Causes and Effects of Pulsations in Compressor

Transcription

technische universität
dortmund
Causes and Effects of Pulsations
in Compressor Systems
A. Brümmer
Chair of Fluid Technology, TU Dortmund
technische
universität dortmund
Contents
1. Definition of pulsations
2. Excitation mechanisms
3. Natural frequencies
4. Effects of Pulsations
5. Examples including measures
6. Vision to discuss
-2-
technische
Definition and example of pulsations
Pulsations are periodic variations in flow-velocity and pressure
about mean values.
Pressure-pulsation inside reciprocating cylinder (red)
and just outside pressure valve (black)
bar
80
pressure
70
60
50
40
80
120
160
200
240
time
ms
-3-
technische
Acoustic Impedance
Relationship between velocity pulsation and pressure pulsation:
Z=p/c
Z
p
c
ρ
a
or
c=p/Z
characteristic acoustic impedance
(Z = ρ* a for plane waves travelling through pipes in one direction)
amplitude of pressure pulsation
amplitude of velocity pulsation
mass density of gas
speed of sound
Speed of sound
a2 = (dp/dρ)s = κ*R*T (ideal gas)
κ
R
T
ratio of specific heats (cp/cv)
gas constant
absolute temperature
-4-
technische
Next chapter
2. Excitation mechanisms
-5-
Excitation mechanisms
technische
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
-6-
Pulsation frequency
technische
compressors (e. g. centrifugal-, screw-, roots-)
f = i*n*rpm
f
i
n
rpm
pulsation frequency
ith harmonic of pulsation (1,2,3,…)
number of blades or lobes (driven male rotor) or active chambers
compressor speed
vortex shedding
f = St*c / d
f
St
c
d
pulsation frequency
Strouhal number (typical values for obstructions St=0.2–0.5)
mean flow velocity
effective diameter of obstructions
-7-
Explanation of thermo-acoustic instability
technische
“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)
t+T
I = ( 1 / T ) ∫ p (t) q' (t) dt
t
I
p(t)
q’(t)
Rayleigh integral (index)
I>0 => amplification of a disturbance
I<0 => damping of a disturbance
pressure pulsation
time-varying component of heat transfer
-8-
Strength of excitation
technische
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
-9-
technische
Next chapter
3. Natural frequencies
- 10 -
Natural frequencies
technische
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
- 11 -
technische
Plane pulse propagation
Pulse reflection at „closed end“:
- closed valve or blind flange
- control valve with high pressure drop
- valves of compressors
pipe
pressure
pipe length
- 12 -
technische
Plane pulse propagation
Pulse reflection at „open end“:
- pipes connected to vessels or pulsation dampers
vessel
- open valves without significant pressure drop
- huge cross-sectional jumps
pipe
pressure
pipe length
- 13 -
Pulse reflection and transmission
at a cross-sectional jump
technische
Cross-sectional jump (m=0.5)
pipe
pressure
pipe length
- 14 -
Superposition of left- and right-going waves
technische
pipe
pipe section
right-going wave
left-going wave
“standing wave”
fixed point
maximum
- 15 -
technische
Plane wave natural frequencies
Half wave length mode (standing wave)
fi= i * a / (2 * L)
fi
a
closed
natural frequency of ith multiple of fundamental mode (half wave)
speed of sound
pressure amplitude
closed
open
pressure amplitude
open
i=1
i=2
i=3
L
L
- 16 -
technische
Plane wave natural frequencies
open
Quarter wave length mode
(standing wave)
pressure amplitude
closed
i=1
fi= (2i-1) * a / (4 * L)
fi
a
L
natural frequency
of ith multiple of
fundamental mode
speed of sound
length of pipe section
i=2
i=3
L
- 17 -
Thermo-acoustically induced “standing wave“
technische
movable heat source
blower
open end
open end
reference: Dr. Lenz, KÖTTER Consulting Engineers KG
- 18 -
Cross-wall acoustic natural frequency
technische
- 19 -
Cross-wall acoustic natural frequency
f(m,n ) =
β (m,n ) ⋅ a
π ⋅d
f(m,n)
a
d
β(m,n)
technische
cross-wall acoustic natural frequency
speed of sound
pipe diameter
zeros of Bessel function
- 20 -
Lateral vibration mode of beams (bending mode)
1
fk =
2π
fk
λk
E
I
µ
⎛ λk ⎞
⎜ ⎟
⎝ l ⎠
2
EI
µ
technische
k = 1, 2, 3,...
natural frequency of kth bending mode
frequency-factor (next slice)
modulus of elasticity
moment of inertia
mass of beam per unit length
- 21 -
Lateral vibration mode of beams (bending mode)
boundary conditions
technische
λk -values
- 22 -
technische
Shall wall natural frequencies
λk ⎛
1/ 2
⎞
E
⎜
⎟
fk =
2 ⎟
⎜
π ⋅ d ⎝ µ ( 1 −ν ) ⎠
1 2s k( k ² − 1 )
λk = 1 / 2
12
d ( 1 + k ²)1 / 2
fk
λk
d
s
E
ν
I
µ
k
natural frequency of kth mode
frequency-factor
mean diameter of pipe wall
pipe wall thickness
modulus of elasticity
Poisson’s ratio
moment of inertia
mass of beam per unit length
mode number (2,3,4…)
- 23 -
Master rule to avoid vibration problems
technische
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
- 24 -
technische
Next chapter
4. Effects of pulsations
- 25 -
Effects of pulsations
technische
Pulsations may cause the following problems:
- compressor and system vibrations
- increased system maintenance
- efficiency losses of the compressor
- flow metering faults
- high noise radiation
- 26 -
technische
Next chapter
5. Examples including measures
- 27 -
technische
Avoid heavy valves at thin stubs
RMS vibration spectrum at
measuring location SKD33x
SKD33x
mm/s eff
60
SKD33x
56 mm/s RMS
40
measure
20
0
0
25
50
75
100
125
150
175
200
Hz
- 28 -
technische
High vibrations at a reciprocating compressor
RMS vibration spectrum at
measuring location SKS13x
SKS13x
mm/s eff
50
41 mm/s RMS
40
SKS13x
30
20
10
0
0
25
50
75
100
125
150
175
200
Hz
- 29 -
technische
Root cause analysis for high vibrations
RMS spectrum of the
acoustic shaking forces
p
Kreisgas_KraftPD_x_058.b
35.000 N (100 Hz)
kN
15
10
5
0
0
50
100
150
200
Hz
- 30 -
Remedial measures
elastomer support
technische
Pulsation damping plate
- 31 -
High frequency vibrations at a screw compressor
technische
Pressure measuring locations
PS1abs
PS1abs
PD1_0, PD1_120
PD2_45, PD2_270
PD4abs
PD3_0, PD3_120
- 32 -
technische
Measured pressure pulsations at discharge side
PD1_120
PD2_270
bar
4
bar
4
3
3
2
2
1
1
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
kHz
s
600
kHz
bar
1.0
s
600
bar
1.0
480
0.8
480
0.8
360
0.6
360
0.6
240
0.4
240
0.4
120
0.2
120
0.2
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0.0
4.0
kHz
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.0
- 334.0
3.5
kHz
technische
Root cause analysis (plane wave modes)
pocket passing frequency: 285 to 585 Hz (variable-speed drive)
speed of sound a= 310 m/s
plane wave mode i
open end - closed end fi
1
52
2
157
3
262
4
367
5
472
6
577
Hz
L = 1462 mm
- 34 -
technische
Root cause analysis (cross-wall modes)
inner pipe diameter d = 168.3 mm and wall thickness s = 4.5 mm
m=
n=
0
1
2
3
0
0
1140
1889
2602
1
2372
3302
4156
4968
Hz
- 35 -
Coincidence chart
(excitation and cross wall natural frequencies)
kth acoustic and structural mode
technische
ith pocket passing frequency
2500
1x Drehzahl
1. Pulsation
2. Harm. Pu
3. Harm. Pu
4. Harm. Pu
5. Harm. Pu
6. Harm. Pu
Quermode
(1
1140
Hz
Quermode (2
Quermode (3
Quermode (0
1. zyl. Scha
2. zyl. Scha
3. zyl. Scha
frequency [Hz].
2000
1500
1000
500
0
1500
2000
2500
3000
motor rotation speed [1/min]
- 36 -
technische
Root cause analysis
PD1_120
PD2_270
bar
4
3
bar
4
plane wave resonances
2
2
1
1
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
cross wall mode
3
3.5
4.0
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
kHz
s
600
kHz
bar
1.0
s
600
bar
1.0
480
0.8
480
0.8
360
0.6
360
0.6
240
0.4
240
0.4
120
0.2
120
0.2
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0.0
4.0
kHz
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.0
- 374.0
3.5
kHz
Remedial measures
technische
cross wall mode
breaker
- 38 -
technische
Disadvantage of both remedial measures
Additional energy costs due to the power loss of orifice plates!
Power loss calculated for a pressure drop of 0.5% of static pressure p.
100
power loss [kW]
80
p=10 MPa
60
5 MPa
40
1 MPa
20
0
0
2000
4000
6000
Volume flow [m³/h]
8000
10000
- 39 -
technische
Next chapter
6. Vision to discuss
- 40 -
Vision
technische
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.
- 41 -
Helmholtz resonator (virtual orifice VO)
technische
reference: Broerman et al., SwRI at GMRC 2008
- 42 -
Vision
technische
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.
- 43 -

Causes and Effects of Pulsations in Compressor

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