Generalized Darcy-Forchheimer law for capturing flow refraction effects in anisotropic porous media

Flow refraction, characterized by a misalignment between the bulk flow direction and the bulk pressure drop direction, has been observed in anisotropic porous media at intermediate and high pore-scale Reynolds number flows. Within these porous media, certain principal geometrical axes exhibit significant flow sheltering, resulting in reduced drag on the flow and causing it to deviate in those directions. Motivated by the use of high porosity porous media for flow control, we studied this phenomenon both numerically, using 2D direct numerical simulations, and experimentally. The results confirm the existence of flow refraction as seen in both simulations and experiments. The standard Darcy-Forchheimer (DF) law, which assumes that the nonlinear permeability tensor is orientation-independent, fails to capture these flow refraction effects. To address this limitation, a generalized DF law is proposed to incorporate these effects by allowing the Forchheimer permeability tensor to vary based on the flow orientation relative to the principal geometric directions of the porous structure. Good agreement of flow refraction angles in simulations, experiments and the proposed model is obtained.