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Numerical studies regarding the influence of entrapped air on the hydraulic performance of gullies are nonexistent. This is due to the lack of a model that simulates the air-entrainment phenomena and consequently the entrapped air. In this work, we used experimental data to validate an air-entrainment model that uses a Volume-of-Fluid based method to detect the interface and the Shear-stress transport k-ω turbulence model. The air is detected in a sub-grid scale, generated by a source term and transported using a slip velocity formulation. Results are shown in terms of free-surface elevation, velocity profiles, turbulent kinetic energy and discharge coefficients. The air-entrainment model allied to the turbulence model showed a good accuracy in the prediction of the zones of the gully where the air is more concentrated.

The accurate prediction of self-aerated flow is not always easy to obtain, particularly if the computational performance is the main concern. Two-fluid formulation is suitable to simulate the dispersed air in a continuous water phase (e.g. bubbly flows) in a fine mesh, whereas the interface tracking methods are used for sharp interfaces with two continuous and contiguous phases (e.g. free-surface flows). Several approaches have emerged to combine both methods; however all found a gap in the transition between resolved and unresolved scales of air at the interface. Including a source term that predicts the self-aeration process is viewed as a promising step to overcome such difficulty. In this work, we added to the volume-of-fluid formulation an extra advection-diffusion equation connected to a source of air at the free surface to simulate the dispersed bubble phase. One-way coupling and two-way coupling versions of this model are tested along with sensitivity tests to show the accuracy of the new source term that does not require calibration. The location of the aeration is analysed and investigated. Results are obtained in terms of free-surface flow depths, air–concentration profiles and velocity fields and compared to experimental data acquired in a scaled stepped spillway model with good agreement. The free-surface given by the air-entrainment model is in good agreement in both non-aerated and aerated zone of the spillway.