On the two-reactant one-step activation-energy asymptotics for steady, adiabatic, planar flames with Lewis numbers of unity

TL;DR

This paper investigates the dependence of flame burning velocity on equivalence ratio using asymptotic and numerical methods, revealing that maximum velocity can occur without chemical kinetics or diffusivity differences.

Contribution

It introduces a new asymptotic analysis for steady planar flames with equal Lewis numbers, showing maximum burning velocity can arise from activation-energy effects alone.

Findings

Maximum burning velocity can occur in fuel-rich mixtures without detailed kinetics.

Asymptotic analysis applies to all equivalence ratios under specified conditions.

Numerical computations support the theoretical predictions.

Abstract

Aspects of predictions of activation-energy asymptotics concerning the dependence of the burning velocity on the equivalence ratio are examined here through both asymptotic analyses and numerical computation. In typical hydrocarbon-air flames, the burning velocity achieves its maximum value for fuel-rich mixture, the cause being generally attributed to the effects of detailed chemical kinetics and unequal diffusivities of the reactants. The present results demonstrate the possibility of this attribute of the burning velocity occurring even when these two effects are absent. This is accomplished by parametrically studying the burning-velocity formula valid for all equivalence ratios under the conditions specified in the title of this article, with special attention paid to implications for hydrocarbon-air flames.