Evaluating a Simple Model for Laminar-Flame-Propagation Rates. II. Spherical Geometry

Abstract

The propagation of a spherical flame radially outward (from an unspecified ignition with purely local and transient consequences) is examined by approximate analysis for an initially homogeneous gaseous premixture. A direct one-step irreversible bimolecular second-order chemical reaction with large Arrhenius activation energy is adopted, but account is taken of the modified exothermicity owing to the partial dissociation of product species and to other causes of incomplete oxidation. The effects arising from differing diffusivities for heat transfer and reactant-species mass transfer, and from varying the equivalence ratio of the premixture, are considered. Algebraic expressions and a simple quadrature are derived which suffice to describe the evolution of the spherical flame speed to the asymptotic planar-flame value, as the magnitude of the flame radius increases from values modestly in excess of the diffusive scale to values which are large multiples of the diffusive scale, for a flame with a two-zone (convective-diffusive, diffusive-reactive) structure. Limited published data on the variation of flamefront-speed-versus-time behavior with equivalence ratio for simple-hydrocarbon/air mixtures are examined in view of the results.