本研究針對電漿熔射奈米金屬微粒之噴塗鍍膜系統整體進行數值計算及分析。電漿熔射成膜的過程中，影響薄膜品質的關鍵在於噴塗粒子撞擊基材的熔融狀態與動能，因此如何使噴塗粒子維持高溫及高速是製程中關切的重點。過去有學者以線上診斷系統來觀察粒子在噴塗過程中的熔融狀態，但是由於粒子在噴塗過程的滯留時間極為短暫，因此只能由儀器取得局部的粒子運動概況，無法掌握完整的噴塗資訊。因此本研究著眼點在忽略其中電漿離子化程度之微觀行為以及物質相變化的情況下，探討不同腔體幾何尺寸、電磁作用強度以及噴塗奈米金屬粒徑對於靶材面上熱流分佈及噴塗粒子的影響。並利用數值計算結果進行參數最佳化，以此分析流程找出能夠使噴塗粒子於轟擊基材時溫度、速度以及噴塗分佈均勻之最佳腔體設計及邊界操作條件。
在數值計算方面，以GAMBIT繪圖軟體進行建模再使用計算流體力學軟體ANSYS-FLUENT進行模型內電漿熱流場以及噴塗粒子之計算研究。數值計算方法上聯立求解連續方程式、動量方程式、能量方程式以及電位能方程式，來求得電漿腔體內速度場、溫度場、電場以及噴塗粒子的速度、溫度和運動軌跡；並依據文獻中所使用的電漿熔射噴塗系統建立相同尺寸以及操作條件之模型，驗證本數值求解系統之可靠性。
在研究中探討不同電位勢強度、不同操作條件、不同腔體幾何尺寸以及不同的噴塗粒徑作用下，對電漿熔射鈦金屬微粒並噴塗於基材時的成膜影響。並定義出一參數判斷是否足以兼顧噴塗粒子的熔融狀態、溫度、速度以及噴塗範圍；再利用數值計算結果進行參數最佳化，發現電極間電位勢與噴塗粒子粒徑的交互作用項為主導成膜噴塗粒子性質的因素，因此界定出在不同電位勢與不同噴塗粒徑之配置下，對於成膜好壞影響之分區圖；同時也發現將現今製程中的噴嘴出口形狀由直圓管更改為外擴圓弧形噴嘴可以增加噴塗範圍與避免直圓管噴嘴所造成的溫度累積現象。最終驗證其最佳化後之腔體尺寸及操作條件的確能獲得較佳的噴塗粒子成膜條件，本研究之分析結果可作為電漿熔射噴塗製程腔體設計與操作之參考。

This study analyzed the plasma-sprayed metal nanoparticles coating system via numerical computation. In the process of plasma spray coating, the melting behavior and momentum of nanoparticles impacting the substrate can influence the quality of film very much, so how to keep the nanoparticle’s temperature and velocity in the high level is a top priority in the processes. Some people used on-line particle monitor to get the particle in-flight properties, but the monitor can only diagnose part of the particle properties due to very short dwell time. So under ignoring ionization degree in the plasma system and the phase change effects, this research want to investigate the temperature distribution and velocity profile on the substrate and the particle properties impacting substrate, according to different chamber design、different electric potential and different particle diameter. After that, the computation result were applied into optimization process with response surface method to find out the best chamber design and system operating condition, which can give consideration to particles melting behavior、temperature、velocity and spray range when particles are coating on the substrate.
For the purpose of solve numerical computation, we use GAMBIT to create the model of plasma spray coating system and then compute the velocity and temperature solutions of the model by using ANSYS-FLUENT package. The program will solve simultaneous equations as follow：mass continuity equation、momentum equation、energy equation and electric potential equation, to get the temperature distribution、velocity profile、electrical distribution in the plasma chamber and particles melting behavior、temperature、velocity and spray range. In order to verify the numerical computation we used is reliable, we create a model with same boundary conditions depend on the reference, and compare the experiment data with predicted results.
We discuss the film made by plasma spray coating will have different quality, because of the different chamber design、different operating conditions and different particle diameters. And we define a brand new parameter to determine whether chamber design or operating conditions give consideration to all of properties which particles need to coat on the substrate. As the result, we verify that we do have the better particle properties to coat film after optimization analysis. The results provided in this research can be useful for the plasma spray coating system’s chamber design or operating conditions.

[1] Harting M., Woodford S., “Stress in hydrogenated amorphous silicon determined by X-ray diffraction”, Thin Solid Film, Vol. 430, No. 1, p.153-156, 2003.
[2] Schuegraf K., “Handbook of thin-film deposition processes and techniques: Principles, methods, equipment, and applications”, Noyes Publications, Bracknell, UK, 1988.
[3] 工業材料雜誌253期.
[4] Mckelliget J., Szekely J., Vardelle M. and Fauchais P., “Temperature and velocity fields in a gas stream exiting a plasma torch. A mathematical model and its experimental verification”, Plasma Chemistry and Plasma Processing, Vol. 2, No. 3, p.317-332, 1982.
[5] Lee Y. C. and Pfender E., “Particle dynamics and particle heat and mass transfer in thermal plasmas. Part III. Thermal plasma jet reactors and multiparticle injection”, Plasma Chemistry and Plasma Processing, Vol. 7, No. 1, p.1-27, 1987.
[6] Vardelle A., Vardelle M. and Fauchais P., “Influence of velocity and surface temperature of alumina particles on the properties of plasma sprayed coatings,” Plasma Chemistry and Plasma Process., Vol. 2, No. 3, p.255-291, 1982.
[7] Scott D. A., Kovitya P. and Haddad G. N., “Temperatures in the plume of a dc plasma torch”, Journal of Applied Physics, Vol. 66, No. 11, p.5232-5239, 1989.
[8] Westhoff R. and Szekely J., “A model of fluid, heat flow, and electro-magnetic phenomena in a non-transferred arc plasma torch”, Journal of Applied Physics, Vol. 70, No. 7, p.3455-3466, 1991.
[9] Dilawari A. H. and Szekely J., “Some perspectives on the modeling of plasma jets”, Plasma Chemistry and Plasma Processing, Vol.7, No. 3, p.317-339, 1987.
[10] Dilawari A. H., Szekely J., Batdorf J., Detering R. and Shaw C. B., “The temperature profile in argon plasma issuing into an argon atmosphere : a comparison of measurements and prediction”, Plasma Chemistry and Plasma Processing, Vol. 10, No. 2, p.321-337, 1990.
[11] El-Kaddah N., Mckelliget J., Szekely J., “Heat transfer and fluid flow in plasma spraying ”, Metallurgical Transactions B, Vol. 15B, p.59-70, 1984.
[12] Zagorski A.V. and Stadelmaier F., “Full-scale modelling of a thermal spray process”, Surface and Coatings Technology, Vol. 146-147, p.162-167, 2001.
[13] Pfender E., “Thermal plasma technology: where do we stand and where are we going?”, Plasma Chemistry and Plasma Processing, Vol. 19, No. 1, 1999.
[14] Zhao, L., K. Seemann, A. Fischer, and E. Lugscheider, “Study on atmospheric plasma spraying of Al2O3 using on-line particle monitoring”, Surface and Coating Technology, Vol. 168, No. 2-3, p.186-190, 2003.
[15] 高正雄譯, “超LSI時代:電漿化學”, 工業調查會電子材料編集部, 1984
[16] Grill A. , “Cold Plasma in Materials Fabrication：From Fundamentals to Applications”, Wiley-IEEE Press, p.64-80, 1994.
[17] Roth J. R., “Industrial Plasma Engineering – Volume 1: Principles”, Institude of physics publishing, Knoxville, USA, 1995.
[18] 張家豪, 魏鴻文, 翁政輝, 柳克強, 李安平, 寇崇善, 吳敏文, 曾錦清, 蔡文發, 鄭國川, “電漿源原理與應用之介紹”, 物理雙月刊, 28卷2期, 2006.
[19] 陳瑾惠, “電漿噴塗氫氧基磷灰石批覆金屬基植入材料之研究Ⅲ介面研究”, 行政院國家科學委員會專題研究計畫成果報告, 1992
[20] Schwenk A., “The influence of inner nozzle contour on the plasma torch performance for atmospheric plasma spraying”, Proceedings of 16th International Symposium on Plasma Chemistry, 2003.
[21] 張煥修, “電漿噴塗超導塗層之研究”, 行政院國家科學委員會專題研究計畫成果報告, 1990.
[22] Prochazka Z., Khor K. A. and Cizek J. , “Influence of input parameters on splat formation and coating thermal diffusivity in plasma spraying”, Advanced Engineering Materials, Vol. 8, No. 7, p.645-650, 2006.
[23] 吳子健、吳朝軍、曾克裏、王全勝, “熱噴塗技術與應用”, 機械工業出版社, 2006.
[24] FLUENT 12.0 User Guide, Fluent Inc, 2009.
[25] Rajeev B., “Fundamentals of Engineering Electromagnetics”, CRC/Taylor & Francis, New York, USA, 2006.
[26] 賴耿楊, “電漿工學的基礎”, 復文書局, 2002.
[27] Cheng D. K., “2nd Field and Wave Electromagnetic”, Addison-Wesley Publishing Company, Boston, USA, 1989.
[28] Ahmed I. and Bergman T. L., “Three-dimensional simulation of thermal plasma spraying of partially molten ceramic agglomerates”, Journal of Thermal Spray Technology, Vol. 9, No.2, p.214–224, 2000.
[29] Sun X. L., “Combustion-aided suspension plasma spraying of Y2O3 nanoparticles：Synthesis and modeling”, Journal of Applied Physics, Vol. 103, No. 3, 2008.
[30] 吳玉印, “新版實驗計劃法”,中國經營管理叢書, 1988.
[31] Box G. E. P., Wilson K. B., “On the experimental attainment of optimum conditions”, Journal of the Royal Statistical Society, Vol. 13, No.1, p.1–45, 1951.
[32] 溫正, 石良辰, 任毅如, “FLUENT流體計算應用教程”, 清華大學出版社, 2009.
[33] 吳心怡, “運用多目標模擬最佳化演算法求解生產控制與庫存管理問題”, 國立高雄第一科技大學運籌管理所碩士論文, 2006.
[34] Riaby V. A., Savinov V. P., Patziora A. V. and Tkachenko D. P., “Evaluation of the mean argon plasma conductivity and temperature at the exit of an atmospheric DC arc plasma torch”, Journal of Physics, Vol. 223, No.1, p.012007, 2010.
[35] Yunus A., “Heat and Mass Transfer：A Practical Approach”, McGraw-Hill Science, Reno, USA, 2006.
[36] 林永發, “電漿熔射鋯基高熵合金塗層之顆粒沖蝕磨耗特性檢討”, 國立成功大學材料科學及工程學系碩士論文, 2004.
[37] 鄭弘彬, “加熱溫度對真空熱處理氫氧基磷灰石(HA)塗層鍵結強度之效應探討”, 國立成功大學材料科學及工程學系碩士論文, 2004.
[38] 葉俊傑, “高速火焰熔射碳化鎢/鈷塗層之特性研究”, 逢甲大學材料科學與工程研究所碩士論文, 2004.