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technische universitt
dortmund
Causes and Effects of Pulsationsin Compressor Systems
A. Brmmer
Chair of Fluid Technology, TU Dortmund
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technische
universitt dortmundContents
1. Definition of pulsations
2. Excitation mechanisms
3. Natural frequencies4. Effects of Pulsations
5. Examples including measures
6. Vision to discuss
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technische
universitt dortmundDefinition and example of pulsations
Pulsations are periodic variations in flow-velocity and pressureabout mean values.
40
50
60
70
80
bar
80 120 160 200 240
mstime
pressure
Pressure-pulsation inside reciprocating cylinder (red)
and just outside pressure valve (black)
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technische
universitt dortmundAcoustic Impedance
Relationship between velocity pulsation and pressure pulsation:
Z = p / c or c = p / Z
Z characteristic acoustic impedance
(Z = * a for plane waves travelling through pipes in one direction)p amplitude of pressure pulsation
c amplitude of velocity pulsation
mass density of gasa speed of sound
Speed of sound
a2 = (dp/d)s = *R*T (ideal gas)
ratio of specific heats (cp/cv)R gas constant
T absolute temperature
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technische
universitt dortmundNext chapter
2. Excitation mechanisms
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technische
universitt dortmundExcitation mechanisms
Main sources of pulsation
positive displacement compressors
(pocket passing frequency and harmonics)
centrifugal compressors
(blade-pass frequency and harmonics)
vortex shedding(flow around a obstruction)
high flow turbulence
(e. g. close to control valves) thermo-acoustic instability
(heat exchanger, combustion chamber)
reference: NEA Group
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technische
universitt dortmundPulsation frequency
compressors (e. g. centrifugal-, screw-, roots-)
f = i*n*rpm
f pulsation frequency
i ith harmonic of pulsation (1,2,3,)
n number of blades or lobes (driven male rotor) or active chambers
rpm compressor speed
vortex shedding
f = St*c / d
f pulsation frequencySt Strouhal number (typical values for obstructions St=0.20.5)
c mean flow velocity
d effective diameter of obstructions
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technische
universitt dortmundExplanation of thermo-acoustic instability
+
=
Tt
t
dt(t)q'(t)p)T/(I 1
If heat be given to the air at the moment of greatest condensation,
or be taken from it at the moment of greatest rarefaction,
the vibration is encouraged.(Rayleigh`s criterion, by 1878)
I Rayleigh integral (index)
I>0 => amplification of a disturbanceI damping of a disturbance
p(t) pressure pulsation
q(t) time-varying component of heat transfer
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technische
universitt dortmundStrength of excitation
In most cases the strength of pulsation excitation is
proportional to the flow-velocity fluctuations of the source!
Examples:- flow velocity fluctuations at pistons or valves of recips
- flow velocity fluctuations at the inlet or outlet of screws
- flow velocity fluctuations at the internal passages of turbo-compressors
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technische
universitt dortmundNext chapter
3. Natural frequencies
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technische
universitt dortmundNatural frequencies
Acoustic natural frequencies
- plane waves (low frequencies)
- cross-wall modes
- three dimensional modes
Structural natural frequencies
- bending modes (low frequencies)
- shell wall natural frequencies- three dimensional modes
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technische
universitt dortmundPlane pulse propagation
pressure
pipe length
pipe
Pulse reflection at closed end:
- closed valve or blind flange
- control valve with high pressure drop
- valves of compressors
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technische
universitt dortmundPlane pulse propagation
pressure
pipe length
pipe
vessel
Pulse reflection at open end:
- pipes connected to vessels or pulsation dampers
- open valves without significant pressure drop- huge cross-sectional jumps
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Pulse reflection and transmission
at a cross-sectional jump
pressure
pipe length
pipe
Cross-sectional jump (m=0.5)
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technische
universitt dortmundSuperposition of left- and right-going waves
pipe
right-going wave
left-going wave
standing wave
fixed point maximum
pipe section
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technische
universitt dortmundPlane wave natural frequencies
closed closed open open
Half wave length mode (standing wave)
fi= i * a / (2 * L)
fi natural frequency of ith multiple of fundamental mode (half wave)a speed of sound
L L
pressure amplitude pressure amplitude
i=1
i=2
i=3
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technische
universitt dortmundPlane wave natural frequencies
closedopen
L
Quarter wave length mode
(standing wave)
fi= (2i-1) * a / (4 * L)
fi natural frequency
of ith multiple of
fundamental mode
a speed of sound
L length of pipe section
pressure amplitude
i=1
i=2
i=3
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technische
universitt dortmundThermo-acoustically induced standing wave
blower
open end open end
movable heat source
reference: Dr. Lenz, KTTER Consulting Engineers KG
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technische
universitt dortmundCross-wall acoustic natural frequency
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technische
universitt dortmundCross-wall acoustic natural frequency
( )( )
d
af
nm,
nm,
=
f(m,n) cross-wall acoustic natural frequency
a speed of sound
d pipe diameter
(m,n)
zeros of Bessel function
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technische
universitt dortmundLateral vibration mode of beams (bending mode)
,...3,2,12
1 2
=
= kEI
lf kk
fk natural frequency of kth bending mode
k frequency-factor (next slice)E modulus of elasticity
I moment of inertia mass of beam per unit length
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technische
universitt dortmundLateral vibration mode of beams (bending mode)
k -valuesboundary conditions
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technische
universitt dortmundShall wall natural frequencies
21
21
/
k)(
E
=
df k
21211
12
12
1//
k
)k(
)k(k
d
s
+
=
fk natural frequency of kth mode
k frequency-factord mean diameter of pipe wall
s pipe wall thickness
E modulus of elasticity
Poissons ratioI moment of inertia
mass of beam per unit lengthk mode number (2,3,4)
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technische
universitt dortmundMaster rule to avoid vibration problems
Avoid coincidences of main excitation frequencies and natural
frequencies (acoustic and structure) of the compressor system !
e. g. reciprocating compressors design according to API 618 (new 5th edition):
- lowest mechanical natural frequency is 2.4 times above the highest
compressor speed
- higher mechanical natural frequencies must have a separation margin of20% to significant acoustic excitation frequencies
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technische
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4. Effects of pulsations
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technische
universitt dortmundEffects of pulsations
Pulsations may cause the following problems:
- compressor and system vibrations
- increased system maintenance
- efficiency losses of the compressor
- flow metering faults
- high noise radiation
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5. Examples including measures
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technische
universitt dortmund
SKD33x
0
20
40
60mm/s eff
0 25 50 75 100 125 150 175 200
Hz
56 mm/s RMS SKD33x
Avoid heavy valves at thin stubs
RMS vibration spectrum at
measuring location SKD33x
measure
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SKS13x
0
10
20
30
40
50mm/s eff
0 25 50 75 100 125 150 175 200
Hz
High vibrations at a reciprocating compressor
41 mm/s RMS
SKS13x
RMS vibration spectrum at
measuring location SKS13x
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technische
universitt dortmund
Kreisgas_KraftPD_x_058.b
0
5
10
15kN
0 50 100 150 200Hz
RMS spectrum of the
acoustic shaking forces
Root cause analysis for high vibrations
p 35.000 N (100 Hz)
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technische
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elastomer supportPulsation damping plate
Remedial measures
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technische
universitt dortmundHigh frequency vibrations at a screw compressor
PD3_0, PD3_120
PD2_45, PD2_270
PD1_0, PD1_120
PD4abs
PS1abs
PS1abs
Pressure measuring locations
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technische
universitt dortmund
0
120
240
360
480
600s
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
kHz
0.0
0.2
0.4
0.6
0.8
1.0bar
0
120
240
360
480
600s
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
kHz
0.0
0.2
0.4
0.6
0.8
1.0bar
0
1
2
3
4bar
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
kHz
0
1
2
3
4bar
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
kHz
PD1_120 PD2_270
Measured pressure pulsations at discharge side
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universitt dortmund
plane wave mode i 1 2 3 4 5 6
open end - closed end fi 52 157 262 367 472 577 Hz
pocket passing frequency: 285 to 585 Hz (variable-speed drive)
speed of sound a= 310 m/s
L = 1462 mm
Root cause analysis (plane wave modes)
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technische
universitt dortmundRoot cause analysis (cross-wall modes)
m= n= 0 1
0 0 2372
1 1140 3302
2 1889 4156
3 2602 4968
inner pipe diameter d = 168.3 mm and wall thickness s = 4.5 mm
Hz
C
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technische
universitt dortmund
0
500
1000
1500
2000
2500
1500 2000 2500 3000
motor rotation speed [1/min]
frequency
[Hz]
1x Drehzahl
1. Pulsation
2. Harm. Pu
3. Harm. Pu
4. Harm. Pu
5. Harm. Pu
6. Harm. PuQuermode (
Quermode (
Quermode (
Quermode (
1. zyl. Scha2. zyl. Scha
3. zyl. Scha
ith pocket passing frequencykth acoustic and structural mode
Coincidence chart
(excitation and cross wall natural frequencies)
1140 Hz
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technische
universitt dortmund
0
120
240
360
480
600s
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
kHz
0.0
0.2
0.4
0.6
0.8
1.0bar
0
120
240
360
480
600s
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
kHz
0.0
0.2
0.4
0.6
0.8
1.0bar
0
1
2
3
4bar
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
kHz
0
1
2
3
4bar
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
kHz
PD1_120 PD2_270
plane wave resonances cross wall mode
Root cause analysis
h i h
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technische
universitt dortmundRemedial measures
cross wall mode
breaker
t h i h
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technische
universitt dortmundDisadvantage of both remedial measures
Additional energy costs due to the power loss of orifice plates!
0
20
40
60
80
100
0 2000 4000 6000 8000 10000
Volume flow [m/h]
powerloss[kW]
1 MPa
5 MPa
p=10 MPa
Power loss calculated for a pressure drop of 0.5% of static pressure p.
technische
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6. Vision to discuss
technischeVi i
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technische
universitt dortmundVision
Design compressor systems without orifice plates as damping device!
Approach:
1. Design pulsation bottles to residual pulsations of 0.5% (1%) ptp.
2. Use Helmholtz resonators (virtual orifice) to attenuate cylinder
nozzle resonances.
technischeH l h lt t ( i t l ifi VO)
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technische
universitt dortmundHelmholtz resonator (virtual orifice VO)
reference: Broerman et al., SwRI at GMRC 2008
technischeVi i
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technische
universitt dortmundVision
Design compressor systems without orifice plates as damping device!
Approach:
1. Design pulsation bottles to residual pulsations of 0.5% (1%) ptp.
2. Use Helmholtz resonators (virtual orifice) to attenuate cylinder
nozzle resonances.
3. For trouble shooting think about a side branch resonator or
control valve instead of an orifice plate.