Two-phase modeling of turbulence in dilute sediment-laden, open-channel flows

In this paper, we focus on assessing the performance of diverse turbulence closures in the simulation of dilute sediment-laden, open-channel flows. To that end, we base our analysis on a framework developed in a companion paper of this special issue, which puts forward a standard sediment transport model (SSTM), a partial two-fluid model (PTFM) and a complete two-fluid model (CTFM), in three- and one-dimensional (3D and 1D) versions. First, we propose in this paper extensions of the transport equations for the Reynolds stresses, and of the equations of the K–ω model to two-phase flows, starting from the general two-fluid model. We consider the drag force to be the predominant force amongst all the interactions between the two phases (water and sediment). Second, under the framework of models formed by the SSTM, the PTFM and the CTFM, we discuss simulation results obtained by employing the Reynolds stress model (RSM), the algebraic stress model (ASM), and the K–\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon$$\end{document} and the K–ω models (in their standard and extended versions), paired with each member of the framework. To assess the accuracy of the models, we compare numerical results with the experimental datasets of Vanoni, Trans ASCE 111:67–133, 1946; Coleman, Water Resour Res 22(10):1377–1384, 1986; Muste and Patel, J Hydraul Eng 123(9):742–751, 1997; Nezu and Azuma, J Hydraul Eng 130:988–1001, 2004; Muste et al. Water Resour Res 41:W10402, 2005 . Third, we obtain from those comparisons the values of the Schmidt number that facilitate the agreement of model predictions with data. We conclude that the standard K–\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon$$\end{document} model, the ASM and the K–ω models all provide satisfactory descriptions of flow variables and sediment concentrations in open-channel flows; further, we show that the more complicated RSM does not provide much improvement in dilute sediment transport as compared to those previous models, even when it is paired with the CTFM. We also show that the inclusion of model extensions in the turbulence closures does not improve the predictions for dilute mixtures either. We find that our values for the Schmidt number agree well with available data, and we provide an explanation for the variation of the Schmidt number with the ratio of the fall velocity and the wall-friction (shear) velocity. Finally, we corroborate that the Schmidt number is the key parameter to obtain satisfactory predictions of sediment transport in suspension.