本文主要利用拉格朗日連結結構(Lagrange coherent structure, LCS)方法分析空蝕紊流流場中的動態行為。空蝕現象指的是液體在流場中，當壓力低於蒸氣壓時，流體將從液體蒸發成氣體的一個現象，其通常伴隨著噪音、震動、阻塞、破壞等情況發生，造成機械的破壞或者機械功率降低等不好的影響。而為了日後能有效的降低或利用空蝕效應，故本文將針對空蝕流場的動態行為進行研究。
本研究將採用攻角8度的Clark-Y水翼作為數值空蝕流場之幾何結構，並搭配計算流體力學軟體Fluent 14.0版本進行數值模擬，最後輔以額外撰寫的程式將數值計算之結果轉換成Finite-time Lyapunov exponent(FTLE)與拉格朗日連結結構，再透過質點追蹤將流場中不同的動態行為做一分區，藉以分析空蝕流場的複雜動態行為。
研究結果顯示，LCS結構涵蓋面積的增減能代表空蝕現象強弱的變化，此外也利用LCS結構捕捉了迴向射流的位置及動態行為，並發現水翼下表面來流會被尾部新生之逆時針渦旋吸引至水翼上表面區域內之現象，進而發現尾部反向射流的角度會隨尾部氣泡密度大小而有所偏移，因而造成尾部渦旋的消長。

Turbulent cavitating flows are ubiquitous in our daily life and technologies, which will induce the noises, material removal, and efficiency reduction of the flow machinery. As the result, it is important to investigate the flow structures of the cavitating flow to predict its dynamical behaviors effectively. In the present study, we utilize the volume of fraction techniques to time-dependent turbulent cavitating flows.
Lagrangian Coherent Structures (LCS) have been developed to highlight the flow structures recently. It is a trajectory-basedapproach from a Lagrangian perspective by considering the fluid as a dynamical system of fluid particles rather than a continuum. This method is frame-independent and more useful to capture the dynamical features of the flows, which can be missed in the traditional Eulerian analyses based on the velocity or vorticity fields.

This dissertation utilizes the finite-time Lyapunov exponent(FTLE) and LCS to get a better understanding of the flow dynamics and underlying physics of the simulated cavitating flows for different representative phenomena during the corresponding stages. It is found that LCS can capture the re-entraint jet front and also indicate that fluid around lower surface could be attracted to the upper surface of the hydrofoil when the induced cavity grows around the trailing edge. This dissertation also analyzes the complicated flow interaction around the trailing edge when the multiple circulation and cavitation regions are formed by particle tracking method.

中文摘要 i
ABSTRACT ii
目錄 iii
圖目錄 v
表目錄 vii
符號說明 viii
第一章 緒論 1
1.1空蝕簡介 1
1.2文獻回顧 3
1.2.1空蝕現象文獻之回顧 3
1.2.1.1熱力學性質 3
1.2.1.2實驗之觀察 4
1.2.1.3數值模擬 5
1.2.1.4空蝕效應之減低方法 6
1.2.2拉格朗日連結結構文獻之回顧 7
1.3研究動機 8
第二章 研究方法 10
2.1數學模型 10
2.2空蝕模型 11
2.3紊流模型 13
2.3.1 Filter-based model(FBM) 14
2.3.2 Density-correction-based model(DCM) 15
2.3.3 Hybrid FBM and DCM model 15
2.4數值方法 16
2.4.1計算區域與邊界條件 16
2.4.2網格測試及驗證 18
2.5拉格朗日連結結構 18
2.6空蝕現象研究流程 21
第三章 結果與討論 24
3.1數值結果與實驗之驗證 24
3.2週期氣泡各階段初步分析 25
3.3拉格朗日連結結構之解析 26
3.3.1 LCS結構之分析-A結構 27
3.3.2 LCS結構之分析-B結構 28
3.3.2.1 B結構各階段之分析 29
3.3.2.2 B結構與迴向射流之關係 32
3.3.3 LCS結構之分析-C結構 33
3.3.4 LCS結構之分析-D結構 35
第四章 結論與建議 81
4.1拉格朗日連結結構方法解析空蝕流場之結論 81
4.2未來研究建議 82
參考文獻 85

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