The objectives of this study are to propose exact numerical methods for the compressible cryogenic cavitating flows and investigate the cavitation behaviors and vortex structures. A numerical modeling framework including large eddy simulations, vapor–liquid equations of state, and a modified mass transport model is presented in this paper. The modified transport model is proposed based on the convective heat transfer in which the convective heat transfer coefficient is associated with the material properties and local temperature. To validate the applicability of the modified model, the liquid nitrogen cavitating flows in the inertial and thermal modes (σ ≈ 0.50, Tthroat = 77.24 K and Tthroat = 85.23 K) are simulated, respectively. Meanwhile, the influence of thermodynamic effects on compressibility is investigated. The numerical method is further utilized to visualize the detailed cavity and vortex structures in different cavitating flow patterns (Tthroat ≈ 77 K, σ = 0.58, 0.39, 0.18). The results show that the predicted cavity structures with the modified mass transport model agree better with the corresponding experimental data. For the thermal mode, since the significant thermal effects restrain the development of cavity, the area of the low sound speed region is smaller than that of the inertial model. The value of the minimum sound speed is larger, so that the Mach number in the cavitation region is reduced. Therefore, the compressibility of the liquid nitrogen cavitation in the thermal mode is weaker. For different cavitating flow patterns, the core region of attached cavities near the throat remains stable during an evolutionary cycle. Compared to the attached cavity region, since some hairpin vortices break into many small-scale discrete vortices, the multi-scale effect of vortex distribution is more remarkable in the shedding cavity region.
REFERENCES
1.
K.
Mani
,
A.
Cervone
, and
J.-P.
Hickey
, “
Turbulence modelling and cavitation dynamics in cryogenic turbopumps
,” in Proceedings of the 5th Space Propulsion
(2016
).2.
K. J.
Petersen
and
J. R.
Brinkerhoff
, “
On the lattice Boltzmann method and its application to turbulent, multiphase flows of various fluids including cryogens: A review
,” Phys. Fluids
33
, 041302
(2021
).3.
A.
Wei
,
L.
Yu
,
L.
Qiu
, and
X.
Zhang
, “
Cavitation in cryogenic fluids: A critical research review
,” Phys. Fluids
34
, 101303
(2022
).4.
B.
Huang
,
Y. L.
Young
,
G.
Wang
, and
W.
Shyy
, “
Combined experimental and computational investigation of unsteady structure of sheet/cloud cavitation
,” ASME J. Fluids Eng.
135
, 071301
(2013
).5.
6.
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
(2015
).7.
M.
Dular
and
O.
Coutier-Delgosha
, “
Thermodynamic effects during growth and collapse of a single cavitation bubble
,” J. Fluid Mech.
736
, 44
(2013
).8.
M.
Ge
,
M.
Petkovsek
,
G.
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
).9.
S.
Watanabe
,
A.
Furukawa
, and
Y.
Yoshida
, “
Theoretical analysis of thermodynamic effect of cavitation in cryogenic inducer using singularity method
,” Int. J. Rotating Mach.
2008
(8
), 125678
.10.
Z.
Zuo
,
H.
Zhang
,
Z.
Ren
,
H.
Chen
, and
S.
Liu
, “
Thermodynamic effects at Venturi cavitation in different liquids
,” Phys. Fluids
34
, 083310
(2022
).11.
T.
Chen
,
H.
Chen
,
W.
Liu
,
B.
Huang
, and
G.
Wang
, “
Unsteady characteristics of liquid nitrogen cavitating flows in different thermal cavitation mode
,” Appl. Therm. Eng.
156
, 63
(2019
).12.
Y.
Utturkar
,
J. Y.
Wu
,
G. Y.
Wang
, and
W.
Shyy
, “
Recent progress in modeling of cryogenic cavitation for liquid rocket propulsion
,” Prog. Aerosp. Sci.
41
, 558
(2005
).13.
Y.
Ito
,
A.
Tsunoda
, and
T.
Nagasaki
, Experimental Comparison of Backflow-Vortex Cavitation on Pump Inducer between Cryogen and Water
(
Ecole Polytechnique Federale Lausanne
,
Lausanne, Switzerland
, 2015
).14.
L. R.
Sarósdy
and
A. J.
Acosta
, “
Note on observations of cavitation in different fluids
,” J. Basic Eng.
83
, 399
(1961
).15.
J. P.
Franc
,
C.
Rebattet
, and
A.
Coulon
, “
An experimental investigation of thermal effects in a cavitating inducer
,” ASME J. Fluids Eng.
126
, 716
(2004
).16.
Y.
Yoshida
,
K.
Kikuta
,
S.
Hasegawa
,
M.
Shimagaki
, and
T.
Tokumasu
, “
Thermodynamic effect on a cavitating inducer in liquid nitrogen
,” ASME J. Fluids Eng.
129
, 273
(2007
).17.
Y.
Yoshida
,
K.
Kikuta
,
K.
Niiyama
, and
S.
Watanabe
, Thermodynamic Parameter on Cavitation in Space Inducer
(
ASME
,
Rio Grande, Puerto Rico
, 2012
).18.
A.
Cervone
,
R.
Testat
,
C. L.
Bramanti
,
E.
Rapposello
, and
L.
d'Agostino
, “
Thermal effects on cavitation instabilities in helical inducers
,” J. Propul. Power
21
, 893
(2005
).19.
J. P. R.
Gustavsson
,
K. C.
Denning
, and
C.
Segal
, “
Hydrofoil cavitation under strong thermodynamic effect
,” ASME J. Fluids Eng.
130
, 091303
(2008
).20.
J.
Zhu
,
S.
Wang
, and
X.
Zhang
, “
Influences of thermal effects on cavitation dynamics in liquid nitrogen through venturi tube
,” Phys. Fluids
32
, 012105
(2020
).21.
J.
Zhu
,
H.
Xie
,
K.
Feng
,
X.
Zhang
, and
M.
Si
, “
Unsteady cavitation characteristics of liquid nitrogen flows through venturi tube
,” Int. J. Heat Mass Transfer
112
, 544
(2017
).22.
T.
Chen
,
H.
Chen
,
W.
Liang
,
B.
Huang
, and
L.
Xiang
, “
Experimental investigation of liquid nitrogen cavitating flows in converging-diverging nozzle with special emphasis on thermal transition
,” Int. J. Heat Mass Transfer
132
, 618
(2019
).23.
W.
Liang
,
T.
Chen
,
G.
Wang
, and
B.
Huang
, “
Experimental investigations on transient dynamics of cryogenic cavitating flows under different free-stream conditions
,” Int. J. Heat Mass Transfer
178
, 121537
(2021
).24.
K.
Ohira
,
T.
Nakayama
, and
T.
Nagai
, “
Cavitation flow instability of subcooled liquid nitrogen in converging-diverging nozzles
,” Cryogenics
52
, 35
(2012
).25.
T.
Chen
,
B.
Huang
,
G.
Wang
, and
X.
Zhao
, “
Numerical study of cavitating flows in a wide range of water temperatures with special emphasis on two typical cavitation dynamics
,” Int. J. Heat Mass Transfer
101
, 886
(2016
).26.
A.
Hosangadi
and
V.
Ahuja
, “
Numerical study of cavitation in cryogenic fluids
,” J. Fluids Eng.
127
, 267
(2005
).27.
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
).28.
M.
Gavaises
,
F.
Villa
,
P.
Koukouvinis
,
M.
Marengo
, and
J. P.
Franc
, “
Visualisation and les simulation of cavitation cloud formation and collapse in an axisymmetric geometry
,” Int. J. Multiphase Flow
68
, 14
(2015
).29.
A.
Gnanaskandan
and
K.
Mahesh
, “
Large eddy Simulation of the transition from sheet to cloud cavitation over a wedge
,” Int. J. Multiphase Flow
83
, 86
(2016
).30.
W.
Liang
,
T.
Chen
,
G.
Wang
, and
B.
Huang
, “
Investigation of unsteady liquid nitrogen cavitating flows with special emphasis on the vortex structures using mode decomposition methods
,” Int. J. Heat Mass Transfer
157
, 119880
(2020
).31.
A. K.
Singhal
,
M. M.
Athavale
,
H. Y.
Li
, and
Y.
Jiang
, “
Mathematical basis and validation of the full cavitation model
,” ASME J. Fluids Eng.
124
, 617
(2002
).32.
R. F.
Kunz
,
D. A.
Boger
,
D. R.
Stinebring
,
T. S.
Chyczewski
,
J. W.
Lindau
,
H. J.
Gibeling
,
S.
Venkateswaran
, and
T. R.
Govindan
, “
A preconditioned Navier-Stokes method for two-phase flows with application to cavitation prediction
,” Comput. Fluids
29
, 849
(2000
).33.
P. J.
Zwart
,
A. G.
Gerber
, and
T.
Belamri
, “
A two-phase flow model for predicting cavitation dynamics
,” in 5th International Conference on Multiphase Flow
(ICMF
, 2004
).34.
A.
Hosangadi
and
V.
Ahuja
, “
A generalized multi-phase framework for modeling cavitation in cryogenic fluids
,” in 33rd American Institute of Aeronautics and Astronautics Fluid Dynamics Conference and Exhibit
, Orlando
, 2003
(AIAA
, 2003).35.
B.
Huang
,
Q.
Wu
, and
G.
Wang
, “
Numerical investigation of cavitating flow in liquid hydrogen
,” Int. J. Hydrogen Energy
39
, 1698
(2014
).36.
T.
Sun
,
X.
Ma
,
Y.
Wei
, and
C.
Wang
, “
Computational modeling of cavitating flows in liquid nitrogen by an extended transport-based cavitation model
,” Sci. China Technol. Sci.
59
, 337
(2016
).37.
S.
Zhang
,
X.
Li
, and
Z.
Zhu
, “
Numerical simulation of cryogenic cavitating flow by an extended transport-based cavitation model with thermal effects
,” Cryogenics
92
, 98
(2018
).38.
M. G.
Rodio
,
M. G.
De Giorgi
, and
A.
Ficarella
, “
Influence of convective heat transfer modeling on the estimation of thermal effects in cryogenic cavitating flows
,” Int. J. Heat Mass Transfer
55
, 6538
(2012
).39.
Y.
Iga
,
M.
Nohml
,
A.
Goto
, and
T.
Ikohagi
, “
Numerical analysis of cavitation instabilities arising in the three-blade cascade
,” ASME J. Fluids Eng.
126
, 419
(2004
).40.
L.
Zhang
and
B. C.
Khoo
, “
Dynamics of unsteady cavitating flow in compressible two-phase fluid
,” Ocean Eng.
87
, 174
(2014
).41.
Y.
Saito
,
R.
Takami
,
I.
Nakamori
, and
T.
Ikohagi
, “
Numerical analysis of unsteady behavior of cloud cavitation around a NACA0015 foil
,” Comput. Mech.
40
, 85
(2007
).42.
B.
Budich
,
S. J.
Schmidt
, and
N. A.
Adams
, “
Numerical simulation and analysis of condensation shocks in cavitating flow
,” J. Fluid Mech.
838
, 759
(2018
).43.
M.
Bhatt
and
K.
Mahesh
, “
Numerical investigation of partial cavitation regimes over a wedge using large eddy simulation
,” Int. J. Multiphase Flow
122
, 103155
(2020
).44.
C.
Wang
,
B.
Huang
,
G.
Wang
,
Z.
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
(2018
).45.
X.
Li
,
T.
Shen
,
P.
Li
,
X.
Guo
, and
Z.
Zhu
, “
Extended compressible thermal cavitation model for the numerical simulation of cryogenic cavitating flow
,” Int. J. Hydrogen Energy
45
, 10104
(2020
).46.
J.
Hord
, “
Cavitation in liquid cryogens. III. Ogives
,” Report No. NASA-CR-2242 (1973
).47.
J.
Hord
, “Cavitation in liquid cryogens. IV. Combined correlations for venturi, hydrofoil, ogives, and pumps
,” Report No. NASA-CR-2448 (1974
).48.
A.
Kubota
,
H.
Kato
, and
H.
Yamaguchi
, “
A new modeling of cavitating flows—A numerical study of unsteady cavitation on a hydrofoil section
,” J. Fluid Mech.
240
, 59
(1992
).49.
J.
Sauer
and
G. H.
Schnerr
, “
Unsteady cavitating flow -a new cavitation model based on a modified front capturing method and bubble dynamics
,” in Proceedings of 2000 ASME Fluid Engineering Summer Conference
, 11
–15
(
ASME
, 2000
).50.
F.
Nicoud
and
F.
Ducros
, “
Subgrid-scale stress modelling based on the square of the velocity gradient tensor
,” Flow Turbul. Combust.
62
, 183
(1999
).51.
J.
Smagorinsky
, “
General circulation experiments with the primitive equations. I: The basic experiment
,” Mon. Weather Rev.
91
(3
), 99
(1963
).52.
H. T.
Chen
and
R.
Collins
, “
Shock wave propagation past an ocean surface
,” J. Comput. Phys.
7
, 89
(1971
).53.
H. B.
Karplus
, “
Velocity of sound in a liquid containing gas bubbles
,” J. Acoust. Soc. Am.
29
, 1261
(1957
).54.
See https://www.nist.gov/srd/refprop for
E.
Lemmon
, “
Reference fluid thermodynamic and transport properties (REFPROP)
,” (
NIST Standard Reference Database
, 2007
).55.
M. S.
Plesset
, “
The dynamics of cavitation bubbles
,” J. Appl. Mech. Transac. ASME
16
, 277
(1949
).56.
J.
Franc
and
J.
Michel
, Fundamentals of Cavitation
(
Springer Science and Business Media
, 2006
).57.
T.-H.
Phan
,
E.
Kadivar
,
V.-T.
Nguyen
,
O.
el Moctar
, and
W.-G.
Park
, “
Thermodynamic effects on single cavitation bubble dynamics under various ambient temperature conditions
,” Phys. Fluids
34
, 023318
(2022
).58.
D.
Colombet
,
E. G.
Da Silva
, and
R.
Fortes-Patella
, “
On numerical simulation of cavitating flows under thermal regime
,” Int. J. Heat Mass Transfer
105
, 411
(2017
).59.
T.
Chen
,
Z.
Mu
,
B.
Huang
,
M.
Zhang
, and
G.
Wang
, “
Dynamic instability analysis of cavitating flow with liquid nitrogen in a converging-diverging nozzle
,” Appl. Therm. Eng.
192
, 116870
(2021
).60.
A.
Wei
,
L.
Yu
,
R.
Gao
,
W.
Zhang
, and
X.
Zhang
, “
Unsteady cloud cavitation mechanisms of liquid nitrogen in convergent-divergent nozzle
,” Phys. Fluids
33
, 092116
(2021
).61.
H.
Stahl
and
A. J.
Stepanoff
, “
Thermodynamic aspects of cavitation in centrifugal pumps
,” J. Basic Eng.
78
, 1691
–1693
(1956
).62.
X.
Long
,
H.
Cheng
,
B.
Ji
,
R. E. A.
Arndt
, and
X.
Peng
, “
Large eddy simulation and Euler-Lagrangian coupling investigation of the transient cavitating turbulent flow around a twisted hydrofoil
,” Int. J. Multiphase Flow
100
, 41
(2018
).63.
J.
Hunt
,
A. A.
Wray
, and
P.
Moin
, “
Eddies, streams, and convergence zones in turbulent flows
,” in Proceedings of CTR Summer Program
(
Stanford University
, 1988
).© 2023 Author(s). Published under an exclusive license by AIP Publishing.
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