两空泡运动特性研究

本文应用边界方法研究了两个相邻空泡的运动特性,得到了空泡的演化规律,以及空泡溃灭时的射流速度与溃灭时间的变化趋势,对于两个空泡之间的距离和半径比的影响进行了讨论。计算结果表明：不同大小的空泡在一起时则小泡会先溃灭,且人泡的存在时间与两泡的半径比成正比;大泡对小泡来说其作用相当于－固壁面,小泡会形成－指向大泡的溃灭射流。相同大小的空泡在一起溃灭时,会同时形成指向中间的射 流,与单空泡在固壁面附近的溃     

A calculation of the parameters of the high-speed jet formed in the collapse of a bubble

As is known, the collapse of vapor bubbles in a liquid can cause the intensive destruction of solid boundary surfaces. Experimental and theoretical investigations of bubble collapse have led to the conclusion that the surface of a bubble can deform and a liquid jet directed toward the solid surface can form in the process [1, 2]. In the theoretical reports [3, 4] too low jet velocities were obtained, inadequate to explain the destruction of the surface in a single impact. In [5] it was found as a result of numerical calculations that the formation of jets possessing enormous velocities is possible. It was also found that two fundamentally different schemes of jet formation are possible in the collapse of a bubble near a wall. The transition from one scheme to the other occurs upon a relatively small change in the initial shape of the bubble. In the present report we investigate the case of sufficiently small initial deformations of a bubble when the region occupied by the bubble remains simply connected during the formation of the jet; i.e., the separation of a small bubble from the bubble does not occur. In the case of the second scheme of bubble collapse near a wall the connectedness of the free boundary is disrupted and a small bubble separates off during the formation of the jet.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 94–99, May–June, 1979.     

固壁空蚀数值研究

空蚀是空泡在固壁附近溃灭对固壁材料产生破坏的现象。本文将空泡界面假设为自由面，并由VOF(Volume of Fluid)中界面构造精度较高的Youngs方法求解，通过直接计算原始变量的Navier-Stokes方程，数值模拟了空泡距固壁不同位置时溃灭对固壁造成的空蚀破坏。计算发现空泡溃灭产生高压脉冲相对于高速射流对空蚀形成起主导作用；空泡在流场中位置不同，高压脉冲对固壁上的空蚀破坏结果不同，并给出了距离界限。     

不同环境下气泡脉动特性实验研究

水下爆炸气泡对舰船结构造成严重的毁伤, 海上实船爆炸实验是考核水下爆炸气泡对舰船毁伤威力最直接、最有效的方法, 然而真实情况的舰船水下爆炸实验难以进行.为此, 在已有研究成果的基础上, 设计实验电路, 利用电容在相对较低的电压下放电打火产生的电火花气泡来模拟水下爆炸气泡, 设计多组实验工况来模拟气泡在不同环境下的运动特性. 研究气泡在不同环境下的脉动特性、射流特征, 揭示一些特殊的实验现象, 总结环境对气泡运动的影响规律.      

瞬态空化泡演变过程的数值模拟

采用边界积分方程方法，对无粘流体中三个空化泡以及自由面附近二个空化泡相互作用的演变过程进行了数值模拟。计算中边界用二阶有限元离散，影响系数矩阵非对角线元素用六点高斯数值积分方法计算，对第一类、第二类完全椭圆积分用高次多项式近似，对计算系数矩阵对角线元素中遇到的奇异积分进行了特殊处理。结果表明，在不同的给定参数下，空化泡的溃灭形态各异，柱状射流和环形射流都有可能发生，使空化泡演变成双泡或环形泡。     

Numerical analysis of gas bubbles in close proximity to a movable or deformable body

The growth and collapse of gaseous bubbles near a movable or deformable body are investigated numerically using the boundary element method and fluid–solid coupling technique. The fluid is treated as inviscid, incompressible and the flow irrotational. The unsteady Bernoulli equation is applied on the bubble surface as one of the boundary conditions of the Laplace’s equation for the potential. Good agreements between the numerical and experimental results demonstrate the robustness and accuracy of the present method. The translation and rotation of the rigid body due to the bubble evolution are captured by solving the six-degrees-of-freedom equations of motion for the rigid body. The fluid–solid coupling is achieved by matching the normal component of the velocity and the pressure at the fluid–solid interface. Compared to a fixed rigid body, the expansion of the bubble is not affected too much but much faster collapsing velocities during the collapsing phase of bubble can be observed when considering the motion of the rigid body. The rigid body is pushed away as the bubble grows and moved toward the bubble as the bubble collapses. The motion of two bubbles near a movable cylinder is also simulated. The large rotation of the cylinder and obvious deformation and distortion for the bubble in close proximity to a curved wall are observed in our codes. Finally, the growth and collapse of bubble near a deformable ellipsoid shell are also simulated using the combination of boundary element method (BEM) and finite element method (FEM) techniques. The oscillations of the ellipsoid shell can be observed during the growth and collapse of bubble, which much differs from the results obtained by only considering effects of a rigidly movable body on the bubble evolution.     

Strong interaction between a buoyancy bubble and a free surface

The growth and collapse of buoyant vapor bubbles close to a free surface in an inviscid incompressible fluid is investigated in this paper. The strong interaction between the deforming bubble and the free surface is simulated numerically by a boundary-integral method (Taib 1985; Blake et al., 1987). Improvements are made in the calculation of the singular integrals, the use of nonuniform boundary elements, and the choice of time-step size. The present numerical results agree better with the experimental observations of Blake and Gibson (1981) than previous numerical predictions for bubbles initiated at one maximum radius from the free surface. There is also concurrence of flow features with the experiments for a bubble initiated as close as half maximum radius from the free surface, where other numerical efforts have failed. The effects of buoyancy on bubbles initiated close to a free surface are also investigated. Vastly different features, depending on the distance of the bubble to the free surface and the buoyancy-force parameter, have been observed.     

近自由面的多个水下爆炸气泡相互作用研究

将气泡运动阶段周围的流场假设为无黏、无旋、不可压缩的理想流体,运用边界积分法模拟流场中气泡的运动,并开发了三维计算程序,计算值与实验值吻合较好.用该方法模拟了近自由面多气泡之间的相互作用,包括同相气泡和异相气泡. 通过计算发现,气泡的周期随两气泡中心的距离减小而增大,这是由于多气泡之间存在抑制作用,特别是对异相气泡,这种抑制作用更加明显,称之为多气泡之间的抑制效应. 无论有、无自由面存在,多气泡之间均存在抑制效应,由于抑制效应导致同相与异相气泡相互耦合作用的动态特性存在巨大的差异,这些现象可为将来研究多个同时或延时产生的水下爆炸气泡的威力提供参考.      

复杂边界条件下近场水下爆炸对固支方板的毁伤效应

近场水下爆炸会产生复杂的载荷模式,而复杂的边界条件使结构在近场水下爆炸作用下的毁伤形态更加难以预测。因此,采用耦合的欧拉-拉格朗日算法探究了水下爆炸气泡在多边界耦合作用下（自由面、弹塑性板、泥沙边界）的演化过程及其对固支方板的毁伤效应。首先,开展了2.5 g TNT在不同尺寸（板边长为0.46、0.92和1.61倍最大气泡直径）固支方板底部10 cm起爆的水下爆炸试验,验证了有限元方法的准确性。然后,结合试验和有限元结果分析了不同边界条件下板的毁伤机理。最后,通过系列数值模拟发现：随着板尺寸和爆距的增大,气泡会出现溃散、下射流和上射流3种不同的演化方式;随着板尺寸的增大,爆距对板中心最终变形的影响减小;泥沙边界能减缓气泡收缩,使气泡从中部塌陷形成方向相反的对射流,降低固支方板的位移和应变,对于气泡提前溃散的工况,泥沙边界基本无影响。

     

A novel numerical scheme for the investigation of surface tension effects on growth and collapse stages of cavitation bubbles

In the present study the effects of surface tension on the growth and collapse stages of cavitation bubbles are studied individually for both spherical and nonspherical bubbles. The Gilmore equation is used to simulate the spherical bubble dynamics by considering mass diffusion and heat transfer. For the collapse stage near a rigid boundary, the Navier–Stokes and energy equations are used to simulate the flow domain, and the VOF method is adopted to track the interface between the gas and the liquid phases. Simulations are divided into two cases. In the first case, the collapse stage alone is considered in both spherical and nonspherical situations with different conditions of bubble radius and surface tension. According to the results, surface tension has no significant effects on the flow pattern and collapse rate. In the second case, both the growth and collapse stages of bubbles with different initial radii and surface tensions are considered. In this case surface tension affects the growth stage considerably and, as a result, the jet velocity and collapse time decrease with increasing surface tension coefficient. This effect is more significant for bubbles with smaller radii.     

简单Green函数法模拟三维水下爆炸气泡运动

假定水下爆炸气泡脉动阶段的流场是无旋、不可压缩的,运用势流理论导出气泡边界面运动的控制方程,采用高阶曲面三角形单元离散了维气泡表面,用边界积分法求解气泡的运动．并将计算结果与Rayleigh-Plesset气泡模型和试验数据进行对比分析,分析结果表明高阶曲面单元能够高精度的模拟水下爆炸气泡运动,且比线性单元有多方面的优越性．分别模拟了有、无重力场和刚壁时对气泡运动的影响,并预测了气泡在流场中膨胀、坍塌、迁移、射流形成等苇要动力学行为,同时建立了水下爆炸气泡与圆柱简相互作用的三维模型,模拟了自由液面、圆柱筒附近三维气泡的动力学特性．     

Numerical analysis of the interaction of 3D compressible bubble clusters

Based on the bubble dynamic theory and the compressible two-phase flow solver of the open source software Open FOAM, a numerical simulation study is carried out on the interactions of bubble clusters in a closed volume. The bubble dynamics and interactions of a single bubble, two bubbles, and four bubbles are investigated under the working conditions without and with the presence of a free surface. Through a parametric study, the qualitative patterns of the variations of the bubble collapse period,the volume compressibility, the bubble pressure peak value, and the breakdown, fusion,and separation phenomena with the parameters such as the bubble pressure, the radius size, the bubble spacing, and the distance from the free surface are obtained. The main factors affecting the bubble morphology and the dynamic characteristics are summarized from numerous parameter experiments. It is shown that, in the absence of a free surface,the main factors are the relative size of the bubbles, the pressure of the liquid, and the pressure differences among the bubbles, while in the presence of a free surface, the main factor is the pressure of the liquid between the upper surface of the bubble and the free surface.     

Vortex ring modelling of toroidal bubbles

During the collapse of a bubble near a surface, a high-speed liquid jet often forms and subsequently impacts upon the opposite bubble surface. The jet impact transforms the originally singly-connected bubble to a toroidal bubble, and generates circulation in the flow around it. A toroidal bubble simulation is presented by introducing a vortex ring seeded inside the bubble torus to account for the circulation. The velocity potential is then decomposed into the potential of the vortex ring and a remnant potential. Because the remnant potential is continuous and satisfies the Laplace equation, it can be modelled by the boundary-integral method, and this circumvents an explicit domain cut and associated numerical treatment. The method is applied to study the collapse of gas bubbles in the vicinity of a rigid wall. Good agreement is found with the results of Best (J. Fluid Mech. 251 79–107, 1993), obtained by a domain cut method. Examination of the pressure impulse on the wall during jet impact indicates that the high-speed liquid jet has a significant potential for causing damage to a surface. There appears to be an optimal initial distance where the liquid jet is most damaging.     

基于高速摄影的直角壁面附近柱形空泡动力学行为研究

本文基于高速摄影实验,对直角壁面附近的柱形空泡动力学行为进行了研究。空泡由激光聚焦诱导产生,形成于具有较小间距的两片平行玻璃板之间的液体环境中,从而具有了较为明显的柱形特征。通过改变柱形空泡距离直角壁面顶点的无量纲距离l^*和位置角度θ,分别探究了对称和非对称处柱形空泡的完整溃灭行为及变化趋势,并揭示了柱形空泡与直角壁面的相对位置对柱形空泡泡壁变形、形心移动距离及方向等泡动力学特性的影响。研究发现：在第一周期溃灭过程中,柱形空泡远离直角壁面一侧的泡壁将会出现凹陷,并且逐渐发展直至将柱形空泡分为两部分;当空泡位于对称位置时,随着无量纲距离l^*的逐渐增大,柱形空泡表面凹陷程度逐渐减弱,且空泡在溃灭阶段的形心移动距离逐渐减小;当空泡位于非对称位置时,随着空泡位置角度θ的减小（对θ < 45°的情况而言）,柱形空泡形心的移动方向由指向壁面顶点逐渐变为指向下壁面。

     

A boundary element method for the simulation of non-spherical bubbles and their interactions near a free surface

The basic principle and numerical technique for simulating two three-dimensional bubbles near a free surface are studied in detail by using boundary element method. The singularities of influence coefficient matrix are eliminated using coordinate transformation and so-called 4 π rule. The solid angle for the open surface is treated in direct method based on its definition. Several kinds of configurations for the bubbles and free surface have been investigated. The pressure contours during the evolution of bubbles are obtained in our model and can better illuminate the mechanism underlying the motions of bubbles and free surface. The bubble dynamics and their interactions have close relation with the standoff distances, buoyancy parameters and initial sizes of bubbles. Completely different bubble shapes, free surface motions, jetting patterns and pressure distributions under different parameters can be observed in our model, as demonstrated in our calculation results.     

Single cavitation bubble generation and observation of the bubble collapse flow induced by a pressure wave

This study utilizes a U-shape platform device to generate a single cavitation bubble for a detailed analysis of the flow field characteristics and the cause of the counter jet during the process of bubble collapse caused by sending a pressure wave. A high speed camera is used to record the flow field of the bubble collapse at different distances from a solid boundary. It is found that a Kelvin–Helmholtz vortex is formed when a liquid jet penetrates the bubble surface after the bubble is compressed and deformed. If the bubble center to the solid boundary is within one to three times the bubble’s radius, a stagnation ring will form on the boundary when impinged by the liquid jet. The fluid inside the stagnation ring will be squeezed toward the center of the ring to form a counter jet after the bubble collapses. At the critical position, where the bubble center from the solid boundary is about three times the bubble’s radius, the bubble collapse flow will vary. Depending on the strengths of the pressure waves applied, the collapse can produce a Kelvin–Helmholtz vortex, the Richtmyer–Meshkov instability, or the generation of a counter jet flow. If the bubble surface is in contact with the solid boundary, the liquid jet can only move inside-out without producing the stagnation ring and the counter jet; thus, the bubble collapses along the radial direction. The complex phenomenon of cavitation bubble collapse flows is clearly manifested in this study.     

气泡碰撞亲疏水曲壁的行为特性研究

气泡碰撞固壁行为和影响因素的研究一直以来都是科学界关注的重点之一, 其在矿物浮选、气膜减阻等工业领域中的应用也极具科研价值. 论文聚焦曲壁对于气泡撞击行为特性的影响研究. 采用高速摄像技术记录气泡碰撞不同曲率半径下亲疏水曲壁的撞击过程, 分析了曲壁润湿性、曲率半径对气泡碰撞固体曲壁的影响规律. 结果表明, 气泡碰撞亲水曲壁时会发生多次弹跳直至离开曲壁; 曲率半径越大, 弹跳次数越少, 且第一次反弹的最远距离越近, 再次发生碰壁时的速度越小. 而碰撞疏水曲壁时会出现碰撞?滑移?附着的现象, 此外针对液膜挤压破裂的现象, 建立理论模型推导出液膜诱导时间的预测公式, 其主要与液膜厚度、液膜临界破裂厚度和液膜被压缩速度有关, 预测误差小于5.0%.      

The influence of viscoelasticity on the collapse of cavitation bubbles near a rigid boundary

An understanding of the phenomena associated with cavitation is important in many areas of science and engineering. This paper is concerned with the influence of viscoelasticity on the dynamics of cavitation bubbles near rigid boundaries. Viscoelastic effects are modelled using a Maxwell constitutive equation, and a generalized Bernoulli equation is derived. The governing equations are solved using the boundary element method in which both the bubble surface and the potential are represented by cubic splines. The numerical scheme is validated through comparisons with results in the literature for the inviscid case. The introduction of viscoelasticity introduces some interesting bubble dynamics including the occurrence of oscillations during collapse. Most importantly, it is shown that viscoelasticity can serve to suppress the formation of a liquid jet. The subsequent reduced pressures compared with the inviscid case suggest that viscoelasticity has a mitigating effect on cavitation damage.     

Numerical study on the hydrodynamic behavior of the dielectric fluid around an electrical discharge generated bubble in EDM

In the process of EDM, due to the electrical current, very small bubbles are created within the gap. These bubbles are connected to each other and generate a single bubble. The vapor bubble continues to grow until it finally collapses to small bubbles. The bubble behavior can be ascertained on the distribution of the pressure in the dielectric fluid around the bubble. In this paper, velocity fields and pressure distribution in the dielectric fluid around the bubble that is generated in the process of EDM are investigated numerically. The tool and the workpiece are assumed as two parallel rigid boundaries with dielectric liquid between them. The boundary integral equation method is applied for the numerical solution of the problem. This study can lead to better understanding of the bubble importance in the performance of the electrical discharge machining process.     

The interaction of background ocean air bubbles with a surface ship

A two-fluid model suitable for the calculation of the two-phase flow field around a naval surface ship is presented. This model couples the Reynolds-averaged Navier–Stokes (RANS) equations with equations for the evolution of the gas-phase momentum, volume fraction and bubble number density, thereby allowing the multidimensional calculation of the two-phase flow for monodisperse variable size bubbles. The bubble field modifies the liquid solution through changes in the liquid mass and momentum conservation equations. The model is applied to the case of the scavenging of wind-induced sea-background bubbles by an unpropelled US Navy frigate under non-zero Froude number boundary conditions at the free surface. This is an important test case, because it can be simulated experimentally with a model-scale ship in a towing tank. A significant modification of the background bubble field is predicted in the wake of the ship, where bubble depletion occurs along with a reduction in the bubble size due to dissolution. This effect is due to lateral phase distribution phenomena and the generation of an upwelling plume in the near wake that brings smaller bubbles up to the surface. © 1998 John Wiley & Sons, Ltd.