Multistage cooling and freezing of a saline spherical water droplet

In this paper, the thermal behaviour of a saline water droplet during flight over a marine vessel in cold weather conditions is investigated by analytical and semi-analytical techniques. To predict and analyze the droplet cooling and freezing processes, three stages are employed: a liquid cooling stage, a solidification stage, and a solid cooling stage. The theoretical model considers heat transfer via conduction inside the droplet as well as convection, evaporation (just for the liquid cooling stage), and radiation heat transfer from the droplet's surface to the ambient air. A novel semi-analytical solution technique is developed to analyze the inward moving boundary problem for the solidification stage. The results show that the liquid cooling stage is very short, and the temperature at the droplet's center remains close to the initial droplet temperature. During the solidification stage, the velocity of the inward freezing front within the droplet is approximately constant, and the temperature variations are linear when the temperature inside the droplet reaches the freezing temperature. The solid cooling stage is much longer than the other stages, and the temperature changes are non-linear. For a case study, theoretical predictions show that the average temperature of a droplet with a diameter of 1 mm at the moment of impact on the deck is approximately −1.95°C. Moreover, there is an ice shell with a thickness of 0.06 mm on the surface of the water droplet at the moment of impact.