臺灣博碩士論文加值系統

本研究的模擬對象是軸對稱彈體的超空化流場，並嘗試在一廣義的空化係數下進行空化空泡的計算，主要是預測其形狀，包括無攻角之軸對稱問題以及有攻角之三維非軸對稱問題。
對於空化流場模擬而言，因為空泡形狀未知，為解的一部份，因此問題為非線性，需要迭代求解。在本論文中我們假設一穩定、無旋性、無熱傳遞、無黏性且不可壓縮之勢流場來模擬片狀空泡的彈體流場，然後運用低階勢基小板法來求解。除了預測外形的迭算，由於在勢流場中並無法決定空泡長度與空化係數的關係，所以針對這個問題，我們還必須在設定的空化係數下迭算空泡長度，因此是屬直接法。片狀空化空泡尾緣的真實流況相當複雜，本研究也將對這些現象加以了解，為了盡量滿足物理現象，並在數學上求得惟一解，我們採用等切速度結尾模型，也將稍加探討文獻上現存之數種結尾模型。
最後我們發現超空化彈體在模擬上會在結尾附近產生異常大的源流分佈導致發散，而在空泡前緣也出現異常的厚度增加量使得空泡外形出現凹陷，所以本研究也將針對這些問題進行修正。

This thesis focused on the simulation of the supercavitating flow field of an axisymmetric projectile. We attempted to compute the cavity at a cavitation number based on cavity pressure, and mainly focused on their bubble shape due to the axisymmetric problem with zero angle of attack and the three-dimensional non-axisymmetric problem with an angle of attack.
In the flow field simulation, because the shape is part of the solution, the problem is nonlinear; it needed an iteration procedure for solution. We assumed that the flow field is steady, irrotational, without heat transfer, inviscid and incompressible. Under these assumptions, the simulation of the sheet bubble becomes a potential flow problem, and then we applied a low-order panel method to solve its shape and flow field. In addition to the iterations for predicting the shape, we had to iterate directly the cavity length with fixed cavitation number, due to the fact that the relation between cavity length and the cavitation number cannot be explicitly expressed. The phenomenon at the bubble tail is very complicated; we simply use the constant tangential velocity termination closure model for satisfying the uniqueness of the physical and mathematical solution.
Finally, we found an unusual source distribution at the cavity tail and the front of bubble in the simulation, the former caused the convergence in the computations and the later made for an uneven shape. Therefore the present work would discuss the improved approaches against these problems.

中文摘要.........................................................................................................................i
英文摘要........................................................................................................................ii
謝誌...............................................................................................................................iii
目錄...............................................................................................................................iv
表目錄..........................................................................................................................vii
圖目錄.........................................................................................................................viii
第一章 緒論................................................................................................................1
1.1 空化流場研究回顧........................................................................................1
1.2 邊界元素法與其空化流場的應用................................................................5
1.3 空化流場數值方法新發展..........................................................................11
1.4 入水空泡的研究..........................................................................................13
第二章 水翼與彈體空化流場..................................................................................20
2.1 空化現象的種類..........................................................................................20
2.2 真實的空化流場現象..................................................................................23
2.3 模擬空化空泡..............................................................................................33
2.4 結尾模型......................................................................................................32
2.5 穿水通氣空泡..............................................................................................42
2.6 研究目標......................................................................................................44
第三章 理論方程式與數值方法..............................................................................45
3.1 理論方程式..................................................................................................45
3.2.1 基本假設..............................................................................................45
3.2.2 統御方程式..........................................................................................46
3.2.3 邊界條件..............................................................................................48
3.2 邊界元素法..................................................................................................53
3.2.1 格林第三恆等式..................................................................................53
3.2.2 離散方程式..........................................................................................54
3.2.3 影響係數..............................................................................................57
3.2.4 離散化邊界條件..................................................................................60
3.3 空泡形狀計算..............................................................................................61
第四章 計算結果與討論..........................................................................................67
4.1 無空化彈體流場..........................................................................................67
4.2 軸對稱超空化彈體流場..............................................................................70
4.2.1 收斂條件與結尾現象..........................................................................70
4.2.2 修正結尾模型......................................................................................74
4.2.3 空泡前緣修正......................................................................................80
4.2.4 SCVA程式結構...................................................................................83
4.2.5 解之存在性、惟一性與一致性..........................................................86
4.2.6 流場模擬結果......................................................................................90
4.2.6.1 彈體幾何的影響..................................................................90
4.2.6.2 空化係數的影響..................................................................92
4.2.6.3 收斂之空泡外形與壓力分佈..............................................94
4.2.6.4 不同空泡起始點與彈頭濕表面形狀的影響......................98
4.3 非軸對稱超空化彈體流場........................................................................101
4.3.1 首尾解一致條件................................................................................101
4.3.2 空泡外形問題....................................................................................103
4.3.3 CFL條件與橫向流分佈問題............................................................105
第五章 結論與建議................................................................................................108
參考文獻...................................................................................................................110
附錄A 超空化武器發展現況................................................................................120
附錄B 空化與通氣現象........................................................................................124
附錄C 水彈道導論................................................................................................127
附錄D 數學基礎....................................................................................................134
D.1 格林恆等式........................................................................................134
D.2 奇異點................................................................................................140
D.3 多連通計算域....................................................................................144
D.4 存在性、惟一性與一致性................................................................146
附錄E 二維影響係數.............................................................................................150
附錄F 二維空泡形狀計算.....................................................................................154
附錄G SCAV程式使用手冊.................................................................................157
G.1 輸入檔說明........................................................................................157
G.2 執行過程............................................................................................159
G.3 輸出檔說明........................................................................................162
G.4 範例....................................................................................................162

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