Two-dimensional laminar flow of a power-law fluid passing two square cylinders in a tandem arrangement is numerically investigated in the ranges of 1< Re< 200 and 1 ≤ G ≤ 9. The fluid viscosity power-law index lies in the range 0.5 ≤ n ≤ 1.8, which covers shear-thinning, Newtonian and shear-thickening fluids. A finite volume code based on the SIMPLEC algorithm with nonstaggered grid is used. In order to discretize the convective and diffusive terms, the third order QUICK and the second-order central difference scheme are used, respectively. The influence of the power-law index, Reynolds number and gap ratio on the drag coefficient, Strouhal number and streamlines are investigated, and the results are compared with other studies in the literature to validate the methodology. The effect of the time integration scheme on accuracy and computational time is also analyzed. In the ranges of Reynolds number and power-law index studied here, vortex shedding is known to occur for square cylinders in tandem. This study represents the first systematic investigation of this phenomenon for non-Newtonian fluids in the open literature. In comparison to Newtonian fluids, it is found that the onset of leading edge separation occurs at lower Reynolds number for shear-thinning fluids and is delayed to larger values for shear-thickening fluids.

References

References
1.
Zdravkovich
,
M. M.
,
1997
,
Flow Around Circular Cylinders
, Vol.
1
Fundamentals, Oxford University
,
New York
.
2.
Zdravkovich
,
M. M.
,
2003
,
Flow Around Circular Cylinders
, Vol.
2
Applications, Oxford University
,
New York
.
3.
Okajima
,
A.
,
1990
, “
Numerical Simulation of Flow Around Rectangular Cylinders
,”
J. Wind Eng. Ind. Aerodyn.
,
33
, pp.
171
180
.10.1016/0167-6105(90)90033-9
4.
Johnson
,
S. A.
,
Thompson
,
M. C.
, and
Hourigan
,
K.
,
2001
, “
Flow Past Elliptical Cylinders at Low Reynolds Numbers
,”
Proc. 14th Australasian Fluid Mechanics Conference
, Adelaide University, South Australia, Dec. 9–14, pp.
343
346
.
5.
Coelho
,
P. M.
, and
Pinho
,
F. T.
,
2003
, “
Vortex Shedding in Cylinder Flow of Shear-Thinning Fluids I. Identification and Demarcation of Flow Regimes
,”
J. Non-Newtonian Fluid Mech.
,
110
, pp.
143
176
.10.1016/S0377-0257(03)00007-7
6.
Coelho
,
P. M.
, and
Pinho
,
F. T.
,
2003
, “
Vortex Shedding in Cylinder Flow of Shear-Thinning Fluids II. Flow Characteristics
,”
J. Non-Newtonian Fluid Mech.
,
110
, pp.
177
193
.10.1016/S0377-0257(03)00008-9
7.
Dhiman
,
A. K.
,
Chhabra
,
R. P.
, and
Eswaran
,
V.
,
2008
, “
Steady Flow Across a Confined Square Cylinder: Effects of Power-Law Index and of Blockage Ratio
,”
J. Non-Newtonian Fluid Mech.
,
148
, pp.
141
150
.10.1016/j.jnnfm.2007.04.010
8.
Bilus
,
I.
,
Ternik
,
P.
, and
Zunic
,
Z.
,
2011
, “
Further Contributions on the Flow Past a Stationary and Confined Cylinder: Creeping and Slowly Moving Flow of Power Law Fluids
,”
J. Fluids Struct.
,
27
, pp.
1278
1295
.10.1016/j.jfluidstructs.2011.06.004
9.
Sahu
,
A. K.
,
Chhabra
,
R. P.
, and
Eswaran
,
V.
,
2009
, “
Two-Dimensional Unsteady Laminar Flow of a Power Law Fluid Across a Square Cylinder
,”
J. Non-Newtonian Fluid Mech.
,
160
, pp.
157
167
.10.1016/j.jnnfm.2009.03.010
10.
Sahu
,
A. K.
,
Chhabra
,
R. P.
,
Eswaran
,
V.
,
2010
, “
Two-Dimensional Laminar Flow of a Power-Law Fluid Across a Confined Square Cylinder
,”
J. Non-Newtonian Fluid Mech.
,
165
, pp.
752
763
.10.1016/j.jnnfm.2010.03.011
11.
Bouaziz
,
M.
,
Kessentini
,
S.
, and
Turki
,
S.
,
2010
, “
Numerical Prediction of Flow and Heat Transfer of Power-Law Fluids in a Plane Channel With a Built-In Heated Square Cylinder
,”
Int. J. Heat Mass Transfer
,
53
, pp.
5420
5429
.10.1016/j.ijheatmasstransfer.2010.07.014
12.
Ehsan
,
I.
,
Mohammad
,
S.
,
Reza
,
N. M.
, and
Ali
,
J.
,
2012
, “
Laminar and Turbulent Power Law Fluid Flow Passing a Square Cylinder
,”
Int. J. Phys. Sci.
,
7
, pp.
988
1000
.10.5897/IJPS11.797
13.
Sumner
,
D.
,
2010
, “
Two Circular Cylinders in Cross-Flow: A Review
,”
J. Fluids Struct.
,
26
, pp.
849
899
.10.1016/j.jfluidstructs.2010.07.001
14.
Wong
,
K. L.
, and
Chen
,
C. K.
,
1986
, “
The Finite Element Solution of Laminar Combine Convection From Two Horizontal Cylinders in Tandem Arrangement
,”
J. AIChE
,
32
, pp.
557
565
.10.1002/aic.690320405
15.
Mizushima
,
J.
, and
Suehiro
,
N.
,
2005
, “
Instability and Transition of Flow Past Two Tandem Circular Cylinders
,”
Phys. Fluids
,
17
, pp.
104
107
.10.1063/1.2104689
16.
Nejat
,
A.
,
Mirzakhalili
,
E.
,
Aliakbari
,
A.
,
Fallah Niasar
,
M. S.
, and
Vahidkhah
,
K.
,
2012
, “
Non-Newtonian Power-Law Fluid Flow and Heat Transfer Computation Across a Pair of Confined Elliptical Cylinders in the Line Array
,”
J. Non-Newtonian Fluid Mech.
,
172
, pp.
67
82
.10.1016/j.jnnfm.2012.01.007
17.
Nejat
,
A.
,
Abdollahi
,
V.
, and
Vahidkhah
,
K.
,
2011
, “
Lattice Boltzmann Simulation of Non-Newtonian Flows Past Confined Cylinders
,”
J. Non-Newtonian Fluid Mech.
,
166
, pp.
689
697
.10.1016/j.jnnfm.2011.03.006
18.
Sohankar
,
A.
, and
Etminan
,
A.
,
2009
, “
Forced-Convection Heat Transfer From Tandem Square Cylinders in Cross Flow at Low Reynolds Numbers
,”
Int. J. Numer. Meth. Fluids
,
60
, pp.
733
751
.10.1002/fld.1909
19.
Patil
,
R. C.
,
Bharti
,
R. P.
, and
Chhabra
,
R. P.
,
2008
, “
Steady Flow of Power Law Fluids Over a Pair of Cylinders in Tandem Arrangement
,”
Ind. Eng. Chem.
,
47
, pp.
1660
1683
.10.1021/ie070854t
20.
Turan
,
O.
,
Chakraborty
,
N.
, and
Poole
,
R. J.
,
2012
, “
Laminar Rayleigh-Bénard Convection of Yield Stress Fluids in a Square Enclosure
,”
J. Non-Newtonian Fluid Mech.
,
171–172
, pp.
83
96
.10.1016/j.jnnfm.2012.01.006
21.
Ternik
,
P.
,
2009
, “
Planar Sudden Symmetric Expansion Flows and Bifurcation Phenomena of Purely Viscous Shear-Thinning Fluids
,”
J. Non-Newtonian Fluid Mech.
,
157
, pp.
15
25
.10.1016/j.jnnfm.2008.09.002
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