Head-on quenching of a premixed flame by a cold wall

We examine the premixed flame (PF) quenching problem, where an initially steadily propagating flame front impinges on a cold isothermal wall. We employ the simplest possible kinetics, R → P with a reaction order of unity, and we restrict ourselves to unit Lewis number. We formulate the problem in terms of the excess enthalpy function, H = τ + Y − 1. Interpretations are provided for the inflection points and maxima of various functional behaviors: for instance, flame arrest occurs at the inflection point of Y(0, t) whereas extinction occurs at the maximum of the cold wall H-gradient. The numerical solution code FRAPPE integrates formulae obtained from a simplified set of the conservation equations. Our results compare well qualitatively and quantitatively with the full numerical solutions of the original equations.