Skip to main content

A general two-phase mixture model for sediment-laden flow in open channel

Abstract

This work extends the sediment-laden mixture model with consideration of the turbulence damping and particle wake effects under the framework of improved efficiency and accuracy. The mixture model consists of the continuity and momentum equations for the sediment-laden mixture, and the continuity equation for the sediment. A theoretical formula is derived for the relative velocity between the water and sediment phases, with consideration of the effects of the pressure gradient, the shear stress and the lift force. A modified expression of the particle wake effect, inducing the local turbulence enhancement around the sediment particle, is employed to improve the turbulent diffusion of the coarse sediment. The km-εm model is proposed to close the mixture turbulence, with the turbulence damping effect due to the high sediment concentration expressed by the density-stratification term without an empirical parameter. The km-εm turbulence model requires smaller computational work and offers better results than an empirical density-stratification turbulence model in high sediment concentration cases. Consequently, with the proposed mixture model, the sediment transport in the open channel under a wide range of sediment sizes and concentrations can be revealed with the results in good agreement with experimental data for the velocity, the sediment concentration and the turbulent kinetic energy.

This is a preview of subscription content, access via your institution.

References

  1. Li Y., Xie L., Su T. C. Profile of suspended sediment concentration in submerged vegetated shallow water flow [J]. Water Resources Research, 2020, 56(4): e2019WR025551.

    Article  Google Scholar 

  2. Shi H., Yu X. An effective Euler-Lagrange model for suspended sediment transport by open channel flows [J]. International Journal of Sediment Research, 2015, 30(4): 361–370.

    Article  Google Scholar 

  3. Huai W., Yang L., Wang W. Predicting the vertical low suspended sediment concentration in vegetated flow using a random displacement model [J]. Journal of Hydrology, 2019, 578: 124101.

    Article  Google Scholar 

  4. Hsu T. J., Jenkins J. T., Liu P. L. F. On two-phase sediment transport: Sheet flow of massive particles [J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2004, 460(2048): 2223–2250.

    Article  Google Scholar 

  5. Chen X., Li Y., Niu X. et al. A general two-phase turbulent flow model applied to the study of sediment transport in open channels [J]. International Journal of Multiphase Flow, 2011, 37(9): 1099–1108.

    Article  Google Scholar 

  6. Liang L., Yu X., Bombardelli F. A general mixture model for sediment laden flows [J]. Advances in Water Resources, 2017, 107: 108–125.

    Article  Google Scholar 

  7. Liang L., Yu X., Bombardelli F. A general formulation of relative motion between two phases in sediment-laden water flows [J]. International Journal of Multiphase Flow, 2018, 109: 63–83.

    MathSciNet  Article  Google Scholar 

  8. Bagchi P., Balachandar S. Response of the wake of an isolated particle to an isotropic turbulent flow [J]. Journal of Fluid Mechanics, 2004, 518: 95–124.

    Article  Google Scholar 

  9. Wang X., Qian N. Turbulence characteristics of Sedimentladen flow [J]. Journal of Hydraulic Engineering, ASCE, 1989, 115(6): 781–800.

    Article  Google Scholar 

  10. Cellino M., Graf W. H. Sediment-laden flow in open channels under noncapacity and capacity conditions [J]. Journal of Hydraulic Engineering, ASCE, 1999, 125(5): 456–462.

    Article  Google Scholar 

  11. Coleman N. L. Effects of suspended sediment on the open-channel velocity distribution [J]. Water Resources Research, 1986, 22(10): 1377–1384.

    Article  Google Scholar 

  12. Winterwerp J. C. Stratification effects by cohesive and noncohesive sediment [J]. Journal of Geophysical Research: Oceans, 2001, 106(C10): 22559–22574.

    Article  Google Scholar 

  13. Jha S. K., Bombardelli F. Toward two-phase flow modeling of nondilute sediment transport in open channels [J]. Journal of Geophysical Research: Earth Surface, 2010, 115(F3): F001347.

    Article  Google Scholar 

  14. Lee C. H., Huang Z., Chiew Y. M. A multi-scale turbulent dispersion model for dilute flows with suspended sediment [J]. Advances in Water Resources, 2015, 79: 18–34.

    Article  Google Scholar 

  15. Huang H., Zhan H., Zhong D. et al. Turbulent mechanisms in open channel sediment-laden flows [J]. International Journal of Sediment Research, 2019, 34(6): 550–563.

    Article  Google Scholar 

  16. Shi H. Two-phase flow models and their applications to sediment transport [D]. Doctoral Thesis, Beijing, China: Tsinghua University, 2016 (in Chinese).

    Google Scholar 

  17. Kundu S., Ghoshal K. Effects of non-locality on unsteady nonequilibrium sediment transport in turbulent flows: A study using space fractional ADE with fractional divergence [J]. Applied Mathematical Modelling, 2021, 96: 617–644.

    MathSciNet  Article  Google Scholar 

  18. Eggenhuisen J. T., Tilston M. C., de Leeuw J. et al. Turbulent diffusion modelling of sediment in turbidity currents: An experimental validation of the Rouse approach [J]. The Depositional Record, 2020, 6: 203–216.

    Article  Google Scholar 

  19. Nezu I., Azuma R. Turbulence characteristics and interaction between particles and fluid in particle-laden open channel flows [J]. Journal of Hydraulic Engineering, ASCE, 2004, 130(10): 988–1001.

    Article  Google Scholar 

  20. Zhang B., Wu B., Li S. et al. Large eddy simulation of sediment transport in high flow intensity by discrete particle method [J]. Journal of Hydraulic Research, 2020, 59(4): 605–620.

    Article  Google Scholar 

  21. Muste M., Yu K., Fujita I. et al. Two-phase versus mixed-flow perspective on suspended sediment transport in turbulent channel flows [J]. Water Resources Research, 2005, 411(10): 312–321.

    Google Scholar 

  22. Salimi-Tarazouj A., Hsu T. J., Traykovski P. et al. A numerical study of onshore ripple migration using a Eulerian two-phase model [J]. Journal of Geophysical Research: Oceans, 2021, 126(2): e2020JC016773.

    Google Scholar 

  23. Li Z. W., Huai W. X., Han J. Large eddy simulation of the interaction between wall jet and offset jet [J]. Journal of Hydrodynamics, 2011, 23(5): 544–553.

    Article  Google Scholar 

  24. Chang H. K., Liou J. C. Discussion on a fall-velocity equation by Nian-Sheng Cheng [J]. Journal of Waterway Port Coastal and Ocean Engineering, 2001, 127(4): 250–251.

    Article  Google Scholar 

  25. Graf W. H., Cellino M. Suspension flows in open channels, experimental study [J]. Journal of Hydraulic Research, 2002, 40(4): 435–447.

    Article  Google Scholar 

  26. Matinpour H., Bennett S., Atkinson J. et al. Modulation of time-mean and turbulent flow by suspended sediment [J]. Physical Review Fluids, 2019, 4(7): 074605.

    Article  Google Scholar 

  27. Herrmann M. J., Madsen O. S. Effect of stratification due to suspended sand on velocity and concentration distribution in unidirectional flows [J]. Journal of Geophysical Research: Oceans, 2007, 112(2): C02006.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xin Chen.

Additional information

Project supported by the National Natural Science Foundation of China (Grant Nos. 41961144014, 51836010), the Chinese Universities Scientific Fund (Grant No. 2019TC133).

Biography: Jia-xing Li (1995-), Male, Ph. D. Candidate

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Li, Jx., Chen, X. A general two-phase mixture model for sediment-laden flow in open channel. J Hydrodyn 34, 286–298 (2022). https://doi.org/10.1007/s42241-022-0023-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42241-022-0023-6

Key words

  • Sediment-laden flow
  • two-phase mixture model
  • particle wake effect
  • turbulence damping effect
  • density stratification