Abstract

In this study, wake of an elliptic cylinder is analyzed in the presence of a fluid–fluid interface. The interactions between the interface and flow affect each other and hence different wake dynamics and interface topologies are observed. The numerical solver developed for this study has immersed boundary method (IBM) coupled with level-set method (LSM). The proximity of the elliptical cylinder to the interface (H/D), Froude number (Fr), and angle of incidence (AOI) are the parameters considered. Three different Froude number regimes are considered for this study, namely, subcritical (Fr < 1), critical (Fr = 1.0), and supercritical (Fr >1) regime. In this paper, the interface topology, wake dynamics, and force values are compared for the variation of these parameters.

References

References
1.
Anderson
,
D. M.
,
McFadden
,
G. B.
, and
Wheeler
,
A. A.
,
1998
, “
Diffuse-Interface Methods in Fluid Mechanics
,”
Annu. Rev. Fluid Mech.
,
30
(
1
), pp.
139
165
.10.1146/annurev.fluid.30.1.139
2.
Yue
,
P.
,
Feng
,
J. J.
,
Liu
,
C.
, and
Shen
,
J.
,
2004
, “
A Diffuse-Interface Method for Simulating Two-Phase Flows of Complex Fluids
,”
J. Fluid Mech.
,
515
, pp.
293
317
.10.1017/S0022112004000370
3.
Jacqmin
,
D.
,
2000
, “
Contact-Line Dynamics of a Diffuse Fluid Interface
,”
J. Fluid Mech.
,
402
, pp.
57
88
.10.1017/S0022112099006874
4.
Osher
,
S.
, and
Sethian
,
J. A.
,
1988
, “
Fronts Propagating With Curvature-Dependent Speed: Algorithms Based on Hamilton–Jacobi Formulations
,”
J. Comput. Phys.
,
79
(
1
), pp.
12
49
.10.1016/0021-9991(88)90002-2
5.
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
6.
Min
,
C.
,
2010
, “
On Reinitializing Level Set Functions
,”
J. Comput. Phys.
,
229
(
8
), pp.
2764
2772
.10.1016/j.jcp.2009.12.032
7.
Shu
,
C.-W.
,
2009
, “
High Order Weighted Essentially Non-Oscillatory Schemes for Convection Dominated Problems
,”
SIAM Rev.
,
51
(
1
), pp.
82
126
.10.1137/070679065
8.
Olsson
,
E.
, and
Kreiss
,
G.
,
2005
, “
A Conservative Level Set Method for Two Phase Flow
,”
J. Comput. Phys.
,
210
(
1
), pp.
225
246
.10.1016/j.jcp.2005.04.007
9.
Sharma
,
A.
,
2015
, “
Level Set Method for Computational Multi-Fluid Dynamics: A Review on Developments, Applications and Analysis
,”
Sadhana
,
40
(
3
), pp.
627
652
.10.1007/s12046-014-0329-3
10.
Fedkiw
,
R. P.
,
Aslam
,
T.
,
Merriman
,
B.
, and
Osher
,
S.
,
1999
, “
A Non-Oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method)
,”
J. Comput. Phys.
,
152
(
2
), pp.
457
492
.10.1006/jcph.1999.6236
11.
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
12.
Enright
,
D.
,
Fedkiw
,
R.
,
Ferziger
,
J.
, and
Mitchell
,
I.
,
2002
, “
A Hybrid Particle Level Set Method for Improved Interface Capturing
,”
J. Comput. Physics
,
183
(
1
), pp.
83
116
.10.1006/jcph.2002.7166
13.
Hieber
,
S. E.
, and
Koumoutsakos
,
P.
,
2005
, “
A Lagrangian Particle Level Set Method
,”
J. Comput. Phys.
,
210
(
1
), pp.
342
367
.10.1016/j.jcp.2005.04.013
14.
Li
,
Z.
,
Jaberi
,
F. A.
, and
Shih
,
T. I.-P.
,
2008
, “
A Hybrid Lagrangian–Eulerian Particle-Level Set Method for Numerical Simulations of Two-Fluid Turbulent Flows
,”
Int. J. Numer. Methods Fluids
,
56
(
12
), pp.
2271
2300
.10.1002/fld.1621
15.
Ciortan
,
C.
,
Wanderley
,
J.
, and
Soares
,
C. G.
,
2012
, “
Free Surface Flow Around a Ship Model Using an Interface-Capturing Method
,”
Ocean Eng.
,
44
, pp.
57
67
.10.1016/j.oceaneng.2012.01.015
16.
Zhang
,
C.
,
Zhang
,
W.
,
Lin
,
N.
,
Tang
,
Y.
,
Zhao
,
C.
,
Gu
,
J.
,
Lin
,
W.
,
Chen
,
X.
, and
Qiu
,
A.
,
2013
, “
A Two-Phase Flow Model Coupling With Volume of Fluid and Immersed Boundary Methods for Free Surface and Moving Structure Problems
,”
Ocean Eng.
,
74
, pp.
107
124
.10.1016/j.oceaneng.2013.09.010
17.
Karim
,
M. M.
,
Prasad
,
B.
, and
Rahman
,
N.
,
2014
, “
Numerical Simulation of Free Surface Water Wave for the Flow Around NACA 0015 Hydrofoil Using the Volume of Fluid (VOF) Method
,”
Ocean Eng.
,
78
, pp.
89
94
.10.1016/j.oceaneng.2013.12.013
18.
Esmaeilifar
,
E.
,
Djavareshkian
,
M. H.
,
Feshalami
,
B. F.
, and
Esmaeili
,
A.
,
2017
, “
Hydrodynamic Simulation of an Oscillating Hydrofoil Near Free Surface in Critical Unsteady Parameter
,”
Ocean Eng.
,
141
, pp.
227
236
.10.1016/j.oceaneng.2017.06.037
19.
Colicchio
,
G.
,
Landrini
,
M.
, and
Chaplin
,
J. R.
,
2005
, “
Level-Set Computations of Free Surface Rotational Flows
,”
ASME J. Fluids Eng.
,
127
(
6
), pp.
1111
1121
.10.1115/1.2062707
20.
Ikram
,
Z.
,
Avital
,
E.
, and
Williams
,
J.
,
2016
, “
Effects of Submergence on Low and Moderate Reynolds Number Free-Surface Flow Around a Matrix of Cubes
,”
ASME J. Fluids Eng.
,
138
(
5
), p.
051102
.10.1115/1.4031852
21.
Reichl
,
P.
,
Hourigan
,
K.
, and
Thompson
,
M. C.
,
2005
, “
Flow Past a Cylinder Close to a Free Surface
,”
J. Fluid Mech.
,
533
, pp.
269
296
.10.1017/S0022112005004209
22.
Bouscasse
,
B.
,
Colagrossi
,
A.
,
Marrone
,
S.
, and
Souto-Iglesias
,
A.
,
2017
, “
SPH Modelling of Viscous Flow Past a Circular Cylinder Interacting With a Free Surface
,”
Comput. Fluids
,
146
, pp.
190
212
.10.1016/j.compfluid.2017.01.011
23.
Wu
,
C.
, and
Young
,
D.
,
2014
, “
Simulations of Free-Surface Flows With an Embedded Object by a Coupling Partitioned Approach
,”
Comput. Fluids
,
89
, pp.
66
77
.10.1016/j.compfluid.2013.10.030
24.
Benitz
,
M.
,
Carlson
,
D.
,
Seyed-Aghazadeh
,
B.
,
Modarres-Sadeghi
,
Y.
,
Lackner
,
M.
, and
Schmidt
,
D.
,
2016
, “
CFD Simulations and Experimental Measurements of Flow Past Free-Surface Piercing, Finite Length Cylinders With Varying Aspect Ratios
,”
Comput. Fluids
,
136
, pp.
247
259
.10.1016/j.compfluid.2016.06.013
25.
Carberry
,
J.
,
Sheridan
,
J.
, and
Rockwell
,
D.
,
2004
, “
Cylinder Oscillations Beneath a Free-Surface
,”
Eur. J. Mech.-B/Fluids
,
23
(
1
), pp.
81
88
.10.1016/j.euromechflu.2003.08.006
26.
Srinidhi
,
N.
, and
Vengadesan
,
S.
,
2017
, “
Ground Effect on Tandem Flapping Wings Hovering
,”
Comput. Fluids
,
152
, pp.
40
56
.10.1016/j.compfluid.2017.04.006
27.
Subburaj
,
R.
,
Khandelwal
,
P.
, and
Vengadesan
,
S.
,
2018
, “
Numerical Study of Flow Past an Elliptic Cylinder Near a Free Surface
,”
Phys. Fluids
,
30
(
10
), p.
103603
.10.1063/1.5046745
28.
Subburaj
,
R.
, and
Vengadesan
,
S.
,
2019
, “
Flow Features for Two Cylinders Arranged in Tandem Configuration Near a free surface
,”
J. Fluids Struct.
,
91
, p.
102770
.10.1016/j.jfluidstructs.2019.102770
29.
Osher
,
S.
, and
Fedkiw
,
R. P.
,
2001
, “
Level Set Methods: An Overview and Some Recent Results
,”
J. Comput. Phys.
,
169
(
2
), pp.
463
502
.10.1006/jcph.2000.6636
30.
Jiang
,
G.-S.
, and
Peng
,
D.
,
2000
, “
Weighted ENO Schemes for Hamilton–Jacobi Equations
,”
SIAM J. Sci. Comput.
,
21
(
6
), pp.
2126
2143
.10.1137/S106482759732455X
31.
Taira
,
K.
, and
Colonius
,
T.
,
2007
, “
The Immersed Boundary Method: A Projection Approach
,”
J. Comput. Phys.
,
225
(
2
), pp.
2118
2137
.10.1016/j.jcp.2007.03.005
32.
Popinet
,
S.
, and
Zaleski
,
S.
,
1999
, “
A Front-Tracking Algorithm for Accurate Representation of Surface Tension
,”
Int. J. Numer. Methods Fluids
,
30
(
6
), pp.
775
793
.10.1002/(SICI)1097-0363(19990730)30:6<775::AID-FLD864>3.0.CO;2-#
33.
Hysing
,
S.-R.
,
Turek
,
S.
,
Kuzmin
,
D.
,
Parolini
,
N.
,
Burman
,
E.
,
Ganesan
,
S.
, and
Tobiska
,
L.
,
2009
, “
Quantitative Benchmark Computations of Two-Dimensional Bubble Dynamics
,”
Int. J. Numer. Methods Fluids
,
60
(
11
), pp.
1259
1288
.10.1002/fld.1934
34.
Paul
,
I.
,
Arul Prakash
,
K.
,
Vengadesan
,
S.
, and
Pulletikurthi
,
V.
,
2016
, “
Analysis and Characterisation of Momentum and Thermal Wakes of Elliptic Cylinders
,”
J. Fluid Mech.
,
807
, pp.
303
323
.10.1017/jfm.2016.625
35.
Naik
,
S. N.
,
Vengadesan
,
S.
, and
Prakash
,
K. A.
,
2018
, “
Linear Shear Flow Past a Rotating Elliptic Cylinder
,”
ASME J. Fluids Eng.
,
140
(
12
), p.
121202
.10.1115/1.4040365
36.
Haller
,
G.
, and
Yuan
,
G.
,
2000
, “
Lagrangian Coherent Structures and Mixing in Two-Dimensional Turbulence
,”
Phys. D: Nonlinear Phenom.
,
147
(
3–4
), pp.
352
370
.10.1016/S0167-2789(00)00142-1
37.
Childs
,
H.
,
Brugger
,
E.
,
Whitlock
,
B.
,
Meredith
,
J.
,
Ahern
,
S.
,
Pugmire
,
D.
,
Biagas
,
K.
,
Miller
,
M.
,
Harrison
,
C.
,
Weber
,
G. H.
,
Krishnan
,
H.
,
Fogal
,
T.
,
Sanderson
,
A.
,
Garth
,
C.
,
Bethel
,
E. W.
,
Camp
,
D.
,
Rübel
,
O.
,
Durant
,
M.
,
Favre
,
J. M.
, and
Navrátil
,
P.
,
2012
, “
VisIt: An End-User Tool For Visualizing and Analyzing Very Large Data
,”
High Performance Visualization–Enabling Extreme-Scale Scientific Insight
, CRC Press, Boca Raton, FL, pp.
357
372
.
38.
Gadde
,
S. N.
, and
Vengadesan
,
S.
,
2017
, “
Lagrangian Coherent Structures in Tandem Flapping Wing Hovering
,”
J. Bionic Eng.
,
14
(
2
), pp.
307
316
.10.1016/S1672-6529(16)60399-2
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