On the use of a Darcy–Forchheimer like model for a macro-scale description of turbulence in porous media and its application to structured packings

In this paper, we propose a methodology to derive a macro-scale momentum equation that is free from the turbulence model chosen for the pore-scale simulations and that is able to account for large-scale anisotropy. In this method, Navier–Stokes equations are first time-averaged to form a new set of equations involving an effective viscosity. The resulting balance equations are then up-scaled using a volume averaging methodology. This procedure gives a macro-scale generalized Darcy–Forchheimer equation to which is associated a closure problem that can be used to evaluate the apparent permeability tensor including inertia effects. This approach is validated through 2D and 3D calculations. Finally, the method is used to evaluate the tensorial macro-scale properties for a gas flow through structured packings.