绕水翼空化流动多尺度数值研究

空化的多尺度效应是一种涉及连续介质尺度、微尺度空化泡以及不同尺度间相互转化的复杂水动力学现象, 跨尺度模型的构建是解析该多尺度现象的关键. 本文基于欧拉-拉格朗日联合算法, 通过界面捕捉法求解欧拉体系下大尺度空穴演化, 通过拉格朗日体系下离散空泡模型求解亚网格尺度离散空泡的运动及生长溃灭. 同时, 通过判断空泡与网格尺度间的关系判定不同尺度空化泡的求解模型. 基于建立的多尺度算法对绕NACA66水翼空化流动进行模拟, 将数值结果与实验进行对比, 验证了数值计算方法的准确性. 研究结果表明, 离散空泡数量与空化发展阶段密切相关, 在附着型片状空穴生长阶段, 离散空泡数量波动较小, 离散空泡主要分布在气液交界面位置; 在回射流发展阶段, 离散空泡逐渐增加并分布在回射流扰动区; 在云状空穴溃灭阶段, 离散空泡数量增多且主要分布在气液掺混剧烈的空化云团溃灭区. 在各空化发展阶段, 离散空泡直径概率密度函数均符合伽玛分布. 空化湍流流场特性对拉格朗日空泡空间分布具有重要影响, 离散空泡主要分布在强湍脉动区、旋涡及回射流发展区域.      

Parametric Analysis for a Single Collapsing Bubble

This work presents a sensitivity analysis for cavitation processes, studying in detail the effect of various model parameters on the bubble collapse. A complete model (Hauke et al. Phys Rev E 75:1–14, 2007) is used to obtain how different parameters influence the collapse in SBSL experiments, providing some clues on how to enhance the bubble implosion in real systems. The initial bubble radius, the frequency and the amplitude of the pressure wave are the most important parameters determining under which conditions cavitation occurs. The range of bubble sizes inducing strong implosions for different frequencies is computed; the initial radius is the most important parameter characterized the intensity of the cavitation processes. However, other parameters like the gas and liquid conductivity or the liquid viscosity can have an important effect under certain conditions. It is shown that mass transfer processes play an important role in order to correctly predict the trends related with the effect of the liquid temperature, which translates into the bubble dynamics. Moreover, under some particular circumstances, evaporation can be encountered during the bubble collapse; this can be profitably exploited in order to feed reactants when the most extreme conditions inside the bubbles are reached. Thus, this paper aims at providing a global assessment of the effect of the different parameters on the entire cycle of a single cavitating spherical bubble immersed in an ultrasonic field. This work has been partially supported by Ministerio de Ciencia y Tecnologia, under grant number CTM2004-06184-C02-02.     

射流对绕水翼云空化流动抑制机理研究

为理解绕水翼云空化流动的发展机理和探究水翼吸力面开孔射流的影响,采用密度 修正的RNG $k$-$\varepsilon $湍流模型和Schnerr-Sauer空化模型对原始NACA66(mod) 水翼和采用射流后的 水翼的云空化非定常过程进行模拟和对比分析;采用在水翼吸力面近壁区设立监测线的方法对近壁区的流场进行监测,得到 近壁区汽相体积分数、回射流速度、压力及压力梯度的时空分布云图;开展了云空化流场特性的涡动力学分析,进而分析水 翼云空化的发生机理和射流抑制空化的抑制机理. 结果表明:游离型空泡在下游溃灭时产生强烈的局部高压,其向上游传播 导致前缘空穴的一次回缩,而空穴的二次回缩受回射流的影响. 回射流的发展区域受限于较高的压力梯度,高的压力梯度一 直存在,但回射流在一个周期内的首次出现需要时间的积累. 在水翼吸力面射流使得射流孔附近压力升高,弥补了由于空化 和绕流造成的压降,压力梯度增大,抗逆压能力增强,对回射流起到阻挡作用;另一方面,射流使得回射流区域面积和回射 流的强度也有所减小,从而对云空化的发展起到抑制的效果. $Q$准则的涡结构云图相比于汽相体积分数云图能显示复杂的 流动结构,前缘附着型空穴和尾缘游离型空穴内存在旋涡,回射流对空穴存在剪切作用造成空穴脱落. 而射流对空穴和回射 流的剪切和阻挡使云空化发展得到抑制.      

On the collapse of cavities

The collapse of a single cavity, or a cloud of bubbles has several physical consequences when in proximity to a structure or resident within a material during deformation. The earliest recognized of these was cavitation erosion of the propellers of steam ships. However, other processes include the rapid collapse of cavities leading to hot spots in explosives from which reaction ensues, or the more recent phenomenon of light generation by oscillating single bubbles or clouds. In the collapse of a cavity, the least considered but the most important mechanism is asymmetric closure. One of the consequences of this is the formation of jets leading to local high pressures and shears that result in the damage or reaction mechanisms observed. The challenge for the future remains in understanding the effects of cloud cavitation since it is likely that only one bubble in perhaps millions in a cloud catalyses an event. The review follows the author's work in the understanding of shock-induced cavity collapse and highlights several results which indicate the importance of this problem in a variety of fields. Received 27 July 2001/ Accepted 25 January 2002     

nfluence of exciting parameters on the vibration of single cavitation bubble driven by intensive sound

根据考虑了液体可压缩性的改进的微气泡动力学方程,采用改进的初始半径对单泡超声空化现象进行了数值计算研究. 结果表明,微气泡振动对一些参量很敏感：微气泡振动半径与初始半径的比值随振动频率的增大而减小;提高声场声压会加剧气泡崩塌程度,但过高的声压又不能使微气泡崩塌;微气泡崩塌速率随气泡初始半径的增加而增大,在一定范围内能保证空化泡稳定振动,在初始半径为1.6\,$\mu$m 处空化程度最强,如果继续增大初始半径则空化程度减弱、甚至消失;微气泡崩塌程度随黏滞系数和表面张力的增大而减弱,过大的黏滞系数和表面张力会使微气泡崩塌难以发生. 计算结果与他人的实验数据相比,发现液体的可压缩性使单泡空化强度增强, 对最佳空化区域范围的确定有较大的影响.     

DYNAMICAL BEHAVIORS OF DOUBLE CAVITATION BUBBLES UNDER ULTRASONIC HONING

为了探讨超声珩磨作用下磨削区的空化机理,基于速度势叠加原理,考虑超声珩磨速度和珩磨压力,建立了磨削区两空化泡的动力学模型. 数值模拟了磨削区空化泡初始半径、两空化泡间距、超声声压幅值、珩磨压力、珩磨头转速对磨削区两空化泡动力学特性的影响. 研究表明,考虑两空化泡之间的相互作用时,要想获得良好的空化效果,可将两空化泡初始半径之比控制在3 倍以内;选择较高的超声波声压幅值与较低的珩磨压力,并且使超声波声压幅值与珩磨压力和液体静压力之差介于0.66~1.89MPa 之间;增大珩磨头转速空化泡溃灭也略有加速;通过试验测量材料表面粗糙度的方法间接验证了理论分析的合理性.     

超声珩磨作用下两空化泡动力学特性

为了探讨超声珩磨作用下磨削区的空化机理,基于速度势叠加原理,考虑超声珩磨速度和珩磨压力,建立了磨削区两空化泡的动力学模型. 数值模拟了磨削区空化泡初始半径、两空化泡间距、超声声压幅值、珩磨压力、珩磨头转速对磨削区两空化泡动力学特性的影响. 研究表明,考虑两空化泡之间的相互作用时,要想获得良好的空化效果,可将两空化泡初始半径之比控制在3 倍以内;选择较高的超声波声压幅值与较低的珩磨压力,并且使超声波声压幅值与珩磨压力和液体静压力之差介于0.66~1.89MPa 之间;增大珩磨头转速空化泡溃灭也略有加速;通过试验测量材料表面粗糙度的方法间接验证了理论分析的合理性.      

Air transport in chute flows

The air bubble rise velocity in still water depends mainly on the bubble size and is basically influenced by buoyancy, viscosity and surface tension. In high-speed flows the number of forces acting on air bubbles increases with turbulence, non-hydrostatic pressure gradient, shear forces, bubble clouds and free-surface entrainment. Air bubbles in these flows are used for cavitation protection of hydraulic structures such as chutes, spillways and bottom outlets. Here, air is normally added by means of aerators upstream of regions where the cavitation number falls below a critical value mainly to reduce the sonic velocity of the fluid and cushion the cavitation bubble collapse process. The distance between successive aerators depends basically on the bubble rise velocity. Until today, the bubble rise velocity in high-speed flows was not thoroughly investigated because of limited laboratory instrumentation. The present project focused on the streamwise development of air concentrations in high-speed flows along a 14 m long model chute. The bubble rise velocity was indirectly derived from the air detrainment gradient of the air concentration contour lines downstream of an aeration device. It accounts for the main hydraulic parameters chute slope, Froude number and air concentration. It is demonstrated that the bubble rise velocity in high-speed flow and stagnant water differ significantly due to fracturing processes, turbulence, and the ambient air concentration.     

Shock-induced collapse of a vapor nanobubble near solid boundaries

The collapse of a nano-bubble near a solid wall is addressed here exploiting a phase field model recently used to describe the process in free space. Bubble collapse is triggered by a normal shock wave in the liquid. The dynamics is explored for different bubble wall normal distances and triggering shock intensities. Overall the dynamics is characterized by a sequence of collapses and rebounds of the pure vapor bubble accompanied by the emission of shock waves in the liquid. The shocks are reflected by the wall to impinge back on the re-expanding bubble. The presence of the wall and the impinging shock wave break the symmetry of the system, leading, for sufficiently strong intensity of the incoming shock wave, to the poration of the bubble and the formation of an annular structure and a liquid jet. Intense peaks of pressure and temperatures are found also at the wall, confirming that the strong localized loading combined with the jet impinging the wall is a potential source of substrate damage induced by the cavitation.     

潜射导弹垂直出水过程中肩部空化的演化与弹体姿态的变化

在潜射导弹高速出水之前,弹体的肩部会出现明显的空化现象。为了研究潜射导弹在出水过程中肩部空化的发展演化过程及相应的弹体姿态角变化,以高速摄影为基本手段,采用边缘检测技术测算弹体姿态角以及肩部空化泡边界,通过对比分析不同出水阶段、不同时刻弹体肩部空化发展的状态,用来寻找出水过程中肩部空化现象和弹体姿态的发展规律。研究表明,高速出水条件下弹体在出水过程中有三种形式的空化现象先后出现,弹体肩部一开始形成的是片状空化,其轴向起始位置不同,周向也为随机分布;弹体运动过程中片状空化以两种方式转化为云状空化,一种是先脱落为旋涡型空化,然后再扩散为云状空化;另一种为片状空化尾部直接脱落为云状空化。出水过程中弹体姿态角变化幅度很小,而且在肩部空化泡出水溃灭的瞬间,弹体姿态角并未产生明显变化。     

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.     

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。     

基于相变松弛法则的水下爆炸空化模型研究

水下爆炸过程中存在着大量的空化现象,空化的产生、演化及其溃灭过程对于水下冲击波传播、爆炸气泡运动以及水下结构物冲击损伤都会产生重要影响。本文基于多相可压缩流体理论模型,考虑空化发生过程中汽-液两相流体亚平衡状态下两相之间发生的热力学-化学平衡机制,分析汽-液两相介质之间的质量和热量交换,从而实现对相变过程的自动捕捉。该系统的控制方程采用分步法处理,首先利用二阶MUSCL-Hancock格式和HLLC黎曼求解器来求解齐次双曲型方程,再采用牛顿迭代法求解相变方程。数值测试结果表明,本文的计算模型对于空化相变过程具有较好的捕捉能力。最后将该模型应用到水下近水面爆炸空化的数值模拟当中,研究发现空泡的溃灭压力峰值约为冲击波压力峰值的15%,有效作用时间是冲击波载荷有效作用时间的2倍以上。本文的空化相变模型能够为水下爆炸空化现象的机理研究提供重要支撑。     

泡内气体热力学性质对空泡溃灭的影响

数值研究固壁附近轴对称空泡溃灭问题. 忽略泡内气体与周围流体之间的质量和热交换, 假设气体瞬时处于热平衡状态, 通过引入不同的热力学模型, 考察泡内气体在空泡溃灭过程中的作用. 采用原始变量的Navier-Stokes方程作为流场的控制方程, 用流体体积方法跟踪运动空泡壁. 数值结果显示空泡溃灭过程中, 伴随空泡变形, 空泡发出多个高压脉冲和高速射流. 对于不同的热力学模型, 等温, 绝热和准绝热过程, 绝热过程能够最大程度抑制空泡溃灭, 从而减弱空泡溃灭对固壁造成的空蚀破坏. 在绝热及其类似过程中, 出现空泡回弹现象.     

High-speed visualization and PIV measurements of cavitating flows around a semi-circular leading-edge flat plate and NACA0015 hydrofoil

Cavitating flows around a flat plate with semi-circular leading edge and a NACA0015 hydrofoil at attack angles ranging from 0° to 9° and with varying cavitation number are investigated using high-speed-imaging visualization (HIV) and particle-imaging velocimetry (PIV). Several known types of cavitation common to both foils, but also some different patterns, were observed. At small angles of incidence (less than 3°), cavitation on the plate begins in the form of a streak array (bubble-band) whereas on the hydrofoil as traveling bubbles. For the regimes with developed cavitation on the NACA0015 hydrofoil, the scattered and discontinuous bubble streaks branch and grow but subsequently merge into bubble clouds forming a remarkably regular lattice pattern. Once the incidence angle increased to 9°, the cavitation on the hydrofoil changed to a streaky pattern like that on the plate at small attack angles, whereas the regime on the plate showed no significant changes. The PIV method proved to be usable for measuring the instantaneous velocity also in the gas–vapor phase, albeit with reduced accuracy that was evaluated and accounted for on the basis of the effective (validation-surviving) number of imaging samples. The time-averaged velocity and turbulence moments show that the incipience of cavitation is governed by the development of the carrier-fluid flow around the foil leading edges, but the subsequent flow pattern depends strongly on the cavitation regime displaying markedly different distributions compared to the non-cavitating case. The main cavitation parameters: the maximum cavity length, the cloud cavity streamwise dimensions and the cloud shedding Strouhal number are analyzed and presented in function of the cavitation number and the attack angle in different scaling. The measurements confirm qualitatively the trends reported in the literature, but show also some quantitative differences, notably between the two foils considered.     

Multiscale tow-phase flow modeling of sheet and cloud cavitation

A multiscale two-phase flow model based on a coupled Eulerian/Lagrangian approach is applied to capture the sheet cavitation formation, development, unsteady breakup, and bubble cloud shedding on a hydrofoil. No assumptions are needed on mass transfer. Instead natural free field nuclei and solid boundary nucleation are modelled and enable capture of the sheet and cloud dynamics. The multiscale model includes a micro-scale model for tracking the bubbles, a macro-scale model for describing large cavity dynamics, and a transition scheme to bridge the micro and macro scales. With this multiscale model small nuclei are seen to grow into large bubbles, which eventually merge to form a large scale sheet cavity. A reentrant jet forms under the sheet cavity, travels upstream, and breaks the cavity, resulting in the emission of high pressure peaks as the broken pockets shrink and collapse while travelling downstream. The method is validated on a 2D NACA0015 foil and is shown to be in good agreement with published experimental measurements in terms of sheet cavity lengths and shedding frequencies. Sensitivity assessment of the model parameters and 3D effects on the predicted major cavity dynamics are also discussed.     

Modèle multi-bulles pour la cavitation

In this study we propose new multi-bubble model for cavitation, in which, to simulate the interactions within a cloud of cavitation at the initial stage, the dynamic behaviour of two nonidentical bubbles localised in a volume of control is studied. The presence of two bubbles introduces an instability in which the exchange of volume seems an additional degree of freedom. Depending on the conditions of expansion, the small bubble can disappear or not. If the small bubble disappears, the volume of control is readjusted to introduce a new small bubble and to continue calculation in a new sequence. The model makes it possible for many small bubbles to disappear as in the appearance of cavitation, which is at the origin of certain phenomena observed in the zone of the appearance, such as emission of the noise. The model reveals especially the pressure rather like a result than a datum.The comparison of the size of the bubbles and the pressure varying in time, obtained with the model are coherent with the measurements taken by Ohl [Phys. Fluids 14 (10) (2002) 3512–3521]. To cite this article: M. Adama Maiga, D. Buisine, C. R. Mecanique 337 (2009).     

On the modeling and simulation of a laser‐induced cavitation bubble

Single cavitation bubbles exhibit severe modeling and simulation difficulties. This is due to the small scales of time and space as well as due to the involvement of different phenomena in the dynamics of the bubble. For example, the compressibility, phase transition, and the existence of a noncondensable gas inside the bubble have strong effects on the dynamics of the bubble. Moreover, the collapse of the bubble involves the occurrence of critical conditions for the pressure and temperature. This adds extra difficulties to the choice of equations of state. Even though several models and simulations have been used to study the dynamics of the cavitation bubbles, many details are still not clearly accounted for. Here, we present a numerical investigation for the collapse and rebound of a laser‐induced cavitation bubble in liquid water. The compressibility of the liquid and vapor are involved. In addition, great focus is devoted to study the effects of phase transition and the existence of a noncondensable gas on the dynamics of the collapsing bubble. If the bubble contains vapor only, we use the six‐equation model for two‐phase flows that was modified in our previous work [A. Zein, M. Hantke, and G. Warnecke, J. Comput. Phys., 229(8):2964‐2998, 2010]. This model is an extension to the six‐equation model with a single velocity of Kapila et al. (Phys. Fluid, 13:3002‐3024, 2001) taking into account the heat and mass transfer. To study the effect of a noncondensable gas inside the bubble, we add a third phase to the original model. In this case, the phase transition is considered only at interfaces that separate the liquid and its vapor. The stiffened gas equations of state are used as closure relations. We use our own method to determine the parameters to obtain reasonable equations of state for a wide range of temperatures and make them suitable for the phase transition effects. We compare our results with experimental ones. Also our results confirm some expected physical phenomena. Copyright © 2013 John Wiley & Sons, Ltd.     

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。     

An experimental study of liquid jets formed by bubble-shock wave interaction in dilute polymer solutions

 This paper describes experiments in which a shock wave, emanating from the collapse of a cavitation bubble, causes a second bubble to collapse, thereby producing a liquid jet. A comparison of the jets formed by bubble collapse in dilute solutions of polyacrylamide and polyethylene oxide, and in their Newtonian counterparts, shows that in the polymer solutions liquid jet development is markedly suppressed. The implications of these findings are discussed in the context of cavitation damage. Received: 3 September 1998/Accepted: 23 July 1999