The Asymptotic Structure of Methanol-Air Diffusion Flames

Abstract

The asymptotic structure of counterflow nonpremixed methanol flames is analyzed using a reduced four-step mechanism, deduced from a starting mechanism containing twenty-seven elementary reactions. The four overall steps represent I) fuel-consumption reaction, where the fuel reacts with radicals to form H₂ and CO, II) water-gas shift reaction where CO reacts with radicals to form CO₂, III) radical-recombination reaction, and IV) chain-branching reaction. The outer structure of the flame is the classic Burke-Schumann structure governed by the overall one-step reaction CH₃0H + 1.50₂ – CO₂ +2H₂O. The inner structure is presumed to consist of two layers, an inner layer of thickness of orderδ6, and an oxidation layer of thickness of order E. The asymptotic analysis is performed forδ ≪E ≪ 1. The structure of the inner layer is presumed to be influenced primarily by the fuel-consumption reaction and the radical-recombination reaction, and the equations governing the structure of the inner layer are similar to those for premixed, methanol flames analyzed previously using the same reduced chemical-kinetic mechanism. Therefore, results of this previous analysis modified for diffusion flames are used here. In the oxidation layer all radicals are presumed to be in steady-state, In the analysis of the structure of the oxidation layer, a parameter D appears, which is roughly proportional to the square of the ratio of the thickness of the region where the global recombination reaction occurs, to the thickness of theregion where the water-gas shift reaction is not in equilibrium. The structure of the oxidation layer is resolved by treating the quantity D to be of order unity (referred here as the full asymptotic model), and in the limit for large values of D. Results are obtained for the quantity X_q, which is proportional to the strain rate at extinction, Q_q, for values of pressure p between 1 atm. and 10 atms, and for various levels of dilution of the oxidizer stream The predictions of the asymptotic models of the critical conditions of flame extinction were found to agree reasonably well with the predictions of previous detailed numerical calculations at p = 1 atm., and for various levels of dilution of the oxidizer stream. However, the deviations between the predictions of the asymptotic models and the results of the detailed numerical calculations increased with the increasing values of p. These differences are attributed to the inaccuracies associated with the asymptotic description of the inner layer.