Acceleration Effects on the Stability of Flame Propagation

We consider the effect of acceleration on the diffusional thermal instability of a plane flame front in a premixed gaseous mixture. We recall that the diffusional thermal instability occurs if the Lewis number L of the mixture is less than a critical value L₀. We show that the diffusional thermal instability is inhibited if the acceleration in the direction of the cold unburned gas is sufficiently high. If the acceleration is sufficiently low, plane flames are unstable, and perturbations of the flame front may evolve to fronts exhibiting cellular structure. Thus we are able to explain the phenomenon that for some mixutres, cellular fronts are observed only for upward propagating flames, while downward propagating plane flames remain stable.