dynaflow lectures – reciprocating compressors … shape of the sawtooth is determined by the...

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

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EXAMPLECompressor piping vibration analysis

Two parts:

1. Acoustical/pulsation study

2. Mechanical response analysis

•Labor intensive modeling

•Large number of load cases.

Copyright 2009 © Dynaflow Research Group BV

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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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Elements of Acoustics

Aspects of Mechanical Response

Examples of Mechanical Response

Agenda


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

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Double acting cylinder:Piston displacement opens and closes

suction and discharge valves


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

Copyright 2009 © Dynaflow Research Group BV 7

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

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The shape of the sawtooth is determined by the rotational speed of the compressor, the geometry of the cylinder and the pressure ratio.


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


Resulting Flow Frequency Spectrum (discrete) for single acting cylinder


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


Uneven frequency components finite but small due to imperfect symmetry

Flow Frequency Spectrum (discrete) for double acting unsymmetrical cylinder


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


Example of acoustical natural frequency result


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


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).


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

18Copyright 2009 © Dynaflow Research Group BV

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EXAMPLEPulsation Bottles located near the compressor

Two bottles per compressor

Multiple pistons per compressor

Inlet scrubbers

COMPRESSORS


Guidelines for Pulsation Bottle sizing

1. SINGLE CYLINDER BOTTLE 2. MULTICYLINDER BOTTLE


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


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)


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

Many vibration problems related to attached components

Examples:Valve Actuators

Small bore branch connections

Instrument connections

Level indicators

Stairs & Ladders


Mechanical properties and pulsations

Rule of thumb: minimum mechanical natural frequency 20% above second compressor harmonic. Question: is this feasible???


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

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


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Acoustics

Mechanical Response

Example of Mechanical Response analysis in design

Agenda


EXAMPLE

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Example: Mechanical Response of NAM Oude Pekela Compressor plant Air cooler A-174


Focal area

EXAMPLEAcoustical results of suction piping


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


Focal area

EXAMPLEAcoustical results of interstage piping


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


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


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


Additional discharge volumes EXAMPLE


EXAMPLEHarmonic frequency assessment in CAESAR IISweep from 4 -56 Hz with 1 Hz steps


Harmonic forces are inserted in the modelConservative Shaking force set taken from acoustic pulsation report

EXAMPLE


EXAMPLEMaximum dynamic stress amplitude calculationMax amplitude 6 MPa


Carbon Steel Fatigue Curve in the high cycle range

EXAMPLEAt a stress amplitude level of 6 MPa the number ofcycles is > 1011

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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


Compressor plant


Structure and support details around the compressor (II)


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


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)


1

2

3

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


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


END


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