On the Interfacial Flow Over Porous Media Composed of Packed Spheres: Part 2-Optimal Stokes–Brinkman Coupling with Effective Navier-Slip Approach

Abstract

The Stokes–Brinkman coupling has been employed to investigate the flow through porous media composed of packed spheres. By matching the slip velocity using the Navier-slip condition, optimal values of the effective viscosity in the continuous stress condition and of the stress jump coefficient in the stress jump condition could be accurately determined. The correlations between the slip length (which has been accurately determined in Part 1) and the effective viscosity as well as the stress jump coefficient have been specified. The accuracy of these two optimal parameters (i.e., the effective viscosity and stress jump coefficient) has been assessed by comparing the velocity profiles in both the fluid and porous regions obtained from the Stokes–Brinkman coupling, with those obtained from the corresponding direct simulations. It is observed that the stress jump condition with the optimal stress jump coefficient yields a superior prediction in the velocity field. The optimal effective viscosity decreases as the solid volume fraction increases, whereas the stress jump coefficient increases with the solid volume fraction. By selecting the optimal parameters, the Stokes–Brinkman coupling with both the continuous stress condition and stress jump condition is applied to solve two example flow problems: a stick–slip–stick flow and a pressure-driven flow in a rectangular channel. Both the stress conditions in the Stokes–Brinkman coupling exhibit good performances in reproducing the velocity fields within the entire domain.