Causes and Effects of Pulsations in Compressor...
Transcript of Causes and Effects of Pulsations in Compressor...
technische universität dortmund
Causes and Effects of Pulsationsin Compressor Systems
A. BrümmerChair of Fluid Technology, TU Dortmund
- 2 -
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
- 3 -
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)
- 4 -
technische universität dortmund
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
- 5 -
technische universität dortmund
Next chapter
2. Excitation mechanisms
- 6 -
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
- 7 -
technische universität dortmund
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
- 8 -
technische universität dortmund
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
- 9 -
technische universität dortmund
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
- 10 -
technische universität dortmund
Next chapter
3. Natural frequencies
- 11 -
technische universität dortmund
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
- 12 -
technische universität dortmund
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
- 13 -
technische universität dortmund
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
- 14 -
technische universität dortmund
Pulse reflection and transmission at a cross-sectional jump
pressure
pipe length
pipe
Cross-sectional jump (m=0.5)
- 15 -
technische universität dortmund
Superposition of left- and right-going waves
pipe
right-going wave
left-going wave
“standing wave”
fixed point maximum
pipe section
- 16 -
technische universität dortmund
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
- 17 -
technische universität dortmund
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
- 18 -
technische universität dortmund
Thermo-acoustically induced “standing wave“
blower
open end open end
movable heat source
reference: Dr. Lenz, KÖTTER Consulting Engineers KG
- 19 -
technische universität dortmund
Cross-wall acoustic natural frequency
- 20 -
technische universität dortmund
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
- 21 -
technische universität dortmund
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
- 22 -
technische universität dortmund
Lateral vibration mode of beams (bending mode)
λk -valuesboundary conditions
- 23 -
technische universität dortmund
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…)
- 24 -
technische universität dortmund
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
- 25 -
technische universität dortmund
Next chapter
4. Effects of pulsations
- 26 -
technische universität dortmund
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
- 27 -
technische universität dortmund
Next chapter
5. Examples including measures
- 28 -
technische universität 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
- 29 -
technische universität dortmund
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
- 30 -
technische universität dortmund
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)
- 31 -
technische universität dortmund
elastomer support Pulsation damping plate
Remedial measures
- 32 -
technische universität dortmund
High frequency vibrations at a screw compressor
PD3_0, PD3_120PD2_45, PD2_270PD1_0, PD1_120
PD4abs
PS1abs
PS1abs
Pressure measuring locations
- 33 -
technische universität dortmund
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
Measured pressure pulsations at discharge side
- 34 -
technische universität dortmund
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)
- 35 -
technische universität dortmund
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
- 36 -
technische universität dortmund
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
- 37 -
technische universität dortmund
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
- 38 -
technische universität dortmund
Remedial measures
cross wall mode breaker
- 39 -
technische universität dortmund
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.
- 40 -
technische universität dortmund
Next chapter
6. Vision to discuss
- 41 -
technische universität dortmund
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.
- 42 -
technische universität dortmund
Helmholtz resonator (virtual orifice VO)
reference: Broerman et al., SwRI at GMRC 2008
- 43 -
technische universität dortmund
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.