Abstract
A theoretical study of extinction of a tubular flame was made by means of asymptotic analysis based on the flame surface model. The numerical calculation was made as well so as to make a comparison with and assure the validity of the analysis. The flame temperature at extinction was found to increase over the adiabatic flame temperature when Lewis number Le < 1, while it decreases when Le > 1. The extinction Reynolds number increases, while the flame radius at extinction decreases, with a decrease in Le. It was found that the general extinction behavior predicted by the analysis agrees with that of the numerical solution. The discrepancy in the details could be explained in terms of the overestimated reaction rate and of the zero reaction zone width of the flame surface model. The relevant parameter which describes the extinction behavior was found to be the flame stretch, and the flame is extinguished when it exceeds the critical value. The value was a function of a single parameter, which contains kinetic, transport, and thermodynamic properties of the mixture simultaneously in a very simple form. The extinction behavior of the axisymmetric tubular flame was found to be different from that of the plane flame in stagnation flows due to the effect of curvature, which provides the increased cooling.
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