Numerical and Physical Modelling of Aerated Skimming Flows over Stepped Spillways

Stepped spillways are commonly used to control overflows from reservoirs, as they dissipate significantly more energy than smooth spillways. At high discharges, skimming flow occurs over stepped spillways, in which significant air entrainment occurs. Numerical modelling has the potential to provide a useful tool to predict the important features of skimming flows over stepped spillways. However, numerical models must be validated against physical data sets, in order to determine whether they are able to accurately predict the required flow characteristics. This project investigates the ability of the Volume of Fluid (VOF), mixture and Eulerian multiphase models, in combination with a range of turbulence models, to predict a range of variables in skimming flows over stepped spillways, with particular focus on the ability of the models to predict air entrainment. A complex pattern of 3D vortices which occur in the step cavities is also investigated, both experimentally and numerically. The pressures acting on the step faces and spillway side walls are also studied. A narrow experimental stepped spillway was studied and pressures, flow depths and the locations of the inception point of air entrainment were measured. The spillway was numerically modelled in 3D, using a range of multiphase and turbulence models, and the results were compared to the experimental data. Experimental data from a second, significantly wider, stepped spillway was provided for this project. This spillway was numerically modelled in 2D and the numerical results were compared to the experimental data. A complex pattern of 3D vortices occurs in the step cavities of the narrow experimental stepped spillway. The direction of circulation of these vortices reverses at each consecutive step. The direction of circulation of the vortices is affected bythe flow rate and was observed to vary unpredictably over time. The Eulerian and mixture models were both shown to predict air entrainment, whereas the VOF model did not. All numerical models predicted the 3D vortex structures observed in the narrow experimental stepped spillway, and their associated effect on pressure. The time dependant behaviour of the vortices, however, was not predicted by the numerical models. 2D modelling using the Eulerian model, with the SST k-ω turbulence model, was found to be able to accurately predict velocities, AVFs, flow depths and the location of the inception point of air entrainment. The pressures and flow depth were also predicted reasonably accurately in 3D, using the Eulerian model with the SST k- ω model. The VOF model made accurate predictions of certain flow characteristics, however, the model’s performance is limited by the its inability to predict air entrainment. The mixture model was found to be significantly less accurate than the Eulerian model. Numerical modelling of spillways of various widths showed that, as the width of the channel increases, the 3D vortex structures in the step cavities repeat across the channel. This behaviour was confirmed experimentally, by modifying the narrow experimental spillway, in order to change the ratio of step height to channel width. An expression is presented, based on the channel width and step height, which is able to accurately predict the number of repetitions of the 3D vortices for all spillway geometries investigated in this project. The 3D vortex structures were shown to have a small effect on the velocities above the steps, however, these effects were highly localised and did not effect the width averaged velocities. The 3D vortex structures were also observed in channels of varying slope. The pressures acting on the step faces and side walls of the narrow stepped spillway were shown, both experimentally and numerically, to be significantly affected by the 3D vortex structures. This resulted in large pressure variations over short distances, which can pose a risk to masonry stepped spillways. Air entrainment was shown to reduce the high pressures acting on the step faces. The low pressures, however, were not significantly affected by the presence of air in the flow. Low pressures have the potential to cause damage to both concrete and masonry stepped spillways. The results of this project suggest that potentially damaging low pressures may occur in both the non-aerated and aerated regions of skimming flow over stepped spillways. This study demonstrates that a complex pattern of 3D vortices may occur in the step cavities of stepped spillways with varying geometries. This may have important implications for stepped spillways which are currently in service. The Eulerian multiphase model, in combination with the SST k-ω turbulence model, is able to accurately predict a range of important flow features over the two spillways investigated in this project. This shows that, this combination of multiphase model and turbulence model has the potential to provide a valuable tool for the design and inspection of stepped spillways. This study also shows that low pressures, which can potentially cause damage to both concrete and masonry spillways, may occur in both the non-aerated and aerated regions of skimming flows over stepped spillways.