• Author / Uploaded
• Prashant Agrawal

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Dynaflow Lectures – Reciprocating compressors Acoustics and Mechanical Response Rotterdam, December 10th 2009

Compressor piping vibration analysis

EXAMPLE

Two parts: 1. Acoustical/pulsation study 2. Mechanical response analysis

•Labor intensive modeling •Large number of load cases.

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Sequence of dependence f Acoustics is about propagation of pressure pulsations in piping systems f Source of Pressure pulsations:  Reciprocating compressors and pumps

f Pressure waves are propagated thru the piping system. f Pressure waves are reflected (partly) and transmitted (partly) at geometrical discontinuities f Pressure pulsations generate unbalanced forces that are the source of piping vibration f Sustained vibration may result in fatigue failures Copyright 2009 © Dynaflow Research Group BV

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Agenda

f Elements of Acoustics f Aspects of Mechanical Response f Examples of Mechanical Response

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Reciprocating compressors and pumps inherently produce pulsations in the suction and discharge piping

Double acting cylinder: Piston displacement opens and closes suction and discharge valves

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Actual Piston movement (not purely sinusoidal) due to finite rod length

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Valve openings result in a “Sawtooth” type of gas flow Due the sequence of piston movement and valve opening and closing

The shape of the sawtooth is determined by the rotational speed of the compressor, the geometry of the cylinder and the pressure ratio. Copyright 2009 © Dynaflow Research Group BV

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Flow time history for a single acting cylinder With ideal instantaneous reacting valves

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Resulting Flow Frequency Spectrum (discrete) for single acting cylinder

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Double acting cylinder (slightly unsymmetrical) Head end ≠ cranck end because of the piston rod volume

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Flow Frequency Spectrum (discrete) for double acting unsymmetrical cylinder

Uneven frequency components finite but small due to imperfect symmetry

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Flow pulsations result in pressure pulsations

f Pressure pulsations propagate thru the piping system at the speed of sound f Speed of sound depends on:  Gas composition  Gas Temperature  Gas Density f Pressure/Flow pulsations reflect at geometrical discontinuities f Wave length of propagating wave depending on speed of sound and pulsation frequency c λ= f f Wave reflection and wave interaction results in system acoustical natural frequencies. e.g. for wave length/frequency that match a geometrical length scale standing waves may occur f Presence of Acoustical natural frequencies may result in Acoustical resonance f System will show an acoustical response to an acoustical excitation Copyright 2009 © Dynaflow Research Group BV

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Example of acoustical natural frequency result

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Limited accuracy of acoustical model

f Accuracy of prediction of acoustical natural frequencies relatively large f Error margin relatively small: +/- 5% f Errors controlled by limited number of parameters:  Geometry  Speed of sound  Compressor RPM

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Guidelines for acoustical pulsation levels according API618

f Guidelines for acceptable pulsation levels. f Acceptable levels are related to (inversely proportional to) frequency, pipe diameter and (proportional to) average pressure level f Measures to control pulsation levels:  Geometry changes (controlling acoustical natural frequencies)  Changing pipe diameters to reduce pulsation level  Introduction of damping (orifice plates at location of max oscillating flow)  Introduction of additional volumes with or without internals (creating filters)  Increasing size of bottles (“windkessel” function).

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Pulsation Bottles are a way to reduce pulsations Bottles serve two effects: (1) Surge volume and (2) Filter function 1. SURGE VOLUME

2. FILTER FUNCTION

Pulsation reduction is proportional to surge volume size

Maximum filter function for pulsations with a wave length that matches the bottle length

Minimum filter function (attenuation) for pulsation with a half wave length that matches the bottle length

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Pulsation Bottles located near the compressor

EXAMPLE

COMPRESSORS Inlet scrubbers

Two bottles per compressor

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Multiple pistons per compressor

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Guidelines for Pulsation Bottle sizing 1. SINGLE CYLINDER BOTTLE

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2. MULTICYLINDER BOTTLE

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Acoustical filters

Volumes connected by choke tubes Filter frequency fh:

Filter frequency response

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Agenda

f Elements of Acoustics f Mechanical Response f Example of Mechanical Response

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Mechanical response calculation fifth edition of API 618

f Guidelines for pulsation levels. f If pulsation levels exceed guidelines system may be qualified by means of mechanical response analysis. f Vibration control by mechanical means is a possible option f Large uncertainty margin in mechanics during design (minimum 10-20%) f Acoustic is more accurate (typically +/- 5%) f Preference for reduction of pulsations and thereby shaking forces by means of acoustical measures e.g. filtering (e.g. Helmholtz resonator)

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Accuracy of prediction of mechanical natural frequencies Error margin: 10-20% or many time even larger

f Modeling of Boundary conditions f Modeling of rack structures f Support clearance f Support lift off (thermal), support settling f Support stiffness i.e. stiffness of clamps and restraints f Influence of friction f Nonlinear supports (supports with gaps or single acting supports) f Uncertainties in masses f Differences between “as built” and “design” f Interaction between parallel pipes in pipe racks f Stiffness of concrete sleepers and pedestals Copyright 2009 © Dynaflow Research Group BV

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Many vibration problems related to attached components

Examples: f Valve Actuators f Small bore branch connections f Instrument connections f Level indicators f Stairs & Ladders

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Mechanical properties and pulsations

Rule of thumb: minimum mechanical natural frequency 20% above second compressor harmonic. Question: is this feasible??? Copyright 2009 © Dynaflow Research Group BV

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Mechanical properties and pulsations (2)

f Mechanical resonance difficult to avoid due to uncertainty in mechanical nat. freq.. f Variable speed compressor makes separation virtually impossible. f At resonance condition amplitude limited by damping only (typical damping factors of 2%-3% of critical) f High stiffness results in lower amplitudes. Copyright 2009 © Dynaflow Research Group BV

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Application of filters in combination with high mechanical natural frequencies looks ideal

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Agenda

f Acoustics f Mechanical Response f Example of Mechanical Response analysis in design

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Example: Mechanical Response of NAM Oude Pekela Compressor plant

EXAMPLE

Air cooler A-174

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Acoustical results of suction piping

EXAMPLE

Focal area

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Unbalanced shaking forces in [kN peak to peak] per pipe section and per compressor harmonic

EXAMPLE

Nodal correspondence: 3360-3430 = C2 node 1085 3350-3360 = C2 node 1070 3000-3350 = C2 node 1033

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Acoustical results of interstage piping

EXAMPLE

Focal area

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Unbalanced shaking forces in [kN peak to peak] per pipe section and per compressor harmonic

EXAMPLE

Nodal correspondence: 3330-3340 = C2 node 5060 3340-3350 = C2 node 5076 3380-3350 = C2 node 5097

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EXAMPLE

Summary of shaking forces Conservative selection: maximum value of all harmonics

Acoustic pipe section

Caesar II node number

Force [N.] [peak-peak]

Force [N.] [0-peak]

3330-3340

5060

131

65.5

3340-3350

5076

355

177.5

3350-3380

5097

815

407.5

3360-3430

1085

535

267.5

3350-3360

1070

240

120

3000-3350

1033

81

40.5

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Two-stage compression combined model

EXAMPLE

Suction (partly), Interstage (upto cooler), Discharge (complete)

Compressor discharge bottles Interstage Line

Additional discharge volumes to reduce pulsation levels in remaining piping

Discharge Line Copyright 2009 © Dynaflow Research Group BV

Aircooler E-174 nozzles

Suction Line

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Additional discharge volumes

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EXAMPLE

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Harmonic frequency assessment in CAESAR II

EXAMPLE

Sweep from 4 -56 Hz with 1 Hz steps

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Harmonic forces are inserted in the model

EXAMPLE

Conservative Shaking force set taken from acoustic pulsation report

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Maximum dynamic stress amplitude calculation

EXAMPLE

Max amplitude 6 MPa

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At a stress amplitude level of 6 MPa the number of cycles is > 1011

EXAMPLE

Carbon Steel Fatigue Curve in the high cycle range

6 MPa

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Agenda

f Acoustics f Mechanical Response f Example of Mechanical Response analysis “as built”

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Issue: Unacceptably high vibration level in compressor suction piping

EXAMPLE

In 5 steps to solution

1. Vibration Measurements: identification of main contributions in frequency domain 2. Acoustical Resonance: verification of acoustical natural frequencies 3. Mechanical Resonance: verification of mechanical natural frequencies 4. Identification of source of vibration problem 5. Modification proposal

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Compressor plant

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Structure and support details around the compressor (I)

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Structure and support details around the compressor (II)

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Details of the compressor location

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EXAMPLE

Step 1. Vibration Measurements

120.00

33 Hz 66 Hz

49 Hz

100.00

16 Hz

99 Hz 83 Hz

Amplitude (dB)

80.00

60.00

40.00

20.00

0.00 0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0

Frequency (Hz)

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Intermediate conclusion from step 1

f Vibrations are at compressor harmonics f Vibrations must be result of f 1 Acoustical resonance or f 2 Mechanical resonance or f 3 High pulsation forces without resonance (compressor bottle sizing problem)

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Step 2. Acoustical natural frequencies & Compressor Harmonics

EXAMPLE

250

16 Hz 200

Amplitude

150

100

50

0 10.00

20.00

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30.00

40.00

50.00

60.00

Frequency (Hz)

70.00

80.00

90.00

100.00

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Intermediate conclusion from step 2

EXAMPLE

f Maybe near-to-resonance condition at first compressor harmonic (16.5 Hz.) f No further acoustical resonance f Vibration peak at 16.5 Hz, most probably is due high shaking forces as a result of near resonant condition f The other vibration peaks must be the result of: 1

Mechanical resonance or

2

High pulsation forces without resonance (compressor bottle sizing problem)

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EXAMPLE

Step 3. Vibration Measurements & Calculated Mechanical Natural Frequencies (Search for Mechanical Resonance)

100.00

66 Hz

90.00

83 Hz

33 Hz

80.00

Amplitude (dB)

70.00 60.00 50.00 40.00 30.00 20.00

Purple vertical lines represent pipe system natural frequencies

10.00 0.00 0.0

10.0

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20.0

30.0

40.0

50.0 Frequency (Hz)

60.0

70.0

80.0

90.0

100.0

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Conclusion from step 3 & Identification of cause of vibration problem f Apparently there is mechanical resonance at 33 Hz and 66 Hz and near mechanical resonance at 83 Hz f No mechanical resonance condition at the first compressor harmonic (16.5 Hz.) and at 49 Hz. and 99 Hz f The high vibration levels 33 Hz, 66 Hz and 83 Hz are of mechanical nature f The high vibration level at 16.5 Hz most probably is an acoustical resonance problem f The high vibration level at 49 Hz and 99 Hz. must be the result of High pulsation forces without resonance (compressor bottle sizing problem)

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Step 4. Identification of cause of vibration problem

EXAMPLE

f The high vibration level at 16.5 Hz most probably is an acoustical resonance problem. f Apparently there is mechanical resonance at 33 Hz and 66 Hz and near mechanical resonance at 83 Hz. f The high vibration levels 33 Hz, 66 Hz and 83 Hz are of mechanical nature f No mechanical resonance condition at the first compressor harmonic (16.5 Hz.) and at 49 Hz. and 99 Hz. f The high vibration level at 49 Hz and 99 Hz. must be the result of:  High pulsation forces without resonance (compressor bottle sizing problem)

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Examination of mechanical behavior

EXAMPLE

Example of 66 Hz. mode shape

Large amplitude movement in suction manifold

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Step 5. Modifications

EXAMPLE

1. The high vibration levels 33 Hz, 66 Hz and 83 Hz are of mechanical nature and need a mechanical solution  Better supporting  Improved support stiffness 2. The high vibration level at 16.5 Hz is due to acoustical resonance and needs an acoustical solution, I.e. different bottles and/or orifice plates to introduce more damping 3. The high vibration level at 49 Hz and 99 Hz. are the result of high pulsation forces without resonance and must be resolved by compressor bottle (re)sizing.

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Modified structure implemented and connected to attached piping AS BUILT SITUATION

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EXAMPLE

IMPROVED AND IMPLEMENTED SITUATION

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Conclusion from example

EXAMPLE

f Compressor vibration problems many cases are of a mixed nature f Part is mechanical f Part is acoustical f Each category requires a different approach and result in different solutions f Not all vibration problems can be solved by mechanical measures.

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