causes and effects of pulsations in compressor...
TRANSCRIPT
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Causes and Effects of Pulsationsin Compressor Systems
A. BrümmerChair of Fluid Technology, TU Dortmund
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technische universität dortmundContents
1. Definition of pulsations
2. Excitation mechanisms
3. Natural frequencies
4. Effects of Pulsations
5. Examples including measures
6. Vision to discuss
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technische universität dortmundDefinition and example of pulsations
Pulsations are periodic variations in flow-velocity and pressure about mean values.
40
50
60
70
80
bar
80 120 160 200 240mstime
pressure
Pressure-pulsation inside reciprocating cylinder (red) and just outside pressure valve (black)
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Acoustic Impedance
Relationship between velocity pulsation and pressure pulsation:
Z = p / c or c = p / Z
Z characteristic acoustic impedance (Z = ρ* a for plane waves travelling through pipes in one direction)
p amplitude of pressure pulsationc amplitude of velocity pulsationρ mass density of gasa speed of sound
Speed of sound
a2 = (dp/dρ)s = κ*R*T (ideal gas)
κ ratio of specific heats (cp/cv) R gas constantT absolute temperature
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Next chapter
2. Excitation mechanisms
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technische universität 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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Pulsation frequency
compressors (e. g. centrifugal-, screw-, roots-)f = i*n*rpm
f pulsation frequencyi ith harmonic of pulsation (1,2,3,…)n number of blades or lobes (driven male rotor) or active chambersrpm compressor speed
vortex sheddingf = St*c / d
f pulsation frequencySt Strouhal number (typical values for obstructions St=0.2–0.5)c mean flow velocity d effective diameter of obstructions
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Explanation 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<0 => damping of a disturbance
p(t) pressure pulsationq’(t) time-varying component of heat transfer
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Strength 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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Next chapter
3. Natural frequencies
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Natural 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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Plane 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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Plane pulse propagation
pressure
pipe length
pipe
vesselPulse 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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Superposition of left- and right-going waves
pipe
right-going wave
left-going wave
“standing wave”
fixed point maximum
pipe section
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Plane 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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Plane 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 soundL length of pipe section
pressure amplitude
i=1
i=2
i=3
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Thermo-acoustically induced “standing wave“
blower
open end open end
movable heat source
reference: Dr. Lenz, KÖTTER Consulting Engineers KG
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Cross-wall acoustic natural frequency
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Cross-wall acoustic natural frequency
( )( )
dπaβ
f nm,nm, ⋅
⋅=
f(m,n) cross-wall acoustic natural frequencya speed of soundd pipe diameterβ(m,n) zeros of Bessel function
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Lateral vibration mode of beams (bending mode)
,...3,2,121 2
=⎟⎠⎞
⎜⎝⎛= kEI
lf k
k µλ
π
fk natural frequency of kth bending modeλk frequency-factor (next slice)E modulus of elasticityI moment of inertiaµ mass of beam per unit length
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Lateral vibration mode of beams (bending mode)
λk -valuesboundary conditions
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Shall wall natural frequencies
21
21
/
k )(E
⎟⎟⎠
⎞⎜⎜⎝
⎛−⋅
=νµ
λdπ
f k
2121 112
121
//k²)k(
)²k(kds
+−
=λ
fk natural frequency of kth modeλk frequency-factord mean diameter of pipe walls pipe wall thicknessE modulus of elasticityν Poisson’s ratioI moment of inertiaµ mass of beam per unit lengthk mode number (2,3,4…)
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Master 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 of 20% to significant acoustic excitation frequencies
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Next chapter
4. Effects of pulsations
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Effects 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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Next chapter
5. Examples including measures
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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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Kreisgas_KraftPD_x_058.b
0
5
10
15kN
0 50 100 150 200
Hz
RMS spectrum of the acoustic shaking forces
Root cause analysis for high vibrations
p 35.000 N (100 Hz)
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elastomer support Pulsation damping plate
Remedial measures
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High frequency vibrations at a screw compressor
PD3_0, PD3_120PD2_45, PD2_270PD1_0, PD1_120
PD4abs
PS1abs
PS1abs
Pressure measuring locations
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0
120
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360
480
600s
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0kHz
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 4.0kHz
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 4.0kHz
0
1
2
3
4bar
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0kHz
PD1_120 PD2_270
Measured pressure pulsations at discharge side
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plane wave mode i 1 2 3 4 5 6open 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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Root cause analysis (cross-wall modes)
m= n= 0 10 0 23721 1140 33022 1889 41563 2602 4968
inner pipe diameter d = 168.3 mm and wall thickness s = 4.5 mm
Hz
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0
500
1000
1500
2000
2500
1500 2000 2500 3000motor rotation speed [1/min]
frequ
ency
[Hz]
.
1x Drehzahl1. Pulsation2. Harm. Pu3. Harm. Pu4. Harm. Pu5. Harm. Pu6. Harm. PuQuermode (1Quermode (2Quermode (3Quermode (01. zyl. Scha2. zyl. Scha3. zyl. Scha
ith pocket passing frequencykth acoustic and structural mode
Coincidence chart (excitation and cross wall natural frequencies)
1140 Hz
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0
120
240
360
480
600s
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0kHz
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 4.0kHz
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 4.0kHz
0
1
2
3
4bar
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0kHz
PD1_120 PD2_270
plane wave resonances cross wall mode
Root cause analysis
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Remedial measures
cross wall mode breaker
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Disadvantage 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 [m³/h]
pow
er lo
ss [k
W]
1 MPa
5 MPa
p=10 MPa
Power loss calculated for a pressure drop of 0.5% of static pressure p.
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6. Vision to discuss
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Vision
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.
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Helmholtz resonator (virtual orifice VO)
reference: Broerman et al., SwRI at GMRC 2008
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Vision
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.