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 simulatedby a periodic array of square cylinders. in the first step, calculations based on microscopic v - fmodel 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 fromthe microscopic solution of v -f model. then, employing the volume average technique, themacroscopic 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 solutionof microscopic v - f model. finally a v - f based macroscopic k-s model is developed andvalidated successfully for a wide range of porosities by comparing the macroscopic data to thosepredicted 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.