Collapse of a single bubble in a Shvedov-Bingham fluid under pulsating external pressure

The behavior of a spherical bubble in an ideal fluid, a viscous medium, and an incompressible viscoplastic medium with a yield stress is studied numerically and analytically when a time-varying periodic pressure is exerted at a sufficient distance from the surface of the bubble. Various modes of collapse are examined and classified. The critical values of the key parameters that characterize the behavior of this system are found; one of these parameters is the dimensionless frequency of external pressure fluctuations.     

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.     

Optimization of shock-wave action on a spherical bubble in an ideal incompressible liquid

The possibility of controlling the oscillations of a spherical gas bubble in an ideal incompressible liquid is subjected to theoretical analysis. Liquid surface tension forces are not taken into account. The optimization process realizing a maximum of the radius amplitude and a maximum of the gas pressure in the bubble for a given impulsive change of pressure at infinity is considered. A shock-resonance bubble oscillation procedure giving stepwise pressure changes at the extrema of the radius is constructed. This problem is of interest in connection with the investigation of cavitation erosion [1] and processes in biological tissues [2–4]. Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 175–178, September–October, 1988.     

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.     

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.     

Visualization of a confined accelerated bubble

High-speed photography was used to study the collapse of a confined two-dimensional, air cavity in water, subjected to a propagating pressure disturbance. The 5–6 mm diameter cavity was confined in a rectangular duct. A sustained pressure disturbance was created by an accelerating piston in contact with the water 240 mm away from the bubble. The pressure increased from 0.1 MPa to about 0.12 MPa with a rise time of the order of 2 ms. The pressure pulse was not reflected until its arrival at the end of the duct, 320 mm from the piston. A microjet was produced at the proximal wall which penetrated the distal cavity wall, thereby producing a pair of bubbles which was thought to be regions of intense vorticity. The features of such confined bubble collapse were not found in previous investigations of unconfined bubble accelerations by weak pressure disturbances. Confinement apparently intensified the effect of the disturbance significantly. Received 18 August 1998 / Accepted 12 May 1999     

The Horton–Rogers–Lapwood Problem Revisited: The Effect of Pressure Work

The problem of the onset of convective roll instabilities in a horizontal porous layer with isothermal boundaries at unequal temperatures, well known as the Horton–Rogers–Lapwood problem, is revisited including the effect of pressure work and viscous dissipation in the local energy balance. A linear stability analysis of rolls disturbances is performed. The analysis shows that, while the contribution of viscous dissipation is ineffective, the contribution of the pressure work may be important. The condition of marginal stability is investigated by adopting two solution procedures: method of weighted residuals and explicit Runge–Kutta method. The pressure work term in the energy balance yields an increase of the value of the Darcy–Rayleigh number at marginal stability. In other words, the effect of pressure work is a stabilizing one. Furthermore, while the critical value of the Darcy– Rayleigh number may be considerably affected by the pressure work contribution, the critical value of the wave number is affected only in rather extreme cases, i.e. for very high values of the Gebhart number. A nonlinear stability analysis is also performed pointing out that the joint effects of viscous dissipation and pressure work result in a reduction of the excess Nusselt number due to convection, when the Darcy–Rayleigh number is replaced by the superadiabatic Darcy–Rayleigh number.     

Law of flow of a viscoplastic fluid through a porous medium with allowance for inertial losses

A macroscopic law of flow of a viscoplastic Schwedoff-Bingham fluid through a porous medium is obtained on the basis of percolation theory with allowance for viscous and inertial losses. The asymptotics of the flow law are estimated and expressions for determining the limiting pressure gradient as a function of the microinhomogeneity parameters are given. Satisfactory qualitative agreement between the theoretical and known experimental data is observed. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 68–73, January–February, 1999.     

Forced nonlinear oscillations of a gas bubble in a large spherical flask (resonator) filled with a fluid

Radial oscillations of a gas bubble in a large spherical flask filled with a fluid are considered. We derive an equation of the change of the bubble radius by the known law of pressure variation at the boundary of the liquid volume (the law of motion of the piston) for a period of time during which, repeatedly reflected from the piston, the leading front of the reflected-from-the bubble perturbations reaches the bubble. For further calculations of the change of the bubble radius, recurrent relations which include the wave reflected from the bubble in the previous cycle and its subsequent reflection from the piston are obtained. Under harmonic action of the piston on the fluid-bubble system, a certain periodic regime with a package of bubble oscillations is established. Institute of Mechanics, Ural Scientific Center, Russian Academy of Sciences, Ufa 450000. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 5, pp. 77–87, September–October, 1998.     

单液滴内空化气泡的生长及溃灭研究

超空化燃油射流使得喷雾中部分燃油分裂液滴内含有空化气泡;空化气泡的生长及溃灭对液滴的分裂与雾化具有重要影响. 基于VOF 方法首次对超空化条件下燃油液滴内空化气泡的生长及溃灭过程进行了数值模拟. 通过研究发现,单液滴内空化气泡的生长过程可以按控制机理划分为表面张力控制阶段、综合竞争阶段和惯性力控制阶段;在第I 阶段,空泡的生长主要受表面张力的控制作用,惯性力对空泡生长的促进作用及黏性力对空泡生长的抑制作用可以忽略;在第II 阶段,空泡的生长受表面张力、惯性力及黏性力三者的综合作用,空泡的生长速率是促进空泡生长的惯性力和抑制空泡生长的表面张力及黏性力相互竞争、共同作用的结果;在第III 阶段,空泡的生长主要受惯性力的控制作用,抑制空泡生长的表面张力及黏性力的作用基本可以忽略. 单液滴内空化气泡的溃灭过程由多个溃灭阶段和反弹阶段构成,类似于有阻尼弹簧振子的振动过程;根据每个溃灭周期结束时空泡半径随时间的变化历程,可以将空泡的溃灭分为快速溃灭期、缓慢溃灭期以及稳定期;溃灭初期空泡溃灭压力的变化非常剧烈,但空泡溃灭体积的变化则要相对平缓得多;空泡反弹压力随时间的变化与空泡反弹体积随时间的变化基本对应.      

Level set method for numerical simulation of a cavitation bubble,its growth,collapse and rebound near a rigid wall

A level set method of non-uniform grids is used to simulate the whole evolution of a cavitation bubble, including its growth, collapse and rebound near a rigid wall. Single-phase Navier–Stokes equation in the liquid region is solved by MAC projection algorithm combined with second-order ENO scheme for the advection terms. The moving interface is captured by the level set function, and the interface velocity is resolved by “one-side” velocity extension from the liquid region to the bubble region, complementing the second-order weighted least squares method across the interface and projection inside bubble. The use of non-uniform grid overcomes the difficulty caused by the large computational domain and very small bubble size. The computation is very stable without suffering from large flow-field gradients, and the results are in good agreements with other studies. The bubble interface kinematics, dynamics and its effect on the wall are highlighted, which shows that the code can effectively capture the “shock wave”-like pressure and velocity at jet impact, toroidal bubble, and complicated pressure structure with peak, plateau and valley in the later stage of bubble oscillating. The project supported by the National Natural Science Foundation of China (10272032 and 10672043). The English text was polished by Keren Wang.     

Forced oscillations of two gas bubbles in a fluid in the vicinity of bubble contact

For a theoretical derivation of bubble coalescence conditions, nonlinear forced oscillations of two closely spaced spherical bubbles subjected to the action of a periodic external pressure field are considered. The equations, asymptotic with respect to a small distance between the bubble surfaces, are derived to describe the approach of the bubbles under the action of (i) the Bjerknes attraction force averaged over the oscillation period and (ii) the viscous drag. It is shown that due to nonlinear interaction of the viscous drag with the radial and translational oscillations of the bubbles a unidirectional repulsive force is generated, which prevents the approach of the bubbles. The coalescence of the bubbles is possible when the nondimensional parameter combined from the amplitude and frequency of the external pressure field, the bubble radius, and the fluid viscosity is greater than a certain critical value. The obtained coalescence condition is qualitatively confirmed by experiments.     

Flow field at collapse of a cavity

Employing Rayleigh’s method, the collapse of a vaporous bubble in an incompressible liquid with surface tension is analysed. The expressions of time versus radius, bubble-wall velocity and pressure developed at collapse are thus introduced.Finally, the numerical solution of velocity and pressure field in the liquid surrounding the cavity is also given.     

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.     

Numerical analysis of an asymptotic model for the collapse of a vapor bubble

In this work, we analyze the thermal collapse of a vapor bubble immersed in a unbounded and subcooled liquid. In this thermal regime, controlled basically by Jakob number (Ja), we present an asymptotic limit of the governing equations by identifying the appropriate temporary and spatial scales to solve numerically the mathematical model. In the limit of Ja ≫ 1, the governing equations describe the spatial and temporal evolution of the adjacent thermal boundary layer to the radius of the bubble. In particular, we prove that the influence of curvature effects due to conductive and convective heat terms of the energy equation for the liquid are responsible to characterize the thermal collapse regime. The numerical results for the evolution of the nondimensional radius of the bubble, a, and the corresponding nondimensional temperature profiles, θ, for different values of the Ja, show that the ending collapse state has a singular behavior, which we have denoted as a “thermal runaway”.     

近场水下爆炸气泡脉动及水射流的实验与数值模拟研究

海上作战时,近场水下爆炸形成的水射流能造成水面舰船结构的严重局部毁伤。为了研究近场爆炸时舰船底部水射流的形成机理及规律,开展了TNT当量2.5 g的炸药在固支方板底部不同爆距下起爆的水下爆炸实验。结果表明,气泡坍塌形成水射流的过程随着爆距的增加由吸附式向非吸附式转化。接着,基于ABAQUS软件采用CEL方法开展了系列数值模拟,结果表明:爆距在0.821～0.867倍最大气泡半径时,存在吸附式射流向非吸附式射流转化的临界点;固支方板加快了气泡坍塌的进程,炸药与钢板间的距离越小则射流形成的时间越早;射流形成过程中最大速度和射流击中钢板时速度均随着爆距的增大先增大后减小,并在临界点附近达到最大值,射流速度最大可达621 m/s,射流击中钢板时速度最大可达269 m/s。最后,给出了射流开始形成时间、射流最大速度、射流最大速度出现时间、射流击中钢板速度和射流击中钢板时间与距离参数的函数关系式。     

圆锥泡声致发光气泡动力学过程的理论分析

在绝热压缩模型的基础上, 详细讨论了圆锥泡声致发光中气泡运动的动力学过程,得到 了气泡塌陷速度方程、气泡内压强方程以及温度方程. 结果显示在气泡进入圆锥腔的初始阶 段,气泡的塌陷速度随着压缩半径的不断减小近似线性地增加;然后随着压缩半径的进一步 减小,气泡塌陷的加速度逐渐减小;当气泡塌陷速度达到最大值后,随着气泡压缩半径的 进一步减小, 塌陷速度迅速下降至零. 在假设初始气压为1000\,Pa的基础上,理论分析 得到气泡的最高塌陷速度可以达到5.8\,m/s; 气泡的最小压缩半径可以达 到1.37\,cm, 相应的气泡内极限压强超过$4.5\times10^5$\,Pa, 极限温度超 过3\,150\,K, 而液流能够提供给气泡的能量达到0.02\,J. 理论推导得到的结果 可以比较好地用来解释实验中的现象. 最后分析得到气泡内的初始气 压对气泡所能达到的极端条件有着重要的影响.     

自由场空泡溃灭过程能量转化机制研究

综合应用实验与数值模拟方法, 深入讨论了自由场空泡溃灭过程中的能量转化机制. 在实验研究中, 应用纹影法记录了空泡溃灭的演变过程, 提取了空泡在溃灭过程中的半径, 溃灭速度等数据, 结合空泡势能和动能方程, 描述了空泡能量的转化过程. 在开展数值模拟分析时, 运用弱可压缩流体质量守恒方程和动量方程, 建立了三维数值模型用以模拟空泡在自由场中的溃灭过程, 并且由结果中获取了空泡溃灭过程中的压力及速度变化规律, 揭示了空泡在溃灭过程中能量转化机制. 研究结果表明: (1) 自由场空泡在溃灭过程中, 空泡势能与空泡半径具有相同的演化趋势, 空泡动能与势能变化趋势相反; 当空泡达到最大半径处时, 空泡势能最大, 流场动能为零. (2) 溃灭后期在空泡周围会形成高压区域, 该区域的压力梯度与速度梯度较高, 随着空泡收缩, 高压区域面积逐渐减小. (3) 空泡在自由场中发生溃灭时, 空泡势能不断转化为流场动能, 在溃灭时刻可以明显观察到冲击波现象, 空泡的大部分能量会在此时转化为冲击波的波能.      

Deformation of a Bingham viscoplastic fluid in a plane confuser

A review is given to and comprehensive numerical-analytic study is carried out of the problem of steady Bingham viscoplastic flow in a plane confuser. The solution is constructed in the first approximation with the yield stress as a small parameter and the solution of the Jeffery-Hamel problem (steady radial motion of an incompressible viscous material in a plane confuser) as the zero-order approximation. The numerical analysis is based on the modified accelerated-convergence method proposed earlier by the authors. The bifurcations of the deformation pattern occurring when the parameters reach some critical values are discussed and commented on. The asymptotic boundaries of the rigid zones that appear at infinity upon perturbation of the yield stress are determined __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 4, pp. 3–45, April 2006.     

Motion of a variable-volume sphere in an ideal fluid near a plane surface

The motion of a spherical cavity in a fluid is investigated. The radius of the sphere varies under the action of a constant pressure at infinity. The problems of the collapse of a cavity moving in an unbounded fluid and of the collapse of a cavity near a plane are solved in the exact formulation. The occurrence of an initial translational velocity or the presence of a solid surface, by contrast with the collapse of a sphere at rest in an unbounded fluid [1], yields a limiting radius at which the process of collapse ceases. A sphere initially at rest near a plane always comes into contact with the plane as a result of collapse. The radius and velocities at which the sphere arrives the plane are calculated for various initial distances from the latter. The possible mechanism of the action of a cavitation bubble on a solid surface is discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 94–103, September–October, 1971.