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研究生： 周昱成
Chou, Yu-Cheng
論文名稱： 過水障礙物流形對壅塞明渠流況之影響
The Shape Effects of a Submerged Obstacle on the Choked Open-Channel Flow
指導教授： 唐啟釗
Tang, Chii-Jau
學位類別： 碩士
Master
系所名稱： 工學院 - 水利及海洋工程學系
Department of Hydraulic & Ocean Engineering
論文出版年： 2017
畢業學年度： 105
語文別： 中文
論文頁數： 104
中文關鍵詞： von Mises轉換 、曲線流 、流線座標 、越臨界流 、最佳化 、未知流量
外文關鍵詞： critical flow, streamline coordinate, unknown flow discharge, optimization, choked flow
相關次數： 點閱：154  下載：5 
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    • 明渠水流通過潛水堰等結構物後，所產生的轉換(transition)流況，一直都是水利工程師所感興趣的問題。這些轉換流況通過臨界點的越臨界流流況，更是相當重要，因為臨界點將是整體渠道流量的控制點。此控制點的存在，也是淹水發生的必要因素；當發生淹水時，下游將無法適量排出上游提供之流量，必須抬升水位以增加可通過流量，因此形成壅塞流(choked flow)，而其壅塞位置就是臨界點的位置。從傳統明渠水力學，可知臨界點處將發生於底床最高點及比能最小處，但從實際過堰水流的觀察中，可知堰頂處水流將不再是靜水壓力分布，且臨界點不可能同時出現在同高的堰頂處，因此這個結果將不再適用。為此，本研究考慮自由液面中水面斜率的完整效應，使得越臨界點之明渠水流分析更符合實況。
    本研究採用流線座標數值方法，計算越臨界流經不同堰形(包含底床斜率與曲率變化)之流況。並搭配流線座標及使用擴充型von Mises轉換，來解決傳統卡氏座標應用不規則邊界計算的困難。但因涉及未知自由液面的計算，且發生臨界條件下的流量為未知值，使得用一般的求解方法，例如：迭代法或牛頓法的計算將遇到許多衍生困難。為此，本研究使用最佳化的方法來計算，來解決此非線性的問題。
    本文併用一維和二維計算，以得到自由液面形狀和臨界流量，並進一步分析其斷面速度和壓力分布。得知二維越臨界流，使用一維流管概念的計算將是可行的。除此之外，不同堰形的水力特性也將是本研究的分析重點。從而得知改變堰形的斜率與曲率，將能對底床負壓力有直接的改善功效。並推論底床斜率的影響似乎較曲率來的明顯。

    Floods occur when the flow chokes in the transition from the subcritical flow at upstream to the supercritical flow at downstream, for example, the flow over a high submerged weir. In this case, the curvilinear flow path makes non-hydrostatic pressure distribution and non-uniform flow velocity in the cross section. In consequence, the complete dynamic condition at curved free-surface involves the square of free-surface slope in addition to the conventional one-dimensional open channel flow theory because the ratio of vertical to horizontal velocity component there is exactly the slope of free-surface. To deal with the unknown variables of flow discharge, critical point and free-surface elevations, we used the one-dimensional (1-D) approach by sequential quadratic programming optimization. For the two-dimensional transitional choked flow, the 1-D optimization approach is utilized to calculate the free-surface elevation by using many 1-D streamtubes, for each streamtube bounded by the free-surface and a varied streamline below the free surface. Moreover, the extend von Mises transformation for given x=x(ξ) and stream function ψ=ψ(η) were used to find out the position of internal streamlines y=y(ξ,η) in the streamline coordinate (ξ,η). To this end, the elevations of all internal streamlines were obtained by solving the Laplace equation under the calculated free-surface elevation. Using them in this study, different shapes of a submerged obstacle were first investigated for the choked open-channel flow. Then the channel bottom with different slopes and curvatures are used to test their influences on the choked flow.

    摘要................................................. I 誌謝...............................................XXII 目錄..............................................XXIII 表目錄............................................ XXVI 圖目錄............................................XXVII 符號說明.......................................... XXXI 第一章緒論................................................. 1 1.1 前言............ ................................ 1 1.2 文獻回顧......................................... 3 1.2.1 座標轉換....................................... 4 1.2.2 曲線流(curvilinear flow)研究................... 4 1.3 研究動機及目的................................... 8 1.4 論文架構......................................... 8 第二章理論分析...................................... 10 2-1 應用流線座標法.................................. 10 2-1.1 二維控制方程式................................ 12 2-1.2 邊界條件...................................... 14 2-1.3 二維速度和壓力場計算.......................... 15 2-2 傳統一維明渠水力學壅塞流理論回顧與檢討.......... 16 2-2.1 一維臨界流條件................................ 17 2-3 包含水面斜率效應下之越臨界流.................... 21 2-3.1 一維臨界流條件................................ 22 2-3.2 二維越臨界流方法.............................. 25 2-4 最佳化方法介紹.................................. 25 2-4.1 限制條件之最佳化.............................. 25 2-4.2 目標函數與限制式.............................. 27 2-4.3 函數演算法簡述................................ 28 第三章數值方法...................................... 31 3-1 有限差分法...................................... 31 3-1.1 有限差分法在流線座標之應用.................... 31 3-2 一維計算自由液面的流程.......................... 34 3-3 二維計算內部流場流程............................ 36 3-3.1 Laplace 方程式求解流線位置.................... 37 3-3.2 二維越臨界流自由液面求解...................... 38 3-4 完整計算流程.................................... 39 第四章結果與討論.................................... 42 4-1 傳統明渠水力學越臨界流.......................... 42 4-1.1 底床及格網條件................................ 42 4-1.2 自由液面形狀與速度、壓力場.................... 42 4-2 考慮水面斜率下之一維越臨界流.................... 46 4-3 最佳化方法的選擇和應用於一維越臨界流之過程評估...50 4-3.1 無移動格網方法................................ 50 4-3.2 θ求解法....................................... 51 4-3.3 y求解法....................................... 57 4-4 一維計算結果與討論.............................. 61 4-4.1 經高斯斯曲線底床形狀之越臨界流................ 62 4-4.2 經三角形底床之越臨界流........................ 66 4-5 二維流況結果與討論.............................. 74 4-5.1 二維流經高斯曲線形狀底床之分析................ 74 4-5.2 二維流經三角形底床之分析...................... 77 4-6 障礙物流形計算與結果............................ 84 4-6.1 不同定坡度斜率底床流形效應.................... 84 4-6.2 底床流形曲率效應.............................. 91 第五章結論與建議.................................... 99 5-1 結論............................................ 99 5-2 建議........................................... 101 參考文獻........................................... 102

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