Edge-flame structure and oscillations for unit Lewis numbers in a non-premixed counterflow

We examine the structure and oscillatory instability of low Peclet number, non-premixed edge-flames in a fixed rectangular channel, closed at one end, with constant side-wall mass injection, one surface supplying fuel, the other oxidizer. Both reactant components have unit Lewis numbers. This study is motivated by issues regarding the nature of combustion that may occur in a propellant crack formed at the interface between the fuel-binder and oxidizer in a heterogeneous propellant. Flux conditions are imposed on the fuel and oxidizer at the injection walls, while the temperature on the boundary walls is held constant. For situations in which steady burning occurs, the flame has two components: an edge that faces towards the closed end of the channel and a trailing one-dimensional diffusion flame. A large Damk?hler number study of the trailing, planar, strained diffusion flame structure is conducted and a new solvability condition uncovered in this limit, whereby the flame may not exist if the supply mixture strength is sufficiently far from stoichiometric. Numerical calculations also reveal that axial oscillations of the edge-flame in the channel may occur, but for a finite range of mixture strengths sufficiently far from stoichiometric values. The importance of mixture strength, heat losses to the relevant injection surface and the channel end-wall, and the role of the injection surface reactant flux conditions in inducing the oscillations are emphasized. Finally we explore the effect on the combustion structure of varying Peclet number and of different injection velocity magnitudes on the side-wall surfaces.