Theoretical Analysis of Two-dimensional Depth-averaged Flows in Contraction Channels
Date Issued
2004
Date
2004
Author(s)
Su, Tung-Hung
DOI
zh-TW
Abstract
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.
Subjects
束縮段
斜震波
水深平均
channel contractions
oblique shock wave
depth-averaged
Type
thesis
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