An Integrated Numerical Model for Unsteady Flows in Pressurized and Open-Channel Circular Pipes

圓管下水道系統流況之複雜，在於常發生明渠流與滿管流交替發生亦或同時存在之情形，而兩種流況在水理特性上的差異在於前者由重力引起，後者則靠壓力驅動，故在計算上無法以單一流況來進行，必須發展可以兼顧明渠管流及受壓管流之數值模式，方能滿足下水道水理分析之需要。 本文旨在於建立一套可同時處理下水道管線中之明渠流況與壓力流況之模式，主要以一維不恆定流方程式配合第二類多方式特徵法的數值模式；前人在滿管流況時常以普里斯曼細縫(Preissmann Slot)法處理，如此一來可避免渠頂寬度為零之困擾，持續以明渠流況處理之，而本研究以管壁材料之彈性討論滿管流時管壁受壓後面積之微小變化以取代細縫法，且對於滿管流況時之壓力波速，假設其等於常溫下之聲速，來模擬下水道管線可能發生的種種流況，如由明渠流轉變至壓力管流以及管線中發生局部滿管等情形。在網路水流系統方面，考慮匯、分流點之流量守恆及能量守恆原理，亦可有效處理網路水流管線中發生局部滿管之流況及管線逆向坡之問題。Analysis of flows in drainage or sewer system with circular pipes is complicated, due to open channel and pressurized flows often occur alternatively or exist simultaneously. The difference between these two flow conditions is that open channel flow is drived by gravity force and pressurized flow is induced by pressure differences. It is impossible to analyse pipe system based on only one individual flow condition. An integrated numerical model for simultaneous pressurized and open-channel flows is needed. The objective of this thesis is to develop an integrated model to simultaneously deal with open-channel and pressurized flows. One dimensional unsteady flow equations and multimode method of characteristics of the second kind are employed. To overcome the difficulty of the zero width at the top of circular pipes, a novel approach based on material elastic area deformation under pressures is used to replace previously popular Preissmann slot. Assuming that pressure velocity in pressurized flows is equal to sound velocity in normal temperature in order to simulate all possible conditions in sewer system. An example of open-channel flow converts to fully or partial pressurized flows is given. For a pipe network system , validity of present model is assured by checking with conservation and energy conservation in junction problem. It is shown that present model can efficiently deal with integrated flow problems in network system with reversed pipe slopes