A general mixture model for sediment laden flows

Abstract

A mixture model for general description of sediment-laden flows is developed based on an Eulerian-Eulerian two-phase flow theory, with the aim at gaining computational speed in the prediction, but preserving the accuracy of the complete two-fluid model. The basic equations of the model include the mass and momentum conservation equations for the sediment-water mixture, and the mass conservation equation for sediment. However, a newly-obtained expression for the slip velocity between phases allows for the computation of the sediment motion, without the need of solving the momentum equation for sediment. The turbulent motion is represented for both the fluid and the particulate phases. A modified k-ε model is used to describe the fluid turbulence while an algebraic model is adopted for turbulent motion of particles. A two-dimensional finite difference method based on the SMAC scheme was used to numerically solve the mathematical model. The model is validated through simulations of fluid and suspended sediment motion in steady open-channel flows, both in equilibrium and non-equilibrium states, as well as in oscillatory flows. The computed sediment concentrations, horizontal velocity and turbulent kinetic energy of the mixture are all shown to be in good agreement with available experimental data, and importantly, this is done at a fraction of the computational efforts required by the complete two-fluid model.