The prediction of stone stability by a three-dimensional eddy resolving simulation technique

Abstract

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.