On Closure in Activation Energy Asymptotics of Premixed Flames

Abstract

Recognizing that the conventional activation energy asymptotic analysis of premixed flames lacks an additional relation for complete closure except for some special cases, the present study has identified that this deficiency is caused by either implicit or explicit approximation of the reaction term as a delta function in the reaction-sheet limit, and that imposition of arbitrary closure relations could lead to 0(1) errors in the solution. It is subsequently demonstrated that closure, to the needed O(ε) accuracy in the solution, can be achieved by locating the reaction sheet at the "center of reaction", which is based on the first moment of the reaction rate function about the location of its maximum point. A generalized analysis of the reaction region structure then shows that this closure relation is equivalent to the requirement that the outer solutions of temperature and concentration be continuous to O(ε) at the reaction sheet, that there exist some special situations which are closure independent for the determination of the bulk flame properties, and that a loss-induced absolute extinction limit can also be identified. The importance of proper closure is further demonstrated by applying the present and various literature closure expressions for a comprehensive analysis of the stabilization and extinction of a non-unity Lewis number counter flow flame,with the stagnation surface being either adiabatic or nonadiabatic, and by showing that quantitatively and qualitatively different solutions can result depending on the applied closure.