Rough-wall layer modeling using the Brinkman equation

A flow model to facilitate the Reynolds-averaged Navier-Stokes (RANS) type of calculations of the turbulent flow over rough walls is proposed. Given that the roughness region is thin compared to the thickness of the boundary layer, the turbulent flow is viewed as consisting of two regions: (1) where the medium is entirely fluid and the RANS equations can be applied, and (2) a region of two phases where the fluid meanders around the solid roughness elements. The method of volume-averaging often used in the study of porous medium flows is applied in the rough-wall layer region. The resulting parameters such as porosity allow a direct inclusion of the geometric characteristics of the roughness element and their pattern in the model equations. In this formulation, the Brinkman equation, a reduced form of the volume-averaged Navier-Stokes (VANS) equations has been used. We have experimented with adapting an existing low Reynolds number eddy-viscosity, two-equation turbulence model developed for smooth walls, to provide closure to the RANS equations. The results shown are for a NACA 0012 airfoil with three different surface coverage using the same roughness.