Abstract

The current research focuses on the laminar flow through permeable side-by-side bars of a square cross section in a channel-confined domain. Vorticity generation on the leeward sides of the permeable bodies further necessitates the study for a better understanding of underlying physics. Reynolds number (Re) and Darcy number (Da) are varied from 5 to 150 and 10−6 to 10−2, respectively, at transverse gap ratios s/d = 2.5–10. In the perspective of periodic unsteady flow, critical Re for the onset of vortex shedding is analyzed. Streamlines, vorticity, pressure coefficient distribution, and velocity profiles are discussed to identify the wake patterns. In lower permeability level, vortex-shedding from the permeable square cylinders is observed either in synchronized antiphase mode or a single large vortex street with a synchronized in-phase pattern in the near wake. A steady-state wake pattern symmetric and flocked toward the centerline is observed for all s/d at a higher permeability level regardless of Re. Wake patterns are not altered for Da = 10−6 to 10−3; instead, prompt extermination of the two vortex streets downstream is observed at Da = 10−3 as compared to Da = 10−6. The impact of s/d, Re, and permeability on the drag is examined. A jump in the flow characteristics and drag forces is noticed at higher Re for the midrange Da remarkably at lower s/d. For the extent of high permeability, the drag coefficient asymptotically gets closer to zero.

References

1.
Zhao
,
F.
,
Kinoshita
,
T.
,
Bao
,
W.
, and
Itakura
,
H.
,
2009
, “
Theoretical and Experimental Study on a Porous Cylinder Floating in Waves
,”
ASME J. Offshore Mech. Arct. Eng.
,
4
, pp.
1261
1268
.10.1115/OMAE2009-79089
2.
Camarri
,
S.
,
Fallenius
,
B. E. G.
, and
Fransson
,
J. H. M.
,
2013
, “
Stability Analysis of Experimental Flow Fields Behind a Porous Cylinder for the Investigation of the Large-Scale Wake Vortices
,”
J. Fluid Mech.
,
715
, pp.
499
536
.10.1017/jfm.2012.532
3.
Noymer
,
P. D.
,
Glicksman
,
L. R.
, and
Devendran
,
A.
,
1998
, “
Drag on a Permeable Cylinder in Steady Flow at Moderate Reynolds Numbers
,”
Chem. Eng. Sci
,
53
(
16
), pp.
2859
2869
.10.1016/S0009-2509(98)00117-1
4.
Cummins
,
C.
,
Seale
,
M.
,
Macente
,
A.
,
Certini
,
D.
,
Mastropaolo
,
E.
,
Viola
,
I. M.
, and
Nakayama
,
N.
,
2018
, “
A Separated Vortex Ring Underlies the Flight of the Dandelion
,”
Nature
,
562
(
7727
), pp.
414
418
.10.1038/s41586-018-0604-2
5.
Sanyal
,
A.
, and
Dhiman
,
A.
,
2017
, “
Wake Interactions in a Fluid Flow Past a Pair of Side-by-Side Square Cylinders in Presence of Mixed Convection
,”
Phys. Fluids
,
29
(
10
), p.
103602
.10.1063/1.5005118
6.
Burattini
,
P.
, and
Agrawal
,
A.
,
2013
, “
Wake Interaction Between Two Side-by-Side Square Cylinders in Channel Flow
,”
Comput. Fluids
,
77
, pp.
134
142
.10.1016/j.compfluid.2013.02.014
7.
Agrawal
,
A.
,
Djenidi
,
L.
, and
Antonia
,
R. A.
,
2006
, “
Investigation of Flow Around a Pair of Side-by-Side Square Cylinders Using the Lattice Boltzmann Method
,”
Comput. Fluids
,
35
(
10
), pp.
1093
1107
.10.1016/j.compfluid.2005.05.008
8.
Durga Prasad
,
A. V. V. S.
, and
Dhiman
,
A. K.
,
2014
, “
CFD Analysis of Momentum and Heat Transfer Around a Pair of Square Cylinders in Side-by-Side Arrangement
,”
Heat Transfer Eng.
,
35
(
4
), pp.
398
411
.10.1080/01457632.2013.828561
9.
Sanyal
,
A.
, and
Dhiman
,
A.
,
2018
, “
Effect of Thermal Buoyancy on a Fluid Flowing Past a Pair of Side-by-Side Square Bluff-Bodies in a low-Reynolds Number Flow Regime
,”
Phys. Fluids
,
30
(
6
), p.
063603
.10.1063/1.5025652
10.
Ma
,
S.
,
Kang
,
C. W.
,
Lim
,
T. B. A.
,
Wu
,
C. H.
, and
Tutty
,
O.
,
2017
, “
Wake of Two Side-by-Side Square Cylinders at Low Reynolds Numbers
,”
Phys. Fluids
,
29
(
3
), p.
033604
.10.1063/1.4979134
11.
Anirudh
,
K.
, and
Dhinakaran
,
S.
,
2018
, “
On the Onset of Vortex Shedding Past a Two-Dimensional Porous Square Cylinder
,”
J. Wind Eng. Ind. Aerodyn.
,
179
, pp.
200
214
.10.1016/j.jweia.2018.03.004
12.
Ledda
,
P. G.
,
Siconolfi
,
L.
,
Viola
,
F.
,
Gallaire
,
F.
, and
Camarri
,
S.
,
2018
, “
Suppression of Von Kármán Vortex Streets Past Porous Rectangular Cylinders
,”
Phys. Rev. Fluids
,
3
(
10
), p.
103901
.10.1103/PhysRevFluids.3.103901
13.
Yu
,
P.
,
Zeng
,
Y.
,
Lee
,
T. S.
,
Bai
,
H. X.
, and
Low
,
H. T.
,
2010
, “
Wake Structure for Flow Past and Through a Porous Square Cylinder
,”
Int. J. Heat Fluid Flow
,
31
(
2
), pp.
141
153
.10.1016/j.ijheatfluidflow.2009.12.009
14.
Wu, H. W., and Wang, R. H., 2010, “
Convective Heat Transfer Over a Heated Square Porous Cylinder in a Channel
,”
Int. J. Heat Mass Transfer.
,
53
, pp. 1927–1937.
15.
Klausmann
,
K.
, and
Ruck
,
B.
,
2017
, “
Drag Reduction of Circular Cylinders by Porous Coating on the Leeward Side
,”
J. Fluid Mech.
,
813
, pp.
382
411
.10.1017/jfm.2016.757
16.
Bruneau
,
C. H.
,
Mortazavi
,
I.
, and
Gilliéron
,
P.
,
2008
, “
Passive Control Around the Two-Dimensional Square Back Ahmed Body Using Porous Devices
,”
ASME J. Fluids Eng.
,
130
(
6
), p.
061101
.10.1115/1.2917423
17.
Arcondoulis
,
E. J. G.
,
Liu
,
Y.
,
Li
,
Z.
,
Yang
,
Y.
, and
Wang
,
Y.
,
2019
, “
Structured Porous Material Design for Passive Flow and Noise Control of Cylinders in Uniform Flow
,”
Materials (Basel).
,
12
(
18
), p.
2905
.10.3390/ma12182905
18.
Rashidi
,
S.
,
Tamayol
,
A.
,
Valipour
,
M. S.
, and
Shokri
,
N.
,
2013
, “
Fluid Flow and Forced Convection Heat Transfer Around a Solid Cylinder Wrapped With a Porous Ring
,”
Int. J. Heat Mass Transfer
,
63
, pp.
91
100
.10.1016/j.ijheatmasstransfer.2013.03.006
19.
Ledda
,
P. G.
,
Siconolfi
,
L.
,
Viola
,
F.
,
Camarri
,
S.
, and
Gallaire
,
F.
,
2019
, “
Flow Dynamics of a Dandelion Pappus: A Linear Stability Approach
,”
Phys. Rev. Fluids
,
4
(
7
), p.
071901
.10.1103/PhysRevFluids.4.071901
20.
Bruneau
,
C.-H.
, and
Mortazavi
,
I.
,
2004
, “
Passive Control of the Flow Around a Square Cylinder Using Porous Media
,”
Int. J. Numer. Methods Fluids
,
46
(
4
), pp.
415
433
.10.1002/fld.756
21.
Vijaybabu
,
T. R.
,
Anirudh
,
K.
, and
Dhinakaran
,
S.
,
2017
, “
Mixed Convective Heat Transfer From a Permeable Square Cylinder: A Lattice Boltzmann Analysis
,”
Int. J. Heat Mass Transfer
,
115
, pp.
854
870
.10.1016/j.ijheatmasstransfer.2017.08.033
22.
Dhinakaran
,
S.
, and
Ponmozhi
,
J.
,
2011
, “
Heat Transfer From a Permeable Square Cylinder to a Flowing Fluid
,”
Energy Convers. Manag.
,
52
(
5
), pp.
2170
2182
.10.1016/j.enconman.2010.12.027
23.
Bhattacharyya
,
S.
,
Dhinakaran
,
S.
, and
Khalili
,
A.
,
2006
, “
Fluid Motion Around and Through a Porous Cylinder
,”
Chem. Eng. Sci
,
61
(
13
), pp.
4451
4461
.10.1016/j.ces.2006.02.012
24.
Yu
,
P.
,
Zeng
,
Y.
,
Lee
,
T. S.
,
Chen
,
X. B.
, and
Low
,
H. T.
,
2011
, “
Steady Flow Around and Through a Permeable Circular Cylinder
,”
Comput. Fluids
,
42
(
1
), pp.
1
12
.10.1016/j.compfluid.2010.09.040
25.
Rashidi
,
S.
,
Bovand
,
M.
,
Pop
,
I.
, and
Valipour
,
M. S.
,
2014
, “
Numerical Simulation of Forced Convective Heat Transfer Past a Square Diamond-Shaped Porous Cylinder
,”
Transp. Porous Media
,
102
(
2
), pp.
207
225
.10.1007/s11242-014-0272-0
26.
Saha
,
A. K.
,
Muralidhar
,
K.
, and
Biswas
,
G.
,
2000
, “
Vortex Structures and Kinetic Energy Budget in Two-Dimensional Flow Past a Square Cylinder
,”
Comput. Fluids
,
29
(
6
), pp.
669
694
.10.1016/S0045-7930(99)00021-3
27.
Williamson
,
C. H. K.
,
1996
, “
Vortex Dynamics in the Cylinder Wake
,”
Annu. Rev. Fluid Mech.
,
28
(
1
), pp.
477
539
.10.1146/annurev.fl.28.010196.002401
28.
Kang
,
S.
,
2003
, “
Characteristics of Flow Over Two Circular Cylinders in a Side-by-Side Arrangement at Low Reynolds Numbers
,”
Phys. Fluids
,
15
(
9
), pp.
2486
2498
.10.1063/1.1596412
29.
Fu
,
W. S.
,
Huang
,
H. C.
, and
Liou
,
W. Y.
,
1996
, “
Thermal Enhancement in Laminar Channel Flow With a Porous Block
,”
Int. J. Heat Mass Transfer
,
39
(
10
), pp.
2165
2175
.10.1016/0017-9310(95)00208-1
30.
Breuer
,
M.
,
Bernsdorf
,
J.
,
Zeiser
,
T.
, and
Durst
,
F.
,
2000
, “
Accurate Computations of the Laminar Flow Past a Square Cylinder Based on Two Different Methods: Lattice-Boltzmann and Finite Volume
,”
Int. J. Heat Fluid Flow
,
21
(
2
), pp.
186
196
.10.1016/S0142-727X(99)00081-8
31.
Turki
,
S.
,
Abbassi
,
H.
, and
Nasrallah
,
S. B.
,
2003
, “
Effect of the Blockage Ratio on the Flow in a Channel With a Built-in Square Cylinder
,”
Comput. Mech
,
33
(
1
), pp.
22
29
.10.1007/s00466-003-0496-2
32.
Nield
,
D. A.
, and
Bejan
,
A.
,
2006
,
Convection in Porous Media
,
Springer
, New York.
33.
Tachibana
,
M.
,
Nobuyoshi
,
K.
, and
Chen
,
C.
,
1991
, “
Two-Dimensional Flow Around a Square Cylinder at Low Reynolds Number
,”
J. Jpn. Soc. Fluid Mech.
,
10
, pp.
253
268
.10.11426/nagare1982.10.253
34.
Ng
,
Z. Y.
,
Vo
,
T.
,
Hussam
,
W. K.
, and
Sheard
,
G. J.
,
2016
, “
Two-Dimensional Wake Dynamics Behind Cylinders With Triangular Cross-Section Under Incidence Angle Variation
,”
J. Fluids Struct.
,
63
, pp.
302
324
.10.1016/j.jfluidstructs.2016.04.003
35.
Kieft
,
R.
,
Rindt
,
C. C. M.
, and
van Steenhoven
,
A. A.
,
2007
, “
Near-Wake Effects of a Heat Input on the Vortex-Shedding Mechanism
,”
Int. J. Heat Fluid Flow
,
28
(
5
), pp.
938
947
.10.1016/j.ijheatfluidflow.2007.03.002
36.
Sohankar
,
A.
,
Norberg
,
C.
, and
Davidson
,
L.
,
1998
, “
Low-Reynolds-Number Flow Around a Square Cylinder at Incidence: Study of Blockage, Onset of Vortex Shedding and Outlet Boundary Condition
,”
Int. J. Numer. Methods Fluids
,
26
(
1
), pp.
39
56
.10.1002/(SICI)1097-0363(19980115)26:1<39::AID-FLD623>3.0.CO;2-P
37.
Jue
,
T. C.
,
2004
, “
Numerical Analysis of Vortex Shedding Behind a Porous Square Cylinder
,”
Int. J. Numer. Methods Heat Fluid Flow
,
14
(
5
), pp.
649
663
.10.1108/09615530410539964
38.
Masliyah
,
J. H.
, and
Polikar
,
M.
,
1980
, “
Terminal Velocity of Porous Spheres
,”
Can. J. Chem. Eng.
,
58
(
3
), pp.
299
302
.10.1002/cjce.5450580303
39.
Schlichting
,
H.
,
1979
,
Boundary Layer Theory
, 7th ed.,
McGraw-Hill
, New York, pp.
664
665
.
40.
Jain
,
A. K.
, and
Basu
,
S.
,
2012
, “
Flow Past a Porous Permeable Sphere: Hydrodynamics and Heat-Transfer Studies
,”
Ind. Eng. Chem. Res.
,
51
(
4
), pp.
2170
2178
.10.1021/ie201647p
41.
Bearman
,
P. W.
, and
Wadcock
,
A. J.
,
1973
, “
The Interaction Between a Pair of Circular Cylinders Normal to a Stream
,”
J. Fluid Mech.
,
61
(
3
), pp.
499
511
.10.1017/S0022112073000832
42.
Kumar
,
S. R.
,
Sharma
,
A.
, and
Agrawal
,
A.
,
2008
, “
Simulation of Flow Around a Row of Square Cylinders
,”
J. Fluid Mech.
,
606
, pp.
369
397
.10.1017/S0022112008001924
43.
Vijaybabu
,
T. R.
,
Anirudh
,
K.
, and
Dhinakaran
,
S.
,
2018
, “
LBM Simulation of Unsteady Flow and Heat Transfer From a Diamond-Shaped Porous Cylinder
,”
Int. J. Heat Mass Transfer
,
120
, pp.
267
283
.10.1016/j.ijheatmasstransfer.2017.11.010
44.
Valipour
,
M. S.
,
Rashidi
,
S.
,
Bovand
,
M.
, and
Masoodi
,
R.
,
2014
, “
Numerical Modeling of Flow Around and Through a Porous Cylinder With Diamond Cross Section
,”
Eur. J. Mech. B/Fluids
,
46
, pp.
74
81
.10.1016/j.euromechflu.2013.12.007
45.
Chen
,
X. B.
,
Yu
,
P.
,
Winoto
,
S. H.
, and
Low
,
H. T.
,
2009
, “
Numerical Analysis for the Flow Past a Porous Trapezoidal-Cylinder Based on the Stress-Jump Interfacial-Conditions
,”
Int. J. Numer. Methods Heat Fluid Flow
,
19
(
2
), pp.
223
241
.10.1108/09615530910930982
46.
Chen
,
X. B.
,
Yu
,
P.
,
Winoto
,
S. H.
, and
Low
,
H. T.
,
2008
, “
Numerical Analysis for the Flow Past a Porous Square Cylinder Based on the Stress-Jump Interfacial-Conditions
,”
Int. J. Numer. Methods Heat Fluid Flow
,
18
(
5
), pp.
635
655
.10.1108/09615530810879756
47.
Barta
,
E.
, and
Weihs
,
D.
,
2006
, “
Creeping Flow Around a Finite Row of Slender Bodies in Close Proximity
,”
J. Fluid Mech.
,
551
(
1
), pp.
1
17
.10.1017/S0022112005008268
You do not currently have access to this content.