Transport Formula for Collisional Sheet Flows with Turbulent Suspension
Publication: Journal of Hydraulic Engineering
Volume 139, Issue 4
Abstract
The prediction of the transport of sediments in streams is of crucial importance for many geophysical and industrial applications. Most of the available formulas for sediment transport are empirical and apply to situations near initiation, where a few erratic particles are seen jumping and rolling over an immobile bed. However, they are commonly adopted for predicting massive transport of sediments, although more rigorous approaches exist. The latter make use of constitutive relations from kinetic theories of granular gases, but require the numerical integrations of complicated, nonlinear differential equations, hence discouraging their usage for practical purposes. A new, explicit formula for predicting intense sediment transport is proposed here, based on kinetic theories of granular gases and incorporating in a simple yet rigorous way the possibility of turbulent suspension of the particles. It is shown that this formula, unlike others, can quantitatively reproduce physical experiments on steady, uniform flows of natural and artificial particles and water over horizontal, movable beds taken from the literature. These findings suggest that granular physics is now mature enough to provide practical tools in fields that were so far mainly empirically oriented.
Get full access to this article
View all available purchase options and get full access to this article.
References
Abrahams, A. D. (2003). “Bed-load transport equation for sheet flow.” J. Hydraul. Eng., 129(2), 159–163.
Armanini, A., Capart, H., Fraccarollo, L., and Larcher, M. (2005). “Rheological stratification in experimental free-surface flows of granular-liquid mixtures.” J. Fluid Mech., 532, 269–319.
Berzi, D. (2011). “Analytical solution of collisional sheet flows.” J. Hydraul. Eng., 137(10), 1200–1207.
Berzi, D., Di Prisco, C. G., and Vescovi, D. (2011). “Constitutive relations for steady, dense granular flows.” Phys. Rev. E, 84(3), 031301.
Berzi, D., and Jenkins, J. T. (2011). “Surface flows of inelastic spheres.” Phys. Fluids, 23(1), 013303.
Boyer, F., Guazzelli, E., and Pouliquen, O. (2011). “Unifying suspension and granular rheology.” Phys. Rev. Lett., 107, 188301.
Capart, H., and Fraccarollo, L. (2011). “Transport layer structure in intense bed-load.” Geophys. Res. Lett., 38, L20402.
Ferguson, R. I., and Church, M. (2004). “A simple universal equation for grain settling velocity.” J. Sediment. Res., 74(6), 933–937.
Frey, P., and Church, M. (2009). “How river beds move.” Science, 325, 1509–1510.
Garzo, V., and Dufty, J. W. (1999). “Dense fluid transport for inelastic hard spheres.” Phys. Rev. E, 59(5), 5895.
Goldhirsch, I. (2003). “Rapid granular flows.” Annu. Rev. Fluid Mech., 35, 267–293.
Hsu, T.-J., Jenkins, J. T., and Liu, P. L.-F. (2004). “On two-phase sediment transport: Sheet flow of massive particles.” Proc. R. Soc. London A, 460, 2223–2250.
Jenkins, J. T. (2006). “Dense shearing flows of inelastic disks.” Phys. Fluids, 18(10), 103307.
Jenkins, J. T. (2007). “Dense inclined flows of inelastic spheres.” Granul. Matt., 10, 47–52.
Jenkins, J. T., and Berzi, D. (2010). “Dense inclined flows of inelastic spheres: Tests of an extension of kinetic theory.” Granul. Matt., 12, 151–158.
Jenkins, J. T., and Hanes, D. M. (1998). “Collisional sheet flows of sediment driven by a turbulent fluid.” J. Fluid Mech., 370, 29–52.
Jenkins, J. T., and Savage, S. B. (1983). “A theory for the rapid flow of identical, smooth, nearly elastic particles.” J. Fluid Mech., 130, 187–202.
Joseph, G. G., Zenit, R., Hunt, M. L., and Rosenwinkel, A. M. (2001). “Particle-wall collisions in a viscous fluid.” J. Fluid Mech., 433, 329–346.
Kumaran, V. (2009). “Dynamics of dense sheared granular flows. Part II. The relative velocity distributions.” J. Fluid Mech., 632, 145–198.
McTigue, D. F. (1981). “Mixture theory for suspended sediment transport.” J. Hydraul. Div., 107(6), 659–673.
Meyer-Peter, P., and Müller, R. (1948). “Formulas of bed-load transport.” Proc. 2nd Congress IAHR, Int. Association for Hydr. Res., Stockholm, Sweden.
Mitarai, N., and Nakanishi, H. (2007). “Velocity correlations in dense granular shear flows: Effects on energy dissipation and normal stress.” Phys. Rev. E, 75(3), 031305.
Nnadi, F. N., and Wilson, K. C. (1992). “Motion of contact-load particles at high shear stress.” J. Hydraul. Eng., 118(12), 1670–1684.
Pasini, J. M., and Jenkins, J. T. (2005). “Aeolian transport with collisional suspension.” Phil. Trans. R. Soc. A, 363, 1625–1646.
Sumer, B. M., Kozakiewicz, A., Fredsoe, J., and Deigaard, R. (1996). “Velocity and concentration profiles in sheet-flow layer of movable bed.” J. Hydraul. Eng., 122(10), 549–558.
Wong, M., and Parker, G. (2006). “Reanalysis and correction of bed-load relation of Meyer-Peter and Müller using their own database.” J. Hydraul. Eng., 132(11), 1159–1168.
Information & Authors
Information
Published In
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Feb 22, 2012
Accepted: Oct 1, 2012
Published online: Oct 3, 2012
Published in print: Apr 1, 2013
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.