Analysis of Brinkman-Extended Darcy Flow in Porous Media and Experimental Verification Using Metal Foam

Abstract

Momentum transport in porous media exists in numerous engineering and process applications, e.g., ground water pollution, storage of nuclear waste, heat exchangers, and chemical reactors. In many of such applications, the porous medium is confined by solid boundaries. These impermeable boundaries give rise to shear stress and boundary layers. The Brinkman-extended Darcy equation describes the momentum transport due to Newtonian fluid flow in confined porous media. This equation is solved analytically in a cylindrical system, employing an existing fully-developed boundary-layer concept particular to porous media flows. The volume-averaged velocity increases as the distance from the boundary increases reaching a maximum at the center. The mean and maximum velocities are obtained and their behavior is investigated in terms of pertinent flow parameters. The friction factor is defined based on the mean velocity and is found to be inversely proportional to the Reynolds number, the Darcy number, and the mean velocity. The analytical results are verified by experiments using two types of metal foam. In the Darcy regime, reasonably good agreement is found between the analytical and the experimental friction factors for the 20-pore-per-inch foam, while a poor agreement is found for the 10-pore-per-inch foam.