Abstract
An unsteady two-dimensional transport equation is considered to investigate the distribution of suspended sediment in an open channel turbulent flow, where the mechanism of hindered settling is also taken into account. Due to the consideration of concentration-dependent settling velocity on sediment transportation, the transport equation is a partial differential equation with a highly nonlinear term, which has been solved numerically by using the alternating direction implicit (ADI) finite-difference method. It is found that the sediment concentration increases along the vertical direction due to the inclusion of hindered settling effect.
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References
Hjelmfelt, A., Lenau, C.W.: Nonequilibrium transport of suspended sediment. In: Journal of the Hydraulics Division: Proceedings of the American Society of Civil Engineers (ASCE), pp. 1567–1587. ASCE, New York (1970). http://www.vliz.be/en/imis?refid=143170
Liu, X., Nayamatullah, M.: Semianalytical solutions for one-dimensional unsteady nonequilibrium suspended sediment transport in channels with arbitrary eddy viscosity distributions and realistic boundary conditions. J. Hydraul. Eng. 140, 04014011 (2014). https://doi.org/10.1061/(ASCE)HY.1943-7900.0000874
Liu, X.: Analytical solutions for steady two-dimensional suspended sediment transport in channels with arbitrary advection velocity and eddy diffusivity distributions. J. Hydraul Res. 54, 389–398 (2016). https://doi.org/10.1080/00221686.2016.1168880
Jing, H., Chen, G., Wang, W., Li, G.: Effects of concentration dependent settling velocity on non-equilibrium transport of suspended sediment. Environ. Earth Sci. 77, 549 (2018). https://link.springer.com/article/10.1007/s12665-018-7731-9
Richarson, J.F., Zaki, W.N.: Sedimentation and fluidisation: part 1. Chem. Eng. Res. Des. 75, S82-S100 (1997). https://doi.org/10.1016/S0263-8762(97)80006-8
Peaceman, D.W., Rachford Jr., H.H.: The numerical solution of parabolic and elliptic differential equations. J. Soc. Ind. Appl. Math. 3, 28–41 (1955). https://doi.org/10.1137/0103003
Douglas, J., Rachford Jr., H.H.: On the numerical solution of heat conduction problems in two and three space variables. Trans. Am. Math. Soc. 82, 421–439 (1956). https://www.jstor.org/stable/1993056
Rouse, H.: Modern conceptions of the mechanics of fluid turbulence. Trans ASCE. 102, 463–505 (1937). https://ci.nii.ac.jp/naid/10029236933/
Acknowledgements
The last three authors are thankful to the Science and Engineering Research Board (SERB), Department of Science and Technology (DST), Government of India for providing financial support through Research Project No. EMR/2015/002434.
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Mohan, S., Debnath, S., Ghoshal, K., Kumar, J. (2020). Distribution of Two-Dimensional Unsteady Sediment Concentration in an Open Channel Flow. In: Bhattacharyya, S., Kumar, J., Ghoshal, K. (eds) Mathematical Modeling and Computational Tools. ICACM 2018. Springer Proceedings in Mathematics & Statistics, vol 320. Springer, Singapore. https://doi.org/10.1007/978-981-15-3615-1_6
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DOI: https://doi.org/10.1007/978-981-15-3615-1_6
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