Steady and Pulsating Modes of Sequential Flame Propagation

Steady and pulsating modes of flame propagation through a premixed combustible mixture are studied for the case in which the flame is characterized by the sequential production and depletion of a significant intermediate species. We employ the method of matched asymptotic expansions to derive a model valid for large activation energies, and show that the pulsating solution is the result of a supercritical Hopf bifurcation from the steadily propagating solution (which becomes unstable). Through a nonlinear bifurcation analysis, we calculate the pulsation amplitude and other characteristics of the flame along the bifurcated branch. It is shown that the average thickness of the pulsating flame, by which we mean the average effective separation distance between production and depletion of the intermediate species, is greater than that predicted by a steady-state theory. In addition, we find that the mean propagation speed is less than that of the steadily propagating solution, but that the instantaneous peak concentration of the intermediate species is a constant equal to its steady-state value.