光滑宽浅明渠流动垂线流速分布公式研究
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摘要
对于宽浅光滑明渠流而言,目前工程上常用的是对数流速分布公式,但是对数公式在y+=u*y/ν=0处无意义,这一点在理论上是不合理的。本文从N-S方程入手推导出内区外区的流速导数公式,在此基础上给出了适用于整个水深范围内的流速导数公式,对其求积分得出了宽浅明渠流速分布统一公式并通过试验数据求出了公式中的未知参数。作者公式u+不仅是无因次水深y+的函数,而且也是y/h的函数,这一点与对数补偿公式相似。利用647组试验数据,将作者公式与现存的三家流速分布统一公式对比,发现作者模型计算精度最高。另外,对作者公式求导发现,当在y+=h+处,du+/dy+=0,满足极值定理,说明作者公式的结构比其它公式更合理。
A widely used formula in engineering for velocity distribution of flows in smooth wide open channel is the log law,but it is unreasonable at the bottom y+= 0.This paper presents a unified differential equation for the dimensionless velocity u+that is derived from the Reynolds-averaged Navier-Stokes equations and a unified formula of velocity distribution valid in the full depth range of smooth wide open channel.This formula relates u+not only to y+but also to dimensionless water depth ε = y / h,a similar case to the wake law.Its velocity gradient at the water surface is zero and satisfies the axial symmetrical condition.Its parameters were determined from experimental data.To verify the new formula,647 sets of experimental data were used and three generalized formulae were selected from the literature for comparison.The results show that the authors' formula gives the best prediction among the formulae and thus is recommended for engineering calculation of velocity distribution of flows in smooth wide open channel.
A widely used formula in engineering for velocity distribution of flows in smooth wide open channel is the log law,but it is unreasonable at the bottom y+= 0.This paper presents a unified differential equation for the dimensionless velocity u+that is derived from the Reynolds-averaged Navier-Stokes equations and a unified formula of velocity distribution valid in the full depth range of smooth wide open channel.This formula relates u+not only to y+but also to dimensionless water depth ε = y / h,a similar case to the wake law.Its velocity gradient at the water surface is zero and satisfies the axial symmetrical condition.Its parameters were determined from experimental data.To verify the new formula,647 sets of experimental data were used and three generalized formulae were selected from the literature for comparison.The results show that the authors' formula gives the best prediction among the formulae and thus is recommended for engineering calculation of velocity distribution of flows in smooth wide open channel.
引文
[1]胡春宏,惠遇甲.明渠挟沙水流运动的力学与统计规律[M].北京:科学出版社,1995.HU Chunhong,HUI Yujia.Mechanics and statistical laws of sediment-laden flow movement in open channels[M].Beijing:Science Press,1995.(in Chinese)
[2]Nezu I,Nakagawa H.Turbulence in open-channel flows[M].A.A.Balkema Publishers,Rotterdam NL,1993:48-81.
[3]Nezu I,Rodi W.Open-channel flow measurements with a Laser Doppler Anemometer[J].Journal of Hydraulic Engineering,ASCE,1986,112(5):335-355.
[4]钱宁,万兆惠.泥沙运动力学[M].北京:科学出版社,1983.QIAN Ning,WAN Zhaohui.Mechanics of sediment transport[M].Beijing:Science Press,1983.(in Chinese)
[5]Swamee P K.Generalized inner region velocity distribution equation[J].Journal of Hydraulic Engineering,ASCE,1993,119(5):651-656.
[6]Cheng N S.Comparison of formulas for drag coefficient and settling velocity of spherical particles[J].Powder Technology,2009,189:395-398.
[7]Guo J,Julien P.Modified log-wake law for turbulent flow in smooth pipes[J].Journal of Hydraulic Research,IAHR,2003,41(5):493-501.
[8]董贵明,束龙仓,田娟,等.矩形明渠二维恒定均匀层流断面流速分布及阻力研究[J].水力发电学报,2010,29(6):95-98.DONG Guiming,SHU Longcang,TIAN Juan,et al.Study on cross-section velocity distribution and resistance of steady twodimensional uniform laminar flow in rectangular open channel[J].Journal of Hydroelectric Engineering.2010,29(6):95-98.(in Chinese)
[9]Yang S Q.Influence of sediment and secondary currents on velocity[C]∥Proceedings of the Institution of Civil Engineers,2009,162(5):299-307.
[10]Pierre Y,Julien.Erosion and Sedimentation[M].Cambridge University Press,2010,113-117.
[11]Grass A J.Structural features of turbulent flow over smooth and rough boundaries[J].Journal of Fluid Mechnics,1971,50(2):233-255.
[12]Cardoso A.Spatially accelerating flow in a smooth open channel[D].Ecole Polytechnique Federale Lausanne,1989.
[2]Nezu I,Nakagawa H.Turbulence in open-channel flows[M].A.A.Balkema Publishers,Rotterdam NL,1993:48-81.
[3]Nezu I,Rodi W.Open-channel flow measurements with a Laser Doppler Anemometer[J].Journal of Hydraulic Engineering,ASCE,1986,112(5):335-355.
[4]钱宁,万兆惠.泥沙运动力学[M].北京:科学出版社,1983.QIAN Ning,WAN Zhaohui.Mechanics of sediment transport[M].Beijing:Science Press,1983.(in Chinese)
[5]Swamee P K.Generalized inner region velocity distribution equation[J].Journal of Hydraulic Engineering,ASCE,1993,119(5):651-656.
[6]Cheng N S.Comparison of formulas for drag coefficient and settling velocity of spherical particles[J].Powder Technology,2009,189:395-398.
[7]Guo J,Julien P.Modified log-wake law for turbulent flow in smooth pipes[J].Journal of Hydraulic Research,IAHR,2003,41(5):493-501.
[8]董贵明,束龙仓,田娟,等.矩形明渠二维恒定均匀层流断面流速分布及阻力研究[J].水力发电学报,2010,29(6):95-98.DONG Guiming,SHU Longcang,TIAN Juan,et al.Study on cross-section velocity distribution and resistance of steady twodimensional uniform laminar flow in rectangular open channel[J].Journal of Hydroelectric Engineering.2010,29(6):95-98.(in Chinese)
[9]Yang S Q.Influence of sediment and secondary currents on velocity[C]∥Proceedings of the Institution of Civil Engineers,2009,162(5):299-307.
[10]Pierre Y,Julien.Erosion and Sedimentation[M].Cambridge University Press,2010,113-117.
[11]Grass A J.Structural features of turbulent flow over smooth and rough boundaries[J].Journal of Fluid Mechnics,1971,50(2):233-255.
[12]Cardoso A.Spatially accelerating flow in a smooth open channel[D].Ecole Polytechnique Federale Lausanne,1989.