Accurate determination of acousto-elastic natural frequencies in centrifugal compressors is important in order to avoid resonance events that may lead to machine failure. Compressors operating with CO2 at high pressures, especially near its transition to supercritical state, deal with a wide variation in density and speed of sound. Natural frequency behavior under these conditions is studied here. A finite element method (FEM) based coupled acousto-elastic solver has been developed to study the modal coupling and interactions between the impeller and the side-cavity modes for an idealized compressor geometry. Pressure in the side-cavities is increased up to a very high value of 20 MPa and existence of fluid- and structure-dominant acousto-elastic modes is observed. The variation of the natural frequencies of these modes with pressure exhibits contrasting trends as CO2 transitions from gaseous to supercritical state.

References

1.
de Noronha
,
R. F.
,
Cavalca
,
K. L.
,
Miranda
,
M. A.
,
Memmott
,
E. A.
, and
Ramesh
,
K.
,
2014
, “
Stability Testing of CO2 Compressors
,” 43rd Turbomachinery and 30th Pump Users Symposia (
Pump and Turbo 2014
), Houston, TX, Sept. 23–25.http://turbolab.tamu.edu/proc/turboproc/T43/TurboLecture9.pdf
2.
Norihisa
,
W.
,
Tsunenori
,
S.
,
Akinori
,
T.
, and
Jyou
,
M.
,
2004
, “
High Performance, High Reliability Re-Injection Compressors for Green House Gas (CO2)
,”
Tech. Rev. Mitsubishi Heavy Ind. Ltd.
,
41
(
1
), pp.
1
3
.https://www.mhi.com/company/technology/review/pdf/e411/e411038.pdf
3.
Eisinger
,
F. L.
,
2002
, “
Acoustic Fatigue of Impellers of Rotating Machinery
,”
ASME J. Pressure Vessel Technol.
,
124
(
2
), pp.
154
160
.
4.
Eisinger
,
F. L.
, and
Sullivan
,
R. E.
,
2002
, “
Acoustically-Induced Structural Fatigue of Impeller Discs: A Brief Note
,”
ASME
Paper No. GT2002-30604.
5.
Atalla
,
N.
, and
Bernhard
,
R. J.
,
1994
, “
Review of Numerical Solutions for Low-Frequency Structural-Acoustic Problems
,”
Appl. Acoust.
,
43
(
3
), pp.
271
294
.
6.
Sandberg
,
G.
,
1995
, “
A New Strategy for Solving Fluid-Structure Problems
,”
Int. J. Numer. Methods Eng.
,
38
(
3
), pp.
357
370
.
7.
Everstine
,
G. C.
,
1997
, “
Finite Element Formulations of Structural Acoustics Problems
,”
Comput. Struct.
,
65
(
3
), pp.
307
321
.
8.
Sandberg
,
G.
,
Wernberg
,
P.-A.
, and
Davidsson
,
P.
,
2009
,
Fundamentals of Fluid-Structure Interaction
,
Springer
,
Vienna, Austria
, pp.
23
101
.
9.
Hou
,
G.
,
Wang
,
J.
, and
Layton
,
A.
,
2012
, “
Numerical Methods for Fluid-Structure Interaction: A Review
,”
Commun. Comput. Phys.
,
12
(
2
), pp.
337
377
.
10.
Ross
,
M. R.
,
2006
, “
Coupling and Simulation of Acoustic Fluid-Structure Interaction Systems Using Localized Lagrange Multipliers
,”
Ph.D. thesis
, University of Colorado, Colorado Springs, CO.https://pdfs.semanticscholar.org/0c04/2d3f0e09d470933b907110651e641407d2e7.pdf
11.
Dowell
,
E.
,
Gorman
,
G.
, and
Smith
,
D.
,
1977
, “
Acoustoelasticity: General Theory Acoustic Natural Modes and Forced Response to Sinusoidal Excitation, Including Comparisons With Experiment
,”
J. Sound Vib.
,
52
(
4
), pp.
519
542
.
12.
Magara
,
Y.
,
Narita
,
M.
,
Yamaguchi
,
K.
,
Takahashi
,
N.
, and
Kuwano
,
T.
,
2008
, “
Natural Frequencies of Centrifugal Compressor Impellers for High Density Gas Applications
,”
ASME
Paper No. IMECE2008-67278.
13.
Magara
,
Y.
,
Yamaguchi
,
K.
,
Miura
,
H.
,
Takahashi
,
N.
, and
Narita
,
M.
,
2013
, “
Natural Frequency Shift in a Centrifugal Compressor Impeller for High-Density Gas Applications
,”
ASME J. Turbomach.
,
135
(
1
), p.
011014
.
14.
Tassios
,
D. P.
,
1993
,
Applied Chemical Engineering Thermodynamics
,
Springer
,
Berlin
.
15.
Soave
,
G.
,
1972
, “
Equilibrium Constants From a Modified Redlich-Kwong Equation of State
,”
Chem. Eng. Sci.
,
27
(
6
), pp.
1197
1203
.
16.
Peng
,
D.-Y.
, and
Robinson
,
D. B.
,
1976
, “
A New Two-Constant Equation of State
,”
Ind. Eng. Chem. Fundam.
,
15
(
1
), pp.
59
64
.
17.
Lee
,
B. I.
, and
Kesler
,
M. G.
,
1975
, “
A Generalized Thermodynamic Correlation Based on Three-Parameter Corresponding States
,”
AIChE J.
,
21
(
3
), pp.
510
527
.
18.
Pitzer
,
K. S.
, Lippmann, D. Z., Curl, R. F., Jr., Huggins, C. M., and Petersen, D. E.,
1955
, “
The Volumetric and Thermodynamic Properties of Fluids. II. Compressibility Factor, Vapor Pressure and Entropy of Vaporization
,”
J. Am. Chem. Soc.
,
77
(
13
), pp.
3433
3440
.
19.
Span
,
R.
, and
Wagner
,
W.
,
1996
, “
A New Equation of State for Carbon Dioxide Covering the Fluid Region From the Triple-Point Temperature to 1100 K at Pressures Up To 800 MPa
,”
J. Phys. Chem. Ref. Data
,
25
(
6
), pp.
1509
1596
.
20.
Morse
,
P. M.
, and
Ingard
,
K. U.
,
1968
,
Theoretical Acoustics
(International Series in Pure and Applied Physics), 1st ed.,
McGraw-Hill
, New York.
21.
Landau
,
L.
, and
Lifshitz
,
E.
,
1970
, “
Theory of Elasticity
,”
Course of Theoretical Physics
, 2nd ed.,
Pergamon Press
, London.
22.
Bermúdez
,
A.
,
Gamallo
,
P.
,
Hervella-Nieto
,
L.
,
Rodríguez
,
R.
, and
Santamarina
,
D.
,
2008
,
Fluid–Structure Acoustic Interaction
,
Springer
,
Berlin
, pp.
253
286
.
23.
Kundu
,
P. K.
, and
Cohen
,
I. M.
,
2004
,
Fluid Mechanics
, 3rd ed.,
Elsevier Academic Press
, Amsterdam, The Netherlands.
24.
Brenner
,
S. C.
, and
Scott
,
L. R.
,
2008
,
The Mathematical Theory of Finite Element Methods
(Texts in Applied Mathematics), Vol.
15
,
Springer
,
New York
.
25.
Guruswamy
,
G. P.
,
2002
, “
A Review of Numerical Fluids/Structures Interface Methods for Computations Using High-Fidelity Equations
,”
Comput. Struct.
,
80
(
1
), pp.
31
41
.
26.
Saad
,
Y.
,
2011
,
Numerical Methods for Large Eigenvalue Problems, Revised edition
,
SIAM
, Philadelphia, PA.
27.
Ern
,
A.
, and
Guermond
,
J.-L.
,
2004
,
Theory and Practice of Finite Elements
(Applied Mathematical Sciences), Vol.
159
,
Springer
,
New York
.
28.
Louisell
,
W.
,
1960
,
Coupled Mode and Parametric Electronics
,
Wiley
, New York.
29.
Pan
,
J.
, and
Bies
,
D. A.
,
1990
, “
The Effect of Fluid Structural Coupling on Sound Waves in an Enclosure Theoretical Part
,”
J. Acoust. Soc. Am.
,
87
(
2
), pp.
691
707
.
30.
Basten
,
T.
,
Mateboer
,
A.
, and
Tijdeman
,
H.
,
1998
, “
Spatial Matching of Structural and Acoustic Modes in an Airtight Box
,”
International Conference on Noise and Vibration Engineering
(
ISMA
), Leuven, Belgium, Sept. 16–18, pp.
639
646
.http://doc.utwente.nl/58804/
31.
Pereboom
,
H. P.
,
van Beek
,
P. J. G.
, and
Smeulers
,
J. P. M.
,
2016
, “
Experimental Investigation of Fluid Structure Interaction of Impeller Like Disks in Super Critical Carbon Dioxide
,”
ASME
Paper No. GT2016-58032.
32.
Konig
,
S.
,
Petry
,
N.
, and
Wagner
,
N. G.
,
2009
, “
Aeroacoustic Phenomena in High-Pressure Centrifugal Compressors—A Possible Root Cause for Impeller Failures
,”
38th Turbomachinery Symposium
, Houston, TX, Sept. 14–17, pp.
103
122
.https://www.semanticscholar.org/paper/Aeroacoustic-Phenomena-in-High-pressure-Centrifuga-K%C3%B6nig/e8cca232e98d9523eac62ecfbabfcfdc5d039977
33.
Ziada
,
S.
,
Oengören
,
A.
, and
Vogel
,
A.
,
2002
, “
Acoustic Resonance in the Inlet Scroll of a Turbo-Compressor
,”
J. Fluids Struct.
,
16
(
3
), pp.
361
373
.
34.
Hirschberg
,
A.
, and
Rienstra
,
S.
,
1992
, “
An Introduction to Acoustics
,” Eindhoven University of Technology, Eindhoven, The Netherlands, Technical Report No.
IWDE 9206
.https://pure.tue.nl/ws/files/1755770/546195.pdf
35.
Genta
,
G.
,
2005
,
Dynamics of Rotating Systems
(Mechanical Engineering Series),
Springer
,
New York
.
36.
Assael
,
M. J.
,
Trusler
,
J. P. M.
, and
Tsolakis
,
T. F.
,
1996
,
Thermophysical Properties of Fluids: An Introduction to Their Prediction
,
Imperial College Press
, London.
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