Interaction of Pulsating and Spinning Waves in Nonadiabatic Flame Propagation

We consider nonadiabatic premixed flame propagation in a long cylindrical channel. A steadily propagating planar flame exists for heat losses below a critical value. It is stable provided that the Lewis number and the volumetric heat loss coefficient are sufficiently small. At critical values of these parameters, bifurcated states, corresponding to time-periodic pulsating cellular flames, emanate from the steadily propagating solution. We analyze the problem in a neighborhood of a multiple primary bifurcation point. By varying the radius of the channel, we split the multiple bifurcation point and show that various types of stable periodic and quasi-periodic pulsating flames can arise as secondary, tertiary, and quaternary bifurcations. Our analysis describes several types of spinning and pulsating flame propagation which have been experimentally observed in nonadiabatic flames, and also describes additional quasi-periodic modes of burning which have yet to be documented experimentally.