Brinkman – Forchheimer – Darcy 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 studied numerically considering valid the Brinkman-Forchheimer-Darcy (or Brinkman-Hazen-Dupuit-Darcy) model. The flow is viscous, laminar, axisymmetric, steady and incompressible. The porous medium is isotropic, rigid and homogeneous. The stream function - vorticity equations were solved numerically in spherical coordinates system by a multigrid method. The influence of the Darcy number and Forchheimer term on the velocities field was investigated for two boundary conditions on the surface of the sphere: slip and no - slip.

Keywords

• saturated porous medium
• sphere
• axisymmetric flow
• stream function
• vorticity
• no slip boundary condition
• slip boundary condition