The Influence of the Lewis Numbers of the Reactants on the Asymptotic Structure of Counterflow and Stagnant Diffusion Flames

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Abstract
The asymptotic structure of counterflow and stagnant diffusion flames are analyzed in the limit for large values of the overall, nondimensional activation energy, Ta , characterizing the rate of the reaction and results are given for small values of the stoichiometric fuel to oxygen mass ratio. The chemical reaction between the fuel and the oxidizer is represented by a one-step, irreversible process. A new approach is developed to characterize the influence of the Lewis number of the fuel, LF and the Lewis number of the oxidizer, L0 , on the outer and inner structure of near equilibrium diffusion flames. Explicit algebraic formulas to predict the critical conditions of flame extinction are also given. For counterflow diffusion flames at fixed values of L0 , the flame moves significantly toward the oxidizer stream and the heat losses toward the oxidizer region of the flame increase significantly with decreasing values of LF . The value of the maximum flame temperature is relatively insensitive to the variations in LF although the value of the rate of strain at extinction, A, increases significantly with decreasing values of LF and increasing values of Ta . At fixed values of LF and decreasing values of L0 , the flame moves slightly toward the fuel stream; the heat losses toward the fuel stream increase slightly and there is a moderate increase in the value of the maximum flame temperature. The value of A increases with decreasing values of L0 for large values of Ta and is relatively insensitive to variations in L0 for moderate values of Ta . The inner and outer structure for stagnant diffusion flames where convection is absent are qualitatively similar to those for counterflow diffusion flames. However, the value of the maximum flame temperature increases significantly with decreasing values of L0 and fixed values of LF . The results developed here are used to obtain overall chemical kinetic rate parameters characterizing the gas phase oxidation of methane using previously measured values of the critical conditions of flame extinction.