A general formulation of relative motion between two phases in sediment-laden water flows. (December 2018) - Liang, Lixin; Yu, Xiping; Bombardelli, Fabián
Highlights: The relative velocity between two phases in sediment-laden flows is formulated. The formula is based a well validated two-phase flow model. The formula is shown to be simple but generally applicable. Abstract: A general formulation for the relative velocity between the two phases in sediment-laden water flows is established in this study. The purpose of this effort is to obtain more affordable tools for the simulation of sediment-laden flows at different scales. To this end, an enhanced Eulerian–Eulerian two-phase flow model, which encompasses the mass and momentum conservation equations for both water and sediment phases and a modified k − ɛ model including sediment effects on fluid turbulence, is first presented and then validated for steady-state, open-channel as well as oscillatory flows. Starting from the aforementioned two-phase flow model, the relative velocity between the two phases is obtained by manipulating the momentum equations for the two phases, thus leading to a simplified expression which saves computational time. Based on numerical experiments, it is found that that in the vertical direction pressure and shear stress are predominant as compared to other factors, while in the horizontal direction, lift force and advection effect are also important to some extent, particularly when accurate results are expected. Interestingly, the simplified form of the formulation is shown to provide similar accuracy as the two-phase flow model does.