A SIMPLIFIED REACTION-RATE MODEL AND ITS APPLICATION TO THE ANALYSIS OF PREMIXED FLAMES

A simple reaction rate model which eliminates much of the non-linearity associated with the Arrhenius model is suggested. The model is applied to one-dimensional flame problems: the unstrained flame at unity and non-unity Lewis numbers and the strained flame at unity Lewis number. Exact expressions for the temperature and species profiles and consumption rates are obtained; in the strained flame, these require numerical evaluation. The solutions demonstrate that the model agrees in all essentials with the Arrhenius model and is much simpler mathematically. For the strained flame problem, the exact solution involves integral functions. Analytical temperature profiles and the consumption rate can be obtained for low and high strain rate. Many of the results obtained via activation energy asymptotics and numerical solution for the Arrhenius model are reproduced by the current model with much less analytical complexity. In the strained flame solutions one can identify two regimes of the flame response to strain. At low strain, we find migration of the flame front downstream as the strain increases. At high strain rates, the direction of migration is reversed. The consumption rate as a function of strain rate is in excellent agreement with the numerical solutions of Darabiha et al. This agreement suggests that the mathematical form of the model is not important to the global flame response and simplification of reaction rate models is justifiable for many flame problems. Moreover, the analytical tractability of the proposed model makes it a good pedagogical tool.