Numerical simulation on the freezing of deposited or impinged water droplets on a cold surface

The freezing of water droplets deposited or impinged on cold surfaces causes many problems in traffic lights, power transmission wires and heat exchangers. Thus, the suppression of the freezing of these droplets is very important. In this study, we carried out two-dimensional numerical simulation on the freezing of the water droplets on a horizontal cold surface using a Phase-field method. A new equation was developed to predict an increase in the total volume of the droplets due to the freezing. The changes in the physical properties of supercooled water with temperature were taken into account for an impinged droplet. The computational results for deposited droplets showed that a projection was formed on the cap of a frozen droplet and that the volume of ice was 8.8% higher than the volume of a deposited water droplet in its unfrozen state. However, the change in the mass due to the freezing was less than 0.001%. Also, a concave shape of the freezing front was predicted after an ice layer was formed. This was consistent with the results for freezing droplets observed by other researchers. Moreover, similar results were obtained in the case of impinged droplets. With these, a projection was formed. The volume of ice was 8.1% higher than the volume of the impinging droplet in the air, while the change in the mass was less than 0.0023%. The predicted freezing fronts were similar to that observed in previous studies.