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Steady flow around and through a permeable circular cylinder. (English) Zbl 1271.76332
Summary: The steady flow around and through a porous circular cylinder was studied numerically. The effects of the two important parameters, the Reynolds and Darcy numbers, on the flow were investigated in details. The recirculating wake existing downstream of the cylinder is found to either penetrate into or be completely detached from the cylinder. It is also found that, contrary to that of the solid cylinder, the recirculating wake develops downstream of or within the porous cylinder, but not from the surface of it. These new findings provide additional evidence to L. G. Leal’s conclusion in [Phys. Fluids A, No. 1, 124–131 (1989)] that the appearance of recirculating wakes at finite Reynolds number is due to vorticity accumulation, but not a result of the same physical phenomena associated with separation in boundary layers in adverse pressure gradients. Also presented in the current study are the variation of the critical Reynolds number for the onset of a recirculating wake as a function of Darcy number and the variation of a newly defined parameter, the penetration depth, as a function of the Reynolds number and Darcy number.

76S05 Flows in porous media; filtration; seepage
76D05 Navier-Stokes equations for incompressible viscous fluids
76D25 Wakes and jets
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[1] Coutanceau, M.; Bouard, R., Experimental determination of the main features of the viscous flow in the wake of a circular cylinder in uniform translation. part 1. steady flow, J fluid mech, 79, 231-256, (1977)
[2] Fornberg, B., A numerical study of steady viscous flow past a circular cylinder, J fluid mech, 98, 819-855, (1980) · Zbl 0428.76032
[3] Li, G.P.; Humphrey, J.A.C., Numerical modelling of confined flow past a cylinder of square cross-section at various orientations, Int J numer methods fluids, 20, 1215-1236, (1995) · Zbl 0840.76054
[4] Sohankar, A.; Norberg, C.; Davidson, L., 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, 39-56, (1998) · Zbl 0910.76067
[5] Anderson, J.M.; Streitlien, K.; Barrett, D.S.; Triantafyllou, M.S., Oscillating foils of high propulsive efficiency, J fluid mech, 360, 41-72, (1998) · Zbl 0922.76023
[6] Yu, P.; Lee, T.S.; Zeng, Y.; Low, H.T., Fluid dynamics and oxygen transport in a micro-bioreactor with a tissue engineering scaffold, Int J heat mass transfer, 52, 316-327, (2009) · Zbl 1156.76448
[7] Joseph, D.D.; Tao, L.N., The effect of permeability on the slow motion of a porous sphere in a viscous liquid, Z angew math mech, 44, 361-364, (1964) · Zbl 0125.19202
[8] Neale, G.; Epstein, N.; Nadar, W., Creeping flow relative to permeable spheres, Chem eng sci, 28, 1865-1874, (1973)
[9] Masliyah, J.H.; Polikar, M., Terminal velocities of porous spheres, Can J chem eng, 58, 299-302, (1980)
[10] Nandakumar, K.; Masliyah, J.H., Laminar flow past a permeable sphere, Can J chem eng, 60, 202-211, (1982)
[11] Hsu, H.J.; Huang, L.H.; Hsieh, P.C., A re-investigation of the low Reynolds number uniform flow past a porous spherical shell, Int J numer anal methods geomech, 28, 1427-1439, (2004) · Zbl 1084.76068
[12] Bhattacharyya, A.; Raja Sekhar, G.P., Viscous flow past a porous sphere with an impermeable core: effect of stress jump condition, Chem eng sci, 59, 4481-4492, (2004)
[13] Ochoa-Tapia, J.A.; Whitaker, S., Momentum transfer at the boundary between a porous medium and a homogeneous fluid I: theoretical development, Int J heat mass transfer, 38, 2635-2646, (1995) · Zbl 0923.76320
[14] Ochoa-Tapia, J.A.; Whitaker, S., Momentum transfer at the boundary between a porous medium and a homogeneous fluid II: comparison with experiment, Int J heat mass transfer, 38, 2647-2655, (1995) · Zbl 0923.76320
[15] Jue, T.C., Numerical analysis of vortex shedding behind a porous cylinder, Int J numer methods heat fluid flow, 14, 649-663, (2004) · Zbl 1078.76545
[16] Ochoa-Tapia, J.A.; Whitaker, S., Momentum jump condition at the boundary between a porous medium and a homogeneous fluid: inertial effect, J porous media, 1, 201-217, (1998) · Zbl 0931.76094
[17] Chen, X.B.; Yu, P.; Winoto, S.H.; Low, H.T., 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, 635-655, (2008)
[18] Noymer, P.D.; Glicksman, L.R.; Devendran, A., Drag on a permeable cylinder in steady flow at moderate Reynolds numbers, Chem eng sci, 53, 2859-2869, (1998)
[19] Bhattacharyya, S.; Dhinakaran, S.; Khalili, A., Fluid motion around and through a porous cylinder, Chem eng sci, 61, 4451-4461, (2006)
[20] Fransson, J.H.M.; Koniecznyb, P.; Alfredssona, P.H., Flow around a porous cylinder subject to continuous suction or blowing, J fluids struct, 19, 1031-1048, (2004)
[21] Leal, L.G., Vorticity transport and wake structure for bluff-bodies at finite Reynolds-number, Phys fluids A - fluid dyn, 1, 124-131, (1989)
[22] Dandy, D.; Leal, L.G., Buoyancy driven motion of a deformable drop through a quiescent liquid at intermediate Reynolds numbers, J fluid mech, 208, 161-192, (1989)
[23] Dandy, D.; Leal, L.G., Boundary-layer separation from a smooth slip surface, Phys fluids, 29, 1360-1366, (1986)
[24] Leal, L.G.; Acrivos, A., The effect of base bleed on the steady separated flow past bluff objects, J fluid mech, 38, 735-752, (1969)
[25] Yu, P.; Lee, T.S.; Zeng, Y.; Low, H.T., A numerical method for flows in porous and open domains coupled at the interface by stress jump, Int J numer methods fluids, 53, 1755-1775, (2007) · Zbl 1370.76110
[26] Gartling, D.K.; Hickox, C.E.; Givler, R.C., Simulation of coupled viscous and porous flow problems, Comput fluid dyn, 7, 23-48, (1996) · Zbl 0879.76104
[27] Alazmi, B.; Vafai, K., Analysis of fluid flow and heat transfer interfacial conditions between a porous medium and a fluid layer, Int J heat mass transfer, 44, 1735-1749, (2001) · Zbl 1091.76567
[28] Ferziger, J.H.; Perić, M., Computational methods for fluid dynamics, (1999), Springer Berlin · Zbl 0869.76003
[29] Lilek, Ž; Muzaferija, S.; Perić, M.; Seidl, V., An implicit finite-volume method using nonmatching blocks of structured grid, Numer heat transfer B, 32, 385-401, (1997)
[30] Dennis, S.C.R.; Chang, G.Z., Numerical solutions for steady flow past a circular cylinder at Reynolds numbers up to 100, J fluid mech, 42, 471-490, (1970) · Zbl 0193.26202
[31] Arcas, D.R.; Redekopp, L.G., Aspects of wake vortex control through base blowing/suction, Phys fluids, 16, 452-456, (2004) · Zbl 1186.76032
[32] Schlichting, H., Boundary-layer theory, (1968), Mcgraw-Hill New York
[33] Rivkind, V.Y.; Ryskin, G.M., Flow structure in motion of a spherical drop in a fluid medium at intermediate Reynolds numbers, Fluid dyn, 11, 5-12, (1976)
[34] Underwood, R.L., Calculation of incompressible flow past a circular cylinder at moderate Reynolds numbers, J fluid mech, 37, 95-114, (1969) · Zbl 0175.51902
[35] Noack, B.; Eckelmann, H., A low-dimensional Galerkin method for the three-dimensional flow around a circular cylinder, Phys fluids, 6, 124-143, (1994) · Zbl 0826.76071
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