Novel boundary conditions for turbulent flows enclosed by porous media

Abstract

In this paper we present the new boundary conditions for the turbulent flows enclosed by porous medium. Such flows play a crucial role in many areas such as filters, oil wells, heat exchangers, catalytic reactors, ground water pollution, scouring and deposition of pollutions at river bed. Since the porous media always consist of multi-scale structures starting from the dimension of the porous medium itself down to pore scale. Resolving all of these structures is too expensive considering the uncertainty of the porous media geometry representation. Under certain conditions, the effects of the porous media to the turbulent flows can be modeled as boundary conditions. However, the approach adopted in [1], [2] and [3] lacks some physical property of the flow at the porous media interface because in those works, either the slip velocity or the interface-normal velocity is assumed zero. The boundary conditions proposed in this work, are validated against the pore scaled simulation in which the whole porous media are resolved. The proposed boundary conditions deliver excellent normalized mean velocity and fluctuations. The numerical simulation using boundary conditions only uses 0.92 Million grid cells and it is computed on a simple workstation compared to 230 Million grid cells of the pore scaled simulation which is computed on a cluster with 512 nodes. The proposed boundary conditions allow accurate predictions of such flows to be accessible by the computing resources available in Thailand.