在高能量密度雷射或者是電子束之鑽孔過程中，我們試著去研究與了解該鑽孔的熔融金屬層在充滿蒸氣與液體粒子的孔洞產生崩塌的現象與條件。並且研究液層的崩塌現象對於在鑽孔過程中所產生的氣孔之形成機制是不可或缺的。
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況視為相似。並且在本研究中，假設孔洞核心區域中的混合物為均質的情況下，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流體可為超音速，本研究所考慮之重要因素為液層表面滲入孔洞之質量傳遞，二相流可依液體粒子的滲入與沉澱為特徵劃分出兩個區域，孔洞的崩塌是液體粒子的滲入所造成，與氣孔之形成有著密切關係。基於環狀二相流的基本了解下，本研究在此提出液體滲入對孔洞中各物理性質的影響且造成氣孔的形成。

This text pursues the causes and phenomena in the course of the collapse of the molten metal layer surrounding a keyhole which is full of vapor and liquid particles during the high energy laser or electron beam drilling process. And the formation mechanism of the pores for the drilling process, to study the collapse phenomenon of the liquid layer is essential.
In the research the collapse of the keyhole is taken as approximated to a transition between the slug and annular two-phase flows in a vertical pipe of varying cross-section. We develop and solve a quasi-steady, one-dimensional model for two phase flow with the assumption that the mixture in the core homogenous, ignoring the friction of the liquid layer, regarding the flow in the keyhole as supersonic, considering the mass transfer of the liquid layer to the keyhole. Two-phase flow can be liquid particle entrainment characteristics, infiltration precipitation, divided into two regions. The collapse of keyhole resulted from the infiltration of the liquid particles is chained to the pore formation. Based on the realization of annular two phase flow, In this text, that the liquid into the holes in the physical properties and caused pores formation.

論文審定書…………I
中文摘要…………II
英文摘要…………III
目錄…………IV
圖次…………VI
符號說明…………VII

第 一 章 緒論…………1
1.1 本文架構 1
1.2 前言與文獻回顧 2
1.3 研究動機 5
1.4 研究方法與目標 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 13
2.4 液層中之液體壓力 16
2.5 液層與固體交界面形狀 17

第 三 章 結果與討論…………19

第 四 章 結語與未來展望…………25

圖…………26

參考文獻…………40

[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(l999).
[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(l1), 6353-6360 (1995).
[9] Y. Lee, S. H. K0, 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 App]. 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.]. 26, 345 (1980).
[21] Ishii, “Chapter 2.4, Wave Phenomena and Two-Phase Flow

Instabi1ities,” 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. Amold, 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, AlChE 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. Szymanski and J. Kurzyna, J. Appl. Phys. 76, 7750 (1994).
[34] R. Miller and T. DebR0y, .1. 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)