在本研究論文裡，我們試圖確認在高能量密度雷射或電子束之焊接過程中，環繞在充滿蒸氣與液體粒子的孔洞周圍之熔融金屬層產生崩塌的條件。研究液層的崩塌現象對於在孔洞焊接中氣孔形成的基本瞭解是不可或缺的。我們將孔洞的崩塌與不同截面之垂直管中栓塞流與環狀二相流的過渡情形視為相似。本研究中，在假設孔洞核心區域中的混合物為均勻的情況下，發展一個擬穩態平均一維之二相流模型，並求解。我們忽略液層的摩擦力並考慮孔洞中為超音速流，二相流域可依液體粒子的滲入與沉澱為特徵，分為四個區域。孔洞的崩塌是由液體粒子的滲入所造成，而孔洞自由表面產生波動是由液體粒子的沉澱所造成。基於環狀二相流的基本瞭解下，本研究在此提出巨孔洞形成的條件。

Here we seek to identify the conditions for the collapse of the molten metal layer surrounding a keyhole filled with vapor and liquid particles during high power density laser and electron beam welding processes. Investigating the collapse of the liquid layer is essential for a fundamental understanding of pore formation in the keyhole mode welding. We treat the collapse of the keyhole as similar to a transition between the slug and annular two-phase flows in a vertical pipe of varying cross-section. A quasi-steady, one-dimensional model for two-phase flow is developed and solved assuming that the mixture in the core is homogenous. Ignoring friction within the liquid layer and considering supersonic flow in the keyhole, the two phase flow regimes can be divided into four regions characterized by entrainment and deposition of liquid particles. Keyhole collapse occurs from entrainment, whereas the keyhole exhibits wavy shape from deposition. A condition for the formation of macro-porosity based on a fundamental understanding of annular two-phase flow is presented.

謝誌 Ⅰ
目錄 Ⅱ
圖目錄 Ⅳ
符號說明 Ⅵ
中文摘要 IX
英文摘要 X

第一章 序論 1
1.1 前言與文獻回顧 1
1.2 研究動機 4
1.3 研究目的 6
1.4 本文架構 7

第二章 系統模型假設與分析 8
2.1 理論模型與假設 8
2.2 自由表面之形狀 10
2.3 孔洞中之蒸氣流動 12
2.4 液層中之液體壓力 15
2.5 液層與固體之交界面形狀 16

第三章 結果與討論 17

第四章 結論 23

圖 26

參考文獻 36

[1] T. DebRoy and S. A. David, Rev. Modern Phys. 67, 85(1995).
[2] S. A. David and T. DebRoy, Science 257, 497 (1992).
[3] H. Zhao and T. DebRoy, J. Appl. Phys. 93(12), 10089-10096 (2003).
[4] M. Pastor, H. Zhao, R. P. Martukanitz, and T. DebRoy, Weld. J. 78, 207s(1999).
[5] F. H. Kaplan, M. Mizutani, S. Katayama, and A. Matsunawa, J. Phys. D: Appl. Phys. 35, 1218 (2002).
[6] Kawaguchi, S. Tsukamoto, H. Honda, and G. Arakane, Proc. the 22nd Int. Congress on Applications of Lasers and Electro-Optics 2003, LMP – Section A, pp. 168-175.
[7] S. Tsukamoto, G. Arakane, H. Honda, and S. Kuroda, 2004, Proc. the 23th Int. Congress on Applications of Lasers and Electro-Optics 2004, pp. 11-17.
[8] Kar and J. Mazumder, J. Appl. Phys. 78(11), 6353-6360 (1995).
[9] Y. Lee, S. H. Ko, D. F. Farson, and C. D. Yoo, J. Phys. D: Appl. Phys. 35, 1570 (2002).
[10] R. Rai and T. DebRoy, J. Phys. D: Appl. Phys. 39, 1257(2006).
[11] R. Rai R, G. G. Roy, and T. DebRoy, J. Appl. Phys. 101(5), Article Number: 054909 (2007).
[12] R. Rai, P Burgardt, J.O. Milewski, T. J. Lienert and T. DebRoy, J. Phys. D: Appl. Phys. 42(2), Article Number: 025503 (2009).
[13] R. Rai, J. W. Elmer, T. A. Palmer, and T. DebRoy, J. Phys. D: Appl. Phys. 40(18), 5753-5766 (2007).
[14] Zhou, H. L. Tsai, and P. C. Wang, J. Heat Transfer 128, 680 (2006).
[15] X. Zeng, X. Mao, S. S. Mao, J. H. Yoo, and R. Greif, J. Appl. Phys. 95, 816 (2004).
[16] G. B. Wallis, One-Dimensional Two-Phase Flow (McGraw-Hill, New York, 1969).
[17] G. F. Hewitt, “Chapter 2, Liquid-Gas Systems,” in Hetsroni, G. (editor), Handbook of Multiphase Systems (Hemisphere Pub., New York, 1982).
[18] P. B. Whalley, Boiling, Condensation, and Gas-Liquid Flow (Clarendon Press, Oxford, 1987).
[19] J. G. Collier and J. R. Thome, Convective Boiling and Condensation, 3rd ed.(Clarendon Press, Oxford, 1994).
[20] Y. Taitel, D. Bornea, and A. E. Dukler, AIChE J. 26, 345 (1980).
[21] Ishii, “Chapter 2.4, Wave Phenomena and Two-Phase Flow Instabilities,” in Hetsroni, G. (editor), Handbook of Multiphase Systems (Hemisphere Pub., New York, 1982).
[22] H. Han and K. Gabriel, J. Fluids Eng. 129, 293 (2007).
[23] C. R. Arnold, and G. F. Hewitt, J. Photogr. Sci. 15, 97 (1967).
[24] Petalas and K. Aziz, J. Canadian Petroleum Tech., 39, 43(2000).
[25] V. F. Reznichenko and A. M. Verigin, Svar. Proiz. 6, 25 (1986).
[26] J. C. B. Lopes and A. E. Dukler, AIChE J. 32, 1500 (1986).
[27] L.Cheng, Chem. Eng. Comm. 194, 975(2007).
[28] R. Viskanta, 50th Anniversary Issue, J. Heat Transfer 110, 1205(1988).
[29] W.D. Bennon and F.P. Incropera, Int. J. Heat Mass Transfer 30, 2161(1987).
[30] S. I. Anisimov, Soviet Physics JETP 27, 182(1968).
[31] C. J. Knight, AIAA J. 17, 519(1979).
[32] Poueyo-Verwaerde, R. Fabbro, G. Deshors, A. M. de Frutos, and J. M. Orza, J. Appl. Phys. 74, 5773 (1993).
[33] Z. Szyma ski and J. Kurzyna, J. Appl. Phys. 76, 7750 (1994).
[34] R. Miller and T. DebRoy, J. Appl. Phys. 68, 2045(1990).
[35] F. Modest, J. Heat Transfer 128, 653 (2006).
[36] S. Wei and C. Y. Ho, Int. J. Heat Mass Transfer 41, 3299 (1998).
[37] H. Shapiro, The Dynamics and Thermodynamics of Compressible Fluid Flow, 2 vols. (Wiley, New York, 1953)