Macroscopic turbulence modeling for incompressible flow through undeformable porous media

The literature presents two different methodologies for developing turbulent models for flow in a porous medium. The first one starts with the macroscopic equations using the extended Darcy–Forchheimer model. The second method makes use, first, of the Reynolds-averaged equations. These two methodologies lead to distinct set of equations for the k–e model. The present work details a mathematical model for turbulent flow in porous media following the second path, or say, space-integrating the equations for turbulent flow in clear fluid. In order to account for the porous structure, an additional term is included in the sources for k and e. A methodology is followed for determining the additional constant proposed. The equations for the microscopic flow were numerically solved inside a periodic elementary cell. The porous structure was approximated by an infinite array of circular rods. The method SIMPLE and a non-orthogonal boundary-fitted coordinate system were employed. Integrated parameters where compared to the existing data for fully developed homogeneous flow through porous media. Preliminary results are in agreement with numerical experiments presented in the literature.