A “v2-f Based” Macroscopic K-Ε Model for Turbulent Flow through Porous Media

Abstract

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 v2 − 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 v2 − 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 v2 − f model. Finally a “ v2 − 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 v2 − 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.