Liquid hydrogen is considered clean energy and is usually pressurized by cryogenic pumps in various industries. To ensure the safe operation of cryogenic pumps, the inducer is installed in front of the pump to improve the impeller inlet pressure but causes cavitation instabilities. This paper aims to investigate the mechanisms of the tip leakage vortex (TLV) cavitating flow in a cryogenic inducer with liquid nitrogen. The large eddy simulations model was used to analyze the thermodynamic effects on the tip leakage vortex cavitation (TLVC). The cavity structure and the pulsation mechanisms of the TLVC were analyzed through the flow characteristics and the vorticity transportation process. The predicted cavitation performance is in good agreement with the experimental measurements. The numerical results showed that the TLVC is suppressed and forms the separation point between the primary TLVC and the secondary TLVC due to the thermodynamic effects. The inhibition rate of the vapor volume fraction at the leading edge is 30%. The pressure fluctuations are caused by the propagation pattern of the detached cavity interacting with the adjacent blade periodically. The velocity triangles near the detached cavity were proposed to reveal the development of the TLVC. It indicates that TLVC instability is caused by the periodic coupling effect of the cavity development, the flow rate magnitude, and the local incidence angle variation. The vorticity transport equation is utilized to investigate the interaction of cavitation and vortex. Comparing the three terms reveals that the stretching and bending term dominates in the vorticity production of the TLV cavitating flow. The dilatation term controls the transportation of vorticity inside the TLV cavity, while the contribution of the baroclinic torque term is negligible in comparison to the other terms. This study provides a reference for optimizing the TLV cavitating flow and instabilities for designing the cryogenic pump.
REFERENCES
1.
A.
Wei
,
L.
Yu
,
L.
Qiu
, and
X.
Zhang
, “
Cavitation in cryogenic fluids: A critical research review
,” Phys. Fluids
34
(10
), 101303
(2022
).2.
X.
Bu
,
H.
Cong
,
Z.
Sun
, and
G.
Xi
, “
Influence of thermodynamic effects on rotor-stator cavity flow in liquid oxygen turbopump
,” Phys. Fluids
35
, 026106
(2023
).3.
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
).4.
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
).5.
C.
Wang
,
Y.
Zhang
,
H.
Hou
,
J.
Zhang
, and
C.
Xu
, “
Entropy production diagnostic analysis of energy consumption for cavitation flow in a two-stage LNG cryogenic submerged pump
,” Int. J. Heat Mass Transfer
129
, 342
–356
(2019
).6.
M.
Zhang
,
B.
Huang
,
Q.
Wu
,
M.
Zhang
, and
G.
Wang
, “
The interaction between the transient cavitating flow and hydrodynamic performance around a pitching hydrofoil
,” Renewable Energy
161
, 1276
–1291
(2020
).7.
Y.
Sun
,
H.
Peng
,
W.
Liu
,
J.
Guo
, and
Y.
Guo
, “
Comparison of the hydrodynamic performance of front and rear-stator pump-jet propulsors in an oblique wake under the cavitation condition
,” Phys. Fluids
34
, 033317
(2022
).8.
X.
Jia
,
Y.
Zhang
,
H.
Lv
, and
Z.
Zhu
, “
Study on external performance and internal flow characteristics in a centrifugal pump under different degrees of cavitation
,” Phys. Fluids
35
, 014104
(2023
).9.
Y.
Wan
,
M.
Manfredi
,
A.
Pasini
, and
Z.
Spakovszky
, “
Dynamic model-based identification of cavitation compliance and mass flow gain factor in rocket engine turbopump inducers
,” J. Eng. Gas Turbines Power
143
(2
), 021011
(2021
).10.
Z.
Mu
,
T.
Chen
, and
W.
Liang
, “
Numerical investigation of rotating cavitation in a three blade inducer numerical investigation of rotating cavitation in a three blade inducer
,” J. Phys.: Conf. Ser.
2217
, 012017
(2022
).11.
L.
Xiang
,
Y.
Tan
,
H.
Chen
, and
K.
Xu
, “
Experimental investigation of cavitation instabilities in inducer with different tip clearances
,” Chin. J. Aeronaut.
34
(9
), 168
–177
(2021
).12.
A.
Goto
, “
The effect of tip leakage flow on part-load performance of a mixed-flow pump impeller
,” J. Turbomach.
114
, 383
–391
(1992
).13.
D.
Li
,
Z.
Ren
,
Y.
Li
,
B.
Miao
,
R.
Gong
, and
H.
Wang
, “
Thermodynamic effects on pressure fluctuations of a liquid oxygen turbopump
,” J. Fluids Eng. Trans. ASME
143
(11
), 111401
(2021
).14.
H.
Zhang
,
B.
Xia
,
F.
Kong
,
G.
Li
, and
P.
Cao
, “
Experimental investigation cavitation characteristics for a high-speed inducer with a great flow rate
,” Adv. Mech. Eng.
14
(3
), 1
–15
(2022
).15.
H.
Wang
,
J.
Feng
,
K.
Liu
,
X.
Shen
,
B.
Xu
,
D.
Zhang
, and
W.
Zhang
, “
Experimental study on unsteady cavitating flow and its instability in liquid rocket engine inducer
,” J. Mar. Sci. Eng.
10
, 806
(2022
).16.
Y.
Yoshida
,
M.
Eguchi
,
T.
Motomura
,
M.
Uchiumi
,
H.
Kure
, and
Y.
Maruta
, “
Rotordynamic forces acting on three-bladed inducer under supersynchronous/synchronous rotating cavitation
,” J. Fluids Eng. Trans. ASME
132
(6
), 061105
(2010
).17.
J.
Kim
and
S. J.
Song
, “
Visualization of rotating cavitation oscillation mechanism in a turbopump inducer
,” J. Fluids Eng. Trans. ASME
141
(9
), 091103
(2019
).18.
D.
Rains
, “
Tip clearance flows in axial flow compressors and pumps
,”
Ph. D. thesis
(
California Institute of Technology
, 1954
).19.
R. L.
Miorini
,
H.
Wu
, and
J.
Katz
, “
The internal structure of the tip leakage vortex within the rotor of an axial waterjet pump
,” J. Turbomach.
134
(3
), 031018
(2011
).20.
B.
Xu
,
X.
Shen
,
D.
Zhang
, and
W.
Zhang
, “
Experimental and numerical investigation on the tip leakage vortex cavitation in an axial flow pump with different tip clearances
,” Processes
7
(12
), 935
(2019
).21.
D.
Tan
,
Y.
Li
,
I.
Wilkes
,
E.
Vagnoni
,
R. L.
Miorini
, and
J.
Katz
, “
Experimental investigation of the role of large scale cavitating vortical structures in performance breakdown of an axial waterjet pump
,” J. Fluids Eng. Trans. ASME
137
(11
), 111301
(2015
).22.
Y.
Long
,
M.
Zhang
,
Z.
Zhou
,
J.
Zhong
,
C.
An
,
Y.
Chen
,
C.
Wan
, and
R.
Zhu
, “
Research on cavitation wake vortex structures near the impeller tip of a water-jet pump
,” Energies
16
, 1576
(2023
).23.
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
).24.
A. G.
Galeev
, “
Review of engineering solutions applicable in tests of liquid rocket engines and propulsion systems employing hydrogen as a fuel and relevant safety assurance aspects
,” Int. J. Hydrogen Energy
42
(39
), 25037
–25047
(2017
).25.
Z.
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
–552
(2017
).26.
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
–76
(2019
).27.
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
–630
(2019
).28.
D.
Kang
,
D.
Nakai
, and
Y.
Iga
, “
Thermodynamic effect of tip-leakage-vortex cavitation on two-dimensional hydrofoils with tip clearance for hot water
,” Int. J. Fluid Mach. Syst.
12
(4
), 368
–379
(2019
).29.
C.
Wang
,
L.
Xiang
,
Y.
Tan
,
H.
Chen
, and
K.
Xu
, “
Experimental investigation of thermal effect on cavitation characteristics in a liquid rocket engine turbopump inducer
,” Chin. J. Aeronaut.
34
(8
), 48
–57
(2021
).30.
D. J.
Kim
,
H. J.
Sung
,
C. H.
Choi
, and
J. S.
Kim
, “
Cavitation instabilities of an inducer in a cryogenic pump
,” Acta Astronaut.
132
, 19
–24
(2017
).31.
Y.
Ito
,
A.
Tsunoda
,
Y.
Kurishita
,
S.
Kitano
, and
T.
Nagasaki
, “
Experimental visualization of cryogenic backflow vortex cavitation with thermodynamic effects
,” J. Propul. Power
32
(1
), 71
–82
(2016
).32.
Y.
Ito
, “
The World's First Test Facility that enables the experimental visualization of cavitation on a rotating inducer in both cryogenic and ordinary fluids
,” J. Fluids Eng. Trans. ASME
143
(12
), 121105
(2021
).33.
Y.
Liu
,
X.
Li
,
Z.
Lin
,
L.
Li
, and
Z.
Zhu
, “
Numerical analysis of thermo-sensitive cavitating flows with special emphasises on flow separation and enstrophy conversion
,” Int. J. Heat Mass Transfer
125
, 105336
(2021
).34.
J.
Chen
,
W.
Dong
,
L.
Han
,
Y.
He
, and
T.
Chen
, “
Numerical investigation of compressible cryogenic cavitating flows by a modified mass transport model
,” Phys. Fluids
35
, 043304
(2023
).35.
Y.
Liu
,
X.
Li
,
M.
Ge
,
L.
Li
, and
Z.
Zhu
, “
Numerical investigation of transient liquid nitrogen cavitating flows with special emphasis on force evolution and entropy features
,” Cryogenics
113
, 103225
(2021
).36.
B.
Xu
,
J.
Feng
,
X.
Shen
,
D.
Zhang
, and
W.
Zhang
, “
Numerical investigation of cavitation suppression in an inducer for water and liquid nitrogen with emphasis on thermodynamic effect
,” J. Braz. Soc. Mech. Sci. Eng.
43
(4
), 212
(2021
).37.
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
).38.
Y.
Zhang
,
X.
Ren
,
Y.
Wang
,
X.
Li
,
Y.
Ito
, and
C.
Gu
, “
Investigation of the cavitation model in an inducer for water and liquid nitrogen
,” Proc. Inst. Mech. Eng., Part C
233
, 6939
–6952
(2019
).39.
Y.
Fan
,
T.
Chen
,
W.
Liang
,
G.
Wang
, and
B.
Huang
, “
Numerical and theoretical investigations of the cavitation performance and instability for the cryogenic inducer
,” Renewable Energy
184
, 291
–305
(2022
).40.
L.
Xiang
,
Y. H.
Tan
,
H.
Chen
, and
K.
Xu
, “
Numerical simulation of cryogenic cavitating flow in LRE oxygen turbopump inducer
,” Cryogenics
126
, 103540
(2022
).41.
N.
Tani
,
N.
Yamanishi
, and
Y.
Tsujimoto
, “
Influence of flow coefficient and flow structure on rotational cavitation in inducer
,” J. Fluids Eng. Trans. ASME
134
(2
), 021302
(2012
).42.
C.
Hah
, “
Investigation of turbulent tip leakage vortex in an axial
,” paper presented at Fluids Engineering Division Summer Meeting (FEDSM 2012), 2012
.43.
Z.
Wang
,
H.
Cheng
,
B.
Ji
, and
X.
Peng
, “
Numerical investigation of inner structure and its formation mechanism of cloud cavitating flow
,” Int. J. Multiphase Flow
165
, 104484
(2023
).44.
Q.
Guo
,
X.
Huang
, and
B.
Qiu
, “
Numerical investigation of the blade tip leakage vortex cavitation in a waterjet pump
,” Ocean Eng.
187
, 106170
(2019
).45.
F.
Zheng
,
X.
Zhang
,
T.
Chen
,
B.
Huang
,
J.
Xu
, and
G.
Wang
, “
Strong transient characteristics in axial flow waterjet pump during rapid starting period with special emphasis on saddle zone
,” Ocean Eng.
269
, 113506
(2023
).46.
X.
Shen
,
X.
Zhao
,
B.
Xu
,
D.
Zhang
,
G.
Yang
,
W.
Shi
, and
B. P. M.
(Bart) van Esch
, “
Unsteady characteristics of tip leakage vortex structure and dynamics in an axial flow pump
,” Ocean Eng.
266
, 112850
(2022
).47.
L.
Yan
,
B.
Gao
,
D.
Ni
,
N.
Zhang
, and
W.
Zhou
, “
Numerical study of unsteady cavitating flow in an inducer with omega vortex identification
,” J. Fluids Eng. Trans. ASME
144
(9
), 091203
(2022
).48.
Z.
Chen
,
S.
Yang
,
X.
Li
,
Y.
Li
, and
L.
Li
, “
Investigation on leakage vortex cavitation and corresponding enstrophy characteristics in a liquid nitrogen inducer
,” Cryogenics
129
, 103606
(2023
).49.
A.
Kubota
,
H.
Kato
, and
H.
Yamaguchi
, “
A new modelling of cavitating flows: A numerical study of unsteady cavitation on a hydrofoil section
,” J. Fluid Mech.
240
(3
), 59
–96
(1992
).50.
J.
Smagorinsky
, “
General circulation experiments with the primitive equations
,” Mon. Weather Rev.
91
(3
), 99
–164
(1963
).51.
F.
Nicoud
and
F.
Ducros
, “
Subgrid-scale stress modelling based on the square of the velocity
,” Flow Meas. Instrum.
62
, 183
–200
(1999
).52.
A. K.
Singhal
,
M. M.
Athavale
,
H.
Li
, and
Y.
Jiang
, “
Mathematical basis and validation of the full cavitation model
,” J. Fluids Eng. Trans. ASME
124
(3
), 617
–624
(2002
).53.
L. F.
Richardson
, “
IX. The approximate arithmetical solution by finite differences of physicalproblems involving differential equations, with an application to the stresses in a masonary dam
,” Philos. Trans. R. Soc. London, Ser. A
210
, 307
–357
(1911
).54.
“Procedure for estimation and reporting of uncertainty due to discretization in CFD applications,”
J. Fluids Eng. Trans. ASME
130
(7
), 0780011
(2008
).55.
X.
Zhao
,
T.
Chen
,
X.
Liu
,
B.
Huang
, and
G.
Wang
, “
Characteristics and mechanisms of the tip leakage cavitating flow around a NACA66(mod) hydrofoil under different cavitation states
,” Ocean Eng.
266
, 112704
(2022
).56.
M.
Xu
,
H.
Cheng
,
B.
Ji
, and
X.
Peng
, “
LES of tip-leakage cavitating flow with special emphasis on different tip clearance sizes by a new Euler-Lagrangian cavitation model
,” Ocean Eng.
213
, 107661
(2020
).57.
X.
Wang
,
X.
Bai
,
H.
Cheng
,
A.
Yu
, and
B.
Ji
, “
LES investigation of cavitation harmonic tone around a Delft twist-11 hydrofoil
,” Ocean Eng.
253
, 111313
(2022
).58.
X.
Bai
,
H.
Cheng
, and
B.
Ji
, “
LES investigation of the noise characteristics of sheet and tip leakage vortex cavitating flow
,” Int. J. Multiphase Flow
146
, 103880
(2022
).59.
S.
Kim
,
C.
Choi
,
J.
Kim
,
J.
Park
, and
J.
Baek
, “
Tip clearance effects on cavitation evolution and head breakdown in turbopump inducer
,” J. Propul. Power
29
(6
), 1357
–1366
(2013
).60.
T.
Kimura
, “
Numerical simulation for vortex structure in a turbopump inducer: Close relationship with appearance of cavitation
,” J. Fluids Eng. Trans. ASME
130
(5
), 051104
(2008
).61.
H.
Cheng
,
X.
Bai
,
X.
Long
,
B.
Ji
,
X.
Peng
, and
M.
Farhat
, “
Large eddy simulation of the tip-leakage cavitating flow with an insight on how cavitation influences vorticity and turbulence
,” Appl. Math. Modell.
77
, 788
–809
(2020
).62.
A.
Yu
,
Z.
Qian
,
X.
Wang
,
Q.
Tang
, and
D.
Zhou
, “
Large Eddy simulation of ventilated cavitation with an insight on the correlation mechanism between ventilation and vortex evolutions
,” Appl. Math. Modell.
89
, 1055
–1073
(2021
).63.
H.
Zhang
,
J.
Wang
,
D.
Zhang
,
W.
Shi
, and
J.
Zang
, “
Numerical analysis of the effect of cavitation on the tip leakage vortex in an axial-flow pump
,” J. Mar. Sci. Eng.
9
, 775
(2021
).© 2023 Author(s). Published under an exclusive license by AIP Publishing.
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