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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

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

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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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Next chapter

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.