液滴撞击液面形成的液坑形态特征及其重力势能分析

用高速相机拍摄了不同直径的液滴（纯净水）以不同速度撞击不同深度液池的过程，对液坑的形态特征和规律进行了分析。液池较深时，当液坑体积达到最大时，其形状基本为半球形；液池较浅时，受池底限制，液坑不能充分发展，体积达到最大时，形状呈被横切掉底部的半球形。液池较深时，生成的液柱较粗且低，分离出的次生液滴较少；液池较浅时，液柱较高且细，分离出的次生液滴较多。无量纲液坑最大水平长度和无量纲最大深度均随韦伯数增大而增大，液滴直径越大，无量纲液坑最大水平长度和最大深度越小；液池较深时，无量纲液坑最大水平长度和最大深度随液池深度减小而增大，然而，当液池浅至一定程度时，无量纲液坑最大水平长度和最大深度却明显减小。对已有的液坑重力势能模型进行了扩展，并据此分析了液坑重力势能的变化规律，研究发现:液坑的重力势能随液滴初始动能增大而增大；液池较深时，液坑重力势能随液池深度减小而增大；液池较浅时，液坑重力势能与液滴初始动能的比值更低。

Study of morphological characteristics and gravitational potential energy of crater formed by droplet impact

The processes of single droplets with different diameters and different speeds impacting on the liquid pool with different depths were captured using a high-speed camera. The morphological characteristics of the craters were analyzed. For the deep liquid pools, when the volume of the crater reaches the maximum, its shape is approximately a hemi-sphere. However, for the shallow liquid pools, due to the restriction of the pool bottom, the crater cannot fully develop. Thus, when its volume reaches the maximum, the shape of the crater looks like a hemi-sphere with the bottom being cut-off. For the deep liquid pools, the liquid jet is thick and short, and the number of the secondary liquid droplets is less. For the shallow liquid pools, the liquid jet is fine and high, and the number of the secondary liquid droplets is more. The dimensionless maximum horizontal length and the dimensionless maximum depth of the crater increase with the increase of the Weber number. The larger the diameter of the droplet is, the smaller the dimensionless maximum horizontal length and the dimensionless maximum depth are. For the deep pools, both the dimensionless maximum horizontal length and dimensionless depth increase with the decrease of the pool depth. However, when the pool depth is decreased to a certain value, the dimensionless maximum horizontal length and dimensionless maximum depth decrease significantly. The existing gravitational potential energy model of the crater was extended, and the law of the gravitational potential energy of the crater was analyzed. The gravitational potential energy of the crater increases with the increase of the initial kinetic energy of the droplet. For the deep liquid pools, the gravitational potential energy of the crater increases as the depth of the crater decreases. For the shallow liquid pools, the ratio of the gravitational potential energy to the initial kinetic energy of the droplet is lower.