基于数值模拟的矩形明渠床面切应力分析  

Numerical Analysis of Bed Shear Stress of a Rectangular Open Channel

作　　者：黄宇航 周晓泉[1] 周文桐[1] 姚畅 周芳龄 HUANG Yuhang;ZHOU Xiaoquan;ZHOU Wentong;YAO Chang;ZHOU Fangling(State Key Lab.of Hydraulics and Mountain River Eng.,Sichuan Univ.,Chengdu 610065,China)

机构地区：[1]四川大学水力学与山区河流开发保护国家重点实验室,四川成都610065

出　　处：《工程科学与技术》2022年第3期201-208,共8页Advanced Engineering Sciences

基　　金：长江水科学研究联合基金(U2040219)。

摘　　要：河道流动受边界切应力影响,边界切应力过大会造成河岸被侵蚀,降低河岸的稳定性,并通过影响泥沙的沉积和搬运,引起河流形态变化。探究河流边界切应力,就是探究河流中水流流动状态、结构特性等问题。由于河流中影响边界切应力的因素多且复杂,本文去掉各种不确定的因素,通过数值软件建立一个2维矩形直道明渠流动模型,并运用相似理论对矩形直道明渠模型进行缩尺试验。首先,对5种比尺的均匀流直道模型的流动进行数值模拟,由于该5组直道明渠模型模拟结果统一出来的水位流量关系与曼宁公式推导出的水位流量关系高度一致,因此可以认为该模型模拟出来的参数真实可靠。针对非均匀流的情况,通过欠均匀流和超均匀流的概念,对9组直道模型非均匀流进行数值模拟,运用动量定理对非均匀流直道中心处间隔相同的101个点位进行受力分析,每两个点之间取一次切应力的平均值,再将所有点位的阻力求和,沿程积分得出河床阻力,大大减少水位波动等不确定因素带来的误差影响。最后,推导出通用的床面切应力公式,该公式表明无论矩形明渠的流动是否为均匀流,都可通过水深h、流速u、曼宁糙率系数n这3个参数求出床面切应力。将本文所得公式与现有的4个河床切应力求解公式进行对比,发现本文的公式既符合动量定理,又有物理意义。该研究成果相对于过去常用的方法更为简便,可以将复杂的流体力学问题(求解偏微分方程)变为简单的代数问题。River flow is affected by boundary shear stress,and too large boundary shear stress will lead to erosion and reduce the stability of river banks,and cause river morphology changes by affecting sediment deposition and transport.To study the shear stress of river boundary is equivalent to the study of flow characteristics in river.Because there are too many complex factors affecting the boundary shear stress in rivers,a two-dimensional rectangular straight open channel flow model was established by numerical software after removing all factors,and the laboratory experiments were carried out on the rectangular straight open channel model by using similarity theory.Firstly,numerical simulation was carried out for flows in uniform straight channels of 5 different scales.Since the stage-discharge relation obtained from the simulation results is highly consistent with the stage-discharge relation deduced by Manning formula,it can be considered that the parameters simulated by the model are true and reliable.In the case of non-uniform flow,through the concepts of under-uniform flow and super-uniform flow,9 cases of straight open channels under different discharges were simulated in this paper.The momentum theorem was used to analyze the force at 101 points with the same spacing in the center of the non-uniform straight path.The average value of shear stress was taken between every two points,and then the resistance of all points was summed up to approximate the integral of the river bed resistance,which will greatly reduce the influence of the error caused by uncertain factors such as stage fluctuation.A general formula of bed shear stress was derived,which showed that the bed shear stress could be calculated by the water depth h,flow velocity u and Manning roughness coefficient n,regardless of whether the flow of rectangular open channel is uniform or not.To verify the new formula,the new formula was compared to four existing formulas,and the results showed that the new formula conformed to the momentum theorem and had

关 键 词：水力学 矩形明渠 切应力 数值模拟 

分 类 号：TV143[水利工程—水力学及河流动力学]