Abstract
高分子流體的黏彈性行為及其特異的流變行為常是加工過程中不易克服的問題之一。本論文的目的在發展有效且準確的數值方法，配合不同型態的黏彈性本質方程式，以探討不同型態的黏彈性高分子流體在多種不同擠出流場內的流動行為。本論文共計包含四個部份（１）高彈性單模態微分型態流體的數值模擬；（２）多模態微分與積分型態流體的數值模擬；（３）非恆溫微分型態黏彈性流體高速擠出下的模口膨脹；（４）液晶高分子在二維複雜流場的流動行為。本研究利用混合式修正型SU子元素法，模擬非恆溫White-Metzner 模式流體在高速擠出下的非恆溫黏彈性效應。不僅可降低數值誤差，節省計算時間，同時可以將擠出速率的計算上限提升至可實用的程度。並考慮不同的人工擴散子型態、材料函數型態對膨脹比率的影響，以及冷卻速率的效應等。同時將SU子元素法應用在多模態、微分型態本質方程式的模擬上，在高擠出速率下同樣具有良好的數值穩定性。對於積分型態本質方程式以及液晶高分子模式，本研究所提出的流體追蹤技術，有助於提升此類數學模式模擬的正確性。配合變數轉換與應力張量積分，可模擬高擠出速率下的多模態積分型態流體。對於向列型液晶高分子在二維複雜流場的流動模擬，使用四階Runge-Kutta 積分與流線積分法，可以免除人工數值風側擴散的誤差，並可得到渦流處液晶配向子的排列狀況。同時並提出非等向增量疊代法，可大幅降低數值計算的時間並提高數值計算的穩定性。同時發現，液晶配向子的配向參數主要影響其配向角分佈，對流場的影響甚微；而非等向性黏度則影響流場壓降，但不影響配向子的排列。Some of the problems encountered in polymer extrusion arecaused by the viscoelastic behavior of polymer melts. Thepurpose of this study is to develop more efficient and accuratenumerical algorithms for various kinds of constitutive models.The thesis consists of four major subjects, which are (1)numerical simulation of single-mode differential models at highWeissenberg numbers; (2) numerical simulation of multi- modedifferential or integral type constitutive equations; (3)numerical simulation of non-isothermal extrudate swell at highextrusion rates; (4) simulation of director orientation ofliquid crystalline polymers in 2-D flows, respectively. The non-isothermal extrudate swell problems for viscoelastic fluidswere solved in this present work by employing a modified non-consistent streamline upwind mixed finite element method withthe White-Metzner constitutive equation. The computation wasproved to be stable and converge up to extrusion ratessignificantly higher than those previous studies which employedthe conventional finite element methods. Additionally, theeffects of viscous dissipation at high extrusion rates andvarious cooling rates were discussed. Furthermore, two kinds ofartificial diffusivities and various forms of materialfunctions on the swell ratio and the free surface profiles werealso discussed. In order to investigate the directororientation of nematic polymers and the flow of integral fluidsin complex configurations, a novel algorithm for the fluidparticle tracking technique was developed in this study. Thesimplified Leslie- Ericksen equations were employed andcalculated on the basis of high viscosity approximation. Thedirector orientation parameter was found to have stronginfluence on the director orientation, while the anisotropicviscosities were found affect the pressure drop across the flowfield.