Continuous Thermodynamics Finite Diffusion Model for Multicomponent Fuel Spray Evaporation

INTRODUCTION The different volatility of the components of a fuel mixture will result in different vaporization rates of components at the droplet surface, and the fuel becomes non-uniform inside the liquid phase because of the mass diffusion resistance inside the droplet. For practical, multidimensional simulations of IC engines, zero-dimensional models for the liquid phase are necessary because of their low computational cost and the fact that thousands of computational parcels are typically needed to represent the fuel spray in an engine. Zeng and Lee [1] developed a zero-dimensional model capable of including finite diffusion and preferential vaporization. This model uses discrete component representation. Discrete multicomponent fuel models use a set of components to match the distillation behavior of a real fuel. A large number of components are typically required in order to represent a commercial fuel adequately. However, the computational cost increases quickly as the number of the components increases, since each component adds an additional transport equation. Commercial fuels usually contain hundreds of components, so it is usually not practical to represent every component using a discrete representation for spray simulation. An alternative approach is continuous representation, which uses a probability density function based on the principles of continuous thermodynamics to represent the fuel. For engineering calculations, a typical commercial fuel consisting of hundreds of components can be reasonably represented by a continuous distribution function. As the mixture is assumed of alkanes and properties of the species can be characterized by the variable of molecular weight, so only a few parameters are required to describe the characteristics of the mixture, such as the mean and variance of the distribution. Thus, only the parameters describing the multicomponent fuel have to be determined beforehand, rather than having to solve a transport equation for each component. The method of continuous thermodynamics was previously used by Lippert and Reitz [2], Yi et al.[3] and Zhu et al. [4] for multidimensional engine modeling. These studies made important contributions to the application of continuous thermodynamics to IC engine simulations. However, these studies are based on the assumption of infinite diffusion in the liquid phase, so non-uniformity inside the droplet (i.e., the effects of finite diffusion) is not considered. In this paper, a comprehensive model considering preferential vaporization of a complex fuel mixture using continuous distributions is presented. The model consists of a gas phase sub-model, which determines evaporation fluxes, and a liquid phase sub-model with finite diffusion. This model was validated with experimental data for the vaporization of isolated JP-4 fuel droplet, and then it was used to analyze the vaporization behavior of single diesel fuel droplet. Finally, gasoline hollow-cone spray simulations were made using this model. This model was implemented into KIVA-3V for computations.