COMBUSTION AND FLAME 35:139-153 (1979) 139 Linear Stability Analysis of Nonadiabatic Flames: Diffusional-Thermal Model

The method of matched asymptotic expansions, interms of a suitably reduced activation energy, is applied to investigate he effects of heat losses on linear stability of a planar flame, which is governed by a one-step irreversible Arrhenius reaction. The density change associated with the heat release isneglected inorder to eliminate the Landau hydro-dynamic instability. Attention isfocused on diffusional-thermal instability mechanisms. The dispersion relation is obtained in terms of the diffusive properties of the limiting reactant and of the heat-loss intensity. For a given loss intensity-less than the critical value leading to extinction-the two steady planar egimes have different stability properties: (1) the "slow " regimes (which do not reduce to the adiabatic one when the heat-loss intensity goes to zero) are shown to be always unstable; and (2) for the "fast " regimes (which include and generalize the adiabatic one) cellular structures are predicted to occur when the limiting component is sufficiently light. If the limiting component is moderately ight, the "fast" regimes are stable and unstructured in nearly adiabatic onditions; however, they are destabilized by an increase of heat losses and must exhibit cells before the extinction limit is reached. Similarly, for mixtures involving arealistically heavy limiting component, our analysis predicts the appearance of transverse travel-ling waves near the extinction limit