A water droplet's impact and its subsequent spreading, recoiling and freezing on a smooth substrate at a supercooled temperature is studied numerically using a 3D pseudo-potential lattice Boltzmann method, in combination with a solid-liquid phase-change model with volume expansion of water at 0°C taken into consideration. Simulated results show that a water droplet after its impact on a smooth surface at a supercooled temperature can form either a central-pointy icing pattern with a single ice peak, or a central-concave icingpattern in a donut shape, depending on the contact angle and the supercooled degree of the wall. Itisshown that the recoiling motion of the droplet after its impact on the supercooled substrate plays the dominant role in the formation of the central-pointy icing or central-concave icing pattern. The central-pointyicingpattern is formed on a substrate having a large contact angle where the recoiling motion of the droplet is strong while the central-concave icing pattern is formed on a substrate having a high degree of supercooled temperature (i.e., a large Stefan number) where the recoiling motion is terminated prematurely because of early nucleation of freezing on the supercooled substrate. The volume expansion during liquid to ice phase-change process at 0°C does affect the movement of the liquid phase although its effect on the formation of icing patterns is small. Effects of movement of freezing fronts on the shape of the icing patterns are illustrated. At fixed values of We= 320 and Re = 164.9, a map showing effects of contact angle and Stefan number (bottom wall temperature) on the formation of central-pointy icing or central-concave icingpatterns after a water droplet's impact (with D₀= 100 and Pr = 13.5) on smooth supercooled surfaces is presented.

使用3D伪势格子Boltzmann方法，结合水在30℃时体积膨胀的固液相变模型，对过冷情况下水滴在光滑基底上的撞击及其随后的扩散，回卷和冻结进行了数值研究。考虑到0°C。模拟结果表明，水滴在过冷温度下撞击光滑表面后，可以形成带有单个冰峰的中心尖糖霜图案，也可以形成甜甜圈形状的中心凹糖霜图案，具体取决于接触角和墙的过冷度。结果表明，液滴撞击过冷基体后的回卷运动在形成中心尖结冰或中心凹结冰图案方面起主要作用。中心点结冰图案形成在具有大接触角的基板上，其中液滴的回弹运动很强，而中心凹形结冰图案形成在具有高过冷度（即大的Stefan数）的基板上由于过早在过冷的基材上形成冻结核，因此重新运动提前终止。尽管在0°C时液体到冰的相变过程中的体积膨胀确实会影响液相的运动，尽管其对结冰图案形成的影响很小。说明了冰冻锋面的运动对结冰图案形状的影响。固定值 较大的Stefan数），由于过冷基板上的早期冻结形核，过早终止了回卷运动。尽管在0°C时液体到冰的相变过程中的体积膨胀确实会影响液相的运动，尽管其对结冰图案形成的影响很小。说明了冰冻锋面的运动对结冰图案形状的影响。固定值 较大的Stefan数），由于过冷基板上的早期冻结形核，过早终止了回卷运动。尽管在0°C时液体到冰的相变过程中的体积膨胀确实会影响液相的运动，尽管其对结冰图案形成的影响很小。说明了冰冻锋面的运动对结冰图案形状的影响。固定值我们= 320，Re  = 164.9，该图显示了水滴撞击后接触角和Stefan数（底壁温度）对形成中心尖结冰或中心凹结冰图案的影响（D ₀ = 100和Pr  = 13.5）表示在光滑的过冷表面上。