大量过冷水滴在冷表面发生撞击，进而导致表面覆冰，会在航空、风力发电、电力输运等领域带来许多危害。过冷水滴在撞击过程中发生的枝晶生长则会与水滴流动耦合，给该问题的研究带来挑战。本文通过理论分析、分子动力学模拟以及实验相结合的方法，研究了过冷水滴晶体生长的界面动力学效应及其对枝晶生长的影响规律，提出了一种考虑界面动力学效应的枝晶生长速度修正模型，以及一种考虑枝晶生长的过冷水滴撞击与结冰数值计算方法。 过冷水晶体生长的分子动力学模拟结果表明，液固界面温度会显著低于平衡凝固点。模拟体系的过冷度越大，界面温度与平衡凝固点的偏离也越大。由于界面动力学效应的影响，界面移动速度随着界面过冷度的升高先增大后减小，两者的关系可用Wilson-Frenkel模型来描述。对过冷水晶体生长的一维Stefan问题的数值计算结果表明，采用Wilson-Frenkel模型修正界面温度后可以准确预测分子动力学模拟得到的界面位置。 开展了过冷水滴结冰实验，采用高速摄影记录了过冷水滴内的枝晶生长过程，测量得到了不同过冷度条件下的枝晶生长速度。经典的枝晶生长LM-K模型在过冷度小于7 K时与实验结果符合得较好，但当过冷度进一步增大时，预测结果与实验结果相比显著偏大。为了在较大过冷度范围内准确预测枝晶生长速度，在LM-K模型中引入Wilson-Frenkel模型以修正界面温度，建立了考虑界面动力学效应的枝晶生长修正模型。 提出了一种分区函数方法来考虑枝晶生长对过冷水滴撞击过程的影响。该数值计算方法将冰相作为一种高粘度的流体相，同时给定了一个限定区域称为枝晶云区域，相变只被允许发生在枝晶云区域内。该区域的范围可根据初始的形核点或生长点以及枝晶生长速度来确定，其中枝晶生长速度可通过本文提出的枝晶生长修正模型计算得到。采用该方法模拟了过冷水滴在圆柱形冰台上的撞击与结冰过程，结果表明模拟得到残留冰层厚度与文献中的实验结果一致，验证了模拟方法的可靠性。这种分区函数法也可用于其它涉及快速凝固问题的流体流动数值模拟。

The impact of a large number of supercooled water droplets on cold surfaces can make the surfaces to be covered with ice, causing hazards in many industrial fields such as aviation, wind power generation, and power transmission. The fluid flow during the impact process is involved with dendrite growth of supercooled water, which brings challenges to the research of this problem. In this paper, the methods of theoretical analysis, molecular dynamics simulation, and experimentation are used to study the interface kinetics effect of ice crystal growth in supercooled water droplets and its effect on the dendritic growth, and a numerical method considering rapid ice crystal growth is proposed for the numerical simulation of impact and freezing of supercooled water droplets. The molecular dynamics simulation of ice crystal growth in supercooled water shows that the temperature at the liquid-solid interface can be significantly lower than the equilibrium freezing point. The deviation of the interface temperature from the equilibrium freezing point increases with the supercooling of the simulation system. Due to the influence of the interface kinetics effect, the moving velocity of the interface first increases and then decreases with the increase of the interface supercooling. The relationship between the interface velocity and the interface supercooling can be described by the Wilson-Frenkel model. The one-dimensional Stefan problem of the freezing of supercooled water is numerically solved. The numerical results show that the interface position obtained in molecular dynamics simulations can be accurately predicted by modifying the interface temperature using the Wilson-Frenkel model. Experiments of freezing of supercooled droplets are conducted. The high-speed photography method is used to record dendritic growth in the supercooled water droplets. The dendritic growth velocities at different supercoolings are measured. Compared with the experimental results, the classical LM-K model for dendritic growth accurately predicts the growth velocities of ice at supercoolings lower than 7 K but yields a remarkable overestimation as the supercooling further increases. To accurately predict the dendritic growth velocity of ice in a wide range of supercoolings, we introduce the Wilson-Frenkel model into the LM-K model to correct the interface temperature, and propose a modified dendritic growth model considering the interface kinetics. A subregion function method to deal with the effect of dendritic growth on the impact of supercooled water droplets is proposed. In this numerical method, ice is treated as a type of fluid with high viscosity. A restricted region named the dendrite cloud region is defined, and the phase change is enabled only in this dendrite cloud region, while the evolution of this region is determined by the initial nucleation sites and the dendritic growth velocity of the ice. The dendritic growth velocity can be calculated by using the present modified model for dendritic growth. The impact and freezing of supercooled water droplets on a cylindrical ice block are simulated by using the present numerical method. The calculated residual ice layer thickness at the impact center is consistent with the experimental results reported in literature. This subregion function method can also be extended to the numerical simulations of other types of fluid flows involving rapid solidification.