Simulation of Flame Fronts by Sources of Fluid Volume

Abstract

Gaseous combustion waves are self propagating exothermic chemical reactions. In the low Mach number limit, these waves are the usual premixed flames where a gas mixture, in an initially unstable molecular configuration at a given temperature, reaches its thermodynamical equilibrium at the flame temperature. Heat release by combustion reaction diffuses towards the fresh gas whose volume increases by thermal expansion. Each heated fluid element expands, acting like a piston that pushes the surrounding fluid. A propagating planar flame front is rendered unstable by such a phenomenon because when it becomes slightly corrugated, crests and valleys push themselves away each other. The linear stability analysis of the planar propagation was performed, independent and almost simultaneously, by Darrieus¹ and Landau² who calculated the potential flow induced in the fresh gas by an infinitesimally distorted flame front. By relating the gas thermal expansion effects to appropriate hydrodynamic jump conditions through the flame, they found that the burned gas is in rotational motion and that each Fourier component of the front distortion grows exponentially with a positive growing rate σ_DL that increases linearly with the corrugation wave number k.