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.     

气泡碰壁受力模型和反弹规律

对Mo=10-8~10-12及Re=5~750范围内的上升气泡与壁面垂直碰撞问题进行了理论求解，研究了不同控制参数下气泡碰壁反弹的规律.气泡上升和碰撞过程的运动方程考虑了浮力、液体阻力、附加质量力和与壁面碰撞时引起的薄膜诱导力.气泡碰壁过程气泡界面与壁面形成的液膜厚度变化规律由Stokes-Reynolds方程计算得到.膜内气泡变形引起的流体压强采用Young-Laplace方程求解.结果表明，基于SRYL方程的薄膜诱导力模型可以很好地预测不同Reynolds数下气泡0到多次的反弹轨迹，计算结果与实验结果吻合良好.气泡在碰壁反弹过程中会形成丰富的薄膜形状，如酒窝状变形，丘疹状变形和涟漪状变形.气泡界面变形会引起膜内压强的变化，压强的分布规律与气泡界面形状有着重要的关系.气泡在与壁面碰撞的过程中，薄膜诱导力会起主导作用，且随着Reynolds数的增加薄膜诱导力最大量级增大.气泡碰撞壁面时，反弹次数与Reynolds数有着直接的联系，不同Morton数下的气泡均在相同Reynolds数附近发生气泡反弹次数的变化.      

II. Recirculation flow induced by a bubble stream rising in a viscous liquid

The recirculation flow induced by the rising motion of a bubble stream in a viscous fluid within an open-top rectangular enclosure is studied. The three-dimensional volume averaged conservation equations are solved by a control-volume method using a hybrid finite differencing scheme to describe the liquid phase hydrodynamics. The momentum exhange between the bubbles and the liquid phase is modeled with a source term equals to the volumetric buoyancy force acting on the gas in the bubble stream. The volumetric buoyancy force accounts for in line interactions between bubbles through the average gas volume fraction in the gas liquid column which depends on the size and the rising velocity of bubbles. The fluid flow within an open-top rectangular enclosure is further investigated by particle image velocimetry for a bubble stream rising in a water-glycerol solution. The measured fluid velocities in a vertical plane are compared with the predictions of the numerical model over a wide range of fluid viscosity (43 mPa s-800 mPa s) and gas flow rates. Finally, the recirculation flows resulting from the interaction of two neighbouring vertical bubble streams are studied. Received: 23 July 1997 / Revised: 19 December 1997 / Accepted: 11 May 1998     

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.     

气泡群的动态物理特性研究

假设气泡周围流场为无黏、无旋、不可压缩的理想流体,建立气泡群相互作用的三维数值模型.将多极快速傅里叶变换方法(FFTM)与高阶边界元法(HOBEM)相结合求解气泡群的运动,在达到同样计算精度时显著加快了边界积分方程的求解速度,可以在合理的时间内模拟气泡群的动态物理特性.同时为维持气泡群模拟过程中的数值稳定性,引入了弹性网格技术(EMT),并用算例验证了数值模型及算法的有效性.基于建立的数值模型,研究了不同组合的气泡群之间的相互作用,模拟和解释了各类气泡运动的物理现象,讨论了影响气泡群膨胀、坍塌、迁移及射流 关键词： 气泡群 FFTM 射流 三维     

VOF法模拟剪切流动下液滴的变形和断裂运动

本文对剪切作用下悬浮液滴在另一种不相融的液体中的变形和断裂过程进行了数值模拟.采用VOF(Volume ofFluid)法中的三维PLIC(Piecewise Linear Interface Calculation)算法实现界面的重构和输运,交错网格下投影法离散表面张力为源项的不可压缩Navier-Stokes方程....     

自由上浮气泡运动特性的光滑粒子流体动力学模拟

基于虚功原理, 在Hu X Y等和Grenier N等的研究结果基础上推导了多相流光滑粒子流体动力学(smoothed particle hydrodynamics, SPH)控制方程, 采用精度较高的黏性力和表面张力模型, 发展了一套适用于具有大密度比和大黏性比界面的多相流SPH方法. 首先, 通过施加人工位移修正, 适当背景压力和异相界面力, 使得计算全程粒子分布相对均匀, 改善了界面处的失稳现象, 防止了异相界面处粒子的非物理性穿透; 在此基础上, 利用方形流体团振荡模型对表面张力模型进行了验证, 数值结果与解析解甚为吻合; 然后采用上浮气泡经典数值算例对比研究了不同黏性力计算方法、不同核函数的适用性以及人工位移修正的效果; 最后, 对单个气泡的上浮、变形、撕裂以及垂向两个气泡的追赶、融合等现象进行了模拟, 初步揭示了气泡上浮过程中各种有趣物理现象的细节过程和动力学机理.     

高密度和高粘度比率下气液两相流动的数值模拟

本文在VOF方法的基础上,采用粗细两套网格对高密度和高粘度比率下的气液两相流动模拟进行了研究分析.在细网格中求解流体体积函数方程,在粗网格中采用交错网格求解动量方程和压力修正方程,通过粗细网格间的数据传递获得求解动量方程时需要的准确的界面密度和粘度及控制体密度,克服了高密度和高粘度比率下通过插值方法计算界面密度和粘度及控制体密度带来较大误差的困难,保证了质量和动量同时守恒.高密度和高粘度比率下气液两相流动中气液交界面处密度、速度和压力急剧变化,为了保证格式的有界性和稳定性,采用稳定的有界高阶组合格式STOIC.最后模拟了不同工况下气泡在液体中的运动,并通过实验和模拟结果验证了方法的可行性及准确性.     

Model for the dynamics of two interacting axisymmetric spherical bubbles undergoing small shape oscillations

Interaction between acoustically driven or laser-generated bubbles causes the bubble surfaces to deform. Dynamical equations describing the motion of two translating, nominally spherical bubbles undergoing small shape oscillations in a viscous liquid are derived using Lagrangian mechanics. Deformation of the bubble surfaces is taken into account by including quadrupole and octupole perturbations in the spherical-harmonic expansion of the boundary conditions on the bubbles. Quadratic terms in the quadrupole and octupole amplitudes are retained, and surface tension and shear viscosity are included in a consistent manner. A set of eight coupled second-order ordinary differential equations is obtained. Simulation results, obtained by numerical integration of the model equations, exhibit qualitative agreement with experimental observations by predicting the formation of liquid jets. Simulations also suggest that bubble-bubble interactions act to enhance surface mode instability.     

An examination of the flow induced by the motion of many buoyant bubbles

The results of direct numerical simulations of the motion of many three-dimensional buoyant bubbles in periodic domains are examined. The bubble motion is computed by solving the full Navier-Stokes equations by a parallelized finite difference/front tracking method that allows a fully deformable interface between the bubbles and the ambient fluid and the inclusion of surface tension. The governing parameters are selected such that the average rise Reynolds number is about 25. Two cases are examined. In one, the bubbles are nearly spherical; in the other, the bubbles rise with an ellipsoidal shape. The ellipsoidal bubbles show a much larger fluctuation velocity and by visualizing the flow field it is possible to show that the difference is due to larger vorticity generation and stronger interactions of the deformable bubbles. The focus here is on the early stage of the flow, when both the spherical and the deformable bubbles are nearly uniformly distributed.     

用多块多网格方法数值模拟三维粘性流动

本文给出了一个模拟三维粘性流动的数值方法．该方法来用高分辨率 ＴＶＤ Ｌａｘ－Ｗｅｎｄｒｏｆｆ格式求解三维雷诺平均Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程，使用Ｂａｌｄｗｉｎ－Ｌｏｍａｘ模型估计湍流粘性系数，用多重网格技术加速收敛，采用多块结构化网格处理复杂的物理域．文中给出了叶轮机械多个叶片排和透平排汽缸内的全三维粘性流动的数值结果．     

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     

Simulation of laminar–turbulent transition in compressible Taylor–Green flow basing on quasi-gas dynamic equations

We report the results of numerical simulation of laminar–turbulent transition in the Taylor–Green vortex for viscous compressible gas flow basing on quasi-gas-dynamic (QGD) equations. Here the QGD system is obtained by a temporal averaging of the Navier–Stokes equations. The additional dissipative terms in QGD system serve to model the effects of the unresolved subgrid scales. Comparison with direct numerical simulation and large eddy simulation reference data demonstrates that QGD numerical algorithm provides a uniform and adequate simulation of both laminar and turbulent evolution of the vortex for Reynolds numbers from 100 up to 5000, including transition.     

Calculation of shock wave propagation in water containing reactive gas bubbles

The entry of a shock wave from air into water containing reactive gas (stoichiometric acetylene–oxygen mixture) bubbles uniformly distributed over the volume of the liquid has been numerically investigated using equations describing two-phase compressible viscous reactive flow. It has been demonstrated that a steady-state supersonic self-sustaining reaction front with rapid and complete fuel burnout in the leading shock wave can propagate in this bubbly medium. This reaction front can be treated as a detonation-like front or “bubble detonation.” The calculated and measured velocities of the bubble detonation wave have been compared at initial gas volume fraction of 2 to 6%. The observed and calculated data are in satisfactory qualitative and quantitative agreement. The structure of the bubble detonation wave has been numerically studied. In this wave, the gas volume fraction behind the leading front is approximately 3–4 times higher than in the pressure wave that propagates in water with air bubbles when the other initial conditions are the same. The bubble detonation wave can form after the penetration of the shock wave to a small depth (~300 mm) into the column of the bubbly medium. The model suggested here can be used to find optimum conditions for maximizing the efficiency of momentum transfer from the pressure wave to the bubbly medium in promising hydrojet pulse detonation engines.     

I. Formation and rise of a bubble stream in a viscous liquid

The continuous emission of gas bubbles from a single ejection orifice immersed in a viscous fluid is considered. We first present a semi empirical model of spherical bubble growth under constant flow conditions to predict the bubble volume at the detachment stage. In a second part, we propose a physical model to describe the rise velocity of in-line interacting bubbles and we derive an expression for the net viscous force acting on the surrounding fluid. Experimental results for air/water-glycerol systems are presented for a wide range of fluid viscosity and compared with theoretical predictions. An imagery technique was used to determine the bubble size and rise velocity. The effects of fluid viscosity, gas flow rate, orifice diameter and liquid depth on the bubble stream dynamic were analyzed. We have further studied the effect of large scale recirculation flow and the influence of a neighbouring bubble stream on the bubble growth and rising velocity. Received: 23 July 1997 / Revised: 16 December 1997 / Accepted: 11 May 1998     

三维格子Boltzmann方法研究上升双气泡的运动特性

应用格子Boltzmann三维模型，对双气泡在静水中的运动进行数值研究.采用八点差分和十八点差分格式分别求解一阶▽φ和二阶▽²φ可以有效避免气液密度比过大造成的数值不稳定问题.结果表明：当两个相同直径的气泡在上升时，位置靠上的气泡形状变化像单气泡上升一样，而位置靠下的气泡会受到前一个气泡尾迹的影响，并有很明显的形状变化.当两个气泡直径不同时，不管初始位置如何，大气泡总会对小气泡造成强烈的影响.     

相同尺度下气泡与复杂壁面的耦合特性研究

采用格子Boltzmann方法(LBM)建立了气液固三相耦合的动力学模型,研究了相同尺度下上浮气泡与复杂壁面的相互耦合作用.首先,基于黏性流体理论,通过构建一组格子Boltzmann(LB)方程来描述气液两相的运动,并以LB离散体积力的形式计入了黏性力、表面张力和重力.同时,采用LBM中的Half-way反弹模型与有限差分格式相结合的方式进行固壁边界的处理.然后,利用本文建立的模型,对不同特征尺寸比条件下,气泡与考虑边缘效应的平面固壁和曲面固壁的耦合特性进行了研究.研究发现固壁边界条件以及特征尺寸比对气泡的运动和拓扑结构的变化都具有明显的非线性影响.最后,研究了流体属性对气泡与复杂壁面耦合规律的影响.     

水中浮升气泡的半径和速度变化

根据牛顿运动定律推导了小气泡在水中浮升过程中的速度和位置坐标的表达式;基于理想气体物态方程和球形液面的压强差公式推导了小气泡在水中浮升过程中的半径变化率;考虑小气泡在水中浮升过程的气泡半径和速度的变化,用计算机模拟了不同初始条件下的气泡群在浮升过程中半径和位置随时间的变化规律.     

求解非定常不可压N-S方程的预处理方法

应用预处理技术,对不可压非定常N-S方程使用双时间推进法求解.当沿物理时间层推进时,连续性方程和动量方程沿伪时间方向使用隐式线Gauss-Seidel迭代法求解,对流项采用三阶迎风差分法离散.通过对不同Reynolds数、不同深宽比下非定常驱动腔内流动的模拟,数值研究了预处理法计算非定常不可压粘性流动的收敛特性,分析了沿伪时间层的迭代收敛速度对流场Reynolds数的依赖特征.