Influence of VOF technique, turbulence model and discretization scheme on the numerical simulation of the non-aerated, skimming flow in stepped spillways

An accurate description of the hydrodynamics in the non-aerated region of the skimming flow on stepped spillways is of outmost importance, particularly in small structures at large discharges. In addition, the flow features upstream of the inception point of air entrainment determine the flow behavior in the downstream self aerated region. In this work, numerical models of the flow in the non-aerated region of stepped spillways have been developed using diverse turbulence closures and discretization schemes implemented in two CFD codes: OpenFOAM and FLOW-3D (R). Partial VOF (Volume of Fluid) and True VOF (TruVOF) approaches are employed to capture the position of the free surface. The Standard, RNG and Realizable k-epsilon, in addition to the SST k-omega model, are used for turbulence closure. Numerical results are compared against reference experimental results obtained from a physical model of constant slope of 0.75H:1V. Models with turbulence closures of the k-epsilon family provide nearly the same predictions for the mean flow velocity with maximum differences on average smaller than 1%. Regarding discretization schemes, the first-order upwind method provides predictions for the mean flow velocity which are not significantly different (within 6%) than those obtained with second-order counterparts. However, these differences can be larger when maximum values of turbulent kinetic energy (TKE) and dissipation rate of TKE at the step edges are compared. In spite of the fact that the TruVOF (FLOW-3D (R)) method does not account for the tangential stresses at the air-water interface, differences in the tracking of the free surface position among this method and the Partial VOF method (OpenFOAM) were found to be smaller than 3% along the stepped spillway. In this work, we also provide a physical interpretation of the flow results.