Explicit calculation of natural aeration using a Volume-of-Fluid model

Accurate prediction of the air-entrainment process in air-water two-phase turbulent flows is one of the most computationally challenging subjects under current investigation in hydraulic engineering. An ideal numerical model for air-entrainment needs to be accurate and fast in the definition of a macroscopic interface and simultaneously precise enough to take into account the formation of bubbles through the free-surface, their transport and their natural interactions: bubble-bubble and bubble-fluid. The problem is made more complex by the strong coupling between mesh and solution exhibited by interface capturing schemes which are commonly used for such problems. This paper examines numerical and modelling aspects of the entrainment process for two canonical cases; the 2D dam break and 3D circular plunging jet cases. We start by investigating the capacities of a Volume-of-Fluid based model to detect the free-surface and predict the velocities inside the water phase, examining the effect of coarsening and refining the mesh on the prediction of the interface location. A reformulated explicit term is used to detect bubble formation and air-entrainment at the free-surface, without the need of a calibration process and adapted to run together with Volume-of-Fluid models. The results obtained with this new approach are further compared with similar cases in the literature in terms of bubble formation and free-surface wave's amplitude. The correct definition of the free-surface was found to be strongly dependent on the mesh refinement in a way that has very significant implications for the development of air-entrainment modelling.