Theoretical/numerical model for the transport of non-uniform suspended sediment in open channels

In this paper, we address the transport of multi-disperse suspended sediment mixtures in open channels, via the use of the two-fluid model. To that end, we extend previously developed frameworks for the dilute and non-dilute transport of suspended sediment. Within the scope of the Reynolds-averaged Navier-Stokes (RANS) equations, these modeling frameworks comprise mass and momentum equations for both phases (water and sediment). Here, we calculate the distribution of total volumetric concentration of sediment using two approaches: (1) by considering the mixture as represented by a single size; we call this approach Partial two-fluid model for uniform sediments (PTFMU); and (2) by combining the volumetric concentration of the sediment corresponding to several particle size classes; we call this approach Partial two-fluid model for non-uniform sediments (PTFMNU). In the second approach, we propose a methodology for the computation of the overall velocity of the disperse phase as a function of the velocities of each size class. k-ε type closures to account for the turbulence in the carrier phase (water) are applied. We also consider the coupling between the two phases through the drag force. Velocities of the carrier and disperse phases, and concentrations for each sediment class size are numerically solved by integrating the differential equations over control volumes. In order to validate our models, we compare numerical results to experimental data of Einstein and Chien H.A. Einstein, N. Chien, Effects of heavy sediment concentration near the bed on velocity and sediment distribution, MRD sediment series report, University of California, Berkley, 1955] and Taggart et al. W.C. Taggart, C.A. Yermoli, S. Montes, A. Ippen, Effects of sediment size and gradation on concentration profiles for turbulent flow, Massachusetts Institute of Technology, 1972]. Results of mean velocity of the carrier phase are in close agreement with the experimental data. For the prediction of sediment concentrations, we observe that there is a difference in the results using the two approaches mentioned above. We additionally obtain values of the Schmidt number needed to improve the agreement between predictions of the distribution of suspended sediment and the experimental data, and discuss the effect of sediment size and increasing sediment concentration on the values of the Schmidt number.