On the Total Flow Control Equations and Characteristics of Unsteady Gradually Varied Flow in Open Channels

  • Shi-he Liu (刘士和)Email author
  • Qian-yi Zhao (赵潜宜)
  • Qiu-shi Luo (罗秋实)


Most unsteady channel flows in nature and practical engineering appear as gradually varied wherein the free surface deformation conforms to the long wave hypothesis. Currently one-dimensional total flow models are used to conduct numerical simulation of long-term and long-distance reaches to describe water movements, however, the models are insufficient to connect descriptions of flow field and total flow. Moreover, few studies of the variations of roughness coefficient change with time in unsteady flows have been conducted. The following results were obtained through theoretical analysis and numerical simulations in this paper. (1) One-dimensional total flow control equations of unsteady gradually varied flow in open channels were obtained directly from the mathematical model of viscous fluid motion, and can both reflect the influence of turbulence and provide an explicit expression of the energy slope item. These equations establish a direct connection between the descriptions of three-dimensional flow fields and one-dimensional total flows. (2) Synchronous prototype observation data and planar two-dimensional numerical simulation results were used to extract the one-dimensional total flow information and discuss the total flow characteristics. (3)The magnitude orders of items in the total flow motion equation were compared, and the change of the roughness coefficient with time was analyzed.

Key words

Open channel unsteady flow total flow characteristics control equations 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Graf W. H., Altinakar M. S. Hydraulique fluviale [M]. University of Electronic Science and Technology of China Press, 1997.Google Scholar
  2. [2]
    Henderson F. M. Open Channel Flow [M]. New York, USA: Macmillan Comp, 1966.Google Scholar
  3. [3]
    Akan A. O. Open Channel Hydraulics [M]. Amsterdam, USA: Butterworth–Heinemann, 2006.Google Scholar
  4. [4]
    Nezu I., Kadota A., Nakagawa H. Turbulent structure in unsteady depth–varying open–channel flows [J]. Journal of Hydraulic Engineering, 1997, 123(9): 752–763.CrossRefGoogle Scholar
  5. [5]
    Nezu I. Open–channel flow turbulence and its research prospect in the 21st century [J]. Journal of Hydraulic Engineering, 2005, 131(4): 229–246.CrossRefGoogle Scholar
  6. [6]
    Nezu I., Sanjou M. PIV and PTV measurements in hydro–sciences with focus on turbulent open–channel flows [J]. Journal of Hydro–environment Research, 2011, 5(4): 215–230.Google Scholar
  7. [7]
    Graf W. H., Song T. Bed–shear stress in non–uniform and unsteady open–channel flows [J]. Journal of Hydraulic Research, 1995, 33(5): 699–704.CrossRefGoogle Scholar
  8. [8]
    Song T., Graf W. H. Velocity and turbulence distribution in unsteady open–channel flows [J]. Journal of Hydraulic Engineering, 1996, 122(3): 141–154.CrossRefGoogle Scholar
  9. [9]
    Hirt C. W., Nichols B. D. Volume of fluid (VOF) method for the dynamics of free boundaries [J]. Journal of Computational Physics, 1981, (39): 201–225.Google Scholar
  10. [10]
    Olsen NRB. Three–Dimensional CFD Modeling of Self–Forming Meandering Channel [J]. Journal of Hydraulic Engineering, 2003, 129(5): 366–372.CrossRefGoogle Scholar
  11. [11]
    Khosronejad A., Rennie C. D., Neyshabouri S. A. A. S., Townsend R. D. 3D numerical Modeling of flow and sediment transport in laboratory channel bends [J], Journal of Hydraulic Engineering, 2007, 133(3): 1123–1134.CrossRefGoogle Scholar
  12. [12]
    Kamel B., IIhem K., Ali F., Abdelbaki D. 3. Simulation of Velocity Profile of Turbulent Flow in Open Channel with Complex Geometry [J]. Physics Procedia, 2014, 55: 119–128.CrossRefGoogle Scholar
  13. [13]
    Wu W. M. Depth–averaged two–dimensional numerical modeling of unsteady flow and nonuniform sediment transport in open channels [J]. Journal of hydraulic engineering, 2004, 130(10): 1013–1024.MathSciNetCrossRefGoogle Scholar
  14. [14]
    Xibing Zhang, Ruilan Yin. Planar 2–D flow and sediment mathematical modeling [J]. Advances in water science, 2002, 13(6):665–669 (in Chinese).Google Scholar
  15. [15]
    Lai C. Numerical modeling of unsteady open–channel flow [J]. Advances in Hydroscience, 1986, 14: 161–333.CrossRefGoogle Scholar
  16. [16]
    Dong Y. H., Huang Y. L. A mathemetical model of one–dimentional unsteady flow in long–distance natural channel [J]. Journal of Yangtze River Scientific Research Institute, 1994, 11(2): 10–17(in Chinese).MathSciNetGoogle Scholar
  17. [17]
    Venutelli M. Weighted four–point implicit finite difference schemes for open channel flow [J]. Journal of Hydraulic Engineering, 2002, 128(3): 281–288.CrossRefGoogle Scholar
  18. [18]
    Zhou X. L., Liu J., Luo Q. S. et al. Further research of 1D numerical simulation of unsteady channel flow [J]. Engineering Journal of Wuhan University, 2010, (8): 443–445(in Chinese).Google Scholar
  19. [19]
    Liu S. H., Fan M., Xue J. The mechanical energy equation for total flow in open channels [J]. Journal of Hydrodynamics, 2014, 26(3): 416–423.CrossRefGoogle Scholar
  20. [20]
    Liu S. H., Xue J. Theoretical analysis and numerical simulation of wall resistance and mechanical energy loss for steady open channel flow [J]. Journal of Hydrodynamics, 2016, 28(3): 489–496.CrossRefGoogle Scholar

Copyright information

© China Ship Scientific Research Center 2018

Authors and Affiliations

  • Shi-he Liu (刘士和)
    • 1
    Email author
  • Qian-yi Zhao (赵潜宜)
    • 1
  • Qiu-shi Luo (罗秋实)
    • 2
  1. 1.Key Laboratory of Water Resources and Hydropower Engineering ScienceWuhan UniversityWuhanChina
  2. 2.Yellow River Engineering Consulting Co., LtdZhengzhouChina

Personalised recommendations