A novel model for the dynamics and evaporation of water droplets with deformation considerations

Abstract

Accurate calculation of water droplet dynamics and evaporation are essential for effective forest firefighting. This study proposes a novel model for the dynamics and evaporation of water droplets by integrating a new Deformation Correction (DC) drag model with the optimal infinite thermal conductivity (ITC) liquid and the Ranz and Marshall (RM) gas phase model. The new DC drag model innovatively combines a semi-theoretical deformation correlation with a drag correction correlation. The terminal velocity predicted by the DC model closely aligns with the experimental data for falling water droplets, whereas other traditional models show significant deviations for large-diameter (>2 mm) droplets. Additionally, a critical deformation Weber number, We_d,crit = 2.5, is defined to determine whether droplet deformation should be considered. Three common liquid and gas phase models are evaluated based on empirical studies conducted in high-temperature airflow conditions (300–500 °C). The results indicate that the ITC model and RM model perform best in predicting water droplet evaporation rates, and the mechanism by which these models influence evaporation through the regulation of B_M and $\frac{Sh}{r_s}$ numbers is also elucidated. Consequently, the model incorporating the new DC drag model, ITC liquid phase model, and RM gas phase model is identified to be the optimal model for predicting droplet dynamics and evaporation. For the simulation case of a water droplet drifting in hot updraft, the maximum prediction deviations of other models with different combinations relative to the optimal model are 15.3 % for drift distance and 40.1 % for evaporation ratio.