Large Activation Energy Analysis of Nonadiabatic Strained Premixed Laminar Flames with Nonunity Lewis Numbers

Abstract

ABSTRACT We present an asymptotic analysis of a strained premixed flame in the mixing layer between two counterflowing streams: one with fresh reactants at a temperature and other with the burned gases at temperature , which may be different from the adiabatic combustion temperature of the fresh gases. A one-step irreversible Arrhenius reaction model, of high activation energy, is used for the asymptotic analysis, together with the thermal-diffusive approximation of constant density and transport properties – easily generalized to variable density and transport properties with the use of a heat-conduction-weighted coordinate. The analysis for near unity Lewis numbers of the fuel by Libby, Liñán and Williams (1983) is extended here to arbitrary nonunity Lewis numbers, of relevance to a wide variety of applications, ranging from hydrogen-fueled combustors to heavy fuel systems. In analogy with Liñán’s analysis of counterflow diffusion flames, three asymptotic distinguished regimes are identified for premixed flames for large activation energies and the appropriate Damköhler numbers – the ratio of the characteristic diffusion and reaction times. These regimes are the premixed flame regime, the partial burning regime and the nearly frozen ignition regime. The analytical expressions obtained for these regimes, of the dimensionless reaction rate as a function of the Damköhler number, are seen to describe with good accuracy the results obtained from the numerical integration of the full problem.