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．     

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．     

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.     

颗粒流体系统的格子Boltzmann数值方法研究进展

介绍Euler-Lagrange框架下基于格子Boltzmann方法 LBM(Lattice Boltzmann Method)发展的两种不同层次（即不同时-空尺度和精度）的颗粒流体系统离散模拟方法,即格子Boltzmann颗粒解析直接数值模拟（LB-based PR-DNS）方法和格子Boltzmann离散颗粒模拟（LB-based DPS）方法,总结了Euler-Euler框架下基于格子Boltzmann双流体模型（LB-based TFM）方面的探索研究。LB-based PR-DNS方法中颗粒尺寸远大于格子步长,能够直接解析出流体在颗粒表面的流动以及颗粒所受完整的动力学信息;LB-based DPS方法中格子步长远大于颗粒直径,其在计算精度、时间耗费和计算效率之间能达到很好的平衡,可获得流体的宏观平均流动及颗粒的运动轨迹信息。LB-based DNS和DPS是探索颗粒流体系统的有力手段,但LB-based TFM应用于模拟颗粒流体系统仍需进一步探索。     

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.      

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。     

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．     

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．     

直角和贴体坐标系下两种格子Boltzmann方法的比较研究

采用格子Boltzmann方法(LBM)和改进的插值格子Boltzmann方法(GILBM)研究了45°斜方腔的顶盖驱动流和Roach通道内的流动特性,并与基准解进行了对比。结果表明,对于45°斜方腔的顶盖驱动流,当雷诺数较小时,两种方法的计算结果与基准解吻合较好;但当雷诺数较大时,采用LBM的计算结果准确性降低,而基于GILBM方法得到的结果准确度升高,且计算稳定性好。对于Roach通道内的流体流动而言,两种方法的计算精度和复杂边界的复杂程度与雷诺数大小有关。根据流场边界形状的复杂程度,网格划分与计算精确度的不同要求,两种方法各有利弊。     

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．     

Extrudate swell in some dilute elastic solutions

An experimental programme has been carried out to obtain data for the isothermal swelling of dilute viscoelastic fluids based on the polyisobutylene-polybutene system. The fluid was thus a constant viscosity one and so the observed swell was predominantly due to elastic effects alone. To establish the experimental rig and procedure, preliminary results for the creeping flow of a Newtonian fluid, based on a polybutene, were acquired. The Newtonian results, showing a creeping flow swell of 13.8%, demonstrated that the rig and procedure were satisfactory for the formation of free, isothermal jets. The viscoelastic results were quite unexpected, showing that dilute elastic solutions can exhibit significant swelling despite the fact that the recoverable shear is small (S _R < 0.1). These results qualitatively confirm a recent numerical study [1].     

Extrudate swell through an orifice die

The extrudate swell of a viscoelastic fluid through an orifice die is investigated by using a mixed finite element and a streamline integration method (FESIM), using a version of the K-BKZ model. The free surface calculation is based on a local mass conservation scheme and an approximate numerical treatment for the contact point movement of the free surface. The numerical results show a vortex growth and an increasing swelling ratio with the Weissenberg number. Convergence with mesh refinement is demonstrated, even at a high Weissenberg number of O(587), where the swelling ratio reaches a value of about 360%. In addition, it is found that the effective flow channel at the entrance region next to the orifice die is reduced due to the enhanced vortex growth, which may be a source of flow instability.     

Delayed die swell

The experiments reported here establish that there is a general critical condition associated with die swell which we call delayed die swell. This condition is defined by a critical speed which is the area-averaged velocity, the extrusion velocity, at the exit of the pipe when the swell is first delayed. The delayed swell ratio and delay distance first increase for larger, post-critical values of the extrusion velocity; then the increases are terminated either by instabilities or by smoothing. The maximum post-critical velocity at the pipe exit was always greater than the shear wave speed measured on the shear-wave-speed meter. The post critical area averaged velocity at the position of maximum swell before termination was always less than the shear wave speed. There were always points in the region of swelling where the ratio of the local velocity to the shear wave speed, the viscoelastic Mach number, was unity. The swelling of the jet is a nonlinear phenomenon which we suggest is finally terminated either by instability or when the variations of the velocity, vorticity and stress field are reduced to zero by the inward propagation of shear waves from the free surface of the jet. This propagation is generated by discontinuous “initial” data along χ in which the prescribed values of velocity at the boundary change from no-slip in the pipe to no-shear in the jet. The measurements raise the possibility that the delay may be associated with a change of type from supercritical to subcritical flow.     

A finite difference analysis of the extrudate swell problem

The extrudate swell phenomenon of a purely viscous fluid is analysed by solving simultaneously the Cauchy momentum equations along with the continuity equation by means of a finite difference method. The circular and planar jet flows of Newtonian and power-law fluids are simulated using a control volume finite difference method suggested by Patankar called SIMPLER (semi-implicit method for pressure-linked equations). This method uses the velocity components and pressure as the primitive variables and employs a staggered grid and control volume for each separate variable. The numerical results show good agreement with the analytical solution of the axisymmetric stick-slip problem and exhibit a Newtonian swelling ratio of 13.2% or 19.2% for a capillary or slit die respectively in accordance with previously reported experimental and numerical results. Shear thinning results in a decrease in swelling ratio, as does the introduction of gravity and surface tension.     

A boundary element investigation of extrudate swell

Numerical studies of die swell have until now dealt perimarily with the Maxwell or Oldroyd-B viscoelastic models. However, these models exhibit features that often make them unsuitable for numerical work. Furthermore, they are not realistic representations of actual viscoelastic fluids. In this report a comparison is made between the behaviour of a variety of different viscoelastic models when applied to the die swell problem. A wide range of elongational and shear behaviour is exhibited by the models examined. Both types of behaviour are shown to be important in the die swell problem, and the observed swelling is related to these characteristics of the models.     

Modeling and simulation of three‐dimensional extrusion swelling of viscoelastic fluids with PTT,Giesekus and FENE‐P constitutive models

The investigation of the extrusion swelling mechanism of viscoelastic fluids has both scientific and industrial interest. However, it has been traditionally difficult to afford theoretical and experimental researches to this problem. The numerical methodology based on the penalty finite element method with a decoupled algorithm is presented in the study to simulate three‐dimensional extrusion swelling of viscoelastic fluids flowing through out of a circular die. The rheological responses of viscoelastic fluids are described by using three kinds of differential constitutive models including the Phan‐Thien Tanner model, the Giesekus model, and the finite extensible nonlinear elastic dumbbell with a Peterlin closure approximation model. A streamface‐streamline method is introduced to adjust the swelling free surface. The calculation stability is improved by using the discrete elastic‐viscous split stress algorithm with the inconsistent streamline‐upwind scheme. The essential flow characteristics of viscoelastic fluids are predicted by using the proposed numerical method, and the mechanism of swelling phenomenon is further discussed.Copyright © 2013 John Wiley & Sons, Ltd.     

Numerical simulation of delayed die swell

In a recent paper, Joseph et al. showed that, for a number of viscoelastic fluids, one can observe the phenomenon of delayed die swell beyond a critical extrusion velocity, or beyond a critical value of the viscoelastic Mach number. Giesekus had also observed that delayed die swell is a critical phenomenon.In the present paper, we find a set of material and flow parameters under which it is possible to simulate delayed die swell. For the viscoelastic flow calculation, we use the finite element algorithm with sub-elements for the stresses and streamline upwinding in the discretized constitutive equations. For the free surface, we use an implicit technique which allows us to implement Newton's method for solving the non-linear system of equations. The fluid is Oldroyd-B which, in the present problem, is a singular perturbation of the Maxwell fluid. The results show very little sensitivity to the size of the retardation time. We also show delayed die swell for a Giesekus fluid.This paper is dedicated to Professor Hanswalter Giesekus on the occasion of his retirement as Editor of Rheologica Acta.