Pulsation Course Bruemmer

8/21/2019 Pulsation Course Bruemmer

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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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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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universitt dortmund

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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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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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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universitt 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


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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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universitt dortmund

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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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.

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Pulsation Course Bruemmer