A Robust Statistical Model for the Evaporation of Multicomponent-Fuel Drops

Abstract

A statistical formulation is developed describing the composition in an evaporating multicomponent-fuel liquid drop and in the gas phase surrounding it. The initial fuel composition is speciÞed by a Gamma Probability Distribution Function (PDF) according to Continuous Thermodynamics (CT) results. Using a discrete-component model and the classical quasi-steady gas phase assumption with respect to the liquid, it is shown that when drops are immersed in a carrier gas containing fuel vapor, condensation of species onto the drop results in the development of a minor peak in the liquid composition PDF. This peak changes the mathematical form of the PDF to a shape that can be viewed as a superposition of two Gamma PDFs. Based on such a superposition of two Gamma PDFs, called the double-Γ−PDF, and using CT concepts combined with the quasi-steady gas phase assumption, a model is developed for calculating the parameters of the double-Γ−PDF. Extensive tests of the model for diesel fuel show that the double-Γ−PDF results replicate accurately the discrete model predictions. Most important, the mean and variance of the composition at the drop surface, which determine the gas phase composition, are in excellent agreement with the discrete model. Results from the model show that although the second peak is minor for the liquid PDF, its corresponding peak for the vapor distribution at the drop surface has a comparable magnitude to and sometimes exceeds that which corresponds to the Þrst peak.