Momentum transport in the free fluid-porous medium transition layer: one-domain approach

Abstract

In this work, we consider the momentum transport of a incompressible fluid in a like Beavers and Joseph (1967) system. For this purpose, in the context of the volume averaging method, we use a one-domain approach (ODA). Thus, the momentum generalized transport equations (GTE), which are written in terms of position-dependent effective medium coefficients, are valid everywhere in the system and contains two Brinkman corrections in addition to a Darcy’s term. The ODA predictions are tested against the results obtained from averaging the local profiles resulting from pore-scale simulations. One of the key points for solving the ODA remains on the prediction of the permeability, which in this work is obtained either by solving the associated local closure problem or from pore-scale profiles. Our analysis shows that the GTE for momentum transport accurately predicts the average velocity profiles everywhere in the system. To this end, the first and the second Brinkman’s corrections, as well as a position-dependent intrinsic permeability tensor in Darcy’s term must be included.