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

Abstract

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 f...