冰封河道综合糙率计算方法比较与分析
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摘要
综合糙率是冰封河道水力计算的重要输入参数。根据水流连续性和力的平衡原理,分别推导得到冰封河道综合糙率的通用公式,并选取抛物线形、矩形和梯形作为典型断面,系统地总结Pavlovskiy、Einstein、Lotter、Sabaneev、Larsen、改进的Larsen等常见公式由通用公式基于何种假定(分区的湿周、流速或水力半径相等)简化得到。采用水槽实测数据和野外观测资料,对比上述公式的计算精度,结果表明改进的Larsen公式的计算结果与实测值吻合较好,推荐在工程设计中使用。前5种公式误差较大的原因在于分区的流速、水力半径相等对于冰封河道不具有普适性,尤其是Lotter公式和Pavlovskiy公式在冰盖和河床糙率差异较大时会明显低估冰封河道的综合糙率,在工程设计中应慎重采用。
Composite roughness is a vital input parameter for hydraulic calculations of ice-covered channels.Two general equations for deriving composite roughness coefficient in ice-covered streams,based on the principles of flow continuity or force balance,are presented in this paper.Taking parabolic,rectangular,and trapezoidal under-ice flow sections as the representative geometries,this paper systematically summarizes the assumptions(e.g.,equalities of wetter perimeters,subsectional mean velocities,and hydraulic radii) used in the derivation of six formulae:those of Pavlovskiy,Einstein,Lotter,Sabaneev,Larsen and its modified form.Laboratory measurements and field observations were used to examine the performance of those above-mentioned formulae.Comparative results indicated that the modified Larsen formula had the best overall performance and therefore its use is recommended in engineering practice.The first five formulae produced relatively large errors in the prediction of composite roughness of ice-covered streams because the main assumptions of equalities of velocities and hydraulic radii are only valid for few special cases.In particular,care should be taken when using the Lotter and Pavlovskiy formulae because of their underestimation of the composite roughness in high-grade asymmetric channels.
Composite roughness is a vital input parameter for hydraulic calculations of ice-covered channels.Two general equations for deriving composite roughness coefficient in ice-covered streams,based on the principles of flow continuity or force balance,are presented in this paper.Taking parabolic,rectangular,and trapezoidal under-ice flow sections as the representative geometries,this paper systematically summarizes the assumptions(e.g.,equalities of wetter perimeters,subsectional mean velocities,and hydraulic radii) used in the derivation of six formulae:those of Pavlovskiy,Einstein,Lotter,Sabaneev,Larsen and its modified form.Laboratory measurements and field observations were used to examine the performance of those above-mentioned formulae.Comparative results indicated that the modified Larsen formula had the best overall performance and therefore its use is recommended in engineering practice.The first five formulae produced relatively large errors in the prediction of composite roughness of ice-covered streams because the main assumptions of equalities of velocities and hydraulic radii are only valid for few special cases.In particular,care should be taken when using the Lotter and Pavlovskiy formulae because of their underestimation of the composite roughness in high-grade asymmetric channels.
引文
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[3]AMBTMAN K D,HICKS F.Field estimates of discharge associated with ice jam formation and release events[J].Canadian Water Resources Journal,2012,37(1):47-56.
[4]张防修,席广永,张晓丽,等.凌汛期槽蓄水增量过程模拟[J].水科学进展,2015,26(2):201-211.(ZHANG F X,XI GY,ZHANG X L,et al.Simulation of channel-storage increment process in ice flood period[J].Advances in Water Science,2015,26(2):201-211.(in Chinese))
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[11]LOTTER G K.Considerations on hydraulic design channels with different roughness of walls[J].Transactions of the Vedeneev AllUnion Scientific Research Institute of Hydraulic Engineering,1933,7:55-88.
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[19]杨开林.明渠冰盖下流动的综合糙率[J].水利学报,2014,45(11):1310-1317.(YANG K L.Composite roughness of icecovered flows in open channels[J].Journal of Hydraulic Engineering,2014,45(11):1310-1317.(in Chinese))
[20]陈刚,张玉蓉,周密,等.冰盖下矩形河道的综合糙率[J].水科学进展,2016,27(2):290-298.(CHEN G,ZHANG Y R,ZHOU M,et al.Composite roughness of rectangular ice-covered rivers[J].Advances in Water Science,2016,27(2):290-298.(in Chinese))
[21]王军.冰冻河道下流速分布和阻力问题探讨[J].水科学进展,2005,16(1):28-31.(WANG J.Discussion of velocity distribution and resistance under ice cover[J].Advances in Water Science,2005,16(1):28-31.(in Chinese))
[22]PARTHASARATHY R N,MUSTE M.Velocity measurements in asymmetric turbulent channel flows[J].Journal of Hydraulic Engineering,1994,120(9):1000-1020.
[23]TATINCLAUX J C,GGˇS M.Asymmetric plane flow with application to ice jams[J].Journal of Hydraulic Engineering,1983,109(11):1540-1554.
[24]SMITH B T,ETTEMA R.Flow resistance in ice-covered alluvial channels[J].Journal of Hydraulic Engineering,1997,123(7):592-599.
[25]HANJALIC K,LAUNDER B E.Fully developed asymmetric flow in a plane channel[J].Journal of Fluid Mechanism,1972,51(2):301-335.
[26]CHEN G,GU S X,HUAI W X,et al.Boundary shear stress in rectangular ice-covered channels[J].Journal of Hydraulic Engineering,2015,141(6):06015005.
[27]EINSTEIN H A.Formulas for the transportation of bed-load[J].Transactions of the American Society of Civil Engineers,1942,107(2140):561-597.
[28]CHEN G,ZHOU M,GU S X,et al.Analytical model for stage-discharge prediction in rectangular ice-covered channels[J].Journal of Hydraulic Engineering,2016,142(7):06016006.
[29]YEN B C.Dimensionally homogeneous Manning's formula[J].Journal of Hydraulic Engineering,1992,118(9):1326-1332.
[30]ENGMANN E O.The turbulent diffusion in channels with a surface cover[J].Journal of Hydraulic Research,1977,15(4):327-335.
[2]BENNETT K E,PROWSE T D.Northern Hemisphere geography of ice-covered rivers[J].Hydrological Processes,2010,24:235-240.
[3]AMBTMAN K D,HICKS F.Field estimates of discharge associated with ice jam formation and release events[J].Canadian Water Resources Journal,2012,37(1):47-56.
[4]张防修,席广永,张晓丽,等.凌汛期槽蓄水增量过程模拟[J].水科学进展,2015,26(2):201-211.(ZHANG F X,XI GY,ZHANG X L,et al.Simulation of channel-storage increment process in ice flood period[J].Advances in Water Science,2015,26(2):201-211.(in Chinese))
[5]SHEN H T.Research on river ice processes:progress and missing links[J].Journal of Clod Regions Engineering,2003,17(4):135-142.
[6]徐国宾,李大冉,赵焱,等.南水北调中线输水工程若干冰力学问题试验研究[J].水科学进展,2010,21(6):808-815.(XU G B,LI D R,ZHAO Y,et al.Laboratory study of problems in ice mechanics encountered in the Middle Route of South-toNorth water transfer project[J].Advances in Water Science,2010,21(6):808-815.(in Chinese))
[7]ATTAR S,LI S S.Data-fitted velocity profiles for ice-covered rivers[J].Canadian Journal of Civil Engineering,2012,39(3):334-338.
[8]UZUNER M S.The composite roughness of ice-covered streams[J].Journal of Hydraulic Research,1975,13(1):79-102.
[9]GHAREH AGHAJI ZARE S,MOORE S A,RENNIE C D,et al.Estimation of composite hydraulic resistance in ice-covered alluvial streams[J].Water Resources Research,2016,52:1306-1327.
[10]PAVLOVSKIY N N.On a design formula for uniform flow in channels with nonhomogeneous walls[J].Transactions of the Vedeneev All-Union Scientific Research Institute of Hydraulic Engineering,1931,3:157-164.
[11]LOTTER G K.Considerations on hydraulic design channels with different roughness of walls[J].Transactions of the Vedeneev AllUnion Scientific Research Institute of Hydraulic Engineering,1933,7:55-88.
[12]EINSTEIN H A.The hydraulic cross section radius[J].Schweizersche Bauzeiung,1934,103(8):89-91.
[13]SABANEEV A A.Calculation of uniform flow in a channel with inhomogeneous walls[J].Trudy LPI,1948,5:5-12.
[14]LARSEN P A.Head losses caused by an ice cover on open channels[J].Journal of the Boston Society of Civil Engineers,1969,56(1):45-67.
[15]陈仁升,康尔泗,吴立宗,等.中国寒区分布探讨[J].冰川冻土,2005,27(4):469-475.(CHEN R S,KANG E S,WU LZ,et al.Cold regions in China[J].Journal of Glaciology and Geocryology,2005,27(4):469-475.(in Chinese))
[16]隋觉义,方达宪.江河冰塞糙率的分析研究[J].水利学报,1993,24(8):10-18.(SUI J Y,FANG D X.Roughness coefficient of river ice jams[J].Journal of Hydraulic Engineering,1993,24(8):10-18.(in Chinese))
[17]茅泽育,马吉明,佘云童,等.冰封河道的阻力研究[J].水利学报,2005,36(5):59-64.(MAO Z Y,MA J M,SHE Y T,et al.Hydraulic resistance of ice-covered river[J].Journal of Hydraulic Engineering,2005,36(5):59-64.(in Chinese))
[18]魏良琰,黄继忠.冰盖流阻力与综合Manning糙率[J].武汉大学学报(工学版),2002,35(4):1-8.(WEI L Y,HUANG JZ.Composite Manning roughness coefficient of ice-covered flows[J].Engineering Journal of Wuhan University,2002,35(4):1-8.(in Chinese))
[19]杨开林.明渠冰盖下流动的综合糙率[J].水利学报,2014,45(11):1310-1317.(YANG K L.Composite roughness of icecovered flows in open channels[J].Journal of Hydraulic Engineering,2014,45(11):1310-1317.(in Chinese))
[20]陈刚,张玉蓉,周密,等.冰盖下矩形河道的综合糙率[J].水科学进展,2016,27(2):290-298.(CHEN G,ZHANG Y R,ZHOU M,et al.Composite roughness of rectangular ice-covered rivers[J].Advances in Water Science,2016,27(2):290-298.(in Chinese))
[21]王军.冰冻河道下流速分布和阻力问题探讨[J].水科学进展,2005,16(1):28-31.(WANG J.Discussion of velocity distribution and resistance under ice cover[J].Advances in Water Science,2005,16(1):28-31.(in Chinese))
[22]PARTHASARATHY R N,MUSTE M.Velocity measurements in asymmetric turbulent channel flows[J].Journal of Hydraulic Engineering,1994,120(9):1000-1020.
[23]TATINCLAUX J C,GGˇS M.Asymmetric plane flow with application to ice jams[J].Journal of Hydraulic Engineering,1983,109(11):1540-1554.
[24]SMITH B T,ETTEMA R.Flow resistance in ice-covered alluvial channels[J].Journal of Hydraulic Engineering,1997,123(7):592-599.
[25]HANJALIC K,LAUNDER B E.Fully developed asymmetric flow in a plane channel[J].Journal of Fluid Mechanism,1972,51(2):301-335.
[26]CHEN G,GU S X,HUAI W X,et al.Boundary shear stress in rectangular ice-covered channels[J].Journal of Hydraulic Engineering,2015,141(6):06015005.
[27]EINSTEIN H A.Formulas for the transportation of bed-load[J].Transactions of the American Society of Civil Engineers,1942,107(2140):561-597.
[28]CHEN G,ZHOU M,GU S X,et al.Analytical model for stage-discharge prediction in rectangular ice-covered channels[J].Journal of Hydraulic Engineering,2016,142(7):06016006.
[29]YEN B C.Dimensionally homogeneous Manning's formula[J].Journal of Hydraulic Engineering,1992,118(9):1326-1332.
[30]ENGMANN E O.The turbulent diffusion in channels with a surface cover[J].Journal of Hydraulic Research,1977,15(4):327-335.