Stoichiometry Effects in the Point-Source Initiation of Lean Flames of a Light Fuel

Abstract

We numerically study a non-linear, integro-differential equation which has recently been obtained in the context of analytical theories of flame initiation. It describes the dynamics of a spherical flame kernel, the growth of which is triggered by a time-dependent, localized source of heal in a mixture of a light fuel, a heavier oxidizer and a diluent in large excess; actually, this equation pertains to situations in which the concentrations of both reactants are small at the reaction zone (nearly-stoichiometric burning).

By performing go-no-go numerical experiments, we obtain the critical energy for successful initiation of an expanding, autonomous flame and we show how it depends on the energy-input duration and shape, the mixture initial equivalence ratio, and the diffusive properties of both reactants.

We show that lean mixtures can provisionally lead to locally-rich burning as the flame kernel grows or shrinks, as a consequence of differential diffusion effects.

For mixtures characterized by a fixed initial amount of deficient reactant, the minimum critical energy is found to markedly increase as the equivalence ratio crosses a known, Lewis-number-dependent, critical value. This is due to a differential-diffusion-induced leakage of the deficient reactant across the reaction zone, and to the corresponding increase in steady flame size.