Modelling of automotive fuel droplet heating and evaporation: mathematical tools and approximations

摘要

Results of the investigation of biodiesel fuel droplet heating and evaporation, using previously developed models, are presented. Temperature gradient, recirculation and species diffusion within the droplets are taken into account. The results of calculations, taking into account the contribution of all components of biodiesel fuels (up to 16) and assuming that these fuels can be treated as a one component fuel, are discussed. It is pointed out that there are serious problems with the application of the approach, based on the analysis of diffusion of individual components, to the modelling of heating and evaporation of realistic Diesel fuel droplets, as the latter include more than 100 components. In our earlier papers, a new approach to the modelling of heating and evaporation of multi-component droplets, suitable for the case when a large number of components are present in the droplets, was suggested. This approach was based on the introduction of quasi-components, and the model was called the `quasi-discrete` model. It is pointed out that there are two main problems with the application of the quasi-discrete model to realistic Diesel fuels. Firstly, even if we restrict our analysis to alkanes alone, it appears not to be easy to approximate this distribution with a reasonably simple distribution function. Secondly, the contributions of other hydrocarbon families in addition to alkanes cannot be ignored in any realistic model of Diesel fuels. Results of the development of the generalised multi-dimensional version of the quasi-discrete model and its application to realistic Diesel fuel droplets are presented. As in the original quasi-discrete model suggested earlier, the components of Diesel fuel with close thermodynamic and transport properties are grouped together to form quasi-components. In contrast to the original quasi-discrete model, the new model takes into account the contribution of not only alkanes, but also various other groups of hydrocarbons in Diesel fuels; quasi-components are formed within individual groups. Also, in contrast to the original quasi-discrete model, the contributions of individual components are not approximated by the distribution function of carbon numbers. The formation of quasi-components is based on taking into account the contributions of individual components without any approximations.