The 3D sediment scour model for non-cohesive soils was first introduced to FLOW-3D in version 8.0 to simulate sediment erosion, transport and deposition. It was coupled with the fluid dynamics and considered entrainment, drifting and settling of sediment particles. In version 9.4, the model was extended with the addition of bedload transport and multiple sediment species.
In version 11.0, the packed sediment bed was described with the FAVOR™ technique. The area and volume fractions describing the packed sediment distribution were recalculated at each time step to reflect the new shape of the packed bed (Wei, 2014), giving a more direct representation of the interface between the packed and suspended sediments. This in turn allowed the solver to more accurately capture viscous boundary layers along the packed bed, which is the primary driving force for erosion. It also simplified and enhanced visualization of the complex phenomena of sediment transport.
Increased Accuracy and Robustness
In the upcoming release of FLOW-3D v12.0, the robustness, accuracy and stability of the model has been enhanced by systematically addressing mass conservation issues for sediment species. Due to the complexity of the physical processes involved in sediment transport and erosion, and to a wide range of numerical approximations used to describe these processes, mass conservation of sediment is a challenge. Each sediment species constantly transitions between suspended and packed states, moves with the mean flow as well as settles under gravity, and is transported along the surface of the packed bed by the bedload fluxes; all while interacting with other species, and constrained by physical and numerical limits such as packing density, free surface, non-eroding solids and mesh resolution. The resulting uncertainties, approximations and assumptions inevitably translate into some loss of mass conservation. The goal of this latest development is to broaden the range of applicability of the model and improve its accuracy.
An additional effort went into reducing the dependency of the solution on mesh resolution and cell aspect ratio. As a result, the processes of sediment entrainment and settling, bedload transport, and suspended sediment transport have received a substantial makeover. These changes are illustrated below.
If all sediment is eroded in a mesh cell, erosion continues to the neighboring cell below.
If a mesh cell is filled due to deposition, the deposition continues in the neighboring cell above.
Eroded Sediment Volume
At each time step, the eroded sediment volume does not exceed the sum of the sediment volumes in the cell and its neighboring cell below.
Volume erosion ≤ Vp1+Vp2
Deposited Sediment Volume
At each time step, the deposited sediment volume does not exceed the sum of the open volumes in the cell and its neighboring cell above.
Volume deposition ≤ Vo1+Vo2
Conserving the Suspended Sediment Mass
When the open volume changes in a cell due to erosion or deposition, the suspended sediment concentration in that cell is adjusted to conserve the suspended sediment mass.
Sediment Scour Model Validation Case
A flow-over-a-weir test case shows the improvements in the sediment mass conservation. The simulation has a packed bed consisting of 3 sediment species of diameters 0.001m, 0.0069m, and 0.0105m, with a density of 2650 kg/m3. Fluid comes into the domain at the upstream boundary (x-min). The downstream boundary (x-max) is closed off. From the plot of the total sediment mass over time shown below, we can see that in the previous version of FLOW-3D we lose sediment mass at a much higher rate than in version 12.0.
An animation of this simulation with v12.0 is shown here:
Next we present a validation case of scour around a horizontal cylindrical pipeline. The experimental work was performed by Mao (Mao, 1986) to obtain scour profiles of bed erosion underneath underwater horizontal pipelines. Below we compare the results obtained using FLOW-3D v12.0 with those from the paper.
Plot (A) compares the maximum scour depth under the pipeline over time, while plots B through F overlay the scour profiles from the study, shown as red dots, with those from FLOW-3D. The results obtained from FLOW-3D compare very well with the data.
In conclusion, the accuracy and stability of the 3D sediment transport and scour model in FLOW-3D version 12.0 has been greatly enhanced. Mass conservation of each sediment species are enforced within a few percent, and the dependency on the mesh density and aspect ratio has been reduced.
Wei, G., Brethour, J. M., Grüenzner M., and Burnham, J., 2014, The Sediment Scour Model in FLOW-3D, Technical Note FSI-14-TN-99, Flow Science, Inc.
Mao, Y., 1986. The interaction between a pipeline and an erodible bed, PhD thesis, Institute of Hydrodynamics and Hydraulic Engineering, Technical University of Denmark, Lyngby, Denmark.