Stretch effects extracted from inwardly and outwardly propagating spherical premixed flames

Abstract

Unsteady propagation of spherical flames, both inward and outward, are studied numerically extensively for single-step reaction and for different Lewis numbers of fuel/oxidizer dependence of flame speed ratio (s) and flame temperature ratio are obtained for a range of Lewis numbers and stretch (κ^~) values. These results of s versus κ^~ show that the asymptotic theory by Frankel and Sivashinsky is reasonable for outward propagation. Other theories are unsatisfactory both quantitatively and qualitatively. The stretch effects are much higher for negative stretch than for positive stretch, as also seen in the theory of Frankel and Sivashinsky. The linearity of the flame speed ratio vs stretch relationship is restricted to nondimensional stretch of ±0.1. It is shown further that the results from cylindrical flames are identical to the spherical flame on flame speed ratio versus nondimensional stretch plot thus confirming the generality of the concept of stretch. The comparison of the variation of (ds/dκ^~)_κ^~=0 with β(Lc - 1) show an offset between the computed and the asymptotic results of Matalon and Matkowsky. The departure of negative stretch results from this variation is significant. Several earlier experimental results are analysed and set out in the form of s versus κ^~ plot. Comparison of the results with experiments seem reasonable for negative stretch. The results for positive stretch are satisfactory qualitatively for a few cases. For rich propane---air, there are qualitative differences pointing to the need for full chemistry calculations in the extraction of stretch effects.