An investigation of inertial one-phase flow in homogeneous model porous media

Abstract

Our interest in this work is the stationary one-phase Newtonian flow in a class of homogeneous porous media at large enough flow rates requiring the introduction of the inertial forces at the pore-scale. At the macroscale, this implies a nonlinear correction to Darcy's law i.e. a nonlinear between the filtration velocity and the pressure gradient. The objective here is to analyze the nonlinear correction on some periodic models of porous media with respect to the Reynolds number and the pressure gradients orientation relative to the principal axes of the periodic unit cell.