当液体局部压力瞬间低于饱和蒸汽压，会发生相变形成空化，这一现象普 遍存在于自然界及工程领域中。空泡非球形演化和溃灭过程，生成高速射流、 冲击波等，包含了相变传质、非稳态及可压缩等复杂因素。当空泡与自由液面 相互作用时，由于自由面的惯性约束非常小，进一步涉及到自由面的非线性变 形、破碎及飞溅等现象，是流体力学和气泡动力学研究的前沿。因此，本文以 单空泡与自由面的相互作用为研究对象，以理论分析与实验观测为主要研究手 段，结合数值模拟方法，建立了自由面约束下空泡溃灭动力学模型，分析了近 自由面空泡溃灭和运动规律，发展了空泡运动影响下自由面大变形和飞溅的理 论计算方法，揭示空泡溃灭过程中气液界面的演化规律。本文主要包括以下几 个方面的工作：

(1) 结合镜像法与势流理论，提出了自由面约束下的基于拉格朗日力学和 哈密顿力学的两种不同的气泡动力学理论模型。针对空泡与自由面间接作用， 即 γ≥1 工况下自由面变形高度，结合量纲分析给出了关于控制参数的标度关系。 同时在气泡运动方程基础上，推导了空泡溃灭期间半径随时间变化的近似解析 解，并基于该解结合流体力学中广义的 Biot-Savart 公式，分析了空泡溃灭过程 中内部无量纲射流速度的发展规律。

(2) 针对空泡与自由面弱耦合，即 0.4 ≤γ≤0.7 的工况，研究该工况下空化 气泡脉动引起的两相界面失稳问题。建立了一个由描述瑞利-泰勒不稳定性演化 的线性模型和预测液滴动力学行为的气泡运动模型组成的二维解析模型。利用 该模型分析扰动的增长和演化，分析了不同参数下空泡界面演化规律，划分了 表征空泡的界面失稳的三种不同的状态:正不稳定、负不稳定和稳定状态。

(3) 针对空泡与自由面强耦合，即 γ≤0.3 的情况，基于脉冲激光水下聚焦， 建立了空泡与自由面相互作用的实验方法，通过在空气一侧加入有机玻璃板进 行折射率补偿，形成一种以折射率补偿为核心的拍摄方法，保证自由面上下两 侧可以同时在高速摄影机中清晰成像，获得气泡与自由面相互作用的精细演化 图像。并且借鉴光滑粒子流体力学思想，建立了自由面冠状水层受力与运动模 型，分析了自由面飞溅水花演化及闭合规律。

When the local pressure of liquid is lower than the saturated vapor pressure instantaneously, phase transition will occur to form cavitation, which is a common phenomenon in nature and engineering. The evolution and collapse process of the non spherical cavity, the formation of high-speed jet, shock wav e and other complex factors, including phase change mass transfer, unsteady state and compressibility. When the cavity interacts with the free surface, because the inertial constraint of the free surface is very small, it further involves the nonlinear deformation, breakage and splash of the free surface, which is the frontier of fluid mechanics and bubble dynamics. Therefore, in this paper, the interaction between a single cavity and a free surface is taken as the rese arch object, the theoretical analysis and experimental observation are taken as the main research means, combined with the numerical simulation method, the dynamic model of cavitation collapse under the constraint of a free surface i s established, and the laws of cavitation collapse and motion near the free surface are analyzed, The evolution of gas-liquid interface in the process of bubble collapse is revealed. This paper mainly includes the following aspects (1) Combining the image method and potential flow theory, two different bubble dynamics models based on Lagrangian mechanics and Hamiltonian mechanics are proposed. In view of the indirect interaction between the cavity and the free surface, that is, the deformation height of the free surface under the working condition, the scaling relationship of the control parameters is given by combining with the dimensional analysis. At the same time, on the basis of the bubble motion equation, the approximate analytical solution of the radius changing with time during the bubble collapse is derived. Based on the solution and the generalized Biot-Savart formula in fluid mechanics, the development law of the internal dimensionless jet velocity in the process of bubble collapse is analyzed.

(2) Aiming at the condition of weak coupling between cavitation and free sur face, that is, the instability of two-phase interface caused by cavitation bubble pulsation is studied. A two-dimensional analytical model is established, which consists of a linear model describing the evolution of Rayleigh-Taylor instability and a bubble motion model predicting the dynamic behavior of droplet s. The model is used to analyze the growth and evolution of the disturbance, and the evolution law of the void interface under different parameters is analyzed. Three different states of the void interface instability are divided: positive instability, negative instability and stable state.

(3) In view of the strong coupling between the cavity and the free surface, that is, the experimental method of the interaction between the cavity and the free surface is established based on the underwater focusing of pulsed laser. By adding a plexiglass plate on one side of the air for refractive index compensation, a shooting method with refractive index compensation as the core is formed, which ensures that both sides of the free surface can be clearly imaged in the high-speed camera at the same time, The fine evolution image of the interaction between bubble and free surface is obtained. Based on the ide a of smoothed particle hydrodynamics, the force and motion model of free surface coronal water layer is established, and the evolution and closure law of free surface splash are analyzed.