Kinetic modelling of fuel droplet heating and evaporation: calculations and approximations

Simple approximate formulae describing temporal evolution of diesel fuel droplet radii and temperatures predicted by the kinetic model are suggested. These formulae are valid in the range of gas temperatures relevant to diesel engine-like conditions and fixed values of initial droplet radii, or in the range of initial droplet radii relevant to diesel engine-like conditions and fixed values of gas temperature. During the time period before the hydrodynamic model predicts complete droplet evaporation, these approximations are based on the calculation of the correction to the prediction of the hydrodynamic model. At longer times, the approximations at the earlier times are extrapolated up until the total evaporation of the droplet, using quadratic fittings. The new approximations are shown to be reasonably accurate for predicting the temporal evolution of droplet radii and droplet evaporation times. The predictions of droplet temperature turned out to be less accurate than those of droplet radii, but this accuracy is believed to be sufficient for many practical applications.