Numerical Study of the Dynamics of Traveling Bubbles around a Body

我们推导了气泡团在任意势流中的运动方程。阐明了方程压力项的物理意义。提出了一种基于二维涡方法和运动方程相结合的气泡团运动空化数值模拟方法。研究了有限个气泡的二维分析方法的有效性。将该方法应用于物体周围的空化流动。结果表明，在流动演化的早期阶段，气泡在近体附近生长和破裂。然而，在涡团在物体后面发展后，气泡在涡团周围生长。研究还表明，气泡-气泡相互作用降低了气泡的长大程度。用边界元方法研究了两个不同初始半径的气泡和一个气泡在不同壁面附近的破裂和回弹，其中考虑了环形气泡的动力学特性。主要研究结果如下：(1)壁面压力取决于气泡的平移运动和微射流穿透形成的高压区。(2)气泡的运动受壁面特性的影响。当壁面柔顺且其固有频率接近驱动频率时，气泡振动明显减小。数值研究了内部气体对非球形气泡运动的热效应。结果表明，内部气体的温度分布很大程度上取决于初始气泡半径。热阻尼力减小了气泡的振荡。

We derive the equations of motion for a bubble cluster in an arbitrary potential flow. The physical meaning of the pressure term for the equations is clarified. A numerical method based on the two-dimensional vortex method that combined with the equations of motion for a bubble cluster is proposed to simulate traveling cavitation. The validity of two-dimensional analysis for finite numbers of bubbles is investigated. The method is applied to the cavitation flow around a body. The results show that the bubbles grow and collapse near the body in the early stage of the flow evolution. However, after the vortex cluster is developed behind the body, the bubbles grow around the vortex cluster. It is also shown that the degree of bubble growth is reduced by bubble-bubble interactions. When a particular bubble growa much faster than the other bubbles, the growth rate of the other bubbles is much lower than that predicted using single-bubble theory.The collapse and rebound of two bubbles with different initial radii and those of a bubble near various kinds of walls are studied using the boundary element method in which the dynamics of toroidal bubbles is considered. The results are summarized as follows : (1) The wall pressure depends on the translational motion of bubbles and the formation of a high pressure region due to the penetration of the microjet. (2) The bubble motion is affected by the characteristic of a wall. When the wall is compliant and its natural frequency is close to the driving frequency, the bubble oscillation is reduced significantly.Thermal effects of the internal gas on the motions of nonspherical bubbles are also studied numerically. It is shown that the temperature distribution of the internal gas is much dependent on the initial bubble radius. The thermal damping reduces the bubble oscillations.