Rate-ratio asymptotic analysis of the influence of stoichiometric mixture fraction on structure and extinction of laminar, nonpremixed methane flames with comparison to experiments

Abstract

Activation energy asymptotic analysis and rate-ratio asymptotic analysis of combustion in laminar, nonpremixed flames are often carried out using conserved scalar quantities as independent variables. One such representation of a conserved scalar quantity is the mixture fraction, ξ, based on thermal diffusivity. These analyses are carried out in the asymptotic limit of large Damköhler number, with chemical reactions presumed to take place in a thin reaction zone that is located at ξ=ξst. The quantity ξst is the stoichiometric mixture fraction. A characteristic diffusion time is given by the reciprocal of the scalar dissipation rate, χ. Previous computational studies have shown that the scalar dissipation rate at extinction depends on ξst and the maximum flame temperature, Tst. Here, a rate-ratio asymptotic analysis is carried out using reduced chemistry to elucidate the influence of ξst on critical conditions of extinction of methane flames. The scalar dissipation rate at extinction was predicted as a function of ξst with the mass fractions of reactants so chosen that the adiabatic flame temperature, Tst, is fixed. The predictions of the analysis show that with increasing values of ξst, the scalar dissipation rate at extinction first increases and then decreases. To test the predictions of the asymptotic analysis, critical conditions of extinction are measured on nonpremixed methane flames stabilized in the counterflow configuration. With increasing values of stoichiometric mixture fraction, the strain rate at extinction was found to increase, and the scalar dissipation rate at extinction was found to first increase and then decrease. The predictions of the asymptotic analysis agreed with experiments. A key outcome of the analysis is that with increasing ξst, the thickness of the regions where oxygen and fuel are consumed first increase and the decrease. This is responsible for the observed non-monotonic changes in the values of the scalar dissipation rate at extinction with changes in ξst.