Hydrodynamic Lift on Sediment Particles at Entrainment: Present Status and Its Prospect
Publication: Journal of Hydraulic Engineering
Volume 146, Issue 6
Abstract
The hydrodynamic force on sediment particles is decomposed into two components, hydrodynamic drag and lift, whose estimations are made semiempirically by the introduction of drag and lift coefficients. A remarkable agreement on the estimation of drag coefficient has been attained in the literature. However, a generic consensus on the determination of lift coefficient so far remains unachievable. This article presents a state-of-the-art review of the hydrodynamic lift on sediment particles at an entrainment, highlighting the present status of lift coefficient in light of experimental observations and the theoretical foundation. The uncertainty in the estimation of hydrodynamic lift and different components of hydrodynamic lift in modeling the entrainment threshold of sediments are discussed. This article shows, for the first time, that there remains a prospect to obtain a generic consensus on the lift coefficient. Compiling and analyzing the lift coefficient data obtained from theoretical predictions, experimental observations, and numerical simulations, it is revealed that the lift coefficient data are somewhat collapsed to a thick band. This band, although subject to inevitable uncertainties, is found to provide a general consensus on the lift coefficient over a wide range of the particle Reynolds number. Finally, the article offers an insight into open questions and sheds light on how these challenges could be resolved.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code generated or used during the study are available from the corresponding author by request.
Acknowledgments
The authors acknowledge the J. C. Bose Fellowship for pursuing this work.
References
Aksoy, S. 1973. “Fluid forces acting on a sphere near a solid boundary.” In Vol. 1 of Proc., 15th Congress of International Association for Hydraulic Research, 217–224. Istanbul, Turkey: International Association for Hydro-Environment Engineering and Research.
Ali, S. Z., and S. Dey. 2016. “Hydrodynamics of sediment threshold.” Phys. Fluids 28 (7): 075103. https://doi.org/10.1063/1.4955103.
Apperley, L. W. 1968. “Effect of turbulence on sediment entrainment.” Ph.D. thesis, Univ. of Auckland.
Bagnold, R. A. 1974. “Fluid forces on a body in shear flow; experimental use of ‘stationary flow.’” Proc. R. Soc. London Ser. A 340 (1621): 147–171. https://doi.org/10.1098/rspa.1974.0145.
Benedict, B. A., and B. A. Christensen. 1972. “Hydrodynamic lift on a stream bed.” In Proc., Sedimentation—Symp. to Honor Professor H. A. Einstein, edited by H. W. Shen. Fort Collins, CO: Colorado State Univ.
Bose, S. K., and S. Dey. 2013. “Sediment entrainment probability and threshold of sediment suspension: Exponential-based approach.” J. Hydraul. Eng. 139 (10): 1099–1106. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000763.
Brayshaw, A. C., L. E. Frostick, and I. Reid. 1983. “The hydrodynamics of particle clusters and sediment entrainment in coarse alluvial channels.” Sedimentology 30 (1): 137–143. https://doi.org/10.1111/j.1365-3091.1983.tb00656.x.
Cheng, E. D. H., and C. G. Clyde. 1972. “Instantaneous lift and drag forces on large roughness elements in turbulent open channel flow.” In Proc., Sedimentation—Symp. to Honor Professor H. A. Einstein, edited by H. W. Shen. Fort Collins, CO: Colorado State Univ.
Cheng, N.-S. 2009. “Comparison of formulas for drag coefficient and settling velocity of spherical particles.” Powder Technol. 189 (3): 395–398. https://doi.org/10.1016/j.powtec.2008.07.006.
Cheng, N.-S., and Y.-M. Chiew. 1998. “Pickup probability for sediment entrainment.” J. Hydraul. Eng. 124 (2): 232–235. https://doi.org/10.1061/(ASCE)0733-9429(1998)124:2(232).
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.
Chepil, W. S. 1961. “The use of spheres to measure lift and drag on wind-eroded soil grains.” Proc. Soil Sci. Soc. Am. 25 (5): 343–345. https://doi.org/10.2136/sssaj1961.03615995002500050011x.
Coleman, N. L. 1967. “A theoretical and experimental study of drag and lift forces acting on a sphere resting on a hypothetical stream bed.” In Vol. 3 of Proc., 12th Congress of the International Association for Hydraulic Research, 185–192. Fort Collins, CO: International Association for Hydro-Environment Engineering and Research.
Davies, T. R. H., and M. F. A. Samad. 1978. “Fluid dynamic lift on a bed particle.” J. Hydraul. Div. 104 (8): 1171–1182.
Dey, S. 1999. “Sediment threshold.” Appl. Math. Model. 23 (5): 399–417. https://doi.org/10.1016/S0307-904X(98)10081-1.
Dey, S. 2014. Fluvial hydrodynamics: Hydrodynamic and sediment transport phenomena. Berlin: Springer.
Dey, S., and S. Z. Ali. 2017a. “Mechanics of sediment transport: Particle scale of entrainment to continuum scale of bedload flux.” J. Eng. Mech. 143 (11): 04017127. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001343.
Dey, S., and S. Z. Ali. 2017b. “Stochastic mechanics of loose boundary particle transport in turbulent flow.” Phys. Fluids 29 (5): 055103. https://doi.org/10.1063/1.4984042.
Dey, S., and S. Z. Ali. 2019. “Bed sediment entrainment by streamflow: State of the science.” Sedimentology 66 (5): 1449–1485. https://doi.org/10.1111/sed.12566.
Dey, S., S. Z. Ali, and E. Padhi. 2019. “Terminal fall velocity: The legacy of Stokes from the perspective of fluvial hydraulics.” Proc. R. Soc. London Ser. A 475 (2228): 20190277. https://doi.org/10.1098/rspa.2019.0277.
Dey, S., H. K. Dey Sarker, and K. Debnath. 1999. “Sediment threshold under stream flow on horizontal and sloping beds.” J. Eng. Mech. 125 (5): 545–553. https://doi.org/10.1061/(ASCE)0733-9399(1999)125:5(545).
Dwivedi, A., B. W. Melville, A. Y. Shamseldin, and T. K. Guha. 2011. “Analysis of hydrodynamic lift on a bed sediment particle.” J. Geophys. Res. Earth Surf. 116 (F2): F02015. https://doi.org/10.1029/2009JF001584.
Egiazaroff, I. V. 1965. “Calculation of nonuniform sediment concentrations.” J. Hydraul. Div. 91 (4): 225–247.
Einstein, H. A. 1950. The bed-load function for sediment transportation in open channel flows. Technical Bulletin 1026. Washington, DC: USDA, Soil Conservation Service.
Einstein, H. A., and E. A. El-Samni. 1949. “Hydrodynamic forces on a rough wall.” Rev. Mod. Phys. 21 (3): 520–524. https://doi.org/10.1103/RevModPhys.21.520.
Gessler, J. 1966. Geschiebetrieb bei mischungen untersucht an naturlichen, abpflasterungserscheinungen in kanalen. Zürich, Switzerland: ETH Zürich.
James, C. S. 1990. “Prediction of entrainment conditions for nonuniform, noncohesive sediments.” J. Hydraul. Res. 28 (1): 25–41. https://doi.org/10.1080/00221689009499145.
Komar, P. D., and Z. Li. 1986. “Pivoting analyses of the selective entrainment of sediments by shape and size with application to gravel threshold.” Sedimentology 33 (3): 425–436. https://doi.org/10.1111/j.1365-3091.1986.tb00546.x.
Lamb, M. P., F. Brun, and B. M. Fuller. 2017. “Direct measurements of lift and drag on shallowly submerged cobbles in steep streams: Implications for flow resistance and sediment transport.” Water Resour. Res. 53 (9): 7607–7629. https://doi.org/10.1002/2017WR020883.
Lee, H., and S. Balachandar. 2012. “Critical shear stress for incipient motion of a particle on a rough bed.” J. Geophys. Res. Earth Surf. 117 (F1): F01026. https://doi.org/10.1029/2011JF002208.
Ling, C.-H. 1995. “Criteria for incipient motion of spherical sediment particles.” J. Hydraul. Eng. 121 (6): 472–478. https://doi.org/10.1061/(ASCE)0733-9429(1995)121:6(472).
Morsi, S. A., and A. J. Alexander. 1972. “An investigation of particle trajectories in two-phase flow systems.” J. Fluid Mech. 55 (2): 193–208. https://doi.org/10.1017/S0022112072001806.
Nath, J. H., and T. Yamamoto. 1974. “Forces from fluid flow around objects.” In Vol. 14 of Proc., 14th Congress on Coastal Engineering, 1808–1827. Reston, VA: ASCE. https://doi.org/10.1061/9780872621138.109.
Papanicolaou, A. N., P. Diplas, N. Evaggelopoulos, and S. Fotopoulos. 2002. “Stochastic incipient motion criterion for spheres under various bed packing conditions.” J. Hydraul. Eng. 128 (4): 369–380. https://doi.org/10.1061/(ASCE)0733-9429(2002)128:4(369).
Patnaik, P. C., N. Vittal, and P. K. Pande. 1994. “Lift coefficient of a stationary sphere in gradient flow.” J. Hydraul. Res. 32 (3): 471–480. https://doi.org/10.1080/00221689409498747.
Rouse, H. 1938. Fluid mechanics for hydraulic engineers. New York: Dover.
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.
Saffman, P. G. 1968. “The lift on a small sphere in a slow shear flow—Corrigendum.” J. Fluid Mech. 31 (3): 624. https://doi.org/10.1017/S0022112068999990.
Schmeeckle, M. W., J. M. Nelson, and R. L. Shreve. 2007. “Forces on stationary particles in near-bed turbulent flows.” J. Geophys. Res. Earth Surf. 112 (F2): F02003. https://doi.org/10.1029/2006JF000536.
Shields, A. F. 1936. “Application of similarity principles and turbulence research to bed-load movement.” In Vol. 26 of Mitteilungen der Preussischen Versuchsanstalt für Wasserbau und Schiffbau, 5–24. Berlin: Das Anstalt.
Slingerland, R. L. 1977. “The effects of entrainment on the hydraulic equivalence relationships of light and heavy minerals in sands.” J. Sediment. Petrol. 47 (2): 753–770. https://doi.org/10.1306/212F7243-2B24-11D7-8648000102C1865D.
Sumer, B. M. 1984. “Lift forces on moving particles near boundaries.” J. Hydraul. Eng. 110 (9): 1272–1278. https://doi.org/10.1061/(ASCE)0733-9429(1984)110:9(1272).
van Rijn, L. C. 1984. “Sediment transport, Part I: Bed load transport.” J. Hydraul. Eng. 110 (10): 1431–1456. https://doi.org/10.1061/(ASCE)0733-9429(1984)110:10(1431).
Velikanov, M. A. 1955. Dynamics of alluvial stream Vol. 2. Moscow: State Publishing House of Theoretical and Technical Literature.
Vollmer, S., and M. G. Kleinhans. 2007. “Predicting incipient motion, including the effect of turbulent pressure fluctuations in the bed.” Water Resour. Res. 43 (5): W05410. https://doi.org/10.1029/2006WR004919.
Watters, G. Z., and M. V. P. Rao. 1971. “Hydrodynamic effects of seepage on bed particles.” J. Hydraul. Div. 97 (3): 421–439.
White, C. M. 1940. “The equilibrium of grains on the bed of a stream.” Proc. R. Soc. London Ser. A 174 (958): 322–338. https://doi.org/10.1098/rspa.1940.0023.
Wiberg, P. L., and J. D. Smith. 1987. “Calculations of the critical shear stress for motion of uniform and heterogeneous sediments.” Water Resour. Res. 23 (8): 1471–1480. https://doi.org/10.1029/WR023i008p01471.
Willetts, B. B., and K. F. Naddeh. 1986. “Measurements of lift on spheres fixed in low Reynolds number flows.” J. Hydraul. Res. 24 (5): 425–435. https://doi.org/10.1080/00221688609499318.
Wu, F.-C., and Y.-J. Chou. 2003. “Rolling and lifting probabilities for sediment entrainment.” J. Hydraul. Eng. 129 (2): 110–119. https://doi.org/10.1061/(ASCE)0733-9429(2003)129:2(110).
Yalin, M. S. 1963. “An expression for bed-load transportation.” J. Hydraul. Div. 89 (3): 221–250.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 146 • Issue 6 • June 2020
Copyright
©2020 American Society of Civil Engineers.
History
Published online: Mar 24, 2020
Published in print: Jun 1, 2020
Discussion open until: Aug 24, 2020
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.