Traveling waves along the front of a pulsating flame

A diffusional-thermal model describing the combustion of a premixed gas is considered. It is shown that a uniformly propagating plane flame is unstable to two-dimensional disturbances when the Lewis number L exceeds a critical value L sub c. A nonlinear analysis is employed to show that for L greater than L sub c two types of solutions bifurcate from the uniformly propagating plane flame. One type corresponds to a pulsating flame with traveling waves along its front while the other corresponds to a pulsating flame with standing waves along its front. The latter describes a pulsating cellular flame. A linear stability analysis of the bifurcated states shows that the traveling wave solutions are stable and the pulsating cellular solutions are unstable. The analysis also shows that the average speeds of the pulsating solutions are less than that of the uniformly propagating plane flame.