Numerical Modelling of Air Entrainment in a Stepped Spillway

Air entrainment in hydraulics are typically modeled by interface capturing methods. The volume of fluid model (VOF) has been used for this purpose. In this method the interface is captured by solving an advection equation for the volumetric water fraction. In this work the VOF solver of OpenFOAM, interFoam, has been modified aiming to improve the capabilities of predicting the amount of air in the water.

The advection equation is designed to keep the interface between the two fluids sharp. This equation do not contain any diffusion term. As this α equation is designed to resolve the case of insolvable two-fluid flow, no diffusion would be expected. Nevertheless, in the case of numerical simulation of air entrainment in free surface flow, where the grid size is insufficient to resolve the smallest bubbles, the air entrainment process can be viewed as a diffusion process. Then it might be relevant to add a diffusion term to the advection equation. Another way to account for the air that is entrained into the water is to add a source term to this equation.

As the entrainment is a function of the turbulent forces, the choice of turbulent modeling will be of importance. As a starting point the relisable k-epsilon model is used. Due to the vertical stratification of the fluid as a result of the air-water mixing, the turbulence might be overestimated. Damping terms will be implemented to the turbulence models to reduce the amount of turbulence in such occasions. A stepped spillway experiment will be used as reference case for validation of the model.