流体黏性及表面张力对气泡运动特性的影响

基于气泡边界层理论,引入黏性修正,采用边界积分法,考虑黏性效应和表面张力在单气泡以及双气泡耦合作用过程中的影响.首先将建立的数值模型与Rayleigh-Plesset的解析解进行对比,发现二者符合良好,验证了数值模型的有效性;在此基础上,建立考虑流体弱黏性效应的双气泡耦合模型,研究流体黏性和表面张力作用下,气泡表面变形、射流速度、流场能量转换等物理量的变化规律;最后研究雷诺数和韦伯数对于气泡脉动特性的影响规律.结果表明,流体黏性会抑制气泡脉动和气泡射流发展,降低气泡半径和射流速度;表面张力不改变气泡脉动幅值,但缩短了脉动周期,提升气泡势能.     

气泡与弹性膜的耦合效应数值模拟

本文在前人研究的基础上,计入浮力、表面张力、不同流体密度比等因素对弹性膜附近气泡运动的影响,结合不可压缩理想流体理论,建立气泡与弹性膜耦合动力学数值模型,采用边界元方法进行求解,计算值与Turangan等的实验结果符合良好.通过对弹性膜附近气泡运动的数值模拟,详细分析了弹性膜两侧为同种密度液体以及不同密度液体时气泡的运动,随后又分析气泡在弹性膜和浮力的共同作用下气泡的射流特性.旨在为相关气泡与弹性膜相互作用特性的研究提供参考. 关键词： 弹性膜 边界元法 气泡 浮力     

气泡在自由液面破碎后的射流断裂现象研究

在势流假设下, 考虑表面张力以及黏性修正, 建立自由液面在气泡破碎后全非线性运动的数值模型, 给出射流断裂和水滴撕裂的数值处理方法. 同时进行上浮气泡在自由液面破裂的实验研究, 数值解与实验值符合良好.为了研究自由液面在气泡破碎后的运动学机理和规律, 运用开发的程序研究了不同尺寸气泡破碎后的动态特性, 包括从气泡底部顶起的射流、射流断裂以及水滴分裂等复杂的物理现象, 总结了从射流上撕裂出的第一个水滴尺寸、撕裂时间以及最大射流速度的变化规律. 最后讨论了雷诺数与韦伯数对气泡破碎后自由液面运动的影响. 关键词： 气泡 自由液面 破碎 断裂     

上浮气泡在壁面处的弹跳特性研究

本文针对毫米量级的上浮气泡在壁面处的弹跳现象进行数值研究.基于势流方法求解气泡的运动,同时考虑气泡的表面张力作用.在伯努利方程中,对气泡与壁面之间水膜中因黏性引起的压力梯度进行修正,开发相应的计算程序,计算值与实验值符合良好.从气泡弹跳的基本现象入手,研究了特征参数对气泡弹跳过程的动态特性以及最终平衡形态的影响.发现随着泡在撞击壁面之前上浮距离增大,气泡回弹距离和弹跳周期增加,但是当上浮距离增加到一定程度后将不会影响气泡的弹跳特性;表面张力是影响气泡弹跳特性的重要因素,气泡的弹跳周期随其增大逐渐减小,但回弹距离却呈现先增后减的规律;最后,影响气泡最终平衡形态的主要因素是气泡的浮力参数与韦伯数.     

Dynamics of a cavitation bubble near a solid wall

The cavitation bubble dynamics, the variation of pressure and velocity fields of the surrounding liquid in the process of the bubble axisymmetric compression near a planar solid wall are considered. It is assumed that the liquid is at rest at the initial moment of time, and the bubble has a spheroidal shape. The liquid is assumed inviscid and incompressible, its motion being potential. The bubble surface deformation and the liquid velocity on the surface are computed by the Euler scheme using the boundary element method until the moment of the collision of some parts of the bubble surface with one another. The influence of the distance of the bubble from the wall and its initial nonsphericity on the liquid pressure and velocity fields, the bubble shape, and the pressure inside the bubble at the end of the time interval under consideration are studied. The maximum pressure in liquid is shown to realize at the bottom of the cumulative jet arising at the bubble collapse with direction to the wall. In the upper part of this jet, the velocity and pressure are practically constant, and the pressure in the jet is approximately equal to the pressure in the bubble.     

Multi-relaxation-time lattice Boltzmann front tracking method for two-phase flow with surface tension

<正>In this paper,an improved incompressible multi-relaxation-time lattice Boltzmann-front tracking approach is proposed to simulate two-phase flow with a sharp interface,where the surface tension is implemented.The lattice Boltzmann method is used to simulate the incompressible flow with a stationary Eulerian grid,an additional moving Lagrangian grid is adopted to track explicitly the motion of the interface,and an indicator function is introduced to update the fluid properties accurately.The interface is represented by using a four-order Lagrange polynomial through fitting a set of discrete marker points,and then the surface tension is directly computed by using the normal vector and curvature of the interface.Two benchmark problems,including Laplace’s law for a stationary bubble and the dispersion relation of the capillary wave between two fluids are conducted for validation.Excellent agreement is obtained between the numerical simulations and the theoretical results in the two cases.     

对流梯形微通道内气液两相流动的数值研究

采用VOF方法,对梯形微通道内不可压缩气液两相流动进行了数值模拟研究,详细分析了气泡形成过程,以及当量直径、截面形状、液体表面张力和粘度等对气泡液柱形成过程和长度的影响,拟合出微通道气泡液柱长度计算公式。结果表明:气泡液柱的长度受表观气速和表观液速的影响较大;表面张力对气泡尺寸的影响较小,当液体粘度增加为水粘度的10倍时,形成的气泡形状不规则。增大表面张力,形成气泡的时间增加;增大粘度,形成气泡的时间减小。     

Influences of different forces on the bubble entrainment into a stationary Gaussian vortex

Simulations of bubble entrainment into a stationary Gaussian vortex are performed by using the combined particle tracking method (PTM) and boundary element method (BEM). Before the bubble is captured by the vortex core, oscillation and migration of the quasi-spherical nucleus are solved by using improved RP equation and the momentum theorem in the Lagrangian reference frame simultaneously, and the trajectory of the nucleus presents a kind of reduced helix shape. After captured by the vortex core, the bubble grows immediately and moves and deforms along the vortex core axis. The non-spherical evolution and deformation of the bubble is simulated by adopting a mixed Eulerian-Lagrangian method. The output of quasi-spherical stage is taken as the input of non-spherical stage, and all the behaviors of the entrained bubble can be simulated such as inception, motion, deformation and split. Numerical results agree well with published experimental data. On this basis, the influences of various factors such as viscosity, surface tension, buoyancy are studied systemically. Hopefully the results from this paper would provide some insight into the control on vortex bubble entrainment.     

静止水中单个上升气泡的直接数值模拟

本文发展了基于Front Tracking的直接数值模拟方法研究气液两相界面的迁移特性,该方法对气液两相采用半隐式的分步法直接求解N-S方程,耦合Front Tracking Method获得两相界面的三维变形。针对无边界以及垂直壁面附近静止水中的单个气泡上升过程进行模拟,研究气泡运动的机理以及气泡与壁面的相互作用。数值模拟准确再现了气泡的上升过程和变形,不同Re数下气泡的上升速度计算结果同经验关联式非常吻合,验证了该方法的有效性。随后分析了气泡周围流场的结构,发现壁面对气泡周围流场的抑制是壁面对气泡作用力的主要原因,将导致气泡逐渐偏离垂直壁面。     

Comparison between level set and phase field method for simulating bubble movement behavior under electric field

In this study, based on different numberical simulation methods, the gas-liquid two-phase flow is taken as the research object. By coupling the continuity equation of incompressible fluid, Navier-Stokes equation, electric field equation and other control equations, a multi-field coupling model for rising bubbles in viscous fluids is established, and numerical simulations are carried out. The two-phase popularity of coupled electric field is studied, and the effect of electric field on bubble motion is analyzed.The Level-set and phase field method are used to track the changes of deformation and rupture during the rising of the bubble. The accuracy and validity of the two methods are verified by mass conservation. At the same time, the calculation area is determined for the accuracy of calculation, and the optimal mesh size is calculated by using mesh independence test. Compared with the level set method, the phase field method has a certain improvement in the calculation efficiency and accuracy. Among them, the calculation efficiency of the phase field calculation method in the same grid is increased by 5 times, and by 3 times in the vertical electric field environment. Moreover, using the phase field method is easier to capture the bubbles slight changes while they are rising, and the quality of the simulation results is better.The simulation analysis of bubble rising process under coupled electric field by two methods shows that under the interaction of electrostatic force, buoyancy and surface tension, the bubble is stretched into an ellipsoid along the direction of the electric field line, and the ratio of the length to the short axis is proportional to the applied electric field strength. In addition, the bubble rising velocity is affected by the electric field, and the vertical electric field accelerates the rising of the bubble.     

Three-dimensional multi-relaxation-time lattice Boltzmann front-tracking method for two-phase flow

We developed a three-dimensional multi-relaxation-time lattice Boltzmann method for incompressible and immiscible two-phase flow by coupling with a front-tracking technique. The flow field was simulated by using an Eulerian grid, an adaptive unstructured triangular Lagrangian grid was applied to track explicitly the motion of the two-fluid interface, and an indicator function was introduced to update accurately the fluid properties. The surface tension was computed directly on a triangular Lagrangian grid, and then the surface tension was distributed to the background Eulerian grid. Three benchmarks of two-phase flow, including the Laplace law for a stationary drop, the oscillation of a three-dimensional ellipsoidal drop,and the drop deformation in a shear flow, were simulated to validate the present model.     

Dynamic behavior of a single bubble between the free surface and rigid wall

The objective of this paper is to apply high-speed photography and schlieren method to investigate the bubble dynamics between the free surface and a rigid wall. The temporal evolution of the bubble shape and the free surface motion are recorded by two synchronous high-speed cameras. Experiments are carried out for a single bubble generated at various normalized stand-off distances from bubble center to the free surface and to the rigid wall. The results show that (1) three distinctive patterns are identified with the morphology of the bubble and free surface, namely single toroidal bubble without spike (STB), single toroidal bubble with a spike (STBS) and double toroidal bubbles with a spike (DTBS). (2) The dynamic characteristics of the bubble at collapse and rebound stage vary evidently at different patterns, including the bubble shape variations and free surface motion. In detail, the schlieren images show the formation and propagation of shock waves, which explains the radiative process of bubble collapse energy. (3) Qualitative comparisons are carried out for the bubble and free surface at the same pattern. And quantitative analyses are conducted for the jet velocity, bubble collapse position, bubble collapse time and spike height, etc. for different values of bubble-rigid wall distance.     

Surface tension effects on the behaviour of a rising bubble driven by buoyancy force

In the inviscid and incompressible fluid flow regime,surface tension effects on the behaviour of an initially spherical buoyancy-driven bubble rising in an infinite and initially stationary liquid are investigated numerically by a volume of fluid (VOF) method. The ratio of the gas density to the liquid density is 0.001, which is close to the case of an air bubble rising in water. It is found by numerical experiment that there exist four critical Weber numbers We₁,~We₂,~We₃ and We₄, which distinguish five different kinds of bubble behaviours. It is also found that when 1≤We2, the bubble will finally reach a steady shape, and in this case after it rises acceleratedly for a moment, it will rise with an almost constant speed, and the lower the Weber number is, the higher the speed is. When We >We₂, the bubble will not reach a steady shape, and in this case it will not rise with a constant speed. The mechanism of the above phenomena has been analysed theoretically and numerically.     

非理想流体中Rayleigh-Taylor和Richtmyer-Meshkov不稳定性气泡速度研究

在随气泡顶端运动的坐标系中, 通过将理想流体模型推广到非理想流体的情况, 研究了流体黏性和表面张力对Rayleigh-Taylor (RT)和Richtmyer-Meshkov (RM)不稳定性气泡速度的影响. 首先得到了RT和RM不稳定性气泡运动的控制方程 (自洽的微分方程组); 其次给出了二维平面坐标和三维柱坐标中气泡速度的数值解和渐近解, 并定量分析了流体黏性和表面张力对RT和RM气泡速度和振幅的影响. 结果表明: 从线性阶段到非线性阶段的全过程中, 非理想流体中的气泡速度和振幅小于理想流体中的气泡速度和振幅. 也就是说, 流体黏性和表面张力对RT和RM不稳定性的发展都具有致稳作用. 关键词： Rayleigh-Taylor不稳定性 Richtmyer-Meshkov不稳定性 气泡速度 非理想流体     

水中上浮气泡动态特性研究

针对水中的上浮气泡,计入表面张力的作用,然后将气泡边界层内黏性效应分为法向和切向两部分,其中附加法向黏性应力通过Young-Laplace关系考虑;附加切向黏性力是基于黏性耗散能量等效原理,引入黏性修正压力代替.首先建立了轴对称和三维上浮气泡边界元模型,将数值结果与理论值和实验值进行对比分析,有良好的符合度,验证了数值模型的有效性;然后针对毫米量级上浮气泡的平衡速度与形态,讨论了气泡初始条件、表面张力和黏性对气泡上浮过程中动力学行为的影响;最后,提出了一种处理三维上浮气泡融合的数值方法,计算结果与实验现象符合良好,并且能够反映气泡融合后的复杂现象细节.     

Deformation of liquid droplets during collisions with hot walls: Experimental and Numerical Results

Measurements of droplet deformation during wall impingement were performed for ethanol droplets and water droplets with diameters ranging from 100 to 200 μm. The wall temperature is well above the Leidenfrost temperature of the droplet liquid. With monodisperse droplet streams and a special illumination technique, slow motion images of the phenomena can be obtained. Measurements with high temporal resolution below 1 μs are possible using a standard video camera. The experimental results are compared with numerical results, which were obtained by solving the three-dimensional Navier-Stokes equations for incompressible fluids including surface tension effects. The fluids are treated with the volume-of-fluid method and the free surface is modeled according to the continuum-surface-force model. Numerical and experimental results show good agreement.     

Nonlinear vibrations of a charged drop in an electrostatic suspension

The problem of nonlinear vibrations of a charged drop of an ideal incompressible conducting fluid in an electrostatic suspension is analytically solved in an approximation quadratic in two small parameters: vibration amplitude and equilibrium deformation of the shape of the drop in an electrostatic field. To solve the problem analytically, the desired quantities are expanded in semiinteger powers of the small parameters. It is shown that the charge of the drop and the gravitational field influence the shape of the drop, nonlinear corrections to the vibration frequencies, and critical conditions for instability of the drop against the surface charge. At near-critical values of the charge, the shape of the nonlinearly vibrating drop falls far short of being a sphere or a spheroid, which should be taken into account in treating experimental data.     

Modeling of surface cleaning by cavitation bubble dynamics and collapse

Surface cleaning using cavitation bubble dynamics is investigated numerically through modeling of bubble dynamics, dirt particle motion, and fluid material interaction. Three fluid dynamics models; a potential flow model, a viscous model, and a compressible model, are used to describe the flow field generated by the bubble all showing the strong effects bubble explosive growth and collapse have on a dirt particle and on a layer of material to remove. Bubble deformation and reentrant jet formation are seen to be responsible for generating concentrated pressures, shear, and lift forces on the dirt particle and high impulsive loads on a layer of material to remove. Bubble explosive growth is also an important mechanism for removal of dirt particles, since strong suction forces in addition to shear are generated around the explosively growing bubble and can exert strong forces lifting the particles from the surface to clean and sucking them toward the bubble. To model material failure and removal, a finite element structure code is used and enables simulation of full fluid–structure interaction and investigation of the effects of various parameters. High impulsive pressures are generated during bubble collapse due to the impact of the bubble reentrant jet on the material surface and the subsequent collapse of the resulting toroidal bubble. Pits and material removal develop on the material surface when the impulsive pressure is large enough to result in high equivalent stresses exceeding the material yield stress or its ultimate strain. Cleaning depends on parameters such as the relative size between the bubble at its maximum volume and the particle size, the bubble standoff distance from the particle and from the material wall, and the excitation pressure field driving the bubble dynamics. These effects are discussed in this contribution.     

Evolution of the shape of a bubble deformed at the zero time in a viscous fluid

The boundary-value problem of the shape of a charged bubble in a viscous incompressible insulating fluid as a function of time is solved in an approximation linear in the initial deformation amplitude. Both centrosymmetric pulsations and vibrations at constant volume are considered. It is shown that the time evolution of the shape of the bubble, as well as of the velocity and pressure fields of the fluid in its neighborhood, can be represented by finite sums over the numbers of initially excited modes, which involve two terms. The first term is a sum over the roots of the dispersion relation; the second, an improper integral. In the low-and high-viscosity limits, the relevant analytical expressions simplify, i.e., become free of integrals. It turns out that the damping constant of bubble surface vibrations varies with viscosity nonmonotonically in the case of radial pulsations and this dependence is different in the different limits. The frequencies of radial pulsations and surface vibrations vary with viscosity monotonically.