assumption dictates that the time step should be small, that is, on the order of 10 s [41]. Equation 53.21 is successively applied up to the time duration of interest. For the ISO 834 test, Tf at any time, t, can be estimated by the following expression [22]: T f ¼ CT log10 ð0:133t þ 1Þ þ T 0
Numerical Methods Many numerical methods are available to estimate the temperature rise in steel structural elements. The equations are derived from simplified heat transfer approaches. Unprotected Steel Members The temperature in an unprotected steel member can be calculated using a quasi-steady-state, lumped heat capacity analysis. This method assumes that the steel
ð53:21Þ
ð53:22Þ
Where CT ¼ 620 with Tf, T0 in F 345 with Tf, T0 in C t ¼ time (sec) T0 ¼ initial temperature F, C Protected Steel Members For protected members, the thermal resistance provided by the insulating material must be considered. If the thermal capacity of the insulation layer is neglected [23],
53
Analytical Methods for Determining Fire Resistance of Steel Members
1929
Table 53.7 Effective emissivity [40] Type of construction 1. 2. 3. 4.
ΔT s ¼
Effective Emissivity Column exposed to fire on all sides Column outside facade Floor girder with floor slab of concrete, only the underside of the bottom flange being directly exposed to fire Floor girder with floor slab on the top flange Girder of 1 section for which the width-depth ratio is not less than 0.5 Girder of 1 section for which the width-depth ratio is less than 0.5 Box girder and lattice girder
ki T f T s Δt cs hW=D
ð53:23Þ
where all parameters are as defined in Equation 53.21, and ki ¼ Thermal conductivity of insulation material (Btu/fts F) (W/m C) h ¼ Protection thickness (ft) (m) Malhotra suggests that the thermal capacity of the insulation material may be neglected if the following inequality is true (see parameter definitions for Equation 53.21 [23]: cs W=D > 2ci ρi h If the thermal capacity must be accounted for, as in the case of gypsum and concrete insulating materials, then T f Ts ki ΔT s ¼ Δt ð53:24Þ h cs ðW=DÞ þ 1=2ci ρi h where all parameters are as defined for Equation 53.21, and ci ¼ Specific heat of insulating material (Btu/lb· F) (J/kg· C) ρi ¼ Density of insulating material (lb/ft3) (kg/m3) An evaluation of the predictive capability of the lumped heat capacity approach using Equation 53.24 for protected steel sections was conducted by Berger for steel columns protected with a spray-applied cementitious material [42]. The analysis consisted of comparing predicted versus measured temperatures for steel columns
0.7 0.3 0.5
0.5 0.7 0.7
exposed to the standard fire exposure. A comparison of the predicted versus measured times for the steel column to reach 538 C is provided in Table 53.8. A comparison of the predicted temperature with that measured for one protected steel column assembly is provided in Fig. 53.17. Predictions of temperature rise in steel beams by the lumped heat capacity approach are prone to be inherently less accurate than those for steel columns [43]. As noted previously, a steel beam in contact with a slab has only three sides exposed to a fire and also will lose heat to the slab [44]. Consequently, the temperature of a steel beam exposed to fire is likely to vary appreciably from the bottom flange to the top flange, stretching the validity of the uniform temperature assumption. Nonetheless, for many engineering applications, the lumped heat capacity approach can provide a conservative estimate of the average temperature rise of a steel beam [45]. Heat losses to the slab may be compensated for by reducing the effective flame emissivity to 0.5 [40]. However, if the temperature gradient across the beam is important, another analytical approach will need to be applied [43]. Exterior Steel Columns and Steel Spandrel Beams A design guide is available for calculating the exposure of exterior steel columns and steel spandrel beams [46]. The guide is based on research by Law and basic radiation heat transfer principles [47]. A similar calculation procedure is available in the Eurocodes [10].
1930
J.A. Milke
Table 53.8 Comparison of predicted time from lumped heat capacity analysis and measurements for protected steel column to reach 538 C h (cm) 1.9 3.8 7.6 3.5 8.3 9.5 1.9 5.6 3.8 1.4 2.9
Shape W 6 16
W 8 28
W 10 49 W 12 106 W 14 228 W 14 233
700
Test (min) 58 112 210 122 291 355 70 217 200 123 225
Calc (min) 56 119 251 121 298 352 62 220 203 140 251
Test Calc
600
Temperature (°C)
500
400
300
200
100
member. For this method, a specific design is considered unacceptable if the steel temperature exceeds 1000 F (538 C). Liquid-Filled Columns The design calculations for liquid-filled columns are based on the thermal capacity of the liquid. The design of a liquid-filled column fire protection system consists of three major steps: 1. Heat transfer analysis 2. Determination of volume of liquid required 3. Pipe network design The heat transfer analysis is used to assess the impact of fire exposure on the liquid-filled column. The heat transfer analysis considers radiation and convection heat transfer from the fire to the column surface, conduction through the column wall, and convection with localized boiling into the liquid. Both temperature of the steel column and total amount of heat transferred to the liquid causing evaporation are determined as a result of this analysis. The liquid volume calculation is important to ensure the column remains full of liquid for the entire fire exposure period. Because heat transferred to the liquid will cause some evaporation, a supplemental amount of liquid must be provided in a storage tank. The final step in the design method is a hydraulic analysis of the tubular column and pipe network. This analysis assesses the ability of the liquid to circulate based on friction losses, elevation changes, and buoyancy of the heated liquid. A comprehensive design aid for liquid-filled columns is available [48]. Because the procedure is rather lengthy, it will not be reviewed here.
0 0
10
20
30
40
50
60
70
Time (min)
Fig. 53.17 Predicted steel column temperature [42]
The temperature of the steel member is calculated from a steady-state conduction analysis. The exposure boundary conditions consist of radiant heating from a fully developed room fire and flames emitting from windows near the steel
Graphical Solutions Because heat transfer analyses can be very tedious and may involve the use of complex computer programs, graphic solutions have been formulated to simplify the estimation of steel temperature. Graphs of the temperature of protected steel members have been developed by Malhotra [23], Jeanes [13], Lie [16], and others.
Analytical Methods for Determining Fire Resistance of Steel Members
Temperature (°C)
1100 1000 900
1931
1000 t = 120 min t = 90 min
h = 0.05 ki
t = 60 min
800 700 600 500 400 300 200 100 0
t = 30 min
900 800 Temperature (°C)
53
h = 0.2 ki
t = 120 min
700
t = 90 min
600
t = 60 min
500 400 300
t = 30 min
200 100 0 50
100
150
200
250
50
300
100
150
1000
Temperature (°C)
800
250
300
1000 h = 0.1 ki
700
t = 120 min
900
t = 90 min
800
t = 60 min
600 500 t = 30 min
400 300
Temperature (°C)
900
200 D/A
D/A
700
t = 120 min
600
t = 90 min
500
t = 60 min
400 300
200
200
100
100
0
h = 0.3 ki
t = 30 min
0 50
100
150
200
250
300
50
D/A
100
150
200
250
300
D/A
Fig. 53.18 Relationship of heated area to steel weight with temperature [23]
The series of graphs developed by Malhotra [23], presented in Fig. 53.18, for estimating the temperature of steel members exposed to the standard exposure are based on the lumped heat capacity approach described in the previous section. Steel temperatures are plotted versus the D/A ratio (analogous to the inverse of W/D) for selected time periods of exposure and thermal resistances of the insulating material. Time periods of 30–120 min are noted in the graphs. The range of thermal resistances of the insulating material covered by these graphs is 0.01–0.30 (W/m2· C)1 (0.003–0.10) (Btu/ft2h F)1. Based on the application of FIRES-T3, a heat transfer computer program that will be described in the next section, Jeanes formulated a series of time-temperature graphs of protected steel beams [13]. The steel beams are protected by a proprietary specific spray-applied cementitious material with a range of thicknesses of 0.5–1.5 in. (12.7–38.1 mm). Graphs are available for a variety of common wide-flange beam shapes [13]. Examples of these graphs are presented in Fig. 53.19 with graphs addressing the average and single-point steel temperatures relating to the maximum endpoint criteria from ASTM
E119 [1]. Average and single-point steel temperatures are represented by the dashed lines. These graphs can be used to determine the thickness of protection material required to provide a desired level of fire resistance. Alternatively, the fire endurance can be estimated for a particular steel beam and insulation thickness design that has not been tested [14]. Information from numerous applications of FIRES-T3 examining the time-temperature response of steel beams protected with a sprayapplied cementitious material exposed to the standard fire exposure is summarized in Fig. 53.20. Using this graph, the fire endurance of protected steel beams with a W/D ratio of 0.4–2.5 lb/ft-in. can be determined for thicknesses of the spray-applied protection between 1.3 and 3.8 cm (0.5 and 1.5 in.). Example 4 A W 24 76 steel beam is protected with 0.50 in. (12.7 mm) of spray-applied cementitious material. Based on the temperature endpoint criteria noted in ASTM E119, determine the fire resistance of the beam by two methods: 1. Graphical approach from Jeanes [13] 2. Quasi-steady-state approach by Malhotra [23]
1932 Fig. 53.19 Predicted steel beam temperature by FIRES-T3 [13]
J.A. Milke Average section temperature of steel beam, W 12 × 14 (W/D = 0.40), for various thicknesses of direct-applied fire protection 1500
Temperature (°F)
1/2⬙
1⬙
1-1/2⬙
Maximum
1000
Average
FIRES-T3 analysis based on the ASTM E119 exposure
500
0 1
2
3
4
Time (hr) Maximum steel beam temperature, W 12 × 14 (W/D = 0.40), for various thicknesses of direct-applied fire protection
Temperature (°F)
1500 1/2⬙
1⬙
1-1/2⬙
Maximum Average
1000
FIRES-T3 analysis based on the ASTM E119 exposure
500
0
1
2
3
4
Time (hr)
Solution A W 24 76 steel beam has a W/D ratio of 1.03 lb/ftin. or 12.36 lb/ft2. The material properties are evaluated at mean temperatures expected during the exposure. The fire resistance can be assessed using the temperature endpoint criteria in ASTM E119. Mean temperatures of 500 F (260 C) and 750 F (400 C) are selected (arbitrarily) for the steel and insulation, respectively, to determine the thermal properties. The following material property values are assumed [13]:
Thermal conductivity Specific heat Density
Steel 25.6 Btu/fth F (44.3 W/m K) 0.132 Btu/lb F (551 J/kg K) 490 lb/ft3 (7860 kg/m3)
Insulation 0.067 Btu/fth F (0.12 W/m K) 0.304 Btu/lb F (1270 J/kg K) 15 lb/ft3 (240 kg/m3)
Jeanes’s Graph Using Fig. 53.21 with a W/D of 1.03 lb/ftin. (0.060 kg/m2) and an insulation thickness of 0.50 in. (12.7 mm), the fire endurance is estimated to be 1.33 h or 80 min.
53
Analytical Methods for Determining Fire Resistance of Steel Members
Fig. 53.20 Fire endurance of steel beams versus fire protection thickness for average section temperature of 1000 F (538 C) (Based on FIREST3 analysis of ASTM E119 fire exposure) [13]
1933
4
Fire endurance (hr)
1-1/2⬙ 3 1⬙ 2
1/2⬙
1
0 0.0
0.5
1.0
1.5
2.0
2.5
W/D of beam
1.0 1.0 N
=5 1
0.6
=
10
0.9
0.3
5
N
0.9
2
0.
15
0.8 2
0.
0.8
10
0.7 1
08
0.
0.7
0.
0.6 0.6
06
0.
0.6
θ 0.5
0.4 0.4
0.3
04
0.
3
0.4
0.2
0.3
0.2
0.1 0.08 0.06 0.04
0.1
0.0
2
0.0
0.3
5 0.1
05
0.
θ 0.5
0.2
0.1
0.02
0.4
0.8
1.4
1.8
2.2
2.6
3.0
2
4
Fo
6
8 10 12 14 16 18 20 22 24 26 28 30 Fo
Fig. 53.21 Dimensionless steel temperature versus Fourier numbers [16]
Quasi-Steady-State Approach First, a check is performed to determine whether the thermal capacity of the insulation material must be considered. cs W=D > 2ci ρi h 0:132 12:36 > 2 0:304 15 0:50=12 1:63 > 0:38 ð53:25Þ
Disregarding the thermal capacity of the insulation, Equation 53.23 is used to predict the steel temperature rise for each time step. 0:067=3600 T f T s Δt 0:0132 0:50=12 12:36 ¼ 2:74 104 T f T s Δt
ΔT s ¼
ð53:26Þ
1934
Time 10 20 30 40 50 3220 3230 3240 3250 3260 3270 3280
J.A. Milke Steel temperature ( C) 20.0 20.1 20.3 20.5 20.8 534.2 535.3 536.5 537.7 538.9 540.1 541.2
Fire temperature ( C) 46 72 96 120 143 888 888 888 889 889 890 890
Fire-steel temperature ( C) 26 51 76 99 122 353 353 352 351 350 350 349
W/m2K k/h 9.13 9.13 9.13 9.13 9.13 9.13 9.13 9.13 9.13 9.13 9.13 9.13
ΔTs ( C) 0.1 0.2 0.3 0.3 0.4 1.2 1.2 1.2 1.2 1.2 1.2 1.2
Thus, the fire endurance is 54 min. The fire endurances calculated by the two methods can be compared as follows: Jeanes (FIRES-T3) Quasi-steady-state
80 min 54 min
The significantly reduced fire endurance calculated using the quasi-steady-state approach is attributable to the approximate nature of the lumped heat capacity method assuming an adiabatic surface condition at the beam-slab interface.
Computer-Based Analyses Several computer-based analyses are available to estimate the temperature rise of steel members. The analyses range from a spreadsheet procedure to perform the iterative calculations for the quasi-steady-state approach to finite element models. Spreadsheets are one example of providing a framework to perform the iterative, quasi-steady calculations [42, 43, 49]. Typically, the spreadsheet procedures mimic the quasi-steady analysis procedure described previously, including the evaluation of material properties at a mid-range temperature for the exposure of interest. Although temperature-dependent material properties can be included within the spreadsheet framework, the accuracy implied by considering temperature-dependent properties is not consistent with the first-order nature of the quasi-steady approach.
Another framework for conducting computerbased analyses includes the numerous mathematical-equation-solver software packages. This software can be used to conduct the iterations associated with the quasi-steady approach or to solve the partial differential equations exactly. Harmathy and Lie developed a twodimensional finite difference model to predict the temperature rise in protected steel columns [50]. The two-dimensional network is formulated over the cross section of the insulation layer, assuming the temperature to be independent of length. The steel is assumed to be a perfect conductor (i.e., the temperature is uniform throughout the steel). Heat transfer via radiation is considered across any air spaces enclosed by the insulation and steel. The boundary conditions included by Harmathy are those associated with the ASTM E119 test [1]. To simplify the model, convection is disregarded, because convection comprises a minor portion of the heat transfer process in the furnace test. Pettersson et al. [40] include a finite difference formulation to predict the temperature rise of steel beams protected with a suspended ceiling exposed to a specified fire. The formulation uses a one-dimensional approximation accounting for conduction through the suspended ceiling and floor slab (above the beam), and radiation and convection in the air space between the slab and beam. The temperature of the steel is assumed to be uniform. The assembly is divided into several elements, as depicted in Fig. 53.22. A system of simultaneous equations is derived for the temperature rise in each of the assembly elements. A numerical integration technique such as Runge-Kutta is used to obtain the solution. A comparison of the calculated versus experimentally observed temperatures for a steel beam is presented in Fig. 53.23. General heat transfer finite-element programs have been available for many years [51]. FIREST3, TASEF-2, SAFIR, SUPER-TEMPCALC, and HEATING 7, among others, have been developed specifically to address the heating of assemblies with steel structural members exposed to fire conditions [52–55].
53
Analytical Methods for Determining Fire Resistance of Steel Members
Fig. 53.22 Division of the floor slab into elements [40]
1935
ϑo
αu
ϑY
4
ϑn
ϑ1
α2
ϑY
3
ϑY
2
ϑt
α1 ϑY
1
Temperature (°C)
400
200
1.0
0.5
1.5
Time (hr)
Fig. 53.23 Calculated (- -) and measured (—) steel temperature-time (θs – t) curve for a floor girder IPE 140 with insulation in the form of a suspended ceiling of 40-mm-thick mineral wool slabs of density γ ¼ 150 kg/m3. The figure also gives the calculated (– –) and measured (–x–) temperature-time curve for the top of the 50-mm-thick concrete floor slab [40]
TASEF-2 examines the conduction heat transfer through assemblies [52]. Assemblies may include internal voids, in which convection and radiation heat transfer modes are considered. Two time-temperature curves are available: (1) the ISO 834 standard time-temperature curve and (2) a time-temperature curve from a ventilationcontrolled fire. SUPER-TEMPCALC can also be used to analyze the conduction heat transfer through assemblies with air gaps. Numerous fire curves are included within the software. FIRES-T3 was specifically developed to examine the heating of structural members exposed to fire conditions [53]. FIRES-T3 has been applied successfully to predict the temperature rise in protected steel beams and columns [13, 56]. Almand used a finite-difference heat transfer model to estimate the protection thickness of spray-applied cementitious material required for tubular steel columns [57]. The input data requirements for the heat transfer computer models can be grouped into two categories: 1. A description of the assembly 2. A description of the fire exposure
1936 1000 FIRES-T3 900
750 Column temperature (°F)
The information necessary to describe the assembly includes geometric factors (dimensions, shape of member) and material property values (thermal conductivity, specific heat, and density). The fire exposure is characterized in terms of the temperature of the surrounding environment and appropriate heat transfer coefficients. The geometry of the assembly is established by formulating an element mesh for the assembly of interest. Required material property data consists of the density, specific heat, and thermal conductivity of the steel and insulation. Material property data are available for a limited number of insulation materials [13, 58]. For models using an explicit transient solution technique, such as FIRES-T3, caution must be exercised in selecting the time step and mesh size to obtain correct results that are numerically stable. TASEF-2 internally determines a numerically stable time step. Most heat transfer models do not address the effects of phase changes or chemical reactions that may influence the heating process. Phase changes and chemical reactions have been accounted for by altering the value of the material properties. Milke addressed the evaporization of free water in a spray-applied cementitious material by increasing the specific heat in a narrow temperature region around 100 C (212 F) [56]. Agreement between the predicted and experimental average steel temperatures is quite good in both applications of FIRES-T3 by Jeanes and Milke. A comparison of the temperature history for a steel column protected with a sprayapplied cementitious material subjected to the ASTM E119 test is presented in Fig. 53.24. A similar comparison is presented in Fig. 53.25 for steel beams protected with the same material [13]. FIRES-T3 has also been used to conduct a preliminary analysis of the heating of partially protected steel columns (i.e., where a portion of the spray-applied protection is missing) [59, 60]. The analysis indicated that even a small portion of missing protection significantly decreased the fire resistance of the column, especially for cases involving small columns. Results of the analysis are indicated in Fig. 53.26.
J.A. Milke
W 10 × 49 3/4 in. of protection
600
UL data 450
300
150
25
50 Time (min)
75
100
Fig. 53.24 Comparison of predicted and measured average steel column temperature [53]
Structural Analyses Much of the previous testing and analysis has concentrated on the response of a single isolated member to fire exposure. Recent events, including the Broadgate fire, Cardington tests, and performance of buildings in or near the World Trade Center complex, have indicated that analyses need to account for interactions between structural members for more realistic assessments of behavior in fire. In the fire at the Broadgate construction site, a major fire exposed steel elements that were not yet protected. However, no collapse was observed. In the Cardington tests, no collapses were observed in any of the six tests despite steel temperatures that reached 900 C in some tests [61]. In the many steel frame buildings involved in the World Trade Center terrorist incident on September 11, 2001, the variety of outcomes
Analytical Methods for Determining Fire Resistance of Steel Members
Average steel temperature (°F)
1500
Beam: W 8 × 28 (W/D = 0.80) Fireproofing: 1⬙ thick (monokote)
1500
Average steel temperature (°F)
53
1000
500
0 0.0
1937
Beam: W 12 × 27 (W/D = 0.63) Fireproofing: 7/8⬙ thick (monokote)
1000
500
FIRES-T3 prediction
FIRES-T3 prediction
Test data
Test data
2.0
1.0
0 0.0
3.0
2.0
1.0
Time (hr)
3.0
Time (hr)
Fig. 53.25 Comparison of experimental data and FIRES-T3 analysis [13]
180 Fire resistance (min) (ASTM E119)
Fig. 53.26 Fire resistance versus percent protection loss for W 10 49 column, flange exposure
160
One hour
140
Two hours Three hours
120 100 80 60 40 20 0 0
2
observed has been attributed to the response of subframes or the interaction of exposed structural members with adjacent structural members [62]. In the North and South Towers, the ability of the towers to remain standing for a period of time after the aircraft impact is attributed to load transfer from the severed exterior columns to core columns. In neighboring buildings, impacts by the debris from the collapsing North and South Towers were withstood because of load transfer. One of the lower buildings in the World Trade Center complex, WTC 5, withstood
4
6
8
10
12
14
16
18
almost complete burnout of fuels, though beams were significantly deflected. The interaction of structural components has been an area of increased research in recent years, as will be discussed later in this chapter relative to computer modeling efforts. Part of this interest has concentrated on joints [63]. In WTC 5, a shear plate failed, leading to a partial collapse of the building [61]. The structural analysis methods calculate one of three parameters: deflection, critical temperature, or critical load. In several of the
1938
methods, all three of the parameters may be considered because they are interrelated. Algebraic equations, graphs, and computer programs are available to perform a structural analysis for the purpose of addressing fire resistance.
General Discussion of Three Parameters Addressed in Structural Analysis Deflection The total deflection and rate of deflection can be calculated for loaded and heated steel beams by considering all sources of strain. The total strain comprises components of the elastic and plastic strains due to the applied loads, thermal strain (due to thermal expansion), and creep strain. The calculated deflection and rate of deflection can be compared with established maximum limits of each. The Robertson-Ryan criteria have been widely accepted for this purpose [22, 64, 65]. However, calculation of the deflection of unheated beams is difficult except for simple loadings, geometries, and end conditions. Adding the thermal expansion and creep components further complicates the calculation, virtually requiring computer solution. Critical Temperature As mentioned earlier in the chapter, the material properties of steel change with increasing temperature. The most important material properties for criticaltemperature calculations are yield strength, ultimate strength, and modulus of elasticity. The critical temperature is defined as the temperature at which the material properties have decreased to the extent that the steel structural member is no longer capable of carrying a specified load or stress level. In this context, the factor of safety of the member is considered to be reduced if the member reaches unacceptable stress levels, buckling becomes imminent, or deflections exceed maximum limits. The critical temperature can be calculated as long as the dependence of the material properties with temperature is known. There are numerous algebraic equations to calculate the critical temperature of steel structural members [66]. Often, the critical
J.A. Milke
temperature is defined based on temperature limits stated in the standard test. However, in tests steel members experienced temperatures in excess of 800 C (1470 F) without collapse [66]. Critical Load The critical load is defined as the minimum applied load that will result in failure if the structural member is heated to a temperature, T. The critical load can be expressed as a point load or distributed load. As with critical temperature, the critical load calculation requires the material properties at elevated temperatures. Critical load calculations can be conducted with algebraic equations or with a computer program.
Algebraic Equations: Critical Temperature Beams The critical temperature of Grade 250 steel beams with an allowable stress of 20,000 psi (138 Mpa) can be determined using equations by Lie and Stanzak [35]. The Lie and Stanzak equations account for creep strain and assume the beam is simply supported and thermally unrestrained. Similar approaches have been developed by Malhotra [23], Vinnakota [65], and Kruppa [67]. Differences in the percent reduction in yield stress or modulus of elasticity are related to design method (elastic or plastic), factor of safety, and end conditions. Equations for the ratio of yield stress at elevated temperature with yield stress at ordinary room temperature are presented in Table 53.9. Typical values of Zp/Ze are between 1.13 and 1.15 for I sections [23], and 1.5 for rectangular sections. Another example of the second approach is the analysis of the critical temperature of beams by European Convention for Constructional Steelwork (ECCS) [41, 68]. The ECCS guide addresses the maximum allowable reduction in yield strength by considering the applied loading, beam geometry, structural end conditions, and whether the applied loading results in stresses
53
Analytical Methods for Determining Fire Resistance of Steel Members
Table 53.9 Critical stress equations [22] Design basics Elastic design Plastic design
Critical yield stress σ yT σy σ yT σy
¼ F1e
Ze Zp
¼ F1p
where σyT ¼ critical yield stress at elevated temperature, T σy ¼ yield stress at ordinary room temperature Fe ¼ factor of safety, elastic design Fp ¼ factor of safety, plastic design Ze ¼ elastic section modulus Zp ¼ plastic section modulus
in the elastic or plastic range. Critical temperature calculations based on the ECCS analysis are presented in Table 53.10. Example 5 Determine the critical temperature of a simply supported W 12 26 steel beam supporting a 53-in. (1.35-m) thick rectangular slab. The applied moment is 41,750 ftlb (15,480 Nm). The rectangular slab is 8 ft (2.4 m) wide. The section properties of the beam are Z e ¼ 33:4 in:3 547 103 mm3 l ¼ 204 in:4 84:9 106 mm4 Assume σy ¼ 36,000 psi (248 MPa). Solution Using Lie and Stanzak’s equation for a beam, 33 96 12 ¼ 216 in:4 5:19 104 m4
Id ¼
ð53:27Þ
70, 000 460 45:62 4:23ðI d =I Þ 70, 000 ¼ 460 ð53:28Þ 45:62 4:23ð216=204Þ
T cr ¼
¼ 1240 F ð671 CÞ
1939
temperature for the onset of elastic buckling for columns under maximum permissible applied stress conditions. The Euler buckling stress at which elastic buckling is imminent is given by σcr ¼
π 2 ET λ2
ð53:29Þ
where σcr ¼ Euler buckling stress (MPa) (psi) ET ¼ Modulus of elasticity at temperature T (MPa) (psi) λ ¼ Slenderness ratio ¼ Kl/r r ¼ Radius of gyration (ft) (m) Kl ¼ Effective length of column (ft) (m) Included in the ECCS guide [41] are dimensionless buckling curves for steel columns at elevated temperatures. These curves are presented in Fig. 53.27. Equation 53.29 is valid only for columns that buckle in the elastic range. Generally, slender columns having a slenderness ratio in excess of approximately 90 can be expected to buckle elastically. Buckling stresses for stout columns (slenderness ratio less than 90) are in the plastic range, requiring a more complex analysis. The failure mode for columns with a slenderness ratio between 80 and 100 cannot be reliably predicted [69]. The tangent modulus can be used instead of the modulus of elasticity in Equation 53.29 for stout columns. However, predictions of the critical temperature using Equation 53.29 may not be accurate, due to residual stresses from the steel fabrication process [69]. Thus, for stout columns, a conservative estimate for the critical temperature of steel columns may be obtained by determining the temperature at which the yield stress is equal to the applied stress.
General Columns Lie and Stanzak calculated a critical temperature of 941 F (505 C) for slender, axially loaded columns [35]. The calculation was based on the
Malhotra has observed that critical temperatures determined from the structural analysis algebraic equations will be somewhat low when compared to experimental data [23]. Thus, the following
1940
J.A. Milke
Table 53.10 Critical temperature of steel beams [43]
Θ = 1.33 Θ = 1.0 Θ = 1.47 Θ = 1.12 Θ = 1.47
Fig. 53.27 Dimensionless buckling curves for steel columns [41]
1.0
0.8 20 ° 20 C 0°C 300 °C 400 °C 450 °C 500° C 550° C 600°C
0.6 Ncrθ 0.4
0.2
0
0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
λ
correction factors, V, are suggested by Malhotra to improve the prediction capabilities of the approach: 1. Columns: V ¼ 0.85 2. Statically determinate beams: V ¼ 0:77þ 0:15PPus 3. Statically indeterminate beams: V ¼ 0:25þ 0:77PPus
where Ps ¼ Service (applied) load (N or N/m) (lb or lb/ft) Pu ¼ Load to induce ultimate stress at midspan (N or N/m) (lb or lb/ft) Example 6 Determine whether the following steel column is expected to buckle if it achieves
53
Analytical Methods for Determining Fire Resistance of Steel Members
an average temperature of 1100 F (593 C). The column is simply supported, is 15 ft (4.6 m) long, and has an applied load of 12,000 psi (82.8 MPa). Assume the yield stress is 36,000 psi (248.4 MPa) and the modulus of elasticity is
ET ¼
1þ
1941
30,000,000 psi (207 GPa). The characteristics of the column are A ¼ 8.23 in.2 (5310 mm2) I ¼ 21.6 in.4 (8.99 106 mm4) Kl ¼ 180 in. (4572 mm) At 1100 F (593 C):
T 593 E0 ¼ 1 þ 15:6 106 ¼ 8:11 106 2000 lnðT=1100Þ 2000 lnð593=1100Þ ð53:30Þ
Solution Calculate the slenderness ratio to determine the failure mode. λ¼
Kl 180 ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 113 r 21:6=8:23
buckle due to the applied load and elevated temperature.
ð53:31Þ
Critical Stress
Because the slenderness ratio exceeds 90, the column is susceptible to buckling. The buckling stress at 1100 F (595 C) is 12,700 psi (87.6 MPa). Thus, the column does not
Columns Simple expressions for determining the critical stress for steel columns [35] are noted below.
1 π2 E T P2cr Pcr σ yT þ 4:8 105 π2 ET þ 2 þ σ y T A 2 ¼ 0 λ λ
ð53:32Þ
where Pcr ¼ Critical point load (N) (lb) σyT ¼ Yield stress at temperature T (Pa) (psi) ET ¼ Modulus of elasticity at temperature T (Pa) (psi) λ ¼ Kl/r In order to improve the prediction capabilities of the critical stress approach for slender columns, the modulus of elasticity should be replaced by the reduced modulus of elasticity [16]. The reduced modulus is defined as 4EET Er ¼ pffiffiffi pffiffiffiffiffi2 E þ Et
ð53:33Þ
where Et ¼ Tangent modulus In addition, the 0.2 % proof stress may be replaced by the 0.5 % proof stress in the yield stress parameter [70].
Results of a buckling analysis on concretefilled square hollow sections are provided in Fig. 53.28. Beams The expressions for the critical loads for beams assume at failure that the beam is in a state of full plasticity at the location of the maximum moment [70]. Obviously, in order to calculate the critical stress, the material property–temperature relationships must be known. The critical distributed load for a simply supported beam is [66] qcr ¼
8σ yT Z p L2
ð53:34Þ
where qcr ¼ Critical distributed load (N/m) (lb/ft) Zp ¼ Plastic section modulus (m3) (in.3) L ¼ Span of beam (m) (ft)
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J.A. Milke
Hollow structural section 400 × 10 Fire class R60
Steel grade
Reinforcing bars S 400
7000 (9) 6000
(7) C40 1.0 (8) C40 2.5 (9) C40 4.0
(3) (4) (2) 3000
(1)
Steel grade
Fe 360
Reinforcing bars S 400
6000
(9) 5000 (8) (6) Buckling load N cr, θ (kN)
Buckling load N cr, θ (kN)
(7) (5)
4000
Fire class R90
μ% (1) C20 1.0 (2) C20 2.5 (3) C20 4.0 (4) C30 1.0 (5) C30 2.5 (6) C30 4.0
(8) (6) 5000
Hollow structural section 400 × 10
Fe 360
4000
(7) (5) (3)
3000
(4) (2) (1)
2000
2000
1000
1000
0
3 1 2 Buckling length L cr, θ (m)
0
4
3 1 2 Buckling length L cr, θ (m)
4
Concrete (C20, C30, C40)
Reinforcing bars S 400
Hollow structural section 400 × 10
Fig. 53.28 Design graphs for ISO fire resistance requirements R60 and R90. For the concrete-filled square hollow structural section 400 10, the axial buckling
load is a function of the buckling length, of the concrete quality, and of the percentage m of reinforcement; this design diagram is based on a simple calculation model [9]
σyT ¼ Yield stress at elevated temperature (MPa) (psi) Considering a cantilever beam with a point load applied one-third of the span from the fixed end, a plastic hinge can be expected at the fixed end. The critical load can be determined by
beams, Pettersson et al. include a load ratio, β, to determine the critical distributed stress [40].
pcr ¼
7:5σ yT Z L
ð53:35Þ
The above equations in this section do not account for creep strain. Based on an analysis of the deflection history of heated, loaded
qcr ¼ β
8σ z L2
ð53:36Þ
where the yield stress is evaluated at ordinary room temperature, relaxing the need to know the yield stress–temperature relationships. β is defined as the ratio of the load causing a maximum allowable deflection under fire conditions to the load inducing stresses equal to the yield stress at ordinary room temperature. Thus, the parameter β takes into account the dependence
53
Analytical Methods for Determining Fire Resistance of Steel Members
1000°F (538°C) 1025°F (552°C) 1060°F (571°C) 1110°F (600°C) 1150°F (620°C) 1200°F (650°C)
Fig. 53.29 Isothermal sections of beam
of both the yield stress and the creep on temperature. Graphs of β are available for a variety of thermal restraint and structural end conditions. The Eurocodes include a method of analysis using algebraic equations to consider the moment capacity of steel beams that have a temperature gradient through the depth of the beam [10]. The method involves dividing the beam into small isothermal sections and treating these isothermal sections as a composite beam (Fig. 53.29). In this case, the moment capacity of the beam is given as Mcap ¼
n X
σi Ai zi
ð53:37Þ
i¼1
where Mcap ¼ Moment capacity (Nm) (lbft) σi ¼ Applied stress in isothermal element (Pa) (psi) Ai ¼ Area of isothermal element (m2) (ft2) zi ¼ Distance from neutral axis to centroid of isothermal element (m) (ft)
Computer Programs Several finite element computer models are available to assess the structural response of fire-exposed structural members or frames. Sullivan et al. indicate that most of the existing finite element models used for structural fire protection analyses were developed originally for research applications [71]. FASBUS-II is an example of a finite element model developed in the United States to evaluate
1943
the structural response of complex building assemblies such as floor assemblies consisting of a two-way concrete slab, steel deck, and steel beam [72]. Sullivan et al. and Franssen et al. provide extensive reviews and comparisons of existing finite element models for structural fire protection applications [72, 74]. At the time of the review, Sullivan et al. noted that all of the models make the following assumptions: • Plane sections remain plane (NavierBernoulli hypothesis). • Perfect composite action is assumed for steelconcrete assemblies, disregarding any slippage between the steel and concrete. • Torsion is disregarded. • Moisture effects are disregarded. • Large displacements are not accurately modeled. Traditionally, analysis of the response of the structure exposed to fire has been limited to an analysis of the response of single members. However, in structural frames comprising many members, load transfer or membrane action may occur to permit the steel member to maintain its integrity, despite achieving a temperature in excess of that typically associated with failure [73, 74]. Load transfer allows stronger members to support additional loads not capable of being carried by heated, weak members. In order to capture this phenomenon, a frame analysis is required [49]. Numerous software packages are available to conduct the frame analysis. Results of a frame analysis are presented in Figs. 53.30 and 53.31. The frame analyses range from algebraic equation–based methods to finite element analyses. Pettersson et al. include a frame analysis via algebraic equations used to determine displacement [40]. The frames consist of beams supported by one or two columns at midspan. The analysis assumes that each beam or column has a uniform temperature (though the temperature of the beam is not required to be that of a column). A pinned connection between the structural members is assumed. The analysis considers the compatibility of the deformation of each member by requiring that the change in length of the column is equal to the beam deflection at the point of contact.
1944
J.A. Milke
P = 972 kN
6000 mm q = 94.2 kN/m
ΔH 4480 mm 1/2 HE 180M
HE 400 AA Full-scale composite frame highly loaded/ fire class F 150
2400 mm
HE 400 AA
ΔH (mm) 150
Horizontal displacement of frame column during ISO fire test t
Test ultimate 150 min
t
Simulation ultimate 149 min
Fire test 3.10 March 15, 1985 100
50
0
Numerical simulation
30
60
90
120
150
ISO fire exposure time t (min)
Fig. 53.30 Deformations measured and calculated by a numerical model for a composite frame [9]
Schleich et al. describe the application of CEFICOSS for a frame analysis [75, 76]. The frame consists of a single beam and column, where one end of the column is connected to an end of the beam. Reasonable agreement is indicated between predicted and measured results.
El-Rimavi et al. describe the application of another finite element model, NARR2, for the evaluation of a large building frame involving numerous beams and columns [77]. The large frame is divided into several subframes for computational ease. Good agreement is noted between predictions of deflections and force
53
Analytical Methods for Determining Fire Resistance of Steel Members
1945
2.12 240
t 210
Simulation ultimate Test ultimate
= 0.9 1.15 B 2.13
180 2.11 1.4
Test ultimate, t (min)
1.8 150
3.10
1.2 1.5 C 1.6
120
t A
Simulation ultimate Test ultimate
= 1.1
1.3 1.7 2.14
90
T3 60
30
0
Test station
4 3 A2II 1 5
30
Structure element
2
Gent B
1.1 6
60
90
Braunschweig D
Maizieres lès–Metz F
Borehamwood UK
Failure criterion
Beam
f ≤ L/30
Column
Buckling
Frame
Buckling
120 150 Simulation ultimate, t (min)
180
210
240
Fig. 53.31 Fire resistance times measured and calculated by a numerical model for columns, beams, or frames of any cross-section types (bare steel, protected steel, composite) [6]
resultants obtained involving simulations of the full building frame and subframes. Slightly greater failure temperatures were determined for semirigid connections as compared to rigid connections. More recently, applications of ABAQUS, SAFIR, and VULCAN to study frame behavior have been described in several references [74, 78, 79]. In contrast to the models reviewed by Sullivan et al., these models have the capability to consider nonlinear effects, large deformations, and torsion. Part of the challenge in conducting frame analyses is to model the response of a joint to fire exposure. This is a current area of research [63, 74].
Nomenclature a A As b bf c cc ci cs C1
Characteristic dimension Cross-section area of steel tube, steel column Cross-section area of steel column Characteristic dimension Width of flange Characteristic dimension Specific heat of concrete Specific heat of protection material Specific heat of steel Constant
1946
C2 d d D E0 Er Et ET F Fe Fp Fo h H I k kc ki K l L L m M N P Pcr Ps Pu qcr r R R0 t t tw Δt T Tf Tm T0
J.A. Milke
Constant Outer diameter of steel pipe Depth of section Heated perimeter of steel section Modulus of elasticity at ambient temperature Reduced modulus Tangent modulus Modulus of elasticity at temperature T Factor of safety Factor of safety, elastic design Factor of safety, plastic design Fourier number Thickness of protection material Thermal capacity of steel section at ambient temperature Second moment of cross sectional area Thermal conductivity of steel Thermal conductivity of concrete Thermal conductivity of protection material End condition factor Unsupported length of column Inside dimension of one side of square concrete box protection Span of beam Moisture content of concrete Flexural moment Ratio of thermal capacity of protection material to that of steel Perimeter of steel tube Critical point load Service (applied) load Ultimate load Critical distributed load Radius of gyration Fire resistance Fire resistance with zero moisture content of concrete Wall thickness of steel pipe Time Width of web Time step Steel temperature Fire temperature Mean fire temperature Ambient temperature
Ts ΔTs V W Ze Zp
Steel temperature Change in steel temperature Correction factor Weight of steel section per unit length Elastic section modulus Plastic section modulus
Greek Letters α α αc αr αT β εf λ θ ρ ρi σcr σy0 σyT
Thermal diffusivity (when used with Fourier number) Heat transfer coefficient Convective heat transfer coefficient Radiative heat transfer coefficient Coefficient of thermal expansion at temperature T Ratio of distributed load causing maximum allowable deflection to distributed load inducing yielding Fire emissivity Slenderness ratio Dimensionless temperature Density Density of insulation material Critical stress for buckling Yield strength at ambient temperature Yield strength at temperature T
References 1. ASTM, ASTM E119, Standard Test Methods for Fire Tests of Building Construction and Materials, American Society for Testing and Materials, Philadelphia (2008). 2. L.G. Seigel, “Fire Test of an Exterior Exposed Steel Spandrel,” Materials Research and Standards, 10, 2, pp. 10–13 (1970). 3. Fire Resistance Directory, Underwriters Laboratories, Northbrook, IL (2012). 4. SFPE Engineering Standard on Calculating Fire Exposures to Structural Elements, Society of Fire Protection Engineers, Bethesda, MD 2011. 5. NFPA 251, Standard Methods of Tests of Fire Resistance of Building Construction and Materials, National Fire Protection Association, Quincy, MA (2006). 6. UL 263, Fire Tests of Building Construction and Materials, Underwriters Laboratories, Northbrook, IL (2003).
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Analytical Methods for Determining Fire Resistance of Steel Members
7. R.G. Gewain and E.W.J. Troup, “Restrained Fire Resistance Ratings in Structural Steel Buildings,” Engineering Journal, 2nd Quarter, pp. 78–88 (2001). 8. T.T. Lie (ed.), Structural Fire Protection, American Society of Civil Engineers, New York (1992). 9. International Fire Engineering Design for Steel Structures: State of the Art, International Iron and Steel Institute, Brussels, Belgium (1993). 10. Eurocode 3: Design of Steel Structures—Part 1-2: General Rules—Structural Fire Design, European Committee for Standardization (CEN), Brussels, Belgium (1995). 11. ASCE/SFPE 29, Standard Calculation Methods for Structural Fire Protection, American Society of Civil Engineers, New York (2005). 12. D. Boring, J. Spence, and W. Wells, Fire Protection through Modern Building Codes, American Iron and Steel Institute, Washington, DC (1981). 13. D.C. Jeanes, Technical Report 84-1, Society of Fire Protection Engineers, Boston (1984). 14. T.Z. Harmathy, NRCC 20956 (DBR Paper No. 1080), National Research Council of Canada, Ottawa (1983). 15. M.S. Abrams, ASTM STP 685, Behavior of Inorganic Materials in Fire, American Society for Testing and Materials, Philadelphia (1979). 16. T.T. Lie, Fire and Buildings, Applied Science, London (1972). 17. T.T. Lie and W.W. Stanzak, “Empirical Method for Calculating Fire Resistance of Protected Steel Columns, Engineering Journal, 57, 5–6, pp. 73–80 (1974). 18. D.R. Boring, “An Analytical Evaluation of the Structural Response of Simply Supported, Thermally Unrestrained Structural Steel Beams Exposed to the Standard Fire Endurance Test,” Master’s Thesis, Ohio State University, Columbus, OH (1970). 19. AISC, ANSI/AISC 360-05, Specification for Structural Steel Buildings, American Institute of Steel Construction, Chicago (2005). 20. “Structural Use of Steelwork in Building: Part 8: Code of Practice for Fire Resistant Design,” BS 5950-8, British Standards Institute, London, UK (2003). 21. R.A. Lindberg, Processes and Materials of Manufacture, Allyn and Bacon, Boston (1978). 22. D.C. Jeanes, Methods of Calculating Fire Resistance of Steel Structures, Engineering Applications of Fire Technology Workshop, SFPE, Boston (1980). 23. H.L. Malhotra, Design of Fire-Resisting Structures, Chapman and Hall, New York (1982). 24. T.Z. Harmathy, “A Comprehensive Creep Model,” ASME Journal of Basic Engineering, 89, pp. 496–502 (1967). 25. T.Z. Harmathy, ASTM STP422, Deflection and Failure of Steel-Supported Floors and Beams in Fire, American Society for Testing and Materials, Philadelphia (1967). 26. J.L. Gross and T.P. McAllister, “Structural Fire Response and Probable Collapse Sequence of the World Trade Center Towers,” NIST NCSTAR 1-6, National Institute of Standards and Technology, Gaithersburg, MD (2005).
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27. Fire Resistant Steel Frame Construction, American Iron and Steel Institute, Washington, DC (1974). 28. Designing Fire Protection for Steel Columns, American Iron and Steel Institute, Washington, DC (1980). 29. W.W. Stanzak and T.T. Lie, Fire Tests on Protected Steel Columns with Different Cross-Sections, National Research Council of Canada, Ottawa (1973). 30. PABCO, Pabco Super Firetemp Fireproofing Board Fire Protection Guide, Ruston, LA (1984). 31. V.K.R. Kodur and T.T. Lie, “Fire Performance of Concrete-Filled Hollow Steel Columns,” Journal of Fire Protection Engineering, 7, 3, pp. 89–98 (1995). 32. V.K.R. Kodur and T.T. Lie, “Evaluation of Fire Resistance of Rectangular Steel Columns Filled with FibreReinforced Concrete,” Canadian Journal of Civil Engineering, 24, pp. 339–349 (1995). 33. L.G. Seigel, “Designing for Fire Safety with Exposed Steel,” Fire Technology, 6, 4, pp. 269–278 (1970). 34. T.T. Lie and W.W. Stanzak, “Fire Resistance of Protected Steel Columns,” Engineering Journal, American Institute of Steel Construction, 10, pp. 82–94 (1973). 35. Designing Fire Protection for Steel Beams, American Iron and Steel Institute, Washington, DC (1985). 36. Load and Resistance Factor Design Specification for Structural Steel Buildings, American Institute of Steel Construction, New York (1993). 37. J.L. Ruddy, S.A. Ioannides, and F. Alfawakhiri, “Fire Resistance of Structural Steel Framing,” Steel Design Guide 19, American Institute of Steel Construction, Chicago (2003). 38. Designing Fire Protection for Steel Trusses, American Iron and Steel Institute, Washington, DC (1980). 39. Fire Resistance Design Manual, Gypsum Association, Evanston, IL (1984). 40. O. Pettersson, S. Magnusson, and J. Thor, Bulletin 52, Lund Institute of Technology, Lund, Sweden (1976). 41. European Convention for Constructional Steelwork, Technical Committee 3, European Recommendations for the Fire Safety of Steel Structures, Elsevier, Amsterdam (1983). 42. G.S. Berger, Estimating the Temperature Response of Wide Flange Steel Columns in the ASTM E119 Test, Department of Fire Protection Engineering, University of Maryland, College Park (unpublished) (1987). 43. J.A. Milke, “A Simplified Model for Estimating the Thermal Response of Steel Beam/Concrete Slab Ceiling Assemblies,” in 2nd International Conference of Fire Research and Engineering (ICFRE2), Society of Fire Protection Engineers, Bethesda, MD (1997). 44. W.W. Stanzak and T.Z. Harmathy, “Effect of Deck on Failure Temperature of Steel Beams,” Fire Technology, 4, 4, pp. 265–270 (1968). 45. I.A. Smith and C. Stirland, “Analytical Methods and Design of Fire Safe Steel Structures,” in International Seminar on Three Decades of Structural Fire Safety, Fire Research Station, Borehamwood, UK (1983). 46. Fire-Safe Structural Steel, A Design Guide, American Iron and Steel Institute, Washington, DC (1979).
1948 47. M. Law, “Prediction of Fire Resistance,” AISC Engineering Journal, pp. 16–29 (1978). 48. G.V.L. Bond, Fire and Steel Construction—Water Cooled Hollow Columns, Constrado, London (1974). 49. W.L. Gamble, “Predicting Protected Steel Member Fire Endurance Using Spreadsheet Programs,” Fire Technology, 25, 3, pp. 256–273 (1989). 50. T.T. Lie and T.Z. Harmathy, Fire Study No. 28, National Research Council of Canada, Ottawa (1972). 51. O.C. Zienkewicz, The Finite Element Method, McGraw-Hill, New York (1983). 52. U. Wickstro¨m, TASEF-2 – A Computer Program for Temperature Analysis of Structures Exposed to Fire, Lund Institute of Technology, Lund, Sweden (1979). 53. R.H. Iding, Z. Nizamuddin, and B. Bresler, UCB FRD 77-15, University of California, Berkeley (1977). 54. A. Anderberg, PC-TEMPCALC, Institutet for Brandtekniska, Fragor, Sweden (1985). 55. K. Childs, Heating 7, Version 7.3, Computer software, Oak Ridge National Laboratory, 486 PC-DOS 4 MB, CD-ROM (1997). 56. J.A. Milke, “Estimating Fire Resistance of Tubular Steel Columns,” in Proceedings of Symposium on Hollow Structural Sections in Building Construction, American Society of Civil Engineers, Chicago (1985). 57. K. Bardell, ASTM STP826, Fire Resistive Coatings: The Need for Standards, American Society for Testing and Materials, Philadelphia (1983). 58. D. Gross, NBSIR 85-3223, National Bureau of Standards, Gaithersburg, MD (1985). 59. D.V. Tomecek and J.A. Milke, “A Study of the Effect of Partial Loss of Protection on the Fire Resistance of Steel Columns,” Fire Technology, 29, 1, pp. 3–21 (1993). 60. N.L. Ryder, S.D. Wolin, and J.A. Milke, “An Investigation of the Reduction in Fire Resistance of Steel Columns Caused by Loss of Spray-Applied Fire Protection,” Journal of Fire Protection Engineering, 12, 1, pp. 31–44 (2002). 61. C.G. Bailey, T. Lennon, and D.B. Moore, “The Behaviour of Full-Scale Steel Framed Buildings Subjected to Compartment Fires,” Structural Engineer, 77, 8, pp. 15–21 (1999). 62. World Trade Center Building Performance Study, FEMA Report 403, Washington, DC (2002). 63. F.M. Block, I.W. Burgess, and J.B. Davison, “Numerical and Analytical Studies of Joint Component Behaviour in Fire,” in Proceedings of 3rd International Workshop Structures in Fire, Ottawa, Canada, pp. 383–396 (2004). 64. A.F. Robertson and J.V. Ryan, “Proposed Criteria for Defining Load Failure of Beams, Floors, and Roof Constructions during Fire Tests,” Journal of Research, 63C, 2, pp. 121–124 (1959). 65. S. Vinnakota, Calculation of the Fire Resistance of Structural Steel Members, American Society of Civil Engineers, New York, p. 105 (1979). 66. J. Kruppa, “Collapse Temperature of Steel Structures,” Journal of Structural Division, 105, pp. 1769–1788 (1979).
J.A. Milke 67. European Convention for Constructional Steelwork, Fire Resistance of Steel Structures, ECCS 89, Brussels, Belgium (1995). 68. B.R. Kirby and D.E. Wainman, The Behaviour of Structural Steelwork in Natural Fires, British Steel PLC., Rotherham, UK (1997). 69. A. Chajes, Principles of Structural Stability Theory, Prentice-Hall, Englewood Cliffs, NJ (1974). 70. T.T. Lie and W.W. Stanzak, “Structural Steel and Fire: More Realistic Analyses,” AISC Engineering Journal, 13, 2, pp. 35–42 (1976). 71. P.J.E. Sullivan, M.J. Terro, and W.A. Morris, “Critical Review of Fire Dedicated Thermal and Structural Computer Programs,” Journal of Applied Fire Science, 3, 2, pp. 113–135 (1994). 72. J.-M. Franssen, J.-B. Schleich, L.-G. Cajot, D. Talamona, B. Zhao, L. Twilt, and K. Both, “A Comparison Between Five Structural Fire Codes Applied to Steel Elements,” in Proceedings of Fourth International Symposium of Fire Safety Science, International Association of Fire Safety Science, Ottawa, Canada, pp. 1125–1136 (1994). 73. C.G. Bailey and D.B. Moore, “The Structural Behaviour of Steel Frames with Composite Floorslabs Subject to Fire: Part 1: Theory, Structural Engineer, 78, 11, pp. 19–27 (2000). 74. D.I. Nwosu and V.K.R. Kodur, “Behaviour of Steel Frames Under Fire Conditions,” Canadian Journal of Civil Engineering, 26, pp. 156–167 (1999). 75. J.M. Franssen, E´tude du Comportement au Feu des Structures Mixtes Ancier—Be´ton (CEFICOSS), A Study of the Behaviour of Composite Steel-Concrete Structures in Fire, Ph.D. Dissertation, Universite´ de Lie`ge, Belgium (1987). 76. J.B. Schleich, J.C. Dotreppe, and J.M. Franssen, “Numerical Simulations of Fire Resistance Tests on Steel and Composite Structural Elements on Frames,” in Proceedings of First International Symposium of Fire Safety Science, Hemisphere Publishing, Gaithersburg, MD, p. 311 (1986). 77. J.A. El-Rimawi, I.W. Burgess, and R.J. Plank, “Model Studies of Composite Building Frame Behaviour in Fire,” in Proceedings of Fourth International Symposium of Fire Safety Science, International Association of Fire Safety Science, Ottawa, Canada, pp. 1137–1148 (1994). 78. Z. Huang, I.W. Burgess, and R.J. Plank, “ThreeDimensional Analysis of Composite Steel-Framed Buildings in Fire,” Journal of Structural Engineering, 126, 3, pp. 389–397 (2000). 79. G.R. Flint and A.S. Usmani, “Investigation into the Impact of Fire on the Twin Towers,” in Proceedings of 3rd International Workshop Structures in Fire, Ottawa, Canada, pp. 147–155 (2004).
James A. Milke is a professor in the Department of Fire Protection Engineering at the University of Maryland. His research activities have included the impact of fires on the structural response of steel and advanced composite members.
Analytical Methods for Determining Fire Resistance of Concrete Members
54
Charles Fleischmann, Andy Buchanan, and Anthony Abu
Introduction Concrete structures have a reputation for excellent behavior in fires. Many reinforced concrete buildings that have experienced severe fires have been repaired and put back into use. Concrete is by nature noncombustible and has a low thermal conductivity. Concrete tends to remain in place during a fire, protecting the reinforcing steel, with the cool inner core continuing to carry the load. Catastrophic failures of reinforced concrete structures in fires are rare, but some occasionally occur [1]. Analytical methods developed to predict the fire resistance of structural assemblies can be divided into two groups: (1) standard and (2) nonstandard fire exposure. For the case of the standard fire exposure, a large database exists from referenced standard tests. The analytical methods use empirically based correlations and minimum dimensions to determine fire resistance. For nonstandard fire exposure, the analysis is more complicated, requiring both heat transfer and structural analyses. Analytical methods are an alternative to conventional methods that require destructive testing of exemplar systems in accordance with standard testing procedures, for example, ASTM E119 or ISO 834. Fire resistance calculations typically use the same acceptance criteria specified in standard C. Fleischmann (*) • A. Buchanan • A. Abu Department of Civil Engineering, University of Canterbury, in Christchurch, New Zealand
test methods, that is, heat transmission and structural integrity. The analysis can be broadly divided into two parts: (1) heat transfer and (2) structural analysis. Heat transfer calculations are used to evaluate the unexposed surface temperature and the temperature distribution throughout the member, in order to evaluate material strength. The structural integrity analysis applies the strength theory [2] used to design reinforced concrete members. The reduced strength of the concrete and steel resulting from elevated temperature is taken into account by using experimental results for the compressive and yield strengths as a function of temperature. This procedure is known as the rational design method. As the fire protection field advances into performance-based engineering, techniques like the rational design method are more likely to be used. In the rational design approach, a design time-temperature curve, based on the expected fire, is specified. The engineer then performs the heat transfer analysis to determine the temperature profile and unexposed surface temperature. Knowing the temperature distribution of the member, a structural analysis is conducted to determine the fire endurance. This chapter presents an overview of the analytical methods for calculating the fire resistance of concrete structural members and provides a description of the mechanical properties for concrete and steel at elevated temperatures. A brief discussion of heat transfer for a concrete assembly is given, along with temperature
M.J. Hurley (ed.), SFPE Handbook of Fire Protection Engineering, DOI 10.1007/978-1-4939-2565-0_54, # Society of Fire Protection Engineers 2016
1949
1950
profiles from ASTM E119 test results. The structural calculations for simply supported and continuous members are explained. A simple example is shown to further demonstrate the basics of the design concept. Fire resistance for columns and walls is also presented. The methodology in this chapter is based largely on ACI216.1-07—Code Requirements for Determining Fire resistance of Concrete and Masonry Construction Assemblies [3], (ACI216) commonly used in North America. Throughout Europe, the Eurocodes for structural design provide comprehensive chapters on fire design. For reinforced concrete, Eurocode 2: Design of concrete structures—Part 1–2: General rules—Structural fire design [4], (EN1992-1-2) gives minimum dimensions and minimum cover necessary to achieve fire resistance ratings for slabs, walls, tensile members, beams, and columns. It also provides information on thermal and mechanical properties of concrete at high temperatures, with recommended design methods. Other than using the given design solutions, Eurocode 2 allows for two overall types of design: “simplified” calculation methods and “advanced” calculation methods. The simplified calculation method is essentially the same as that described in this chapter. The advanced calculation methods include those that provide a more realistic analysis of concrete structures exposed to fire, based on fundamental physical behavior including high temperature effects. The advanced calculation methods are the only option for design of complex structures regardless of the type of fire exposure, because the interaction between different structural members is critical to the fire resistance. Design of composite steel-concrete slabs in fire conditions is given in: Eurocode 4: Design of Composite Steel and Concrete Structures, EN1994-1-2: General Rules— Structural Fire Design [5]. More comprehensive discussions of the rational design methods for calculating the fire resistance of concrete structural members can be found elsewhere [1–8]. For more detailed overview of the “State-of-Art” for fire design of concrete structures the reader is directed to bulletin 38 [9] and 46 [10] written by Task Group 4.3 of the fib ( fe´de´ration internationale du be´ton / The International Federation for Structural Concrete).
C. Fleischmann et al.
Material Properties of Concrete and Steel Most of the material properties for concrete and steel change significantly at elevated temperatures. In order to accurately predict the structural fire resistance of concrete members, these changes must be taken into account. Temperature-dependent values of strength and modulus of elasticity are presented in a graphical format to aid in the design process. Values have been taken from both ACI216 and EN1992-1-2. The thermophysical properties that are required for a heat transfer analysis, i.e., thermal conductivity, specific heat, and density are also functions of temperature. These values are not included in ACI216; therefore only the EN19921-2 values are given below.
Strength The strength of the reinforcing steel changes significantly with temperature and must be taken into account in any structural calculation. Figure 54.1 shows the strength–temperature relationship for hot-rolled, cold-drawn, and highstrength alloy steels from both the ACI216 and EN1992-1-2. Yield strength versus temperature relationship is given for hot-rolled steel, used for reinforcing bars. Tensile strength versus temperature relationship is shown for the cold-drawn steel and high-strength alloy steel, used for prestressing bars, wire, or strands. The change from yield strength to tensile strength for the two steel types relates to the design parameters used for reinforced versus prestressed concrete assemblies. Like steel, the strength of concrete is also diminished at elevated temperatures. Figure 54.2a–c show the strength–temperature relationship for carbonate, siliceous, and sand-lightweight aggregate concretes, respectively. The compressive strength is not only a function of temperature but is also affected by the applied load as shown in ACI216 values given in Fig. 54.2. In Fig. 54.2 the values labeled as (Stressed 0.4f’c) were obtained from specimens initially loaded to 40 % of their
54
Analytical Methods for Determining Fire Resistance of Concrete Members
1951
Temperature (°F)
32
212
392
572
752
932
1112
1292
1472
100 ACI(hot rolled) (Yield strength) ACI(cold worked) (tensile strength) ACI(high strength) (tensile strength) EC2-Class N (hot rolled)
90
% Strength at 20°C (70°F)
80 70
EC2-Class X (hot rolled)
60
EC2-Class N (cold drawn) EC2-Class X (cold drawn)
50 40 30 20 10 0 0
100
200
300
400
500
600
700
800
Temperature (°C)
Fig. 54.1 Strength–temperature relationships for hot-rolled, cold-drawn, and high-strength alloy steels [3, 4]
compressive strength during the heating process; when the desired temperature was reached the samples were then loaded to failure. The values labeled (Unstressed) were heated to the desired temperature and then loaded to failure. Those labeled (Unstressed Residual) were heated, allowed to cool back to ambient temperature and then loaded to failure. Figure 54.2b illustrates that for the Stressed 0.4f’c results the compressive strength of concrete remains relatively unchanged up to 500 C (900 F). Above 500 C (900 F), the compressive strength of the siliceous aggregate concrete starts to decrease rapidly and is considered ineffective at temperatures above 650 C (1200 F), where the compressive strength has been reduced by approximately 50 % of the value at normal temperatures. However, for (Stressed 0.4f’c) carbonate and lightweight aggregates, compressive strength remains relatively unchanged up to 650 C (1200 F) and is not considered to be ineffective until it reaches a temperature of 760 C (1400 F). The experimental method used may influence the reported compressive strength.
Specimens heated without compressive loads and then loaded to failure while hot have lower compressive strengths than those heated while loaded [7]. The EN1992-1-2 results are closest to the ACI Unstressed results.
Modulus of Elasticity The modulus of elasticity for steel decreases as the temperature increases, as shown in Fig. 54.3. Figure 54.4 shows the modulus of elasticity–temperature curve for three different concrete aggregates. In each case, the modulus of elasticity of concrete is greatly reduced at elevated temperatures. This large reduction of the elastic modulus is helpful in reducing induced thermal stresses in concrete members due to fire [7].
Thermophysical Properties The thermophysical properties required for heat transfer calculations are also strong functions of
1952
C. Fleischmann et al. Temperature (°F)
32 100
212
392
572
752
932
1112
1292
400
500
600
700
1472
1652
800
900
% of initial compressive strength
90 80 70 60 50 40 30
(ACI) Stressed 0.4f'c (ACI) Unstressed
20
(ACI) Unstressed Residual 10
EC (Calcareous)
0 0
100
200
300
Temperature (°C)
Carbonate Aggregate
Temperature (°F) 32
212
392
572
752
932
1112
1292
400
500
600
700
1472
1652
800
900
100
% of initial compressive strength
90 80 70 60 50 40 30
(ACI) Stressed 0.4f'c (ACI) Unstressed
20
(ACI) Unstressed Residual EC (Siliceous)
10 0 0
100
200
300
Temperature (°C)
Fig. 54.2 (a) Strength–temperature relationship for carbonate aggregate concretes for different loading conditions [3, 4]. (b) Strength–temperature relationships for siliceous aggregate concretes for different loading
Siliceous Aggregate
conditions [3, 4]. (c) Strength–temperature relationships for sand-lightweight aggregate concretes for different loading conditions [3, 4]
54
Analytical Methods for Determining Fire Resistance of Concrete Members
1953
Temperature (°F) 32
212
392
572
752
932
1112
1292
1472
1652
500
600
700
800
900
100
% of initial compressive strength
90 80 70 60 50 40 (ACI) Stressed 0.4f'c (sanded)
30
(ACI) Unstressed (sanded)
20
(ACI) Unstressed (unsanded)
10 0
(ACI) Unstressed Residual (sanded) 0
100
200
300
400
Temperature (°C)
Lightweight Aggregate
Fig. 54.2 (continued)
Temperature (°C) Modulus of elasticity (% of initial)
Fig. 54.3 Modulus of elasticity for hot-rolled steel at elevated temperatures [11]
204
100
427
649
800 400 Temperature (°F)
1200
90 80 70 60 50 0
temperature especially for concrete. The evaporation of water as well as changes within the cement and aggregate all play a role in the thermophysical properties. Density. Figure 54.5 shows the percentage change in concrete density with temperature. From ambient to 1200 C there is 12 % reduction in the density, with the greatest change occurring between 115 and 200 C. The following relationship can be found in EC1992-1-2 [4].
ρ(θ) ¼ ρ(20 C) ρ(θ) ¼ ρ(20 C) (10.02(θ115)/85) ρ(θ) ¼ ρ(20 C) (0.980.03(θ200)/200) ρ(θ) ¼ ρ(20 C) (0.950.07(θ400)/800)
For 20 C θ 115 C For 115 C < θ 200 C For 200 C < θ 400 C For 400 C < θ 1200 C
Specific Heat. The specific heat, cp(θ), for both siliceous and carbonate aggregates is assumed to be identical for dry concrete with zero moisture content. Specific heat varies slightly with
1954
C. Fleischmann et al.
Fig. 54.4 Modulus of elasticity, at elevated temperatures, for carbonate, siliceous, and lightweight concretes [12]
Temperature (°C) 204
Modulus of elasticity (% of initial)
100
427
649
800 400 Temperature (°F)
1200
Carbonate aggregate
80
60 Siliceous aggregate
40
Lightweight aggregate
20
0 0
Temperature (°F) 32 1
212
392
572
100
200
300
752
932
1112
1292
1472
1652
400
500
600
700
800
900
% of ambient density
0.98 0.96 0.94 0.92 0.9 0.88 0.86
0
Temperature (°C)
Lightweight Aggregate
Fig. 54.5 Percentage change in concrete density as a function of temperature based on the ambient density [4]
54
Analytical Methods for Determining Fire Resistance of Concrete Members
1955
Temperature (°F) 32
212
392
572
752
932
1112
1292
1472
1652
2200 2000 0% MC
Specific Heat (kJ/kg K)
1800
1.5% MC 3% MC
1600 1400 1200 1000
800 600 400 200 0 0
100
200
300
400
500
600
700
800
900
Temperature (°C)
Fig. 54.6 Specific heat for siliceous and carbonate aggregate concrete as a function of temperature incorporating the moisture content [4]
temperature, ranging from 900 J/kg K at ambient to 1100 J/kg K above 400 C. The following relationship can be found in EC1992-1-2 [4].
following values are given in EC1992-1-2 [4] for the constant cp between 100 and 115 C. cp(peak) ¼ 900 J/kg K
cp(θ) ¼ 900 (J/kg K) cp(θ) ¼ 900 + (θ100) (J/kg K) cp(θ) ¼ 1000 + (θ200)/2 (J/kg K) cp(θ) ¼ 1100 (J/kg K)
For 20 C θ 100 C For 100 C < θ 200 C
cp(peak)
For 200 C < θ 400 C
cp(peak)
For moisture content of 0 % of concrete weight ¼ 1470 J/kg K For moisture content of 1.5 % of concrete weight ¼ 2020 J/kg K For moisture content of 3 % of concrete weight
For 400 C < θ 1200 C
However, when moisture is not explicitly included in the analysis and is to be included in the cp value, the specific heat is modelled as a constant value (dependent on the moisture content) from 100 to 115 C and a linear decline from 115 to 200 C as shown in Fig. 54.6. The
Conductivity. The conductivity of concrete can be modeled as a quadratic equation of temperature over the range of 201200 C. Due to the variability in concrete a range is recommended for the conductivity in EC1992-1-2 [4]. Figure 54.7 shows the band between the upper and lower limits.
Upper limit k ¼ 2 0:2451 ðθ=100Þ þ 0:0107 ðθ=100Þ2 W=m K for 20 C θ 1200 C Lower limit
k ¼ 1:36 0136 ðθ=100Þ þ 0:0057 ðθ=100Þ2 W=m K for 20 C θ 1200 C
1956
C. Fleischmann et al. Temperature (°F)
32 2.0
212
392
572
752
932
1112
1292
1472
1652
Upper limit Lower limit
1.8
Conductivity (W/m K)
1.6 1.4
1.2 1.0 0.8 0.6 0.4 0.2 0.0 0
100
200
300
400
500
600
700
800
900
Temperature (°C)
Fig. 54.7 Conductivity for siliceous and carbonate aggregate concrete as a function of temperature showing the upper and lower limit [4]
Heat Transmission The temperature of the unexposed side of concrete floors, roofs, and walls is usually limited to prevent ignition of combustibles in contact with the unexposed surface. In ASTM E119 the criteria are 121 C (250 F) average and 163 C (325 F) single-point temperatures. These criteria often govern the fire resistance of the assembly. In addition to the unexposed surface temperature, the temperature distribution throughout the member is required in order to evaluate the material strengths in the structural calculations. Similar criteria are specified in the ISO 834. Heat is mainly transferred through a solid concrete member by conduction. The temperature of the unexposed side of the slab is a function of the slab thickness and the type of aggregate used. The fire endurance versus slab thickness is presented in Fig. 54.8 for three types of concrete typically used in building
construction. The data is based on actual fire tests of concrete slabs [7]. For the normal-weight concretes used in the fire tests, the maximum aggregate size was 20 mm (0.75 in.) and the air content was about 6 %. The maximum aggregate size for the structural lightweight concretes was slightly less than 20 mm (0.75 in.) and the air content was about 7 %. Although the slab thickness and type of aggregate are the main factors that affect heat transmission through the concrete, other factors do have some impact. These factors include moisture content, unit weight, air content, and maximum aggregate size. Within the usual range of values, water-cement ratio, strengths, and age have been shown to have insignificant effects on the heat transfer process [7]. Floor and roof slabs are often composites of materials, for example, a concrete base slab with overlays or undercoatings of either insulating materials or other types of concrete. Research has been conducted on two-course composite assemblies. An example of a composite slab
54
Analytical Methods for Determining Fire Resistance of Concrete Members
Fig. 54.8 Fire endurance of concrete slabs—effect of thickness and type of aggregate, based on heat transmission [7]
1957
Slab thickness (mm) 5
50
75
100
125
150
175
Structural concretes
Fire endurance (hr)
4
Lightweight Sand-lightweight
3
2 Air-cooled slag Carbonate
1
Siliceous 0 2
of normal and lightweight concrete is shown in Fig. 54.9. Similar plots for different composite assemblies can be found in Abrams and Gustaferro [13]. The temperature on the unexposed side is not the only temperature of concern. The temperature distribution within the member is used to determine the temperature of the reinforcing or prestressing steel. The temperature of the reinforcing bars is approximately equal to the temperature of the concrete at the level of the center of the bar; [7] that is, the presence of the steel is neglected in the heat transfer analysis. Thus, temperature distribution is primarily affected by the type of concrete, shape of the member, and exposure conditions. During fire tests, slabs and walls are typically heated on one side only; beams are heated from one, two, to three sides; and columns are heated on all four sides. Data on the temperature distribution within concrete members are available from results of fire tests. Figures 54.10, 54.11, and 54.12 show the temperatures within a slab exposed to the standard ASTM E119 timetemperature curve for carbonate, siliceous, and sand-lightweight aggregates, respectively. These data apply to any slab thickness, as long as the
3
4 5 Slab thickness (in.)
6
7
slab is at least 25 mm (1 in.) thicker than the point in question. The temperature distribution within a 250 300 mm (10 12 in.) rectangular concrete beam exposed to the ASTM E119 standard time-temperature curve is illustrated in Fig. 54.13. Because the temperature distribution is a function of the beam size, it is not practical to present a complete set of figures. A procedure has been developed in which the temperature distribution can be constructed [7]. With the advent of fast, affordable computers, such empirical techniques are rapidly being replaced by complete numerical modeling of the temperature distribution. Computer models such as FIRES T3 [15], TASEF-2 [16], and SAFIR [17] can accurately predict the temperature distribution in various types of concrete members. These models are capable of handling one-, two-, or threedimensional heat transfer, with time-dependent nonlinear boundary conditions, and temperaturedependent thermal properties. None of these models incorporate mass transfer or moisture migration, and thus require modification to the thermal properties to account for latent heat absorption of the water. All three programs use a finite-element technique to solve the energy
1958
C. Fleischmann et al.
a Normal weight concrete Lightweight concrete Thickness of lightweight concrete base slab (mm) 0 50 75 100 125 25 50 75
25
Carbonate overlay
4
100
125
Siliceous overlay
125 100
4 hr 3
3
3
2 2
75
4 hr
2
1
50
1 25
1
Overlay thickness (mm)
Overlay thickness (in.)
5
0
0
0 0
1
2
3
4
5
0
1
2
3
4
5
Thickness of lightweight concrete base slab (in.) Normal weight concrete overlay on lightweight concrete slab
b Lightweight concrete Normal weight concrete Thickness of normal weight concrete base slab (mm) 25
50
Overlay thickness (in.)
5
75
100
125
0
25
50
Carbonate base slab
75
100
125 125
Siliceous base slab
100
4 4 hr
4 hr
3 3 2
2
2
50
1
1
1
75
3
25
Overlay thickness (mm)
0
0
0 0
1
2
3
4
5
0
1
2
3
4
5
Thickness of normal weight concrete base slab (in.) Lightweight concrete overlay on normal weight concrete slab
Fig. 54.9 Fire endurance of base slabs and overlays of normal weight or lightweight concretes, based on heat transmission [13]
equation and thus require a skilled operator. Recent improvements to SAFIR include element generation, significantly simplifying the input, and reducing time required. Although these models are not necessary for typical analysis
assuming a standard time-temperature curve, with the increased emphasis on performancebased design and more realistic time-temperature curves, the use of such models is likely to increase in the future.
Analytical Methods for Determining Fire Resistance of Concrete Members
Fig. 54.10 Temperatures within solid or hollow-core concrete slabs during fire tests, carbonate aggregate [14]
1959 871
1600 1500
Carbonate aggregate concrete (normal weight)
816 760
1400 1300
1100
m
m
m
(½
704 . in
)
rfa su
m
m
(
ce
538 in
1½
37
800
.)
0
m
m
(2
482 .) in
426
(3
m
m
5
700
649 593
m
m
19
900
(
.)
d se po x e .) m in ro 1 f ( .) m in m ¾
12
1000
in
25
Temperature (°F)
m
6
1200
(¼
75
600 500 1/2
1
1½
Temperature (°C)
54
2
in
.)
371
m 316 m 0 in.) 0 1 4 ( 260 3 4
Fire test time (hr)
871
1600 1500
Siliceous aggregate concrete (normal weight)
816 760 su rfa ed po s .)
fro
593
m
m
(1
in
in .) (¾ m
538 (1
½
in
.)
25
m
1000
649
m
12
1100
19
482 in .
)
m
m
900
426 in
371
600 500 1/2
10 (4 0 m in m .)
75
m m
(3
700
.)
50
m
m
800
(2
37
Temperature (°F)
1200
704
ex
m m
6
(½
m
m
1300
in .)
(¼
in
ce
.)
1400
316 260
1
1½
Fire test time (hr)
2
3
4
Temperature (°C)
Fig. 54.11 Temperatures within solid or hollow-core concrete slabs during fire tests, siliceous aggregate [14]
1960
C. Fleischmann et al.
Fig. 54.12 Temperatures within solid or hollow-core slabs during fire tests, sandlightweight concrete [14]
871
1600 1500
Sand-lightweight concrete
816 760 ce rfa
in
su
m
649
in .
)
25
m
482 426
m
m
(2
37
800
in
m
.)
m
(1 ½
900
538
m
m
1000
m
(¾
(1
in
.)
in .)
fr o
593
Temperature (°C)
m 12
1100
19
Temperature (°F)
1200
704
ex po se d
m
6
(½
m
m
1300
.)
(¼
in
.)
1400
371 (3
in .)
50
700
316
75
m m
600
260
500 1/2
1
1½
2
3
4
700°C (1300°F)
480°C (900°F) 590°C (1100°F) 700°C (1300°F) 820°C (1500°F) 930°C (1700°F)
370°C (700°F)
260°C (500°F)
480°C (900°F) 590°C (1100°F)
260°C (500°F)
150°C (300°F)
Fig. 54.13 Temperature distribution within a 250 mm 300 mm (10 in. 12 in.) lightweight concrete beam, 1- and 3-h exposure time [7]
370°C (700°F)
Fire test time (hr)
C 0° F) 82 00° 5 1 (
125 mm (5 in.)
125 mm (5 in.)
1 hr
3 hr
300 mm (12 in.)
54
Analytical Methods for Determining Fire Resistance of Concrete Members
a M n ¼ As f y d 2
Simply Supported Slabs and Beams Simply supported, unrestrained members are not typically cast in place. However, a discussion of simply supported members will make the discussion of continuous members easier to understand. A simply supported, reinforced concrete slab is illustrated in Fig. 54.14. Note: The calculation methodology closely follows the procedures outlined in ACI216: 2007 [3]. A similar methodology is available in the Eurocode, EN1992-1-2 [4]. The slab is supported by a “frictionless” rollers and a “frictionless” pin, so that the slab is free to expand without resistance but should not deflect at the support. The load, w, is evenly distributed over the surface of the slab, and the reinforcing steel runs the entire length of the slab. Considering these conditions without a fire, the moment diagram for the slab is illustrated in Fig. 54.14b. The moment strength of the slab will be constant along the entire length:
1961
where As ¼ Area of the reinforcing steel fy ¼ Yield stress of the reinforcing steel d ¼ Distance from the extreme compression fiber to the centroid of the reinforcing steel a ¼ Depth of the equivalent rectangular stress block [2]
a¼
As f y 0
0:85 fc b
0
Simply supported one-way slab
Mn
aθ ¼ 1 M = — wL2 8
Normal conditions (no fire)
c
ð54:3Þ
where θ denotes the effects of elevated temperature. The reduced moment strength diagram is shown in Fig. 54.14c. With a reduction in the yield stress, fyθ, there is a corresponding reduction in the size of the equivalent stress block, aθ [7].
W
L
b
ð54:2Þ
fc ¼ Compressive strength of the concrete b ¼ Width of the beam or slab During exposure to a fire, the temperature of the reinforcing steel will increase. As the temperature of the steel increases, the yield strength decreases (see Fig. 54.14c). This reduction in the steel strength causes a reduction of the moment strength of the slab [7]: aθ Mnθ ¼ As f y θ d 2
a
ð54:1Þ
Mnq
1 M = — wL2 8 At 2 hr of fire exposure
Fig. 54.14 Applied moments and reduced moment strength diagrams for simply supported one-way slab [7]
As fyθ 0
0:85 fc b
ð54:4Þ
Typically, the temperature at the top of a slab remains relatively unchanged from normal conditions even after 2 h of fire exposure, since the concrete is a good insulating medium (see Figs. 54.10, 54.11, 54.12). Thus, the values 0 for fc and d are not affected. However, if the temperatures in the compression zone exceed 480 C (900 F) for a siliceous aggregate or 650 C (1200 F) for a carbonate aggregate, 0 the concrete compressive strength, fc , should be reduced (see Fig. 54.2).
1962
C. Fleischmann et al.
As previously noted, the compressive strength of concrete is reduced significantly at a critical temperature, selected here as 650 C (1200 F) for a siliceous aggregate or 760 C (1400 F) for a carbonate aggregate. To account for this substantial reduction in strength, regions of concrete in the compression zone at temperatures above the critical temperature are neglected in the design process. As a result, the depth and/or width of the compression zone are reduced by subtracting the area of the concrete, which is heated in excess of the critical temperature. For a simply supported slab it is unlikely that the compression zone would be heated to above the critical temperature without the steel failing first, but it should be noted that, if the section of concrete is reduced, the value of d in Equation 54.3 must be adjusted accordingly. Flexural failure occurs when the moment strength is reduced to the applied service load moment, M, at the center of the span [7] M¼
wL2 8
ð54:5Þ
where M ¼ Applied service load moment L ¼ Length of the span w ¼ Applied live load plus dead load, with “factor of safety” ¼ 1.0 The factor of safety used in fire endurance calculations is a decision for the authority having jurisdiction. In this section, the fire safety factor has been set equal to 1.0. Load combinations for structural fire design should give lower design loads than those for cold conditions. Guidance on selecting the appropriate safety factors can be found in regulatory documents such as ASCE 7-05 [18]. In North America, guidance is given by ASCE-07 with the recommended load combination for fire conditions being 1.2 dead load + 0.5 live load. Similar load combinations are specified in many other countries. As indicated in Equation 54.3, the structural fire endurance of a simply supported one-way slab or beam is a function of the load intensity, strength– temperature characteristics of the reinforcing
steel, and the depth of protection given to the reinforcement by the concrete cover. There is no benefit of continuity or restraint of thermal expansion with a simply supported slab; the total slab depth, based on heat transmission, ht, required to obtain the desired fire rating is probably as small or smaller than the total slab thickness, hs, required for gravity loads [7]. Therefore, there is no advantage of doing a structural fire endurance analysis for unrestrained, simply supported structural members [7].
Continuous Unrestrained Flexural Members Continuous unrestrained members have a considerably longer fire endurance than simply supported members because of their ability to redistribute the applied moments. Figure 54.15a shows an interior span of a continuous unrestrained slab. The applied moment diagram for a normal condition, with no fire, is shown in Fig. 54.15b. The maximum positive moment occurs near the center of the span, and the maximum negative moments are located over the supports. When the slab is exposed to fire conditions from below, the moments will be redistributed within the slab. This redistribution may be sufficient to cause the negative moment reinforcement to yield. This yielding generally occurs within the first half hour of the fire, based on observation made during standard fire tests [7]. Figure 54.15c shows the redistribution of moments after 2 h of fire exposure (2 h was selected at random). The American Concrete Institute (ACI) warns that increasing the negative reinforcement will increase the attracted negative moment, possibly leading to a compressive failure. It is important that flexural tension governs the design of concrete members. Thus, to avoid compressive failure in the negative moment region, the negative reinforcement should be small enough so that [6]:
54
Analytical Methods for Determining Fire Resistance of Concrete Members
Fig. 54.15 Moment redistribution in interior span of continuous unrestrained one-way slab due to fire exposure [7]
1963
a
W
L Interior span
b
+M max
–M max Normal conditions (no fire), applied moments
c
+M max
–M max At 2 hr of fire exposure, applied moments
As f yθ 0
bθ dθ fc θ
< 0:30
ð54:6Þ
Flexural failure of continuous members occurs when three hinges are formed within a span. One of the hinges will form near the midspan and the other two at the adjacent supports. A hinge is formed at the point where the applied moment is equal to the flexural strength at that point. The flexural strength at any point can be calculated using Equation 54.3 for simply supported members. Figure 54.16 shows the moment diagram for a one-way span with unequal end moments, that is, when the spans are of unequal lengths. This diagram represents the general case and can be used for other conditions, that is, end spans and slabs with equal spans. The member fails when the sum of the flexural strengths is less than the applied moment, wL2/8. The negative moments are calculated at the supports, and the
positive flexural strength is calculated at the center of the span. The negative flexural strength is then used in the following equation for the minimum positive flexural strength [7]: Minimum positive M M Mnθ1 flexural strength Mnθ ¼ nθ1 2 nθ2 2 2wL required 2 Mnθ2 wL þ 2 8 ð54:7Þ If the minimum positive flexural strength required is less than the positive flexural strength, the member has the calculated fire endurance. The location of the maximum positive moment, X1, is calculated from X1 ¼
L þ 2
M nθ1 Mnθ2
wL
ð54:8Þ
1964
C. Fleischmann et al.
Fig. 54.16 Redistributed applied moment diagram at structural endpoint for span of a uniformly loaded continuous one-way slab or beam with unequal end moments [7]
X1 M+ nθ M– nθ
wL2 —— 8
1
M– nθ
2
L /2 L
Fig. 54.17 Redistributed applied moment diagram at structural endpoint for end span of a continuous one-way slab or beam [7]
L X2 = 2X1
X0
X1 M+ nθ wL2 —— 8
M –nθ
L/2
End Span
Equation 54.8 becomes
Equations 54.7 and 54.8 can be modified and used for the end span of a continuous member (Fig. 54.17). For the end span, Mn ¼ 0, leaving Minimum required 2 Mnθ M wL2 þ Mnθ ¼ nθ þ 2 2 8 2wL X1 ¼
L M nθ 2 wL
ð54:9Þ
ð54:10Þ
Interior Span with Equal End Moments Equations 54.7 and 54.8 can also be modified for spans with equal end moments, as indicated in Fig. 54.18. For this case, M nθ1 ¼ M nθ2 , changing Equation 54.7 to Minimum required Mþ nθ ¼
wL2 M nθ ð54:11Þ 8
X1 ¼
L 2
ð54:12Þ
The location of the points of inflection, X0, is dependent on the magnitude of the negative flexural strengths and can be calculated using rffiffiffiffiffiffiffiffiffiffiffi 2Mþ L nθ X0 ¼ ð54:13Þ 2 w The negative moment reinforcement must be extended a sufficient distance beyond the point of inflection to allow the bar strength to become fully developed. Design criteria for the development length are outlined in the ACI Building Code Requirements for Reinforced Concrete [2]. It is further recommended that at least 20 % of the maximum negative moment reinforcement in the span extends throughout the entire length of the span.
54
Analytical Methods for Determining Fire Resistance of Concrete Members
Fig. 54.18 Redistributed applied moment diagram at structural endpoint for symmetrical interior span of a uniformly loaded continuous one-way slab or beam [7]
1965
M+ nq wL2 —— 8
M –nq X0
X2
X0
L
Fig. 54.19 Maximum thrust for allowed expansion of reference specimens [21]
Allowed longitudinal expansion in 5.5 m (mm) 6
12
19
Maximum thermal thrust (kips)
500
25
32
A
Normal weight concrete conventionally reinforced
B
Normal weight concrete prestressed
C
Lightweight concrete conventionally reinforced
400 D
38 2670
2225
1780
Lightweight concrete prestressed
1335
300 A B
200
890
Maximum thermal thrust (kN)
600
0
C
445
100 D
0 0
Fire Endurance of Concrete Structural Members Restrained Against Thermal Expansion When a fire occurs beneath an interior portion of a floor or roof slab, the heated portion of the slab tends to expand. As this portion of the slab expands, the surrounding cooler portions resist the expansion and exert a resistive force on the heated portion of the slab. This resistive force is referred to as the thermal thrust force. Most U.S. fire tests of floor slabs are conducted with the specimen mounted within a restraining frame which restricts the thermal expansion [19]. The amount of restraining force provided by the restraining frame varies from
0.25 0.50 0.75 1.00 1.25 Allowed longitudinal expansion in 18 ft (in.)
0 1.50
one laboratory to another, based on factors such as frame design, specimen design, and specimen tightness. Prior to 1960, no research had been conducted to measure the magnitude of the thermal thrust force. In 1960, the Portland Cement Association (PCA) began operation of its floor furnace [20]. This furnace allowed for both variable and monitored restraint during the fire test. Restraining the slab against expansion greatly affects the thermal thrust, as indicated in Fig. 54.19. Notice that with no expansion allowed, the thermal thrust force would be very high, which would cause compression failure of the concrete. However, with only a slight increase in the allowed expansion, there is a significant decrease in the thermal thrust force.
1966
C. Fleischmann et al.
.0005
.0002
300 5
.0001
200
9
8
7
10 d
100
0
se
es
str
.0005
a
( LL )
.001
Re in fo rc ed
6
e Pr
0
Z
4
Strain parameter
.001
A in — = S
) m
4
10
100
3
m
5 m 00 )6 (2 m 200 50 m m) 7 5 8 m 6 )1 9 0 7 8 9
2
.002
.
2 3
m
m )4
= A — S in .
m
m )3
400
5
(2
(1 50
.002
(2
300
m
.005
1
(1 00
5
1
1
m m )2
Z
(7
500
( AET )
(5 0
400
.005
) m m ) 0 m (5 m 2 ) 5 m (7 m 3 00 ) (1 m 4 m ) 50 5 m 1 ( m ) 6 0 m m 7 (20 8 50 9 0 (2 1
Thrust parameter
( AET )
)1
Thrust parameter
m
a
m
( LL )
5
.01 Lightweight concrete (expanded shale aggregate)
Strain parameter
(2
500
600 × 10–6
.01
Normal weight concrete (carbonate aggregate)
Re Pr info es r tre ced ss ed
600 × 10–6
.0002
.0001
Fig. 54.20 Nomographs relating thrust parameter, strain parameter, and ratio of cross-sectional area to heated perimeter [21]
It should also be noted that the thermal thrust force developed in lightweight concrete is considerably less than is developed within normalweight concrete. This condition is believed to be due to the lower modulus of elasticity and the lower coefficient of expansion of the lightweight concrete [7]. As a result of the fire research done at PCA, the thermal thrust force was found to vary with the initial modulus of elasticity and the heated perimeter [22]. The heated perimeter, S, is defined as that portion of the perimeter of a section of the specimen, normal to the direction of the thermal thrust, that is exposed to fire. Having assembled a large database of “reference specimens,” the thermal thrust from these specimens can be used to predict the thermal thrust within a concrete member [21]: T1 T 0 Z0 ¼ A1 E 1 A0 E0 Z 1
ð54:14Þ
where Z0 ¼ A0/S0 Z1 ¼ A1/S1 S0 ¼ Heated perimeter of the reference member S1 ¼ Heated perimeter of the member in question T1 ¼ Maximum thermal thrust of the member in question T0 ¼ Maximum thermal thrust of the reference member
A0 ¼ Cross-sectional area normal to the direction of thermal thrust of the reference member A1 ¼ Cross-sectional area normal to the direction of thermal thrust of the member in question E1 ¼ Modulus of elasticity of the member in question E0 ¼ Modulus of elasticity of the reference member The parameter T/(AE) is dimensionless, thus the units used for T, A, and E must be consistent. Nomographs, presented in Fig. 54.20, are used to solve Equation 54.14. For any given partially restrained expansion of a concrete member exposed to fire, there is a compatible thermal thrust developed in the fireexposed portion. The effect of the thermal thrust on the structural behavior of a reinforced concrete slab is the same as that of a prestressing force along the line of action of the thrust. In structural fire endurance calculations, the flexural strength is the primary interest, for which case the thermal thrust can be considered a “fictitious reinforcement” along the line of an action of the thrust [23]. The moment due to the thermal thrust, referred to as the thrust moment, is equal to the thrust force multiplied by the distance between the line of action of the thermal thrust and the centroid of the compression block [21]
Analytical Methods for Determining Fire Resistance of Concrete Members
aþ MT ¼ T d 1 Δ θ 2
ð54:15Þ
where aθ þ ¼
þ T þ Aþ S f y0
ð54:16Þ
0
0:85 fc θ bθ
T ¼ Magnitude of the thermal thrust dt ¼ Distance from extreme compression fiber to the line of action of the thermal thrust, T Δ ¼ Deflection of the slab at the point in question MT ¼ Thrust moment strength The line of action of the thermal thrust must act below the resultant of the equivalent rectangular stress block in order to contribute to the fire endurance of the slab. Results from fire tests have shown that the line of action for the thermal thrust is near the bottom of the member throughout the fire test in most cases, particularly when the thrust is small [21]. Although the line of action acts near the bottom, the actual position changes during the fire test. The exact location of the line of action depends on the shape of the member, type of concrete, amount of reinforcement, stiffness of the restraining frame, and the amount of expansion permitted. Table 54.1 is used to locate the line of action of the thermal thrust for floor systems developing a minimal restraint to thermal expansion. The guidelines
presented in Table 54.1 are based on results from standard fire tests [21]. In order to calculate the thrust moment, the deflection must be estimated. Since the deflections at the supports are assumed to be zero, the only other deflection of interest is at the midspan. The midspan deflection can be approximated using the following equation derived from the deflection equation for simply supported members [21] Δ1 ¼
L21 Δ0 3500yb1
ð54:17Þ
where Δ1 ¼ Deflection for the member (in.) Δ0 ¼ Deflection for the reference member (in.) (Fig. 54.21) L1 ¼ Length of the span of the member (in.) yb1 ¼ Distance from the centroidal axis to the extreme fiber (in.) Table 54.1 Location of thermal thrust line [6] Type of construction Solid slab
Slab-and-joist
Fire exposure (h) 2 3 4 2 2–4
Location of thrust line at supportsa 25 mm (1 in.) 32 mm (1.25 in.) 38 mm (1.5 in.) 0.1 h 0.15 h
Distance above bottom of member where h ¼ overall depth of the joist and slab
a
5
Midspan deflection, Δ0 (in.)
Fig. 54.21 Idealized midspan deflection, Δ0, of reference specimens with minimal restraint [7]
1967
125
4
100
Lightweight concrete
75
3
Normal weight concrete
2
50
25
1
0 0
1
2 Fire test time (hr)
3
4
Midspan deflection, Δ0 (mm)
54
1968
C. Fleischmann et al.
In SI units, Equation 54.17 becomes Δ1 ¼
L1 Δ0 88,900yb1
where Δ, L, and yb1 are all in mm. Equation 54.17 is for members with minimal restraint to thermal expansion. Another equation should be used when the thrust is greater than minimal [7].
In order to summarize and illustrate how to apply this information to calculate the structural fire endurance for reinforced concrete members, a step-by-step procedure is presented. This procedure was taken from the Concrete Reinforcing Steel Institute (CRSI), Reinforced Concrete Fire Resistance (Table 54.2) [7].
Table 54.2 Step-by-step procedure—structural analysis for fire endurance Step no. 1 2 3 4 4a
Description From the building code governing the project (model, municipal, state, etc.), look up the required fire ratings Determine the total depths of slabs, ht, based on heat transmission to provide the required fire ratings Compare ht vs. hs, total slab thickness If ht < hs, no further fire endurance considerations are necessary If the governing building code permits a reduced fire rating for heat transmission as long as the required structural fire rating is provided, then proceed to Step 5 5 Only if ht > hs (or as in step 4a), compute the structural fire endurance, in hours, based on continuity and/or restraint to thermal expansion Structural fire endurance for simply supported or continuous slabs with no axial restraint 6 Solid slabs. Compute the reduced nominal positive and negative flexural strengths, Mþ nθ and Mnθ , available at the required fire rating, for example, 3 h 7 Interior spans. If the absolute sum of available nominal flexural strengths is equal to or greater than the 2 applied moment, that is, if Mþ nθ þ Mnθ wL =8 the fire endurance is equal to or greater than the required fire rating 7a Exterior spans. Using either the reduced nominal negative or positive flexural strength available at the specified fire endurance, compute the minimum required nominal flexural strength 8 If the nominal flexural strength available is equal to or greater than the minimum required nominal flexural strength, the structural fire endurance is adequate—go to Step 9 8a If the nominal flexural strength available is less than the required nominal flexural strength, the structural fire endurance based on continuity only is not sufficient—go to Step 10 9 If continuity only is considered in the structural fire endurance calculations, and restraint to thermal expansion is neglected, check the lengths of the top reinforcing bars to make sure the bars are long enough to develop the required nominal negative flexural strength Note: The procedure for analyzing continuous beams and joist systems is the same as for the solid slab above, except that isothermal diagrams would be required for determining the available nominal flexural strengths Structural fire endurance based on restraint to thermal expansion 10 Estimate the deflection Δ1, of the heated slab, assuming minimal restraint occurs 11 Locate the line of action of the thermal thrust force at the supports 12 Compute the moment, MT, that the thermal thrust force has to develop to provide the required additional nominal positive flexural Strength for the specified fire endurance MT ¼ Min: reqd Mþ nθ Available Mnθ 13 Compute the thermal thrust, T1, required to produce MT using Equation 54.15 14 Compute the thrust parameter, T1/A1E1 15 Compute the value of z ¼ A1/s 16 With T1/A1E1 and z, determine the strain parameter 17 Compute the expansion ΔL, by multiplying the strain parameter by the heated length, Lh, of the member 18 Determine if the restraining elements, that is, spandrel or effective edge beams, columns, walls, and so forth, can withstand the thermal thrust, T1, with a displacement no greater than the expansion, ΔL
54
Analytical Methods for Determining Fire Resistance of Concrete Members
Fig. 54.22 One-way continuous slab, supported on beams [7]
1969 6.1 m (20 ft)
6.1 m (20 ft) 200 mm (8 in.)
A
Ext. cols. — 16 in. × 16 in. 3.65 m (12 ft)
A 3.65 m (12 ft)
Partial framing plan
400 mm (16 in.)
400 mm (16 in.)
h = 100 mm (4 in.)
3.25 m (10 ft 8 in.) 3.7 m (12 ft 0 in.)
3.0 m (10 ft 0 in.)
Section A–A
Example of Continuous One-Way Span The continuous one-way span example has been included to illustrate the step-by-step procedure for structural analysis for fire endurance that is used. The example problem is for a one-way continuous slab with no thermal restraint assumed. The slab is found to have the desired fire endurance, but the development length of the steel bars required for the negative moment strength is significantly longer than is required for standard gravity loading. The development length is then recalculated assuming minimal thermal restraint. Given. A one-way, multispan continuous slab supported on beams as shown in Fig. 54.22. The slab is 100 mm (4 in.) thick with 3.7 m (12-ft) beam spacing. The concrete for the slab is made from siliceous aggregate with a compressive strength of 20.7 MPa (3000 psi). The slab is
subjected to a 3.8 kPa (80 psf) superimposed live load and a 0.25 kPa (5 psf) dead load. The reinforcement consists of No. 4 bars that meet the requirements of ASTM for A615 Grade 60 (415 MPa). Reinforcing bars are placed in accordance with the 1984 CRSI Handbook [24]. Problem: Determine if the slab has a 2 h fire endurance. Step 1: Determine the required fire rating: 2 h, as stated in the problem. Step 2: Determine the total depth of the slab, ht, based on heat transmission: From Fig. 54.8, ht ¼ 125 mm (5 in.). Step 3: Compare ht versus hs:ht ¼ 125 mm (5 in.) > 100 mm (4 in.) ¼ hs. Step 4: In this example, the authority having jurisdiction has waived the requirements for heat transmission, as long as the required structural fire endurance is provided. Step 5: Because 125 mm (5 in.) is greater than 100 mm (4 in.), the fire endurance for the end span must be computed based on continuity only.
1970
C. Fleischmann et al.
aθ þ 570ð174Þð75 5:6=2Þ þ Mnθ þ ¼ Aþ f d þ ¼ s yθ 2 1 106
Structural Fire Endurance Based on Continuity Only Step 6: Compute the reduced positive and nega– tive moment strengths, M+nθ and Mnθ , respectively, available after 2 h. Step 6a: Mþ nθ available at 2 h. U+ for bottom bars, U þ ¼ 19 þ 6 ¼ 25 mm (1.0 in.) (Fig. 54.23). At 2 h, U+ ¼ 25 mm (1.0 in.), θs+ ¼ 360 C (1170 F) (see Fig. 54.17). f þyθ ¼ 0:42ð414Þ ¼ 174 M pa ð25:2 ksiÞ (see Fig. 54.1). Reinforcing is 12.5-mm bars at 215 mm (#4 bars at 9 in.) 2 2 Aþ s ¼ 570 mm =m 0:27 in: =ft Aþ is calculated from the rebar spacing s requirements. aþ θ ¼
þ Aþ s f yθ 0
0:85 f c b
¼
570ð174Þ 0:85ð20:7Þð1000Þ
¼ 5:6 mmð0:22 inÞ½from Equation 54:4
Fig. 54.23 Mþ nθ calculation for bottom bars
¼ Mþ nθ ¼ 7:3 kN m=m ð1:64 ft kips=ftÞ ½from Equation 54:3
Step 6b: Mþ nθ available at 2 h The bottom 25 mm (1 in.) has been neglected, because the concrete temperature is above 0 650 C (1200 F) with a significantly reduced fc . Top bars,U ¼ 100 ð19 þ 6Þ ¼ 75 mm(3.0 in.) (Fig. 54.24). At 2 h, U ¼ 75 mm ð3:0 in:Þ, θ ¼ 270 C (520 F). (see Fig. 54.11). f yθ ¼ 0:83 ð414Þ ¼ 344 MPa ð49:8 ksiÞ (see Fig. 54.1). The f yθ stress block, a θ , is estimated to be about 16 mm (0.625 in.) with a temperature ranging from 650 to 480 C (1200–900 F). Temperature values are estimated from Fig. 54.11. The average temperature is approximately 565 C (1050 F). In this example the 0 stressed fcθ curve was accepted by the AHJ as the appropriate strength for this design.
12.5 mm bars at d + = 75 mm (3 in.) 215 mm (#4 at 9 in.)
100 mm (4 in.)
0.85f ⬘c
d+ – a +q
0.5a + q
99 kN (20 kips)
570(174) = 99 kN (20 kips)
19 mm (3/4 in.) CLR u + = 25 mm (1 in.)
Fig. 54.24 M nθ calculation for top bars
19 mm (3/4 in.) CLR.
100 mm (4 in.)
a –q
510(344) = 175 kN (39 kips)
d –q = 50 mm (2 in.) 0.85f ⬘c q Neglect 25 mm (1 in.) 12.5 mm bars at – u = 75 mm 25 mm 240 mm (#4 at 10 in.) ( 1 in.) (3 in.)
d –q – 0.5a –q 175 kN (39 kips)
54
Analytical Methods for Determining Fire Resistance of Concrete Members
Fig. 54.25 Top bar lengths at 2 h of fire exposure
1971 1.2 m (3 ft 10 in.)
1.25 mm at 240 mm (#4 at 10 in.)
0.6 m (2 ft)
100 mm (4 in.) 400 mm (16 in.)
400 mm (16 in.) 3.25 m (10 ft 8 in.) 3.65 m (12 ft 0 in.) 0
fcθ ¼ 0:65 ð20:7Þ ¼ 13:5 MPa ð1:95 ksiÞ (see Fig. 54.2). d θ ¼ 100 ð19 þ 6 þ 25Þ ¼ 50 mm ð2:0 in:Þ. Reinforcing is 12.5-mm bars at 240 mm (#4 at 10 in.) 2 2 A s ¼ 510 mm =m 0:24 in: =ft a θ ¼
A s f yθ 0
0:85 fcθ b
¼
510ð344Þ 0:85ð13:5Þð1000Þ
¼ 15 mm ð0:60 in:Þ½from Equation 54:4 8 aθ 510ð344Þð50 15=2Þ > > > Mnθ ¼ As f yθ d θ 2 ¼ < 1 106 ¼ Mnθ ¼ 7:5 kN m=m > > > : ð1:69 ft kips=ftÞ ½from Equation 54:3
strength, structural fire endurance is adequate. Because the moment strength available, 7.3 kN · m/m (1.64 ft · kips/ft), is for practical purposes equal to the required moment strength, 7.3 kN · m/m (1.64 ft · kips/ft), the structural fire endurance for the end span is 2 h. Step 9: Check the lengths of the top reinforcing bars to make sure the bars are long enough to develop the required negative moment strength. The length of the top bars under normal conditions, considering only gravity loads and no fire, is taken from the CRSI Handbook [24] (Fig. 54.25). Step 9a: Top bar lengths, at first interior support, neglecting restraint to thermal expansion The distance to the point of inflection at first interior support for structural fire endurance is calculated using
Step 7: Calculate the minimum positive moment required at 2 h. Minimum required 2 Mnθ M wL2 þ Mnθ ¼ nθ þ 2 2 8 2wL w ¼ 0:1ð24Þ þ 0:25 þ 3:8 ¼ 6:45 kN=m ð0:44 kips=ftÞ Minimum required ð7:5Þ2 7:5 6:45ð3:65Þ2 Mþ þ nθ ¼ 2 2 8 2ð6:45Þð3:65Þ
X0 ¼
2M nθ wL
Because the negative reinforcement generally yields early in the fire, as discussed previously, within the first half hour, the value for the negative moment used in Equation 54.13 should be the maximum negative moment that the beam can support.
Mþ nθ ¼ 7:3 kN m=mð1:64 ft kips=ftÞ
510ð415Þ ¼ 12 mm ð0:47 in:Þ 0:85ð20:7Þð1000Þ a 510ð415Þð75 12=2Þ ¼ A f d M s y n 2 1 106 ¼ Mn ¼ 14:6 kN m=mð3:28 ft kips=ftÞ
Step 8: If the positive moment strength available is greater than the required positive moment
The value used for w is left to engineering judgment based on the expected loading during a fire.
Minimum required
a¼
As f y 0
0:85 f c b
¼
1972
C. Fleischmann et al.
X0 wL 1:2ð4:55Þð3:65Þ ¼ 2 2 ¼ 10 kN m=mð2:25 ft kips=ftÞ
For this example, the full dead load and one-half the live load is used. w ¼ 0:1ð24Þ þ 0:25 þ 1:9 ¼ 4:55 kN=mð0:31 kips=ftÞ X0 ¼
2ð14:6Þ ¼ 1:75 m ð5 ft 9 in:Þ 4:55 3:65
The distance the top bars have to be embedded beyond the point of inflection is given in the ACI Building Code [2]. At least one-third of the bars should be embedded 1/16 of the clear span, d, or 12db, whichever is greater. In this example, the 1/16 of the clear span criterion governs (250 mm or 10 in.). Thus, some of the top bars must extend 2.0 m (6 ft 6 in.) into the end span. The length of the top steel, 2.0 m (6 ft 6 in.), is nearly twice the required length for the gravity load (1.2 m or 3 ft 10 in.). The maximum negative moment strength, Mn, used in Equation 54.13, represents the most severe condition for the development length. However, the assumption of frictionless roller bearing supports used in the above example neglected the restraining force in all calculations. The restraining force, or thermal thrust, T, is developed early in the fire, producing a moment opposite the support moment, which acts to reduce the magnitude of the support moment. The net support moment will then be less than the moment strength, M n , used in the calculation above, thereby overestimating the development length required for the desired fire endurance [7]. The restraint criteria discussed will be used to determine if there is sufficient restraint developed in the longitudinal direction, to reduce the development lengths to that required for the gravity load. Step 9b: Top bar lengths, at first interior support, including restraint to thermal expansion Using X0 ¼ 1.2 m (3.83 ft), the length required for gravity loading, we can determine the net moment at the support required. X0 ¼
2M n wL
ð54:18Þ
M n ¼
The thermal thrust must produce a moment equal to MT ¼ 14:6 10:0 ¼ 4:6 kN m=mð1:04 ft kips=ftÞ Early in the fire, T will act at or near the bottom of the slab (see Table 54.1). T is assumed to act 12 mm (1/2 in.) above the bottom of the slab (taking the fire exposure as approximately one-half hour): d T ¼ 100 12 ¼ 88 mmð3:5 in:Þ Δ ¼ 0 at the support The depth of the stress block, aþ θ , is assumed initially to be zero because the required thrust is small. T¼
MT 4:6ð1000Þ þ ¼ 88 0 0 d T Δ aθ
¼ 52:3 kN=mð3:6 kips=ftÞ Recalculating aþ θ, aþ θ ¼ T¼
T 52:2 ¼ 3 mmð0:13 in:Þ ¼ 0 0:85 f c b 0:85ð20:7Þ
4:6ð1000Þ ¼ 53:2 kN=mð3:65 kips=ftÞ 88 0 3=2
Compute the expansion, L, that corresponds to T ¼ 53:2 kN=mð3:65 kips=ftÞ E1 ¼ 25, 000 MPa 3:6 106 psi A1 ¼ 1:0ð0:1Þ ¼ 0:1 m2 =m 48 in:2 =ft T1 53:2 ¼ 21 106 ¼ A1 E1 0:1ð25Þ Z¼
A1 0:1 ¼ 0:1 m ¼ 100 mmð4 in:Þ ¼ 1 s
54
Analytical Methods for Determining Fire Resistance of Concrete Members
ΔL ¼ 0:006 ðfrom Fig: 54:18Þ Lh L ¼ 0:006 3652 ¼ 22ð0:86 in:Þ In order to maintain equilibrium of the horizontal forces and compatibility of the displacements, the restraining elements must withstand T ¼ 53.2 kN/m (3.65 kips/ft) and not deflect more than ΔL ¼ 22 mm (0.86 in.). The next step would be to check the strength and stiffness of the restraining elements, that is, the exterior spandrel beams and columns of the exterior support and the plane floor area of the first interior support. In this example, it is not necessary to check the strength and stiffness toward the interior of the structure, because there is considerable restraint from the large unheated floor area and many columns to provide the thrust moment at the first interior support [7]. However, the spandrel beams and columns at the exterior support should be checked to ensure that there is sufficient strength and stiffness to resist the thrust moment. Determining the strength and stiffness of the spandrel beams and columns requires a long and complex structural analysis and is not shown here. An explanation of the structural analysis of spandrel beams and columns can be found in the literature [7]. Assuming there is sufficient restraint in the spandrel beams and columns to resist the thrust moment, the required length of the top bars over the first interior support at 2 h of fire exposure must be determined. Neglecting restraint to thermal expansion, X0 ¼
2M 2ð7:5Þ nθ ¼ 0:90 mð2:96 ftÞ ¼ ð4:55Þð3:65Þ wL
As previously discussed, at least one-third of the top bars should be embedded 1/16 of the clear
1973
span at the point of inflection, X0, therefore the top steel should extend 1.1 m (3 ft 8 in.) into the end span. This length is less than the top bar length required for gravity loads, so no adjustment in the length of the reinforcement steel is required to obtain the desired fire endurance.
Reinforced Concrete Columns Throughout the history of concrete construction, reinforced concrete columns have performed well when exposed to fire. The reason for this is threefold: 1. Columns are generally large enough to prevent the center core from losing a significant amount of strength even in prolonged fire exposure. 2. Ties or spirals contain the concrete within the core. 3. The vertical reinforcing bars are generally protected by at least 48 mm (1–7/8 in.) of concrete cover, thereby insulating the steel bars [7]. Most of the building codes in the United States assign 3- and 4-h fire resistance to reinforced concrete columns larger than 300 300 mm (12 12 in.) for square shapes, or a diameter of at least 300 mm (12 in.) for round columns. ACI recommends that columns with a specified compressive strength f’c 82.7 MPa (12,000 psi) should have the least dimension of the column sized in accordance with Table 54.3. In addition, minimum concrete cover thickness over the main longitudinal reinforcements should be at least 25 mm (1 in.) times the number to hours of required fire resistance to a maximum of 50 mm (2 in.). The detailing of the ties is also
Table 54.3 Minimum concrete column size
Carbonate Siliceous Semi-lightweight
Minimum column dimension for fire resistance rating, mm (in) 1h 1.5 h 2h 3h 200 (8) 225 (9) 255 (10) 280 (11) 200 (8) 225 (9) 255 (10) 305 (12) 200 (8) 216 (8.5) 225 (9) 270 (10.5)
4h 305 (12) 356 (14) 305 (12)
1974
quite important. ACI216.07 specifies that the ties should be formed with hooks having a six-diameter extension that engage the longitudinal reinforcements and project into the interior of the hoop. Detailed assessments of reinforced concrete columns exposed to fires have been made by Anderberg [25] and Lie and Irwin [26]. EN1992-1-2 uses a more detailed methodology for assessing fire resistance of concrete columns which accounts for the height of the column, slenderness ratio and eccentricity of the loading.
Reinforced Concrete Frames It is not possible to use simple hand calculation methods for accurate structural design of reinforced concrete frame structures exposed to fires. Individual concrete members can be designed by the methods described above, but for moment-resisting frames, a special purpose computer program is necessary for detailed analysis and design. Available programs include FIRES-RC-II [27], CONFIRE [28], SAFIR [17], and DIANA [29].
Reinforced Concrete Walls Typically, the fire endurance of concrete and concrete masonry walls is determined by heat transmission criteria as opposed to structural performance [6, 7]. As a result, estimating the fire resistance of walls can be accomplished using a heat transfer analysis only. For this reason, the discussion of thickness requirements presented in the heat transmission section can be used. The required thickness can be determined graphically or by applying a heat transfer computer model. The distinction between bearing and nonbearing walls is based on building code structural requirements and not fire endurance. For example, some building codes require bearing walls to be thicker than nonbearing walls. Such a requirement has not been justified by results of a fire test. [7] ASTM E119 requires that a superimposed load be applied and maintained at
C. Fleischmann et al.
a constant magnitude throughout the test of a bearing wall. When testing nonbearing walls, there is no applied load; however, the edges of the walls may be restrained against thermal expansion, in which case a thermally induced load is applied during the fire test. This thermally induced load is of much greater magnitude than the load applied to bearing walls [7].
Prestressed Concrete Assemblies Most of this chapter refers to reinforced concrete. The same principles apply to prestressed concrete, which is often more vulnerable in fires for the following reasons: prestressing steels are much more sensitive to elevated temperatures than mild steel reinforcing bars; prestressed concrete is often manufactured in slender components with thin cover concrete; and some failure modes such as debonding, shear, and spalling are more critical in prestressed concrete. Procedures are also available to calculate the fire resistance of prestressed concrete members. The reader is directed to Design for Fire Resistance of Precast Prestressed Concrete [30].
Composite Steel-Concrete Construction Composite steel-concrete construction refers to concrete slabs cast on permanent steel-deck formwork and steel beams which act compositely with the concrete slab to resist bending moment, as shown in Fig. 54.26. Composite steel-concrete slabs have excellent integrity in fire conditions because even if cracks occur in the concrete slab, the continuous steel deck will prevent any passage of flames or hot gases through the floor. To meet the insulation criterion, it is simply necessary to provide sufficient thickness of slab. A solid slab of uniform thickness requires the same thickness as a normal reinforced concrete slab, but for other profiles it is necessary to evaluate an effective thickness. Generic listings are given in some codes including Eurocode 4 [5], and manufacturers of steel
54
Analytical Methods for Determining Fire Resistance of Concrete Members
Fig. 54.26 Composite steel-concrete construction
1975
Concrete slab
Steel decking
Welded stud Steel beam
decking have proprietary ratings for their products. It is possible to spray the underside of the steel sheeting with spray-on insulation, but this method is rarely economical. The strength of composite steel-concrete slabs is severely influenced by fire because the steel sheeting, acting as external reinforcing, loses strength rapidly when exposed to the fire. However, composite slabs can achieve good fire resistance because of three contributing factors: axial restraint, moment redistribution, and fire emergency reinforcement. Composite slabs often have different fire resistance ratings for restrained and unrestrained conditions [31]. During a fire test, if a composite slab is built into a rigid testing frame which allows almost no axial expansion, the slab can achieve a fire resistance rating with no reinforcing other than the steel sheeting, because of the thermal thrust developed at the supports. Some buildings are sufficiently stiff and strong to provide such restraint to a fire-exposed floor system, but because the amount of restraint is difficult to assess accurately, it is usual to rely on some reinforcing within the slab. If the nominal reinforcing provided to control shrinkage cracking is placed near the top of the concrete and if the slab is continuous over several supports, it can develop significant negative flexural capacity through moment redistribution and hence retain sufficient load capacity during the fire. If a slab is simply supported, or if
moment redistribution is insufficient to resist the applied loads, it is common practice to place fire emergency reinforcing in the slab, consisting of steel reinforcing bars in the troughs of the sheeting, with sufficient cover from the bottom surface to control temperatures in the bars. The flexural strength of the slab can be calculated in the usual way using the temperature of the rebars. Further design recommendations are given by ECCS [32], Lawson [33], and Eurocode 4 [5].
Recent Developments There is continuing international research on fire performance of reinforced concrete. Several recent developments are described below.
Calculation of Temperatures Recent publications on thermal and mechanical properties of concrete at high temperatures are given by Harmathy [34], Schneider [35], Bazant and Kaplan [36], and Neville [37]. A simple, approximate formula for calculating internal temperatures in reinforced concrete members exposed to the standard fire has been developed by Wickstro¨m [38]. Internal temperatures in concrete slabs and beams exposed to realistic fires are given by Wade [39].
1976
Spalling The design methods in this chapter are based on the assumption that the concrete remains intact for the duration of the fire. This assumption is invalid if the cover concrete spalls off during the fire, exposing reinforcing steel to the fire temperatures. Experiments and real fire experience have shown that most normal weight concrete members can withstand severe fires without spalling, but spalling does occur sometimes. In some cases spalling is related to the type of aggregate, but it is more often linked to the behavior of cement paste. It is generally agreed that spalling most often occurs when water vapor is driven from the cement paste during heating, with high pore pressures creating high tensile stresses in the concrete. Spalling can also occur as result of the presence of high compressive stresses [40]. Susceptibility to spalling results from high free-moisture content (such as in fresh concrete), rapid rates of heating, low water-cement ratio, large aggregate size, low tensile strength of concrete, dense reinforcement, nonuniform thickness of the member, and prestressing. Recent reviews of concrete spalling in normal weight concrete are provided by Hertz [41] and Connolly [42], and in high strength concrete by Ali [43] and Phan [44]. The most promising new development to reduce spalling is the addition of fine polypropylene fibers to the concrete mix so that the polypropylene melts during the fire exposure, leaving cavities through which the water vapor can escape [45].
C. Fleischmann et al.
400 C, with explosive spalling being a problem in some cases. High-strength concrete is more susceptible to spalling since it has smaller freepore volume (higher paste density), so that the pores become filled with high-pressure water vapor more quickly than in normal weight concrete. Fire tests on high-strength columns are reported by Aldea et al. [46] and Kodur [45], and fire tests on high-strength beams are reported by Felicetti and Gambarova [47]. Design recommendations are given by Tomasson [48], who suggests a simple method that ignores concrete above 500 C (950 F) for slabs and beams and above 400 C (750 F) for columns. A study on residual mechanical properties of highstrength concrete after exposure [49] shows that strength and stiffness of high-strength concrete decrease significantly in fire, and the recovery of strength afterwards is negligible.
Fiber-Reinforced Concrete Thermal and mechanical properties of steel-fiber reinforced concrete at elevated temperatures are described by Lie and Kodur [50]. They show that the presence of steel fibers increases the ultimate strain and improves the ductility of the concrete during fire exposure. An extensive survey of the mechanical behavior of steel-fiber reinforced concrete at high temperatures has been conducted by Colombo [51], who expresses the flexural behavior as a thermal-mechanical damage model with consideration of irreversible thermal strains.
High-Strength Concrete Hollow-Core Concrete Slabs There has been considerable recent interest in high-strength concrete as a construction material. High-strength concrete contains additives such as silica fume and water reducing admixtures, which result in compressive strength in the range 60–120 MPa (8400–18,000 psi). An extensive survey of high-strength concrete properties at elevated temperatures by Phan [44] shows that they tend to have a higher rate of strength loss than normal concrete at temperatures up to
With the increasing popularity in recent years of precast prestressed concrete panels in construction, research is being carried out on the behavior of hollow-core concrete slabs in fire, which is more complicated than reinforced concrete because of the effect of prestressing, the small amount of reinforcing, and variable restraint from the surrounding structure. The fire behavior of composite hollow-core concrete units supported on
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Analytical Methods for Determining Fire Resistance of Concrete Members
steel beams is described by Borgogno and Fontana [52]. Several fire tests on hollow-core concrete slabs have been carried out [53–55]. The performance of hollow-core concrete flooring systems in fire has been studied extensively by Fellinger [56] with special focus on the shear and anchorage behavior, and a simulation model of hollow-core concrete flooring systems for design purposes has been proposed by Chang [57].
References 1. A.H. Buchanan, Structural Design for Fire Safety, John Wiley and Sons, Chichester, UK (2001). 2. Building Code Requirements for Reinforced Concrete, ACI 318-89, American Concrete Institute, Detroit, MI (1989). 3. American Concrete Institute, ACI 216.1-07/TMS0216-07 – Code Requirements for Determining Fire Resistance of Concrete and Masonry Construction Assemblies, USA, 2007. 4. EN1992-1-2:2004, Eurocode 2: Design of concrete structures – Part 1-2: General rules – Structural fire design, European Committee for Standardisation, Brussels, Belgium (2004). 5. EN1994-1-2:2005, Eurocode 4: Design of Composite Steel and Concrete Structures, EN1994-1-2: General Rules—Structural Fire Design, European Committee for Standardisation, Brussels, Belgium (2005). 6. Guide for Determining the Fire Endurance of Concrete Elements, ACI 216-89, American Concrete Institute, Detroit, MI (1989). 7. Reinforced Concrete Fire Resistance, Concrete Reinforcing Steel Institute, Chicago (1980). 8. A.H. Gustaferro and T.D. Lin, “Rational Design of Reinforced Concrete Members for Fire Resistance,” Fire Safety Journal, 11, pp. 85–98 (1986). 9. Fire design of concrete structures – material’s, structures, and modelling, state-of-art report, bulletin 38, fib (fe´de´ration internationale du be´ton / the International Federation for Structural Concrete), July 2008. 10. Fire design of concrete structures – structural behaviour and assessment, state-of-art report, bulletin 46, fib (fe´de´ration internationale du be´ton / the International Federation for Structural Concrete), April 2007. 11. R.L. Brockenbrough and B.G. Johnston, Steel Design Manual, U.S. Steel Corporation, Pittsburgh, PA (1968). 12. C.R. Cruz, “Elastic Properties of Concrete at High Temperatures,” PCA Research Bulletin, 191, Portland Cement Association, Skokie, IL (1966). 13. M.S. Abrams and A.H. Gustaferro, “Fire Endurance of Two-Course Floors and Roofs,” Journal of American Concrete Institute, 66, p. 2 (1969).
1977
14. M.S. Abrams and A.H. Gustaferro, “Fire Endurance of Concrete Slabs as Influenced by Thickness, Aggregate Type, and Moisture,” PCA Research Bulletin, 223, Portland Cement Association, Skokie, IL (1968). 15. R.H. Iding, Z. Nizamuddin, and B. Bresler, “FIRES T3, A Computer Program for the Fire Response of Structures—Thermal-Three-Dimensional Version,” UCB FRG 77-15, University of California, Berkeley (1996). 16. U. Wickstro¨m, “TASEF-2—A Computer Program for Temperature Analysis of Structures Exposed to Fire,” Report No. 79-2, Lund Institute of Technology, Lund, Sweden (1979). 17. J.-M. Franssen, V.K.R. Kodur, and J. Mason, User’s Manual for SAFIR 2002: A Computer Program for Analysis of Structures Subjected to Fire, University of Lie`ge, Belgium (2002). 18. ASCE 7-05, Minimum Design Loads for Buildings and Other Structures, American Society of Civil Engineers, Reston, VA (2006). 19. Symposium on Fire Resistance of Concrete, ACI Publication SP 5, American Concrete Institute, Detroit, MI (1962). 20. C.C. Carlson, “Function of New PCA Fire Research Laboratory,” PCA Publication RX109, Portland Cement Association, Skokie, IL (1959). 21. L.A. Issen et al., “Fire Tests of Concrete Members: An Improved Method for Estimating Restraint Forces,” Fire Performance, ASTM STP 464, American Society for Testing and Materials, Philadelphia (1970). 22. S.L. Selvaggio and C.C. Carlson, “Restraint in Fire Tests of Concrete Floors and Roofs,” ASTM STP 422, American Society for Testing and Materials, Philadelphia; also PCA Research Department Bulletin 220, Portland Cement Association, Skokie, IL (1967). 23. E.A.B. Salse and A.H. Gustaferro, “Structural Capacity of Concrete Beams During Fires as Affected by Restraint and Continuity,” in Proceedings, 5th CIB Congress, Paris (1971). 24. CRSI Handbook, Concrete Reinforcing Steel Institute, Chicago (1984). 25. Y. Anderberg, “Computer Simulations and a Design Method for Fire Exposed Concrete Columns,” Report 92-50, Fire Safety Design, Lund, Sweden (1993). 26. T.T. Lie and R.J. Irwin, “Method to Calculate the Fire Resistance of Reinforced Concrete Columns with Rectangular Cross Section,” ACI Structural Journal, 90, 1, pp. 52–60 (1993). 27. R. Iding, B. Bresler, and Z. Nizamuddin, “FIRES-RC II, A Computer Program for the Fire Response of Structures—Reinforced Concrete Frames,” Fire Research Group Report No. UCB FRG 77-8, University of California, Berkeley (1977). 28. N.E. Forsen, “A Theoretical Study of the Fire Resistance of Concrete Structures,” FCB-SINTEF Report STF65 A82062, SINTEF, Trondheim, Norway (1982). 29. DIANA. Diana User’s Manual, Non-Linear Analysis, Rel. 6.1, TNO Bouw (1996).
1978 30. Design for Fire Resistance of Precast Prestressed Concrete, 2nd ed., Prestressed Concrete Institute, Chicago (1988). 31. UL2007, Fire Resistance Directory, Underwriters Laboratories Inc., Northbrook, IL (2007). 32. ECCS, “Calculation of the Fire Resistance of Composite Concrete Slabs with Profiles Steel Sheet Exposed to the Standard Fire,” Publication No. 32, European Commission for Constructional Steelwork, Brussels (1983). 33. R.M. Lawson, “Fire Resistance of Ribbed Concrete Floors,” CIRIA Report 107, Construction Industry Research and Information Association, London (1985). 34. T.Z. Harmathy, Fire Safety Design and Concrete, Concrete Design and Construction Series, Longman Scientific and Technical, Harlow, UK (1993). 35. U. Schneider, “Concrete at High Temperatures—A General Review,” Fire Safety Journal, 13, pp. 55–68 (1988). 36. Z.P. Bazant and M.F. Kaplan, Concrete at High Temperatures—Material Properties and Mathematical Models, Concrete Design and Construction Series, Longman Group Ltd., Harlow, UK (1996). 37. A.M. Neville, Properties of Concrete, 4th ed., John Wiley and Sons, New York (1997). 38. U. Wickstro¨m, “A Very Simple Method for Estimating Temperatures in Fire Exposed Structures,” New Technology to Reduce Fire Losses and Costs (S.J. Grayson and D.A. Smith, eds.), Elsevier Applied Science, London, pp.186–194 (1986). 39. C.A. Wade, “Performance of Concrete Floors Exposed to Real Fires,” Journal of Fire Protection Engineering, 6, 3, pp. 113–124 (1994). 40. Purkiss J.A, Fire Engineering Design of Structures, Butterworth and Heinemann, 2007 41. K.D. Hertz, “Limits of Spalling of Fire-Exposed Concrete,” Fire Safety Journal, 38, pp. 103–116 (2003). 42. R. Connolly, “The Spalling of Concrete,” Fire Engineers Journal, 57, 186, pp. 38–40 (1997). 43. F.A. Ali, D. O’Conner and A. Abu-Tair, “Explosive Spalling of High-Strength Concrete Columns in Fire,” Magazine of Concrete Research, 53, 3, pp. 197–204 (2001). 44. L.T. Phan, “Fire Performance of High Strength Concrete: A Report of the State-of-the-Art,” NISTIR 5934, National Institute of Standards and Technology (1996). 45. V.K.R. Kodur, “Studies on the Fire Resistance of High Strength Concrete at the National Research Council of Canada,” Proceedings—International Workshop on Fire Performance of High Strength Concrete, NIST Special Publication 919, National Institute of Standards and Technology, Gaithersburg, MD, pp. 75–86 (1997). 46. C.-M. Aldea, J.-M. Franssen, and J.-C. Dotreppe, “Fire Test on Normal and High Strength Reinforced Concrete Columns,” in Proceedings—International
C. Fleischmann et al. Workshop on Fire Performance of High Strength Concrete, NIST Special Publication 919, National Institute of Standards and Technology, Gaithersburg, MD (1997). 47. R. Feticetti, P.G. Gambarova, ASCE Member, and M. Semiglia, “Residual Capacity of HSC Thermally Damaged Deep Beams,” Journal of Structural Engineering, 125, 3, pp. 319–327 (1999). 48. B. Tomasson, “High Performance Concrete—Design Guidelines,” Report, Department of Fire Safety Engineering, Lund University, Sweden (1998). 49. R. Felicetti and P.G. Gambarova, “Effects of High Temperature on the Residual Compressive Strength of High-Strength Siliceous Concretes,” ACI Materials Journal, 95, 4, pp. 395–406 (1998). 50. T.T. Lie and V.K.R. Kodur, “Thermal and Mechanical Properties of Steel Fibre Reinforced Concrete at Elevated Temperatures,” Canadian Journal of Civil Engineering, 23, 2, pp. 511–517 (1996). 51. M. Colombo, FRC Bending Behaviour: A Damage Model for High Temperatures, PhD Thesis, Politecnico di Milano, Italy (2006). 52. W. Borgogno and M. Fontana, Versuche zum Tragverhalten von Betonhohlplatten mit flexibler Auflagerung bei Raumtemperatur und Normbrandbedingungen, IBK ETH Zu¨rich, Zurich, (2006). 53. N.E. Andersen and D.H. Lauridsen, Danish Institute of Fire Technology Technical Report X 52650 Part 2—Hollow-Core Concrete Slabs, Danish Institute of Fire Technology, Denmark (1999). 54. FeBe Studiecommissie SSTC, Re´sistance au Cisaillement de Dalles Alveole´es Pre´contraintes, Laboratorium voor Aanwending der Brandstoffen en Warmteoverdracht, Belgium (1998). 55. M. Breccolotti, A.L. Materazzi, and I. Venanzi, “Fire Performance of HPLWC Hollow-Core Slabs,” Proceedings—4th International Workshop on Structures in Fire, pp. 587–598, Aveiro, Portugal (2006). 56. J.H.H. Fellinger, Shear and Anchorage Behaviour of Fire Exposed Hollow-Core Slabs, DUP Science, Netherlands (2004). 57. J. Chang, Computer Simulation of Hollowcore Concrete Flooring Systems in Fire, PhD Thesis, University of Canterbury, NZ (2007).
Charles Fleischmann is a professor in the Department of Civil Engineering, University of Canterbury, in Christchurch, New Zealand. Andy Buchanan is an emeritus professor in the Department of Civil Engineering, University of Canterbury, in Christchurch, New Zealand. Anthony Abu is a senior lecturer in the Department of Civil Engineering, University of Canterbury, in Christchurch, New Zealand.
Analytical Methods for Determining Fire Resistance of Timber Members
55
Robert H. White{
Introduction The fire resistance ratings of wood members and assemblies, as with other materials, have traditionally been obtained by testing the assembly in a furnace in accordance with ASTM International (ASTM) Standard E119 “Standard test methods for fire tests of building construction and materials”, International Organization for Standardization (ISO) Standard 834 “Fire-resistance tests-Elements of building construction”, and similar standards. In the U.S., these ratings are published in listings, such as Underwriters Laboratories Fire Resistance Directory, Gypsum Association’s Fire Resistance Design Manual, American Wood Council’s Design for Code Acceptance publications, and those in building codes. The ratings listed are limited to the actual assembly tested and normally do not permit modifications such as adding insulation, changing member size, changing interior finish, or increasing the spacing between members. Code interpretation of test results sometimes allows the substitution of larger members, thicker or deeper assemblies, smaller member spacing, and thicker protection layers, without reducing the listed rating. Two procedures for calculating fire resistance ratings have U.S. building code acceptance: the methodologies for calculating fire resistance ratings of exposed wood members in the R.H. White (*) { Deceased
American Wood Council’s National Design Specification® for Wood Construction (NDS®) and the component additive method (CAM) for protected wood-frame walls, floors, and roofs [1]. A third methodology developed by T.T. Lie [2] is expected to be withdrawn from future editions of the U.S. codes in favor of the NDS methodology. The T.T. Lie methodology and the CAM procedures were developed in Canada and currently have both U.S. and Canadian code acceptance [3]. In Europe, the Eurocode 5 of the European Committee for Standardization (EN 1995-12:2004 Eurocode 5: Design of timber structures-Part 1–2: General-Structural fire design and its corrigendum EN 1995-1-2:2004/ AC:2009) on design of timber structures provides calculation methods for the fire design of timber structures. A review of the development of EN 1995-1-2, improvements from the earlier ENV 1995-1-2 published in 1994, and references for the research results used to support its provisions are provided by Ko¨nig [4, 5]. Provisions of Eurocode 5 and more recent developments in Europe are extensively discussed in “Fire Safety in Timber Buildings— Technical guideline for Europe [6]. When attention is given to all details, the fire resistance of a wood member or assembly depends on three items: 1. Performance of its protective membranes (if any) 2. Extent of charring of the structural wood element
M.J. Hurley (ed.), SFPE Handbook of Fire Protection Engineering, DOI 10.1007/978-1-4939-2565-0_55, # Society of Fire Protection Engineers 2016
1979
1980
R.H. White
Fire
t1
t2
t 12
t1
t2
t1
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Fire
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t2 t2 > t1
Rule 1
Rule 2
Rule 3
Rule 4
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Fire
Fire
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Fire
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t2
Dry
Fire
Moist
t2 > t1
Low conductivity High conductivity
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t 12 > t 1 + t 2
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t1 > t2
t1 ≠ t2
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Rule 5
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Rule 8
Beam tested as part of floor
For the floor assembly
Beam tested separately
For a beam when tested separately
t1
t1
t2
t2
B
A
t1 > t2
Beam A can be replaced by beam B if t 2 > t1
Rule 9
Rule 10
Fig. 55.1 Harmathy’s ten rules of fire endurance [7]
3. Ratio of the load-carrying capacity of the remaining uncharred portions of the structural wood elements to the applied load
Contribution of the Protective Membrane Gypsum wallboard and wood paneling are two common types of protective membrane that provides the first line of resistance to fire in wood construction. The effects of the protective membrane on the thermal performance of an assembly are included in Harmathy’s ten rules of fire endurance rating [7]. These ten rules (Fig. 55.1) provide guidelines to evaluate the relative effects of
changes in materials on the fire resistance rating of an assembly. However, there are exceptions to some of these general rules. The rules apply primarily to the thermal performance of the assembly. In the U.S., testing of assemblies often include the reporting of “finish ratings” of the protective membrane. A finish rating of a protective membrane is generally defined as the time to reach either an average temperature rise of 139 C (250 F) or a maximum rise of 181 C (325 F), as measured on the plane of the wood framing member nearest the fire. Also in the U.S., these same temperature criteria are used in the fire resistance testing of protective membranes (i.e. “thermal barriers”) required for the
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Analytical Methods for Determining Fire Resistance of Timber Members
protection of foam plastic insulation [8]. In Europe, these same temperature increase criteria (140 K average, 180 K maximum) are used for layers in the CAM in the Eurocode 5. The contribution of the protective membrane to the fire resistance rating of a light-frame assembly is clearly illustrated in the CAM. The North American CAM is initially discussed in the following subsection. In Europe, a new classification system for the abilities of building panels to provide fire protection has been developed [6]. The “K” classes are determined by testing for fire resistance using a temperature rise on the unexposed surface of 250 C and horizontal orientation of the test panel.
Component Additive Method The CAM is a calculation procedure to determine fire resistance ratings of light-frame wood floor, roof, and wall assemblies. With this procedure, as with Harmathy’s rules 1 and 2, one assumes that a time can be assigned to the type and thickness of the protective membrane and that an assembly with two or more protective membranes has a fire resistance rating at least that of the sum of the times assigned for the individual layers plus the time assigned to the framing. CAM was developed by the National Research Council of Canada (NRCC) and has code approval in both the United States [1] and Canada [3]. Richardson and Batista [9] evaluated the methodology using results from tests of lightframe walls lined with gypsum board. The times assigned to the protective membranes (Table 55.1), the framing (Table 55.2), and other factors are added together to obtain the fire resistance rating for the assembly. The times are based on empirical correlation with actual ASTM E119 tests of assemblies. The ratings obtained in these tests ranged from 20 to 90 min. The times given in Table 55.1 are based on the membrane’s ability to remain in place during fire tests. In this North American CAM, the times assigned to the protective membranes in the component additive method are not the “finish ratings” of the material cited in test reports or listings.
1981
Table 55.1 Time assigned to protective membranes Description of finish 9.5 mm (3/8 in.) Douglas fir plywood, phenolic bonded 13 mm (½ in.) Douglas fir plywood, phenolic bonded 16 mm (5/8 in.) Douglas fir plywood, phenolic bonded 9.5 mm (3/8 in.) gypsum board 13 mm (½ in.) gypsum board 16 mm (5/8 in.) gypsum board 13 mm (½ in.) type X gypsum board 16 mm (5/8 in.) type X gypsum board Double 9.5 mm (3/8 in.) gypsum board 13 mm + 9.5 mm (½ in. + 3/8 in.) gypsum board Double 13 mm (½ in.) gypsum board
Time (min) 5 10 15 10 15 20 25 40 25 35 40
The applicable building code should be checked for acceptance of, modification to, and limitations on the procedure. There are specific requirements for the installation of some of the membranes
Table 55.2 Time assigned for contribution of wood frame Description of frame Wood wall studs, 406 mm (16 in.) on center Wood floor and roof joists, 406 mm (16 in.) on center Wood floor and roof truss assemblies, 610 mm (24 in.) on center
Time (min) 20 10 5
Minimum size for studs is nominal 51 mm by 102 mm (2 in. by 4 in.). Wood joists must not be less than nominal 51 mm (2 in.) in thickness. The spacing between studs or joists cannot exceed 406 mm (16 in.) on center. The applicable building code should be checked for acceptance of, modification to, and limitations on the procedure
The type of fasteners and their spacing on the protective membrane can be critical factors in the performance of the membrane in a fire resistance test. Reference should be made to similar tested assemblies. The addition of insulation to a wall assembly can increase its fire resistance [10]. Adding rock wool or slag mineral wool insulation batts for additional protection to the wood stud wall generally has an assigned time of 15 min in the CAM procedure, which is added to the sum of the times for the framing and the protective membrane to obtain the rating for the
1982
wall assembly. Assigned times for glass fiber insulation depend on the codes. The effect of adding insulation to the fire resistance of a floor or roof assembly in a fire test depends on its location within the assembly and the method of attachment. In tests of single layer I-joists systems, the addition of insulation above the unbacked joints in the gypsum board ceiling has been beneficial. In the case of floor assemblies, adding insulation can also decrease the fire resistance of the assembly [10]. Using the results of the series of wall tests conducted in Canada, Sultan and Kodur [11] examined the effects of insulation type, insulation width between studs, resilient channel location, gypsum board thickness, number of gypsum board layers, glass fiber in the gypsum board core, gypsum board mass per unit area, and stud type. For load-bearing wood stud walls, the fire resistance is reduced when resilient channels are used to attach the gypsum boards on the fire-exposed side of the studs [12]. For asymmetrical wall assemblies, the rating in the CAM procedure is based on the side with the lesser fire resistance. For floor/ceiling assemblies, roof/ceiling assemblies, and exterior walls rated only from the interior, there are minimal requirements for the membrane on the face of the assembly not directly exposed to the fire, in order to ensure that the wall or floor/roof assembly does not fail because of fire penetration or heat transfer through the assembly. Specific alternative membranes are identified for the face of wood stud walls not exposed to fire (exterior) and for the flooring or roofing over wood joist framing. The membrane on the side not exposed to fire (the outside or top) may also be any membrane listed in Table 55.1 with an assigned time of 15 min or greater. The application of the method in the building codes is generally limited to 60 or 90 min. Additional information can be found in publications of the American Wood Council [1] and the Canadian Wood Council [3]. When code acceptance is required, the applicable building code must be checked for acceptance of, modifications to, and limitations of the procedure. There are differences between the codes in what is accepted. CAM gives flexibility, for example, in
R.H. White
calculations for plywood and gypsum board combined as an interior finish. Example 1 The calculated fire resistance rating of a wood stud exterior wall (nominal 2 in. 4 in. [51 mm 102 mm] studs, 16 in. [406 mm] on center) with 0.625 in. (16 mm) Douglas fir phenolic-bonded plywood over 0.5-in. (13-mm) type X gypsum wallboard on the side exposed to fire is From Table 55.1: 16 mm (0.625 in.) Douglas fir plywood, 15 min phenolic bonded 13 mm (0.5 in.) type X gypsum board 25 min From Table 55.2: Wood stud framing 20 min Calculated rating (total) 60 min Mineral wool insulation could be used to increase the fire rating to 75 min
There is also a CAM in Eurocode 5 based on work in Sweden [13, 14]. In the CAM described in Eurocode 5, the fire separation function of wall and floor assemblies is calculated as the sum of the contribution to fire resistance from each layer of material: X tins ¼ tins, 0, i kpos, i k j,i ð55:1Þ i
where tins,0,i ¼ Basic insulation value of layer i (min) kpos,i ¼ Position coefficient of layer i in relation to the fire kj,i ¼ Joint coefficient of layer i The temperature increase criteria of 140 K average or 180 K maximum are used in the determination of the basic insulation value, tins,0, for a single layer. Application of this CAM to address the insulation aspect of fire resistance includes consideration of the different paths for heat transfer through the assembly. The position coefficient adjusts the basic insulation value for the position of the layer within the assembly, and the joint coefficient adjusts for the configuration of any joints in the layer. Research in Switzerland [15, 16] has resulted in improvements to the methodology. These suggested modifications to the current Eurocode 5 procedure include the impact of the adjacent
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Analytical Methods for Determining Fire Resistance of Timber Members
layers on the position coefficient and introduce a basic protection value. The position coefficient of Equation 55.1 is modified to be the product of two position coefficients—a position coefficient that takes into account the influence of layers on the fire exposed side of the layer and a position coefficient that takes into account the influence of layers on the non-fire exposed side of the layer. The basic protection value is used instead of the basic insulation value of Equation 55.1 for all layers except the last layer on the unexposed side. The determination of the basic protection value is based on temperature rise criteria of 250 K average or 270 K maximum. Assuming an initial temperature of 20 C, the 270 K temperature rise corresponds to a temperature of 290 C which is close to the 300 C temperature criteria commonly used for the base ¨ stman et al. [6] provide of the char layer. O detailed information on this methodology, including design examples. The Eurocode 5 also includes design procedures for fire resistance of load-bearing, insulated, light-frame floors and walls that consider charring of the wood joist or stud. There are separate procedures for wall and floor assemblies with and without cavities filled with rock (mineral wool) or glass fiber insulation. In New Zealand publications [17], an approach described as the onset of char method is used to determine the fire ratings of light-frame assemblies. Because the charring of wood is associated with a temperature of 300 C (550 F), another method is to assume that the membrane will protect any wood framing for at least the time of the finish rating of the membrane in a test involving wood framing. As with the onset of char method, the fire rating of the entire assembly with the substituted member is assumed to be at least equal to the finish rating of the protective membrane in the test with the solid-sawn wood framing.
Models for Light-Frame Construction The protective membrane contributes to fire resistance by providing thermal protection. Numerical
1983
heat transfer methodologies are available to evaluate this thermal protection. In most cases, the models were developed for light-frame wall assemblies. An extensive literature review of efforts to model the fire resistance of light-frame construction is provided by Be´nichou and Sultan [18]. In early work, Fung [19] developed a one-dimensional finite difference model and computer program for thermal analysis of walls. Gammon [20] developed a two-dimensional finite element heat transfer model for wood-stud wall assemblies. WALL2D, developed by Forintek Canada, is a two-dimensional finite-difference model for predicting heat transfer through wood stud walls exposed to fire [21, 22]. Difficulties in modeling the charring of wood, and the physical deterioration of the panel products complicate these numerical methodologies. Other research on models for light-frame construction includes activities in Canada [23, 24], Sweden [25], New Zealand [26, 27] and Australia [28, 29]. In addition to modeling heat transfer, these efforts have included the modeling of the structural capacity of the light-frame assemblies. WALL2D has been used with a simple structural model to predict structural collapse [30]. In a manner similar to the bilinear char model of Eurocode 5 for initially protected wood, Frangi et al. [31] developed a charring model for timber frame floor assemblies with void cavities. Clancy [32] used his model to examine the effects of various variables on the times for structural collapse. As part of the development of such models, research has been done on the properties of gypsum board. Cramer et al. [33] examined mass loss and mechanical properties of gypsum board at elevated temperatures. Be´nichou and Sultan [34] reported test results for thermal conductivity, specific heat, mass loss, and thermal expansion/contraction for wood, gypsum, and insulation. Craft et al. [35] developed Arrhenius rate constants for the calcinations of the gypsum. Thomas [36] reviewed thermal data for gypsum board and made modifications to obtain apparent values for the properties that were suitable for a heat transfer model.
1984
Direct Protection of Wood Members The steel industry improves the fire resistance of steel members by directly covering them with fire-resistive panels or coatings. Currently, the marketing of fire-resistive coatings for use on wood is almost nonexistent. The fire-retardant coatings marketed for wood are designed and recognized only for use to reduce the spread of flames over a surface (flame spread). Depending on its thickness and durability under fire exposure, a coating may merely delay ignition of the wood for a few minutes or may provide an effective insulative layer that reduces the rate of charring. For both fire-retardant coatings and fire-resistive coatings, their performance as a fire-resistant membrane on wood has been evaluated [37–39]. In some full-scale testing of beams, those coated with an intumescent fire retardant produced improvements less than that obtained in earlier tests in a small-scale furnace [40]. Bending of the beams during the fire test resulted in adhesion problems. Tests on coated timber members were also reported in Finland and the U.S.S.R [41]. There are published data on the protection provided by directly covering a wood member with gypsum board or other nonwood panel products. Gardner and Syme [42] found that gypsum board not only delayed the onset of char formation but also reduced the subsequent rate of char formation. In their 2 h tests, 13-mm (0.5in.) thick gypsum board on wood beams reduced the depth of char by approximately 40 %. Of the 40 %, only 17 % was credited to the initial delay in char formation. Tsantaridis et al. [43] provided information on the charring of wood protected by gypsum board when exposed to 50 kW/m2. Richardson and Batista [44] tested wood decks with and without gypsum board protection. A 16-mm (0.625-in.) thick Type X gypsum board increased the times for flame penetration from 4.5 to 44 min. In a study of engineered wood rim board products, White [45] investigated the charring rates of wood composite rim boards with and
R.H. White
without the protection of one or two layers of gypsum board when subjected to ASTM E119 exposure. Based on tests in a cone calorimeter and a series of tension tests, White [46] concluded that a single layer of U.S. 16 mm (0.625-in.) thick type X gypsum board could be used to add 30 min to the rating of an unprotected wood member and two layers could be assigned a time of 60 min. The charring of wood beneath cladding is addressed in the Eurocode 5 by adjusting the charring rate of the wood for the period before and after the failure of the different types of protective panel products [6]. Osborne et al. [47] and Dagenais et al. [48] found that using two layers of directly attached 13 mm (0.5-in.) type X gypsum boards delayed the onset of charring of cross-laminated timber (CLT) assemblies by 40 min; while a single layer of 16 mm (0.625-in.) provides 30 min. In a manner consistent with the design equations in Eurocode 5, Just et al. [49] developed specific design equations for a wide range of different types of gypsum boards.
Fire-Resistive Exposed Wood Members As the wood member is exposed to fire, charring reduces the cross section of the member. In addition to charring of the member, the residual structural capacity is affected by the elevated temperature gradient within the uncharred wood. The fire-resistive characteristics of exposed wood members are due to the insulative characteristics of the char layer and the sharp temperature gradient beneath the base of the char layer. As a result, even an unprotected structural wood member retains its structural stability in a fire for a period of time. In an engineering analysis of the fire resistance of an exposed wood member, information is needed on charring rate, ratio of ultimate strength to design values, and reduction in strength due to temperature gradient within the uncharred cross section.
55
Analytical Methods for Determining Fire Resistance of Timber Members
Using such engineering analyses, Lie [2] developed simple formulas for calculating the fire resistance of large wood beams and columns that require the user to know only the dimensions of the structural element and load as a fraction of the full design load. These equations were extensively discussed in previous editions of this chapter. In terms of U.S. code acceptance, the formulas of T. T. Lie [2, 50] for beams and columns are expected to be phased out in favor of the NDS methodology. In contrast to the more flexible NDS method, the Lie’s methodology is applicable only to large wood beams and columns with common loading and bracing conditions. It also does not allow the user to adjust the charring rate. Other procedures such as the NDS method (discussed later in this chapter) and the various methods described in Eurocode 5 allow the user to specify the applicable charring rate.
Charring of Wood Wood undergoes thermal degradation (pyrolysis) when exposed to fire (Fig. 55.2). The thermal degradation process depends on the temperatures and inorganic impurities such as fire-retardant chemicals [51]. The pyrolysis and combustion of wood have been studied extensively. Past literature reviews include publications by Browne [52], Schaffer [53, 54], Hall et al. [55], and Hadvig [56]. Babrauskas [57] reviewed literature on wood charring and the use of charring rate of wood as a tool for fire investigations. By converting wood to char and gas, pyrolysis results in a reduction in the wood’s density. The pyrolysis gas undergoes flaming combustion as it leaves the charred wood surface. Glowing combustion and mechanical disintegration of the char eventually erode or ablate the outer char layer. Charring rate generally refers to the linear rate at which wood is converted to char. Under standard fire exposure, charring rates tend to be fairly constant after a higher initial charring rate.
1985
Establishing the charring rate is critical to evaluating fire resistance, because char has virtually no load-bearing capacity. There is a distinct demarcation between char and uncharred wood. A temperature of 300 C is widely used to define the base of the char layer. Early U.S. research used a temperature of 550 F, and SI conversion from inch-pound units resulted in 288 C, 290 C, and 300 C being used for 550 F. To determine charring rate, both empirical models based on experimental data and theoretical models based on chemical and physical principles are used.
Standard ASTM E119 Fire Exposure Expressions for charring rate in the standard ASTM E119 test are the result of many experimental studies. As given in the Eurocode 5, the normal equation for the char depth at a given time is of the form dchar ¼ βt
ð55:2Þ
where dchar ¼ Char depth β ¼ Charring rate t ¼ Time The design values for charring rate depend on the fire resistance methodology being used. The empirical model that is most generally used assumes a constant transverse-to-grain char rate of 0.6 mm/min. (1.5 in./h) for all woods, when subjected to the standard fire exposure. This is for one-dimensional charring in a semiinfinite slab. There are differences among species associated with their density, chemical composition, and permeability. In addition, the moisture content of the wood affects the charring rate. Schaffer [58] reported transverse-to-grain charring rates as a function of density and moisture content for Douglas fir, southern pine, and white oak. The regression equations for C (minutes/ mm, the reciprocal of charring rate β) were
1986
R.H. White
Fig. 55.2 Degradation zones in a wood section
Char layer Char base Pyrolysis zone Pyrolysis zone base Normal wood
C ¼ 1=β ¼ ð0:002269 þ 0:00457uÞρ þ 0:331 for Douglas‐fir ð55:3Þ C ¼ 1=β ¼ ð0:000461 þ 0:00095uÞρ þ 1:016 for southern pine ð55:4Þ C ¼ 1=β ¼ ð0:001583 þ 0:00318uÞρ þ 0:594 for white oak ð55:5Þ where u ¼ Moisture content (fraction of oven-dry mass) ρ ¼ Density (dry mass, volume at moisture content u, kg/m3) White and Nordheim [59] developed an empirical model based on eight species. The char rate equation was of the form t ¼ mx1:23 c where t ¼ Time (min) m ¼ Char rate coefficient xc ¼ Char depth (mm)
ð55:6Þ
This nonlinear char model is used in the NDS calculation procedure for exposed wood members. The char rate coefficients ranged from 0.42 to 0.84 mm/min1.23 for the eight species [59]. Average values for the char rate coefficients were 0.555 for southern pine, 0.554 for western red cedar, 0.598 for redwood, 0.734 for Engelmann spruce, 0.498 for basswood, 0.653 for hard maple, 0.747 for red oak, and 0.607 for yellow poplar. The char rate coefficient was found to be correlated to density, moisture content, and a char contraction factor, defined as the thickness of the char layer at the end of the fire exposure divided by the original thickness of the wood layer that was charred (char depth). The application of this nonlinear model to composite wood products is discussed by White [60, 61]. Other researchers have concluded that there is not a correlation between the char rate and density [62]. Results from theoretical charring models have also shown that density has an impact on the charring rate [63]. The equation developed for the influence of density and moisture content was:
55
Analytical Methods for Determining Fire Resistance of Timber Members
βρ, w ¼ kρ kw β450:12
ð55:7Þ
with sffiffiffiffiffiffiffiffi 450 kp ¼ ρ12
ð55:8Þ
and kw ¼
1:12 1:5 1þw
ð55:9Þ
where β450,12 ¼ charring rate of wood with density of 450 kg/m3 and 12 % moisture content, mm/min ρ12 ¼ density of wood at 12 % moisture content, kg/m3 w ¼ moisture content, kg/m3 For charring in the longitudinal direction, i.e. along the grain, there is very little available data [63]. The charring rate parallel to the grain of wood has been reported as being approximately twice that transverse to the grain [55]. Based on results from a theoretical model on the impact of variations in thermal conductivity on charring rate, Cachim and Franssen [63] proposed the following relationship between a multiplication factor for thermal conductivity perpendicular to grain, kλ, and the corresponding charring rates, parallel (βjj ) and perpendicular to grain β⊥ . 2 kλ ¼ βjj =β⊥ ð55:10Þ Consistent with a doubling of charring rate, a value of 4 was suggested for kλ. Per the Wood Handbook [64], thermal conductivity along the grain has been reported as greater than conductivity across the grain by a factor of 1.5–2.8, with an average of about 1.8. While not generally required for fire design, further work is needed on this question. In Eurocode 5, the design charring rate, βo, in Equation 55.2 is the rate observed in one-dimensional experiments. The listed design charring rates for timbers include 0.65 mm/min for solid-sawn or glued-laminated softwood
1987
timber (characteristic density of 290 kg/m3 or greater), solid-sawn or glued-laminated hardwood timbers (characteristic density of 290 kg/ m3), and laminated veneer lumber (LVL) (characteristic density of 480 kg/m3 or greater); and 0.50 mm/min for solid or glued-laminated hardwood with a characteristic density of 450 kg/m3 or greater. The effect of the rounding of the charred member can be taken into account by increasing the values for char rate, as is done in Eurocode 5. Eurocode 5 notional design charring rate, βn, includes 0.7 mm/min for glued-laminated softwood and beech timbers (characteristic density of 290 kg/m3 or greater), solid-sawn or gluedlaminated hardwood except beech timbers (characteristic density of 290 kg/m3), and LVL (characteristic density of 480 kg/m3 or greater); 0.8 for solid softwood and beech timber (characteristic density of 290 kg/m3 or greater); and 0.55 mm/min for solid-sawn or glued-laminated hardwood except beech (characteristic density of 450 kg/m3 or greater). Except for beech, the charring rates for hardwoods with characteristic densities between 290 and 450 kg/m3 are linear interpolations of charring rates for 290 and 450 kg/m3. The concept of notional charring rates in the Eurocode 5 is discussed by Ko¨nig [65]. Using results from a conductive/finite element model, Cachim and Franssen [63] suggested modifications to the Eurocode 5 values to address the effects of density, moisture content, and anisotropy on charring rates. Assumption of a constant charring rate is reasonable when the member or panel product is thick enough to be treated as a semi-infinite slab. For smaller dimensions, the charring rate increases once the temperature has risen above the initial temperature at the center of the member or at the unexposed surface of the panel. In tests of solid timber beams, Frangi and Fontana [62] observed an increase in the charring rate when the residual cross section was smaller than 40–60 mm. As discussed later, the elevated temperature profile beyond the base of the char layer is estimated to be about 40 mm thick. In Eurocode 5, design charring rate listed for panels (20 mm thick and characteristic density of
1988
R.H. White
450 kg/m3) includes 0.9 mm/min for wood paneling and wood-based panels other than plywood and 1.0 mm/min for plywood. Kanury and Holve [66] suggest the model ‘ 2 b‘ 1 ð55:11Þ t a a where ‘ ¼ Thickness of slab (mm) t ¼ Fire resistance time (min) a,b ¼ Constants They consider the 2/a factor an ideal charring rate and the ratio b‘/a as a correction factor accounting for thickness and thermal diffusion ¨ stman [67] provided the effects. Noren and O equation bm ¼ 1:128x þ 0:0088x2
ð55:12Þ
where bm ¼ Contribution to fire resistance (min) x ¼ Panel thickness (mm) The equation is based on data for various wood-based panel products.
Effect of Adhesives and Treatments The effect of fire-retardant treatment and adhesives on the char rates depends on the type of adhesive or treatment. The charring rate of wood laminates bonded with phenol adhesives is considered to be consistent with that of solid wood. Early tests of a phenol-resorcinol adhesive and a melamine adhesive showed no delamination at the glueline in the wood beneath the char layer [68]. Delamination beneath the base of the char layer occurred at the gluelines for a polyvinyl adhesive [68]. With the introduction of Cross-Laminatedtimber (CLT) construction in Europe and North America, there has been testing of more products with non-resorcinol/phenol adhesives. CLT construction panels are solid wood components built of dimension lumber in manner similar to plywood in which the grain direction of each layer is perpendicular to the adjacent layers. Frangi et al. [69] and Osborne et al. [47] observed the falling off of charred laminates during tests of CLT and the resulting increased charring rate
compared with homogeneous specimens. The effect of adhesives on load capacity during a fire is discussed later in this chapter. Fire-retardant treatments that involve the pressure impregnation of the chemicals are designed to reduce flame spread. However, few fire retardants have been found to improve charring resistance [70].
Nonstandard Fire Exposures The above equations were stated to apply to the standard ASTM E119 or ISO 834 fire exposure. Data on charring rates for other fire exposures have been limited. Schaffer [58] provided data for constant temperatures of 538 C (1000 F), 815 C (1500 F), and 927 C (1700 F). Lau et al. [71] presented data for constant 500 C and an empirical model for constant or variable temperatures. The charring rate is a function of the external flux. For a range of 20–33 kW/m2, Butler [72] calculated the char rate (mm/min) to be 0.022 times the irradiance (kW/m2). Because of increased testing with heat release rate calorimeters, such as the cone calorimeter, char rate and temperature profile data as a function of external heat flux are becoming more available [73–80]. In tests of spruce, charring rates obtained were 0.56, 0.80, and 1.02 mm/min for external heat fluxes of 25, 50, and 75 kW/m2, respectively [78]. In tests of southern pine, the linear charring rate ranged from 0.44 mm/min at 18 kW/m2 to 0.85 mm/min at 55 kW/m2 [73, 74]. Charring rate has been found to be proportional to the ratio of external heat flux over density [77, 78]. Eurocode 5 includes equations for parametric fire exposures in which the load-bearing function must be maintained during the complete duration of the decay phase or for a specified period of time.
Hadvig’s Equations for Nonstandard Fire Exposure Hadvig [56] developed equations for nonstandard fire exposure. The charring rate in a real fire depends on the severity of the fire to which
55
Analytical Methods for Determining Fire Resistance of Timber Members
1989
Table 55.3 The transfer coefficient, k [56, 81] Type of fire compartmenta A B C D E Fb G H
Geometrical opening factor, F0 0.02 0.04 1.0 1.0 0.85 0.85 3.0 3.0 1.35 1.35 1.65 1.50 1.0–0.5 1.0–0.5 1.50 1.45 3.0 3.0
0.06 1.0 0.85 3.0 1.35 1.35 0.8–0.5 1.35 3.0
0.08 1.0 0.85 3.0 1.50 1.50 0.7–0.5 1.25 3.0
0.10 1.0 0.85 3.0 1.55 1.75 0.7–0.5 1.15 3.0
0.12 1.0 0.85 2.5 1.65 2.00 0.7–0.5 1.05 2.5
A ¼ (Standard fire compartment) The average consisting of brick, concrete, and gas concrete B ¼ Concrete, including concrete on the ground C ¼ Gas concrete (density 500 kg/m3) D ¼ 50 % concrete, 50 % gas concrete (density 500 kg/m3) E ¼ 50 % gas concrete (density 500 kg/m3), 33 % concrete, and 17 % laminate consisting of (taken from the inside) 13 mm plasterboard (density 500 kg/m3), 10 cm mineral wool (density 50 kg/m3), and brick (density 1800 kg/m3) F ¼ 80 % steel plate, 20 % concrete. The fire compartment is comparable to a storehouse or other building of a similar kind with an uninsulated roof, walls of steel plate, and floor of concrete G ¼ 20 % concrete and 80 % laminate consisting of a double plasterboard (2 13 mm) (density 790 kg/m3), 10 cm air space, and another double plasterboard (2 13 mm) (density 790 kg/m3) H ¼ Steel plate on either side of 100 mm mineral wool (density 50 kg/m3) b The higher values apply to q < 60 MJ/m2; the lower values apply to q > 500 MJ/m2. Intervening values are found by interpolation a
the wood is exposed. The fire severity depends on such factors as available combustible material (fire load) and available air supply (design opening factor) [81]. The design fire load density is q¼k
Q At
ð55:13Þ
where q ¼ Design fire load density (MJ/m2) k ¼ Transfer coefficient (dimensionless) Q ¼ Sum of the products of mass and lower calorific value of materials to be found in the compartment (MJ) At ¼ Total internal area of the compartment, including floor, walls, ceiling, windows, and doors (m2) The transfer coefficients are given in Table 55.3 for different types of compartments and geometrical opening factors. In the case of fire compartments whose bounding structures do not come under any of the types A–H, k is usually determined by a linear interpolation in the table between appropriately chosen types of compartments.
The geometrical opening factor is pffiffiffi A h 0 F ¼ At
ð55:14Þ
where F0 ¼ Geometrical opening factor (m½) A ¼ Total area of windows, doors, and other openings in walls (i.e., vertical openings only) (m2) h ¼ Weighted mean value of the height of vertical openings, weighted against the area of the individual openings (m) The design opening factor is 0
F¼F k f
ð55:15Þ
where F ¼ Design opening factor (m1/2) F0 ¼ Geometrical opening factor (m1/2) k ¼ Transfer coefficient of bounding structure (dimensionless) f ¼ Coefficient (dimensionless) to account for horizontal openings
1990
R.H. White
Fig. 55.3 Diagram for the determination of f for fire temperatures of 500 C and 1000 C [56]
Ah /A = 0.5
Ah /A = 0.1
1000°C 500°C
Ah /A = 1.0
1.5
1.0
0.5
0.1
Ah
2
3
X ¼ β0 τ for 0 τ
h1 h/2 h A
Fig. 55.4 Simplified sketch of vertical cross section of ventilated compartment with notation [56]
The dimensionless coefficient, f (Figs. 55.3 and 55.4), increases the opening factors when there are horizontal openings. For only vertical openings, f is equal to 1. Hadvig’s [56] equations are θ ¼ 0:0175 β0 ¼ 1:25
q F
ð55:16Þ
0:035 F þ 0:021 ð55:17Þ for 0:02 F 0:30
4
5
f
Ah • √h A • √h
θ 3
1 3 3 τ2 X ¼ β0 θ þ τ 12 2 4θ θ for τ θ 3
ð55:18Þ
ð55:19Þ
where θ ¼ Time at which maximum charring is reached for the values used for F and q (min) β0 ¼ Initial value of rate of charring (mm/min) X ¼ Charring depth (mm) F ¼ Design opening factor (m1/2) (defined in Equation 55.15) q ¼ Design fire load density (MJ/m2) (defined in Equation 55.13) τ ¼ Time (min) These equations are valid for fire exposures less than 120 min and for a room where the combustible material is wood. Plastic burns more intensely and for a shorter time than wood. When the combustible materials in the room are plastics, Equations 55.16 and 55.17 are therefore modified for faster char rate (β0 is 50 % higher), shorter time is allowed for maximum charring (θ is cut in half), and Equation 55.18 is applicable for τ less than θ. Equations 55.16 through 55.19 are for gluedlaminated timber with a density of 470 kg/m3, including a moisture content of 10 % and minimum width of 80 mm or greater or square members of minimum 50 50 mm.
55
Analytical Methods for Determining Fire Resistance of Timber Members
Equations 55.18 and 55.19 are valid only for 0 < X < b/4, where b is the dimension of the narrow face of a rectangular member. For dimensions of nonsquare cross sections between 30 and 80 mm, the ratio of the original dimensions must be equal to or greater than 1.7, the charring depth perpendicular to the wide face is X, and the charring depth perpendicular to the narrow face is determined by multiplying Equation 55.18 or 55.19 by the dimensionless quantity 1:35 0:0044ðbÞ
F ¼ ð0:048Þð1:0Þð2:4Þ ¼ 0:115m1=2 The design fire load density (Equation 55.13) is q¼k
Example 2 The room is a standard fire compartment consisting of brick, concrete, and gas concrete. The floor area is 5 10 m, and the height is 3 m. The openings are one window 1.5 m high and 2.0 m wide, three windows 1.5 m high and 1.0 m wide, and one skylight 1.5 3.0 m. The skylight is 2 m above the midheight of the windows. The fire load is 6 m3 of wood. Assuming a fire temperature of 1000 C, a wood density of 500 kg/m3, and a lower calorific value of 17 MJ/kg, describe the charring of a 38 250 mm wood beam exposed on three sides after 8 min of the fire. The geometrical opening factor (Equation 55.14) is pffiffiffiffiffiffiffi pffiffiffi A h ½1ð1:5 2Þ þ 3ð1:5 1Þ 1:5 0 F ¼ ¼ At ½2ð5 10Þ þ 2ð3 5Þ þ 2ð3 10Þ pffiffiffiffiffiffiffi 7:5 1:5 ¼ 0:048m1=2 ¼ 190 The design opening factor (Equation 55.15) is
Q ð6 500 17Þ 51, 000 ¼ ¼ ð1:0Þ At 190 190
¼ 268 MJ=m2 Maximum charring rate will be reached at θ min (Equation 55.16):
ð55:20Þ
where b equals the dimension of the narrow face (mm).
1991
θ ¼ 0:0175
268 MJ=m2 ¼ 41min 0:115 m1=2
The initial charring rate (Equation 55.17) will be β0 ¼ 1:25
0:035 ¼ 1 mm=min 0:115 þ 0:021
At 8 min, the char depth (Equation 55.18) will be X ¼ 1 8 ¼ 8 mm for 0 8
41 3
The smaller dimension b of the beam is 38 mm. The charring depth criterion 0 < x < b/4 is 0 < 8 < 9.5 mm, so Equations 55.18 and 55.19 are valid. The ratio of the original dimensions is 25/3.8, or 6.6. Because 38 mm is less than 80 mm, the multiplying factor (Equation 55.20) is 1:35 0:0044ð38Þ ¼ 1:18 At 8 min, the uncharred area of the beam will be approximately 38 mm 2ð8 mmÞ ¼ 22 mm wide and
0
F¼F k f
250 mm ð1:18 8 mmÞ ¼ 240 mm high
The k is obtained from Table 55.3 (k ¼ 1.0 for type A, F0 ¼ 0.048). The f is obtained from Figs. 55.3 and 55.4. pffiffiffi pffiffiffi pffiffiffiffiffi A1 h1 ð1:5 3Þ 2 4:5 2 pffiffiffi ¼ pffiffiffiffiffiffiffi ¼ pffiffiffiffiffiffiffi ¼ 0:69 A h 7:5 1:5 7:5 1:5 Ah 4:5 ¼ 0:6 ¼ 7:5 A pffiffiffiffiffi pffiffiffi For Ah h1 =A h of 0.69 and Ah/A of 0.6, the f from Fig. 55.3 is 2.4.
As the charring proceeds after (9.5 mm)/(1 mm/ min), or 9.5 min, the b/4 criterion of the equations no longer holds. This is because the charring rate increases as the temperature at the center of the beam starts to increase. Using an opening factor method and parametric time-temperature curves, equations for natural fires are provided in Eurocode 5. The approach is a simplification of Hadvig’s equations. In the 1994 edition of the Eurocode
1992
R.H. White
5, the equation for the parametric charring rate during the period τ0 is β par ¼ 1:5β0
5F 0:04 4F þ 0:08
ð55:21Þ
where F ¼ F0 of Equation 55.14 β0 ¼ Design charring rate of Eurocode 5 The time period τ0 is τ0 ¼ 0:006
q F
ð55:22Þ
where q is the design fire load density of Equation. 55.13. At τ0, the char rate decreases to zero at 3τ0. The maximum charring depth during the fire exposure and the subsequent cooling period is 2β0τ0. Equations are valid for F between 0.02 and 0.30 m1/2, τ0 of 40 min or less, and char depths less than one-quarter of the dimensions. Buchanan [82] provides a table of char rate, char time, and char depth results from the above equations for a range of opening factors. The equations in the 1994 edition were modified for the 2004 edition of the Eurocode 5. In the 2004 equations, the 5F and 4F in Equation 55.21 were modified to be a function of the thermal properties of the compartment boundaries. Oleson and Ko¨nig [83] tested glued-laminated beams and found agreement with Hadvig’s equations for the wide vertical side of a member. Oleson and Ko¨nig [83] noted that, compared with conditions at standard exposure, the mechanical behavior at natural fire exposure is different due to the changes of temperature in the residual cross section during the cooling period. The influence of elevated temperature is no longer concentrated to the outer layer of the residual cross section.
Theoretical Models Considerable efforts have gone into developing theoretical models for wood charring, and work in this area is continuing. Janssens [84] observes that more than 50 wood pyrolysis models have been developed since World War II. Moghtaderi [85] provides a review of pyrolysis models of
wood developed over the past 60 years. Theoretical models allow calculation of the charring rate for geometries other than a semi-infinite slab and for nonstandard fire exposures. Roberts [86] reviewed problems associated with the theoretical analysis of the burning of wood, including structural effects and internal heat transfer, kinetics of the pyrolysis reactions, heat of reaction of the pyrolysis reactions, and variations of thermal properties during pyrolysis. He considered the major problems to be in the formulation of a mathematical model for the complex chemical and physical processes occurring and in the acquisition of reliable data for use in the model. Many models for wood charring are based on the standard conservation of energy equation. The basic differential equation includes a term for each contribution to the internal energy balance. An early model for wood charring was given by Bamford et al. [87]. The basic differential equation used by Bamford was cρ
∂T ∂2 T ∂w ¼K 2q ∂t ∂t ∂X
ð55:23Þ
where K ¼ Thermal conductivity T ¼ Temperature X ¼ Location w ¼ Weight of volatile products per cubic centimeter of wood t ¼ Time q ¼ Heat liberated at constant pressure per gram of volatile material evolved c ¼ Specific heat ρ ¼ Density In Equation 55.23, the term on the left side of the equal sign represents the energy stored at a given location as indicated by the increase or decrease of the temperature with time at that location. The first term on the right side of the equal sign represents the thermal conduction of energy away from or into the given location. The second term on the right side represents the energy absorbed (endothermic reaction) or the energy given off (exothermic reaction) as the wood undergoes pyrolysis or thermal degradation. Numerical solutions using computers are normally used to solve these differential equations.
55
Analytical Methods for Determining Fire Resistance of Timber Members
In Bamford’s calculations using Equation 55.23, the rate of decomposition was given by an Arrhenius equation. The heat of decomposition, q, was the difference between the heat of combustion of the wood and that of the products of decomposition. Thermal constants for wood and char were assumed to be the same, and the total thickness of char and wood was assumed to remain constant. Thomas [88] added a convection term to Bamford’s equation to obtain ρc
∂T ∂2 T ∂T ∂w ¼ K 2 þ Mcg q ∂t ∂X ∂t ∂X
ð55:24Þ
where M ¼ Local mass flow of pyrolysis gases cg ¼ Specific heat of the gases The convection term represents the energy transferred in or out of a location due to convection of the pyrolysis gases through a region with a temperature gradient. The Factory Mutual Research Corporation model (SPYVAP) includes terms for internal convection of volatiles and thermal properties as functions of temperature and density. It was developed by Kung [89] and later revised by Tamanini [90]. Atreya [91] has further revised this model to include moisture absorption. His energy conservation equation is ∂T ∂T ∂ K ρa C pa þ ρc C pc þ ρm Cpm ¼ ∂X ∂t ∂X ! ∂H g ρ þ i 1 j c Mg ρf ∂X
ρf ∂ρs ρs Q þ H a H c = 1 Hg ∂t ρw ρw
∂ρm Qm þ H m H g ∂t
where Cp ¼ Specific heat (J/[kgK]) K ¼ Thermal conductivity (W/[m K]) T ¼ Temperature (K) t ¼ Time (s) X ¼ Distance (m) ρ ¼ Density (kg/m3)
ð55:25Þ
1993
Mg ¼ Outward mass flux of volatile gases (kg/m2s) H ¼ Thermal-sensible specific enthalpy (J/kg) Q ¼ Endothermic heat of decomposition of wood for a unit mass of volatiles generated (J/kg at Tx) i,j ¼ Parameters to simulate cracking, between 0 and 1 Subscripts: 1 ¼ Ambient w ¼ Virgin wood c ¼ Char g ¼ Volatile gases a ¼ Unpyrolyzed active material m ¼ Moisture f ¼ Final value s ¼ Solid wood Equation 55.25 is similar to the previous equations except the material has been broken up into its components (wood, water, and char). The parameter j eliminates the convection term if the pyrolysis gases are escaping through cracks or fissures in the wood. The last term represents the heat absorbed with vaporization of the water. The conservation of mass equation is ∂Mg ∂ρs ∂ρm ¼ þ ∂X ∂t ∂t
ð55:26Þ
and ensures that the mass of the gases equals the mass loss due to thermal degradation of the wood and vaporization of the moisture. As noted before, the decomposition kinetics equation for wood is the Arrhenius equation ρs ρ f
∂ρs expðE=RT Þ ð55:27Þ ¼ A ∂t 1 ρ f =ρw where A ¼ Frequency factor (1/s) E ¼ Activation energy (J/mol) R ¼ Gas constant Atreya [91] uses a moisture desorption kinetics equation for vaporization of the water in the wood, which is ∂ρm ¼ Am ρm expðEm =RT Þ ∂t
ð55:28Þ
1994
The CMA model [92] developed for NASA provides good results for oven-dry wood because it includes surface recession. Parker [93, 94] has taken char shrinkage parallel and normal to the surface into account in the model. Parker also includes different Arrhenius equations for each of the three major components of wood: (1) cellulose, (2) hemicelluloses, and (3) lignin. There may be not only moisture desorption but also an increase in moisture content behind the char front caused by moisture movement away from the surface [95]. A model of Fredlund [96] includes mass transfer as well as heat transfer and provides for surface recession due to char oxidation. In a model for wood combustion, Bryden et al. [97] modeled the wood pyrolysis kinetics, including tar decomposition, using three competing primary reactions and two secondary reactions. The surface boundary layer includes both char shrinkage and surface recession due to char combustion. To describe the natural smoldering of logs after a forest fire, Costa and Sandberg [98] modeled the steady one-dimensional propagation of infinitesimally thin fronts of drying, pyrolysis, and char oxidation. Kanury and Holve [66] have presented dimensional, phenomenological, approximate analytical, and exact numerical solutions for wood charring. Other models include those of Havens [99], Knudson and Schniewind [100], Kansa et al. [101], Hadvig and Paulsen [102], Tinney [103], and Janssens [84]. Badders et al. [104] examined the ability of four commercial finite element analysis programs (FIRES-T3, SAFIR, TASEF, COMSOL) to model exposed wood beams. The option of theoretical models or advanced calculations for the determination of charring rates and temperature profiles is addressed in the Eurocode 5. For purpose of such calculations, the Eurocode 5 provides values for the equivalent conductivity, specific heat capacity and the char/ wood density ratio as a function of temperature. Cachim and Franssen [63] used the finite element program SAFIR and the Eurocode property data to examine the effects of density, moisture content, and anisotropy on charring rates.
R.H. White
Janssens [105] used the finite element software package COMSOL Multiphysics and the Eurocode 5 data to model some glued laminated beams in fire resistance test. A major issue in the use of the more sophisticated models is the adequacy of the available data to use as input. The thermophysical properties for wood pyrolysis models are discussed by Janssens [106, 107]. Wood properties are discussed at the conclusion of this chapter. Most theoretical models for wood charring not only define the charring rate but also provide results for the temperature gradient. This temperature gradient is important in evaluating the load-carrying capacity of the wood remaining uncharred.
Load-Carrying Capacity of Uncharred Wood In the standard ASTM E119 test of a wood member, structural failure occurs when the member is no longer capable of supporting its design load. The charring of the wood reduces the crosssectional area of the member such that the ultimate capacity of the residual member is exceeded. During the charring of the wood member, the temperature gradient is steep in the wood section remaining uncharred. The temperature at the innermost zone of the char layer is assumed to be 300 C. Because of the low thermal conductivity of wood, the temperature 6 mm inward from the base of the char layer is about 180 C once a quasi-steady-state charring rate has been obtained. Some loss of strength undoubtedly results from elevated temperatures. The peak moisture content occurs where the temperature of the wood is about 100 C, which is about 13 mm from the char base. Schaffer et al. [108] have combined parallel-to-grain strength and stiffness relationships with temperature and moisture content and the gradients of temperature and moisture content within a fireexposed slab to obtain graphs of relative modulus of elasticity, compressive strength, and tensile strength as a function of distance below the char layer (Fig. 55.5).
Analytical Methods for Determining Fire Resistance of Timber Members
Fig. 55.5 Relative modulus of elasticity and compressive and tensile strength as a function of distance below char layer in softwood section under fire exposures (Expressed in percentage of that at 25 C and initial moisture content of 12 %.) Duration of fire exposure should be equal to or greater than 20 min to apply results of this figure
1995
100 Modulus of elasticity 80 Relative strength (%)
55
Tensile 60
40 Compressive 20
0 0.5
1
1.5
2
Depth below char layer (in.)
Various equations for the temperature gradient within the charred wood slab have been developed [62, 109, 110]. An equation based on a power term is x 2 T ¼ T i þ ð300 T i Þ 1 ð55:29Þ d where T ¼ Temperature ( C) Ti ¼ Initial temperature ( C) x ¼ Distance from the char front (mm) d ¼ Thermal penetration depth (mm) In the tests of White and Nordheim [59], an average value for the thermal penetration depth was 33 mm. Based on European tests, a more conservative value of 40 mm was recommended for the thermal penetration depth [110]. The power term does not provide for the plateau in temperatures that often occurs at 100 C in moist wood. The power term has also been used to estimate the temperature profile in wood exposed to a constant heat flux [74]. Frangi and Fontana [62] observed that the thermal penetration depth was dependent on time and developed an alternative equation:
α βt T ðxÞ ¼ 20 þ 180 x
ð55:30Þ
where T ¼ Temperature at depth x ( C) β ¼ Charring rate (mm/min) t ¼ Time (min) x ¼ Distance from the surface of the cross section (mm) and αðtÞ ¼ 0:025t þ 1:75
ð55:31Þ
Equation 55.30 was derived assuming the char front at 200 C and char rate of 0.7 mm/min. Frangi and Fontana [62] also developed the following equation for a timber beam exposed to fire on three sides: T ðx; yÞ ¼ 20 þ 180ðβtÞα α α
α 1 1 1 þ þ x bx y
ð55:32Þ
where T, t, α, and β are as defined for Equation. 55.30, and x and y are the depths from the
1996
R.H. White
surfaces of the cross section in millimeters. The theoretical models discussed previously can be used to determine the temperature gradient within the wood remaining uncharred. There are two approaches to evaluating the load-carrying capacity: to evaluate the remaining section either as a single homogeneous material or as a composite of layers or elements with different properties. In the single homogeneous material approach, one uses either reduced material properties or the room-temperature material properties. A greater reduction in cross-sectional area is calculated if the material properties are not reduced.
Reduced Properties Models One approach in accounting for the loss in strength in the section remaining uncharred is to assume that the strength and stiffness of the entire uncharred region are fractions α of their room-temperature values. For bending rupture of a beam, an equation of this type would be M ¼ ασ0 Sð t Þ
ð55:33Þ
Where α ¼ fraction of room-temperature values M ¼ Applied moment (design load) S ¼ Section modulus of charred member σ0 ¼ Modulus of rupture at room temperature t ¼ Time Assuming the residual cross section is rectangular in shape before and during fire exposure, the section modulus of charred solid rectangular bending members with the neutral axis perpendicular to depth at center is [109] SðtÞ ¼
i 1h ðB 2C1 tÞðD jC2 tÞ2 6
ð55:34Þ
where B ¼ Original breadth of beam D ¼ Original depth of beam (depth>breath) C1 ¼ Charring rate in breadth direction C2 ¼ Charring rate in depth direction
j ¼ 1 for three-sided fire exposure (top edge covered) or 2 for four-sided fire exposure (Fig. 55.6) Alternative to Equations 55.33 and 55.34 are the following, Equations 55.35 through 55.36: 2 B k d d D B ¼ ð55:35Þ α D 1D D for exposure on all four sides [111], and 2 k B=D d ¼ ð55:36Þ α ½B=D 2ð1 d=DÞ D for exposure on three sides [112], [113], where k ¼ Load, as fraction of room temperature ultimate load of original member d ¼ Critical depth of the uncharred beam The fire resistance is equal to the time to reach the critical depth, or t ¼ ðD d Þ= jC
ð55:37Þ
Proposed α values ranged from 0.5 in New Zealand to 0.83 in France [109]. The differences in α values are due to uncertainty, differences in design load, and desired level of safety. The application of the above equations is generally limited to large wood members. In light-frame members, α values would be substantially lower [114]. In Eurocode 5, this approach is called the “reduced properties method.” The reduction factors are a function of the perimeter of the fire-exposed residual cross section divided by the area of the cross section. In addition to bending rupture, the fire resistance of a beam may depend on lateral buckling of the beam [111]. Similar expressions can be developed for columns and tension members [2, 109, 113, 115]. Early reviews of fire resistance design methodologies for large wood members include those of Schaffer [109], Pettersson [116], and Barthelemy and Kruppa [117]. Kirpichenkov and Romanenkov [118] discussed the calculation procedures in the Soviet Union. The fire resistance of wood structures is also briefly discussed by Odeen [119]. In developing a model for fire-exposed
55
Analytical Methods for Determining Fire Resistance of Timber Members
1997
Fig. 55.6 Fire exposure of beams on three or four sides
unprotected wood joist floor assemblies, Woeste and Schaffer [120, 121] evaluated various timedependent geometric terms that could be used to modify the strength reduction factor. The selected term was α¼
1
1þ
Bþ2D BD
γt f
ð55:38Þ
where tf ¼ Failure time γ ¼ Empirical thermal degrade parameter The model has been experimentally evaluated [122, 123], extended to floor-truss assemblies [121, 124] and used as part of a first-order second-moment reliability analysis of floor assemblies [120, 121]. Reliability-based design of the fire resistance of light-frame construction is also discussed by Lau and Barrett [114]. In a model for metal plate–connected wood trusses [125], the strength degradation factors for the wood are calculated as a function of the duration of exposure and the temperature profile within the wood component. The models for load-bearing floor joist and wall studs in Annex C of Eurocode 5 incorporate the notional char depth within the calculation of the modification factor for the strength
properties. Ko¨nig and Ka¨llsner [126, 127] developed such a modification factor for wood I-joists.
Reduced Cross-Section Area Models A more common approach is to assume an equivalent zero-strength layer, δ, and then evaluate the rest of the member using room-temperature property values [128]. In the model of Schaffer et al. [108] for beams, the δ was estimated to be 8 mm (0.3 in.) thick. This zero-strength layer, δ, was added to the char depth, βt, to obtain the total zero-strength layer. This zero-strength layer model was incorporated within a reliability-based model to predict the strength of glued-laminated beams with individual laminates of various grades of lumber [129]. This zero-strength layer approach is called the “reduced cross-section method” in Eurocode 5 [6]. In Eurocode 5, δ is a linear fraction of 7 mm for the initial 20 min and 7 mm after 20 min. In the NDS method [130, 131], a 20 % increase in the charring rate is used to account for a zero-strength layer. Schmid et al. [128] presented an analysis that indicates that various
1998
factors such as fire exposure, shape, and dimensions of the cross-section may affect the optimum thickness for the zero-strength layer. Further analysis by Klippel et al. [132] also indicated that members in compression would be better modeled using a zero layer thickness greater than the 7 mm currently specified. For fire-damaged members, Williamson [133] recommended 6 mm (0.25 in.) for designs controlled by compression (16 mm [0.625 in.] if design is controlled by tension) and the use of 100 % of the original basic allowable stresses in calculation of load capacity. Performance of the structural member in a fire will depend on the ratio of the applied load to the ultimate capacity of the residual member. Calculations of the structural capacity of the remaining cross section are normally made using ultimate strength values. Design or characteristic strength values are used in the Eurocode 5 calculations. In Eurocode 5, the design value of strength is the 20th percentile of the cold strength divided by a partial factor equal to one. The design stress to member strength adjustment factors in the NDS are discussed in the next section. Design methods account for the various factors affecting performance in different manners. Care must be taken to verify that all the design values and the methodologies are compatible. The reduced cross-section area approach is being used to predict the fire resistance ratings of walls and floors built of cross-laminated-timber (CLT) construction as described by Dagenais et al. [48]. Frangi et al. [134] developed a reduced cross-section model for calculating fire resistance of timber slabs with hollow core elements. Reduced cross-section methodologies are also used to evaluate the load capacity aspect of fire resistance for both unprotected [130] and protected light-frame assemblies [6].
NDS Method for Exposed Wood Members The National Design Specification for Wood Construction (NDS®) method for the fire design
R.H. White
of exposed wood members is a mechanics-based design method that is applicable to all wood structural members covered under the NDS. With explicit equations for the residual fire resistance of the wood members, it is possible to adjust the equations for other member types and loading conditions. The charring rate can be modified for specific wood products. It is described in a chapter of the NDS and other articles [131]. Full documentation is provided in Technical Report 10 of the American Wood Council [130]. In the United States, code recognition is via adoption of the 2005 or later editions of the NDS. It is limited to ratings of 2 h or less. This effective cross-section method uses the nonlinear charring model of Equation 55.6 and strength values at ambient temperatures. An increased char rate accounts for reduced strength and stiffness properties and accelerated charring at the corners. The increase in char depth is 20 % over a nominal char rate that is based on 1 h of fire exposure. Thus, the effective char rate is given by βeff ¼
1:2βn t0:187
ð55:39Þ
where βeff ¼ Effective char rate (mm or in. per hour) adjusted for exposure time, t βn ¼ Nominal char rate (mm or in. per hour) linear char rate based on 1-h exposure t ¼ Exposure time A nominal char rate, βn, of 38 mm (1.5 in.) per hour is normally assumed for solid-sawn and glued-laminated softwood members. The effective char depth is βeff multiplied by time. Thus, the effective char depth at 1 h is 46 mm (1.8 in.); the actual char depth is 38 mm (1.5 in.) and the equivalent zero-strength layer thickness is 7.6 mm (0.3 in.). The section properties of the members are reduced by the effective char depth for the surfaces that are exposed to the standard fire exposure. The resisting strength or average ultimate residual strength properties are calculated by multiplying the allowable design stress values
55
Analytical Methods for Determining Fire Resistance of Timber Members
in the NDS by design stress-to-member strength adjustment factors. Values for this adjustment factor are 2.85 for bending and tensile strength, 2.58 for compression strength, and 2.03 for beam-buckling and column-buckling strength. As appropriate, the allowable design stress values are also multiplied by a size factor, volume factor, flat use factor, beam stability factor, and column stability factor as described in the NDS. For a fire resistance rating of time t, the induced stress of the reduced section of the charred member at time t shall not exceed the resisting strength of the member. For glued-laminated timber bending members with tension laminations, the NDS has requirements for the substitution of core laminations with tension laminations. The specifics depend on the fire resistance rating and the details of the beam construction.
Decks The NDS method addresses the structural requirements for fire resistance of timber decks. Decks are specified to have a thickness of at least 51 mm (2 in.). Butt-jointed decking is designed as a series of beams that have reduced charring on the partially protected sides and normal charring on the exposed bottom surface. The char rate for the sides is one-third of the effective char rate (Equation 55.39). Single and double tongue-and-groove (T&G) decking is assumed to have charring on only the one bottom face. Janssens [135] applied a transformed section analysis of a timber deck and the Eurocode 5 effective cross-section method to develop a simplified design equation (thickness and load factor as variables) for timber decks that was similar to the T.T. Lie equations. In addition to the requirement of structural stability, the fire resistance rating of a timber deck also depends on requirements for thermal protection. Thermal protection criteria provide for excessive temperature rise on the unexposed surface and flame penetration.
1999
In the United States, there is no recognized procedure for solid wood floors or roofs that include the thermal failure criteria of ASTM E119. The equations for the temperature profile in a wood slab discussed previously can be used to estimate the required thickness to prevent excessive temperature rise [135, 136]. A deck is likely to have joints and gaps between the boards that become the controlling factor in the fire resistance of the deck. Joints can be a critical factor in the fire resistance of a wood barrier. Eurocode 5 provides some guidance for joints in wood-based panel products. The estimated failure times for such panel products with a butt joint, lap joint, single T&G joint, or double T&G joint are 20, 30, 40, and 60 %, respectively, of the failure times for a solid wood barrier calculated using charring rates for wood. The application of these adjustments developed for panel products to gaps in decks has been investigated. Based on a series of tests of timber decks, Richardson and Batista [44] concluded that the failure times for simple butt joints, single T&G joints, and double T&G boards were 10, 40, and 40 %, respectively, of the times for a solid wood member estimated using charring rates for wood. In the tests, the specification for the gaps between boards was 2 mm (0.08 in.) or less. These tests also illustrated the effect of increasing the thickness of gaps, particularly with butt joints. For gaps of 1 mm (0.04 in.), the tests suggested that failure times for simple butt joints were 30 % of those for solid-sawn lumber instead of the 10 % for gaps of 2 mm (0.08 in.) or less. Adding wood flooring or panel products on top of the timber deck improved the failure times in the tests of Richardson and Batista [44]. Paneling on top of the decks provided the most benefits to the fire resistance of decks when the butt joints had 4 mm (0.16 in.) gaps, compared with decks of T&G joints or narrow gaps. Given the limited ability to control gaps between deck boards over time, the best method to address the joint issue is to provide a
2000
multilayer deck assembly by adding panel products or other floor topping, such as gypsum concrete or lightweight or normal concrete toppings, on top of the heavy timber decks. Frangi and Fontana [62] found that the fissures between nailed-laminated timber planks did not increase the char rate but noted that the nonexposed surface must be sealed airtight to obtain such results.
Connections Connectors and fasteners relating to support of the member must be protected for equivalent fireresistive construction. Carling [137] summarizes work done in Europe on the fire resistance of joint details in load-bearing wood construction. Buchanan [82] also reviews the literature on the fire performance of connections. Eurocode 5 provides rules for the fire resistance of connections and protecting connections in firerated timber members, and the subject is ¨ stman discussed by Ko¨nig [4, 5, 138] and by O et al. [6]. Rules are given for connections made with nails, bolts, dowels, screws, split-ring connectors, shear-plate connectors, and toothedplate connectors. Moss et al. [139] determined values for embedment strength as a function of temperature and predicted failure times for fire exposed bolted connections with steel and wood splice plates by applying the data to Johansen’s yield equations. Racher et al. [140] used a threedimensional finite element model to examine the thermal and mechanical behavior of dowelled timber connections exposed to fire. Peng et al. [141] reviewed recent studies on fire performance of connections and provided equations for failure times of double shear connections with either bolts or wood dowels. Configurations for the double sheer connections included wood-wood-wood (W-WW), wood-steel-wood (W-S-W), and steel-woodsteel (S-W-S). The equations for W-W-W and W-S-W connections incorporated char rate, load ratio, wood side member thickness, and fastener diameter. In the case of S-W-S
R.H. White
connections, the equation of Peng et al. [141] included the load ratio and the thickness of the wood component. Peng et al. [141] reported that a single layer of 16 mm (0.625 in.) Type X gypsum board improved the fire resistance of the connections by about 33 min and reviewed results for intumescent paints. In U.S. procedures with building code recognition, the protection of connections is addressed by prescriptive requirements. Where minimal 1 h fire resistance is required, the International Building Code (U.S.) requires connectors and fasteners must be protected from fire exposure by 38 mm (1.5 in.) of wood or other approved covering or coating for a 1 h rating. Industry publications [130] include diagrams giving typical details of such protection.
Adhesives There have been a number of recent investigations on the potential impact of new adhesives on the fire resistance of structural wood products. These new adhesives are replacing the traditional resorcinol-formaldehyde and phenol-resorcinolformaldehyde in structural wood products. A note in the Eurocode 5 states that the softening temperature is considerably below the charring temperature of the wood for some adhesives. In response to concerns about the fire performance of non-phenol resorcinol adhesives in finger-jointed lumber, there were efforts in the United States to develop qualification tests for the performance of adhesives in fire-rated wood assemblies. An initial effort was a test protocol (ASTM D 7247 “Test method for evaluating the shear strength of adhesive bonds in laminated wood products at elevated temperatures”) for evaluating the shear strength of adhesive bonds in laminated wood products at elevated temperatures [142]. Performance criteria based on this test were added to specifications for laminated wood products. To address the specific concerns of finger-jointed lumber, two related ASTM standards (ASTM D7374 “Practice for evaluating elevated temperature performance of
55
Analytical Methods for Determining Fire Resistance of Timber Members
adhesives used in end-jointed lumber and D7470 “Practice for evaluating elevated temperature performance of end-jointed lumber studs” were developed as performance criteria for the “Heat Resistant Adhesives” (HRA) grade stamp on end-jointed lumber. End-jointed lumber with the HRA grade stamp was allowed to continue to be an acceptable substitution in fire-rated assemblies tested with solid-sawn lumber. In Europe, Frangi et al. [143] tested the shear behavior of five one-component polyurethane (PUR) adhesives as well as a resorcinolformaldehyde (RF) and an epoxy adhesive as controls at temperatures up to 170 C. The performance of the five PUR adhesives ranged from the very good high temperature performance of the RF adhesive to the poor high temperature performance of the epoxy. Finite element calculations using the reduced elevated temperature shear properties were consistent with an unexpected shear failure within a glued laminated beam in a fire resistance test of a timber-concrete composite slab. While generally not used in structural wood products, tests have shown that epoxy-based adhesives can have poor fire performance [82]. Ka¨llander and Lind [144] conducted a comparative study of six different adhesives before and after exposure of glulam beams to fire. Ko¨nig et al. [145] tested small-sized glued laminated beams in bending. The fire resistance of the beams made with the two polyurethane adhesives and the melamine urea formaldehyde adhesive were less than that for the beam made with the traditional phenolic resorcinol formaldehyde adhesive. Frangi et al. [146] reported substantial differences in temperature dependent strength reduction and failure between several different types of adhesives, particularly when tested in tension. It is expected that concerns about the non-phenol adhesives can continued to be successfully addressed either by improvements in the formulations of the adhesives to comply with appropriate performance criteria or modifications to the fire resistance calculation methodologies to accurately reflect the performance of the structural wood composite products.
2001
Composite Models The most complex approach to evaluating the fire resistance of a wood member is to assume that the uncharred region consists of layers or elements at different temperatures and moisture contents. The strength and stiffness properties depend on the temperature and moisture content profiles. These are referred to as “advanced methods” in Eurocode 5. In one model with layers, the compressive and tensile strengths and modulus of elasticity of each layer are assumed to be fractions of the room-temperature values. Using one 38 mm (1.5 in.) heated layer with reduced properties, Schaffer et al. [108] analyzed a beam using transformed section analysis. In the similar elastic transformed section model of King and Glowinski [147], the heated zone of the remaining wood section is divided into two layers at elevated temperatures. Transformed section analysis is also used by Lee-Gun Kim and Jun-Jae Lee [148] and by Janssens [135]. Finite difference and finite element methods have been used to solve the governing equations for heat and mass transfer. A finite difference model for wood beams and columns was developed by Tavakkol-Khah and Klingsch [149]. The finite element analysis software COMSOL Multiphysics was used by Janssens [105] to predict failure times of glulam beams tested with load levels of zero, 27 %, 44 % and 91 % of design load. Schnabl at al. [150] examined timber composite beams used the finite element method to solve the Luikov’s equations for simultaneous heat and mass transfer. Fragiacomo et al. [151] used the general purpose finite element code Abaqus to conduct 3-D finite modeling of the thermo-structural behavior of laminated veneer lumber (LVL) loaded in tension and exposed to fire. Do and Springer [152–154] proposed a fire resistance model for wood beams based on mass loss versus strength data. The work included a program to predict the temperatures and mass loss within the wood member. The input data came from small-scale tension,
2002
compression, and shear tests done on specimens that had previously been heated in an oven. Examples of models that use a grid of elements to analyze the residual load capacity of the structural member include ones for wood joists [155], compression members [156], and wood studs [28].
Property Data Proper input data are critical to the use of any model. For the models discussed in this section, property data include strength and stiffness properties and thermal properties. General property data for clear wood can be found in various chapters of Wood Handbook: Wood as an Engineering Material [64], which also includes a chapter on fire safety. Reviews of available data on properties needed to model thermal degradation, charring, and residual load capacity of wood members can be found in the literature [82, 107]. Equations and graphs of the strength and stiffness of wood as functions of temperature and moisture content are available [157–159]. Recent research in the development of fire resistance models has provided additional data specific for application to such models. An extensive study on fire-exposed wood in tension was done by Lau and Barrett [160]. Recent efforts have been on the compression properties of wood [161, 162]. The strength reductions given in Eurocode 5 include the time-dependent effects of creep, moisture, and mechanosorption. Such effects are among the reasons for differences reported in the literature. Preheating samples in an oven is not the same as exposing samples to simultaneous thermal and structural loads. Other methodology differences, such as rate of loading, affect the experimental results reported. Thermal properties can also be found in the various references for charring models and Annex B of Eurocode 5 (EN 1995-1-2). As discussed by Ko¨nig [163], the thermal properties of EN 1995-1-2 and other sources are often
R.H. White
effective property values that depend on the assumptions of the model and the experiments used to calibrate the input data. Due to the complexity of wood, thermal degradation, and the heat and mass transfer within the wood element, some aspects of the complexity are accommodated by adjusting the thermal property data. Thus, such thermal property data may be applicable only to the standard fire exposure used in their development and can produce erroneous results when applied to natural fires and parametric fire curves [163]. This is particularly the case for the thermal properties of the char layer. As discussed by Hadvig [56], the “char” of the char layer is complex and its thermal characteristics are not the same as those of charcoal. Lattimer et al. [164] used inverse heat transfer analysis of fire test data for balsa wood to obtain thermal properties, physical properties and decomposition kinetics constants needed for their decomposition model. Although assuming constant property values is often less complicated, these properties are very often a function of other properties or factors. Most wood properties are functions of density, moisture content, grain orientation, and temperature. Chemical composition may also be a factor. Because an understanding of these factors is important to the application of property data, the factors are defined in the rest of this section. The oven-dry density of wood can range from 160 kg/ m3 (10 lb/ft3) to over 1040 kg/m3 (65 lb/ft3), but most species are in the 320- to 720-kg/m3 (20- to 45-lb/ft3) range [64]. The density of wood relative to the density of water (i.e., specific gravity) is normally based on oven-dry weight and volume at some specified moisture content, but in some cases the oven-dry volume is used. As the empirical equations for charring rate show, materials with higher density have slower char rate. In the Eurocode 5 discussion of advanced calculations, the suggested char/ dry wood ratios are 1.0, 1.0, 0.93, 0.76, 0.52, 0.38, 0.28, 0.26, and 0 for temperatures of 20, 200, 250, 300, 350, 400, 600, 800, and 1200 C, respectively.
55
Analytical Methods for Determining Fire Resistance of Timber Members
Wood is a hygroscopic material, which gains or loses moisture depending on the temperature and relative humidity of the surrounding air. Moisture content of wood is defined as the weight of water in wood divided by the weight of oven-dry wood. Green wood can have moisture content in excess of 100 %. However, air-dry wood comes to equilibrium at moisture content less than 30 %. Thirty percent moisture content is also considered the approximate moisture content at which the cell walls are saturated with water, but there is no water in the cell lumens. This condition is known as the fiber saturation point. At higher moisture contents, water exists in the cell lumens. Many physical and mechanical properties of wood change with moisture content only at moisture contents below the fiber saturation point. Under the conditions stated in ASTM E119 (50 % relative humidity), the equilibrium moisture content is about 9 %. Moisture generally reduces the strength of wood but also reduces the charring rate. Both density and moisture content affect the thermal conductivity of wood. The average thermal conductivity perpendicular to the grain is [64] k ¼ Sð0:0001941 þ 0:000004064MÞ þ 0:01864 ð55:40Þ where k ¼ Thermal conductivity (W/mK) S ¼ Density based on volume at current moisture content and oven-dry mass (kg/m3) M ¼ Moisture content (percent) Equation 55.40 is valid for moisture contents of 25 % or less, densities greater than 300 kg/m3, and temperature of 24 C. Conductivity increases about 2–3 % per 10 C [64]. In the Eurocode 5 discussion of advanced calculations, the suggested values for “apparent thermal conductivity” of the wood/char as a function of temperature are 0.12, 0.15, 0.07, 0.09, 0.35, and 1.50 W/ mK for 20. 200. 350, 500, 800, and 1200 C, respectively.
2003
The fiber (grain) orientation is important because wood is an orthotropic material. The longitudinal axis is parallel to the fiber or grain. The two transverse directions (perpendicular to the grain) are the radial and tangential axes. The radial axis is normal to the growth rings, and the tangential axis is tangent to the growth rings. For example, the longitudinal strength properties are usually about ten times the transverse properties, and the longitudinal thermal conductivity is 1.5–2.8 times the transverse property. In fire resistance analysis, temperature can have a significant influence on the properties of wood. The preponderance of property data is often limited to temperatures below 100 C. The effect of temperatures on the strength properties of wood is shown in Figs. 55.7, 55.8, and 55.9. Using data from a variety of sources, Buchanan [82] also provides graphs of the temperature effect on mechanical properties. The heat capacity, cρ (kJ/kg K), of dry wood is approximately related to temperature, T (in K), [64] by. cρ ¼ 0:1031 þ 0:003867T
ð55:41Þ
In the Eurocode 5, the suggested apparent specific heat capacity values are 1.53, 1.77, 13.60, 13.50, 2.12, 2.00, 1.62, 0.71, 0.85, 1.00, 1.40, 1.65, and 1.65 kJ/kg-K for 20, 99, 99, 120, 120, 200, 250, 300, 350, 400, 600, 800, and 1200 C, respectively. These values results in a sharp peak between 99 and 120 C to address water vaporization. These values are tied to the suggested char/wood ratios with the addition of the moisture content to the ratio for temperatures between 20 and 99 C. For moist wood below the fiber saturation point, the heat capacity is the sum of the heat capacity of dry wood and that of water and an additional adjustment factor for the wood-water bond [64]. Studies on thermal properties of wood and char continue to be active areas of research. The major components of wood are cellulose, lignin, hemicelluloses, extractives, and inorganic materials (ash). Softwoods have lignin contents
2004 200
Relative modulus of elasticity (%)
Fig. 55.7 The immediate effect of temperature on modulus of elasticity parallel to the grain at two moisture contents relative to value at 20 C. The plot is a composite of results from several studies. Variability in reported trends is illustrated by the width of bands [64]
R.H. White
12 percent moisture content
150
0 percent moisture content
100
50
0 –200
100 0 Temperature (°C)
200
300
250
18 percent moisture content
200 Relative modulus of rupture (%)
Fig. 55.8 The immediate effect of temperature on modulus of rupture in bending at three moisture contents relative to value at 20 C [64]
–100
150
12 percent moisture content
0 percent moisture content
100
50
0 –200
–150
–100
–50 0 50 Temperature (°C)
100
150
55
Analytical Methods for Determining Fire Resistance of Timber Members
Fig. 55.9 The immediate effect of temperature on compressive strength parallel to the grain at two moisture contents relative to the value at 20 C [64]
2005
300
Relative compressive strength (%)
250
12 percent moisture content
200
150
100
0 percent moisture content
50
0 –200
–100
0
100
200
300
Temperature (°C)
of 23–33 %, whereas hardwoods have only 16–25 %. The types and amounts of extractives vary. Cellulose content is generally around 50 % by weight. The component sugars of the hemicelluloses are different for the hardwood and softwood species. Chemical composition can affect the kinetics of pyrolysis (Equation 55.27) and the percentage weight of the residual char. In the degradation of wood, higher lignin content results in greater char yield.
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Forest Service, Forest Product Laboratory, Madison, WI (1981). 122. R.H. White, E.L. Schaffer, and F.E. Woeste, “Replicate Fire Endurance Tests of an Unprotected Wood Joist Floor Assembly,” Wood and Fiber, 16, p. 374 (1984). 123. E.L. Schaffer and R.H. White, “Fire Endurance Model Validation by Unprotected Joist Floor Fire Testing,” in Proceedings of 1988 International Conference on Timber Engineering, Forest Products Research Society, Madison, WI (1988). 124. E.L. Schaffer and F.E. Woeste, “Reliability Analysis of a Fire-Exposed Unprotected Floor Trusses,” in Proceedings, Metal Plate Wood Truss Conference, Forest Products Research Society, Madison, WI (1985). 125. R.H. White, S.M. Cramer, and D. Shrestha, “Fire Endurance Model for a Metal-Plate-Connected Wood Truss,” Research Paper FPL 522, USDA Forest Service, Forest Products Laboratory, Madison, WI (1993). 126. J. Ko¨nig and B. Ka¨llsner, “Modeling Resistance of Wooden I-Joists Exposed to Fire,” in Proceedings of SiF’06: Fourth International Workshop Structures in Fire, University of Aveiro, Aveiro, Portugal, p. 951 (2006). 127. J. Ko¨nig, “Fire Exposed Simply Supported Wooden I-Joists in Floor Assemblies,” SP Report 2006:44, SP National Testing and Research Institute, Stockholm, Sweden (2006). 128. J. Schmid, J. Ko¨nig, and A. Just, “The Reduced Cross-Section Method for the Design of Timber Structures Exposed to Fire - Background, Limitations, and New Developments,” Structural Engineering International, 22, 4, p. 514 (2012). 129. D.A. Bender, F.E. Woeste, E.L. Schaffer, and C.M. Marx, “Reliability Formulation for the Strength and Fire Endurance of Glued-Laminated Beams,” Research Paper FPL 460, USDA Forest Service, Forest Prod. Laboratory, Madison, WI (1985). 130. American Wood Council, “Calculating the Fire Resistance of Exposed Wood Members,” Technical Report 10, American Forest & Paper Association, Washington, DC (2003). 131. B.K. Douglas, “Calculating the Fire Resistance of Exposed Wood Members,” Wood Design Focus, 9, 3, p. 15 (1999). 132. M. Klippel, J. Schmid, and A. Frangi, “The Reduced Cross-Section Method for Timber Members Subjected to Compression, Tension and Bending in Fire,” in Proc. CIB-18 Meeting 45, Paper 45-15-1. Ingenieurholzbau und Baukonstruktionen, Karlsruhe Institute of Technology, Karlsruhe, Germany (2012) 133. T.G. Williamson, “Rehabilitation of Fire-Damaged Timber—The Filene Center,” in Evaluation, Maintenance, and Upgrading of Wood Structures, American Society of Civil Engineers, New York (1982).
2010 134. A. Frangi, M. Knobloch, and M. Fontana, “Fire Design of Timber Slabs Made of Hollow Core Elements,” Engineering Structures, 31, p. 150 (2009). 135. M.L. Janssens, “A Method for Calculating the Fire Resistance of Exposed Timber Decks,” in Fire Safety Science—Proceedings of the Fifth International Symposium, International Association for Fire Safety Science, Boston (1997). 136. R.H. White, “Fire Resistance of Exposed Wood Members,” in Proceedings of the 5th Wood and Fire Safety Conference, Technical University of Zvolen, Zvolen, Slovak Republic, p. 337 (2004). 137. O. Carling, “Fire Resistance of Joint Details in Loadbearing Timber Construction—A Literature Survey,” Study Report No. 18, Building Research Association of New Zealand, Judgeford, NZ (1989). 138. J. Ko¨nig and M. Fontana, “The Performance of Timber Connections in Fire-Test Results and Rules of Eurocode 5,” in Proceedings of International Rilem Symposium “Joints in Timber Structures,” University of Stuttgart, Germany (Sept. 2001). 139. P. Moss, A. Buchanan, M. Fragiacomo, and C. Austruy, “Experimental Testing and Analytical Prediction of the Behavior of Timber Bolted Connections Subjected to Fire,” Fire Technology, 46, p. 129 (2010). 140. P. Racher, K. Laplanche, D. Dhima, and A. Bouchaı¨r, “Thermo-Mechanical Analysis of the Fire Performance of Dowelled Timber Connection,” Engineering Structures, 32, p. 1148 (2010). 141. L. Peng, G. Hadjisophocleous, J. Mehaffey, M. Mohammad, and L. Lu, “Calculating Fire Resistance of Timber Connections,” in Proceedings of Fire and Materials 2011 Conference, Interscience Communications Ltd., London, p. 455 (2011). 142. B. Yeh and R. Brooks, “Evaluation of Adhesive Performance at Elevated Temperatures for Engineered Wood Products,” in Proceedings of the 9th World Conference on Timber Engineering, Oregon State University, Corvallis (2006). 143. A. Frangi, M. Fontana, and A. Mischler, “Shear Behavior of Bond Lines in Glued Laminated Timber Beams at High Temperatures,” Wood Sci Technol., 38, p. 119 (2004). 144. B. Ka¨llander and P. Lind, “Strength Properties of Wood Adhesives After Exposure to Fire,” in Proceedings of Wood Adhesives 2005, Forest Products Society, Madison, WI, p. 211 (2006). 145. J. Ko¨nig, J. Nore´n, and M. Sterley, “Effect of Adhesives on Finger Joint Performance in Fire,” in Proc. CIB W18 Meeting 41, Lehrstuhl fu¨r Ingenieurholzbzu, University of Karlsruhe, Karlsruhe, Germany (2008). 146. A. Frangi, M. Bertocchi, S. Clauß, and P. Niemz, “Mechanical Behavior of Finger Joints at Elevated Temperatures,” Wood Sci. Technol., 46, p. 793, (2012).
R.H. White 147. E.G. King and R.W. Glowinski, “A Rationalized Model for Calculating the Fire Endurance of Wood Beams,” Forest Products Journal, 38, 10, p. 31 (1988). 148. Lee-Gun Kim and Jun-Jae Lee, “Studies on Prediction about Behavior of Wood Beam Under Standard Fire Condition,” Mokchae Konghak, 23, 4, p. 10 (1995). 149. M. Tavakkol-Khah and W. Klingsch, “Calculation Model for Predicting Fire Resistance Time of Timber Members,” in Fire Safety Science—Proceedings of the Fifth International Symposium, International Association for Fire Safety Science, Boston (1997). 150. S. Schnabl, I. Planinc, G. Turk, and S. Srpcˇicˇ, “Fire Analysis of Timber Composite Beams with Interlayer Slip,” Fire Safety Journal, 44, p. 770 (2009). 151. M. Fragiacomo, A. Menis, P.J. Moss, I. Clemente, A.H. Buchanan, and B. DeNicolo, “Predicting the Fire Resistance of Timber Members Loaded in Tension,” Fire and Materials, published on-line, DOI: 10.1002/fam.2117, (2012). 152. M.H. Do and G.S. Springer, “Mass Loss of and Temperature Distribution in Southern Pine and Douglas Fir in the Range 100 to 800C,” Journal of Fire Sciences, 1, p. 271 (1983). 153. M.H. Do and G.S. Springer, “Model for Predicting Changes in the Strengths and Moduli of Timber Exposed to Elevated Temperatures,” Journal of Fire Sciences, 1, p. 285 (1983). 154. M.H. Do and G.S. Springer, “Failure Time of Loaded Wooden Beams During Fire,” Journal of Fire Sciences, 1, p. 297 (1983). 155. N. Be´nichou. “Predicting the Structural Fire Performance of Solid Wood-Framed Floor Assemblies,” in Proceedings of SiF’06: Fourth International Workshop Structures in Fire, University of Aveiro, Aveiro, Portugal, p. 909 (2006). 156. I.M. VanZeeland, J.J. Salinas, and J.R. Mehaffey, “Compressive Strength of Lumber at High Temperatures,” Fire and Materials, 29, p. 71 (2005). 157. C.C. Gerhards, “Effect of Moisture Content and Temperature on Mechanical Properties of Wood: An Analysis of Immediate Effects,” Wood and Fiber Science, 14, p. 4 (1982). 158. F.C. Beall, “Effect of Temperature on the Structural Uses of Wood and Wood Products,” in Structural Use of Wood in Adverse Environments, Van Nostrand Reinhold, New York (1982). 159. B.A.-L. Ostman, “Wood Tensile Strength at Temperature and Moisture Contents Simulating Fire Conditions,” Wood Science and Technology, 19, p. 103 (1985). 160. P.W. Lau and J.D. Barrett, “Modeling Tension Strength Behaviour of Structural Lumber Exposed to Elevated Temperatures,” in Fire Safety Science— Proceedings of the Fifth International Symposium, International Association for Fire Safety Science, Boston (1997).
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161. S.A. Young and P. Clancy, “Compression Mechanical Properties of Wood at Temperatures Simulating Fire Conditions,” Fire and Materials, 25, p. 83 (2001). 162. F.J. Francisco and P. Clancy, “Compression Properties of Wood as Function of Moisture, Stress and Temperature,” Fire and Materials, 28, p. 209 (2004). 163. J. Ko¨nig, “Effective Thermal Actions and Thermal Properties of Timber Members in Natural Fires,” Fire and Materials, 30, p. 51 (2006).
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164. B.Y. Lattimer, J. Ouellette, and J. Trelles, “Measuring Properties for Material Decomposition Modeling,” Fire and Materials, 35, p. 1 (2010). Robert H. White was a wood scientist at the USDA, Forest Service, Forest Products Laboratory. His research in a wide range of topics pertaining to fire performance of forest products have included studies on wood charring and fire resistance of wood assemblies.
Egress Concepts and Design Approaches
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Richard W. Bukowski and Jeffrey S. Tubbs
Introduction Among the most important concepts in fire safety in buildings is to manage those potentially exposed to the fire and its effects, either by protecting them in place or by moving them to a place of safety. Protected spaces and paths of travel needed to accomplish this are the egress components, systems and procedures that are discussed in this chapter. The chapter presents an overview of considerations, concepts, methods, and strategies utilized globally for emergency egress system design. Approaches to full or partial evacuation using stairs or elevators, egress for people with disabilities, protect-inplace strategies, and alternatives to evacuation, are presented. Prescriptive and performancebased approaches are discussed and strategies for selecting specific systems are summarized. Additional information on performance-based evacuation modeling, occupant movement simulation, human behavior during emergencies, and occupant and scenario factors is detailed in other chapters. Chapter 57 presents methods for considering occupant factors within designs.
R.W. Bukowski, P.E., FSFPE (*) Jensen Hughes, 2001 N Main St #510, Walnut Creek, CA 94597 J.S. Tubbs, P.E., FSFPE Arup, 955 Massachusetts Avenue, Fourth Floor, Cambridge, MA 02139
Chapters 61 and 63 present methods for assessing tenability and criteria for use in engineering studies. Chapter 58 presents human behavior concepts and theory and how data is collected. Chapter 64 presents studies of flow rate and walking speed applicable for use in engineering studies. Chapters 59 and 60 present evacuation calculation and simulation methods and techniques. The purpose of this chapter is to present the historical evolution of emergency egress provisions in public buildings and the varying approaches utilized to facilitate egress along with their scientific basis. By understanding the scientific basis the engineer should understand the intended performance in the context of performance based design and alternate approaches utilized to address the special needs of specific occupants or unique facilities. The chapter begins with the history of emergency egress systems including the scientific basis for the 44 in. (1100 mm) egress stair width, the concept of exit capacity used in US Codes, flow rate, fire escapes and the 7/11 stair geometry. This should help to understand the goals and objectives of the codes and the levels of performance anticipated from the common prescriptive approaches to egress system arrangements. Next, a discussion of common strategies that address specific objectives and the expanding list of egress system components are discussed in their context of use along with related systems that notify people of the need to
M.J. Hurley (ed.), SFPE Handbook of Fire Protection Engineering, DOI 10.1007/978-1-4939-2565-0_56, # Society of Fire Protection Engineers 2016
2012
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take action and that provide route guidance during the action. Finally, performance-based design concepts that are frequently used to justify alternative egress system designs in unique or constrained buildings are presented.
Historical Perspective For many years, buildings were short enough that stairs provided for access were sufficient for safe and rapid egress for most occupants in the event of fire. Until passage of the Americans with Disabilities Act (PL101-336) in 1990, buildings were rarely accessible, and emergency egress of people with disabilities was not a national priority. Even in single stair (mostly residential) buildings, experience indicated that this stair was sufficient for fire egress as long as the fire did not expose or block access to the stair. Fire resistant apartment doors shielded the stair from most fires and exterior fire escapes provided a second egress path beginning early in the Twentieth Century. The 1854 invention of the elevator safety brake enabled the passenger elevator. This system is credited with facilitating increases in building height beyond six floors and the first so-called skyscraper in Chicago in 1885 [1]. Model building regulations in the US started with the National Building Code published by the National Board of Fire Underwriters (NBFU) following the Great Fire of Boston in 1872. Property loss claims from this fire resulted in more than 70 insurance companies being driven into bankruptcy, causing insurance interests to form the NBFU and to develop building fire safety rules aimed at reducing property losses in fires. These rules became the first model building code, called the National Building Code (NBC), first published in 1905. The NBFU was able to tie compliance with their rules to their Municipal Grading Schedule on which insurance rates are based. Cities needed favorable rates to attract investment, so they were motivated to adopt regulations consistent with the National Building Code. The first edition of the NBC required exit stairs to have a minimum width of 20 in. (510 mm) [2].
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Origins of the 44 in. Exit Stair in the US In the 1913 National Fire Protection Association (NFPA) Proceedings, the Committee on Fireproof (later, Fire-Resistive) Construction reported a number of recommendations, including a minimum unobstructed width of 44 in (1100 mm) exit stairs. Handrails were permitted to intrude not more than 3.5 in. (89 mm) on each side. That same year, NFPA formed their Committee on Safety to Life. That committee’s first activity was to conduct a comprehensive review of fire safety issues and regulatory approaches found in building codes and local regulations in several, geographically diverse cities. At the meeting [1], they reported that [3], . . . existing laws are exceedingly deficient in this very important matter of egress. A number of states report frankly that they have no real legislation upon the subject, many City Ordinances are of the most indefinite character, and in some the matter is simply left to the discretion of the fire department or other officials.
In the 1914 NFPA Proceedings section on egress, the Safety to Life Committee cites the 1913 NFPA Annual Meeting report of the Committee on Fire-Resistive Construction in which they said was presented [1]. . . . a splendid set of specifications for the construction of a standard building. Egress received detailed attention;—specifications for smokeproof towers, for stairs, for horizontal exits, and for the capacity of vertical and horizontal exits were included.
The committee also cites the 1913 laws of the New York State Department of Labor which, “. . . as regards fundamentals appear to agree entirely with the requirements of our Committee . . .”. Extracting from the referenced New York statute, they cite [1], (a) For buildings erected in the future, a minimum of 22 in. (550 mm) of stair width shall be required for not to exceed 14 persons on any one floor. (b) On buildings already erected this figure is reduced to 18 in. (450 mm) as a minimum. (c) A 44-in. (1100 mm) stair in new buildings permits 28 persons to be housed on each floor above the first one.
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(d) In arriving at this decision the idea has been that all of the persons on all floors shall be able to remain in the stair tower without any movement, a person requiring about 22 in. (550 mm) in width, and one person to stand on every other stair. This committee further characterizes the New York laws’ stair geometry (7.75 in. riser height by 10 in. tread) as “good”, and that they recommend a minimum 44 in. wide stair for new buildings as this width is “sufficient to prevent three persons from forming an arch and blocking traffic” [4].
Exit Capacity The above explains why the US designs exits for “capacity” and why the capacity is based on the population of a single floor. The exit is sized to “store” people, motionless within the protected exit enclosure, such that the population of one floor will fit entirely within the stair between that floor and the next floor below, with each person in a space 22 in. wide and standing on every other step. This philosophy was recognized in the 1935 National Bureau of Standards (NBS now NIST) publication, Design and Construction of Building Exits [5]. Developed by the Department of Commerce Building Code Committee, this report included survey data on exit sizes and configurations drawn from eight cities chosen, “. . . with a view to covering places varying in size and sufficiently distributed to give a fair cross section of building construction.” The survey included population counts on typical floors and compiled data on movement of people in buildings, as well as railway terminals (particularly at rush hour which was considered to be similar to emergency movement in a fire) and schools. Studies of the flow of occupants in government buildings during fire drills and of the general public exiting railway terminals at rush hour were conducted, and the data resulted in discharge rates for stairs (as a function of width and stair geometry), ramps, and doorways. The data was used to suggest possible approaches to calculating the minimum width
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of exits necessary to provide for occupant safety. These included five, proposed methods (text paraphrased from the 1935 NBS report): 1. Capacity Method, which is based on the concept of storing occupants on the stairs within a protected stair enclosure, and allowing for the subsequent safe and orderly evacuation of the building. It recognized that travel down a long series of stairs in high buildings is exhausting even to normal persons. Objections of building owners over the loss of rentable space are noted as well as the comment by some authorities that people may not stand still in stairways, even in relatively taller buildings, preferring instead to proceed to the street. 2. Flow Method, which is based on the concept that people will move down the stairs at a typical flow, assumed to be 45 persons per 22 in. unit of width per minute and 60 persons per minute through doorways. It is stated that this method is usually coupled with an assumed time in which it is safe to exit the building and that this method calls for considerably less stairway width than the capacity method. However, the committee felt that it would be limited to a few occupancies and to buildings of low to moderate height since continuous movement down stairways in relatively taller buildings cannot be expected without serious effects on some occupants. 3. Combined Method suggests the flow method for lower buildings shifting to the capacity method for taller buildings also accounting for type of construction and use. Once again NBS pointed out that taller buildings would require a disproportionate amount of space devoted to stairways as compared with useable floor area. 4. Probability Method considers only the population of the six most densely populated floors since it was considered improbable that simultaneous evacuation of all floors of a large building would be needed. This is the first time that phased evacuation, as currently practiced in tall buildings, was suggested. 5. Floor Area Method relates area to units of exit width needed as a function of construction type and use. As in the probability
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method, simultaneous evacuation of all floors is not considered; however, the number of floors that were considered to simultaneously evacuate varied with occupancy. In the end, the 1935 report suggests that the needs of the vast majority of buildings can be met with the provision of two, two-unit-width (44 in. or 1100 mm) stairs. The capacity method, which includes occupants waiting within the exit enclosure, is appropriate for shorter buildings with a gradual shift to the flow method for taller buildings where people will be less comfortable waiting in the stair. For tall buildings the floor area method has some application as these are of fire resistive construction and only those near the floor of fire origin are initially at risk. NBS suggests half of the floors should be considered with the floor area method.
Early Thoughts on Elevators as a Means of Egress Both the 1914 NFPA Proceedings [1] and the 1935 NBS report [5] discuss the possible use of elevators for egress from tall buildings. In 1914 the Committee on Safety to Life expressed the opinion that, “. . . elevator shafts properly enclosed and with openings adequately protected have decided value from an escape standpoint, and are absolutely necessary in high buildings.” They cited as “. . . loss of life possibilities in many modern so-called fireproof buildings . . .” the common practice of unenclosed stair and elevator shafts that might permit a fire in lower stories to, “. . . spread with unexpected speed . . .” which “. . . could result in a loss of life which would stagger the civilized world.” The Committee called for enclosing elevator shafts, improving the fire resisting powers of elevator doors, ensuring the integrity of the electric current applied to elevators, and “drilling” elevator operators in emergency procedures, including that persons in the upper stories “shall first be taken to the ground.” The 1935 NBS report discusses a credit for elevators against required aggregate exit width.
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They discount automatic elevators as unsuitable, as their “. . .capacity and rate of speed is not great,” and “. . . they are not subject to a single will as in the case of an elevator operator, but to demands from many tenants.” While there was a suggestion in the formulae of the flow method that five elevators might be equal to a single unit of exit stair width for some construction types and use, in the end they concluded that the uncertainties were such that no direct credit be given for elevators but to recognize their availability in high buildings.
Early Regulatory Approaches in the US The 1914 report of the Committee on Safety to Life included detailed recommendations for the design and arrangement of egress stairs and fire escapes with the intent that this material would be incorporated by others into building regulations. No code or standard was produced by the Committee until the 1927 publication of the first edition of the NFPA Building Exits Code (NFPA 101-T) [6] which later became the Life Safety Code. The 1927 edition of NFPA 101-T defined stairs as Class A, B, or C. Class A stairs were the main stair of a newly-constructed Assembly occupancy, and were 44 in. (1100 mm) wide (handrails could intrude not more than 3.5 in. (89 mm) on each side) with a rise of not more than 7 in. (178 mm) and a tread of not less than 10.5 in. (267 mm). Class B stairs were for new construction of all stairs not required to be Class A, and for existing construction where Class A stairs would be required if new. Class B stairs were the same width as Class A but the rise was permitted to be not more than 7.75 in. (197 mm) with a tread of not less than 9.5 in. (241 mm). Class C stairs covered existing stairs in existing buildings and were at least 36 in. (900 mm) wide (not less than 32 in. or 810 mm between handrails, but stairs less than 44 in. (1100 mm) wide only required a handrail on one side). Occupant load on a floor dictates the capacity (total width of stairs in number of
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22 in. (550 mm) units) to be provided in a minimum of two stairs located “as remote as practical.” The 1935 NBS report included recommended code language in an appendix that did not follow any of the five methods for calculating minimum exit widths discussed previously. They explained that tentative requirements were drawn up and compared against the results of the field studies. Eventually a consensus of the Committee was reached and was presented in the recommended code language. The suggested code requirements largely followed the capacity method for at least two stairs of two 22 in. (550 mm) units of exit width each, with the floor area method used, by means of occupancy load factors consistent with those found in current regulations, to determine aggregate width. No suggestions of maximum egress time, including no references to fire resistance times associated with construction types, building height, and use, that might facilitate the use of the flow method, and no mention of partial evacuation of tall buildings as discussed in the probability and floor area methods was made. These recommendations were consistent with those in the 1927 edition of NFPA 101-T, but this is not surprising since the Committee on Safety to Life was well represented on the NBS Committee. The requirements suggested in the NBS report and NFPA 101 were generally adopted in the model codes and building regulations throughout the US until the mid-1980s when the 22 in. (550 mm) unit of exit width was abandoned for assessing exit capacity in units of people per inch, but retaining the 44 in. (1100 mm) minimum width. This method provides similar results for aggregate exit width but provides more capacity credit for fractions of the 22 in. (550 mm) unit.
Early Scientific Studies of Flow Rate The 1935 NBS report [5] included field surveys of discharge rates down exit stairs and through
R.W. Bukowski and J.S. Tubbs
doors for various government buildings during drills and for subway and rail terminals at rush hours. The data collected was discussed by the Committee and a consensus reached that there was a clear correlation between width and flow. The committee agreed that “. . . rates of 45 persons per 22-in. unit per minute for travel down stairways, and 60 persons per 22-in. unit per minute through doorways, which had been in use on the basis of earlier observations, were sufficiently confirmed to warrant their retention in connection with the requirements under development.” Almost from the start there were issues raised with the assumed flow rate on stairs of 45 persons per minute per 22 in. (550 mm) unit of exit width. Togawa [7] in Japan conducted research in the 1940s and 1950s, that showed for densities above one person per square meter (10 ft2), flow rates decreased significantly. His data suggested a flow rate of 26 persons per minute per (22 in.) unit of exit width. Pauls [8] has published extensively on this topic and continues to be the scientific conscience of stair design in the US codes. Pauls [8] and Fruin [9] both discussed the concept of effective width of a stair, which is generally 0.3 m (1 ft) narrower than the actual width due to the natural tendency of people to keep a distance from walls and handrails. Fruin further spoke of the personal space (buffer) around people that increases their effective space requirement. Pauls found that for people walking on stairs, their body sways from side to side and they desire sufficient space so that they do not make contact with the person beside them. Pauls work confirmed that of Togawa, finding flow rates in stairs at typical densities to be approximately 27 persons per minute per (22 in.) unit of exit width. Extensive studies in Russia also confirmed the effects of density on flow rates and confirmed the values suggested by Pauls [8] and Togawa [10]. Chapter 64 details flow rate and walking speed studies applicable for use in engineering simulation and studies.
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Early Scientific Studies of Exit Width The current 44 in. (1100 mm) minimum exit stair width is intended to support two, 22 in. (550 mm) queues of occupants either standing still (capacity method) or moving down the stair. This also allows counterflow, which occurs when a single queue of occupants moving down are passed by firefighters or other responders moving up. The 22 in. (550 mm) dimension for the width of a person was offered in 1914, originating from soldiers standing in a line [3]. Challenges to the adequacy of the 22 in. (550 mm) dimension include the need to provide for body sway as people move down the stair [8], and the need to allow for some personal space [9,10]. Recently, the adequacy of the basic 22 in. dimension has been questioned in light of the increasing size and weight of the typical person, especially in the US. The 22 in. dimension refers to the width of a person at the shoulders, which is assumed to be the widest part. Predtechenskii and Milinskii suggest that 4 in. (100 mm) be added to each side to allow for a personal buffer except that for low obstructions (like handrails) the additional space is not needed since one’s shoulders are at a higher level and will extend over the obstruction. From anthropometric data for modern Americans, the width at the hip is approaching the width at the shoulder, and it seems that this exception may no longer be valid. Thus, with the shoulder width of the 97.5th percentile adult male reaching 20 in. (510 mm) [11] and allowing the 4 in. on each side for handrail and personal space, the new unit of exit width should be 28 in. (700 mm) and the minimum stair width 56 in. (1400 mm), see Fig. 56.1. Arguably the most comprehensive studies of movement on stairs were conducted by Templer [12], beginning with his doctoral research [13] and including work at NBS in the 1980s. Templer observed the movement of many individuals up and down stairs of varying width and tread geometry, tabulating variables ranging from quantitative (speed, number of stumbles) to qualitative (perceived comfort). From this work
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Templer concluded that the minimum width of an egress stair should be 56 in. (1400 mm).
Scientific Studies of Tread Geometry One of the earliest studies of stair geometry was conducted by a seventeenth century architect in France named Francois Blondel [14]. Blondel was primarily interested in comfort rather than safety and observed that the main stairs of classic cathedrals were comfortable to use and accommodated large numbers of people attending services. He made measurements and found that the ratio of stair height to tread depth was a constant, and he related this dimension to the length of the human gait. His formula was 2R þ G ¼ 24 in., where R is the rise and G is the going (or run). Templer [15] adjusted Blondel’s formula for the use of the old (pre French Revolution) inch and a modern gait more like 28 in. (710 mm) and arrived at the formula, 2R þ G ¼ 710 mm. The 7 in. rise, 11 in. run stair geometry commonly required in US codes meets the relation 2R þ G ¼ 635 mm. Templer [15] summarizes a number of research studies of stair geometry and safety. Many such studies were conducted by observing people moving up or down stairs in buildings. Observations in subway or train stations at rush hours provided data for higher population densities. A few studies were conducted in laboratory settings on specially constructed stair sections where the geometries and stair angle could be varied systematically. Templer himself conducted several of these studies, including some at NBS. Most of the studies reviewed concluded that the measure of Total Energy Cost per Meter Rise [15] is a useful metric for the evaluation of stair design for normal use and comfort; however, stair safety is more closely related to the likelihood of missteps which is a function of how the stair relates to the human gait. In both cases, the effect is different for ascent and descent, with descent being more hazardous.
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R.W. Bukowski and J.S. Tubbs
Fig. 56.1 Anthropometric data (in mm.) for adults; males and females of average, 50th percentile, size; some dimensions apply to very large, 97.5 percentile (97.5 P), adults (Reprinted with permission from NFPA 101®-2012, Life Safety Code®, Copyright # 2011,
National Fire Protection Association, Quincy, MA). This reprinted material is not the complete and official position of the NFPA on the referenced subject, which is represented only by the standard in its entirety
When ascending a stair, a person walks on the ball of the foot with less of the foot placed on the step. Shorter treads (goings) and higher risers produce fewer missteps. When descending a stair, the heel and most of the foot needs to be placed on the tread. Too much of the front of the foot extending over the nosing results in rotation of the foot and a fall, or a distorted gait while trying to place more of the foot on the tread. Tread depths of at least 11 in. (280 mm) are recommended to accommodate the 95th
percentile foot, but considering only gait and accident history, treads (goings) of at least 9 in. (230 mm) are required. Riser heights of 6.3–7.2 in. (160–183 mm) had the fewest missteps. Other dimensions apply to curved stairs [16]. Other factors relevant to stair safety include lighting, slip resistance, single steps (most codes prohibit flights of fewer than three steps), handrails, and inability to detect the edge of the tread due to lack of visual contrast.
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Fire Escapes As with so many building code provisions relating to fire safety, requirements for exterior, non-combustible fire escapes began with tragedy. The mid-nineteenth century saw significant numbers of European immigrants settling in New York City, mostly in tenement buildings. The term generally refers to a substandard multifamily dwelling in the urban core, frequently old and occupied by the poor. These wood-frame, six-story buildings (six stories was considered the practical height limit before elevators) were crowded together in ethnic neighborhoods, generally home to several dozen families each crammed into one or two rooms with the only access and egress by a single, narrow stairway. Doors to family living rooms were usually wood panel doors with little fire resistance and the buildings often had commercial space on the ground floor. Fires starting in the commercial space or in a tenant space would quickly burn through the thin door and race up the stair, cutting off egress and trapping occupants who perished in full view of the street crowds attracted by the fire [17]. After a particularly gruesome fire that killed ten women and children in 1860 [18], New York City passed its first egress regulation, Chapter 470, Section 25 of the New York City Acts, entitled,—An Act to Provide Against Unsafe Buildings in the City of New York. This law applied to buildings housing more than eight families and required a ‘fire-proof’ stair attached to an exterior wall in a fire-proof building with the stair separated from all living spaces by doors. In buildings that were not fire-proof, the law required fire-proof balconies on each story of the exterior of the building connected by fireproof stairs with all rooms communicating with the balconies and separated by doors. Since fireproof construction was far too costly for tenement buildings, iron fire escapes became ubiquitous throughout the city. It is interesting to note that in 1867, the Tenement House Act was enacted that required existing buildings to be furnished with fire
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escapes; perhaps the first example of a requirement applicable to existing buildings [17]. However, subjective provisions made enforcement difficult and many buildings were exempted or were equipped with fire escapes that collapsed, were not accessible from all rooms, or exited to narrow spaces or enclosed courtyards. Tragic losses continued in buildings without or with inadequate fire escapes, leading to several amendments to the laws, including requirements in 1871 to maintain fire escapes, transfer of responsibility from the health department to the fire department in 1882 and to the building department in 1892. The 1871 legislation extended requirements for fire escapes to hotels and other public buildings including theaters, schools, factories and hospitals. By the beginning of the twentieth century a New York Tenement Commission surveyed tenement laws in 27 US cities and found that nearly all had some sort of egress regulation requiring fire escapes but often the details were left to the discretion of inspectors. Many disastrous fires with high death counts were attributed to occupants being trapped by the fire on upper floors or fires blocking the single exit. Fires that attracted national attention such as the Brooklyn Theater in 1876 (294 fatalities) and Chicago’s Iroquois Theater in 1903 (605 fatalities), Ohio’s Lake View school in 1908 (170 fatalities), and the Fifth-Avenue Hotel in St. Louis (100 fatalities) led to fire escape regulations in most major cities and to NFPA’s development of the Building Exits Code in 1927. The Triangle Shirtwaist Fire in 1911 (146 fatalities) had a fire escape that collapsed under the weight of too many workers, which contributed to the high death count [19].
Egress Strategies Egress strategies provide systems and features to allow people to safely exit structures, reach a place of safety, or safely remain in place during emergency conditions. These strategies need to be aligned with and support the overall life safety
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goals and objectives, and be developed in concert with the overall fire protection and life safety program. Strategies form the basis of design for egress and other supporting features. Effective egress strategies are appropriate to the facility size and complexity, and reflect the facility, how it is used, characteristics of its occupants, fire protection and life safety systems, security features and arrangements, and hazards within the facility. Systems are typically designed to allow occupants who are not intimate with the initial fire or emergency to escape the area of immediate hazard in order to reach a place of relative safety. The concept of protecting those “not intimate” with the incident is important. A common example of intimate with the ignition is a person involved with a fire igniting a bed, a chair or a couch while smoking [20]. Egress strategies should be based on the specific hazards expected to occur over the life of the facility. Typical egress strategies include evacuating all occupants to the exterior of the building (simultaneous full evacuation), evacuating a portion of the occupants (partial evacuation), defending occupants in place (defend or shelter in place), or relocating occupants to a safe place within the building (relocation). Partial evacuation relies on protectin-place strategies for non-evacuating occupants. The process can be phased, initially evacuating only a portion of the occupants, or all occupants can be notified to exit simultaneously. For many structures, a single response for all events is appropriate. For others, a scalable approach that escalates from partial evacuation and protect-inplace to simultaneous full building evacuation may be necessary. Regardless of the strategy, wheelchair users, occupants with mobility impairments, or others with mobility or cognitive conditions that may hinder self-directed egress need to be considered. An overview of these strategies follows [20–23].
Simultaneous Full Building Evacuation Simultaneous full-building evacuation has been the norm for most buildings up to six stories for
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many years and tends to be the most common strategy for life safety. This is usually arranged through unprotected paths of travel, with distances appropriate to the building use, to protected stairs that discharge to the public way. For tall buildings, iconic structures, large assembly buildings, or other facilities that require full-building evacuation, a performancebased engineered approach may be necessary to evaluate the impact of evacuating a large number of people simultaneously [20]. Timed egress analysis or computer-based evacuation simulation methods can help to better understand the potential impacts of specific features and strategies on evacuation times. Chapters 59 and 60 provide detail on developing timed egress analysis and computer-based evacuation simulation methods. These tasks can be completed as part of an informal qualitative process or through a formal threat and risk assessment. For tall buildings, evacuation elevators can be used to support simultaneous full-building evacuation and substantially reduce evacuation times while addressing the needs of people with disabilities. Simultaneous full-building evacuation will require considerably longer times for many occupants to make their way out of a tall building. This leads to questions on messaging strategies and how occupants will react during the evacuation, such as “Are additional features and functionality of the life safety systems necessary to provide an appropriate level of situational awareness?” Special messaging strategies with enhanced voice communication systems and additional zoning to keep occupants informed of the situation in real-time can help to address these issues. Such situational awareness features can provide specific real-time information about an event, allowing occupants to make better decisions regarding whether to stay or leave, or more informed decisions about route choice and adapting route choice to the situation [24–27]. As noted in referenced discussion on these topics, careful planning is necessary to be sure that these systems do not become too complicated, that messages are appropriate, and that increased reliability is built into systems.
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Simultaneous full building evacuation messages should be coordinated and directed by the responding local fire authorities or properly trained staff utilizing the voice communication system or the growing range of emergency communication system devices. Messages should follow established procedures defined in the emergency plan developed for the facility [11, 28–30]. When using full building evacuation strategies, attention should be given to notification messages and their effectiveness. Particular concern should be given to assumptions regarding pre-movement time, occupant characteristics, and assumptions regarding mobility and evacuation time, and building features that could restrict or impede occupant flow. Narrow doors or corridors, and other obstructions can impede flow [20]. The time required for evacuation raises concerns related to occupant and staff training. Occupants benefit from training to give people a feeling for the length of time necessary to exit the building. This would be particularly powerful if occupants understood how staff would manage the process and what process and information decision makers use during emergencies. Consideration should be given to how occupants move and disperse once leaving the structure, particularly for tall buildings or other high occupant load structures in dense urban environments. For these examples, occupants will need a clear path for a safe distance from the structure.
Protect-in-Place Protect-in-place strategies are also known as defend-in-place or shelter-in-place strategies. These strategies involve providing adequate safety features to allow occupants to remain in place during the event, and they are used in facilities with occupants that have a limited ability to be moved, either because they are incapacitated or they are immobile due to medical or physical restraint. Protect-in-place strategies also are used in highly compartmented
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structures, such as residential occupancies, where building separations provide protection and allow a portion of the population to safety use phasing strategies [20]. Designs using protect-in-place strategies use a combination of active and passive fire protection features and management procedures to provide an appropriate level of safety for occupants to remain in the initial compartment. Structures using a protect-in-place strategy are typically protected throughout with automatic sprinklers, and include fire-rated compartments to reduce smoke and fire spread. Typical examples of facilities needing protect-in-place strategies are health care facilities, and detention and correctional occupancies. In hospital surgical suites and intensive care units, it may be difficult—if not impossible—for patients to initiate and complete escape without assistance. Some patients cannot be moved without significantly jeopardizing their safety. For these situations, a protect-in-place may even be used within the compartment of origin. US building codes have required features for many years in high-rise buildings to allow protect-in-place strategies. In residential buildings, and similar occupancies, tenant and corridor separations compartmentalize floors, which can offer a level of safety that permits protect-in-place strategies. For example, in United Kingdom Approved Document B (Fire Safety), Provision 2.7 a single stair is permitted in sprinkler protected residential buildings regardless of height because general evacuation is not contemplated [31]. For some specific and isolated events, evacuation may not be the most appropriate action because the process of evacuation exposes occupants to higher risk. For example, consider a deadly 1988 fire within a New York City residential high-rise building—four occupants attempting to escape tragically died during this fire, while other occupants that remained in place were not injured [32]. A study of fires in hotel occupancies in the 1980s concluded that guests not in the room of origin may have been safer
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sheltering in their rooms because most fatalities occurred during evacuation [33]. Other examples can be drawn from terrorist actions. Terrorists can use the fire alarm system to evacuate occupants to the street, and then detonate a car bomb. DHS [34] provides specific guidance for active shooter situations, which includes sheltering-in-place. Occupants may need to ignore evacuation alarms, as the alarms can be used by the shooter to entice potential victims out of safe locations.
Relocation Relocating occupants from an area of potential hazard to a protected area of refuge or other safe place within a building can be a safe and effective strategy, and represents a variation on the protect-in-place strategy. The ICC Performance Code [35] defines a safe place as “. . . an interior or exterior area wherein protection from hazards is provided by construction or appropriate separation distance.” As with protect-in-place strategies, relocation requires attention to management procedures and may require special detection and notification systems or other appropriate life safety features. Hospitals, nursing homes, detention and correctional facilities, and institutional facilities are examples of facilities that use relocation strategies. These facilities typically use horizontal exits, smoke barriers, protected floor separations, or other appropriate means to protect relocated occupants [22]. Relocation strategies can be used in tall buildings. Here, occupants are directed to relocate to floors below the fire and away from any fire impact. With relocation strategies, the floor and shaft fire ratings and structural fire protection are critical, as the lower floors are relied upon to provide a safe area perhaps for the duration of the incident [22].
Phased or Partial Evacuation Phased and partial evacuation strategies combine evacuating or relocating a portion of the
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occupants—those in immediate danger from the incident—with allowing occupants remote from an incident to protect-in-place. In this way, phased evacuation helps to optimize the use of the available egress components. With phased evacuation, occupants remote from the fire initially remain in place, but can be evacuated later if conditions warrant evacuation of the entire building. Partial evacuation strategies require features to protect occupants remote from the incident [20]. In high-rise buildings in the US, typically the event floor and two floors above and below the event floor are evacuated [11, 36]. In theory, this allows occupants on the fire floor unobstructed use of the exit stairs, thus optimizing use of the exit components and reducing the evacuation time for the affected floor or areas. For both phased and partial strategies, occupants remote from the event floor and those in the evacuation floor zones are notified. Occupants not in the affected zone are asked to remain in place to await further instructions [20,22]. Notification of occupants outside of the affected zone is common practice in Canada. In hospitals, phasing may be necessary for larger incidents if such incidents might compromise adjacent evacuation zones. Large assembly spaces also may allow remote occupants to remain in place, while those closer to and intimate with the incident immediately evacuate. Assembly examples include large convention centers with multiple event halls. Where convention center halls are appropriately separated, it may be possible to phase the evacuation using individual halls as evacuation zones. Two fundamental assumptions are critical with this strategy: (1) the event will not impact occupants outside of the affected zone during the time necessary to evacuate the affected zone; and (2) occupants in the unaffected areas will remain in place. This concept works well for ‘traditional’ events, such as a sprinkler-controlled fire in a high-rise building, because automatic suppression systems in high-rise buildings are designed with a degree of resilience and have proven to be generally effective and reliable in controlling or
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suppressing fires. In sprinkler-controlled highrise fire events, fire-rated floor and shaft separations minimize hazards to occupants on the unaffected floors. If it is deemed that the building will need to address events other than ‘traditional’ events, additional or more reliable fire safety measures may be necessary. Changes in risk perception resulting from the September 11, 2001 attacks have impacted public acceptance of phased evacuation. Occupants may become aware of events through communication technologies, such as texting, and social media, rather than the building notification system. In the event of a disaster, occupants might ignore “standby” messages and instead decide to immediately exit the building, particularly where they are afraid that the building might collapse. This has been reported during drills in New York City high rises. Another complicating factor is that today’s emergency response procedures are being developed for a broad range of potential threats, not just fires, many of which requiring significantly different actions. To accomplish this, designers need to account for occupant response to non-‘traditional’ events, such as wide-spread power loss, severe weather events, crowd incidents or civil disturbances, terrorisms, large scale hazardous material incidents, or transportation incidents [23].
Egress Strategies for People with Disabilities Egress system designs need to accommodate the needs of people with disabilities. The Americans with Disabilities Act (ADA) mandates that expected disabilities be accommodated, and that structures allow for equal access. The 2010 edition of the ADA references the IBC (2003 Edition) for requirements related to means of egress and areas of refuge. At least one accessible means of egress is required for every accessible space and at least two accessible means of egress are required where more than one means of egress is required. The technical criteria for accessible means of egress allow the use of exit stairways and evacuation elevators
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when provided in conjunction with horizontal exits or areas of refuge. While typical elevators are not designed to be used during an emergency evacuation, evacuation elevators are designed with standby power and other features according to the elevator safety standard and can be used for the evacuation of individuals with disabilities. Codes typically require an elevator to serve an accessible floor that is four or more levels above the level of exit discharge [11, 36]. Evacuation elevators provide for occupant self-evacuation through elevators that are intended to be used during fire events [11, 36]. In buildings over 30 m in height, UK standards [37] require a fire service elevator that is also intended to provide egress assistance to people with disabilities. The IBC provides requirements for areas of refuge, which are fire-rated spaces on levels above or below the exit discharge levels where people unable to use stairs can go to register a call for assistance and wait for evacuation. Individual floors within fully sprinkler protected buildings are considered to meet the requirements for area of refuge [11,20,36]. In general, codes require audible and visible notification appliances throughout public areas of all buildings and structures. Fire alarm systems are required to have capacity to add these devices in other occupancies to address the needs of persons with hearing impairments if hired. Egress designs that serve those with disabilities need to consider the specific needs of the occupants. Emergency action plans may need to involve the disabled person to ensure that his/her needs are addressed [11,28]. People with service animals will be reluctant to leave those animals behind. Some wheelchairs are equipped with life support equipment and may weigh hundreds of pounds exclusive of the user. Plans may need to allow for these people to evacuate with the wheelchair. Stair descent devices, also known as evacuation chairs, can be provided on floors occupied by a person with a mobility limitation to help when evacuation is required. Traditional “buddy systems” that pair the disabled
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with a co-worker to provide assistance are effective; however, this needs the co-worker to be available at the time of the emergency. Guidance on the development of customized plans for occupants of offices was developed after the 1993 WTC bombing [38].
Performance-Based Strategies Prescriptive codes provide egress design guidance for a broad range of building types, occupancy, and use groups, and allow for many common arrangements. The Life Safety Code Handbook [39] and IBC Commentary [40] include helpful comments and explanations for prescriptive egress design approaches. Prescriptive approaches have been generally successful in providing safe egress from most structures. However, design flexibility is often compromised in order to create a comprehensive set of code provisions that apply to a broad range of uses and occupancies [22]. In contrast, performance-based egress approaches combine first-principles fire engineering analysis with estimates of evacuation times that assess the ability of occupants to safely exit buildings for a range of fire conditions or other events. Performance-based approaches require safety systems to be designed to meet specific life safety goals for a range of hazards and events. This can result in increased design flexibility, as it affords the opportunity to align overall building objectives with fire safety objectives. With this flexibility, however, comes an additional design burden, as analysis is needed to demonstrate that occupants can safely exit under the range of expected design scenarios. Performance-based designs are discussed later in this chapter [22].
Selecting and Evaluating Options When selecting an appropriate egress strategy, the strategy needs to match the ability, activity and responsiveness of the occupants, the technology used, and the ability and reliability of staff or occupants to assist in the process. The selection
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of an appropriate egress strategy hinges upon the emergency scenarios considered, and evacuation and emergency response planning. The communication and messaging strategies need to match the evacuation strategy. Other considerations include the number of people who will need to evacuate, whether all occupants within the facility will be exposed to hazardous conditions, and the occupants’ familiarity with the exits and egress routes. Egress strategies should be developed to guide the design of egress features, rather than be developed after the building is built [22]. For complex facilities, it is often necessary to develop an overall fire and life safety strategy to coordinate these features. Voice communication, suppression, and detection system zones need to match with the evacuation zones. Emergency lighting is necessary in exit pathways to allow safe movement during power outages. Exiting components will likely require appropriate fire ratings. In some cases, additional voice communication zones, two-way communication, message boards, or other communications systems may be necessary to provide occupants with an appropriate level of situational awareness and a general understanding of the incident. Zones require specific fire separations and structural fire ratings appropriate to the strategy. Other features also may be necessary: elevators may need to be protected and provided with special controls, stair door unlocking may be necessary, and life safety systems will likely need emergency power. All of these features need to coordinate with security systems [22]. A single solution may not be appropriate for complex facilities. These facilities may benefit from adaptive or event-based strategies. With adaptive or event-based evacuation, conditions dictate the specific actions and egress strategy. During an event, the situation is assessed and a strategy is selected based on that assessment. For example, consider a fire event on a single floor, a strategy including relocation through exit stairs and protecting in place those on unaffected floors may be appropriate. For the same building, a building power outage may require full building evacuation.
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Adaptive evacuation concepts are particularly useful for facilities that may be exposed to a range of events, this is important when those events can involve threats both inside and outside of the building. Events occurring outside the building may require a very different response than those occurring inside. The presence of an active shooter will likely need a protect-in-place lockdown where spaces can be secured against entry by the shooter. Civil unrest or a hazardous material event outside a building may require occupants to be secured within the building. Release of a biological agent within a building may require potentially contaminated occupants to be secured within the building until it can be determined that they will not contaminate others. This strategy places a large burden on the decision makers and the decision-making process. Decision makers need relevant information and the authority to make critical decisions. While flexibility can be beneficial, simplicity creates increased reliability. Substantial training is required to minimize confusion, particularly where differing responses are expected for different events. Appropriate systems and methods are needed for decision makers to quickly obtain credible information about the event and to empower decision makers with the appropriate authority to make egress decisions based on that information. Training can help, but the provision of real-time instructions is necessary to increase the
Fig. 56.2 Exit components
likelihood of obtaining the correct response from a wide range of potential responses [20].
Exit Components In the US codes, a means of egress consists of three parts; the exit access, the exit itself, and the exit discharge. The exit access is any portion of a means of egress that leads to an exit and the exit discharge is any portion of a means of egress between the termination of an exit and a public way. The exit is defined as [11], That portion of a means of egress that is separated from all other spaces of a building or structure by construction or equipment as required to provide a protected way of travel to the exit discharge.
Figure 56.2 illustrates the relationship between exit access, exit, and exit discharge. A means of egress is generally considered to be a protected path of travel to the exit discharge. On floors above grade, this is typically through an exit stair. The exit stair is required to discharge on grade to a path leading to the public way. US codes generally define the public way as a street, alley, or other space open to the air that is dedicated to public use. Exit stairs need to be arranged so that once entered, occupants are not required to leave the stair until reaching the exit discharge. There are exceptions. In some cases, an exit discharge can lead to a space of sufficient
Exit Access
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• Exterior Exit Doors • Exit Stairs • Exit Passageways • Horizontal Exits • Evacuation Elevators
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size to accommodate all of the occupants expected to use the exit and be located at a safe distance from the building. In other cases, exit stairs are allowed to discharge through an on-grade level floor where a direct and obvious path is provided [11, 36]. Egress systems require that at least two means of egress be provided from any point in a building. One exit can be provided for spaces that meet limits on common paths of travel. Additional exits are required based upon occupant load: three exits for spaces with 500 occupants, and four exits for spaces with 1000 or more occupants. Exits are also required to be located to meet travel distance limits. Stairs enclosed by a fire and smoke rated shaft are the most common exits. Horizontal exits can serve as a means provided that the horizontal exit passes through a rated wall that is continuous from exterior wall to exterior wall and continuous to grade. Occupants are deemed to be in a safe area after exiting through the horizontal exit. Requirements for exit capacity, which affect the number and width of stairs and doors, are based upon the occupant load of each floor, either estimates of the actual number of occupants including visitors, or an occupant density derived from surveys of actual buildings. The load factors specified for specific occupancies are quite consistent across many international building codes. For example, the occupant load for office occupancies is 100 ft2 (10 m2) per person in US, Australia and Spain, 90 ft2 (9 m2) per person in Hong Kong and 60 ft2 (6 m2) per person in the UK. Some of the traditional load factors are being questioned since most of the surveys on which they are based were taken more than 50 years ago. Egress stairs are required to be protected from the entry of smoke that could slow evacuation or harm occupants. Besides having a fire rated and smoke resistant shaft enclosure, egress stairs in high-rise buildings are typically pressurized to prevent smoke leakage through construction cracks and doors opened to provide access. Stair pressurization systems are discussed further later in this chapter.
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Occupant Evacuation Elevators Walking down many flights in tall buildings can be a difficult task for many occupants and may be impossible for some. Elderly, disabled, or injured occupants, occupants with other medical issues like heart conditions, or those with or mobilityimpairing injuries may have difficulty negotiating stairs or may be incapable of evacuating using stairs. Changes in technology, an aging population, the events of September 11, 2001, and the practicalities of designing for very tall buildings, have converged to make elevators a viable option, and perhaps a necessary alternative, for emergency evacuation in tall buildings. Protected evacuation elevators can provide a safe and effective alternative to walking down many flights of stairs. With appropriate design, it may be possible to allow protected elevators use for a large segment of the building population [20,22]. The use of elevators can speed evacuation within tall buildings. This has been proven in real events. For example, reports indicate that 16 % of World Trade Center Tower Two occupants escaped through the elevators before the second airplane struck the building [41]. Utilizing elevators can result in the total evacuation of any building of any height in less than one hour, without increasing the number, size, or speed of the elevators normally provided for routine use [42]. Fire service access elevators that are also used for assisting disabled or injured occupants have been required in British codes and others following the British system since the mid-1980s [37]. No building regulation has recognized elevators for occupant evacuation in fires until the 2009 editions of the US codes, although some systems (e.g., Stratosphere Tower, Petronas Towers, Taipei 101) were approved as performance-based designs [43]. One strategy is to shuttle occupants from upper levels. Another would be to attempt to restrict elevator usage to those who simply cannot take the stairs due to health or mobility
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limitations. If restricted access is planned, training of all occupants, stringent controls enforced by operators or fire wardens, and a management plan would be necessary to prioritize and discern between those that need the elevators versus those that simply choose to use the elevators. Another strategy is to allow occupants to descend stairs from the fire floor to a refuge floor, or a specially designed sky lobby, then to use the elevator from that floor or continue down the stairs [22]. In all cases, strategies need to be well-defined, well-engineered, and coordinated. Special care is necessary to help educate and train occupants in the use of such systems. Elevators must be protected, and appropriate fire and life safety features, appropriate signage and way-finding, and a well-constructed evacuation plan with training are required. Figures 56.3a and b provide two examples of tall buildings using elevators for evacuation. In Fig. 56.3a, elevators serve the fire floor. In Fig. 56.3b, elevators only serve the sky lobbies. Taller and taller buildings are be designed and constructed around the world. For these structures protected elevators are an important egress design component. Both the International Building Code [36] and the Life Safety Code [11] allow elevators to serve as one means of egress. The Life Safety Code has allowed emergency evacuation elevators to serve as the second exit within observation, control, operation, and signaling towers since its 1988 edition. These approaches potentially use all public use elevators to minimize evacuation times and to prioritize evacuation of occupants from the most threatened floors. ASME A17.1/CSA B44 Safety Code for Elevators and Escalators [44] includes specific operational protocol and design features for elevator evacuation—Occupant Evacuation Operation. Requirements include manual elevator recall switches in the elevator lobby and in the fire command, controls to initiate “Elevator Total Building Evacuation” in the fire command center, appropriate fire alarm signs, and variable message signs to indicate elevator status and estimate time duration for the next elevator [44].
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Note that in all cases, emergency evacuation elevators only operate prior to Phase I Emergency Recall Operation. This means that elevators only operate in evacuation mode until recalled to the first level by the activation of a smoke detector adjacent to the elevator opening. Phase I recall can be activated manually by the fire department to recall individual elevators while keeping others in service. Some concerns have broad societal implications—e.g., the overall public reaction to the use of elevators is unknown. Usage of elevators during emergencies is in direct contrast to the message given for years from the life safety community: in case of fire, do not use elevators. Given this message, how will occupants react and what percentage of occupants will use elevators? These questions need to be addressed on a case-by-case basis through planning and training.
Escalators Escalators are not generally credited to required egress capacity. NFPA 130, Standard on Fixed Guideway Transit Systems [45] is an exception. NFPA 130 allows non-combustible escalators to be counted for up to 50 % of required capacity from subway stations, so its acceptance in other occupancies may eventually change. Escalators are present in many buildings, are familiar to occupants through daily use, and there is no prohibition against using them for egress in fires. Thus, evacuation modeling in buildings with escalators performed as part of a performance design or a supporting egress analysis could incorporate the escalators where appropriate and acceptable to the Authority Having Jurisdiction. NFPA 130 contains specific guidance on escalators used for egress. Escalators moving in the direction of egress travel continue to move, and those moving in the opposite direction are stopped. Note that stopping a moving escalator while people are riding must be done with extreme care to avoid falls—escalators should slow to a stop [45].
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Fig. 56.3 (a) Elevators serving the fire floor (left) (b) Elevators serving sky lobbies (right) [20]
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Capacity of typical escalators is credited the same as egress stairs, defined as 1.41 persons per inch-minute (0.0555 p/mm-min). Escalator speeds have been standardized by ASME A17.1 at 100 ft per minute (33 m/min), although some faster speeds can be found in special applications, especially on very long runs [44]. The egress travel speed on a stopped escalator is defined by NFPA 130 as 48 ft per minute (14.63 m/min) in the down direction and 40 ft per minute (12.19 p/mm-min) in the up direction. NFPA 130 requires that the calculation of egress time must assume at least one escalator out of service. The main reasons that escalators are not credited as a means of egress component are their lack of a fire rated enclosure and the tread geometry does not comply with typical code requirements. Typical code compliant egress stairs are required to have a 7 in. (178 mm) rise and an 11 in. (280 mm) tread depth. Escalator steps (except at the top and bottom where they are collapsing) have a greater riser height, not more than 8.5 in. (220 mm), and a tread depth of not less than 15.75 in. (400 mm). The increased depth is not an issue since the 11 in. stair depth is a minimum. In a survey of egress stair geometry requirements in a select number of countries, Bukowski [4] found that the maximum riser height permitted for an egress stair is 7.5 in. (190 mm). Escalators do not have intermediate landings, and slopes are not more than 30 where the slope of an egress stair is 32 . In addition, the collapsing riser heights at the top and bottom can interrupt gait which slows movement and pose a potential for tripping.
Refuge Floors Refuge floors are required in high-rise buildings in Asia and the Middle East to provide an area of temporary refuge and an ability to cross over between stairways. Refuge floors are typically provided every 15–20 floors or more, depending on occupancy, and are frequently co-located on mechanical floors. The refuge space is typically
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required to be at least 50 % of the floor area and separated from mechanical equipment by fire rated partitions. Exterior walls are required to be at least 50 % open to provide for natural smoke control. Perimeter deluge sprinkler systems are required to reduce the potential for smoke or fire spread into the space. Some have expressed concerns about the practicality of refuge floors. During drills, it is reported that occupants often evacuate to the nearest refuge floor and await the call to return to their workplace. This can result in overcrowding of the refuge floor with occupants backing up into the stairs and blocking egress flow. It is unclear whether such behavior would be seen in a real emergency. Another concern is storage. Storage is not allowed in refuge areas; however, if items are stored, the area available for occupants to rest would be further reduced. Storage also introduces a fire load into the evacuation path. For these and other reasons, there is controversy over the use of refuge floors.
Pedestrian Walkways and Skybridges Elevated pedestrian walkways are increasingly popular architectural features of urban buildings that can be found in several US cities connecting downtown buildings, usually at the second floor level. Pedestrian walkways provide a means to access portions of a downtown area protected from the outdoor weather and often connect hotels to shopping and to convention centers. Skybridges connect buildings at higher levels and are less common—the Petronas Towers skybridge is a well-known example. Pedestrian walkways provide exit paths to adjacent buildings. This can be significant for tall buildings, as this provides an alternative evacuation path. Legal issues regarding responsibility for operating costs, maintenance, and liability must be addressed when Pedestrian walkways connect buildings under different ownership but these clearly can be addressed because such walkways are found in many cities.
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Features in Codes Internationally It is important to understand country specific requirements or cultural norms that may affect the design. The following provides some examples of egress features and design conventions used internationally. In addition to requirements for refuge floors discussed in previously, Chinese and Korean Codes require vestibules at the entrances to egress stairs and elevators on each floor of a high-rise building. Chinese regulations permit common vestibules but Korean codes require them to be separate and integrated with an area of refuge staging floor. Korean regulations further require that a fire service access elevator be located within 30 m (98 ft) of the building exterior. In Tokyo where buildings are crowded together and many streets are quite narrow, numerous public parks serve as protected spaces in which people who have evacuated nearby buildings can be sheltered. These parks are surrounded with trees intended to provide shielding from radiant energy from the event. The provision of parks as shelters began after the Great Kanto Earthquake (1923) where the large death toll was mostly from fires and proved its worth in the fire bombing late in WWII. US codes allow longer travel distances, even for the reduced travel distances required for non-sprinkler protected facilities. In Hong Kong and Macau, travel to an exit must be within 40 m (130 ft). In Australia, the maximum travel distance depends on the type of building, but ranges between 20 (65 ft) and 40 m (130 ft). For comparison, the US is 61–91 m (200–300 ft) depending on the occupancy served. Some countries utilize scissor stairs to meet code mandates for two egress stairs. In most cases these are required to have the entrance doors separated by at least 9 m (30 ft) and be fully fire separated. Other than in New York City where they are common, scissor stairs are generally not permitted to serve as separate exits due to the perceived difficulties in separating the enclosures and the resulting
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possibility of simultaneously contaminating both exit enclosures. In the US, two exits are required for nearly all multi-story buildings. Single exits are common for residential high-rise buildings outside the US. This allowance is typically limited to smaller floor areas so that exits can be reached within 20 m (65 ft). Design can include merging stairs in the International Building Code, such as basement stairs meeting and combining with tower stairs at the discharge level. In the Middle East, and China, Hong Kong, and other countries [46], designs follow an approach similar to NFPA 5000 and rising and descending flights of stairs need to be separated so that the stairs are separated and there are two independent exit discharges. Horizontal exits are recognized in the US and Australia as a means of egress. Horizontal exiting concepts are not incorporated within Chinese Codes, but have been used in projects following the International Building Code or Life Safety Code.
Systems and Features That Support Egress The egress strategy forms the basis for life safety and needs to be designed as part of a coordinated life safety program that integrates the fire protection and life safety features of the building. Notification, way finding, and fire and smoke protection of egress components are fundamental features that support both prescriptive and performance-based egress concepts because they support the efficient use of the egress system.
Notification Timely evacuation begins with emergency notification. Most public buildings have a notification system initiated by automatic fire detectors or the detection of water flow in the sprinkler system.
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Notification appliances in modern systems are usually voice systems since they provide the flexibility to tailor messages to a range of events. Research has shown that people are more likely to respond to voice messages because many may not understand the meaning of an audible signal or occupants may think it is a false alarm [47]. A significant improvement in voice systems can be attributed to the development of a method to make objective, quantitative measurements of the intelligibility of voice messages coupled with explicit requirements in the Notification Appliances Chapter of the National Fire Alarm Code [30]. Notification systems generally include visible appliances for the hearing impaired and may also include tactile devices. Smaller buildings are not typically required to be provided with voice communication systems. The effectiveness of messages broadcast over voice systems can vary significantly. Effective messages are more likely to result in the desired response [48]. Attributes of an effective message including being: • Short but informative • Easy to understand what is expected • Authoritative • Provides information to support effective decisions • Repeated but not repetitive In some cases, such as in health care or in detention/correctional occupancies where occupants are restrained or unable to evacuate without assistance, it is unwise to directly notify people of an emergency through public mode alerting systems because of the anxiety that results in those who cannot respond to the call to evacuate. Here, notification appliances can operate in what is called private mode. Private mode signals are presented only to specific parties who then notify and assist others. In contrast, public mode alerts the general population. Systems need to be audible and intelligible. If occupants can hear the message, it is audible. If occupants can understand the message, it is intelligible. Chapter 40 and the National Fire Alarm Code Handbook [49] describe methods for designing audible and intelligible messages.
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Where people may be sleeping, notification appliances need special attention. As required by the National Fire Alarm and Signaling Code [30], audible appliances need to produce sound pressure levels of 75 dBA or more that are at least 15 dBA above the average sound pressure level of any background noises. Visible appliances need to operate at least 177 candela at the pillow to wake occupants. This is significantly higher than the 15 candela minimum at the device for visual notification of alert people. The National Fire Alarm and Signaling Code includes new requirements for low frequency alarm signals in sleeping areas to increase the ability of the waking sleeping occupants. Tactile notification provides an alternative [30].
Wayfinding Buildings that may contain occupants who are unfamiliar with the egress system are usually required to install some features to guide wayfinding. The traditional wayfinding aid is the exit sign over exit doors and signs that direct people to these exits. Hotels usually have a floorplan map located on the back of the door in every room showing the location of the exit stairways in relation to that room. In recent years, some regulations have been changed to move signage lower in hotels so that it is not obscured by smoke. In Europe and South America, some countries install lighted chevrons in the baseboards of exit access hallways. For the visually impaired, there are “talking signs” that transmit an audio channel that can be heard on special devices carried by the disabled person and heard as the sign is approached. Another new technology is directional sound transmitted from speakers mounted over exit doors. Even without being able to see, these sounds give the impression of direction, guiding the person to the exit. Dynamic signage can direct occupants to specific locations, guiding evacuees away from hazards. One example is the use of dynamic signage within stairways to direct occupants to a specific exit or to direct evacuees to cross over
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to another stair to avoid hazards. Some have proposed the use of messages transmitted to handheld devices including smart phones to provide way finding guidance in emergencies.
Illumination and Exit Marking With a few exceptions, the means of egress including the exit discharge is required to be illuminated to at least 1 ft-candle when the building is occupied. Recently, illumination requirements have been supplemented by requirements for luminous egress path markings, including photoluminescent marking. Requirements in the Life Safety Code [11] state that, where photoluminescent markings are used, light levels sufficient to charge the material are required to be provided for at least 60 min before the building is occupied. Energy conservation systems that turn off lights when the stairs are not occupied cannot be used. Chapter 7 in Facilities Standards for the Public Buildings Service contains additional information [50].
Fire and Smoke Protection Egress stairs typically require fire-rated shaft construction and protection from the entry of smoke. Egress stairs in high-rise or tall buildings are typically pressurized to prevent smoke leakage through construction cracks and doors opened to provide access. Stair pressurization systems typically require pressures of at least 25 pa (0.1 in. of water) to prevent smoke infiltration but not more than 67 pa (0.25 in. of water) which could result in excessive door opening forces. Systems need to meet both limits at every door, and account for pressures resulting from stack effect and the fire itself. Shaft height, high indoor to outdoor temperature differences, and requirements for designing for open stairway doors add complexity to the design. Chapter 50 includes additional information on stair pressurization.
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Simple stair pressurization systems can be designed with hand calculations. Complex arrangements such as buildings with adjacent vestibules or corridors pressurized separately from the stairs, buildings with multiple shafts, buildings with shafts taller than 75 ft, or buildings with shafts that connect to spaces that are open to the outside such as parking garages, should be addressed by use of a network model that can account for the multiple flow paths involved [51]. Before pressurization systems there were stair designs called smoke-proof towers that employ stair access through a vestibule that is naturally ventilated to the outside. Smoke-proof towers now combine mechanically vented or purged vestibules with stair pressurizations systems. Smoke-proof towers were found to be reliable and effective as long as the vestibule ventilation is not blocked.
Performance-Based Evacuation Design The prescriptive egress provisions of the codes have been developed to provide robust evacuation features for a wide range of buildings types, uses and occupancies. While these provisions have worked well for many years, they cannot address all situations. The performance-based evacuation design process is an important tool to address situations that are either not appropriately addressed by prescriptive codes, or to address owner and designer needs that cannot be solved with traditional prescriptive code solutions. The SFPE Engineering Guide to PerformanceBased Fire Protection Analysis and Design in Buildings [52] defines a process to undertake performance-based design, which includes defining scope, developing goals and objectives, developing performance criteria, developing design fire scenarios, developing trial designs, evaluating trial designs and selecting final design, and preparing documentation. Chapters 37 and 57 provide information to help implement this process. Table 56.1 illustrates this process when applied to the evaluation of evacuation designs for fire
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Table 56.1 Sample performance-based evacuation design process for fire scenarios SFPE PBD process Step 1—Define project scope
Step 2—Identify goals Step 3—Define objectives
Step 4—Develop performance criteria
Step 5—Develop fire scenarios
Step 6—Develop trial designs
Step 7—Evaluate trial designs and select final design
Step 8—Prepare documentation
Potential performance-based evacuation assessment tasks Define prescriptive requirements Applicable codes Define performance–based egress features and strategy Chapter 37 Identify life safety goals Chapter 37 Define stakeholder objectives Chapter 37 Define egress design objectives Chapter 37 Determine tenability criteria Chapter 61 Chapter 63 Determine fire and smoke detection criteria Chapter 40 Determine fire sizes, locations, and simulation parameters Chapter 37 Chapter 26 Design retained prescriptive–based egress features and requirements Applicable codes Design performance–based egress features and requirements Chapter 59 Determine occupant scenarios—occupant loads, pre-movement times, and movement parameters Chapter 58 Chapter 57 SFPE Engineering Guide: Human Behavior in Fire [53] Determine fire/smoke detection and occupant notification time Chapter 40 Determine Required Safe Evacuation Time (RSET)—Simulate occupant pre-movement (or delay time) and movement time (see Chapter 60 SFPE Engineering Guide: Human Behavior in Fire [53] Determine Available Safe Evacuation Time (ASET)—Simulate smoke movement, and fire affects, and determine time to untenable conditions Chapter 50 Compare occupant movement and tenability results Chapter 37 SFPE Engineering Guide: Human Behavior in Fire [53] Review factors of safety Chapter 59 Document analysis, assumptions, results, and limitations Chapter 37 Peer review (if necessary) SFPE Guidelines for Peer Review in the Fire Protection [54] Design Process
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scenarios. The process can be applied to other non-fire emergencies as well as crowd related hazards. The following sections further discuss the process.
Design Considerations
The following list considerations related to evacuation, defend in place, and relocation designs that may be relevant for performance-based evacuation design and analysis [20]. Will occupants investigate alarm signals before deciding to leave? Will occupants be committed to or be involved in an activity that will slow their reaction to alarm signals? Will families or other groups attempt to find other group members before beginning to evacuate? Will all exits be available, or will one or more exits become unusable during specific events? Will occupants be familiar with or aware of the closest escape route? Will occupants use the available exits uniformly, or will the main exit be more congested than others? Will all occupants have similar abilities? Will some of the population need special assistance?
Define Project Scope (Step 1) The first step in the process includes gathering information about the structure and the occupants, identifying the stakeholders, and determining the level of application. The project budget and approvals process should also be determined [52]. Stakeholders should agree on the project scope, goals and objectives. The SFPE Guide [52] lists the following example stakeholders: building owner, building manager, design team, authority having jurisdiction, accreditation agencies, construction team, tenants, building operations and
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maintenance, emergency responders, and peer reviewer. Other stakeholders might include commissioning agents. The project scope also defines the level of application and clearly identifies systems or components designed using prescriptive code requirements and those designed using performance methods. The scope can include individual fire protection safety components or overall systems, partial buildings, whole buildings, and multiple buildings [52]. Project Scope Examples The following provides typical examples where the performance-based process may be employed to help realize designer, or owner vision. Performance-based assessments can include developing solutions to safely extend travel distance, extend common paths of travel, or reduce exit widths within large facilities. An integrated strategy including fire detection, smoke management, and carefully planned evacuation features can allow a safe alternative for architectural designs that differ from typical prescriptive code requirements. The process can be used to test the ability of a strategy to meet established goals and objectives, based on the expected hazards. The process can support evacuation planning and crowd management planning assessments. For example, designs may need to optimize evacuation through the use of elevators in tall and super tall buildings. In these examples, evacuation simulations may be used to facilitate comparison of specific strategies, and elevator operations during emergencies. The process can help inform crowd management planning and can help to understand crowd movement under a range of conditions. The process also can be used to optimize evacuation for large assembly spaces. Sime [55] notes a strong relationship between normal circulation routes and exit pathways used during emergencies. Exit paths that serve as normal circulation paths will more likely be used than other exits, even if the path of travel is further along the normal circulation route. The
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assessment can evaluate strategies to minimize occupant crowding and optimize occupant flow at critical evacuation components, and allow alignment of normal circulation routes with emergency exit paths.
Define Goals and Objectives (Steps 2 and 3) The next step is for the stakeholder team to agree on fire safety goals and objectives for the project. Chapter 37, the SFPE Engineering Guide to Performance-Based Fire Protection [52], Life Safety Code, NFPA Building and Safety Code, and the ICC Performance Code (ICC 2012), and Code for Fire Protection of Historic Structures [56] provide information and guidance on selecting goals and objectives. Goals and objectives can relate to limiting sources of fire ignition, preventing fire ignition and growth, limiting fire impact, limiting consequences from hazardous materials, protecting people during egress and rescue operations, managing people safely, protecting responders from unreasonable risks, providing notification for emergency responders, providing access and facilities for emergency responders, and providing notification for life safety and property protection [35, 52]. The Life Safety Code states in part that “a structure shall be designed, constructed, and maintained to protect occupants not intimate with the initial fire development for the time needed to evacuate, relocate, or defend in place.” Section 5.3 of the Life Safety Code refers to Retained Prescriptive Requirements, which are features that need to follow prescriptive methods or provide an equivalent design. Retained prescriptive requirements within the Life Safety Code include design details for: changes in elevation, guards, doors, stairs, ramps, fire escape ladders, alternating tread devices, capacity of means of egress, impediments to egress, illumination of means of egress, emergency lighting, and marking of egress [11].
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The ICC Performance Code states in part that “the construction, arrangement and number of means of egress, exits, and safe places for buildings shall be appropriate to the travel distance, number of occupants, occupant characteristics, building height, and safety systems and features.” The ICC Performance Code requires performance-based egress designs to address the following: exit identification, exit illumination and safety of means of egress, providing unobstructed egress paths, protecting occupants from untenable conditions, provisions to address human biometrics and expectation of consistence, maintenance of means of egress systems, maintenance of clear path, maintaining identification of exits, maintaining ease of use, and maintenance of illumination [35].
Develop Performance Criteria (Step 4) Performance criteria are “threshold values, bounded ranges of threshold values, or distributions of expected performance,” [52] and form the basis for assessment of the design. For fire evacuation events, performance criteria are typically described in terms of occupant tenability. Where performance-based assessments are used for evacuation for events other than fires, such as crowd movement events, performance criteria matching the specific hazards associated with those events is needed. The Life Safety Code [11] lists four methods that provide context to tenability assessments for performance-based egress approaches for fire events. Method One accounts for designs that expose occupants to heat, smoke, or other toxic or damaging products of combustion while evacuating a structure. This method requires a tenability assessment. The Fractional Effective Dose (FED) method can be used to determine if occupants can safety exit through contaminated egress paths. Chapter 63 describes the FED method in detail. Exposures to lower doses of contaminants over a long period of time may be as severe as a higher dose over a shorter exposure. The FED method accounts for low and high exposures.
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Method Two compares timed egress and smoke-movement simulation results to determine if occupants are able to evacuate before egress paths become contaminated. Method Three requires the calculated smoke layer to be maintained 6 ft or more above the floor in all egress paths throughout the required egress time. Method Four relies upon passive smoke and fire barriers, or active smoke pressurization systems to maintain pressures across barriers to keep smoke from reaching egress paths. Depending upon geometry and configurations, computer fire models may be necessary to appropriately assess smoke movement. Chapter 50 details smoke pressurization methods. Chapter 51 calculation methods for simulating smoke movement. Tenability in fires can be quantified in terms of thermal effects, visibility through smoke, smoke toxicity, or limiting impact from falling materials. Some occupants, such those that are ill, young, or elderly can be particularly vulnerable to exposure. Criteria may need to reflect these vulnerabilities. Chapter 63 provides methods for quantifying thermal effects, visibility, and smoke toxicity. Sub-lethal effects may also be important. Thermal Effects Thermal effects are evaluated based upon occupant exposures to heated gases or flame. Radiant and convective exposures are cumulative. The FED method allows the combined assessment of radiant and convective exposures. Visibility Visibility estimates the distance occupants can read exit signs or distinguish exit paths through smoke. Visibility is based upon smoke density, illumination, and distance. Smoke Toxicity Combustion products can be toxic, and can cause reduced decision-making capacity and impaired motor activity. Inhalation of toxic combustion products can lead to incapacitation or death.
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Impact Falling objects, airborne building materials, or structural collapse can cause injury or death [57]. Sub-lethal Effects Sub-lethal effects can lead to severe injury and incapacitation. For example, smoke exposure can be irritating to an occupant’s eyes and this physiological effect can reduce the ability to see over time. Another example would be an occupant who survives, but sustains permanent damage due to smoke inhalation. Kuligowski [58] details criteria on sub-lethal effects. Chapter 63 includes information on assessing sub-lethal effects. Events Other Than Fire Historically, fires have been the primary incident of concern for prescriptive building codes. Earthquakes are also considered in seismic design zones. Since the September 11, 2001 attacks on the World Trade Center, there has been more consideration of planning for appropriate response to emergencies other than fire and focus has shifted to address a wider range of events. For example, the Life Safety Code states [11]: Life safety in buildings includes more than safety from fire. Although fire safety has been the longstanding focus of NFPA 101, its widely known title, Life Safety Code, and its technical requirements respond to a wider range of concerns, including, for example, crowd safety.
The ICC Performance Code similarly addresses a wide range of events, although the approach is different. In this code, maximum damage or outcome from event scenarios is mandated. Events are categorized as mild, moderate, and severe. For example, a mild event requires: no structural damage, fully operational non-structural systems for both normal and emergency operations, minimal damage to facility or contents, minimal hazardous material released to environment, and only minor occupant injuries with low likelihood of life loss. A moderate event would allow more severe damage. Moderate events are characterized by greater damage
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requiring repair prior to reoccupation and an increased likelihood of death and injury. Severe events result in sufficient damage that re-use is unlikely and multiple deaths are likely [35].
Develop Design Scenarios (Step 5) The next step in the process is to develop design scenarios. The SFPE Guide and Robbins, Gwynne, and Kuligowski [59] detail processes for developing fire safety scenarios, which entails identifying possible fire scenarios, paring the possible scenarios into a sub-set of design scenarios, and quantifying the design scenarios. Design scenarios include the building components and characteristics, occupant scenarios, and fire scenario(s). There are a range of methods and analysis techniques that can be used to identify possible fire scenarios and rationalize these scenarios into the design scenarios. SFPE [52] describes probabilistic and deterministic approaches and outlines these methods. Robbins et al. [59] further describe this process. Chapter 72 and the SFPE Engineering Guide to Fire Risk Assessment [60] provide detail on fire risk assessment. Building Characteristics Building characteristics include building height and size, occupancy and uses, architectural features, structural fire protection, egress features, fire protection and life safety systems and features, building services, functions and processes, fire department response features, environmental factors, and expected hazards and threats, criticality, and importance [20, 52, 59]. Occupant Characteristics Occupant characteristics include occupant loads, occupant ages and cognitive and physical abilities, presence of groups, and occupant response characteristics. Chapter 57 overviews occupant scenarios. Occupant loads are determined through use classification of the spaces. Codes provide prescriptive factors for occupant loads [11,36]. In
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some cases, occupant loads can be determined through the expected actual use. Occupant loads will vary based upon the event considered. In many cases, larger occupant loads will increase risk, but this may not always be the case. Consider a convention center used for lecture seating and boat shows. While lecture seating would pose a lower fire hazard, when compared to a boat show, the expected occupant loads would be significantly higher. Other uses may include exhibits with cooking or concerts with pyrotechnics. Each scenario has varying occupant loads, varying occupant conditions, varying hazards, and ultimately varying levels of safety. For these conditions, it may not be intuitive which poses a higher risk, scenarios with higher occupant loads or scenarios with higher fire hazards. The analysis would need to review a representative range of expected scenarios to appropriately characterize the level of safety [57]. Performance-based approaches require a comprehensive understanding of expected reaction times, and occupant movement. Chapter 57 and the SFPE Guide discuss factors that influence pre-movement and movement times. Factors include whether the person is alone or with others, the occupants familiarity with the building’s exit paths, emergency procedures, distribution within the space or throughout the building, pre-event activities, occupant alertness, occupant physical and mental ability, social affiliation, role in the evacuation or the organization structure, location, commitment to activities or others, age, culture, occupant condition, and gender. Table 56.2 describes specific characteristics emphasized in the Life Safety Code [11] and ICC Performance Code [35]. People have a wide range of abilities, and response characteristics. Prescriptive building and safety codes traditionally use occupancy groups to imply the characteristics and typical behavior of occupants in a building. The life safety strategies and egress features required by prescriptive codes are based upon the number and location of occupants, and the building characteristics.
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Table 56.2 Code mandated occupant characteristics Life safety code Number of occupants Length of occupancy Response characteristics Location Staff assistance Emergency response personnel Post-construction conditions Off-site conditions Consistency of assumptions Special provisions
ICC performance code Number of occupants (LSC) Sleeping characteristics Familiarity Vulnerability Relationships
Most public buildings classified as Assembly, Business, and Mercantile occupancies by prescriptive building codes are assumed to contain people that are awake and generally capable of unassisted egress. Higher occupant densities associated with large crowds within Assembly buildings pose additional challenges and crowd manager requirements are included to address challenges associated with large crowds. Industrial and Storage occupancies are not typically open to the public and contain people that can be trained in the specific hazards present in the building. Residential occupancies contain occupants of all ages and may require awakening from sleep. Educational, Day Care and Ambulatory Health Care contain children or adults that may need assistance to respond appropriately. Health Care and Detention/Correctional buildings contain occupants that are restrained or incapable of response and may need to be protected in place. Design Fire Scenarios Fire scenarios include a sequence of events that includes the fire location, source of ignition, and growth rate. If the fire continues to grow the event might reach flashover and full development, and finally decay and extinction. SFPE [52], Chaps. 26, 37, and 38 provide detail on development of design fire scenarios. The Life Safety Code [11] mandates
use of eight (8) specific design scenarios, where applicable. Other references include the ICC Performance Code [35], NFPA 92, Standard for Smoke Control Systems [61], and Babrauskas and Grayson [62].
Develop Trial Designs (Step 6) After the design scenarios are developed, the team develops trial designs. Trial designs may need to provide features to protect against hazards other than fire. Minimally, the trial design should include the development of clear intuitive egress components and features. Depending upon the level of analysis, a comprehensive and coordinated fire engineering strategy may be necessary to address structural fire protection, fire compartments, fire detection and notification fire suppression, interior finish, smoke control, and emergency power. Fire strategies can also rely upon controlling ignition and controlling the initial spread of fire. SFPE [52] provides additional detail on comprehensive fire strategies. NFPA 550, Guide to the Fire Safety Concepts Tree [63] can assist to identify comprehensive conceptual approaches.
Evaluate Trial Designs (Step 7) The next step includes evaluating the trial design for compliance with the design objectives and performance criteria. For performance-based evacuation designs, this evaluation typically involves a review of Required Safe Evacuation Time (RSET) against Available Safe Evacuation Time (ASET). Required Safe Evacuation Time is the total time between notification of occupants that they need to move to a safe place and the time that the last occupant reaches that place. Available Safe Evacuation Time is the time between notification of the occupants and the onset of untenable conditions or other conditions that might impede egress or cause harm at any location that is occupied or will be traversed by occupants during egress. A timeline can be
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developed to compare RSET and ASET for each design scenario. SFPE [52] outlines a detailed process for evaluating trial designs. ASTM E1355 Standard Guide for Evaluating the Predictive Capability of Deterministic Fire Models [64] and “Guidelines for Substantiating a Fire Model for a Given Application,” Society of Fire Protection Engineers [31] provide guidance on selecting tools for the analysis. Lord et al. [65] also provides guidance. Analysis can follow probabilistic and deterministic approaches and outlines these methods. Refer to Chap. 37 and SFPE Engineering Guide to Fire Risk Assessment [60], for details on using fire risk assessment. Hazard Assessment Fire growth simulation and smoke movement simulation can be used to estimate exposure to smoke, heat and thermal radiation. Other non-fire emergency and crowd related hazards can also be evaluated. Refer to Chap. 62 for information related to assessing and quantifying hazards associated with fire events. Evacuation Overview Evacuation times consist of detection, notification, pre-movement, and movement times, and represents RSET. Figure 56.4 illustrates the evacuation process. Detection and Notification The time between ignition of fire and the time for occupants to become aware of the situation is the detection and notification time. Buildings with egress issues that are of particular concern typically require detection and
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notification systems. Detection can be through automatic systems, such as air sampling, smoke, heat, linear heat, projected beam, gas, radiant energy, video, multi-criteria, and multi-sensor detectors, sprinkler water flow devices, or through manual alarms. Chapter 40 and the National Fire Alarm Code Handbook [49] describe methods for calculating detection times. Analysis should include transport lag time and system and detector processing times. Systems using positive alarm sequence and alarm verification should incorporate these inherent delays. The National Fire Alarm Code specifies a maximum time of 10 s for fire alarm systems to actuate alarm notification appliances or voice communication after a detection device activates. Positive alarm sequence allows a delay of up to 180 s for staff to investigate and evaluate conditions to determine if evacuation is necessary. Alarm verification allows a 60 s delay to reconfirm alarm conditions in smoke detectors and reduce unwanted alarms [30]. Audible notification can be through horns, bells, sirens, or speakers. Where a message is necessary to initiate evacuation or other action like shelter-in-place, the message needs to be audible and intelligible. Visual notification is required to alert hearing impaired occupants. Visual notification devices (strobes) are the most common. Textual and tactile appliances are also permitted. Examples of textual devices are private mode LCD devices or public mode messages in areas on large message boards. Examples of tactile appliances are bed shaking devices to wake hearing impaired occupants [30].
Detection and Notification
Pre-Movement
Pre-Movement
Time for detection systems to actuate and initiate notification sequence
Time for occupants to decide to initiate evacuation
Time for occupants to exit or otherwise reach a place of safety
Fig. 56.4 Evacuation time
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Pre-movement Time Pre-movement times, or delay times, start when occupants are notified and end when they start to evacuate or take other appropriate action that leads to evacuation. Pre-movement times are impacted by occupant activities prior to notification, method of notification, occupant training, staff assistance, and familiarity with the buildings. For example, a sleeping occupant would need to wake-up and get dressed before exiting. A mother, father, or caregiver would likely locate and assist their children before leaving. Fahy and Proulx [66] reported actions performed by occupants after the 1993 bombing of the World Trade Center. The most frequent actions included: investigate, seek information, prepare to evacuate, alert others or report incident, assist others, seek refuge, and wait. Fahy [67] lists reasons occupants gave for not voluntarily leaving during this event: occupants “were waiting for information or instructions,” occupants felt it was “better to wait or they were told to wait,” occupants were not aware of the problem, occupants were “making sure others left,” health reasons, “too much smoke,” occupants were “waiting for better conditions,” or occupants were “waiting for the fire department” as requested. Chapter 58 details pre-movement times. Movement Time A broad range of engineering calculations are available from algebraic calculations suitable for simple egress systems to detailed models that incorporate behavior sub-models and graphically display results within the building. Regardless of the method employed, the process involves the estimation of the total evacuation time needed for all occupants to get to a safe place and the conditions to which they may be exposed during the evacuation. Models and engineering calculations are discussed in Chaps. 59 and 60; behavioral aspects of evacuation can be found in Chap. 58. Speed of movement on horizontal egress components and stairs is well documented for non-disabled occupants. Data is available to
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simulate specific disabilities in Chap. 64. Movement speeds must be reduced to account for higher people densities, occupants exposed to smoke, and queuing at doors and other pinch points. While hand calculations can be used for simple systems, computer models may be necessary to account for higher occupant loads and complex designs. Evaluate Results and Select Final Design The Required Safe Egress Time is compared with the Available Safe Egress Time to determine if sufficient time is available for occupants to escape, with appropriate safety factors. Results can also be used to determine areas of crowding, to estimate exit usage, and to input into evacuation plans and crowd management plans. When the stakeholders agree that the trial satisfies the objectives, and performance criteria, the final design is selected. To obtain a realistic yet conservative estimate of RSET, common actions and behaviors need to be explicitly included and factors of safety accounting for human variability need to be applied. The factors most often neglected in analyses are pre-movement times (or delay times) and factors of safety sufficient to account for expected variability. Limitations Analysis of results should consider the limitations inherent with the methodologies. One limitation is that methods typically estimate the optimum egress times rather than simulate a range of expected egress times. Analysis may also need to account for non-simultaneous evacuation start times, uneven use of exits, complications associated with way finding, occupant interaction with smoke, temporary flow stoppages, merging flows, and counter flows. Chapter 64 contains additional information regarding limitations. Safety Factors and Uncertainties Engineering models and analysis inherently contain limitations, simplifying assumptions, variability, and uncertainty. There may be variability in occupant reactions and behaviors. Models may be based
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upon “best fit curves” to represent a set of data. Input data may introduce uncertainties. Assumptions may either increase or decrease the evacuation time or the time to onset of hazards. For example, doubling the fire size may result in predicting more smoke, but it may also decrease the predicted detection time. Using a single walking speed or a single flow through doors may not appropriately represent the range of expected occupant movement. The interaction and influence of these results may not be intuitive. Safety factors provide one method of accounting for uncertainty and variability associated with limitations and simplifying assumptions inherent to engineering analysis. Safety factors are typically applied to the analysis results, as changes to specific parameters may have a non-linear effect on the results. For a discussion on addressing uncertainty with safety factors, see Frantzich [68]. Probabilistic approaches can be used to account for uncertainty and variability. Chapter 72 outlines risk informed analysis methods. Chapter 76 provides methods for understanding and accounting for uncertainty and variability. Section 5.5.3.8 of the Life Safety Code [11] requires consideration of a design scenario that includes independently rendering each active or passive fire protection system ineffective. Examples include discounting a single stair, or discounting a single exhaust fan. Systematically testing scenarios with less than fully effective systems provides the designers with a better understanding of the consequences of these failures, which helps to understand the robustness and appropriateness of the selected safety factor.
Prepare Documentation (Step 8) The final step is to document the analysis and design. SFPE [52] states that the following should minimally be included: project scope, designer’s capability, goals and objectives, performance criteria, design scenarios, final design, evaluation, critical assumptions, critical design features, and references.
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Design and Operational Considerations The following outlines design and operational considerations for specific buildings and transport infrastructure.
Buildings and Transport Infrastructure For some complex facilities, such as malls, healthcare facilities, detention and correctional facilities, following the prescriptive code can provide an acceptable and appropriate level of safety. Hospitals are among the most complex and highly regulated buildings due to the condition of most of the occupants. Since some or many patients must remain in their beds, most hospitals depend on horizontal exits to relocate occupants to a safe place on the same floor. For other buildings, a level of assessment beyond typical code compliance is warranted. The following suggests considerations for tall buildings, large assembly spaces, airports, rail stations, and rail and road tunnels. Life Safety Code Handbook [39], IBC Code and Commentary [40], NFPA 5000, Building and Safety Code [46], Appendix A of the ICC Performance Code for Buildings and Facilities [35], and Tubbs and Meacham [20] provide additional insight on a wide range of occupancies. Systems Coordination and Integration Simple egress strategies provide safe evacuation through simple stair and exit discharge configurations, emergency notification, and emergency lighting. Complex evacuation strategies need to integrate and coordinate with the fire protection and life safety strategy. Comprehensive fire protection and life safety strategies include structural fire protection, fire-resistive compartmentation, fire detection, emergency communication and notification, fire suppression, smoke control, emergency lighting, and emergency power. These systems can have complex interactions. Based on these complexities, egress systems may need to be assessed even when the approach
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does not directly relate to the egress systems [57]. Chapter 49 includes additional information on systems coordination and integration. Tall Buildings Tall and super tall buildings pose particular challenges with respect to egress, as exiting through conventional stairway systems in tall buildings can mean walking down hundreds of flights of stairs. A portion of the population simply may not have the ability to travel down a stair system within a tall building, even with opportunities to rest along the way. Since passing in a crowded stair can be problematic, a person descending slowly due to physical limitations, injury or fatigue may delay everyone behind them. Before the World Trade Center disaster, typical evacuation schemes for high-rise buildings included partial evacuation of only those occupants thought to be in immediate danger, by evacuating the ‘fire’ floor, along with one or two floors above and below the ‘fire’ floor. Code required stair widths have evolved to accommodate three to five floors evacuating simultaneously. If simultaneous full building evacuation from a tall building becomes necessary, it will involve a large number of people—many more than that anticipated by typical building egress designs. This inherent imbalance will result in significant delays and crowding in stairs [23]. The 2009 edition of the International Building Code introduced a requirement for buildings over 420 ft (128 m) in height to be provided with an additional stair to compensate for the high-rise fire-fighting practice of designating one of the stairs as the “attack stair” and fighting the fire from that position. The thought being that once firefighters start operations within the stair, the stair will become impassible at the level of the fire floor due to the presence of charged hose lines. These actions may contaminate the stair with smoke because the fire hoses will hold the door to the fire floor partially open. The IBC requirements further state that the required exit capacity must be met without the additional stair. Occupant additional evacuation elevators can substitute for the stair.
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Large Assembly Spaces Large assembly facilities pose a range of competing challenges: airports need to balance security and continuity of operations with safety concerns, sports facilities need to balance sight-lines with providing safe steps for aisles serving seating, arenas and stadia need to provide guardrails to help prevent falls. There are many more examples. Given the level of risk in large assembly spaces, the Life Safety Code [11] requires a Life Safety Evaluation when more than 6000 occupants are present, and when festival seating is used (e.g., when no seating is provided requiring patrons to stand or to provide their own seat). Both the International Building Code [36] and Life Safety Code (2012a) require a Life Safety Evaluation when the reduced egress widths, increased aisle lengths, and increased travel distances allowed by smoke protected assembly seating are used. Life Safety Evaluations are required to include the following [11]: • Nature of the events and the participants and attendees • Access and egress movement, including crowd density problems • Medical emergencies • Fire hazards • Permanent and temporary structural systems • Severe weather conditions • Earthquakes • Civil or other disturbances • Hazardous materials incidents within and near the facility Crowd management also can be particularly important in directing the emergency actions of large crowds in assembly spaces. Fruin [69] defines crowd management as “. . . the systematic planning for, and supervision of, the orderly movement of people. . .” and provides a comprehensive discussion of crowd management. Information includes crowd communication, crowd motivation, the nature of crowds, crowd management centers, staff training, emergency response, responsibilities of performers, responsibility of staff, ticketing, owner/management duty to warn, appropriate space for occupants, occupant
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metering, and ingress/egress pressure points [69]. The International Association of Venue Managers the NFPA Handbook for Fire Protection Engineering, NFPA 101, and Tubbs and Meacham [22] provide additional information on crowd management. Rail Stations Rail stations are unique structures built to serve large transient occupant loads. In these facilities, customers tend to arrive in groups, based upon train arrival schedules. Stations can be at grade, above grade, or below grade. Underground stations pose greater challenges. The approach described within NFPA 130, Standard for Fixed Guideway Transit and Passenger Rail Systems [45] is a hybrid between prescriptive and performance-based approaches. Specific aspects are prescribed, such as the maximum platform travel distance and maximum egress times, where other aspects are based on performance concepts, such as the occupant loads, egress widths, separations to adjoining spaces, and smoke management systems [20]. Occupant loads are based on ridership, and system surge factors are used to account for variability of arrivals to the station. Egress arrangements need to result in a maximum of four minutes to clear platforms, and a maximum of six minutes to reach a point of safety [45]. Rail and Road Tunnels Rail and road tunnels can be constructed through mountains, underwater, or under urban landscapes. Air-rights structures continue to be constructed over railways and roadways to create a tunnel. NFPA 130 and NFPA 502, Standard for Road Tunnels, Bridges, and Other Limited Access Highways address egress in rail and road tunnels. Means of egress include exits to grade at the exit portals, exit stairs discharging at grade, cross passage exit doors to adjacent tunnels, and exits to a protected exit passageway. The exiting strategy needs to be coordinated with the life safety program and specifically with the smoke management concepts [20].
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Operational Concerns Emergency Plans Emergency plans may include a wide range of events, including natural hazards such as hurricanes, tornados, tsunamis, winter storms, floods or flash floods, and earthquakes; technological events, such power outages, vehicle impacts, hazardous material releases, gas releases, and explosions; and deliberate events, such as civil disturbances, bomb threats, and acts of terrorism [70]. Depending on the facility, evacuation strategies may need to address some or all of these hazards. These considerations have led to more complex emergency plans and the need for real-time communication systems to direct occupants in the desired response. Despite this additional complexity, evacuation through protected stairways remains the primary strategy, since they provide safe, protected paths out of a structure. Emergency planning for appropriate responses to specific threats is an active area that has evolved significantly in the past decade. When planning for events other than fire, risk assessment principles can provide guidance, in identifying and quantifying events [20]. • What threats are possible given the building location and use? • How likely is each threat? • What are the potential consequences? • For each event, what strategies will limit the potential for harm to people? • What holistic strategy provides an appropriate balance of safety? In some cases, strategies need to balance the level of safety for differing events, as a strategy optimized for one event may not be appropriate for other events. This is particularly true for iconic buildings and spaces. Evacuation Drills Evacuation drills are an important means of training occupants on what they are expected to do, especially where there are different responses to different threats. The US General Services Administration (GSA) is responsible for approximately 9600 federally owned or leased properties. The GSA conducts
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two drills per year in every federal office building, with one a fire evacuation and the other an evacuation for some non-fire event. In hotels, drills are important for training staff in their duties since staff are responsible for the safety of guests and it is not feasible to train guests in the procedures of the facility. Most fire codes include a requirement for regular drills, but often owners or operators terminate the drill early for fear of liability for injuring an occupant in a drill. For example, a review of high-rise drill requirements in fire codes conducted by NIST in their investigation of the September 11, 2001 WTC attacks revealed that drills conducted in New York City terminate with occupants meeting at the door to the egress stairs on their floor. In Chicago, occupants are required to enter the stairway and travel down not more than two floors. In Los Angeles occupants are required to follow the entire evacuation plan, traveling down stairs to the street level and gathering at the assembly point. This practice of following the complete plan is particularly important to familiarize the occupants with the entire egress system including any transfer corridors, and the exit discharge including assembly for accountability.
Summary This chapter first overviewed the evolution of emergency egress provisions to provide a better understanding of current egress requirements and strategies. Next, considerations, concepts, and methods for egress strategies were outlined. Features and components that support and facilitate evacuation and protect in place methods are an essential component of building and transport infrastructure life safety strategies. In summary, egress strategies need to be appropriate to the building design, safety features, function and use, and occupant characteristics. It is important that evacuation strategies coordinate with the overall fire and life safety strategy and specifically address occupants with disabilities or mobility impairments. Occupant evacuation
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elevators can be used to help occupants evacuate from tall and very tall buildings quickly and can assist those with mobility impairments. Various methods are available to assess evacuation times and are discussed in other Chapters. Evacuation times and queuing information developed as part of a timed evacuation assessment can be used to better understand the evacuation and crowd management concerns. This information can also be used as part of a performance-based evacuation design. Other chapters provide specific methodologies, data and detail to assess strategies and implement these concepts.
References 1. NFPA. (1914). Proceedings of the 18th Annual Meeting. Quincy, MA: National Fire Protection Association 2. Bukowski, R.W. (1997). “Progress Toward a Performance-Based Codes System for the United States.” Applications of Fire Safety Engineering. Symposium for ’97 FORUM. Proceedings. Tianjin, China: Tianjin Fire Research Institute and Shanghai Yatai Fire Engineering Co., Ltd. 3. NFPA. (1913). Proceedings of the 17th Annual Meeting. Quincy, MA: National Fire Protection Association 4. Bukowski, R.W. (2009). “NIST Technical Note 1623: Emergency Egress from Buildings.” Gaithersburg, MD: National Institute of Standards and Technology 5. NBS (1935). Design and Construction of Building Exits. National Bureau of Standards Miscellaneous Publication M151. Washington. DC: National Bureau of Standards 6. NFPA (1927). Building Exits Code. NFPA 101-T. Boston, MA: National Fire Protection Association 7. Togawa, K. (1976). “Study on Fire Escapes Basing on the Observations of Multitude Current, in Building Research Institute of Japan, U.S./Japan Government Cooperative Program on Natural Resources (UJNR).” Panel on Fire Research and Safety. Human Behavior 2: 1-13 8. Pauls, J. L. (1997). “Building Evacuation and Other Fire Safety Measures: Some Research Results and their Application to Building Design and Regulation.” McLean, VA: Environmental Design Research Association 9. Fruin, J.J. (1987). Pedestrian Planning and Design. (rev. ed.). Mobile, AL: Elevator World 10. Predtechenskii, V.M., Milinskii, A.I. (1978). Planning for Foot Traffic Flow in Buildings. New Delhi: Amerind Publishing
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11. NFPA (2012). NFPA 101: Life Safety Code®. Quincy, MA: National Fire Protection Association 12. Templer, J. (1974). Stair Shape and Human Movement. Ph.D. dissertation. Colombia University 13. Templer, J., Mullet, G.M., Archea, J., Margulis, S.T. (1978). An Analysis of the Behavior of Stair Users. NBSIR 78-1554. Washington, DC: National Bureau of Standards 14. Blondel, F. (1675-1683). Cours d’Architecture Enseigne dans l’Academie Royale d’Architecture, Paris. 15. Templer, J. (1994). The Staircase, Studies of Hazards, Falls, and Safer Design. Cambridge, MA: MIT Press: 16. Bukowski, R.W., Kuligowski, E.D. (2004). “The Basis for Egress Provisions in U.S. Building Codes.” Edinburgh, UK: InterFlam 17. De Forest, R.W. and Veiller, L. (1903), The Tenement House Problem (New York: Arno Press, 1903), 230-1. 18. New York Times (1860), Calamitous Fire, February 3, 1860, Proquest Historical Newspapers, http:// proquest.umi.com 19. Hall, J. (2006) Significant Fires Involving Egress, historical data summary provided to ASME Emergency Operations task groups. 20. Tubbs, J., Meacham B.J. (2007). Egress Design Solutions: A Guide to Evacuation and Crowd Management Planning. Hoboken, NJ: John Wiley and Sons 21. Tubbs, J., Meacham, B.J. (2008) “Evacuation Design Strategies and Considerations for Tall Buildings: Suggested Best Practices.” ASHRAE Transactions. Atlanta, GA: American Society of Heating, Refrigeration and Air Conditioning Engineers 22. Tubbs, J., Meacham, B.J. (2008). “Selecting Appropriate Evacuation Strategies.” Consulting-Specifying Engineer, Reed Elsevier Inc., September Vol. 44, No. 3, p 20-28 23. Tubbs, J., Meacham, B.J. (2009) “Selecting Appropriate Evacuation Strategies for Super Tall Buildings: Current Challenges and Needs.” Proceedings of the 4th International Symposium on Human Behaviour in Fire. London: Interscience Communications Ltd 24. Bukowski, R.W. (2010). “Addressing the Needs of People using Elevators for Emergency Evacuation”, Fire Technology, Special issue containing selected papers from the NIST Pedestrian Dynamics Conference 25. Meacham, B.J. (2009). “Application of Adaptive Management Concepts to Building Evacuation and Emergency Response.” Proceedings of the 4th International Symposium on Human Behaviour in Fire. London: Interscience Communications Ltd. 26. Pauls, J., Groner, N., Gwynne, S., Kuligowski, E., Meacham, B., Proulx, G., Ripley, A., Thomas, I. (2009). “Informed Emergency Responses through Improved Situational Awareness, Discussion Panel Paper.” Proceedings of the 4th International Symposium on Human Behavior in Fire, London: Interscience Communications Ltd.
2045 27. Kuligowski, E.D., Gwynne, S.M., Butler, K.M., Hoskins, B.L., Sandler, S., (2012). NIST Technical Note 1733: Developing Emergency Communication Strategies for Buildings, Gaithersburg, MD: National Institute of Standards and Technology. 28. ICC (2012) International Fire Code. Falls Church, VA: International Code Council 29. NFPA (2010). NFPA 1600: Standard on Disaster/ Emergency Management and Business Continuity Programs. Quincy, MA: National Fire Protection Association 30. NFPA (2013). NFPA 72: National Fire Alarm and Signaling Code. Quincy. MA: National Fire Protection Association 31. SFPE Engineering Guide to Substantiating a Fire Model for a Given Application, Bethesda, MD: Society of Fire Protection Engineers. 32. Proulx, G. 2001. “High-Rise Evacuation: A Questionable Concept?,” Human Behaviour in Fire – Understanding Human Behaviour for Better Fire Safety Design, Proceedings of the 2nd International Symposium, London: Interscience Communications, Ltd., pp. 221-230. 33. MacDonald, J.N. (1985) Non-evacuation in compartmented fire resistive buildings can save lives and its makes sense, NBS SP83-1985. 34. DHS (2008) Active Shooter: How to Respond. Washington, DC: US Department of Homeland Security 35. ICC (2012b) International Code Council Performance Code. Falls Church, VA: International Code Council 36. ICC (2012a). International Building Code. Falls Church, VA: International Code Council 37. HMG (2012) Building Regulations 2012, Approved Document B (Fire Safety), England: HM Government 38. FEMA and USFA. (1993). Emergency Procedures for Employees with Disabilities in Office Occupancies. FA-154 and FA-154s, United States Fire Administration Emmitsburg, MD: 39. Cote´, R. and Harrington, G. (2012). Life Safety Code Handbook, Quincy, MA: National Fire Protection Association. 40. ICC (2012d). International Building Code and Commentary (Vol 1 and 2). Falls Church, VA: International Code Council 41. Averill, J. (2005). “Occupant Behavior, Egress, and Emergency Communications.” Federal Building and Fire Safety Investigation of the World Trade Center Disaster. Gaithersburg, MD: National Institute of Standards and Technology 42. Bukowski, R.W. and Li, F. (2010). “Use of Elevators in Fires.” Consulting Specifying Engineer, February 2010 43. Bukowski, R.W. (2010), International Applications of Elevators for Egress in Fires, Proc SFPE Engineering Technology Conference, October 2010 and ASME Workshop on Elevators in Fires. 44. ASME. (2010). ASME A17.1 / CSA B44 Safety Code for Elevators and Escalators. New York, NY: American Society of Mechanical Engineers
2046 45. NFPA (2010). NFPA 130: Standard for Fixed Guideway Transit and Passenger Rail Systems. Quincy, MA: National Fire Protection Association 46. NFPA (2012b). NFPA 5000: Building and Safety Code. Quincy, MA: National Fire Protection Association 47. Proulx, G. (2000) Strategies for Ensuring Appropriate Occupant Response to Fire Alarm Signals, NRCC Construction Technology Update No. 43. 48. Kuligowski, E.D. (2011) Elevator Messaging Strategies, Fire Protection Research Foundation Report, Quincy, MA: Fife Protection Research Foundation 49. Richardson, L., Roux, R. (2010). National Fire Alarm and Signaling Code Handbook. Quincy, MA: National Fire Protection Association 50. GSA (2010). Facilities Standards for the Public Buildings Service (P100) Washington, DC: US General Services Administration 51. Walton, G., Dols, W. (2010). NISTIR 7251. CONTAM. USER Guide and Program Documentation. Gaithersburg, MD: National Institute of Standards and Technology 52. SFPE (2007). SFPE Engineering Guide to Performance-Based Fire Protection. Bethesda, MD: Society of Fire Protection Engineers 53. SFPE (2010). SFPE Engineering Guide to Human Behavior in Fire. Bethesda, MD: Society of Fire Protection Engineers 54. SFPE (2009). SFPE Guidelines for Peer Review in the Fire Protection Design Process. Bethesda, BD: Society of Fire Protection Engineers 55. Sime, J. D. (2001). “Advancing Human Behavior Theory: Visual Access and Occupancy Research, Modeling and Applications,” 2nd International Symposium on Human Behavior in Fire. London: Interscience Communications Ltd. 56. NFPA (2010). NFPA 914: Code for Fire Protection of Historic Structures. Quincy, MA: National Fire Protection Association 57. Tubbs, J. (2004). “Pedestrian Movement and Safety,” in Performance-Based Building Design Concepts, Meacham, B.J. Ed. Falls Church, VA: International Code Council 58. Kuligowski, E. (2009). “NIST Technical Note 1644 – Compilation of Data on the Sublethal Effects of Fire Effluent.” Gaithersburg, MD: National Institute of Standards and Technology 59. Robbins, A., Gwynne, S., Kuligowski, E. “NIST Technical Note 1743: Proposed General Approach to
R.W. Bukowski and J.S. Tubbs Fire-Safety Scenarios.” Gaithersburg, MD: National Institute of Standards and Technology 60. SFPE (2006). SFPE Engineering Guide to Fire Risk Assessment. Bethesda, MD: Society of Fire Protection Engineers 61. NFPA (2012). NFPA 92: Standard for Smoke Control Systems. Quincy, MA: National Fire Protection Association 62. Babrauskas, V.; Grayson, S. (1992) Heat Release in Fires. New York, NY: Elsevier Applied Science 63. NFPA (2012). NFPA 550: Guide to the Fire Safety Concepts Tree. Quincy, MA: National Fire Protection Association 64. ASTM (2012). ASTM E1355 Standard Guide for Evaluating the Predictive Capability of Deterministic Fire Models. West Conshohocken, PA: ASTM International 65. Lord, J., Meacham, B. J., Moore, A., Fahy, R. F., Proulx, G. (2005). “NIST GCR 06-886 – Guide for Evaluating the Predictive Capabilities of Computer Egress Models.” Gaithersburg, MD: National Institute of Standards and Technology 66. Fahy, R.F., Proulx, G. (2009) "Panic and human behavior in fire" Proceedings of the 4th International Symposium on Human Behaviour in Fire. London: Interscience Communications Ltd. 67. Fahy, R.F., Proulx, G. (1995) Collective common sense: a study of human behavior during the World Trade Center evacuation. NFPA J 89(2):59–67 68. Frantzich, H. (1997). "Uncertainty and risk analysis in fire safety engineering." PhD Dissertation, LUND UNIVERSITY OF TECHNOLOGY, LUND (SWEDEN). 208: 208. 69. Fruin, J.J. (1993). “The Causes and Prevention of Crowd Disasters.” Proceedings of the International Conference on Engineering for Crowd Safety. London: Elsevier Science Publishers 70. FEMA (1993). Emergency Management Guide for Business and Industry. Washington, DC: Federal Emergency Management Agency
Richard W. Bukowski is a Senior Consultant with Rolf Jensen and Associates and has authored numerous publications on elevator egress systems and strategies. Jeffrey S. Tubbs is a Principal with Arup in Boston and is an author of the text Egress Design Solutions: A Guide to Evacuation and Crowd Management.
Selecting Scenarios for Deterministic Fire Safety Engineering Analysis: Life Safety for Occupants
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Daniel Nilsson and Rita Fahy
Introduction In many cases, the principle goal of a fire safety engineering (FSE) design is the life safety of the users of a structure. There are, however, other potential fire safety goals to consider, e.g., property protection, continuity of operations, protection of the environment and protection of cultural heritage [1]. Whatever the goal, users of the building, both building managers and occupants, will have a role in its achievement. The process of evaluating an FSE design involves the development of scenarios that will test the ability of building protection and other design features to meet the fire safety goals of the analysis. The evaluation of the design involves comparing the predicted development of fire and smoke for a selected set of design fire scenarios against the time required to move any occupants to locations of safety. Little attention has been focused in the past on the combinations of occupant characteristics and other factors that would constitute ‘design occupant scenarios’ analogous to design fire scenarios. The selection of fire scenarios for fire safety engineering (FSE) analysis is outlined in Chap. 38 of this handbook. As discussed in that chapter, there are several fundamental fire safety goals for a building, one of which is to provide life D. Nilsson (*) Lund University R. Fahy National Fire Protection Association
safety for building occupants. This chapter will refine the fire scenario selection process for the specific fire safety goal of life safety for the occupants by showing the designer how to consider egress issues through each step. The aim of this chapter is (1) to provide the designer with a systematic method of incorporating occupants in the design fire scenario selection process, and (2) to give guidance on how, in this process, to identify specific occupant characteristics that should be included in the subsequent analysis, i.e., determine the design occupant scenarios that should be analyzed with each design fire scenario.
Chapter Outline In the initial part of this chapter (section “Use of Deterministic Analysis in FSE Design”), a general description of the use of deterministic analysis in FSE design is given. This is followed by a section which highlights the importance of a clear definition of the context of a FSE analysis before the scenario selection process is initiated (section “Informing the Scenario Selection Process: Establishing the Context”). In this section, an example illustrating the complexity of scenario selection for the goal of providing life safety for building occupants is also presented. In subsequent sections, the scenario selection process is described in detail (section “Scenario Selection Process”) and an example of the selection of scenarios for a hypothetical building is presented (section “Example”). The example is
M.J. Hurley (ed.), SFPE Handbook of Fire Protection Engineering, DOI 10.1007/978-1-4939-2565-0_57, # Society of Fire Protection Engineers 2016
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an expanded version of a sub-set of the scenario selection example presented in Chap. 38 of this handbook. The scenario selection process described in this chapter is based on the procedure outlined in the document ISO/TS 16733—Selection of design fire scenarios and design fires [2]. However, the procedure is only described for the specific fire safety goal of life safety for occupants, and it focuses on the appropriate incorporation of occupants in the scenario selection process.
Use of Deterministic Analysis in FSE Design In performance-based FSE design, the designer needs to show that the proposed design delivers a sufficient level of safety. This is often done using some form of risk analysis, but these risk analyses can vary in complexity from simple qualitative reasoning to full quantitative risk analyses [3, 4]. In many cases, a deterministic analysis is chosen because it involves a manageable number of scenarios that can be handled with reasonable work effort. In deterministic analyses, the hazards are mainly described in terms of their consequences [5], which corresponds to level 2 according to the classification by Pate´-Cornell [6] of treatment of uncertainty in risk analyses. (Level 2 is defined there as ‘quasi-worst case’ or ‘plausible upper bounds.’) The deterministic analysis, sometimes also called scenario analysis, can be compared to putting the building through a severe fire test. If the proposed building design passes the test, it has also been shown that it will survive most other fires according to the deterministic analysis. Because it is imperative that the included scenarios represent the worst credible cases, it is essential that the scenario selection process is both thorough and systematic. A deterministic analysis hence involves the selection of severe but reasonable scenarios that
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challenge the proposed fire safety design of the building. The fact that the scenario should challenge the design means that it must be chosen in relation to the goal of the analysis. For example, if the goal is to provide life safety for building occupants, a small and limited trash fire close to the main exit might be highly relevant as it can block the most important means of escape. However, the same fire is probably not particularly relevant, due to its limited size, if the goal is to prevent structural collapse of the building. When the goal is to provide life safety for building occupants, the building use and users will always influence which fire scenarios are relevant. This is illustrated by the example above involving the small trash fire at the main exit. It is well-recognized that people tend to use the main exit in case of emergencies [7]. Hence, the fact that the building has a main exit (building use) and the fact that people tend to use the main exit in emergencies (behaviour of users) makes the fire scenario suitable for deterministic analysis, i.e., a credible scenario that severely challenges the fire safety design. The selection of this particular fire scenario also implies that the designer has already started to consider possible occupant scenarios. In this particular case, an occupant scenario involving building occupants initially heading towards the main exit is considered highly relevant, and it is the reason that the small trash fire is considered in the analysis. In FSE analyses, designers often spend a lot of time and effort on the fire problem, e.g., estimating design HRR curves or simulating smoke spread, but occupant aspects may not always be incorporated appropriately in the design. As illustrated by the trash fire example above, there is always an occupant scenario paired with each fire scenario. This means that the selection of fire scenarios and occupant scenarios for deterministic analysis cannot be done independently, but it is instead a process of finding combined scenarios, i.e., coupled fire and occupant scenarios, which challenge the proposed fire safety design.
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Selecting Scenarios for Deterministic Fire Safety Engineering Analysis. . .
Informing the Scenario Selection Process: Establishing the Context Before scenario selection begins, there are three elements that must be specified—the project scope, the Fire Safety Goals (FSG) and the Fire Safety Objectives (FSO)—because they dictate which scenarios are relevant for consideration in the deterministic analysis. These elements are therefore explained below, followed by a case showing that the scenario selection process is not always simple and straightforward. Because deterministic analysis involves the identification of the worst credible cases, it is of fundamental importance to know (1) what should be protected (FSG), and (2) how this can be achieved (FSO). As previously mentioned, a deterministic analysis can be compared to putting the building through a severe fire test. This test will be different depending on what aspect is evaluated.
Project Scope Every performance-based design process starts off with the definition of the project scope [8]. The scope is the project context, e.g., if it is an entirely new building or an existing building, if it involves the whole building or just specific components, etc. Proper definition of the project scope is important since it dictates the boundaries of the analysis. The scope is always project specific, and so for the purposes of this chapter, it will be assumed that it has been defined and will not be discussed further.
Fire Safety Goal (FSG) The FSG, which is defined next in the performance-based design process, is often expressed in quite general terms. It describes the focus of the analysis, i.e., what is worth protecting? Examples of goals can be to protect property, the environment and/or occupants. In this chapter, only the goal to provide life safety
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for building occupants is treated. This definition of the FSG will inform the scenario selection process.
Fire Safety Objective (FSO) Based on the FSG, the FSO is then defined. The FSO can be seen as a specification of how the goals will be achieved. Examples of objectives for life safety are that people should not be exposed to specified critical fire conditions, e.g., heat and smoke, or that queuing time should be within defined limits. In this chapter, only the objective to not expose people to critical fire conditions will be treated since this is an often-mentioned objective in rules and regulations [9, 10]. Specific critical fire conditions, i.e., performance criteria, are sometimes given in rules and regulations [9] and often involve limiting values (or doses) for temperature, radiation, toxic gases, visibility and/or smoke layer height [9, 11, 12]. In this chapter, however, critical fire conditions are not specified, but they are assumed to involve limiting values (or doses) related to the effects of fire.
Discussion of Scenario Relevance: A Case Study Before presenting the steps required for selecting design scenarios, it is important to emphasize that the analysis is an integrated process, where the designer has to consider the fire, building uses and users simultaneously. The choice of scenarios is not necessarily intuitive. It is not sufficient to merely choose the biggest fire, i.e., the fire with the fastest growth rate or the highest peak heat release rate. Such a fire will not necessarily be the fire that presents the greatest challenge when the FSG is life safety for building occupants. For example, it might instead be a smaller fire close to the main entrance, e.g., in the foyer of a hotel, that presents the greatest risk of exposing evacuating occupants to critical fire conditions, i.e., that challenges the achievement of the FSO.
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Fig. 57.1 Ground floor of the building
One example that illustrates the complexity of scenario selection is a case study involving cable fires in a university building [13]. The goal of the study was to select the fire scenario that would most severely challenge the FSG, which in this case was life safety for building occupants. The structure is an existing four-story university building with lecture rooms, computer labs, offices, a small food service area and a combined dining/ exhibition area. However, only the combined dining/exhibition area and the adjacent food service area, lecture rooms and computer labs were included in the analysis, see Figs. 57.1 and 57.2. This part of the building covers two floors, referred to as the ground floor and the upper floor. The dining/exhibition area, which has a slanted ceiling, is open from the ground floor to the balcony on the upper floor, see Fig. 57.3. As the fire under consideration involved burning cables in a vertical cable tray, the heat release
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Fig. 57.2 Upper floor of the building
rate of the fires was prescribed. Hence, the main variable for the analysis was determining the fire location. Based on an inventory of the fire load in the building, i.e., locations where a significant amount of cable would be expected, it was clear that there were only a limited number of areas where fire could be expected to occur. A pilot study of people’s movement patterns in this building revealed that Exit A is the main exit for most people going to the food service area, lecture rooms and computer labs. People using the lecture rooms on the upper floor most often use Stair 1, which is a spiral staircase in the open area of the dining/exhibition area, near Exit A. This means that the dining/exhibition area is a location that most people pass through every day and therefore also the preferred evacuation route in emergency situations. A key feature in any building is the main exit/entrance of the building, as it is well-established that people tend to move
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Fig. 57.3 View of the dining/exhibitions area of the building from the top of Stair 2
towards familiar exits in emergencies [7]. This makes a fire in the dining/exhibition, or the adjacent food service area (no fire separation), most challenging for the achievement of the FSO. Given that most occupants would move toward Exit A, it might make intuitive sense simply to place the ignition point in the foyer at the exit. In this case study, however, a number of different specific fire locations within the dining/ exhibition area and food service area were identified, and the most challenging of these was found with the help of CFD simulations. The food service area was the first fire location that was tested, see Fire Location I in Fig. 57.4. This location was chosen since it has many possible ignition sources as well as many areas with a considerable amount of cables. CFD simulations showed that smoke spread out through the opening between the food service area and the dining/ exhibition area, creating a wide plume at the balcony. Eventually, a relatively well-mixed smoke layer was created at the balcony on the upper floor. Although this smoke layer would engulf people on the balcony, the smoke would not be very dense, according to the simulations.
Fig. 57.4 Fire locations in the building (ground floor)
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The second fire location was a cable shaft underneath the balcony at the ground floor, see Fire Location II in Fig. 57.4. This location was chosen mainly because of the considerable amount of cables in the cable shaft. CFD simulations of the smoke spread showed that a relatively wide balcony plume was generated, which eventually led to a smoke layer that covered the upper part of the balcony. The conditions in the smoke layer were considerably worse than for the fire in the canteen, which makes it a more challenging scenario in relation to the FSO. The third and final fire location was close to the food service area but in the part of the dining/ exhibition area with the slanted ceiling, see Fire Location III in Fig. 57.4. This location was chosen because cables can be expected during exhibitions and a fire occurring at that time could potentially threaten large numbers of people. CFD simulations of the smoke spread revealed that, once the plume hit the slanted ceiling, the smoke travelled along the ceiling towards the balcony. At the balcony the smoke hit a structural beam, which created a swirl that made the smoke move very rapidly along the ceiling at the balcony towards Stair 1. On hitting the wall, the smoke was pushed down quickly, creating severe conditions at the top of Stair 1. The third fire location was deemed to be the most severe as it involves a conflict between smoke spread and evacuation. The conditions quickly became severe at the top of Stair 1, which is most likely the preferred evacuation route for people in the lecture rooms on the upper floor. Also, these people could be expected to still be moving through that area. Another important issue is that the fire is located in the far end of the dining/exhibition area, i.e., away from Stair 1, which means that people will move towards Stair 1 if they try to move away from the fire. Also, the rapid deterioration of the conditions at the top of Stair 1 means that people might be caught by the smoke. This conflict between evacuation and smoke spread makes the fire in the dining/exhibition area, under the slanted ceiling, the scenario that most severely challenges the FSO.
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In this case study, simulations were used to determine the most challenging fire location, and showed that the most challenging location was not the one that conventional wisdom might have led the designer to choose. Simulations are not always necessary, and the selection process can be based on simpler and more straightforward approaches, e.g., theoretical reasoning. As illustrated by the case study, it is, however, an iterative process that considers both occupant and fire aspects simultaneously. This is necessary for finding the scenarios that challenge the achievement of the FSO. In order for the selection process to be possible, the designer hence needs to know the characteristics of the building users, which depend on the building features and building use.
Scenario Selection Process After the FSG and FSO are defined, the scenario selection process begins. A key element in appropriate scenario selection for life safety of occupants is to carefully consider the expected uses of the building and the type of people who would, as a result, be the expected users of the building. Selection of fire scenarios has often not tied the process as specifically to a particular building design as is necessary for the selection of scenarios for life safety. The focus on a particular design is necessary in order to assist the designer in considering the full range of users, and the variation in the types of users, who might occupy the building and need protection.
Identification of Building Uses Specifying the building use can be simple (and almost trivial) for a single-use building. It is, however, still important to focus on the function a building is intended to fulfil, in order to fully account for the types of people who will use that building. Most buildings with engineered design will likely have multiple uses, for example, a hotel with sleeping rooms, meeting spaces,
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restaurants, pool, etc., or an arena suited for various uses such as sporting events, conventions, entertainment, etc. One illustrative example of a building with multiple uses is an arena and events centre [14]. This type of building may host a wide range of events, e.g., everything from sporting events to conferences, which in turn will influence the number and composition of occupants. It is therefore imperative for the designer to list all uses that the building is designed for. This is particularly important for structures that are inherently multi-functional, e.g., transit stations, airports, shopping malls, etc. For example, a typical transit station may contain functions such as a bus station, rail station, parking area and shops. Each of these functions or uses of the transit station might be associated with distinctly different users. The use of a building is not only linked to the abovementioned functions, but also depends on the internal building layout. This layout influences how people move in the building during normal operation, i.e., the circulation paths, and how they usually enter and exit. There might also be specific functions that are important waypoints during everyday use, e.g., a parking garage in a shopping mall or the cash desk in a store. Since everyday physical use also influences the physical use in emergency situations, e.g., the egress paths and choice of exits [7, 15], it is imperative that the designer is familiar with the expected physical use and identifies the: – circulation paths, – main exits/entrances, – important waypoints Ideally, the emergency egress design of a building should be based on the everyday physical use, but for technical reasons this might not always be possible. When possible, it makes perfect sense to use the everyday exit/entrance of a building as an emergency exit, however, legislation might require a certain maximum length of egress paths, which can result in the installation of several emergency exits between a person’s original position and the main exit/entrance. When these emergency exits are not used regularly during everyday building operations, they are likely to be overlooked or ignored during emergency
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evacuations [15, 16]. They still are an integral part of the emergency egress design, but the designer cannot assume that unfamiliar building features will always be used in an emergency. This is hence an example of why it is essential for the designer to always identify the expected physical use of the building.
Identification of Users and Their Characteristics The uses of the building should provide a strong indication of the expected users. Once the uses of the building have been specified, the next step is to consider the types and numbers of people who will make use of the building in those ways.
Inventory of Characteristics For the purpose of this chapter it is appropriate to divide occupant characteristics into the following categories: – permanent/transitory, – trained/untrained, – potential age ranges, – cognitive, sensory or mobility issues, – potential vulnerabilities, – awake/asleep/unconscious/intoxicated, – social groupings or not, – role The number of people in any category for any characteristic will vary over time. As part of the scenario selection process, the designer must be aware of the distributions of occupant characteristics that may be present. For example, a hospital would have permanent staff and transitory patients (in some expected proportion); the staff should be trained, the patients would not be; the staff would be working age, the patients’ ages would depend on the hospital’s specialities; the staff would have an expected distribution of physical disabilities, the patient vulnerabilities would depend on the hospital’s speciality; the variability in the composition of the occupant groups would be limited to what would be expected for the hospital’s speciality, i.e., the patients would all be sick or injured to some degree.
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Similarly, a hotel would have a permanent staff and transitory guests (in some expected proportion); the staff should be trained, the guests would not be; the staff would be working age, the guests could be any age but generally mostly adults; the staff would have an expected distribution of physical disabilities, the guests could have any disabilities and the proportion of guests with disabilities could range from low to high; the hotel guests would be using sleeping rooms as well as function rooms/public spaces and would vary widely—function rooms full of children, drinkers, meetings of people with disabilities need to be considered; sleeping rooms could be filled with guests with special needs attending conferences, possibly. Shopping centres and offices would have permanent staff and transitory customers and visitors who might have some familiarity with the space (in some expected proportion). The permanent staff may or may not be trained, but the customers and visitors would not. Again, there would be variation in the distribution of occupants with disabilities and of different age groups. All occupants would be awake. The potential for occupants to be intoxicated would have to be considered.
Why These Characteristics Are Issues Each of the characteristics listed above are important because of the impact they can have on evacuation. These impacts can affect awareness of cues, including alarms, delay times after notification but before movement to exits, travel speeds and vulnerability to toxic exposures, etc. These effects can vary over time and the designer must take this variance into consideration in the scenario selection. A brief description of the eight characteristics is given below: – permanent/transitory—Permanent staff or residents can be expected to be more familiar with a building and its systems than people who are in a building only once or occasionally. This can affect each occupant’s ability to recognize alarm signals, identify alternate escape routes, or have any familiarity with a building’s emergency management plan. Per-
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–
–
–
–
–
manent occupants who are familiar with a building may provide guidance to transitory occupants, either proactively or simply by example, but if they are vastly outnumbered by transitory occupants, that effect may be muted. trained/untrained—Trained occupants should be familiar with a building’s emergency management plan, its alarm signals, procedures and emergency exits. Designers dealing with a building with many untrained people cannot assume that their reactions and actions will be optimal. potential age ranges—Mobility, sensory and cognitive ability vary with age. Children and those with age-related cognitive issues cannot be assumed to make independent decisions that will lead to self-rescue. Young children will need assistance in evacuating a building, and they and older adults may move more slowly than others. The ages of people present in the building can vary with the current use of a building. For example, an assembly property can be used by an audience of adults or an audience of children or families, with very different ranges of cognitive abilities. cognitive, sensory or mobility issues—Some of the building users may have disabilities not related to age that would affect their ability to perceive or recognize fire cues and/or react to an emergency. These occupants can be either permanent or transitory users of the building. potential vulnerabilities—The effect of toxic products can vary according to the vulnerability of those exposed, so the designer must recognize that there will be some range of vulnerability among the building users, i.e., one cannot assume that all building occupants will be healthy adults who will be able to tolerate the same level of smoke or other products of combustion. awake/asleep/unconscious/intoxicated—People who are asleep are likely slow to respond to fire cues [17]. If people sleep through much of a fire incident, the evacuation conditions can be very challenging when they wake up and decide to escape. The fact that people
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can be intoxicated might make the problem even worse since studies have shown that even small amounts of alcohol influence the probability of people waking up from a fire alarm [18]. Alcohol has also been shown to impair decision making abilities and increase reaction time [19]. – social groupings or not—family groups will assemble before evacuating and will likely move together, at the speed of the slowest member, so the presence of family groups can have an impact on evacuation [7]. This may be true of other groups as well, e.g., friends, colleagues, etc. Social influence has an impact on decision making, so the presence of groups, or of a high proportion of occupants present on their own, can affect how rapidly cues are acted upon [20]. – role—It has been observed in real fires that occupants may continue to function in certain roles, particularly those they fill during the normal use of the building; for example, servers in a restaurant assisting the guests at their tables, and the guests looking to the servers for guidance [21]. Similarly, students may look to teachers for guidance, employees may look to managers or supervisors, etc. The types of people using a building, i.e., the proportion of people in those listed categories, may vary over time. For example, the guests registered in a hotel could be family groups one week and convention attendees another week. Depending on the appeal of special events, the proportion of the occupant population with certain issues or vulnerabilities can vary widely. In places such as specialized hospitals, where the characteristics of the occupants will tend to be the same over time, the number of occupants and the presence of staff might vary.
Determination of Life Safety Challenges Because the aim of the deterministic analysis is to test the fire safety design using a selection of severe but credible scenarios, it is imperative to identify any issues or conflicts that, in
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combination with fire, could potentially lead to the failure of the design. These issues and conflicts are referred to here as life safety challenges. Such issues are often occupant characteristics that lead to non-optimal response or movement in emergency situations. Conflicts often involve a mismatch between building uses and users or between users and building layout. An example of an issue that can result in a life safety challenge is intoxication. It has been shown in previous studies that alcohol has an effect on a person’s ability to waken and respond to an alarm [18]. Intoxication can therefore pose an important life safety challenge in a hotel where guests can be expected to be asleep. Similarly, a designer will have to consider the effect of large numbers of intoxicated occupants who might be using any place of assembly, either free-standing, e.g., a concert venue, arena or nightclub, or part of a larger complex, e.g., a hotel ballroom. One example of a life safety challenge involving the conflict between the building layout and building users may occur if people with movement impairments are forced to evacuate via the stairs. If the elevators cannot be used for evacuation, wheelchair users might not be able to leave their floor in case of a fire. Although, it is possible to wait in protected evacuation stairs, this is not an optimal situation for wheelchair users. Similar problems also apply to people who do not use wheelchairs but have other types of movement disabilities. A typical life safety challenge involving a conflict between building uses and users is people’s tendency to use familiar exits [7]. This tendency means that people will try to move towards the main entrance/exit, which is a potential major evacuation bottleneck in case of fire. A fire that quickly renders the main entrance unusable is therefore a scenario that severely challenges the fire safety design. The case study in section “Discussion of Scenario Relevance: A Case Study” showed that uncovering the life safety challenge of a design is an iterative process that requires consideration of the building layout, fire, building use and users. In that case, the placement of the fire resulted in a choice of exits that itself resulted in a dangerous bottleneck.
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Steps in Selecting Scenarios
Table 57.1 Steps in the scenario selection process according to ISO TS 16733
Once the building uses and users, as well as the relevant life safety challenges, have been identified, the scenario selection process described in Chap. 38 of this handbook can be initiated. This selection is based on the 10-step procedure described in the document ISO/TS 16733. The 10 steps are listed in Table 57.1. For deterministic analyses, the first five steps involve identification of the fire-related factors/ aspects that most severely threatens the achievement of the FSO. The identification of these factors/aspects is always done in relation to the life safety challenges. In steps 6 to 10, the factors/aspects are combined into fire scenarios from which design fire scenarios are then selected.
SCENARIO SELECTION PROCESS in ISO TS 16733 A process for selecting design fire scenarios and design fires involves 10 steps: Step 1—Location of fire Identify the location of the fire Step 2—Type of fire Specify the type of fire, e.g., initial intensity, rate of growth, items involved, etc. Step 3—Potential fire hazards Consider potential fire hazards associated with the use of the property or design Step 4—Systems and features impacting on fire Identify fire safety systems and features that can impact fire growth and smoke spread Step 5—People response Occupant response following ignition, i.e., responses impacting on fire Step 6—Event tree Construct an event tree that represents the sequence from ignition to outcome Step 7—Consideration of probability Consider the probability of each event in the event tree Step 8—Consideration of consequence Estimate the consequence of each scenario Step 9—Risk ranking Rank the scenarios in order of risk Step 10—Final selection and documentation Final selection of design scenarios and documentation of the reasons for selection Steps 6 to 10 all belong to the Scenario Selection Process, i.e., the process in which a set of design scenarios are chosen from the range of identified scenarios
Location of Fire (Step 1) In keeping with the FSG of life safety for occupants, fire locations most likely to threaten people will be the focus at this step. Locations are chosen in relation to identified life safety challenges. This could be due to the fire’s proximity to occupied spaces, escape routes or its potential for spread of fire or toxic products into occupied spaces or escape routes and stairs. The designer has to be sensitive to potential life safety challenges—bottlenecks in the design, critical route junctions where exit paths converge, and access to the main entrance/exit (favoured route), for example. Occupant characteristics can also impact the selection of ignition location. For example, if intoxication is an expected life safety challenge for the building, then consideration must be given to the ways that intoxication can impact an individual’s ability to handle complicated way-finding tasks. Ignition locations that would require occupants to make decisions about a travel path could be a challenge for those cognitively impaired by intoxication. Fuel packages near sensitive locations might not be involved in ignition but are vulnerable to spread. Fires in remote locations can spread smoke into escape routes. The case study in
section “Discussion of Scenario Relevance: A Case Study” illustrated the situation where a fire remote from the main entrance would produce smoke in the locations where occupants would move in their efforts to reach the main entrance. Fires that will not develop, spread into, or damage areas where occupants are located (originally or during evacuation) can be ignored for this fire safety objective.
Type of Fire (Step 2) The issues critical to occupant movement and survivability must be considered in this step. The primary issues are visibility (due to either
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smoke obscuration or irritants), heat and toxicity. Long-term effects of toxic exposure must also be considered, especially for vulnerable populations. Visibility will be reduced by fires that generate a lot of soot, due to inefficient combustion or involvement of materials that generate soot. Lack of visibility will slow occupant movement, resulting in longer evacuation times. Exit signs will be obscured, complicating way-finding for occupants, even for those familiar with the building. Irritants, e.g., hydrogen chloride, formaldehyde, acrolein, isocyanates, etc., can be a factor as a result of pain and discomfort, e.g., people cannot keep their eyes open, and may also be lethal. Toxic levels of irritants and asphyxiants can threaten occupants in under-ventilated fires or fires involving items such as PVC furniture. Plastics and cables, when burning, can generate compounds that are lethal in small quantities. More details on toxicity can be found in Chap. 63 of this handbook. Slow-growing fires may create more irritants, with potential for long-term consequences in vulnerable people; fast-growing fires can expose people to heat sooner and result in entrapment. In considering the type of fire, the designer should evaluate the potential fire growth and toxicity of the involved materials. For example, for a fire involving a sofa composed of polyurethane foam and some wood, the focus should be on the foam, which will have a higher rate of burning than the wood and a smoke potential that is a factor of 5 or more higher [22] On the other hand, if a small piece of furniture is located close to a large quantity of wood, the greater threat may be presented by the wood.
Potential Fire Hazards (Step 3) ISO/TS 16733 lists several hazards that should be considered in this step, including earthquakes and terrorist events that can result in multiple fires or disable multiple safety systems simultaneously; non-fire events that can impair structural stability; and the presence of high-hazard materials and operations that can initiate fires or complicate their suppression. Some events might
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also eliminate the power supply, thus knocking out the building’s notification, lighting and communications systems. Potential fire hazards should be considered in this step as they relate to occupant safety or evacuation. For example, an earthquake or terrorist attack could completely change the evacuation from what is expected. That is, the physical environment is changed and things not included in an ordinary evacuation would have to be considered, such as debris in travel paths, routes eliminated due to broken stairwells, etc. This type of change of physical environment was observed in the explosion test of the METRO project. In this test, a small explosive device not only destroyed the interior of the primary railway car, but also jammed the doors of the adjacent cars [23]. In some areas, a combination of earthquake and fire should be considered. This can be particularly dangerous as an earthquake might damage existing fire safety features or systems. This was the case in the Kobe earthquake where the sprinkler systems in some buildings were damaged by the earthquake [24]. The motion of a building in an earthquake can also distort doorframes and damage locks, affecting the passive resistance of doors and impeding evacuation [25]. This specific potential fire hazard will, however, not be relevant for all parts of the world.
Systems and Features Impacting on Fire (Step 4) In this step, the designer must consider how the presence and functioning of passive and active protection systems in the building might affect evacuation and life safety. This should also include how the expected occupants might use or misuse the fire safety systems and features of a design, and how that might impact fire development and smoke spread from an evacuation point of view. Among the passive systems and features that must be considered are doors, windows, structural elements, contents and furnishings and size of compartment. For example, the composition of the occupant population might influence the likelihood that a door will be closed or left open.
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If a door is open, fire and smoke can spread into occupied areas and evacuation routes. If a door is closed, the scenario might not be relevant for life safety, as the closed door might afford some protection to occupants on the other side of the door. If occupants will have to move through a closed door, there could be difficulties presented by the latching mechanism or door handle, or by the opening force required by the door. Active systems include smoke control and suppression systems; detection, warning and communication systems; fire safety management; and firefighting operations. There are various issues to consider as to how life safety can be impacted by the presence and functioning of active systems. With smoke control systems, for example, occupants in high-rise buildings might regularly prop open the doors into pressurized stairwells. This might influence the functioning of the pressurization in a fire, hence allowing smoke to enter occupied spaces, i.e., the stairwell. A fire management plan or building maintenance program could minimize the likelihood of such a practice. Without an operating sprinkler system, the smoke layers may be more stratified, with better visibility below the smoke layer. A sprinkler system will be expected to prevent a small fire from becoming an uncontrolled fire, but the increased mixing may result in reduced visibility in travel paths. The designer will have to factor in the effect that that will have on the evacuation or smoke exposure to vulnerable occupants. Other systems that might influence the consequences of a specific fire scenario, such as notification and egress systems, are important to consider even if they do not directly affect fire or the smoke spread. Notification systems can alert and guide occupants in their evacuation. Determining the effectiveness of the system will have to take into consideration the abilities and disabilities of the expected occupant population. For example, how will people with different sensory impairments, e.g., hearing or vision, be alerted? Egress systems, such as emergency elevators, will impact the evacuation, as will a fire safety
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management plan that will establish the likelihood of trained staff present, quality of any training provided, and overall planning and preparation for emergencies.
People Response (Step 5) For any fire safety objective, the designer has to consider how the expected occupants might impact the development and spread of the fire. Under Step 4, the use or misuse of the fire safety systems and features of a design were discussed. In Step 5, consideration is given to the presence of trained occupants, who might begin warning or suppression activities. Occupants might change the conditions in ways that affect the evacuation or exposure to fire and smoke, in positive or negative ways, such as opening a manual smoke hatch (if trained to do this correctly), or inadvertently opening too many doors in a pressurized stairwell, for example. Opening too many doors might influence the functioning of the pressurization system. The mobility of the expected population will affect the likelihood of many doors being open for a long time. A fire management plan, e.g., a phased evacuation, and training could minimize the likelihood of this happening. Scenario Selection Process (Step 6 to 10) At this point in the process, the designer has compiled a large number of potential fire scenarios that have factored in issues related to occupant characteristics. The next series of steps (Steps 6 to 10) present a quantitative approach for the selection of design fire scenarios using an event tree. Alternatively, a more qualitative approach for selecting design fire scenarios can be followed, e.g., using a risk matrix. In either case, at this point, the designer needs to consider the specific descriptions of expected occupants that will complement the design fire scenarios. For example, in order to develop an event tree, the likelihood of occupants attempting fire fighting or interfering in the operation of safety systems will depend on the composition and location of the occupant population. In Step 6, an event tree is constructed describing the possible chronological sequences of
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Fig. 57.5 An example of a part of an event tree that combines the aspects/factors identified in Steps 1 to 5 in a chronological order
events from the start of the fire to the final outcome for life safety. This event tree should combine the different factors/aspects identified in Steps 1 to 5, see example in Fig. 57.5. It is not necessary to combine all aspects/factors with each other as some combinations might not even be possible or might not be relevant for life safety. For example, the combination of a fire location with a specific fire safety system may be omitted simply because there is no such system in that part of the building. In Step 7, the probability of occurrence of each event in the event tree is estimated. These estimates can be based on available statistics or, if no such statistics exist, on engineering judgement. In this step, it is important to consider how the occupant population might influence the
probabilities associated with different events. For example, as mentioned in section “Systems and Features Impacting on Fire (Step 4)”, the mobility of the expected population might affect the likelihood of failure of any stairwell pressurisation systems. Finally, the probabilities of events are combined to provide the probability of each branch of the event tree, i.e., the probability for each scenario. In Step 8, the consequences for life safety of each scenario are quantified. If possible, these estimates can be based on available statistics, but in many cases engineering judgement must instead be applied. This step usually involves rough estimates of the consequences in terms of the number of people exposed to critical conditions for each scenario. During this
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documentation of the design fire scenarios, as well as documentation of the non-selected scenarios including possible reasons for these not being chosen. The scenario selection process and the methods/tools that can be applied are not described in great detail in this chapter. The reader is instead referred to the discussion on selection of fire scenarios in Chap. 38 of this handbook. It is, however, important to point out that the selection process for the type of deterministic analysis described in this chapter will focus on finding worst credible cases, i.e., design scenarios that challenge the achievement of the FSO.
Deriving Design Occupant Scenarios Fig. 57.6 An example of a risk matrix with scenarios (X) and a possible region with worst credible cases
estimation process, it is particularly important to recall the thought process behind the identification of aspects/factors in Steps 1 to 5. For example, a particular system might have been identified in Step 4 due to the potential high impact on life safety if it fails. Therefore, the consequence of scenarios involving failing of that system should most likely be high. In Step 9, the probabilities and consequences of each scenario are combined into a measure of risk. According to ISO/TS 16733, the relative risk can be estimated by multiplying the probability with the consequence for each scenario. An alternative way to illustrate the risk is to insert the different scenarios in a risk matrix, see Fig. 57.6. Because the axes of the risk matrix are expressed in terms of probability and consequence, the matrix offers a more refined view of the risk associated with each scenario. It is also a useful tool for the deterministic analysis because it can be used to identify worst credible cases, e.g., scenarios with moderate or higher probability and high consequence, see Fig. 57.6. Finally, the highest ranked scenarios in Step 9 are selected for the deterministic analysis in Step 10. These scenarios constitute the design fire scenarios. Step 10 also includes
The identification of fire-related factors/aspects that threaten the achievement of the FSO (Steps 1 to 5) and the selection of design fire scenarios (Steps 6 to 10) are linked to the fire safety challenges. Hence, each design fire scenario is linked to occupant-related issues or conflicts that, in combination with fire, could potentially lead to the failure of the design. In fact, every single design fire scenario in the deterministic analysis should have been chosen because of an expected evacuation problem or concern. For example, a fast growing fire in the main entrance of a department store in combination with a failing sprinkler system, i.e., the design fire scenario, might have been chosen because there is a conflict between building uses and users (people’s tendency to use familiar exits), i.e., a specific life safety challenge. A severe fire in the main entrance of the department store would result in many people potentially being exposed to critical fire conditions. Determination of design occupant scenarios is the process of re-examining the basis for the identification of fire-related factors/aspects (Steps 1 to 5) and selection of design fire scenarios (Steps 6 to 10). For the example above involving a severe fire at the main entrance of a department store, the design occupant scenario might involve a large number of untrained
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occupants moving towards the everyday exit. Evacuees can be expected to be mainly shoppers, which for a specific combination of time and day might include a significant proportion of elderly, family groups and people with disabilities. Fire experience data can be used to determine the time of day the selected type of fire would most likely occur, and demographic data could help determine the appropriate mix of occupants at that time. In combination, these occupant-related factors/aspects make up the design occupant scenario for the design fire scenario involving the fire at the main entrance of the department store. Together, the design fire and occupant scenarios represent a severe but still credible case, which is the essence of the deterministic analysis. The design occupant scenario is merely a qualitative description of the relevant occupant factors/aspects to be included in the deterministic analysis. Hence, the scenarios need to be expressed in quantitative terms in order to enable fire safety analysis. This involves the quantification of occupant- and evacuation-related variables for each of the chosen design occupant scenarios. These variables must include, but are not limited to: – number of occupants and their location, – exact combination of occupant characteristics, – initial response of occupants, and – initial route choice of occupants. These variables are combined to form a qualitative description of the design occupant scenario related to each design fire scenario. The quantification of variables has to produce severe but reasonable conditions. However, much of the work related to the combination has already been considered during the identification of life safety challenges. For data and research that will assist in quantifying the occupant-related variables, the reader is referred to in Chap. 64.
Evacuation Variables for Sensitivity Analysis Because the deterministic analysis involves a selection of a small subset of all the endless
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number of possible scenarios, i.e., the worst credible cases, it is important to investigate the effect of reasonable changes of different variables on the end result. If a small change of one variable, e.g., the proportion of people in wheelchairs, leads to the FSO not being achieved, the designer should question the level of safety. A sensitivity analysis, i.e., the process of changing different variables one at a time within reasonable limits [26], is one way to test the robustness of the fire safety design. A sensitivity analysis should involve both fireand occupant-related variables. The selection of occupant-related variables for the sensitivity analysis can be based on the occupant- and evacuation-related variables (see section “Deriving Design Occupant Scenarios”). In relation to the combination of occupant characteristics (second bullet in section “Deriving Design Occupant Scenarios”), the previously listed characteristics can be used as a starting point (see section “Inventory of Characteristics”).
Example In the following section, an example that illustrates the incorporation of human behaviour aspects in the scenario selection process is presented. The example is a subset of the example given in the chapter about fire scenarios in Chap. 38 of this handbook, but an expanded explanation of the motives behind the scenario selection is given in this presentation. The designs used in this example are for a new building complex. This means that the plans are not final and could potentially change depending on the outcome of the analysis. In this example, however, the design is only analysed once, i.e., no modifications are considered. Ideally, the design process should be iterative in order to achieve an acceptable building design at the end of the analysis. However, in this simple example the building design is treated as if it were final.
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Fig. 57.7 A schematic drawing of the building complex
Description of the Building The example is a building complex with multiple occupancies, see Fig. 57.7. The four floors underground constitute a parking garage. There is also a shopping area on the first four floors of the building, which are connected through an atrium. At one end of the building there is a 20-story hotel tower. The building is sprinklered and there is a fire alarm system. In case of emergency, people are notified by means of a voice alarm. Also, the atrium is equipped with a smoke exhaust system. This analysis does not include the entire building complex, but instead focuses on the 20-story hotel tower. The ground floor of the hotel includes a lobby, restaurant, kitchen, three elevators and two independent evacuation stairs, see Fig. 57.8. The ground floor has an open layout, which means that there are no partitions between the lobby and the restaurant. All floors above the ground floor have a similar layout and include hotel rooms, storage rooms, three elevators and two independent evacuation stairs, see Fig. 57.9. One hotel room per floor is designed to be accessible. All accessible rooms are located close to the elevators.
Fig. 57.8 The layout of the ground floor
Fig. 57.9 The layout of the 2nd to 20th floor
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Fire Safety Goal and Fire Safety Objectives
Identification of Users and Their Characteristics
The only FSG used in this example is the goal to provide life safety for building occupants. This goal is assumed to be reached by achieving the FSO to not expose people to critical fire conditions. The critical conditions are not specified in this example, but include limiting values for species (CO2, CO, O2, HCN, etc), temperature, visibility and radiation.
The uses of the building are each associated with a number of different users. The main users in the example are the hotel guests. Most guests are likely unfamiliar with the building as it is only temporary accommodation (transitory and untrained). However, other characteristics of the guests may vary widely. It can be expected that the hotel is used by people on, for example, business trips, romantic getaway weekends and family holidays, which implies that the users can be single persons, couples and families (social groupings). Both adults and children can be expected (age range). It is also expected that people with disabilities will use the hotel, and the types of disabilities can include everything from a hearing impairment to a movement disability (vulnerabilities). More specifically, it can be expected that some guests use wheelchairs as the hotel offers accessible rooms (vulnerabilities). Another user characteristic that might be relevant for the scenario selection is the level of intoxication (unconscious/intoxicated). Finally, guests might be awake or asleep (awake/asleep). The restaurant guests constitute another important group of users in the example. Many of the restaurant guests might also be hotel guests, but others might be people who are just visiting the 20-story hotel tower for a meal (transitory). Guests might visit the restaurant in a variety of different combinations, such as families, groups of friends, couples and single individuals (social groupings). As the restaurant is not a place that most guests visit frequently, they are expected to be relatively unfamiliar with the environment (untrained). Also, a restaurant is a setting in which people’s roles and associated rules can be very important, i.e., guest versus server (role). This relationship is associated with rules that dictate people’s behaviour, and it is, for example, likely that the guests will display more passive behaviour compared to that of servers [27]. Also, since guests have often invested in the situation, e.g., waited for a long time for their food, they might be unwilling to
Identification of Building Uses This building has several uses. It is mainly used as a hotel, i.e., a temporary place of accommodation. As can be seen in Fig. 57.9, there are both regular rooms and accessible rooms on each hotel floor. On the ground floor of the building there is also a restaurant. All types of meals might be served in the restaurant, e.g., breakfast, lunch and dinner, but it might also host other types of events, e.g., private parties or receptions. However, the restaurant is not intended to be used as a nightclub or bar. Finally, the hotel is also the workplace of the hotel/restaurant staff. For example, people will be working in the restaurant, kitchen, hotel lobby, hotel floors, etc. The most important aspects of physical use of the building are linked to the main exit/entrance and important waypoints. For the 20-story hotel tower, the main exit/entrance of the complex is the entrance door near the hotel lobby. It is expected that this is the main way in and out from the building during everyday use. Two major waypoints for the hotel guests are (1) the hotel lobby, where people can get information or assistance, and (2) the elevator lobby (or elevators), which people usually pass on their way to or from their room. For restaurant guests, one major waypoint is the entrance to the restaurant where the coatroom is also located. As the movement patterns are relatively simple for the 20-story hotel tower, e.g., occupants moving to and from their hotel room or to and from the restaurant, there are no complicated circulation paths.
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Table 57.2 Occupant characteristics Characteristic Familiarity Training Ages Disabilities Vulnerabilities Level of intoxication Awake Social groupings Role
Hotel guests Transitory None Adults and children Wide range possible Possible Intoxication possible Awake or asleep Individuals, couples, families Guest (expects assistance)
Restaurant patrons Transitory None Adults; children possible Wide range possible Possible Intoxication possible Awake Individuals, couples, families, groups Guest (expects assistance)
evacuate [28]. Level of intoxication is also a very important characteristic to consider as guests might be consuming alcoholic beverages (intoxicated). Finally, the restaurant is presumably accessible and different types of disabilities are therefore always relevant (vulnerabilities). Hotel staff are typically familiar with the building since they spend a lot of their time there (permanent and trained). The staff represent a range of different occupations, and some examples include server, cook, hotel receptionist, hotel manager, housekeeper and security guard. These different occupations are associated with different roles and associated rules, which will govern how they behave in fire emergencies (role). For example, the role of manager versus the role of receptionist may significantly impact how willing the receptionist is to activate a fire alarm without confirmation or permission from his/her boss. As mentioned previously, the different roles of guests and staff may make staff more responsive and staff may also take on more of the responsibility in emergencies. These varying characteristics are shown in Table 57.2.
Determination of Life Safety Challenges One potential life safety challenge is that guests might be asleep in their hotel rooms, which can lead to slow response in case of a fire emergency. Also, guests with movement disabilities will experience difficulties during evacuation because there are no evacuation elevators.
Hotel employees Permanent Yes Adults Small range possible Possible Conscious Awake Individuals, co-workers Manager/subordinate
Another life safety challenge is the fact that the entrance door near the hotel lobby is the everyday main exit for both the people in the hotel rooms and the restaurant. In case of an evacuation, there is hence a risk that people will try to head through the lobby on their way out, which is a severe potential challenge.
Location of Fire (Step 1) In the example given in Chap. 38 of this handbook, a number of different fire locations were identified, but only the following two are relevant for the 20-story hotel tower: – Fire in a hotel room – Fire in the restaurant of the hotel adjacent to the hotel lobby These two locations are both identified since they are possible fire locations that severely threaten the achievement of the FSO. As previously mentioned, the fact that hotel guests can be asleep in their room and that some guests can have movement disabilities makes the evacuation situation especially challenging. A fire in close vicinity of hotel rooms is therefore highly relevant. On the 2nd to 20th floors of the hotel tower there are a number of possible fire locations, but a fire in a hotel room is estimated to be one of the most relevant. The number of fuel packages in the evacuation stairs, hotel corridor, elevators and elevator lobby can be expected to be very limited, and fires at these locations are thus both unlikely and relatively minor. Hotel rooms on the
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other hand have a significantly higher fuel load. Also, rooms are occupied by guests who engage in activities that might result in fires, e.g., smoking and ironing, and rooms have electronic equipment that might malfunction, e.g., TVs and refrigerators. This makes a hotel room a credible fire location. Storage rooms are similar to hotel rooms as they contain a large amount of combustible material, but they are typically locked and only accessed by staff. This makes a fire in a storage room much less likely than a fire in a hotel room. Given the reasoning above, a hotel room appears to be a credible location that threatens the achievement of the FSO. The hotel lobby was identified as a major waypoint, i.e., a potential life safety challenge, and a fire in the adjacent restaurant is therefore considered most relevant. The lobby of the hotel is most likely sparsely furnished and has limited possible ignition sources. A fire in the lobby would therefore be unlikely and relatively minor. However, in the adjacent restaurant there are likely an abundance of possible sources of ignition, e.g., candles on tables or hot surfaces in the kitchen. Also, the restaurant has many fuel sources, e.g., furniture in the dining area or frying oil in the kitchen. Due to the open plan of the ground floor, smoke from a fire in the restaurant can easily spread to the hotel lobby. The restaurant, either the seating area or the kitchen, is therefore a credible location that severely threatens the achievement of the FSO.
Type of Fire (Step 2) A rapidly growing flaming fire with a high heat release rate is considered the most relevant type of fire for the hotel room since it most severely threatens the achievement of the FSO. Many types of hotel room fires are possible. Firstly, the ignition source might relate to activities that the guests engage in, e.g., smoking or ironing, as well as malfunction of electronic equipment, e.g., TVs and refrigerators. The resulting fire growth characteristics might also vary and include anything from a slowly developing smouldering fire to a rapidly growing flaming
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fire. For the hotel room example, a rapidly growing flaming fire with a high peak heat release rate is deemed most relevant since it has the potential to make the evacuation situation unacceptable before people have responded to the initial fire cues, which relates to the previously mentioned life safety challenge. This type of fire might be ignited with a cigarette that is thrown in a garbage bin that ignites curtains and subsequently spreads to large fuel items, e.g., a bed and/or a sofa. For the restaurant location, a rapidly growing flaming fire with a high heat release rate is also considered most relevant since it has the potential to generate a lot of toxic and hot smoke that may quickly fill the hotel lobby, thereby threatening the achievement of the FSO. One example could be a candle that falls over and ignites a tablecloth and then a large fuel item, e.g., a sofa or table/chairs. Alternatively, a fire might start at a deep fryer in the kitchen and subsequently spread to uncleaned and greasy parts of the duct system. Both of these fires have the potential to create and uphold difficult evacuation conditions in the hotel lobby.
Potential Fire Hazards (Step 3) In this example, one potential fire hazard that could severely threaten the achievement of the FSO is an arson attack. This type of attack may involve combustible liquid, e.g., gasoline, which is carried into the building complex and ignited. Although unlikely, this type of attack has been known to occur, see for example the PUB incident in Stockholm [29]. The liquid might be ignited in the lobby as it is a public area and hence easily accessible. Also, this is a location that relates to one of the previously mentioned fire safety challenges. In an area susceptible to serious earthquake damage, consideration should be given to the impact of a possible post-quake fire, where occupants might have to deal with damage to components of the egress system, such as doors jammed in distorted doorframes that could result in entrapments.
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Systems and Features Impacting on Fire (Step 4) Some of the systems that are used in the 20-story hotel tower to mitigate the fire effects on people are the automatic sprinkler system, the fire alarm system and the fire barriers. A failing or compromised barrier, i.e., a hotel room door that does not close properly or a stairwell door that is propped open, would make conditions outside the room of origin unacceptable quickly. Similarly, a failing sprinkler system, or a sprinkler system unable to control a shielded fire, could allow a fire to grow bigger more rapidly and a failing fire alarm or voice messaging system would potentially delay people’s response. Failure of any of these systems would hence severely threaten the achievement of the FSO for both the fire in a hotel room and a fire in the restaurant.
People Response (Step 5) The building users may engage in activities that can make conditions either better or worse. In this example, manual suppression is an activity that can improve the chances of achieving the FSO. This occupant response is deemed more likely for the restaurant fire due to the presence of trained staff that is familiar with the building. One activity that threatens the achievement of the FSO is if occupants do not close doors, e.g., a hotel room door, which would make fire barriers ineffective, or if opening too many doors in a pressurized stairwell affects its proper functioning.
Scenario Selection Process (Step 6 to 10) Steps 6 to 10 of the example, i.e., the compilation of scenarios, the scenario selection process and the documentation, are not described in this chapter and the interested reader is referred to the description in Chap. 38 of this handbook. It should, however, be pointed out that each scenario is evaluated in relation to the achievement of the FSO. The evaluation in the example
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resulted in the selection of the following design scenario involving a fire in a hotel room in the 20-story hotel tower: Fire started in a garbage container and spread to the curtain and mattress. Nobody was in the room of fire origin. The sprinkler system did not activate because the water supply was turned off for repairs. The fire spread from the room door to the corridor of the hotel. For life safety calculations, assume that occupants were asleep when the fire started. (Chap. 38)
It is important to note that a number of scenarios believed to challenge the system must be selected in order to adequately test the design. This example will follow only one—a fire in a hotel room.
Deriving Design Occupant Scenarios No details about the occupants were included in the example in Chap. 38, other than that the occupants outside the room of origin were asleep. In order to do the evaluation of the design, assumptions must be made about the characteristics of the occupants so as to formulate a scenario that will challenge the fire safety design. A suitable design occupant scenario in this example is therefore that all guests are asleep in their rooms and that one accessible room per floor is occupied. All rooms are assumed occupied to their maximum capacity. As hotel guests are transitory occupants, it will also be assumed that they are unfamiliar with the layout of the building and they are not trained in evacuation. As a result, there will be delays in evacuation as they assess the situation after waking, prepare for evacuation and attempt to find the exits. These conditions are believed to represent a worst credible case.
Evacuation Variables for Sensitivity Analysis In previous sections, a number of occupant characteristics for hotel guests were highlighted in relation to the hotel use of the building. These characteristics are also the evacuation variables that should be the variables included in a
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sensitivity analysis. For this example, the evacuation variables for the sensitivity analysis include: – transitory—familiarity with the building – social groupings—alone, couples, families – age ranges—adults, children – vulnerabilities—types of disabilities – intoxicated—level of intoxication These characteristics are mainly concerned with the ability of building occupants to mitigate or cope with a fire event. All these variables can be varied with regards to their magnitude, e.g., the degree of familiarity with the building, and frequency, e.g., the number of guests who are very unfamiliar with the building. It might also be relevant to vary the initial behaviour and the initial route choice in the sensitivity analysis. For example, in the baseline scenario, the hotel guests were asleep, but not intoxicated. The sensitivity analysis would assume some percentage of occupants were intoxicated, with the resulting additional delays in waking, and possibly more difficulty in decision making and way-finding. Similarly, the sensitivity analysis can test the effect of varying the ages of the occupants. The sensitivity analysis will test the robustness of the safety design, which could result in changes to the design or refinements to the fire safety management plan for the building.
Summary The intent of this chapter has been to extend the discussion on the selection of scenarios for deterministic fire safety engineering analysis according to ISO/TS 16733 when the Fire Safety Goal is life safety. In this case, the fire, building and occupants all play an important role in determining scenario relevance. Before the scenario selection process can be initiated, the designer must first define the project context by setting the scope, Fire Safety Goal (life safety for building occupants in this chapter), Fire Safety Objectives and critical fire conditions. The subsequent step involves identification of possible building uses, as well as the subsequent users and their characteristics. In this
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chapter, characteristics are divided into eight categories commonly used in the identification process. Once the uses and users are known, the designer needs to determine the life safety challenges, which are any issues or conflicts that, in combination with fire, could potentially lead to the failure of the design. These life safety challenges are essential for the scenario selection process because it is in relation to them that the severe but credible scenarios, i.e., the worst credible cases, are chosen in the deterministic analysis. In the first five steps of the fire scenario selection process of ISO/TS 16733, fire-related factors/aspects, e.g., fire locations and types of fire, that severely threaten the achievement of the FSO are identified. This identification is always done in relation to the life safety challenges as described in this chapter. In Steps 6 to 10 of ISO/TS 16733, design fire scenarios are then chosen for the deterministic analysis from the multitude of possible fire scenarios. Because the entire fire scenario selection process is linked to the fire safety challenges, each design fire scenario is also linked to occupantrelated issues or conflicts. This means that for every design fire scenario there is already a design occupant scenario. The process of determining these design occupant scenarios involves re-examination of the basis for the identification of fire-related factors/aspects (Steps 1 to 5) and selection of design fire scenarios (Steps 6 to 10). Scenario selection is an iterative process as occupants can impact the fire, the fire can impact the occupants, and the building and its features impact both the fire and the occupants. A failing design might be addressed by changing, for example, the building layout, which in turn might influence both potential fires and occupants. This means that the described process might need to be repeated several times before an acceptable design is found. The evaluation of the safety of a design involves comparing the expected growth and spread of challenging fires (the design fire scenarios) against the ability of occupants to avoid or survive the effects of those fires. There is a great deal of interaction between the
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occupants of a building and the likelihood of fire ignitions and fire spread. While this chapter has focused on life safety, parts of the process could be applied to the consideration of other fire safety objectives, where the number and type of occupants could impact fire ignition, growth, spread and suppression.
References 1. Watts, J.M. (2008). Systems Approach to Fire-Safe Building Design, NFPA Handbook (20th ed), 1–159. 2. ISO/TS 16733:2006 – Selection of design fire scenarios and design fires (2006) Geneva: ISO. 3. BBRAD 1 - Boverkets allma¨nna ra˚d om analytisk dimensionering av byggnaders brandskydd, BFS 2011:26 med a¨ndringar t.o.m. BFS 2012:13 (2011) Karlskrona: Boverket. 4. INSTA/prTS 950 - Fire Safety Engineering - Verification of fire safety design in buildings (2013) Inter Nordic Standardisation Organisation 5. Frantzich, H. (1998). Uncertainty and Risk Analysis in Fire Safety Engineering. Report 1016, Lund: Department of Fire Safety Engineering, Lund University. 6. Pate´-Cornell, M. E. (1996). Uncertainties in risk analysis: six levels of treatment. Reliability Engineering and Systems Safety, 54(2), 95–111. 7. Sime, J.D. (1985). Movement towards the familiar Person and place affiliation in a fire entrapment setting. Environment and Behaviour, 17(6), 697–724. 8. SFPE (2007) SFPE Engineering Guide to Performance-Based Design (2nd ed.). Bethesda, MD: Society of Fire Protection Engineers. 9. BBR19 - Regelsamling fo¨r byggande, Boverkets byggregler, BFS 2011:6 med a¨ndringar t.o.m. BFS 2011:26 (2011) Karlskrona: Boverket. 10. NFPA 101: Life Safety Code® (2012). Quincy, MA: National Fire Protection Association. 11. NKB (1994). Funktionsbestemte brandkrav og teknisk vejledning for beregningsmeassig eftervisning, NKB Utskotts- och arbetsrapporter 1994:07, Helsinki: NKB. 12. ISO/TS 13571:2002 - Life-threatening components of fire - Guidelines for the estimation of time available for escape using fire data. (2002) Geneva: ISO. 13. van Hees, P., Nilsson, D., & Berggren, E. (2009). Simulation of critical evacuation conditions for a fire scenario involving cables and comparison of two different cables. Lund: Department of Fire Safety Engineering and Systems Safety, Lund University. 14. Gwynne, S., Kuligowski, E., & Nilsson, D. (2012). Representing Evacuation Behaviour in Engineering Terms. Journal of Fire Protection Engineering, 22 (2), 133–150.
D. Nilsson and R. Fahy 15. Nilsson, D. (2009). Exit choice in fire emergencies Influencing choice of exit with flashing lights, Report 1040, Lund: Department of Fire Safety Engineering and Systems Safety, Lund University. 16. McClintock, T., Shields, T.J., Reinhardt-Rutland, A. H., & Leslie, J.C. (2001). A behavioural solution to the learned irrelevance of emergency exit signage. Proceedings of the 2nd International Symposium on Human Behaviour in Fire, London, UK, pp. 23–33. 17. Bruck D. & Brennan P. (2001). Recognition of fire cues during sleep. Proceedings of the 2nd International Symposium on Human Behaviour in Fire, London, UK, pp. 241–252. 18. Ball, M., & Bruck, D. (2004). The effect of alcohol upon response to different fire alarm signals in sleeping young adults. Proceedings of the 3rd International Symposium on Human Behaviour in Fire, Belfast, UK, pp. 291–302. 19. Anderson, B.M., Stevens, M.C, Meda, S.A., Jordan K., Calhoun, V.D., & Pearlson, G.D. (2010). Functional Imaging of Cognitive Control During Acute Alcohol Intoxication, Alcoholism: Clinical & Experimental Research; DOI: 10.1111/j.1530-0277.2010. 01332.x. 20. Latane´, B.,& Darley, J.M. (1968). Group Inhibition of Bystander Intervention in Emergencies, Journal of Personality and Social Psychology, 10(3), 215–221. 21. Swartz, J.A. (1979). Human Behavior in the Beverly Hills Fire. Fire Journal, 73(3), 73–74, 108. 22. Drysdale, D. (2011). An Introduction to Fire Dynamics.(3rd ed.) West Sussex: John Wiley & Sons, Ltd. 23. Ingason, H., Kumm, M., Nilsson, D., Lo¨nnermark, A., ˚ kerstedt, R., Claesson, A., Li, Y.Z., Fridolf, K., A Nyman, H., Dittmer, T., Forse´n, R., Janzon, B., Meyer, G., Bryntse, A., Carlberg, T., NewloveEriksson. L., Palm, A. (2012). The METRO project Final report. SiST 2012:8, Va¨stera˚s: School of Sustainable Development of Society and Technology, Ma¨lardalen University. 24. Sekizawa, A., Ebihara, M., & Notake, H. (2003). Development of Seismic-induced Fire Risk Assessment Method for a Building. Fire Safety Science – Proceedings of the 7th International Symposium, International Association for Fire Safety Science, pp. 309–320. 25. Kim, J.K., Park, H. & Meacham, B.J. (2013). “Fire Performance of Earthquake-Damaged Buildings: Overview and Preliminary Analysis of Full-Building Earthquake and Fire Tests,” Proceedings, Interflam 2013, Interscience Communication, Ltd., London, UK, 1407–1418. 26. Hamby, D.M. (1995). A Comparison of Sensitivity Analysis Techniques. Health Physics, 68(2), 195–204. 27. Levin, B.M. (1984). Human Behavior in Fire: What We Know Now. SFPE Technology Report 84–3, Boston, MA: Society of Fire Protection Engineers.
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28. Purser, D.A. and Bensilum, M. (2001). Quantification of behaviour for engineering design standards and escape time calculations, Safety Science, 38, 157–182. 29. Harne (1998). Polisen utan spa˚r efter pyromanen [Police without any trace after pyromaniac], Aftonbladet, 24th December, 1998.
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Daniel Nilsson, PhD is an Associate Professor in the Department of Fire Safety Engineering at Lund University, Sweden, and Chair of ISO TC92/SC4 on Fire Safety Engineering. Rita F. Fahy, PhD is the manager of fire databases and systems at NFPA and convenes the ISO TC92/SC4 working group on behaviour and movement of people.
Human Behavior in Fire
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Erica D. Kuligowski
Introduction Human behavior in fire is at the core of all life safety projects completed by fire safety or fire protection engineers. A better understanding of how people respond to building emergencies can aid in safer building design; improved use or development of calculation tools used to ensure the level of safety afforded by these designs; and more effective emergency procedures, emergency communication systems, and pre-event emergency training for buildings and communities. The purpose of this chapter is to provide a basic understanding of human behavior in fire concepts and theory for use by engineers. The chapter contains the following aspects of human behavior in fire and other emergencies: a definition of human behavior in fire, including a discussion of the types of disciplines employed in the study of people in fires; a presentation on what human behavior in fire is not, including examples of disaster myths; an overview of the disaster-based decision-making process in fires and other emergencies; a discussion relating theory to practice (highlighting studies from fire events that support the decision-making theory); the identification of important factors that influence the decision-making process; and a conclusion highlighting what is missing in the field of human behavior in fire. Each section of this E.D. Kuligowski (*) National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, MD 20899
chapter will include an implications section that outlines the reasons why these ideas or theories are important for engineers to understand and incorporate.
Definition of Human Behavior in Fire Human behavior in fire is the study of human response, including people’s awareness, beliefs, attitudes, motivations, decisions, behaviors, and coping strategies in exposure to fire and other similar emergencies in buildings, structures and transportation systems. The study of human behavior in fire is highly multidisciplinary, involving practitioners from the fields of engineering, architecture, computer science, mathematics, law, sociology, psychology, human factors, communications and ergonomics, to mention just a few. The primary focus of human behavior research and its translation into practice is to minimize the risk to people from fire. This is achieved by generating and collecting quantitative and qualitative data on human responses which can be used to develop human fire response theory.1 A comprehensive theory of human response is key to improve current fire safety engineering design, performance based regulatory systems, egress-
1
This definition of human behavior in fire was first presented in the brochure advertising the 2012 Human Behaviour in Fire Symposium, developed by consensus of program committee members (Interscience Communications).
M.J. Hurley (ed.), SFPE Handbook of Fire Protection Engineering, DOI 10.1007/978-1-4939-2565-0_58, # Society of Fire Protection Engineers 2016
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Fig. 58.1 Timeline of a human response to a building fire emergency
Pre-evacuation period
Ignition
Alarm/ Cues
Evacuation Decision
Seek information
Movement period
Movement begins…
Prepare, Protect others, Protect self
Protect self and others
Time
related computational models and fire safety management. The ultimate goal of improving life safety analyses in performance-based design is to develop a comprehensive theory of human fire response. Human behavior is complex and there is more work to be done to achieve this goal. A focus on case studies of specific building fires [1–3], and research on particular aspects of a fire evacuation has left the field of human behavior in fire with a series of partial-theories, rather than a comprehensive theory of human behavior in fire. As a result, human response to fires is often crudely categorized into two main periods: the pre-evacuation period2 and the movement period, with little understanding of the behavioral processes that take place within each one. The pre-evacuation period estimates the time when ignition begins until the point when an individual or group begins purposive evacuation movement to a place of safety. The time period in which purposive movement to safety occurs is then considered the evacuation or movement period. As shown in Fig. 58.1, and as will be presented throughout this chapter, the pre-evacuation and movement periods consist of additional sub-phases that the engineer should understand. For example, within the pre-evacuation period, at least three sub-phases can exist: • The pre-alarm phase, which is the time from the point when fire ignition begins until the 2
Other terms have been used to express the pre-evacuation period, including pre-movement or pre-response.
point when the building alarm initiates and/or building occupants are exposed to cues from the fire event (i.e., seeing smoke or being told about the fire event by a staff member) • The evacuation decision-making phase, where building occupants are exposed to or seek out cues/information from the fire event and others in the building, and after processing this information, must decide whether or not it is necessary to protect themselves (e.g., evacuate) • The protective action phase, whereby individuals engage in certain actions, e.g., gathering personal belongings or assisting others to prepare for evacuation that allows them to protect themselves or others before beginning evacuation. These phases are important to understand, because in certain types of buildings or emergencies within a building, the pre-evacuation period can be significantly longer than the movement period in a building evacuation. Additionally, the same types of decisions and actions can take place during the movement period, especially when people are faced with additional environmental cues. The purpose of this chapter is to aid the engineer in understanding the current state of knowledge regarding the entire process of human behavior in fire emergencies. This process is important to understand because it is often the goal of fire safety or fire protection engineers (as well as fire marshals, authorities having jurisdiction, and other emergency responder personnel) to ensure that a particular structure or transportation system provides the appropriate
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level of life safety to its users. With this goal in mind, it becomes an almost impossible task to assess life safety (credibly or reliably) without understanding how the structure or transportation system will be used during a fire emergency. In a building, for example, an engineer must understand how the building occupants will respond to a fire in order to assess whether the building and the fire safety features provide an adequate level of safety during a fire emergency event. Therefore, this chapter focuses on communicating current understanding of human behavior in fire, including all phases of the human response, for use in fire safety and life safety analyses of structures and other systems.
Discarded Theories in Human Behavior in Fire Before we can achieve an understanding of human behavior in fire, we must first discuss what human behavior in fire is not. This is critical since our understanding of human behavior in fire has direct implications to the engineering design process. Since behavior in fires has been studied since the 1950s (and for other disasters, earlier than that), certain claims have been made and then subsequently refuted as explanations of human behavior in fires. In this chapter, and elsewhere [4], these claims are labeled as disaster myths. In some cases, these disaster myths are true for a small minority of the population, but have become overgeneralized to hold for the entire population. In other cases, the disaster myth is completely invalid [5]. Three disaster myths will be discussed in this section: panic, disaster shock, and group mind. All three myths have been overgeneralized by society and the media to account for negative situations in some disaster scenarios, but, in reality, are very rare. These are chosen as discussion points in this section, since they have been used in the past to characterize occupant response to building fire disasters. These are not the only disaster myths promulgated by past events, nor the only disaster myths that may be promoted by future events.
E.D. Kuligowski
Panic Behavior The concept of panic is often used to explain the occurrence of multiple fatalities in fires. Representatives of the media and public officials often label various types of fire incident behavioral responses as panic [6, 7], often going so far as specifically asking about the presence of the behavior when interviewing disaster survivors [8]. According to most definitions, panic is a flight or fleeing type of behavioral response that also involves extravagant and injudicious effort. Panic is not necessarily limited to a single individual, and may be mimicked and adopted by a body of persons (i.e., mass panic or collective flight). Johnson describes panic as the following: “. . .selfish competition uncontrolled by social and cultural constraints—i.e., unregulated” and the breakdown of social order [9, 10]. Wenger et al. [11] includes a definition for “panic flight” as “the competitive mass behavior of individuals involved in fleeing from an imminent threat that results in increasing the danger to themselves and others”. Quarantelli [7] characterizes panic not only as withdraw (or flight) behavior, but also as a behavior that encompasses a lack of consideration for others (i.e., competition). Often, however, the concept of selfdestructive or animalistic panic-type behavioral responses to fire incident stimuli, such as the presence of flames or smoke, has not been supported by the research on human behavior in fire incidents. As indicated by Sime [12], Quarantelli [13], and others [14–17], panic behavior in which the flight response is characterized by actual physical competition between the participants and personal injuries is rare. For example, Best studied extensive interviews with survivors of the Beverly Hills Supper Club fire (1977) to find that the staff and patrons of the club did not exhibit panic behavior, despite media accounts attributing the large loss of life to the phenomenon [18]. Also, several studies have been conducted on the 2001 World Trade Center Disaster (WTC), allowing researchers to assess the accuracy of the headline of a BBC News Online article, entitled: “Panic on
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the stairs” [8, 19]. Studies of both media accounts [20, 21] and survivor interviews [1, 22, 23] of this deadly terrorist attack revealed overall trends of calm and altruism. While there were reported situations of emotion, i.e., crying or being anxious or nervous about the situation, the majority of stories reported rational, orderly, and often times, delayed responses to the disaster event. Therefore, the use of the concept of panic must be separated from the use of the terms anxiety or fear. These are natural emotions in emergency situations that do not necessarily lead to competitive, injudicious flight behavior (i.e., panic). Additionally, research has shown that survivors of fire emergencies (or other disasters) may mistakenly categorize their own behavior or the behavior of others as panic, whereas further description of actual actions barely reflect panic behavior [12, 24]. Ramachandran [25], in his review of studies on human behavior in fires in the United Kingdom, has developed the following conclusion relative to nonadaptive behavior: In the stress of a fire, people often act inappropriately but rarely panic or behave irrationally. Such behavior, to a large extent, is due to the fact that information initially available to people regarding the possible existence of a fire and its size and location is often ambiguous or inadequate.
In reality, and in stark contrast to panic behavior, engineers should be aware that people’s first assumption in many disasters, regardless of the intensity of the information perceived, is that nothing unusual is happening, and thus, no response is required. This phenomenon is known as normalcy bias [26–29]. It is our challenge, as engineers, to ensure that disaster victims (i.e., those who are in danger) become aware that a dangerous situation is taking place, and that they perceive personal risk. If not, they are unlikely to take actions to protect themselves from harm. Even in an event as large and intense at the 2001 WTC disaster, building occupants had to be convinced of the danger to which they were exposed, sometimes taking several minutes, before evacuating the building [30]. Additionally, in reference to the assumption of competition, engineers should acknowledge that
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altruistic behavior is more likely to occur. Researchers have found that even though disasters can cause shifts in the pre-existing situation, the breakdown of social order is rare [31, 32]. Many of the societal norms and social roles evident before the disaster carry over into the new, evolving situation. Therefore, occupants are likely to engage in pro-social behaviors, including helping others rather than competing with others, as they would do in non-disaster situations. Engineers should also be aware of these types of pro-social behavior, since they could lead to delays in the evacuation process, among other issues. The delays associated with altruist behavior, such as helping, should be accounted for in fire protection and emergency procedural design for buildings in the event of fire emergencies.
Disaster Shock An additional disaster myth suggests that individuals who do not act irrationally (i.e., panic) are often immobilized by fear in emergency events [4, 33]. This myth creates an image of large numbers of individuals dazed or shocked; i.e., unable to cope with the new disaster-created situation at hand. This myth also extends into the disaster recovery stage, suggesting that the paralyzing shock created by the situation is followed by longer-term personal effects, often labeled as post-traumatic stress disorder, or PTSD. Although this may at first seem irrelevant to fire emergencies, since much of the research on disaster shock is reported in response to the natural or technological disasters, the myth of disaster shock is directly applicable to fire emergencies. In a building fire, the fire ignites and continues to grow as building occupants are made aware of the event and are encouraged to take protection (e.g., evacuate). In fires, different from a tornado event, for example, building occupants are warned about the event after it has already started to cause destruction. Thus, it is possible to assume in building fire events that individuals
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will go into shock in response to the fire, and thus rendering themselves incapable of evacuating on their own. Researchers have found that following disasters, documented reports of disaster shock are rare. Melick [34], after reviewing disaster studies conducted between 1943 and 1983, found the following three conclusions regarding disaster shock: (1) Disaster shock occurs more frequently in sudden onset disaster events that are accompanied by little forewarning and extensive physical and social destruction; (2) Disaster shock affects a relatively small proportion of the population in any one event [7, 35]; and (3) Disaster shock usually occurs within the immediate postimpact period of a disaster, lasting no longer than a few hours or days [5]. Other researchers have shown that this phenomenon is rare and the state is usually short-lived [36]. Disaster researchers attempt to dispel this myth by explaining that disaster response behavior is often performed in an active manner [7]. Instead of waiting for assistance, in a dazed or disoriented manner, disaster victims are more likely to show considerable personal initiative, performing search and rescue activities, casualty care, and restoration of essential services even before emergency responders arrive on scene [11]. This kind of response was observed in the 2001 WTC disaster [30], where survivors were often the first individuals to respond to the needs of their coworkers, assisting them to reach safety before first responders could reach the upper floors. Belief in this assumption could cause engineers to focus more on emergency response officials and their role in evacuation. However, it is important for engineers to understand that building occupants will react in an emergency and proactively engage in their own (and others’) safety. In turn, engineers must ensure sufficient and efficient evacuation routes and strategies to ensure safety for all occupants in the building. One note that should be made here regarding this myth is the inability to interview those who perish from building fires, and the effect that this gap may have on our overall understanding of disaster shock. The fires and disaster fields may
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not fully understand the role of disaster shock in consequences (i.e., injuries and deaths), and therefore future research should focus on obtaining a better understanding of the circumstances of fatalities from fires (when possible). One way to obtain this type of data is to interview individuals who were physically with (or in contact with) the deceased during the fire emergency.
Group Mind A third disaster myth is the oversimplification that the group is something other than the sum of individuals responses; i.e., that the group has a “mind” of its own when making decisions in a disaster [37]. Another way of thinking about group mind is the assumption that when a disaster occurs, individuals become a part of a group and the group (as a whole or as one entity) acts in response to the disaster. This assumption can also be characterized as mob behavior or herd behavior. However, sociologists have stated that thinking that the group acts or thinks in a certain way is “often a serious oversimplification” [37]. Making this assumption can cause the engineer or researcher to be blinded by any diversity associated with the group, including individual characteristics, experiences, decision-making or behavior. If we make this assumption, we may then assign attributes to the group, including a mind, a sense of responsibility, a conscience, or even a lack of self-control (related to mass panic described above). What is more likely, and what has been seen in actual disaster events, is that groups consist of a variety of different individuals. During disasters, it is more likely that groups engage in what is called “a division of labor” in that certain individuals take on particular roles based upon their experiences and/or relationships with others in the group, which complement each other and allow the group to function [37]. It is therefore important to understand the division of labor within the groups and the characteristics,
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experience, decision-making and behavior of the individuals within the group to truly understand human behavior in fire. It should be noted; however, that there is extensive research in group dynamics and how groups “act” in disasters and building fires. This research will be described later in this chapter. Overall, it is neither the description of the group (only) nor the description of the individual (only) that is sufficient in understanding human behavior in fire. Instead, identifying both his/her attitudes toward the object (or issue at hand, in this case, the fire cue or cues) [38] and attitudes toward the group and others in the building (i.e., the processes of group dynamics) leads to the true understanding of human response in emergencies [37].
Engineering Implications of Disaster Myths or Why Should the Engineer Care? Unfortunately, these disaster myths can have negative implications on fire safety in our society. Images of human behavior during disasters are often the basis for critical decisions made by engineers and other fire protection designers on building design requirements, emergency communications systems design and guidance, as well as emergency response procedures for fire events. The assumptions of irrationality or human frailty can inappropriately shape the way that engineers and emergency officials plan for response to fires in their buildings, as well as how evacuation models represent evacuation behavior during fires. Instead, it is important for engineers to understand the true needs of building occupants so that engineering and emergency procedural designs and methods more accurately reflect realistic occupant behavior during building fire events. One example of how a disaster myth has had negative implications on fire safety is the influence of panic on emergency communication during fires [33]. The view that people would panic in response to an incident (and specifically to information describing the incident) has influenced both the notification procedures
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employed and the language used (by survivors) to report the exhibited behavior [39]. This assumption influenced a difficult and harmful cycle consisting of the following steps: people report that they panicked, emergency officials continue to believe that panic is a normal response, emergency information is withheld in the next disaster so that people do not panic, human response is delayed and inefficient, and the situation becomes more dire. Over the last 25 years, this point of view has been slowly replaced with the recognition that people need detailed and credible information as early as possible in order to initiate and inform their response. The availability of this information encourages people to accept the emergency procedures and to improve their familiarity with the required response, and later informs the decision-making process that determines their response. People need information in order to act. Detailed information by no means guarantees the desired response; however, without this information, an uninformed approach (ignorant of the conditions and the options available) is much more likely. It is now broadly accepted that depriving evacuees of information is more likely to lead to an inefficient and inappropriate response; e.g., misinterpreting the incident and the threat it poses, delaying response, engaging in an inappropriate response, and ignoring safe egress routes. During an incident, people will seek information regarding the nature of the incident and what they should do in response to it. Unfortunately, this information may not always be easy to find, reliable, consistent or accurate. It is critical that an information vacuum is avoided and that accurate, credible information is provided. The previous section discussed the factors and theories that do not accurately describe human behavior during building fires and other events. Therefore, the following section will focus on describing the theory of human behavior in fires and the foundation upon which this and other related theories were built. This understanding of human behavior focuses on decision-making at the level of the individual, independent of whether the individual is on his/her own, a
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member of a group, or a member of a larger crowd during the emergency. Social psychological theories of decision-making during emergencies will be presented in the following section.
Social Psychological Theories of Human Behavior in Emergencies Everyday, individuals go about their normal lives—attending meetings at work, watching movies at the local cinema, and shopping at the mall or the grocery store for all of their necessities. These are activities in which individuals have engaged so often that they have become routine in nature. When an emergency occurs, these activities may suddenly seem irrelevant. When an alarm is sounding or smoke is billowing into a room from an air conditioning duct, individuals are faced with a potentially new and unique situation where previous actions may no longer apply. Under these new conditions, individuals are required to make a concerted effort to create meaning out of new and unfamiliar situations, often under time pressure. From this meaning, a set of actions, different from those that have become routine, must be created. Emergent norm theory (ENT), explains the process of meaning-making in the face of uncertain conditions [37], stating that in situations where an event occurs that creates a normative crisis (i.e., an event where the institutionalized norms [e.g., sitting at a desk and working] no longer apply), such as a building fire, individuals interact collectively to create an emergent situationally-specific set of norms to guide their future behavior. In other words, individuals must work together to redefine the situation and propose a new set of actions, which is the product of processes labeled “milling” and “keynoting”. Milling is a communication process whereby individuals come together in an attempt to define the situation, propose and adopt new appropriate norms for behavior, and seek coordinated action to find a solution to the shared problem at hand [40]. The group engages in both physical and
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verbal communication in order to ask the three following questions: (1) what happened? (2) what should we do? and (3) who should act first? (known as leadership selection) [41, 42]. Leaders emerge as keynoters, or those who advance suggested interpretations of the event or suggestions on what do to next [37, 43]. The consequences of the milling process are that individuals become sensitized to one another, that a common mood develops, and that a collective definition of the situation is decided upon that minimizes initial ambiguity [44]. Overall, in the face of new and uncertain situations, milling and the keynoting processes allow the group to define the situation and to propose next steps for alternative schemes of social action [40, 43, 44]. The new situation and next steps developed do not emerge in a social vacuum, however. Rather, individuals within a group bring with them certain aspects of the “normal” or non-emergency situation that influence decisions made in the new situation. First, individuals bring their “social stock of knowledge” to the situation. The social stock of knowledge consists of an individual’s internal set of knowledge about the disaster (or disasters in general), experiences from previous disasters or building evacuations, and his/her relationships and roles within the building, especially those related to building fires and other types of disasters [45]. Second, individuals bring conventional norms, i.e., previous ways of acting within the building and/or society as whole, which are likely to influence the newly developed “next steps for action” during the current disaster situation [31].
Protective Action Decision Model—A Background A decision-making model has been developed that extends and applies ENT’s explanation of the meaning-making process in crises to disaster situations. The Protective Action Decision Model (PADM), which is based on over 50 years of empirical studies of hazards and disasters [28, 38, 46–49], provides a framework that describes the information flow and decision-
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making that influences protective actions taken in response to natural and technological disasters [50]. The model posits that cues from the physical environment (e.g., the sight of smoke) as well as information from the social environment (i.e., emergency messages or warnings), if perceived as indicating the existence of a threat, can interrupt normal activities of the recipient. Depending upon the perceived characteristics of the threat (e.g., what is going on and how dangerous is it?), indicative of the milling and keynoting processes described above, individuals will either seek additional information, engage in actions to protect people or property, perform actions to reduce psychological stresses, or resume normal activities [50]. In addition to perceptions of the threat, responses are also determined by the perceived feasibility of protective actions. Before describing the stages of the PADM in detail, it is necessary to introduce the additional research and social models that it draws upon. Studies of social influence provide insight on the types of cues and information that affect behavior. Research and studies on the decision-making process shed light on the steps in which people engage to make decisions on their next course of action. Additionally, the PADM is based upon other theories and conceptual models that link together cues, cognitive processes and subsequent protection actions. First, since people perceive information from both the physical and social environment, the PADM incorporates insights from social influence research. Theories of social influence posit that the actions of others and the risk communication process can influence human response in disasters. In ambiguous situations, the presence or actions of others helps to define what behavior is appropriate in a particular situation. If people are seen to be taking protective action, for example, moving to the same stair, others are likely to follow suit [51, 52]. Conversely, if people are not taking emergency action, others are also less likely to engage in emergency actions. Additionally, research has shown the influence of information (for example, warnings provided via emergency communication systems), on a person’s beliefs, attitudes, and subsequent
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behavior [53, 54]. Aspects of the risk communication process, e.g., the source, the message, the channels, and the receiver characteristics (i.e., the receiver’s perceptions of the credibility of the message, message comprehension, and channel preferences), can ultimately predict whether or not protective action is taken before or during crisis [38, 50]. As a decision-making model, the PADM also relies on behavioral decision theory. In a perfect world, in which those at risk behave like rational actors, decisions would be made based upon all of the necessary information available to the individual, which would be weighed based on costs and benefits of the various outcomes, leading ultimately to an optimal decision on the best course of action. More often, however, people lack the necessary information needed to make decisions, and they do not always search for additional information. Instead, they make decisions based on their beliefs about the situation, and many times, these beliefs can reflect poor understandings of the situation [55]. For example, in the Beverly Hills Supper Club fire when an employee took the stage and announced the presence of a fire, some of the patrons thought that the announcement was part of the evening’s entertainment and in turn, remained in place rather than moving to the exits [18]. Decision scientists argue that people are often poor judges both of the likelihood of a disaster event and of the range and severity of impacts disasters can produce. This is because people use a variety of “quick and dirty” heuristics, which are simple rules or “cognitive short cuts” through which they judge a situation or event [56, 57]. One example of a heuristic that people employ is the availability heuristic, or judging the likelihood of an event based on the ease of recalling similar instances from memory [57, 58]. For example, people often think that deaths due to plane incidents are more frequent than deaths due to car accidents because they can recall more easily dramatic media coverage of large-scale plane crashes [59]. Another short cut, similar to social influence research, is an over-reliance on the actions of others [60]. In cases of procedural uncertainty, where individuals have little
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experience dealing with high-stakes decisions, individuals are likely to adopt the decision strategies of others and follow their behavior [60]. Unfortunately, the individuals who are followed may also be using cognitive short-cuts and taking inappropriate action. Heuristics can result in biased understandings of the situation, which may then be used to make sub-optimal decisions during a disaster. Research in the area of judgment and decisionmaking under uncertainty also provides insights into the ways in which people make decisions on their next course of action based on their beliefs. “Rational-actor”-based research claims that individuals will optimize decision-making by weighing all options and choosing the best one [61, 62]. In situations of uncertainty or crisis, however, individuals or groups are unlikely to search for a large number of options due to significant time pressures [63–66]; limited mental resources (e.g., when they are under stress) [67–69]; or if they perceive themselves as experienced in or knowledgeable concerning recommended protective procedures [56, 70]. In situations with greater time pressure, dynamic conditions, and ill-defined goals [56], all of which are likely to characterize building emergencies, people are likely to satisfice. Satisficing [67, 69, 71] is a method in which an individual chooses what s/he sees as a sufficient rather than optimal option, “not to find the best [option] but to find the first one that works” [56]. For highly trained and experienced individuals, for example, fire fighters, satisficing may in fact lead to quicker, more effective and appropriate decisions for the task at hand. The decision-making technique may be detrimental, however, for occupants who are less experienced in building fires, increasing their delay to safety or even leading to more severe consequences, like injury or death. Finally, the PADM is based upon theories that link cues, cognitive (internal) processes, and subsequent protective action. Much of that research seeks to establish links between the perception of risk and the performance of protective action. Janis and Mann [72] developed the conflict model to describe the process of emergency decision-making. An individual’s
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response to a warning is based upon his/her perception of the severity and immediacy of the threat, the perceived effectiveness of the possible protective action, and the possibility of gaining more information about the event and possible actions. Mileti and Sorensen [38] developed a model that describes the influence of cognition on warning response. Whereas the PADM focuses on responses of people to various types of cues before or during a disaster, this model summarizes the determinants and consequences of public responses to disaster warnings. The warning response model outlines a process in which the receiver must hear, understand, believe, and personalize the warning message in order to respond in an appropriate way. The first stage of the process is perceptually receiving the alert or warning; Mileti and Sorensen [38] note that before anyone can respond to a message, they must receive it first. Once the warning is received, it must be understood, and in this instance, “understanding does not refer to correct interpretation of what is heard, but rather to the personal attachment of meaning to the message” [38]. For example, what does a flood warning mean to one person, versus another? The next stage involves whether the person believes the warning or not—involving whether they believe that the warning is authentic and the contents of the message are accurate. Finally, the last stage in the process before response is personalization. This is the stage in which people think of the warning in personal terms, in that they begin to consider the implications of the risk for themselves and others around them. If the individual has heard, understood, believed, and personalized the warning, s/he will then decide what to do about the risk. Mileti and Sorensen [38] do not discuss the decision-making process and subsequent actions in depth, but generally state that people do next what they think is best for them. An important part of this process is confirmation. In threat situations, people are constantly seeking new information to confirm prior information, whether from family, friends, neighbors, and co-workers, or from various media sources and authorities. Confirmation
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affects each stage of the warning process, in that it helps people to better understand warnings, believe them, personalize the risk, and make decisions.
Protective Action Decision Model—The Stages of Decision-Making Although the PADM is similar to the Mileti and Sorensen warning response model, the PADM provides a more general framework that describes information flow and decision-making specifically in response to various types of cues that originate from natural and technological disasters [50, 73]. The PADM asserts that the process of decision-making begins when people witness cues from the disaster event. Individuals can encounter only one type of cue (for example, seeing smoke) or may be presented with a variety of different cues, for example, environmental cues, the behavior of others, and warning messages. Warning messages can consist of both official and unofficial messages; i.e., official messages are those that come from official warning providers (e.g., emergency managers in a building fire) and unofficial messages are those that come from unofficial sources, such as others in the building. The introduction of these cues initiates a series of pre-decisional processes that must occur in order for the individual to perform protective actions. First, the individual must perceive or receive the cue(s). Then, s/he must pay attention to the cue(s). Finally, the individual must comprehend the cue(s). Comprehension means understanding the information that is being conveyed. If the message uses a different language or highly technical terms, comprehension will be difficult. Comprehension also refers to the development of an accurate understanding of environmental cues. For example, will the individual understand that the smoke s/he smells is coming from a building fire rather than from burnt toast in the kitchen? People go into any disaster with widely varying pre-event perceptions or beliefs about the elements that go into a disaster—the event itself,
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the actions that they have taken (or should take) before the disaster occurs, and the individuals involved in the response to a disaster. The differences in these perceptions are important to understand because they often are predictors of the individuals’ response behaviors when the disaster occurs. The PADM labels these pre-event perceptions as core perceptions or schemas and highlights as important three main core perceptions: perceptions of threat, perceptions of protective actions, and perceptions of stakeholders [73]. First, perceptions of environmental threats include people’s beliefs about the probability and consequences of certain types of disasters as well as their expectations about personal impacts, including death, injury, property damage, and disruption of daily activities (i.e., work, school, shopping, etc.). These can vary from individuals’ beliefs that they are very unlikely to be involved in any type of disaster to individuals’ severe worry or dread that the next disaster is coming specifically for them. Also associated with perceptions of environmental threats is what Lindell and Perry call “the degree of hazard intrusiveness” [73]. This refers to how often individuals are personally concerned with disaster consequences, the time they spend talking about disasters, and the amount of information they receive (passively) about hazards and disasters. The second pre-event perception includes people’s perceptions of protective actions; i.e., the actions that they can take to prepare for a disaster. Essentially, this perception captures individuals’ attitudes about engaging in preparatory actions before a disaster occurs. This can also vary widely, from individuals taking no preparatory action at all and believing that these types of actions are not necessary to individuals taking extensive preparation in their homes and/or work places. The third pre-event perception consists of individuals’ perceptions toward stakeholders in a disaster. Stakeholders in a disaster can be authorities (i.e., federal, state or local government), evaluators (e.g., scientists, universities, medical professionals), watchdogs (e.g., news
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media), industry/employers, and individuals themselves (i.e., in their homes or places of work). Here, it is important to understand the ways in which people perceive stakeholders in terms of three factors: their expertise about disasters (in this case, fires), trustworthiness, and responsibility when a disaster or building fire takes place. This pre-event perception is more applicable to community-based disasters, such as hurricanes or tornadoes, but could be applied to fires in instances where, for example, building occupants do not trust warning information provided by a building manager. All three of these perceptions have been shown in research to vary from individual to individual involved in the disaster situation. More importantly, these factors (among others) have been linked to the decisions that individuals make in disasters, and in turn, their protective actions (discussed below). After the three pre-decisional processes are completed and the three core perceptions are activated (i.e., it is understood that there are differences among individuals in these three areas), the decision-making model consists of a series of five questions [50]: • Is there a real threat that I need to pay attention to? [If yes, then the individual believes the threat] • Do I need to take protective action? [If yes, then the individual decides that s/he needs to take protective action] • What can be done to achieve protection? [The individual begins searching for possible protective action strategies] • What is the best method of protection? [The individual chooses one of the action strategies developed in the previous stage and develops a protective action strategy or plan] • Does protective action need to be taken now? [If yes, the individual follows the plan developed in the previous stage] Individuals must “answer” each question in order to proceed through the perceptualbehavioral sequence, in which the outcome of the process is the performance of a behavioral action. A graphic of the process is shown in Fig. 58.2.
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The first stage of the decision model involves the issue of risk or threat identification. If the individual perceives, pays attention to, and comprehends cues associated with an event, s/he first asks “Is there a real threat that I should pay attention to?” In this stage, according to Lindell and Perry, the individual decides if there is actually something occurring that may require her action, sometimes referred to as warning belief [74], “but this term unnecessarily excludes people’s reactions to environmental cues so the term threat belief is generally more appropriate” [50]. This stage corresponds to the phase in ENT in which members of a population realize that the norms and behaviors for “stable times” no longer apply [37]. If the individual’s answer is yes, then s/he is said to believe the threat, and s/he subsequently moves on to consider the next question in the process. The second stage of the decision model is referred to as risk assessment. Research has shown that a person’s perception of personal risk, or “the individual’s expectation of personal exposure to death, injury, or property damage” is highly correlated with disaster response [50]. In this stage, also known as personalizing risk [38], the individual determines the likelihood of personal consequences that could result from the threat and asks oneself the following: “Do I need to take protective action?” At this point, which is also discussed in human factors research as “situation awareness” [75], the individual tries to gain insight on the potential outcomes of the disaster and what those potential outcomes mean for his safety. The internal dialogue that takes place at this stage can be thought of as mental simulation or mental modeling [56], in which the individual develops a mental model of what is going on in his environment, based on perceived cues, and then expands the mental model to predict the personal consequences of the event. The more certain, severe, and immediate the risk is perceived to be, the more likely the individual is to perform protective actions [76]. In the third and fourth stages, the individual engages in a decision-making process to identify (1) what can be done to achieve protection; and (2) the best available method of achieving this
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Environmental cues
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Social context
Information sources
Information channels
Message content
Receiver characteristics
Predecisional processes
Threat perceptions
Protective action perceptions
Stakeholder perceptions
Risk identification: “Is there a real threat that I need to pay attention to?” Information needs assessment: “What information do I need?” Risk assessment: “Do I need to take protective action?”
Protective action search: “What can be done to achieve protection?”
Protective action assessment: “What is the best method of protection?”
Communication action assessment: “Where and how can I obtain this information?”
Communication action implementation: “Do I need the information now?”
Protective action implementation: “Does protective action need to be taken now?”
Fig. 58.2 The protective action decision model [73]
protection. The outcome of the third stage is a set of possible protective actions from which to choose. After establishing at least one protective action option, individuals engage in the fourth stage of the PADM: protective action assessment. This stage involves assessment of the
potential option(s), evaluating the option(s) in comparison with taking no action and continuing with normal activities, and then selecting the best method of protective action (e.g., evacuating, sheltering in place). Once an action is chosen, the end result of stage 4 is an adaptive plan,
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which can vary in its specificity. For example, for households under threat conditions, [a]t a minimum, a specific evacuation plan includes a destination, a route of travel, and a means of transportation. More detailed plans include a procedure for reuniting families if members are separated, advance contact to confirm that the destination is available, consideration of alternative routes if the primary route is unsafe or too crowded, and alternative methods of transportation is [sic] the primary one is not available [50].
After a protective action is chosen and the adaptive plan is developed, the final step in the decision process involves the implementation of the protective action plan or strategy. Here, the individual asks whether the protective action needs to be taken now. If the answer is yes, then s/he engages in that action. However, Lindell and Perry [50] note and other studies confirm [18, 77, 78] that individuals are still likely to delay the performance of protective action, even when the threat is perceived as imminent. Passage through these stages is often problematic. If at any stage the individual is uncertain about the answer to a question, s/he engages in additional information-seeking actions. Information seeking is especially likely to occur when individuals think that time is available to gain additional insight on the question at hand. If information seeking is successful, in that the person at risk judges s/he has obtained enough information to answer the question, then the individual moves on to the next stage or question in the decision-making process. However, if the information-seeking action is unsuccessful, there will be additional searching for information as long as s/he is optimistic that other sources or channels can help [50]. If s/he is pessimistic regarding future information seeking success, s/he is likely to attempt to decide on a protective action based solely on whatever information is available. This description is not meant to imply that decision processes are linear and straightforward. For example, information feedback loops allow for the receipt of new environmental and social cues after initial engagement in information-
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seeking actions. An individual who gains additional information is likely to carry on with the decision-making process until s/he is ready to implement a protective action. Additionally, individuals do not have to go through each stage or question in the decision flow chart [50]. For example, if an individual is presented with information about the event from a credible source or if s/he is ordered to evacuate, s/he may move on to later stages in the decision process rather than going through each one in succession. This decision-making framework describes the process of how individuals respond to disasters. Even though the focus of the models discussed so far is on community-wide disasters, it is clear that the models also apply to decisionmaking during more localized types of events, such as building fires.
Engineering Implications of the Protective Action Decision Model Engineers must understand that response to fires and other disasters is the result of a process. Individuals or groups of individuals engage in a decision-making process (i.e., a series of steps) before they respond, based upon the cues presented from their environment (including information), the social context, personal characteristics, past experience [23, 76, 79–81] and hazard knowledge [82]. With this understanding, the engineer should recognize that occupants of a building are unlikely to evacuate immediately, and simultaneously, and instead, recognize that occupants are required to receive and process information on an individual- (or group-) basis. Also important is that if, at any time in the process, the answer to a decisionmaking question is unclear (See Fig. 58.2), then the individual will engage in informationseeking actions. Information-seeking actions take time to complete and delay the occupant from reaching safety. Additionally, just because cues or information are provided to building occupants does not necessarily mean that they will act appropriately.
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The cues or information must be perceived (e.g., heard or seen), paid attention to, and then comprehended first before any actions take place. Therefore, engineers must ensure that any information meant for building occupants must be provided in such a way to ensure that these three processes take place. One example of this is to ensure that the public address announcements disseminated in a building fire are set to an appropriate volume level such that all occupants in the buildings can hear them; and if not and in order to reach occupants with hearing disabilities, other means of disseminating the information are used (e.g., visual signage) [83]. Engineers should also acknowledge that occupants must perceive a credible threat and personalize the risk before taking action. Research has shown that individuals are more likely to identify and personalize the risk if they perceive a larger number of cues [43, 84, 85] that are intense or extreme in nature [86, 87]. In building fires, for example, occupants who witness heavy, thick, black smoke that decreases visibility and irritates the eyes are more likely than those noting less intense cues to realize that a serious event has taken place that puts them in danger [88]. However, it is always the responsibility of the engineer to protect building occupants, which includes limiting their exposure to fire effluent. The main way to prompt safe, effective, and appropriate action from building occupants is to disseminate warning messages during fire emergencies that will positively influence risk identification and assessment. Research has shown that a successful warning message contains the following factors or qualities: • Specific about the threat and the risk involved [89–91], • Repetitive [50], • Consistent [92], • Disseminated via multiple channels [93], • Provided by a credible source [49, 76, 81, 94]. Source credibility is defined in terms of the source’s expertise, including access to special skills or information, and trustworthiness, or the perceived ability to communicate information
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about the disaster without bias [50, 54]. Source credibility can differ depending upon a number of factors, including the type of disaster, characteristics of the source, such as social role and believability, and characteristics of the warning receiver, such as past experience in disasters and social location [95–100]. For some warning receivers, credible sources may be friends and relatives, and for others, credible sources may be disaster authorities, such as government officials [101, 102] or fire fighters [38]. As far as content, a warning message should contain five important topics to ensure that building occupants have sufficient information to respond with little or no additional delay and information seeking [38, 103]. These five topics, labeled here as the five W’s of any effective warning message, are as follows: 1. Who is providing the message? (i.e., the source of the message, which should be perceived as credible by the building occupants) 2. What should people do? (i.e., what actions occupants should take in response to the emergency and if necessary, how to take these actions) 3. When do people need to act? (i.e., in rapidonset events, the “when” is likely to be “immediately”) 4. Where is the emergency taking place? (i.e., who needs to act and who does not) 5. Why do people need to act? (including a description of the hazard and its dangers/ consequences). Another way to prompt safe, effective, and appropriate action from building occupants is through training. An individual’s past experiences in emergencies, specifically the actions that s/he has performed previously, can influence the actions that s/he considers as options during the current emergency [50, 56, 104]. The individual uses memories of the protective actions s/he performed in the past as options for actions to perform in the current emergency. Similarly, an individual’s emergency-based training and knowledge, for example, knowledge about evacuation procedures, can influence the options that s/he develops during an emergency [78, 105–108].
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Relating Theory to Practice— Protective Actions in Fires As shown in the earlier section, research has established the theoretical process through which community residents or building occupants make decisions in response to fires and other disasters [50]. However, these theories do not provide sufficient information on the specifics or the types of protective actions in which occupants engage and why they engage in these types of actions during fire emergencies. Research has been performed that identifies the types of actions that people perform during a building fire evacuation, with a focus on the pre-evacuation period. Both summary research [77, 87, 109] and research on specific incidents [1, 3, 18] highlight certain actions in which occupants are likely to engage. These actions, depending upon the situation, can include seeking information, waiting, investigating the incident, alerting others, preparing for evacuation (or deciding not to evacuate), assisting others, fighting the fire, and searching for or rescuing others. One factor that has been used to differentiate one set of actions from another set of actions is the type of building in which the emergency occurs. For example, individuals who are at home (especially at night) may engage in a different set of preparatory actions than individuals who are awake in their offices when the alarm sounds, for example. Therefore, in this section, studies that have been performed on different types of structures will be presented to identify the actions in which individuals most frequently engaged.
U.S. and UK Residential Studies One of the first studies of behaviors performed during residential fire evacuations was by Wood [15]. The study involved 2193 fire-department conducted interviews with residents from 952 residential fire incidents in Great Britain. Within the same decade, Bryan [14] also studied residential fire incidents by analyzing on-scene interviews
E.D. Kuligowski
conducted by fire service personnel with 584 participants from 335 fire incidents in the United States. Both researchers found that behavioral responses to fires could be categorized into the following actions: notifying others, searching for the fire, fighting the fire, calling the fire department, getting dressed, getting the family, asking others to call the fire department, gathering personal property, closing the door to the fire area, turning off appliances, doing nothing, attempting to evacuate, and evacuating; among other more specific actions. The most frequent behavioral responses to fire in both the UK and US studies were identified as evacuating the building, fighting or containing the fire, and notifying other individuals or the fire brigade. Bryan and Wood also organized these actions into first, second, and third actions in an attempt to begin to order the actions taken during the residential evacuation process. In both studies, it was found that investigation actions, such as searching for the fire; notification actions, such as notifying others, pulling the fire alarm or getting family; and preparation actions, such as fighting the fire, turning off appliances, and getting dressed; were performed. In the U.S. study, Bryan [14] indicated that the action of “investigate” was very common as a first action by 45 % of occupants in the sample and as a second action by 23 %. These authors also report that actions such as “mitigate the fire,” “help others,” and “call for help” were in the middle of the actions sequence, and “escape” or “go for help” were at the end of the usual sequence of four to five actions. “Call the fire brigade” was generally a fourth action, and “fight the fire” usually occurred between the second and sixth actions. Bryan [14] and Wood [15] also identified actions that were specifically linked to engagement with the fire and/or subsequent toxic products produced by the fire during these residential evacuations. Some percentage of occupants in both studies engaged in fire-fighting behavior, re-entry behavior (i.e., they returned to the structure after leaving), moved some distance through smoke, and/or turned back (i.e., stopped their movement to or into smoke and redirected
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based on environmental conditions) [77]. These results show that individuals were likely to engage in potentially risky behavior, such as fire-fighting or re-entry behavior, during the fire incident. For more information on the psychophysical effects of smoke on individual movement and actions, including the visibility distances in which people moved through smoke or turned back, please see Chaps. 61, 63, and 64.
MGM Grand Hotel Fire Analysis was also performed on the behaviors engaged in during the MGM Grand Hotel fire in Clark County, Nevada, on November 21, 1980 [110]. This hotel fire involved both injuries and fatalities among the guests. The management of the MGM Grand Hotel, and the Clark County Fire Department, in cooperation with the National Fire Protection Association (NFPA) [111], conducted an intensive study of the guests registered in the hotel for the evening of November 20 to 21, 1980, to determine how the occupants became aware of the fire incident and their behavioral responses. The MGM Grand Hotel fire was discovered by an employee of the hotel who entered the delirestaurant located on the casino level of the hotel at approximately 7:10 a.m. on November 21, 1980. The fire reached a flashover condition in the deli area, immediately spread from east to west through the main casino area, and extended out the west portico doors on the casino level immediately following the arrival of the initial fire department personnel. The heat and smoke extended from the casino area through seismic joints, elevator shafts, and stairways throughout the 21 residence floors of the hotel. The heat was intense enough on the 26th (top) floor to activate automatic sprinkler heads located in the lobby area adjacent to the elevator shafts. Due to the rapid early evacuation of the telephone staff, guests in their rooms were not alerted by the hotel public address system nor the local fire alarm system. Guests who were alerted early in the fire incident, or guests already
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awake and dressed, were able to escape prior to the smoke conditions becoming untenable on the residential floors. Guests alerted later in the progression of the fire incident remained in their rooms or moved to other rooms, often with other occupants. The flame propagation did not extend above the casino level, with the exception of very minor extension into two guests’ rooms on the 5th floor. The fire resulted in 85 fatalities to guests and hotel employees in the following areas of the hotel [110]: 14 persons were found on the casino level, 29 persons were found in guest rooms, 21 persons were found in corridors and lobbies, 9 persons were found in the stairways, and 5 persons were found in elevators. The victims were located on the casino level, and the 16th through 25th floors, with the majority of fatalities found between the 20th and the 25th floors. Various estimates have been provided of the number of guests and fire department personnel that suffered injuries at the MGM Grand Hotel fire. Morris [112] indicated that 619 persons were transported to hospitals from the fire scene, and another 150 guests were treated at the Las Vegas Convention Center, where the survivors had been transported. Behavioral responses from survivors of this fire were elicited from 554 returned mailsurveys. Similar to the residential studies, one topic of interest was to collect information on the types of behaviors in which survivors engaged. The initial five behavioral responses of the 554 guests as elicited from the NFPA questionnaire study are presented in Table 58.1. The five most frequent first behavioral responses were “dressed,” “opened door,” “notified roommates,” “dressed partially,” and “looked out window.” The guests involved in the first responses were predominantly engaged in attempting to define and structure the fire cues relative to the severity of the threat to themselves. Only a small percentage, approximately 8 % of the study population, initiated or attempted to initiate their evacuation behavior as the first response. Examination of Table 58.1 indicates the five most frequent behavioral responses reported by guests as second actions were “opened door,”
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Table 58.1 Compilation of the initial five actions of guests in the MGM grand hotel fire incident [111] Actions Dressed Opened door Notified roommates Dressed partially Looked out window Got out of bed Left room Attempted to phone Went to exit Put towels around door Felt door for heat Wet towels for face Got out of bath Attempted to exit Secured valuables Notified other room Returned to room Went down stairs Left hotel Notified occupants Went to another exit Went to other room Went to other room/others Looked for exit Broke window Offered refuge in room Went upstairs to roof Went to balcony Other Total (percent) Number of guests
Percent of population First Second 16.8 11.6 15.9 11.7 11.6 3.0 10.1 7.5 9.7 5.7 4.5 – 4.3 5.4 3.4 3.6 2.5 10.3 1.6 2.5 1.3 2.3 1.3 3.7 1.1 – 1.1 3.0 – 6.8 – 3.4 – – – – – – – – – – – – – – – – – – – – – – – – 14.8 19.5 100.0 99.1 554 549
“dressed,” “went to exit,” “dressed partially,” and “secured valuables.” Whereas approximately 40 % of the population was engaged in evacuation or sheltering actions by the second act, others were engaged in protective actions. Approximately 19 % of the study population reported they were involved in the dressing actions, 10 % were involved in notification activities, and 7 % were gathering valuables prior to initiating evacuation or seeking refuge. Examination of the third behavioral responses of the 537 guests in the study population indicated the responses of the guests generally progressed to evacuation, attempted evacuation,
Third 6.5 6.7 – 4.5 – – 8.1 – 9.5 3.0 – 6.3 – 5.8 4.3 2.2 3.9 3.9 3.4 3.0 – – – – – – – – 28.9 96.9 537
Fourth – 3.4 – – – – 2.4 2.8 16.1 6.8 – 4.6 – 4.3 – – 8.4 5.4 2.6 – 3.6 3.6 3.4 2.4 – – – – 30.2 90.4 501
Fifth – – – – – – 2.0 – 6.7 7.7 – 7.9 – – – – 4.1 21.3 2.0 – 4.8 3.6 8.7 – 4.3 1.8 2.9 1.8 20.4 79.6 441
and notification responses. Thus, approximately 25 % of the MGM Grand Hotel fire incident study population was involved in evacuationrelated behavioral responses, and approximately 10 % of the guests were involved in attempted evacuations as identified by their third responses of “attempted to exit” and “returned to room.” The alerting and notification actions of the guests were involved with the third behavioral responses of “notified occupants” and “notified other room.” The fourth behavioral responses of the guests in the study population indicated a progression of the guests to evacuation, attempted evacuation,
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Table 58.2 Activities prior to evacuation reported in telephone survey by survivors of WTC 1 and WTC 2 [1] Activities before evacuation Talked to others Gathered personal items Helped others Searched for others Talked on telephone Moved between floors Shut down computers Continued working Fought fire or smoke Other activities
Percent reporting the activity (n ¼ 440 in WTC 1) (%) 70 46 30 23 16 8 6 3 6 25
Percent reporting the activity (n ¼ 363 in WTC 2) (%) 75 57 34 32 16 8 7 6 1 20
Source: NIST WTC Telephone Survey Data Note: Total does not add up to 100 % because respondents may have taken multiple actions
and self-protection or room refuge procedural responses. Additionally, the fifth behavioral responses of the guests were primarily for selfprotection, including the improvement of the room as an area of refuge, and evacuation behavior. Overall, in this hotel fire, hotel guests were more likely to take initial actions investigating, notifying others, and preparing for evacuation, which in this case involved getting dressed. This is similar to the residential studies, likely because a hotel and a residence involve similar living circumstances. In both cases, individuals may be alerted to a fire when they are sleeping— meaning that they will require additional time to prepare for evacuation; i.e., getting dressed themselves or getting other family members dressed. Then, after initial investigation, preparation and warning activities ended, and hotel guests engaged in protective actions and evacuation.
2001 World Trade Center Disaster (Office Buildings) Different from a residential or hotel fire, studies were performed on the 2001 World Trade Center (WTC) evacuation of the two office towers [1, 22, 30]. On September 11, 2001, two commercial airplanes flew into World Trade Center (WTC) Towers 1 and 2 and initiated full building
evacuations from both 110-story office buildings. At 8:46 am, Flight 11 slammed into the north face of WTC 1, disconnecting the entire population above the 91st floor from any way out of the building. It was at this moment that the largest full-scale building evacuation in history began for occupants who had the opportunity to evacuate from both WTC 1 and 2. None of them knew, however, that another commercial jet was on its way—one that was heading straight for WTC 2. Sixteen minutes after WTC 1 was struck and after one-third of WTC occupants had already evacuated,3 Flight 175 sliced into floors 78 to 84 of WTC 2 leaving only one of the three stairs available for evacuees above the 78th floor. Occupants who could evacuate continued to pour from the structures until the towers eventually succumbed to structural collapse (WTC 2 collapsed at 9:58:59 am and WTC 1 collapsed at 10:28:22 am). The frequency of actions performed in the 2001 WTC disaster by occupants evacuating Towers 1 and 2 was reported by Averill et al. [1] and Day, Hulse and Galea [113], shown in Tables 58.2, 58.3 and 58.4 below. The focus here is an understanding of the actions taken before evacuation movement in the stairs began. As part of the NIST WTC study [1],
3
21 % from WTC 1 and 41 % from WTC 2.
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803 interviews were conducted via telephone using a computer program that allowed the interviewers to collect data electronically, also known as computer-assisted telephone interviewing (CATI). Quantitative data was captured via an interview schedule designed to measure the following five primary areas: preparedness and training, initial September 11 experience, interim September 11 experience, evacuation experience on September 11, and respondent demographics. The two populations selected for study were all of the people who worked in WTC Tower 1 and WTC 2 who were in the buildings between 8:46 am and the time at which their respective Tower collapsed on September 11, 2001. In the UK, the WTC evacuation was also studied as part of an in-depth research project carried out by the Project Highrise Evacuation Evaluation Database (HEED) research team [22]. Project HEED was a 3-year project to explore human behavior associated with the evacuation of high-rise buildings. The basis for this project was an analysis of the 2001 WTC disaster through both face-to-face interviews with survivors and computer simulation of the evacuation. The project resulted in over 250 face-to-face or telephone interviews with survivors from the 2001 WTC disaster, collected to both inform the development of future
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building regulations and evacuation computer models and to make data available to bona fide building safety researchers in countries around the world. In both cases, the studies’ presentation of actions taken was not ordered in any way (i.e., first, second, and third actions); however, both studies provide an understanding of the actions that were most frequently performed from one tower to another. Averill et al. [1] presented a list of the “general” pre-evacuation actions performed in both towers, shown in Table 58.2, below, acknowledging that not all actions were covered by these categories by including the “other” category at the end of the list. The majority of individuals in both towers engaged in actions that involved talking to others (70 % in WTC 1 and 75 % in WTC 2) and gathering personal items (46 % in WTC 1 and 57 % in WTC 2). Additionally, about a third of occupants in both towers engaged in helping others and searching for others. Day, Hulse and Galea [113], on the other hand, grouped pre-evacuation actions into two different categories: information tasks and actions tasks (shown in Tables 58.3 and 58.4). Information tasks, which involved action taken to obtain or receive information, were further divided into three different areas: seeking
Table 58.3 Comparisons of information tasks by tower [113] Information tasks Seek information tasks Environmental (e.g., window) WTC colleagues/friends Waited for further info People outside WTC (e.g., called family, friends) TV/internet/radio Professional bodies (e.g., port authority, security, police, fire) Communication tasks Instruct others to evacuate Inform others of my situation Debate/challenge Receive information tasks Non-professionals (e.g., managers, family) Professionals (e.g., PA announcements, security, police, fire) WTC1: N ¼ 119, WTC2: N ¼ 121, PPTs participants
WTC1 % PPTs
Freq
WTC2 % PPTs
Freq
53 36 13 8 2 2
66 44 17 17 2 2
83 27 8 3 6 5
142 46 11 4 7 6
34 17 3
51 25 5
40 30 11
89 63 15
12 8
16 9
23 19
35 31
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Table 58.4 Comparisons of action tasks by tower [113] Action tasks Personal tasks Collected personal items (e.g., wallet) Went to toilet/comfort break Changed footwear/glasses Emergency tasks Evacuation facilitation (e.g., searched office/floor, forced exit open) Waited for others so evacuate together Gave others physical assistance (e.g., carried/gave first aid) Protective action (e.g., took refuge, blocked/sealed cracks, got under smoke, made masks) Distributed useful items (e.g., mobiles, masks, bottled water) Work tasks Secured items/areas (e.g., locked files, bank vaults) Tidied desk Latent tasks Denial/Froze/continued working Travelled to another area/floor/stairwell (reason unknown)
WTC1 % PPTs
Freq
WTC2 % PPTs
Freq
60 3 3
141 3 3
63 2 1
145 2 1
19 7 6 7
25 8 7 8
26 14 3 3
47 17 4 4
0
0
1
1
7 3
10 5
3 8
4 14
2 4
2 5
13 3
17 4
WTC1: N ¼ 119, WTC2: N ¼ 121, PPTs participants
information, communicating with others, and receiving information. The action tasks, a term which was not specifically described by the authors, was subdivided into additional categories: personal, emergency, work and latent actions. According to this study, and similar to Averill et al. [1], the majority of tasks undertaken by the participants were “Information tasks” (54 % in WTC 1 and 63 % in WTC 2)—specifically the action termed as “seeking information”. Additionally, the most common “Action Tasks” performed by occupants in each tower were “Personal Tasks”—accounting for 68 % of the “Action Tasks” in WTC 1 and 57 % in WTC 2. Personal tasks involved occupants collecting or packing up their personal possessions before evacuating the building. Day, Hulse and Galea [113] also tracked the number of tasks completed by each participant in the study. The range of tasks completed was between 0 and 13 in WTC 1 and 2 and 21 in WTC 2; with an average number of tasks completed in WTC 1 of 3.96 and an average number of tasks completed in WTC 2 of 5.86.
Table 58.5 Range of times associated with WTC pre-evacuation actions [30] Action Preparation (Action task, personal) Communicating with others (Information task) Looking out the window (Information task) Helping, by authorities (Action task, emergency)
Range of timing (minutes) 0.5–5 3 1–5 4–10
While most empirical studies of actual incidents [114–116] and evacuation drills [117–119] provide overall timing estimates for activities in the pre-evacuation period, very few researchers discuss times associated with specific pre-evacuation actions. From analysis performed by this author on the Project HEED database [30], pre-evacuation action times were reported by some WTC occupants and are presented in Table 58.5 as a range of times (minutes) for each action type.
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University Library Building in the Czech Republic From a study of an unannounced evacuation drill in a university library in the Czech Republic, Galea et al. [120] collected data on the number, type and duration of pre-evacuation actions. To begin the evacuation, the alarm system, consisting of a combination of tones, recorded voice and live voice messages, was activated. The recorded voice message began by stating the word “attention” multiple times, followed by a declaration that an emergency situation was taking place. The message also instructed people to prepare for evacuation and wait for further instruction. Two live messages were also disseminated during the drill. The message made it clear that the evacuation instruction was directed at occupants in the library building only and then gave instructions on the routes to take, depending upon where the individual was located within the library building. The live messages also warned individuals not to use the elevators, and to only use the stairs to evacuate. On the day of the trial, the alarm system failed to operate in certain parts of the library building. Some individuals heard the alarm tone and announcements and some did not. In the places where the alarm failed to function, the evacuation was initiated by staff intervention. Video observation and analysis of the evacuation drill allowed for the collection of pre-evacuation action (or task) type and duration. In this study, similar to the WTC study presented above, pre-evacuation actions were categorized in two different ways: information tasks (or actions that involve the occupant seeking, providing or exchanging information regarding the incident) and action tasks (or all other types of pre-evacuation actions, e.g., preparation, fighting the fire, helping others, etc.). Throughout the evacuation, 235 information tasks and 268 action tasks were completed; the average number of information tasks (per person) was 3.7 and the average number of action tasks (per person) was 4.3. On average, an evacuee in this study
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engaged in a total of 8.0 tasks prior to beginning evacuation movement (e.g., into the stairs). There were differences in task numbers between evacuees who received staff intervention and those who were alerted by the alarm system. For those who were alerted via staff intervention, the average number of information tasks was 2.0 and the average number of action tasks was 3.6; for an average number of total tasks performed prior to beginning evacuation movement of 5.6. For those alerted via the alarm system, the average number of information tasks was 7.4 and the average number of action tasks was 5.7; for an average number of total tasks of 13.1. The authors of this study noted that individuals alerted by the alarm engaged in twice as many tasks during pre-evacuation than individuals notified by a member of staff. Work was also performed to measure the time to undertake each individual task from the video footage [120]. The analysis showed that the average duration of a single action task was 6.4 s and the average duration of an information task was 9.7 s (independent of how an evacuee was alerted to the incident). The authors concluded that, in this study, an information task took 1.5 times as long as an action task. Analysis of task timing was also performed by comparing the two groups alerted to the drill via different means. For the population alerted by staff intervention, the average time for an action task was 6.5 s and for an information task was 6.7 s. On the other hand, for the population alerted by the alarm system, the average time for an action task was 6.4 s and for an information task was 9.9 s. The authors of this research noted that there was a considerable difference in the average time to complete information tasks among the two populations—showing that the population alerted by the alarm system took a longer time (on average) to complete information tasks in comparison to the population alerted by staff intervention. This highlights the greater influence of in-person, official communication/ instruction on a faster response time when compared with an alarm system.
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University of Greenwich Dreadnought Building (Educational and Library Services Building) A study was performed on an evacuation of a university building known as the Dreadnought building, located on the University of Greenwich campus in London, UK [121]. The Dreadnought building is a three-story structure used for a variety of purposes, including library services, student computing facilities, and a small cafeteria. Data were collected by research staff located at 15 key locations throughout the building via handheld video and manual observations. Additionally, questionnaires were handed out to all evacuees to collect information about their experience during evacuation. Last, 62 closed-circuit cameras were used to gather data on the starting locations of evacuees, their behaviors/actions, and response times. Because of camera locations, initial responses and times could only be captured for 247 evacuees of this building: 228 students and 19 members of staff. In this building, once the alarm sounded, nominated members of staff swept each room, “forcing students to leave their work and belongings, and informing them of the routes they should adopt” [121]. During analysis, a dictionary of potential actions was created based upon examination of the video evidence from the evacuation. The list of actions comprised of the following: • Evacuate immediately • Perform a computer shutdown • Disengage socially • Collect items, including bags, coats, paperwork, etc. • Investigate the incident. Additionally, it was found that 27 % of the participants of this study completed one or no actions prior to beginning evacuation, 55 % completed two actions, and 18 % completed three or more.
Engineering Implications of Actions Taken During Evacuation Engineers should understand that actions, both information-related actions and protective
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actions, are performed during fire evacuation. Depending upon the circumstances, these actions can take a considerably long time to complete and will contribute to the time to reach safety. First, engineers must account for these actions in some way when calculating evacuation timing in a proposed design building fire. Actions and delay times associated with these actions can be especially important in certain types of buildings, where individuals are likely to engage in certain types of lengthy actions; i.e., those in which people may be asleep or located on upper floors of uniquely tall buildings. Many times, when performing an evacuation calculation, engineers are asked to provide a specific pre-evacuation time period or distribution as input. Engineers should choose a time that is based upon specific scenarios and resulting occupant actions (and action timing). Additionally, to improve occupant response, engineers should account for evacuation actions when developing fire evacuation plans for buildings. As stated earlier, research has shown that providing specific warning information in certain ways or providing leadership to prompt evacuation response could reduce the need for information seeking, and even the performance of certain protective actions. If engineers understand which evacuation actions they should anticipate in a specific building or fire scenario, they can formulate plans that are successful in decreasing delays caused by evacuation actions. Therefore, it is important to first understand that types of actions that individuals have engaged in previous fires and how these actions can vary from building to building, and from fire event to fire event.
Relating Theory to Practice—The Sequence of Protective Actions in Fires Beyond identifying the types and percentages of actions, including the percentage of actions that were performed first, second, and third, research has been performed to identify the sequence of actions taken in different types of fires. Canter, Breaux, and Sime [78] developed decomposition diagrams for various types of fire events that
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identify the sequence of actions. The study was conducted in the United Kingdom on domestic fires (14 domestic fires and the acts of 41 persons), multiple-occupancy fires (eight multiple-occupancy fires and the acts of 96 persons), and hospital fires (6 hospital fires and the acts of 61 persons). All persons in this study were interviewed about their experiences in the fire; first asking them to give a detailed account of everything that happened starting from the time at which they considered that something out of the ordinary might be occurring. Once individuals had given full accounts, interviewers questioned respondents on certain issues, including recognition of the fire event, location of the occupant, ongoing behavior, sequence of actions, perception of the situation, past experiences, and background information. The results of this analysis were the development of decomposition diagrams. These diagrams are provided here, as Figures 58.3, 58.4, and 58.5. Dashed circles indicate the acts which occurred with a lower frequency. The relationships between acts are indicated by arrows; and if actions are repeated, the circle (representing the action) would have a looped arrow coming back on itself. The numbers next to an arrow refer to the strength of the association. The higher the association number, the greater the association is; i.e., the more likely it is that given the performance of one act, the next action (specified) will follow. The decomposition diagram for domestic fires is shown in Fig. 58.3. The domestic diagram summarizes 1189 acts which occurred in 14 domestic fires. It outlines departure from pre-event activities, such as sleeping, to a range of other investigative, notification, and preparation activities. In these domestic fires, individuals tended to perform actions related to investigating which involved encountering or engaging with the fire in some way, and then evacuating; or discuss the situation, notify or warn others, preparing to evacuate, and then leaving the house. The decomposition diagram for multiple occupancy fires is shown in Fig. 58.4. The multiple occupancy diagram summarizes 1714 acts
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which occurred in all eight multiple-occupancy fires [78]. All fires occurred in the United Kingdom in hotel occupancies. Similar to the domestic fires, occupants went to investigate the receipt of strange noises, which led to them encountering the fire environment and/or warnings about the emergency. If direct contact with the fire environment ensued, the characteristic sequence that followed involved the occupant going to the window, shouting for help, and then being rescued. Also similar to domestic fires, occupants engaged in activities such as warning others, gathering personal items, and closing or opening windows. The decomposition diagram for hospital fires is shown in Fig. 58.5. The hospital diagram summarizes 1104 acts which occurred in all six multiple-occupancy fires [78]. The case studies covered a variety of hospital types, i.e., geriatric, psychiatric and general medicine; however, patterns were still revealed among the entire population, as a whole. Detection and investigation actions are performed relatively early in these fires, possibly because the higher spread of people in the building. Also, the sequence of actions is different in this diagram, when compared with others, due to the nature of the organizational hierarchy of the hospital. Senior nursing staff, whose job it was to investigate the fire, relay information to junior colleagues, who then had a series of actions that they performed in response. The reader should note the inclusion of process-related factors (first described in the PADM) into these action-based diagrams. For example, Figures 58.3, 58.4, and 58.5 contain circles for the receipt of cues, i.e., “hear strange noises” or “encounter difficulties in smoke”, which are not actions. Instead, these are processes in which individuals engage in order to act in a building fire. Also, all three diagrams contains circles for the interpretation of cues, i.e., “misinterpret (ignore)”. The domestic diagram even contains an entry for “feel concern”. These entries also are not actions, but interpretations about the situation and personal risk (first described in the PADM) as direct
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Pre-event activity (typically sleeping)
1
9.84
6.26
4 Misinterpret Hear strange 4.02 (ignore) noises 0.89 0.97 5.81 1.84 0.55 5 .97 12 0 Informed . Investigate (discuss) 2 46 1.34 1.79 Dress 3.13 17 Instruct/ reassure 2
2.68
0.89
Wait for person to return
14
8.88
0.89 Feel concern
3 1.34 10
21
2.24
2.12
Encounter smoke/fire
0.45
3.58
0 Fight fire
1.34 Go to neighbors or return to house
18
Warn (phone fire brigade)
1.72
16
1.79
0.89
Encounter difficulties in smoke
3.58 22
20 Close door
13
0.45
1.79 3.90
0.45
15 0.89
19
8
Enter room of fire origin
Evasive
Rescue attempt
Search for person in smoke
6
14.3 4.47
4.47 Leave house
Note: Numbers on lines indicate strength of association between two acts linked by arrow
25
2.24
4.47
Meet fire brigade on arrival
24 9.39
End of involvement
*
Fig. 58.3 Decomposition diagram—domestic fires [78]
influences of actions. These diagrams truly represent the first attempt at developing an inclusive conceptual model of evacuation actions—that identify not only the action, but also the processes of receiving cues and processing information in order to act in an emergency.
Patterns of behavior exist across all three diagrams (of varying occupancy type). What is important to note here is that certain actions take place in specific locations within the evacuation sequence. First, immediately after the receipt of initial cues, individuals were more likely to
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Pre-event (typically sleeping)
1 24.70 Hear strange noises
1.81 5.20
2 2.68
14.75
6 11.21
3.09
See smoke/glow 2.96 Encounter . 4 92 smoke with difficulties
3
5
Misinterpret (ignore)
Seek information/investigate 1.96 . 1 38
4.02 2.68
0.34 Note persistence of noise 17
3.20
5.36 0.84
4
Re-enter room
12 Close doors
1.73
Warn others
4.05
4.47
3.13 Receive instructions
9
1.57
18
14
1.34 1.78 15 6.37
1.78
2.23
Cope (open window)
2.60
4.02 10
Dress/ gather valuables
4.92
11
6.70
3.57
4.85
Leave immediate area
24
4.92
Seek/receive assistance 11.77
Duty related (clearing up, check lists, post fire actions)
Evasive
1.78
7
6.37
Receive warning
Assess fire state
2.91 8.05
16
23 Out of fire
20 25.49
6.70
Note: Numbers on lines indicate strength of association between two acts linked by arrow
*
End of involvement
Fig. 58.4 Decomposition diagram—multiple-occupancy fires [78]
‘investigate’ the situation and/or ‘misinterpret’ (or ignore) cues that they received early on in the event. Then, after seeing smoke, one of three ‘prepare’ sequences were more likely to be performed, including ‘instruct’, ‘explore’, or ‘withdraw’. Finally, depending upon the particular preparation action chosen, occupants were more likely to engage in the following actions: ‘wait’, ‘warn’, ‘fight’ or ‘evacuate’.
Engineering Implications of the Linkage of Actions Taken During Evacuation Actions follow a specific pattern across all types of building fires, and an understanding of the patterns of behavior is important when attempting to accurately model an evacuation scenario (i.e., the methods outlined in Chap. 57). Take for example, an office building
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Fig. 58.5 Decomposition diagram—hospital fires [78]
that houses a child daycare for its employees on the 10th floor of a 20-story building. It will be important for engineers to understand that occupants will spend some period of time on their floors investigating the situation and making decisions as to what needs to be done; i.e., if evacuation is necessary or not. Therefore, a determination of the fire and smoke conditions on any occupied floor is important immediately after the fire begins. Next, the engineer should understand that some proportion of occupants may travel to the 10th floor to rescue their children from the daycare center, requiring an assessment of the environmental conditions on that
floor for some time period after investigation is complete (i.e., the protective action phase). An understanding of the behavioral process is important also for the design of evacuation procedures for a building. For example, the presence of staff as well as a building alarm for alerting the population of a building fire may decrease time spent investigating and deciding to evacuate. If staff members instruct building occupants to evacuate, especially if they represent a credible source to the population, then building occupants may be more likely to begin evacuation sooner than if left to their own decisions [30].
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Relating Theory to Practice—Group Behavior Research also exists to explain observations from numerous fire studies that people tend to travel or converge into groups during emergencies. There are theories that support the idea that individuals come together and form a group before evacuating, and then continue their evacuation together until they reach safety. This behavior, labeled as affiliative behavior [107], is described first in this section. Individuals also come together in groups to help one another. Helping behavior is found in almost every disaster, and an overview of this behavior will also be provided in this section. Finally, individuals have been found to converge together in groups during emergencies in order to take refuge from the fire conditions. Convergence groups, or clusters as termed by Bryan [77], were found in situations whereby individuals attempted evacuation and decided that is was not possible at the time.
Affiliative Behavior According to Sime, who developed the Affiliative model, there is a relationship between people and their physical settings [107]. This model assumes that individuals with close psychological ties will attempt to escape with other group members during an emergency evacuation. Through his study of the Summerland fire, he found that nucleus family members were more likely than others to maintain group ties during travel to and through exits. Mixed groups, on the other hand, including friends and/or relations, did appear to have been less concerned with maintaining group ties during evacuation than they might have under normal circumstances. Proulx also found this trend in group behavior while studying evacuation timing in apartment building evacuations [122]. Through the analysis of video tapes, it became apparent that people traveled in groups during evacuation: families with children would typically evacuate in a close group with an adult carrying the smallest
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child. However, family groups would split slightly when traveling with children who were a bit older in age. Additionally, seniors also traveled in groups of two or three; noting that they would exit their apartment and gather to discuss the drill, finally proceeding to evacuate together. Overall, Proulx found that 62 % of the occupants (in the four buildings studied) evacuated in groups. One important aspect to note is that Proulx also monitored the speed of movement of building occupants and found that groups tended to assume the speed of the slowest person, which in many cases in the apartment buildings studied were young children or older adults. Also, people tended to stop to converse during evacuation, rather than maintain the same speed throughout the entire evacuation.
Helping Others Occupants also help one another during building emergencies, bringing people together in groups at one time or another. Analysis of building fires [77, 78, 108] and community-wide disasters, such as tornadoes [123, 124] and hurricanes [125, 126], provide many examples of instances where evacuees are often the first responders in any emergency. For example, Johnson, Feinberg and Johnston’s study [127] of the Beverly Hills Supper club event (where a fire broke out in a nightclub in Kentucky in 1977, causing 165 deaths and over 200 injuries) showed that people put themselves in what they categorized as “grave danger” while assisting others in their group—“at times, returning to the burning building to search for loved ones; staff performing heroic acts while trying to save their clients”. Aguirre et al. [128] through their study of another nightclub fire (i.e., The Station Nightclub Fire), which occurred at approximately 11:09 p.m., on February 20, 2003, in West Warwick, Rhode Island [129], found evidence that people cooperated and took care of one another in their group during and after the evacuation, which was a key aspect of their survival. Drury, Cocking, and Reicher [32] discuss the reasons why helping behavior occurs in
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emergencies. They claim that people help others in moments of crisis not only because they know and care about each other, but also because individuals have “internal cognitive categories” that allow identifications with others in certain contexts. In other words, an emergency requires individuals to redefine the situation collectively (as discussed in an earlier section of this chapter), and through this redefinition, individuals can form a sense of ‘we-ness’. In emergencies, the redefinition of most situations, especially building fires, can be one where the evacuees are ‘all in this together’ or ‘all in the same boat’—i.e., in need of protection or in search of survival. This redefinition of ‘we-ness’ then lends itself to the associated behavior of helping others.
Convergence Clusters (for Refuge) The phenomenon of occupant convergence cluster formation in a fire incident was initially noticed in a study of occupant behavior in a 1979 high-rise apartment building fire [130]. Convergence clusters appear to involve the convergence of the occupants of the building in specific rooms selected as being areas of refuge, when evacuation was perceived as not possible. In the MGM Grand Hotel fire, for example, guests tended to select rooms on the north side of the east and west wings, and rooms on the east side of the south wing, due to the prevailing atmospheric conditions and the external smoke migration. In addition, guests reported that people had converged in rooms that had balconies and doors leading to the balconies because of the ease of ventilation, the reduced smoke exposure, improved visibility, and the communication advantages the balconies offered. The guests who reported their participation in convergence behavior in rooms provided either numerical estimates of the persons occupying the room or suite, or indicated only that “others” or “other persons” were present. Bryan also recorded the numbers of individuals in each convergence cluster, noting that the smallest number of people identified as a single cluster involved three persons and the largest was 35 persons.
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Convergence clusters may serve as an anxiety and tension-reducing mechanism for individuals confronted with a fire incident perceived as life threatening. In addition to the detailed human behavior study of the MGM Grand Hotel fire [131], the NFPA conducted a similar questionnaire study of the guests’ behavior in the Westchase Hilton Hotel fire [132] and also found the presence of convergence clusters.
Implications of Describing Behavior in Terms of the Group The main reason for understanding group behavior, especially these three examples provided above, is because groups take time to form and move together as a unit, with decisions made according to the attributes of the group and movement speeds converging to the slowest member of the group to ensure group cohesion. People have been found to delay their own safety in order to help others. Depending upon where others are located in the building, these actions can take a significant amount of time, delaying movement to safety. However, the previous sections on actions taken during an evacuation, action sequences, or a description of group processes do not yet tell the entire story of human behavior in fire. Not included are the causes of the decisions made and actions performed during fires. The studies of convergence clusters did begin to show that individuals reduce stress and anxiety in emergencies when they meet with members of their social circles; more insight is needed here. Therefore, the following section focuses specifically on the factors that affect decisions made or actions taken during a fire evacuation.
Factors that Influence Behavior in Fire People in fires very rarely act in similar manners throughout the fire event. Instead, based on various environmental and individual factors, they internalize and process the information, and then act in kind.
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Research into community disasters and building fires identifies individual and process-related factors that influence behavior [133]. There are some research that identifies the factors that influence various stages of the emergency decision-making process and others that identify factors that they claim directly influences behavior (however, it is more likely that these factors influence some stage in the decision-making process, that then influences behavior). These factors include social influence (or the influence of others in the building), stress, the built environment, leadership, and demographics (notably gender). Each factor will be described in further detail below and supported by appropriate research studies. It is important to identify these factors so that engineers can identify circumstances within fire scenarios in which certain types of behaviors (resulting in times delays) are likely to occur.
Factor 1: The Influence of Other Occupants on Behavior (Social Influence) Research has been performed on the influence of others in the building on an individual’s response to fire cues. This phenomenon is labeled here as social influence. This section will begin by describing psychological experiments performed by Latane and Darley [52] to test the influence of others on behaviors. Then, the section will describe research findings on the effect of groups (i.e., others who have formed a group tie) on the timing of actions during evacuation. Latane and Darley [52] created an experimental situation involving college students. While the students were completing a written questionnaire, the experimenters would introduce smoke into the room through a small vent in the wall. If the subject left the room and reported the smoke, the experiment was terminated. If the subject had not reported the presence of the smoke within a 6-min interval from the time the smoke was first noticed, the experiment was considered completed. In some cases, subjects were alone in the room. In other cases, subjects were
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accompanied by “actors” that were told to remain in the room for as long as the subject did, no matter what. Finally, there were cases where subjects were accompanied by other subjects (or participants) who were unaware of the purpose of the experiment. Subjects alone in the room reported the smoke in 75 % of the cases. When two “actors” were introduced in the room with each subject, only 10 % of the groups reported the smoke. When the total experimental group consisted of three unknowing subjects, one of the individuals reported the smoke in only 38 % of the groups. Of the 24 persons involved in the eight unknowing subject groups, only 1 person reported the smoke within the first 4 min of the experiment. In the situations involving subjects alone in a room, 55% of the subjects had reported the smoke within 2 min and 75 % reported smoke in 4 min. Latane and Darley reported that noticing the smoke was apparently delayed by the presence of other persons, with the median delay of 5 s for single subjects and 20 s for both of the group conditions. These results would appear to indicate the inhibiting influences that may be imposed on individuals in public places. Latane and Darley reported the behavioral response of nine of the unknowing subjects in the ten passive research situations as follows [52]: The other nine stayed in the waiting room as it filled up with smoke, doggedly working on their questionnaire, and waving the fumes away from their faces. They coughed, rubbed their eyes, and opened the window but did not report the smoke.
Latane and Darley suggest that, while trying to interpret ambiguous threat cues as to whether a situation requires a unique response, the individual is influenced by the behavioral response of others who are exposed to identical cues. If these other individuals remain passive and appear to interpret the situation as a nonemergency, this inhibiting social influence may reinforce this nonemergency interpretation for an individual. This behavioral experiment may help explain the reported tendency of persons (1) to disregard initial ambiguous fire incident cues or (2) to interpret the cues as a nonemergency condition when the fire incident occurs with a social
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audience of other persons, as in a restaurant, theater, or department store. This experimental study may also be helpful in understanding the incidents reported to fire departments that have been delayed by occupants for periods of minutes or even hours. In the report of the Arundel Park fire [32], several of the residents indicated that when they re-entered the hall after observing the fire from outside the building, they warned other residents and suggested they leave, but they were laughed at and the warning was disregarded. Latane and Darley indicated that social inhibition, diffusion of responsibility, and mimicking appear to be primarily responsible for the inhibition of adaptive and assistance behavior responses by participants in emergency situations. It would appear that the inhibition of behavioral responses in the early stages of a fire incident (when the fire incident cues are relatively ambiguous) may predispose participants to a nonadaptive type of flight behavior, since the available evacuation time has been expended. In some fire incidents it appears to be difficult to get occupants of a building to evacuate because of the variables of social inhibition and diffused responsibility. The tendency to mimic the interpretation of cues and the behavior responses of others (as established by Latane and Darley) appears to be a frequent occurrence in fire incidents in restaurants, hotels, and other places of public assembly. Similar to the studies that showed occupants were less likely to react if others were not reacting, studies have found that individuals are likely to follow others (i.e., begin their evacuation) if they witness others acting/reacting in emergencies. Occupants in the 2001 WTC disaster were likely to begin evacuation if they saw others evacuating as well, and this was especially the case if they viewed this individual (or individuals) as a credible decision-maker [30]. Even more interesting is the choice between stairs and elevators in WTC 2. As discussed earlier in this chapter, there were 16 min between the time that WTC 1 was hit and when WTC 2 was subsequently struck by the second plane. Therefore, occupants of WTC 2 who decided to
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evacuate before their own building was hit had access to both stairs and elevators. There were individuals in WTC 2 who decided to use the elevators for evacuation. One of the factors that influenced their decision was the presence of other individuals also using elevators for evacuation that day. In addition, similar to elevators, a stair route was not considered an option if no one was using it or if people encountered barriers, such as toxic conditions, that inhibited use. Research has also been performed on the effect of groups on evacuation timing, or the timing to initiate evacuation behavior. First, Aguirre, Wenger and Vigo [40] performed a quantitative study of the 1993 bombing of the World Trade Center Tower 1 (the north tower). After the bombing occurred, researchers sent 690 mail surveys to management representatives to distribute to the 776 occupants selected using a stratified random sampling technique. Overall, the total sample included 415 respondents (161 from WTC 1 and 254 from WTC 2), for an overall response rate of 53.4 %. In this analysis, the dependent variable was the length of time (in minutes) that respondents took to join the evacuation, with the independent variables of interest being group size (large group of 20 or more people [1] or not [0]) and social interaction (a scale starting with: the respondent did not know anyone in group [0] and ending with the respondent knew everyone very well [11]). Results of this analysis showed that the more people whom respondents knew in their evacuating group, and the better that they knew each one, the longer it took them to initiate their evacuation. Further, respondents in large groups took 6.7 min longer to initiate their evacuation than others. Also of interest was the influence of perceived risk on time to evacuate. The study showed that people who perceived more danger tended to initiate evacuation earlier; however, the opposite was true if they were people in large groups who knew people more thoroughly. In other words, people who perceived risk, but were in larger groups of people whom they knew well, took longer to initiate evacuation. According to the researchers, this finding is
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likely due to the importance of interacting within the group pro-socially; i.e., spending time trying to help friends or known others to decide to evacuate or prepare themselves before beginning evacuation movement. Much of the focus of this chapter has been on the behavioral actions taken during evacuation, since other chapters in the handbook focus primarily on movement (e.g., Chap. 59). However, research on social influence has also found that group formation can delay the speed at which the group moves throughout the building during an emergency [122]. This finding is a direct result of the members of the group moving at the speed of the slowest member, so as to keep together during the emergency. Other movement aspects of an evacuation are outside of the scope of this chapter and more information on these can be found in Chap. 59.
Engineering Implications of Social Influence on Behavior It is important to understand the effects of others on evacuees, especially in highly occupied buildings. In many buildings, occupants are surrounded by others, some of whom they find credible and others they may not. Social influence is especially important to remember when using current evacuation modeling or simulation tools to assess life safety of a structure. Many times, evacuation models simulate each individual (or agent) as if they are not behaviorally influenced by anyone else around them. For example, some models will randomly distribute pre-evacuation times throughout the simulated population, and, when one simulated agent in a room leaves, all other agents remain in place until their assigned pre-evacuation time has expired. This example does not represent a realistic scenario and engineers should be aware of social influence when running simulation tools. Additionally, a proper understanding of social influence can aid engineers in developing new and more effective evacuation procedures. For example, if a building manager or engineer is aware that designated fire wardens are more likely than anyone else in the building to respond
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quickly during a fire evacuation, one potential evacuation scenario might be to strategically place these “quick responders” throughout the building (rather than all in one place) to promote faster response from other building occupants. This is simply one example of many for how an understanding of social influence can also help improve occupant response through smarter emergency procedure development.
Factor 2: The Influence of Stress on Behavior (Perception) Research has also been performed to understand the effect of stress on emergency or evacuation behavior. Stress can be brought on in an emergency via several different complex conditions or states. Other than the obvious threat from physical harm due to the fire, fires can cause other conditions or states, including uncertainty/ambiguity, information overload, and time pressure. Uncertainty for building occupants [56, 134] can occur due to missing information, unreliable information (actual or perceived), ambiguous or conflicting information (more than one way to interpret the information) [87, 135], and/or overly complex information. Information overload occurs when the individual or group perceives that there is too much information to filter though in the time available, and it is posited that time pressure is necessary to produce the perception of information overload [136]. Last, with time pressure, occupants may perceive their situation as urgent and that they only have a limited amount of time to perform certain actions [137]. All of these conditions mentioned above can be considered as stressors for the building occupant [56, 134, 138, 139], leading the occupant to experience a physical state of stress and/or anxiety. In order for the individual to experience acute stress, some of the stressors must be present and the individual must be aware of the presence of stress, motivated to resolve the situation and uncertain of the outcome [138].
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One of the main ways in which stress affects evacuation decision-making is through the narrowing of an individual’s perceptive field. In this instance, stress makes it more difficult to perceive cues from the event [56, 137], and in turn, individuals may only pay attention to a select number of cues from their physical environment. Because of this, they could very well miss important pieces of information about the event which they would need to make safer or more effective decisions. Additionally, the ability to process information is skewed in three major ways under stress [140]: • They process information at a faster rate, without carefully connecting the appropriate pieces of information together into an coherent story • They can engage in the avoidance of optimal decision-making, i.e., making random choices • Subjectively, the important data are chosen for consideration in the decisions Another effect of stress on behavior and decision-making is that individuals are more likely to make choices that are less risky, thus, for example, providing additional support for the use of more familiar exits rather than unknown exits during evacuation [66].
Engineering Implications of Stress on Behavior It is important for engineers to understand the implications of stress because this understanding can help improve the way we design buildings as well as emergency communications systems for fire safety. If individuals are more likely, in stressful situations, to pay attention to a lower number of cues, for example, engineers should design more noticeable signage or warning cues that easily grab people’s attention. One example of this is providing information via luminous materials, like visual signage, that are central to people’s perception field. Signage should be designed to capture people’s attention and keep their attention during a building fire in as many ways as they can (see Kuligowski and Omori [83] for further information on better communication of emergency information during building emergencies).
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Factor 3: The Influence of the Built Environment on Behavior Research has also been performed on the influence of the built environment, i.e., the building, on evacuation behavior. Much of this work has been performed by Jonathan Sime, and refers back to the Affiliative Model [107] presented in an earlier section of this chapter. Similar to how individuals are likely to move toward individuals who are familiar to them before (or during) evacuation movement, people will attempt to use (or evacuate by) the exits or exits routes that are most familiar to them [107]. In general, in the Summerland fire that took place on the Isle of Man in Great Britain in 1973, Sime found that people attempted to leave via the exit route with which they were familiar; often, that was the exit that they had used to gain entry into the building. The Affiliative model also predicts that because a fire route (or exit) is not in regular use, and thus likely unfamiliar to the population, it is less likely to be used in a fire evacuation. People will prefer to use the most familiar exits, and this is exacerbated in emergencies [107]. Nilsson, building upon Sime’s findings on familiarity, performed several studies on the features of exits that could increase the attractiveness of one exit over another [141]. He based his analysis of exit design on the theory of affordances [142], which states that people perceive objects in terms of what they can offer or afford. Based upon Gibson’s work, Hartson [143] introduces four types of affordances and the types of activities they support: • Sensory affordance—sensing or seeing • Cognitive affordance—understanding • Physical affordance—physically activity (doing or using) • Functional affordance—fulfillment of an individual’s goals Nilsson [141] provides examples of how the theory of affordances can be used to analyze the design of an emergency exit. The first, or sensory affordance, suggests that the exit must be designed such that it is easy to sense. Nilsson provides specific examples of how to increase an
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exit’s sensory affordance in the following ways: clearly distinguish the door from other elements in the space (e.g., by using color or pattern) and equipping them with flashing lights, as long as sufficient contrast is provided by the environment. Cognitive affordance suggests that people understand that the exit should be used in emergencies and that it can lead them to a safer place. Examples of increasing cognitive affordance include providing an emergency exit sign above the door, placing flashing lights next to the exit sign (which would cover both sensory and cognitive affordances), and providing green flashing lights that is associative with safety or emergency exits (especially in countries where the exit signs are green). Physical affordance suggests that the user should be easily able to open and operate the door in an emergency. An example of increasing physical affordance is providing a door that is easy to open (i.e., no large force is required to open the door). Finally functional affordance suggests that the exit aids the user in obtaining their goal—to escape as quickly as possible. The difficulty, according to Nilsson, with functional affordance is that individuals during a building evacuation may have a multitude of goals; i.e., to not be the only one using an exit (for fear of looking foolish) or to avoid unpleasant environments in the building. Therefore, it is difficult to identify specific examples of increasing functional affordance in a building evacuation. Finally, studies have shown that the individual’s definition (or perception) of their environment can influence behavior during a fire evacuation. Donald and Canter’s study of the King’s Cross Disaster [144], where a fire began in the escalators of London, UK’s King’s Cross underground metro station, showed instances of the influence of place. Individuals located in the underground station were told by police officials to evacuate the underground station; however, the location to which they actually traveled depended upon their definition of the underground station. Some were unsure whether “the station” included the ticket hall area or the concourse or both, causing confusion about
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where they should actually travel to reach a safer location.
Engineering Implications of the Built Environment on Behavior In all three studies, individuals’ perceptions of the built environment, including familiarity, exit affordances, and the location of safety, influenced their decisions on and actions toward exit routes during the emergency event. It is important for engineers to understand the factors that influence exit choice for two reasons. First, buildings or emergency procedures can be designed to account for this type of behavior— e.g., increasing the size of the main exit for certain type of buildings. Similarly, evacuation procedures can institute a plan whereby staff members direct individuals to exits that are less familiar or are unknown to many of the population. Second, an understanding of exit choice can aid the engineer in designing more efficient emergency communication systems. This may include specifically telling certain individuals which exits to use in the building or equipping potentially unfamiliar exits with flashing lights (see Kuligowski [83] for further information on better communication of emergency information during building emergencies).
Factor 4: The Influence of Leadership (or Role) on Behavior This section focuses on the influence of leadership (or role) on evacuation behavior. Depending upon the building, leadership may already be in place before an emergency event begins. For example, in office buildings, there usually exist individuals in management positions throughout the building. Similarly, mercantile buildings often consist of customers and employees, some of whom are in management roles. However, in emergencies, leadership has been known to emerge as well [31]. In emergent cases, the individual (or individuals) did not hold a pre-emergency leadership role, but engaged in actions (i.e., helping behavior or the provision
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of instructions) that reflect a certain level of responsibility for others. Jones and Hewitt, for example, studied group formation and leadership during the evacuation of a high-rise office building due to a fire [145]. Overall, a person’s role in the organized hierarchy (pre-event leaders) had an influence on the group actions; i.e., in some cases, the leader’s group listened, relinquished decision-making to this individual, and followed directions. The same type of scenarios were found in Kuligowski’s study of the 2001 WTC evacuation [30] where individuals, more times than not, followed the instructions provided by their management of when and how to evacuate the towers. Jones and Hewitt did find exceptions to this trend, however, noting that when leadership failed to retain influence, new leadership emerged (i.e., even from those who were not previously in leadership roles). Individuals also followed leadership in the King’s Cross Disaster (discussed in the previous section) [144]. Individuals modified their action when they received instructions from people who appeared to hold official authoritative roles, i.e., police officers. In this disaster, even though the police did not have any additional official information and actually gave out incorrect information at times, they felt some responsibility for dealing with the situation and the public looked to them for instructions and guidance. In this particular instance, the reactions of the public to transportation staff was to ignore them, unless their instructions were backed by the police or fire department; showing that the people’s confidence in the transportation staff was fairly low.
Engineering Implications of Leadership on Behavior Leadership studies show the engineer that there are certain people in the building who are more likely than others to assume a leadership position during a fire emergency. These individuals are likely to provide suggestions on what to do, and in turn, influence others’ actions. The more credible these individuals are, the more influence they will have on the rest of the population. For example, if the engineer is aware that managers
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are already more likely to respond and take leadership roles, another possibility is to assign fire safety leadership roles to people who are not already predisposed to help; i.e., empowering other types of occupants, in addition to managers, to enroll in key fire safety roles. Based on previous research, people with previous experiences in disasters or individuals with emergency-related occupations may already hold credibility as emergency experts with the larger population, and as an extension of this research, may be more likely to take interest in fire safety roles. Additionally, if the engineer understands that managers, for example, are already more likely to take leadership roles during a fire event, then managers should receive special fire safety training to ensure that they are providing accurate information and performing appropriate actions during building fires.
Factor 5: The Influence of Demographics (Gender) on Behavior Demographics refer to the characteristics of a population, notably those characteristics that are genetic to the individual. Examples of geneticbased demographics are provided here: gender, age, physical fitness, physical abilities or disabilities, race, and culture. However, demographics can also include other social factors that can define or label an individual in some way, including socio-economic status, location (i.e., where s/he lives), marital status, occupation, etc. In this section, studies are presented that have been performed on one type of demographic (i.e., gender), and its effects on evacuation or emergency decision-making. Bryan [14] and Wood [15] studied the influence of gender on certain residential evacuation behaviors. These researchers tested their respective datasets to see if gender had an influence on the first action taken, the action of fire fighting, and the act of notifying others in the building before evacuating. First, with respect to initial actions taken, Bryan [14] studied the impact of gender. He found statistically significant differences
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between males and females in the categories of “searched for fire,” “called fire department,” “got family,” and “got extinguishers.” Male participants were predominant in fire-fighting activities: 14.9 % of the males participated in the behavioral response of “searched for fire” as opposed to 6.3 % of the females, and 6.9 % of the males were involved in the action of “got extinguishers” as opposed to 2.8 % of the females. In the U.S. population, females differed significantly from the males in the warning and evacuation activities—11.4 % of the females “called fire department” as their initial behavioral response action as opposed to 6.1 % of the males. In relation to the evacuation behavior, 10.4 % of the females “left building” as the first behavioral response action, contrasted with 4.2 % of the males. Bryan [77] stated that the cultural influence of gender on female participants is probably explicitly indicated in the concern for other family members, with the finding that 11 % of the females “got the family” as the first behavioral response, whereas only 3.4 % of the males engaged in this behavioral response. It should be noted that the male actions of “searched for fire” or “fought fire” were matched by the female actions of “called fire department” and “got family.” This identical pattern of behavioral responses has also been observed in fire incidents in health care and educational occupancies. However, considering the fact that these studies took place in the late 1970s and early 1980s, additional and updated research should be performed on these gender roles to test their current applicability. In contrast, studies have been performed on building fires where gender was not identified as a predictor of behavior. For example, Proulx et al. [146] studied the 2 Forest Laneway fire in 1995, a high-rise apartment fire that killed 6 people in Canada. Researchers inquired about behaviors by distributing behavioral surveys to survivors, and found no significant differences between the actions taken by males and females. Horasen and Bruck performed studies of response behavior of students in secondary (junior and senior high) schools [147]. Behavioral
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intention questionnaires; i.e., questionnaires that ask individuals what they would do if a particular situation were to occur, were completed by 170 students across grades 7 to 12. The first section of the questionnaire contained questions on student demographics, the second section presented students with six scenarios to collect information on the most probable actions taken under the given conditions, and the third section asked about students’ previous experiences with evacuation drills and actual fire incidents. Overall, the study found no significant differences in likely behavioral responses of males versus females. However, when asked about scenarios in which they would be alone and with smoke cues, females were more likely to ‘leave the building immediately’, whereas males were more likely to ‘find an extinguisher’. Saunders [148] studied an office building fire, also using behavioral intention questionnaires and found support for gender differences with respect to evacuation actions. Females were more likely than males to report that they would investigate, warn, and evacuate in response to various types of cues. However, neither males nor females wanted to fire fight. These studies may support research showing that women have a higher perception of risk in emergencies, and therefore, are more likely to respond in emergencies. However, there are limitations associated with the use of behavioral intention questionnaires as a means to understand future behavior. In both studies described above, participants were asked to provide insight on what they would do in a series of hypothetical situations. Here, the participant is asked to mentally picture the scenario without physically being a part of the situation. If the scenario is not described in sufficient detail to the participant of the study, he/she will likely be unable to mentally picture the scenario accurately and make estimates of potential response behavior. Also, even if extensive detail is provided on the scenario description, behavioral intention questionnaires deprive participants from experiencing, first-hand, the cues from the physical (i.e., the fire) and social environments. The inability to experience the environment in the hypothetical scenario can cause difficulty in
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determining behaviors that would be performed, since it is the physical and social environments that prompt internal cognitions, decision-making and action in a fire emergency. Additionally, a participant’s prediction of future behavior in a particular scenario may be influenced by previous experiences in building fires or other disasters. Thus, participants who have not experienced an actual building fire emergency may be less inclined to accurately predict response behaviors in future fire emergencies.
Engineering Implications of the Influence of Demographics (Gender) on Behavior As mentioned earlier in this section, there are several demographic factors that could be considered as influential to behavioral actions during emergencies. Gender is simply one demographic factor that is highlighted here in this chapter. While it is important for engineers to understand that demographics can play a role in behavioral response during building fires, engineers must also understand that the relationship between demographics and behavior is complex [133]. Engineers should be aware that individual factors are more likely to be predictors of internal cognitions (such as risk perception), which then influence action, rather than direct influences of action. Rather than stating that all women warn others during fire emergencies, what is more likely to be the case is that situational or emergency-related variables, such as environmental cues and demographics, lead to risk identification and assessment, which then leads to action. Therefore, engineers should inquire how gender and other individual-based factors influence perceptions of the threat and risk, which then directly influence actions performed in response to a fire.
Summary—Behavioral Facts A great deal of information has been provided on human behavior in fire in this chapter. Following each section, engineering implications were discussed, providing the “so what?” to readers. The engineering implications were provided
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after each section so that a reader might be able to see the application of these findings to actual engineering projects. In addition, examples of “behavioral facts,” first introduced by Kuligowski and Gwynne [149] and extended by Gwynne [150], are listed below to summarize the major findings captured by this chapter, which link to the section in which each fact is discussed. A total of 11 behavioral facts are listed here: Behavioral fact #1: Rather than panic, people’s first instinct is to feel (sometimes inappropriately) safe in their environment (Sections “Discarded Theories of Human Behavior in Fire” and “Panic Behavior”). Behavioral fact #2: Just because information is provided in a fire emergency does not mean that appropriate occupant response will take place. Perception of, attention to, and comprehension of information (in a fire event) is a critical part of occupant response (Section “Social Psychological Theories of Human Behavior in Emergencies”). Behavioral fact #3: Occupants must perceive a credible threat and personalize the risk before protective action is taken (Section “Social Psychological Theories of Human Behavior in Emergencies”). Behavioral fact #4: People will engage in information seeking actions, especially when cues are ambiguous and/or inconsistent (Sections “Social Psychological Theories of Human Behavior in Emergencies” and “Relating Theory to Practice—Protective Actions in Fires”). Behavioral fact #5: People are likely to engage in preparation activities before beginning evacuation response. Preparation activities will likely delay their response (Section “Relating Theory to Practice—Protective Actions in Fires”). Behavioral fact #6: Generally, people act rationally and altruistically during building fires (Section “Relating Theory to Practice— Group Behavior”). Behavioral fact #7: The surrounding population will influence the individual’s decisionmaking process (Section “Factor 1: The Influence of Other Occupants on Behavior [Social Influence]”).
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Behavioral fact#8: Stress can narrow a person’s field of perception, causing individuals to miss or ignore certain cues or information (Section “Factor 2: The Influence of Stress on Behavior [Perception])”. Behavioral fact #9: People move to the familiar. The relationships with the structure and people that existed prior to the incident influence response during the incident (Sections “Relating Theory to Practice— Group Behavior” and “Factor 3: The Influence of the Built Environment on Behavior”). Behavioral fact #10: People do not instantaneously switch to a different set of roles in a building fire event. The rules and roles prior to the event form the basis of those employed during the event (Section “Factor 4: The Influence of Leadership [or Role] on Behavior”). Behavioral fact#11: People are heterogeneous and these individual differences in characteristics (or demographics) can influence behavior (Section “Factor 5: The Influence of Demographics [Gender] on Behavior”).
What Is Missing in Human Behavior in Fires? This chapter first presented an overarching theory of human behavior in disasters; i.e., the period of time in which individuals make decisions on whether protective action is necessary and then which actions they will take in response to the threat (the PADM). However, this theory is more general in nature and does not actually identify the factors that would predict the performance of particular actions, such as helping others or taking a particular route in the building. Next, this chapter presented studies from the field of human behavior in fire to support the larger, general theory. These studies identified the actions that people take in response to fires, the approximate timing of action types, as well as began to identify the factors that influenced these types of actions. Most studies
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focused on the pre-evacuation period of a building fire. What is missing in the field of human behavior in fires is a comprehensive theory that brings all of the theory and data from studies together to predict, rather than to simply determine based upon user input, human behavior during evacuations. With a larger comprehensive theory, engineers could perform more accurate calculations for performance-based design (i.e., see Chaps. 57, 59, and 60) and model developers could create more accurate evacuation models that rely less on user input and more on fundamental theory (see Gwynne [150]). One step in the process of reaching this comprehensive theory is to develop models that can predict the actions that people take in response to fires—both before they decide to evacuate (pre-evacuation) and during the evacuation (or movement) time period. Canter, Breaux and Sime’s [78] decomposition diagrams begin to tie various sub-theories together, but focus primarily on the linking of evacuation actions together, and often neglect to identify the interpretations and levels of risk perception that are influential to occupant’s actions. One example is provided here of a qualitative model that predicts the pre-evacuation actions of survivors of the 2001 World Trade Center (WTC) Disaster [30, 151]. Through analyses of transcripts from 245 face-to-face interviews with survivors from both WTC towers, collected by Project HEED [22], this model is the first inductively-developed, individually- (or evacuee-) based model explaining the actions taken during the pre-evacuation period of a building fire/evacuation event. The goal of this research was to describe evacuation decision processes in greater detail than either research on building fires or studies on community-wide evacuation, focusing on how people perceive and interpret environmental cues and warnings, how they seek confirmation during sensemaking and milling processes, and what they do before moving to safety. There are five main findings that can be highlighted from this research. The findings are as follows:
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• The WTC pre-evacuation period was divided into two main phases: the milling/ sensemaking phase and the protective action phase. In the milling/sensemaking phase, WTC occupants engaged in two different actions—continuing to work or seeking additional information. In the protective actions phase, on the other hand, occupants engaged in actions that were focused specifically on protecting themselves or others (i.e., helping others, preparing to evacuate, or defending in place). Both phases took place before moving to the stairs or elevators. • Risk perception, or the feeling of personal danger, was the main predictor of when individuals decided to evacuate—i.e., the transition from the milling/sensemaking phase to the protective action phase. Both individual and environmental factors were identified as influential of risk perception development. • Some individuals made their decisions to evacuate before others on their floor. These “early responders”, as labeled by Kuligowski [30], were primarily higher-level managers, fire wardens, military personnel, or individuals with experiences or occupations in emergency situations. These individuals still required the receipt of information that increased their level of perceived risk, but were also more inclined to act first (before others) because they felt responsibility for others and/or had previously experienced/ witnessed negative consequences associated with fire or building evacuations. • Certain factors, such as personal responsibility, social connections, and the actions of others, influenced which protective actions people engaged. See Kuligowski [30] for further explanation on the conceptual model. Kuligowski’s model is not without limitations, however. The model focuses specifically on the pre-evacuation period of one building event. Additionally, the model does not incorporate any decisions or actions of the decedents. While the findings in the model were
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verified with theory from other events, the factors that influenced each action performed were specific to an office building fire and subsequent evacuation, thus making it difficult to generalize the findings. This is a first start to developing a model to predict actions taken during building fires; however, this effort should be expanded upon to include findings from analysis of other building fires, including fires in different types of structures and with different populations, as well as from analysis of other types of disasters, not limited to building fires. An additional step in the process of reaching this comprehensive theory is to develop models that can predict the timing associated with the performance of certain actions—both before they decide to take protection (e.g., evacuate) and during the evacuation (or movement) time period. First, there are a few studies that attempt to predict how long people delay before evacuating [1, 40, 84, 152] as well as the time it takes individuals to evacuate via stairs [1]. For example, NIST’s federal investigation of the 2001 WTC disaster performed multiple regression analysis to predict pre-evacuation delay and normalized stairwell evacuation time— identifying factors such as action type, floor number, the number of environmental cues and level of perceived risk as predictors of pre-evacuation delay time and factors such as the presence of counterflow, the presence of crowding, the number of environmental cues, floor number, pre-evacuation delay, and evacuation interruption as predictors of normalized stairwell evacuation time [1]. Other research efforts have attempted to quantify human behavior in the form of an empirical model. One such model was developed by NIST [153] based upon the WTC conceptual model [30], presented earlier in this section. A firstorder quantitative model, labeled as the Evacuation Decision Model (EDM), was developed to predict the time when a simulated occupant, or agent, decides to evacuate (i.e., the decision that protective action is necessary). In the EDM, the prediction of the evacuation decision is based upon the agent’s perceptions of risk during the
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pre-evacuation period. In its simplicity, the EDM model attempts only to simulate the evacuation decision, without additional simulation of protective action behaviors. At present, these qualitative and quantitative models scratch only the surface of the development of a larger, comprehensive model of human behavior in fire. These models provide a path forward on the methods that could be used in its eventual development. However, there is much work still to be done to improve our understanding of human behavior in fire, and without this understanding, a comprehensive model is near impossible. Listed here are just a few examples of areas in the field that require further study: • The influence of fire’s toxic products and heat on decision-making and behavior (before incapacitation or death occur) in a building fire • An identification of all of the factors that influence risk perception and how they interact to increase or decrease risk perception levels. • The types of protective actions that are performed in building fire evacuations • The factors that influence the various types of protective actions performed in building fire evacuations • The factors that influence the receipt of cues, the ways in which people pay attention to cues, and the comprehension of cues • The ways in which individual factors, such as gender, disability, age, body size, culture, marital status, past experiences, training and social role, influence decision-making during building fires • The timing associated with the performance of behavior during building fires, and the factors that influence this timing • The influence of urgency or other types of dissemination techniques on the response of building occupants during fires • The influence of group dynamics on individual decision-making and group decisionmaking during fires • The role of place (including building type or building characteristics) on decision-making during fires
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• The role of psychological states, including stress or anxiety, on decision-making during building fires. For the field to reach its goal and develop a larger understanding of human behavior in fire, accurate, rigorous, and comprehensive research must continue. There is still much left to understand, but the ultimate goal of a comprehensive model is in our future.
Chapter Summary Human behavior in fire is a key aspect of understand