Computation of turbulent flow in porous media using a low-reynolds k-ε Model and an infinite array of transversally displaced elliptic rods

Abstract

Through the volumetric averaging of the microscopic transport equations for the turbulent kinetic energy, k, and its dissipation rate, ε, a macroscopic model is proposed for flow in porous media. As an outcome of the volume-averaging process, additional terms appeared in the equations for k and ε. These terms are adjusted assuming the porous structure to be modeled as an infinity array of transversally displaced elliptic rods. This adjustment is obtained by solving the microscopic flow governing equations numerically, using a law-Reynolds formulation, in the periodic cell composing the infinite medium. Different porosity and aspect ratios are investigated. The adjusted model is compared with similar results found in the literature. A general view of the effect of the medium morphology on model assumptions is obtained by comparing results for elliptic, cylindrical, and square rods.