The prediction of cavity length is very important for identifying cavitation state. This paper introduces a sophisticated framework aimed at predicting cavity length, leveraging the combination of neural network architecture with the active subspace method. The model identifies the dominant dimensionless group influencing cavity length in hydrofoil and venturi. For hydrofoil, a linear, negatively correlated relationship is found between cavity length and its dominant dimensionless number. Conversely, for venturi, an exponential, positively correlated relationship is identified. Using the found dominant dimensionless number to predict the dimensionless cavity length, the average relative errors are 0.146 and 0.136, respectively. The expression of the dominant dimensionless number, combined with the input parameters, is simplified into structural and physical functions, thereby significantly reducing the dimensionality of input while increasing the average relative error to 0.338. This study enhances the understanding of data-driven cavitation features and offers guidance for cavitation control and prevention.

1.
R. D.
Moore
and
R. S.
Ruggeri
, “
Method for prediction of pump cavitation performance for various liquids, liquid temperatures, and rotative speeds
,” Paper No. TN D-5292 (
1969
).
2.
V. H.
Arakeri
, “
Cavitation inception
,”
Proc. Indian Acad. Sci.
2
,
149
177
(
1979
).
3.
R. E.
Arndt
, “
Cavitation in fluid machinery and hydraulic structures
,”
Annu. Rev. Fluid Mech.
13
,
273
(
1981
).
4.
J.
Feng
,
B.
Liu
,
X.
Luo
,
G.
Zhu
,
K.
Li
, and
G.
Wu
, “
Experimental investigation on characteristics of cavitation-induced vibration on the runner of a bulb turbine
,”
Mech. Syst. Signal Process.
189
,
110097
(
2023
).
5.
B.
Gong
,
Z.
Zhang
,
C.
Feng
,
J.
Yin
,
N.
Li
, and
D.
Wang
, “
Experimental investigation of characteristics of tip leakage vortex cavitation-induced vibration of a pump
,”
Ann. Nucl. Energy
192
,
109935
(
2023
).
6.
N.
Qiu
,
P.
Xu
,
H.
Zhu
, and
J.
Wu
, “
Pressure fluctuation and cavitation noise characteristics of hydrofoil at different temperatures
,”
Ocean Eng.
286
,
115570
(
2023
).
7.
Q.
Si
,
A.
Ali
,
M.
Liao
,
J.
Yuan
,
Y.
Gu
,
S.
Yuan
, and
G.
Bois
, “
Assessment of cavitation noise in a centrifugal pump using acoustic finite element method and spherical cavity radiation theory
,”
Eng. Appl. Comput. Fluid Mech.
17
,
2173302
(
2023
).
8.
E.
Nakao
and
S.
Hattori
, “
Cavitation erosion mechanisms and quantitative evaluation based on erosion particles
,”
Wear
249
,
839
(
2001
).
9.
J. R.
Laguna-Camacho
,
R.
Lewis
,
M.
Vite-Torres
, and
J. V.
Méndez-Méndez
, “
A study of cavitation erosion on engineering materials
,”
Wear
301
,
467
(
2013
).
10.
X.
Long
,
J.
Zhang
,
J.
Wang
,
M.
Xu
,
Q.
Lyu
, and
B.
Ji
, “
Experimental investigation of the global cavitation dynamic behavior in a venturi tube with special emphasis on the cavity length variation
,”
Int. J. Multiphase Flow
89
,
290
(
2017
).
11.
C. E.
Brennen
,
Cavitation and Bubble Dynamics
(
Oxford University Press
,
1995
).
12.
K.
Sato
,
M.
Tanada
,
S.
Monden
, and
Y.
Tsujimoto
, “
Observations of oscillating cavitation on a flat plate hydrofoil
,”
JSME Int. J. Ser. B
45
,
646
(
2002
).
13.
J. M.
Michel
and
J. P.
Franc
,
Fundamentals of Cavitation
(
Springer
,
2004
).
14.
M. L.
Billet
,
J. W.
Holl
, and
D. S.
Weir
, “
Thermodynamic effects on developed cavitation
,”
J. Fluids Eng.
97
,
507
(
1975
).
15.
F.
Larrarte
,
T. M.
Pham
, and
D. H.
Fruman
, “
Investigation of unsteady sheet cavitation and cloud cavitation mechanisms
,”
J. Fluids Eng.
121
,
289
(
1999
).
16.
Q.
Le
,
J. P.
Franc
, and
J. M.
Michel
, “
Partial cavities: Global behavior and mean pressure distribution
,”
J. Fluids Eng.
115
,
243
(
1993
).
17.
R. E. A.
Amdt
,
M.
Kjeldsen
, and
M.
Effertz
, “
Spectral characteristics of sheet/cloud cavitation
,”
J. Fluids Eng.
122
,
481
(
2000
).
18.
M.
Dular
,
I.
Khlifa
,
S.
Fuzier
,
M.
Adama Maiga
, and
O.
Coutier-Delgosha
, “
Scale effect on unsteady cloud cavitation
,”
Exp. Fluids
53
,
1233
(
2012
).
19.
X.
Lu
,
D.
Wang
,
W.
Shen
, and
C.
Zhu
, “
Experimental investigation of the propagation characteristics of an interface wave in a jet pump under cavitation condition
,”
Exp. Therm. Fluid Sci.
63
,
74
(
2015
).
20.
J.
Wang
,
S.
Xu
,
H.
Cheng
,
B.
Ji
,
J.
Zhang
, and
X.
Long
, “
Experimental investigation of cavity length pulsation characteristics of jet pumps during limited operation stage
,”
Energy
163
,
61
(
2018
).
21.
A.
Sarc
,
T.
Stepisnik-Perdih
,
M.
Petkovsek
, and
M.
Dular
, “
The issue of cavitation number value in studies of water treatment by hydrodynamic cavitation
,”
Ultrason. Sonochem.
34
,
51
(
2017
).
22.
W.
Liang
,
T.
Chen
,
B.
Huang
, and
G.
Wang
, “
Thermodynamic analysis of unsteady cavitation dynamics in liquid hydrogen
,”
Int. J. Heat Mass Transfer
142
,
118470
(
2019
).
23.
B.
Xu
,
J.
Feng
,
F.
Wan
,
D.
Zhang
,
X.
Shen
, and
W.
Zhang
, “
Numerical investigation of modified cavitation model with thermodynamic effect in water and liquid nitrogen
,”
Cryogenics
106
,
103049
(
2020
).
24.
Y.
Yamaguchi
and
Y.
Iga
,
Thermodynamic Effect on Cavitation in High Temperature Water
(
ASME
,
Chicago, IL
,
2014
).
25.
M.
Ge
,
P.
Manikkam
,
J.
Ghossein
,
R.
Kumar Subramanian
,
O.
Coutier-Delgosha
, and
G.
Zhang
, “
Dynamic mode decomposition to classify cavitating flow regimes induced by thermodynamic effects
,”
Energy
254
,
124426
(
2022
).
26.
G.
Shi
,
Y.
Wei
, and
S.
Liu
, “
Cavitation flow characteristics of water and liquid oxygen in the inducer considering thermodynamic effect
,”
Energies
15
,
4943
(
2022
).
27.
Y.
Iga
,
J.
Okajima
,
Y.
Yamagichi
,
H.
Sasaki
, and
Y.
Ito
, “
Thermodynamic suppression effect of cavitation arising in a hydrofoil in 140 °C hot water
,”
J. Fluids Eng.
145
,
011207
(
2023
).
28.
A. J.
Stepanoff
, “
Cavitation properties of liquids
,”
J. Eng. Power
86
,
195
(
1964
).
29.
C.
Rebattet
,
J. P.
Franc
, and
A.
Coulon
, “
An experimental investigation of thermal effects in a cavitating inducer
,”
J. Fluids Eng.
126
,
716
(
2004
).
30.
H.
Zhang
,
Z.
Zuo
,
K. A.
Mørch
, and
S.
Liu
, “
Thermodynamic effects on venturi cavitation characteristics
,”
Phys. Fluids
31
,
097107
(
2019
).
31.
Z.
Zuo
,
H.
Zhang
,
Z.
Ren
,
H.
Chen
, and
S.
Liu
, “
Thermodynamic effects at Venturi cavitation in different liquids
,”
Phys. Fluids
34
,
083310
(
2022
).
32.
J. H.
Evans
, “
Dimensional analysis and the Buckingham Pi theorem
,”
Am. J. Phys.
40
,
1815
(
1972
).
33.
Z.
del Rosario
,
P. G.
Constantine
, and
G.
Iaccarino
, “
Data-driven dimensional analysis: Algorithms for unique and relevant dimensionless groups
,” arXiv:170804303 (
2017
).
34.
L.
Jofre
,
Z.
del Rosario
, and
G.
Iaccarino
, “
Data-driven dimensional analysis of heat transfer in irradiated particle-laden turbulent flow
,”
Int. J. Multiphase Flow
125
,
103198
(
2020
).
35.
S.
Saha
,
Z.
Gan
,
L.
Cheng
,
J.
Gao
,
O. L.
Kafka
,
X.
Xie
,
H.
Li
,
M.
Tajdari
,
H. A.
Kim
, and
W. K.
Liu
, “
Hierarchical Deep Learning Neural Network (HiDeNN): An artificial intelligence (AI) framework for computational science and engineering
,”
Comput. Methods Appl. Mech. Eng.
373
,
113452
(
2021
).
36.
X.
Xie
,
A.
Samaei
,
J.
Guo
,
W. K.
Liu
, and
Z.
Gan
, “
Data-driven discovery of dimensionless numbers and governing laws from scarce measurements
,”
Nat. Commun.
13
,
7562
(
2022
).
37.
K.
Yang
,
Z.
Liang
,
B.
Xu
,
Z.
Hou
, and
H.
Wang
, “
Data-driven dimensional analysis of critical heat flux in subcooled vertical flow: A two-stage machine learning approach
,”
Appl. Therm. Eng.
248
,
123167
(
2024
).
38.
K.
Yang
,
H.
Liao
,
B.
Xu
,
Q.
Chen
,
Z.
Hou
, and
H.
Wang
, “
Data-driven dryout prediction in helical-coiled once-through steam generator: A physics-informed approach leveraging the Buckingham Pi theorem
,”
Energy
294
,
130822
(
2024
).
39.
K.
Gimpel
and
D.
Hendrycks
, “
Gaussian error linear units (GELUs)
,” arXiv:1606.08415 (
2016
).
40.
G. E.
Hinton
and
V.
Nair
, “
Rectified linear units improve restricted Boltzmann machines
,” in
ICML 2012
(
ACM
,
2010
), pp.
807
814
.
41.
J. R.
Kiros
,
J. L.
Ba
, and
G. E.
Hinton
, “
Layer normalization
,” arXiv:1607.06450 (
2016
).
42.
C. B.
Angelo Cervone
,
E.
Rapposelli
, and
L.
d'Agostino
, “
Thermal cavitation experiments on a NACA 0015 hydrofoil
,”
J. Fluids Eng.
128
,
326
(
2006
).
43.
A.
Yu
,
Q.
Tang
, and
D.
Zhou
, “
Entropy production analysis in thermodynamic cavitating flow with the consideration of local compressibility
,”
Int. J. Heat Mass Transfer
153
,
119604
(
2020
).
44.
C.
Esposito
,
J.
Steelant
, and
M. R.
Vetrano
, “
Impact of cryogenics on cavitation through an orifice: A review
,”
Energies
14
,
8319
(
2021
).
45.
C.
Esposito
,
L.
Peveroni
,
J. B.
Gouriet
,
J.
Steelant
, and
M. R.
Vetrano
, “
On the influence of thermal phenomena during cavitation through an orifice
,”
Int. J. Heat Mass Transfer
164
,
120481
(
2021
).
46.
A.
Ficrella
and
M. G.
De Giorgi
, “
Simulation of cryogenic cavitation by using both inertial and heat transfer control bubble growth
,” in
39th AIAA Fluid Dynamics Conference
(
AIAA
,
2012
).
47.
H.
Kim
and
C.
Kim
, “
A physics-based cavitation model ranging from inertial to thermal regimes
,”
Int. J. Heat Mass Transfer
181
,
121991
(
2021
).
48.
D.
Li
,
B.
Miao
,
Y.
Li
,
R.
Gong
, and
H.
Wang
, “
Numerical study of the hydrofoil cavitation flow with thermodynamic effects
,”
Renewable Energy
169
,
894
(
2021
).
49.
J. P. R.
Gustavsson
,
K. C.
Denning
, and
C.
Segal
, “
Hydrofoil cavitation under strong thermodynamic effect
,”
J. Fluids Eng.
130
,
091303
(
2008
).
50.
J. P. R.
Gustavsson
,
K. C.
Denning
,
C.
Segal
, and
D. J.
Dorney
, “
Incipient cavitation studied under strong thermodynamic effect
,”
AIAA J.
47
,
710
(
2009
).
51.
X.
Jiang
and
Z.
Ge
, “
Data augmentation classifier for imbalanced fault classification
,”
IEEE Trans. Automat. Sci. Eng.
18
,
1206
(
2021
).
52.
A.
Vijayan
and
P. K.
P
, “
Characterization of cavitation zone in cavitating venturi flows: Challenges and road ahead
,”
Phys. Fluids
35
,
111301
(
2023
).
You do not currently have access to this content.