Analysis of turbulent combustion in inert porous media

The objective of this paper is to present an extension of a simplified reaction kinetics model that, combined with a thermo-mechanical closure, entails a full-generalized turbulent combustion model for flow in porous media. In this model, one explicitly considers the intra-pore levels of turbulent kinetic energy. Transport equations are written in their time-and-volume-averaged form and a volume-based statistical turbulence model is applied to simulate turbulence generation due to the porous matrix. The rate of fuel consumption is described by an Arrhenius expression involving the product of the fuel and oxidant mass fractions. These mass fractions are double decomposed in time and space and, after applying simultaneous time-and-volume integration operations to them, distinct terms arise, which are here associated with the mechanisms of dispersion and turbulence. Modeling of these extra terms remains an open question and the derivations herein might motivate further development of models for turbulent combustion in porous media.