Sediment Transport under Saltation Regime in Turbulent Flow Part A: Development of the Model

Document Type : Research Article


1 Professor, Water Engineering Research Center, Tarbiat Modares University, Tehran, Iran

2 Professor, Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, New York, USA.


In the present research, a 3D numerical model of the sediment grain movement has been developed based on the Eulerian-Lagrangian perspective. The forces which act on sediment grains are non-linear drag force, the shear lift force, the rotational lift (Magnus) force, the buoyancy force, the added mass force, the Basset history force and torque. Second-order nonlinear ordinary differential equations have been used to calculate linear and angular velocity vectors and also the position of sediment grains. Two parts including turbulent fluctuations in 3D space and a stochastic bed-particle collision model have been considered in the modeling procedure. The verification of the developed model has been examined for two important issues including the minimum number of jumps for statistical convergence and the appropriate value of the time step. The validation of the model has been performed using reliable experimental data in terms of the saltation height, length and streamwise particle velocity for the ranges of fine sand to coarse gravel. To evaluate the qualification of the conceptual model, the effects of the elimination of some forces and turbulent fluctuations, where do not exist consensus on the use of these factors in the previous researches, have been studied. The results indicated that the developed model can be considered as a numerical lab to study different aspects of the sediment transport in the prediction step, which will be performed in the part B of this series.


سرشتی، ف. و کلاهدوزان، م. (1392). "بررسی تأثیر نیروهای هیدرودینامیکی مؤثر بر حرکت ذرات رسوب برای جریان سیال در کانال‌ها،" نشریه هیدرولیک، 8(2)، 41-56.‎
کبورانی، س. و شانه‌ساززاده، ا. (1392). "شبیه‌سازی و بررسی اثر عوامل مؤثر بر حرکت تصادفی ذرات رسوب بار بستر در جریان ماندگار،" مهندسی عمران مدرس، 14(1), 95-104.‎
مهدیزاده، س. س. (1387). "بررسی آزمایشگاهی حرکت ذره رسوبی در نزدیکی بستر با استفاده از دستگاه PIV"، پایان‌نامه کارشناسی ارشد، دانشگاه تربیت مدرس، تهران، ایران.
نصراللهی، ع. (1389). "شبیه‌سازی عددی انتقال بار بستر با استفاده از جریان دوفازی اولری-لاگرانژی"، رساله دکتری، دانشگاه تربیت مدرس، تهران، ایران.
Abbott, J. E., and Francis, J. R. D. (1977). “Saltation and suspension trajectories of solid grains in a water stream.” Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 284(1321), 225-254.
Bagnold, R. A. (1973). “The nature of saltation and of 'bed-load' transport in water.” Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 332(1591), 473-504.
Barati, R., Salehi Neyshabouri, S. A. A., and Ahmadi, G. (2014). “Development of empirical models with high accuracy for estimation of drag coefficient of flow around a smooth sphere: an evolutionary approach,” Powder Technology, 257, 11-19.
Crowe, C. T., Schwarzkopf, J. D., Sommerfeld, M., and Tsuji, Y. (2011). Multiphase flows with droplets and particles. CRC Press.
Francis, J. R. D. (1973). “Experiments on the motion of solitary grains along the bed of a water-stream.” In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 332(1591) 443-471.
García, M. H. (Ed.). (2008). Sedimentation engineering: processes, measurements, modeling, and practice (No. 110). ASCE Publications.
Gosman, A. D., and Loannides, E. (1983). “Aspects of computer simulation of liquid-fueled combustors,” Journal of Energy, 7(6), 482-490.
Ji, C., Ante, M., Eldad, A., Xu, D., and John, W. (2014). “Numerical investigation of particle saltation in the bed-load regime,” Science China Technological Sciences, 57(8), 1500-1511.
Lee, H. Y., and Hsu, I. S. (1994). “Investigation of saltating particle motions.” Journal of Hydraulic Engineering, 120(7), 831-845.
Lee, H. Y., Chen, Y. H., You, J. Y., and Lin, Y. T. (2000). “Investigations of continuous bed load saltating process,” Journal of Hydraulic Engineering, 126(9), 691-700.
Lee, H. Y., Lin, Y. T., Yunyou, J., and Wenwang, H. (2006). “On three-dimensional continuous saltating process of sediment particles near the channel bed,” Journal of Hydraulic Research, 44(3), 374-389.
Lukerchenko, N., Piatsevich, S., Chara, Z., Vlasak, P., Chára, Z., and Vlasák, P. (2009). “3D numerical model of the spherical particle saltation in a channel with a rough fixed bed,” Journal of Hydrology and Hydromechanics, 57(2), 100-112.
Maxey, M. R., and Riley, J. J. (1983). “Equation of motion for a small rigid sphere in a nonuniform flow,” Physics of Fluids, 26(4), 883-889.
Murphy, P. J., and Hooshiar H. (1982). “Saltation in water dynamics,” Journal of the Hydraulics Division, 108(11), 1251-1267.
Nezu, I. (1977). Turbulent structure in open-channel flows. PhD Thesis, Kyoto University, Kyoto, Japan.
Niño, Y. (1995). Particle motion in the near bed region of a turbulent open channel flow: implications for bedload transport by saltation and sediment entrainment into suspension, PhD Thesis, University of Illinois, USA.
Niño, Y., and García, M. (1998). “Using Lagrangian particle saltation observations for bedload sediment transport modelling, ” Hydrological Processes, 12(8), 1197-1218.
Niño, Y., and García, M. (1994). “Gravel saltation: 2. Modeling,” Water Resources Research, 30(6), 1915-1924.
Oberkampf, W. L., Sindir, M. M., and Conlisk, A. T. (1998). Guide for the verification and validation of computational fluid dynamics simulations. American Institute of Aeronautics and Astronautics (AIAA).
Papanicolaou  A. N., Elhakeem M., Krallis G., Prakash S. and Edinger J. (2008). “Sediment transport modeling review—current and future developments,” Journal of Hydraulic Engineering (ASCE), 134(1), 1-14.
Reizes, J. A. (1978). “Numerical study of continuous saltation,” Journal of the Hydraulics Division, 104(9), 1305-1321.
Sekine, M., and Kikkawa, H. (1992). “Mechanics of saltating grains. II,” Journal of Hydraulic Engineering, 118(4), 536-558.
Tian, L., and Ahmadi, G. (2007). “Particle deposition in turbulent duct flows—comparisons of different model predictions,” Journal of Aerosol Science, 38(4), 377-397.
Tsuchiya, Y. (1969). “Mechanics of the successive saltation of a sand particle in a turbulent stream,” Bull. Dis. Pre. Res. Inst., Kyoto Univ., 19(152), 31-44.
Tsuji, Y., Oshima, T., and Morikawa, Y. (1985). “Numerical simulation of pneumatic conveying in a horizontal pipe,” KONA Powder and Particle Journal, 3, 38-51.
van Rijn, L. C. (1984). “Sediment transport, part I: bed load transport.” Journal of Hydraulic Engineering, 110(10), 1431-1456.
Wiberg, P. L., and Smith, J. D. (1985). “A theoretical model for saltating grains in water,” Journal of Geophysical Research: Oceans (1978–2012), 90(C4), 7341-7354.
Yalin, M. S. (1992). River mechanics. Pergamon Press, New York. 
Yeganeh-Bakhtiary, A., Shabani, B., Gotoh, H., and Wang, S. S. (2009). “A three-dimensional distinct element model for bed-load transport” Journal of Hydraulic Research, 47(2), 203-212