A Macroscopic Turbulence Model for Reacting Flow in Porous Media

Abstract

Two macroscopic turbulence models, Pedras and de Lemos (P–dL) and Nakayama and Kuwahara (N–K), have been used previously in the literature for analyzing turbulent flows through porous media. The accuracy of these models is discussed in the present study, and a model is proposed for reacting flows through porous media. The additional source terms of macroscopic $$k-\varepsilon $$ equations representing production and dissipation of turbulent kinetic energy are modeled introducing two unknown model constants based on physical considerations. These unknown constants are determined from the results of microscopic simulations available in the literature and scale analysis in the present study. To substantiate the validity of the present model and its superiority over the previous models, eddy viscosity predicted by the present model is compared against the results of previous models and microscopic simulation of reacting flow through a simple but often used numerical model for porous media, a staggered arrangement of square cylinders. Unlike the previous models, results of the present model are in good agreement with the microscopic results in the preheat zone, and the present model accurately captures the laminarization of flow in the combustion zone.