Stabilization and extinction of diffusion flames in an inert porous medium

Abstract

Diffusion flames established in inert porous media have been reported to present temperatures lower than a comparable gaseous mixture. Therefore, the study of the flame structure, temperature and extinction limits of confined diffusion flames is of importance. In the present work we discuss extinction conditions for such flames. Using an asymptotic model that accounts for the excess/deficient enthalpy at the reaction region, we study the multiscale problem and analyze the effects of the heat exchange between gas and solid phases on the flame structure. When the heat removed from the flame by the solid matrix is large, the flame can extinguish because the lowering in the flame temperature leads to increasingly large leakage of reactants through the flame sheet. We show that this occurs when the porosity or the mass injection rate is small enough. The extinction limit associated with a small value of the mass injection rate adds to the kinetic extinction limit (which is associated with a large value of the mass injection rate) to characterize a dual-extinction-point behavior for this problem. When the porosity of the medium reaches a minimum critical value, these two distinct extinction points collapse, such that for porosities lower than the critical porosity no flame can be established inside the porous chamber. Then, it is possible to construct a flammability map for the confined diffusion flame, where the critical porosity defines an absolute flammability limit.