粘弹流体轴对称流动的格子Boltzmann方法

基于BGK碰撞模型，通过在迁移方程中引入作用力项，建立了粘弹流体的轴对称格子Boltzmann模型．通过Chapman-Enskog展开，获得了准确的柱坐标下轴对称宏观流动方程．采用双分布函数对运动方程和本构方程进行迭代求解，模拟分析了粘弹流体管道流动，获得了流场中的速度和构型张量的分布，通过与解析解进行比较，验证了模型的准确性．研究了作为粘弹流体流动基准问题的收敛流动，对涡旋位置进行了定量分析，将回转长度的计算结果与有限体积法进行了比较，两种数值结果十分吻合．研究结果表明，模型能够准确表征粘弹流体的轴对称流动，具有较广阔的应用前景．     

非等温黏弹性复杂流动的改进SPH方法模拟

非等温黏弹性流体广泛存在于自然界和工业生产中,准确预测黏弹性流体的非等温流动机理和复杂流变特性有着重要的应用价值.文章提出一种改进的光滑粒子流体动力学(smoothed particle hydrodynamics,SPH)方法对非等温黏弹性复杂流动进行了数值模拟,其中流体的黏弹特性通过eXtended Pom-Pom本构模型来表征.为了提高模拟结果的精度,采用了一种核函数梯度的修正算法;为了灵活地施加边界条件,发展了边界粒子和虚拟粒子相联合的边界处理方法;为了消除流动过程中的拉伸不稳定性,施加了粒子迁移技术.运用改进SPH方法数值模拟了液滴撞击固壁和F型腔注塑成型问题,通过与Basilisk软件得到的结果进行比较验证了改进SPH方法求解非等温黏弹性流体的有效性.通过利用不同粒子初始间距进行计算,评价了改进SPH方法的数值收敛性.研究了非等温流动相较于等温流动的不同流动特征,深入分析了不同热流变参数对流动过程的影响.数值结果表明,文章提出的改进SPH方法可稳定、准确地描述非等温黏弹性复杂流动的传热机理、复杂流变特性和自由面变化特性.     

聚合物分子模型的Brown动力学模拟

介绍了研究聚合物分子模拟流变性质的Brown动力学模拟方法,综述了有关这方面的研究工作．在通常情况下,将分子模型的数值模拟与求解流动守恒方程的数值解法相结合,便有可能用分子模型去代替连续介质力学的本构方程,来模拟聚合物流体的复杂流动．本文介绍了这一方法的产生背景、最新进展以及优点．      

纤维悬浮液搅拌流动的数值模拟

由于缺乏适当的本构方程，对纤维悬浮液流动的研究一直局限于纤维的牛顿流体悬浮液。本文采用ＭＵＣＭ模型对作者最近提出的纤维Ｏｌｄｒｏｙｄ－Ｂ流体悬浮液的本构方程作了改进，并对锚式桨搅拌槽的二维Ｏｌｄｒｏｙｄ－Ｂ流体和牛顿流体纤维悬浮液搅拌流动作了数值模拟。模拟的结果表明，本文所用的模型和方法能有效地抑制过大局部应力的影响并合理地处理流体的记忆效应。     

黏弹流体挤出胀大的数值模拟研究进展

主要介绍了黏弹流体挤出胀大的数值模拟研究进展.给出了黏弹流体挤出胀大的数学模型,回顾了近20多年以来挤出胀大的主要数值模拟研究工作,然后对主要模拟方法的计算过程、方法特点和形成的结果进行了一定的总结.最后提出了作者对挤出胀大研究的一些看法,包括目前研究中存在的问题和相关研究的发展趋势.      

广义Maxwell黏弹性流体在两平板间的非定常流动

将分数阶微积分运算引入Maxwell黏弹性流体的本构方程，研究了黏弹性流体在两平板问的非定常流动．对于广义Maxwell黏弹性流体的分数阶导数模型，导出了对时间具有分数阶导数的特殊运动方程，利用分数阶微积分的Laplace变换理论，得到了流动的解析解．     

哑铃式聚合物分子模型流变学数值研究

本文介绍了求解哑铃式分子模型位形空间分布函数扩散方程的数值方法,以及用这种方法计算的若干分子模型的流变性质。在通常情况下,将这一方法与求解流动守恒方程的边界元法相结合,便有可能用一个得不到本构方程的分子模型去代替连续介质力学本构方程,来模拟聚合物流体的复杂流动。本文还讨论了这一方法某些令人感兴趣的特点。      

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．     

基于格子Boltzmann两相模型的粘弹流体挤出胀大分析

挤出胀大的数值模拟是非牛顿流体研究中具有挑战性的问题．本文运用格子Boltzmann方法(LBM)分析Oldroyd-B和多阶松弛谱PTT粘弹流体的挤出胀大现象，采用颜色模型模拟出口处粘弹流体和空气的两相流动，通过重新标色获得两种流体的界面，并最终获得胀大的形状．Navier-Stokes方程和本构方程的求解采用双分布函数模型．将胀大的结果与解析解、实验解和单相自由面LBM结果进行了比较，发现格子Boltzmann两相模型结果与解析解和实验结果相吻合，相比于单相模型，收敛速度更快，解的稳定性更高．研究了流道尺寸对胀大率的影响，并对挤出胀大的内在机理进行了分析．     

离心泵叶轮内宾汉流体湍流流场的数值计算

考虑宾汉流体本构关系特点,建立了任意曲线坐标系（ζ,η）下宾汉流体湍流流动的基本方程,应用压力加权校正算法,实现了速度场和压力场的关联,采用交错网格技术,解决了非物理压力振荡问题,在此基础上,对离心泵叶轮内回转面上宾汉流体湍流流动进行了数值模拟,并分析探讨了离心泵叶轮内宾汉流体湍流流动机理。     

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．     

不可压饱和粘弹性多孔介质的变分原理及其无网格模拟

基于饱和多孔介质理论,在固相和液相微观不可压,固相骨架小变形且满足线性粘弹性积分型本构关系的假定下,建立了流体饱和粘弹性多孔介质动力响应的若干Gurtin型变分原理,包括Hu-Washizu变分原理.利用所建立的变分原理,导出了流体饱和粘弹性多孔介质动力响应无网格数值模拟的离散控制方程,此方程是一个关于时间的对称微分方程组,便于分析计算.作为数值例子,研究了流体饱和粘弹性多孔柱体的一维动力响应,数值结果揭示了流体饱和粘弹性多孔柱体中波的传播特性以及固相粘性的影响.     

Nonlinear waves in fluid flow through a viscoelastic tube

A system of nonlinear equations for describing the perturbations of the pressure and radius in fluid flow through a viscoelastic tube is derived. A differential relation between the pressure and the radius of a viscoelastic tube through which fluid flows is obtained. Nonlinear evolutionary equations for describing perturbations of the pressure and radius in fluid flow are derived. It is shown that the Burgers equation, the Korteweg-de Vries equation, and the nonlinear fourth-order evolutionary equation can be used for describing the pressure pulses on various scales. Exact solutions of the equations obtained are discussed. The numerical solutions described by the Burgers equation and the nonlinear fourth-order evolutionary equation are compared.     

Viscoelastic flow past confined objects using a micro–macro approach

This paper is concerned with the numerical prediction of viscoelastic flow past a cylinder in a channel and a sphere in a cylinder using molecular-based models. The basis of the numerical method employed is a micro–macro model in which the polymer dynamics is described by the evolution of an ensemble of Brownian configuration fields. The spectral element method is used to discretize the equations in space. Comparisons are made between the macroscopic simulations based on the Oldroyd B constitutive model and microscopic simulations based on Hookean dumbbells, and excellent agreement is found. The micro–macro approach can be used to simulate models, such as the finitely extensible nonlinear elastic (FENE) dumbbell model, which do not possess a closed-form constitutive equation. Numerical simulations are performed for the FENE model. The influence of the model parameters on the flow is described and, in particular, the dependence of the drag as a function of the Weissenberg number.     

Nonisothermal two‐ and three‐dimensional flow simulations of inelastic and viscoelastic fluids by a finite‐volume method

This paper applies the finite‐volume method to computations of steady flows of viscous and viscoelastic incompressible fluids in complex two and three‐dimensional geometries. The materials adopted in the study obey different constitutive laws: Newtonian, purely viscous Carreau–Yasuda as also Upper‐Convected Maxwell and Phan‐Thien/Tanner differential models, with a Williams–Landel–Ferry (WLF) equation for temperature dependence. Specific analyses are made depending on the rheological model. A staggered grid is used for discretizing the equations and unknowns. Stockage possibilities allow us to solve problems involving a great number of degrees of freedom, up to 1 500 000 unknowns with a desk computer. In relation to the fluid properties, our numerical simulations provide flow characteristics for various 2D and 3D configurations and demonstrate the possibilities of the code to solve problems involving complex nonlinear constitutive equations with thermal effects. Copyright © 2009 John Wiley & Sons, Ltd.     

On the steady solution of linear advection problems in steady recirculating flows

Numerical modelling of non-Newtonian flows typically involves the coupling between equations of motion characterized by an elliptic behaviour, and the fluid constitutive equation, which is an advection equation linked to the fluid history. In this paper we prove that linear steady advection problems in steady recirculating flows have only one solution when the kinematics differs from a rigid motion. We also give a numerical procedure to determine this steady solution. We will describe this numerical procedure for two linear models the first will be the SFRT flow model and the second will be a simplified linear formulation of the Pom–Pom viscoelastic model.     

A finite element method for computing the flow of multi-mode viscoelastic fluids: comparison with experiments

The numerical computation of viscoelastic fluid flows with differential constitutive equations presents various difficulties. The first one lies in the numerical convergence of the complex numerical scheme solving the non-linear set of equations. Due to the hybrid type of these equations (elliptic and hyperbolic), geometrical singularities such as reentrant corner or die induce stress singularities and hence numerical problems. Another difficulty is the choice of an appropriate constitutive equation and the determination of rheological constants. In this paper, a quasi-Newton method is developed for a fluid obeying a multi-mode Phan-Thien and Tanner constitutive equation. A confined convergent geometry followed by the extrudate swell has been considered. Numerical results obtained for two-dimensional or axisymmetric flows are compared to experimental results (birefringence patterns or extrudate swell) for a linear low density polyethylene (LLDPE) and a low density polyethylene (LDPE).     

Numerical analysis of complex flow of fibre suspensions in a viscoelastic fluid

Research efforts made so far to simulate fibre suspension flows are limited to fibre suspensions in Newtonian fluids. Though short fibre composites are mostly made of polymers, lack of suitable constitutive equations for fibre suspensions in viscoelastic fluids frustrates attempts to simulate flows of these suspensions. A preliminary work done by the author led to a constitutive equation for semiconcentrated fibre suspensions in the Oldroyd-B fluid. This paper describes the mathematical formulation of the flow problems for such a suspension and the numerical procedure to solve them. Some numerical results of flow past a sphere in a tube are also presented. This paper is supported by the University of Melbourne, the National Natural Science Foundation of China and Zhejiang Province.     

Practical comparison of differential viscoelastic constitutive equations in finite element analysis of planar 4:1 contraction flow

Finite element modeling of planar 4:1 contraction flow (isothermal incompressible and creeping) around a sharp entrance corner is performed for favored differential constitutive equations such as the Maxwell, Leonov, Giesekus, FENE-P, Larson, White-Metzner models and the Phan Thien-Tanner model of exponential and linear types. We have implemented the discrete elastic viscous stress splitting and streamline upwinding algorithms in the basic computational scheme in order to augment stability at high flow rate. For each constitutive model, we have obtained the upper limit of the Deborah number under which numerical convergence is guaranteed. All the computational results are analyzed according to consequences of mathematical analyses for constitutive equations from the viewpoint of stability. It is verified that in general the constitutive equations proven globally stable yield convergent numerical solutions for higher Deborah number flows. Therefore one can get solutions for relatively high Deborah number flows when the Leonov, the Phan Thien-Tanner, or the Giesekus constitutive equation is employed as the viscoelastic field equation. The close relationship of numerical convergence with mathematical stability of the model equations is also clearly demonstrated.     

Effect of viscoelasticity on the rotation of a sphere in shear flow

When particles are dispersed in viscoelastic rather than Newtonian media, the hydrodynamics will be changed entailing differences in suspension rheology. The disturbance velocity profiles and stress distributions around the particle will depend on the viscoelastic material functions. Even in inertialess flows, changes in particle rotation and migration will occur. The problem of the rotation of a single spherical particle in simple shear flow in viscoelastic fluids was recently studied to understand the effects of changes in the rheological properties with both numerical simulations [D’Avino et al., J. Rheol. 52 (2008) 1331–1346] and experiments [Snijkers et al., J. Rheol. 53 (2009) 459–480]. In the simulations, different constitutive models were used to demonstrate the effects of different rheological behavior. In the experiments, fluids with different constitutive properties were chosen. In both studies a slowing down of the rotation speed of the particles was found, when compared to the Newtonian case, as elasticity increases. Surprisingly, the extent of the slowing down of the rotation rate did not depend strongly on the details of the fluid rheology, but primarily on the Weissenberg number defined as the ratio between the first normal stress difference and the shear stress.In the present work, a quantitative comparison between the experimental measurements and novel simulation results is made by considering more realistic constitutive equations as compared to the model fluids used in previous numerical simulations [D’Avino et al., J. Rheol. 52 (2008) 1331–1346]. A multimode Giesekus model with Newtonian solvent as constitutive equation is fitted to the experimentally obtained linear and nonlinear fluid properties and used to simulate the rotation of a torque-free sphere in a range of Weissenberg numbers similar to those in the experiments. A good agreement between the experimental and numerical results is obtained. The local torque and pressure distributions on the particle surface calculated by simulations are shown.