Verification of the boundary condition at the porous medium–fluid interface

Abstract

We study the hydrodynamic stability of liquid flowing down over the inclined layer of uniform porous medium and compare the results obtained in the different frameworks. The flow in porous medium is described by the Brinkman model and by the Darcy model with corresponding boundary conditions at the interface between the homogeneous fluid and porous medium. It is shown the critical Reynolds number is calculated for the Darcy model much lower than in case of the Brinkman model, while the flow velocity is the same in the both models. It is a pure mathematical effect, which can be used to verify the models and to determine the empirical coefficients in the boundary conditions from an experimental study of flow instability.

Flow Simulation in a combined Region

“…The first direction is associated with Darcy's law for a porous layer and the Navier-Stokes equation in the pure region. In [1][2][3][4][5][6], the flow in the combined region was investigated using the Darcy and Stokes/Navier-Stokes model. In the Darcy model, it is believed that the flow inertia is small, and in the case of highly porous media and in large Reynolds numbers, the results of this model give large errors.…”