Theoretical analysis of ultra-lean premixed flames in porous inert media

Abstract

The structure of stationary adiabatic premixed flames within porous inert media under intense interphase heat transfer is investigated using the asymptotic expansion method. For the pore sizes of interest for combustion in porous inert media, this condition is reached for extremely lean mixtures where lower flame velocities are found. The flame structure is analysed in three distinct regions. In the outer region (the solid-phase diffusion length scale), both phases are in local thermal equilibrium and the problem formulation is reduced to the one-equation model for the energy conservation. In the first inner region (the gas-phase diffusion length scale), there is local thermal non-equilibrium and two equations for the energy conservation are required. In this region, the gas-phase temperature at the flame is limited by the interphase heat transfer. In the second inner region (the reaction length scale), the chemical reaction occurs in a very thin zone where the highest gas-phase temperature is found. The results showed that superadiabatic effects are reduced for leaner mixtures, smaller pore sizes and smaller fuel Lewis numbers. The results also show that there is a minimum superadiabatic temperature for the flame propagation to be possible, which corresponds to the lean flammability limit for the premixed combustion in porous inert media. A parameter that universalizes the leading-order flame properties is identified and discussed.