Analytical study of a flame propagation front in a solid phase driven by chain-branching reactions at large Zel’dovich numbers: Steady states, stability and influence of the radicals Lewis number

Abstract

The combustion wave propagation in the condensed phase is investigated analytically in the large Zel’dovich number limit. The study is based on a two-step chain branching model for combustion reactions in which the flammability limit is explicitly present. As is common in gasless combustion, the diffusion of the initial fuel is assumed to be negligible. However, the effect of intermediate product diffusion on wave propagation velocity is analyzed, along with the stability of the corresponding dynamic response. With heat release as the controlling parameter, a Hopf bifurcation is encountered as the parameter decreases, leading to the emergence of an oscillatory instability. It is found that this instability ultimately leads to the extinction of the combustion wave, even under adiabatic conditions. Additionally, the effect of heat loss on flame stability and dynamics is examined.

Novelty and significance statement For the first time, the analysis of combustion wave propagation in the solid phase using a two-stage chain branching combustion model is performed in analytical form. In the absence of fuel diffusion, which is natural for combustion in the condensed phase, the effect of the final diffusion of intermediate radicals is investigated. The effect of volumetric losses is also studied. The results are obtained for stationary solutions of propagation and their stability is investigated. It is shown that even in the absence of heat loss, there is a region of parameters in which the combustion wave is unstable, which leads to its extinction.