A 3rd-order polynomial temperature profile model for the heating and evaporation of moving droplets

Droplet heating and evaporation is of fundamental importance in various engineering applications. Based on the assumption that droplets' internal temperature follows a third-order polynomial distribution, a new liquid phase model is proposed, taking into account both temperature gradient and internal circulation inside the droplet in terms of Hill's spherical vortex. The new liquid model and other commonly used liquid models are compared with the experimental data outlined in the literature. The internal temperature predicted by the new model matches the experimental data of an n-Decane droplet heating best, whereby the enhancement of heat transport by internal circulation is correctly reflected. In comparison, other models always predict the monotonic variation of internal temperature during the initial heating period, which deviates widely from the experimental data. The new model displays the best performance with regard to predicting droplet evaporation in the later vaporizing period, whereas the parabolic temperature profile model and conduction limit model significantly underestimate and overestimate the droplet evaporation rate, respectively. The CPU requirement for the new model is far less than that for the conduction limit model and the effective thermal conductivity model with an order of magnitude, which shows its potential for implementation into CFD codes.