复式河槽水位流量计算误差分析及方法对比
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摘要
水位流量关系是推算水面线的重要依据。复式河槽的水流漫滩时,直接运用曼宁公式计算水位流量关系会产生很大的误差,并会出现流量随水深增加而减小的不合理现象,为此分析了复式河槽垂线平均流速的横向分布及曼宁公式中流量-水深函数的单调性,探讨了这种误差及现象出现的原因;然后以实测资料为依据,对比分析了以曼宁公式为基础的水平分割法、垂直分割法、对角线分割法、湿周修正法及权重分割法与传统理论方法(谢汉祥法、河槽协同度法)计算复式河槽水位流量关系的精度,进而讨论了改进后的曼宁公式在复式河槽中的适用性。结果表明,主槽与滩地的流速差使漫滩水流发生横向运动,并在滩槽交界处形成大量的动量交换,其作用机理完全不同于单一河槽,故曼宁公式不能直接应用于复式河槽;复式断面的水力半径增长率与湿周增长率满足一定的条件时,曼宁公式中流量-水深函数单调递减,漫滩初期流量随水深增加而减小;对比不同计算方法的结果发现,湿周修正法精度最低而不推荐使用;水平分割法、垂线分割法、对角线分割法及权重分割法的精度与传统理论方法接近甚至更高,因此这些改进后的曼宁公式能够较好地适用于复式河槽。由于对角线分割法在所有方法中精度最高且计算简便,故计算复式河槽水位流量关系时推荐采用对角线分割法。
The stage-discharge relationship is an important basis for estimating water surface line. Using the Manning formula directly to calculate the relationship of water level and flow will produce great errors,and the unreasonable phenomenon is that the decrease of flow with the increase of water depth will occur when flood is out of bank. In this paper,the transverse distribution of the average vertical velocity and the monotonicity of the flowdepth function of the Manning formula are first analyzed,and then the reasons for such errors and unreasonable phenomena are discussed. In addition, the calculation accuracy of different methods such as horizontal segmentation,vertical segmentation,diagonal segmentation,wetted perimeter correction,weight segmentation,Xie Hanxiang method and synergism method is compared to demonstrate the applicability of the improved Manning formula in the compound channel. The results show that the velocity difference between the main channel and the floodplain makes the flow move laterally,which will lead to produce a large amount of momentum exchange at the junction,and its mechanism of action is completely different from the single channel,so the Manning formula cannot be applied directly to the compound channel. When the growth rate of hydraulic radius and the wetted perimeter satisfy a certain condition,the flow-depth function is monotonically decreasing,and the flow decreases with the increase of water depth. Compared with the results of different calculation methods,it is found that the precision of wetted perimeter correction is the lowest and not recommended. The precision of horizontal segmentation,vertical segmentation,diagonal segmentation and weight segmentation is close to the traditional theoretical method,so the improved Manning formula can be better applied to the compound channel. Diagonal segmentation is recommended in this paper because the diagonal segmentation method has the highest accuracy and the most simple calculation in all the methods.
The stage-discharge relationship is an important basis for estimating water surface line. Using the Manning formula directly to calculate the relationship of water level and flow will produce great errors,and the unreasonable phenomenon is that the decrease of flow with the increase of water depth will occur when flood is out of bank. In this paper,the transverse distribution of the average vertical velocity and the monotonicity of the flowdepth function of the Manning formula are first analyzed,and then the reasons for such errors and unreasonable phenomena are discussed. In addition, the calculation accuracy of different methods such as horizontal segmentation,vertical segmentation,diagonal segmentation,wetted perimeter correction,weight segmentation,Xie Hanxiang method and synergism method is compared to demonstrate the applicability of the improved Manning formula in the compound channel. The results show that the velocity difference between the main channel and the floodplain makes the flow move laterally,which will lead to produce a large amount of momentum exchange at the junction,and its mechanism of action is completely different from the single channel,so the Manning formula cannot be applied directly to the compound channel. When the growth rate of hydraulic radius and the wetted perimeter satisfy a certain condition,the flow-depth function is monotonically decreasing,and the flow decreases with the increase of water depth. Compared with the results of different calculation methods,it is found that the precision of wetted perimeter correction is the lowest and not recommended. The precision of horizontal segmentation,vertical segmentation,diagonal segmentation and weight segmentation is close to the traditional theoretical method,so the improved Manning formula can be better applied to the compound channel. Diagonal segmentation is recommended in this paper because the diagonal segmentation method has the highest accuracy and the most simple calculation in all the methods.
引文
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[2]SHAO Quanxi,DUTTA D,KARIM F,et al.A method for extending stage-discharge relationships using a hydrodynamic model and quantifying the associated uncertainty[J].Journal of Hydrology,2018,556:154-172.
[3]SHIONO K,KNIGHT D W.Turbulent open-channel flows with variable depth across the channel[J].Journal of Fluid Mechanics,1991,222:617-646.
[4]许唯临.复式河道漫滩水流计算方法研究[J].水利学报,2002(6):21-26,31.(XU Weilin.Study on computational method of overbank flow in channels with compound cross section[J].Journal of Hydraulic Engineering,2002(6):21-26,31.(in Chinese))
[5]杨华,廖华胜,李连侠,等.SKM模型在天然河道的适用性研究[J].水利水电科技展,2011,31(3):53-56.(YANGHua,LIAO Huasheng,LI Lianxia,et al.Applicability of SKM model in natural channels[J].Advances in Science and Technology of Water Resource,2011,31(3):53-56.(in Chinese))
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[7]刘达,芦妍婷,李连侠,等.明渠流动S-K模型在具有垂直壁面的复式断面下的数值模拟[J].武汉大学学报(工学版),2012,45(2):148-151,156.(LIU Da,LU Yanting,LI Lianxia,et al.Numerical simulation of SKM in open-channel with vertical wall[J].Engineering Journal of Wuhan University,2012,45(2):148-151,156.(in Chinese))
[8]谢汉祥.漫滩水流的简化计算法[J].水利水运科学研究,1982(2):84-92.(XIE Hanxiang.Simplified calculation of water flow in floodplain[J].Journal of Nanjing Hydraulic Research Institute,1982(2):84-92.(in Chinese))
[9]刘沛清,冬俊瑞.复式断面渠道中均匀流的水力计算[J].长江科学院院报,1995,12(3):61-66.(LIU Peiqing,DONGJunrui.Hydraulic calculation of uniform flow in compound channel[J].Journal of Yangtze River Scientific Research Institute,1995,12(3):61-66.(in Chinese))
[10]ACKERS P.Flow formulate for straight two-stage channel[J].Journal of Hydraulic Research,1993,31(4):509-531.
[11]TANG Xiaonan.An improved method for predicting discharge of homogeneous compound channels based on energy concept[J].Flow Measurement and Instrumentation,2017,57:57-63.
[12]刘士和,黄伟,罗秋实.复式明渠水流运动的数值模拟[J].武汉大学学报(工学版),2006,39(6):1-5.(LIU Shihe,HUANG Wei,LUO Qiushi.Numerical simulation of compound open channel flow[J].Engineering Journal of Wuhan University,2006,39(6):1-5.(in Chinese))
[13]石荣荣,刘兴年,杨克君.复式河槽漫滩水流的三维数值计算[J].水利水电科技进展,2006(2):13-16,25.(SHIRongrong,LIU Xingnian,YANG Kejun.Three-dimensional numerical calculation of overbank flow in compound channel[J].Advances in Science and Technology of Water Resource,2006(2):13-16,25.(in Chinese))
[14]林斌良,SHIONO K.复式断面明渠三维紊流的数值模拟[J].水利学报,1995(3):52-61.(LIN Binliang,SHIONO K.Three dimensional numerical modelling of compound open channel flows[J].Journal of Hydraulic Engineering,1995(3):52-61.(in Chinese))
[15]WORMLEATON P R,ALLEN J,HADJIPANOS P.Discharge assessment in compound channel flow[J].Journal of Hydraulic Division,ASCE,1982,108(9):975-994.
[16]ZENG Y H,GUYMER I,SPENCE K J,et al.Application of analytical solutions in trapezoidal compound channel flow[J].River Research and Applications,2012,28(1):53-61.
[17]LAMBERT M F,MYERS W R C.Estimating the discharge capacity in straight compound channels[J].Civil Engineers Water Maritime Energy,1998,130:84-94.
[18]KHATUA K K,PATRA K C,MOHANTY P K.Stage-discharge prediction for straight and smooth compound channels with wide flood plains[J].Journal of Hydraulic Engineering,2012,138(1):93-99.
[19]吴持恭.水力学[M].北京:高等教育出版社,2016.(WU Chigong.Hydraulics[M].Beijing:Higher Education Press,2016.(in Chinese))
[20]杨克君,曹叔尤,刘兴年,等.复式河槽流量计算方法比较与分析[J].水利学报,2005,36(5):563-568.(YANGKejun,CAO Shuyou,LIU Xingnian,et al.Comparison of methods for calculating flow capacity of channels with compound cross section[J].Journal of Hydraulic Engineering,2005,36(5):563-568.(in Chinese))
[2]SHAO Quanxi,DUTTA D,KARIM F,et al.A method for extending stage-discharge relationships using a hydrodynamic model and quantifying the associated uncertainty[J].Journal of Hydrology,2018,556:154-172.
[3]SHIONO K,KNIGHT D W.Turbulent open-channel flows with variable depth across the channel[J].Journal of Fluid Mechanics,1991,222:617-646.
[4]许唯临.复式河道漫滩水流计算方法研究[J].水利学报,2002(6):21-26,31.(XU Weilin.Study on computational method of overbank flow in channels with compound cross section[J].Journal of Hydraulic Engineering,2002(6):21-26,31.(in Chinese))
[5]杨华,廖华胜,李连侠,等.SKM模型在天然河道的适用性研究[J].水利水电科技展,2011,31(3):53-56.(YANGHua,LIAO Huasheng,LI Lianxia,et al.Applicability of SKM model in natural channels[J].Advances in Science and Technology of Water Resource,2011,31(3):53-56.(in Chinese))
[6]芦妍婷,刘达,李连侠,等.不同形状断面河槽下SKM模型解析解与数值解的比较分析[J].广东水利水电,2012(7):3-6.(LU Yanting,LIU Da,LI Lianxia,et al.Comparison and analysis of analytic solution of SKM model and numerical solution in different compound channels[J].Guangdong Water Resources and Hydropower,2012(7):3-6.(in Chinese))
[7]刘达,芦妍婷,李连侠,等.明渠流动S-K模型在具有垂直壁面的复式断面下的数值模拟[J].武汉大学学报(工学版),2012,45(2):148-151,156.(LIU Da,LU Yanting,LI Lianxia,et al.Numerical simulation of SKM in open-channel with vertical wall[J].Engineering Journal of Wuhan University,2012,45(2):148-151,156.(in Chinese))
[8]谢汉祥.漫滩水流的简化计算法[J].水利水运科学研究,1982(2):84-92.(XIE Hanxiang.Simplified calculation of water flow in floodplain[J].Journal of Nanjing Hydraulic Research Institute,1982(2):84-92.(in Chinese))
[9]刘沛清,冬俊瑞.复式断面渠道中均匀流的水力计算[J].长江科学院院报,1995,12(3):61-66.(LIU Peiqing,DONGJunrui.Hydraulic calculation of uniform flow in compound channel[J].Journal of Yangtze River Scientific Research Institute,1995,12(3):61-66.(in Chinese))
[10]ACKERS P.Flow formulate for straight two-stage channel[J].Journal of Hydraulic Research,1993,31(4):509-531.
[11]TANG Xiaonan.An improved method for predicting discharge of homogeneous compound channels based on energy concept[J].Flow Measurement and Instrumentation,2017,57:57-63.
[12]刘士和,黄伟,罗秋实.复式明渠水流运动的数值模拟[J].武汉大学学报(工学版),2006,39(6):1-5.(LIU Shihe,HUANG Wei,LUO Qiushi.Numerical simulation of compound open channel flow[J].Engineering Journal of Wuhan University,2006,39(6):1-5.(in Chinese))
[13]石荣荣,刘兴年,杨克君.复式河槽漫滩水流的三维数值计算[J].水利水电科技进展,2006(2):13-16,25.(SHIRongrong,LIU Xingnian,YANG Kejun.Three-dimensional numerical calculation of overbank flow in compound channel[J].Advances in Science and Technology of Water Resource,2006(2):13-16,25.(in Chinese))
[14]林斌良,SHIONO K.复式断面明渠三维紊流的数值模拟[J].水利学报,1995(3):52-61.(LIN Binliang,SHIONO K.Three dimensional numerical modelling of compound open channel flows[J].Journal of Hydraulic Engineering,1995(3):52-61.(in Chinese))
[15]WORMLEATON P R,ALLEN J,HADJIPANOS P.Discharge assessment in compound channel flow[J].Journal of Hydraulic Division,ASCE,1982,108(9):975-994.
[16]ZENG Y H,GUYMER I,SPENCE K J,et al.Application of analytical solutions in trapezoidal compound channel flow[J].River Research and Applications,2012,28(1):53-61.
[17]LAMBERT M F,MYERS W R C.Estimating the discharge capacity in straight compound channels[J].Civil Engineers Water Maritime Energy,1998,130:84-94.
[18]KHATUA K K,PATRA K C,MOHANTY P K.Stage-discharge prediction for straight and smooth compound channels with wide flood plains[J].Journal of Hydraulic Engineering,2012,138(1):93-99.
[19]吴持恭.水力学[M].北京:高等教育出版社,2016.(WU Chigong.Hydraulics[M].Beijing:Higher Education Press,2016.(in Chinese))
[20]杨克君,曹叔尤,刘兴年,等.复式河槽流量计算方法比较与分析[J].水利学报,2005,36(5):563-568.(YANGKejun,CAO Shuyou,LIU Xingnian,et al.Comparison of methods for calculating flow capacity of channels with compound cross section[J].Journal of Hydraulic Engineering,2005,36(5):563-568.(in Chinese))
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