本研究採用相位場法與磁性流體力學，將氬氣電漿以二相流模擬金屬自由表面在電漿環境下受出入口熱通量影響後，其鎔融或固化之暫態熱流行為。本研究考慮質量守恆方程式、動量方程式、能量方程式、相位場函數、電場及磁場效應、黏滯力效應、電離及重組效應、以及離子電子及中性粒子動量交換之間的碰撞效應，求流場的溫度、壓力、流線與相位場函數之分佈。本研究探討在氬氣電漿環境下，由不同的邊界條件預測製造加工與加工件固化後金屬自由表面流體之變化，譬如固化、渦流、漣漪或湧起形成，此等反應會直接影響表面熱處理與焊接成品的品質。

This study uses the phase-field method and magnetohydrodynamics method to simulate thermocapillary flow under argon plasma condition on surface of a metallic material, molten or solidified by the heat flux during process. This research consider by mass conservation equation, momentum equation, energy equation, phase-field function, electric fields and magnetic fields, viscous, ionization and recombination effects, momentum exchange collisions between electrons and ions particles, to solve flow field temperature, pressure, streamline and phase-field function distribution. This project is to explore under plasma condition, formed on the surface morphology after curing and processing parts, such as surface filled, depression, or the formation of ripple, these reaction will directly affect the surface heat treatment and welding quality of the finished product.

論文審定書 ....................................................................................................................... i
誌謝 .................................................................................................................................. ii
中文摘要 ......................................................................................................................... iii
Abstract ............................................................................................................................ iv
目錄 .................................................................................................................................. v
圖次 ................................................................................................................................ vii
表次 .................................................................................................................................. x
符號說明 ......................................................................................................................... xi
第一章 緒論 .................................................................................................................... 1
1.1 研究背景 ........................................................................................................... 1
1.2 二相流、相位場法與磁性學模擬方法簡介 ................................................... 1
1.3 本論文研究內容簡介 ....................................................................................... 2
1.4 論文架構 ........................................................................................................... 3
第二章 理論分析與模型設定 ........................................................................................ 4
2.1 模型之統御方程式 ............................................................................................ 4
2.1.1 相位場法方程式 ..................................................................................... 4
2.1.2 質量守恆方程式 ..................................................................................... 6
2.1.3 動量方程式 ............................................................................................. 8
2.1.4 能量方程式 ........................................................................................... 18
2.1.5 馬克士威方程式 ................................................................................... 21
2.2 模型區域設定 .................................................................................................. 23
2.2.1 模型幾何 ............................................................................................... 23
2.2.2 網格設定 ............................................................................................... 25
2.2.3 邊界條件設定 ....................................................................................... 27
2.2.4 初始值設定 ........................................................................................... 33
2.2.5 各流體性質 ........................................................................................... 36
2.2.6 研究模擬之流程圖 ............................................................................... 37
第三章 結果與討論 ...................................................................................................... 38
3.1 模擬條件與說明 .............................................................................................. 38
3.2 基本性質的模擬圖 .......................................................................................... 38
3.3 模擬結果與討論 .............................................................................................. 41
3.3.1 電位變化 ............................................................................................... 41
3.3.2 磁場變化 ............................................................................................... 44
3.3.3 密度與速度變化 ................................................................................... 47
3.3.4 溫度變化 ............................................................................................... 58
第四章 結論 .................................................................................................................. 66
參考文獻 ........................................................................................................................ 67

[1]K. Ishizaki, N. Araki, and H. Murai, 1965, “Penetration in arc welding and convection in molten metal”, J. Japan Welding Society, Vol.34, pp.146-153.
[2]E. Friedman, 1978, “Analysis of weld puddle distortion and its effect on penetration”, J. Welding, Vol.57, pp.161-s-166-s.
[3]S. Kuo and Y. H. Wang, 1986, “Weld pool convection and its Effect”, J. Welding, Vol.65, pp.63-s-70-s.
[4]C. R. Heiple and J. R. Roper, 1982, “Mechanism for minor element effect on GTA fusion zone geometry”, J. Welding, Vol.61, pp.97-s-102-s.
[5]C. Chan, J. Mazumder and M. M. Chan, 1984, “A two-dimension transient model for convection in laser Melted Pool”, Metal. Trans., Vol.15A, pp.2175-2184.
[6]A. Paul and T. Debroy, 1988, “Free surface flow and heat transfer in conduction mode laser welding”, Metal. Trans. Vol.19B, pp.851-858.
[7]L. C. Wrobel and M. H. Aliabadi, 2003, “The boundary element methods”, Wiley, UK.
[8]V. Cristini, J. Bławzdziewicz, and M. Loewenberg, 1998, “Drop breakup in three-dimensional viscous flows”, Physics fluids, Vol.10, pp.1781-1783.
[9]H. H. Hu, N. A. Patankar and M. Y. Zhu, 2000, “Direct numerical simulations of fluid–solid systems using the arbitrary lagrangian–eulerian technique”, Journal of Computational Physics 169, pp.427-462.
[10]S. Ramaswamy and L.G. Leal, 1999, “The deformation of a viscoelastic drop subjected to steady uniaxial extensional flow of a Newtonian fluid”, J. Non-Newtonian fluid mech 85, pp.127-163.
[11]S. Osher and N. Paragios, 2003, “Geometric level set methods in imaging, vision, and graphics. Springer-Verlag”, New York.
[12]H. Emmerich, 2003, “The diffuse interface approach in materials science, Springer-Verlag”, New York.
[13]J. S. Rowlinson, 1979, “The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density”. Journal of Statistical Physics, Vol.20, No.2, pp.200-244.
[14]O. Penrose and P. C. Fife, 1990, “Thermodynamically consistent models of phase-field type for the kinetic of phase transitions”, Physica D 43, North-Holland, pp.44-62.
[15]P. Yue and J. J. Feng, 2004, “A diffuse-interface method for simulating two-phase flows of complex fluids”, J. Fluid Mech, Vol.515, pp.293-317.
[16]P. C. Hohenberg and B. I. Halperin, 1977, “Theory of dynamic critical phenomena”, Rev. Mod. Physics, Vol.49, pp.435-479.
[17]D. Jacqmin, 1999, “Calculation of two-phase Navier–Stokes flows using Phase-Field modeling”, Journal of Computational Physics 155, pp.96-127.
[18]M. Verschueren, F. N. Van De Vosse and H. E. H. Meijer, 2001, “Diffuse-interface modolling of thermocapillary flow instabilities in a Hele-Shaw cell”, J. Fluid Mech., Vol.434, pp.153-166.
[19]S. I. Braginskii, 1965, “Review of Plasma Physics. Consultants Bureau”, New York, vol.1, pp.205-311.
[20]J. W. Cahn and J. E Hilliard, 1958, “Free energy of a nonuniform system. I. Interfacial free energy”, J. Chem. Phys. 28, pp.258-267.
[21]T. Kunugi, 1995, “Numerical simulation of heat transfer and fluid flow of a non-equilibrium argon plasma jet with confined wall”, Fusion Engineering and Design 28, pp.63-71.
[22]M. A. Lieberman and A. J. Lichtenberg, 1994, “Principles of plasma discharges and materials processing”, Wiely.
[23]F. Kong, H. Zhang and G. Wang, 2008, “Numerical simulation of transient multiphase field during hybrid plasma-laser deposition manufacturing”, J. Heat Transfer, Vol.130, NO.112101, pp.1-7.
[24]Y. Sun and C. Beckermann, 2007, “Sharp interface tracking using the phase-field equation”, Journal of Computational Physics 220, pp.626-653.
[25]Comsol, 1998–2008, “Chemical engineering module”, Boiling water, pp.155-156.
[26]L. M. Montierth and W. A. Neuman, 1992, “Fluid model treatment of surface plasma structures”, Phys. Fluids B4, pp.784-795.
[27]C. S. Wu, 1999, “Modeling the anode boundary layer of high-intensity argon arcs”, Computational Materials Science 15, pp.302-310.