利用表面流速量測推估矩形斷面流量之研究

Application of Surface Velocity Measurements for Discharge Estimate in Rectangular Cross-section Channels

石欣軒(Sin-Syuan Shih)

指導教授 ： 李天浩

國立臺灣大學/工學院/土木工程學研究所/碩士(2012年)

https://doi.org/10.6342/NTU.2012.01803

摘要

本研究嘗試以非接觸式方法，建立推估河川或渠道流量的量測技術。在矩形斷面明渠水流中，邊壁和角落的壁效應比圓形滿管流顯著，雷諾應力會在角落產生二次流，兩者使得斷面流速分佈會因寬深比(B/H)而異。若矩形渠道的寬�深比大於10，最大流速會在渠道斷面中垂線的水面上，可以使用美國地質調查所的標準方法估計河川流量；若寬�深比小於10，最大流速會出現在中垂線的水面以下，若以非接觸式方法估計水面流速，並假設流速分布如美國地質調查所的寬矩形渠道曲線分布，便會低估斷面流量。除了當寬�深比外，邊壁粗糙率是影響流速分布的另一項重要因素。因為矩形斷面流速分布並無理論解，需要建立數值模式配合表面流速遙測估計值，求解矩形斷面速度分佈，才能正確推求流量。
本研究採用粒子追蹤測速法（Particle Tracking Velocimetry）遙測估計表面流速。處理影像和分析判斷粒子移動軌跡、估計水面流速分佈，是應用卡艾瑋教授團隊所研發的軟體。演算已知水深矩形斷面流速分佈的方法，是自行撰寫 紊流數值模式，期望以表面流速分佈作為自由水面的流速邊界條件，透過調整參數獲得斷面的流速分布，再作面積分推估流量。 模式是由四條方程式組成，除了連續方程式和動量方程式外；另外引進紊流動能 和消散率 兩個變數，推演出與紊流動能和消散率相關的兩條方程式，以描述紊流中相對重要的渦流粘度(eddy viscosity)。因為聯立方程組為非線性，需要交互迭代求解速度分佈、動能和消散率等變數。
方法驗證部分，除了以文獻中的矩形斷面流速分佈，檢驗本研究方法計算的結果外；另外，以不同寬深比矩形渠道穩態水流試驗的水面流速和流量量測數據，檢驗本研究方法模式推估流量的正確性。

關鍵字

粒子追蹤測速法 ； k-ε模式 ； 表面流速 ； 二次流 ； 寬深比 ； 渦流粘度

並列摘要

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.

並列關鍵字

Particle Tracking Velocimetry Method ； k-ε model ； surface velocity ； secondary flow ； aspect ratio ； eddy viscosity

參考文獻

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