二維水深平均束縮渠道流場之解析

Theoretical Analysis of Two-dimensional Depth-averaged Flows in Contraction Channels

蘇騰鋐(Tung-Hung Su)

指導教授 ： 許銘熙

國立臺灣大學/生物資源暨農學院/生物環境系統工程學研究所/博士(2004年)

https://doi.org/10.6342/NTU.2004.02345

摘要

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。

關鍵字

束縮段 ； 斜震波 ； 水深平均

並列摘要

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.

並列關鍵字

channel contractions ； oblique shock wave ； depth-averaged

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