Diffusional–thermal instability of cylindrical burner-stabilized premixed flames

Abstract

Steady burning behavior and diffusional–thermal instability of cylindrical burner-stabilized premixed flames are studied via activation energy asymptotics. For the steadily burning flame, the analysis yields a solution of the flame temperature and standoff distance as functions of the mass flow rate supplied by the burner. The result shows that the flame may be stabilized by either heat loss to the burner or flow divergence, in agreement with an earlier investigation by Eng et al. In addition, the flame exhibits two dual flame behaviors; namely, there exist two flame speeds either for the same heat loss rate to the burner or at the same standoff distance, which is consistent with earlier investigations on the one-dimensional, planar burner-stabilized flame. The linear stability analysis reveals that there exists a critical wave number on both the angular and axial directions for which the flame is the most unstable, that the critical wave number on the angular direction increases with increasing flow supply rate from the burner, that the effect of flow divergence–induced flame curvature is to stabilize the flame so that the cylindrical burner-stabilized flame is more stable than its one-dimensional counterpart, that the stability boundaries of a cylindrical flame approach those of the adiabatic, freely propagating planar flame by continuously increasing the burner supply rate, and that a flame stabilized by a larger burner is less stable than that supported by a smaller burner.