泄水建筑物反弧急流水深的显式解  

Explicit solution of the supercritical flow depth at the bucket of the outlet structures

作　　者：宁利中[1] 张珂[1] 宁碧波[2] 田伟利[3] NING Lizhong;ZHANG Ke;NING Bibo;TIAN Weili(State Key Laboratory of Eco-hydraulics in Northwest Arid Region of China,Xi'an University of Technology,Xi'an 710048,China;College of Civil Engineering and Architecture,Jiaxing University,Jiaxing 314001,China;College of Fine Arts,Shanghai University,Shanghai 200444,China)

机构地区：[1]西安理工大学省部共建西北旱区生态水利国家重点实验室,陕西西安710048 [2]嘉兴学院建筑工程学院,浙江嘉兴314001 [3]上海大学美术学院,上海200444

出　　处：《水资源与水工程学报》2019年第6期130-134,共5页Journal of Water Resources and Water Engineering

基　　金：国家自然科学基金项目(10872164);省部共建西北旱区生态水利国家重点实验室基金项目(2017ZZKT-2)

摘　　要：泄水建筑物反弧急流水深是泄水工程下游水流衔接、反弧半径设计、反弧段动水压力计算的重要参数。本文的目标就是探讨具有足够精度又计算方便的泄水建筑物反弧急流水深计算方法。在利用恒定急变流的能量方程对于泄水建筑物的反弧水流进行分析基础上,对恒定急变流的能量方程建立的反弧段水深方程,通过级数展开近似处理,得到泄水建筑物反弧急流水深的显式解。精确解和显式解的误差分析表明,当急变流流速系数在0.85到1.0之间变化时,反弧急流水深的误差随着流速系数的增大而减小;当流能比在0.01到0.3之间变化时,反弧急流水深的误差随着流能比的减小而减小。建议的公式最大误差小于1.85%。可见,在实际工程的参数变化范围内,本文建议的泄水建筑物反弧急流水深的显式解形式简单、计算方便、又具有足够的精度,因此可应用于实际工程泄水建筑物反弧急流水深的水力计算。The supercritical flow depth at the bucket of the outlet structures is an important parameter for flow connection in the downstream of outlet work,design of bucket radius and dynamic water pressure calculation.The aim of this paper is to seek a calculation method of supercritical flow depth at the bucket of the outlet structures with sufficient accuracy and convenient calculation.Based on the analysis of the supercritical flow at the bucket of the outlet structures using the energy equation of the rapidly varied steady flow,the water depth equation of the bucket derived by the energy equation of the rapidly varied steady flow was approximated by series expansion,and the explicit solution of the supercritical flow depth at the bucket of the outlet structures was obtained.Error analysis of exact solution and explicit solution showed that the error of the supercritical flow depth at the bucket decreases with the increase of the velocity coefficient when the velocity coefficient of the rapidly varied flow varied from 0.85 to 1.0.The error of the supercritical flow depth at the bucket decreased with the decrease of the flow-energy ratio when the flow-energy ratio varied from 0.01 to 0.3.The maximum error of the proposed formula was less than 1.85%.It can be seen that the explicit solution of the supercritical flow depth at the bucket of the outlet structures proposed in this paper is simple,convenient,and accurate in the range of the parameters of the actual project.Therefore,it can be applied to the hydraulic calculation of the supercritical flow depth at the bucket of the outlet structures in practical engineering.

关 键 词：泄水建筑物 反弧段 急流水深 能量方程 恒定急变流 显式解 

分 类 号：TV135.2[水利工程—水力学及河流动力学]