R. Bahoosh-Kazerooni - Mechanical Engineering, Sharif University of Technology
S. Kazemzadeh Hannani - Mechanical Engineering, Sharif University of Technology

In this paper a new macroscopic k-ε 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 v۲ − f model are conducted using a Galerkin/Least-Squares finite element formulation, employing equalorder 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 v۲ − f model. Then, employing the volume average technique, the macroscopic transport equations of continuity, momentum and k-ε model are derived and modeled. Inthe third step and during the volume averaging process, additional terms appeared in the k-ε model are interpreted and compared with the volume averaged properties that are extracted from the solutionof microscopic v۲ − f model. Finally a “ v۲ − f based” macroscopic k-ε model is developed and validated successfully for a wide range of porosities by comparing the macroscopic data to those predicted by microscopic v۲ − 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.

Porous, Turbulence, K, ε, v۲ − f