液态金属熔池中气泡-液体两相湍流的数值模拟研究

应用欧拉-欧拉双流体模型,以及分别描述气泡和液体湍流的两相湍流模型,描述液态金属中气体射流发泡过程的两相流动及气泡分布。与实验结果的对比表明,本模型的预测能力优于前人未考虑气相湍流的模型。考查了液体物性和气泡尺寸对流场特性的影响,结果发现,液体密度越低,气泡尺寸越小,气泡分布就越均匀。     

垂直壁面附近上升单气泡的弹跳动力学研究

采用高速摄影技术结合阴影法,对静止水中垂直壁面附近上升单气泡运动进行实验研究,对比气泡尺度及气泡喷嘴与壁面之间的初始无量纲距离(S~*)对气泡上升运动特性的影响,分析气泡与壁面碰撞前后,壁面效应与气泡动力学机制及能量变化规律.结果表明,对于雷诺数Re≈580～1100,无量纲距离S~*2～3时,气泡与壁面碰撞且气泡轨迹由无约束条件下的三维螺旋转变成二维之字形周期运动;当S~* 2～3时,壁面效应减弱,有壁面约束的气泡运动与无约束气泡运动特性趋于一致.气泡与壁面碰撞前后,壁面效应导致横向速度峰值下降为原峰值的70%,垂直速度下降50%;气泡与壁面碰撞前,通过气泡中心与壁面距离(x/R)和修正的斯托克斯数相关式可预测垂直速度的变化规律.上升气泡与壁面碰撞过程中,气泡表面变形能量单向传输给气泡横向动能,使得可变形气泡能够保持相对恒定的弹跳运动.提出了气泡在与壁面反复弹跳时的平均阻力系数的预测模型,能够很好地描述实验数据反映出的对雷诺数Re、韦伯数We和奥特沃斯数Eo等各无量纲参数的标度规律.     

基于Level Set方法的气-液-固三相流动模型与模拟

采用基于Level Set方法与离散颗粒模型相结合的方法,建立了一个用于描述气液固三相流动的新模型.模型耦合了颗粒与气泡、颗粒与液相以及气泡与液相之间的相互作用.应用该模型对液固悬浮液中的典型现象--气泡的单孔及多孔形成过程以及颗粒夹带现象进行了三维模拟,检验了其可行性.并进一步研究了颗粒的存在对气泡的形成与上升过程的影响以及气泡诱导的液相流动对颗粒行为的影响.研究结果表明,所提出的模型能够真实地预测三相流中气泡与颗粒分散相的特征,为研究多尺度的三相流动提供了一种新途径.     

利用欧拉-拉格朗日方法预测层流泡状流的含气率分布

利用欧拉-拉格朗日方法，提出了用于预测竖直管道内绝热层流泡状流中含气率分布的三维模型。该模型能够跟踪单独的气泡轨迹，从而获取更多的界面力信息；同时气泡尺寸可以作为参数之一引入模型，使含气率分布的计算更为方便。模型中分析了绝热层流泡状流中气泡的各项受力表达式，建立了两种描述方法下的气液两相间的耦合关系。利用现有实验数据对模型进行的检验表明，该模型能够预测一定尺寸范围内气泡的分布；气泡径向分布主要取决于气泡所受侧向提升力。对于更大尺寸的气泡，气泡变形和气泡尾迹与当地流场间相互作用将对侧向提升力产生很大影响。     

垂直壁面附近上升单气泡的弹跳动力学研究

采用高速摄影技术结合阴影法,对静止水中垂直壁面附近上升单气泡运动进行实验研究,对比气泡尺度及气泡喷嘴与壁面之间的初始无量纲距离 ($S^{\ast}$)对气泡上升运动特性的影响,分析气泡与壁面碰撞前后,壁面效应与气泡动力学机制及能量变化规律.结果表明,对于雷诺数$Re \approx 580 \sim 1100$,无量纲距离$S^{\ast } <2 \sim3$时,气泡与壁面碰撞且气泡轨迹由无约束条件下的三维螺旋转变成二维之字形周期运动;当$S^{\ast } >2 \sim3$时,壁面效应减弱,有壁面约束的气泡运动与无约束气泡运动特性趋于一致.气泡与壁面碰撞前后,壁面效应导致横向速度峰值下降为原峰值的70%,垂直速度下降50%;气泡与壁面碰撞前,通过气泡中心与壁面距离($x/R$)和修正的斯托克斯数相关式可预测垂直速度的变化规律.上升气泡与壁面碰撞过程中,气泡表面变形能量单向传输给气泡横向动能,使得可变形气泡能够保持相对恒定的弹跳运动.提出了气泡在与壁面反复弹跳时的平均阻力系数的预测模型,能够很好地描述实验数据反映出的对雷诺数${Re}$、韦伯数${We}$和奥特沃斯数${Eo}$等各无量纲参数的标度规律.      

基于遗传算法的低压液压管路模型参数识别

为了合理预测伴随气泡和气穴的低压液压管路压力瞬态脉动,提出了用改进遗传算法对低压液压管路压力瞬态脉动模型进行参数辨识的新方法.给出了用来描述管路流动特性的瞬态脉动数学模型,建立了用来计算伴随气泡和气穴的液压管路瞬态下气泡体积和气穴体积的数学模型.构造了基于最小二乘法的适应度模型,探讨了遗传操作方式及算法终止准则,采用了算术交叉同线性逼近相结合的改进算术交叉算子进行交叉操作,给出了模型参数寻优的算法流程.实现了对低压液压管路压力瞬态脉动数学模型的参数识别,得到了参数优化后的低压液压管路压力瞬态脉动模型.仿真结果与实验数据的比较表明在低压液压管路瞬态模型中,用改进遗传算法来识别模型中的未知参数的方法是可行的、有效的.     

通气空泡尾部气泡流仿真和特性分析

基于欧拉-欧拉双流体模型对通气空泡尾部气泡流进行数值仿真, 并采用基于多尺寸分组模型的总体平衡方法预估气泡尺寸分布. 应用改进后湍流耗散系数计算模型, 考虑了气泡体积含量对在湍流作用下气泡扩散现象的影响. 基于上述模型对两种试验工况下流场进行了数值仿真.结果表明模型对空泡尾部回流区特性进行了准确预示, 在回流区高湍流度作用下气泡迅速破碎成小气泡. 并进一步得到试验体尾流区空泡体积分数和速度分布. 尾流区水流速度分布保持了流体经过非流线型对称体时产生的尾流分布规律. 仿真结果与试验数据相一致, 模型适用性得到验证.      

同相气泡耦合特性实验研究

设计实验, 利用电火花打火生成气泡来研究两个气泡之间以及两个气泡与自由面的相互作用, 在实验过程中, 精确控制打火电路, 使两个电火花气泡的生成时间间隔控制在67\mus以内, 实现了气泡的同相生成. 大量实验后发现, 两气泡相互作用过程中可能会出现融合、蘑菇状气泡、对射流、射流方向逆转、反向射流等现象, 自由面附近不同安置方式的两同相气泡会出现不同的脉动形式. 通过系列实验提出了气泡之间的无量纲距离、无量纲周期差等参数来描述气泡耦合特性, 为气泡群的相互作用提供实验依据.}      

橡胶弹性材料的一种混合本构模型

该文探讨不可压缩橡胶弹性材料的本构模型.考虑到小变形时分子链的端矢分布符合高斯函数,而大变形时符合非高斯函数,提出一个混合模型,用高斯链网络模型来描述小变形而用8链网络模型来描述大变形.引入权重函数,使小变形和大变形情况下混合模型分别退化或趋于高斯链网络模型和8链网络模型.由Treloar拉伸实验数据拟合得到模型参数,通过这些材料参数混合模型对等双轴拉伸和纯剪切变形模式的预测结果与Tre-loar实验数据基本吻合,说明混合模型具有同时描述不同变形模式的能力.通过比较分析,混合模型的总体预测精度均优于高斯链网络模型和8链网络模型,特别是对剪切变形.     

气泡多周期运动时引起的流场压力与速度

假设水下爆炸气泡的内部气体在膨胀收缩过程中满足绝热条件,周围流体无黏无旋不可压缩. 基于势流理论,采用边界元法研究气泡动力学行为,重点关注气泡引起的流场脉动载荷以及滞后流特性,给出了相关的理论推导和数值计算方法. 通过将数值结果与解析解、实验值进行对比,数值模型的收敛性和有效性能够得到保证. 利用编写的程序进行计算和分析,发现在气泡加速膨胀阶段,流场压力在气泡径向不一定是逐渐衰减,还有可能以先增后减的规律变化;气泡射流后,为了能够继续描述环状气泡的运动以及流场特性,将此时的流场分为无旋场和一个布置在气泡内部涡环的叠加,计算过程中采用了一些数值技巧处理气泡的拓扑结构,得以连续模拟多个周期的气泡运动. 环状气泡具有相对较高的上浮迁移速度,而且在其顶部和底部附近分别形成两个高压区,顶部的高压区峰值相对较大,底部的高压区范围相对较大. 环状气泡中心轴上的流场速度会在气泡中心有一个加速过程,在气泡顶部附近又迅速减小.      

Comparison of several models for multi-size bubbly flows on an adiabatic experiment

This paper deals with the modelling and numerical simulation of isothermal bubbly flows with multi-size bubbles. The study of isothermal bubbly flows without phase change is a first step towards the more general study of boiling bubbly flows. Here, we are interested in taking into account the features of such isothermal flow associated to the multiple sizes of the different bubbles simultaneously present inside the flow. With this aim, several approaches have been developed. In this paper, two of these approaches are described and their results are compared to experimental data, as well as to those of an older approach assuming a single average size of bubbles. These two approaches are (i) the moment density approach for which two different expressions for the bubble diameter distribution function are proposed and (ii) the multi-field approach. All the models are implemented into the NEPTUNE_CFD code and are compared to a test performed on the MTLOOP facility. These comparisons show their respective merits and shortcomings in their available state of development.     

Properties and Averaged Equations for Flows of Bubbly Liquids

Averaged properties of bubbly liquids in the limit of large Reynolds and small Weber numbers are determined as functions of the volume fraction, mean relative velocity, and velocity variance of the bubbles using numerical simulations and a pair interaction theory. The results of simulations are combined with those obtained recently for sheared bubbly liquids [19] and the mixture momentum and continuity equations to propose a complete set of averaged equations and closure relations for the flows of bubbly liquids at large Reynolds and small Weber numbers.     

A novel fuzzy-logic based method for determination of individual bubble velocity and size from dual-plane ultrafast X-ray tomography data of two-phase flow

Ultrafast X-ray tomography enables non-invasive imaging of gas-liquid flows with high spatial and temporal resolution. While it is relatively straightforward to extract e.g. gas fraction profiles from cross-sectional tomographic images, the extraction of bubble and gas-liquid interface information requires advanced image processing techniques. Thereby it is an important necessity to transform the temporal scale in the scanned sequences into a corresponding length scale for obtaining correct volumetric information. For bubbly flows this means that the velocity of the dispersed phase, e.g. the gas bubbles, has to be determined from dual-plane scans. A common and widely applied method to obtain gas phase velocities is cross-correlating the image sequences of the two scanning planes. This gives an averaged velocity for each position in the cross-section. In the present work, a new method is introduced, which determines the velocity of individual gas bubbles. This new method is termed as “bubble twinning method”, because it tries to identify twin-bubbles in both scanning planes. The developed algorithm compares essential bubble parameters, that is, volume, position and residence time in the slice, by applying a fuzzy-logic based membership function approach. The algorithm was tested for bubbly flow as well as slug flow conditions. Results are compared with established theoretical predictions as well as the cross-correlation method.     

Interfacial area concentration in gas–liquid bubbly to churn flow regimes in large diameter pipes

This study performed a survey on existing correlations for interfacial area concentration (IAC) prediction and collected an IAC experimental database of two-phase flows taken under various flow conditions in large diameter pipes. Although some of these existing correlations were developed by partly using the IAC databases taken in the low-void-fraction two-phase flows in large diameter pipes, no correlation can satisfactorily predict the IAC in the two-phase flows changing from bubbly, cap bubbly to churn flow in the collected database of large diameter pipes. So this study presented a systematic way to predict the IAC for the bubbly-to-churn flows in large diameter pipes by categorizing bubbles into two groups (group 1: spherical or distorted bubble, group 2: cap bubble). A correlation was developed to predict the group 1 void fraction by using the void fraction for all bubble. The group 1 bubble IAC and bubble diameter were modeled by using the key parameters such as group 1 void fraction and bubble Reynolds number based on the analysis of Hibiki and Ishii (2001, 2002) using one-dimensional bubble number density and interfacial area transport equations. The correlations of IAC and bubble diameter for group 2 cap bubbles were developed by taking into account the characteristics of the representative bubbles among the group 2 bubbles and the comparison between a newly-derived drift velocity correlation for large diameter pipes and the existing drift velocity correlation of Kataoka and Ishii (1987) for large diameter pipes. The predictions from the newly-developed two-group IAC correlation were compared with the collected experimental data in gas–liquid bubbly to churn flow regimes in large diameter pipes and their mean absolute relative deviations were obtained to be 28.1%, 54.4% and 29.6% for group 1, group 2 and all bubbles respectively.     

On the numerical study of bubbly flow created by ventilated cavity in vertical pipe

The dispersion of bubbles into a down-liquid flow in a vertical pipe is investigated. At low flow rates, the intended design of a swarm of discrete bubbles is achieved. At high flow rates, a ventilated cavity is nonetheless formed, which is attached close to the gas sparger. Behind this ventilated cavity, three different flow regimes characterize the complex bubbly flow field downstream of the down-liquid flow: vortex region with high void fraction, transitional region and pipe flow region. In this study, a numerical model that solved the entire development of the gas–liquid flow including the extended single-phase liquid region upstream to the wall-jet and recirculating-vortex zones in order to allow a more realistic determination of the boundary conditions of the down-liquid flow was adopted. Coupling with the Eulerian–Eulerian two-fluid model to solve the respective gas and liquid phases, a population balance model was also applied to predict the bubble size distribution in the wake right below the cavity base as well as further downstream in the transitional and fully-developed pipe flow regions. The numerical model was evaluated by comparing the numerical results against the data derived from theoretical, numerical and experimental approaches. Prediction of the Sauter mean bubble diameter distributions by the population balance approach at different axial locations confirmed the dominance of breakage due to the high turbulent intensity below the ventilated cavity which led to the generation of small gas bubbles at high void fraction. Further downstream, the coalescence effect dominated leading to merging of the small bubbles to form bigger bubbles.     

A DNS study of laminar bubbly flows in a vertical channel

Direct numerical simulations are used to examine laminar bubbly flows in vertical channels. For equal size nearly spherical bubbles the results show that at steady state the number density of bubbles in the center of the channel is always such that the fluid mixture there is in hydrostatic equilibrium. For upflow, excess bubbles are pushed to the walls, forming a bubble rich wall-layer, one bubble diameter thick. For downflow, bubbles are drawn into the channel center, leading to a wall-layer devoid of bubbles, of a thickness determined by how much the void fraction in the center of the channel must be increased to reach hydrostatic equilibrium. The void fraction profile can be predicted analytically using a very simple model and the model also gives the velocity profile for the downflow case. For the upflow, however, the velocity increase across the wall-layer must be obtained from the simulations. The slip velocity of the bubbles in the channel core and the velocity fluctuations are predicted reasonably well by results for homogeneous flows.     

Direct numerical simulation of wall turbulent flows with microbubbles

The marker‐density‐function (MDF) method has been developed to conduct direct numerical simulation (DNS) for bubbly flows. The method is applied to turbulent bubbly channel flows to elucidate the interaction between bubbles and wall turbulence. The simulation is designed to clarify the structure of the turbulent boundary layer containing microbubbles and the mechanism of frictional drag reduction. It is deduced from the numerical tests that the interaction between bubbles and wall turbulence depends on the Weber and Froude numbers. The reduction of the frictional resistance on the wall is attained and its mechanism is explained from the modulation of the three‐dimensional structure of the turbulent flow. Copyright © 2001 John Wiley & Sons, Ltd.     

Numerical simulation of circulation in gas-liquid column reactors: isothermal, bubbly, laminar flow

The gas-liquid flow inside a circular, isothermal column reactor with a vertical axis has been studied using numerical simulations. The flow is assumed to be in the laminar, bubbly flow regime which is characterized by a suspension of discrete air bubbles in a continuous liquid phase such as glycerol water. The mathematical formulation is based on the conservation of mass and momentum principle for the liquid phase. The gas velocity distribution is calculated via an empirically prescribed relative velocity as a function of void fraction. The interface viscous drag forces are prescribed empirically. For some cases a profile shape is assumed for the void ratio distribution. The influence of various profile shapes is investigated. The results are compared with those where the void ratio distribution is calculated from the conservation of mass equation. The mathematical model has been implemented by modifying a readily available computer code for single-phase newtonian fluid flows. The numerical discretization is based on a finite volume approach. The predictions show a good agreement with measurements. The circulation pattern seems not to be so sensitive to the actual shape of the void fraction profiles, but the inlet distribution of it is important. A significantly different flow pattern results when the void fraction distribution is calculated from the transport equation, as compared to those with a priori prescribed profiles. When the void fraction is uniformly distributed over the whole distributor plate, no circulation is observed. Calculations also show that even the two-phase systems with a few discrete bubbles can be simulated successfully by a continuum model.     

EULERIAN–LAGRANGIAN COMPUTATIONS ON PHASE DISTRIBUTION OF TWO-PHASE BUBBLY FLOWS

A comprehensively theoretical model is developed and numerically solved to investigate the phase distribution phenomena in a two-dimensional, axisymmetric, developing, two-phase bubbly flow. The Eulerian approach treats the fluid phase as a continuum and solved Eulerian conservation equations for the liquid phase. The Lagrangian bubbles are tracked by solving the equation of motion for the gas phase. The interphase momentum changes are included in the equations. The numerical model successfully predicts detailed flow velocity profiles for both liquid and gas phases. The development of the wall-peaking phenomenon of the void fraction and velocity profiles is also characterized for the developing flow. For 42 experiments in which the mean void fraction is less than 20 per cent, numerical calculations demonstrate that the predictions agree well with Liu's experimental data. © 1997 by John Wiley & Sons, Ltd.