Drift Velocity of Suspended Sediment in Turbulent Open Channel Flows
Publication: Journal of Hydraulic Engineering
Volume 140, Issue 1
Abstract
The drift velocity, at which sediment disperses relative to the motion of water-sediment mixtures, is a key variable in two-phase mixture equations. A constitutive relation for the drift velocity, expressed as a power series in the particle bulk Stokes number, was obtained by solving the momentum equation for sediment with the perturbation approach. It shows that gravity and turbulent diffusion are the primary dispersion effects on sediment, whereas flow inertia, particle-particle interactions, and other forces such as lift are the first-order particle inertial corrections that also play significant roles in sediment suspension. Analysis proves that studies based on turbulent diffusion theory are the zeroth-order approximations to the present formulation with respect to the particle inertia effect. The vertical concentration and velocity distributions of sediment in simple flows were investigated with the two-phase mixture equations closed by the drift velocity acquired in the research reported in this paper. The calculated concentration profiles agree well with measurements when the first-order particle inertial effect is considered. The calculated velocity of sediment coincides with available experiments that sediment lags behind water in open-channel flows as a result of turbulence-induced drag.
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Acknowledgments
Financial support from the Natural Science Foundation of China (NSFC, grant number 51039004) and the National Key Technologies Research and Development Program of China during the 12th Five-Year Plan Period (number 2012BAB05B01) is gratefully acknowledged. The writers benefited considerably from the anonymous reviewers for their important comments. The Associate Editor’s suggestions and comments also have a significant contribution to this paper, which made publication of this paper possible.
References
Bagnold, R. A. (1973). “The nature of saltation and bedload transport in water.” Proc. R. Soc. Lon. A, 332(1591), 473–504.
Bakhtyar, R., Yeganeh-Bakhtiary, A., Barry, D. A., and Ghaheri, A. (2009). “Two-phase hydrodynamic and sediment transport modeling of wave-generated sheet flow.” Adv. Water Resour., 32(8), 1267–1283.
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.
Cao, Z. X., Egashira, S. J., and Carling, P. A. (2003). “Role of suspended-sediment particle size in modifying velocity profiles in open channel flows.” Water Resour. Res., 39(2), WR000394.
Cao, Z. X., Wei, L. Y., and Xie, J. H. (1995). “Sediment-laden flow in open channels from two-phase flow viewpoint.” J. Hydraul. Eng., 725–735.
Celik, I., and Gel, A. (2002). “A new approach in modeling phase distribution in fully developed bubbly pipe flow.” Flow Turbul. Combust., 68(4), 289–311.
Cheng, N. S. (2004). “Analysis of velocity lag in sediment-laden open channel flows.” J. Hydraul. Eng., 657–666.
Chien, N., and Wan, Z. (1999). Mechanics of sediment transport, ASCE, Reston, VA.
Chow, V. T. (1959). Open-channel hydraulics, McGraw-Hill, New York.
Coleman, N. L. (1986). “Effects of suspended sediment on the open-channel velocity distribution.” Water Resour. Res., 22(10), 1377–1384.
Csanady, G. T. (1963). “Turbulent diffusion of heavy particles in the atmosphere.” J. Atmos. Sci., 20(3), 201–208.
Drew, D. A. (1975). “Turbulent sediment transport over a flat bottom using momentum balance.” J. Appl. Mech., 42(1), 38–44.
Druzhinin, O. A. (1995). “Dynamics of concentration and vorticity modification in a cellular-flow laden with solid heavy-particles.” Phys. Fluids, 7(9), 2132–2142.
Einstein, H. A., and Chien, N. (1955). “Effects of heavy sediment concentration near the bed on velocity and sediment distribution.” Rep. Prepared for the U.S. Army Corps of Engineers, Washington, DC.
Elata, C., and Ippen, A. T. (1961). “Dynamics of open channel flow with suspensions of neutrally buoyant particles.” Rep. Prepared for Massachusetts Institute of Technology, Cambridge, MA.
Enwald, H., Peirano, E., and Almstedt, A. E. (1996). “Eulerian two-phase flow theory applied to fluidization.” Int. J. Multiphase Flow, 22(1), 21–66.
Fu, X. D., Wang, G. Q., and Shao, X. J. (2005). “Vertical dispersion of fine and coarse sediments in turbulent open-channel flows.” J. Hydraul. Eng., 877–888.
Greimann, B. P., and Holly, F. M. (2001). “Two-phase flow analysis of concentration profiles.” J. Hydraul. Eng., 753–762.
Greimann, B. P., Muste, M., and Holly, F. M. (1999). “Two-phase formulation of suspended sediment transport.” J. Hydraul. Res., 37(4), 479–500.
Guo, J. K., and Julien, P. Y. (2001). “Turbulent velocity profiles in sediment-laden flows.” J. Hydraul. Res., 39(1), 11–23.
Herrmann, M. J., and Madsen, O. S. (2007). “Effect of stratification due to suspended sand on velocity and concentration distribution in unidirectional flows.” J. Geophys. Res. Oceans, 112(C2), C02006.
Hibiki, T., and Ishii, M. (2003). “One-dimensional drift-flux model and constitutive equations for relative motion between phases in various two-phase flow regimes.” Int. J. Heat Mass Tran., 46(25), 4935–4948.
Horender, S., and Hardalupas, Y. (2009). “Turbulent particle mass flux in a two-phase shear flow.” Powder Technol., 192(2), 203–216.
Hsu, T. J., Jenkins, J. T., and Liu, P. L. F. (2003). “On two-phase sediment transport: Dilute flow.” J. Geophys. Res. Oceans, 108(C3), C33057.
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. Lon. A, 460(2048), 2223–2250.
Hunt, J. N. (1954). “The turbulent transport of suspended sediment in open channels.” Proc. R. Soc. Lon. A, 224(1158), 322–335.
Ishii, M., and Hibiki, T. (2006). Thermo-fluid dynamics of two-phase flow, Springer, New York.
Jha, S. K., and Bombardelli, F. A. (2010). “Toward two-phase flow modeling of nondilute sediment transport in open channels.” J. Geophys. Res. Earth, 115(F3), F03015.
Jha, S. K., and Bombardelli, F. A. (2011). “Theoretical/numerical model for the transport of non-uniform suspended sediment in open channels.” Adv. Water Resour., 34(5), 577–591.
Jiang, J. S., Law, A. W. K., and Cheng, N. S. (2004). “Two-phase modeling of suspended sediment distribution in open channel flows.” J. Hydraul. Res., 42(3), 273–281.
Johansen, S. T. (1991). “The deposition of particles on vertical walls.” Int. J. Multiphase Flow, 17(3), 355–376.
Kovacs, A. E. (1998). “Prandtl’s mixing length concept modified for equilibrium sediment-laden flows.” J. Hydraul. Eng., 803–812.
Lun, C. K. K., Savage, S. B., Jeffrey, D. J., and Chepurniy, N. (1984). “Kinetic theories for granular flow—Inelastic particles in Couette flowand slightly inelastic particles in a general flowfield.” J. Fluid Mech., 140, 223–256.
Lyn, D. A. (1988). “A similarity approach to turbulent sediment-laden flows in open channels.” J. Fluid Mech., 193, 1–26.
Maxey, M. R., and Riley, J. J. (1983). “Equation of motion for a small rigid sphere in a nonuniform flow.” Phys. Fluids, 26(4), 883–889.
McTigue, D. F. (1981). “Mixture theory for suspended sediment transport.” J. Hydr. Div., 107(6), 659–673.
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.
Muste, M., Yu, K., Fujita, I., and Ettema, R. (2005). “Two-phase versus mixed-flow perspective on suspended sediment transport in turbulent channel flows.” Water Resour. Res., 41(10), W10402.
Nezu, I., and Rodi, W. (1986). “Open-channel flow measurements with a laser doppler anemometer.” J. Hydraul. Eng., 335–355.
Nguyen, K. D., Guillou, S., Chauchat, J., and Barbry, N. (2009). “A two-phase numerical model for suspended-sediment transport in estuaries.” Adv. Water Resour., 32(8), 1187–1196.
Ni, J. R., and Wang, G. Q. (1991). “Vertical sediment distribution.” J. Hydraul. Eng., 1184–1194.
Oliveira, P. J., and Issa, R. I. (2003). “Numerical aspects of an algorithm for the Eulerian simulation of two-phase flows.” Int. J. Numer. Meth. Fluids, 43(10–11), 1177–1198.
Parker, G., and Coleman, N. L. (1986). “Simple-model of sediment-laden flows.” J. Hydraul. Eng., 356–375.
Peirano, E., and Leckner, B. (1998). “Fundamentals of turbulent gas-solid flows applied to circulating fluidized bed combustion.” Prog. Energy Combust., 24(4), 259–296.
Peirano, E., and Minier, J. P. (2002). “Probabilistic formalism and hierarchy of models for polydispersed turbulent two-phase flows.” Phys. Rev. E, 65(4), 046301.
Pittaluga, M. B. (2011). “Stratification effects on flow and bed topography in straight and curved erodible streams.” J. Geophys. Res., 116(F3), F03026.
Richardson, J. F., and Zaki, W. N. (1954). “The sedimentation of a suspension of uniform spheres under conditions of viscous flow.” Chem. Eng. Sci., 3(2), 65–73.
Rouse, H. (1937). “Modern concepts of the mechanics of fluid turbulence.” Trans. ASCE, 102(1), 463–505.
Soo, S. L. (1990). Multiphase fluid dynamics, Science Press and Gower Technical, Beijing.
Sumer, B. M. (1974). “Mean velocity and longitudinal dispersion of heavy particles in turbulent open-channel flow.” J. Fluid Mech., 65(1), 11–28.
Toorman, E. A. (2008). “Vertical mixing in the fully developed turbulent layer of sediment-laden open-channel flow.” J. Hydraul. Eng., 1225–1235.
Umeyama, M. (1992). “Vertical-distribution of suspended sediment in uniform open-channel flow.” J. Hydraul. Eng., 936–941.
van Rijn, L. C. (1984). “Sediment transport, part II: Suspended load transport.” J. Hydraul. Eng., 1613–1641.
Wang, X. K., and Qian, N. (1992). “Velocity profiles of sediment laden flow.” Int. J. Sediment Res., 7(1), 27–58.
Wright, S., and Parker, G. (2004). “Density stratification effects in sand-bed rivers.” J. Hydraul. Eng., 783–795.
Wu, W. M., and Wang, S. Y. (2000). “Mathematical models for liquid-solid two-phase flow.” Int. J. Sediment Res., 15(3), 288–298.
Yalin, M. S. (1977). Mechanics of sediment transport, Pergamon, Toronto.
Zhong, D. Y., Wang, G. Q., and Sun, Q. C. (2011). “Transport equation for suspended sediment based on two-fluid model of solid/liquid two-phase flows.” J. Hydraul. Eng., 530–542.
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Published In
Journal of Hydraulic Engineering
Volume 140 • Issue 1 • January 2014
Pages: 35 - 47
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Feb 24, 2013
Accepted: Jun 27, 2013
Published online: Jul 1, 2013
Discussion open until: Dec 1, 2013
Published in print: Jan 1, 2014
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