On the Stability of Near-Equidiffusional Strained Premixed Flames

In this paper we examine the effect of stretch on the stability of premixed flames. The stability problem is posed within the asymptotic limits of large activation energy and of disturbances of wavelength much larger than the flame thickness. Only disturbances that are independent of the direction of flow divergence are considered here. It is shown that stretch stabilizes the long wavelength disturbances which are otherwise unstable as a result of the Darrieus-Landau instability. On the other hand it is known that diffusion may have a stabilizing influence on the short wavelength disturbances. Thus, for a sufficiently large strain rate, a flame may become absolutely stable even in the absence of gravity or other stabilizing effects. We identify here the critical value of the strain rate above which stability may be attained and determine the stability boundaries in terms of a scaled Lewis number and of stretch, for representative values of thermal expansion.