Influence of Lift Force on the Settling Velocities of Rotating Particles in Two-Dimensional Shear Flow
Publication: Journal of Hydraulic Engineering
Volume 139, Issue 12
Abstract
We derive a simple theoretical model for estimating the change in the magnitude of the particle slip velocity and the deflection in the trajectory of a particle induced by the lift force acting on a freely rotating particle settling under gravity in a shear flow. The lift force on the particle in small, intermediate, and large particle Reynolds number, is studied. We have found that the magnitude of the slip velocity is always reduced by the lift force, implying reduced particle settling velocities. The reduction in the slip velocity and the angle of deflection are the greatest when the shear is the greatest and the particle Reynolds number is the smallest. However, these effects decrease as the particle Reynolds number becomes larger. The derived equations are applied to evaluate the effect of the lift force on particle transport within turbidity currents, on the entrainment of small particles embedded in the lower boundary of a shear flow, and on sediment-laden open-channel flow.
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Acknowledgments
This research was funded by the Turbidites Research Group Consortium (Anadarko, BG, BP, ConocoPhilips, Devon Energy, Maersk, Marathon, Nexen, Petronas, Statoil and Woodside).
References
Bagchi, P., and Balachandar, S. (2002a). “Effect of free rotation on the motion of a solid sphere in linear shear flow at moderate Re.” Phys. Fluids, 14(8), 2719–2737.
Bagchi, P., and Balachandar, S. (2002b). “Shear versus vortex-induced lift force on a rigid sphere at moderate Re.” J. Fluid Mech., 473(1), 379–388.
Best, J., Bennett, S., Bridge, J., and Leeder, M. (1997). “Turbulence modulation and particle velocities over flat sand beds at low transport rates.” J. Hydraul. Eng., 1118–1129.
Bluemink, J. J., Lohse, D., Prosperetti, A., and Wijngaarden, L. V. (2008). “A sphere in a uniformly rotating or shearing flow.” J. Fluid Mech., 600(1), 201–233.
Camenen, B. (2007). “Simple and general formula for the settling velocity of particles.” J. Hydraul. Eng., 229–233.
Cheng, N. S. (1997). “Simplified settling velocity formula for sediment particle.” J. Hydraul. Eng., 149–152.
Cheng, N. S. (2004). “Analysis of velocity lag in sediment-laden open channel flows.” J. Hydraul. Eng., 657–666.
Dallavalle, J. (1948). Micrometrics: The technology of fine particles, Pitman, London.
Dandy, S. D., and Dwyer, H. A. (1990). “A sphere in shear flow at finite Reynolds number: effect of shear on particle lift, drag and heat transfer.” J. Fluid Mech., 216(1), 381–410.
Drew, D. A., and Lahey, R. T., Jr. (1987). “The virtual mass and lift force on a sphere in rotating and straining inviscid flow.” Int. J. Multiphase Flow, 13(1), 113–121.
Fu, X., Wang, G., and Shao, X. (2005). “Vertical dispersion of fine and coarse sediments in turbulent open-channel flows.” J. Hydraul. Eng., 877–888.
Huppert, H. E., and Simpson, J. E. (1980). “The slumping of gravity currents.” J. Fluid Mech., 99(4), 785–799.
Kim, I. (2006). “Forces on a spherical particle in shear flow at intermediate Reynolds number.” Int. J. Comput. Fluid Dyn., 20(2), 137–141.
Kneller, B. C., Bennett, S. J., and McCaffrey, W. D. (1999). “Velocity structure, turbulence and fluid stresses in experimental gravity currents.” J. Geophys. Res., 104(C3), 5381–5391.
Kurose, R., and Komori, S. (1999). “Drag and lift forces on a rotating sphere in a linear shear flow.” J. Fluid Mech., 384(1), 183–206.
Lahey, R. T., Jr., Lopez de Bertodano, M., and Jones, O. C., Jr. (1993). “Phase distribution phenomena in complex geometry conduits.” Nucl. Eng. Des., 141(1–2), 177–201.
Mei, R. (1992). “An approximate expression for the shear lift force on a spherical particle at finite Reynolds number.” Int. J. Multiphase Flow, 18(1), 145–147.
Meiburg, E., and Kneller, B. (2010). “Turbidity currents and their deposits.” Annu. Rev. Fluid Mech., 42(1), 135–156.
Moraga, F. J., Bonetto, F. J., and Lahey, R. T., Jr. (1999). “Lateral forces on spheres in turbulent uniform shear flow.” Int. J. Multiphase Flow, 25(6–7), 1321–1372.
Muste, M., and Patel, V. C. (1997). “Velocity profiles for particles and liquid in open-channel flow with suspended sediment.” J. Hydraul. Eng., 742–751.
Niño, Y., Lopez, F., and Garcia, M. (2003). “Threshold for particle entrainment into suspension.” Sedimentology, 50(2), 247–263.
Rubinow, S. I., and Keller, J. B. (1961). “The transverse force on a spinning sphere moving in a viscous fluid.” J. Fluid Mech., 11(3), 447–459.
Saffman, P. G. (1965). “The lift on a small sphere in a slow shear flow.” J. Fluid Mech., 22(2), 385–400.
Xu, J. P. (2010). “Normalized velocity profiles of field-measured turbidity currents.” Geol., 38(6), 563–566.
Xu, J. P., Noble, M., Eittreim, S. L., Rosenfeld, L. K., Schwing, F. B., and Pilskaln, C. H. (2002). “Distribution and transport of suspended particulate matter in Monterey Canyon, California.” Mar. Geol., 181(1–3), 215–234.
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Published In
Journal of Hydraulic Engineering
Volume 139 • Issue 12 • December 2013
Pages: 1277 - 1285
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Aug 17, 2012
Accepted: Jun 13, 2013
Published online: Jun 15, 2013
Discussion open until: Nov 15, 2013
Published in print: Dec 1, 2013
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