Abstract

Flow around a cube is numerically studied in the laminar vortex shedding regime. The objective is to examine the three-dimensional vortex shedding mechanism and understand the temporal behavior of the wake. Vortices were identified using λ2 criterion for Re = 250–770. The wake of the cube sheds paired hairpin vortices, which moves in the streamwise direction and attains a constant shape with time. The analysis of separation distance and angular orientation of hairpin vortices for flow around a cube are presented here for the first time in the literature. The separation (d) between the paired hairpin vortices scales as t1/2. The orientation of hairpin vortices changes with time and attains a near-normal orientation with respect to the axial direction. At Re 339, the hairpin twists with respect to axial direction losing the axisymmetry in one plane noted for 276 Re 300. The hairpin vortices disintegrate into smaller vortices at higher Re = 570 and 770. A quasi-periodic nature of the flow has been revealed by the phase plots. The drag and side forces generated due to the flow are studied with pressure force mostly contributing to the drag. One of the side force coefficients dominates owing to the asymmetry of the wake in one plane and symmetry in the other orthogonal streamwise plane. These results clearly bring out the asymmetric nature of flow in the shedding regime.

References

References
1.
Carranza
,
F.
, and
Zhang
,
Y.
,
2017
, “
Study of Drag and Orientation of Regular Particles Using Stereo Vision, Schlieren Photography and Digital Image Processing
,”
Powder Technol.
,
311
, pp.
185
199
.10.1016/j.powtec.2017.01.010
2.
Guan
,
Y.
,
Guadarrama-Lara
,
R.
,
Jia
,
X.
,
Zhang
,
K.
, and
Wen
,
D.
,
2017
, “
Lattice Boltzmann Simulation of Flow Past a Non-Spherical Particle
,”
Adv. Powder Technol.
,
28
(
6
), pp.
1486
1494
.10.1016/j.apt.2017.03.018
3.
Ouchene
,
R.
,
Khalij
,
M.
,
Tanière
,
A.
, and
Arcen
,
B.
,
2015
, “
Drag, Lift and Torque Coefficients for Ellipsoidal Particles: From Low to Moderate Particle Reynolds Numbers
,”
Comput. Fluids
,
113
, pp.
53
64
.10.1016/j.compfluid.2014.12.005
4.
Ouchene
,
R.
,
Khalij
,
M.
,
Arcen
,
B.
, and
Tanière
,
A.
,
2016
, “
A New Set of Correlations of Drag, Lift and Torque Coefficients for Non-Spherical Particles and Large Reynolds Numbers
,”
Powder Technol.
,
303
, pp.
33
43
.10.1016/j.powtec.2016.07.067
5.
Bagheri
,
G.
, and
Bonadonna
,
C.
,
2016
, “
On the Drag of Freely Falling Non-Spherical Particles
,”
Powder Technol.
,
301
, pp.
526
544
.10.1016/j.powtec.2016.06.015
6.
Wang
,
J.
,
Qi
,
H.
, and
Zhu
,
J.
,
2011
, “
Experimental Study of Settling and Drag on Cuboids With Square Base
,”
Particuology
,
9
(
3
), pp.
298
305
.10.1016/j.partic.2010.11.002
7.
Hölzer
,
A.
, and
Sommerfeld
,
M.
,
2009
, “
Lattice Boltzmann Simulations to Determine Drag, Lift and Torque Acting on Non-Spherical Particles
,”
Comput. Fluids
,
38
(
3
), pp.
572
589
.10.1016/j.compfluid.2008.06.001
8.
Raul
,
R.
,
Bernard
,
P. S.
, and
Buckley
,
F. T.
,
1990
, “
An Application of the Vorticity–Vector Potential Method to Laminar Cube Flow
,”
Int. J. Numer. Methods Fluids
,
10
(
8
), pp.
875
888
.10.1002/fld.1650100803
9.
Johnson
,
T. A.
, and
Patel
,
V. C.
,
1999
, “
Flow Past a Sphere Up to a Reynolds Number of 300
,”
J. Fluid Mech.
,
378
, pp.
19
70
.10.1017/S0022112098003206
10.
Sakamoto
,
H.
, and
Haniu
,
H.
,
1990
, “
A Study on Vortex Shedding From Spheres in a Uniform Flow
,”
ASME J. Fluids Eng.
,
112
(
4
), pp.
386
392
.10.1115/1.2909415
11.
Taneda
,
S.
,
1956
, “
Experimental Investigation of the Wake Behind a Sphere at Low Reynolds Numbers
,”
J. Phys. Soc. Jpn.
,
11
(
10
), pp.
1104
1108
.10.1143/JPSJ.11.1104
12.
Saha
,
A. K.
,
2004
, “
Three-Dimensional Numerical Simulations of the Transition of Flow Past a Cube
,”
Phys. Fluids
,
16
(
5
), pp.
1630
1646
.10.1063/1.1688324
13.
Saha
,
A. K.
,
2006
, “
Three-Dimensional Numerical Study of Flow and Heat Transfer From a Cube Placed in a Uniform Flow
,”
Int. J. Heat Fluid Flow
,
27
(
1
), pp.
80
94
.10.1016/j.ijheatfluidflow.2005.05.002
14.
Khan
,
M. H.
,
Sooraj
,
P.
,
Sharma
,
A.
, and
Agrawal
,
A.
,
2018
, “
Flow Around a Cube for Reynolds Numbers Between 500 and 55,000
,”
Exp. Therm. Fluid Sci.
,
93
, pp.
257
271
.10.1016/j.expthermflusci.2017.12.013
15.
Khan
,
M. H.
,
Sharma
,
A.
, and
Agrawal
,
A.
,
2020
, “
Simulation of Flow Around a Cube at Moderate Reynolds Numbers Using the Lattice Boltzmann Method
,”
ASME J. Fluids Eng.
,
142
(
1
), p.
011301
.10.1115/1.4044821
16.
Klotz
,
L.
,
Goujon-Durand
,
S.
,
Rokicki
,
J.
, and
Wesfreid
,
J.
,
2014
, “
Experimental Investigation of Flow Behind a Cube for Moderate Reynolds Numbers
,”
J. Fluid Mech.
,
750
, pp.
73
98
.10.1017/jfm.2014.236
17.
Richter
,
A.
, and
Nikrityuk
,
P. A.
,
2012
, “
Drag Forces and Heat Transfer Coefficients for Spherical, Cuboidal and Ellipsoidal Particles in Cross Flow at Sub-Critical Reynolds Numbers
,”
Int. J. Heat Mass Transfer
,
55
(
4
), pp.
1343
1354
.10.1016/j.ijheatmasstransfer.2011.09.005
18.
Tiwari
,
S. S.
,
Bale
,
S.
,
Patwardhan
,
A. W.
,
Nandakumar
,
K.
, and
Joshi
,
J. B.
,
2019
, “
Insights Into the Physics of Dominating Frequency Modes for Flow Past a Stationary Sphere: Direct Numerical Simulations
,”
Phys. Fluids
,
31
(
4
), p.
045108
.10.1063/1.5083917
19.
Magarvey
,
R.
, and
MacLatchy
,
C.
,
1965
, “
Vortices in Sphere Wakes
,”
Can. J. Phys.
,
43
(
9
), pp.
1649
1656
.10.1139/p65-154
20.
Achenbach
,
E.
,
1974
, “
Vortex Shedding From Spheres
,”
J. Fluid Mech.
,
62
(
2
), pp.
209
221
.10.1017/S0022112074000644
21.
Mittal
,
R.
, and
Najjar
,
F.
,
1999
, “
Vortex Dynamics in the Sphere Wake
,”
30th Fluid Dynamics Conference
,
Norfolk, VA
, June 28–July 1, p.
3806
.
22.
Leweke
,
T.
,
Provansal
,
M.
,
Ormieres
,
D.
, and
Lebescond
,
R.
,
1999
, “
Vortex Dynamics in the Wake of a Sphere
,”
Phys. Fluids
,
11
(
9
), p.
S12
.10.1063/1.4739162
23.
Przadka
,
A.
,
Miedzik
,
J.
,
Gumowski
,
K.
,
Goujon-Durand
,
S.
, and
Wesfreid
,
J.
,
2008
, “
The Wake Behind the Sphere; Analysis of Vortices During Transition From Steadiness to Unsteadiness
,”
Arch. Mech.
,
60
(
6
), pp.
465
472
.https://am.ippt.pan.pl/am/article/view/v60p467
24.
Hunt
,
J. C.
,
Wray
,
A. A.
, and
Moin
,
P.
,
1988
, “
Eddies, Streams, and Convergence Zones in Turbulent Flows
,”
Studying Turbulence Using Numerical Simulation Databases 2, Proceedings of the Summer Program
,
Center for Turbulence Research, Stanford University
,
Stanford, CA
, pp.
193
208
.
25.
Eshbal
,
L.
,
Rinsky
,
V.
,
David
,
T.
,
Greenblatt
,
D.
, and
van Hout
,
R.
,
2019
, “
Measurement of Vortex Shedding in the Wake of a Sphere at Re = 465
,”
J. Fluid Mech.
,
870
, pp.
290
315
.10.1017/jfm.2019.250
26.
Eshbal
,
L.
,
Kovalev
,
D.
,
Rinsky
,
V.
,
Greenblatt
,
D.
, and
van Hout
,
R.
,
2019
, “
Tomo-PIV Measurements in the Wake of a Tethered Sphere Undergoing VIV
,”
J. Fluids Struct.
,
89
, pp.
132
141
.10.1016/j.jfluidstructs.2019.02.003
27.
Issa
,
R. I.
,
1986
, “
Solution of the Implicitly Discretised Fluid Flow Equations by Operator-Splitting
,”
J. Comput. Phys.
,
62
(
1
), pp.
40
65
.10.1016/0021-9991(86)90099-9
28.
Eça
,
L.
, and
Hoekstra
,
M.
,
2014
, “
A Procedure for the Estimation of the Numerical Uncertainty of CFD Calculations Based on Grid Refinement Studies
,”
J. Comput. Phys.
,
262
, pp.
104
130
.10.1016/j.jcp.2014.01.006
29.
Celik
,
I. B.
,
Ghia
,
U.
,
Roache
,
P. J.
,
Freitas
,
C. J.
,
Coleman
,
H.
, and
Raad
,
P. E.
,
2008
, “
Procedure for Estimation and Reporting of Uncertainty Due to Discretization in CFD Applications
,”
ASME J. Fluids Eng.
,
130
(
7
), p.
078001
.10.1115/1.2960953
30.
Jeong
,
J.
, and
Hussain
,
F.
,
1995
, “
On the Identification of a Vortex
,”
J. Fluid Mech.
,
285
(
1
), pp.
69
94
.10.1017/S0022112095000462
31.
Wu
,
J.-Z.
,
Ma
,
H.-Y.
, and
Zhou
,
M.-D.
,
2007
,
Vorticity and Vortex Dynamics
,
Springer Science & Business Media
,
Berlin
.
32.
Okajima
,
A.
,
1982
, “
Strouhal Numbers of Rectangular Cylinders
,”
J. Fluid Mech.
,
123
, pp.
379
398
.10.1017/S0022112082003115
33.
Sharma
,
A.
, and
Eswaran
,
V.
,
2004
, “
Heat and Fluid Flow Across a Square Cylinder in the Two-Dimensional Laminar Flow Regime
,”
Numer. Heat Transfer, Part A
,
45
(
3
), pp.
247
269
.10.1080/10407780490278562
34.
Gollub
,
J.
, and
Benson
,
S.
,
1980
, “
Many Routes to Turbulent Convection
,”
J. Fluid Mech.
,
100
(
3
), pp.
449
470
.10.1017/S0022112080001243
35.
Saha
,
A.
,
Muralidhar
,
K.
, and
Biswas
,
G.
,
2000
, “
Transition and Chaos in Two-Dimensional Flow Past a Square Cylinder
,”
J. Eng. Mech.
,
126
(
5
), pp.
523
532
.10.1061/(ASCE)0733-9399(2000)126:5(523)
36.
Guzmán
,
A.
, and
Amon
,
C.
,
1996
, “
Dynamical Flow Characterization of Transitional and Chaotic Regimes in Converging–Diverging Channels
,”
J. Fluid Mech.
,
321
, pp.
25
57
.10.1017/S002211209600763X
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