D scour around a complex foundation
The mesh used in this study was selected to have the same dimensions as the flume in which the experimental measurements of Tavouktsoglou et al. (2017) were made. Thus the numerical flume was 15 m long 1.2 m wide and 0.5 m deep. The mesh was comprised of a total of 1,500,000 cells with an increasing refinement closer to the structure (see Figure 10). This was done to capture as accurately as possible the flow separation off the structure’s surface. The sediment box (i.e., Lagrangian field) is confined in a 0.5 x 0.5 m inverted
Figure 9: Comparison of scourFOAM results with Sumer and Fredspe (1990) for scour due to waves. Red line: model; dots: Sumer and Fredspe (1990) physical model results.
pyramid surrounding the base of the structure in the centre of the domain (see Figure 10). The inverted pyramid was selected in order to reduce the amount of Lagrangian particles needed to fill the virtual sand pit and thus reduce the computational time.
The equilibrium scour depth induced by a structure is the most important engineering aspect of scour. Numerous empirical methods for the prediction of the equilibrium scour depth exist which can be applied with some success, but their shortcoming is that they cannot provide an estimate of the overall 3D scour features. This section presents the results of the numerical simulation and provides a comparison with experimental measurements for a cylindrical base structure. Figure 11 presents the results of this comparative study.
As can be seen from the figure, the numerical model predicts well the 3D scour around the structure. The discrepancies and variation shown in Figure 11 are mainly attributed to the slight variation of the location of scour features in the x-y plane rather than the underestimation or overestimation of scour. This is expected as the locations of these features are highly effected by the slightest of variations in the starting flow and bed conditions. It can be seen that the maximum scour depth in both cases occurs at an angle of 45 degrees relative to the flow direction which agrees with potential flow theory. There is a small tendency for the model to over predict the equilibrium scour depth in front of the structure. This is mainly attributed to the slightly different flow profile which is used in the numerical model. According to Tavouktsoglou et al. (2017) higher near-bed velocities (as is the case
Figure 10: Computational domain for the complex 3D foundation test.
Figure 11: Equilibrium scour depth for the complex 3D foundation test.
in the numerical model) induce a stronger depth-averaged horizontal pressure gradient and thus deeper scour depths. Further observation of the data reveals that the model captures accurately the lateral extent of the scour hole both in the streamwise and cross-flow direction. This aspect is also important for design purposes as it controls the lateral extent of the scour protection. Therefore, the overestimation of the extent of the scour hole may lead to the overdesign of the scour protection system. In the case of the underestimation of the scour extent, the scour protection may be designed to be less extensive than required and thus pose a threat to the stability of the foundation.
The scourFOAM solver also captures accurately the secondary scour holes which radiate away from the structure at an angle ±130 degrees relative to the flow direction at the lee of the structure. This scour feature is associated with the lee-wake vortices which are induced by the flow structure interaction and are a common feature in cylindrical geometries (Olsen and Melaaen, 1993). These secondary scour features are also of significance for the design of scour protection systems as they may destabilize the edge detail of the scour protection and thus make the entire protection susceptible to failure. The simulation of this feature is also important as many existing sediment transport solvers have difficulties reproducing.
A final feature which is picked-up by the scourFOAM model and shows its ability to accurately capture the physical processes associated with scour around complex geometries is the deposition zone at the lee of the structure. This feature is caused by a secondary scour mechanism, the large-scale counter-rotating streamwise phase-averaged vortices (LSCSVs), which effectively creates a strong up-ward pressure gradient which re-suspends sediment from the lee of the structure. The LSCSVs are mainly driven by the longitudinal counterrotating vortices which are created partly by the horseshoe vortex and the variation of the shedding frequency over the height of the structure (Baykal et al., 2015). In the case of the cylindrical base structure the interaction between the flow and the components of the foundation with different diameters leads to the disruption of the LSCSVs. This in turn, reduces the erosion rate at the lee of the structure and thus more deposition takes place. Figure 11 shows that the sediment mound at the lee of the structure is not in line with the principal flow axis. This is attributed to a small flow asymmetry of around 5% which was present in the flume. A closer examination of this feature shows that the depression in the middle of this deposition zone is deeper in the case of the experimental results. This is also explained by the flow asymmetry which produces a stronger lee wake vortex on one side and thus a stronger upward flow gradient at the lee.
After the pile is installed the scour depth develops rapidly; however, it is important to predict the time evolution of scour for several reasons:
Numerous methods for predicting the time evolution of scour around monopiles have been developed (Harris et al., 2010 contains a brief review). The shortcoming of these methods is that they have all been developed based on laboratory data. This means that their accuracy is subject to scale effects and their performance varies from case to case. Therefore, the accurate predict ion of scour development using a numerical model can provide an invalauble tool for use in engineering analysis, design and practice. Figure 12 presents the results of the comparison between the experimental and numerical results. In this figure the scour depth is measured adjacent to the structure at an angle of 45 degrees relative to flow direction. It can be seen that the present model predicts well the time development of scour. The model has a tendency to over predict the scour but this is attributed to the stronger pressure gradient induced by the flow in the simulation case. The difference between the experimental and numerical results is small enough to be attributed to the slightly different flow profiles that were present in each case. To verify this, the scour prediction correction factor of Tavouktsoglou et al. (2016) is applied to the simulation data. By applying a 90% correction factor recommended by Tavouktsoglou et al. (2016) to the simulation results
Figure 12: Effect of correction factor on the model prediction.
we can obtain the dashed line in Figure 12 which shows that the agreement between the two data-sets has significantly improved, with the numerical solution following more closely but slightly underestimating the scour depth during the stabilization phase of the measured process. In conclusion, the scourFOAM model appears to represent a valuable tool to aid the design of coastal structures in real world engineering practice.