A kinetic model of droplet heating and evaporation: effects of inelastic collisions and a non-unity evaporation coefficient

The previously developed kinetic model for droplet heating and evaporation into a high pressure air is generalisedto take into account the combined effects of inelastic collisions between molecules in the kineticregion, a non-unity evaporation coefficient and temperature gradient inside droplets. It is pointed out thatfor the parameters typical for Diesel engine-like conditions, the heat flux in the kinetic region is a linearfunction of the vapour temperature at the outer boundary of this region, but practically does not dependon vapour density at this boundary for all models, including and not including the effects of inelastic collisions,and including and not including the effects of a non-unity evaporation coefficient. For any giventemperature at the outer boundary of the kinetic region the values of the heat flux are shown to decreasewith increasing numbers of internal degrees of freedom of the molecules. The rate of this decrease isstrong for small numbers of these degrees of freedom but negligible when the number of these degreesexceeds 20. This allows us to restrict the analysis to the first 20 arbitrarily chosen degrees of freedomof n-dodecane molecules when considering the effects of inelastic collisions. The mass flux at this boundarydecreases almost linearly with increasing vapour density at the same location for all above-mentionedmodels. For any given vapour density at the outer boundary of the kinetic region the values of the massflux are smaller for the model, taking into account the contribution of internal degrees of freedom, thanfor the model ignoring these degrees of freedom. It is shown that the effects of inelastic collisions leadto stronger increase in the predicted droplet evaporation time in Diesel engine-like conditions relativeto the hydrodynamic model, compared with the similar increase predicted by the kinetic model consideringonly elastic collisions. The effects of a non-unity evaporation coefficient are shown to be noticeable forgas temperatures of 1500 K. The application of the rigorous kinetic model, taking into account the effectsof inelastic collisions and a non-unity evaporation coefficient, and the model taking into account the temperaturegradient inside droplets, is recommended when accurate predictions of the values of droplet surfacetemperature and evaporation time in Diesel engine-like conditions are essential.