Hostname: page-component-7c8c6479df-995ml Total loading time: 0 Render date: 2024-03-28T23:48:35.281Z Has data issue: false hasContentIssue false

Pressure-driven flow in a two-dimensional channel with porous walls

Published online by Cambridge University Press:  17 July 2009

QUAN ZHANG
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
ANDREA PROSPERETTI*
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA Faculty of Science & Technology and Burgerscentrum, University of Twente, AE 7500 Enschede, The Netherlands
*
Email address for correspondence: prosperetti@jhu.edu

Abstract

The finite-Reynolds-number two-dimensional flow in a channel bounded by a porous medium is studied numerically. The medium is modelled by aligned cylinders in a square or staggered arrangement. Detailed results on the flow structure and slip coefficient are reported. The hydrodynamic force and couple acting on the cylinder layer bounding the porous medium are also evaluated as a function of the Reynolds number. In particular, it is shown that, at finite Reynolds numbers, a lift force acts on the bodies, which may be significant for the mobilization of bottom sediments.

Type
Papers
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Adler, P. M., Mills, P. M. & Quemada, D. C. 1978 Application of a self-consistent model to permeability of a fixed swarm of permeable spheres. A.I.Ch.E. J. 24, 354357.Google Scholar
Agelinchaab, M., Tachie, M. & Ruth, D. 2006 Velocity measurement of flow through a model three-dimensional porous medium. Phys. Fluids 18, 017105.Google Scholar
Beavers, G. S. & Joseph, D. D. 1967 Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30, 197207.Google Scholar
Brinkman, H. 1947 A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Appl. Sci. Res. A1, 2734.Google Scholar
Choi, H. G., & Joseph, D. D. 2001 Fluidization by lift of 300 circular particles in plane Poiseuille flow by direct numerical simulation. J. Fluid Mech. 438, 101128.Google Scholar
Goharzadeh, A., Khalili, A. & Jørgensen, B. B. 2005 Transition layer thickness at a fluid-porous interface. Phys. Fluids 17, 057102.Google Scholar
Hill, R., Koch, D. & Ladd, A. 2001 Moderate-Reynolds-number flows in ordered and random arrays of spheres. J. Fluid Mech. 448, 243278.Google Scholar
Hou, S., Zou, Q., Chen, S., Doolen, G. & Cogley, A. 1995 Simulation of cavity flow by the lattice Boltzmann method. J. Comp. Phys. 118, 329347.Google Scholar
James, D. & Davis, A. 2001 Flow at the interface of a fibrous porous medium. J. Fluid Mech. 426, 4772.Google Scholar
Koch, D. & Ladd, A. 1997 Moderate Reynolds number flow through periodic and random arrays of aligned cylinders. J. Fluid Mech. 349, 3166.Google Scholar
Koplik, J., Levine, H. & Zee, A. 1983 Viscosity renormalization in the Brinkman equation. Phys. Fluids 26, 28642870.Google Scholar
Larson, R. & Higdon, J. 1986 Microscopic flow near the surface of a two-dimensional porous medium. Part 1. Axial flow. J. Fluid Mech. 166, 449472.Google Scholar
Larson, R. E. & Higdon, J. J. L. 1987 Microscopic flow near the surface of two-dimensional porous media. Part 2. Transverse flow. J. Fluid Mech. 178, 119136.Google Scholar
Le Bars, M. & Worster, M. G. 2006 Interfacial conditions between a pure fluid and a porous medium: implications for binary alloy solidification. J. Fluid Mech. 550, 149173.Google Scholar
Martys, N., Bentz, D. & Garboczi, E. 1994 Computer simulation study of the effective viscosity in Brinkman's equation. Phys. Fluids 6, 14341439.Google Scholar
Ouriemi, M., Aussillous, P., Medale, M., Peysson, Y. & Guazzelli, E. 2007 Determination of the critical Shields number for particle erosion in laminar flow. Phys. Fluids 19, 061706.Google Scholar
Patil, D. V., Lakshmisha, K. N. & Rogg, B. 2006 Lattice Boltzmann simulation of lid-driven flow in deep cavities. Comput. Fluids 35, 11161125.Google Scholar
Pozrikidis, C. 2001 Shear flow over a particulate or fibrous plate. J. Engng Math. 39, 324.Google Scholar
Sahraoui, M. & Kaviany, M. 1992 Slip and no-slip velocity boundary conditions at interface of porous, plain media. Intl J. Heat Mass Transfer 35, 927943.Google Scholar
Sangani, A. & Acrivos, A. 1982 Slow flow through a periodic array of spheres. Intl J. Multiphase Flow 8, 343360.Google Scholar
Sangani, A. & Behl, S. 1989 The planar singular solutions of Stokes and Laplace equations and their application to transport processes near porous surfaces. Phys. Fluids A1, 2137.Google Scholar
Sangani, A. & Yao, C. 1988 Transport properties in random arrays of cylinders. II. Viscous flow. Phys. Fluids 31, 24352444.Google Scholar
Shen, C. & Floryan, J. M. 1985 Low Reynolds number flow over cavities. Phys. Fluids 28, 31913202.Google Scholar
Smith, S. H. 1987 Stokes flow past slits and holes. Intl J. Multiphase Flow 13, 219231.Google Scholar
Tachie, M., James, D. & Currie, D. 2003 Velocity measurement of a shear flow penetrating a porous medium. J. Fluid Mech. 493, 319343.Google Scholar
Tachie, M., James, D. & Currie, I. 2004 Slow flow through a brush. Phys. Fluids 16, 445451.Google Scholar
Takagi, S., Oguz, H., Zhang, Z. & Prosperetti, A. 2003 PHYSALIS: a new method particle simulation. Part II. Two-dimensional Navier–Stokes flow around cylinders. J. Comput. Phys. 187, 371390.Google Scholar
Zhang, Z. Z. & Prosperetti, A. 2003 A method for particle simulation. J. Appl. Mech. 70, 6474.Google Scholar
Zhang, Z. & Prosperetti, A. 2005 A second-order method for three-dimensional particle flow simulations. J. Comput. Phys. 210, 292324.Google Scholar