A mathematical model for supercooling process and its application to frazil ice evolution.

The calculation of the number of ice crystals for the model of frazil ice evolution is very important and affects the whole frazil events. In this paper, the general formula for the number of frazil ice crystals was established considering secondary nucleation, flocculation, gravity and turbulent entrainment, and ice crystals by melting. Meanwhile, two physical processes of secondary nucleation and flocculation were expressed by introducing critical impact velocity and the probability of flocculation from previous models. It has been found that the simulation results of frazil ice evolution are in good agreement with the experimental data and actual project. Then, Sobol method is carried out to judge parameters' influence degree, which found the number of nuclei produced [Formula: see text] is the most sensitive and has the greatest influence on the model results. In addition, sensitivity analysis of these parameters shows that they can affect the maximum supercooling and the period of supercooling. Therefore, the calculation method of the number of ice crystals is applied, which provides technical support for exploring the water temperature and internal relationship of frazil ice evolution.