A numerical model for air concentration distribution in self-aerated open channel flows

The self-aeration in open channel flows, called white waters, is a phenomenon seen in spillways and steep chutes. The air distribution in the flow is always an important and fundamental issue. The present study develops a numerical model to predict the air concentration distribution in self-aerated open channel flows, by taking the air-water flow as consisting of a low flow region and an upper flow region. On the interface between the two regions, the air concentration is 0.5. In the low flow region where air concentration is lower than 0.5, air bubbles diffuse in the water flow by turbulent transport fluctuations, and in the upper region where air concentration is higher than 0.5, water droplets and free surface roughness diffuse in the air. The air concentration distributions obtained from the diffusion model are in good agreement with measured data both in the uniform equilibrium region and in the self-aerated developing region. It is demonstrated that the numerical model provides a reasonable description of the self-aeration region in open channel flows.