本研究模擬單一翼片擺動於二維非穩態流場中所產生的動態失速現象，以尤拉及拉格朗日兩種不同的觀點對模擬之結果進行分析。尤拉觀察法係以渦度場與流線的變化中觀察前緣渦旋(leading edge vortex，LEV)與後緣渦旋(trailing edge vortex，TEV)的演變過程，將分為渦度η與無因次化之速度梯度張量的第二不變量Λ兩種不同形式進行分析，在本研究中將點出渦度η的缺點，並改用Λ得以更完整呈現LEV與TEV的演變，以及從動態失速現象發生前後壓力場之變化，找出其渦旋與升力變化之關係，並由Λ傳輸方程探討動態失速延遲期間對流、壓力與擴散各項的影響。拉格朗日觀察法則是使用拉格朗日連結結構(Lagrangian coherent structures，LCS)，藉此區分出具有不同動態行為的區域，由LCS的變化並配合質點群追蹤找出這些被LCS分隔開的區域內質點動態行為的差異之處。藉由LCS與尤拉方法一同分析擺動機翼之流場讓我們更了解動態失速現象。

This study investigates two-dimensional flow over a pitching airfoil by numerical simulation. The simulation results are analyzed by two different viewpoints based on Eulerian and Lagrangian. In Eulerian viewpoints, we have observed that the evolution of leading edge vortex (LEV) and the trailing edge vortex (TEV) by the vorticity η and the normalized second invariant of the velocity gradient tensor Λ. In this study, we have suggested that Λ can present the rotation strength of the LEV and TEV better than the vorticity, and the relationship between the vortex interaction and the variation of lift force are evaluated by the pressure field. Furthermore, the convective, pressure, and diffusion effects during the dynamic stall are discussed by the transport equation of Λ. In Lagrangian viewpoints, we have used Lagrangian coherent structures (LCS) to distinguish regions with different dynamic behavior and observed the variation of LCS by particle group tracking. The underlying flow dynamics of LEV and TEV is observed under this methodology. This study shows that better understandings of the dynamic stall of a pitching foil are acquired by using the LCS approach and the Eulerian method together.

論文審定書 i
中文摘要 ii
Abstract iii
目錄 iv
圖次 vi
表次 vii
符號說明 viii
第一章緒論 1
1.1 研究背景與目的 1
1.2 文獻回顧 2
1.2.1 動態失速 2
1.2.2 紊流模型 5
1.2.3 拉格朗日連結結構 7
第二章研究方法 8
2.1 數值方法與紊流模型 8
2.2計算相關設定 11
2.2.1邊界條件 11
2.2.2機翼運動模式 12
2.2.3網格設定 13
2.2.4 數值結果與實驗之驗證 14
2.3 渦度η 與 Λ 以及Λ傳輸方程 16
2.3.1 渦度η 與 Λ 16
2.3.2 Λ傳輸方程 16
2.4 拉格朗日連結結構分析法 18
第三章分析－尤拉觀察法 21
3.1 渦度場 22
3.2 壓力場 25
3.3 Λ傳輸方程 26
第四章分析－拉格朗日觀察法 29
第五章結論與建議 35
參考文獻 37

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