Asymptotic study of premixed flames in inert porous media layers of finite width: parametric analysis of heat recirculation phenomena

Abstract

In this paper, we present an investigation on super-adiabatic premixed flames in an inert porous medium layer of finite length. The combustion process is modeled by a one-step Arrhenius kinetics in which density variations are taken into account. The asymptotic case of large ratio of thermal conductivities of solid to gas phases and the high activation energy limit are explored. The results obtained for these limiting cases are compared to those for finite values of these parameters. The use of the flame sheet model allows us to obtain steady-state solutions in an analytical form thus facilitating the parametric analysis. The investigation focuses on the phenomenon of multiplicity of steady-state solutions. It is shown that two or three (nontrivial) steady-state solutions are possible, depending on the flow rate intensity. The critical values of the parameters for the existence of multiple solutions are also determined. The stability of the obtained solutions is finally investigated by means of time-dependent simulations.