A v2-F BASED MACROSCOPIC k-£ MODEL FOR TURBULENT FLOW THROUGH POROUS MEDIA

In this paper a new macroscopic k-e model is developed and validated for turbulent flow through porous media for a wide range of porosities. The morphology of porous media is simulated by a periodic array of square cylinders. In the first step, calculations based on microscopic v - f model are conducted using a Galerkin/Least-Squares finite element formulation, employing equal order bilinear velocity-pressure elements. Calculations are validated by comparing the results to available data in the literature. In the second step, the volume averaged properties are extracted from the microscopic solution of v -f model. Then, employing the volume average technique, the macroscopic transport equations of continuity, momentum and k-e model are derived and modeled. In the third step and during the volume averaging process, additional terms appeared in the k-s model are interpreted and compared with the volume averaged properties that are extracted from the solution of microscopic v - f model. Finally a v - f based macroscopic k-s model is developed and validated successfully for a wide range of porosities by comparing the macroscopic data to those predicted by microscopic v -f model. Moreover, the results of the calculations are compared with the result of an experimental work in the literature in order to validate the accuracy of the model.