基于跌坎压力自相似分布的明渠水深−流量关系推求  

Quasi-theoretical End-depth-Discharge Relationship Based on the Pressure Distribution at the End of Free Overfall for Rough Rectangle Channels

作　　者：李乃稳[1,2] 黄滟淳 陈小攀 李龙国[2] 刘超[1,2] LI Naiwen;HUANG Yanchun;CHEN Xiaopan;LI Longguo;LIU Chao(State Key Lab.of Hydraulics and Mountain River Eng.,Sichuan Univ.,Chengdu 610065,China;College of Water Resource&Hydropower,Sichuan Univ.,Chengdu 610065,China;Henan Tianchi Pumped Storage Power Co.,Ltd.,Nanyang 473000,China)

机构地区：[1]四川大学山区河流保护与治理全国重点实验室,四川成都610065 [2]四川大学水利水电学院,四川成都610065 [3]河南天池抽水蓄能有限公司,河南南阳473000

出　　处：《工程科学与技术》2024年第1期218-227,共10页Advanced Engineering Sciences

基　　金：国家自然科学基金面上项目(52079084,52379073);四川省重大科技专项(2018SZDZX0027);四川省科技支撑计划项目(2022YFS0472,2023YFS0377);四川大学–泸州校地合作项目(2020CDLZ–6)。

摘　　要：明渠流量计量是高效灌溉、合理分配水资源和进行用水有效管理的重要手段。跌水是常见的明渠水流上下游衔接的水利设施。当跌落水流不受跌坎下游水流影响时形成自由跌流,可用于明渠流量的精确计量。受自由跌流影响,跌坎断面水流由缓流向急流转变,压力分布显著偏离静水压力分布规律。而获得跌坎压力分布及其准确描述方程则正是明渠自由跌流流量公式推求的关键,其准确与否决定了利用跌流进行流量计量的精度。本文首先通过模型试验和数值计算对矩形明渠自由跌流的断面压力分布特征进行研究,而后利用理论推导建立了明渠跌流的水深−流量关系公式。研究发现,明渠跌水跌坎断面压力呈典型自相似分布规律,其无量纲压力值分布倾向于一条曲线,压力最大值为0.238he(he为跌坎水深),出现在竖向距跌坎0.209he水深处,并且压力自相似分布规律与明渠流量、渠道底坡和边壁糙率无关。在此基础上,结合幂函数和尾迹函数提出了描述跌坎断面压力分布的函数方程,并给出了最大压力和最大压力位置的计算公式,然后根据动量方程和流量连续方程推求了明渠自由跌流的流量计算公式。最后,对本文和其他研究者提出的流量计算公式采用试验数据进行了对比分析,结果表明:本文提出的流量公式在明渠流量为5~100 L/s,底坡为–0.0112~0.0534、糙率为0.0930~0.0193的研究范围内,具有更高的精度和适用性,计算误差在±5%之内,可适用于该流量、底坡和边壁糙率范围内矩形明渠自由跌流的流量精确计算。本文研究结果对于利用自由跌流进行明渠流量计量提供了理论与技术支撑,具有重要的工程应用价值。Flow measurement is an important means for irrigation,efficient allocation of water resources and water diversion management.In the open channel,the overfall is usually applied as a facility connecting the upstream and downstream.When the overfall is not affected by the flow of downstream,the overfall is classified as a free one,which can be used as a discharge measurement by a single measurement of depth at the end of the channel.At this condition,the flow pattern changes from a subcritical flow into a supercritical one,and the pressure distribution in the end section deviates greatly from the hydrostatic pressure distribution with a skewed shape,which is the key to derive the discharge formula by energy equation and momentum equation.In this study,the characteristics of sectional pressure distribution of free overfall in a rectangular open channel were studied by model test and numerical calculation,and then the water depth-flow relationship formula of open channel with free overfall was established.It was found that the pressure of the end section was conformed to the self-similar distribution law,as the distribution of dimensionless pressure values tended to be the same curve,in which the maximum value was 0.238he(here he was water depth of end section)and it occurred at 0.209he distancing from the end fall.The above findings are independent of the flow discharge,bottom slope and side wall roughness.Based on these findings,a simple formula combining a power function and wake function was proposed to describe the pressure distribution at the end section.Then using the momentum equation and continuity equation,a quasi-theoretical end-depth–discharge relationship was proposed.With the known end depth,bed slope and Manning’s coefficient,the discharge could be direct solved by the proposed equations.The proposed equation was valid over the entire practical ranges of Q=5~100 L/s,S=–0.0112~0.0534,n=0.0930~0.0193,and they showed excellent agreement with the available experimental data in this paper and from oth

关 键 词：明渠 自由跌水 压力分布 水深−流量关系 流量计量 

分 类 号：TV131.4[水利工程—水力学及河流动力学]