Impact of Particle Shape on Saltating Mode of Bedload Transport Sheared by Turbulent Flow
Publication: Journal of Hydraulic Engineering
Volume 146, Issue 5
Abstract
The saltating mode of sediment transport is the dominant mechanism of bedload transport in a fluvial stream, especially in mountainous rivers. In most simulation studies, the actual shapes of sediment particles are simplified considering the spherical shape of particles, which can affect the accuracy of the estimation of bedload transport rate. In this study, a model of sediment particle saltation by streamflow is presented, simulating the wall-shear turbulent flow over a sediment bed by large-eddy simulation and calculating the forces acting on the saltating particles by Newton’s second law of motion. The model was calibrated by using the experimental data from previous studies on particle saltation. To study the impact of particle shapes, the computational results of saltation lengths, heights, and velocities of different-shaped particles were analyzed. Then, three key parameters were used to estimate bedload transport rates: bedload concentration, saltation height, and particle velocity. By summarizing the above results, this work presents a formula of bedload transport rate that improves upon a previous well-celebrated formula from the literature. The proposed formula introduces shape factors of natural sediment particles.
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Acknowledgments
The authors gratefully acknowledge the National Natural Science Foundation of China (91647210), National Key Research and Development Program of China (2016YFC0402506), and 111 Project (B18031) for providing the financial support for this research.
References
Abbott, J. E., and J. R. D. Francis. 1977. “Saltation and suspension trajectories of solid grains in a water stream.” Philos. Trans. R. Soc. London, Ser. A 284 (1321): 225–254. https://doi.org/10.1098/rsta.1977.0009.
Anderson, R. S., and B. Hallet. 1986. “Sediment transport by wind.” Geol. Soc. Am. Bull. 97 (5): 523–535. https://doi.org/10.1130/0016-7606(1986)97%3C523:STBWTA%3E2.0.CO;2.
Bai, J., H. W. Fang, and T. Stoesser. 2013. “Transport and deposition of fine sediment in open channels with different aspect ratios.” Earth Surf. Process. Landf. 38 (6): 591–600. https://doi.org/10.1002/esp.3304.
Basset, A. B. 1888. Vol. 2 of A treatise on hydrodynamics: With numerous examples. Cambridge, UK: Bell and Company.
Bialik, R. J., V. I. Nikora, M. Karpiński, and P. M. Rowiński. 2015. “Diffusion of bedload particles in open-channel flows: Distribution of travel times and second-order statistics of particle trajectories.” Environ. Fluid Mech. 15 (6): 1281–1292. https://doi.org/10.1007/s10652-015-9420-5.
Bialik, R. J., V. I. Nikora, and P. M. Rowiński. 2012. “3D Lagrangian modelling of saltating particles diffusion in turbulent water flow.” Acta Geophys. 60 (6): 1639–1660. https://doi.org/10.2478/s11600-012-0003-2.
Bombardelli, F. A., A. E. González, and Y. I. Niño. 2008. “Computation of the particle Basset force with a fractional-derivative approach.” J. Hydraul. Eng. 134 (10): 1513–1520. https://doi.org/10.1061/(ASCE)0733-9429(2008)134:10(1513).
Bomminayuni, S., and T. Stoesser. 2011. “Turbulence statistics in an open-channel flow over a rough bed.” J. Hydraul. Eng. 137 (11): 1347–1358. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000454.
Bridge, J. S., and D. F. Dominic. 1984. “Bed load grain velocities and sediment transport rates.” Water Resour. Res. 20 (4): 476–490. https://doi.org/10.1029/WR020i004p00476.
Brown, P. P., and D. F. Lawler. 2003. “Sphere drag and settling velocity revisited.” J. Environ. Eng. 129 (3): 222–231. https://doi.org/10.1061/(ASCE)0733-9372(2003)129:3(222).
Brush, L. M., H. W. Ho, and B. C. Yen. 1964. “Accelerated motion of a sphere in a viscous fluid.” J. Hydraul. Div. 90 (1): 149–160.
Cevheri, M., R. McSherry, and T. Stoesser. 2016. “A local mesh refinement approach for large-eddy simulations of turbulent flows.” Int. J. Numer. Methods Fluids 82 (5): 261–285. https://doi.org/10.1002/fld.4217.
Challabotla, N. R., L. Zhao, and H. I. Andersson. 2016. “Orientation and rotation dynamics of triaxial ellipsoidal tracers in wall turbulence.” Phys. Fluids 28 (12): 123304. https://doi.org/10.1063/1.4971318.
Chepil, W. S. 1958. “The use of evenly spaced hemispheres to evaluate aerodynamic forces on a soil surface.” EOS Trans. Am. Geophys. Union 39 (3): 397–404. https://doi.org/10.1029/TR039i003p00397.
Crowe, C., M. Sommerfeld, and M. Tsuji. 1998. Multiphase flow with droplets and particles. Boca Raton, FL: CRC Press.
Cundall, P. A., and O. D. Strack. 1979. “A discrete numerical model for granular assemblies.” Géotechnique 29 (1): 47–65. https://doi.org/10.1680/geot.1979.29.1.47.
Dey, S. 2014. Fluvial hydrodynamics: Hydrodynamic and sediment transport phenomena. Berlin: Springer.
Donahue, C. M., C. M. Hrenya, R. H. Davis, K. J. Nakagawa, A. P. Zelinskaya, and G. G. Joseph. 2010. “Stokes’ cradle: Normal three-body collisions between wetted particles.” J. Fluid Mech. 650 (May): 479–504. https://doi.org/10.1017/S0022112009993715.
Einstein, H. A. 1941. “Formulas for the transportation of bed load.” Trans. Am. Soc. Civ. Eng. 107: 561–577.
Einstein, H. A. 1950. The bed-load function for sediment transportation in open channel flows. Washington, DC: United States Dept. of Agriculture, Soil Conservation Service.
Fang, H. W., H. M. Zhao, Z. H. Chen, M. H. Chen, and Y. F. Zhang. 2015. “3D shape and morphology characterization of sediment particles.” Granul. Matter 17 (1): 135–143. https://doi.org/10.1007/s10035-014-0545-x.
Fernandez-Luque, R., and R. van Beek. 1976. “Erosion and transport of bed-load sediment.” J. Hydraul. Res. 14 (2): 127–144.
Foerster, S. F., M. Y. Louge, H. Chang, and K. Allia. 1994. “Measurements of the collision properties of small spheres.” Phys. Fluids 6 (3): 1108–1115. https://doi.org/10.1063/1.868282.
Fraga, B., T. Stoesser, C. Lai, and S. Socolofsky. 2016. “A LES-based Eulerian-Lagrangian approach to predict bubble plume dynamics.” Ocean Modell. 97 (Jan): 27–36. https://doi.org/10.1016/j.ocemod.2015.11.005.
Francis, J. R. D. 1973. “Experiments on the motion of solitary grains along the bed of a water stream.” Proc. R. Soc. London, Ser. A 332 (1591): 443–471. https://doi.org/10.1098/rspa.1973.0037.
Gilbert, G. K. 1914. Transportation of debris by running water. Washington, DC: USGS.
Hill, K. M., L. DellAngelo, and M. M. Meerschaert. 2010. “Heavy-tailed travel distance in gravel bed transport: An exploratory enquiry.” J. Geophys. Res. Earth Surface 115 (F2): F00A14. https://doi.org/10.1029/2009JF001276.
Ikeda, S. 1971. “Some studies on the mechanics of bed load transport.” In Vol. 1971 of Proc., Japan Society of Civil Engineers: 61–69. Tokyo: Japan Society of Civil Engineers.
Joseph, G. G., and M. L. Hunt. 2004. “Oblique particle-wall collisions in a liquid.” J. Fluid Mech. 510 (Jul): 71–93. https://doi.org/10.1017/S002211200400919X.
Lajeunesse, E., L. Malverti, and F. Charru. 2010. “Bed load transport in turbulent flow at the grain scale: Experiments and modeling.” J. Geophys. Res. Earth Surface 115 (F4): F04001. https://doi.org/10.1029/2009JF001628.
Lee, H.-Y., Y.-H. Chen, J.-Y. You, and Y.-T. Lin. 2000. “Investigations of continuous bed load saltating process.” J. Hydraul. Eng. 126 (9): 691–700. https://doi.org/10.1061/(ASCE)0733-9429(2000)126:9(691).
Liu, X., C. Ji, X. Xu, D. Xu, and J. J. Williams. 2017a. “Distribution characteristics of inertial sediment particles in the turbulent boundary layer of an open channel flow determined using Voronoï analysis.” Int. J. Sediment Res. 32 (3): 401–409. https://doi.org/10.1016/j.ijsrc.2017.07.004.
Liu, Y., T. Stoesser, H. W. Fang, A. Papanicolaou, and A. G. Tsakiris. 2017b. “Turbulent flow over an array of boulders placed on a rough, permeable bed.” Comput. Fluids 158 (Nov): 120–132. https://doi.org/10.1016/j.compfluid.2017.05.023.
McLaughlin, M. H. 1968. “An experimental study of particle-wall collision relating to flow of solid particles in fluid.” Ph.D. thesis, Dept. of Engineering and Applied Science, California Institute of Technology.
Meunier, P., F. Métivier, E. Lajeunesse, A. S. Mériaux, and J. Faure. 2006. “Flow pattern and sediment transport in a braided river: The ‘torrent de St Pierre’ (French Alps).” J. Hydrol. 330 (3–4): 496–505. https://doi.org/10.1016/j.jhydrol.2006.04.009.
Meyer-Peter, E., and R. Müller. 1948. “Formulas for bed-load transport.” In Vol. 3 of Proc., 2nd Meeting IAHR, 39–64. Stockholm, Sweden: International Association for Hydraulic Structures Research.
Mrokowska, M. M. 2018. “Stratification-induced reorientation of disk settling through ambient density transition.” Sci. Rep. 8 (1): 412. https://doi.org/10.1038/s41598-017-18654-7.
Nicoud, F., and F. Ducros. 1999. “Subgrid-scale stress modelling based on the square of the velocity gradient tensor.” Flow Turbul. Combust. 62 (3): 183–200. https://doi.org/10.1023/A:1009995426001.
Nikora, V. 2005. “Flow turbulence over mobile gravel-bed: Spectral scaling and coherent structures.” Acta Geophys. Pol. 53 (4): 539–552.
Niño, Y., and M. García. 1994. “Gravel saltation. 2: Modeling.” Water Resour. Res. 30 (6): 1915–1924. https://doi.org/10.1029/94WR00534.
Niño, Y., and M. García. 1998a. “Experiments on saltation of sand in water.” J. Hydraul. Eng. 124 (10): 1014–1025. https://doi.org/10.1061/(ASCE)0733-9429(1998)124:10(1014).
Niño, Y., and M. García. 1998b. “Using Lagrangian particle saltation observations for bedload sediment transport modelling.” Hydrol. Processes 12 (8): 1197–1218. https://doi.org/10.1002/(SICI)1099-1085(19980630)12:8%3C1197::AID-HYP612%3E3.0.CO;2-U.
Ouro, P., B. Fraga, U. Lopez-Novoa, and T. Stoesser. 2019. “Scalability of an Eulerian-Lagrangian large-eddy simulation solver with hybrid MPI/OpenMP parallelisation.” Comp. Fluids 179 (Jan): 123–136. https://doi.org/10.1016/j.compfluid.2018.10.013.
Roseberry, J. C., M. W. Schmeeckle, and D. J. Furbish. 2012. “A probabilistic description of the bed load sediment flux. 2: Particle activity and motions.” J. Geophys. Res. Earth Surface 117 (F3): F03032. https://doi.org/10.1029/2012JF002353.
Rubinow, S. I., and J. B. Keller. 1961. “The transverse force on a spinning sphere moving in a viscous fluid.” J. Fluid Mech. 11 (3): 447–459. https://doi.org/10.1017/S0022112061000640.
Saffman, P. G. 1965. “The lift on a small sphere in a slow shear flow.” J. Fluid Mech. 22 (2): 385–400. https://doi.org/10.1017/S0022112065000824.
Schiller, L., and A. Naumann. 1935. “A drag coefficient correlation.” Z. Ver. Dtsch. Ing. 77: 318–320.
Schmeeckle, M. W. 2014. “Numerical simulation of turbulence and sediment transport of medium sand.” J. Geophys. Res. Earth Surface 119 (6): 1240–1262. https://doi.org/10.1002/2013JF002911.
Schmeeckle, M. W., J. M. Nelson, J. Pitlick, and J. P. Bennett. 2001. “Interparticle collision of natural sediment grains in water.” Water Resour. Res. 37 (9): 2377–2391. https://doi.org/10.1029/2001WR000531.
Sekine, M., and H. Kikkawa. 1992. “Mechanics of saltating grains. II.” J. Hydraul. Eng. 118 (4): 536–558. https://doi.org/10.1061/(ASCE)0733-9429(1992)118:4(536).
Shim, J., and J. G. Duan. 2017. “Experimental study of bed-load transport using particle motion tracking.” Int. J. Sediment Res. 32 (1): 73–81. https://doi.org/10.1016/j.ijsrc.2016.10.002.
Stoesser, T., R. McSherry, and B. Fraga. 2015. “Secondary currents and turbulence over a non-uniformly roughened open-channel bed.” Water 7 (12): 4896–4913. https://doi.org/10.3390/w7094896.
Stokes, G. G. 1851. On the effect of the internal friction of fluids on the motion of pendulums. Cambridge, UK: Pitt Press.
Tsakiris, A. G., A. T. N. Papanicolaou, and T. J. Lauth. 2014. “Signature of bedload particle transport mode in the acoustic signal of a geophone.” J. Hydraul. Res. 52 (2): 185–204. https://doi.org/10.1080/00221686.2013.876454.
Vanoni, V. A. 1975. Sedimentation engineering. New York: ASCE.
van Rijn, L. C. 1984. “Sediment transport. I: Bed load transport.” J. Hydraul. Eng. 110 (10): 1431–1456. https://doi.org/10.1061/(ASCE)0733-9429(1984)110:10(1431).
Wiberg, P. L., and J. D. Smith. 1985. “A theoretical model for saltating grains in water.” J. Geophys. Res. Oceans 90 (C4): 7341–7354. https://doi.org/10.1029/JC090iC04p07341.
Yalin, M. S. 1977. Mechanics of sediment transport. Oxford, UK: Pergamon Press.
Zhang, J., L. S. Fan, C. Zhu, R. Pfeffer, and D. Qi. 1999. “Dynamic behavior of collision of elastic spheres in viscous fluids.” Powder Technol. 106 (1–2): 98–109. https://doi.org/10.1016/S0032-5910(99)00053-4.
Zhang, Y. F., and Y. Q. Long. 1997. “Modification of Einstein’s bed-load formula.” J. Sediment. Res. 12 (4): 61–67.
Zhao, T., G. T. Houlsby, and S. Utili. 2014. “Investigation of granular batch sedimentation via DEM-CFD coupling.” Granul. Matter 16 (6): 921–932. https://doi.org/10.1007/s10035-014-0534-0.
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Published In
Journal of Hydraulic Engineering
Volume 146 • Issue 5 • May 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Jul 27, 2018
Accepted: Oct 16, 2019
Published online: Mar 6, 2020
Published in print: May 1, 2020
Discussion open until: Aug 6, 2020
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