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ASME-PTC10 ADOPTION NOTICE ASME-PTC10, "Compressors and Exhausters,'' was adopted on (DoD). October 3 , 1994 for use by the Department of Defense Proposed changes by DoD activities must be submitted to the DoD Adopting Activity: Director, US Army Mobility Technology Center/Belvoir, ATTN: AMSTA-RBES, Fort Belvoir, VA 22060-5606. DoD activities may obtain copies of this standard from the Standardization Document Order Desk, 700 Robbins Avenue, Building 4D, Philadelphia, PA 19111-5094. The private sector and other Government agencies may purchase copies from the American Society of Mechanical Engineers, 345 East 47th Street, New York, NY 10017. Custodians: Army - ME Navy - YD-1 Air Force - 99

Adopting Activity Army - ME

FSC 4310

DISTRIBUTION STATEMENTA. Approved for public release; distribution is unlimited.

COPYRIGHT American Society of Mechanical Engineers Licensed by Information Handling Services

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COPYRIGHT American Society of Mechanical Engineers Licensed by Information Handling Services

ASME PTC 10-1997

Performance Test Code on Lompressors and Exhausters

COPYRIGHT American Society of Mechanical Engineers Licensed by Information Handling Services

STD.ASME PTC L O - E N G L 1977

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0757b70 Oh05923 158

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Date of Issuance: September 30, 1998

This document will be revised when the Society approves the issuance edition. There will be no addenda issued to ASME PTC 10-1997.

of a n e w

Please Note: ASME issues written replies to inquiries concerning interpretation of technical aspects of this document. The interpretations are part not of the document.

PTC 10-1997 is being issued with an automatic subscription service to the interpretations that will be issued to it up to the publication of the next edition.

ASME is the registered trademark of The American Society of Mechanical Engineers.

This code or standard was developed under procedures accredited as meeting the criteria for American National Standards. The Standards Committee that approved the code or standard was balanced to assure that individuals from competent and concerned interests have had an opportunity toparticipate. The proposed code or standard was made available for public review and comment which provides an opportunityfor additional public input industry, fromacademia, regulatory agencies, and the public-at-large. ASME does not "approve," "rate," or "endorse" any item, construction, proprietary device, or activity. ASME does not take any position with respect to the validityof any patent rights asserted in connection with any items mentioned in this document, andundertake does not to insure anyone utilizing a standard against liability for infringement of any applicable LettersPatent, nor assume any such liability. Users of a code or standard are expressly advised that determination of the validity of any such patent rights, and the risk of infringement of such rights, is entirely their own responsibility. Participation by federal agency representative(s)or personb) affiliated with industry is not to be interpreted as government or industry endorsement of this codeor standard. ASME acceptsresponsibilityfor onlythose interpretations issued in accordancewith governing ASME procedures and policies which preclude the issuance of interpretations by individual volunteers.

No part of this document may be reproduced in any form, in an electronic retrieval system or otherwise, without the prior written permission of thepublisher.

The American Society of Mechanical Engineers Three Park Avenue, New York, NY 10016-5990 Copyright (B 1998 by THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS All Rights Reserved Printed in U.S.A.

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FOREWORD (This Foreword is not a part of ASME PTC 10-1997.)

PTC 10 was last revised in 1965 andit has been reaffirmed many times in the intervening period. The PTC 1O Committee has been in various states of activity for approximately the past20 years. During that time the Codehas been completely rewrittento be far more explanatory in nature. The performance testing of compressors is complicated by the need in virtually every case to consider and make correction for the differences between the test and specified conditions.Thetechniques used to do so arebased upontherules of fluid-dynamic similarity. Some familiarity with this fundamental technique will be a significant aid to the users of PTC IO. Compressors and exhausters come in all sorts of configurations. A very simple case is a single section compressor with one impeller, and single inlet and outlet flanges. Many morecomplex arrangementsexist with multiple inlets,outlets,impellers,sections, intercoolersandside seams. Typical gases handled areair, its constituents,andvarious hydrocarbons. Tests are commonly run in the shop or in the field, at speeds equal to or different from the specified speed, and with the specified or a substitute gas. In order to handle this vast array ofpossibilities PTC 10 reduces the problemto the simplest element, the section, and provides the instructionsfor combining multiple sections to compute the overall results. Uncertainty analysis can play a very important role in compressortesting, from the design of the test to interpretation of the test results. In all but the very simplest of cases the development of an analytic formulation, ¡.e., in simple equation form, for overall uncertainty computation is formidable. The test uncertainty will always be increasingly more complex to evaluate with the complexity of the compressor configuration, and by the very nature of the test will be a function of the performance curves. The modern personal computer is readily capable of completing the calculations required. The Committee developed software and used it to perform both the basic code calculations and uncertainty analysis computationsfor widea range of possible compressor configurations. This Code was approved by the PTC 1O Committee on January 18,1991. It was approved and adopted by the Council as a standard practice of the Society by action of the Board on Performance Test Codes on October 14, 1996. It was also approved as an American National Standard by the ANSI Board of Standards Review on April 22, 1997.

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STD-ASME

P T C LO-ENGL L997 D 0759b70 Ob05925 T20

NOTICE All PerformanceTestCodesMUST adhere to therequirements ofPTC 1, GENERAL INSTRUCTIONS. The following information is based on that document and is included here for emphasis and for the convenience of the user of this Code. It is expected that the Code user is fully cognizant of Parts I and III of PTC I and has read them prior to applying this Code.

ASME Performance Test Codes provide test procedures which yield results of the highest level of accuracy consistent with the best engineering knowledge and practice currently available. They were developedby balanced committees representing all concerned interests. Theyspecifyprocedures,instrumentation,equipmentoperatingrequirements,calculation methods, and uncertainty analysis. When tests are run in accordance with thisCode, the test results themselves, without adjustment for uncertainty, yield the best available indication of the actual performance of the tested equipment. ASME Performance Test Codes do not specify means to compare those it is recommended that the partiesa commercial to results to contractual guarantees. Therefore, test agree before starting the test and preferably before signing the contract on the method to be used for comparing the test results to the contractual guarantees. It is beyond the scope of any code to determine or interpret how such comparisons shall be made. Approved by Letter Ballot #95-1 and B E C Administrative Meeting of March 13-14, 1995

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PERSONNELOFPERFORMANCE

TEST CODECOMMITTEE NO. 10

ON COMPRESSORS AND EXHAUSTERS (The following is the roster of the Committee atthe time of approval of this Code.)

OFFICERS Gordon J. Gerber, Chair Richard J. Gross, ViceChair jack H. Karian, Secretary

COMMITTEEPERSONNEL Helmut B. Baranek, Public Service Electric & GasCompany John J. Dwyer, Consultant Gordon J. Gerber, Praxair Richard J. Gross, The University of Akron Jack H. Karian, ASME Robert E. Lawrence, Consultant Jack A. Lock, LockEngineering Vincent J.Polignano, IMO Delaval Frank H. Rassmann, ElliottCompany Norman A. Samurin, DresserRandCompany Joseph A. Silvaggio,Jr., Alternate to Polignano, IMO Delaval

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S T D - A S M E P T C L O - E N G L L777 m 0 7 5 7 b 7 0 Ob05427 A T 3 m

BOARD ON PERFORMANCE TEST CODES OFFICERS

D. R. Keyser, Chair P. M. Cerhart, Vice Chair W. O. Hays, Secretary

C O M M l l T E E PERSONNEL R. P. Allen R. L. Bannister B. Bornstein J.M. Burns J. R. Friedman G. J. Gerber

P. M. Gerhart

R. S. Hecklinger

R. W. Henry D. R. Keyser S. Korellis

J.

J. W. Milton G. H. Mittendorf, ]r. S. P. Nuspl

R. P. Perkins A. L. Plumley

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COPYRIGHT American Society of Mechanical Engineers Licensed by Information Handling Services

S. B. Scharp J. Siegmund J. A. Silvaggio, Jr. R. E. Sommerlad W. G. Steele, Jr. J. C. Westcott J. G. Yost

S T D - A S M E P T C LO-ENGL

CONTENTS

Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CommitteeRoster ................................................ BoardRoster ....................................................

Section 1 2 3 4

5 6

Figures 3.1 3.2 3.3 3.4 3.5 3.6 3.7 4.1 4.2

4.3 4.4

4.5 4.6

4.7 4.8 4.9

4.1O 4.1 1 4.1 2 5.1

Objectandscope ........................................ Definitions and Description of Terms .......................... Guiding Principles ........................................ Instruments and Methods of Measurement ...................... Computation of Results .................................... ReportofTest ...........................................

Section Control Volumes ................................... Typical Sideload Sectional Compressors ........................ Allowable Machine Mach Number Departures. Centrifugal Compressors .......................................... Allowable Machine Mach Number Departures. Axial Compressors. . . . Allowable Machine Reynolds Number Departures. Centrifugal Compressors .......................................... Schultz Compressibility Factor - Function Y versus Reduced Pressure Schultz Compressibility Factor- Function X versus Reduced Pressure Inlet and Discharge Configuration ............................ OpenInlet .............................................. Vortex Producing Axial Inlet ................................ OpenDischarge ......................................... Diffusing Volute Discharge With Nonsymmetric Flow . . . . . . . . . . . . . TypicalClosedLoop ...................................... Typical Closed Loop With Sidestream Straighteners and Equalizers................................. Inlet Nozzle on an Open Loop .............................. Discharge Nozzle on an Open Loop, Subcritical Flow . . . . . . . . . . . . . Discharge Nozzle on an Open Loop, Critical Flow. . . . . . . . . . . . . . . . Typical Sidestream Inlet Area ................................ Specified Condition Capacity Coefficient for SpecifiedCondition Capacity of Interest .....................................

.........................

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1 3 11 23 39

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14 16 18 19

20 21 22

24

24 25 25 26 26

27 29 32

33 33 35

49

Tables 3.1

Permissible Deviation From Specified Operating Conditions for Type1 Tests...........................................

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3.2 3.3 3.4 5.1

5.2 5.3

5.4

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Permissible Deviation From Specified Operating Parameters for Type1 and2Tests Limits of DepartureFromIdeal GasLaws of Specifiedand TestGases Permissible Fluctuations of Test Readings ....................... Ideal Gas Dimensionless Parameters Real Gas Dimensionless Parameters Total Work Input Coefficient. All Gases Typical Conversion Dimensionless of Parameters

......................................

............................................ .......................... ........................... ........................ .................

Nonmandatory Appendices AUse of Total Pressureand TotalTemperature to Define Compressor Performance B Properties of Gas Mixtures .................................. Sample C Calculations C.l Type 1 Test for a Centrifugal Compressor Using anIdeal Gas C.2Type2Test for a CentrifugalCompressorUsinganIdealGas ........ C.3 Ideal Gas Application to Selection of TestSpeed and TestGas and Methods of PowerEvaluation C.4 Treatment of Bracketed TestPoints C.5 Selection of aTestGas for aType2Test Using Ideal and RealGas Equations............................................. C.6 Type 2Test Using RealGasEquations forDataReduction C.7 Treatment of a Two SectionCompressor With ExternallyPiped Intercoolers,CondensateRemoval .......................... C.8 Application of Uncertainty Analysis ........................... D References E Rationale for Calculation Methods ............................ F Reynolds Number Correction G Refined Methods for Calculating Total Conditions H SIUnits ................................................

.......................................... ...................................... ........

..............................

............................

..........

..............................................

................................

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13 14 40 41 48 50

59 61 63

65 85 109 119

123 139 151 159 165 167 183 185 187

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SECTION 1 1.1

10-1 997

- OBJECTANDSCOPE nally pipedintercoolersand for compressors with interstage side loadinletsoroutlets. Internally cooled compressorsare includedprovided that test conditions are held nearly identical to specifiedconditions. Compressors, as thenameimplies,areusually intended to produceconsiderabledensitychange as aresultof the compressionprocess.Fansare normally considered to be air or gas moving devices and are characterized by minimal densitychange. A distinction betweenthe two at timesmaybe unclear. As a veryroughguide,either PTC 10 or PTC 11 maybeused for machines falling into the approximatepressure ratio rangeof 1.05 to 1.2. Themethodsof PTC 10, which provide for the pronouncedeffectsofdensitychangeduringcompression,have no theoretical lower limit. However, practical considerations regarding achievable accuracy become important in attempting to apply PTC 10 to devicescommonlyclassified as fans. For example,the low temperatureriseassociated with fans may lead to large uncertainty in power requirement if theheatbalancemethod i s chosen.Fans also may require traversing techniques for flow and gas state measurementsdue to the inlet and discharge ducting systems employed. Refer to PTC 11 on Fans for further information.

OBJECT

Theobjectof this Code is to providea test procedure to determine the thermodynamic performance of an axial or centrifugal compressororexhauster doing work on a gas of known or measurable propertiesunderspecifiedconditions. This Code is written to provide explicit test procedures which will yield the highest level of accuracy consistent with the best engineering knowledge and practice currently available. Nonetheless, no single universal value of the uncertainty is, or should be, expected to apply to everytest.The uncertainty associated with any individual PTC 10 test will dependupon practical choicesmade in terms of instrumentationandmethodology. Rulesare provided to estimate the uncertainty for individual tests.

1.2

SCOPE

1.2.1 General. Thescope of this Codeincludes instructionson test arrangement and instrumentation, testprocedure,andmethods for evaluationand reportingof final results. Rulesare provided for establishing the following quantities,corrected as necessary to representexpected performance under specified operatingconditions with the specified gas: (al quantity of gas delivered (b) pressure rise produced (c) head (d) shaft power required (e) efficiency (0 surge point (g) choke point Other than providing methods for calculating mechanicalpower losses, this Code does notcover rotor dynamicsorothermechanicalperformance parameters.

1.3

BY THIS

The calculation procedures provided in this Code are based on thecompressionof a singlephase gas.They should not be used for a gas containing suspendedsolids or any liquid, when liquid could be formed in thecompression process, orwhen a chemicalreaction takes place in the compression process. Thisdoes not preclude the use of thisCodeon a gas where condensation occurs in a cooler providing the droplets are removed prior tothe gas entering the next stage of compression.

1.2.2 CompressorArrangements. ThisCode is designed to allowthe testing of single multiple or casing axial or centrifugal compressors orcombinations thereof, with oneormore stages ofcompression percasing.Proceduresarealso included for exter1

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EQUIPMENTNOTCOVERED CODE

ASME PTC 10-1 997

1.4

COMPRESSORS AND EXHAUSTERS

configuration is used, thisshall be agreed upon in writing prior to the test by the participating parties. However, no deviationsmaybemadethat will violate anymandatoryrequirementsof this Code when the tests are designated as tests conducted in accordance with ASMEPTC 10. The mandatory rules of this Code are characterized by the use of the word "shall." If a statement is of an advisory nature it is indicated by the use of the word "should"or is stated as a recommendation.

TYPES OF TESTS

ThisCodecontainsprovisions for two different types of tests. A Type 1 test must be conducted on the specified gas with a limited deviation between test and specifiedoperatingconditions. A Type 2 test permitsthe use ofasubstitutetest gas and extends the permissible deviations between test and specifiedoperatingconditions.

1.5

PERFORMANCE RELATION TO GUARANTEE

This Code provides a means for determining the performance of a compressor at specified operating conditions. It also provides a method for estimating the uncertainty of the results. The interpretation of the results relative to any contractual guarantees is beyond the scope of this Code and shouldbe agreed upon i n writing prior to the test by the participating parties.

1.7

TheCode on GeneralInstructions, PTC 1, shall bestudiedand followed whereapplicable.The instructions in PTC 10 shall prevail over other ASME Performance Test Codes where there is any conflict.

1.8

1.6

ALTERNATE PROCEDURES

REFERENCES

Unlessotherwisespecified,references to other Codes refer to ASME Performance Test Codes. Literaturereferencesareshown in Appendix D.

Definitive procedures for testing compressors are describedherein. If anyotherprocedureortest

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INSTRUCTIONS

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S T D - A S M E P T C 10-ENGL L777 m 0 7 5 9 6 7 0 Ob05q32 L b 0 COMPRESSORS AND EXHAUSTERS

SECTION 2

ASME PTC 10-1997

- DEFINITIONSANDDESCRIPTION OF TERMS

2.1

BASIC SYMBOLS AND UNITS Symbol

Description

Units

A a

Flow channel cross sectional area Acoustic velocity Tip width Coefficient of discharge Molal specific heat (Appendix B only) Specific heat . Specific heat at constant pressure Specific heat at constant volume Diameter Diameter of fluid meter Relative error Polytropic work factor Dimensional constant, 32.1 74 Molal enthalpy Humidity ratio Enthalpy Coefficient of heat transfer for casing and adjoining pipe Mechanical equivalent of heat, 778.1 7 Flow coefficient Ratio of specific heats, cp/cy Common logarithm (Base 10) Naperian (natural) logarithm Molecular weight Machine Mach number Fluid Mach number Polytropic exponent for a path on the P-T diagram Mass (Appendix B only) Rotative speed Polytropic exponent for a path on the P-v diagram Number of moles (Appendix B only) Isentropic exponent for a path on the p-v diagram Power Pressure Velocity pressure Other external heat losses Total mechanical losses (equivalent)

ft2

b C C C CP CV

D

d

e f gc

H HR

h h, j K

k log In MW

Mm M m m

N n n ns

P P Pv Qext

Om

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COPYRIGHT American Society of Mechanical Engineers Licensed by Information Handling Services

ftlsec

ft dimensionless Btu/lbm mole "R Btu/lbm "R Btu/lbm "R Btu/lbm "R in. In. dimensionless dimensionless Ibm ft/lbf sec2 Btu/lbm-mole Ibm H20/lbm dry air Btu/lbm Btu/hr f t 2 "R e

ft Ibf/Btu dimensionless dimensionless dimensionless dimensionless Ibmllbmole dimensionless dimensionless dimensionless Ibm rPm dimensionless

lb mole dimensionless hP

psia

PSi Btu/min Btu/min

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S T D D A S M E PTC LO-ENGL L997

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0759b70 Ob05433 UT7 W

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ASME PTC 10-1997

0, QSl

9

R RA, RB, RC Re Rem RH RP Rt

r

'r 'P '9 rt

r"

S Sc S

T t U

U V V

W W

X X

Y Y

Z

Heat transfer from the section boundaries External seal loss equivalent Rate of flow Gas constant Machine Reynolds number correction constants Fluid Reynolds number Machine Reynolds number Relative humidity Reduced pressure Reduced temperature Pressure ratio across fluid meter Recovery factor Pressure ratio Flow rate ratio Temperature ratio Ratio of specific volumes Molar entropy Heat transfer surface area of exposed compressor casing and adjoining pipe Entropy Absolute temperature Temperature Internal energy Blade tip speed Velocity Specific volume Work per unit mass Mass rate of flow Compressibility function Mole fraction Compressibility function Elevation head or potential energy Compressibility factor as used in gas law,

Btu/min Btulmin ft3/min ft IbWlbm . "R dimensionless dimensionless dimensionless percentage dimensionless dimensionless dimensionless dimensionless dimensionless dimensionless dimensionless dimensionless Btullbmmole fi2

Btu/lbm "R

"R "F Btu/lbm filsec ftlsec ft3/lbm ft Ibf/lbm Ibm/m in dimensionless dimensionless dimensionless ft Ibfllbm dimensionless

-

144 pv = ZRT

ß Y

a

rl P EL in

PP PS Y

P

c T E

R d

Diameter ratio of fluid meter, d/D1 Isentropic exponent Partial derivative Efficiency Absolute viscosity Work input coefficient Polytropic work coefficient Isentropic work coefficient Kinematic viscosity Density Summation Torque Surface roughness Total work input coefficient Flow coefficient

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dimensionless dimensionless dimensionless dimensionless Ibm/ft sec dimensionless dimensionless dimensionless ft2/sec Ibm/ft3 dimensionless I bf-ft

in. dimensionless dimensionless

- "R

STD-ASME PTC LO-ENGL

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ASME PTC 10-1997

Subscripts

2.2.2 Gage Pressure. The gage pressure i s that pressure which i s measured directly with the existing barometric pressure as the zero basereference.

a

Ambient a,b,c,j Component of gas mixture (Appendix B only) Average av C Casing Correction corr crit. Fluid’s critical point value d Compressor discharge conditions Dry air da

db des dg

S

sh

Shaft

g hb i lu

Id m

P rotor

2.2.3 Differential Pressure. The differential pressure is thedifferencebetweenany two pressures measured with respect to a common reference (e.g., the difference between two absolutepressures). 2.2.4Static Pressure. Thestaticpressure i s the pressuremeasured in such a manner that no effect is produced by the velocity of the flowing fluid.

Dry-bulb Design Dry gas Gas Heat balance Compressor inlet conditions Leakage upstream Leakage downstream Gas mixture Polytropic Flow location reference Isentropic

2.2.5 Total (Stagnation) Pressure. The total (stagnation) pressure is an absoluteor gagepressure that would exist when a moving fluid i s brought to rest andits kinetic energy is converted to an enthalpy rise by an isentropic process from the flow condition to the stagnation condition. In a stationary body of fluid thestaticand total pressuresareequal. 2.2.6Velocity(Kinetic)Pressure. Thevelocity (kinetic) pressure is thedifferencebetweenthe total pressureandthestaticpressure at the same point in a fluid.

Specified conditions su sidestream upstream sd sidestream downstream SV Saturated vapor Test conditions t Wb Wet-bulb 1, l n Upstream of fluid meter 2, 2n Downstream or at throat of fluid meter (Y Compressor inlet conditions (static, Appendix A only) Compressor discharge conditions (static, Y Appendix A only) static Static meas. Measured SP

2.2.7 InletTotal Pressure. The inlet total pressure is the absolute total pressure that exists at the inlet measuringstation (seepara. 4.6.8). Unless specifically statedotherwise, this i s thecompressor inlet pressure as used in this Code. 2.2.8 Inlet StaticPressure. The inlet static pressure is the absolute static pressure that exists at the inlet measuringstation(seepara.4.6.7). 2.2.9 Discharge Total Pressure. The discharge total pressure is the absolute total pressure that exists at thedischargemeasuringstation (see para. 4.6.9). Unless specifically stated otherwise, this is the compressordischargepressure as used in this Code. 2.2.1 O DischargeStaticPressure. Thedischarge staticpressure is theabsolutestaticpressure that exists at thedischargemeasuringstation(seepara. 4.6.7).

Superscripts (

l’

()

Condition at dischargepressure with entropy equal to inlet entropy Determined at static conditions

2.3

2.2

is

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TEMPERATURES

2.3.1AbsoluteTemperature. The absolute temperature is thetemperaturemeasuredaboveabsolute zero. It is stated in degreesRankineorKelvin.The Rankinetemperature i s the Fahrenheittemperature plus 459.67 and the Kelvin temperature is the Celsius temperature plus 273.1 5.

PRESSURES

2.2.1AbsolutePressure. Theabsolutepressure the pressuremeasuredaboveaperfectvacuum.

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2.3.2StaticTemperature. The statictemperature is the temperature determined in such a way that no effect is produced by the velocity of the flowing fluid.

2.4.4AbsoluteViscosity. Absolute viscosity is that property of any fluid which tends to resist a shearing force.

2.3.3 Total (Stagnation) Temperature. The total (stagnation) temperature is the temperature that would exist when a moving fluid is brought to rest and its kinetic energy is converted to an enthalpy rise by an isentropic process from the flow condition to the stagnation condition. In a stationary body of fluid the static and the total temperatures are equal.

2.4.5KinematicViscosity. The kinematic viscosity of a fluid is theabsoluteviscosity divided by the fluid density. 2.4.6 Specific Heat at Constant Pressure. The specific heat at constant pressure, (c,) = (dh/aT), is the change in enthalpy with respect to temperature at a constantpressure.

2.3.4 Velocity (Kinetic) Temperature. The velocity (kinetic) temperature is the difference between the total temperature and the static temperature at the measuringstation.

2.4.7Specific Heat at Constant Volume. Thespecific heat at constant volume, (c,,) = (au/aT), is the change in internal energy with respect to temperature at a constant specific volume.

2.3.5 Inlet Total Temperature. The inlet total temperature is the absolute total temperature that exists at the inlet measuring station(see para. 4.7.7). Unless specifically stated otherwise, this i s the compressor inlet temperatureused in this Code.

2.4.8 Ratio of Specific Heats. heats, k, is equal to cpIc,,.

The ratio of specific

AcousticVelocity(SonicVelocity). A pressure wave or acoustic wave of infinitesimal amplitude is described by an adiabaticandreversible (isentropic) process. The corresponding acoustic velocity for suchwaves in any medium is given by:

2.4.9

2.3.6 Inlet Static Temperature. The inlet static temperature is the absolute static temperature that exists at the inlet measuring station.

($)

2.3.7DischargeTotalTemperature. Thedischarge total temperature is the absolute total temperature that exists at the dischargemeasuringstation (see para. 4.7.8). Unless specifically statedotherwise, this i s the compressor discharge temperatureas used in this Code.

2.4.10Fluid Mach Number. The Fluid Mach number is the ratio of fluid velocity to acoustic velocity.

2.3.8 Discharge Static Temperature. The discharge static temperature is the absolute static temperature that exists at the discharge measuring station.

2.5

2.4

a2

=

5

MACHINE CHARACTERISTICS

2.5.1Capacity. Thecapacity of a compressor is the rate of flow which is determined by delivered mass flow rate divided byinlet total density. For an exhauster it is determined by the inlet mass flow rate dividedbyinlet total density. Forsidestream machines, this definition must be applied to individualsections.

OTHER GAS (FLUID) PROPERTIES

2.4.1

Density. Density is the mass ofthe gas per unit volume. It is a thermodynamic property and is determined at a point once the total pressureand temperature are known at the point. 2.4.2SpecificVolume. Specific volume is the volume occupied by a unit mass of gas. It is a thermodynamic propertyand is determined at a point once the total pressure and temperature are known at the point.

2.5.2 Flow Coefficient. The flow coefficient is a dimensionless parameter defined as the compressed mass flow rate divided by the product of inlet density, rotational speed, and the cube of the blade tip diameter. Compressed mass flow rate i s the net mass flow rate through the rotor.

2.4.3 Molecular Weight. Molecular weight is the weight of a molecule of a substance referred to that of an atom of carbon-1 2 at 12.000.

2.5.3Pressure Ratio. Pressure ratio i s the ratio of the absolute discharge total pressure to the absolute inlet total pressure.

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COMPRESSORS AND EXHAUSTERS

2.5.4 PressureRise. Pressurerise is thedifference betweenthedischarge total pressureandthe inlet total pressure.

streams enteringandleavingcanbequantitatively defined as well as the powerinput and heat exchange by conduction and radiation. Such a region can be considered to be in equilibrium for both a mass andenergybalance.

2.5.5Temperature Rise. Temperaturerise is the differencebetweenthedischarge total temperature andthe inlet total temperature.

2.5.14 CompressorSurge Point. Thecompressor surge point is the capacity below whichthe compressor operation becomesunstable.Thisoccurswhen flow is reduced and thecompressorbackpressure exceeds the pressure developed by the compressor and a breakdown in flow results.This immediately causes a reversal in the flow direction and reduces thecompressorbackpressure.The moment this happensregularcompression i s resumedandthe cycle is repeated.

2.5.6 Volume FlowRate. The volume flow rate as used in this Code is the local mass flow rate divided by local total density. It is used to determine volume flow ratio. 2.5.7VolumeFlowRatio. is the ratio ofvolume the flow path.

Thevolume flow ratio flow rates at two points in

2.5.8Specific Volume Ratio. Thespecificvolume ratio is the ratio of inlet specific volume to discharge specific volume.

2.5.15ChokePoint. Thechoke point is the point where the machine is run at a given speed and the flow is increased until maximum capacity is attained.

2.5.9 Machine Reynolds Number. The Machine Reynolds number is defined by the equation Rem = Ub/v, where U is thevelocity attheouterblade tip diameter of the first impeller or of the first stage rotor tip diameter of the leading edge, Y is the total kinematicviscosityofthe gas at thecompressor inlet, and b is a characteristic length. For centrifugal compressors, b shallbetaken as the exit width at the outer blade diameter of the first stage impeller. For axial compressors, b shall be taken as the chord length at the tip of the first stage rotor blade. These variablesmustbeexpressed in consistent units to yield a dimensionless ratio.

2.6

WORK, POWER, AND EFFICIENCY

These definitions apply to a section. 2.6.1IsentropicCompression. Isentropiccompression as used in thisCoderefers to a reversible, adiabaticcompressionprocess. 2.6.2 Isentropic Work (Head). Isentropic work (head) is the work requiredto isentropically compress a unit mass of gas from the inlet total pressure and total temperature to thedischarge total pressure. The total pressureandtemperatureareused to account for thecompressionofthe gas andthe change in the kinetic energy of the gas. The change in the gravitational potentialenergyofthe gas is assumed negligible.

2.5.10 Machine Mach Number. The Machine Mach number is defined as the ratio oftheblade velocity at the largest blade tip diameterof the first impeller for centrifugal machinesoratthe tip diameter of the leading edge of the first stage rotor blade for axial flow machines to the acoustic velocity of the gas at the total inlet conditions.

2.6.3PolytropicCompression. Polytropic compression is a reversiblecompressionprocessbetween the inlet total pressure andtemperatureandthe discharge total pressureandtemperature.The total pressures and temperatures are used to account for thecompressionofthe gas and thechange in the kinetic energy of the gas.Thechange in the gravitational potential energy is assumed negligible. The polytropic process follows a path such that the polytropic exponent is constant during the process.

NOTE: This is not to be confused with local Fluid Mach number.

2.5.11 Stage. A stage for a centrifugal compressor is comprised of a single impeller and itsassociated stationary flow passages. A stage for an axial compressor i s comprisedofasingle row of rotating blades and its associated stationary blades and flow passages. 2.5.12Section. Section is defined as oneormore stages having the samemass flow without external heat transfer other than natural casing heat transfer.

2.6.4 Polytropic Work (Head). Polytropic work (head) is thereversible work required to compress a unit mass of gas by a polytropic process from the inlet total pressure and temperature to the discharge total pressureandtemperature.

2.5.13 Control Volume. The controlvolume is a region of space selected for analysis where the flow 7

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COMPRESSORS AND EXHAUSTERS

ASME PTC 10-1997

station, the characteristic length D is the inside pipe diameter at the pressure measuring station and the kinematicviscosity, Y is that which existsforthe statictemperatureandpressureat the measuring station.Thepressureandtemperaturemeasuring stations for flow metering calculations shallbe specified as in Section 4 and the accompanying illustrations.Thevariables in theReynoldsnumbermust beexpressed in consistentunits to yield a dimensionless ratio.

2.6.5 Gas Work. Gas work is the enthalpy rise of a unit mass of the gas compressedanddelivered by thecompressorfromthe inlet total pressure and temperature to the discharge total pressure and temperature. 2.6.6 Cas Power. Gas power is the power transmitted to the gas. It is equal to the product of the mass flow rate compressed and the gas work plus the heat loss fromthecompressed gas. 2.6.7 Isentropic Efficiency. The isentropic efficiency is the ratio of the isentropic work to the gas work.

2.7.2 Dimensional Constant. The dimensional constant, gc, is required to accountfortheunitsof length, time, and force. It i s equal to 32.174 ft-lbm/ Ibf sec2. The numerical value is unaffected by the local gravitationalacceleration.

2.6.8 Polytropic Efficiency. The polytropic efficiency is the ratio of the polytropic work to the gas work.

2.7.3Specified Operating Conditions. Thespecified operating conditions arethose conditions for which the compressor performance is to be determined. Refer to paras.6.2.3 and 6.2.4.

2.6.9ShaftPower(BrakePower). The shaft power (brake power) is the power deliveredto the compressor shaft. It is the gas power plusthemechanical losses in thecompressor.

2.7.4 Test Operating Conditions. The test operating conditions are theoperating conditions prevailing during thetest.Refer to paras.6.2.7 and 6.2.8.

2.6.10Isentropic Work Coefficient. The isentropic work coefficient is thedimensionless ratio of the isentropic workto the sum of the squares ofthe blade tip speeds of all stages in a givensection.

2.7.5Equivalence. The specifiedoperating conditions and the test operating conditions, for the purpose of this Code, are said to demonstrate equivalence when, for the sameflow coefficient the ratiosof the three dimensionless parameters (specific volume ratio, Machine Machnumber, and Machine Reynolds number) fall within the limits prescribed in Table 3.2.

2.6.1 1 Polytropic Work Coefficient. The polytropic work coefficient is thedimensionless ratio of the polytropic work to the sum ofthe squares of the blade tip speeds of all stages in a givensection. 2.6.1 2Mechanical losses. Mechanical lossesare the total powerconsumedby frictional losses in integral gearing,bearings,andseals.

2.7.6Raw Data. Raw data is the recorded observation of an instrument taken during the testrun.

2.6.13 WorkInput Coefficient. The work input coefficient is the dimensionless ratio of the enthalpy rise to the sum of the squares of the tip speeds of all stages in a givensection.

2.7.7Reading. A reading i s theaverageofthe corrected individual observations (raw data) at any givenmeasurementstation. 2.7.8TestPoint. Thetest point consists of three or more readings that have been averaged and fall within thepermissiblespecified fluctuation.

2.6.14 Total WorkInput Coefficient. The total work input coefficient is the dimensionless ratio of the total work input to the gas to the sum of the squares oftheblade tip speeds of all stages in a givensection.

2.7

2.7.9 Fluctuation. The fluctuation of a specific measurement is defined as the highest reading minus thelowestreading divided by the average of all readingsexpressed as a percent.

MISCELLANEOUS

2.7.1FluidReynolds Number. The Fluid Reynolds number is the Reynolds number for the gas flow in a pipe. It is defined by theequation Re = VD/v, where the velocity, characteristic length, and static kinematic viscosity are to be used as follows: velocity V is the average velocity at the pressure measuring

2.8INTERPRETATION

2.8.1 Certainvaluesforthermodynamicstateand mass flow rateareused in the computation of the dimensionless performance parameters M, Re, r,, 4, P,,, pi, T,, and Unlessotherwise specifically

s1.

a

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ASME PTC 10-1997

COMPRESSORS A N D EXHAUSTERS

stated, the thermodynamic total conditions are used. The subscripts usedin these equations are interpreted as follows. 2.8.1.1 The subscript "i" on thermodynamic state variablesdenotes inlet conditions. For singleentry streams it refers to conditions at the section inlet measurementstation.For multiple inlet streams it refers to a calculated mixed state.Seepara. E.5 of Appendix E. 2.8.1.2 The subscript "d" on thermodynamic state variables denotes discharge conditions. It refers to conditions at the mainstream discharge measurement station. 2.8.1.3 Thesubscript "rotor" i s used on mass flow rate to denote the netmass flow rate compressed by the rotor. Its determination requires that all measured flows and calculated leakages are considered.

9

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S T D * A S M E P T C LO-ENGL L797 W 0757b70 UbO5439 515 H COMPRESSORSANDEXHAUSTERS

SECTION 3 3.1

ASME PTC 10-1997

- GUIDING

PLANNING THE TEST

3.2

3.1.1 Before undertaking a test in accordance with the rules of this Code, the Code on General Instructions,PTC 1, shallbeconsulted. It explainsthe intended use of the Performance Test Codes and i s particularly helpful in the initial planning of the test.

TYPES OF TESTS

ThisCodedefines two typesof test which are based on the deviations between test and specified operating conditions. 3.2.1 Type 1 testsare conducted with the specified gas at or very near the specified operating conditions. Deviations in the specified gas and operating conditions are subject to the limitations imposed by Table 3.1. These limitations are subject to thefurther restriction that their individual and combined effects shall not exceedthe limits ofTable 3.2.

3.1.2 When a test is to be conducted in accordance with this Code, thescopeandprocedures to be used shall be determined in advance.Selections of pipe arrangements, test driver, instruments, and test gas, if applicable,shallbe made.Estimates ofthe probable uncertainty in the planned measurements shouldbe made.

3.2.2 Type 2 testsare conductedsubject to the limits ofTable 3.2 only. Thespecified gas ora substitute gas may be used. The test speedrequired is often different from the specified operatingcondition speed.

3.1.3 The scope of the test shall be agreed to by the interested parties. This may be dictated in advance by contractual commitments or may be mutually agreed upon prior to the start of the test. This Code contains procedures for a single point performance test and gives guidance on determining a complete performancecurve.

3.2.3 Theselection of test type shall bemade in advanceof the test. In theinterestof maximizing accuracy of test results it is desirable that test conditions duplicatespecifiedoperatingconditions as closely as possible.The limits in Table 3.1 provide maximum allowable deviations of individual parametersforType 1 tests.The limitations of Table 3.2 providemaximumallowabledeviationsofthe fundamental dimensionless parameter groupings for both types.Theemphasis in conducting either a Type 1 or Type 2 test should be toward minimizing these deviations. The mostreliable test results would be expected when the deviations in both tables are minimized.

3.1.4 Specifiedconditions, that is, mass flow rate, inlet conditions of pressure,temperature, humidity, discharge pressure, cooling water temperature if applicable, speed, gas properties,andinputpower expectedshallbedefined. 3.1.5 A detailed written statement of the test objectives shall be developed prior to conducting the test.

3.2.4 Calculationprocedures are given in Section 5 for gases conforming to Ideal GasLaws and for Real Gases. Where the compressibility values depart from the limits prescribed in Table 3.3 the alternate calculation procedures provided for Real Gases shall be used. These alternate procedures applyto calculations foreitherType 1 orType 2 tests.

A test facility shall be selected. Typically this is themanufacturer’stest stand orthe user’s installation site. 3.1.6

3.1.7 Thenumberoftestpersonnelshouldbe sufficient to assure a careful and orderly observation ofall instruments with timebetweenobservations to check for indications of error in instrumentsor observations.

3.3

3.1.8 An individual shall be designated as responsible for conducting the test.

LIMITATIONS

3.3.1 Compressorsconstructed withliquid cooled diaphragms,or built-in heatexchangers,shallbe 11

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PRINCIPLES

S T D D A S M E P T C L O - E N G L L777 m 0757b70 ObOSqqO 237 M ASME

10-1997

COMPRESSORS AND EXHAUSTERS

TABLE 3.1 PERMISSIBLEDEVIATION FROM SPECIFIEDOPERATINGCONDITIONS TYPE 1 TESTS

FOR Permissible

Symbol

Variable Inlet pressure Inlet temperature S P d Molecular weight Cooling temperature difference Coolant flow rate Capacity

596 8%

psia

Pi Ji

OR

N

rPm Ibm/lbmole

MW

2%

2%

5%

O R

gal/min ft3/m in

4i 4%

3yo

GENERALNOTES: (a) Type 1 tests are to be conductedwith the specifiedgas. Deviations are based on the specified values where pressures and temperatures are expressedin absolute values. (b) The combined effect of inlet pressure, temperature and molecular weight shall not produce more than an 8% deviation in the inlet gas density. (c) The combined effect of the deviationsshall not exceed the limited of Table 3.2. Cooling temperature difference is defined as inlet gas temperature minus inlet cooling water temperature.

TABLE 3.2 PERMISSIBLE DEVIATION FROM SPECIFIED OPERATING PARAMETERSFOR TYPE 1 AND 2 TESTS limit of Test Values as Percent of Design Values Parameter Specific volume ratio

105

Flow coefficient

Symbol

Min

vh’d

95

4

96

Milx

104

Machine Mach number Centrifugal compressors Axial compressors

See Fig. 3.3 See Fig. 3.4

Machine Reynolds number Centrifugal compressors [Note Rem(111

See Fig. 3.5

Axial compressors where the Machine Reynolds number at specified conditions is below 100,000 105

90 [Note (111

Axial compressors where the Machine Reynolds number at specifiedconditions is above 100,000

10

200

NOTE:

(1) Minimum allowable test Machine Reynolds number is 90,000.

12

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PTC

COMPRESSORS ASME AND EXHAUSTERS

10-1997

TABLE 3.3 LIMITS OF DEPARTURE FROM IDEAL CAS LAWS GASES

OF SPECIFIED A N D TEST

~~

1.12

Pressure

Maximum Ratio

Ratio

k rnaxlk min

1.4 2

4

1

8 16 32

1.10 1.o9

.O8 1.O7 1 .O6

~~

Allowed Range for Function X

~~

~

Allowed Range for Function Y

Min

Max

Min

-0.344 -0.1 75 -0.073 -0.041 -0.031 -0.025

0.279 0.1 67 0.071 0.050 0.033 0.028

0.925 0.964 0.982 0.988 0.991

0.993

Max 1.O71 1 .O34

1 .o1 7 1 .o1 1 1 .O08 1.006

GENERALNOTES: (a)Where: X =

T av - 1 and v a-r

-

Y = 72)(See Figs. 3.6 and3.7) V

ap T

(b) Maximum and minimum values of k shall apply to both the specified andtest gas over the complete range of conditions. (c) When these limits are exceeded by either the specified gas or the test gas at any point along the compression path real gas calculation methods shall be usedfor that gas. Ideal or real gas method may be used if these limits are not exceeded.

test providing all conditions, including those at the sidestream,meettherequirementsofTable 3.1. Compressors with sidestreamsmayalsobetested by individual sections utilizing the criteria for a Type 2 test.

tested on thespecified gas and at theoperating conditions specified for the inlet pressure, inlet temperatureand speed, and with the flow rateand the temperature specified for the cooling fluid. The fluctuations of the test readings shall be controlled within the limits ofTable 3.4. Theresultsshallbe computed by themethodsprovidedfor a Type 1 test, andreported “as run.”

3.3.5 Where condensation can take place between compression sections; for example, intercooled compressors handlingmoist air; thecapacityshall be measured a t thecompressordischarge.(Foratmosphericexhausters the flow shall bemeasuredat theinlet.)Care shall be taken to assure that there is no liquid carry-overfromthe intercoolers.

Themethodsof this Codemay be applied for conversion of testresults to specified operating condition results for compressors which maybe treated as oneormoresections. A section is that portion of a compressorwherenointermediate streamleavesorentersbetweenone impeller inlet andthe sameoranother following impeller discharge. See Table 3.2. Heat exchangers are excluded from the interior of the section boundaries. Section boundaries are indicateddiagrammatically in Fig. 3.1. The gas state and flow rate shall be established for each stream where it crosses the section boundary.Thepowerabsorbedandheatloss or gain by naturalambientheattransfermustalso be determined.

3.3.2

in practice differ between test and specified operating conditions due to leakagedifferences.Forexample, it is common to test at reduced inlet pressure andthereduced differential pressureacross a seal to atmosphere could result in zero or negative leakage. As a result, volume flow ratio equalitycannot be achieved betweentestandspecifiedconditions. Therefore, it shall be necessary to estimatethe leakage ratio; that is, the leakage mass flow divided bythe inlet mass flow for both test andspecified conditions. If theleakage ratio differencebetween test andspecified is significant,theseeffectsshall be appliedto the calculations of capacity and power.

3.3.6 Volume flow ratiosmay

3.3.3 Compressors with externallypiped intercoolersmaybegiven a Type 1 test ortheymaybe tested by individual sectionsusing a Type 2 test. 3.3.4 Compressors with inlet or outlet sidestreams may be testedusingtheproceduresfor a Type 1 13

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PTC

ASME

1 O- 1997

COMPRESSORS AND EXHAUSTERS

TABLE 3.4 PERMISSIBLE FLUCTUATIONSOF TEST READINGS' Symbol

Measurement ~~~

~

~

Inlet pressure Inlet temperature Discharge pressure Nozzle differential pressure Nozzle temperature Speed Torque Electric motor input Molecular weight Cooling water inlet temperature Cooling water flow rate Line voltage

MW T

2%

psia "R psia

0.5% 2%

PSi "R

2% 0.5%

rPm

0.5%

Ibf ft

1 Yo

kW lbdlbmole

0.25%

"R

0.5% [Note (2)1

gal/min volts

2%

1Yo

2%

GENERALNOTES: (a) A fluctuation is the percent difference between theminimum and maximum test reading divided by the average of all readings. (b) Permissible fluctuations apply to Type 1 and Type 2 tests. NOTES (1) Seepara.5.4.2.3. (2) See para. 4.1 6 for further restrictions.

Power in

r--

I

L

-7 -

c

-------

/1

lest section boundary

Multiple entry streams

I I ""-

I

" I

I

4

-

FIG. 3.1 SECTIONCONTROLVOLUMES 14

I I

" " "

Heat transfer

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Multiple exit

S T D - A S M E P T C 10-ENGL L997

0 7 5 9 b 7 0 Ob05YY3 T q b

COMPRESSORS AND EXHAUSTERS

ASMEPTC 10-1997

In many cases it is not practical to measurethe leakage flow and it is permissible to use calculated values of leakage for test and specified conditions.

speeds of rotating equipment in selectingthetest speed. shall not exceed Testpressuresandtemperatures the maximum allowable pressures and temperatures for thecompressor.

3.3.7 Where the efficiency is to be determined by shaft input power measurementsthebearingand seallosses shouldnotexceed 10 percent of the total test power. This will minimize theeffectof uncertainties in the bearing and seal loss determination of gas power.

3.5

3.5.2 It is necessary to maintain a consistency betweenspecifiedvolume flow rate ratio and test volume flow rate ratio for each section. Permissible deviationsfromtheseratiosare listed in Fig.3.2. As an example, in the first section ofa multisection compressor,the ratio of inlet volume flow rate to dischargevolume flow rate for thespecifiedand test conditions must be held to within +S percent which is the same as that required for conventional compressors in Table 3.2. In addition, it is required thatthe ratio of first stage sectiondischarge flow rate to secondsection inlet volume flow rate for the specified and test conditions be held to within 2 1 O percent.This is required so that the total pressure determined at thesidestreamflange will havethesame relationship to the total pressure actually existing atthe exit of the first section boundary for specified and test conditions. For thesecondandsucceedingsectionstherequirements are similar. The ratio of inlet volume flow rate to discharge volume flow rate for specified andtest conditionsmustbeheld to within +5 percent. Also, the preceding section discharge volume flow rate to sidestream inlet volume flow rate ratio for specified and test conditions must be held to 21O percent.Finally,the ratio ofthedischargevolume flow rateofthesectionbeingtested to thenext sidestream volume flow ratemustalsobeheld to 2 1 O percent. This requirement is most important in the second section of a three section machine where both inlet anddischarge total pressuresare being determined at the sidestreamflanges andvelocity similarities arenecessary for test accuracy. Code requirements arealsodescribed in equationform in Fig. 3.2.

3.3.9 When power is to be determined by the heat balancemethod, the heatlossesdue to radiation andconvection,expressed in percentof the total shaftpower,shall not exceed 5 percent. 3.3.10 ForType 2 tests, the inlet gas condition shallhave a minimum of 5°F of superheat.

TEST CAS AND SPEED

3.4.1 The physicalandthermodynamicproperties of thespecified and test gas shall beknown.The option of using tabulated data, an equation of state correlation, or experimental determination as a source for theseproperties shall be agreed upon prior to the test. 3.4.2 The following physicalproperties of thetest gas throughout the expected pressure and temperature range shall be known or accurately determined: (a) molecular weight (b) specific heat at constant pressure (cf) (c) ratio of specific heats (c&) (d) compressibility factor (Z) (e) dew point (fl viscosity (g) isentropic exponent (h) enthalpy (i) acoustic velocity 3.4.3 Thetestspeedshallbeselected so as to conform to the limits of Table 3.2.Thetestspeed shall not exceedthe safe operating speed of the compressor. Consideration shouldbe given to critical 15

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INTERMEDIATE FLOW STREAMS

3.5.1 Section Treatment. Compressors having flowsaddedorremoved at intermediatelocations betweenthe inlet and final dischargearehandled by treating the compressor by sections. The gas state and flow rateshallbeestablished for eachstream where it crosses the section boundary.

3.3.8 Evaluation of performanceofcomponents between sections, if any,such as heatexchangers, piping, valves,etc., is generallybeyondthescope of this Codeandshallbeagreeduponbyparties to the test.The specifiedoperating condition performance of suchcomponentsorthetechnique for correctionof testresults to specifiedoperating conditions shall be agreed upon by parties to the test.

3.4

m

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subscript

whelre:

go

h2-2)t

93 = 42

‘q3-2

Section 1 inlet from measurements

Section 1 diiharge from measurementa side&earn

Section 2 inlet from measurement,

1 -

2 =

3 =

(r~-2)sp

95

- (rq7-2lt (rql-2M.J

q’ 92

Min.

=

1

‘ql-2

Section

flange

computed before

flange

,,o

105

Max.

FIG. 3.2

(rpl-5)t

9 44 = 45

Section

TYPICAL SIDELOAD

46

= 45

subscript7

Q8

rq7a = 41

QL%5

SECTIONAL COMPRESSORS

flange

Section 3 inlet from measurements

6 -

inlet computed

110

105

110

Max.

Section 2 discharge computed from internal measurements before ridestream

2 mixed

go

95

9o

Min.

2

5 -

4 = Section

(r,&sp

(rq8-5)t

(r++p

(rq3-2)t (rql.2)sp

(13

= -

subscript

re5=$

w-5

rq3-2

---------

h&t

3 mixed

105

110

Max.

from

inlet computed

95

w

Min.

3

8 = Section 3 discharge flange measurements

= Section

&8-5)w

section

S T D - A S M E P T C LO-ENGL L997 m 0 7 5 9 b 7 0 0 b 0 5 4 4 5 8 1 9 m COMPRESSORS AND EXHAUSTERS

ASMEPTC 10-1997

3.5.3 Inward Sidestreams. Whenthe sidestream flow is inward,thedischargetemperatureofthe precedingsectionshallbe measured prior to the mixing ofthe two streams. This temperature measurement shall bemade in a portion ofthedischarge flow stream where the sidestream cannot affect the raw data. Raw data may be affected by heat transfer froma cold sidestream to a hotmainstream flow or fromrecirculation which mayoccur within the flow passage. The discharge temperature is needed to compute the performanceof the preceding section and to computethereferencemixedtemperature for the nextsection inlet. It is possible for internal total pressures to exceed flange total pressure dueto the higher internal velocities. The higher internal velocities are accompanied by a lower static pressure which provides a pressure difference for inward flow. 3.5.4 Temperature Stratification. It is common for sideload sectional compressors to have temperature differences between the mainstream and sidestream. When testing all sections of a multisection compressor (threeormoresections)simultaneously,large differences between the sidestream and mainstream temperatures may occur. It is possible, due to these differences, for thermal flow stratification to exist within thecompressorsections. This stratification mayresult in inaccurate measurements of internal temperatures in downstreamsections.Undertest conditions, the stream temperature differences should be maintained as close to specified as practical.

3.5.7 It is recommended that eachsection of a multisectionmachinehaveits own performance curvedefinedby a number of testpoints.This enables synthesis of the combined overall performance curve and provides data on the interrelations of the individual sections. The ratios of Fig. 3.5 will apply at all points unless other specified operating ratiosare identified.

3.6

SAFETY

3.6.1 Thetest gas usedshallbe in compliance with local regulationsandprudentpractice with regard to flammability and/or toxicity. Testgasesused in a closed loop shall be continuously monitored for composition and avoidance of combustible mixtures. Air or other oxidizing gases shallnotbeused in aclosedloop.

3.6.2

3.6.3 The party providing thetestsite will be responsible for establishing the requirements of systemprotection.Considerationshouldbegiven to the needfor relief valves for accidental overpressure. Therequirement of alarmsand/orautomaticshutdown devicesforsuchitems as high temperature, loss of cooling water, low oil pressure,compressor overspeed, or other possible malfunctions should be reviewed,

3.5.5 Performance Definition. Thesectionalhead, efficiencies,and pressures are definedflange to flange. The only internal measurementsneededare the sectional discharge temperatures for computing the mixed temperature conditions and sectional performance.Thepressureusedforcalculatingthe sectionalperformance is assumed to be equal to the sidestreamflange total pressure. The internal mixedtemperatureshould be computed on a mass enthalpy basis (real gas evaluation) for obtaining the inlet temperature for succeeding sections. Simplified mixing based on mass temperaturemaybedone for ideal gases with constant specific heat.Forfurther information see para. E.5 of Appendix E.

3.7

PIPING

3.7.1 Piping arrangements required to conducta test under the Code are detailedin Section 4. Permissible alternatesaredescribed for convenienceand suitability. A selection suitable for the prevailing test conditions shall be made and described in thetest report. When the choke point is to be determined, care should be taken to assure that the compressor pressurerise shall exceedsystemresistance. 3.7.2 Minimum straightlengths ofpiping at the inlet, discharge, and on both sides of the flow device arespecified in Section 4. When compressorsaretreated as anumber of individual sections, these piping requirements apply to each section. Such piping between sections may not occurnaturally in thedesign. When it does

3.5.6 Extraction Sidestreams. Whentheintermediate flows are removed (¡.e., bleed-off) fromthe compressor,they will cross asectionboundary. 17

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The internal temperatureandpressurecanbe assumed to be equal to the external flange temperatureand pressure oftheprimary internal stream. The ratio of flow raterestrictions in Fig. 3.2 shall also apply to outward flowing sidestreams.

ASME PTC 10-1997

EXHAUSTERS

AND

COMPRESSORS

O .3

0.2

0.1

8

BI

0.0

Ë

S

-0.1

-0.2

I -0.3 I O

I

I

I

I

I I

0.2

I I

I I

0.4

I I

I I

1

I

I

I

I

I

I

I

I

I

I

1

I

I

I

0.6

0.8

Mach No. Specified

FIG. 3.3

-

1.o Mmsp

A L L O W A B L EM A C H I N EM A C HN U M B E R CENTRIFUGAL COMPRESSORS

I I

I

I

I

I

I

I

I

1.2

1.4

1.6

DEPARTURES,

not, the parties to the test should elect by mutual agreement to: (a) install additional piping between the sections (6) take measurementsin the availablespace. Consideration shall be given to any compromise in measurement accuracy and its effect upon the final test objective. (c) remove components such as external heat exchangers and replace them with the required piping. When this alternate is selected it is important that the removal of the component have a negligible effect upon the section entry or exit flowfield so as not to affect the section performance parameters.

shall be designed for the maximum pressure plus a suitable safety factor and the cooler shall be sized to dissipatethe maximum heatload. Additional lengthsof piping beyondthe minimum prescribed may be requiredto provide additional system capacitance.Provisionsmay be necessary toallow for expansion of the piping and the piping design shall beofsufficientstrength to withstandthe stresses imposed during compressorsurge.

3.7.3 Where externalintercoolerperformanceand

Test instruments shall be selected, calibrated, and installed in accordance with therequirements of Section 4.

3.8

pressure drop are known for the specified operating conditions,ordeterminedon a separatetest, the compressor may be tested as separate sections and the combined performance computed by the method described in Section 5.

INSTRUMENTATION

3.7.4 If a closed loop test i s to beperformed, the 3.9 PRETEST maximum messure to be obtained and themaximum heat load shallbeestimated.The piping andcooler Pretest inspection may be of interest to either from thecompressordischarge to the throttle valveparty.Refer to PTC 1 forguidance. 18

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S T D - A S M E P T C LO-ENGL L997 D 0 7 5 7 b 7 0 O h 0 5 4 4 7 bqL COMPRESSORS ASME AND EXHAUSTERS

PTC 10-1 997

Mach No. Specified - Mmsp

FIG. 3.4

3.10

A L L O W A B L EM A C H I N EM A C HN U M B E R COMPRESSORS

(i) lubricant temperatures, inlet and outlet of bearings, seals, and speed changing gear, if applicable (j) coolant and lubricant flows, if applicable fk/ barometric pressure (I) gas analysis, if atmospheric air is not the test gas (m) time

PRETEST R U N

3.10.1 Thecompressorshallbeoperated for sufficient time at the required conditions to demonstrate acceptable mechanical operation and stable values of all measurements to be takenduringthe test, Preliminarydatashallbetaken to familiarize test personnel, to determine if all instrumentsare functioning properly,and to ascertain if thereading fluctuations fall within the limits prescribed in Table 3.4.

3.10.3 A set ofcalculationsshall be madeusing the preliminary testdata to assure that the correct test speed has been selected, that the test parameters required in Tables 3.1 or 3.2, as applicable,were obtainedand that theoverallperformancevalues arereasonable.

3.10.2 All instrumentobservationspertinent to the testshall be taken during the pretest run. They commonly include the following: (a) inlet pressure (b) inlet temperature (c) relative humidity orwet bulb temperature, if atmospheric air is the test gas (d) discharge pressure (e) discharge temperature and/orshaft power input (0 flow device pressures and temperatures (gl speed (h) cooler inlet and outlet temperatures,gas and coolant sides, if applicable

3.10.4 Thepretestrunmaybeconsidered as part of the test if it meets all requirementsofthetest.

3.11

TEST OPERATION

3.11.1 Thecompressor shall be operated at the requiredconditions for a sufficient period of time to demonstrate that all variables have stabilized. 3.11.2 When all variableshavestabilized,the test personnelshall take thefirst set ofreadings of all 19

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DEPARTURES, AXIAL

~~

S T D - A S M E P T C 10-ENGL L797

m

0757b70. Ob05448 528

m EXHAUSTERS

ASME PTC 10-1997

GENERAL NOTE: 90,000 is cutoff

FIG. 3.5

ALLOWABLE MACHINE REYNOLDSNUMBER CENTRIFUGAL COMPRESSORS

greater of specified capacity). When the compressor is used with a variable speed driver additional points maybe run onselectedspeedlines, provided that an equivalent speed is generated for each operating point selected.

essentialinstruments.Three sets of readingsshall be taken during eachtest point. 3.1 1.3 The minimum duration of a test point, after stabilization, shall be 15 minutesfromthe start of the first set of readings to the end of the third set of readings.

3.11.6 The flow at which surgeoccurscan be determined by slowly reducing the flow rate at the test speed until indications of unstable or pulsating flow appear. The severity of surge will vary widely as a function of pressure ratio, type of compressor, andcapacitanceofthe piping system.Surgemay be identified by noise, fluctuations in the differential pressure of the flow nozzle, or a drop and/or fluctuation of the pressure and/or temperature. When the surge flow has been identified, the flow shouldbeincreased slightly until stableoperation is restored so that a complete set ofperformance datamaybetaken.Thisprocessmayberepeated a second time to demonstrate the reliability of the initial setting. It should be understood that a surge flow established in a shoptestmay not definethe surge conditions which will occur in the field due to

3.11.4 When a test is only to verify a single specified condition, the test shall consist of two test points which bracket the specified capacity within a range of 96 percent to 104 percent.

3.1 1.5 When performancecurves are required to verify the complete compressor range of operation, a multipoint test shall beperformed. Each point selected along the curve shall be assumed to be a specified point andcheckedforequivalency.This may require a different equivalent speed foreach test point. Usually five pointsshouldbe used to complete a curve. A point shall be taken at approximately the specified capacity. The additional points should consist of one point nearsurge, two points between specified capacity andsurge, and one point in the overload range (preferably 105 percentor 20

COPYRIGHT American Society of Mechanical Engineers Licensed by Information Handling Services

DEPARTURES,

PTC 10-1997

COMPRESSORS ASME AND EXHAUSTERS

12

10 9

FIG. 3.6

SCHULTZ COMPRESSIBILITYFACTOR

differences in piping configurationand sponse.

- FUNCTION

3.12

system re-

INCONSISTENCIES

3.12.1 Where four independent instruments are used to measure a pressure ortemperaturevalue andonerecordedobservation is inconsistentdue to measurementerror, its valueshall be discarded and the value determined from the average of the otherthree.Wherefewerthanfourindependent measuring devices are used, all values shall be used and averaged to determine the measurement value.

3.11.7 Thechoke flow maybedeterminedby gradually opening the discharge throttle valve while maintaining speed and inlet pressure until the flow remainsessentiallyconstant with decreasing dischargepressure. If the compressoris to be operated as an exhauster ortested with an opendischarge,thechoke flow may be determined by gradually opening the inlet valve whileholding speed anddischargepressure constant. If choke flow is to bedetermined,the facilities shall be designed so as not to limit maximum flow.

3.12.2 Thethreereadings for eachtest point shall be within thefluctuationtolerances listed in Table 3.4. 21

COPYRIGHT American Society of Mechanical Engineers Licensed by Information Handling Services

Y VERSUS REDUCED PRESSURE

ASME PTC 10-1997

COMPRESSORS AND EXHAUSTERS

Reduced Pressure, Pr

FIG. 3.7 SCHULTZCOMPRESSIBILITYFACTOR

3.13

- FUNCTION X VERSUSREDUCEDPRESSURE

ERRORS AND UNCERTAINTIES

3.14 TEST LOG SHEETS Thetest log sheet shall identify thecompressor manufacturer, model, and serial number. Test location, driver identification, test instruments used, and test date shall be listed. Raw data for each test point shall be recorded as observed on the test log sheet as well as the time of each set of data. Corrections and corrected readings shall be listed separately in the test report. At the completion of the test the log sheets shall be signed by therepresentatives of theinterested parties. Copies of the complete log sheets shall be furnished to the interestedparties.The test report shall be completed in accordance with the instructions in Section 6.

3.13.1 It should be recognizedthattheresults of the test calculations are subject to errorcaused by theinaccuracies of the testinstrumentsand/or procedures. It is recommendedthat an uncertainty analysis be made prior to the test to assure that the test objectives can be met. The detailed procedures are given in PTC 19.1 and arediscussed in para. 5.7 of this Code.

3.13.2 The uncertainty is a measure of the quality ofthe test andshouldnot beused as a measure of the quality of the machine.

22

COPYRIGHT American Society of Mechanical Engineers Licensed by Information Handling Services

S T D - A S M E P T C LO-ENGL L777 H 0 7 5 7 b 7 0 Ob0545L 0 3 2 ASME PTC 1O- 1997

COMPRESSORS AND EXHAUSTERS

SECTION 4

- INSTRUMENTSANDMETHODSOF MEASUREMENT 12 taps displaced 45 deg. fromthemandatleast in. downstream. In special cases when atmospheric conditions satisfytherequirements,thecompressormayberun without an inletpipe as shown in Fig.4.2.The inlet opening shall be protected with a screenand bellmouth suitably designed to eliminate debris and minimize entrancelosses(seepara.4.4).The total inlet pressure is equal to atmospheric pressure. Temperature measuring devices shall be located on the screen to measure the temperature of the air stream at thecompressor inlet. Forcompressors with an axial inlet, the impeller may,undersomeconditions, produce a vortexat the pressure station to cause substantial error in the measurement of inlet pressure.Users of this Code, by agreement,mayusevanes suitably designed for low pressure loss to prevent rotation at the pressure taps.Thestaticpressurestationsshall notbe less than four pipe diameters upstream of the compressor flange as shown in Fig.4.3.

4.1 METHODS 4.1.1 The choice of methods provided in this Code will depend on the compressor,thespecified gas, andthetypeoftestselected.

4.2

INSTRUMENTATION

4.2.1 ThePerformanceTestCodeSupplements in the PTC 19 series on InstrumentsandApparatus provide authoritative information concerning instrumentsand their use andshouldbeconsultedfor suchinformation.Theselection of instrumentation shall be determined by the uncertainty limit requirementsofthetest as well as suitability forthetest siteconditions.Theinstrumentselectionshallbe justified by calculation that the uncertainty in results meets the statedtestobjectives. Instrumentation is required to determine the inlet and discharge gas states, flow rate, and compressor speed. Depending upon the method selected, additional instrumentation may be required to determine test power.

4.3

4.3.3 Typicaldischarge piping required for compressors are outlined in Fig.4.1.The minimum straight length of discharge pipe required before and after the instrumentation is specified. The four static pressuretapsarea minimum of 12 in. downstream ofthedischargeopening.Thepressuretapsare followed by the four temperature taps displaced 45 deg. fromthemandatleast 8 in. downstream. Analternatearrangementmaybeusedwhen a compressoroperating as an exhauster on air has a dischargevelocitypressure less than 5 percent of the total pressure. In this case the compressor can berun without a discharge pipe as shown in Fig. 4.4. The discharge temperature of the gas stream is measuredat the compressor discharge. When the compressor has a volute that produces unsymmetrical flow at thedischargeopeningthe static pressure taps shall be a minimum of six diametersdownstream as shown in Fig.4.5.The other minimum dimensions are specified in Fig. 4.1. Straightening vanesdesigned for low pressure loss,

PIPING

4.3.1 The location of the pressure and temperature measuring stations have specificrelation to the compressor inlet and outlet openings.The pipe sizes shall match theseopenings, Minimum lengthsof straight pipe are mandatory for certain pressure and temperaturemeasurementstationsand for certain flow devices.Pipearrangementsandallowableexceptionsaredescribed in thisSection.Appropriate selectionsshallbemadeanddescribed in thetest report. 4.3.2 Typical inlet piping required for compressors is outlined in Fig. 4.1. The minimum straight length of inlet pipe is determined by what is upstreamof the inlet opening. The four static pressure taps are a minimum of 24 in. upstream of the inlet opening. Downstream of the pressure taps arefour temperature 23

COPYRIGHT American Society of Mechanical Engineers Licensed by Information Handling Services

ASME PTC 10-1997

COMPRESSORS AND EXHAUSTERS

6 minimum

I

12 in. minimum

r

7

12 in. minimum

6 in. minimum

8 in. minimum

h temperature Inlet Inlet static pressure 4 taps spaced 90 deg. apart

Inlet Opening Preceded By Straight run Elbow Reducer Valve Flow device

i

Discharge static pressure 4 measuring from taps spaced 90 deg. apart

4 measuring stations spaced 90 deg. apart (45 deg. from static pressure)

Discharge Opening Followed By

Minimum Dimension A

6

2D

30

20

30 60 IOD

30 ED 3D

I

Straight run Elbow Reducer Valve Flow device

5D

I

L

Discharge temperature 4 measuring taps spaced 90 deg. apart (45 deg. pressure) static

Minimum Dimension

A

6

20 20 30 30 80

30 30 50 5D IOD

~

For open inlet, see Fig. 4.2.

For open discharge, see Fig. 4.4.

For vortex producingaxial inlet, see Fig. 4.3.

For diffusing volute with unsymmetrical flow, see Fig. 4.5. Discharge Configuration

Inlet Configuration

FIG. 4.1

INLETANDDISCHARGECONFIGURATION

Protecting screen

Inlet pressure by barometer

7

Inlet temperature 4 measuring stations spaced 90 deg. apart

FIG. 4.2 OPEN INLET 24

COPYRIGHT American Society of Mechanical Engineers Licensed by Information Handling Services

ASMEPTC

COMPRESSORS AND EXHAUSTERS

r

10-1997

See Fig. 4.1 for

minimum dimensions 1D min

Inlet static pressure 4 taps spaced 90 deg. apart

Inlet temperature 4 measuring taps spaced 90 deg. apart (45 deg. from static pressure)

A-

4Dmin.

v

L Straightener (optional) See Fig. 4.8, para. 4.5

FIG. 4.3VORTEX

PRODUCING AXIALINLET

Discharge static pressure by barometer (when discharge velocity pressure exceeds 5% of total pressure use discharge pipe arrangement, Fig. 4.1)

Discharge temperature 4 measuring locations spaced 90 deg. apart

U

FIG. 4.4

OPEN DISCHARGE

as covered in para. 4.5, maybeused by mutual agreement to minimize the effect of the unsymmetrical flow.

for the conditions. In general, a screen on the inlet must be strongenough to preventcollapse in the event of accidental clogging. The mesh of a screen shall be selected to prevent entry of foreign matter which might damage thecompressorandimpair itsperformance.Reliable tests cannot be made on atmospheric air laden with dust, oil-fog, paint spray, orotherforeignmatter which may foul the flow passage of thecompressor.Protectivescreensshall have an open area at least two timesthat of the compressor inlet or the nozzle pipe. When screens with very small mesh orfilters are used, inlet pressure

4.3.4 Figures 4.6 and 4.7 show a typical arrangement for testing with ageneralclosed loop and closed loop with sidestreams.

4.4 PROTECTIVE

SCREENS

4.4.1 Compressors operating with an open inlet shall beprotected with ascreen orfilter,suitable 25

COPYRIGHT American Society of Mechanical Engineers Licensed by Information Handling Services

S T D - A S M E PTC L O - E N G L L797 ASME PTC 10-1997

m

0757b70 Ob05454 821 W

EXHAUSTERS

AND

COMPRESSORS

Discharge static pressure 4 measuring taps spaced

minimum dimensions

Discharge temperature 4 measuring tapsspaced 90 deg. apart (45 deg. from static pressure)

Straightener (optional) See Fig. 4.8, para. 4.5

FIG. 4.5

DIFFUSINGVOLUTEDISCHARGEWITHNONSYMMETRICFLOW

Cooling water inlet temp.

arrangement

straightener and

III

v”

Drain pot

a Drain tank

FIG. 4.6

TYPICALCLOSED

26

COPYRIGHT American Society of Mechanical Engineers Licensed by Information Handling Services

Gauge

LOOP

S T D . A S M E P T C LO-ENGL

L777

COMPRESSORS AND EXHAUSTERS Flow equalizer measuring straightenerand

Nozzle arrangement (See PTC 19.5)

Y-

Drain pot

-i!&+ Drain tank Gauge

II-I Cooling

,

0757b70 O b 0 5 4 5 5 7bB

water inlet temp.

ASMEPTC 10-1997

Inlet

Inlet measuring stations (See Fig. 4.1

'

""" jJ

Valves for charging and venting gas

Nozzle measuring arrangement (See PTC 19.5)

Throttle valve

Relief valve

n -

I m

Flow equalizer and straightener

-" LJ

\ Flow nozzle

Drain tank Gauge

? i l + FIG. 4.7

TYPICALCLOSEDLOOP

27

COPYRIGHT American Society of Mechanical Engineers Licensed by Information Handling Services

WITH SIDESTREAM

S T D - A S M E P T C 10-ENGL 2 9 9 7

0759b70 O b 0 5 4 5 b bTq COMPRESSORSANDEXHAUSTERS

ASME PTC 10-1997

shall be measured by static taps as provided in Fig. 4.1 for straight pipe.Where screens or filters are used in a closed loop, precautions such as measurement of the differential pressurearerecommended.

4.5

4.6 PRESSURE MEASUREMENTS 4.6.1 Reference should be made to PTC 19.2, forgeneral information on instruments to measure pressure.For therangeofpressures likely tobe measured in compressortest, the manometerand thedeadweightgage shall beused as standards. Pressure transducers and other pressure measurement devices can be used. These can be calibrated using deadweight testers or manometers. Deadweight testers shall be certified by a competentlaboratory. Where gage lines are filled with liquids, means shall be provided to measure the liquid level, and a correction shallbe applied forunbalanced liquid head.

FLOW STRAIGHTENERS A N D EQUALIZERS

4.5.1 Flow straighteners may be installed by mutual agreementof the parties to the test as shown in Figs. 4.3 and 4.5.These flow straighteners may be of the simple vane type, Fig. 4.8, sketch (a), where L/D will beequal to orgreaterthanunity, or of the multitube type,Fig. 4.8, sketch (b), wherethe length-diameter ratio of the tube shall be equal to or greater than eight and a maximum tube diameter of '/sD.

4.6.2 Bourdontubesorsimilar gages shouldbe selected to operate in themid-range of the scale. Thediameters ofthe scalesand thearrangement of thegraduations shall permit easy reading.The temperature of the gage during calibration shall be within 40°F of theambienttemperature prevailing during the test.

Flowequalizers shall be installed if required in PTC 19.5. See Fig. 4.8, sketch (c). Flow equalizers shall be a multihole plate,designed to produce a minimum staticpressure dropof two timesthe calculated velocity pressure forthe pipe section. The total area required of the holes may be determined from the following formula:

4.5.2

4.6.3 Manometerscanbeeither U-tube orsingle leg design. Smallboremanometers are subject to appreciableerrorresultingfrom capillary forces, variable meniscus,andrestrictedseparationofentrained gas bubbles. These errors vary with the type of fluid, the tube diameter, and the tube cleanliness. Singlelegmanometers shall be checkedforzero position before and after test. Manometer fluid shall be chemically stable when in contact with the test gases andmetalpartsof the instrument. The specific gravity andthe coefficient of temperatureexpansion of the fluid shall be determined before the test. See PTC 19.2 for further guidance.

where Ah= total area of holes in plate, sq in. Ap= area of cross section or pipe, sq in. q = inlet volume flow, cfm pi= inlet density,Ibmper CU ft Dp= diameter of pipe, in. pp= densityof gas in pipe upstreamofplate, Ibm per CU ft Ap= pressure drop acrossplate, psi

4.6.4 Deadweight gages andtesters shall be selected to suit the pressure range. Deadweight gages cannotmeasure rapid pressurechangesand where necessarytheyshallbe installed in parallel with a Bourdon tube gage, transducer, or other instrument.

The plate should contain not less than 50 holes persquare foot of area, uniformly spaced, but not less than50holes minimum.

4.6.5 Transducersshallbeselected with pressure ranges appropriate for the expectedtestpressures. They must be calibrated before and after each test. When automated data collection equipment is used with a pressure switching device, and a single transducer, that transducer shall be selected to cover theentirerangeofpressure.Whenusingpressure switching devices, sufficienttime between successive switch points shall be allowed so that the transducer pressure will reach equilibrium for the selected pres-

4.5.3 A combined flow equalizer and flow straightener is used with flow nozzleswhererequiredby PTC 19.5. See Fig. 4.8, sketch (dl. The flow straightener shall be the multitube type as shown in Fig. 4.8, sketch (b), preceded by a flow equalizer onehalf pipediameter upstream. Alternatively three flow equalizers spaced one pipe diameter apart may be used as shown in Fig. 4.8, sketch (e). 28

COPYRIGHT American Society of Mechanical Engineers Licensed by Information Handling Services

ASME PTC 10-1997

lal Simple-Vane Flow Straightener

I

I

L14 (bl Multi-Tube Flow Straightener

(cl Equalizer (Perforated Plateor Screen)

k

4

min.

Id) Combination Equalizer and Straightener

IfD-"-J (e) Multi-Tube Type Equalizer and Straightener

FIG. 4.8

STRAIGHTENERS AND EQUALIZERS

29

COPYRIGHT American Society of Mechanical Engineers Licensed by Information Handling Services

S T D * A S M E P T C LO-ENGL L777 W 0757b70 O b 0 5 q 5 8 477 W COMPRESSORS AND EXHAUSTERS

ASME PTC 10-1997

Themeasurement obtained by a total pressure probe can be influenced to varying extent by spatial location. In the event of significant unresolved differences from the total pressure deduced from the static pressureandaverage velocity, thestatic-pressurebasedresult shall prevail.

sure tap. Equilibrium shouldbe verified as part of the measurementsystem operatingprocedures. Velocity pressure shall becomputed on the basis of average velocity. (Seepara. 5.4.3.)

4.6.6

Static pressure shall be taken as the arithmetic average ofindividual rawdataobservations from four stations,spaced 90 deg. in the same plane of the pipe. Thediameter of the static hole shall not exceedfour-tenths of the pipewall thicknessand it should not be greater than V,, in. in normal circumstances.The hole shallbe drilled smoothandfree of burrs. A preferred connection is obtained by welding a coupling to the pipe and then drilling thehole.Total pressureprobesmaybeused to measurepressure at the samestations thestatic measurements are made. Where the absolute values from four stations differ by more than one percent, the cause shall bedetermined and the condition corrected. SeePTC 19.2 forfurtherguidance.

4.6.7

4.6.10 Barometerreadingsand thetemperature at theinstrument shall be recorded at the beginning and end of each test point. The instrument shall be located at the site of the test. It shall be protected from weather, direct sunlight, and fluctuating temperature changes. Precautions shall be taken to prevent negativepressures in the vicinity of the barometer which may be caused by strong winds, compressor intakes, or ventilating fans. The instrument elevation with respect to the compressor shall be determined and propercorrections applied. SeePTC19.2 for further guidance. 4.6.1 1 Internal pressure measurements are required only if thesectionalperformance is defined for internal conditions (as an alternative the Codedefinition in para. 3.5.6). Due to the many configurations of the internal passages in sidestreamcompressors, this Codecannotspecifypreciselywhereor how internal pressure instrumentation may be placed.As a guide, four pressure probes (either static ordynamic) should beinserted in themainstream flow. These probes should belocated so the incoming sidestream does not affecttheraw data (see Fig. 4.12). It is usually difficult to makeaccurate internal pressure measurements at a stagedischargesince this is normally a region of high velocity with local variations of velocity, flow angle,andpressure.This measurement uncertainty should be reflected in the error analysis and in thevalue of the uncertainty assigned to thesestations.

4.6.8 Inlet pressure i s the total pressure prevailing at the compressor inlet. It i s the sum of thestatic pressure and the velocity pressure.Staticpressure shall be measured as specifiedfor inlet pipes in Figs. 4.1 or 4.3. Where no inletpipe is used, as in Fig. 4.2, the inlet total pressure shall be measured by a barometer. Total pressuremay be directly measured by the use of total probes inserted into the flow stream (such probes shall be properly oriented or directionally compensated to insureproper measurement).The measurement obtained by a total pressure probe can be influenced to varying extent by spatial location. In the event of significant unresolved differences from the total pressure deduced from thestaticpressure and average velocity, the static-pressure-based result shall prevail. 4.6.9 Discharge pressure i s the total pressureprevailing at the compressor discharge. It shall be taken as the sum of thestaticpressureandthe velocity pressure. Static pressure shall be measured as illustrated in Fig.4.1. When no discharge pipe i s used, as illustrated in Fig. 4.4, the discharge static pressure shall be measured by a barometer. If the velocity pressure (based on discharge opening area) exceeds 5 percent of the static pressure,an open discharge shall not be used. Total pressuremaybe directly measured by the use of total probes inserted into the flow stream (such probesshallbe properly oriented or directionally compensated to insureproper measurement).

4.7

4.7.1 Reference should be made to PTC 19.3, Temperature Measurement, for guidance on instruments fortemperaturemeasurement.Temperature shall be measured by thermocouples or mercury-inglass thermometers or other devices with equivalent accuracy. The range of their scales, the sensitivity, and the required accuracy shall be chosen for each of the significant measurements according to the particular need.The following generalprecautions arerecommendedwhen making any temperature measurement: the instrument installation should assure that thermal conductance by radiation, convec30

COPYRIGHT American Society of Mechanical Engineers Licensed by Information Handling Services

TEMPERATURE MEASUREMENTS

ASME PTC 1 O- 1997

COMPRESSORS AND EXHAUSTERS

temperature measured is a value between static and total temperature. The velocity temperature is then corrected for the recovery factor and added to the measured observation (see para. 5.4.4). Special temperature probes made to measure total temperature need little ornocorrection.

tion, and conduction between the temperaturesensitive elementand all externalthermalbodies(pipe wall, externalportions of thermometerwellsand thermocouple, etc.) shall be negligible in comparison to theconductancebetweenthe sensor andthe mediumbeing measured. Insulationofthoseparts of thermometer well, thermocouple sheath, etc., that extendbeyondthe pipe outsidediametermaybe a means of accomplishing this objective if necessary. In somecases, insulation of the pipe wall near the thermometerorpossiblyinsulation of thesection of the pipe upstreamof the thermometermaybe necessary. The temperature measuring device shall extend a sufficient distance into the fluid stream to minimize unavoidable conduction of heat. They need not be perpendicular to the wall. Oil or other heat conducting fluid should be used in thermowells to improve heat transfer. Precaution shall betaken to avoid insertion of thetemperaturemeasuringdevice into astagnant area when measuring the temperature of a flowing medium.

4.7.7 Inlet temperature is the total temperature prevailing at the compressor inlet. When the compressor is tested with an inlet pipe, four temperature taps shallbespaced 90 deg.apartand displaced Figs. 45 deg. fromthestaticpressuresensors(see 4.1 or 4.3). When machines are assembled with an open inlet as in Fig. 4.2, inlet total temperature is the atmospheric temperature, andit shall be measuredby fourinstrumentsattached to the protecting screen. In general, when the 4 (four) raw data observations differ by morethan 0.5 percent of theabsolute temperature the cause shall be determined and corrected.For low temperaturerisemachinesuncertainty analysis should be used to determine acceptable limits. Variations of more that 0.5 percent caused by factors other than instrument error such as design may require more than 4 (four) measuring stations.

4.7.2 When selecting a liquid-in-glass thermometer there may be a need for an emergent stem correction. Refer to PTC19.3 for further information.

4.7.8 Dischargetemperature i s the total temperature prevailing at thecompressordischarge.When a compressor is assembled for test with a discharge pipe,theinstruments shall be located as shown in Figs, 4.1 or 4.5 andspaced 90 deg. apart and displaced 45 deg. fromthe pressuretaps. Where the compressor is operated without a discharge pipe, four instruments shall be anchored to the discharge opening with asuitableprojection into the gas stream. Whenthefourraw dataobservations differ by more than 0.5 percent of the absolute temperature, the cause shall be determined and corrected. Variationof morethan 0.5 percentcaused by factors otherthaninstrumenterrorsuch as designmay requiremorethanfourmeasuringstations.

4.7.3 Thermocouples shall have junctions silver brazedorwelded.Theselectionofmaterialsshall be suitable for the temperature and the gases being measured. Calibration shall be made with the complete assembly, including theinstrument,thereferencejunction,andthe lead wires. If the well is integral with the thermocouple,the well shall also be included in the calibration. 4.7.4 Thermometer wells shall be as small in diameter and with walls as thin as conditions will permit. Wells shall be evaluated for the conditions of anticipated use to determine the time lag and the corrections to be applied. Thermocouples should be welded to the bottomof a well toreduce orminimize the correction for well error.

4.7.9 Forsidestreamcompressors,due to the many possibleconfigurations of internal passages, this Code cannot specify where orhow internal temperature instrumentation may be placed (see paras. 3.5.5 and 3.5.6). As a guide,fourtemperatureprobes shouldbeinserted in themainstream flow. These probes should be locatedso the incoming sidestream does notaffecttherawdata(seeFig. 4.12). It is usually difficult to make accurate internal temperature measurements at a stage discharge since this is normally a regionof high velocity. This measurement

Resistancetemperaturedetectorsorthermistorsshouldbeselected for the appropriate range. Cautionshould be takenbecausesome of these deviceshave a relatively slow responsetime. 4.7.5

4.7.6 Total temperature is the sum of static temperatureandvelocitytemperature.Wherethe Mach number is lowerthan 0.1 1 for gases,or for air where the velocity is below 125 ft/sec, the velocity temperature may be negligible. Normally, the actual 31

COPYRIGHT American Society of Mechanical Engineers Licensed by Information Handling Services

ASME PTC 10-1997

COMPRESSORS AND EXHAUSTERS

Nozzle temperature

r

m I

Nozzle pressure 2 taps spaced 90 dag.

" 4 "

I

para.

Protecting screen See 4.4

FIG. 4.9

SD minimum

INLET NOZZLE ON A N OPEN LOOP

uncertainty shouldbereflected in theuncertaintybarometer pressure. Differential pressure i s measured analysisand in the value of the uncertainty assigned from two statictaps located 112Ddownstream of the to thesestations.The internal temperaturemeasurenozzle flange.Temperature is measuredbysensors ment i s always required when sidestreamand mainat the screen. stream flows mix internally.

4.8 CAPACITY MEASUREMENTS 4.8.1 Flowmaybemeasuredbyusingan ASME flow nozzle, concentric square edgeorifice, Herschel type venturi tube, or alternative devices of equal or betteraccuracy.Reference shall be made to PTC 19.5, Flow Measurement, for general instruction and detailed description of the various primary elements and their applications. Other references are provided in Appendix D. The interested parties shall mutually agree upon the type of metering device to be used and the choice shall bestated in the test report. 4.8.2 The flow measuring device may be located on either the inlet or discharge side of the compressor. It shall be usedto determine the net capacity delivered, or in the case of anexhauster,the netcapacity exhausted, which excludeslosses by shaftleakage, balancing pistons,condensation,andothernormal leakage that maybeinherent in the compressor design. Multiple devicesare required for multiple inlet or discharge flow sections. The nozzle may be used with an open inlet. The nozzle arrangement shown in Fig. 4.9 may be used for the test of compressors as exhausters. The 4.8.3

minimum length of straight pipe, following the noz-

4.8.5 Formulasfor calculating mass flow for a variety offlow measuringdevices as provided in PTC 19.5 shallbeused.Methodsare included for the determination of the discharge coefficient, fluid expansionfactor,andmeteringelementthermal expansion coefficient for various flow elements.

zle, shall be equal to five times the pipe diameter, and the pipe diameter shall be a minimum of 1.66 times the nozzle throat diameter. A protecting screen shall be used in accordance with the instructions of para. 4.4. Upstream total pressure is equal to the 32

COPYRIGHT American Society of Mechanical Engineers Licensed by Information Handling Services

4.8.4 The nozzle maybeused with an open discharge: Figs. 4.1 O and 4.1 1 show optional arrangements of the flow nozzle on the outlet end of a pipe for use where it is convenient to discharge the gas to atmosphere. For a subcritical flow, the nozzle differential pressure, A,, will be less than the barometric pressure and it shall be measured fromimpact tubes, as shown in Fig. 4.10. Where theavailable gaspressures permit,the nozzle maybesizedfor operation at critical flow. In this case the differential pressure will begreaterthanbarometric pressure, and it shall be measured fromstatic taps located 1 D upstream of the nozzle as indicated in Fig. 4.1 l . In both cases the minimum length of straight pipe precedingthe nozzle shall be 1OD andthe pipe diameter shall be a minimumof 1.66 timesthe nozzle throat diameter. Temperature measuring Stations shall be located6 0 upstream. The flow straightenerand/or flow equalizer, as described in para. 4.5, shall be used.Users of these arrangements are cautioned to observe the distinction between critical and subcritical flow. It shouldbenotedthatthe velocity ofapproach is included in measurements made with impact tubes.

S T D - A S N E P T C 1 0 - E N G L L797

m

0 7 5 7 b 7 0 ObOSLIbL T b l

COMPRESSORS ASME AND EXHAUSTERS

PTC 10-1997

pressure NozzletemperatureNozzle 2 measuring stations spaced 90 deg.

Flow equalizer and straightener (See Fig. 4.9)

II

Il II

II I I

Not greater than

-

Il

.-

20

====

1.. .

r1

t

" " " "

-

One impact tubefor d 5 5 in. act tubes ford > 5 in.

I.

" " " "

Efzz

" "

0.23d

1OD minimum

4

SPECIAL NOTE: d not more than 0.6D for any nozzle arrangement

FIG. 4.10

DISCHARGENOZZLE ON ANOPENLOOP,SUBCRITICALFLOW

i

Nozzle temperature 2 measuring stations spaced

deg-

7 1ODminimum

, - / , - -

FIG. 4.11

4.9

Nozzle pressure 2 measuring stations spaced 90 deg.

""-I

DISCHARGENOZZLE ON ANOPENLOOP, CRITICALFLOW

CAS COMPOSITION

the compressor or the sampling points. This analysis shallconsist of identification of theconstituents,a measure of mole percent of each and evaluation of the molecular weight. If the test gas is air no samples arenecessary.However, relative humidity ordewpoint shall be measured during eachtest point.

4.9.1 Thetest gas must be defined.At the minimum, sampling will betaken at thestartand end of each test. 4.9.2 Special precautions shall be taken when testingwith theclosed loopto eliminate all liquids fromthe gas stream andstaticinstrumentlines. When dealing with gas mixtures subject to variation, samplesshallbetaken at eachtest point andbe analyzed by spectrographic,chromatographic,or chemical methods. The sample shall be taken from the piping such that there i s no condensation before

4.9.3 Note that while the gas under test conditions may not exhibit condensation, the gas in the instrumentlines will be cooler (¡.e., roomtemperature) and,undersome conditions,condensation could occur. 33

COPYRIGHT American Society of Mechanical Engineers Licensed by Information Handling Services

COMPRESSORS AND EXHAUSTERS

ASME PTC 10-1997

torque meters shall be of a type suitable for calibration. The torsion member shall be selected for readability and accuracy at thespeed and load prevailing during test.

4.1 O SPEED MEASUREMENT 4.10.1 Instruments shall beselected to provide a continuous indicationof speed fluctuation where variable speed drivers are used. Use of two independentinstruments,one to provide a check on the other, i s alsorecommended.

4.14SHAFTPOWER BYELECTRICAL MEASUREMENTS

4.10.2 Thespeed of a compressor driven by synchronous motors may be determined from the number of poles in themotorandthefrequency of the power systems. If gearsareused betweenthe measuring point and the compressor shaft, the speed ratio shall be computed from a count of the number of teeth.

4.14.1 Theshaft power input to a motor driven compressormay be computedfrom measurements of the electrical input to the motor terminals under certainconditions. The powerrequirement of the compressor should be above mid-point of the motor rating.The output of a motorshallbecalculated bysubtracting losses from the measured electrical input,or as the product of input and efficiency. Efficiency shall be determinedby an input-output test where output is measured on a calibrated dynamometer or other appropriate device. For efficiency determination, the supply line voltage used for calibration shallbethe same as that used forthe compressor test.

4.10.3 Detailed instructionson speed measuring instrumentation is given in PTC 19.1 3, Measurement of RotarySpeed.

4.1 1 TIME MEASUREMENT 4.11.1 Thedateand time of day at which test readingsaretaken shall be recordedon all data records.

4.12

4.14.2 Efficiency determination by input-output measurements may not be practical for large motors. For large motors the loss method may be used. The segregated losses of an induction motor shall include friction and windage, core loss, 12R loss of the rotor and the stator, and a load loss. These measurements shallbemade in accordance with current ANSI standards.

METHODS OF SHAFTPOWER MEASUREMENT

4.12.1 Theshaft power input at thecompressor coupling or the drive shaft maybemeasured directly by: (a) torque meters (b) reaction mounted drivers or evaluated from: (c) measurementof electrical input to a driving motor (d) a heat balance method (e) heat input to a loop cooler

4.14.3 The electric power input to the motor shall bemeasured by theinstrumentsconnected at the motorterminals.Thedetailedinstructionsforthe measurement of electrical power are as given in IEEE 120. The indicating electric meters should be selected to readabove one-third of the scalerange. 4.14.4 Calculations of electrical power shall include calibration corrections for the meter and current transformers. The transformersshall be measured for ratio andphaseangle at the load conditions prevailing during the test.

4.1 2.2

The precautions, limitations, and the permiseach of thesemethodsare describedseparately.Codeusersshallselect the method bestsuitedforthe application. Detailed instruction on the measurement of shaft power will be found in PTC 19.7, Measurement of Shaft Power.

sible applicationsfor

4.13

4.15SHAFTPOWER BY HEATBALANCE MEASUREMENTS

SHAFTPOWER BY TORQUE MEASUREMENTS

4.15.1 When it i s not possible or practical to measureshaft power by direct means, it may be computedfrom measuredvalues of thecapacity, gas properties at inlet and discharge, heat exchange

4.13.1 Torque may be directly measured by devices installed in a drive shaftinterposedbetweenthe driver and the compressor. For tests under this Code, 34

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k-

Location C

Location A

Location B

GENERAL NOTE: Mainstream instrumentation to be located between stationsA and B.

FIG. 4.12

TYPICALSIDESTREAMINLETAREA

surement of the temperature rise (suchas with differential thermocouples). Evidence of nonuniform temperature distribution morethan 2 percentofthe temperature rise at either the inlet or the discharge measurement station, may require one of the following procedures be used at the offending measurement station: (7) Apply insulation to the piping upstreamof the temperature measurement station in an effort to minimize thermal gradient.If successful, the temperature measurement installation need not be changed. (2) Move the temperature measurement station away from the compressor and add pipe insulation. This might beparticularly effective when temperature

through the casing, mechanical losses, and gas leakage - loss from the shaft seals. Methods to account for mechanical losses are discussed in para. 4.18. External heat loss from

4.15.2

''

the casing may be evaluated para. 4.1 7.

with

4.15.3 Theheatbalancemethod shall be used with the following precautionsand limitations. (a) The inlet and discharge temperatures shall be measured with instruments suitably selected and applied toprovide combined accuracywithin 1 percent of the temperature rise. When the rise is less than SOOF, consideration should be given to direct mea35

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stratification causes the problem at a compressor discharge. (3) Perform a temperature traverse using 1O locations along each of two diametral traverse lines spaced 90 deg. apart at the same pipe crosssection.The 1 O sensing locations along each traverse line should correspond closelyto the average radii offive annular regions of equal area which comprise the entirepipe cross section. (The central region actually would be a circular rather than annular area.)Themeasured temperature would be the averageof the 20 individual measurements. (b) In sidestream machines, whereinternal temperature measurements areto be made,ideally four locations should be used. However, this may not prove to bepractical. In all cases, the upstream temperatures of the two streams mixing internally should be measured, A measurement ofthe downstream mixed temperature would be unreliable and should not be used for calculation purposes dueto inherent poorinternal mixing conditions in a machine. (c) Temperature equilibrium shallbeestablished before starting the test reading. Acceptable equilibrium will be demonstrated by six or more readings, uniformly timed, fora period not less than 1 O minutes, during which the temperature rise drift does not exceed 5 percent of the temperature rise. (cf) The heat losses due to radiation and convection expressed in percent of total shaft power shall not exceed 5 percent. (See para. 4.1 7.) (e) The inlet gas conditions shall have a minimum of 5 deg. superheat for Type 2 tests.

4.16

SHAFTPOWER

BY HEATEXCHANGER

METHODS 4.16.1 When it is not possible or practical to measureshaft power directly or by a compressor heat balance, and a heat exchanger is incorporated in the test arrangement, the heat transferred to the cooling watermaybeused to determinethenet compressorshaft power. 4.16.2 Methods to accountforthemechanical losses are discussed in para. 4.18. External heat loss from the casing, piping, and coolermay be evaluated in accordance with para. 4.17.

4.17

HEAT LOSS

4.17.1 When using either the heat balance or heat exchanger method for determining power, it is recommendedthatheat loss be minimizedby the application of a suitable insulating material. If the compressedgas temperature rise is less than S O O F , the inlet piping, compressor casing, and exit piping shall be insulated atleast to the measuring station. Theexternalheat loss fromthecompressorcasing andconnecting piping may be computed with acceptableaccuracyfrommeasurementsoftheexposedsurfacearea, the average temperature of the surface, and theambienttemperature. Where a hot surfacetemperaturevarieswidely, as in large multistage compressors, it is advisable to divide the casing into arbitrary sections and determine the area and temperature of each separately, and thus obtain an approximateintegratedaveragetemperaturefor the total surface. 4.1 7.2 Where cooling occurs between the inlet and outlet measuring stations as part of the compressor design, measurement of temperatures and flow rates ofthe cooling fluids arerequired.Examplesare compressors incorporating cooled diaphragms, interstage coolers, or aftercoolers as part of the compressorpackage being tested.

4.16.3 Theheatexchanger methodshall beused with the following precautionsand limitations. (a) The cooling fluidsupply shall be stablein pressure and temperature so that the fluctuation of flow rates will not deviate more than 2 percent and the

36

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fluctuation of the temperature rise by not more than 1 percent of the temperature rise. (b) The cooling fluid flow meter shall be selected and calibrated to maintain the uncertaintylimit within 1/2 percent at test conditions. (c) The cooling fluid flow rate shall be regulated so that the temperature rise i s not less than 20°F. (d) Two or more temperature measuring devices shall be used at each cooling fluid inletand outlet. (e) Spinners or similar devices shall be used to insure thorough mixing of the outlet stream prior to temperature measurement. (0 The heat losses dueto radiation and convection from the gas loop piping, the compressor,and the cooler shall not exceed 5 percent of the total shaft power. It is recommended that the piping between the compressor discharge flange and the cooler inlet be insulated. (g) Temperature equilibrium shall be established before starting the test reading. Acceptable equilibrium will be demonstrated by six or more readings, uniformly timed, fora period not less than 1 O minutes, during which the temperature rise drift does not exceed 5 percent of the temperature rise.

COMPRESSORS AND EXHAUSTERS

4.18MECHANICAL

ASME PTC 10-1997

LOSSES

4.1 9.2 Pressure measurement devices (Bourdon tube gages and transducers, etc.) shall be calibrated with a deadweight standard or manometer at approximately 5 percent intervals for the anticipated measurementrange. Instruments affected by temperature shall be calibrated in the same temperaturerangeprevailing during their use.

4.18.1 Whenpractical,theheatequivalent of the mechanical losses (integral gears, bearings, and seals) shall bedeterminedfromthetemperatureriseof the cooling fluid. The quantity of fluid flowing shall be determined by calibrated flow meters.Theheat equivalentoftheexternal losses as well as the frictional loss in the mechanical seals, if used, shall be determined and included in the total mechanical losses. Where the mechanical losses are well known and documented, the calculated values or those values determinedfrom prior testing may be used by agreement by testparties.

4.1 9.3 Temperature measurement devices (thermocouples, mercury-in-glass thermometers, RTDs, thermisters,etc.) shall becalibrated with certified standards at 20 percent intervalsfor the measurement range. The standardshall be suitable for the measurementrangeoftheinstruments to becalibrated. Procedures described in PTC 19.3, Temperature Measurement, shall be followed for checkingthe accuracy of temperature measuring instruments. Thermocouplecalibrationchecksshall include the hotjunction, the leadwires,andthe indicating instrument. RTDs and thermisters shall be calibrated with the total system.

4.18.2 Where speed changing gears (not partof thecompressor)areusedbetween a driverand a compressor,and shaft power is measured onthe input side of the gear, it willbe necessary to subtract the friction and windage loss of the gear to obtain the shaft power input to thecompressor.Thegear power loss to the lubricating fluid may be determined by measuring the flow rate and the temperature rise. The additional external loss to the atmosphere may be determined by the methods of para. 4.17. When gear loss measurements are madeon an independent geartest, careshouldbetaken to assure that the load, lubricating oil temperature, viscosity, and flow ratesare similar to those for thecompressortest.

4.1 9

4.19.4 Instruments for measuring electric power such as wattmeters, ammeters, and voltmeters shall be calibrated with primary standards. The zero adjustments shall be checked. They shall be examined for pivot friction. Instruments showing pivot friction shall notbe used. Dynamometertypesmay be calibrated on either ac or dc current. Current transformersshallbemeasured for transformation ratio and phase angle at the range of burdens prevailing in the circuit duringthe test.The transformation ratio of potential transformers shall bemeasured at theapproximateprimaryvoltageandfrequency prevailing during the test.

INSTRUMENT CALIBRATION

4.19.1 All instrumentsused for measurement shall be currently certified by comparisonwith appropriate standards before the test. Those instruments subject to change in calibrationsdue to use, handling,or exposure to injurious conditions, shall be compared again with standardsafterthetest.

4.19.5 Torque meters shall be calibrated by applying torque with certified standard weights, load cells, or other appropriate devices spaced to cover the working range. For strain gage types, the calibration shall includethe brushes, leadwires,andthe indicatinginstrument.

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ASME PTC 10-1997

SECTION 5 - COMPUTATIONOFRESULTS percent one in efficiency and two percent in dischargespecificvolume.'The ideal gas equation of The Calculation The process Of state, 14dPv = RT, and the correspondingderived establishing compressor performance from test data equations in Tables and may be involves a number of calculation steps. This Section Forgases with variablespecific heats,average is presented in the following chronologicalorder: properties are calculated at the arithmetic mean

FORMAT 5.1

0 0 0

0 0

0 0

Perfect real or gas treatment is selected. section temperature. The appropriate test speed is calculated if a Type 2 test is to be performed. The raw test data is processed. Test performance is calculated. Test performance is expressed in dimensionless form. Reynolds number correction is applied. The corrected dimensionless expressions are used to predict performance at specified operating conditions.

Theimportantsubjectofuncertainty is treated separately. The section format is intended to guide the user in basic calculation procedure and to present the necessary equations. Appendix E is provided as a background theory source and further explanation of the equations.

5.2COMPUTATIONALMETHODS AND REALGASES

5.2.1.3 Tabulated Properties and Equation of StateMethods. Puregases and gas mixtures for which tabulated data properties exist may be treated as real gases. There are many gas property correlation equations of state for purecomponentsand gas mixtures. Many of the generalized equations of state provide sufficiently accurate predictions of gas properties to be used in conjunction with the calculation methods. Theuse ofeitherofthesemethods will require iterative procedures to satisfy the equations in Tables 5.2 to 5.4.

FORIDEAL

5.2.1Choice of Methods. Thetest andspecified gases maybetreated as eitherperfectorrealdependingupon their respectivethermodynamicbehavior. For thepurposesofthisCode ideal gases are those which fall within the limits of Table 3.3. Gases which exhibit deviations beyond these limits are considered real. Threedistinct treatments of gases are recognized in the computational procedures. The appropriatechoice will dependupontheselected gas, knowledge of itsproperties,andthedesired accuracy.

the limits imposed h Table 3.3. 'Th;! table limik aredefined so that the use of ideal gas laws will introducemaximumuncertaintyofapproximately

5.3.1 Test Gas Selection. The gas to be used in establishingtheperformance of thecompressor to betestedcanbethespecifiedoperating gas ora

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5.2.1.2 Schultz Method. Thegasmay be treated as a real gas usingthemethodofSchultz[see Ref.(D.1311 when the compressibility functions are known.Thereal gas equationof state, 144pv = ZRT, andthecorrespondingderivedequationsof Tables 5.2 to 5.4 areused.The arithmeticmean between inlet and discharge conditions shall be used forevaluatingcompressibility,specificheat, X and Y. TheSchultzmethod is normally used whenthe discharge conditions are unknown and an estimate ofthepolytropicexponent, n, is needed. Iteration is required to obtain the arithmetic mean conditions. Thecurves provided for X (Fig. 3.6) and Y (Fig. 3.7) are for reference. They were derived from the generalizedcompressibility charts.Specificvalues of X and Y may bedeveloped for anytest or specified gas composition.

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TABLE 5.1 IDEAL GAS DIMENSIONLESS Parameter

PARAMETERS

Mathematical Description at Test Operating Conditions

Eq. No.

Assumption

[Pinlsp [5.1T-21

=

Flow coefficient

Work input coefficient

Isentropic work coefficient

-RT;.

-31 15.1

[PinIr

IPslsp = [PJf Rem,

k-1

I5.1 T-41

Polytropic work coefficient [Pdf =

where nt =

[1-

(5.1T-51

In

PiTd

Isentropic efficiency [%If =

Polytropic efficiency hplf

Total work

input coefficient

=

See Table 5.3

For ideal gases with constant specific heats

k.1

and, [rlplr =

GENERAL NOTE:Appropriate unitsmust be chosen to render the parameters dimensionless. Further explanation of the equationsis available in Appendix E.

40

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ASMEPTC 10-1997

COMPRESSORS AND EXHAUSTERS

TABLE 5.2 REAL GASDIMENSIONLESS PARAMETERS Parameter Mathematical Operating Description Test Conditions at !

Eq. No.

Flow coefficient

[5.2T-1j

Assumption 4sp

=

4f

t

Work input coefficient

where [ndr =

[T]

15.2T-41

In -

t

(5.2T-51 and f, =

Polytropic work coefficient

Irplr =

where nt =

[T] -

[5.2T-7j

In

I

[5.2T-8]

Isentropic efficiency [ d r =

hd

[vSlsp= I

d t

Remccllr

- hi [Table continued on next pagel

41

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PTC

ASME

COMPRESSORS AND EXHAUSTERS

1O- 1997

TABLE 5.2 (CONT'D) REAL GAS DIMENSIONLESS PARAMETERS Eq. No.

Parameter Mathematical Operating Test Description Conditions at

Assumption

Polytropic efficiency

Total work input coefficient

See Table 5.3

GENERAL NOTE: Appropriate units mustbe chosen to render the parameters dimensionless. Further explanation of the equationsis available in Appendix E.

¡.e.,

gas which allows for similarity testing at equivalent conditions.

(E)

5.3.2 Test Speed Selection. The volume ratio limitation of Table 3.2 may be met by controlling the test speed. The appropriate test speed i s calculated from

1

The Machine Reynolds number correction, Rem ,,, is explained in para. 5.6.3. In order to apply theseequations it is necessary to knowthe polytropic exponent, which is a function of polytropic efficiency. Foranygas,

where

[5.3.61 n l():

and,

Foran

ideal gas, n

-T

"

n- 1

k p

E

i5.3.71

For a real gas usingtheSchultzmethod, with the restriction that,

k"1t

= 1r"lsp

n =

[5.3.4]

42

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1 Y-m(l

+x)

I5.3.81

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where m =

?(L+ x) CP TP

5.4.2.3 Fluctuation. Threeormorereadingsare used to obtain the test point. The allowable fluctuation ofthereadings is shown in Table3.4.The fluctuation is computedbytakingthedifferencesof the highestreadingand the lowestreadingand the average of all the readings*

[5-3.91

60th the test and specified operating condition &iciencies are known only approximatelybeforethe test. Where no betterapproximation is available, estimated be may design they the from value,

AF=

,

1 O0 (AH - AL)

15.4.1 1

where TestSpeed Validation.When the actualtest conditions differ from the estimated values, the most appropriate test speedwill depart fromthe previously calculated testspeed.Some deviation is allowable. Thetestspeed is acceptablewhenthedeviation satisfies the limits of Table 3.2.

5.3.3

5.4

AF=

fluctuation expressed in

YO (Table 3.4)

AH= highest reading

AL= lowest reading Ai= ith reading n= total number of readings If the fluctuation values of Table 3.4aresatisfied, thenthe point i s assumed to be valid.

CALCULATIONS FOR TEST OPERATING CONDITIONS

5.4.2.4 Test Point Data. The individual readings and summed are divided the by total ofnumber readings to establishanaverage.Thisaverage is Performanceat the test conditions is calculated then used as thetest point data. by the following procedures.

5.4.1 Raw DataAcceptability.Theobserved data shall be checked for compliance with the limitations imposed in Sections 3 and4. See PTC 19.1 for guidance on examining data for outliers. 5.4.2

ProcessingRawData.Acceptableraw

5.4.2.5 TotalConditions. Gas state static test point data shallbeconverted to total condition values for thecomputationalprocedure.This does notpreclude final presentation in terms of static conditions, but total values are usedin the intermediate computations. The relationship between static and total properties is velocitydependent.Average total properties are estimatedhereinfromtheaveragevelocity at the measurementstation. Theaverage velocity atthemeasurementstation is givenby

data

shall beprocessed to provide values to be used in thecomputationofresults. 5.4.2.1 CalibrationsandCorrections.Applicable instrument and system calibrations shall be applied to the raw data. The need for corrections and calibrations arises from both the indicating system components andmeasurementtechnique.Rawdata shall be corrected as required based on: (a) instrument and instrument system calibrations (b) liquid legs in pressure measurement lines (c) temperature effects (d) thermometer emergent stem corrections (e) local gravitational variation

5.4.2.2 Data Conversion. The corrected raw data is then averaged from the total number of observations(rawdata)ateachmeasurementstation. This averaged data becomesthereading.Thereading i s thenconverted to absolute units of pressure, temperature,etc,

Simplified methods for converting between static and total conditions at low Fluid Mach numbers are presented in the following paragraphs. A refined method for higher Mach numbers is given in Appendix G. The Fluid Mach numberfor ideal gases is given by 43

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COMPRESSORS AND EXHAUSTERS

ASME PTC 10-1997

M =

5.4.3

Thetest total temperature is calculated from the measured temperature taking into account the effect of recovery factor.

V

5.4.4.2Simplified Method. Thedifferencebetween total andstatictemperaturesmaybeevaluated from

Test Pressure

5.4.3.1 Simplified Method. Formeasurement station Fluid Mach numbers of 0.2 orless theeffects of compressibility are small, A good approximation of velocity pressuremaybe obtained by assuming incompressible flow at the measurement station and calculating anapproximatedensityfromthemeasuredstaticpressureandmeasuredtemperature. Thus

Va, = ~ / 6 0 p A

[5.4.61

Thisequation is accurate for ideal gases (using an average c&. It is less accurate for real gases and should be used with caution for real gases for Fluid Mach numbersabove 0.2 (see Appendix G). The above equation and thedefinition of recovery factor rf combine to give

15.4.31

5.4.4.3Refined Method. For cases wherethe measurementstationFluid Mach number exceeds 0.2 for areal gas, thediscussion in Appendix G gives guidelines for more accurate methodsfor relating total temperature to measured temperature. For cases involving extremevariationfrom ideal gas behavior,such as near the critical point, the total temperature may differ greatly from the value indicated by para. 5.4.4.1 and the methods outlined in Appendix G shouldbe used.

5.4.3.2Refined Method. For cases wherethe measurementstation Fluid Mach numberexceeds 0.2, or when abetteraveragevelocityestimate is desirable,therefinedmethodofAppendix G may be used. This method is based upon the assumption of uniform compressible flow at themeasurement station. 5.4.4 Test

5.4.4.4 Test DischargeTemperatureFrom Shaft Power. An alternative method for determining test discharge temperature is discussed in para. 5.4.7.6.

Temperature

5.4.4.1RecoveryFactor. Thetemperature indicated by asensing element is normallyavalue somewhere between thestatic and total temperature, depending upon the ability of the sensor to recover the converted kinetic energy of the gas stream. This ability is defined in terms of a recoveryfactor,

5.4.5TestDensityandSpecificVolume. Thetest total density is calculated from the test total pressure and total temperature as

[5.4.81

for ideal gases,and, The recovery factor i s primarily dependent upon geometric configuration, orientation, and FluidMach number. Standardized Performance Test Code wells (PTC 19.3) used at velocities below 300 fthec have arecoveryfactor for air equal to 0.65. Recovery factors for various sensorsmay beavailablefrom the instrument manufacturer.

[5.4.9]

for real gases. The test total specific volume is the reciprocal of the total density 44

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TC

COMPRESSORS ASME AND EXHAUSTERS

1

v, = -

10-1997

[5.4.10]

Pt

where

5.4.6 Test Flow Rate. Themeasured flow rate is calculated according to theformulasapplicable to the indicating instrument used. In somecasessecondary flows such as leakages may be wholly calculated ratherthanmeasuredwhenmutuallyacceptablemethodsareavailable,

[Coutwh - Lnwhl

indicates thesum of mass flow rate-enthalpy products for all flowscrossingthesectionboundaries. QI i s the heat transfer from the section boundaries. 5.4.6.1 Mass Flow Rate. Test flow ratesareexShaft power i s the sum of gas powerplus any pressed as mass rateof flow at thestationofinterest.parasitic losses,

5.4.6.2Volume Flow Rate. ThisCodeuses a flow rate definition in the calculation process which has the units of volume flow rate. It is q=-

W

Psh,

=

[5.4.14]

Pg, iPparasitic,

5.4.7.3 Heat Exchanger Method. Closed loop heat input tests are a form of the heat balance method.The gas power is given by,

[5.4.11]

P

where mass flow rate P= total density This definition is consistent with the use of total properties in the calculation procedure. It does not represent the actual local volume flow rate because it is based upon total rather than static density. All references to calculated volume flow rate imply this definition unless otherwise stated. W=

Pg,

+

Qextl

[5.4.15] 33000

W,=

cooling fluid massrate of flow

CP',

cooling fluid specific heat

t2= cooling fluid outlet temperature = cooling fluid inlet temperature heattransfer from the section boundaries QIxt= other external heat loss equivalent, for example,sealleakage tl

Qr=

5.4.7.4Casing Heat Transfer. Theexternalheat loss or gain fromthesectionmaybecomputed from measurements of the exposed surface area, the average temperature of the surface, and the ambient temperature from

5.4.7.1ShaftPowerMethods. Whenpower input i s measured by instrumentssuch as a torque meter, dynamometer, or calibrated motor, the shaft power is calculated using the appropriate formula. Gas power is calculated by subtracting the parasitic losses fromthe shaft power (seepara. 5.4.7.5 for parasiticlosses).

Qr

= ISA tc -.

1

ta)

hl60

15.4.1 61

where Sc= heat transfer surface area of exposed compressorandadjoiningpipeforsection of interest tc= casing surface temperature ta= ambient temperature hr= coefficient ofheattransfer for area (combinedconvectionand radiation) Where the casing surface temperature varies be widely,theaccuracy of thiscalculationmay improved by treating small areas of the surface

= measured value

5.4.7.2 Heat Balance Method. Gas power is calculatedfromtheFirst Law ofThermodynamics applied to the compressor section of interest,yielding 45

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- tl) + Qr

where

5.4.7TestPower. The calculationof test power dependsupon the methodof measurement.Both shaft power and gas power may be of interest. Shaft power is the power input to thecompressordrive shaft.Gas power is the power delivered to the gas in thesection(s1ofinterest.

Psh,

= [wwcpW(r2

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separately and summing the results. See paras. 4.1 5, 4.16, and 4.17.

Pg = Psh

- Ppararitic

[5.4.19]

(b) Calculate the enthalpy rise from the gas power

5.4.7.5 Parasitic Losses. Parasiticlossesarethe difference between shaft power and gas power for the section(s) of interest.Theyarecomprisedof mechanical losses andotherpowerrequirements which do not contribute to theenergyriseofthe gas in thesection of interest,

33000

( h 7 Qr)

yielding Pparasitic

=

Pmech

=

Pother

15.4.1 71

(a) Mechanical Losses. Mechanical lossesare always considered to be parasitic losses. Those losses due to lubricated gears, bearings, seals, etc., may be estimated from the lubricating oil temperaturerise. Othermechanical losses from seals, bearing,etc., which do not contribute to the lubricating oil temperature rise shall be determined separately. Thatportion of the mechanical loss evident in the lubricating oil temperature rise is given by:

(c) Determinethedischargestagnationtemperature fromthe calculated discharge stagnation enthalpy and discharge stagnation pressure, according to the properties of the gas. NOTE: An iterative calculation is required for real gases.

5.5 Prnech

I

= [wcpAtl 33000

The following dimensionless parameters are calculated for the test conditions to provide verification that the limits of Table 3.2 havebeenmet.

[5.4.18]

Machine Mach Number. The Machine Mach number is given by

5.5.1

where mass flow rate of the lubricating or sealing fluid cp= specific heat of the lubricating orsealing fluid At= temperature rise of the lubricating or sealing fluid (b) Other Parasitic Losses. When the shaft power method is used, power supplied to drive auxiliary equipment is treated as parasitic. Also, power supplied to sections’of a multisection compressor other than the section being tested i s considered parasitic. When the heat balance method is used, and total shaft power i s defined toinclude power to drive auxiliary equipment, theauxiliary power requirement is treated as parasitic. W=

M m = U/ai

i5.5.1 I

For ideal gases,

For real gases,

di

=

Yi

=G

(5.5.31

5.5.2 Machine Reynolds Number. The Machine Reynoldsnumber is given by

5.4.7.6 Alternate Method For Determining Test DischargeTemperature. Forcases wherethedischarge temperature cannot be measured with sufficient accuracy, it may be possible to obtain a value from the measuredshaft power. Themethod is as follows: fa) Calculate gas power from theshaft power measurement

Rem = Ublu

[5.5.41

(a) For Centrifugal Compressors U= velocity at the outer blade tip diameter of the first impeller, ft/sec b= first stage impeller exit width, ft

46

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DIMENSIONLESS PARAMETERS

ASMEPTC 10-1997

COMPRESSORS AND EXHAUSTERS

5.6.1TheSingleSectionCompressor

kinematic viscosity of thegas at inlet conditions,ft2/sec (b) For Axial Compressors U = velocity at first stage rotor blade outer diameter,ft/sec b= chord at tip of first stage rotor blade, ft v = kinematic viscosity of the gas, ft2/sec Y=

5.6.1.1 Description. Thesinglesectioncompressor from inlet to outlet measurement stations experiences no gas cooling otherthannaturalradiation and convection. No gas flow is added or removed other than that lost through seal or balance piston leakage. No condensationoccurs.

5.5.3Specific Volume Ratio. Thespecificvolume ratio is the ratio of inlet to discharge total specific volume.

5.6.1.2 Calculation ProcedureforSingleSection Compressors. The first step i s to calculate thefollowing values: (a) flow coefficient (b) work input coefficient (c) polytropic work coefficient (d) polytropic efficiency (e) total work input coefficient Theequationsneeded todo this are shown in Tables 5.1, 5.2, and 5.3, and are explained in detail in Appendix E. Some of these parameters are subject to correction for the difference in Machine Reynolds number between test and specified operating conditions, as explained in para. 5.6.3. Theright-hand columns show the relationship between the test and specified condition values. The second step is an interpolation process. Compressor performance at a single specified condition operating point is determinedfrom atleast two bracketing test points. To perform the interpolation, the specified operating condition dimensionless parametersaretreated as functionsofthespecified operatingcondition flow coefficient. Thespecified operating condition dimensionlessparameters for each point may be plotted as shown in Fig. 5.1. A smooth curve i s drawn connecting the data points. For two pointsthis is simplylinear interpolation. Improved data interpolation may bepossible with additional test points and nonlinear curve fitting. The third step is to establish the compressor performance in dimensionlesstermsatthespecified operating conditionflow ofinterest.Todothis, a specifiedoperating conditionflow coefficient is calculated fromthe flow rate, speed, and inlet conditions of interest. The remaining dimensionless performance parameters are defined from the interpolation process of step 2. This information is simply 5.1 at the flow coefficient read from the curves of Fig. of interest. The compressor performance at the specified operating conditionpoint of interest is now defined in dimensionlessterms. Thefourth step is to calculatethe compressor performance in thedesireddimensionalform.This is donebysolvingthedimensionlessparameter

5.5.4VolumeFlowRatio. Thevolume flow ratio betweenany two points x and y in thesection is given by

Forcompressors without sidestreams the inlet to discharge volume flow ratio is limited by the specific volume ratio limit. Forsidestreamcompressors the volume flow ratio limits of Fig. 3.2 also apply. 5.5.5 Flow given by

Coefficient. The flow coefficient is

where wrotori s the mass flow rate which enters the rotor and i s compressed. It differs from the measured mass flow rate by the amount of leakage and sidestream flow which occursbetweenthe rotor entry and the flow measurement station. Figure E.2 gives a schematic representation of mainstream, sidestream, andleakageflows.

5.6

CALCULATIONS FORSPECIFIED OPERATING CONDITIONS

Performance at specified conditions

is calculated

by the following procedures. Certain additional

di-

mensionlessparametersarecalculated for thetest conditions and extended to specified conditions. 47

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S T D - A S M E PTC LO-ENGL L997 m 0 7 5 9 b 7 0 Ob0597555b ASME

10-1997

m

COMPRESSORS AND EXHAUSTERS

TABLE 5.3 TOTAL WORK INPUT COEFFICIENT, ALL GASES Parameter Mathematical Operating Conditions Test Description at Total work input coefficient (Note (heat balance method)

Eq. No.

llspwmption

(1 )I

(Pd

coefficient input work Total (heat balance method)

[arlt=

- fpdtie)33000

It

[5.3T-21

1nSh1rp = Iadlt

GENERAL NOTE Appropriate units mustbe chosen to render the parameters dimensionless. Further explanation of the equationsis available in Appendix E. NOTE (1 1 This equation applies to a particular model as presented in Appendix E, para. E.3.12. Some of the terms may not apply in a particular case. Additional terms may apply. The analysis of para. E.3.12 may be followed to develop appropriate equations.

(a) It shall be possibleto gather test information for each single sectionas though it were an independent single section compressor. That is, the testspeed, flow rate, and inlet and outlet states must be available for each single section. In the special case of sidestream mixing internally in a compressor, the inlet mixed condition shall be determined from the inlet states of the incoming streams. (b) When a component such as an external heat exchanger exists between sections, the performance of that component shall be known for specified operating conditions. (c) Differences in the intermediatecomponent performance between test and specified operating conditions shall havea negligible or known effect uponthe single section performance. That is, a negligible or known effect upon thedimensionlessperformance parameters.

equationsforthosequantitiesofinterest. Typical equationsused to do this areshown in Table 5.4. For example, to calculate the discharge pressure at the specified condition flow the following steps are taken: (1 ) the pressure ratio is calculated from the now known specified operating condition polytropic efficiency and polytropic work coefficients, and (2) the discharge pressure is the product of this pressure ratio and the specifiedoperating conditioninlet pressure. 5.6.2The

Multisection Compressor

5.6.2.1Description. A multisection compressor is a compressor which may be treated as a number ofindividual singlesectioncompressorsoperating in series.The output from each single section provides input to the next section. The section boundaries may be drawn to exclude intermediate components such as externalheatexchangers. The following conditions shall bemet to treat a compressor as a multisection compressor.

5.6.2.2 Calculation Method for Multisection Compressors. The specified operating condition per48

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S T D - A S M E PTC LO-EFJLL

L197

0759b70 ObU5q7b q92

COMPRESSORS AND EXHAUSTERS

m ASME PTC 10-1 997

I m p

I

t

I

Test F

FIG. 5.1

SPECIFIED CONDITION CAPACITYCOEFFICIENT FOR SPECIFIED CONDITION CAPACITY OF INTEREST

formance for multisection compressors is calculated from the specified operating condition performance of the individual calculated sections. The basic calculation procedure for each section is the same as for singlesection tests.Thetest data for eachsection is reduced to the form of dimensionless performance parameters which apply at thespecifiedoperating conditions.Theperformanceofthefirstsection is calculated just as is done for a singlesection compressor. This yields the discharge conditions from the first section. If an intermediatecomponent such asan intercooler existsbeforethenextsectionentry,the 49

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effects onflow rateand gasstateare taken into account. For a heat exchanger these effects are temperature reduction,pressuredrop,andcondensateremoval. For the case ofmixed streamsseepara. E.5. The resulting condition becomes the specified operating condition gas state at the entry to the second section. The flow coefficient calculated from the known flow rate becomesthe interpolating flow coefficient for the second section. The calculation process is repeated through the second section, remaining intermediate componentsandsections,and on to the final discharge. It i s not necessary that an intermediate

C

ASME

10-1 997

COMPRESSORS AND EXHAUSTERS

TYPICAL CONVERSION

TABLE 5.4 OF DIMENSIONLESS PARAMETERS

Parameter Mathematical Description Test Operating at Conditions

Eq. No. 15.4T-1]

[5.4T-21

(5.4T-31 Capacity

[5.4T-4]

Polytropic work (head) per section

I5.4T-51

Pressure ratio (ideal gas with constant specific heats)

[5.4T-6]

n-1

where

n k = -( t l d s p (n - 1 (k - 1)sp

I5.4T-71

[5.4T-81

Pressure ratio (real gas)

[5.4T-9]

[5.4T-1 O]

I5.4T-11I

In

W

[5.4T-12] [Table continued on next page]

50

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ASMEPTC

COMPRESSORS AND EXHAUSTERS

TABLE 5.4 (CONT'D) TYPICAL CONVERSION O F DIMENSIONLESS PARAMETERS Eq. No.

Parameter Mathematical Description Test Operating at Conditions Pressure ratio (real gas) (Cont'd)

or, where the Schultz method is used 15.4T-131

m5P

=

[-ZR (-1

+

Cf

[5.4T-141

x)]sf

Discharge pressure

[5.4T-15]

Pressure rise

I5.4T-161

Discharge enthalpy

15.4T-171

Temperature ratio (ideal gas)

15.4T-191

The discharge temperature may also be obtained from the discharge pressure and enthalpy when the appropriate data is available.

[5.4T-201

Gas power per section

Shaft power

Assumption,

n = &h

or, Sf

ash

Sf

GENERAL NOTE: Consistent units must be used in defining dimensional properties.

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~~

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ASME PTC 10-1997

The correction to be applied is as follows: (a) For Centrifugal Compressors

component exist in order to treat a compressor in multiple sections. The exit of one section and entry of another may coincide. The specified operating condition flowcoefficients for the second and succeeding sections are functions of the performance of the preceding sections. This dependence upon preceding section performance is an effect commonly referred to as section matching. When the individual section performance curves are as thenumberof individual sections steep,and increase,the overall compressorperformance becomes increasinglysensitive. It is because of this effect that it is important to follow the calculation method presented. What mayappear to be small differences betweentest and specified operating conditions in each section may combine to show up as important effects in overall performance. Calculation methods which attempt to make overall corrections without explicit consideration of the section matching effectcanlead to erroneousresults.

5.6.3

RA = 0.066

Rem

Rem

RB =

RC

[5.6.2]

f

13.67\

15.6.31

log ( €+ -)

Rem

RC =

General. Theperformanceof a compres-

sor is affected by the Machine Reynolds number. Frictional losses in the internal flow passagesvary in a mannersimilar to friction losses in pipesor other flow channels. If the Machine Reynolds number at test operating conditions differs from that at specified operatingconditions, a correction to the test results is necessary to properly predict the performance of the compressor. The flow patterns of axial and centrifugal compressors are relatively complex. Theterm“Machine Reynoldsnumber” is used to provide a basis for definition in this Code. The Machine Reynolds number correction forcentrifugal compressors recommended in thisSection is based onRef. (D.3) but simplified for ease of application. The Machine Reynoldsnumber correction for axial compressors is unchanged from the previous issue of the Code and is based on Ref. (D.7). If anothermethodof correction is used it shall be agreed on by theparties prior to the test (See Appendix F).

0.988 ~~~0.243

i5.6.41

where

b= as defined in para. 5.5.2, ft v= the average surface roughness

of the flow passage, in. The polytropicwork coefficient should be correctedfor Machine Reynoldsnumber in the same ratio as the efficiency.

(b) For Axial Compressors The correction for axial compressors continues to be based on Ref. (D.7), and is a function only of the Machine Reynoldsnumber ratio and not the absolute value of the Machine Reynolds number.

5.6.3.2 Correction Factor. Since frictional losses in the compressorare a function of the Machine Reynoldsnumber it is appropriate to apply the correction to the quantity (1 - 7 ) . Themagnitude of the correction is a function of both the Machine Reynoldsnumber ratio andtheabsolutevalueof the Machine Reynolds number, with increasing effect as the Machine Reynoldsnumberdecreases.

Again, as for the centrifugal compressor case,

The limitations of Table 3.2 apply. 52

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]

(4.8 x lo6 x b)

+ 0.934

0.000125 + -

Machine Reynolds Number Correction

5.6.3.1

m

0757b70 Ob05477 1 T 1

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ASME PTC 10-1997

estimated error limit of a measurement or result for agivencoverage.Coverage is thefrequencythat an interval estimate of a parameter may be expected to contain the true value. Forexample, 95 percent uncertaintyintervalsprovide 95 percentcoverage of the truevalue.That is, in repeatedsampling, when a 95 percent uncertaintyinterval is constructed foreachsample,overthe longrun, the intervals will contain the true value 95 percent of the time. Uncertainty analysis i s theprocess of identifying and quantifying the errors in test measurements and propagating these errors to estimate the uncertainty in the final result. The methodology of ASMEPTC 19.1 is the standard for ASMEPTC 1O tests. If other methods areto be used they are subjectto agreement by parties to thetest.

5.6.3.3 limits of Application. Since the performance variations increase substantiallyas the Machine Reynoldsnumberdecreases,tests of compressors designed for operation at low MachineReynolds numbers should be tested at conditions closeto those specified.Therefore,themaximumand minimum permissibleratiosbetween Reml and Rem, are shown in Fig. 3.4. Also, see Appendix F and Table E.2. 5.6.4 Mechanical losses. Whenthemechanical losses at specifiedoperatingconditions are not known they may be determined from the following equation:

5.7.5 Scope of Uncertainty Analysis. Thescope of the uncertainty analysis required for a given test is intimately related to the test objectives. The scope of suchanalysis is subject to agreementbythe parties to the test.Suchagreements shall be made prior to undertaking the test.

The exponent in the preceding equation may vary with thedesign of bearings,thrustloads, oiling It usually has avaluebetween 2.0 systems,etc. and 3.0.

5.7 TREATMENT OF ERRORS 5.7.1 Source. The information presented Section is derivedfrom PTC 19.1.

in this

5.7.2 Errors. All measurementshaveerrors.Errors arethedifferencebetweenthe measurementsand thetruevalue. The total error is made up of two components. One i s called bias error. Bias errors are thesystematicerrors which may includethose which are known and can be calibrated out, those which are negligibleand areignored,andthose which are estimated and included in the uncertainty analysis. The other type of error is called precision error. Precision errorsare the random errors observed in repeatedmeasurements.Exactagreement in repeated measurements does not and is not expected to occur because of numerous error sources. 5.7.3TheImportance of Errors. One chooses.to run a performance test with certain objectives in mind.Theymaybe as varied as establishing a benchmark for maintenance or to verify guarantee performance.Acceptableerror limits will depend upon the test objectives. The error in the final result shall be sufficiently small so as not to mask the test objective. 5.7.4Uncertainty. Somemeansarenecessary to quantifyerrors to make a judgement in terms of acceptable error limits for a test. Uncertainty is the 53

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5.7.6 The Methods of PTC 19.1. PTC 19.1 includes discussionsandmethods which enable the user to select an appropriate uncertainty model for analysis andforreporting testresults. It defines,describes, and illustrates the various terms and methods used to provide meaningful estimates of the uncertainty of measurements and results. It is in essential agreement with various national and international standards on the samesubject. The uniquenessof PTC 1 O test objectives precludes exhaustive treatment of uncertaintyin this document. It is anticipated that the user will refer to PTC 19.1 for detailed information to apply to individual tests. The uncertainty analysis can thereby be tailored to meet the individual testobjectives. The following discussion is includedto indicate thecalculationmethod in generalterms.Asimple sample demonstration case is given in Sample Calculation C.8 of this Code. Another simple compressor example may be found in PTC 19.1. Both are intended simply to demonstrate the method. Neither shouldbeconstrued as exhaustive in detail nor necessarilygenerallyindicative of usualor anticipateduncertainty. PTC 19.1 presents a step-by-step calculation procedure to be conducted before and after each test. It is summarized in brief as follows: Step 1 - Definethemeasurementprocess. (a) Review test objectives and test duration.

ASME

COMPRESSORS AND EXHAUSTERS

10-1997

(b) List all independent measurement parameters and their nominal levels. (c) List all calibrations and instrument setups. (d) Define the functional relationship between the independent parameters and the test result. Step 2 - List elemental error sources. (a) Exhaustive list of all possible measurement error sources (b) Group error sources according to calibration, data acquisition,anddata reduction . Step 3 - Estimateelementalerrors. (a) Obtain estimate of each errorin Step 2 above. (6) Classify as precision or bias error. Step 4 - Calculate bias and precision errors for eachparameter. Step 5 - Propagate the bias and precision errors. (a) Bias and precision errors of the independent parameters are propagated separately all the way to the final result. (b) Propagate according to the functional relationship defined in Step l(d) above using sensitivity factors. Step 6 - Calculate uncertainty.' (a) Select UADDand/or URSSmodels. (bl Obtain uncertainty. Step 7 - Report (a) Calculations (b) Tabulated elemental errors (c) Bias (d) Precision [rssSl,where S = [CS,2/Ni]"

'

The UADD and URSS models are the mathematical models which are usedto combine bias and precision errors to a single uncertainty value. UAODprovides approximately 99 percent coverage while URSS provides approximately 95 percent coverage when neither bias errors nor precisionerrors are negligiblecompared to the other. If the bias error is negligible, both UADD and U R S S provide95 percent coverage.

54

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ASMEPTC 10-1997

SECTION 6 6.1

- REPORT OF

(e) Description of compressor cooling system and coolant properties

CONTENTS

The Report of test shallinclude applicable portions of the informationshown in para. 6.2, andmay include otherdata as necessary. Copiesofthe original testdata log, certificates of instrument calibration, primemover(motoror othertype)efficiency data as needed, description of testarrangementandinstrumentation,andany special written agreements pertaining to thetestor thecomputation of results shall be included. When testsare runover a rangeofoperating conditions the results shall also be presented in the form of curves. The curves shall be clearly marked to denote use of staticor total conditions.

6.2TYPICAL

6.2.3Specified Operating Conditions (a) Gas composition and source for properties (b) Inlet gasstate (7) Total and static pressure' (2) Total and static temperature' (3) Total and static density', (4) Relative humidity if applicable' (c) Gas flow rate (7) Inlet and discharge mass flow rate (2) Inlet and discharge volume flow rate (3) Capacity (dl Discharge static and/or total pressure (e) Coolant type, properties,flow rate, and temperature for cooled compressors (0 Speed (g) Others as needed

REPORT INFORMATION

6.2.4 Expected Performance Specified at eratingConditions (a) Developed head (b) Efficiency (c) Power requirement (d) Discharge total temperature (e) Others as needed

6.2.1 General Information (a) Date of test (b) Location of test (c) Manufacturer (d) Manufacturer'sserialnumbersandcomplete identification (e) Party or parties conducting test ff) Representatives of interested parties (g) Detailed written statement of the test (h) Agreement made by parties to the test

Op-

6.2.5 Derived Parameters at Specified Operating Conditions (a) Machine Mach number (b) Pressure ratio (c) Volume ratio (d) Flow coefficient (e) Machine Reynolds number (0 Others as needed

6.2.2Description of Test Installation (al Type of compressor;radial flow, axial flow, etc. ( 1 ) Type of impellers; open, shrouded, cast, fabricated, etc. (2) Number of stages (3) Arrangement of casing and piping (4)Pipe sizes; inlet and discharge (51 Arrangement of intercoolers, if used (6) Impeller diameter and blade tip widths (b) Description of lubricating system and lubricant properties (c) Type of shaft seals (d) Type and arrangements of driver; turbinedirect connected, motor direct connected, motor and gear, etc.

6.2.6SetupofInstrumentsandMethodsof

Mea-

suring (a) Description of all allowed departures from this Code which have been authorized by agreement (b) Piping arrangementwith sketches and diagrams (c) Location ofall measuring stationswith diagrams and sketches 'Pressures, temperatures, and densitiesshould be clearly identified as static or total conditions.

55

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TEST

ASME

10-1997

COMPRESSORS AND EXHAUSTERS

(ee) Casing surface area Leakage flow rates

(d) Method of measuring flow rates

(m

(e) Instruments usedfor the measurement of pressure, temperature, speed, composition ofgas, density, and power (0 Procedures andfacilities used for the calibration of instruments (g) Calibration data (h) Instrument accuracy (i) Source of test gas property data 0) Method of determining powerlosses, if any, between the power measurement station and the compressor input shaft (k) Description of sampling and analysis method for test gas

6.2.8 Computed Results for Test Operating Conditions (a) Type of test (b) Test run number (c) Barometricpressure (d) Gas composition (e) Mass flow rate (0 Inlet static conditions ( 1 ) Pressure (2) Temperature2 (3) Compressibility factor (4) Density’ (5) Enthalpy (6) Others as needed (g) Inlet volume flow rate (h) Inlet velocity temperature2 (i) Inlet velocity pressure 0) Inlet total conditions (7) Pressure (2)Temperature (3) Compressibility factor (4) Density (5) Enthalpy (6) Others as needed (k) Capacity (I) Discharge static conditions ( 1 ) Pressure (2)Temperature2 (3) Compressibility factor (4) Density2 (5) Enthalpy (6) Others as needed (m)Discharge volume flow rate (nl Discharge velocity temperature2 (o) Discharge velocity pressure (p) Discharge total conditions (7) Pressure (21 Temperature (3) Compressibility factor (4) Density (5) Enthalpy (6) Others as needed (q) Leakages (7) Mass flow rate (2) Enthalpy (3) Energy loss or gain (r) Secondary flow streams ( I ) Mass flow rate

6.2.7 Mean Observations Derived FromTest Data (All calibrationsandinstrumentcorrectionshaving beenapplied) (a) Test run number (b) Duration of run (c) Speed (d) Inlet temperature (e) Barometer reading (0 Ambient temperature at barometer (g) Inlet static pressure (h) Dry bulb temperature if required (i) Wet bulb temperature if required Dew point temperature if required (k) Gas density if measured (I) Gas composition if measured (m)Discharge static pressure (n) Discharge temperature (0)Flowmeter data, typically: ( 1 ) Pressure differential across flowmeter (2) Pressure upstream side of flowmeter (3) Temperature upstream side of flowmeter (4) Flowmeter throat diameter [Items (P) to (W) apply to cooled compressors:] (p) Coolant flow rate CS,, Coolant inlet temperature (r) Coolant outlet temperature (S) Gas temperature at inlet of cooler (t) Gas temperature at outlet of cooler (u) Gas pressure at inlet of cooler (v) Gas pressure at outlet of cooler (W) Condensate drained from cooler (x) Power input (y) Torque (z) Lubricant flow rate (aa) Lubricant inlet temperature (bb) Lubricant outlet temperature (cc) Mean casing surface temperature (dd) Ambient temperature

u)

*Iterativesolutionmay be required.

56

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ASMEPTC 10-1997

COMPRESSORS AND EXHAUSTERS

(I) Pressure ratio

(2) Enthalpy (3) Average mixed gas state (4) Energy loss or gain (S) Rotor mass flow rate (t) Mechanical loss (u) Heat transfer loss (v) Gas power (W) Shaft power (x) Head

6.2.10 Machine Reynolds NumberCorrection (a) Test operatingcondition Machine Reynolds number (b) Specified operating condition Machine Reynolds number (c) Machine Reynolds number correction (d) Specifiedoperating condition polytropic efficiency (e) Specified operating condition polytropic work coefficient

6.2.9Computed Test PerformanceParameters (a) Isentropic total discharge conditions (7) Temperature (2) Density (3) Enthalpy (6) Polytropic work coefficient (7) Overall isentropic volume exponent (2) Polytropic work factor (3) Polytropic exponent (4) Polytropic work (5) Impeller blade tip velocity (6) Polytropic work coefficient (c) Isentropic work coefficient (7) Isentropic exponent (2) Isentropic work (3) Isentropic work coefficient (d) Polytropic efficiency (e) Isentropic efficiency (0 Work input coefficient (g) Total work input coefficient ( 1 ) Energy lost or gained via leakage (2) Energy lost or gained via secondary flows (3) Energy lost via casing heat transfer (4) Mechanical loss (h) Flow coefficient (i) Volume ratio ci., Machine Mach number (k) Specific heat ratio, inlet and discharge

6.2.1 1 Computed Results for Specified Operating Conditions (Speed and inlet gasstate given) (a) Flow rate (7) Capacity (2) Inlet and/or discharge mass flow rate (3) Inlet and/or discharge volume flow rate (4) Leakage flow rate (5) Cooler condensate (6) Secondary flow rates (7)Others as needed (b) Discharge conditions (7) Static and total pressure (2) Static and total discharge temperature (3) Compressibility factor (4) Static and total density (5) Others as needed (c) Work related terms (7) Polytropic head (2) Enthalpyrise (3) Gas power (4) Shaft power (5) Others as needed 6.2.12Uncertainty

6.2.13 SuggestedSummary of Results, Comparing the Test, TestResults,and IntendedValues

57

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Analysis

APPENDIX A USE OF TOTAL PRESSURE A N D TOTAL

TEMPERATURE TO DEFINECOM.PRESSOR PERFORMANCE (This Appendixisnot

a part of ASME PTC 10-1 997.)

A.l Theperformancecharacteristicsofacompressor which depend upon thermodynamic properties for their definition are, under the provisions of this Code,based on stagnation (total) conditions.This procedurecan cause confusion if theprinciples involved are not kept clearly in mind. Compressor performancemaybespecified atstaticpressures andtemperaturesor at stagnationpressures and temperatures, as desired, and the following explanation serves topointout thedifferencesbetween the two.

Subscripts i and d refer to stagnation inlet and dischargeconditions,respectively, as determined bystagnationpressuresandtemperatures. In the stagnationprocess

[A-41

A.2

When the FirstLaw ofThermodynamics, written as the generalenergyequation, is applied to a compressor section with the system boundaries defined as the interior wall ofthecasingandthe transverseplanesacrossthe inlet anddischarge flanges in the absence of leakageandsidestreams, the following expressionresults:

The difference between static and stagnation conditions is shown graphically on a Mollier Diagram, Fig. A.l. A.4 As will be notedfrom Fig. A.1, theprocess ofcompressiontakesplacebetweenstates (Y and y. Some calculations regarding theinternal compression process might requirethe use ofstatic states intermediate to (Y and y. However, as shown by Eqs. [A-1I through [A-51, use of the stagnation properties for the external energy balanceof the compressor is an excellent approximation because: (a) "Charging" the compressor with receipt of gas at the stagnation enthalpy hi (at stagnation pressure pi) i s equivalent to charging it withreceipt of gas at the static enthalpy h,a (at static pressure pa) plus kinetic energy

Subscripts aand yrefer to static inlet and discharge conditions,respectively.The inlet anddischarge flanges may be considered to be at the same elevation so that y. and yr the elevation heads, become equal.Solving Eq. [A-11 for W s h gives

Thisresultinvolvesstaticenthalpiesdetermined

by staticpressures andtemperatures. A.3 When the stagnation concept is employed, Eq. [A-21 becomes 59

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h

FIG. A.l

COMPRESSORSTATE POINTS STATIC AND TOTAL thermodynamic or otherwise, taking place within thecompressorproper.Should a study of events internal to the compressor be desired, a new system mustbe defined andtheappropriate conditions stated. Studies of events internal to the compressor not included within the scope of this Code.

and,

(b) “Crediting” the compressorwith delivery of gas at the stagnation enthalpy hd (at stagnation pressure

p& is equivalent to crediting it with delivery of gas at the static enthalpyh, (at staticpressurep,) plus kinetic are energy

A.6

v; 2gcJ

A.5

The precedinganalysiscanbe applied only becausethesystemboundarieswerecarefullydefined so as to preclude any consideration of events,

Theotheruse of thestagnationpressureand stagnation temperaturein this Code is for the determination capacity. Capacity of is a volumetric flow related rate inlet to conditions. Capacity is defined herein as thedelivered mass flow rate divided by inlet total density correspondingto total pressure and temperature. This is convenient because it permits a clear definition of volume flow rate consistent with mass flowwithout referring to thedesign of the compressor. 60

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APPENDIX B PROPERTIES OF GAS MIXTURES (This Appendix is not a part of ASME PTC 10-1997.)

partial pressureof that constituent by

B.l The testing of modern compressors may require the use of a gas mixture as the test“gas”either becausethespecified gas is itselfamixtureor because it is necessary, foronereasonoranother, to substitute for thespecified gas duringthe test a mixture is the only satisfactory program,and method of obtainingthedesiredproperties in the substitute gas.Theuse ofa gas mixture presents, in essence, a two-part problem. If thestate of the mixture is such that it maybeconsidered as a mixture of ideal gases, the usual methods of classical thermodynamicscan be applied to determine the state of each constituent gas,If,however,the state of themixture is such that themixtureand the constituentsdeviatefromthe ideal gaslaws, other methods must be used which recognize this deviation. In either case there is the necessity that accurate thermodynamic dataforthegases beavailable. If accurate thermodynamic properties for a gas, based on experimentaldataor reliable mathematical and physical methods are available, these properties shouldbe used with preferencegiven to thatdata based on experimental work. So far as this Code is concerned, the problem is one of determining density, enthalpy, specific heats, and entropy of constituent gases at thepressureandtemperatureeach experiences.

The molal (volumetric) analysis of the mixture is oneoftheitems of testdataandgivesthe mole fraction readily. With a homogeneousmixture, all constituent gases will havethe sametemperatures as the mixture thus providing the second of the two independentpropertiesneeded to definethe gas state. (This excludessaturatedvapors.) With the state of each constituent thus defined, the individual property of interestmaybedeterminedandthe equivalent mixture properly calculated by the methods outlined below.

B.4 With properties of the individual gases determined, the equivalent value of the property for the gas mixture maybecalculated by summingthe individual propertyvalues on a total basis, ¡.e., quantity of the gas times property value. The equations are summarizedbelow. Enthalpy:

B.2 Whenthethermodynamic state is such that the gas mixtureand its constituent gases must be treated as real gases, themethodofdefiningthe thermodynamic state oftheconstituent gases and thus arriving at their properties shall be agreed upon in writing prior to thetest. Once the state of the gas i s defined, presumably by pressureandtemperature,theotherproperties of interestmaybeobtainedfromcharts,tables,or equations of state.

nmHm= naHa+ nbHb + ncHc+

Entropy:

B.3 For ideal gases, the mole fraction, xi, of any constituent gas j maybeused to determinethe 61

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e + n,Hj

18-31

In the preceding series of equations, lB-21, [B-S], and [B-81 are on a massbasis; [B-31, [B-61, and [B-9] are on a mole basis, and [B-41,[B-71, and [B-101 are on a mole fraction basis. It shouldbe noted that the determination of theend point of theisentropic processstarting at inlet conditions and ending at thedischargepressureandentropy value correspondingto inlet conditions will probably involve a trial-and-error solution.

62

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APPENDIX C SAMPLE CALCULATIONS (This Appendix is not a part of ASME PTC 10-1 997.)

The sample calculations contained in this Appendix demonstrate the basic calculation principles of this Code. Each sample highlights one or morefacets of the necessary procedures for application oftheCode to realmachines.Thedatapresented is typical and does notrepresentanyactual operating unit. Additionally this data should not be taken as expected for any actual conducted test.

Sample C.l

Sample

Sample Sample Sample

Sample Sample Sample

demonstrates a Type 1 testfor a centrifugal compressorusingan ideal gas.The conversionofstaticreadings to total conditionsandcalculationofresults by heatbalanceand shaft powermethods arecovered. ideal gas. C.2 demonstrates a Type 2 testfor a centrifugalcompressorusingan Application of Reynoldsnumbercorrections, heat loss to ambient and variable speedeffectsarecovered. C.3 demonstrates the ideal gas application to selectionoftestspeedandtestgasand alsocoversthemethods of power evaluations. C.4 demonstrates the treatment of bracketed test points. C.5 demonstrates how to select a test gas for a Type 2 testusing ideal andreal gas equations. A flow chart procedure is presented to assist in outlining the required steps. C.6 demonstratesaType 2 testusingreal gas equations for data reduction. C.7 demonstratesthetreatmentofa two sectioncompressor with externally piped intercooler. C.8 demonstrates the application of uncertainty analysis to this Code.

63

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SAMPLE CALCULATION C.l TYPE 1 TEST FOR A CENTRIFUGALCOMPRESSOR USING A N IDEAL GAS Thissample calculation is intended to demonstrate: (a) Type 1 test (6) Test gas same as specified gas (c) Ideal gas (d) No heat loss (except to lubricating oil) (e) No flow leakages (0 Centrifugal machine (g) No flexibility to change compressor speed (h) Single section machine The purpose of this calculation is to determine the quantity of gas delivered and the compressor head,pressurerise,efficiency, and shaft inputpower. Paragraph3.1 1.4 of theCoderequires that whena test is only to verify asinglespecified condition,the test shall consistof two test points which bracketthespecifiedcapacity. The calculations demonstrated in this sample calculation would be used on both of these bracketing points.

Description of Test Installation (seepara.6.2.2) (a) Type of compressor - centrifugal (7) type of impellers - shrouded (2) number of stages - single section, five stages (3) arrangement of casing and piping - not applicable to this sample (4) pipe sizes; inlet and discharge- inlet pipeis 18 in., schedule 40 (Di = 16.876 in.); discharge pipe i s 10 in., schedule 40 ( D d = 10.020 in.) (5) arrangement of intercoolers, if used no intercooler (6) impeller diameter and blade tip widths - impeller diameters 0 1 = D2 = D3 = 18.4 in. and D4 = D5 = 16.6in.; first stage impeller tip width = 6 = 1.SOO in. (b) Description of lubricating system and lubricant properties- Lubricating sytem oil flow rate is 4 gpm per bearing for a total flow rate of 8 gpm. Oil density i s 55.6 Ibm/ft3 so the oil flow rate is 59.5 Ibm/min [8 gpmA7.48 gal/ft3) x 55.6 Ibm fi3]. Oil has constant pressure specific heat of cp = 0.462 Btu/lbm "R. (c) Type of shaft seals - Not applicable to sample (dl Type and arrangementsof driver; turbine direct connected, motor direct connected, motor and gear, etc. - Not applicable to sample (e) Description of compressor cooling system and coolant properties- No cooling system

-

Simpliving AssomptionsforThisSample (al The gas (air) may be treated as an ideal gas with a constant specific heat (evaluated at the average of the inlet and discharge temperatures). (b) The Reynolds number correction i s negligible.

Specified Operating Conditions (seepara. 6.2.3) (a) Air with constant pressure specific heats of dry air and water vapor givenin Fig. C.1, MWda = 28.97 and MW, = 18.02 65

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(b) Inlet gas state (7) pslatic i = 14.00 psia at inlet flange (2) TStatic &i = 560.0 "R at inlet flange (3) have to calculate inlet densities (4) RHinlet = 81.7 percent (c) Gas flow rate (7) inlet mass flow rate = discharge mass flow rate =

W = 600 Ibm/min (2)inlet and discharge volume flow rates have to be calculated

(3) capacity to be calculated

(d) Discharge static pressure = 45.00 psia at discharge flange (e) Compressor coolant not applicable (0 N = 10,000 rpm (g) Not applicable

Expected Performance at Specified Operating Conditions (see para. 6.2.4) (a) Developed polytropic head = 44100 ft Ibf/lbm (based on total conditions) (b) Efficiency (polytropic) = np = 0.80 (c) Power requirement = Psh = 101 9 hp (d) Discharge total temperature = 844.1 "R (The discharge static temperature is assumed given as 842.8 "R.) The following preliminary calculationsestablish the givenspecifiedoperating conditions in a form convenient for the Code calculations. (a) Partial pressure of water vapor is found using the steam tables: [Ref. (D.20)]

(b) Air humidity ratio at inlet flange [Ref. (D.20)1

(HRi)sp

= (0.6220

-(

")

0.6220 Ibm (0.7825 psia) Ibm da

(1 4.00

- 0.7826) psia

)

lbmole W (28.97 ibm da) 180.02 ibrn W lbrnole da

= 0.05921

lbmole W lbrnole da

(c) Air molecular weight [Ref. (D.2011 (MWaIsp =

mole da ( M W d + mole

W

mole da + mole

W

(MW,)

Ibm da

-

) + 0.05921 lbmole

1 .O00lbrnole da 66

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+ 0.05921 lbmole

W

W

S T D - A S M E P T C LO-ENGL L777

m 0757b70

Ob05492 h35

m

Ibm = 28.36 lbmole

(d) Air specific heat at constant pressure is found using dry air and steam properties (Fig. C.l)

(cp)sp

(

=

mass da

(Cpda)

mass da

) + 0.03683 Ibrn (O 448 Ibrn w"R

1 .O00 Ibrn da 0.240 (cpi)sp=

= 0.247

Ibrn & " R 1 .O00 Ibrn da

\

*

+ 0.03683

Btu

Ibrn da "R

) + 0.03683 Ibrn (O 462 Ibrn w o R W

'

1.000 Ibrn da + 0.03683 Ibrn

(D.20)]

Btu Ibrn "R

0.247 (0.247

m)Btu

(1.986

0.252

-)

Btu Btu (0.252 Ibrn "R

)(

Btu lbmole

=

W

Btu [note: ( H R i ) s p = Ibrn "R

(e) Air specific heat ratio [Ref.

=

W

Btu

(

= 0.252

(kd)sp

Ibrn

Ibrn "R

=

(kAp

W

-

1.000 Ibrn da 0.2445 ,

Wpdsp

+ mass W (cpw) + mass W

"R

Btu Ibrn "R

- (1.986

lbmole "R

lbmole

)=

28.36 Ibrn

)(

lbmole

)=

28.36 Ibrn

(0 Static specific volume at inlet and discharge flanges is found using the ideal gas law 67

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S T D - A S M E P T C LO-ENGL 1777 m 0757b70 U b 0 5 Y 9 3 571 m

(

(vstatic Jsp

=

)

(1545 ft lbf) lbmole (560.0 "R) lbmole "R 28.36 Ibm (14.00

S) $) (144

)

(

(1545 ft lbf) lbmole (842.8 "R) lbmole "R 28.36 Ibm (45.00

fi3

= 15.13 Ibm

S)

(144

$-)

= 7.086 I bm ft3

fg) Average fluid velocity at inlet and discharge flanges (see para. 5.4.3.1)

( 6 0 0 2 ) (15.13 (Vilsp

ft3

=

(600 (vd)sp

)

= 97.40

g) L) (7.086

=

= 129.4

ft sec

ft

sec

(h) Fluid Mach number at inlet and discharge flanges (see para. 5.4.2.5)

97.40 (M;)sp

=

ft sec

lb

(1545 lbmfole "R

68

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) (28.36 lbmole ) (560 "R) Ibm

= 0.0832

129.4 (Md)sp

=

Ibm2)(1545 Ibf sec

(

1.385 32.1 74

ft sec

-

ft lb lbrnole "R

) (28.36 lbmole ) (842.8 "R) Ibm

= 0.0905

(i) Totaltemperaturesatinletanddischargeflangesarefoundusingtheenergyequationand assuming an adiabatic process (see Eq. [5.4.6])

(97.40 (TJsp

=

560.0 "R

+

k)

(

Ibf sec2 (0.247

= 842.8 "R

+

(

E)(32.1

2 778.1 7 Btu

Btu

k)

(1 29.4 (TdlSp

= 560.8 "R

ft Ibrn

2 7 7 8 . 1 7Btu E ) (32.174-)

= 844.1 "R

ft Ibrn

747) (0.252 Ibf sec Ibm "R

ci,, Since the Fluid Mach number isless than 0.2, the total pressure may be calculated according to the simplified Eq. i5.4.41

(97.40 (pi)sp

= 14.00 psia

+

(

J:,'

2 1 5.1 3 -

(32.174-

(1 29.4 (pd)sp

= 45.00 PSia

i-

2 (7.086

S)

ft Ibrn in2 ft2) Ibf sec2) 144 -

= 14.07 psia

(

A) -)

(32.1 74ft Ibrn (1 44 Ibf sec2 69

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2)

g)

= 45.26 psia

(k) Total density at the inlet and discharge flanges is found using the ideal gas law

1 (40.7): (pi)sp

= ($)*P

=

Ibm

( 1 4 4in2 ~lbf)

) (lbmole) 1

ft Ibf

= 0.06632 (560.8 "R)

fi3

"

(1545 lbmole "R

28.36Ibm

(45.26 (Pd)sp

=

( g ) s p =

(1 545

ft Ibf lbmole "R

S) $) (144

)(

lbmole) 1 28.36. Ibm

I bm = 0.141 7 (844.1 "R)

ft3

"

(I) The sum of the squares of the blade tip speeds is

\ lo4 min) j= 1

13 (18.4 inIL + 2 (16.6 il.,

,

= 2.983

fi2

X

lo6-

j= 1

sec2

mln

Mean Observations Derived fromTest Data (seepara. 6.2.7) (a) Test run number 1 (b) Duration of test = 30 minutes (c) Compressor speed = 10,000 rpm id) Inlet temperature = T&ic dbi = 540.0 "R (e) Barometer reading = 14.1 7 psia (0 Ambient temperature at barometer = 540.8 "R (g) Inlet static pressure = 14.10 psia (h) Dry bulb temperature at inlet flange = = 540.0 "R (i) Wet hulb temperature at inlet flange = TStatic wbi = 530.0 "R 0) Dew point at inlet flange = 524.4 "R (k) Gas density not measured (1) MWda = 28.97 and MW, = 18.02 (m) Discharge static pressure = fstatic d = 47.00 psi in) Discharge static temperature = Tstatic dbd = 830.0 "R (o) Mass flow rate = 38,000 Ibm/hr (dto (W) Not applicable to this sample (x) Shaft power input = Psh = 1097 hp (y) Shaft torque = 57.62 ft lb (z) Lubricating system oil flow rate is 4 gpm per bearing fora total flow rate of 8 gpm. Oil density is 55.6 Ibm/ft3 so the oil flow rate is W, = 59.5 Ibm/min. Oil has constant pressure specific heat cw = 0.464 Btu/lbm. (aa) Lubricant inlet temperature = Toin = 530.0 "R (bb) Lubricant outlet temperature = Toout= 561 .O O R (cc) to (fi3 Not applicable to this sample Computed ResultsforTest OperatingConditions (similar to para. 6.2.8) The previous test data is converted into a form convenient for Code calculations. (a) The air humidity ratio ofthe inlet air is found using air and steam properties [Ref. (D.20)]

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0.3667 psia Ibrn W = 0.01661 14.1 O psia 0.3667 psia Ibrn da

= 0.6220

Btu Ibrn da

-

-

(540.0 O R

Btu - 530.0) R t (0.01661 G Ibm ") (1092.2 - 38.35) Ibrn Btu (1095.5 - 38.35) Ibrn W

W

0.01881

=) (L lbmole 7 (28.97 Ibrn lbmole da Ibrn18.02 da W

=

0.03024

lbmole

W

lbmole da

(b) Air molecular weight [Ref. (D.20)] (MW,), =

-

=

(MWdJ + mole [mole damole + mole da

(

1.000 lbmole da 28.97

W

(MW,)

W

I, ) + 0.03024 lbmole

Ibm da lbmole da

1.00 lbmole da

28.65

W

+ 0.03024 lbmole W

I bm lbmole

(c) Air specific heat is found using dry air and steam properties (see Fig. C.1)

(c,), =

(

mass da (Cpda) + mass W (cpw) mass da + mass W

I,

1 .O00 Ibrn da 0.240 (Cp;)t

=

= 0.244

Ibrn da "R

1 .O00 Ibrn da + 0.01 881 Inm

Btu Ibrn " R 71

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) + 0.01881 Ibrn ( 0.447 Ibm w"R W

S T D - A S M E PTC LO-ENGL L 7 7 7 D 0 7 5 7 b 7 D Ob05q77 1 1 7

)

Btu + 0.01 881 Ibrn (0.460 da OR 1.O00Ibrn da + 0.01881 Inrn W

1 .O00Ibrn da (0.244 cc,,,, = Btu = 0.248 Ibrn "R

A verage specific heat 0.244

+ 0.248 Btu Btu

- 0.246 Ibrn "R

"

2

Ibrn "R

(dl Air specific heat ratio

=

(Mt

=

(0.244

S)-

(Z),

=

Btu 0.244 Ibrn "R

(0.1 986

0.248 (kd)t

lbmole Btu O R )

Btu Ibrn O R

=

Btu (o'248

= 1.397

Btu

-)Ibrn "R - (0.1 986 lbmole"R

(G 1 r lbmole )

)(

1

lbmole)

28.65

Ibrn

= 1.388

(e) Static specific volume at inlet and discharge flanges is found using the ideal gas law

(1 545 (vstatic d t

=

ft Ibf

lbmole O R

) (28.65 1 lbmole) 540.0 "R Ibm "

(14.10%)

(144$) 72

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= 14.34

ft3

I brn

(1 545 (Vstatic

d)r

=

ft Ibf lbmole "R

) (28.65 1 lbmole) 830.0 "R Ibrn "

S) $)

(47.00

CO

ft3

= 6.613

I bm

(1 44

Fluid velocity at inlet and discharge flanges (see para. 5.4.3.1)

?)hr

(1 4.34

4 (T16.87ft)

(3600

(38,000 (VJt =

TT

(38,000%) hr (6.613 (vd)t

=

ft

777 (F 10.020ft)'

E) Ibm

T)

ft

= 97.45sec

E) Ibrn

(3600

y)

= 127.5 sec

[g) Fluid Mach numbers at inlet and discharge flanges (see para. 5.4.2.5)

ft 97.45 -

(Mi), =

sec

(

-)

ft m J I .397 32 174Ibf!ec2

(I545

ft

lb

) (L28.65-) Ibm

lbmole "R

ft sec

= 0.0852 (540.0 "R)

127.5 -

(Md)( =

(

-)

ft Ibrn 41.388 32.1 74 Ibf sec2 (1 545

lb

lbmole "R

(h) Totaltemperatureatinletanddischargeflanges adiabatic process (see Eq. [5.4.6]) 73

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= 0.0902

)( 1 e (830.0) "R) 28.65 Ibrn

is foundusingtheenergyequationforan

~~

~~

S T D - A S M E P T C LO-ENGL L997

m

0759b70 Ob05499 T 9 T

(97.45

(Ti), = 540.0 "R

+

= 830.0 "R

+

(Td)t

Z)

0 . 2 4 4 Btu ~ ) ( 7 7 8 . 1 7 E ) ( 3 2 . 1 7 4 - ft Ibm Btu Ibf sec2)

(

m

ft ,bm

-) Btu

= 540.8 "R

) = 831.3 "R

E) 7 (32.174 Btu Ibf secz

2 0.248 Ibrn "R (778.1

(i) Since the Fluid Mach number is less than 0.2, the total pressure may be calculated according to the simplified method of Eq. (5.4.41

(97.45 ( p h = 14.10 psia

+

&)

2

(Pd)(

(14.34

(

2 6.61 3

-)Ibm ft3

7

= 14.1 psia

lbfsec~(144%)

A)'

(32.1 74

74

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2

(32.174 ' I b m )

(1 27.5

= 47.00 psia +

&)

Ibf Ihm) sec2 (144

= 47.27 psia

$)

fj) Total density at the inlet and discharge flanges is found using the ideal gas law

(Pu)sp =

(14.17

(&),=

S) 5)

) (28.65 lbmole) (540.8"F) Ibm

Ibf (1545lbmole "R

(Pd)sp

=

(&),

S)

)(

ft Ibf

= 0.06997 ft3

"

(47.26

=

Ibm

(144

1

$)

I bm

(1 44 lbmole)

= 0.1518 ft3 (831.3"F)

"

(1545lbmole O R

28.65 Ibm

(k) The sum of the squares of the blade tip speeds is

[x 5

[TE 5

Ur],=

[Tz 5

Dr], =

j= 1

j= 1

Dr] = 2.983 X lo6-secZ ft*

j=l

(I) The shaft power was measured by the shaft power method to be (Psdt= 1097 hp (shaft power method) Theshaftpowercanalsobedeterminedusing Eq. 15.4.141:

where Eqs. [5.4.17] and [5.4.18] showtheparasiticlosses by the lubricating oil temperaturerise). Also using Eq. [5.4.13] gives

Ihm) (

to bemechanical losses(represented

ft Ibf ) (831.1 - 540.8)"R Ibm "R

(38,000 0.2459

) (60 F) (42.440mln hp ~

(59.5

%)

(0.462

~~

~~

Btu

) (31.O "R)

= 1065 hp + 20.1 hp = 1085 hp (heat balance method) 75

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(m) The gas power can be calculated from the heat balance method using ,Eq. [5.4.13]

The gas power canalsobe calculatedfromthe Using Eqs. [5.4.12], l5.4.171, and [5.4.181 P&= (Psh)t wo c p A To = 1097 hp 20.1 hp = 1077 hp (shaft power method) (n) The capacity is

-

shaft powerusingtheshaft

power method.

-

(38,000

9f =

T) -k) (60

=

(0.06997

Check for a Type 1 Test The following calculations confirm thatthe Type 1 test in Table 3.1. (a) Inlet pressure departure

*)

ft3

= 9051 min

ft3

test conditions meetthe

limits prescribedfor

Thetest inlet total pressure is within the Table 3.1 limit of 5%. (b) Inlet temperature departure (T;)sp

- (Ti), x 100 = 650.8 - 540.8 X 100 = 3.6%

( T;)sp

560.8

Thetest inlet temperature is within the Table 3.1 limit of 8%. (c) Speed departure (NJsp

- (Ni)(x 100 = 10,000 - 10,000 x 100 = 0%

( N;)sp

10,000

Thetestspeed is within the Table 3.1 limit of 2%, (dl Molecular weight departure (MW;Isp- (MW;)t 28.36 - 28.65 x 100 = x 100 = -1.02% 28.36 (MW;)sp

Thetest molecular weight is within the Table 3.1 limit of 2%. 76

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a

S T D - A S M E P T C L O - E N G L L997

0 7 5 9 b 7 0 D b 0 5 5 0 2 304 9

fe) Capacity departure

I

36,000 38,000 "

=

0.06632

0.06997

36,000

X

100 = -0.049%

0.06632

Thetest inlet capacity is within the Table 3.1 limit of 4%. (0 Density departure

(pdsp

- (pJr x 100 = 0.06632 - 0.06997 x 100 = -5.5% 0.06632

(P ilsp

Thetest inlet total density is within theTable 3.1 limit of 8%. Thetest coolanttemperaturedifferenceandcoolant flow ratewere not checked with the specified values since there is no coolant at the specified condition. Since all thetestparameters listed in Table 3.1 (excluding the coolantparameters) satisfy the Table 3.1 limits,thetest is a Type 1 test. Computed TestDimensionlessParameters (similar to para. 6.2.9) The dimensionless parameterswhich form the basis for the conversion fromtest data to specified operating conditions are calculated in this section. (a) Polytropic efficiency is found as follows: Averagespecificheat ratio

kr=

0.246

-= CP

(cp -

Btu Ibm "R

tí Ibf

-)Ibm "R

Btu

- (1.986 lbmole "R

)(

lbmole) 28.65 Ibm 1

Polytropicexponent (see Eq. [5.1T-51)

47.26 psia

In (14.1 7 pia)

=

In

(47.26 psia) (540.8 O R ) (14.17 psia) (831.3 O R ) 77

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= 1.555

= 1.392

Polytropic efficiency (see Eq. [5.1T-91)

(b) Flow coefficient (see Eq. [5.1T-11) (38,000

P)(5 (-) ) 60hr min

2.rrrad

-)

4t =

(0.06997 F Ibm)(1 0,000 rev

( 18.4y ft)

= 0.03996

min

(cl Polytropic work coefficient (see Eq. [5.1T-4])

(F)

ft Ibf

lbmole

1

(S K) (2.983 x l o 6 sec L (32.174 *)ft Ibm

- o 555

545 lbmole "R)

[ 47 26 -- 1 1 0.555

(540.8 "R)

q)

= 0.4734

(d) Total work input coefficient using the shaft power method (see Eqs. [5.4.18] and [5.3T-21)

(59.5 (om) t

=

wotp0ATo

=

e) min

(0.462

(42.44

Btu m) (31.O "R)

-) Btu

= 20.1 hp

minhr

--

T) 2)(h=) -)mm hp

(1 097 hp - 20.1 hp) (33,OO ft Ibf

(38.000

T)

(2.983

X

lo6

(60

= 0.6052

(e) Total work input coefficient using the heat balance method (see Eq. [5.3T-11) 78

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) (831.3- 540.8)"R + O1 778.1Btu6 ft lb

-

= 0.5996

(0 Work input coefficient (see Eq. [5.2T-2])

(g) Volume ratio at stagnation conditions (for information only) Ibm 0.1 851

ft3

0.6997

Ibrn fi3

= 2.170

Computed Resultsfor Specified Operating Conditions (similar to para. 6.2.1 1) The performance at the specified operating conditions is calculated from the test dimensionless parameters.Thesevalues apply directly sincetheReynoldsnumbercorrections are negligible. (a) Discharge total pressure at specified conditions is obtained as follows: Averagespecificheat Btu

Btu

0.247-+ 0.252 Ibrn "R Ibrn "R Btu = 0.250 2 Ibrn "R

-

hasbeenused

(Thedesigndischargetemperature

to estimate cpd)

Average specific heat ratio

0.250

-)

Btu Ibrn "R

(0.250 Btu - (1.986 Btu Ibm "R lbmole "R

)(

1 lbmole) 28.36 Ibrn

= 1.389 Polytropic exponent is found assuming equality of the polytropic efficiency at test and specified conditions (see Eq. [5.4T-71)

79

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= 0.7905

1.389 (-)0.389

= 2.823

2.823

nSP

= 0.4734

(

(2.983

(-)0.549 (1 545 lbmole 1 549

(pd)sp

X

-

= 1.823 = 1.549

1 O6

5)(L

sec ft lb "R

=) 32.174 ft Ibm

)(

1 28.36 Ibm

lbmole)

2.823

= 3.196

(560.8 "R)

= 3.196 (pjlSp= 3.1 96(14.07 psia) = 44.97 psia

(b) Capacity at specified conditionsis found using the definition of theflow coefficient and equating the flow coefficients at test and specified conditions (see Eq. (5.4T-11).

=

(

0.03996 10,000

2)

(2.") 80

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rad

18.4 ft3 (T ft)3 = 9051 min

S T D m A S M E P T C 10-ENGL L997 D 0759b70 Ob055Uh T 5 T

m

(c) The inlet mass flow rate is

WSP

=

(E)sp

(pi)sp = (9051

min Ibm ft3 ,in) (0.06631 F) (60 7)

Ibrn Ibm = 600.3 hr min

= 36,020

(cf) The specific volume ratio based on total conditions is (for information only)

(e) Discharge total temperature is found using Eq. [5.4T-18]

Since this temperature is nearly equal to the design value of 844.1°R, the average specific heat chosen for the calculations is assumed appropriate. (0 Gas power is found using the equality of the total work input coefficient between the test and the specified operating condition. Using the shaft power method and Eq. (5.4T-201 gives

Usingtheheatbalancemethod,

Wsp (&b)sp

(PghJsp

=

Eq. [5.4T-201gives

(y)sp c. u2 (600.3 x) Ibm (0.5996) -

33,000

(2.983 X lo6

-)

ft Ibf (33,000mm hp (60

= 1011 hp

$)

(g) Since the specified speed and the test speed are equal, the mechanical losses are assumed equal. The shaft power is then ( p s h ) ~ h= (Pg,,,

+ Q , A P = 1021

hp + 20.1 hp = 1041 hp (shaft power method)

or (Ps&,

= (Pghb+

= 1011 hp + 20.1 hp = 1031 hp(heatbalance

method)

(h) Static discharge temperature and pressure may be calculated from the mass flow rate, flow area, and total temperature and pressure. Since the flow Mach number is below 0.2,Eqs. [5.4.21, [5.4.31,f5.4.41, and [5.4.61 may be used. 81

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With a guessed velocity of 130.5 ft/sec, obtainedbytrialanderror,

(Tstatic d)sp

=

(Td)sp

- 2 ) gVdc c p

= 846.5

Ibm

(pstatic d)sp

=

(pd)sp

-

ft'

(130.5)'

- 2 778.1 7

sec

(Pstatic d)sp

( Ibf

-ft) Ibf

sec2

= 845.2

-)

(32.1 74 ft Ibm (0.252

Btu

--

Vd = 44.97 I bf

2gc (1 44)

"R

F)

(130.5)'

(0.1 40

ft Ibm)

(

2 32.174-

sec2Ibf

ft2 -

Ibf ( sec2 inn) = 44.7 in' 144

-

Checking

V=Ibstatic

\(0.140-Ibm) - (1;;2)

A/

T

ft3

(Pstatic d)sp

=

144 R

I = 130.5

II

(pstatic d)sp

(Trtatic d)sp

--

4

(1 44

-)

ft Ibf (1545 ibm "R

82

COPYRIGHT American Society of Mechanical Engineers Licensed by Information Handling Services

ft2/

ft sec

-

$) $) (44.7

(Lm) 28.36 Ibm (854.2 "R)

= 0.140-

Ibm ft3

OR

S T D - A S M E P T C LO-ENGL L777 U 0 7 5 7 b 7 0 0 b 0 5 5 0 8 8 2 2

TABLE C.l.l CALCULATION SUMMARY Test Corrected to specified Operating Test Operating Quantity

l. Quantity of gas delivered

Condition Symbol ConditionValue

Expected at specified

Units

W

Ibm/hr

38,000 36,000 36,000

rise 2. Pressure

*P

psi

33.1

(total) 3. Head

WP

ft Ibf/lbm 44,100 43,900 43,900

(Psh)sh

hP 1020 1040 1100

(Psh)hh

hP 1020 1030 1080

30.9

4. Shaft power Shaft

(a) method method (b) Heat

5. Polytropic efficiency

ratio

0.80

VP

0.790 0.790

6. Flow coefficient

4

7. Machine Mach no.

Mm

-

-

-

8. MachineReynoldsno.

Rem

-

-

-

9. Specific volume ratio (total)

(vi/v&

heat10. Specific coefficient 11.work Polytropic

12. Work input coefficient 13. Total work input coefficient method Shaft (a) method Heat (b) 14. Capacity

0.0400 0.0400

2.17

k

1.39

1.39

pp

0.473 0.473

Pmin

0.600 0.600

ash nhP

0.605 0.600

9 = (w/oJ

ft3/min

2.1 1

0.605 0.600

9050 9050

15. Inlet gasstate (a) Static temperature

T

(bl Staticpressure

P T P

(c) Total temperature (d)Total pressure

560 O R 560 14.0psia 14.0 O R 561 561 14.1psia 14.1

540 14.1 541 14.2

16. Discharge gasstate (a)Statictemperature

(b) Staticpressure (c)Totaltemperature (d) Total pressure

T P

OR

psia "R psia

T P

845 830 44.7 47.0 831 45.0 47.3

847

843.5 45.0 844.8 45.3

17. Cas power (a) Shaft method

(pg)sh

(b) Heat method

( pg)hb

hP hP

1o m

1O20 1010

1 O00

1060

10,000

18. Cooling condition

Not applicable

19. Speed

N

rPm

10,000

10,000

20. Mechanical losses

Qm

hu

20.120.0

20.1

83

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1 000

1200

1100 400

lo00SOO

900

700

1300

0.600

0.490

0.450

0.440 600

600

800

700

900

loo01200

1100

Steam Temperature PR)

FIG. C.l(b)

IDEAL GASSPECIFICHEAT

84

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FOR STEAM

1300

SAMPLE CALCULATION C.2 TYPE 2 TEST FOR A CENTRIFUGALCOMPRESSOR USING AN IDEAL GAS Thissamplecalculation is intended to demonstrate: fa) Type 2 test (b) Testgassameas specified gas (c) Ideal gas (d) No heat loss to lubricating oil and to ambient (e) No flow leakages (0 Centrifugal machine (gl No flexibility to change compressor speed (h) Single section machine The purpose of this calculation is to determine the quantity of gas delivered and the compressor head,pressurerise,efficiency,andshaft input power. Paragraph 3.1 1.4 of theCoderequires that when a test is only to verify asinglespecified condition,the test shall consist of two testpoints which bracketthespecifiedcapacity.The calculations demonstrated in this sample calculation would be used on both of these bracketing points.

Description of Test Installation (seepara. 6.2.2) (a) Type of compressor - centrifugal (7) type of impellers - shrouded (2) number of stages - single section, ten stages (3) arrangement of casing and piping - not applicable to this sample (4)pipe sizes; inlet and discharge- inlet pipeis 18 in., schedule 40 (Di = 16.876 in.); discharge pipe is 10 in., schedule 40 (Dd = 10.020 in.) (5) arrangement of intercoolers, if used - no intercooler (6) impeller diameter and blade tip widths - impeller diameters D1 = D2 = D3 = D4 = D5 = D6 = 20 in. D7 = D8 = D9 = Dl0 = 18.0 in.;firststage impeller tip width b = 1.5 in. (b) Description of lubricating system and lubricant properties - Lubricating system oil flow rate is 4 gpm per bearing for a total flow rate of 8 gpm. Oil density is 55.6 Ibm/ft3 so the oil flow rate is 59.5 Ibm/min [8gprnA7.48 gal/ft3) x 55.6 Ibm ft3]. Oil has constant pressure specific heat of cp = 0.462 Btu/lbm "R. (c) Type of shaft seals - Not applicable to sample (d) Type and arrangements of driver; turbinedirect connected, motor direct connected, motor and gear, etc. - Not applicable to sample (e) Description of compressor cooling system and coolant properties - No cooling system Simplitjhg Assumptionsfor This Sample (a) Thegas (air) may be treated as an ideal gas with a constant specific heat (evaluated at the average of the inlet and discharge temperatures). Specified Operating Conditions (seepara. 6.2.3) (a) Air with constant pressure specific heats of dry air and water vapor givenin Fig. C.1, MWda = 28.97 and MW, = 18.02 (b) Inlet gasstate 85

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(1)

hatic i

= 7.50 psia at inlet flange

(2) T& dbi = 600.0 O R at inlet flange (3) inlet densities; to be calculated (4) RHinlH = 50.0 % (c) Gas flow rate (7) inlet mass flow rate = discharge mass flow rate = W = 17,300 Ibmhr = 288.3 Ibm/min (2) inlet and discharge volume flow rates have to be determined (3) capacity has to be determined (d) Discharge static pressure = 48.00 psia at discharge flange (e) Compressor coolant not applicable (fl N = 10,000rpm (g) Compressor internal roughness = E = 0.00012 in. Expected Performance at Specified Operating Conditions (see para. 6.2.4) (a) Developed polytropic head = 88200 ft Ibf/lbm (based on total conditions) (6) Efficiency (polytropic) = np = 0.82 (c) Power requirement = Psh = 1025 hp (d) Discharge total temperature (The discharge static temperature is assumed given as 1103"R.) The following preliminary calculations establish the given specified operating conditions in a form convenient for the Code calculations. (a) Partial pressure of water vapor is found using the steam tables: [Ref, (D.20)]

(6) Air humidity ratio at inlet flange [Ref. (D.20)l (HRi)sp= (0.6220

-

-(

0.6220 Ibm (1.456 psia) Ibm da (7.50 - 1.456) psia

)

lbmole W (28.97 Ibm da) 18.02 Ibm W lbmole da

= 0.2408

lbmole W lbmole da

(c) Air molecular weight [Ref. (D.2011

Ibm da

) + 0.2408 lbmole

W

1 .O00 lbmole da t 0.2408 lbmole W

= 26.04

Ibm lbmole 86

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(d) Air specific heat at constant pressureis found using dry air and steam properties. The specific heat at constant pressure for both the dry air (da)and water vapor( W ) are given in Sample Calculation C.1. (Fig. C.1)

(cplsp

=

(Cpda) + mass W (cpw) mass da + mass W

mass da

)

Btu + 0.1498 Ibrn W O 448 Ibm da "R * Ibm W "R 1 .O00 Ibrn da + 0.1 498 Ibrn W

(

1.000 Ibrn da 0.240 (cpi)sp

=

0.267

Btu Ibrn "R

1.000 Ibrn da (0.251 kp&p

=

) + 0.1498 Ibm (0.480 Ibrn w o R W

da

OR

1 .O00 Ibrn da

= 0.281

(

+ 0.1 498 Ibrn W

Btu Ibrn "R

(e) Air specific heat ratio

0.267 k)sp

= (0.267

BtuBtu

- (1.986

G)

0.281 (kd)sp

=

(0.281

Btu Ibrn "R lbmole "R

26.4 Ibrn

Btu

Ibrn "R

-) Btu - (1.986 Ibrn "R

) ( lbmole ) =

Btu lbmole "R

)(

lbmole 26.84

)=

Ibrn

(0 The inlet flange kinetic viscosity is found from Ref. (D.20) and is assumed to be that of dry air at the inlet pressure and temperature ( ~ i ) s p=

4.00

87

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X

1 O4

ft* sec

(g) Static specific volume at inlet and discharge flanges is found using the ideal gas law

(

(Vstatic i)sp

=

)

(1545 ft Ibf) lbmole (600.0"R) lbmole "R 26.84 Ibm (7.50

(1545 ft lbf)

lbmole "R

5)

(1 44

(

= 31.98

$)

Ibm

)

lbmole (1 103.0 O R ) 26.84 Ibm

(48.00

ft3

-

$)(1 44 $)

= 9.186 Ibm ft3

(h) Average fluid velocity at inlet and discharge flanges (see para. 5.4.3.1)

Ihm) (

(Vi)sp

(1 7,300 - -h r ) (31.98 hr 3600 sec = ?r i16.876 , \ 2

88

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$) = 98.94

ft sec

{i) Fluid Mach number at inlet and discharge flanges (see para.

(-)W V

=

""

sec

(Mi)sp =

= (32'174

= 0.0798

lbmole lb "R

80.61 (Md)sp

T SP

ft -

98.94.

(1545

S)

(

2 778.1 7

) (26.84 lbmole Ibm) (1 103.0 "R)

is foundusingtheenergyequationforan

sec/

ft Ibm E) (32.1 74 7) (0.267 Btu Btu Ibf sec

(80.61

(Td)sp = 1103.0

"R +

2

= 0.0484

lbmole lb "R

\

"R +

) (26.84 lbmole Ibm) (600.0 "R)

ft sec

ci,, Totaltemperatureatinletanddischargeflanges adiabatic process (see Eq. [5.4.6])

(Tilsp= 600.0

5.4.2.5)

-)

(778.1 ft Ibf 7 (32.1 Btu

k)2

-)

74ft Ibm (0.281 Ibrn Ibf sec2

= 600.7 "R

= 1 1 03.46 "R "R

(k) Since the Fluid Mach number is less than 0.2, the total pressure may be calculated according to the simplified Eq. [5.4.4] 89

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(pi), = 7.50 psia +

=

7.53 psia

2(31.98$)(32.1741bfre;i)(144$) ft Ibm

48.00 psia + 2 (9.186

$)

(32.174

ft Ibm m) (144

G)

= 48.08 psia

(I) Total density at the inlet and discharge flanges is found using the ideal gas law

(7.53

S) $)

Ibm

(1 44

) ( ' lbmole)(600.7 "R) (1545 lbmole "R 26.84 Ibm Ibf

(48.08 (Pd)sp = (&)sp

=

h Ibf

= 0.03136 ft3

"

)(

z) S) 1

Ibm = 0.1090 ft3

(1 44 lbmole)

(1 103.5 "R)

"

(lS4' lbmole "R

26.84 Ibm

(m)The sum of the squares of the blade tip speeds is

j=l

-

= 7.037

X

-

lo6 h2

sec2

Mean Observations Derived from Test Data Thetest is to berun with air at atmosphericpressureandtemperature as the inlet pressure and temperature. These give (pstatic i ) l = 14.1 O psia and Ustatic &i),= 560.0 "R. Both the specified gas and the testgasareassumed ideal gases.Assuming equality of the (total) volume ratio between the testand specified operating conditions gives 90

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Assuming equality of the polytropic

efficiencies between the test and specified conditions gives

Since thesame gasi s used i n the test and at the specified operating conditions, assume kt = ksp Then,

as the approximate (total) discharge pressure for the test. Thetestspeed is found by assumingequality of the polytropic work coefficient between the test and the specified operating condition to give

(E),(3)

c u2 sp

CU2

which can be obtained from equality Thenumericalvaluesgive

of Machine Mach numbers.

= 9841 rpm

Nt = 10,000 rpm

as the approximate appropriate test speed. Not that no Reynolds number correction (as used later in converting the testdata to the specified operating condition) is used in this estimation of the testspeed.Also, note that the Code speed rule (para. 5.3.2) reduces to the equality of Machine Mach numbers between the test and the specified operating conditions for ideal gases with equal values of the specific heat ratios. See para. 6.2.7. fa) Test run number 4 fbl Duration of test = 40 minutes (c) Compressorspeed = 9,500 rpm fd) Inlet temperature = TStatic dbi = 540.0 "R 91

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(e) Barometer reading = 14.1 O psia (0 Ambient temperature at barometer = 540.0 "R (g) Inlet static pressure = Pstatic i = 14.1 O psia (h) Dry bulb temperature at inlet flange = Tstatic dbi = 540.0 "R (i) Wet bulb temperature at inlet flange = TStatic di = 530.0 "R 0) Dew point at inlet flange = 525.1 "R (k) Gas density not measured (I) MW& = 28.97and MW, = 18.02 (m) Discharge static pressure = PStatic d = 99.6 psia (n) Discharge static temperature = Tstatic d&j = 1042.2 "R (o) Mass flow rate = 36,500 Ibm/hr (pl to (W) Not applicable to this sample (x) Shaft power input = Psh = 1851 hp (determined by measuring shaft input torque of speed) (y) Shaft torque = 1023 ft lb (zl Lubricating system oil flow rate is 19.3 gpm. The oil density is 55.45 Ibm/ft3 so the oil flow rate is 143.1 Ibm/min (19.3 x 55.45/7.48), The oil has constant pressure specific heat cp = 0.462 Btu/lbm "R. (aa) Lubricant inlet temperature = Toin = 525.0 "R (bb) Lubricant outlet temperature = Toout= 568.5 "R (cc) to (eel Casing heat loss = 6740 Btu/hr (ft7 Not applicable m

Computed Results for Test Operating Conditions (similar to para. 6.2.8) The previous test data is converted into a form convenient for Code calculations. (a) The air humidity ratio of the inlet air is found using air and steam properties [Ref, (D.20)]

= 0.6220

-

0.240

Btu

Ibm da "R

0.3667 psia Ibm W = 0.01661 14.10 psia - 9.3667 psia Ibm da

-

(540.0 - 530.0) R

(1095.5

0.01881

= 0.03024

Btu - 38.35) Ibm W

Ibm W ) ( 1 lbmole W) (28.97 Ibm da 18.02 Ibm W

lbmole W lbmole da 92

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Btu (1092.2 - 38.35) Ibm W

+

lbmole da

(b) Air molecular weight [Ref. (D.20)]

=

-

mote da (MW&) + mole W (MW,) mole da + mole W

(

1.O00 lbmole da 28.97

I, ) + 0.03024 lbmole

Ibm da lbmole da

1 .O0 lbmole da + 0.03024 lbmole

= 28.65

W W

Ibm lbmole

(c) Air specific heat is found using dry air and steam properties

mass da (Cpda) + mass c (wp,) mass da

(

1 .O00 Ibrn da 0.240 (cp,.)r =

= 0.244

W "R

W

Btu Ibrn "R

(

=

Ibrn da "R

1.O00 Ibrn da

= 0.253

I,

) + 0,01881 Ibrn (O 447 Ibrn

1.O00 Ibrn da + 0.01 881 Inm

1.000 tbm da 0.249 (cpd)t

Btu Ibrn da "R

+ mass W

) + 0.01881 Ibm (0.475 Ibrn w " R + 0.01 881 Inm W

Btu Ibrn "R

Average specific heat

(C,),

=

Btu - = 0.244 +2 0.253 IbrnBtu"R - 0.249 Ibrn "R

('pi

"

93

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(d) Air specific heat

ratio

Btu 0.244 (kilt

=

Ibrn "R Btu 986 lbrnole "R

m)- (0.1

(0.244

Btu

0.253

=

-

(

0.1 986

Btu Ibrn "R

)(

1 lbmole) 28.65 Ibrn

)(

Btu lbmole "R

1 lbmole) 28.65 Ibrn

= 1.397

= 1.37

(e) The inlet flange kinematic viscosity is found from Ref. (D.20) and is assumed to be that of dry air at atmospheric pressure and the existing temperature = 1 .TOx 10-4ft2 sec

(0 Static specific volume at inlet and discharge flanges is found using the ideal gas law

(vstatic i ) t

=

(lS4'

ft Ibf lbmole "R

)(

1 lbmole) 540.0 "R 28.65 Ibrn

"

(14.10

ft Ibf

5)

(144

)(

$)

lbmole)

1

= 14.34

ft3

Ibrn

1042.3 "R

"

(vstatic d)r

=

(1545 lbrnole "R

28.65 Ibrn

5)

(99.6

(1 44

$)

[g) Fluid velocity at inlet and discharge flanges (see para. 5.4.3.1) 94

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ft3

= 3.919 I bm

S T D * A S M E P T C LO-ENGL L777 E 0757b70 Ob05520 3 2 T m

(36,500 (Vi),

=

%) hr

(1 4.34

E) Ibrn

4( 16.8767 fi)'(3600 F)

= 93.60

-)hr

(36,500 Ibrn (3.919 (vd)t

= 77

Ibrn

= 72.56

r)

10.020

4 (F

ft sec

T

ft

sec

h) (3600 (h) Fluid Mach numbers at inlet and discharge flanges (see para. 5.4.2.5)

93.60

(Milt =

f-t sec

lb

lbmole "R

72.56

(&)r

=

ft sec

) (-S) (540.0 "R) 28.65 Ibm

) (-

lbmole "R

(i) Totaltemperatureatinletanddischargeflanges adiabatic process

= 0.0818

1

1

28.65

-)

(1 042.2

= 0.0459 "R)

Ibrn

is foundusingtheenergyequationforan

(93.60

(T;)( = 540.0 "R

+

0.244

E)Btu

(778.1

-ft)7Ibf Btu

95

COPYRIGHT American Society of Mechanical Engineers Licensed by Information Handling Services

- = 540.7 "R

(32.1 74 ft Ibrn

Ibf sec2)

(72.56 (Td)l

1042.2 'R

+2

m)

(0.253 Btu

A)'

= 1042.6 "R E)(32.174 ft Ibm

(778.17

Ibf secz)

Btu

(j) Since the Fluid Mach number is less than 0.2, the total pressure may be calculated according to the simplified method of Eq. [5.4.41

=

Pl

193.60

\-

(pi), = 14.1 O psia +

(

2 14.34

(Pd),

(&I

= 99.6 pS¡a +

~

~

~

f t z -\secl

=

-)Ibm (32.1 74 m Ihm)(144 $) ft3

14.1 7 psia

= 99.74 psia ) ( inn) 2 (3.91 9 2) (32.1 74 lbfsec~ 144 ft Ibm

Total density at the inlet and discharge flanges is found using the ideal gas law

S) $)

(14.17

ft Ibf (1545 lbmole "R

(Pd)sp

=

)(

1

lbmole)

(540.7 )

"

28.65

(99.74

(&),

Ibm

(144

Ibm

E)

(144

= 0.06993

fi3

O R

$)

Ibm

= 0.2555

=

-

ft3

(I) The sum of the squares of the blade tip speeds is (9,500 1'1

z)'

I6 (20 in)'

+ 4 (1 8 in)'] = 6.35

j=1

X

lo6

ft2 5ec2

mm

(m)The shaft power was measured by the shaftpower method) 96

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method to be ( f s h ) , = 1851 hp (shaft power

S T D e A S M E P T C 30-ENGL 1 7 7 7 II 0 7 5 1 b 7 0 Ob05522 L T 2

Theshaft powercanalsobecalculatedfromthe and Eq. [5.5.14]

m

gas powerusingtheheatbalancemethod

Equations L5.4.171 and [5.4.181 show the parasitic losses to be mechanical losses. Also, using

Eq. [5.4.131 gives

-)

E) (1042.6 - 540.7) "R

(36,500 Ibrn (0.2459

Ibm "R

hr (psh)t

(42.44

&) F) x) -

-)

= (1791.4

+

(60

(143.1 min Ibrn (0.462 ,bm

(568.5

6740 (42.44

Btu

hr

S) T) (60

525.0) "R

+ 2.65 + 67.8) hp

= 1862 hp (heat balance method)

(n) The gas power can be calculated from the heat balance methodas done above to get (P,),

(W C p ) t (Td - Ti), + Qr = (1791 4 + 2.65)hp = 1794 hp (heat balance method)

Thegas power can also be calculated from the shaft power using the shaft power method

(P,),=

(Psh)r

- W o Cpo ATO

= (1 862 - 67.8) hp = 1794 hp (shaft power method)

Check for a Type 1 Test Theabovetestdoes notqualify as a Type 1 testdue to thelargedifferences pressures. To formalize this observation,the inlet pressuredeparture is (Pi),

- (piIr x

(pi)sp

100 =

7.53

- 14.16 X

7.53

in the inlet

100 = -88.0%

which is outside the range of the Table 3.1 limit of 5%; therefore, the test is not a Type 1 test. Therefore, wemustconduct a Type 2 test; however, we will verify that this i s aType 2 test, ¡.e.,satisfies the Table 3.2 requirements. 97

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S T D - A S M E P T C 10-ENGL 1997

0 7 5 9 b 7 0 0605523 O34

Computed Test Dimensionless Parameters (similarto para.6.2.9) The dimensionless parameters which form the basis for the conversion from test data to specified operatingconditionsarecalculated in thissection. (a) Polytropic efficiency is found as follows: Average specific heat ratio

0.249

fi Ibf

Btu Ibm "R Btu

-)Ibm "R - (1.986 lbmole "R

)(

1

lb mole)

28.65

Ibrn

Polytropic exponent (see Eq. [5.1T-51)

(99.74 psia) 14.1 7 psia = 1.507 (99.74 psia) (540.7 "R) In (14.17 psia) (1042.6 "R)

Polytropic efficiency (see Eq. [5.1T-91)

(b) Flow coefficient (see Eq. l5.1T-11)

-

2)(L (-) )

(36,500

2

T

rad

(0.06993 F Ibm )(9,500

S)( 1 2 ft)

98

COPYRIGHT American Society of Mechanical Engineers Licensed by Information Handling Services

hr

60 min

20.0

= 0.03148 3

= 1.386

STDmASME PTC 10-ENGL L977

075'1b70

Ob05524 T 7 5

(c) Polytropic work coefficient (see Eq. [5.1T-41)

-

0.507

)( 28.65 L F Ibm ) (540.7"R) [(-)99.74 1.507 - 1 1 14.17 ft2 ) ( 1 Ibf sec2) 6.35 lo6--

(-)

1 507 (1 545 lbmole ft Ibf "R 0.507

X

(143.1 (Q,,,)t= wocpJT0 =

?)

32.174 ft Ibm

sec2

(0.462 G)Btu

mm

(42.44

(568.5 - 525.0) "R

= 67.8 hp

-mln ) hr Btu

Ibf ) (60 mrn hp

(1851 hp - 67.8 hp) 33,000

F)

(36,500

W-

(

gc

(6.35 x

F) = 0.4901

lo6 E)(LF) sec2

32.174 ft Ibm

(e) Total work input coefficient using the heat balance method (see Eq. [5.3T-l])

(0.249

-

-)llbmBtu"R

(1042.6- 540.7)"R +

ft' (6.35 lo6 -()-

sec2

(0

Btu

36,500 hr

= 0.4935

32.174 ft Ibm

Work input coefficient (see Eq. [5.2T-2])

b¡"h

=

- Ti) I - (0.249E)Btu CU' -

cp (Td

(1042.6- 540.6)"R (778.1 7

gc

99

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*)Btu

= 0.4927

(g) Volume ratio at stagnation conditions (for information only)

c)r

Ibm -

0.2555

(;)r

=

ft3

=

0.6993

I bm = 3.65

ft3

Computed Results forSpecified Operating Conditions (similar to para. 6.2.1 1) The performance at the specified operating conditions is calculated from the test dimensionless parameters. The effect of the difference between test and specified operating condition Reynolds numbers is estimatedfromthe PTC 10 Reynoldsnumbercorrection. (a) Discharge total pressure at specified conditions is obtained as follows: Average specific heat Btu

Btu

0.267-+ 0.281 Ibrn "R Ibrn "R = 0.274 2

(Thedesigndischargetemperaturehasbeenused Average specific heat ratio

to estimate cps)

0.274

Btu Ibrn "R

Btu Ibrn "R - (1.986 lbmole "R

-)

Btu Ibrn "R

Btu

)(

lb mole) 28.36 Ibrn 1

= 1.370

Polytropic efficiency correction is now used to accountforthedifferences in the Machine Reynoldsnumbers.TheReynoldsnumber limits forthis correction are found using Eqs. [5.4.41 and 15.6.11 to 15.6.41

(F)

= 2.73 x 105

SP

NDib

T)

(9,500 min (2 T$)

(=E) 20 rad

sec

1O0

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(E) 1 .5

ft

= 6.10 x

105

or Remt < 4.775 Remsp = 4.775 (2.73x Remt > 0.2094 Rem,

= 0.2094

lo5) =

1.3 x

lo6

(2.73 x 1Os) = 5.72 x lo4

Sincethetest Machine Reynoldsnumber (6.10 x lo5)fallsintheaboverange,thefollowing Reynoldsnumbercorrectionmaybeused. The correctedpolytropicefficiency forthespecified operatingcondition is relatedtothe test polytropicefficiency by

where = 0.988(2.73 x 105)4.243= 0.04718

0.988

(6.10 x 105)-0.243 = 0.03881

RCt= 0.988 Remt0.243= 0.988

RA,=

0.066 + 0.934

RA,=

0.066 + 0.934

RAsp= 0.066 + 0.934

RA,=

0.066 + 0.934

46 X 10' Rem

1,

RCsp

4 (I.5 in) x 1 os 2.73 X 105

]

46 X

[

On4718

= 1.0354

lo5 RCt

Rem

Il

4 (I.5 in) x 1 o5

]

6.10 X 105

0~13881

= .O99940

0.000125 + Reml

RBI =

13.67

( Remt)

log c +

13.67 6.10 x lo5) = 0.9961 13.67 log 0.00012 + 6.10 x 105)

(

1 o1

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Then,

1

-(

~

~ =) 11~

1 .O354 ) (0.9967) = 0.1785 -p0.828) (0.99940 0.9961

and 0.822

(vsp)sp

The polytropic exponent is found from

or

3.054 2.054

nsp = -- 1.49 The polytropic work coefficient ratio for the specified operating condition is 0.822

(pplsp

= (pph-- 0.4075 -= 0.4044 0.828

(qp)r

Discharge pressure ratio is found using the definition of the polytropic work coefficient to give

r

[(E)

(7.037x

=

r.4044

(1 545

(-Ibf secz)

f i l z )1

lo6 -

3.042

= 6.400

sec 32.174 fi Ibm fi l b (600.70R) lbmole "R 28.36 Ibm

)( ' 3 )

Dischargepressure is found using Eq. [5.4T-151 Pd

= 6.400 (pi)sp = 6.400 (7.53 psia) = 48.2 psia

(b) Capacity at specifiedconditions is found using thedefinition ofthe flow coefficient and equating the flow coefficients at test and specified conditions (see Eq. [5.4T-11)

(

z)

= 0.03148 10,000

102

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rad

fi)

20

(277~)

2

fi3

= 9157- min

S T D - A S M E P T C 10-ENGL 1997 W 0 7 5 7 b 7 0 Ob05528 b 1 0

m

(cl The inlet mass flow rate is

= 17,230-Ibm

= ( 9 1 5 f t73 ~ ()0 . 0 3 1 3 6 F ) 6)0(:

hr

(d) The specific volume ratio based on total conditions is

(2) = [ Vd sp

(F)q 1

1 -

= 6.4007.49 = 3.48

*P

(e) Discharge total temperature is found using Eq. [5.4T-181

(E)7] n-1

(TdlSp

= [Ti

0.49

= 600.7 "R (6.400)'.49 = 1 1 .O6 "R 5P

Since this temperature is nearlyequal to the designvalue of 1103.5"R, the average specific heatchosen for the calculations is assumed appropriate. ffl Gas power is found using the equality of the total work input coefficient between the test and the specified operating condition. Using theshaft power method, Eq. [5.4T-20], and Table 5.3 gives

-

= 932.8 hp (shaft power method1

Eq. [5.4T-201, andTable 5.3 gives

Usingtheheatbalancemethod,

33,000 (1 7,230

F) min

(0.4935) (7.037 X 10'

= 939.3 hp (heat balance method) 103

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ft2

) (1 Ibf sec2) -

sec2

32.174 ft Ibm

S T D - A S M E PTC LO-ENGL L797

m

0 7 5 9 b 7 0 Ob05529 557

m

(g., The shaft power is found by assuming the mechanical losses are proportional to a power of the rotational speed (see Eq. 15.6.81)

N (2) = 2.5

(Qmlsp

=

(Qm)r

67.8 hp

(

10,000

rev -

2.5

-

= 77.1 hp

9,500 min

The shaft power is found using Eqs. [5.4.14],[5.4.17],and[5.4.181

= 1O 1 0 hp (shaft power method)

or

=

101 6 hp (shaft power method)

(h) Static discharge temperature and pressure may be calculated from the mass flow rate, flow area, and total temperature and pressure. Since the flow Mach number is below 0.2, Eqs. 15.4.21, (5.4.33,i5.4.41, and 15.4.61may be used. With a guessed velocity of 80.2 fthec, obtained by trial anderror,

(802)2 = 1106.

-

sec2 ft2

-)

ft Ibm 2 778.17- Ibf) (32.1 74 (0.281 Btu Ibf sec

(

= 48.2

Ibf

--

(0.1 O9

F)

= 1 105.5 'R

;J= 48.12 -in2 -) (144 -

104

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ft* e c ~

(80.2)2~

ft Ibm 2 32,174 Ibf sec2

(

Btu

Ibf

S T D - A S M E P T C LO-ENGL L797

m

0 7 5 7 b 7 0 Ob05530 2 7 7

Checking

ft sec

= 80.2 -

(144

(1545

$) $)

Ibrn

(48.2

ft Ibf -)Ibm ('W) 28.36 Ibm

= 0.109 -

(1105.5 "R)

ft3

O R

Check for a Type 2 Test (a) Specific volume ratio (see Eq. [5.5.51)

i

a

x

,oo -

3.65 3.48

X

100 = 1.049%

The test specific volume flow ratio is just within the Table Thedifference is duelargely to theassumption of equal specified conditions made when determining the testspeed. A reduce this deviation. (b) Capacity - speed (flow coefficient) ratio (see Eqs. [5.2T-11

3.2 range of 95% to 105%. gas propertiesbetweentestand retest at an adjusted speed would and [5.4T-43

F)

(36,500 hr

-)

(0.06993 Ibm ft3 (9,500 x 100 =

E) min X

F)

(1 7,300 hr

")

(0.03 136 TI bm fi) (1 0,000 min 105

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100 = 99.6%

-

Thetest capacity speed ratio is within the Table 3.2range (c) Test Machine Mach number (see para. 5.5.1)

of 96% to 104%.

= 0.710

Mm, =

(9,500

Mmt

2)($

=

(-

h) (2

TE)(Az)

= 0.708

1 moe 26.84 “Ibm (540.7 “R)

2)

Thetest Machine Mach number is within the Fig.3.4range (0.71O + 0.105). (cf) Machine Reynolds number ratio (see Eq. [5.5.51)

Rem,

=

of 0.625(0.710

= 2.73

X

- 0.085)to 0.815

105

sec

?)

(9,500 mm

(hg) (S (gfi) h)

= 6.10 x 105

Remt =

Remt 6.10 x 105 x 100 = 2.73 x 105 Remsp

X

100 = 223.4%

Thetest Machine Reynoldsnumber is abovetheTable 3.2 lower limit of 90,000 andthe Machine Reynoldsnumber is between the Fig. 3.6 limits of 0.17 and 6.5. Since all the Table 3.2 requirementsaresatisfied,thetest is a Type 2 test. 106

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0759b70 Ob05532 O'+& H

STD ASME P T C 10-ENGL

TABLEC.2.1 CALCULATION SUMMARY

Test QuantityValue

Units

Symbol

Test Corrected to Specified Operating Condition

Expected at Specified Operating Condition

1, Quantity of gas delivered

lbmhr

36,500

17,230

17,300

2.Pressurerise

psi

85.6

40.7

40.6

3. Head (total)

ft . Ibf/lbm

80,400

88,450

88,200

4.Shaftpower (a)Shaft method (b) Heat method

hP

1851 1862

1010 1016

1025 1025

5. Polytropic efficiency

0.828

0.822

0.82

6. Flow coefficient

0.031 5

0.031 5

0.031 6

7. Machine Mach no.

0.724

0.703

0.703

8. Machine Reynolds no.

610,000

273,000

273,000

9. Specific volume ratio (total)

3.48

3.48

3.48

10. Specific heat ratio

1.39

1.37

1.37

11. Polytropic work coefficient

0.408

0.44

-

12. Work input coefficient

0.493

0.493

-

13. Total work input coefficient (a) Shaft method (b) Heatmethod

0.490 0.494

0.490 0.494

-

8700

9160

9190

540 14.1 S41 14.2

660 7.50 601 7.53

600 7.50 601 7.53

psia

1042 99.6 1043 99.7

1106 48.1 1106 48.2

1103 48.0 1103 48. I

17. Gas power (a) Shaft method (b) Heat method

hP hP

1794 1794

933 939

18. Casing heat loss

hP

2.65

19. speed

rPm

9,500

10,000

20. Mechanical losses

hP

67.8

77.1

14.Capacity 15. Inlet gasstate (a) Static temperature (b) Static pressure (c) Total temperature (dl Totalpressure 16. Discharge gasstate (a) Static temperature (b)Staticpressure (cl Totaltemperature (d)Totalpressure

hP

Whin

OR

psia OR

psia "R

psia O R

107

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-

10,000

-

SAMPLE CALCULATION C.3 IDEAL GAS APPLICATIONTOSELECTION OF TEST SPEED AND TEST GAS ANDMETHODS OF POWEREVALUATION

Thissamplecalculation is intended to demonstrate: (a) Test speed selection (b) The effect of substitute gas use on achievement of flow similarity (c) Methods of power evaluation The following information is givenaboutthedesign: Number of stages = 6 1 st stage diameter = 1 1.459 Discharge in. pressure Impeller exit tip width = 0.5 Polytropic in. efficiency Shaft rotational speed = 16000 rpm Gas - Methane Inlet pressure = 30 psia Inlet temperature = 570"R W 2 / g c = 1.1 1006 x 1O5 ft-lbf/lbm

At an inlet flow

of 3000 ft3/min

= 90 psia = 0.76 Shaft power = 690 hp

Thedata in the left hand column above indicate the specified operating conditions. This data describes the compressor geometry, the operational speed, and inlet gas conditions. The data in theabove right hand column describestheintendedperformanceofthecompressor at the specifiedoperatingconditions. It is thepurpose of thetest to verify these intendedvaluesor establishtheactualvalues. It i s assumed thatcircumstances prohibit testing with methane. Air i s available at 14.7 psia, 520"R, and 50 percent relative humidity. The driver has variable speed capability. The following assumptions are made to simplify the calculation process so that focus may be madeondemonstrationpoints. (a) Both the test gas, air, and the specifiedgas, methane, will be treatedas ideal gases with constant specific heats. Average values will be used. (The alternative is to use actual gas thermodynamic data and the Type 2 calculation procedure. This would lead to slightly more accurate results.) (b) Leakages will be assumed negligible at both test and specifed conditions. The rotor mass flow rate is then the inlet mass flow rate. The test speed required to provide equivalence betweentest and specified conditions is obtained fromthe speed selection rule. For ideal gases,

1o9

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TABLE C.3.1 PRETEST C A L C U L A T I O N S U M M A R Y Methane

CaS Pd Pi

90. 30.

psia psia

Ti

"R

570.

R

ft-lbf/lbmOR

96.31 1.28 0.078693 0.769 x 16000. 800. 0.532 3.411 X lo5 0.76

k P P

Ibm/ft3 Ibmh . sec

u

ft/sec

N

rPm

Mm

Rem TP

1.6

pd/pi n qi/qd

51.597 14.7 520. 53.53 1.396 0.0761 1.27x 10-5 12704.

635 0.5675 1.583 X lo5 0.76 (excludes Reynolds Number correction) 3.51

3.0 1.4 2.19 0.00343

4

Air

2.1 9

with 1

1

and

n n-1

k

"

'Ip-

k - 1'

and Remco,, = 1

Precise values of pressure ratio, efficiency, and polytropic exponent for both specified and test conditions are of course unknown before test. However,theappropriatetestspeedmaybe estimated by making the following assumptions: (al Thepressure ratio and efficiency at specified operating conditions are equal to the design values. (b) The efficiency at test conditions is also equal to the design value.While the Reynolds number effect might be taken into account here, it is small and the current calculation is only an estimate. It is ignored simply for computational ease. The firstassumptionallows calculation of thespecified conditionpolytropic exponent.The second allows calculation of the test polytropic exponent. With these a test pressure ratio estimate and a required testspeedestimatemaybecalculated.This speed may be used to calculate Machine Mach andReynoldsnumbers. Thegasdataused andresults of the computations indicated abovearesummarized in Table C.3.1. Thevalues in thistable may be used to determine if it is possible to accomplish the proposedtest within the allowable deviations in similarity parameters. Mach NumberCheck:The test Mach number is = 6.6 percentgreaterthanthedesign Mach number. This is an unavoidableconsequenceof gas selection with 110

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different k valueswhenspecificvolume ratio equality i s maintained. Thedeviation is, however, within the limits of Fig.3.2. ReynoldsNumberCheck:ThetestReynoldsnumber is -46 percent of thedesignReynolds number.This is within thedeviation limits of Fig.3.4, andthe correction relationship applies. The correction has not been applied to the tabulated values,sincethe computations are preliminary. The compressor is run to obtain a bracketing point. A bracketing point lies within 2 4 percent of the specified operating condition flow coefficient of interest, which is

3000

= 0.03427

(y)3 12

2~(16000)

The desired test inlet flow may be calculated from test and specified operating coefficient equality, which yields

9;,= 9i

'P

(9 NS

= 3000

12704 (-)16000

= 2383

condition flow

ft3 rnln

Thetest yields the following data: W = 2.9595 Ibm/sec pi= 14.7 Ibf/in3 Ti= 520 "R

RH;= 50% 50.4 Ibf/in2 Td= 832 "R 20 hp (from lubricating oil temperature rise and flow rate) 5574.5 Btu/hr(calculatedcasingheat loss) Psh= 339. hp (shaftpower,perhaps from a torquemeter) N= 12690 rpm R = 53.53 ft-lbf/lbm*"R The next step is to compute the following dimensionless parameters from the test SpecificVolumeRatio: pd=

om= or=

(3; 1

r", =

= 2.14286

Flow Coefficient:

111

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data.

Polytropic Work Coefficient:

(-)n -n 1 ClPt =

RF

xu2

[

- 1 1 = 0.62702

Work InputCoefficient:

PolytropicEfficiency:

Total Work InputCoefficient: (Heat balancemethod)

Total Work InputCoefficient:(Shaftpowermethod)

gc

MachineMach Number:

Mmt =

U -

Remt =

- = 1.583 X lo5

Machine ReynoldsNumber: Ub V

whichhavebeenevaluated

using

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S T D - A S M E P T C LO-ENGL 1777

W;

0 7 5 7 b 7 0 Ob05537 b 2 3

= (2.9595 Ibm/sec) (60 sec/min) = 177.57 Ibm/min

N = 12690 rev/min

D = 11.459 in.

R = 53.53 ft-lbf/lbm*"R

CU2

1.11006 X 10' = 6.9828 X

k = 1.396

Btu Ibm "R

cp =

(5574.5Btu/hr) (1/60hr/min) = 92.91 Btu/min

113

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ft

lo4 Ibm

14.7 p i = - -Pi =

R Ti

53.53

Ibf (5) 144 ):(

ti Ibf

(-)Ibm "R

2.9595 Wi

q,=-= Pi

(20hp) 33000

o m .... =

f-\ti

778.1 6

u =" 2lrN

D

60 24

- (2.-) (12690;)Rad rev

mm

1.27x

10-5

P

y="=

ft3

520 "R

(E) 60 sec

0.076047

Ibm = 0.076047 -

(=) min

I bm (F)

(-)minft Ibfhp Ibf

Btu

min

(--)601 min sec ( r Ibm ) sec

11.459

(?in.)

= 1.67 X

Ibm

(-121-)fin.t

min

= 848.2 -

0.076047 (F)

b = 0.5 in,

ft3

= 2335 -

(--)121 fin.t

= 634.5

-)secft

ti2 -

sec

= 0.041 7 ft

The preliminary assumptionis madethatthesecoefficients withappropriateReynoldsnumber correction,alsoapplyatspecifiedconditions.Thelimitsforallowabletest Machine Reynolds numberaregivenby

114

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or

6.41 x

lo4 5

Thetest Machine Reynoldsnumberdoes maybe used.Thus

1 -

VPsp

= (1

- VPt)

RASPRBsp

Rem, 5 1.81 x

lo6

fall within these limits and the efficiency correction

0.97798 (0.99648) = 0.2476 184 (0.9971 8)

- (1 - 0.744)1 .O1

where

RASP = 0.066 + 0.934

RAI = 0.066

RB,

(4.8X 1 O6 b) RCsp Rem,

7

+ 0.934

=

= 0.97798

RCr

= 1.01184

= 0.99648

with RC, = 0.988 Remsf-0.243= 0.044696 RCt= 0.988 Rem,p-0.243 = 0.053862 b= 0.5 in. Remsf= 3.411 x lo5 Remr= 1.593 x lo5 E= 0.000120 in.

so, ‘PSP

0.752

vpsP= 0.7524,and Remco,, = - = -= 1.0118

’

Pt

The Reynolds number correction work coefficient.

0.744

is applied to both the polytropic efficiency and the polytropic

115

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In summary,the preliminary assumption is thatthe applies at specified operating conditions.

drp

“p*p

=

= 4, =

qpt Remcorr=

following dimensionless coefficient set

0.3363

0.744 (1 .O1

18) = 0.752

This assumption is taken to be valid to the approximation involved if: (a) the test specificvolume ratio is within 2 5 percent of the specifiedcondition volume ratio (Table 3.2). The specified operating condition volume ratio is calculated to determine if this requirement is met. This is done by using the polytropic work coefficient and polytropic efficiency to calculate the specified condition discharge gas state, ¡.e.,

= [0.6344

1.11006 x lo5 ((3.4395) ) + 11 96.31 (570)

3.4395

= 2.9750

where n

1.28

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0.7524 = 3.4395

S T D O A S M E P T C 20-ENGL 2 7 7 7

m

0759b70 Ob05542 O 5 4

m

which yields nsp = 1.4099, Thespecificvolume ratio is then

(which is within the + 5 percent limit). (b) the test Machine Mach number is within the limits of Fig. 3.4, which is seen to be satisfied; (c) the test Machine Reynolds number is within the limits as already described; (d) the test flow coefficient is within ?4 percent of the specified operating condition flow coefficient of interest, It is concludedthatthedimensionless coefficient set developed is valid for thespecified operating conditions. The following quantities of interest at the specified operating conditions are established from this set as follows. Thesectionpressure ratio hasalreadybeenestablished in thevolume ratio calculationusing the polytropic efficiency and polytropic work coefficient. Thedischarge gasstate is then

(3,

Tdsp =

($sp

The flow is determined from the

D 3

gi = [ 4 s p 2 7 ( ~ )

]

SP

(3" n-1

=

Tisp= 1.373 (570) = 782.6 "R

flow coefficient

= 0.03363 2 min

wj = pigi =

0.4099

= 2.975 1.4099 = 1.373

11.459 3 ft 3 16000 rev 1 2 ft) = 2944 rev min

144 (30) Ibm

[96.31 (570)

ft3 Ibm 2944 - = 231.7 mm mln

F I 117

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(

rad 7-

The power requirement at the specified operating conditions is determined from the total work input coefficient.

Ibm

sec

sec

min

ft Ibf 1.11006~lo5Ibm

= 3.862-60-0.849

min

hp

(G=)= 697.3 hp

where, Om,

I

-=" 33000

Om,

I

(

Nsp)2'5

= 20 hp

33000 Nt

In this example both the shaft method and heat balance method give exactly the same power requirement. This may not always be true because of differences in the independent measurements which areused.Thisexamplewas specifically constructedusingvaluessuchthatthepowers would match.

118

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ASME PTC 10-1997

SAMPLE CALCULATION C.4 TREATMENT OF BRACKETEDTEST POINTS

This sample problem is an extension of Sample Calculation C.3. It demonstratestreatmentof bracketing points. Supposethat a seconddata point forthecompressorofSample Calculation C.3 is available. The data is shown in the upper portion ofthesecond column in Table C.4.1. Calculations were done for this data set following thesame procedure as in Sample Calculation C.3. Theresults are summarized in the lower portion of column 2. The calculated efficiency and work coefficients are plotted as functions of flow coefficient in Fig. C.4.1.The flow coefficient of interest is for 3000 ft3/min at specified conditions, or

ft3

3000 min

d =

= 0.03427

in Fig.C.4.1.Thedata points are valid which fallsabout midway betweenthedatapoints bracketing points in that they are well within 4 percent of the flow coefficient of interest (Table 3.2). In the absence of additional data points, the values of the dimensionless coefficients at the flow coefficient ofinterestaredetermined by linear interpolation. Linear interpolation gives

These values are used to calculate the compressor performance in dimensional terms as follows: Flow rate: 3000 ft3/min as above Dischargepressure:

n

=

[

1.11006 x l o 5 (3.430196.31(570) +

119

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'1,

3.4304

= 2.9497

d

ASME PTC 10-1997

COMPRESSORS AND EXHAUSTERS

TABLE C.4.1 Point

Data

1st

Units Test Data

Data Point

12690.Irpml 3.0799 [lbm/sec]

N Wi

Pi

Ipsial

520.

Ti

PR1

RH¡

[%I

Pd Td

[psial

Om

psh QI

R

k

12690. 2.9595 14.7 520. 50. 50.4 832. 20. 339. 5574.5 53.53 1.396

IORI

20.

lhpl

Ihpl

330.39

5495. [Btuhrl [fi-lbf/lbmoR] 1.396

14.7 50. 49.4 828.

53.53

Calculation Summary: 2nd Data Point

1st Data Point

Test Specified Opentill# Operating Operating Conditions Conditions

Test

opentill#

conditions Conditions

0.034 4 0.843Ph

0.035

PP

0.838 0.794

0.748 'IP 0.849 nhb 0.84900 0.5320 Mm

ah

Rem q&d

0.035

0.034 0.843 0.627 0.61 0.739 0.744 0.849 0.84900 0.5674 0.5675 1.583 x Id 2.1429

0.832 0.634 0.752

0.832 5

0.5320 3.411 X 105 2.1351 2. 1668

1 .S83 x 1Os 2.1105

where

n

=

(E) k

tsp

= 0.750

(z = ) 1.28

3.4304

n = 1.41145

and, Pd

specified

= (pd/pi) pi =

(2.9497)30

120

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=

88.49 lbf/in2

0.623

3.41 1 x 1Os

S T D * A S M E P T C L O - E N G L L977 M 0 7 5 9 b 7 0 Ob05545 7 T T M

FIG. C.4.1

Power requirement: Heat balance method:

=+ "- wi n h b PShhb

xu2

33000 g,

Qml 33000

-- (236.08)0.848(1.11006x 1 Os)+ 35.7 hp = 705.79 hp 33000

where

W¡

= pi q., = H3011 44(3000)1/[(96.31)(570)1 = 236.08 Ibm/min

121

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S T D - A S M E P T C 10-ENGL L997 ASME

10-1997

COMPRESSORS AND EXHAUSTERS

Shaft power method:

- (236.08)0.823(1.11006

x 1Os)

33000

t 35.7 hp

= 689.43 hp

Notice thatthe shaft power andheatbalancemethods yield two different results in contrast to Sample Calculation C.3. This is due to the contradictory measurementsfor the seconddata point, reflected in the two different values for total work input coefficient. One of the values is clearly in error, indicating an error in measurement. With mutualagreement by parties to the test, the optionsmayinclude: (a) retest, eliminating the error; (b) neglecting the error should the difference in results be deemed negligible; (c) assuming one or the other measurement correct and ignoring the other; (d) comparison with other data points if available. In this case the error would appear quite large.Since only two data points are available it might well beprudent to retestfor verification. As the methodsagreeforthefirstpoint, the seconddata point is questionable. Further,since the testshaft power is smaller for the second data point despite a largermass flow rate, the shaft power measurement is especially suspect. Assume that further investigation leads to disqualification of the shaft power measurement for the second data point. The final results from the bracketing data points may be summarized as Design

Calculated

16000 Methane

16000 Methane

570.

570.

30. 3000. 90. 0.76 690.

30.

2.1 9

2.1 52

3000. 88.49 0.750

705.79

Comparison of the design and actual results indicates that the compressor falls short of meeting its designpressuregoal at design flow. The implication of this fact to the parties involved are beyond the scope of this Code, as they would be also had the compressor exceeded its design goals.However, typical industrial reaction in lieuof mutualacceptance as tested is hardware modification or specified condition speed adjustment, In the event of hardware modification the testmust be repeated.Forsmallspeedadjustmentsthetestresultsmayremainvalid.This is determined by conversion of the testresults to the new specified condition speedand verifying that the limits in departurebetweentestandspecified conditions are not exceeded.

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STDmASME P T C 1 0 - E N G L

1 9 9 7 D 0 7 5 9 b 7 0 06055’i7 5 7 2 D

SAMPLE CALCULATION C.5 SELECTION OF A TEST GAS FOR A TYPE 2 TEST USING IDEALAND REAL GAS EQUATIONS This sample calculation is intended to demonstrate how to select a test gas and determine the testspeed. A compressor designed for use on a hydrocarbon mixture is to be tested in the shop with aclosed loop for an ASME test.TableC.5.1gives thespecifiedoperatingconditionsand predictedperformance for the pointto be tested. Additionally, it gives mechanicaldesign requirements of theequipmentsuch as themaximumtemperature, pressure, rotating speed requirements, the impellerdesign data neededfortheevaluationoftestequivalency,andthe critical speeds of thecompressorrotorsystem. Theselectionofthetest gas andcomputation of therequired compressorspeed is a multistepprocess.TableC.5.2 outlinesthebasic steps involved in flow chartform.Thefirst step involves computation of the specified conditions; Reynolds number,Mach number, pressure ratios, volume ratios, etc. This data is contained in TableC.5.4.The next step is to select the possible testgases. In this problemnitrogen,carbondioxide,refrigerant134a(R134a)andrefrigerant 22 (R22)havebeenselected as possibletestgases.’ Knowing a closed loop is to be used, 20 psia and 100°F were used for afirstestimateof inlet conditions.Theselectionofthe 20 psiawas to allow a loop with a positive pressure and therefore, no inward leakage of air as a contaminant would occur. Table C.5.3 lists the test gas inlet conditions for each of the gasses.The next step is thedeterminationwhether ideal gas orreal gas calculationmethodsshould be used. The X factor and Y factor of Schultz were computed for the specified gasas well as for each of the test gases. It was found that the specified gas required real gas calculations, nitrogen could be assumed to beideal,and CO2,R134a,R22 requiredreal gas calculations.Fromthe X and Y factors,anestimateofthe cp andthecompressibility Z, thetestpolytropicexponent was computed.Sincethespecificvolume ratio attest shouldequalthespecificvolume ratio at specified operating conditions, the test pressure ratio was computed along with the test discharge pressure and temperature;see Table C.5.4. At this point, a check with mechanical design conditions found that nitrogenand COZtestdischargetemperatureswere in excess of maximum allowed by themechanicaldesignand a furthercomparisonof speedsalso indicatedextremelyhigh rotational testspeeds in excess ofmechanical design.Further computation was not needed for nitrogen and COZ, as thesegaseswere eliminated.Firstestimates of temperature and speed for refrigerant 134a and refrigerant 22 (See Table C.5.4) indicated possible testgasessince they did not exceed mechanical limitations. However, the rotative speed for the preliminary R22 selection was only 3 percent below the first critical speed and the rotative speed for the R134a selection was approximately 14 percentbelowthefirst critical speed.For the first pass, there was no Reynoldsnumberscorrection, verification ofspecificvolume ratio, efficiency,or anestimate of real gas correction factors. The final testspeed should be checked so that it is not too close to a critical speed. Thenext step is thecomputationofthe testhead, dischargeenthalpy,isentropicdischarge condition, and the real gas correction polytropic work factor. Table C.5.5 has the computed data

l It is recognizedthatthere is apotentialenvironmentalproblem demonstrate the calculation method.

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of usingrefrigerant

22. Theusehere

is only to

TABLE C.5.1 SPECIFIEDOPERATINGCONDITIONSANDPREDICTEDCONDITIONS Inlet Pressure,psia Temperature, O R 0.2602 Specific volume ft3/lbm 0.7981 Z 373 0.01 Viscosity centipoise 0.6266 heat Btu/lbm-"R Specific Specific heat ratio 820. Sonic velocity hhec 209.8 Enthalpy Btu/lbm Entropy Btu/lbm-"R

Discharge

200 575 0.7578 0.8768 0.01 0.4894 1.1 28 830. 164.9 1

704.8

021

.S77

650

1 .O98

1 .S92

Cas properties: Hydrocarbon mixture Critical pressure: 646.4 psia Critical temperature: 577.2 'R Critical specific volume: 0.7943 ft3/lbm Mol weight: 35.67 Volume flow rate: 22734 d m Mass flow rate: 30000 Ibm/min Polytropic efficiency: 0.781 Polytropic head: 27310 h-lbf/lbm Speed:Gas 3600rpm Mechanical 1 0 0 hp Mechanical design: Max. temp 350 O F Max. pressure 900 psia Max. speed 3775 rpm 1st critical speed: 2600 rpm 2nd critical speed: 4700 rpm 1 2.5

in.

Impeller 2nd Diam., in. 36 Width, Tip f, in.

st 36

36

36

-

3rd 5th 36 1.25

4th -

-

1 .5

0.000125

for R134a.Thetestspecific volume ratio comparedtospecified indicated that the R134agas conditions are very close (within the accuracy of estimated gas properties) to that of the specified. Furthercheck on the assumed efficiency also indicated it was within 4 percent of specified. The polytropic headwas computed along with Reynoldsnumber correction factorand a new speedwasalsocomputed.Furthercheck of this speedagainst the critical s p e e d of the unit indicated a margin of 8.6 percent, which should be within a reasonable range for unit operation; therefore,R134a could be used. Table C.5.6 has the basic R22 checkdata.Thetestspecificvolume ratio is considerably off from that specified.Thetest speed is 2556 rpm which is too close to the first critcal speed. This problem demonstrated the extent of calculation necessary to come up with the test speed for a given unit. The final test power may be increased by changing the inlet pressure and then re-computing all the values.Effectivelythetemperature ratio shouldremainconstantand test speedmay vary slightly with increase of inlet pressure. Thetestspeed computed is only an estimate. Once the unit is on test, the 9/N should be set and the specific volume ratio, r", checked from test data. If the volume ratio is not correct, the testspeed should be adjusted and the q/N reset.

124

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~~

S T D - A S M E P T C LO-ENGL L997 m 0 7 5 9 b 7 0 Ob05547 345 m

TABLE C.5.2

GENERALFLOWCHART

FOR TESTGASSELECTION

Y I

+ +

Compute Test Speed

Rem, Mach No., qIN, Wp, tlp. rp. ' y

Verify Mechanical Design for Critical Speed, Max Speed, etc.

-ONAssume InletTest Conditions

P. f

Verify Volume Ratio

Compute X and Y for Real Gas Requirements (Table 3.3)

Estimate New Discharge Pressure

+

Compute Test Polytropic Exponent

Compute Corrected Test Speed Temperature andPressure

1 Verify Test Temperature Pressure Lower Than Max. Design

+

No

Compute Q and Test W

1.

l

Compute Test Head Discharge Enthalpy and Isentropic Discharge and Real Gas Correction

I

125

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+

Compute Mach No., Verify Test Volume Ratio

No

Compute Test Power

I

TABLEC.5.3 TEST GASINLET CONDITIONS

560

560

pi, psia Ti, 'R 560 vi, ft3/lbm

4

0.982

p, centipoise

c, Btu/lbm-'R

k ai, ft/sec

204.8 721.9 102.

673.8 TO 'R 547.7 590.3 po psia 1069.9 MW 44.01 h&Btu/lbm si Xi Yi

R134a

c02

N2

20 560 10.73 1 .o0 0.975 0.017 0.2499 1.396 1 178. 227.4 493. 28.01

20

20

6.778 0.993 0.015 0.21 03 1.273 894.

121.2 0.02 -

-

R22

20

2.871 6

3.41

0.01 o9 0.2098 1 .O98 538.8

0.01 1 0.161 1.166 598.5

122.3

-

0.07 1 .O27

-

1 .O3

GENERAL NOTE It is recognized that thereis a potential environmental problem of using refrigerant22. The use here is only to demonstrate the calculation method.

TABLE C.5.4 FIRST PASS FORGASSELECTION specified

Ca 3.25 2.912 1.226 1 .O273 0.781 0.509/1 .O56 1.1 50b.287 Real

1.1 027 2731 0.0 2.266 x lo7 0.681 565.5

CO2

N2

R22

5.358 2.912 1.840

4.309 2.91 2 1.495

3.296 2.91 2 1.157

3.551

0.781

0.781 0.01 1 .o1

0.781 0.08 1 .O3

0.781 0.02 1 .O3

-

-

-

2.91 2 1.261

Ideal

Real

Real

Real

1 S74 71 422

1.366 34860

1.185 13750

107.2 1030. [Note (111

86.2 836.6

1.116 1 o499 3.473 x 106 0.65 350 65.9 648

[Note (1 11

5822

4067

[Note (111

[Note (111

-

3600

R134a

-

-

0.983 2232

70.0 706

2554 [Note (311

NOTES (1 1 Test values exceed the mechanical designlimit for the tested unit. (2)No Reynolds number correction or verification of volume ratio, efficiency, or real gas correction, (3)Test speed too close to rotor critical speed.

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22

S T D - A S M E P T C 10-ENGL L997

0759b70 O b 0 5 5 5 1 T T 3

TABLE C.5.5 Specified CaS Polytropic work factor f RemdRem,

1.004

Allowable range (minimum) r, check qp check W, ft Ibf/lbm

2.912 0.781 2731O

Remcon N, rpm

3600 0.681 22734 31790

Mm

9 hP

R134a

1 .o1 0.1 53 0.1 2.92 0.779 10605 1.O03 2247 0.655 14190 2039

Supplement C.5.A PredictedConditionsSpecifiedGas PressureRatio rp = pd/pi = 650/200 = 3.25 Volume Ratio r, = Vi/Vd = 0.7578/0.2602 = 2.912 kmaxkmin = 1.1283 /1 .O975 = 1 .O28 S/N = 2273413600 = 6.315 CheckSpecifiedGasforTypeofCalculation

FromSchultzCharts

=

Xmi"

Xmax

= 0.509 Ymin = 1 .I50 = 0.056 Ymax = 1.287

Based on Table 3.3

UseRealGas

CalculationMethod forSpecified

-

Gas

1.128 (200)(0.7578)(32.2) 144 1.15

= 830.2 ftfsec. 127

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Tip Speed

-

T

(36) (3600) fi = 565.5 sec 720

MachineMach Number

Mm =

U/&

= 565.5f830.2= 0.681

Machine Reynolds Number

Rem = Ulbl/pv

= 0.01021 centipoise = 0.01

,U

021

/(1488.2)

= 6.86 x lov6Ibm/ft-sec

2.5 (565.5)(E) Rem =

6.86 x

= 2.266 X

(0.7678)

lo7

Test Gas Nitrogen (N21 Initial Estimate:Assume

Ideal Gas

Y = 1.0

x

= 0.0

f = 1.0

ComputePolytropicExponent

npt = nPsp= 0.781

COPYRIGHT American Society of Mechanical Engineers Licensed by Information Handling Services

Remco,, = 1 .O

=-

(1.396

1

- 1)

1.396 0.781

= 0.3632

nt = 1.574

Compute TestGasPressureRatio

rvt = r,

SP

1.574

= 3.25

1.1027

n-1

= 5.358

rt, = ( r p ) T 5.358°.3632= 1.840

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Test Polytropic Head

W, =

W, =

n

=pi

vi

n-1 n - 1) 144

(rp

1 .S704 1.5704

- 1) 144 - 1 (20) 10.725 (5.358°*3632

= 71422 ft-lbf/lbm TestSpeed

Nt = 3600

NOTE Testtemperatureexceedsmechanicaldesignlimit.

Test Gas

= 5822 rpm

Test speed exceedsmechanicaldesignlimit.

Co;!

Initial Estimate:

Assume NonidealGas Useinletconditionsfor initial calculations. ReducedTemperature = R, = Ti /Tc,it = 560/547.7 = 1.022 Reduced Pressure = Rp = pi = 20/1069.9 = 0.0187 x = 0.01 Y = 1.01 Z = 0.993 cp = 0.2103 130

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S T D - A S M E P T C 111-ENGL 1917 W 0757b70Ob05555

ComputePolytropicExponent

n=

-

1 Y - m (1

+ X)

1 ( 778.1 7 (0.21 03) (44.01 0.781 0.993 (1 545)

+ 0.01)

= 0.2749

n=

1

1.01

- 0.2755 (1 + 0.01) = 1 .3655

Compute TestPressureRatio

Pdr

= rppi, = 4.304 x 20 = 86.1 psia

Compute Test TemperatureRatio

Td, = r( T; = 1494 (560 "R) = 836.6 "R

z T ~ , 0.993 (-)44.01 = -1545

"'t

P i(

144 (20) 131

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(560)

= 6.778

h119

m

n1

n

Wp,

Wpt=

= -pi .(rp

" - 1) 144

n-1

(1.3655 1*3655 ) 20 (6.778)(4.304°.2677- 1 ) 144 -1

= 34860 ft-IbWlbm

Test Speed

= 3600

NOTE:Testtemperature

-- 4067

rpm

is marginal.Test s p e e d exceedsmechanicaldesign.

Test Gas R734a Initial Estimate

Assume NonidealGas UseInletConditions

for Initial Assumptions

ReducedTemperature =

RI

= Tiflcrit

= 5601673.8 = 0.8311

ReducedPressure = Rp =

pdpcrit

= 201590.3 = 0.0339 X = 0.07 132

COPYRIGHT American Society of Mechanical Engineers Licensed by Information Handling Services

Y = 1.027

ComputePolytropicExponent

--

1 ( + 0.07) 778.1 7 (0.2098) (1 02) 0.781 0.975 (1 545)

= 0.1 221 5

1 Y - m (1

n =

-

+X)

1 1 .O27 - 0.1 221 5 (1

+ 0.07)

= 1.1157

Compute Test Gas PressureRatio

Pd

fp,

=

=

fp

1.1157 -

3.25'.'02' = 3.2955

pi

= 3.2955 x 2 0 = 65.91 psia

Compute Test Gas TemperatureRatio

r( =

r6

= (3.2955)0.'22'5= 1.1568

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Compute Test Head

z

vit

= --

1545 (K)

(560)

= 2.8716

144 (20)

P i,

W, =

=

0.9753

..n - 1.

n

pi vi (rp n-1

- 1) 144

[

) 20 (2.871 6) 3.29!jS(*) (1.1157 - 1 57

- 1) 144

fi-l bf Ibrn

= 10499 -

Compute TestSpeed

Nt = 3600

J"= = 2232 rprn

Check Volume Ratio

Vd

=

647.8 - 0.951 (1 545) 144 p M W - 144 (65.911 102 ZRT

= 0.9832

r, = 2.871610.9832 = 2.921 ComputePolytropic Work (RealGas)Factor Isentropic P= 65.91 psia T'= 168.7 "F (628.7 OR) V = 0.9205 ft3/lbm h'= 135.46 Btu/lbm n,= Inrplln r,' r:= VdvJ = 2.8716 /0.9205 = 3.1 196 n,= In 3.2955/1n3.1 196 = 1 .O482 134

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lb ft3

S T D - A S M E P T C LO-ENGL 2777 m 0757b70 O b 0 5 5 5 7 29q m

I (h2 - hi) = (135.46 - 122.3)778.17 = 10241 fi-lbf/lbm

Ws=

ns ns- 1

(Pd

Vd

- pi

Vi)

144

10241

f=

1.O482

1.O482 - 1

= 1.01

[65.91 (0.9205) - 20 (2.871 6)] 144

ComputeReynoldsNumberandReynoldsNumberCorrection Use Preliminary TestSpeed Rem = Ubfp v U= rDN/720 = IT 36 (2232)/720 = 350.6 ft/sec. 3 5 0 . 62 (.5~ ) Remt=

7.324 x 1O-6 (2.871 6)

= 3.473 x 106

ReynoldsNumberRatio Remt

- 3.473 x lo6 = 0.153

"

2.266 x l o 7

Rem,

Allowable Ratio Remt/Remsp 2 0.1

Therefore,theReynoldsnumber ratio of 0.153meets ComputeReynoldsnumberconditions.

RA = 0.66

conditions.

lo6 bIRC + 0.934 (4.8 xRem

RB= log (0.000125 + 13.67/Rem)/log (e + 13.67/Rem) RC = 0.988/(Rem)0.243 RC =, 0.01 61 2 135

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RA,=

0.66 + 0.934

RB,=

1 .O

RC,=

0.988

= 0.02543

[3.473 X 1O6lo."3

0.66 t 0.934

R A = I

RBI= 1.0

(1

- S&=

(1

- .781),

1 565 1 O (-)1.548 (-)1.0

= 0.224

qPr= 0.7786

Remco,,= 0.781/0.7786 = 1 .O03

(z p () r p 7n

"P=

1.1157

f

n-1

1) 144

v

0.1 157

.O11

(20) 6)(2[3.2955'."57 .871

- 1] (144)

= 10605 ft-lbf/lb Correct Preliminary Test Speed

NI

= 3600

= 2247 rpm 136

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NOTE Test s p e e d within 8-1/2 percent of 1st rotor CriticalSpeed

Calculate Mach Number Mm= U/ai U= ~ D N / 7 2 0 = [~36(2247)1/720 = 353 fVsec. Mm= 3531539 = 0.655 Mach NumberRatioDifference Mmt

- Mmsp= 0.655 - 0.681

= -0.026

Test Gas R22 (Chlorodifluoromethane) Initial estimate

TP,=

?Psp

Remco,,= 1.O f= 1.0 Usereal gas calculation Useinletconditionsfor initial estimate ComputePolytropicExponent

m=

(-

0.982 (1 545) 2 + 0.02) = 0.1821 778.17 (0.161) 86.48 0.781

n = 1/[Y - m (1 + XII t~=1/[1.03 - 0.1821(1 n= 1.1 845

+ 0.0211

Compute TestPressureRatio

-

'P(

=

1.1 845 3.251.1027

= 3.546

pd = rptpi = 3.546 (20)= 70.9 psia

137

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Compute TestTemperatureRatio

rtt

Compute Test

= rpT = 3.546L0~'82'' = 1.259

Head

Z Ti,

-

1545 0.982 86.48 (560)

(-)

=P it -

144 (20)

= 3.4113

n- 1

1.1845

= 13750 ft-lbf/lbm Compute TestSpeed

= 3600

= 2554 rpm

Testspeed

is tooclosetothefirst

critical of 2600 rpm.

138

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-1

S T D - A S M E P T C L O - E N G L L997

0 7 5 9 b 7 0 Ob85563 715

m

SAMPLE CALCULATION C.6 TYPE 2 TEST USING REAL GAS EQUATIONS FOR DATA

REDUCTION A mixed hydrocarbon compressor which wasset up in the Sample Calculation C.5 was tested on refrigerant134ausingaType2test. Table C.6.1 outlinestheconditions for which this compressorwasdesigned. It tabulatesthe inlet anddischargeconditions, as well as theisentropicdischargeconditions. Table C.6.2 showsthe gas compositionand critical properties for this hydrocarbonmixture. The molecular weight and the calculated gas constantareshown in this table. Table C.6.3 shows thederiveddesignfunctions, specifically pressureratio,temperatureratio, volumeratio, as well as polytropicexponent,volumeflow, head, efficiency, andpower.The test is supposed to verify thesevalues.The calculationof thesevalues is shown in Sample Calculation CS. The unit was tested on refrigerant 134a.' The test data are shown in Table C.6.4. It wasat a test speed of 2245 rpm. The inlet pressure was held at 20 psia at an inlet temperature of 100OF. Dischargeconditionsachievedwere 67.5psiaand187.4"F.Thedatashown is the average of the actual test data readings. It is assumed that all scatter was within the allowable test requirements for thesedata point positions. The derived test functions, pressure ratio, temperature ratio, volume flow ratio, etc., are shown in Table C.6.5.This is the reduced data from the test point of Table C.6.4.The calculations are shown in Supplement C.6.A for obtainingeach of the individual items.

TABLE C.6.1 SPECIFIC DESIGNCONDITIONS

-

Mass Flow 30,000 Ibm/min Speed 3,600 - rpm Inlet

Discharge

Isentropic

~~

650 Pressure,psia 227.7 Temperature

650 244.8 0.2465 Specific volume, ft3/lbm 0.7749 Compressibility factor

P T V 0.2602 0.7981 Z

Viscosity, centipoise P 0.6266 Specific heat, Btu/lbm-OR CP Specific heat ratio k a Sonic velocity, ft/sec 820 199.05 209.84h Enthalpy, Btu/lbm 1.577 1.592S Entropy,Btu/lbm-"R

200. 115 0.7578 0.8768 373 0.01 021 0.01 0.4894 2831.1 830 164.9 1.577

1 .O975

It is recognized that there is a potential environmental problem of using refrigerants. The use here is only to demonstrate the calculation method.

139

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TABLE C.6.2 GAS COMPOSITION A N D PROPERTIES Composition: Methane Ethane Propane N-Butane

20% 25% 50% 5%

Critical properties:

=

PC

=

TC

--

v, Molecular weight

=

Gas constant R

=

646.4 psia 577.2 "R 0.7943 fi3/lbm 35.67 43.31 ft-lbf/lbm O R

TABLE C.6.3 DERIVED DESIGN FUNCTIONS ~~~

~~~

Pressure ratio Temperature ratio Volume ratio hax/kmin

9,ICFM S/N,ICFM/rpm Reduced temp min/max Reduced pressure min/max Schultz factors XmdXmax YmdYnux

1st stage tip speed, Wsec Machine Mach no. Machine Reynolds no. Polytropic exponent n Isentropic exponent n, Polytropic work factor f Isentropic head, ft-lbf/lbm Polytropic head, ft-lbf/lbm Polytropic efficiency Unit gas power, hp

3.25 1.226 2.91 2 1.O281 22734 6.31 5 0.996/1.221 0.30911 .O06 0.509/1 .O56 1.1 50/1.287 565.5 0.681 2.266 x 10' 1.1027 1 .o495 1 .o04 26570 2731O 0.781 31 790

Table C.6.6 compares the test data and the test data converted to specified operating conditions with the predicted performance at the specified operating conditions. Supplement C.6.B demonThe calculation ofdischargeconditions, pressure, strates the calculationsfortheconversion. temperature, and volume is shown in SupplementC.6.C, which alsoillustrates the use of an iterative procedure. As canbe seen the inlet capacityfortheconverted test conditions was within 1 percent of the original specifieddesign point andthehead was within 2 percent.Theconvertedspecific volume ratio was within the specified 4 percent allowed. Supplement C.6.A

Calculations: Derived Test Functions 140

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S T D - A S M E P T C L O - E N G L L777

m

0757b713 Ob055b5 5 7 8

m

TABLE C.6.4 TEST DATA Mass flow SPd

4,923 - Ibm/min 2,245 - rprn Inlet

P Pressure, psia T Temperature Specific volume, ft3/lbm0.9639 0.9234 V 6 Compressibility factor 0.944 0.955 Z Viscosity, centipoise CL Specific heat, Btu/lbm-OR =P Specific heat ratio k Sonic velocity, ft/sec a Enthalpy, Btu/lbrn 140.04 h Entropy,Btu/lbrn-OR 0.2639 0.2731 S

Isentropic Discharge

67.520 1 O0 167.49 2.871 0.975 0.01 o9 0.2098 1.O98 538.8 122.3 0.2639

67.5 187.4

135.80

Gas - Refrigerant 134a Mole weight 102 PC

TC

590.3 psia 213.8

OF

TABLE C.6.5 DERIVED TEST FUNCTIONS

14143

Pressure ratio Temperature ratio ratio Volume q ICFM qhV ICFWrpm 1st stage tip speed (ft/sec) Machine Mach no. Machine 3.49 Reynolds Rem no. exponent Isentropic factor Polytropic work exponent Polytropic Polytropic head (ft-lbf/lbm) efficiency Polytropic Unit gas (hp) power

Pressure Ratio

3.375 1.1 56 2.980

'P '1 'V

6.3 352.6 0.654 x 106 1.O718 7 1.o01 1.1139 10735.2 0.778 2059

U Mm ns

f n WP VP

p.

rp = p&i

=

67.5 20

= 3.375

TemperatureRatio

rt = T&;

=

(460 + 187.4) (460 + 100) 647.4

=-

560

= 1.156 141

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0759b70 O b O 5 5 b b 42q D

S T D - A S M E P T C 10-ENGL L977

TABLE C.6.6

DATA SUMMARY Test Data Converted To Specified Test Data operating Conditions

N 9 9m WP 7lP

PS Pi 660.8 Pd ti

246.7 b 0.7578 Vi

4.8 0.7578

Vd

rPm ICFM

2245 141 37 6.297 10736 0.778 2059 20 67.5 115 1O0 187.4 2.871 0.9635 2.98 122.3 140.04

ft-lbf/lbm hP psia psia OF

OF

ftVbm 6 V/lbm

Vr

164.9

hi hd

164.9 Btu/lbrn Btu/lbrn

InletSpecific

Volume

vi

Predicted Performance At Specified Operating Conditions

3600 22670 6.297 27690 0.780 32180 200

3600 22734 6.31 5 2731O 0.781 31790 200 650

115 0.2562 2.958

0.2602 2.91 2

210.5

=

ZiR Ti

-=

209.84

0.975

1545 ( x (560) ) = 2.8716

(20) 144pi 144

Specified Volume Ratio

r, =

=

V&

2.8716 0.96347

= 2.9805

InletCapacity

9 = mvi = 4923 x 2.8716 = 141 37ICFM

Capacity/Speed Ratio

q/N =

141 37 2245

= 6.297 142

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S T D - A S M E P T C 10-ENGL 1997 II 0759b70 Ub055b7 3bI1

TD N =

U=

1st Stage Tip Speed 720

a 3 6 . 0 x 2245

720

= 352.6 ft/sec

Mm = U/a =

MachineMachnumber

352.6 538.8

= 0.654

= Ub/pv

Machine Reynolds number Rem

-

352.6 (2.5/12)(1488.2) 0.01 O9 (2.871 6)

=

n,

Isentropic Exponent

= In(pdpi)/ln =

=

f=

(1 38.50

1 .O7212 0.072 1 2

n

In (67.5/20)

In (2.871 6/0.9234) 1.07212

- 20 (2.871 6)]144

= In (rp)/ln(rv)= =

1.1138

143

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(vM)

- 122.3) 778.1 7

(67.5 (0.9234)

Polytropic Exponent

3.493 x 106

= 1.002

In (3.3750) In (2.9805)

~

S T D - A S M E P T1C0 - E N G L

Polytropic Head

0 7 5 9 b 7 0 Ob055bB 2 T 7 9

1997

n wp = (7) (PdVd - pivil

1.1138

[67.5 (m)

=

(0.96347) - 20

= 10736 ft-lbf/lbm

= 0.7777

Wpw - 10737 (4923)

pg=”

Gas Power

0.778 (33000)

TIP

= 2059 hp

Supplement C.6.B Calculation:Conversion From TesttoSpecifiedPerformance Inlet Capacity

= 141 35

(-)3600 2245

= 22670 ICFM

Reynolds Number Correction forEfficiency

RC, =

0.988 Remp243

--

0.988

144

COPYRIGHT American Society of Mechanical Engineers Licensed by Information Handling Services

= 0.0254

(3.49 x 106~243

(2.871

611

144

~~~~

~

~~

0 7 5 7 b 7 0 Ob055b9 L33 D

S T D - A S M E P T C L O - E N G L L977

Remf = 1.0 13.67

RBf =

[4.8X lo6 X b] Remf

RAI = 0.66 + 0.934

[

2.5

4.8 X

= 0.66 + 0.934

RC, =

RCt

lo6 X -

0.0254

12] 3.493 x 106

= 1.565

0.988 0.988 = 0.01 61 2 (Rem,p)0.243(2.266 x 1 07)0.245

--

RA, = 0.66 + 0.934

(4.8 X lo6 X Remsp

[

b)"sp

("'1

4.8 x 1 0 6 x -

= 0.66 + 0.934

RB,

1

= 1.548

2.266 x lo7

= 1.0

1 .S48 1 .O = (1 - 0.7777) -

1.565

- qp,

1

- VPsp = 0.2199 145

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o.o1612

1.0

S T D - A S M E PTC LO-ENGL 1997 D 0 7 5 9 b 7 0 Ob05570 755

VPSP

m

= 0.780

Remcorr= 1.O03

Polytropic Head

(2) 2

Wpsp= Wpt

= 110736

Remcorr

3600 (-)2245

1.O03 = 27690

ft-lbf Ibm

Power

3600

(-)

= 14137 2245

Pg =

w~sp SP

1

(-)0.7578

- 27690(2991

= 29915

5) = 32, 8o hp

0.780 (33000)

Supplement C.6.C The conversion from test conditions to computed specified conditions involves an iteration to obtain the discharge pressure from theknown head and discharge enthalpy. Theiteration procedure and calculation involves assuming a dischargepressureat the known dischargeenthalpyand finding the corresponding temperature and specific volume. The polytropic exponent and polytropic head is then calculated for the assumed discharge pressure. This polytropic head is then compared to the actual and, if not the same, then a new discharge pressure is assumed.The new assumed pressure is evaluationforproperties at the known dischargeenthalpy,and a new discharge volume is evaluated and polytropic exponent are computed. This iteration procedure is continued until the conditions matchtherequired head. 146

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FIG. C.6.1 POLYTROPICHEAD vs. PRESSURE, CONSTANTENTHALPY

FiguresC.6 .1 and C.6.2are a plot of discharge conditions at a constantenthalpy of 210.5 Btu/lbm. The finalpoint at 27,605 ft-lb/lbm is 659 psia,246.5"F.This methodcaneither be computerized or done graphically as shown in thisexample. Calculation Procedure: Known Wp= 27,690 ft-lbf/lbm

pi= 200 psia hi= 164.9 Btu/lbm vi= 0.7578 ft3/lbm 147

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~~

~

S T D - A S M E P T C LO-ENGL 1997 D 0759b70 Ob05572 728 D

630

650

660

670

680

Pressure, psia

FIG. C.6.2 TEMPERATURE/SPECIFIC VOLUME vs. PRESSURE, CONSTANT ENTHALPY

148

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690

qp= 0.780

f= 1 .O04 Step 7 - Calculatedischargeenthalpy.

= 165.9 +

Step 2

- Assume

Btu 27690 = 210.5 0.78 (778.1 7) Ibm

a discharge pressure. Pout = 660.8 psia

Step 3 - For pd and hd, obtain the discharge volume Vd =

for the properties.

0.2562 ft3/lbm

Step 4 - Compute the polytropic exponent. n= In rp/ln r, T,= 660.8/200 = 3.304 r,= 0.757810.2562 = 2.958 n= In 3.25/1n 2.905= 1 .lo2 Step 5

- Compute the polytropic

head.

1 .O04

[660.8 (0.2562)- 200 (0.7578)]

144

fi-l bf = 27705 Ibm

Step 6 - Compare the computed W, to the actual. If they are within acceptabletolerance,thenthedischargeconditionsareestablished. If they donot match,then a newdischargepressuremustbeassumedand theprocedure repeatedfrom step 2 thru 6 .

149

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S T D - A S M E P T C LO-ENGL L997 m 075'7b70 Ob05579 S T O

SAMPLE CALCULATION C.7 TREATMENT O F A TWO SECTIONCOMPRESSOR WITH EXTERNALLYPIPEDINTERCOOLERS,CONDENSATE REMOVAL

This sample calculation illustrates the computational procedure, at specified operating conditions, for a multisection compressor havingexternally piped intercoolers. Consider a two stageaircompressor equipped with oneintercoolerand an aftercooler. Section 2 U 1065 D = 12.204 N = 20,000

Section 1

U = 1200 D = 13.751

N = 20,000

-:

After After Cooler

Final discharge discharge Final conditions

" "

I

I

Leakage

Condensate

Leakage

Condensate

Power requirements

* Measurement stations It is desired to calculatethe compressorperformance at thespecifiedoperating conditions shown. The compressor has been tested and the test data reduced to the following dimensionless form. Thedatawas collected with pressureandtemperaturebeingmeasured at the inlet and outlet of eachsection.The flow coefficientswerecalculated based upon test rotor flow rates. The selectionof testmethodandthemeansofestablishingleakageandcondensate flow rates were subject to prior agreementby parties to the test. The first step in calculating thespecifiedoperating condition point of interest is to establish the first section performance, starting with the flow coefficient. Taking the saturation pressure of water vapor at 560"R to be approximately 0.949 Ibf/in2, with the remaining specified operating conditions at the inlet, we obtain

pw = RHpsv= 0.60 (0.949) = 0.569 Ibf/in2 pa = 14.7

and

COPYRIGHT American Society of Mechanical Engineers Licensed by Information Handling Services

- 0.560 = 14.1 31 Ibf/in2

STDOASME PTCLO-ENGL

L997

m

0 7 5 9 b 7 0 Ob05575 437 D

Thegas constant for the mixture is

= 0.0250 Ibrn

a

w/lbm

da

The rotor flow rate is the same as the inlet mass flow rate.The flow coefficient is then Wrotor

Q=

-

-

w~RT~

6.5 (60) 54.13 (560)

(F)

144 (14.17) 27r (20000)

13.751

= 0.0295 3

With the flow coefficient established the corresponding polytropic efficiency, polytropicwork 1 dimensionlesscurves coefficient,and total workinput coefficient areread fromthesection (see Fig.C.7.1).That is = 0.83, ,up = 0.599, and = 0.722 at C$ = 0.0295.To continue the calculationstheproperties of air at thespecifiedoperatingconditionsmust be known. For the purpose of this example we assume that the air-water vapor mixture maybetreated asan

r),

Section 2

Section 1

I

I

0.50

E I

I

L

0.035 0.030 0.025 0.020

U,

I

I

0,040 Q

The Mm, Rem, k, and v;/vdfor the data are assumed to match the specified operating conditions within Table 3.2 Limits. The Rem match is assumed sufficiently close so as to render the Reynolds number correction negligible.

FIG. C.7.1 152

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S T D - A S M E P T C 10-ENGL L777 M 0759b70 O b 0 5 5 7 b 373 D

ideal gas with constant specific heat. k = 1.395 is used as being representative of the end result which might be obtainedby considering the properties of the constituent gases over the compression range. This value will be used for both sections for this example. The average constant pressure specificheat is Btu 0.2457 Ibm "R

.

Usingthe polytropic efficiency of

n

-

vP

= 0.83 gives k

"

n-1

or,

n =

T

p

K

= 0.83

1.395 = 2.931 0.395

1.5178.

Using the polytropic work coefficient of

= [l

Thedischargepressure

+

= 0.599 gives

,up

0.599 (1 20012 (2.931) 54.13 (560) 32.174

1

2.931

= 2.166

is

The temperature ratio and discharge temperature

are

and

The power absorbed in the compressor section is obtained using the total work input coefficient

S1 = 0.722.

The shaft seal which is located downstream of the rotor leaks 0.03 Ibm/sec for these conditions, is

so the mass flow rate at the intercooler entry

w/cooler entry = wrotor-

Weak

= 6.50

- 0.03

= 6.47 Ibm/sec

The intercooler is known to cool the flow to 560"R atthemass flow rate, gas entry state, and specifiedoperating condition coolanttemperatureand flow rate.Theairstreamexperiences a total pressure loss of 0.8 psi across the intercooler. It must now be determined if and how much 153

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condensation occurs in the cooler. Since the cooler exit velocity is assumed, very low stagnation valuesareused in the analysis. Thesaturationpressure of the vapor at 560"R is approximately 0.949 psia. If the exit air is at 100 percent relative humidity, the humidity ratio is HRd =

2 zsv i::;:

Ibrn water --) = 0.0196 Ibrn da p (31 .O4 - 0.949

-

where p = 31.84 0.8 = 31.04 psia Sincethesaturated humidity ratio is less thanthecoolerentry humidity ratio,condensation must occur. The difference between the two is the ratio of condensate to dry air COndenSate/Wda = HRi

- HRd = 0.0250 - 0.0196 = 0.0054 Ibm

w/lbrn da

Themass flow rate of dry air is given by

so, the condensate is Condensate = (condensate/wd,)

=

W/

= 0.0054 (6.312) = Ibm/sec

- water vapor mixture

The exit mass flow rate for the air Wex

Wda

- condensate

is

= 6.47 - 0.0341 = 6.436 Ibrn/sec

The intercooler exit conditions are the second section inlet conditions. The previous calculation sequence is repeated for the second section, starting with calculation of the flow coefficient. Thegas constant changes slightly due to the water vapor removal.

= 53.96 ft-lbf/lbrn "R

And the flow coefficient is

6.436

--

(53.96)

(560)

144 (31.04)

(3

2000 (

y

ni

q

= 0.0197 3

Reading q p = 0.81, p P = 0.560, and = 0.691 from the section 2 dimensionless performance curves(seeFig. C.7.1) for q5 = 0.01 97, andusing 154

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S T D * A S M E P T C LO-ENGL 1 7 7 7

0757b70 Ob05578 L 4 b

53.96 1.395

0.2449

m

Btu Ibm O R

yields pk E =

q

= 0.81 1.395

n

0.395 yielding n

- 2.861, and n

"

n- 1

= 1.537

n n-1

rp=

[

1+

fip

1

gc

(L) RTi n- 1

r

=L1+

0.56

1 0652 -

12.861

J

(2.861) 53.96 (560) gc

= 1.801

ZU2

-60

Wrotor

Gas Power =

-

gc

3300 6.436

(

(0.691 1 10652) 60 32.1 74 = 285.1 hp 3 O00 3

Theshaftsealdownstream ofthe rotor leaks 0.06 Ibm/sec for theseconditions, flow rateattheaftercoolerentry is Wcooler entry

so the mass

= 6.436 - 0.06 = 6.376 Ibm/sec

Theaftercooler is known to cool the flowto 580"R at this mass flow rate,gasstate, and specifiedoperating condition coolanttemperatureand flow rate.Theaftercoolerpressure drop is 1 psi. Assuming a saturation pressure of 1.692 psia and following the intercooler condensation analysisscheme, 155

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HR=

-(R,

Rda

P

psv

1.692 ) =A( 53 34 85.76 54.91 - 1.692

= 0.0198

Ibm W

Ibm da

where p = 55.91 - 1 = 54.91 psia. Sincethesaturatedhumidityratio is greaterthantheentry humidityratio, no condensation occurs in theaftercooler. In summary, the final discharge pressure at the aftercooler exit is 54.91 psia, the final discharge temperatureattheaftercoolerexit is 580°R, andthetotal gas powerrequirement of the two sectionsis 667 hp.

156

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STD. ASME P T C 10-ENGL L777 m 0759b70 Ob05580 8 T 4

TABLE C.7.1 SUMMARY OF RESULTS Conditions:

re

Section:

Specified Inlet mass flow rate total Inlet pressure total Inlet relative Inlet humidity constant, air Gas dry water constant, Gas 1 st Section: Rotational speed Tip diameter 2nd Rotational speed Tip diameter

lbmhec

6.500 14.7 560. 60. 53.34 85.76 20000

psia "R % ft-lbf/lbm-"R ft-lbf/lbm-OR rPm

13.751 20000

rPm

in.

in.

12.204

Intermediate CalculationResults:

Cas constant for mixture Specific heat for mixture Flow coefficient Polytropic efficiency Polytropic work coefficient Work input coefficient Total work input coefficient Polytropic exponent Tip speed Inlet pressure Pressure ratio Discharge pressure Inlet temperature Discharge temperature C a s power Inlet mass flow rate Leakage flow rate Discharge flow rate Cooler condensate flow Cooler pressure drop

1st Section 54.13 0.2457 0.0295 0.83 0.599 0.722 0.722

2nd Section

1.51 78 1200 14.7 2.1 66 31.84 560. 729. 381.9 6.5 0.03 6.47 0.0341 0.8

1.537 1065 3 1 .O4 l. 801 55.91 560. 687.9 285.1 6.436 0.06 6.376 O. 1 .o

Overall results: Final discharge pressure Final discharge temperature Total gas power Delivered mass flow rate

54.9 580. 667 6.38

psia OR

horsepower Ibm/sec

157

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53.96 0.2449 0.01 97 0.81 0.56 0.691 0.691

ft-lbf/lbm-"R Btu/lbm-"R

ft/SeC

psia

-

psia "R

"R horsepower Ibm/sec lbmkec lbm/sec lbmkec psia

SAMPLE CALCULATION C.8

APPLICATION OF UNCERTAINTY ANALYSIS This sample problem highlights some of thefeatures of uncertainty analysis as they apply to a PTC 10 test.The propagation of measurementerror to final results is emphasized. This particular casehasbeenselectedbecause ofthe relative simplicityoftheequations involved.There is nointention toimply that it covers all uncertainties of interest. Nor is it intended to imply achievable or expected accuracy in general. It simply demonstrates the method. Suppose that test results which meet Code requirements are available. It is desired to determine flow rate.Assume that the uncertainty in shaft power for agivenspecifiedoperatingcondition the shaft power measurement method wasused during the test. Uncertainty analysis is done following PTC 19.1, using the step-by-step calculation procedure given i n that document. The steps, excluding final report,are: ( I ) Define the measurement process. (2) List the elemental error sources. (3) Estimate elemental errors. (4) Calculate the bias and precision errors for each parameter. (5) Propagate the bias and precision errors. (6) Calculate uncertainty. Step I - Definition of the measurement process requires expression of the functional relationship involved.FromTable 5.4 weobtain

Assumingasinglesectionand

no leakageorsidestreams

and,

Sincetheshaftpower

is being evaluated for a given flow and speed,

wspand

EU2 (F)

are treated as knowns having no error. SP

159

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Theterms

RshSP and Pparasiticsp arerelated to test conditions,fromTable

ashsp= ash, =

(/%h

- Ppararitic)

5.3, as

33000

Assuming that Qm is the only parasitic loss,

and

where

In general the procedure would now be to break down the individual variables in this equation if the shaft powerweredetermined from a torque meter, that power would be expressed as the product of measured torque and measured speed. Similarly,therotor massrate offlowmight beexpressed in terms of nozzle pressure drop,pressure,temperature,and gas composition. For brevity, in this example Pdt, Q m l r Ut, and wf are treated as individually measuredelementalquantities. Steps 2 rhru 4 - Assume thattheelementalerrorsourceshavebeenlisted,theelemental errorsestimated, and the corresponding bias and precision errors calculated. Many examples of this procedure may be found in PTC 19.1. Thisprocessdepends upon theactualinstrumentation systemand data collection techniques used.Theresultsmay be expressed as follows. The bias limits and precision indicesrepresent the combined effects of the independentmeasurementsforeachparameter. in terms ofindependentmeasurements.Forexample,

Parameter Absolute Bias wt

'

limit Bwr = 0.01

S+

Bpfif

Qm,

W m ,

ut ß

Absolute Precision Index

sw,= 0.01 W,

W,

= o.o1 Phr = 0.01

SPhr= 0.01 Phf Som, = 0.01 Om,

Om,

BU, = 0.01 Ur

B, = 0.2 ß S, only in this section, is the Absolute Precision Index

MeanNQ of the

SU,= 0.01 Ut of the mean = S / a .

In everycase a onepercentvalue hasbeenassigned to each bias limit and precisionindex for themeasuredquantities.This of coursedoes not reflect what might be expected in reality. Thesevalueshavebeenchosen to demonstrate the effect of unit variations. Step 5 - The individual errorsarepropagated into theresultaccording to a Taylorseries expansion. To do so it is necessary to determinesensitivitycoefficients,the precision indexof the result,andbias limit of the result. 160

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Thesensitivity coefficients #i are determined if r = API, P2,P,,

e

PshsP

partial differentiation, ¡.e.,

Pi), then +Pi =

W

[-$($)

#Om, = a

ag,

by

=

u 2 +(%)']J 33000

A bias error is assumed in the mechanical loss conversion equation dueto an assumed unknown error in the exponent ß. It is estimated for this example as 0.2ß. The precision index for the result is the square root of the sum of the squares of the product of sensitivity coefficients and averageindependentparameterprecisionindices.Thus

The bias limit for the result is the square root of the sum of the squares of the product of the sensitivity coefficients and average independentparameterbias limits. Thus

Step 6 - Calculate uncertainty 161

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Uncertainty may be calculated according, by choice, to two models. The models combine the precision index and bias limits of theresult differently.

UA00 psh

=

BpShsp + t9sSpSh SP

SP

Q

The value r is called the Student’s r. It is assigned depending upon the degrees of freedom of the sample, which is usuallyone less thanthenumber of points averaged.SeePTC 19.1 for furtherexplanation.Assuming a large sample, r = 2 maybe used. Results In order to allow expression of the results of this example numerically, assume

The sensitivity factorsare

dpsh,

= 1.20 (1 .OS)’ = 1.323

4QM1 -

-0.00456

33000

= -1.20 (1 .0512(1

dur = -2 (1.20) (1.05)* (1

- 0.1) (%) = -1.1907 w t

- 0.1)

(3) -

= -2.6638

(2) I

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(2)

2.5 (0.1) (1.05)2.5

r

t

S T D - A S M E P T C LO-ENGL L777

The precision index

= 41.418 X

0757b70 Ob05585 3 8 b M

of the result is

+ 1.75 X

+ 7.10 X

+ 3.74 X

+ 1.20 X

10" = 0.0325

Psh,

... (b)

Theuncertaintiesare

Discussion The UADDand URSS uncertaintiesmaybeinterpreted as follows. For UADD= 0.097 P+ the measurement Pshr f 0.097 PSht will be expected to contain the true value 99 percent of the time.

Similarly, for URSS = 0.072 PS+ the measured PShr? 0.072 Psht will be expected to contain the true value within 99 percent of the time. It is reasonable to assume that theuncertainty for this example is so large as to mask the objective of the test (recall that the numerical values for the independent measurement bias limits andprecisionindiceswereselected at 1 percentsimply to demonstrate unit variations). It is a very simple matter to review the calculations to expose the major uncertainty source. Inspection of equations (a) and (b) for the largest terms immediately indicates the speed measurement. Thus, for example, if the bias limit and precision error for speedmeasurement could be reduced to BU, = 0.001 Ut, and SU, = 0.001 U ,

the uncertaintiesbecome

It is clear that such analysis is of great value in both planning a test and evaluating test results.

163

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APPENDIX D REFERENCES (ThisAppendixisnot

a part of ASME PTC 10-1997.)

(D.8)Samurin, N. A., and M. A.Strite.“Equivalent PerformanceTestingofMulti-SectionCompressors.” ASME 81-GT-150, March 9, 1981.

Maretti, A., M. Giovannini,and P. Nava. “Shop Full Load Testing of Centrifugal Compressors.” December 1982 proceedingsof the 1l t h Turbomachinery Symposium, Texas A&

(D.9)Daugherty, R. L., and J. B. Franzini. “Fluids Mechanics with Engineering Application.” McGraw Hill Book Co.; 1977.

M.

F. J. Wiesner. “A New Appraisal of Reynolds Number Effects onCentrifugal Compressor (D.10)Lee, J. F., and F. W. Sears. ”ThermodynamPerformance.” Transactions of the ASME, pp. ics.” Addison Wesley Publication Co.; 2nd 384-395~Vo~.10l,July1979,~ourna/of€ngiedition, 1963. neering for Power. (D.ll)

Huber, M. L., and M. O. McLinden. “Thermodynamic Properties of R134a (1,1,1r2-Tetrafluoroethane).” July 14-1 7,1992 proceedings, International Refrigeration Conference, Purdue University, West Lafayette, IN.

(D.12) J.E. Lay. “Thermodynamics.” Charles E. Merrill Books, Inc., 2nd printing, 1964.

Simon, H., and A. Bulskamper. On the Evaluation of Reynolds Number and Related Surface Roughness Effects on Centrifugal Compressor Performance Basedon Systematic Experimental Investigations. ASME paper no. 83 GT-118: Transactions of the journal of Engineering for Power, presented March 27, 1983. Nathoo, N. S., and W. G. Gottenberg. “Measuring the Thermal Dynamic Performance of Multi-Stage Compressors Operating onMixed Hydrocarbon Gases.’’ December1981proceedings of the 10th Turbomachinery Symposium, Texas A and M.

(D.13) J. M. Schultz.“ThePolytropicAnalysis of CentrifugalCompressors.”Transactions of the ASME, Series A. Vol. 84, lournal of Engineering for Power. January 1962, p. 69-82 and April 1962, p. 22. (0.14)

M. V. Casey. ”The Effects of Reynolds Number on the Efficiency of Centrifugal CompressorStages.” Transaction of the ASME, April 1985, Vol. 107, p. 541 -548.Journal of Engineering for Gas Turbine and Power.

(D.15) A. Schaffler. ”Experimental and Analytical lnvestigation of the Effects of Reynolds Number and Blade Surface Roughness on Multistage Axial FlowCompressors.” Transactions ofthe ASME, January 1980,Vol. 102, p. 5-1 3,journa/ of Engineering for Power.

Herd, T. C., and E. J.Hipp. “Accuracy Expectations for Gas Turbine and Centrifugal Compressor Performance Testing.” Paper ASME 83GT-128.

(D.16)

Carter, A. D. S., C. E. Moss, G. R. Green, and G. G. Annear. “The Effects on Reynolds Number on the Petformanceof a Single Stage Compressor.” Aeronautical Research Council Reports and Memorandum, 1960; memorandum 31 84, May 1957, U.K. 165

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A. H. Shapiro. “Compressible Fluid Flow.“ The Weld Press Co., 1953.

R. A. Strub. “Influence of the Reynolds Number on the Performance of Centrifugal Compressors.” Final Reportof theWorking Group of the Process Compressor Subcommittee of the International Compressed Air and Allied MachineryCommittee(ICAAMC)Zurich, October 1982.

(D.17)Nathoo, W. S., andW. G. Gottenberg."A New Look at Performance Analysis of Centrifugal Compressors Operating with Mixed Hydrocarbon Gases.', Transactions of the ASME, October 1983, Vol. 105,p. 920-926,lournal of Engineering for Power. (D.18) Skoch, Gary J., and Royce D.Moore. NASA Technical Memorandum 7007/5 AJAA-877745. AVSCOM Technical Report 87-C-21 "Performanceof two 10 Ib/sec centrifugal compressors with different blade and shroud thickness operating over a range of Reynolds Numbers." 23rdJointPropulsion Conference cosponsored by theAIAA, SA€,ASME and ASEE, San Diego, CA, June 29-July 2, 1987. (D.19) Moore, M. J.,and H. S. Shapiro. Fundamentals ofEngineeringThermodynamics. John Wiley & Sons, Inc., 1988. (D.20)

F. Kreith. Principles ofHeat Transfer. lntext Educational Publishers, 3rd edition, 1973.

166

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.

APPENDIX E RATIONALE FOR CALCULATION METHODS (This Appendixisnot a part of ASME PTC 10-1997.)

E.l

PURPOSE

The purpose of this Appendix is to describe the Code problem model, background theory, simplifying assumptions.

E.2

and

PROBLEM MODEL

The ultimate aim of a Codetest is to determinecompressorperformancefor conditions. That is, to determine relationships of the form

Dependentparameter

a given set of

= F (many independentparameters)

Examples of dependentparametersaredischargepressure, head, efficiency,etc.Amongthe independentparameters aregeometry,speed, flow rate, inlet gas state, gas properties,etc.The functional relationship f i s unknown. It is to be determined by the test. Themanyindependentparametersrepresentthespecifiedoperatingconditions.Practicaltest situations are often suchthatoneormoreoftheseparameters is precluded from taking on the desired specified operating condition value. Means must then be sought to determine the effects of thedepartures. One method is to employ dimensional analysis. E.2.1 Dimensional Analysis. The theory of dimensionalanalysisand similarity arediscussed in PTC 19.23, Guidance Manual for Model Testing,andmany fluid dynamics textbooks. In essence it provides a means to reduce the numberofparameters in a problemwhich is expressed in dimensional terms. This is done by appropriate grouping of dimensional terms in dimensionless groups.

E.2.2 Basic Model. Considerationof a simplemathematicalmodel of compressor performance illustrates the general features of dimensional analysis as they are applied in this Code. A simple conventional set of dimensionlessparametersoften applied is given by vp= F1 (4, Mm, Rem,gas properties expressed in dimensionlessterms) F,,= F2 (#J, Mm, Rem, gas properties expressed in dimensionlessterms) p i n = F2f FI

The dimensionless parameters are defined in terms of dimensional variables,

.. . n-

n -f144piVj(F) t7p

=

n-1

hd

167

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- hi

1

" -1

with,

In

Vi Vd

dJ=

W

Rem= ULIv

Mm= U/a gas properties

. . . according to

gastypes

k= C&

Z= pv/RT It is presumed in performing a dimensionalanalysisthat all ofthevariablesaffecting the thermodynamicand fluid dynamicperformanceofthecompressorhavebeen included. If so, different sets ofdimensionalvariables which combine to form identical sets of independent dimensionlessgroups (4, Mm, Rem,gas properties) will haveassociated with them identical valuesfor r], , u, and p i . This basic model is generally accepted to adequately describe the main features of compressor performance. It has the immediate advantage of reducing the number of parameters which must beconsidered in developing a test. But of at leastequalimportance it provides a means of accounting for unavoidable departures from desired specified operating conditions. For example, it may be used to establish an appropriate test speed to compensate for the effect of a test inlet temperature which differs from the specified operating condition temperature.

E.2.3 Allowable Departures. It oftenremains impractical to satisfy all theindependent dimensionless parameter requirements. This situation may be addressed by allowing controlleddepartures in certain independent dimensionless groups. The assumption is that the limits placed upon these departures render the effects upon the dependent parameters either negligible or predictable. The following approach is taken in this Code. E.2.3.1 Mach Number. Mach numberdeparturesareassumed to be of increasing relative importance as the Machine Mach number increases, This is reflected in the allowable departures shown in Table 3.2 or Figs. 3.2 and 3.3. It i s assumed that negligible effect is associated with departure within these limits. E.2.3.2 Cas Properties. Allowable departuresfromtheideal gas lawsfor both the test and the specified gasesare given in Table 3.3. When these limits areexceeded the gas must be treated as real. E.2.3.3Reynolds

Number. The allowable departures in Machine Reynoldsnumberare

given

in Table 3.2 and Fig. 3.4. E.2.3.4Specific VolumeRatio. The preceding allowable independentdimensionlessgroup departuresmay combine to alterthespecificvolume ratio between the compressor inlet and discharge. As a result an additional restriction i s placed upon the volume ratio, r,, as shown in Table 3.2. Theeffectsdue to volume ratio departure areassumed to be negligible when these limits are observed. 168

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STD-ASME P T C 1 0 - E N G L

L997

0'759b70 0b0559Cl 743

E.2.4 Secondary Flow Streams. Thebasiccompressorperformancemodelassumessingle entry and exit flow streams. In actual practice secondary flow streams may enter or leave a compressor section.Examplesaresidestreams and leakages,Thesesecondarystreams give rise to a number of additionaldimensionlessgroups. Each additionalentry flow streamhasassociated with it a flow rateand gasstate, orthreeadditionalindependentvariables. If we use volume flow rate, enthalpy, and density to define thestreams we may form three additional independent dimensionless groups by referencingmainstream values, 771 = (q/qx)m

Tz=

(hh,)rn

773 = (p/px)rn

where x denotesthesidestreamvalue,and m denotesthereferencemainstreamvalue. Theapproachtaken in this Code is to require that the ratio of sidestream to reference flow rates remain within the limits of Table 3.5 or leakagesperpara. 3.3.6. When these limits are observed it i s assumed that the effects upon the dependent dimensionless groups are negligible. No specific restriction is placed upon the density or enthalpy ratios. It is assumed that departures in theseratios will produce negligible effects upon the dependent dimensionless groups. Where thorough mixing of inlet streams beforethecompression is doubtful, this assumptionmay not be valid. In suchcases the parties to the testmay elect by mutual agreement to further restrict theseratios as well. Departures in these secondary dimensionless groups do affect results in the dimensional sense. This is accounted for in the calculation procedure.

E.2.5

Code Model Summary. TheCodeperformancemodelmaybesummarized

qpsp= q p ,Remcorr=

F1

( 4 , -,4 x M,,,,

as follows:

r,, dimensionles gas properties), Remcorr

qm

ppSp= pptRemcorr=

F2

( 4 ,-, 4 x M,,,/

r,, dimensionles gas properties)( Remcorr

4m

For agiven flow coefficient 9, certain departures are allowed in theremainingindependent dimensionlessgroups.Thevolume ratio restriction serves to limit theeffectsofthecombined departures in the otherdimensionlessgroups.Thefirstthreedependentgroupshavethesame form as those in preceding issues of this Code. The fourth, is new to this issue as an explicit parameter. It i s a power coefficient which takes on different forms for energy balance and shaft powermethods. It is related to theotherdependentparameters, but is useful explicitly in a bookkeeping sense for complicated arrangements.

as,,,

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E.3

CODE DIMENSIONLESS PARAMETERS

Appropriateunitsanddimensionalconstants computations.

are requiredfor the system of unitselectedfor

E.3.1 Inlet and Exit Conditions. Thestructureofthe problem model is such that it is necessary to carefully define the inlet and exit conditions which are used in calculating the dimensionless groups.The exit conditions are thestagnation condition at thedischargemeasurementstation. The inlet condition is the stagnation state assigned to the flow stream entering the impeller, and is denoted by the subscript i on thermodynamic properties. For a simple single inlet flow stream this is the stagnation state at the inlet flange. For multiple inlet streams it is the stagnationstate computed from the mixing of the individually determined streams. A standard calculation scheme is given in subpara. E.5. E.3.2

Flow Coefficient. The flow coefficient is defined as wrotor 3

Pi 2

Q

N(;)

where wrotor=mass flow rate entering rotor (mass flow ratecompressed) pi= inlet total density N= rotor rotational speed Dis the blade tip diameter of the 1st impeller for centrifugal compressors Dis the diameter at the leading edge of the 1ststage rotor blade for axial compressors. Themass flow rateenteringthe rotor i s determined giving dueconsideration to all section inlet and outlet flow streams and leakages.

E.3.3 Gas Properties. The physical properties of the gasareexpressed in dimensionless form as theisentropicexponents,compressibilityfactors,andcompressibilityfunctions. E.3.4 Specific Volume Ratio. The specific volume ratio is the ratio of inlet to exit total specific volumes. The inlet specific volume is that assigned to the flow entering the rotor. The exit specific volume is that computed for exit total conditions

where

E.3.5 Ratio of Flow Rates. The ratio of flow rates is the ratio of flow ratesat two points in the flow. It i s given by 170

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where W=

local mass flow rate

P= local total density

and x and y denote different points in the section. The flow rates so definedhavethe units ofvolume flow rate, but donot representactual volume rates of flow since they are defined in terms of total densities. It is assumed that there is aconstantrelationshipbetween these flow rates and actualvolume flow rates between test and specified operating conditions. This is true when the test and specified operating condition local Fluid Mach numbers are equal, and the deviations are assumed negligible when the Code Machine Mach numberdeparture limits areobserved.

E.3.6

MachineMach Number. TheMachine Mach number is givenby Mm = U/a

where

U = first stage impeller blade or rotor blade tip velocity a= acoustic velocity at the For ideal gases

inlet total conditions

For real gases

The Machine Mach number so defined i s not an actual Fluid Mach number. It is nearly directly proportional to actualFluid Mach numberswhentheCodedeparture limits areobserved.The Codedeparture limits shown in Figs. 3.2 and 3.3 for centrifugal and axial compressorsarealso given in equationform in Table E.l.

E.3.7

Machine Reynolds Number. The MachineReynoldsnumber

i s given by

Rem = Ub/v For centrifugal compressors, 6 is the exit width ofthefirst stage impeller in thesectionof interest.For axial compressors, b is the chord length at the tip of thefirst stage rotor blade in the section of interest. The viscosity u is taken for inlet (stagnation) conditions. The Code departure limits shown in Fig. 3.4 for centrifugal compressorsaregiven in equationform in Table E.2. E.3.8

Isentropic Work Coefficient, Theisentropic work coefficient is givenby

171

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S T D - A S M E P T C LO-ENGL L777

0759b70 Ob05593 4 5 2

TABLE E.l MACHINE MACH NO. LIMITS CENTRIFUGAL COMPRESSORS Specified Mach No. Upper

Range Limit

Lower

0-0.214 0.215-0.86 0.86 5 Mm,

Limit

- Mm4 c (-0.25 Mm,, + 0.286)