A Mathematical Description of Open and Closed Flame Tips

Abstract

The tips of two-dimensional premixed flames are analyzed for both plane and axisymmetric geometries. Using activation energy asymptotics and slender flame theory the problem of solving the model aerothermochemical equations is reduced to a generalized Stefan problem which is solved numerically. The qualitative nature of the solutions depends critically on the Lewis Number, L. For most values of L they correspond to closed tips, the most commonly observed laboratory situation. But for values of L significantly less than 1 solutions corresponding to open tips are formed, of the kind sometimes seen in the combustion of lean mixtures of hydrogen.