A novel one-domain approach for modeling flow in a fluid-porous system including inertia and slip effects

Abstract

A new one-domain approach is developed in this work yielding an operational average description of one-phase flow in the classical Beavers and Joseph configuration including a porous medium topped by a fluid channel. The model is derived by considering three distinct regions: the homogeneous part of the porous domain, the inter-region, and the free fluid region. The development is carried out including inertial flow and slip effects at the solid–fluid interfaces. Applying an averaging procedure to the pore-scale equations, a unified macroscopic momentum equation, applicable everywhere in the system and having a Darcy form, is derived. The position-dependent apparent permeability tensor in this model is predicted from the solution of two coupled closure problems in the inter-region and in the homogeneous part of the porous medium. The performance of the model is assessed through in silico validations in different flow situations showing excellent agreement between the average flow fields obtained from direct numerical simulations of the pore-scale equations in the entire system and the prediction of the one-domain approach. Furthermore, validation with experimental data is also presented for creeping flow under no-slip conditions. In addition to the fact that the model is general from the point of view of the flow situations it encompasses, it is also simple and novel, hence providing a practical and interesting alternative to models proposed so far using one- or two-domain approaches.