規則渠道變量流在迴水影響下線性解析法

The linearized analytical approach in a regular channel where backwater occurs

劉有棋(Yu-Chi Liu)

指導教授 ： 王士紘

淡江大學/工學院/水資源及環境工程學系碩士班/碩士(2010年)

https://doi.org/10.6846/TKU.2010.00833

摘要

本研究在提出不同斷面的規則渠道，如：矩形渠道、梯形渠道，其渠道變量流在下游邊界迴水影響的情況下以線性解析法模擬河川流量的變化情形，並與數值法和無因次解析解作比較。
解析法求解中，忽略動量方程式中慣性項的影響，僅考慮渠底坡度、壓力坡降及摩擦坡降，則可得擴散波動量方程式。將連續方程式及擴散波動量方程式合併成一個二皆非線性的偏微分方程式，並引進運動波模式加以線性化。且將流量、長度、時間除以個別特徵常數再進行解析解計算，即可得一無因次解析解的模式。
至於數值方法，由連續方程式及動力波動量方程式，利用顯性法有限差分方法，此方法利用中央格點法、前項差分和Lax-Wendroff法求出流量和通水斷面積。
在下游受迴水影響下，越接近下游端受迴水影響越趨明顯，其影響範圍約有數百公尺。在流量歷線不同間距的選取使圖形壓縮變形造成觀察上的不便，甚至影響誤差。取無因次化後，不管流量與時間的大小，均可將流量與時間的圖形座標範圍控制在0~1之間，能夠明顯的表示出流量與時間的關係。進而將此無因次方法推廣到濃度方面來應用。

關鍵字

規則渠道 ； 變量流 ； 迴水影響 ； 線性解析法 ； 無因次解析解

並列摘要

The objective of this study is to develop a linearly analytical solution for simulating unsteady open channel flow in various shapes of the cross sections, such as rectangular and trapezoidal cross sections, where the significant backwater effect from downstream is existed. And comparing with the numerical method and the normalized analytical solution.
Neglecting the inertia terms in the Saint-Venant momentum equation to obtain the linearization of the Saint-Venant equation by the method of small perturbation. And obtaining the normalized analytical model by dividing the discharge, length and time by the individual characteristics of constant.
The nonlinear dynamic-wave model is solved by an explicit finite difference method which calculating the discharge and area of cross section by using the central grid method, forward difference method and Lax-Wendroff method.
Approaching downstream of channel the more effect by the backwater. And the impact area is about several hundred meters. In the hydrograph of different pitch selection, it is hard to do observation and might lead to differences on results. After normalization, the discharge and time could be fitted in the range between 0 and 1. The analytical solution expressed obvious relationship between discharge and time. And the normalized analytical model could be applied to concentration routing problem.

並列關鍵字

Regular channel ； unsteady flow ； backwater effect ； linearized analytical ； normalized analytical solution

參考文獻

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(10) Price, R. K., “Comparison of Four Numerical Methods for Flood Routing＂Journal of the Hydraulics Division, ASCE, Vol.100, No.HY7, July, 1974, pp879-899.

(1) Hayami, S., “On the Propagation of Flood Wave＂, Kyoto University Disaster Prevention Research Institute, Bulletin No.1, Kyoto, Japan, 1951.