突然扩散水跃方程的改进与比较
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摘要
为研究突然扩散水跃方程的特性,根据动量守恒原理,在回流区平均水深作为代表水深的假设下,推导了突然扩散水跃的一般方程。在改进了回流区平均水深具体表达式的基础上,得到了突然扩散水跃的新方程,并给出了有关参数的确定方法。将已有的和改进的突然扩散水跃方程求得的共轭水深比与试验结果进行了比较,结果表明:不同突扩比时改进后的方程求得的共轭水深比与试验结果的平均相对误差和最大相对误差最小,计算精度最高;且改进后的方程具有显式解,计算方便。因此,改进后的方程可用于突然扩散水跃共轭水深的水力设计。
The aim of this paper is to make an improvement on hydraulic jump equation in abruptly expanding channel and compare it with the experimental results of predecessors. Under the assumption that average water depth in the backflow region is taken as representative water depth, the general equation of hydraulic jump in abruptly expanding channel is derived according to the principle of momentum conservation. On the basis of improving the concrete expression of the average water depth in the backflow region, a new equation for hydraulic jump in abruptly expanding channel is obtained, and a method for determining the parameters in the equation is given. The conjugate depth ratios obtained by existing equations and the present improved equation are compared with the experimental results. The comparison demonstrates that the average error and the maximum error between the conjugate depth ratio obtained by the present improved equation and the experimental results are the smallest and the accuracy is the highest in the presence of varying expansion ratio of channel. In addition, the present equation is convenient for calculation with explicit solution. Therefore, we recommend the improved equation for hydraulic design of conjugate water depth of hydraulic jump in abruptly expanding channel.
The aim of this paper is to make an improvement on hydraulic jump equation in abruptly expanding channel and compare it with the experimental results of predecessors. Under the assumption that average water depth in the backflow region is taken as representative water depth, the general equation of hydraulic jump in abruptly expanding channel is derived according to the principle of momentum conservation. On the basis of improving the concrete expression of the average water depth in the backflow region, a new equation for hydraulic jump in abruptly expanding channel is obtained, and a method for determining the parameters in the equation is given. The conjugate depth ratios obtained by existing equations and the present improved equation are compared with the experimental results. The comparison demonstrates that the average error and the maximum error between the conjugate depth ratio obtained by the present improved equation and the experimental results are the smallest and the accuracy is the highest in the presence of varying expansion ratio of channel. In addition, the present equation is convenient for calculation with explicit solution. Therefore, we recommend the improved equation for hydraulic design of conjugate water depth of hydraulic jump in abruptly expanding channel.
引文
[1] 张志昌,张巧玲.明渠恒定急变流和渐变流水力特性研究[M].北京:科学出版社,2016.
[2] 李建中,宁利中.高速水力学[M].西安:西北工业大学出版社,1994.
[3] FINNEMORE E J,FRANZINI J B.Fluid Mechanics with Engineering Applications[M].Edition 10.Beijing:Tsinghua University Press,2003:460-468.
[4] 李连侠,廖华胜,刘德伟,等.进口形式对浅水垫消力池水跃特性的影响[J].水力发电学报,2015,34(5):57-65.
[5] 傅铭焕,郭曙啸,卢志男,等.突扩式水跃跃后水深的分析与计算[J].长江科学院院报,2017,34(5):48-52.
[6] 傅铭焕,卢志男,惠祥明,等.突扩式水跃跃长的计算公式推导与验证[J].长江科学院院报,2017,34(4):48-51.
[7] 代述兵,刘韩生,杨吉健.抛物线类渠道共轭水深的直接计算公式[J].水力发电学报,2015,34(5):88-94.
[8] 罗永钦.突跌渐扩消力池体型优化及水力特性分析[J].水力发电学报,2016,35(2):61-66.
[9] 于志忠.矩形扩散水跃的计算方法[J].水利学报,1982,13(2):39-45.
[10] 宁利中,宁碧波,田伟利,等.矩形扩散水跃方程的近似解[J].西安建筑科技大学学报,2013,45(6):875-879.
[11] ABDELKAWT A M,MC CORQUODALE J A.Simulation of the Radial Hydraulic Jump[J].Journal of Hydraulic Research,1992,30(2):149-164.
[12] 张志恒.矩形扩散水跃的水力计算[J].陕西水利科技,1973,(1):10-26.
[13] ABDELKAWI M K,JOHN A M.Radial Hydraulic Jump[J].Journal of the Hydraulics Division,ASCE,1979,105(9):1065-1078.
[14] HASAN M R,MATIN M A.Experimental Study for Sequent Depth Ratio of Hydraulic Jump in Horizontal Expanding Channel[J].Journal of Civil Engineering,2009,37(1):1-9.
[15] PADMANABHAN M.Hydraulic Jump in Non-prismatic Rectangular Channels[J].Journal of Hydraulic Research,1985,23(1):21-35.
[16] RAJARATNAM N,SUBRAMANYA K.Hydraulic Jumps Below Abrupt Symmetrical Expansions[J].Journal of the Hydraulics Division,ASCE,1968,94(2):481-504.
[17] ZARE H K,BADDOUR R E.Three-dimensional Study of Spatial Submerged Hydraulic Jump[J].Canadian Journal of Civil Engineering,2007,34(9):1140-1148.
[18] 卢士强.两侧突然扩散水跃特性的试验研究[D].南京:河海大学,2000:44-46.
[19] BREMEN R,HAGER W H.T-jump in Abruptly Expanding Channel[J].Journal of Hydraulic Research,1993,31(1):61-78.
[20] 卢士强,邹志业,程胜依.突然扩散水跃共轭水深研究[C]∥第十六届全国水动力学研讨会论文集.北京:海洋出版社,2002:342-349.
[21] HERBRAND K.The Spatial Hydraulic Jump[J].Journal of Hydraulic Research,1973,11(3):205-217.
[22] 宁利中,渠亚伟,宁碧波,等.突然扩散水跃方程的显式解[J].水利水运工程学报,2018(5):24-29.
[2] 李建中,宁利中.高速水力学[M].西安:西北工业大学出版社,1994.
[3] FINNEMORE E J,FRANZINI J B.Fluid Mechanics with Engineering Applications[M].Edition 10.Beijing:Tsinghua University Press,2003:460-468.
[4] 李连侠,廖华胜,刘德伟,等.进口形式对浅水垫消力池水跃特性的影响[J].水力发电学报,2015,34(5):57-65.
[5] 傅铭焕,郭曙啸,卢志男,等.突扩式水跃跃后水深的分析与计算[J].长江科学院院报,2017,34(5):48-52.
[6] 傅铭焕,卢志男,惠祥明,等.突扩式水跃跃长的计算公式推导与验证[J].长江科学院院报,2017,34(4):48-51.
[7] 代述兵,刘韩生,杨吉健.抛物线类渠道共轭水深的直接计算公式[J].水力发电学报,2015,34(5):88-94.
[8] 罗永钦.突跌渐扩消力池体型优化及水力特性分析[J].水力发电学报,2016,35(2):61-66.
[9] 于志忠.矩形扩散水跃的计算方法[J].水利学报,1982,13(2):39-45.
[10] 宁利中,宁碧波,田伟利,等.矩形扩散水跃方程的近似解[J].西安建筑科技大学学报,2013,45(6):875-879.
[11] ABDELKAWT A M,MC CORQUODALE J A.Simulation of the Radial Hydraulic Jump[J].Journal of Hydraulic Research,1992,30(2):149-164.
[12] 张志恒.矩形扩散水跃的水力计算[J].陕西水利科技,1973,(1):10-26.
[13] ABDELKAWI M K,JOHN A M.Radial Hydraulic Jump[J].Journal of the Hydraulics Division,ASCE,1979,105(9):1065-1078.
[14] HASAN M R,MATIN M A.Experimental Study for Sequent Depth Ratio of Hydraulic Jump in Horizontal Expanding Channel[J].Journal of Civil Engineering,2009,37(1):1-9.
[15] PADMANABHAN M.Hydraulic Jump in Non-prismatic Rectangular Channels[J].Journal of Hydraulic Research,1985,23(1):21-35.
[16] RAJARATNAM N,SUBRAMANYA K.Hydraulic Jumps Below Abrupt Symmetrical Expansions[J].Journal of the Hydraulics Division,ASCE,1968,94(2):481-504.
[17] ZARE H K,BADDOUR R E.Three-dimensional Study of Spatial Submerged Hydraulic Jump[J].Canadian Journal of Civil Engineering,2007,34(9):1140-1148.
[18] 卢士强.两侧突然扩散水跃特性的试验研究[D].南京:河海大学,2000:44-46.
[19] BREMEN R,HAGER W H.T-jump in Abruptly Expanding Channel[J].Journal of Hydraulic Research,1993,31(1):61-78.
[20] 卢士强,邹志业,程胜依.突然扩散水跃共轭水深研究[C]∥第十六届全国水动力学研讨会论文集.北京:海洋出版社,2002:342-349.
[21] HERBRAND K.The Spatial Hydraulic Jump[J].Journal of Hydraulic Research,1973,11(3):205-217.
[22] 宁利中,渠亚伟,宁碧波,等.突然扩散水跃方程的显式解[J].水利水运工程学报,2018(5):24-29.