在本研究中，主要是以三維共位體心式有限體積法(collocated cell-centered finite volume method)求解多層共押出(coextrusion)成型程序的系統方程式，以數值計算模擬非恆溫泛牛頓流體在共押出成型進料區塊(feedblock)中的流動行為，以了解其速度場、壓力、溫度與流體界面的在三維立體空間中的分佈，並改變不同的計算流變參數，以分析及討論其模擬計算之結果。
本研究的模擬結果與文獻中的計算結果比較相當吻合，可證明此數值計算方法之正確性，並且由模擬計算之結果可知兩流體在雙層共押出成型進料區塊內的流動行為與界面分佈將與流量比、黏度比及起始接觸高度、接觸角度有關，一般而言，流體界面將會趨向於往低黏度及低流量的流體層偏移，且因應力平衡的結果而流體界面扭曲產生所謂的包覆現象(encapsulation phenomena)，不同的起始接觸高度及接觸角度亦會造成不同程度的界面扭曲。

在修正型Cross模式流體的雙層共押出成型模擬計算中，改變入口進料的流量及溫度做模擬計算，其中對剪切率或溫度較敏感的材料會因流量的增加或溫度的提高而使黏度降低較多，因而間接使得流體界面往該層偏移。而後又將此模擬計算方法推廣應用於三層及五層的共押出成型模擬計算，亦可預測在更複雜的系統中的流動行為及流體界面分佈。

In this study, a collocated cell-centered finite volume method is developed to simulate the multilayer coextrusion process, which co-extrude two or more layers of non-isothermal generalized Newtonian fluid in a feedblock. This research will predict the velocity, pressure, temperature fields and free surface distribution in three-dimensional space. With different computational parameters, we analyze and discuss the simulation results.
Comparing simulation results with past analysis data, we proof that the method used in this study can accurately simulate the flow behavior and free surface distribution in the feedblock of two-layer coextrusion process. We discover that the free surface tends to shift towards the layer with less viscosity or less flow rate, and the encapsulation phenomena occurs for the balance of stresses on free surface. Furthermore, the difference of the initial merging height and contact angle also causes different distortion of free surface.

According to the simulation results of two-layer coextrusion with modified Cross model, we observe that the free surface shifts towards the more sensitive material layer by increasing flow rate or temperature, and it is due to the effect of viscosity decrease. Later, we apply this method to three-layer and five-layer coextrusion simulation, and it can also predict the flow behavior and free surface distribution in these more complex systems.

1.
E. A. Muccio, “Plastics Processing Technology”, ASM International, United States of America (1994).
2.
D. H. Morton-Jones, “Polymer Processing”, Chapman & Hall, London (1989).
3.
W. Michaeli, “Extrusion Dies for Plastics and Rubber”, Hanser Publishers, New York (1992).
4.
C. Rauwendaal, “Polymer Extrusion”, Hanser Publishers, New York (1990).
5.
J. Y. Chiou, P. Y. Wu, C. C. Tsai, and T. J. Liu, “An Integrated Analysis for a Coextrusion Process”, Polym. Eng. Sci., 38, 49 (1998).
6.
J. Dooley, K. S. Hyun, and K. Hughes, “An Experimental Study on the Effect of Polymer Viscoelasticity on Layer Rearrangement in Coextrusion Structures”, Polym. Eng. Sci., 38, 1060 (1998).
7.
A. Hannachi and E. Mitsoulis, “Sheet Coextrusion of Polymer Solutions and Melts: Comparison Between Simulation and Experiments”, Adv. Polym. Tech., 12, 217 (1993).
8.
E. Mitsoulis, “Multilayer Sheet Coextrusion: Analysis and Design”, Adv. Polym. Tech., 8, 225 (1988).
9.
T. C. Yu and C. D. Han, “Stratified Two-Phase Flow of Molten Polymers”, J. Appl. Polym. Sci., 17, 1203 (1973).
10.
C. D. Han and R. Shetty, “Studies on Multilayer Film Coextrusion I. The Rheology of Flat Film Coextrusion”, Polym. Eng. Sci., 16, 697 (1976).
11.
M. E. Nordberg III and H. H. Winter, “Fully Developed Multilayer Polymer Flows in Slits and Annuli”, Polym. Eng. Sci., 28, 444 (1988).
12.
C. D. Han, “A Study of Bicomponent Coextrusion of Molten Polymers”, J. Appl. Polym. Sci., 17, 1289 (1973).
13.
C. D. Han and H. B. Chin, “Theoretical Prediction of the Pressure Gradients in Coextrusion of Non-Newtonian Fluids”, Polym. Eng. Sci., 19, 1156 (1979).
14.
C. D. Han and D. Rao, “Studies on Wires Coating Extrusion. I. The Rheology of Wire Coating Extrusion”, Polym. Eng. Sci., 18, 1019 (1978).
15.
C. D. Han and D. Rao, “Studies on Wires Coating Extrusion. II. The Rheology of Wire Coating Extrusion”, Polym. Eng. Sci., 20, 128 (1980).
16.
E. Uhland, “Stratified Two-Phase Flow of Molten Polymers in Circular Dies”, Polym. Eng. Sci., 17, 671 (1977).
17.
S. Basu, “A Theoretical Analysis Non-Isothermal Flow in Wire-Coating Co-Extrusion Dies”, Polym. Eng. Sci., 21, 1128 (1981).
18.
G. Sornberger, B. Vergnes, and J. F. Agassant, “Two Directional Coextrusion Flow of Two Molten Polymers in Flat Dies”, Polym. Eng. Sci., 26, 455 (1986).
19.
J. Vlcek and J. Vlachopoulos, COEXCAD: Users manual, CAPPA-D, Dept. of Chem. Eng., McMaster University, Hamilton, Canada (1990).
20.
S. Puissant, Y. Demay, B. Vergnes, and J. F. Agassant, “Two-Dimensional Multilayer Flow in a Flat Coat-Hanger Die. Part I: Modeling”, Polym. Eng. Sci., 34, 201 (1994).
21.
R. Y. Chang and K. J. Lin, “Application of Hybrid FEM/FDM for the Flow Analysis of Single Screw Plasticating Extrusion”, Polym. Eng. Sci., 35, 1748 (1995).
22.
W. A. Gifford, “A Three-Dimensional Analysis of Coextrusion”, Polym. Eng. Sci., 37, 315 (1997).
23.
W. F. Ames, “Numerical Methods for Partial Differential Equations”, Academic Press, New York (1977).
24.
O. C. Zienkiewicz, and R. L. Taylor, “The Finite Element Method”, McGRAW-Hill (1989).
25.
J. H. Ferziger, and M. Peric, “Computational Methods for Fluid Dynamics”, Springer, New York (1996).
26.
S. L. Lee, “A strongly implicit solver for two-dimensional elliptic differential equations”, Numer. Heat Transfer, 16B, 161 (1989).
27.
R. Y. Chang, and W. H. Yang, “Numerical Simulation of Mold Filling in Injection Molding Using a Three-Dimensional Finite Volume Approach”, submitted to Int. J. Numer. Methods Fluids (2000).
28.
C. W. Hirt, and B. D. Nichols, “Volume of Fluid (VOF) method for the dynamics of free boundaries”, J. Comput. Phys., 39, 201 (1981).
29.
Richard Barrett, Michael Brry, Tony F. Chan, James Demmel, June M. Donato, Jack Dongarra, Victor Eijkhout, Roldan Pozo Charles Romine, and Henk Van der Vorst, “Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods”, (1994).
30.
S. V. Patankar, “Numerical Heat Transfer and Fluid Flow”, McGRAW-Hill, New York, (1994).
31.
C. M. Rhie and W. L. Chow, “A Numerical Study of the Turbulent Flow Past an Isolated Airfoil with Trailing Edge Separation”, AIAA J., 21, 1525 (1983).