A consistent methodology for the derivation and calibration of a macroscopic turbulence model for flows in porous media

This work aims to model turbulent flows in media laden with solid structures according to porous media approach. A complete set of macroscopic transport equations is derived by spatially averaging the Reynolds averaged governing equations. A two-scale analysis highlights energy transfers between macroscopic and sub-filter kinetic energies (dispersive and turbulent kinetic energies). Additional terms coming from the averaging procedure and representing solids/fluid interactions and turbulent contributions are modeled. Connections between turbulence modeling and dispersion modeling are presented. Other closure expressions are determined using physical considerations and spatial averaging of microscopic computations. A special care is given to the calibration methodology for the phenomenological coefficients. Results of the present model are successfully compared to volume-averaged reference results coming from fine scale computations and show significant improvements with respect to previous macroscopic models.