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 本論文的目的有二，一是開發一多變數的最佳化方法，一是應用此方法於螺槳設計上。本論文選擇拉格朗日乘數法，原因在於其可以將具備限制條件的最佳化問題成為不具限制條件的方程式，同時，由拉格朗日乘數法演化的方法相當多，使得應用上同時具備彈性與深度。在論文中，我們除討論拉格朗日乘數法的基本理論，多變數拉格朗日乘數法的推導，同時也探討由其演化的簡約梯度法等相關議題。在最佳化方法建立後，我們探討其應用於螺槳設計的可能性，開發一個螺槳設計方法。論文中提出的方法是使用最佳化方法搭配勢流邊界元素法直接設計螺槳幾何，而不再經由設定負荷分佈，再設計幾何的過程。此設計方法是根據所需要達到的目標推力，利用所建立的多變數拉格朗日乘數法進行最佳化計算，迭算出滿足此推力且具有最高效率(最小扭力)之螺槳螺距以及拱高分佈。論文中，我們使用一般的三次曲線作為螺距與拱高幾何的描述方法，設計變數即為定義這些幾何的係數。對於相同的螺槳設計，我們同時將應用傳統的設計方法進行設計，再將本論文提出方法設計的結果與之互相比較。結果顯示，本文提出的方法缺點在於無法有效控制螺槳之壓力係數分佈，但足以作為螺槳設計的輔助工具。
 The purpose of this thesis is to develop a multi-variables optimization method, and then apply to the propeller designs. The Lagrange multiplier method is selected as the optimization method. A constrained optimization problem can be transferred to an unconstrained optimization problem by the Lagrange multiplier method, and this method has been extensively used by many applications due to its flexibility. In this thesis, the fundamental theory of Lagrange multiplier method is discussed, and the multi-variable Lagrange multiplier method is derived. The reduced gradient method is also demonstrated to compare to the Lagrange multiplier method. A new propeller design method using this optimization method combined with the potential flow boundary element method is then developed and discussed. The present design method is different from the traditional propeller design method, which separated the design process into two phases: the span-wise load distribution and the chord-wise load distribution. It designs the propeller geometry directly according to the design requirement. In this thesis, the thrust force is given, and the multi-variable Lagrange multiplier method is then used to optimize the efficiency. The propeller pitch and camber distributions are defined by cubic curves, and the coefficients of these cubic curves are designed. The design results show that the objective function is obtained mathematically; however, comparing to the traditional design method, the present method does not provide satisfactory pressure distributions. Still, by properly adjust the design requirements, the present method can be used as an auxiliary tool, and to effectively control the pressure distribution is necessary for the future research.
 摘要 iAbstract ii謝誌 iv目錄 v圖目錄 viii表目錄 xi符號說明 1第一章 緒論 21.1. 研究動機 21.2. 文獻回顧 31.2.1. 最佳化方法 31.2.2. 螺槳設計 41.3. 本文架構 5第二章 設計方法理論 62.1. 拉格朗日及其相關方法 62.2. 廣義簡約梯度法 112.3. 一階梯度法與牛頓法 252.3.1. 一階梯度法 252.3.2. 牛頓法 292.3.3. 一階梯度法與牛頓法的優勢及劣勢 31第三章 計算方法及流程 323.1. 拉格朗日-牛頓法及其變形-廣義簡約梯度法 323.1.1. 拉格朗日-牛頓法 323.1.2. 廣義簡約梯度法 353.1.3. 應用簡單算例驗證拉格朗日-牛頓法與廣義簡約梯度法 ………………………………………………………...393.2. 應用拉格朗日-牛頓法和拉格朗日-梯度法於螺槳設計 423.2.1. 拉格朗日-牛頓法 423.2.2. 拉格朗日-梯度法 453.3. 傳統的螺槳設計流程 47第四章 計算與結果 494.1. 傳統設計方法 494.2. 拉格朗日-牛頓法 494.3. 拉格朗日-梯度法 524.4. 修正法 53第五章 結論與未來展望 75參考文獻 78
 [1].Betz, A., “Schraubenpropeller mit geringstem Energieverlust”, K. Ges. Wiss. Gottingen Nachr. Math.-Phys. Klasse, 1919[2]. Dan Klein,“Lagrange Multipliers without Permanent Scarring”, http://www. cs. berkeley.edu/~klein/.[3].Goldstein, S., “On the vortex theory of screw propellers”, Proc. R. Soc. London Ser. A 123 :440-65[4].Greeley, D.S. and Kerwin, J.E., “Numerical methods for propeller design and analysis in steady flow”, SNAME Trans. Vol. 90, 198[5].Hsin. C.-Y, Wu, J.-L, Chang, S.-F., 2006, “Design and Optimization Method for a Two-Dimensional Hydrofoil”, The Conference of Global Chinese Scholars on Hydrodynamics (CCSH06), July, 2006, Shanghai, China[6].J.A. van Egmond,“Numerical optimization of target pressure distributions for subsonic and transonic airfoil design,” AGARD Conference Proceedings No.463, Computational Methods for Aerodynamic Design (Inverse) and Optimization 11 p (N90-20976 14-05),March 1990。[7].J.Abadie&J.Carpentier,“Generalization of the Wolfe reduced gradient method to the case of nonlinear constraints.”In Optimization(R.Fletcheer, Ed.),Academic press,New York,Chapter 4,USA. ,1969。[8]. John C. Platt Alan H. Barr, “Constraint Methods for Flexible Models,” California Institute of Technology Pasadena, CA 91125.[9].Kerwin, J.E., “The solution of propeller lifting surface problems by vortex lattice methods”, report, Dept. of Ocean Eng., M.I.T.[10].Lerbs, H.W., “Moderately loaded propellers with a finite number of blades and an arbitrary distribution of circulation”, SNAME Trans. Vol. 60, 1952[11].Eckhart, M.K. and Morgan, W.B., “A propeller design method”, SNAME Trans. Vol. 63, 1955[12].M. D. Gunzburger.,“Introduction into mathematical aspects of flow control and optimization. Inverse Design and Optimisation Method”,von Karman Institute for Fluid Dynamics,Lecture Series 1997-05.[13].R.F. van den Dam, J.A. van Egmond,J.W.Slooff, “Optimization of Target Pressure Distributions,” Special Course on Inverse Methods for Airfoil Design for Aeronautical and Turbomachinery Applications 13 p (N91-18035 10-02),AGARD Report No.780,Nov 1990[14]. R.G. MELVIN*, W.P. HUFFMAN, D.P. YOUNG, F.T. JOHNSON, C.L. HILMES AND M.B. BIETERMAN,“ RECENT PROGRESS IN AERODYNAMIC DESIGN OPTIMIZATION,”The Boeing Company, PO Box 24346, M:S 7L-21, Seattle WA, 98124 -0346, USA.[15].Shigenori Mishima and Spyros A. Kinnas.,“ A Numerical Optimization Technique Applied to the Design of Two-Dimensional Cavitating Hydrofoil Section”, Journal of Ship Research, September 1995.[16].Singiresu S. Rao,“Engineering Optimization”, WILEY. INTERSCIENCWE.[17].Stephen J.Wright,“Optimization Software Packages,”Mathematics and Computer Science Division Argonne National Laboratory.[18].Wenbin Song_ and Andrew J. Keane,“A Study of Shape Parameterisation Methods for Airfoil Optimisation”, University of Southampton, Highfield, Southampton, SO17 1BJ, United Kingdom.[19].Wenbin Song, Andy Keane, Hakki Eres, Graeme Pound, and Simon Cox,“Two Dimensional Airfoil Optimisation Using CFD in a Grid Computing Environment”, School of Engineering Sciences University of Southampton High_eld, Southampton, SO17 1BJ, UK.[20].孫建強(2000),“求解等式約束問題的不精確Newton法”,北京工業大學碩士論文。[21].吳佳林(2003),“應用黏性流計算於翼型設計”,國立台灣海洋大學系統工程暨造船學系碩士學位論文。[22].劉惟信, “機械最佳化設計 第二版”,全華科技圖書公司。[23].梁尚明 殷國富,“現代機械憂化設計方法”,化學工業出版社。
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 1 應用拉格朗日乘數法進行多目標翼形設計 2 勢流與黏性流方法應用於螺槳空化計算之比較 3 應用黏性流計算於翼型設計

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