The present study provides a numerical method for liquid jet atomization in supersonic gas crossflow. Compressibility of the gas and incompressibility of the liquid are considered. High-order accurate weighted essentially non-oscillatory schemes and the Harten–Lax–van Leer contact approximate Riemann solver are used for gas flows. Liquid flow is simulated by the Chorin projection method. The motion of the sharp interface between the gas and liquid is simulated by the volume of fluid method. In order to verify the accuracy of the numerical method, numerical and experimental results for the droplet breakup in the supersonic gas flow are compared. The method is employed to simulate the liquid jet atomization in the supersonic gas crossflow. According to numerical results, the breakup process is analyzed for four different stages. The discussion for the effect of the Mach number for the gas crossflow on the liquid jet atomization is given.

1.
N.
Weber
 et al, “
Sloshing instability and electrolyte layer rupture in liquid metal batteries
,”
Phys. Fluids
29
,
054101
(
2017
).
2.
P. A.
Caron
,
M. A.
Cruchaga
, and
A. E.
Larreteguy
, “
Study of 3D sloshing in a vertical cylindrical tank
,”
Phys. Fluids
30
,
082112
(
2018
).
3.
V. T.
Gurumurthy
and
S.
Pushpavanam
, “
Hydrodynamics of a compound drop in plane Poiseuille flow
,”
Phys. Fluids
32
,
072003
(
2020
).
4.
N.
Goyal
,
J.
Shaikh
, and
A.
Sharma
, “
Bubble entrapment during head-on binary collision with large deformation of unequal-sized tetradecane droplets
,”
Phys. Fluids
32
,
122114
(
2020
).
5.
K.
Monroe
 et al, “
Role of pulsatility on particle dispersion in expiratory flows
,”
Phys. Fluids
33
,
043311
(
2021
).
6.
M.
Herrmann
, “
The influence of density ratio on the primary atomization of a turbulent liquid jet in crossflow
,”
Proc. Combust. Inst.
33
,
2079
2088
(
2011
).
7.
H.
Liu
,
Y.
Guo
, and
W.
Lin
, “
Numerical simulations of spray jet in supersonic crossflows using an Eulerian approach with an SMD model
,”
Int. J. Multiphase Flow
82
,
49
64
(
2016
).
8.
P.
Li
 et al, “
Numerical simulation of the gas–liquid interaction of a liquid jet in supersonic crossflow
,”
Acta Astronaut.
134
,
333
344
(
2017
).
9.
F.
Xiao
 et al, “
Large eddy simulation of liquid jet primary breakup in supersonic air crossflow
,”
Int. J. Multiphase Flow
87
,
229
240
(
2016
).
10.
F.
Xiao
 et al, “
Simulation of drop deformation and breakup in supersonic flow
,”
Proc. Combust. Inst.
36
(
2
),
2417
2424
(
2017
).
11.
M.
Behzad
,
N.
Ashgriz
, and
B. W.
Karney
, “
Surface breakup of a non-turbulent liquid jet injected into a high pressure gaseous crossflow
,”
Int. J. Multiphase Flow
80
,
100
117
(
2016
).
12.
X.
Li
 et al, “
High fidelity simulation and analysis of liquid jet atomization in a gaseous crossflow at intermediate Weber numbers
,”
Phys. Fluids
28
(
8
),
1
35
(
2016
).
13.
X.
Li
,
H.
Gao
, and
M. C.
Soteriou
, “
Investigation of the impact of high liquid viscosity on jet atomization in crossflow via high-fidelity simulations
,”
Phys. Fluids
29
(
8
),
082103
(
2017
).
14.
X.
Li
and
M. C.
Soteriou
, “
Detailed numerical simulation of liquid jet atomization in crossflow of increasing density
,”
Int. J. Multiphase Flow
104
,
214
232
(
2018
).
15.
R. S.
Prakash
 et al, “
Liquid jet in crossflow—Effect of liquid entry conditions
,”
Exp. Therm. Fluid Sci.
93
,
45
56
(
2017
).
16.
Z. P.
Tan
 et al, “
The regimes of twin-fluid jet-in-crossflow at atmospheric and jet-engine operating conditions
,”
Phys. Fluids
30
(
2
),
025101
(
2018
).
17.
W. A.
Miller
 et al, “
Transient interaction between a reaction control jet and a hypersonic crossflow
,”
Phys. Fluids
30
(
4
),
046102
(
2018
).
18.
G.
Amini
, “
Linear stability analysis of a liquid jet in a weak crossflow
,”
Phys. Fluids
30
(
8
),
084105
(
2018
).
19.
J.
Huang
and
X.
Zhao
, “
Numerical simulations of atomization and evaporation in liquid jet flows
,”
Int. J. Multiphase Flow
119
,
180
193
(
2019
).
20.
S.
Behera
and
A. K.
Saha
, “
Evolution of the flow structures in an elevated jet in crossflow
,”
Phys. Fluids
32
(
1
),
015102
(
2020
).
21.
T. G.
Theofanous
and
G. J.
Li
, “
On the physics of aerobreakup
,”
Phys. Fluids
20
(
5
),
201
(
2008
).
22.
Y. J.
Kim
and
J. C.
Hermanson
, “
Breakup and vaporization of droplets under locally supersonic conditions
,”
Phys. Fluids
24
(
7
),
507
512
(
2012
).
23.
M.
Jalaal
and
K.
Mehravaran
, “
Transient growth of droplet instabilities in a stream
,”
Phys. Fluids
26
(
1
),
721
735
(
2014
).
24.
N.
Liu
 et al, “
Numerical simulation of liquid droplet breakup in supersonic flows
,”
Acta Astronaut.
145
,
116
130
(
2018
).
25.
D.
Stefanitsis
 et al, “
Numerical investigation of the aerodynamic breakup of droplets in tandem
,”
Int. J. Multiphase Flow
113
,
289
303
(
2019
).
26.
J. W. J.
Kaiser
 et al, “
Investigation of interface deformation dynamics during high-Weber number cylindrical droplet breakup
,”
Int. J. Multiphase Flow
132
,
103409
(
2020
).
27.
E.
Johnsen
and
T.
Colonius
, “
Implementation of WENO schemes in compressible multicomponent flow problems
,”
J. Comput. Phys.
219
(
2
),
715
732
(
2006
).
28.
J. Y.
Lin
 et al, “
Simulation of compressible two-phase flows with topology change of fluid–fluid interface by a robust cut-cell method
,”
J. Comput. Phys.
328
,
140
159
(
2017
).
29.
K.
Ritos
 et al, “
Implicit large eddy simulation of acoustic loading in supersonic turbulent boundary layers
,”
Phys. Fluids
29
(
4
),
1
11
(
2017
).
30.
F.
Harlow
and
A.
Amsden
, “
Fluid dynamics
,” in
Monograph LA-4700
(
Los Alamos National Laboratory
,
Los Alamos, NM
,
1971
).
31.
J. P.
Cocchi
,
R.
Saurel
, and
J. C.
Loraud
, “
Treatment of interface problems with Godunov-type schemes
,”
Shock Waves
5
,
347
357
(
1996
).
32.
R. F.
Warming
and
R. M.
Beam
, “
Upwind second-order difference schemes and applications in aerodynamic flows
,”
AIAA J.
14
(
9
),
1241
1249
(
1976
).
33.
R.
Rannacher
, “
On Chorin's projection method for the incompressible Navier–Stokes equations
,” in
Lecture Notes on Mathematics
(Springer,
1992
), Vol.
1530
, pp.
167
183
.
34.
G. S.
Jiang
and
C. W.
Shu
, “
Efficient implementation of WENO schemes
,”
J. Comput. Phys.
126
,
202
228
(
1996
).
35.
P.
Batten
 et al, “
On the choice of wavespeeds for the HLLC Riemann solver
,”
SIAM J. Sci. Comput.
18
,
1553
1570
(
1997
).
36.
P. L.
Roe
, “
Approximate Riemann solvers, parameter vectors, and difference schemes
,”
J. Comput. Phys.
43
,
357
372
(
1981
).
37.
B.
Einfeldt
 et al, “
On Godunov-type methods near low densities
,”
J. Comput. Phys.
92
,
273
295
(
1991
).
38.
E. F.
Toro
,
Riemann Solvers and Numerical Methods for Fluid Dynamics
(
Springer
,
Heidelberg
,
1999
).
39.
E. F.
Toro
,
M.
Spruce
, and
W.
Speares
, “
Restoration of the contact surface in the HLL-Riemann solver
,”
Shock Waves
4
,
25
34
(
1994
).
40.
S. C.
Schlanderer
,
G. D.
Weymouth
, and
R. D.
Sandberg
, “
The boundary data immersion method for compressible flows with application to aeroacoustics
,”
J. Comput. Phys.
333
,
440
461
(
2017
).
41.
J.
Shentu
 et al, “
Numerical simulations for water entry of hydrophobic objects
,”
Ocean Eng.
190
,
106485
(
2019
).
42.
D.
Li
 et al, “
Numerical investigation of the water entry of a hydrophobic sphere with spin
,”
Int. J. Multiphase Flow
126
,
103234
(
2020
).
43.
H. W.
Liepmann
and
A.
Roshko
,
Elements of Gas Dynamics
(
Wiley
,
1957
).
You do not currently have access to this content.