Evolutionary equations for the disturbed flame stabilised at the flat burner

Abstract

The dynamics of the burner-stabilised flame is investigated theoretically in the frame of diffusive-thermal model. The nonlinear system of equations describing dynamics of curved flame front and the flame front temperature is derived in the quasi-stationary approximation from the basic diffusive-thermal model with one-step chemical reaction of Arrhenius type. The reduced model successfully describes nonlinear flame oscillation that is confirmed by comparison of oscillation characteristics obtained in the reduced and full models with the volumetric chemical reaction. The comparison of the instability increments depending on wave numbers agrees with the increments following from the linear stability analysis. The proposed model makes it possible to significantly reduce calculations by reducing the dimension of the system, as well as to obtain estimates of the critical parameters at which oscillations occur. Specifying the critical parameters by simple model will facilitate the performance of complex calculations in the models with detailed kinetics of chemical combustion reactions. A reduced model that describes the flame front spatial instability is proposed too.