Application of Surface Velocity Measurements for Discharge Estimate in Rectangular Cross-section Channels
Date Issued
2012
Date
2012
Author(s)
Shih, Sin-Syuan
Abstract
The objective of this study is to estimate the discharge in rectangular channels based on the surface velocity measurements via non-contact velocemetry techniques. In rectangular cross-section open channel flow, the wall effect of side-walls and corners is considerably larger than that in a circular pipe. Also, Reynolds stress at corners produces secondary flows. Together, they make the velocity distributions to vary with aspect ratio, B/H. When the aspect ratio is greater than 10, the maximum velocity will occur at the water surface and the central perpendicular bisector of channel of cross-section. In this situation, the standard U.S. Geological Survey river discharge measurement technique may be applied. However, if the aspect ratio is less than 10, the maximum velocity will take place below the water surface of the central perpendicular bisector. Assuming the USGS wide rectangular channel velocity profile applies and utilizes the surface velocities to approximate will underestimate the discharge. In addition to the aspect ratio, sidewall roughness is another major factor to determine the cross-sectional velocity distribution. Since there is no theoretical velocity distribution for rectangular cross-section with different aspect ratio, so a k-ε numerical model is developed in order to derive cross-sectional velocity distribution using the surface velocities as the upper boundary condition for discharge estimate.
In this study, the Particle Tracking Velocimetry (PTV) technique is utilized for surface velocity measurement. The software was developed by Professor H. Capart’s team . Calculus of rectangular cross-section velocity distribution with known depth, it is written in the turbulent k-ε model, the surface velocity distribution as the free surface boundary conditions, and then the velocity distribution of cross-section obtained by adjusting the parameters. Finally, the area integration estimates discharge. The model is composed of four equations. In addition to continuity and two-dimensional momentum equation; it takes introduction of turbulent kinetic energy and dissipation rate of two variables, deducing the kinetic energy and dissipation rate of two equations to describe the relative importance of eddy viscosity in turbulence. Equations are nonlinear, so it needs to interact with the iterative solutions of velocity、kinetic energy and dissipation rate .
For verification purpose, the comparison of the computed velocity distribution results and the estimations of rectangular cross-section distribution in the literatures is done.
The experiments were performed on steady-state rectangular cross-section channel with different aspect-ratio, and the result measured data of the surface velocity and discharge are used to examine the validity of the discharge-estimating model presented.
Subjects
Particle Tracking Velocimetry Method
k-ε model
surface velocity
secondary flow
aspect ratio
eddy viscosity
Type
thesis
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