Computation of the Particle Basset Force with a Fractional-Derivative Approach
This article has a reply.
VIEW THE REPLYPublication: Journal of Hydraulic Engineering
Volume 134, Issue 10
Abstract
Recent empirical and numerical evidence shows that the Basset force plays an important role in the description of acceleration of relatively small sediment particles moving close to solid boundaries. This force can make the numerical solution of the equations of motion computationally time and memory consuming. This technical note presents a two-stage methodology to deal with the difficulties associated with computing the Basset force. The Basset term is first approximated based on a semiderivative (fractional mathematics), and then the integration time is redefined in terms of appropriate flow and particle time scales, thus, avoiding unnecessary computations. Important savings in computational time are reported.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The writers are very grateful to three anonymous reviewers, the associate editor, and the editor for useful comments, which have helped in clarifying the paper. This paper was completed thanks to the startup funds provided by the University of California to Fabián A. Bombardelli.
References
Abramowitz, M., and Stegun, I. (1970). Handbook of mathematical functions, Dover, New York.
Alexander, P. (2004). “High order computation of the history term in the equation of motion for spherical particle in a fluid.” J. Sci. Comput., 21(2), 129–143.
Armenio, V., and Fiorotto, V. (2001). “The importance of the forces acting on particles in turbulent flows.” Phys. Fluids, 13(8), 2437–2440.
Brush, J. S., Ho, H. W., and Yen, B. C. (1964). “Acceleration motion of sphere in a viscous fluid.” J. Hydr. Div., 90, 149–160.
Crowe, C., Sommerfeld, M., and Tsuji, M. (1998). Multiphase flow with droplets and particles, CRC, Boca Raton, Fla.
Ferry, J., and Balachandar, S. (2001). “A fast Eulerian method for disperse two-phase flow.” Int. J. Multiphase Flow, 27, 1199–1226.
González, A. E., Bombardelli, F. A., Calo, V. M., and Niño, Y. (2007). “Simulation of particle motion close to a rigid wall.” Proc., ASME Applied Mechanics and Materials Conf., McMat 2007, oral presentation.
Grass, A. J. (1970). “Initial instability of fine bed sand.” J. Hydr. Div., 96, 619–632.
Kaftori, D., Hetsroni, G., and Banerjee, S. (1995). “Particle behavior in the turbulent boundary-layer. 1. Motion, deposition and entrainment.” Phys. Fluids, 7, 1095–1106.
Lee, H., and Hsu, I. (1994). “Investigation of saltating particle motion.” J. Hydraul. Eng., 120(7), 831–845.
Lee, H., Lin, Y., You, J., and Wang, H. (2006). “On three dimensional continuous saltating process of sediment particles near the channel bed.” J. Hydraul. Res., 44(3), 374–389.
Lukerchenko, N., Chara, Z., and Vlasak, P. (2006). “2D numerical model of particle-bed collision in fluid-particle flows over bed.” J. Hydraul. Res., 44(1), 70–78.
Maxey, M. R., and Riley, J. J. (1983). “Equation of motion for a small rigid sphere in a nonuniform flow.” Phys. Fluids, 26, 883–889.
Mei, R., Adrian, R. J., and Hanratty, T. (1991). “Particle dispersion in isotropic turbulence under Stokes drag and Basset force with gravitational settling.” J. Fluid Mech., 225, 481–495.
Michaelides, E. E. (1992). “A novel way of computing the Basset term in unsteady multiphase flow computations.” Phys. Fluids A, 4(7), 1579–1582.
Mordant, N., and Pinton, J. F. (2000). “Velocity measurement of a settling sphere.” Eur. Phys. J. B, 18, 343–352.
Niño, Y., and García, M. (1994). “Gravel saltation. 2. Modeling.” Water Resour. Res., 30(6), 1915–1924.
Niño, Y., and García, M. (1996). “Experiments on particle-turbulence interactions in the near-wall region of an open channel flow: Implications for sediment transport.” J. Fluid Mech., 326, 285–319.
Niño, Y., and García, M. (1998). “Using Lagrangian particle saltation observations for bedload sediment transport modelling.” Hydrolog. Process., 12, 1197–1218.
Oldham, Y., and Spanier, M. (1974). The fractional calculus, Academic, New York.
Parker, G. (2004). “1D sediment transport morphodynamics with applications to rivers and turbidity currents.” e-book downloadable at: ⟨http://cee.uiuc.edu/people/parkerg/morphodynamics_ebook.htm⟩.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. (1992). Numerical recipes, Cambridge University Press, New York.
Schmeeckle, M. W., and Nelson, J. M. (2003). “Direct numerical simulation of bedload transport using a local, dynamic boundary condition.” Sedimentology, 50, 279–301.
Sekine, M., and Kikkawa, H. (1992). “Mechanics of saltation grains. II.” J. Hydraul. Eng., 118, 1303–1321.
Tatom, F. B. (1988). “The Basset term as a semiderivative.” Appl. Sci. Res., 45, 283–285.
White, F. M. (1974). Viscous fluid flow, McGraw-Hill, New York.
Wiberg, P., and Smith, J. D. (1985). “A theoretical model for saltating grains in water.” J. Geophys. Res., [Oceans], 90(C4), 7341–7354.
Wood, I. R., and Jenkins, B. S. (1973). “A numerical study of the suspension of a non-buoyant particle in a turbulent stream.” Proc., IAHR Int. Symp. on River Mech., Vol. 1, 431–442.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 134 • Issue 10 • October 2008
Pages: 1513 - 1520
Copyright
© 2008 ASCE.
History
Received: Feb 21, 2007
Accepted: Jan 25, 2008
Published online: Oct 1, 2008
Published in print: Oct 2008
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.