Abstract

This study evaluates the dynamic response of a centrifugal impeller to pulsating flow rates using dynamic mode decomposition with control (DMDc) to contribute improving turbomachinery's robustness. A surrogate model, which we developed in this study, was designed to capture both the one-dimensional transient behaviors and the three-dimensional unsteady flow field while reducing computational cost. Comparison with numerical and experimental results revealed that the one-dimensional DMDc (1D-DMDc) model, derived using the Z-transform, successfully reproduces the frequency response of centrifugal impeller under various flow pulsation conditions. Especially, the surrogate model accurately predicted gain and phase delay. The three-dimensional DMDc (3D-DMDc) model effectively captures dominant unsteady flow structures, including pressure rise pulsations and pressure pulsations induced by impeller–volute tongue interactions. These findings demonstrate the effectiveness of DMDc as a reduced-order modeling approach for analyzing unsteady flows in turbomachinery, offering a computationally efficient alternative to high-fidelity simulations.

References

1.
von Karman
,
T.
, and
Sears
,
W. R.
,
1938
, “
Airfoil Theory for Non-Uniform Motion
,”
J. Aeronaut. Sci.
,
5
(
10
), pp.
379
390
.10.2514/8.674
2.
Rubin
,
S.
,
1966
, “
Longitudinal Instability of Liquid Rockets Due to Propulsion Feedback (POGO)
,”
J. Spacecr. Rockets
,
3
(
8
), pp.
1188
1195
.10.2514/3.28626
3.
Sack
,
L. E.
, and
Nottage
,
H. B.
,
1965
, “
System Oscillations Associated With Cavitating Inducers
,”
ASME J. Basic Eng.
,
87
(
4
), pp.
917
924
.10.1115/1.3650844
4.
Dussourd
,
J. I.
,
1968
, “
An Investigation of Pulsations in the Boiler Feed System of a Central Power Station
,”
ASME J. Basic Eng.
,
90
(
4
), pp.
607
616
.10.1115/1.3605204
5.
Ohashi
,
H.
,
1967
, “
Analytical and Experimental Study of Dynamic Characteristics of Turbopumps
,”
Trans. Jpn. Soc. Mech. Eng.
,
33
(
255
), pp.
1779
1788
.10.1299/kikai1938.33.1779
6.
Greitzer
,
E. M.
,
1981
, “
The Stability of Pumping Systems
,”
ASME J. Fluids Eng.
,
103
(
2
), pp.
193
242
.10.1115/1.3241725
7.
Brennen
,
C. E.
, and
Acosta
,
T.
,
1972
, “
Theoretical, Quasi-Static Analysis of Cavitation Compliance in Turbopumps
,”
J. Spacecr. Rockets
, 10(3), pp.
229
236
.10.2514/3.27748
8.
Brennen
,
C.
, and
Acosta
,
A. J.
,
1976
, “
The Dynamic Transfer Function for a Cavitating Inducer
,”
ASME J. Fluids Eng.
,
98
(
2
), pp.
182
191
.10.1115/1.3448255
9.
Brennen
,
C.
,
1978
, “
Bubbly Flow Model for the Dynamic Characteristics of Cavitating Pumps
,”
J. Fluid Mech.
,
89
(
2
), pp.
223
240
.10.1017/S002211207800258X
10.
Brennen
,
C. E.
, and
Braisted
,
D. M.
,
1980
, “
Stability of Hydraulic Systems With Focus on Cavitating Pumps
,”
Proceedings of the 10th IAHR Symposium
, Tokyo, Japan, pp.
255
268
.http://brennen.caltech.edu/PUBPAPERS/papers/BRE042.pdf
11.
Tsujimoto
,
Y.
,
Kamijo
,
K.
, and
Yoshida
,
Y.
,
1993
, “
A Theoretical Analysis of Rotating Cavitation in Inducers
,”
ASME J. Fluids Eng.
,
115
(
1
), pp.
135
141
.10.1115/1.2910095
12.
Tsujimoto
,
Y.
,
Kamijo
,
K.
, and
Brennen
,
C. E.
,
2001
, “
Unified Treatment of Flow Instabilities of Turbomachines
,”
J. Propul. Power
,
17
(
3
), pp.
636
643
.10.2514/2.5790
13.
Shimura
,
T.
,
1995
, “
Geometry Effects in the Dynamic Response of Cavitating LE-7 Liquid Oxygen Pump
,”
J. Propul. Power
,
11
(
2
), pp.
330
336
.10.2514/3.51429
14.
Otsuka
,
S.
,
Tsujimoto
,
Y.
,
Kamijo
,
K.
, and
Furuya
,
O.
,
1996
, “
Frequency Dependence of Mass Flow Gain Factor and Cavitation Compliance of Cavitating Inducers
,”
ASME J. Fluids Eng.
,
118
(
2
), pp.
400
408
.10.1115/1.2817392
15.
Watanabe
,
S.
, and
Tsujimoto
,
Y.
,
2021
, “
One-Dimensional Numerical Simulation of Cavitation Surge in Pumping System Considering Cavity Response Delay
,”
IOP Conf. Ser.: Earth Environ. Sci.
,
774
(
1
), p.
012053
.10.1088/1755-1315/774/1/012053
16.
Watanabe
,
S.
, and
Tsujimoto
,
Y.
,
2021
, “
Prediction of Cavitation Surge Onset Point by One-Dimensional Stability Analysis
,”
Int. J. Fluid Mach. Syst.
,
14
(
2
), pp.
199
207
.10.5293/IJFMS.2021.14.2.199
17.
Kang
,
D.
,
Yonezawa
,
K.
,
Ueda
,
T.
,
Yamanishi
,
N.
,
Kato
,
C.
, and
Tsujimoto
,
Y.
,
2009
, “
Large Eddy Simulation of the Dynamic Response of an Inducer to Flow Rate Fluctuations
,”
Int. J. Fluid Mach. Syst.
,
2
(
4
), pp.
431
438
.10.5293/IJFMS.2009.2.4.431
18.
Yonezawa
,
K.
,
Aono
,
J.
,
Kang
,
D.
,
Horiguchi
,
H.
,
Kawata
,
Y.
, and
Tsujimoto
,
Y.
,
2012
, “
Numerical Evaluation of Dynamic Transfer Matrix and Unsteady Cavitation Characteristics of an Inducer
,”
Int. J. Fluid Mach. Syst.
,
5
(
3
), pp.
126
133
.10.5293/IJFMS.2012.5.3.126
19.
Ashida
,
T.
,
Yamamoto
,
K.
,
Yonezawa
,
K.
,
Horiguchi
,
H.
,
Kawata
,
Y.
, and
Tsujimoto
,
Y.
,
2017
, “
Measurement of Dynamic Characteristics of an Inducer in Cavitating Conditions
,”
Int. J. Fluid Mach. Syst.
,
10
(
3
), pp.
307
317
.10.5293/IJFMS.2017.10.3.307
20.
Maeda
,
T.
,
Tsuru
,
W.
,
Kang
,
D.
,
Tsuneda
,
T.
,
Kagawa
,
S.
,
An
,
B.
,
Nohmi
,
M.
, and
Yokota
,
K.
,
2019
, “
The Suppression of Cavitation Surge in a Double-Suction Centrifugal Pump by Using Branch-Type and Slit-Type Accumulations Installed at a Pump Outlet Pipe
,”
IOP Conf. Ser.: Earth Environ. Sci.
,
240
, p.
032049
.10.1088/1755-1315/240/3/032049
21.
Tanaka
,
Y.
,
Kitabata
,
T.
,
Nasu
,
K.
,
Watanabe
,
S.
,
Ohashi
,
S.
, and
Sakata
,
A.
,
2021
, “
Effect of Suction Pipeline Resistance on Cavitation Surge in a Turbopump With Inducer
,”
J. Phys.: Conf. Ser.
,
1909
(
1
), p.
012068
.10.1088/1742-6596/1909/1/012068
22.
Yamamoto
,
K.
,
Ukai
,
S.
,
Fukuda
,
T.
,
Kawasaki
,
S.
, and
Negishi
,
H.
,
2023
, “
Establishment of Prediction Model for Cavitation Surge Frequency and Onset in an Inducer Considering Dynamic Characteristics of Cavitation Compliance and Mass Flow Gain Factor
,”
ASME J. Fluids Eng.
,
145
(
9
), p.
091501
.10.1115/1.4062377
23.
Kambayashi
,
I.
,
Dou
,
C.
, and
Kang
,
D.
,
2024
, “
Experimental and Numerical Evaluations of Dynamic Transfer Matrix for a Three-Dimensional Centrifugal Impeller Based on Unsteady Energy Conservation
,”
ASME J. Fluids Eng.
,
146
(
9
), p.
091202
.10.1115/1.4064996
24.
Young, W. E., Murphy, R., and Reddecliff, J. M.,
1972
, “
Study of Cavitating Inducer Instabilities
,” National Aeronautics and Space Administration, Washington DC, Pratt & Whitney Research Report No.
NASA-CR-123939
.https://ntrs.nasa.gov/api/citations/19730004572/downloads/19730004572.pdf
25.
Watanabe
,
T.
,
Kang
,
D.
,
Cervone
,
A.
,
Kawata
,
Y.
, and
Tsujimoto
,
Y.
,
2008
, “
Choked Surge in a Cavitating Turbopump Inducer
,”
Int. J. Fluid Mach. Syst.
,
1
(
1
), pp.
64
75
.10.5293/IJFMS.2008.1.1.064
26.
Kang
,
D.
, and
Yokota
,
K.
,
2014
, “
Analytical Study of Cavitation Surge in a Hydraulic System
,”
ASME J. Fluids Eng.
,
136
(
10
), p.
101103
.10.1115/1.4027220
27.
Nohmi
,
M.
,
Yamazaki
,
S.
,
Kagawa
,
S.
,
An
,
B.
,
Kang
,
D.
, and
Yokota
,
K.
,
2016
, “
Numerical Analyses for Cavitation Surge in a Pump With the Square Root Shaped Suction Performance Curve
,”
Proceedings of ISROMAC
, Honolulu, HI, Apr. 10--15, pp. 1--8.https://hal.science/hal-01894396/document
28.
Schmid
,
P. J.
,
Li
,
L.
,
Juniper
,
M. P.
, and
Pust
,
O.
,
2011
, “
Applications of the Dynamic Mode Decomposition
,”
Theor. Comput. Fluid Dyn.
,
25
(
1–4
), pp.
249
259
.10.1007/s00162-010-0203-9
29.
Tu
,
J. H.
,
Rowley
,
C. W.
,
Luchtenburg
,
D. M.
,
Brunton
,
S. L.
, and
Kutz
,
J. N.
,
2014
, “
On Dynamic Mode Decomposition: Theory and Applications
,”
J. Comput. Dyn.
,
1
(
2
), pp.
391
421
.10.3934/jcd.2014.1.391
30.
Proctor
,
J. L.
,
Brunton
,
S. L.
, and
Kutz
,
J. N.
,
2016
, “
Dynamic Mode Decomposition With Control
,”
SIAM J. Appl. Dyn. Syst.
,
15
(
1
), pp.
142
161
.10.1137/15M1013857
31.
Narasingam
,
A.
, and
Kwon
,
J. S.-I.
,
2017
, “
Development of Local Dynamic Mode Decomposition With Control: Application to Model Predictive Control of Hydraulic Fracturing
,”
Comput. Chem. Eng.
,
106
, pp.
501
511
.10.1016/j.compchemeng.2017.07.002
32.
Brunton
,
S. L.
,
Brunton
,
B. W.
,
Proctor
,
J. L.
,
Kaiser
,
E.
, and
Kutz
,
J. N.
,
2017
, “
Chaos as an Intermittently Forced Linear System
,”
Nat. Commun.
,
8
(
1
), p.
19
.10.1038/s41467-017-00030-8
33.
Kutz
,
J. N.
,
Brunton
,
S. L.
,
Brunton
,
B. W.
, and
Proctor
,
J. L.
,
2016
, “
Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems
,”
SIAM Rev.
,
59
(
4
), pp.
430
491
.10.1137/1.9781611974508
34.
Giannakis
,
D.
,
2015
, “
Data-Driven Spectral Decomposition and Forecasting of Ergodic Dynamical Systems
,”
Appl. Comput. Harmonic Anal.
,
39
(
3
), pp.
470
494
.10.1016/j.acha.2017.09.001
35.
Nemoto
,
K.
,
Kang
,
D.
,
Kambayashi
,
I.
,
Tsuru
,
W.
,
Watanabe
,
S.
, and
Yokota
,
K.
,
2022
, “
Stability Analysis of Cavitation Surge in Hydraulic System Considering Response Delay of Cavitating Pump
,”
Int. J. Fluid Mach. Syst.
,
15
(
4
), pp.
401
410
.10.5293/IJFMS.2022.15.4.401
36.
Fung
,
Y.-C.
,
1955
,
An Introduction to the Theory of Aeroelasticity
,
Wiley
,
New York
.
37.
Horlock
,
J. H.
,
1968
, “
Fluctuating Lift Forces on Aerofoils Moving Through Transverse and Chordwise Gusts
,”
ASME J. Basic Eng.
,
90
(
4
), pp.
494
500
.10.1115/1.3605173
38.
Nitzsche
,
J.
,
Ringel
,
L. M.
,
Kaiser
,
C.
, and
Hennings
,
H.
,
2019
, “
Fluid-Mode Flutter in Plane Transonic Flows
,”
Proceedings of the International Forum on Aeroelasticity and Structural Dynamics
(
IFASD
),
Savannah, GA, June 9--13
, pp.
1
12
.https://elib.dlr.de/127989/1/IFASD-2019-006.pdf
39.
Kambayashi
,
I.
,
Kang
,
D.
, and
Nishimura
,
N.
,
2021
, “
Theoretical, Numerical, and Experimental Study on an Unsteady Venturi Flowmeter for Incompressible Flows
,”
ASME J. Fluids Eng.
,
143
(
2
), p.
021308
.10.1115/1.4048689
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