Causes and Effects of Pulsations in Compressor Systems
A. Brümmer Brümmer Chair of Fluid Technology, TU Dortmund
technische
Contents
universität dortmund
1.
Definition of pu pulsations
2.
Excitation mechanisms
3.
Natural frequencies
4.
Effects of of Pu Pulsations
5.
Exam xamples les incl inclu uding ing measu easurres
6.
Vision to discuss
technische
Contents
universität dortmund
1.
Definition of pu pulsations
2.
Excitation mechanisms
3.
Natural frequencies
4.
Effects of of Pu Pulsations
5.
Exam xamples les incl inclu uding ing measu easurres
6.
Vision to discuss
technische
Definition and example of pulsations
universität dortmund
Pulsations are periodic variations in flow-velocity and pressure about mean values. Pressure-pulsation Pressure-pulsation inside reciprocating cylinder (red) and just outside pressure valve (black)
bar 80
pressure 70 60 50 40 80
120
160
200
240
technische
Acoustic Impedance
universität dortmund
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 absol te temperat re
technische
Next chapter
universität dortmund
2. Excitation mechanisms
Excitation mechanisms
technische universität dortmund
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
Pulsation frequency
technische universität dortmund
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
Explanation of thermo-acoustic instability
technische universität dortmund
“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
Strength of excitation
technische universität dortmund
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
Half wave length mode (standing wave) f i= i * a / (2 * L) f i a
closed
natural frequency of ith multiple of fundamental mode (half wave) speed of sound
pressure amplitude
closed
open
pressure amplitude
i=1
i=2
i=3
L
L
open
technische
Plane wave natural frequencies
universität dortmund
open
Quarter wave length mode (standing wave)
pressure amplitude
i=1
f i= (2i-1) * a / (4 * L) f i
a L
natural frequency of ith multiple of fundamental mode speed of sound length of pipe section
i=2
i=3
L
closed
Thermo-acoustically induced “standing wave“
technische universität dortmund
movable heat source blower
open end
open end
Cross-wall acoustic natural frequency
technische universität dortmund
Cross-wall acoustic natural frequency
f (m,n ) =
β (m,n ) ⋅ a π ⋅d
f (m,n) a d
β(m,n)
technische universität dortmund
cross-wall acoustic natural frequency speed of sound pipe diameter zeros of Bessel function
Lateral vibration mode of beams (bending mode)
f k f k
λk E I
µ
=
1
⎛ λ k ⎞
⎜ ⎟ 2π ⎝ l ⎠
2
EI
µ
technische universität dortmund
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
Lateral vibration mode of beams (bending mode)
boundary conditions
λk -values
technische universität dortmund
technische
Shall wall natural frequencies
universität dortmund
f k = λ k = f k
λk d s E
ν I
µ k
1 / 2
⎛ E ⎞ ⎜⎜ ⎟ 2 ⎟ π ⋅ d ⎝ µ ( 1 −ν ) ⎠ λ k
1 1 / 2
12
2 s k ( k ² − 1 )
d ( 1 + k ²)
1 / 2
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…)
Master rule to avoid vibration problems
technische universität dortmund
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
technische
Next chapter
universität dortmund
4. Effects of pulsations
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
