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研究生:陳仲帆
研究生(外文):Chung-FanChen
論文名稱:以二維高階小板法分析起伏浮體之流體動力係數
論文名稱(外文):The Analysis on the Hydrodynamic Coefficients of the Heaving Floating Body Using the Two Dimensional High Order Panel Method
指導教授:方銘川方銘川引用關係
指導教授(外文):Ming-Chung Fang
學位類別:碩士
校院名稱:國立成功大學
系所名稱:系統及船舶機電工程學系碩博士班
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:中文
論文頁數:62
中文關鍵詞:二維B-Spline流體動力係數
外文關鍵詞:two-dimensionB-Splinehydrodynamic coefficients
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以往求解具自由液面浮體流體動力係數之相關問題,多以低階方式來離散物體幾何、源點強度和勢流等,在有限的線段離散下,無法真實地呈現其物理性質,為了不失去其特性,本文透過二維高階小板法建立浮體幾何,並求解起伏運動浮體之流體動力係數。
首先,本文將物體表面的源點強度分佈導入B-Spline概念,以B-Spline曲線的基底函數與控制點來描述。在求解邊界值問題中,基底函數為已知,而其控制點為待求解之變數,當邊界值問題求解後,透過源點強度控制點可計算出源點強度、勢流和流體動壓;沿著浮體浸水面,積分流體動壓後,可得到其流體動力係數─附加質量與阻尼。在邊界值問題中,必須將積分式離散,積分式當中包含了B-Spline曲線中的基底函數,本文則使用高斯積分的數值技巧來處理。
高階小板法中,物體幾何必須以曲線描述,然而一般問題常以多點資訊描述而非曲線。假設待解物體的形狀變化不大,本文在已知幾何點位資訊下,以局部差分技巧重新建立幾何資訊,其建立的曲線必會通過原本的幾何點位。在本文中,探討起伏運動浮體的流體動力係數,並與以往之方法比較,而離散積分所使用數值技巧中(高斯積分),透過數值實驗有找出適當的源點強度控制點數量,且有一定的計算準確性。
The study introduces the B-Spline technique to establish two-dimension high-order panel for solving the hydrodynamic coefficients of heaving floating body. Traditionally, the concerned quantity distributions of the model, such as body shape, source intensity, and potential etc., are discretely approximated. Usually such discrete approximation must be described by enough segments to get the generality sufficiently. Thus, the high-order panel might be applied to formulate geometry and concerned quantity in spline sense without losing generality.
In the present study, we cast the source intensity distribution over body into B-Spline sense. Since that, source intensity is transformed to be formulation related to product of basis function and control points. Then the basis function is well defined and unknown control points are solved as a boundary-value problem (BVP). After solving the BVP, the intensity of control points would lead to the solutions of source intensity, velocity potential and hydrodynamic pressure on body. Ultimately, the relevant hydrodynamic coefficients, i.e. added mass and damping coefficient, can be obtained. Besides, integration of the B-Splined source intensity in the present BVP includes the additional basis function. To deal with this, the Gaussian quadrature technique is applied to perform the numerical integration.
To implement high-order panel, the spline information for body geometry is essential. However, the geometry may be released in sense of points, not spline formulation. If the shape of target geometry is simple and its variation is small, we can just fit the given points on body to reversely estimate the required spline information. Thus, the local interpolation technique, constructing a B-Spline curve precisely passing through a set of geometric data, is incorporated into the implement of high-order panel. Through the comparisons with the computation results by tradition model, we can conclude that the number of control points in the spline intensity and integration point in the Gaussian quadrature technique affect the computation accuracy of high-order panel.
摘要 I
Abstract II
致謝 IV
目錄 V
表目錄 VII
圖目錄 VIII
符號說明 XIII
第一章 緒論 1
1-1 研究動機與目的 1
1-2 文獻回顧 1
1-3 本文架構 4
第二章 理論基礎 6
2-1 參考座標系統 6
2-2 基本假設與邊界條件 6
2-3 格林函數與源點分佈法 8
2-4 流體動力 10
第三章 數值方法 12
3-1 B-Spline曲線 12
3-2 幾何曲線建立 13
3-3 源點分佈法之離散 15
3-4 勢流 21
3-5 主程式流程圖 22
第四章 計算結果與討論 23
4-1 幾何曲線 23
4-2 格林函數 25
4-3 源點強度與流體動力 42
第五章 結論與未來展望 50
參考文獻 51
附錄1 55
附錄2 58
附錄3 60

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