本文展示一考慮黏性流效應的翼形設計方法，並利用此方法設計多目標之翼形幾何。在過去的研究中，我們已發展一以勢流理論為假設的翼形反算設計方法，應用邊界元素法進行計算，並利用B-木條曲線產生幾何，進而由擾動幾何，求解非線性方程式，迭算出所要的目標翼形幾何。但勢流並沒有考慮到黏性所造成的影響，所以在本文中，我們應用XFOIL、商用CFD軟體FLUENT以及網格產生軟體GRIDGEN搭配自行開發的自動化技術，建立設計流程中的計算方法。至於最佳化的設計上，我們利用的是拉格朗日乘數法，配合權重法，將原來的單目標最佳化方法推廣至多目標的拉格朗日乘數法。
本文以多目標的拉格朗日乘數法為基礎，配合文中所提出的翼形設計流程，發展出一多目標翼形的設計流程，使得設計翼形能在不同操作條件下都維持一定的操作效能。由於利用RANS方法來求解黏性流流場是很花時間的，因此我們在應用反算法設計翼形時，改採包含了黏性修正的邊界元素法來作設計，再輔以RANS方法來驗證最後的設計。在進行多目標設計時，則先應用RANS方法計算不同設計參數翼形的性能，由此建立資料庫，再利用資料庫進行多目標設計。我們也實際利用多目標翼形的設計流程設計出兩種翼形，而這些範例也證明了本文提出的設計流程是有效的。此設計方法可用來進行單一目標或多目標的翼形設計，並可推廣至三維螺槳設計。

The purpose of this thesis is to develop a design procedure for designing a multi-objective foil section with the consideration of the viscous effects. A design method which can generate the foil geometry based on a prescribed pressure distribution has already been developed, and the boundary element method is used as the computational tool. In this thesis, we further extend this method to include the viscous effect by using the boundary element method, the boundary layer method XFOIL, and the commercial RANS method FLUENT as the computational tools. Furthermore, in the optimization problem, we extend this design method from a single-objective method to a multi-objective method by using the Lagrange multiplier method combining with aggregate objective function.

This multi-objective design method can design a foil section not only having a satisfactory performance, but also having consistent performance at different design conditions, such as different speeds or different angles of attack. When designing a foil based on the prescribed pressure distribution, the boundary layer method XFOIL is used for the efficiency reason, and the final design is then verified by RANS method. In the multi-objective design procedure, foils with different geometric parameters are first computed by RANS, and a database is then established from these computational results. The gradients used in the optimization method thus can be computed by differentiating the computational results in the database using a finite difference method. In this way, enormous computational time for computing the gradients can be saved. In this thesis, several practical design examples are demonstrated, and the design results show that the presented method is effective.

摘要
Abstract
謝誌
目錄
圖目錄
表目錄
符號說明
第一章 緒論
1.1. 研究動機
1.2. 文獻回顧
1.3. 本文架構
第二章 設計方法理論
2.1. 幾何反算
2.2. 拉格朗日乘數法
2.3. 多目標拉格朗日乘數法
第三章 設計方法
3.1. 翼形設計流程
3.2. 自動化產生網格
3.3. 最佳化程式
3.4. 性能指標
第四章 設計實例
4.1. 實例一
4.2. 實例二
第五章 結論與未來展望
參考文獻

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