Pressure-driven flow in a channel with porous walls

Abstract

The finite-Reynolds-number three-dimensional flow in a channel bounded by one and two parallel porous walls is studied numerically. The porous medium is modelled by spheres in a simple cubic arrangement. Detailed results on the flow structure and the hydrodynamic forces and couple acting on the sphere layer bounding the porous medium are reported and their dependence on the Reynolds number illustrated. It is shown that, at finite Reynolds numbers, a lift force acts on the spheres, which may be expected to contribute to the mobilization of bottom sediments. The results for the slip velocity at the surface of the porous layers are compared with the phenomenological Beavers-Joseph model. It is found that the values of the slip coefficient for pressure-driven and shear-driven flow are somewhat different, and also depend on the Reynolds number. A modification of the relation is suggested to deal with these features. The Appendix provides an alternative derivation of this modified relation.

Improved procedure for the computation of Lamb’s coefficients in the physalis method for particle simulation

“…The central observation at the root of the PHYSALIS method lies in the recognition that, in the immediate neighborhood of the particle, even at finite Reynolds numbers, the modified velocity and pressure fieldsp andũ must be describable as in (11) and (12) due to the smallness of inertia. Thus, provided the coefficients are known, (11) and (12) can be used to ''transfer'' the boundary conditions from the particle surface to a cage of adjacent grid nodes enclosing the particle.…”

“…Thus, provided the coefficients are known, (11) and (12) can be used to ''transfer'' the boundary conditions from the particle surface to a cage of adjacent grid nodes enclosing the particle. After this step, the computation is carried out only on the nodes of the fixed Cartesian grid and the complexity deriving from the geometric mismatch between the particle boundary and the grid is eliminated.…”

“…The method has been thoroughly validated in the original papers and it has proven its value in a number of applications: the sedimentation of 1024 particles [7], the turbulent flow around fixed particles [8,9], the flow induced by a rotating particle [10] and over a porous medium [11,12]. An interesting variant which uses artificial compressibility to generate a timestepping pressure equation has been described and used by Perrin and Hu [13,14].…”

Verification of the boundary condition at the porous medium–fluid interface

“…The drag force in a porous medium leads to the rapid decrease of the tangential velocity, and it permits the flow instability development. The coupled flows have been studied since 1950s [1][2][3][4][5][6][7]. The problem has many applications in the environmental science and technology: contaminant transport in the rivers and atmosphere [8,9], solidification of the liquid metals [10][11][12], heat and mass transfer between the contacting media [13], optimization of the flows in the fuel cells [5], etc.…”

Wicking of a liquid bridge connected to a moving porous surface

“…Similar problems involving coupled flow within and outside a porous medium have been analysed by various researchers, including Tilton & Cortelezzi (2008), who investigated the stability of flows in channels with porous walls, and Liu & Prosperetti (2011), who conducted a numerical study of finiteReynolds-number pressure-driven flows through channels with porous walls, as well as others (e.g. Majdalani, Zhou & Dawson 2002;Dinarvand, Rashidi & Doosthoseini 2009).…”