A model equation for nonlinear unsteady flow through porous media

Abstract We propose a new model for nonlinear unsteady flow through porous media in the framework of the volume-averaged momentum equation. The drag is decomposed into the accelerative pressure drag, the viscous pressure drag, the convective pressure drag and the friction drag. The accelerative pressure drag is given in terms of the tortuosity and the macroscopic pressure gradient. The convective pressure drag is modelled by a Forchheimer-type nonlinearity. The friction drag and the viscous pressure drag are modelled together by a history term that is constructed by blending the equivalent fluid model of Pride et al. (Phys. Rev. B, 1993) with a steady laminar boundary layer scaling.The model is validated against direct numerical simulations of oscillatory flow through a hexagonal sphere pack and compared with models from the literature. The proposed model accurately represents linear flow and significantly improves the prediction of nonlinear flow at intermediate frequencies compared to the existing models. The model errors increase gradually from linear unsteady flow and nonlinear quasi-stationary flow to high-frequency nonlinear flow.