臺灣博碩士論文加值系統

本文以三維翼面尾端跡流為主要研究之對象，尋找均勻流流經此翼面之尾跡流位置。本文假設流場內之流體滿足勢流，利用邊界積分方程式使用高斯積分法對離散後的邊界積分方程式進行積分，求解此翼面表面上之速度勢。將翼面邊界上所求的尾端環流量帶入邊界積分式以求解流場中各點位置的速度勢，再藉由改變尾跡流的形狀來觀察法向速度。本文嘗試利用最小方差的方式將勢流理論解在跡流面上的法向速度最小化為目標，希望能有效的尋找出三維尾翼跡流的位置，而不再需要其他額外的輔助工具。

This study focuses on how to locate the wake position of a three-dimensional airfoil due to a uniform flow. Based on the potential theory, the boundary integral method is applied to solve the velocity potential on the boundary of the airfoil. Once the strength of the velocity potential is solved, it can be substituted into the boundary integral equation and find all the velocity potential in the flow field. By adjusting the shape of the wake, and minimizing the normal velocity components on the surface of the wake, the goal is to select a correct position of wake.

誌謝 I
摘要 II
ABSTRACT III
目錄 IV
圖目錄 VI
表目錄 VIII
第一章 緒論 1
1.1 研究動機及背景 1
1.2 文獻回顧 2
1.3 研究目的與方法 4
第二章 基本理論 6
2.1 基本假設 6
2.2 高斯散度定理、格林第一定理及格林第二定理 6
2.3 邊界積分方程式 8
2.4 三維翼面外流場 11
2.5 奇異點與近似奇異點之處理 17
2.5 處理四邊形環積分範例 21
第三章 數值計算 27
3.1 翼面外流場未考慮尾跡流形狀之數值計算結果 27
3.2 翼面尾端跡流之流場速度勢計算 32
3.3 無窮處的尾跡流流場計算 34
3.4 不同三維翼面尾跡流形狀 35
3.5 尋找尾跡流位置 51
3.6 升力係數的驗證 59
第四章 結論與展望 64
4.1 結論 64
4.2 展望 65
參考文獻 66

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