Numerical Modeling of Turbulent Flow in Porous Media Using a Spatially Periodic Array

Turbulent flowfields within a spatially periodic array were calculated numerically using a finite difference method with a low Reynolds number, two-equation model of turbulence. Exploiting periodic boundary conditions, only a one-structural unit was taken as a calculation domain to simulate a porous medium of regular arrangement in an infinite space. Extensive numerical calculations were carried out for a wide range of Reynolds numbers, to elucidate hydrodynamic behaviors of turbulent flow (post-Forchheimer flow) in porous media. The microscopic numerical results thus obtained at a pore scale were processed to extract the macroscopic hydrodynamic characteristics in terms of the volume-averaged quantities. The macroscopic pressure and flow rate relationship, determined purely from a theoretical basis, has been examined against the existing semiempirical laws, namely, Forchheimer-extended Darcy's law. Thus, departure from Darcy's law resulting from combined nonlinear effects of both porous inertia and turbulence on the macroscopic pressure drop has been investigated numerically and correlated with the porosity and Reynolds number.