Turbulence modeling for flows in wall bounded porous media: An analysis based on direct numerical simulations

Various models are available for simulating turbulent flows in porous media. Models based on the eddy viscosity assumption are often adopted to close the Reynolds stress term. In order to validate the assumptions behind such turbulence models, we studied the dynamics of macroscopic momentum and turbulence kinetic energy in porous media flows by utilizing Direct Numerical Simulation (DNS). The generic porous matrix is composed of regularly arranged spheres. The resulting periodic porous medium is bounded by two walls. The DNS analyses with a Lattice Boltzmann method were performed for various values of the applied pressure gradient, pore size to channel width ratio, and porosity. The DNS results were averaged over time and volume to obtain macroscopic results. The results show that the macroscopic shear Reynolds stress in all Representative Elementary Volumes (REVs), independent of their location, is negligibly small, although the mean velocity gradient takes nonzero values near the wall. The turbulence kinetic energy production rate is generally balanced by the dissipation rate in each REV. The DNS results support a zero-equation turbulence model that accounts for the fact that turbulent structures are restricted in size by the pore scale. The DNS results also suggest that the Brinkman term, which expresses the diffusion of momentum, has an important effect near the wall where the gradient of the shear stress is large. Therefore, the Brinkman term should be taken into account in the macroscopic momentum equation as a component of the total drag. A preliminary macroscopic model for calculating turbulent porous media flows has been proposed and compared with our DNS results.