為了要模擬噴嘴內氣泡震波空蝕現象的發生，在數值模擬方面本文採用了ROE的通量分離法。以推導原始的ROE方程後改寫成代數式的型式，而以此方法可以提高運算的效率。空間離散則使用Muscl+Limiter，而在時間離散上採用具TVD效應之三階Runge-Kutta法。吾人以代數式型式的ROE模擬一維的震波管及爆炸波問題作驗證，得到的結果與真實黎曼解幾乎是一致的。接著模擬二維的噴嘴，在採用 紊流模式時能模擬出週期性變化，及空蝕係數大於1.5後可抑制空蝕氣泡的產生。最後模擬二維及軸對稱注油器，則可看出兩者氣泡震波發生的位置與時間有明顯的差異性。在未來則是希望進行三維測試例的模擬。

The purpose is to simulate the shock-like cavitation phenomena in the nozzle flow. Numerical simulation is based on the Roe type flux splitting method. The original ROE solver is reformulated in the algebraic form. This reformulated method can enhance the efficiency of the computations. Also, the MUSCL type method is used to deal with spatial discretization and a 3-order Runge-Kutta method is chosen to discretize the time evolution. First, one-dimensional shock tube and blast wave problems are validated with numerical calculations. Secondly, the   turbulence model can achieve the periodical revolution of bubble growths of two-dimensional cavitated nozzle flows. In addition, the flow under the cavitation number more than 1.5 is shown that the cavitation will not appear in the nozzle. Finally, the two-dimensional and axis-symmetric injector nozzle cases show that the different location and appearing time for the shock-like cavitated flow are captured. The three-dimensional test cases will be necessary in the further study.

目錄
致謝 i
中文摘要 ii
英文摘要 iii
目錄 iv
圖目錄 vii
符號說明 xi
第一章 緒論 1
1.1前言 1
1.2噴嘴的物理現象	3
1.3空蝕的物理現象	5
1.4震波管原理	5
1.5文獻回顧	7
1.6研究動機與目的	11
第二章 數值計算方法	13
2.1統御方程式	13
2.2狀態方程式	16
2.3數值分法	18
2.4真實黎曼解(Exact Riemann Solver)	20
2.5紊流模式	22
2.6 空蝕模式	24
第三章 模擬結果與討論	26
3.1一維波方程	26
3.2 一維震波管問題	27
3.3 一維爆炸波問題	30
3.4二維噴嘴邊界條件及網格設定	33
3.4.1網格及時間獨立性測試	34
3.4.2測試VOF模型時不同的紊流模式	36
3.4.3測試Mixtue模型時不同的紊流模式	40
3.4.4 選k-ω standard模式 比較VOF與Mixture模型	44
3.4.5 選k-ω standard模式與Mixture模型比較不同K值	45
3.5二維注油器噴嘴	46
3.5.1 網格獨立性測試	48
3.5.2 選定網格數進行模擬	51
3.5.3  採用紊流模式	55
3.5.4 測試不同壓差下氣泡震波生成情形	56
3.6軸對稱注油器噴嘴	58
第四章 結論與未來展望	62
參考文獻	63
附錄A 投稿論文	66
 
圖目錄
圖1-1-1 船用螺旋 2
圖1-1-2注油器 3
圖1-2-1 subsonic flow經過噴嘴之後的變化情形 4
圖1-2-2 supersonic flow經過噴嘴之後的變化情形 4
圖1-4-1 shock tube at t=0 6
圖1-4-2 shock tube at t>0 7
圖1-5-1  8度擴張管空蝕現象 8
圖1-5-2 平均空蝕佔有率 8
圖2-4-1 真實黎曼解示意圖 21
圖3-1-1 三種方法與真實解作比較 27
圖3-2-1震波管密度分佈圖 28
圖3-2-2震波管壓力分佈圖 29
圖3-2-3震波管速度分佈圖 29
圖3-3-1爆炸波密度分佈圖 31
圖3-3-2爆炸波壓力分佈圖 31
圖3-3-3爆炸波速度分佈圖 32
圖3-4-1二維噴嘴網格圖 33
圖3-4-2 [10] 34
圖3-4-3 網格獨立性測試 35
圖3-4-4 時間獨立性測試 35
圖3-4-5氣體體積佔有率隨時間變化 36
圖3-4-6四個時間的氣泡分佈圖 37
圖3-4-7  0.045秒時壓力分佈圖 37
圖3-4-8  0.045秒時壁面壓力分佈圖 37
圖3-4-9氣體體積佔有率隨時間變化 39
圖3-4-10四個時間的氣泡分佈圖 39
圖3-4-11  0.045秒時壓力分佈圖 40
圖3-4-12  0.045秒時壁面壓力分佈圖 40
圖3-4-13氣體體積佔有率隨時間變化 41
圖3-4-14四個時間的氣泡分佈圖 41
圖3-4-15  0.045秒時壓力分佈圖 42
圖3-4-16  0.045秒時壁面壓力分佈圖 42
圖3-4-17氣體體積佔有率隨時間變化 43
圖3-4-18四個時間的氣泡分佈圖 43
圖3-4-19  0.045秒時壓力分佈圖 44
圖3-4-20  0.045秒時壁面壓力分佈圖 44
圖3-4-21氣體體積佔有率隨時間變化 45
圖3-4-22  0.045秒時壁面壓力分佈圖 45
圖3-4-23  0.045秒時氣泡分佈圖 45
圖3-4-24  0.045秒時氣泡分佈圖 45
圖3-4-25不同K值時氣泡分佈圖 46
圖3-5-1二維注油器網格圖 47
圖3-5-2網格獨立性測試圖 49
圖3-5-3網格獨立性測試局部放大圖 49
圖3-5-4 不同網格數時氣泡震波分佈情形 50
圖3-5-5中線壓力變化 52
圖3-5-6   秒時氣泡震波分佈 52
圖3-5-7   秒時壓力分佈 52
圖3-5-8   秒時氣泡震波分佈 52
圖3-5-9   秒時壓力分佈 52
圖3-5-10   秒時氣泡震波分佈 53
圖3-5-11   秒時壓力分佈 53
圖3-5-12   秒時氣泡震波分佈 53
圖3-5-13   秒時壓力分佈 53
圖3-5-14   秒時氣泡震波分佈 53
圖3-5-15   秒時壓力分佈 53
圖3-5-16   秒時氣泡震波分佈 54
圖3-5-17   秒時壓力分佈 54
圖3-5-18 不同時間空蝕氣泡分佈圖 54
圖3-5-19 採用層流與紊流模式時氣泡隨時間變化 55
圖3-5-20   秒時氣泡震波分佈圖 56
圖3-5-21 不同壓差時氣泡震波分佈圖 58
圖3-6-1軸對稱注油器網格圖 59
圖3-6-2二維與三維注油器氣泡隨時間變化 60
圖3-6-3不同時間點氣泡震波分佈圖 61

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