A two-phase mixture turbulence model for sediment-laden flows:theory and verification

Two-phase mixture models are used to reproduce the motion of sediment-laden flows. Empirical constitutive relations, modified single-phase k - ϵ models and two-fluid turbulence models are usually applied to close two-phase mixture models. However, the turbulence model under the framework of the two-phase mixture theory has not been formed yet. In this paper, a two-phase mixture turbulence model was derived based on a two-fluid turbulence model. The equations of turbulent kinetic energy and turbulent dissipation rate of solid-liquid mixtures were derived. A key variable, the dispersion turbulent kinetic energy, defined as the mean relative turbulent kinetic energy of sediment to that of mixtures, is introduced to close the two-phase mixture turbulence model. An algebraic expression of the turbulent dissipation rate of solid phase is proposed. The two-phase mixture turbulence model takes into account interphase interaction and particle collisions, inherits the capabilities of the two-fluid turbulence model to predict turbulent information of both phases separately, and reduces the number of partial differential equations in half. The function of the absolute concentration distribution was adopted to determine the bottom boundary condition of sediment concentration. The partition coefficient of turbulent intensity in each direction was introduced to consider the turbulent anisotropy. A set of experiments were selected to verify the two-phase mixture model closed by the turbulence model acquired in this paper. The results are in satisfactory agreements with the observations. In addition, the experimental observations that the turbulent intensity decreases with the increment of sediment concentration can be reproduced by this model. © 2020, China Water Power Press. All right reserved.