Fully explicit formulae for flame speed in infinite and finite porous media

Abstract

This work proposes new analytical expressions for gaseous flames in inert porous media, based on the existing modelling strategies. The central hypothesis is that interphase heat transfer has negligible impact on the local flame structure. This requires a gradual separation between the length scales of chemical reactions, gas diffusion, and interphase thermal re-equilibriation. By resolving the gas and solid equations without reaction on each side of the reaction sheet, the preheating of the fresh gases ahead of the flame front is analytically computed at leading order. Combustion kinetics are solved separately, assuming the consumption rate to be a sole function of this preheating. Two kinetic models are considered, namely, single-step Arrhenius and power law fits from experiments or detailed computations. Several fully explicit formulae for flame speed in porous media are given accordingly. A universal abacus provides the maximum flame speed attainable in finite porous media. The explicit, ready-to-use nature of the present theory is particularly suitable for practical designs. This work is consistent with previous theoretical, numerical and experimental trends of the literature.