A new multi-dimensional quasi-discrete model is suggested and tested for the analysis of heating and evaporation of Diesel fuel droplets. 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 quasidiscrete 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. Groups contributing small * Corresponding author.Tel. +44 (0)

Biodiesel fuel droplet heating and evaporation is investigated using the previously developed models, taking into account temperature gradient, recirculation, and species diffusion within droplets. The analysis is focused on four types of biodiesel fuels: Palm Methyl Ester, Hemp Methyl Esters, Rapeseed oil Methyl Ester, and Soybean oil Methyl Ester. These fuels contain up to 15 various methyl esters and possibly small amounts of unspecified additives, which are treated as methyl esters with some average characteristics. Calculations are performed using two approaches: 1) taking into account the contribution of all components of biodiesel fuels (up to 16); and 2) assuming that these fuels can be treated as a one component fuel with averaged transport and thermodynamic coefficients. It is pointed out that for all types of biodiesel fuel the predictions of the multi-component and single component models are rather close (the droplet evaporation times predicted by these models differ by less than about 5.5%). This difference is much smaller than observed in the case of Diesel and gasoline fuel droplets, and is related to the 1 Corresponding author, e-mail: S.Sazhin@brighton.ac.uk Preprint submitted to FuelMarch 28, 2013 fact that in the case of Diesel and gasoline fuel droplets the contribution of components in a wide range of molar masses and enthalpies of evaporation needs to be taken into account, while in the case of biodiesel fuels the main contribution comes from the components in a narrow range of molar masses and enthalpies of evaporation. As in the case of Diesel and gasoline fuel droplets, the multi-component model predicts higher droplet surface temperature and longer evaporation times than the single component model.

The paper presents a new approach to modelling of the heating and evaporation of gasoline fuel droplets with a specific application to conditions representative of internal combustion engines. A number of the components of gasoline with identical chemical formulae and close thermodynamic and transport properties are replaced with characteristic components leading to reducing the original composition of gasoline fuel (83 components) to 20 components only. Furthermore, the approximation to the composition of gasoline with these components is replaced with a smaller number of hypothetical quasi-components/components as previously suggested in the multi-dimensional quasi-discrete (MDQD) model. The transient diffusion of quasi-components and single components in the liquid phase as well as the temperature gradient and recirculation inside the droplets, due to the relative velocities between the droplets and the ambient air, are accounted for in the model. In the original MDQD model, n-alkanes and iso-alkanes are considered as one group of alkanes. In this new approach, the contributions of these two groups are taken into account separately. The values for the initial model parameters were selected from experimental data measured in a research engine prior to combustion. The results are compared with the predictions of the single-component model in which the transport and thermodynamic properties of components are averaged, diffusion of species is ignored and liquid thermal conductivity is assumed to be infinitely large, or approximated by those of iso-octane. It is shown that the application of the latter models leads to an under-prediction of the droplet evaporation time by approximately 67% (averaged) and 47% (iso-octane), respectively, compared to those obtained using the discrete component model, taking into account the contributions of 20 components. It is shown that the approximation of the actual composition of gasoline fuel by 6 quasi-components/components, using the MDQD model, leads to an under-prediction of the estimated droplet surface temperatures and evaporation times by approximately 0.9% and 6.6% respectively, for the same engine conditions. The application of the latter model has resulted in an approximately 70% reduction in CPU processor time compared to the model taking into account all 20 components of gasoline fuel.