A Theoretical Study of Propagation and Extinction of Nonsteady Spherical Flame Fronts

Abstract

Freely propagating expanding spherical flame fronts are studied analytically using the method of activation energy asymptotics. Effects of Lewis number, curvature, heat loss, and thermal expansion, on propagation rates and extinction conditions are examined. The behavior of spherical flame fronts is found to be determined primarily by the values of the Lewis number (Le) and a heat loss parameter. Results are compared to recent experimental observations of spherical flame fronts in mixtures near the flammability limits; for ${\text{Le}} < 1$ it is found that many of the features of these experimental results are described by the analysis presented here but for${\text{Le}} > 1$, unrealistic dynamic behavior is predicted due to the nature of diffusive-thermal instabilities under these conditions.