Comparison of Mixture and VOF methods for numerical simulation of air-entrainment in skimming flow over stepped spillways

Because stepped spillways can significantly reduce the depth and size needed for a stilling basin at the toe of a dam and lead to great economic benefit, these spillways are increasingly attractive in hydraulic engineering. It is commonly acknowledged that free-surface aeration is significant in stepped spillways. In this paper, for investigation of Mixture and VOF method's ability, air-entrainment in skimming flow over the stepped spillways is simulated by using Fluent software. The numerical simulation results of free surface, velocity components and air concentration in water and circumstance of air entry into the water have been compared with the experimental results. It was found, downstream of the inception point of free-surface aeration which rapid free-surface aeration is observed, free surface is simulated better by Mixture method. On the steps downstream of the inception point of free-surface aeration, the results of Mixture and VOF methods about velocity distribution are closer together (RMSE is equal to 0.25 and 0.23 for Mixture and VOF Methods, respectively). But on the steps located further downstream by a strong air entrainment, Mixture method gives relatively better results (RMSE is equal to 0.23 and 0.33 for Mixture and VOF Methods, respectively). Also in the Mixture method, convergence time is much less than VOF method. This time reduces about four to five times.