Two-dimensional Numerical modeling of rolling waves in chutes and analyze the factors affecting the formation of them

Document Type : Technical Note

Authors

1 M.Sc. Graduate, Department of Civil Engineering, Faculty of Engineering, Shahid Bahonar University of Kerman, Kerman, Iran

2 Assistant Professor, Department of Civil Engineering, Faculty of Engineering, Shahid Bahonar University of Kerman, Kerman,

Abstract

Roll waves create instabilities and turbulent behavior in channels and chutes that affect downstream
hydraulic structures. The present study aims to provide a numerical model to simulate the roll waves
in the turbulent regime and analyze the conditions and factors affecting the formation of the roll
waves on the free surface. In the present model, the governing equations consist of the depthaveraged
Navier Stokes equations that are discretized by finite volume method. The HLLC method
is selected. To achieve second order accuracy in time and space, the TVD-WAF scheme is used. For
modeling the turbulence effects, the standard k-ɛ turbulence model is used. Then the results of the
present model are compared with the experimental data and the analytical solutions. The results
show that applying a regular perturbation at the inlet of the channel causes periodic roll waves and
the amplitude and period of the periodic roll waves are independent of the perturbation amplitude at
the inlet of the channel. But if the perturbation amplitude is a greater percentage of normal depth, the
distance of formation of roll waves is shorter and waves evolve faster than other conditions. In
addition, the results analysis shows that the Froude number and magnitude of the discharge affect the
formation and evolution of waves.

Keywords

References

Bazargan, J. and Aghebatie, B. (2015). "Numerical analysis of roll waves in chutes". J. Water Science and Technology. 15(3), pp. 517-524.
Brock, R. R. (1967). “Development of roll wave in open channels”, PhD thesis, University of California Institute of Technology, USA.
Dressler, R. F. (1949) "Mathematical solution of the problem of roll waves in inclined channel flows". Communications on Pure and Applied Mathematics. 2, pp. 149–194.
Dressler, R. F. and Pohle, F. V. (1953). "Resistance effects on hydraulic instability". Communications on Pure and Applied Mathematics. 6(1), pp. 93-96.
Huang, Z. (2013). “Open channel flow instabilities modeling the spatial evolution of roll waves”, PhD Thesis, China Institute of Water Resources and Hydropower Research, China.
Huang, Z. and Lee, J. J. (2014). "Numerical investigation on roll-wave properties: wave-wave interactions, generality, and spectrum". J. Engineering Mechanics. 141(2), pp. 060140181-060140188.
Iwasa, Y. (1954). "The criterion for instability of steady uniform flows in open channels". Memoirs of the Faculty of Engineering, Kyoto University, Japan. 16(6), pp. 264-275.
Liu, K. F. and Mei, C. C. (1994). "Roll waves on a layer of a muddy fluid flowing down a gentle slope-A Bingham model". Physics of Fluid. 6(8), pp. 2577-2590.
Montes, S. (1998). Hydraulics of Open Channel Flow. ASCE Press. USA.
Que, Y. T. and Xu, K. (2006). "The numerical study of roll-waves in inclined open channels and solitary wave run-up". International Journal for Numerical Methods in Fluids. 50(9), pp. 1003-1027.
Richard G. L. and Gavrilyuk, S. L. (2012). "A new model of roll wave: comparision with Brock' s experiments". J. Fluid  Mechanics. 698, pp. 374- 405.
Rodi, W. (1993). Turbulence models and their application in hydraulics. IAHR Monograph. Rotterdam.
Rouse, H. (1938). Fluid mechanics for hydraulic engineers. McGraw-Hill. New York.
Toro, E. F. (1997). Riemann solvers and numerical methods for fluid dynamics. Springer-Verlag. Berlin.
Toro, E. F. (2001). Shock-capturing methods for free-surface shallow flows. John Wiley & Sons.
Wu, W. M. (2004). "Depth-averaged two-dimensional numerical modeling of unsteady flow and nonuniform sediment transport in open channels". J. Hydraulic Engineering. 130(9), pp. 1013–1024.
Yu, C. and Duan, J. (2012). "Two-dimensional depth-averaged finite volume model for unsteady turbulent flow". J. Hydraulic Research. 50(6), pp. 599- 611.
 
 

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History

  • Receive Date: 07 May 2017
  • Revise Date: 07 December 2017
  • Accept Date: 15 December 2017

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