A Numerical Study of the Flow Past an Impermeable Sphere Embedded in a Porous Medium

Abstract

The flow past an impermeable sphere embedded in a fluid-saturated porous medium was investigated numerically. The flow is considered viscous, laminar, axisymmetric, steady and incompressible. The generalized model for fluid flow through an isotropic, rigid and homogeneous porous medium was used. The stream function–vorticity equations were solved numerically in spherical coordinates system by a defect correction multigrid method. The computations were focused on the influence of the Darcy number (Da) and Forchheimer constant on the flow field for two boundary conditions on the surface of the sphere: slip and no-slip. The conditions when the macroscopic inertial terms of the generalized model can be neglected are presented. For high-porosity porous media, the macroscopic inertial terms of the generalized model can be neglected if Da \(Re< 1\) (Re is the sphere Reynolds number).