Investigation of the momentum transfer conditions at the porous/free fluid interface: A benchmark solution

In this work, the conformal mapping method is used to obtain the microscopic solution for the velocity distribution in the porous composite system. The corresponding macroscopic solution is determined by using a two-domain approach, in which the momentum transfer at the porous/free fluid interface is governed by the Beavers-Joseph condition or the stress-jump condition. The boundary parameters in the macroscopic solution, including the velocity slip and the stress jump coefficients, are determined by comparing the microscopic and macroscopic solutions. The impacts of the porous structure, flow type and the thickness of the free fluid layer on the velocity slip coefficient and the stress jump coefficient are discussed. In addition, the errors for the interface velocity, predicted by the velocity slip coefficient and the stress jump coefficient, are investigated. The analytical solution obtained in this work can be used as a benchmark for relevant numerical simulation.