Two-phase modeling of granular sediment for sheet flows and scour

Abstract

Even though sediment transport has been studied extensively in the past decades, not all physical processes involved are yet well understood and represented. This results in a modeling deficiency in that few models include complete and detailed descriptions of the necessary physical processes and in that models that do usually focus on the specific case of sheet flows. We seek to address this modeling issue by developing a model that would describe appropriately the physics and would not only focus on sheet flows.

To that end, we employ a two-phase approach, for which concentration-weighted averaged equations of motion are solved for a sediment and a fluid phase. The two phases are assumed to only interact through drag forces. The correlations between fluctuating quantities are modeled using the turbulent viscosity and the gradient diffusion hypotheses. The fluid turbulent stresses are calculated using a modified k-epsilon model that accounts for the two-way particle-turbulence interaction, and the sediment stresses are calculated using a collisional granular flow theory.

This approach is used to study three different problems: dilute flow modeling, sheet flows and scouring. In dilute models sediment stresses are neglected. Near bed processes are instead modeled through the bottom boundary conditions and we consider and compare two widely used approaches. We also introduce and validate a concentration dependent Schmidt number.

The sheet flow model is validated for different flow conditions. Several well-known results and formulae are confirmed such as reduced turbulence in the diluted region, the bed load layer thickness and the dependence of the sediment transport rate on the Shields parameter. It also provides a counterexample to modeling the bed shear stress in phase with the free stream velocity. Finally, it provides information on the vertical sediment flux, which could be used to model the bottom boundary condition in dilute models.

The two-phase model is also shown to be able to represent two-dimensional sediment transport issues. A simple benchmark test case (scouring downstream of an apron) is performed and results are found to reproduce reasonably well existing experimental data.

Future work on sediment transport modeling is also discussed.