Stability of a Premixed Flame in Stagnation-Point Flow Against General Disturbances

Abstract

In a previous analysis, the stability of a premixed flame in a stagnation point How was discussed for a restricted class of disturbances that are self-similar to the basic undisturbed flow. Thus, flame fronts with corrugations only in the cross stream direction have been considered. In this paper, we consider a more general class of three-dimensional flame front perturbations, which permits corrugations in the streamwise direction as well. It is shown that, because of the stretch experienced by the flame, the hydrodynamic instability is limited only to disturbances of short wavelength. If, in addition, diffusion effects have a stabilizing influence, as would be the case for mixtures with Lewis number greater than one, a stretched flame could be absolutely stable. Instabilities occur when the Lewis number is below some critical value less than one. Neutral stability boundaries are presented in terms of the Lewis number, the strain rate and the appropriate wavenumbers. Beyond the stability threshold, the two-dimensional, self-similar modes always grow first. However, if disturbances of long wavelength are excluded, it is possible for the three-dimensional modes to be the least stable ones. Accordingly, the pattern that will be observed on the flame front, at the onset of the instability, will consist of either ridges in the direction of stretch, or the more common three-dimensional cellular structure.