挤出胀大流动的有限元方法研究

本文对Luo-Tanner提出的流线有限元作了重要的改进,提出了沿通过单元高斯点的流线积分本构方程的方法,迴避了速度梯度在单元边界上间断和出口处应力奇点的困难,同时减少了计算量,对比计算表明,采用压力不连续单元来加强不可压缩性限制能使计算质量和收敛性都得到显著的提高,对Maxwell流体的轴对称挤出胀大流动在Weissenberg数1.2下获得了合理的收敛解。  

粘弹性流体的入口收敛流动

本文以聚合物流体为研究对象,对其在入口收敛流动中产生的粘弹效应及机理进行了初步的讨论和分析,并就近10年来国内外有关粘弹性流体入口流动研究及进展作了简要的评述。  

粘弹性流体在旋转圆盘上的流动

利用线性Maxwell模型，研究了粘弹性流体在旋转圆盘上的流动．并应用摄动法：求得涂层厚度的近似解析解．发现增加涂料的弹性，有助于甩涂．  

Stokes＇ first problem for a viscoelastic fluid with the generalized Oldroyd-B model

The flow near a wall suddenly set in motion for a viscoelastic fluid with the generalized Oldroyd-B model is studied. The fractional calculus approach is used in the constitutive relationship of fluid model. Exact analytical solutions of velocity and stress are obtained by using the discrete Laplace transform of the sequential fractional derivative and the Fox H-function. The obtained results indicate that some well known solutions for the Newtonian fluid, the generalized second grade fluid as well as the ordinary Oldroyd-B fluid, as limiting cases, are included in our solutions. The project supported by the National Natural Science Foundation of China (10272067), the Doctoral Program Foundation of the Education Ministry of China (20030422046), the Natural Science Foundation of Shandong Province, China (Y2006A14) and the Research Foundation of Shandong University at Weihai. The English text was polished by Keren Wang.  

黏弹性流体纯弹性不稳定现象研究综述

近年来粘弹性流体流动的弹性不稳定性现象引起了越来越多学者的关注与研究，与牛顿流体惯 性不稳定现象不同，这种现象是由粘弹性流体流动中的弹性应力和粘性力之间相互作用，使得在较 低的雷诺数下即可产生复杂的流动分岔不稳定现象。当流动中的弹性数（表现为 Deborah 数 De 与 Reynolds 数Re 的比值，其中 De 数定义为粘弹性流体的松弛时间和流动的特征时间的比值，Re 数表 征流动中惯性力与粘性力之比）较大时，在 Re<相似文献

同心旋转圆柱间强弹性流的非线性稳定性分析

基于Oldroyd-B型粘弹性流体模型，采用同心旋转圆柱间非线性动力系统分析了流体的弹性对轴对称Taylor涡稳定性的影响．分析结果表明，对于弱弹性流体，Taylor涡出现时，系统存在超临界分岔；而对于强弹性流体则出现亚临界分岔．在小间隙大扰动条件下，采用有限差分法分析了非线性效应对系统稳定性的影响．数值计算结果表明，随着流动速度的增加，润滑油膜的失稳结构与流体的弹性有关，对于弱弹性流，流体以同宿轨道分岔失稳；强弹性流则出现倍周期分岔，直至发生混沌，流场最终发展为湍流．  

Oldroyd粘弹性流体缝隙流问题的解析解

本文得到了满足Oldroyd 四参数模型的粘弹性流体的平板Poiseuille 流问题的解析解.利用所得结果计算了共挤出问题——一种新的聚合物加工过程,并得到了解析解.  

Numerical and analytical investigations of thermosolutal instability in rotating Rivlin-Ericksen fluid in porous medium with Hall current

Numerical and analytical investigations of the thermosolutal instability in a viscoelastic Rivlin-Ericksen fluid are carried out in the presence of a uniform vertical magnetic field to include the Hall current with a uniform angular velocity in a porous medium. For stationary convection, the stable solute gradient parameter and the rotation have stabilizing effects on the system, whereas the magnetic field and the medium permeability have stabilizing or destabilizing effects on the system under certain conditions. The Hall current in the presence of rotation has stabilizing effects for sufficiently large Taylor numbers, whereas in the absence of rotation, the Hall current always has destabilizing effects. These effects have also been shown graphically. The viscoelastic effects disappear for stationary convection. The stable solute parameter, the rotation, the medium permeability, the magnetic field parameter, the Hall current, and the vis-coelasticity introduce oscillatory modes into the system, which are non-existent in their absence. The sufficient conditions for the non-existence of overstability are also obtained.  

粘弹性流体的分数元模型及圆管起动流

分数元模型所描述的非牛顿流体属于复杂粘弹性流体,其应力与应变的分数阶时间导数成正比.本文提出一种用弹簧和油壶连接组成的分形网络结构来比拟分数元模型的应力-应变特性,利用Heaviside运算微积,证明了该分形网络结构对应的粘弹性流体为1/2阶导数的分数元.并证明了构成其他分数阶导数分数元模型需要引入弹簧和油壶的多重分形网络结构.本文还导出了分数元模型的圆管起动流的解析解,研究了分数元模型起动过程振荡特征与该模型导数阶β之间的关系;发现在β≠1的情况下,随时间的进程,圆管内分数元模型的运动最终均将趋于静止,只有β=1的情况是一个例外.  

DECAY OF VORTEX VELOCITY AND DIFFUSION OF TEMPERATURE IN A GENERALIZED SECOND GRADE FLUID

The fractional calculus approach in the constitutive relationship model of viscoelastic fluid was introduced. The velocity and temperature fields of the vortex flow of a generalized second fluid with fractional derivative model were described by fractional partial differential equations. Exact analytical solutions of these differential equations were obtained by using the discrete Laplace transform of the sequential fractional derivatives and generalized Mittag-Leffier function. The influence of fractional coefficient on the decay of vortex velocity and diffusion of temperature was also analyzed.