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Motivated by the pioneering activation-energy asymptotic analysis of strained laminar premixed flames in counterflow by Libby and his coworkers, a rate-ratio asymptotic analysis is carried out to elucidate the structure and predict the critical conditions of extinction of strained premixed methane flames. Steady, axisymmetric, laminar flow of two counterflowing streams: a reactive mixture stream and a product stream toward a stagnation plane is considered. The temperature of the reactive mixture stream isand it is made up of methane (CH 4 ), oxygen (O 2 ) and nitrogen (N 2 ), while the temperature of the product stream is, and it is made up of O 2 , carbon dioxide, water vapor and N 2 . The asymptotic flame structure is presumed to be made up of a thin reaction zone where all chemical reactions take place. On one side of the reaction-zone is an inert, preheat zone containing the reactants and on the other side a post-flame zone made up of products. Analysis of the preheat zone gives matching conditions that is required to analyze the structure of the reaction zone. A four-step, reduced mechanism is used to describe the chemical reactions. The reaction zone is presumed to be made up of an inner layer, where CH 4  is consumed. The hydrogen (H 2 ) and carbon monoxide that are formed in this layer are consumed in an oxidation layer that is made up of two layers: an H 2 -oxidation layer and a CO-oxidation layer. The results of the analysis are used to predict the flame location,, flame temperature,, and the speed of the convective flow,, in the reaction zone as a function of the strain-rate,. Classical C-shaped curves were obtained when,andare plotted as a function ofand they were used to predict extinction. A key finding of this work is thatis proportional to, whereis the crossover temperature predicted by the rate-ratio asymptotic analysis. Whether abrupt extinction will take place or not was found to depend on the value ofrelative to, which is different from the predictions of activation-energy asymptotic analysis wheremust be compared with the value of the adiabatic temperature. Similar to the analysis of Libby and his coworkers, the rate-ratio asymptotic analysis predicts the existence of “negative flame speeds,” where the convective flow and the diffusive flow of reactants in the reaction zone, are in opposite directions. The predictions of the rate-ratio asymptotic analysis were found to agree with the results of computations with detailed chemistry and previous experimental data.

Rate-Ratio Asymptotic Analysis of Strained Premixed Laminar Methane Flame Under Nonadiabatic Conditions