Rate-ratio asymptotic analysis of non-premixed methane flames

The asymptotic structure of laminar, non-premixed methane flames is analyse d using a reduced four-step chemical-kinetic mechanism. Chemical reactions are presumed to take place in two layers: the inner layer and the oxidation layer. In the inner layer the fuel reacts with radicals and the main compo unds formed are the intermediate species CO and H-2. These intermediate spe cies are oxidized in the oxidation layer. The structure of the oxidation la yer is described by two second-order differential equations: one for CO and the other for Hz. Two limiting cases are considered. At one limit the glob al step CO + H2O reversible arrow CO2 + H-2 is presumed to maintain partial equilibrium everywhere in the oxidation layer except in a thin layer adjac ent to the inner layer. At the other limit the steady-state approximation i s introduced for Hz everywhere in the oxidation layer except in a thin laye r adjacent to the inner layer. This limit, called 'slow CO oxidation', has not been analysed previously. The structure of the inner layer is described by two second-order differential equations: one for the fuel and the other for the H radicals. This is a significant improvement over previous models in which either a steady-state approximation is introduced for the H radic als in the inner layer, or the reaction between the fuel and radicals is pr esumed to be very fast. The chain-breaking elementary reaction CH3 + H + M --> CH4 + M is found to have a significant influence on the structure of th e inner layer and on the scaler dissipation rates at extinction. The influe nce of this reaction was either neglected in previous models or was include d as a perturbation to the principal elementary reactions taking place to t he leading order in the inner layer. Using the results of the asymptotic an alysis the scalar dissipation rates at extinction are calculated at a press ure of I bar They are found to agree well with those calculated numerically using a chemical-kinetic mechanism made up of elementary reactions.