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研究生:吳佳林
研究生(外文):Jia-Lin Wu
論文名稱:應用黏性流計算於翼型設計
論文名稱(外文):Foil design by viscous flow computations
指導教授:辛敬業辛敬業引用關係
指導教授(外文):Ching-Yeh Hsin
學位類別:碩士
校院名稱:國立臺灣海洋大學
系所名稱:系統工程暨造船學系
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2005
畢業學年度:93
語文別:中文
論文頁數:88
中文關鍵詞:簡約梯度法NURBS法B-木條曲線黏性流計算
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本論文的目的是在開發一個二維翼型設計方法。首先將勢流設計方法延伸到黏性流計算。此設計方法是依據一已知的目標壓力分佈來設計翼型,並且使用牛頓-拉福森法來產生一個壓力分佈與目標壓力分佈相符的翼型幾何。RANS 法則被運用在黏性流計算上,而與勢流同樣的計算方法也被應用在設計上。黏性流計算的設計結果已經由邊界層計算方法得到驗證,並與勢流計算的結果進行比較。雖然設計者能根據目標的局部特性給定目標壓力分佈,但由此預知目標翼型上的受力是相當困難的。於是,使用拉格朗日乘數法的最佳化方法被發展出來。在本論文中,我們討論了拉格朗日乘數法的基本理論,同時也探討懲罰函數法,加強型拉格朗日乘數法和簡約梯度法。最後為了求解非線性問題,於是我們選擇了簡約梯度法作為我們的設計方法。設計目標是在滿足升力要求下使阻力減到最小。在本論文中,展示一個以此設計目標為基礎的範例,並且利用一形狀函數來滿足指定的壓力分佈。結果顯示,我們所展示的方法能成功地達到設計目標。
The purpose of this thesis is to develop a two-dimensional foil design method. First a previously developed potential flow design method is extended to the viscous flow computations. This design method designs a foil based on a prescribed pressure distribution, and the Newton-Raphson method is used to achieve a foil geometry generating the prescribed pressure distribution. The RANS method is utilized for the viscous flow computations, and the same algorithm is applied to the designs. Design results by the viscous flow computations are validated by a boundary layer calculation method, and are compared to designs based on the potential flow computations. Although designers can specify a pressure distribution based on the desired local characteristics, it is hard to know the forces on the desired foil in advance. Therefore, an optimization method by using the Lagrange multiplier is then developed. The elementary theory of the Lagrange multiplier method, along with the penalty function method, the Augmented Lagrange multiplier method and the reduced gradient method are discussed in the thesis. The reduced gradient method for solving the nonlinear problems are finally applied to the foil designs. The design goal is to satisfy the lift requirement by minimizing the drag force. A design case based on this design goal is demonstrated in the thesis, and a shape function is also specified for the pressure distribution. Results show that the presented method successfully reach the design goals.
摘要 i
Abstract ii
謝誌 iii
目錄 iv
圖目錄 v
第一章 緒論 1
1.1 研究動機 1
1.2 文獻回顧 3
1.2.1進化演算法(Evolutionary Algorithms,EAs) 3
1.2.2限制條件最佳化方法 5
1.2.3 工程設計方法 7
1.3 本文使用方法概述 7
1.4 本文架構 8
第二章 設計方法之理論 10
2.1 NURBS法 10
2.1.1 牛頓法 11
2.1.2 修正式牛頓法 11
2.2 限制條件下的最佳化方法 12
2.2.1拉格朗日乘數法(LM法) 12
2.2.2 懲罰函數法(Penalty Function Method) 18
2.2.3加強型拉格朗日乘數法(ALM法) 22
2.2.4 簡約梯度法(reduced gradient method) 27
第三章 設計方法之設計程序 41
第四章 NURBS方法的應用 44
4.1 設計實例 44
4.2 加入黏性效應進行設計 51
4.3 其他設計實例 58
第五章 限制最佳化方法的應用 66
5.1 問題定義與推導 66
5.1.1設計過程 66
5.2 實例計算 72
第六章 結果與討論 78
參考文獻 80
參考文獻
1. 辛敬業(1995) “應用邊界元素法之二維翼面設計方法”,行政院國家科學委員會專題研究計劃成果報告,NSC-83-0209-E-019-013。
2. 辛敬業(2000) “應用通用螺槳幾何描述法之螺槳葉片設計方法”,行政院國家科學委員會專題研究計畫成果報告。
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5. De Falco. “An introduction to Evolutionary Algorithms and their application to the Aerofoil Design Problem Part II:The Results.” Inverse Design and Optimisation Method. von Karman Institute for Fluid Dynamics,Lecture Series 1997-05.
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7. De Falco. An introduction to Evolutionary Algorithms and their application to the Aerofoil Design Problem Part II:The Results. Inverse Design and Optimisation Method. von Karman Institute for Fluid Dynamics,Lecture Series 1997-05.
8. De Falco, R. Del Balio, A. Della Cioppa and E.Tarantina, “A Parallel Genetic Algorithm for Transonic Airfoil Optimisation,” Evolutionary Computation, 1995., IEEE International Conference on, Volume: 1, PP.429-434, 29 Nov-1 Dec 1996.
9. Eppler, R. and Somers, D.M., “A Computer Program for the Design and Analysis of Low-Speed Aitfoils”, Tech. Rep., NASA TM 80210, 1980
10. Hsin, C.-Y. “Application of the panel method to the design of two-dimensional foil sections”, J. of Chinese Society of Naval Architecture and Marine Engineers, Vol.13, No.2. 1994.
11. Hsin, C.-Y. and Chang, Y.-L., “Solving a Hydrodynamic Design Problem by a Distributed Computing System”, 3rd International Conference on Hydro-dynamics, Seoul Korea, Oct. 1998.
12. Hsin, C.-Y. and Chang, Y.-L., “A Hydrodynamic Design Method Developed on a Distributed Computing System”, Transcations of the Aeronautical and Astronautical Society of the Republic of China, Vol. 32, No.1, pp.89-95, 2000
13. 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
14. Lighthill “A new method of two-dimensional aerodynamic design”, RAND Technical Report M2112, ARC. 1945.
15. M. Drela, “XFOIL: An Analysis and Design System for Low Reynolds Number Airfoils”, in Low Reynolds Number Aerodynamics, Vol. 54, 1989, Springer-Verlag Lecture Notes in Eng.
16. 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.
17. M. Giles, M. Drela, “A two-dimensional transonic aerodynamic design method,” AIAA Journal, Vol.25, No.9, 1986.
18. 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
19. 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.
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21. Sangho Kim, Juan J. Alonso and Antony Jameson, “Design Optimization of High–Lift Configurations Using a Viscous Continuous Adjoint Method,” 40th AIAA Aerospace Sciences Meeting and Exhibit January 14–17, 2002/Reno, NV
22. Siva K. Nadarajah, Antony Jameson, “A COMPARISON OF THE CONTINUOUS AND DISCRETE ADJOINT APPROACH TO AUTOMATIC AERODYNAMIC OPTIMIZATION”, AIAA-2000-0667,Department of Aeronautics and Astronautics Stanford University Stanford, California 94305 U.S.A.
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