空蝕經常發生在許多水力裝置之中，造成劇烈的壓力變化，並導致噪音、震動等現象發生。本研究採用RANS (Reynolds-averaged Navier-Stokes)中的standard k-ε紊流模型、RNG (Re-Normalization Group) k-ε紊流模型以及PANS (Partially-Averaged Navier-Stokes) 紊流模型，並使用user defined function之功能寫入Zwart的空蝕模型與過濾器(filter)，模擬二維Clark Y水翼、NACA66水翼以及三維Delft twist 11 水翼在水中所發生的空蝕現象。
本研究利用四種不同的過濾器尺寸，配合一百組空蝕模型中的蒸發、凝結係數，應用在攻角8度的Clark Y水翼，並逐漸降低流場的空蝕數，將數值模擬結果之平均升、阻力係數和氣泡運動頻率與實驗數據比較，確立可用係數值域。接下來，固定所選用的係數，置換水翼幾何形狀，並與其它的紊流模型所得之數值結果相比較，以證明係數的泛用性(generality)。
接下來，Clark Y水翼的空蝕流場結構也被分析。為了流場結構在數值上的準確性，本研究改變紊流模型，而係數的泛用性也不再被要求。最後，基於在二維空蝕流場的模擬經驗，進一步模擬三維Delft twist 11 水翼之空蝕流場，分析迴向射流與側向射流對流場結構的影響。在結果中發現，除了由於氣泡尾端附近的壓差造成的迴向射流，水翼兩側的壓差、來流與迴向射流的碰撞也促進側向射流的產生，影響整個氣泡結構。

Cavitation models and turbulent models are widely used to predict cavitation phenomenon in numerical simulations. The coefficients which dominate the evaporation and condensation rates in cavitation models are often empirical and tunable. To reduce the sensitivity and raise the generality of the coefficients, unsteady cloud cavitation cases on 2D Clark Y and NACA66 hydrofoils were simulated with different combinations of empirical coefficients and turbulent treatments. The Reynolds-Averaged Navier-Stokes (RANS) and Partially Averaged Navier-Stokes (PANS) turbulent approach was coupled with a homogeneous cavitation model to calculate the time-averaged lift coefficient, time-averaged drag coefficient and frequency of cavitation shedding behavior. The suitable empirical coefficients are presented in this study.
An unsteady 3D simulation on a Delft twist 11 hydrofoil was also performed. The re-entrant jets and structure of the cavitating flow around the hydrofoil was investigated. The results on time-averaged lift coefficient, three dimensional cavity structure and shedding frequency agreed well with experimental observation. Analysis of the flow field reveals that secondary shedding is an omen of primary shedding and induced by a pair of side-entrant jets. These side-entrant jets promote re-entrant jets to move further upstream. Eventually, the attached cavity is cut off by the re-entrant jets, leading to the primary shedding.

論文審定書 i
謝 誌 ii
中文摘要 iii
Abstract iv
目錄 v
圖目錄 vii
表目錄 viii
符號說明 ix
第一章 緒論 1
1.1前言 1
1.2文獻回顧 1
1.2.1空蝕現象 1
1.2.2實驗觀察 3
1.2.3數值模擬 3
1.2.3.1 空蝕模型 3
1.2.3.2紊流模型 4
第二章 研究方法 6
2.1數值方法與統御方程式 6
2.2空蝕模型 8
2.3紊流模型 10
2.3.1 Standard k-ε model 10
2.3.2 RNG k-ε model 12
2.3.3 PANS model 12
2.3.4 Filter-based model (FBM) 13
2.3.5 Density-correction-based model (DCM) 13
2.3.6 Hybrid FBM and DCM (Hybrid model) 14
2.4計算區域與邊界條件 15
2.4.1二維翼型 15
2.4.2三維翼型 16
第三章 結果與討論 19
3.1泛用性 19
3.2流場結構 23
3.2.1二維流場 Clark Y翼型 23
3.2.2三維流場 Delft twist 11 翼型 25
3.2.2.1 次氣泡脫離 27
3.2.2.2 主氣泡脫離 27
第四章 結論與建議 39
參考文獻 41

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