本研究利用套裝軟體Ansys Fluent建立三維暫態模型，模擬螺旋式移動電子束加熱純鈷金屬，利用水冷銅坩鍋在材料邊界進行散熱，並在熔煉過程中考慮，熔池表面之馬蘭戈尼效應與表面蒸發熱損失。
先利用熔池表面積、熔池體積來找出適合的電子束轉速、電子束移動路徑，再利蒸發熱、熔池表面積與熔池體積大小，從三種電子束半徑3、6、9 mm與四種電子束能量5、10、15、20 kW，且邊界溫度在熔煉時須控制小於穩定溫度(800 K)，所以在熔煉10秒中，篩選出最適合的電子束能量15 kW與電子束半徑6 mm。另外討論改善水冷銅坩鍋之冷卻效果，即提升總熱傳係數之影響。
接著再以最適合的熔煉參數，探討熔煉過程熔池表面的熱流現象在10秒內之演變，最後討論定點加熱方式與移動加熱方式於加熱10秒內之差別，移動加熱方式之優點在熔池表面積較大與熱損失比例較小，定點加熱之優點則在於熔池體積較大。

In this study, a three-dimensional model is used to simulate cobalt heated by spiral scanning type of electron beam melting. The copper crucible is used to dissipate heat In boundary of model. During the process of melting, the Marangoni effect and heat losses with surface evaporation are considered in the model.
The suitable electron beam rotation speed, moving path are found by surface area and volume of molten pool. Then, the suitable electron beam radius and power are found from three electron beam radii 3, 6, 9 mm and four electron beam powers 5, 10, 15, 20 kW by evaporation heat, surface area and volume of molten pool. While melting, the temperature of boundary condition is controlled to be smaller than the stable temperature (800K). Result show that the most suitable electron power is 15 kW and the electron radius is 6 mm. The cooling effect of copper crucible improved by enhancing the overall heat transfer coefficient is studied.
The melting process of molten pool thermal fluid phenomenon is discussed with the most suitable parameters in 10 seconds. Then the comparisons of the fixed heat source and moving heat source within 10 seconds are investigated. The advantages of moving heat source are having larger surface area and smaller heat losses. The advantage of fixed moving heat source is larger molten pool.

1. 楊邦朝, 崔紅玲, “濺射靶材的製備與應用,” 真空, 第3期, 2001.
2. 伍秀菁, 汪若文, 林美吟, “真空技術與應用,” 行政院國家科學委員會精密儀器發展中心, 2001.
3. G.S. Choi, J.W. Lim, N.R. Munirathnam, I.H. Kim and J.S. Kim,“Preparation of 5N Grade Tantalum by Electron Beam Melting,” Journal of Alloys and Compounds, Vol. 469, pp. 298-303, 2009.
4. Y. Tan, S. Wen, S. Shi, D. Jiang, W. Dong and X. Guo, “Numerical Simulation for Parameter Optimization of Silicon Purification by Electron Beam Melting,” Vacuum, Vol. 95, pp. 18-24, 2013.
5. B. Basui, J.A. Sekhar 2, R.J. Schaefer 3 and R. Mehrabian, ”Analysis of the Steady State Molten Pool Obtained by Heating a Substrate with an Electron Beam” Acta metall, mater. Vol. 39, No. 5, pp. 725-733, 1991.
6. J.P. Bellot, D. Ablitzer and E. Hess., "Aluminum Volatilization and Inclusion Removal in the Electron Beam Cold Hearth Melting of Ti Alloys," Metallurgical and Materials Transactions B, Vol. 31, pp. 845-854, 2000.
7. Z.H. Shen, S.Y. Zhanga, J. Lub and X.W. Ni, ” Mathematical Modeling of Laser Induced Heating and Melting in Solids” Optics & Laser Technology, Vol. 33, pp. 533-537, 2001.
8. M. Ritchie, S.L. Cockcroft, A. Mitchell, P. D. Lee and T. Wang, “X-ray-Based Measurement of Composition During Electron Beam Melting of AISI 316 Stainless Steel: Part I. Experimental Setup and Processing of Spectra,” Metallurgical and Materials Transactions A, Vol. 34, pp. 851-861, 2003.
9. 韓明臣, 周義剛, 趙鐵夫, 張英明, 周廉, “電子束冷床熔煉參數對熔池表面溫度的影響,” 稀有金屬, 第30卷, 55-59, 2006.
10. D.C. Jiang, Y. Tan, S. Shi, Q. Xu, W. Dong, Z. Gu and R. X. Zou, “Research on New Method of Electron Beam Candle Melting Used for Removal of P from Molten Si,” Materials Research Innovations, Vol. 15, pp. 406-409, 2011.
11. Z. Zhang, “Modeling of Al Evaporation and Marangoni Flow in Electron Beam Button Melting of Ti-6Al-4V,” Master’s Thesis, The University of British Columbia, Vancouver, 2013.
12. C.C. Chao, ”Numerical Analysis on Molten Pool of High Purity Metals By Electron Beam Melting” Master’s Thesis , Department of Mechanical Engineering, National Cheng Kung University, 2014.
13. G.C.A. Devia, ”Numerical Simulation on Molten Pool of High-Purity Cobalt by Different Scanning thpes of Electron Beam Melting”, Master’s Thesis, Department of Mechanical Engineering, National Cheng Kung University, 2015.
14. Y.C. Chen, ”Thermal Analysis of Numeriacl and Experimental Investigation for High Purity Cobalt Melted by Electron Beam” Master’s Thesis, Department of Mechanical Engineering, National Cheng Kung University, 2016.
15. 王永杰,”大功率電子槍電子束行程系統的設計與研究”,碩士論文,東北大學機械工程與自動化學院, 2011.
16. Y. Tan, S. Shuang, “Progress in Research and Development of Electron Beam Technology in Metallurgy Refining Field”, Master’s thesis, Dalian University of Technology,2013
17. 劉喜海, 徐成海, 鄭險峰, “真空熔煉,” 化學工業出版社, pp. 196-233, 2013.
18. D.W. Tripp, “Modelling Power Transfer in Electron Beam Heating of Cylinders,” PhD Thesis, The University of British Columbia, Vancouver, 1994.
19. P.D. Lee, P.N. Quested and M. McLean Modelling of Marangoni effects in Electron Beam Melting," Philosophical Transactions of the Royal Society A, Vol. 356, pp. 1027-1044, 1998.
20. A. Powell, U. Pal, J. Van Den Avyle, B. Damkroger, and J. Szekely, "Analysis of Multicomponent Evaporation in Electron Beam Melting and Refining of Titanium Alloys," Metallurgical and Materials Transactions B, Vol. 28B, pp. 1227-1239, 1997.
21. P. Sahoo, T. Debroy and M.J. Mcnallan, "Surface Tension of Binary Metal – Surface Active Solute Systems under Conditions Relevant to Welding Metallurgy," Metallurgical Transitions B-Process Metallurgy, Vol. 19, pp. 483-491, 1988.
22. 朱承先, “矩形潛熱式熱控裝置之熔解熱傳研究,” 博士論文, 國立成功大學機械系, 1994.
23. Y.P. Lei, H. Murakawa, Y.W. Shi and X.Y. Li, “Numerical Analysis of the Competitive Influence of Marangoni Flow and Evaporation on Heat Surface Temperature and Molten Pool Shape in Laser Surface Remelting,” Computational Materials Science, Vol. 21, pp. 276-290, 2001.
24. I. Utke, P. Hoffmann and J. Melngailis, “Gas-assisted focused electron beam and ion beam processing and fabrication,” Journal of Vacuum Science & Technology B, Vol. 26, pp. 197-1276, 2008.
25. ANSYS, “Ansys Fluent. 14.0 User's Manual,” ANSYS Inc., 2011.
26. V.R. Voller and C. Prakash, “A Fixed Grid Numerical Modelling Methodology for Convection-Diffusion mMushy Region Phase-Change Problems,” International Journal of Heat and Mass Transfer, Vol. 30, pp. 1709-1719, 1987.
27. J. Srinivasan and B. Basu, “A Numerical Study of Thermocapillary Flow in a Rectangular Cavity During Laser Melting,” International Journal of Heat and Mass Transfer, Vol. 29, pp. 563-572, 1986.
28. J.C. Chen and Y.C. Huang, “Thermocapillary Flows of Surface Melting due to a Moving Heat Flux,” International Journal of Heat and Mass Transfer, Vol. 34, pp. 663-671, 1991.
29. K.W. Westerberg, M.A. McClelland and B.A. Finlayson, “Finite Element Analysis of Flow, Heat Transfer, and Free Interfaces in an Electron Beam Vaporization System for Metals,” International Journal for Numerical Methods in Fluids, Vol. 26, pp. 637-655, 1998.
30. K.C. Mills, “Recommended Values of Thermophysical Properties for Selected Commercial Alloys,” Woodhead Publishing, 2002.
31. M.W. Chase, “NIST-JANAF Thermochemical Tables,” 1998
32. L.C. Yaws, “Handbook of Properties of the Chemical Elements,” Norwich, N.Y. : Knovel, c2011., 2011.
33. R.W. Powell and P.E. Liley, "Thermal Conductivity of the Elements: A Comprehensive Review," Journal of Physical and Chemical Reference Data, Vol. 3, pp. I–1 to I–796, 1974.
34. P.F. Paradis, T. Ishikawa and S. Yoda, “Surface Tension and Viscosity of Liquid and Undercooled Tantalum Measured by a Containerless Method,” Journal of Applied Physics, Vol. 97, 053506, 2005.
35. R. Rai, J.W. Elmer, T.A. Palmer and T. DebRoy, “Heat Transfer and Fluid Flow During Keyhole Mode Laser Welding of Tantalum, Ti–6Al–4V, 304L Stainless Steel and Vanadium,” Journal of Physics D: Applied Physics, Vol. 40, 5753, 2007.
36. E.R. Cohen, D. R. Lide and G. L. Trigg, editors., “AlP Physics Desk Reference, 3rd Edition,” New York Springer-Verlag New York, Inc., 2003.
37. J.W. Edwards, H.L. Johnston and P.E. Blackburn, “Vapor Pressure of Inorganic Substances. IV. Tantalum between 2624 and 2943° K. 1,” Journal of the American Chemical Society, Vol. 73, pp. 172-174, 1951.
38. J.W. Edwards, H.L. Johnston, and W.E. Ditmars, “The Vapor Pressures of Inorganic Substances. VII. Iron Between 1356° K. and 1519° K. and Cobalt Between 1363° K. and 1522° K 1.,” Journal of the American Chemical Society, Vol. 73, pp. 4729-4732,1951.
39. M.J. Assael, I.J. Armyra, J. Brillo, S.V. Stankus, J. Wu and W.A. Wakeham, “Reference Data for the Density and Viscosity of Liquid Cadmium, Cobalt, Gallium, Indium, Mercury, Silicon, Thallium, and Zinc.” Journal of Physical and Chemical Reference Data, Vol. 41, 033101, 2012.
40. ANSYS, “Ansys Fluent. 14.0 Theory Guide,” ANSYS Inc. , 2011.
41. T.L. Bergman and B.W. Webb, “Simulation of Pure Metal Melting with Buoyancy and Surface Tension Forces in the Liquid Phase,” International Journal of Heat and Mass Transfer, Vol. 33, pp. 139-149, 1990.