An Accurate and Simple Approach to Allow for the Transient Temperature Gradient in a Vaporizing Droplet

The purpose of this work is to analyze the importance of considering internal temperature gradient in modeling droplet evaporation, and to demonstrate performance of simplified methods in which the temperature gradient is approximately taken into account. Based on three characteristic time scales, two dimensionless criteria have been identified which determine magnitude of the internal temperature gradient and its effect on the evaporation dynamics. Numerical values of these criteria in a wide range of ambient temperatures show that the effect of the internal temperature gradient is more pronounced in more volatile liquid at higher ambient temperatures. Although droplet life time predictions are not sensitive to the internal temperature gradient, its effect might be strong at the initial stages of droplet evaporation, and this substantiates the need in robust and computationally inexpensive methods to take it into account. Two simple and yet accurate approaches (quasi-steady higher order polynomial approximation and the integral balance method) have been favourably tested and recommended for use in CFD spray modeling.