Abstract

A three-dimensional (3D) gradient-augmented level set (GALS) two-phase flow model with a pretreated reinitialization procedure is developed to simulate violent sloshing in a cuboid tank. Based on a two-dimensional (2D) GALS method, 3D Hermite, and 3D Lagrange polynomial schemes are derived to interpolate the level set function and the velocity field at arbitrary positions over a cell, respectively. A reinitialization procedure is performed on a 3D narrow band to treat the strongly distorted interface and improve computational efficiency. In addition, an identification-correction technique is proposed and incorporated into the reinitialization procedure to treat the tiny droplet which can distort the free surface shape, even lead to computation failure. To validate the accuracy of the present GALS method and the effectiveness of the proposed identification-correction technique, a 3D velocity advection case is first simulated. The present method is validated to have better mass conservation property than the classical level set and original GALS methods. Also, distorted and thin interfaces are well captured on all grid resolutions by the present GALS method. Then, sloshing under coupled surge and sway excitation, sloshing under rotational excitation are simulated. Good agreements are obtained when the present wave and pressure results are compared with the experimental and numerical results. In addition, the highly nonlinear free surface is observed, and the relationship between the excitation frequency and the impulsive pressure is investigated.

References

References
1.
Arai
,
M.
,
1984
, “
Experimental and Numerical Studies of Sloshing Pressure in Liquid Cargo Tanks
,”
J. Jpn. Soc. Nav. Archit. Ocean Eng.
, 1984(155), pp.
114
121
.10.2534/jjasnaoe1968.1984.114
2.
Akyildiz
,
H.
, and
Ünal
,
E.
,
2005
, “
Experimental Investigation of Pressure Distribution on a Rectangular Tank Due to the Liquid Sloshing
,”
Ocean Eng.
,
32
(
11–12
), pp.
1503
1516
.10.1016/j.oceaneng.2004.11.006
3.
Faltinsen
,
O. M.
,
Rognebakke
,
O. F.
,
Lukovsky
,
I. A.
, and
Timokha
,
A. N.
,
2000
, “
Multidimensional Modal Analysis of Nonlinear Sloshing in a Rectangular Tank With Finite Water Depth
,”
J. Fluid Mech.
,
407
(
407
), pp.
201
234
.10.1017/S0022112099007569
4.
Ibrahim
,
R. A.
,
2015
, “
Recent Advances in Physics of Fluid Parametric Sloshing and Related Problems
,”
ASME J. Fluids Eng.
,
137
(
9
), p.
090801
.10.1115/1.4029544
5.
Cao
,
X. Y.
,
Ming
,
F. R.
, and
Zhang
,
A. M.
,
2014
, “
Sloshing in a Rectangular Tank Based on SPH Simulation
,”
Appl. Ocean Res.
,
47
(
2
), pp.
241
254
.10.1016/j.apor.2014.06.006
6.
Ozbulut
,
M.
,
Tofighi
,
N.
,
Goren
,
O.
, and
Yildiz
,
M.
,
2017
, “
Investigation of Wave Characteristics in Oscillatory Motion of Partially Filled Rectangular Tanks
,”
ASME J. Fluids Eng.
,
140
(
4
), p.
041204
.10.1115/1.4038242
7.
Daneshvar
,
F. A.
,
Rakhshandehroo
,
G. R.
, and
Talebbeydokhti
,
N.
,
2017
, “
New Modified Gradient Models for MPS Method Applied to Free-Surface Flow Simulations
,”
Appl. Ocean Res.
,
66
, pp.
95
116
.10.1016/j.apor.2017.05.009
8.
Zhao
,
Y.
, and
Chen
,
H. C.
,
2015
, “
Numerical Simulation of 3D Sloshing Flow in Partially Filled LNG Tank Using a Coupled Level-Set and Volume-of-Fluid Method
,”
Ocean Eng.
,
104
, pp.
10
30
.10.1016/j.oceaneng.2015.04.083
9.
Liu
,
D.
, and
Lin
,
P.
,
2009
, “
Three-Dimensional Liquid Sloshing in a Tank With Baffles
,”
Ocean Eng.
,
36
(
2
), pp.
202
212
.10.1016/j.oceaneng.2008.10.004
10.
Chen
,
H. H.
, and
Liu
,
C. S.
,
1978
, “
Numerical Simulation of Liquid Sloshing in a Partially Filled Container With Inclusion of Compressibility Effects
,”
Phys. Fluids
,
21
(
3
), p.
377
.10.1063/1.862236
11.
Jafari
,
A.
, and
Ashgriz
,
N.
,
2015
,
Numerical Techniques for Free Surface Flows: Interface Capturing and Interface Tracking
,
Springer
,
New York
.
12.
Sussman
,
M.
,
Smereka
,
P.
, and
Osher
,
S.
,
1994
, “
A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow
,”
J. Comput. Phys.
,
114
(
1
), pp.
146
159
.10.1006/jcph.1994.1155
13.
Hirt
,
C. W.
, and
Nichols
,
B. D.
,
1981
, “
Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries
,”
J. Comput. Phys.
,
39
(
1
), pp.
201
225
.10.1016/0021-9991(81)90145-5
14.
Ansari
,
M. R.
,
Azadi
,
R.
, and
Salimi
,
E.
,
2016
, “
Capturing of Interface Topological Changes in Two-Phase Gas–Liquid Flows Using a Coupled Volume-of-Fluid and Level-Set Method (VOSET)
,”
Comput. Fluids
,
125
, pp.
82
100
.10.1016/j.compfluid.2015.09.014
15.
Osher
,
S.
,
Fedkiw
,
R.
, and
Piechor
,
K.
,
2003
,
Level Set Methods and Dynamic Implicit Surfaces
,
Springer
,
New York
.
16.
Gu
,
H. B.
,
Qian
,
L.
,
Causon
,
D. M.
,
Mingham
,
C. G.
, and
Lin
,
P.
,
2014
, “
Numerical Simulation of Water Impact of Solid Bodies With Vertical and Oblique Entries
,”
Ocean Eng.
,
75
(
5
), pp.
128
137
.10.1016/j.oceaneng.2013.11.021
17.
Bai
,
W.
,
Liu
,
X.
, and
Koh
,
C. G.
,
2015
, “
Numerical Study of Violent LNG Sloshing Induced by Realistic Ship Motions Using Level Set Method
,”
Ocean Eng.
,
97
, pp.
100
113
.10.1016/j.oceaneng.2015.01.010
18.
Bihs
,
H.
,
Kamath
,
A.
,
Alagan Chella
,
M.
,
Aggarwal
,
A.
, and
Arntsen
,
Ø. A.
,
2016
, “
A New Level Set Numerical Wave Tank With Improved Density Interpolation for Complex Wave Hydrodynamics
,”
Comput. Fluids
,
140
, pp.
191
208
.10.1016/j.compfluid.2016.09.012
19.
Adalsteinsson
,
D.
, and
Sethian
,
J. A.
,
1995
, “
A Fast Level Set Method for Propagating Interfaces
,”
J. Comput. Phys.
,
118
(
2
), pp.
269
277
.10.1006/jcph.1995.1098
20.
Sethian
,
J. A.
,
1999
,
Level Set Methods and Fast Marching Methods
,
Cambridge University Press
,
New York
.
21.
Sussman
,
M.
, and
Puckett
,
E. G.
,
2000
, “
A Coupled Level Set and Volume-of-Fluid Method for Computing 3D and Axisymmetric Incompressible Two-Phase Flows
,”
J. Comput. Phys.
,
162
(
2
), pp.
301
337
.10.1006/jcph.2000.6537
22.
Liu
,
D.
,
Tang
,
W.
,
Wang
,
J.
,
Xue
,
H.
, and
Wang
,
K.
,
2017
, “
Modelling of Liquid Sloshing Using CLSVOF Method and Very Large Eddy Simulation
,”
Ocean Eng.
,
129
, pp.
160
176
.10.1016/j.oceaneng.2016.11.027
23.
Zhao
,
Y.
,
Chen
,
H. C.
, and
Yu
,
X.
,
2015
, “
Numerical Simulation of Wave Slamming on 3D Offshore Platform Deck Using a Coupled Level-Set and Volume-of-Fluid Method for Overset Grid System
,”
5
(
4
), pp.
245
259
.
24.
Enright
,
D.
,
Fedkiw
,
R.
,
Ferziger
,
J.
, and
Mitchell
,
I.
,
2002
, “
A Hybrid Particle Level Set Method for Improved Interface Capturing
,”
J. Comput. Phys.
,
183
(
1
), pp.
83
116
.10.1006/jcph.2002.7166
25.
Cecil
,
T.
,
Qian
,
J.
, and
Osher
,
S.
,
2004
, “
Numerical Methods for High Dimensional Hamilton-Jacobi Equations Using Radial Basis Functions
,”
J. Comput. Phys.
,
196
(
1
), pp.
327
347
.10.1016/j.jcp.2003.11.010
26.
Nave
,
J. C.
,
Rosales
,
R. R.
, and
Seibold
,
B.
,
2010
, “
A Gradient-Augmented Level Set Method With an Optimally Local, Coherent Advection Scheme
,”
J. Comput. Phys.
,
229
(
10
), pp.
3802
3827
.10.1016/j.jcp.2010.01.029
27.
Courant
,
R.
,
Isaacson
,
E.
, and
Rees
,
M.
,
1952
, “
On the Solution of Nonlinear Hyperbolic Differential Equations by Finite Differences
,”
Commun. Pure Appl. Math.
,
5
(
3
), pp.
243
255
.10.1002/cpa.3160050303
28.
Lee
,
C.
,
Dolbow
,
J.
, and
Mucha
,
P. J.
,
2014
, “
A Narrow-Band Gradient-Augmented Level Set Method for Multiphase Incompressible Flow
,”
J. Comput. Phys.
,
273
(
273
), pp.
12
37
.10.1016/j.jcp.2014.04.055
29.
Shi
,
F. L.
,
Xin
,
J. J.
, and
Jin
,
Q.
,
2019
, “
A Cartesian Grid Based Multiphase Flow Model for Water Impact of an Arbitrary Complex Body
,”
Int. J. Multiphase Flow
,
110
, pp.
132
147
.10.1016/j.ijmultiphaseflow.2018.09.008
30.
Xin
,
J. J.
,
Shi
,
F. L.
,
Jin
,
Q.
, and
Lin
,
C.
,
2018
, “
A Radial Basis Function Based Ghost Cell Method With Improved Mass Conservation for Complex Moving Boundary Flows
,”
Comput. Fluids
,
176
(
15
), pp.
210
225
.10.1016/j.compfluid.2018.09.004
31.
Kim
,
J.
, and
Moin
,
P.
,
1985
, “
Application of a Fractional-Step Method to Incompressible Navier–Stokes Equations
,”
J. Comput. Phys.
,
59
(
2
), pp.
308
323
.10.1016/0021-9991(85)90148-2
32.
Van Leer
,
B.
,
1979
, “
Towards the Ultimate Conservative Difference Scheme—V: A Second-Order Sequel to Godunov's Method
,”
J. Comput. Phys.
,
32
(
1
), pp.
101
136
.10.1016/0021-9991(79)90145-1
33.
Anumolu
,
L.
, and
Trujillo
,
M. F.
,
2013
, “
Gradient Augmented Reinitialization Scheme for the Level Set Method
,”
Int. J. Numer. Method Fluid
,
73
(
12
), pp.
1011
1041
.10.1002/fld.3834
34.
LeVeque
,
R.
,
1996
, “
High-Resolution Conservative Algorithms for Advection in Incompressible Flow
,”
SIAM J. Numer. Anal.
,
33
(
2
), pp.
627
665
.10.1137/0733033
35.
Liu
,
D.
, and
Lin
,
P.
,
2008
, “
A Numerical Study of Three-Dimensional Liquid Sloshing in Tanks
,”
J, Comput. Phys.
,
227
(
8
), pp.
3921
3939
.10.1016/j.jcp.2007.12.006
36.
Chen
,
Z.
,
Zong
,
Z.
,
Li
,
H. T.
, and
Li
,
J.
,
2013
, “
An Investigation Into the Pressure on Solid Walls in 2D Sloshing Using SPH Method
,”
Ocean Eng.
,
59
(
2
), pp.
129
141
.10.1016/j.oceaneng.2012.12.013
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