Numerical modeling of turbulent flow in porous media using a spatially periodic array

Turbulent flowfields within a spatially periodic array were calculated nume rically using a finite difference method with a low Reynolds number, two-eq uation 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 ca lculations were carried out for a wide range of Reynolds numbers, to elucid ate hydrodynamic behaviors of turbulent flow (post-Forchheimer flow) in por ous media. The microscopic numerical results thus obtained at a pore scale were processed to extract the macroscopic hydrodynamic characteristics in t erms of the volume-averaged quantities. The macroscopic pressure and flow r ate relationship, determined purely fp om a theoretical basis, has been exa mined against the existing semiempirical laws, namely, Forchheimer-extended Darcy's law. Thus, departure from Darcy's law resulting from combined nonl inear effects of both porous inertia and turbulence on the macroscopic pres sure drop has been investigated numerically and correlated with the porosit y and Reynolds number.