A self-consistent kinetic model for droplet heating and evaporation

A new kinetic model for heating and evaporation of Diesel fuel droplets is suggested. The model is based on the introduction of the kinetic region in the immediate vicinity of the heated and evaporating droplets, where the dynamics of molecules are described in terms of the Boltzmann equations for vapour components and air, and the hydrodynamic region. The effects of finite thermal conductivity and species diffusivity inside the droplets and inelastic collisions in the kinetic region are taken into account. Diesel fuel is approximated by n-dodecane or a mixture of 80% n-dodecane and 20% p-dipropylbenzene. In both cases, the evaporation coefficient is assumed equal to 1. The values of temperature and vapour density at the outer boundary of the kinetic region are inferred from the requirement that both heat flux and mass flux of vapour (or vapour components) in the kinetic and hydrodynamic regions in the vicinity of the interface between these regions should be equal. Initially, the heat and mass fluxes in the hydrodynamic region are calculated based on the values of temperature and vapour density at the surface of the droplet. Then the values of temperature and vapour density at the outer boundary of the kinetic region, obtained following the above-mentioned procedure, are used to calculate the corrected values of hydrodynamic heat and mass fluxes. The latter in their turn lead to new corrected values of temperature and vapour density at the outer boundary of the kinetic region etc. It is shown that this process quickly converges for the cases analysed in the paper, and it leads to self-consistent values for both heat and mass fluxes. The model is applied to the analysis of heating and evaporation of Diesel fuel droplets with initial radii and temperature equal to 5 μm and 300 K, immersed into gas with temperatures in the range 800-1200 K and pressure equal to 30 bar. It is shown that in all cases the kinetic effects lead to a decrease in droplet surface temperature and an increase in the evaporation time. The kinetic effects on the droplet evaporation time are shown to increase with increasing gas temperatures.