Brinkman–Forchheimer-Darcy flow past an impermeable cylinder embedded in a porous medium

Abstract

For the flow past an impervious cylinder embedded in a fluid saturated porous medium only the linear (Darcy and Darcy - Brinkman) models were used. In this work, the flow past an impermeable cylinder embedded in a fluid saturated porous medium was studied numerically considering a nonlinear model valid (the Brinkman – Forchheimer – Darcy or Brinkman – Hazen – Dupuit – Darcy model). The flow is viscous, laminar, steady and incompressible. The porous medium is isotropic, rigid and homogeneous. The stream function - vorticity equations were solved numerically in cylindrical coordinates system. The influence of the cylinder Reynolds number, Darcy number and Forchheimer term on the velocities field and surface pressure was investigated for two boundary conditions on the surface of the cylinder: slip and no - slip.

Keywords

• saturated porous medium
• cylinder
• stream function
• vorticity
• no – slip boundary condition
• slip boundary condition