Due to the presence of a monopile in a turbulent flow swirling vortices, known as horseshoe vortices, can form upstream of the structure near the cylinder-bed junction. Those vortices then travel downstream of the cylinder as they are being dragged along with the current. The horseshoe vortices can scoop up bed material surrounding the cylinder, weakening the foundation of the structure. This phenomenon is known as scour. A common protection method to reduce the effects of scour is the dumping of stones in the vicinity of the cylinder-bed junction. The aim is to alter the flow dynamics near the bed in such a way that the underlying sediment is mostly unaffected. However, the protection material itself is also subject to hydrodynamic forcing and can therefore be entrained as well. This would be described as damage to the protection layer as its effectiveness reduces due to re-exposure of the underlying sediment. It is for this reason that protection layers must be carefully designed depending on their use. The mechanism of the horseshoe vortex system and its damaging aspects are not completely understood yet, making engineering of specific protection layers challenging. To better understand the flow behaviour upstream of a cylinder-bed junction, where the formation of the horseshoe vortices takes place, several tests have been performed at the Eastern Scheldt Flume in the Hydro Hall of Deltares. Here different cylinder and bed protection configurations were subjected to turbulent current and wave conditions where the upstream flow fields were measured with a PIV measurement system. Since the obtained information of the tests is limited to a specific area, there was an interest in modelling the test cases by means CFD, while using the test results as validation. In this thesis several of the test cases have been modelled with the Improved Delayed Detached Eddy Simulation (IDDES) hybrid turbulence model, based on the Spalart-Allmaras formulation, which include the following: a) Open channel with a smooth bed and no monopile b) Open channel with a rough bed and no monopile c) Open channel with a smooth bed and a smooth monopile d) Open channel with a rough bed and a smooth monopile The modelling strategy used starts off with a basic simulation case (a) which is compared to the test results for validation of the simulated flow characteristics. This model is then elaborated on by inclusion of either a rough protection model (b) or a smooth cylinder (c). Both models are again validated with the test results so that the ability of the IDDES model to model the fluid-structure interaction is investigated. Finally, a simulation that includes both a rough bed and a smooth cylinder (d) is performed. For simulation models b, c and d an assessment is made for potential initial particle entrainment by means of hydrodynamic forcing indicators. Additionally, the effects of bed model surface roughness on the entrainment of bed material are briefly considered.

Granular bed protections are a common measure to mitigate scour of the sand bed around hydraulic structures. In view of marching towards cost-effective solutions to tackle erosion-related problems, it is important to accurately predict the loads exerted on the bed and come up with the needed rock grading. To that end, a 3-D eddy resolving modelling technique could help in formulation of a new stability formula, based on extreme local flow conditions It is the aim of this thesis to build a hydrodynamic numerical tool, able to predict governing mechanisms in stone stability. Special attention is paid on the way of representing a rough boundary and predicting wall and free turbulence. That being said, a Wall-Modelled Large Eddy Simulation (WMLES) is suggested and is build using the open-source CFD toolbox OpenFOAM. Firstly, simple open channel flow case simulations are set-up, to evaluate the performance of rough wall functions in the LES environment. Secondly, a backwards facing step kind of flow from the experimental study of Jongeling et. al (2003) is simulated and the performance of the numerical model is evaluated based on the experimental results. Finally, the suitability of this method for the target applications of this study is discussed, including a comparison with previous numerical studies of this research area.

In this thesis, it is studied if the stability of a stone in a granular bed protection, can be predicted by the local output of a three-dimensional (3D) eddy resolving simulation technique.

In earlier studies regarding stone stability, Reynolds-Averaged Navier-Stokes (RANS) models are used to determine the loads on the bed. In the resulting stability formulas, depth-averaged flow parameters are used, and the loads caused by turbulent fluctuations are taken into account by the modelled turbulent kinetic energy k. A load caused by turbulent wall pressures is never explicitly taken into account before. With the use of a 3D eddy resolving modelling technique, turbulence can be resolved to a certain extent, by which local parameters can be used to determine the load on the bed. This may result in a more accurate prediction of stone stability, and a more economical design method for granular bed protections.

Due to the computational requirements needed for the most detailed eddy resolving modelling techniques, it is concluded that for the aim of assessing stone stability, Improved Delayed Detached Eddy Simulation (IDDES) is the most appropriate 3D eddy resolving modelling technique for now and the nearby future. This modelling technique is also applied in a study regarding the influence of tidal energy turbines in one of the gates of the Eastern Scheldt barrier. In this thesis, special attention is paid to develop a stability formula, which can be used to assess the stone stability in the highly turbulent flow region behind the Eastern Scheldt barrier, based on the output of these simulations (hereafter ”Eastern Scheldt case”).

In order to derive a new stability formula, IDDESs are made of the two long sill experiments of Jongeling et al. (2003). In these experiments, an accelerating flow region is present above the sill. At its downstream end, the flow is separating, causing a highly turbulent flow region behind the sill. Thereby, the dominant flow characteristics are similar to those at the Eastern Scheldt barrier. In both regions of the experiments, on top of the sill and in the area downstream of the sill, damages to the granular bed protection are measured.

A new stability formula is proposed. To avoid the new stability formula to be grid dependent, the wall shear stress and the pressure gradient are used to
represent the loads by drag and inertia respectively.

It appeared, that the proposed stability formula does not predict the number of measured stone movements well, for the entire modelled domain of the long sill experiments. Nevertheless, it is hypothesised, that the assumed pre-dominant load terms are right, but that the ratio between those load terms on top of the sill differs from the ratio between the load terms in the downstream area. Two different entrainment mechanisms are described, that may not be predicted accurately by the same stability formula.

With regard to the Eastern Scheldt case, the choice is made to derive a stability formula that is only valid for the entrainment mechanism in a highly turbulent flow region behind a sill of backward-facing step. The data, behind the point of separation in the long sill simulations, is used to derive this stability relation. It appeared that the best results are obtained for a stability formula that is similar to the stability relation proposed earlier, with a Cm:b-value of 1. This is in agreement with the hypothesised entrainment mechanisms for this region.

Finally, the proposed stability formula is applied to the Eastern Scheldt case. A firm conclusion about the exact influence of the tidal energy turbines on the granular bed protection, cannot be drawn based on this study. However, it can be concluded, that the influence on the stability of the stones seems to be insignificant. At the analysed locations, the loads on the bed even seem to be slightly reduced in the simulation with turbines, compared to the simulation without turbines.

At least as important, is the conclusion that IDDES potentially is an appropriate modelling technique to assess the stability of stones in a granular bed protection. For the long sill experiments, the measured flow characteristics are clearly reproduced more accurately when using IDDES, than by applying a RANS model with the same boundary conditions. The computational effort needed for the Eastern Scheldt case is comparable to the computational requirements of the long sill simulations. Nevertheless, in both cases, the effective grid resolution was not yet sufficient to resolve all fluctuations towards the size of 1dn50. Despite the given that the desired resolution is not yet reached in this thesis, the simulated velocity signals of the long sill experiments are in good agreement with the measured ones. The choice between the use of IDDES or a RANS model should depend on the available computational power, time and required accuracy.