dynaflow lectures – reciprocating compressors … shape of the sawtooth is determined by the...
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Dynaflow Lectures – Reciprocating compressors Acoustics and Mechanical ResponseRotterdam, December 10th 2009
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2
EXAMPLECompressor piping vibration analysis
Two parts:
1. Acoustical/pulsation study
2. Mechanical response analysis
•Labor intensive modeling
•Large number of load cases.
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3
Sequence of dependence
Acoustics is about propagation of pressure pulsations in piping systems
Source of Pressure pulsations:Reciprocating compressors and pumps
Pressure waves are propagated thru the piping system.
Pressure waves are reflected (partly) and transmitted (partly) at geometrical discontinuities
Pressure pulsations generate unbalanced forces that are the source of piping vibration
Sustained vibration may result in fatigue failures
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4
Elements of Acoustics
Aspects of Mechanical Response
Examples of Mechanical Response
Agenda
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Reciprocating compressors and pumps inherently produce pulsations in the suction and discharge piping
5
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
8
The shape of the sawtooth is determined by the rotational speed of the compressor, the geometry of the cylinder and the pressure ratio.
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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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Uneven frequency components finite but small due to imperfect symmetry
Flow Frequency Spectrum (discrete) for double acting unsymmetrical cylinder
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Flow pulsations result in pressure pulsations
Pressure pulsations propagate thru the piping system at the speed of sound
Speed of sound depends on:
Gas composition
Gas Temperature
Gas Density
Pressure/Flow pulsations reflect at geometrical discontinuities
Wave length of propagating wave depending on speed of sound and pulsation frequency
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
Presence of Acoustical natural frequencies may result in Acoustical resonance
System will show an acoustical response to an acoustical excitation
fc
=λ
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Example of acoustical natural frequency result
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Limited accuracy of acoustical model
Accuracy of prediction of acoustical natural frequencies relatively large
Error margin relatively small: +/- 5%
Errors controlled by limited number of parameters:
Geometry
Speed of sound
Compressor RPM
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Guidelines for acoustical pulsation levels according API618
Guidelines for acceptable pulsation levels.
Acceptable levels are related to (inversely proportional to) frequency, pipe
diameter and (proportional to) average pressure level
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 pulsationsBottles serve two effects: (1) Surge volume and (2) Filter function
1. SURGE VOLUME 2. FILTER FUNCTION
Maximum filter function for pulsationswith a wave length that matches thebottle length
Minimum filter function (attenuation)for pulsation with a half wave lengththat matches the bottle length
Pulsation reduction is proportional tosurge volume size
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EXAMPLEPulsation Bottles located near the compressor
Two bottles per compressor
Multiple pistons per compressor
Inlet scrubbers
COMPRESSORS
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Guidelines for Pulsation Bottle sizing
1. SINGLE CYLINDER BOTTLE 2. MULTICYLINDER BOTTLE
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Acoustical filters
Volumes connected by choke tubes
Filter frequency fh:
Filter frequency response
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Elements of Acoustics
Mechanical Response
Example of Mechanical Response
Agenda
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Mechanical response calculation fifth edition of API 618
Guidelines for pulsation levels.
If pulsation levels exceed guidelines system may be qualified by means of
mechanical response analysis.
Vibration control by mechanical means is a possible option
Large uncertainty margin in mechanics during design (minimum 10-20%)
Acoustic is more accurate (typically +/- 5%)
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
Modeling of Boundary conditions
Modeling of rack structures
Support clearance
Support lift off (thermal), support settling
Support stiffness i.e. stiffness of clamps and restraints
Influence of friction
Nonlinear supports (supports with gaps or single acting supports)
Uncertainties in masses
Differences between “as built” and “design”
Interaction between parallel pipes in pipe racks
Stiffness of concrete sleepers and pedestalsCopyright 2009 © Dynaflow Research Group BV 24
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Many vibration problems related to attached components
Examples:Valve Actuators
Small bore branch connections
Instrument connections
Level indicators
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???
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Mechanical properties and pulsations (2)
Mechanical resonance difficult to avoid due to uncertainty in mechanical nat. freq..
Variable speed compressor makes separation virtually impossible.
At resonance condition amplitude limited by damping only (typical damping factors
of 2%-3% of critical)
High stiffness results in lower amplitudes.Copyright 2009 © Dynaflow Research Group BV 27
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Application of filters in combination with high mechanical natural frequencies looks ideal
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29
Acoustics
Mechanical Response
Example of Mechanical Response analysis in design
Agenda
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EXAMPLE
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Example: Mechanical Response of NAM Oude Pekela Compressor plant Air cooler A-174
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Focal area
EXAMPLEAcoustical results of suction piping
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Nodal correspondence:
3360-3430 = C2 node 10853350-3360 = C2 node 10703000-3350 = C2 node 1033
EXAMPLE
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Unbalanced shaking forces in [kN peak to peak] perpipe section and per compressor harmonic
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Focal area
EXAMPLEAcoustical results of interstage piping
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Nodal correspondence:
3330-3340 = C2 node 50603340-3350 = C2 node 50763380-3350 = C2 node 5097
EXAMPLEUnbalanced shaking forces in [kN peak to peak] perpipe section and per compressor harmonic
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Summary of shaking forcesConservative 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
EXAMPLE
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EXAMPLE
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Two-stage compression combined modelSuction (partly), Interstage (upto cooler), Discharge (complete)
Aircooler E-174 nozzles
Suction LineDischarge Line
Additional discharge volumesto reduce pulsation levels in remaining piping
Compressor discharge bottles
Interstage Line
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Additional discharge volumes EXAMPLE
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EXAMPLEHarmonic frequency assessment in CAESAR IISweep from 4 -56 Hz with 1 Hz steps
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Harmonic forces are inserted in the modelConservative Shaking force set taken from acoustic pulsation report
EXAMPLE
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EXAMPLEMaximum dynamic stress amplitude calculationMax amplitude 6 MPa
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Carbon Steel Fatigue Curve in the high cycle range
EXAMPLEAt a stress amplitude level of 6 MPa the number ofcycles is > 1011
41
6 MPa
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Acoustics
Mechanical Response
Example of Mechanical Response analysis “as built”
Agenda
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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
EXAMPLEIssue: Unacceptably high vibration level in compressor suction pipingIn 5 steps to solution
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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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0.00
20.00
40.00
60.00
80.00
100.00
120.00
0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0
Frequency (Hz)
Am
plitu
de (d
B)
66 Hz49 Hz
33 Hz
16 Hz
99 Hz
83 Hz
EXAMPLEStep 1. Vibration Measurements
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Intermediate conclusion from step 1
Vibrations are at compressor harmonics
Vibrations must be result of
Acoustical resonance
or
Mechanical resonance
or
High pulsation forces without resonance (compressor bottle sizing problem)
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1
2
3
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50
0
50
100
150
200
250
10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
Frequency (Hz)
Ampl
itude
16 Hz
EXAMPLEStep 2. Acoustical natural frequencies & Compressor Harmonics
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Maybe near-to-resonance condition at first compressor harmonic (16.5 Hz.)
No further acoustical resonance
Vibration peak at 16.5 Hz, most probably is due high shaking forces as a result of near resonant condition
The other vibration peaks must be the result of:
Mechanical resonance
or
High pulsation forces without resonance (compressor bottle sizing problem)
EXAMPLEIntermediate conclusion from step 2
1
2
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0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
100.00
0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0
Frequency (Hz)
Am
plitu
de (d
B)
66 Hz
33 Hz 83 Hz
EXAMPLEStep 3. Vibration Measurements & Calculated Mechanical Natural Frequencies (Search for Mechanical Resonance)
Purple vertical lines represent pipe system natural frequencies
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Conclusion from step 3 & Identification of cause of vibration problem
Apparently there is mechanical resonance at 33 Hz and 66 Hz and near mechanical resonance at 83 Hz
No mechanical resonance condition at the first compressor harmonic (16.5 Hz.) and at 49 Hz. and 99 Hz
The high vibration levels 33 Hz, 66 Hz and 83 Hz are of mechanical nature
The high vibration level at 16.5 Hz most probably is an acoustical resonance problem
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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The high vibration level at 16.5 Hz most probably is an acoustical resonance problem.
Apparently there is mechanical resonance at 33 Hz and 66 Hz and near mechanical resonance at 83 Hz.
The high vibration levels 33 Hz, 66 Hz and 83 Hz are of mechanical nature
No mechanical resonance condition at the first compressor harmonic (16.5 Hz.) and at 49 Hz. and 99 Hz.
The high vibration level at 49 Hz and 99 Hz. must be the result of:High pulsation forces without resonance (compressor bottle sizing problem)
EXAMPLEStep 4. Identification of cause of vibration problem
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Large amplitude movement in suction manifold
EXAMPLEExamination of mechanical behavior Example of 66 Hz. mode shape
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1. The high vibration levels 33 Hz, 66 Hz and 83 Hz are of mechanical nature and need a mechanical solution
Better supportingImproved 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.
EXAMPLEStep 5. Modifications
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EXAMPLEModified structure implemented and connected to attached piping
AS BUILT SITUATION IMPROVED AND IMPLEMENTED SITUATION
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Compressor vibration problems many cases are of a mixed nature
Part is mechanical
Part is acoustical
Each category requires a different approach and result in different solutions
Not all vibration problems can be solved by mechanical measures.
EXAMPLEConclusion from example
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