The structure of premixed methane-air flames with large activation energy

We examine the structure of both lean and stoichiometric premixed methane-air flames with a reduced reaction mechanism. Our starting point is a four-step, C₁-chain mechanism that has been derived previously using a series of steady-state and partial equilibrium assumptions. This same mechanism has been adopted in several recent asymptotic studies that have used the ratio of the branching to propagating reactions as the perturbation parameter to analyze the fuel consumption zone within the flame structure. In the present study, we assume that the activation energy of the intermediate reactions in the fuel consumption zone are sufficiently large to employ the method of large activation energy asymptotics. We obtain temperature and species profiles, as well as a structure problem whose solution determines the burning rate eigenvalue in terms of a parameter that represents the ratio of branching to terminating reactions. When this parameter is set to zero, the results of previous rate-ratio analyses are recovered. In the opposite limit that this parameter becomes large, the structure reduces to that of Liñán's premixed burning regime. In both limiting cases, we determine the parametric dependence of the burning rate on equivalence ratio, pressure, and the ratio of competing rates of branching and termination reactions. The trends are found to be largely in agreement with experimental observations. One advantage of the present approach is that the exponentially nonlinear reaction rate terms are retained, thus permitting the study of the response of methane-air flames to small perturbations.