Abstract
In this study, non-equilibrium transport of suspended sediment from one equilibrium state to another is investigated. Based on a convective-diffusion equation, a numerical model for flow with suspended sediment is developed by considering the effect of concentration-dependent settling velocity. The numerical model is validated by comparing analytical solutions and experimental results. The concentration profiles, mean concentrations and distance necessary to reach a new equilibrium state are examined by comparing them with the results of constant settling velocity. For a high concentration flow, the results indicate that evident differences between the above three indicators can be determined with and without concentration-dependent settling velocity. Additionally, the effects of concentration-dependent settling velocity are sensitive to the sediment mobility parameter (or Rouse number), although they are nearly independent of the diffusion Reynolds number.
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References
Apmann RP, Rumer RR (1970) Diffusion of sediment in developing flow. J Hydraul Div 96(1):109–123
Armanini A, Di Silvio G (1988) A one-dimensional model for the transport of a sediment mixture in non-equilibrium conditions. J Hydraul Res 26(3):275–292
Baldock TE, Tomkins MR, Nielsen P, Hughes MG (2004) Settling velocity of sediments at high concentrations. Coast Eng 51:91–100
Batchelor GK (1972) Sedimentation in a dilute dispersion of spheres. J Fluid Mech 52(2):245–268
Cheng KJ (1984) Bottom-boundary condition for nonequilibrium transport of sediment. J Geophys Res 89(C5):8209–8214
Chien N, Wan Z (1999) Mechanics of sediment transport, vol 1. American Society of Civil Engineers, Reston
Claudin P, Charru F, Andreotti B (2011) Transport relaxation time and length scales in turbulent suspensions. J Fluid Mech 671:491–506
Coles D (1956) The law of wake in the turbulent boundary layer. J Fluid Mech 1(2):191–226
Dorrell RM, Hogg AJ (2011) Length and time scales of response of sediment suspensions to changing flow conditions. J Hydraul Eng 138(5):430–439
Dyer KR, Soulsby RL (1988) Sand transport on the continental shelf. Annu Rev Fluid Mech 20:295–324
Einstein HA, Chien N (1955) Effects of heavy sediment concentration near the bed on the velocity and sediment distribution, Report No. 8, University of California, Berkeley
Guo J, Julien PY (2001) Turbulent velocity profiles in sediment-laden flows. J Hydraul Res 39(1):11–23
Hjelmfelt AT, Lenau CW (1970) Nonequilibrium transport of suspended sediment. J Hydraul Div 96(7):1567–1586
Hsu TJ, Jenkins JT, Liu PL (2004) On two-phase sediment transport: sheet flow of massive particles. Proc R Soc A Math Phys Eng Sci 460(2048):2223–2250
Kundu S (2016) Effect of lateral bed roughness variation on particle suspension in open channels. Environ Earth Sci 75(8):631
Lavelle JW, Thacker WC (1978) Effects of hindered settling on sediment concentration profiles. J Hydraul Res 16(4):347–355
Liu X, Nayamatullah M (2014) 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(5):04014011
Mazumder BS (1994) Grain size distribution in suspension from bed materials. Sedimentology 41(2):271–277
Mazumder BS, Ghoshal K (2006) Velocity and concentration profiles in uniform sediment-laden flow. Appl Math Model 30(2):164–176
Mei CC (1969) Nonuniform diffusion of suspended sediment. J Hydraul Div 95(1):581–584
MoayeriKashani M, Hin LS, Ibrahim S (2017) Experimental investigation of fine sediment deposition using particle image velocimetry. Environ Earth Sci 76(19):655
Pritchard D (2006) Rate of deposition of fine sediment from suspension. J Hydraul Eng 132(5):533–536
Richardson JF, Zaki WN (1954) Sedimentation and fluidisation: Part 1. Trans Inst Chem Eng 32:35–53
Rouse H (1939) Experiments on the mechanics of sediment suspension. In: Proceedings of fifth international congress for applied mechanics, pp 550–554
Stansby PK, Omar Awang MA (1998) Response time analysis for suspended sediment transport. J Hydraul Res 36(3):327–338
Toffolon M, Vignoli G (2007) Suspended sediment concentration profiles in nonuniform flows: is the classical perturbative approach suitable for depth-averaged closures? Water Resour Res 43(4):W04432
Van Rijn LC (1984) Sediment transport, part II: suspended load transport. J Hydraul Eng 110(11):1613–1641
Woo HS, Julien PY, Richardson EV (1988) Suspension of large concentrations of sands. J Hydraul Eng 114(8):888–898
Wu W (2007) Computational river dynamics. Taylor & Francis, Boca Raton
Acknowledgements
The study is financially supported by National Key R&D Program of China (2017YFC0504704) and Natural Science Foundation of Education Department of Shaanxi Province, China (no. 16KJ1543).
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Jing, H., Chen, G., Wang, W. et al. Effects of concentration-dependent settling velocity on non-equilibrium transport of suspended sediment. Environ Earth Sci 77, 549 (2018). https://doi.org/10.1007/s12665-018-7731-9
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DOI: https://doi.org/10.1007/s12665-018-7731-9