A general two-phase mixture model for sediment-laden flow in open channel

This work extends the sediment-laden mixture model with consideration of the turbulence damping and particle wake effects under the framework of improved efficiency and accuracy. The mixture model consists of the continuity and momentum equations for the sediment-laden mixture, and the continuity equation for the sediment. A theoretical formula is derived for the relative velocity between the water and sediment phases, with consideration of the effects of the pressure gradient, the shear stress and the lift force. A modified expression of the particle wake effect, inducing the local turbulence enhancement around the sediment particle, is employed to improve the turbulent diffusion of the coarse sediment. The k(m)-epsilon(m) model is proposed to close the mixture turbulence, with the turbulence damping effect due to the high sediment concentration expressed by the density-stratification term without an empirical parameter. The k(m)-epsilon(m) turbulence model requires smaller computational work and offers better results than an empirical density-stratification turbulence model in high sediment concentration cases. Consequently, with the proposed mixture model, the sediment transport in the open channel under a wide range of sediment sizes and concentrations can be revealed with the results in good agreement with experimental data for the velocity, the sediment concentration and the turbulent kinetic energy.