Macroscopic Modeling of Turbulence in Porous Media Flows

Abstract

A new model to describe turbulent flows within the porous media approximation is presented. The spatial- and time fluctuations in this new model are tied together and treated as a single quantity. This novel treatment of the fluctuations leads to a natural construction of the “k” and “epsilon” type
equations for rigid and isotropic porous media in which all the kinetic energy filtered in the averaging process is modeled. The same terms as those found in the corresponding equations for clear flow, plus additional terms resulting from the interaction between solid walls in the porous media and the fluid characterize the model. These extra terms arise in a boundary integral form, facilitating their modeling. The model is closed by assuming the eddy viscosity approximation to be valid, and using simple models to represent the interaction between the walls in the porous media and the fluid. Preliminary validation of the model is carried out by simulating a free stream entering to an infinite two dimensional porous medium formed by staggered squares (numerical solution based on Reynolds Averaged Navier-Stokes equations, RANS). Simulations are carried out for the 75% porosity case. Different inlet turbulence intensities are imposed on the free stream to test the model under different macroscopic boundary conditions. Microscopic RANS solutions for the turbulence quantities (k and epsilon) are averaged in
space and compared with those yielded by the porous media model. The model is shown to fairly predict macroscopic turbulence quantities under different testing conditions. Results encourage further validation of the model in more complex porous media geometries.