Lattice Boltzmann equation with Bhatnagar–Gross–Krook (BGK) model is applied to simulate unsteady laminar flow around a confined square obstacle, in order to study the vortex shedding and their interaction in the flow on the mass transfer in the parietal zone of a channel. The model was tested by comparing to an experimental study via standard particle image velocimetry (PIV). A post-processing was used to well extract instantaneous vortices contained in the flow downstream obstacles. A sensor with zero concentration on the surface is placed on the channel wall to study the effect of wake instabilities on the parietal mass transfer.
References
1.
Chen
, S.
, and Doolen
, G. D.
, 1998
, “Lattice Boltzmann Method for Fluid Flows
,” Annu. Rev. Fluid Mech.
, 30
(1
), pp. 329
–364
.10.1146/annurev.fluid.30.1.3292.
Flekkoy
, E. G.
, 1993
, “Lattice Bathnagar-Gross-Krook Models for Miscible Fluids
,” Phys. Rev. E
, 47
(6
), pp. 4247
–4257
.10.1103/PhysRevE.47.42473.
Shi
, B.
, and Guo
, Z.
, 2011
, “Lattice Boltzmann Simulation for Non-Linear Convection-Diffusion Equations
,” Comput. Math. Appl.
, 61
(12
), pp. 3443
–3452
.10.1016/j.camwa.2011.01.0414.
Williamson
, C. H. K.
, 1996
, “Vortex Dynamics in the Cylinder Wake
,” Annu. Rev. Fluid Mech.
, 28
(1
), pp. 477
–539
.10.1146/annurev.fl.28.010196.0024015.
Zdravkovich
, M. M.
, 1997
, Flow Around Circular Cylinder: A Comprehensive Guide Through Flow Phenomena, Experiments, Applications, Mathematical Models, and Computer Simulations
, Vol. 1
, Oxford University Press, New York
.6.
Zdravkovich
, M. M.
, 2003
, Flow Around Circular Cylinder: A Comprehensive Guide Through Flow Phenomena, Experiments, Applications, Mathematical Models, and Computer Simulations, Vol. 2
, Oxford University Press, New York
.7.
Rehimi
, F.
, Aloui
, F.
, Ben Nasrallah
, S.
, Doubliez
, L.
, and Legrand
, J.
, 2008
, “Experimental Investigation of a Confined Flow Downstream of a Circular Cylinder Centred Between Two Parallel Walls
,” J. Fluids Struct.
, 24
(6
), pp. 855
–882
.10.1016/j.jfluidstructs.2007.12.0118.
Abassi
, W.
, Aloui
, F.
, Ben Nasrallah
, S.
, and Legrand
, J.
, 2011
, “Lattice Boltzmann Method Used to Simulate an Unsteady Flow Around an Obstacle in Laminar Regime
,” Paper No. AJK2011-13005
, pp. 3047
–3055
.9.
Thomas
, D. G.
, 1966
, “Forced Convection Mass Transfer: Part III. Increased Mass Transfer From a Flat Plate Caused by the Wake From Cylinders Located Near the Edge of the Boundary Layer
,” AIChE J.
, 12
(1
), pp. 124
–130
.10.1002/aic.69012012410.
Abassi
, W.
, Aloui
, F.
, Ben Nasrallah
, S.
, and Legrand
, J.
, 2012
, “Use of Lattice-Boltzmann Method in Mass Transfer for the Wall Shear Stress Calculation in an Unsteady Laminar Flow Downstream of a Cylinder Located in a 2D Rectangular Channel
,” ASME
Paper No. FEDSM2012-72232.10.1115/FEDSM2012-7223211.
Coutanceau
, M.
, and Defaye
, J. R.
, 1991
, “Circular Cylinder Wake Configurations: A Flow Visualization Survey
,” ASME Appl. Mech. Rev.
, 44
(6
), pp. 255
–305
.10.1115/1.311950412.
Okajima
, A.
, 1982
, “Strouhal Numbers of Rectangular Cylinders
,” J. Fluid Mech.
, 123
(1
), pp. 379
–398
.10.1017/S002211208200311513.
Graftieaux
, L.
, Michard
, M.
, and Grosjean
, N.
, 2001
, “Combining PIV, POD and Vortex Identification Algorithms for the Study of Unsteady Turbulent Swirling Flows
,” Measure. Sci. Tech.
, 12
(9
), pp. 1422
–1429
.10.1088/0957-0233/12/9/30714.
Klekar
, K. M.
, and Patankar
, S. V.
, 1992
, “Numerical Prediction of Vortex Shedding Behind Square Cylinders
,” Int. J. Numer. Methods Fluids
, 14
(3
), pp. 327
–341
.10.1002/fld.165014030615.
Davis
, R. W.
, and Moore
, E. F.
, 1982
, “A Numerical Study of Vortex Shedding From Rectangles
,” J. Fluid Mech.
, 116
(3
), pp. 475
–506
.10.1017/S002211208200056116.
Zovatto
, L.
, and Pedrizzetti
, G.
, 2001
, “Flow About a Circular Cylinder Between Parallel Walls
,” J. Fluid Mech.
, 440
(1
), pp. 1
–25
.10.1017/S002211200100460817.
Sumer
, B. M.
, Jensen
, B. L.
, and Fredsoe
, J.
, 1991
, “Effect of a Plane Boundary on Oscillatory Flow Around a Circular Cylinder
,” J. Fluid. Mech.
, 225
(1
), pp. 271
–300
.10.1017/S002211209100205718.
Abassi
, W.
, Aloui
, F.
, Ben Nasrallah
, S.
, Legrand
, J.
, and Labraga
, L.
, 2013
, “Use of the POD and the Coherent Structure Detection Criteria to Study the Flow Dynamics Downstream a Confined Square Obstacle
,” ASME
Paper No. FEDSM2013-16309.10.1115/FEDSM2013-1630919.
Brede
, M.
, Eckelmann
, H.
, and Rockwell
, D.
, 1996
, “On Secondary Vortices in the Cylinder Wake at Right Reynolds Numbers
,” J. Fluids Struct.
, 22
(8
), pp. 757
–771
.10.1063/1.86898620.
Zheng
, G. S.
, and Worek
, W. M.
, 1996
, “Methods of Heat and Mass Transfer Enhancement in Film Evaporation
,” Int. J. Heat Mass Transfer
, 39
(1
), pp. 97
–108
.10.1016/S0017-9310(96)85009-521.
Berger
, F. P.
, Hau
, K.-F.
, and Hau
, F.-L.
, 1979
, “Local Mass/Heat Transfer Distribution on Surfaces Roughened With Small Square Ribs
,” Int. J. Heat Mass Transfer
, 22
(12
), pp. 1645
–1656
.10.1016/0017-9310(79)90081-422.
Deliyang
, Y.
, Shehata
, A.
, Modi
, V.
, and West
, A. C.
, 1997
, “Mass Transfer to a Channel Wall Downstream of a Cylinder
,” Int. J. Heat Mass Transfer
, 40
(18
), pp. 4263
–4271
.10.1016/S0017-9310(97)00091-423.
Bhatnagar
, P. L.
, Gross
, E. P.
, and Krook
, M.
, 1954
, “A Model for Collision Process in Gases
,” Phys. Rev.
, 94
(3
), pp. 511
–525
.10.1103/PhysRev.94.51124.
Skordos
, P. A.
, 1993
, “Initial and Boundary Conditions for the Lattice Boltzmann Method
,” Phys. Rev. E
, 48
(6
), pp. 4823
–4842
.10.1103/PhysRevE.48.482325.
He
, X.
, and Luo
, L. S.
, 1997
, “Theory of Lattice Boltzmann Method: From the Boltzmann Equation to Lattice Boltzmann Equation
,” Phys. Rev. E
, 56
(6
), pp. 6811
–6817
.10.1103/PhysRevE.56.681126.
He
, X.
, Chen
, S.
, and Doolen
, G. D.
, 1998
, “A Novel Thermal Model for the Lattice Boltzmann Method in Incompressible Limit
,” J. Comput. Phys.
, 146
(1
), pp. 282
–300
.10.1006/jcph.1998.605727.
Shan
, X.
, 1997
, “Simulation of Rayleigh-Bénard Convection Using a Lattice Boltzmann Method
,” Phys. Rev. E
, 55
(2
), pp. 2780
–2788
.10.1103/PhysRevE.55.278028.
Rothman
, D. H.
, and Zaleski
, S.
, 1997
, Lattice-Gas Cellular Automata: Simple Models of Complex Hydrodynamics
, Cambridge University
, Cambridge, UK
.29.
Breuer
, M.
, Bernsdorf
, J.
, Zeiser
, T.
, and Durst
, F.
, 2000
, “Accurate Computations of 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)00081-830.
Zhou
, J. G.
, 2003
, Lattice Boltzmann Method for Shallow Water Flows
, Springer-Verlag
, Berlin
.10.1007/978-3-662-08276-831.
Zou
, Q.
, and He
, X.
, 1997
, “On Pressure and Velocity Boundary Conditions for the Lattice Boltzmann BGK Model
,” Phys. Fluid
, 9
(6
), pp. 1591
–1598
.10.1063/1.86930732.
Lundgren
, T. S.
, Sparrow
, E. M.
, and Starr
, J. B.
, 1964
, “Pressure Drop Due to the Entrance Region in Ducts of Arbitrary Cross Section
,” J. Basic Eng.
, 86
(3
), pp. 620
–626
.10.1115/1.365318633.
Paranthoën
, P.
, Browne
, L. W. B.
, Le Masson
, S.
, Dumouchel
, F.
, and Lecordier
, J. C.
, 1999
, “Characteristics of the Near Wake of a Cylinder at Low Reynolds Numbers
,” Eur. J. Mech. B/Fluids
, 18
(4
), pp. 659
–674
.10.1016/S0997-7546(99)00105-334.
Réhimi
, F.
, 2006
, “Experimental Characterization of Vortices Behind a Confined Cylinder With PIV and Polarography
,” Ph.D. thesis, Faculty of Sciences and Techniques, University of Nantes
, Nantes, France
.35.
Guerrouache
, M. S.
, 2000
, “Numerical Study of the Instability of Benard-Karman Behind a Fixed Cylinder or Periodic Motion: Dynamic Flow and Chaotic Advection
,” Ph.D. thesis, Polytechnic School of the University of Nantes
, Nantes, France
.36.
Strawn
, R.
, Kenwright
, C.
, and Ahmad
, D. N.
, 1999
, “Computer Visualisation of Vortex Wake Systems
,” AIAA J.
, 37
(4
), pp. 511
–512
.10.2514/2.74437.
Jeong
, J.
, and Hussain
, F.
, 1995
, “On the Identification of a Vortex
,” J. Fluid Mech.
, 285
(1
), pp. 69
–94
.10.1017/S002211209500046238.
Hunt
, J. C. R.
, Wray
, A.
, and Moin
, P.
, 1988
, “Eddies, Stream and Convergence Zones in Turbulent Flows
,” Center for Turbulence Research, Report CRT-S88
, pp. 193
–208
.39.
Koched
, A.
, Pavageau
, M.
, and Aloui
, F.
, 2011
, “Experimental Investigations of Transfer Phenomena in a Confined Plane Turbulent Impinging Water Jet
,” ASME J. Fluids Eng.
, 133
(6
), p. 061204
.10.1115/1.400409040.
Aloui
, F.
, Berrich
, E.
, and Pierrat
, D.
, 2011
, “Experimental and Numerical Investigations of a Turbulent Flow Behavior in Isolated and Nonisolated Conical Diffusers
,” ASME J. Fluids Eng.
, 133
(1
), p. 011201
.10.1115/1.400323641.
Lévêque
, M. A.
, 1928
, “Les Lois de Transmission de la Chaleur par Convection
,” Ann. Mines
, 13
, pp. 381
–412
.42.
Berrich
, E.
, Aloui
, F.
, and Legrand
, J.
, 2013
, “Analysis of Inverse Method Applied on Sandwich Probes
,” ASME J. Fluids Eng.
, 135
(1
), p. 011401
.10.1115/1.4007888Copyright © 2015 by ASME
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