黏弹性流体扩展及收缩流动的格子Boltzmann模拟分析

本文应用格子Boltzmann 方法(LBM)并结合Oldroyd-B 模型,讨论了不可压缩的 Navier-Stokes 方程和平流扩散本构方程的解耦及各自求解方法,以及两类问题的边界处理格式,实现了黏弹性流体在二维1:3 扩展流道以及3:1 收缩流道中的流动的数值模拟．获得了不同雷诺数Re 和维森伯格数Wi 以及黏度vs 下流动的流线分布,计算给出了漩涡的涡心位置和大小,并分析了参数Re、Wi 和vs 对流动特点的影响．模拟结果表明本文所采用模型和边界处理方法具有良好的精度和稳定性．     

微流道内椭圆粒子黏弹性聚焦数值模拟研究

黏弹性聚焦技术借助微尺度黏弹性流体的惯性和弹性耦合效应,能够实现生物粒子在流道中心的单一位置聚焦排列,被认为是未来生物粒子计数以及检测的理想预处理单元,因而引起了广泛的关注．自然界中的生物粒子往往是非球形的,故而研究不同形状粒子在黏弹性流体中的迁移特性具有十分重要的价值．本文通过格子玻尔兹曼方法耦合浸入边界法,对椭球粒子在直流道内黏弹性流体中的聚焦行为进行了系统的数值模拟研究．结果表明,面积相同但长径比不同的椭圆粒子在黏弹性流体中有不同的旋转周期与迁移速度．长径比更大的粒子旋转周期更长,且长径比大于3.5 的粒子甚至不再有明显的旋转．长径比更大的粒子上下两侧的黏弹性力分布更加平缓,受到指向流道中心的弹性力更小,使得粒子横向迁移速度更慢从而导致了长径比不同的椭圆粒子聚焦至流道中心所需时间的差异．此外,Weissenberg 数Wi 的增加同样能够减弱粒子的旋转,使得长径比稍小的粒子也能和长径比为1.0 的圆形粒子产生明显的分离．上述数值模拟的结论,为不同长径比粒子在黏弹性流体中的聚焦与分选应用提供了重要的理论指导．     

用PSM模型模拟聚合物熔体轴对称收缩流动

采用模拟黏弹流体挤出胀大的方法，计算了IUPAC-LDPE熔体经过4：1轴对称收缩流道的流动．计算的相对涡强度、入口校正和献中的结果基本一致，给出的流场也显示出计算结果是合理的．表明该方法能够适用于用积分型PSM模型表征的黏弹流体在收缩流道内的流动模拟．     

密度不同的颗粒在流体中的沉降特性

采用格子Boltzmann方法(LBM)对雷诺数范围为5≤Re≤12的双颗粒沉降进行了直接数值模拟研究,主要关注颗粒之间的密度差异k对其周期性振动的影响。根据雷诺数颗粒沉降特性可以分成三个阶段,即当Re较小时,颗粒的振动幅度随k的增大而减小,当Re较大时则正好相反,介于两者之间存在一个临界雷诺数,在此雷诺数附近,颗粒的沉降同时具有以上两种特征。同时还研究了两个颗粒的稳定沉降结构以及重颗粒摆脱轻颗粒的条件。     

基于虚拟区域法的黏弹性流体中微生物游动的数值模拟和应用

微生物是自然生态系统的重要组成部分,掌握微生物在复杂流体中的运动特性可以为微型器件的设计制造提供理论指导.壁面效应是微生物游动研究中的重要问题之一,已有研究表明微生物在壁面附近存在复杂的行为特征.然而已有研究大多集中于微生物在牛顿流体中的游动模拟,仅有少数涉及黏弹性流体等非牛顿流体.本文采用直接力虚拟区域法与乔列斯基分解相结合的数值方法,引入Squirmer微生物游动模型,研究了微生物在黏弹性流体中的游动问题.首先给出求解黏弹性流体本构方程的数值格式;并将该方法应用于研究微生物游动中的壁面效应.研究结果表明,游动方向是影响微生物颗粒壁面效应的重要因素.流体弹性应力会对微生物产生一个反向转矩,影响微生物的游动方向,从而阻碍微生物逃离壁面.微生物颗粒在黏弹性流体中与壁面作用时间较长,几乎达到牛顿流体的两倍以上.     

双颗粒沉降的动力学分析

采用格子Boltzmann-虚拟区域方法对雷诺数范围为50≤Re≤200的双颗粒自由沉降进行了直接数值模拟。首先,研究发现双颗粒最终沉降的位置分别在通道的1/4和3/4位置附近,且与颗粒的初始间距、雷诺数以及通道宽度无关。其次,重点研究了颗粒沉降过程中所受的侧向力(与沉降方向垂直),首次揭示了侧向力的振动频率与雷诺数呈二次关系,且单颗粒的结果始终小于双颗粒的结果;研究还发现侧向力的振动频率与通道宽度近似呈幂律函数关系,且幂律指数与雷诺数有关,雷诺数越大,幂律指数的绝对值越小。最后还研究了雷诺数及通道宽度对侧向力振动振幅的影响。     

含液颗粒材料液固耦合分析的离散颗粒模型及特征线SPH法

对含液颗粒材料流固耦合分析建议了一个基于离散颗粒模型与特征线SPH法的显式拉格朗日-欧拉无网格方案。在已有的用以模拟固体颗粒集合体的离散颗粒模型[1]基础上,将颗粒间间隙内的流体模型化为连续介质,对其提出并推导了基于特征线的SPH法。数值例题显示了所建议方案在模拟颗粒材料与间隙流相互作用的能力和性能以及间隙流体对颗粒结构承载能力及变形的影响。     

表面活性剂流体弹性应力对颗粒沉降的影响

颗粒在粘弹性表面活性剂流体中的沉降问题是复杂固液两相流研究的基础问题。采用实验和数值模拟的方法研究了单颗粒在粘弹性表面活性剂流体中的沉降过程。实验结果表明,粘弹性表面活性剂流体的粘弹性会引起颗粒的终端速度随时间产生波动。Giesekus本构方程可以描述颗粒在表面活性剂流体中沉降的非线性剪切变稀行为和弹性导致的拉伸变形。颗粒在粘弹性表面活性剂流体中沉降时其尾部会出现负尾迹现象,负尾迹区随着松弛时间的增大向下游延伸,表征流体弹性的松弛时间越大,负尾迹区越长。颗粒表面剪切速率大于临界剪切速率时,负尾迹的出现使颗粒在粘弹性表面活性剂流体中沉降所受曳力减小,沉降速度增加;颗粒表面剪切速率小于临界剪切速率时,粘弹性表面活性剂流体负尾迹区的拉伸效应与颗粒表面的弹性应力的共同作用,导致颗粒终端速度随着松弛时间的增加先增大后减小。     

非牛顿流体在渐变管中压力和剪切应力的二次摄动解

本文利用双摄动方法求解缓慢变化管道中Johnson-Segalman(J-S)流体流动的渐近解．将管道的扩张（或收缩）角度和粘弹性参数分别作为双摄动的参数，由流函数和涡量函数的形式，推导出压力和壁面剪切应力的渐近解．在此基础上，分析了管道角度，粘弹性参数和雷诺数等参数对压力以及剪切力影响．主要结论如下：(1) 管道扩张角度增加时，流向同一位置处径向压力以及壁面剪切应力随扩张角度减小；(2) 在同一扩张管道中，径向压力随着流向位移减小，收缩管与之相反；(3) 扩张角度与雷诺数对流场起主导作用，粘弹性系数起次要作用．     

饱和黏弹性多孔介质中的平面波及能量耗散

研究了流体饱和不可压黏弹性多孔介质中的非均匀平面波及其能量流和能量耗散规律. 在流 相和固相物质微观不可压、固相骨架宏观服从积分型本构关系和小变形的假定下，利用 Helmholtz分解，得到了饱和黏弹性多孔介质中非均匀平面波的一般解以及纵波、横波相速 度和衰减率等的解析表达式，分析了平面波传播矢量和衰减矢量之间的关系. 数值结果表明 孔隙流体与固相骨架间的相互作用以及固相骨架的黏性对波的相速度、衰减率等有着显著的 影响. 同时，得到了饱和黏弹性多孔介质的能量方程，给出了能量流矢量和能量耗散率. 对 非均匀平面纵波和横波，推导了平均能量流矢量和平均能量耗散率的解析表达式.     

SIMULATION OF SEDIMENTATION OF TWO CIRCULAR PARTICLES WITH COLLISION CONSIDERED IN VERTICAL CHANNEL

D2Q9 model of lattice Boltzmann equation method was used to simulate the sedimentation of two circular particles in a bounded two dimension channel. The characteristics of the sedimentation shows some periodicity for the Reynolds number Re chosen, 0.1-20. The larger the Reynolds number, the stronger the interaction between the two particles and the larger the transversal displacements. For large Re, the two particles leading alternately; for small Re, the initially leading particle will keep its leading position and for moderate Re, the initially upper particle will get leading position and keep it. The influence of the initially relative position of the two particles on sedimentation is small. The width of the channel won＇t change the characteristics of the sedimentation as a whole, but will change the period of the sedimentation. The wider the channel, the longer the period will be.     

Investigation of turbulence and skin friction modification in particle-laden channel flow using lattice Boltzmann method

Interaction between turbulence and particles is investigated in a channel flow. The fluid motion is calculated using direct numerical simulation (DNS) with a lattice Boltzmann (LB) method, and particles are tracked in a Lagrangian framework through the action of force imposed by the fluid. The particle diameter is smaller than the Kolmogorov length scale, and the point force is used to represent the feedback force of particles on the turbulence. The effects of particles on the turbulence and skin friction coefficient are examined with different particle inertias and mass loadings. Inertial particles suppress intensities of the spanwise and wall-normal components of velocity, and the Reynolds shear stress. It is also found that, relative to the reference particle-free flow, the overall mean skin-friction coefficient is reduced by particles. Changes of near wall turbulent structures such as longer and more regular streamwise low-speed streaks and less ejections and sweeps are the manifestation of drag reduction.     

椭圆颗粒在剪切流中旋转特性的数值研究

研究颗粒在流体剪切作用下的运动特性是理解和预测颗粒悬浮流流动行为的关键.当流体的惯性不能忽略时,颗粒的运动往往变得非常复杂.本文采用格子Boltzmann方法对中等雷诺数下椭圆颗粒在剪切流中的旋转运动进行了模拟.首先,研究了雷诺数(0Re 170)的影响,结果表明当雷诺数低于临界值时,颗粒以周期性的方式旋转,角速度最小时对应的长轴方向随着雷诺数的增大而逐渐远离水平方向,而且这一倾角与雷诺数呈分段线性关系;当雷诺数大于临界值时,椭圆形颗粒最终保持静止状态,且静止时的转角与雷诺数呈幂函数关系,雷诺数越大,转角越小,椭圆的长轴越远离水平位置.其次,研究了椭圆颗粒的长短轴之比α(1α10)的影响,结果表明颗粒旋转的周期与α呈幂函数关系,α越大,颗粒旋转周期越小.此外,当α超过临界值时,颗粒也在水平位置附近保持静止状态,此时的转角与α也呈幂函数关系,α越大,转角越小.研究还发现,当雷诺数较大时椭圆颗粒在旋转过程中会产生过冲现象.     

Bingham fluid simulation with the incompressible lattice Boltzmann model

The Bingham fluid flow is numerically studied using the lattice Boltzmann method by incorporating the Papanastasiou exponential modification approach. The He–Luo incompressible lattice Boltzmann model is employed to avoid numerical instability usually encountered in non-Newtonian fluid simulations due to a strong non-linear relationship between the shear rate tensor and the rate-of-strain tensor. First, the value of the regularization parameter in Bingham fluid mimicking is analyzed and a method to determine the value is proposed. Then, the model is validated by pressure-driven planar channel flow and planar sudden expansion flow. The velocity profiles for the pressure-driven planar channel flow are in good agreement with analytical solutions. The calculated reattachment lengths for a 2:1 planar sudden expansion flow also agree well with the available data. Finally, the Bingham flow over a cavity is studied, and the streamlines and yielded/unyielded regions are discussed.     

Investigation of the characteristics of particulate flows through fibrous filters using the lattice Boltzmann method

A fibrous filter is one of the most common systems used to separate suspended particles from air.Two important factors(i.e.,the pressure drop and capture efficiency) are usually used to evaluate the performance of this type of filter.This study considers three two-dimensional arrangements of fibers(parallel,staggered,and random) to geometrically model fibrous media.The lattice Boltzmann method is employed to numerically simulate fluid flow through the filter.The Lagrangian form of the equation of motion of a particle is numerically solved to track the path of each particle in the flow field,where a one-way interaction between the fluid and particles is considered.The effects of pertinent parameters such as the fiber arrangement,solid volume fraction,particle-to-fiber diameter ratio,particle-to-fluid density ratio,Reynolds number,Stokes number,and size of the fibrous medium on the pressure drop and capture efficiency are studied.The obtained results are compared with existing empirical and theoretical findings and discussed.     

Oldroyd-B黏弹性液滴弹跳行为的改进SPH模拟

基于光滑粒子流体动力学SPH(Smoothed Particle Hydrodynamics)方法对Oldroyd-B黏弹性液滴撞击固壁面产生的弹跳行为进行了模拟与分析。首先,为了解决SPH模拟黏弹性自由表面流出现的张力不稳定性问题,联合粒子迁移技术提出了一种改进SPH方法。然后,对Oldroyd-B黏弹性液滴撞击固壁面产生的铺展行为进行了改进SPH模拟,与文献结果的比较验证了方法的有效性。最后,通过降低Reynolds数捕捉到了液滴的弹跳行为;并在此基础上,分析了液滴黏度比、Weissenberg数和Reynolds数对液滴弹跳行为的影响。结果表明,改进SPH方法可有效地模拟黏弹性自由表面流问题;液滴黏度比、Weissenberg数和Reynolds数对液滴最大回弹高度均有显著的影响。     

Numerical analysis of axisymmetric and planar sudden expansion flows for laminar regime

In this study, the Navier–Stokes equations are solved numerically for axisymmetric and planar sudden expansion flows. The flow is considered laminar and steady state, and the fluid is incompressible. Finite difference equations are obtained using a control volume method in a non‐staggered grid arrangement, and solved by line‐by‐line TDMA technique using the SIMPLEM (SIMPLEM‐Modified) algorithm. Calculations are performed for higher expansion ratios, β, ranging from 1.5 to 10 and Reynolds numbers from 0.1 to 500. Results are presented in terms of streamlines, relative eddy intensity, location of the eddy center, and the eddy reattachment length depending on Re number and β values for both axisymmetric and planar sudden expansions. It is aimed to provide a picture of the effects of high values of expansion ratio and Reynolds number on the sudden expansion flow. As a result, it is found that the flow characteristics keep their structure for both higher expansion ratios and higher Reynolds numbers. Further, correlations were developed for the nondimensional eddy reattachment length, location of the eddy center and the relative eddy intensity, which have agreeable results to the computed results available from the literature. Copyright © 2010 John Wiley & Sons, Ltd.     

The simulation of turbulent particle‐laden channel flow by the Lattice Boltzmann method

We perform direct numerical simulation of three‐dimensional turbulent flows in a rectangular channel, with a lattice Boltzmann method, efficiently implemented on heavily parallel general purpose graphical processor units. After validating the method for a single fluid, for standard boundary layer problems, we study changes in mean and turbulent properties of particle‐laden flows, as a function of particle size and concentration. The problem of physical interest for this application is the effect of water droplets on the turbulent properties of a high‐speed air flow, near a solid surface. To do so, we use a Lagrangian tracking approach for a large number of rigid spherical point particles, whose motion is forced by drag forces caused by the fluid flow; particle effects on the latter are in turn represented by distributed volume forces in the lattice Boltzmann method. Results suggest that, while mean flow properties are only slightly affected, unless a very large concentration of particles is used, the turbulent vortices present near the boundary are significantly damped and broken down by the turbulent motion of the heavy particles, and both turbulent Reynolds stresses and the production of turbulent kinetic energy are decreased because of the particle effects. We also find that the streamwise component of turbulent velocity fluctuations is increased, while the spanwise and wall‐normal components are decreased, as compared with the single fluid channel case. Additionally, the streamwise velocity of the carrier (air) phase is slightly reduced in the logarithmic boundary layer near the solid walls. Copyright © 2015 John Wiley & Sons, Ltd.