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.

The Bristol Channel has one of the largest tidal ranges in the world, with a mean tide of nearly 10.5 m at Avonmouth, and speculations on how to harness this energy date back well over a century. One method is tidal range by the use of tidal lagoons, which operates on principles akin to hydropower. The lagoon is essentially an enclosed reservoir near the coast, which can maintain the inside water level while the outside rises and falls with the tide. When a sufficient head difference between the inside and outside water level is achieved, the turbine gates open and the flow drive the turbines.

This thesis explores a novel modelling approach consisting of a 1D channel based on the inertial form of the Saint-Venant Equations, coupled with 0D tidal lagoons. The model was built in Modelica. The 1D channel subsystem was modelled first, and validated by comparison with tidal constituents at multiple measuring stations in the domain. The channel model’s accuracy was deemed sufficient, with root-mean-square deviations ranging from 0.29 to 0.67 m. With the model validated, the nature of the tidal resonance in the channel was investigated, where the natural period was determined to be located between 7-8 hours. It was shown that the natural period is heavily dependent on the tidal wave propagation velocity, which is in accordance with the quarter-wavelength resonance theory.

The 0D tidal lagoon subsystem was coupled with the 1D channel and validated by considering the proposed Swansea lagoon design by Tidal Lagoon Power and comparing the results with the current literature. The lagoon was found to be operating as expected in dual generation, and the annual energy generation was 425 GWh. The energy production is slightly conservative compared to literature, but within reason. The lagoons' impact on the channel hydrodynamics were also investigated, and it was found to have a significant effect, particularly in the narrow section of the estuary. The influence of the lagoon-channel coupling on energy generation was also explored: As the hydrodynamic impact increases, the energy generation from the system as a whole decreases.

A 2D model was also utilised to explore the higher-order and near-field effects that would potentially be lost in a 1D model, like localised dips in water elevation, reduced circulation zones, jets and more. The 2D results indicate that consideration of the localised effects is crucial when designing tidal lagoons.

The tidal lagoons were also implemented, and the Swansea lagoon had an annual energy generation of 408 GWh, closely matching the 1D model. Three larger tidal lagoons were also implemented, however not successfully scaled to match the 1D model due to time constraints. Operational tidal lagoons were also shown to have a tremendous influence on the water elevation in the channel.

In conclusion, the 1D modelling approach is potentially as a powerful tool to supplement more detailed 2D models, and it can potentially replace the 0D models ordinarily used for optimisation and sensitivity analyses in the preliminary investigations.