Asymptotic structure and extinction of methaneair diffusion flames

Abstract

The asymptotic structure of a counterflow methaneair diffusion flame is analyzed using a three-step chemical kinetic mechanism, I CH 4+O 2→CO+H 2+H 2O, II CO+H 2O⇄CO 2+H 2, III O 2+2H 2→2H 2O , which was deduced in a systematic way through steady state and partial equilibrium assumptions from a detailed chemical kinetic mechanism for oxidation of methane. The rates for the three steps are related to the rates of elementary reactions. The outer structure of the diffusion flame is the classical Burke-Schumann structure governed by the overall one-step reaction CH 4 + 2O 2 → CO 2 + 2H 2O, with the flame sheet positioned at Z= Z st, where Z is the mixture fraction used as the independent variable in the analysis. The inner structure consists of a thin H 2CO oxidation layer of thickness O( ϵ) toward the lean side, a thin nonequilibrium layer for the water gas shift reaction of thickness O( ν), and a thin fuel consumption layer of thickness O( δ) toward the rich side. These layers result, respectively, in the limit of large values for the Damköhler number characterizing the rate of reaction III, II, and I, while the ratios of activation temperature to gas temperature for the three reactions are assumed to be of order unity. We also find that ϵ > ν > δ. The results of the asymptotic analysis yield values of the temperature and the main species at the fuel consumption layer as a function of the scalar dissipation rate χ st. We therefore obtain the upper branch and the turning of the classical S-shaped curve where the maximum flame temperature is plotted as a function of χ st −1. The scalar dissipation rate at quenching χ q is derived from the S-shaped plot and its relation to the laminar burning velocity is discussed. A comparison of the diffusion flame structure with that of a premixed flame shows that the rich part of the diffusion flame corresponds to the upstream part of the premixed flame while its lean part corresponds to the downstream part. First the kinetic scheme is based on the most important (principal) reactions to derive the basic structure. When a number of additional elementary chemical reactions are added the results of the asymptotic analysis are found to be in very good agreement with previous numerical calculations that used a complete kinetic mechanism, as well as with experiments.