Inertial effects in nonstationary models of flame front evolution

The objective of the present study is to formulate flame front evolution models capturing the effects of flame extinction, ignition, and oscillations in addition to the conventional regime of flame propagation. The basic equations constituting the one-dimensional thermodiffusion model of combustion are reduced to a system of two ordinary differential equations for the flame front coordinate and flame temperature. These equations admit solutions that describe, for example, ignition, extinction, and nonlinear oscillations of the flame, which are observed during premixed gas combustion in microchannels with an elevated wall temperature or during gasless combustion of condensed systems. Similarity of the basic thermodiffusion models assuming an in-finitely small thickness of the chemical reaction zone allows application of a universal method to derive reduced equations in physically different systems. It is demonstrated that modeling of flame oscillations requires at least considering effects associated with flame acceleration (flame front “inertia”) and the rate of flame temperature variation. The accuracy of the proposed model with inertial effects is checked by results of direct numerical simulations of the original equations.