Characterization of turbulence statistics on the non-aerated skimming flow over stepped spillways: a numerical study

In this work we address the mean flow and turbulence statistics in the non-aerated region of a stepped spillway by using two different numerical strategies in two dimensions. First, we present results regarding the flow in a large portion of the spillway, simulated with a volume of fluid (VoF) method to capture the position of the free surface (case A). Numerically-obtained data are in very good agreement with particle image velocimetry (PIV) data; further, results suggest that profiles of mean velocity, turbulent kinetic energy (TKE) and dissipation rate of TKE at the step edges are approximately self-similar. It was also found that values of TKE and dissipation rate of TKE in the boundary layer development region follow universal similarity laws which are valid for open-channel flows. In addition, the field of simulated dimensionless pressure and pressure distributions at the step edges are qualitatively similar to those reported in a recent experimental work. Second, additional simulations were developed as a pressure-driven flow for only a portion of the spillway (case B). This was possible due to prior knowledge of the water depths. We show that, despite the fact that the pressure field can not be interpreted as in case A, the numerical simulations closely reproduce the experimental data regarding averaged velocity, vorticity, and the turbulence statistics. It was also found that turbulence intensity profiles in the intermediate region are consistent with published experimental results for open-channel flows. These numerical results offer new avenues for the simulation of portions of stepped spillways to assess the physics at the inception point of air entrainment with more sophisticated turbulence closures.