Numerical modeling of self-aerated flows: Turbulence modeling and the onset of air entrainment

Numerical modeling of self-aerated flows is essential for understanding water systems and designing hydraulic structures. This work discusses and extends a theoretical/numerical model to represent air entrainment in self-aerated flows, which includes a criterion to define the occurrence of air entrainment, based on a balance between disturbing and stabilizing energies. The impact of the turbulence closure on the modeling of the onset of air entrainment and the distribution of bubble concentration is studied with particular emphasis. This work shows that uniform-density formulations of Reynolds-averaged Navier–Stokes closures lead to severe overprediction of air entrainment due to unphysical transport of turbulent kinetic energy generated in the air phase to the water phase. In contrast, combining variable-density turbulence closures with the energy balance criterion enables accurate prediction of the regions where air is entrained for stepped spillways and plunging jets. The choice of turbulence closure significantly influences the proposed criterion, emphasizing the importance of selecting an appropriate closure for an accurate description of the air entrainment process. Based on the conducted tests, the standard k−ε and buoyancy modified k−ε models better predict the onset of air entrainment and bubble distribution in stepped spillways, while the k−ω SST model proves to be more effective in capturing air entrainment at the impingement point in plunging jets. This study expands the capabilities of numerical models in predicting air entrainment and provides valuable insights into the effects and interrelations of the turbulence modeling, the air entrainment occurrence criteria, and the bubble transport equations.