颗粒在黏弹性流体扩张和收缩流中沉降的格子Boltzmann模拟分析

对于Oldroyd-B型黏弹性流体，本文应用格子Boltzmann方法(LBM)，实现了流体在二维1:3扩张流道及3:1收缩流道中流动的数值模拟，获得了黏弹性流体在扩张和收缩流道中的流场分布．结合颗粒的受力和运动规则，基于点源颗粒模型，数值分析了颗粒在扩张流和收缩流中的沉降过程和特征，讨论了颗粒相对质量和起始位置以及雷诺数Re和威森伯格数Wi对颗粒沉降特征的影响．结果表明，颗粒相对质量和起始位置以及Re对颗粒沉降轨迹和落点影响较大，而Wi的影响则较小．     

用PSM模型模拟聚合物熔体的长口模挤出胀大

 以作者提出的模拟黏弹流体挤出胀大流动的方法为基础，计算了 IUPAC-LDPE熔体经过长圆形口模的挤出胀大. 计算结果同文献的报道 基本一致，表明作者提出的方法适于黏弹聚合物熔体的挤出胀大模拟.     

积分型Maxwell流体挤出胀大的数值模拟

应用Luo提出的基于常规有限单元的应力计算方法和范毓润回避奇点的方法,模拟了积分型Maxwell黏弹流体的挤出胀大流动,计算得到了Weissenberg数达1．0下的合理结果。     

黏弹流体流动的数值模拟研究进展

综述了黏弹流体流动数值模拟的研究进展,突出介绍近十年来有限元法在黏弹流体流动数值模拟研究中取得的成果,通过动量方程的适当变形和本构方程离散权函数的合理选择,可以显著增强数值计算的稳定性。得到较高Weissenberg数下的解,同时文中对黏弹流体流动数值模拟中本构方程的应用、非等温情况和三维空间下的研究进行了介绍。     

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方法的挤出胀大的数值模拟

将单相格子Boltzmann方法(lattice Boltzmann method, LBM)引入到粘弹流体的瞬态挤出胀大的数值模拟中,建立了基于双分布函数的自由面粘弹性流动格子Boltzmann模型．分析得到的流道中流动速度分布和构型张量结果与理论解十分吻合．对粘弹流体瞬态挤出胀大过程进行了模拟,并分析了运动粘度比和剪切速率对挤出胀大率的影响,得到的胀大率结果与理论分析和其它模拟结果基本一致．表明给出的LBM可以捕捉挤出胀大的瞬态效应．     

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.     

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．     

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.      

基于黏弹性的微注射成型流动模拟

应用有限元方法研究了微注射成型中瞬态、可压缩、非牛顿熔体流动的黏弹性对流动前沿及流动平衡的影响。基于Phan-Thien-Tanner模型建立了熔体流动的本构方程,利用Hele-Shaw假设和简化建立了瞬态、可压缩、非牛顿熔体流动的连续性方程、动量方程、能量方程;为了有效地描述微注射成型的尺寸效应,采用了边界滑移和表面张力边界条件。通过分部积分和待定系数法导出了带有边界信息的变分方程和求解应力分量的半解析公式,构造了有限元离散求解及超松驰迭代算法。模拟结果表明:熔体的黏弹性对浇口附近的压力和后续的熔体流动前沿有重要影响;与黏性模型相比,黏弹性模型可以控制模拟压力的快速增长,减少不同型腔之间的充填差异,与短射实验结果也更吻合。     

Two-dimensional viscoelastic flows: experimentation and modeling

Extensive experimental data on the birefringence in converging and diverging flows of a polymeric melt have been obtained. The birefringence and pressure drop measurements were carried out in working cells of planar geometry having different contraction angles and contraction ratios. For investigation of diverging or abrupt expansion flow, the direction of flow in the cells was reversed. The theoretical predictions are based upon the Leonov constitutive equation and a finite element scheme with streamwise integration.In contrast to Newtonian and second-order fluids, viscoelastic fluids at high shear rates show significant differences in pressure drop and birefringence (i.e. stresses) in converging and diverging flows. For a constant flow rate, the pressure drop is higher and the birefringence smaller in diverging flows than in converging flows. This difference increases with increasing flow rate. Further, for the same contraction ratio but different contraction angles, the birefringence maximum increases considerably with contraction angle. In addition, an increase in contraction ratio has the same effect.The viscoelastic constitutive equation of Leonov has been shown to describe all the above viscoelastic effects observed in the experiments. In general, a reasonable agreement between theory and experiment has been obtained, which shows the usefulness of the Leonov model in describing actual flows.     

Three‐dimensional simulation of planar contraction viscoelastic flow by penalty finite element method

The planar contraction flow is a benchmark problem for the numerical investigation of viscoelastic flow. The mathematical model of three‐dimensional viscoelastic fluids flow is established and the numerical simulation of its planar contraction flow is conducted by using the penalty finite element method with a differential Phan‐Thien–Tanner constitutive model. The discrete elastic viscous split stress formulation in cooperating with the inconsistent streamline upwind scheme is employed to improve the computation stability. The distributions of velocity and stress obtained by simulation are compared with that of Quinzani's experimental results detected by laser–doppler velocimetry and flow‐induced birefringence technologies. It shows that the numerical results agree well with the experimental results. The numerical methods proposed in the study can be well used to predict complex flow patterns of viscoelastic fluids. Copyright © 2009 John Wiley & Sons, Ltd.     

A numerical method for steady and nonisothermal viscoelastic fluid flow for high Deborah and Péclet numbers

A combined finite element/streamline integration method is presented for nonisothermal flows of viscoelastic fluids. The attention is focused on some characteristic problems that arise for numerical simulation of flows with high Deborah and Péclet numbers. The two most important problems to handle are the choice of an outflow boundary condition for not completely developed flow and the treatment of the dissipative term in the temperature equation. The ability of the numerical method to handle high Deborah and Péclet numbers will be demonstrated on a contraction flow of an LDPE melt with isotropic and anisotropic heat conductivity. The influence of anisotropic heat conduction and the difference between the stress work and mechanical dissipation will be discussed for contraction flows. Received:  4 February 1997 Accepted: 23 October 1997     

A method for implementing time-integral constitutive equations in commercial CFD packages

A method is described for obtaining viscoelastic flow solutions, based upon time-integral constitutive equations, using a general purpose CFD package. The method is general enough to be applied to any available software that has rudimentary input and output facilities and can solve a Stoke's flow problem. From this basis, flexibility of choice of constitutive equation and computational techniques is available. The method is presented in a form appropriate for solving both planar and axisymmetric flows. Delaunay triangulation is used to reconstruct a mesh for external code, and stress computation procedures are performed on this mesh. The method has only two particular requirements for the CFD package used – it must be able to output nodal values (of position and velocity) to file and it must be able to read body-forces from a file. Two methods of velocity adjustment were compared: an incremental method and a method whereby the viscoelastic stresses were incorporated directly as body-forces. Results and convergence from the two methods were found to be essentially identical, hence the direct body-force method (which is considerably easier to implement) is described in detail. The method is applied to a well-known flow problem of LDPE melt through a 4 : 1 abrupt contraction axisymmetric die. Convergence was obtained up to nearly the highest value of apparent shear rate for which published simulation results are available. Quantitative results for vortex strength, vortex opening angle and Couette correction are presented which are compared with earlier work on the problem using other methods. Agreement is generally good, giving confidence in the method. Simulations of planar flows of the same melt are performed: a decreasing corner vortex was observed. This phenomenon has been observed experimentally for flows of other substances, but is not expected for flows of LDPE melt. A parametric study of a critical strain hardening parameter is conducted to help explain the cause of the results.     

The effect of slip in the flow of a branched PP melt: experiments and simulations

In this paper visualisation and direct velocity profile measurement experiments for a branched polypropylene melt in a 10:1 axisymmetric contraction demonstrate the onset of wall slip. Video processing of the flow shows the formation of vortices and their diminution with increasing flow rate. Numerical simulations using a multimode K-BKZ viscoelastic and a purely viscous (Cross) model—both of them incorporating a nonlinear slip law—were used to predict the flow kinematics and dynamics as well as to deduce the slip velocity function by performing fitting to the velocity profiles. It was found that the numerical predictions agree well with the experimental results for the velocity profiles, and vortex formation, growth and reduction. It is suggested that such experiments (visualisation of entrance flow and direct velocity profile measurement) can be useful in evaluating the validity of constitutive equations and slip laws in the flow of polymer melts through processing equipment.