The asymptotic structure of premixed tubular flames

The steady isobaric combustion of premixed tubular flames undergoing a direct one-step irreversible Arrhenius-type exothermic global reaction with a constant but general Lewis number is studied in the physically interesting limit of large activation energy. This analysis applies the combustion approximation and differs from previous asymptotic analyses of tubular flames by applying the Hirschfelder boundary condition at the burner exit for chemical species and the application of the delta-function closure scheme. The analysis yields a solution for flame sheet position, flame temperature, heat loss rate to the burner, temperature in the burned region, and stabilization limits as functions of the mass flow rate supplied to the burner and temperature of the burner surface in the near equidiffusional flame limit. Results predict the existence of dual flame behavior consistent with other investigations on the planar and cylindrical burner-stabilized flame. Two stabilization limits are identified, one for approaching flames, consistent with previous studies, and one for receding flames that has not been reported to date. Flame temperature profiles predict a nonmonotonic response, unique to the tubular flame. Consistent with the excess enthalpy of the tubular flame, the results demonstrate a strong dependence of a Lewis number differing from unity. Previous asymptotic analyses of tubular flames with a plug flow boundary condition for mass fraction are reanalyzed with the application of the delta-function closure scheme. Unlike previous results, the analysis predicts an interesting dual response for the temperature in the burned region