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研究生:蘇騰鋐
研究生(外文):Tung-Hung Su
論文名稱:二維水深平均束縮渠道流場之解析
論文名稱(外文):Theoretical Analysis of Two-dimensional Depth-averaged Flows in Contraction Channels
指導教授:許銘熙許銘熙引用關係
學位類別:博士
校院名稱:國立臺灣大學
系所名稱:生物環境系統工程學研究所
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:中文
論文頁數:117
中文關鍵詞:束縮段斜震波水深平均
外文關鍵詞:channel contractionsoblique shock wavedepth-averaged
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渠道二維水深平均模式,一直是水力學上重要的課題。本文的主要目的為分析二維渠道中非旋流及超臨界流之流況,針對二維束縮段非旋流時,利用等勢能函數來計算矩形渠道收縮段之水深及流速分布。由於等勢能函數在二維渠道中可寫成Laplace的方程式,故在本文中利用Schwarz-Christoffel 轉換,來求解等勢能函數之Laplace方程式。將原來的水理參數化成等勢能函數及水深參數,利用等勢能函數之定義,可計算出二維矩形渠道收縮段之速度分布。
  在二維超臨界流束縮段方面,本文針對水平渠道,斜震波折角及最佳束縮段長度進行研究,其中斜震波折角與福祿數及束縮折角的關係也是本文研究的重點。研究發現斜震波折角為福祿數及束縮折角之函數關係,並利用統計的方式求出斜震波折角公式。另外,由斜震波理論出發,建立最佳束縮段長度關係圖,並提出最佳束縮段長度公式,利用福祿數及斷面束縮比直接求解,以代替試誤法之求解(Chow, 1959)。最後,利用數值試驗來驗証本文所提之最佳束縮段長度關係圖。
The analysis of two-dimensional depth-averaged flows in open channel is of great importance in the hydraulics. The main purpose of this study is to find the solution of the two- dimension irrotational flow and supercritical flow in channel contractions. For irrotational flow, the potential function is used to compute the water depth and velocity distributions in constriction channel. The potential function in a two-dimension channel flow can be expressed as the form of Laplace equation. In this study, the Schwarz-Christoffel mapping is used to solve the Laplace equation. The hydraulic variables in the channel are reduced to two variables, the potential function and water depth. By using the definition of potential function, the velocity distribution in two-dimensional constriction channel is solved for.
The oblique shock angles and the optimal transition length for channel contraction with supercritical flows in a horizontal channel are analyzed. The relationships between the shock angles, Froude number and contraction angles have been investigated. Because the shock angles are the function of the Froude number and contraction angle, the explicit shock angles function can be established by statistical method. In addition, a new optimal contraction diagram is developed based on the fundamental relationship between oblique shock waves and optimal contraction equations. The optimal contraction equations expressed in terms of the Froude number and contraction ratio are proposed, in stead of trial-and-error procedures (Chow, 1959) for the determination of the optimal contraction. Moreover, numerical simulations are also used to examine the validity of the new optimal contraction diagram.
中文摘要 I
Abstract II
目錄 III
圖錄 V
表錄 VII
符號表 VIII
第一章 緒論 1
1.1 研究緣起 1
1.2 前人研究 1
1.3 研究目的及內容 5
  1.4 本文組織 5
第二章 基本方程式 7
2.1 流體之動量及質量方程式 7
    2.1.1 質量守恆方程式 7
    2.1.2 動量守恆方程式 8
2.2 水深平均連續及動量方程式 9
    2.1.1 連續方程式 9
    2.1.2 動量方程式 10
2.3 非旋流方程式 13
2.4 超臨界流斜震波 15
第三章  二維束縮渠道等勢能流解析 20
3.1 Schwarz-Christoffel之轉換 20
3.2 等勢能函數轉換 25
3.3 等勢能函數之解 26
3.4 二維矩形渠道收縮段(constriction) 28
第四章  二維束縮段超臨界流解析 29
4.1 束縮段斜震波方程式 29
4.2 頸塞流況 32
4.3 束縮段斜震波折角理論 34
4.4 最佳束縮長度理論 37
第五章 驗証與比較 41
5.1 非旋流解析之比較 41
5.2 二維非旋流矩形束縮渠道解析 43
5.3 二維矩形渠道收縮段等勢能函數 45
5.4 連續型二維矩形渠道非對稱收縮段等勢能函數 47
5.5 最佳束縮長度之驗証 48
5.6 二維超臨界流最佳束縮長度應用 50
第六章 結論與建議 52
6.1 結論 52
    6.1.1 二維非旋流 52
    6.1.2 二維超臨界流 53
6.2 建議 54
參考文獻 55
附錄A 114
簡歷 116
學術著作 117
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