Asymptotic analysis of a planar reaction front in gasless combustion: Higher order effects and the influence of the large but finite Lewis number on the propagation velocity

An asymptotic analysis of a planar combustion front in a condensed phase with an arbitrary temperature dependence of thermal conductivity has been carried out by the method of matched asymptotic expansions. The Zel’dovich number is used as a large parameter, and three expansion terms are obtained for the flame velocity. The asymptotic results are compared with direct numerical calculations, and very good agreement is obtained even at low Zel’dovich numbers. The effect of a large but finite Lewis number on the flame propagation velocity are also examined. It is shown that even at Lewis numbers of the order of the Zel’dovich number, the effect of fuel diffusion becomes significant. The presented asymptotic analysis allows us to write a uniformly valid expression for the propagation velocity that can be used both for large Lewis numbers and for Lewis numbers of order unity. Novelty and significance statement For the first time an analytical expression for the velocity of a planar combustion front in the condensed (gasless) phase was obtained up to third-order terms in the inverse Zel’dovich number, taking into account the arbitrary dependence of the thermal conductivity coefficient on temperature. For the first time, the influence of a small but finite reactant diffusion coefficient on the propagation velocity of a planar combustion front was analytically studied. The result allows us to write a uniformly valid formula for the flame velocity applicable in both the solid and gaseous phases.