本研究主要是以理論分析探討塑膠原料在螺桿內的熔融及輸送過程。利用共位體心式有限體積法(Colocated Cell-centered Finite Volume Method) 針對單螺桿押出程序進行三維的計算分析，求解螺桿溝道三維空間中速度分佈、壓力梯度、溫度分佈。
在章節區分方面，本論文共分為五章討論單螺桿塑化押出程序；首先在第一章對單螺桿的歷史演進及塑料在螺桿內輸送及融化的現象進行簡介。第二章部分為針對相關文獻做一回顧和討論。本研究所使用的本質方程式、數值方法及相關數學模式推導則詳述於第三章。

第四章為計算結果與討論；在熔膠輸送區的模擬方面，針對Fenner螺桿輸送問題進行計算，並與文獻進行比較；結果顯示當螺桿外徑120 ，塑料為PS，入口及料筒溫度均設為220 時，計算結果之比較可得到合理的近似，印證了本研究數值計算的可靠性。另外本研究利用三維空間計算可觀察傳統上二維近似模式所無法觀察之塑料在三維螺旋空間中之流動情形，且可在螺桿設計上所關心的押出流量及出口平均料溫等數據得到合理的結果。

另外，本研究引入熱焓法配合軟化溫度範圍、局部液體分率等以跨相分析塑料的熔融行為，針對不同的螺桿轉速與料筒溫度等操作條件進行模擬，而在熔化長度的計算上與實驗數據得到相當吻合的結果。另外、不同於傳統上Hele-Shaw薄殼近似法只能求解平均液體分率而定性說明螺桿熔化之能力，本研究所採用三維空間計算模式可直接觀察固液兩相分離及固體床被熔化膜包覆之情形。

Three dimensional nonisothermal flow simulations in the single-screw extruder were performed using a collocated cell-centered finite volume method.
For the melt conveying zone of a single screw extruder, through Fenner’s example , the pressure distribution and temperature profile are investigated numerically in this study. Comparing results with conventional 2D FDM for the thermally developing flow, some discussion is proposed in this thesis.

The enthalpy formulation and the local liquid fraction method are introduced to simulate the plasticating phenomena in the single screw extruder. A reasonable agreement is obtained between the simulation result and experimental measurement for fusion length. In additional, not like the 2.5D simulation, 3D simulation can compute the solid bed position, so we can observe the local solid fraction in the screw channel directly.

1 林焜章， “混合有限元素法和有限差分法應用於單螺桿塑化押出程序之流動分析”，博士論文，國立清華大學(1995).
2. G.L. Bata, “The Archimedean Screw as an Extruder, Historical Note”, Polym. Eng. Sci, 24, 624(1984)
3. Z. Tadmor and C.G.Gogos, “Principles of Polymer Processing ”, Wiley , New York (1979).
4. C. Rauwendaal, “Polymer Extrusion”, Hanser, Munich (1985).
5. Z. Tadmor and I. Klein, “Engineering Principles of Plasticating Extrusion”, Van Nostrand Reinhold Company, New York (1970).
6. F. Zhu and L. Chen, “Studies on the Theory of Single Screw Plasti-cating Extrusion. Part I : A New Experimental Method for Extrusion”, Polym. Eng. Sci , 31, 1113 (1991).
7. R.T. Fenner, “Developments in the Analysis of Steady Screw Extrusion of Plymer”, Polymer, 18, 617 (1977).
8. R.M. Griffith, “Fully Developed Flow in Screw Extruder : Theoretical and Experiment Study”, Ind, Eng. Chem. Funadm, 1, 180 (1962)
9. R. T. Fenner, “The Design of Large Hot Melt Extruders”, Polymer, 16, 298 (1975).
10. B. Elbirli and J.T. Lindt, “A Note on the Numerical Treatment of the Thermally Developing Flow in Screw Extruders ”, Polym. Eng. Sci, 27, 504 (1987).
11. C. D. Han, “Analysis of the Performance of Cooling Extruders in Thermoplastic Foam Extrusion”, Polym, Eng. Sci, 28, 1227(1988).
12. S. Gopalakrishna, Y. Jaluria, and M.V. Karwe, “Heat and Mass Transfer in a Single Screw Extruder for Non- Newtonian Materials”, Int. J. Heat Mass Transfer, 35, 221 (1992).
13. J.F.T. Pittman and K.Rashid, “Heat Transfer in Recirculating Extruder Channel Flow”, J. Polym . Eng , 5, 1(1985).
14. C. Rauwendaal and J.F. Igen Housz , “Leakage Flow of an Isothermal Power-Law Fluid”, Adv. Polym. Technol.,8,290(1988).
15. T. Matsuoka and H. Takahashi, “Finite Element Analysis of Polymer Melt Flow in Profile Extrusion Coating Die”, Int. Polym. Proc., 3, 183 (1991).
16. M.A. Spalding, J. Dooley, K.S. Hyun, and S.R. Strand, “Three Dimensional Analysis of the Metering Section of a Single Screw Extruder”, SPE ANTEC Tech Papers, 39,1533 (1993).
17. J.T. Lindt, “Pressure Development in the Melting Zone of a Single Screw Extruder”, Polym. Eng. Sci., 21, 1162(1981).
18. Z. Tadmor, “Fundamentals of Plasticating Extrusion”, Polym. Eng. Sci., 6, 185 (1966).
19. Z. Tadmor, I. Duvdevani, and I. Klein, “Metering in Plasticating Extruders Theory and Experiments”, Polym. Eng. Sci., 7, 198 (1967).
20. R.C. Donovan, “A Theoretical Melting Model for Plasticating Extruders”, Polym. Eng. Sci., 11, 247(1971).
21. A.L. Halmos, J.R.A. Pearson, and Trottnow, “Melting in Single Screw Extruders. Part III : Solutions for a Power Law Temperature Dependent Viscous Melt”, Polymer, 19, 1199(1978).
22. J.T. Lindt, “A Dynamic Melting Model For a Single Screw Extruder”, Polym. Eng. Sci., 16, 284(1976).
23. J.T. Lindt and B. Elbirli, “Effect of the Cross-Channel Flow on the Melting Performance of a Single-Screw Extruder”, Polym. Eng. Sci., 25, 412(1985).
24. I.R. Edmondson and R.T. Fenner, “Melting of Thermoplastics in Single Screw Extruders”, Polymer, 16, 49(1975).
25. B. Elbirli, J.T. Lindt, S.R. Gottgetreu and S.M. Baba, “Mathematical Modeling of Melting of Polymers in a Single Screw Extruder”, Polym. Eng. Sci., 24, 988(1984).
26. K.Y. Lee and C.D. Han, “Analysis of the Performance of Plasticating Single Screw Extruders With a New Concept of Solid-Bed Deformation”, Polym. Eng. Sci., 30, 665(1990).
27. 楊文賢，”有限體積法在塑膠射出成型三維流動分析之研究”，博士論文初審，國立清華大學 (2000)
28. J. H. Ferziger, and M. Peric, “Computational Methods for Fluid Dynamics”, Springer, New York (1996).
29. 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).
30. S. L. Lee, “A strongly implicit solver for two-dimensional elliptic differential equations”, Numerical Heat Transfer, 16B, 161 (1989).
31. R. Barrett, M. Berry, T.F. Chan, J. Dammel,, J. M. Donato, J. Dongarra, V.Eijkhout, P. Pozo, C.Romine and H.V. Vorst, “Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods”,1994.
32. S. V. Patankar, “ Numerical Heat Transfer and Fluid Flow ”, Hemiphere, New York, 1980.
33. RAMAN V. Chiruvella and Y. Jaluria, and V. Sernas “Extrusion of Non-Newtonian Fluids in a Single-Screw Extruder With Pressure Back Flow”, Polym. Eng. Sci., 36, 358(1996).
34. 黃俊欽 “三維有限元素法在非牛頓流體流動分析之研究”，博士論文，國立成功大學(1993).
35. 蔡金津，“高分子加工製程數值模擬”，博士論文，國立清華大學(1995).
36. 張榮語, “射出成型模具設計”.高立圖書有限公司(1998).
37. J.L. White, “Principles of Polymer Engineering Rheology”, Wiley, New York (1990).
38. H. J. Zamodits and J. R. A. Pearson, Trans. Soc. Reol,13, 357(1969).
39. I. Brucker, C. Miaw, A. Hanson, and G. Balch, “Numerical Analysis of the Temperature Profile in the Melt Conveying Section of a Single Screw Extruder: Comparison with Experimental Data”, Polym. Eng. Sci., 27, 504(1987).
40. E. E. Agur and J. Vlachopoulos, “Numerical Simulation of a Single Screw Plasticating Extruder”, Polym. Eng. Sci., 22, 1084(1982)