On the Radiation-Induced Curvature Effects on Particle-Laden Premixed Flames

Abstract

We set up and studied a mathematical model of curved flames propagating in a gaseous reactive premixture which is weakly seeded with small, inert particles. Assuming that:

i) the activation to highest temperature ratio is large, ii) the two-phase mixture is an emitting-absorbing-scattering grey medium, iii) the radiative transfer follows the Eddington law, iv) the flame front is infinitely optically thin, v) the radiant to convective flux ratios are small,

we employ asymptotic techniques to derive non-linear equations describing the shape of weakly wrinkled steady flames. We show that the radiative transfer induces non-local curvature effects which, according to subsequent analytical and numerical investigations, allow for angled flame fronts even when the incoming flow is regular locally. We identify a threshold value of a radiation/convection grouping at which angles appear. Mainly developed for wedge-shaped fronts in a uniform incoming flow, the analysis is also extended to three-dimensional fronts and to weakly non-uniform flows. We show how infinitesimal local curvature effects can nevertheless be important, for they rule out a class of previously obtained non-smooth flame shapes. We finally show how the non-local curvature effects can be incorporated in an equation accounting for the Landau-Darrieus instability, in the framework of the weak-thermal-expansion approximation.