The alteration of physical properties in cavitating flows due to phase transition presents challenges for accurately expressing turbulent viscosity in Reynolds-Averaged Navier–Stokes models. Addressing this issue is crucial for capturing cavitating flow characteristics effectively. This study introduces a modification to turbulent viscosity by considering the compressibility of the vapor–liquid mixture, applied within the k-omega Shear-Stress Transport (SST k ω) model framework. Simulations of cavitating flow around the Clark-Y hydrofoil, National Advisory Committee for Aeronautics 66 hydrofoil, and wedge are conducted to validate the proposed method. Results indicate that the modified model can reproduce the cavity inception, development, cutoff, and shedding processes observed in the experiment. Notably, the modification model accurately reproduces distinct cavitating flow features such as U-shaped cavities, secondary shedding, and high-pressure phenomena resulting from collapse. Moreover, the predicted time-averaged velocity, time-averaged Reynolds stress component, and dominant frequencies of pressure and phase volume fraction surpass those of the original SST k ω model, demonstrating improved performance. These findings highlight the enhanced accuracy and reliability of the proposed SST-multiphase compressibility modification k ω model for simulating cavitating flows, thus contributing to improved understanding and prediction capabilities in relevant engineering applications.

1.
S. J.
Zhang
,
C. Y.
Wang
,
Z. F.
Yao
,
Q.
Zhong
,
J.
Wu
, and
F. J.
Wang
, “
Evaluation of a modified URANS prediction of unsteady cavitating flow around a hydrofoil by comparing with LES results and experimental results
,”
Int. J. Multiphase Flow
162
,
104405
(
2023
).
2.
Z. Y.
Wang
,
H. Y.
Cheng
,
B.
Ji
, and
X. X.
Peng
, “
Numerical investigation of inner structure and its formation mechanism of cloud cavitating flow
,”
Int. J. Multiphase Flow
165
,
104484
(
2023
).
3.
B. Q.
Liu
,
W.
Yang
,
S. E.
Li
,
J.
Chen
,
B.
Huang
, and
X. B.
Huang
, “
Study of unsteady cavitating flow around Clark-Y hydrofoil using nonlinear PANS model with near-wall correction
,”
Mod. Phys. Lett. B
35
(
35
),
2150497
(
2021
).
4.
B. C.
Tian
,
J.
Chen
,
X.
Zhao
,
M. J.
Zhang
, and
B.
Huang
, “
Numerical analysis of interaction between turbulent structures and transient sheet/cloud cavitation
,”
Phys. Fluids
34
(
4
),
047116
(
2022
).
5.
H. Y.
Cheng
,
X. P.
Long
,
B.
Ji
,
X. X.
Peng
, and
M.
Farhat
, “
A new Euler–Lagrangian cavitation model for tip-vortex cavitation with the effect of non-condensable gas
,”
Int. J. Multiphase Flow
134
,
103441
(
2021
).
6.
Z. Y.
Wang
,
H. Y.
Cheng
, and
B.
Ji
, “
Euler–Lagrange study of cavitating turbulent flow around a hydrofoil
,”
Phys. Fluids
33
(
11
),
112108
(
2021
).
7.
C. C.
Wang
,
Q.
Wu
,
B.
Huang
, and
G. Y.
Wang
, “
Numerical investigation of cavitation vortex dynamics in unsteady cavitating flow with shock wave propagation
,”
Ocean Eng.
156
,
424
434
(
2018
).
8.
C. C.
Wang
,
G. Y.
Wang
, and
B.
Huang
, “
Dynamics of unsteady compressible cavitating flows associated with the cavity shedding
,”
Ocean Eng.
209
,
107025
(
2020
).
9.
J. B.
Leroux
,
O.
Coutier-Delgosha
, and
J. A.
Astolfi
, “
A joint experimental and numerical study of mechanisms associated to instability of partial cavitation on two-dimensional hydrofoil
,”
Phys. Fluids
17
(
5
),
052101
(
2005
).
10.
Z. Y.
Wang
,
H. Y.
Cheng
, and
B.
Ji
, “
Numerical investigation of condensation shock and re-entrant jet dynamics around a cavitating hydrofoil using a dynamic cubic nonlinear subgrid-scale model
,”
Appl. Math. Modell.
100
,
410
431
(
2021
).
11.
M. M.
Ge
,
M.
Petkovšek
,
G. J.
Zhang
,
D.
Jacobs
, and
O.
Coutier-Delgosha
, “
Cavitation dynamics and thermodynamic effects at elevated temperatures in a small Venturi channel
,”
Int. J. Heat Mass Transfer
170
,
120970
(
2021
).
12.
Q.
Wu
,
B.
Huang
,
G. Y.
Wang
,
S. L.
Cao
, and
M. M.
Zhu
, “
Numerical modelling of unsteady cavitation and induced noise around a marine propeller
,”
Ocean Eng.
160
,
143
155
(
2018
).
13.
M. J.
Zhang
,
Q.
Wu
,
G. Y.
Wang
,
B.
Huang
,
X. Y.
Fu
, and
J.
Chen
, “
The flow regime and hydrodynamic performance for a pitching hydrofoil
,”
Renewable Energy
150
,
412
427
(
2020
).
14.
B.
Ji
,
J.
Wang
,
X. W.
Luo
,
K.
Miyagawa
,
L. Z.
Xiao
,
X.
Long
, and
Y.
Tsujimoto
, “
Numerical simulation of cavitation surge and vortical flows in a diffuser with swirling flow
,”
J. Mech. Sci. Technol.
30
,
2507
2514
(
2016
).
15.
G.
Wallis
,
One-Dimensional Two-Phase Flow
(
McGraw-Hill
,
NY
,
1967
).
16.
J. P.
Franc
and
J. M.
Michel
,
Fundamentals of Cavitation
(
Springer Science & Business Media
,
2005
).
17.
H.
Shamsborhan
,
O.
Coutier-Delgosha
,
G.
Caignaert
, and
F. A.
Nour
, “
Experimental determination of the speed of sound in cavitating flows
,”
Exp. Fluids
49
,
1359
1373
(
2010
).
18.
R. E.
Bensow
and
G.
Bark
, “
Implicit LES predictions of the cavitating flow on a propeller
,”
J. Fluids Eng.
132
(
4
),
041302
(
2010
).
19.
B.
Huang
,
A.
Ducoin
, and
Y. L.
Young
, “
Physical and numerical investigation of cavitating flows around a pitching hydrofoil
,”
Phys. Fluids
25
,
102109
(
2013
).
20.
B.
Ji
,
X. W.
Luo
,
R. E. A.
Arndt
, and
Y.
Wu
, “
Numerical simulation of three dimensional cavitation shedding dynamics with special emphasis on cavitation-vortex interaction
,”
Ocean Eng.
87
,
64
77
(
2014
).
21.
J.
Chen
,
B.
Huang
,
T. T.
Liu
,
Y.
Wang
, and
G. Y.
Wang
, “
Numerical investigation of cavitation-vortex interaction with special emphasis on the multistage shedding process
,”
Appl. Math. Modell.
96
,
111
130
(
2021
).
22.
R. E.
Arndt
, “
Cavitation in vortical flows
,”
Annu. Rev. Fluid Mech.
34
(
1
),
143
175
(
2002
).
23.
X. J.
Li
,
B.
Li
,
B. X.
Yu
,
Y.
Ren
, and
B.
Chen
, “
Calculation of cavitation evolution and associated turbulent kinetic energy transport around a NACA66 hydrofoil
,”
J. Mech. Sci. Technol.
33
(
3
),
1231
(
2019
).
24.
Y.
Chen
,
J.
Li
,
Z. X.
Gong
,
X.
Chen
, and
C. J.
Lu
, “
Large eddy simulation and investigation on the laminar-turbulent transition and turbulence-cavitation interaction in the cavitating flow around hydrofoil
,”
Int. J. Multiphase Flow
112
,
300
(
2019
).
25.
V.
Hidalgo
,
X. W.
Luo
,
X.
Escaler
,
B.
Ji
, and
A.
Aguinaga
, “
Implicit large eddy simulation of unsteady cloud cavitation around a plane-convex hydrofoil
,”
J. Hydrodyn.
27
,
815
823
(
2015
).
26.
G. Y.
Peng
,
C. X.
Yang
,
Y.
Oguma
, and
S.
Shimizui
, “
Numerical analysis of cavitation cloud shedding in a submerged water jet
,”
J. Hydrodyn.
28
,
986
993
(
2016
).
27.
S. J.
Zhang
,
Z. F.
Yao
,
H. F.
Wu
,
Q.
Zhong
, and
R.
Tao
, “
A new turbulent viscosity correction model with URANS solver for unsteady turbulent cavitation flow computations
,”
J. Fluids Eng.
144
(
9
),
091403
(
2020
).
28.
O.
Coutier-Delgosha
,
J. L.
Reboud
, and
Y.
Delannoy
, “
Numerical simulation of the unsteady behaviour of cavitating flows
,”
Int. J. Numer. Methods Fluids
42
(
5
),
527
548
(
2003
).
29.
O.
Coutier-Delgosha
,
R.
Fortes-Patella
, and
J. L.
Reboud
, “
Evaluation of the turbulence model influence on the numerical simulations of unsteady cavitations
,”
J Fluids Eng.
125
,
38
45
(
2003
).
30.
J.
Wu
,
G. Y.
Wang
, and
W.
Shy
, “
Time-dependent turbulent cavitating flow computations with interfacial transport and filter-based models
,”
Int. J. Numer. Methods Fluids
49
(
7
),
739
761
(
2015
).
31.
J. L.
Reboud
,
B.
Stutz
, and
O.
Coutier-Delgosha
, “
Two phase flow structure of cavitation: Experiment and modeling of unsteady effects
,” in
Proceedings of the Third Symposium on Cavitation
,
Grenoble
,
1998
.
32.
B.
Huang
,
Y. L.
Young
,
G. Y.
Wang
, and
W.
Shyy
, “
Combined experimental and computational investigation of unsteady structure of sheet/cloud cavitation
,”
J. Fluids Eng.
135
,
071301
(
2013
).
33.
B.
Budich
,
S. J.
Schmidt
, and
N. A.
Adams
, “
Numerical simulation and analysis of condensation shocks in cavitating flow
,”
J. Fluid Mech.
838
,
759
813
(
2018
).
34.
C. C.
Wang
,
G. Y.
Wang
, and
B.
Huang
, “
Characteristics and dynamics of compressible cavitating flows with special emphasis on compressibility effects
,”
Int. J. Multiphase Flow
130
,
103357
(
2020
).
35.
C. L.
Hu
,
G. Y.
Wang
,
G. H.
Chen
, and
B.
Huang
, “
A modified PANS model for computations of unsteady turbulence cavitating flows
,”
Sci. China
57
(
10
),
1967
1976
(
2014
).
36.
J. K.
Zhang
,
L.
Hao
,
Q.
Wu
, and
B.
Huang
, “
Numerical investigation on the formation of the re-entrant flow and the transformation of varying shedding modes in cloud cavitation
,”
Ocean Eng.
279
,
114557
(
2023
).
37.
J. K.
Zhang
,
Q.
Wu
,
D.
Liu
,
B.
Huang
, and
G. Y.
Wang
, “
Numerical investigation of cavitation-vortex interaction around the NACA66(mod) hydrofoil with emphasis on multistage shedding process
,”
Ocean Eng.
259
,
111661
(
2021
).
38.
Y.
Chen
,
X.
Chen
,
J.
Li
,
Z.
Gong
, and
C.
Lu
, “
Large eddy simulation and investigation on the flow structure of the cascading cavitation shedding regime around 3D twisted hydrofoil
,”
Ocean Eng.
129
,
1
19
(
2017
).
39.
B.
Ji
,
X. W.
Luo
,
R. E. A.
Arndt
,
X.
Peng
, and
Y.
Wu
, “
Large eddy simulation and theoretical investigations of the transient cavitating vortical flow structure around a NACA66 hydrofoil
,”
Int. J. Multiphase Flow
68
,
121
134
(
2015
).
40.
B.
Huang
,
Y.
Zhao
, and
G. Y.
Wang
, “
Large eddy simulation of turbulent vortex cavitation interactions in transient sheet/cloud cavitating flows
,”
Comput. Fluids
93
,
113
124
(
2014
).
41.
Q.
Wu
,
B.
Huang
,
G. Y.
Wang
, and
S. L.
Cao
, “
The transient characteristics of cloud cavitating flow over a flexible hydrofoil
,”
Int. J. Multiphase Flow
99
,
162
173
(
2018
).
42.
M.
Caciolo
,
P.
Stabat
, and
D.
Marchio
, “
Numerical simulation of single-sided ventilation using RANS and LES and comparison with full-scale experiments
,”
Build. Environ.
50
,
202
213
(
2012
).
43.
L.
Zhou
and
Z.
Wang
, “
Numerical simulation of cavitation around a hydrofoil and evaluation of a RNG j-e model
,”
J. Fluids Eng.
130
(
1
),
011302
(
2018
).
44.
A.
Gnanaskandan
and
K.
Mahesh
, “
A numerical method to simulate turbulent cavitating flows
,”
Int. J. Multiphase Flow
70
,
22
34
(
2015
).
45.
B.
Huang
,
G. Y.
Wang
,
Y.
Zhao
, and
Q.
Wu
, “
Physical and numerical investigation on transient cavitating flows
,”
Sci. China
9
(
56
),
2207
2218
(
2013
).
46.
C. C.
Wang
,
B.
Huang
,
G. Y.
Wang
,
Z. P.
Duan
, and
B.
Ji
, “
Numerical simulation of transient turbulent cavitating flows with special emphasis on shock wave dynamics considering the water/vapor compressibility
,”
J. Hydrodyn.
30
,
573
591
(
2018
).
47.
F. R.
Menter
, “
Two-equation eddy-viscosity turbulence models for engineering applications
,”
AIAA J.
32
(
8
),
1598
1605
(
1994
).
48.
N. I.
Semenov
and
S. I.
Kosterin
, “
Results of studying the speed of sound in moving gas-liquid systems
,”
Teploenergetika
11
,
46
51
(
1964
).
49.
R. E.
Henry
,
M.
Grolmes
, and
H. K.
Fauske
, “
Pressure-pulse propagation in two-phase one and two-component mixtures
,”
Technical Report No. ANL-7792
, Argonne Image Lib.,
1971
.
50.
G. H.
Schnerr
and
J.
Sauer
, “
Physical and numerical modeling of unsteady cavitation dynamics
,” in
ICMF-2001, 4th International Conference on Multiphase Flow
,
2001
.
51.
Q.
Wu
,
G. Y.
Wang
,
M.
Farhat
, and
B.
Huang
, “
An experimental study of cavity shedding mechanisms for unsteady cloud cavitation
,” in
Proceedings of 10th International Symposium on Cavitation
(
ASME Press
,
2018
), pp.
61
65
.
52.
H.
Ganesh
,
S. A.
Makiharju
, and
S. L.
Ceccio
, “
Bubbly shock propagation as a mechanism for sheet-to-cloud transition of partial cavities
,”
J. Fluid Mech.
802
,
37
78
(
2016
).
53.
G. K.
Batchelor
, “
Pressure fluctuations in isotropic turbulence
,”
Math. Proc. Cambridge Philos. Soc.
47
(
2
),
359
374
(
1951
).
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