Effect of heat-loss on flame-edges in a premixed counterflow

We describe the combined influence of heat-loss and strain (characterized here by non-dimensional parameters κ and ε, respectively) on premixed flame-edges in a two-dimensional counterflow configuration. The problem is formulated as a thermo-diffusive model with a single Arrhenius reaction. In order to help classify the various flame-edge regimes, the non-adiabatic one-dimensional problem which characterizes the wings (far downstream) of the flame-edge is briefly revisited and its solutions are delimited in the κ-ε plane. An analytical description of the flame-edges is then presented in the weak-strain limit ε → O. This is complemented by a detailed numerical study. Several combustion regimes are found and their domains of existence are identified in the κ - ε plane. These include ignition fronts, extinction fronts, solutions with propagation speeds that depend non-monotonically on the strain-rate, propagating flame tubes and stationary flame tubes. Multiplicity of solutions and hysteresis phenomena, which are partly but not exclusively associated with the one-dimensional regimes, are also identified and discussed.