Turbulent Flame Velocities In Premixed Sprays Part II. Theoretical Analysis

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Abstract
The process of propagation of a turbulent flame into a premixed spray has been studied theoretically. In general, the flame velocity of a premixed flame is presented theoretically as the eigenvalue of a set of differential equations. In this study, a numerical method was adopted in determining the flame velocity as an eigenvalue, so that a theoretical analysis on a rather realistic model, where the droplet size distribution, the temperature dependences of thermal or transport properties and some other factors were taken into account, was possible. This treatment successfully explained the observed behavior of premixed spray flames in terms of the intensity of turbulence, average droplet diameter and volatility of the fuel. The predicted dependence of the flame velocity on the fuel-air ratio, however, was found to be weaker than the observed one, but this may be explained by the fact that the amplifying effect of the flame on the turbulence level varies with the fuel-air ratio. It was also found that the initial temperature of the mixture exerted a great influence on the flame velocity, but that the effect of the shape of droplet size distribution curve was surprisingly weak.

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