Modelling of the icing processes of sessile supercooled water droplets on cold spheres

Icing widely exists in production and life and always causes great harm. In this study, icing processes of sessile supercooled water droplets on cold spheres are explored. A theoretical model is established and validated by comparing the droplet profiles and freezing times under different parameters with the experimental results. The icing characteristics such as base area, freezing rate and time, and the profile and height of frozen droplets at different surface temperatures, droplet volumes, contact angles, and sphere diameters are obtained. The results demonstrate that the base area and droplet profile are not significantly affected by the surface temperature, yet a higher surface temperature causes a longer freezing time. The increase in droplet volume enlarges the base area and enhances the solid-liquid heat transfer, which results in an increase in freezing time and droplet height. As the contact angle becomes greater, the base area decreases, resulting in prolonged freezing time. For a smaller sphere diameter, the droplet height exhibits an initial decrease followed by an increase; for a larger sphere diameter, the droplet height monotonically increases. Under larger droplet volumes and smaller contact angles, the effect of sphere diameter on the base area and droplet height is more significant, yielding maximum changes of 30.1 % and 22.6 % compared to the values for the planar surface. Likewise, under smaller droplet volumes and higher surface temperatures, the sphere diameter has a more noticeable impact on the freezing time, with an increase of 10.2 %. The tip angle of the frozen droplet is independent of the sphere diameter. The above findings improve the understanding of the icing characteristics of the sessile supercooled water droplets on curved surfaces, and reveal the influence of the sphere size on the icing characteristics, thus providing new ideas for the design of curved anti-/de-icing surfaces.