Characterization of coupled parallel flow through layered heterogeneous porous media

Abstract

In this paper, numerical simulations are used to investigate the flow fields that develop within a triple-layer channel. The middle layer, with flow governed by Navier–Stokes equations, is sandwiched between two heterogeneous permeable layers, with flow governed by well-known non-Darcy type models such as Darcy–Lapwood–Brinkman (DLB) and Darcy–Lapwood–Forchheimer–Brinkman (DFB). As a function of the normal space variable, it is proposed that the permeability varies continuously and logarithmically across the channel and reaches zero on solid walls. All computations are carried out with the open source software package OpenFOAM. In the case of constant permeability, the computations are first validated by comparison to data from earlier literature and homotopy analysis method results. Then, for the case of heterogeneous porous media, a computational investigation is performed to examine the effects of specific geometrical, media, and flow parameters on the quantities of interest, namely, interfacial strain rate and velocity. Specifically, the effect of Darcy number, Reynolds number, porous media model, pressure gradient, free-space layer thickness, symmetry adjustment parameter, and Forchheimer coefficient is determined. It is found that interfacial velocity scales with pressure gradient and Reynolds number for low Reynolds numbers, increases with the Darcy number, and decreases as the Forchheimer coefficient increases. For low Reynolds numbers, the interfacial strain rate is found to scale with pressure gradient, Reynolds number, and free-space layer thickness. Furthermore, the interfacial strain rate is found to be independent of Darcy number when the bounding porous layers have the same thickness, Darcy number, or model equation.