Numerical Simulation of Air–Water Two-Phase Flow on Stepped Spillways Behind X-Shaped Flaring Gate Piers under Very High Unit Discharge

Abstract

Stepped spillways are commonly used under relatively low unit discharge, where cavitation pitting can be avoided by self-aerated flow. However, there are several dams in China with stepped spillways in combination with X-shaped flaring gate piers with unit design discharge considerably larger than specified in the available guidelines. Consequently, air–water two-phase flow on stepped spillway behind X-shaped flaring gate piers under very high unit discharge was investigated using Computational Fluid Dynamics (CFD) simulations. The 3-D Reynolds-averaged Navier–Stokes equations were solved, including sub-grid models for air entrainment, density evaluation, and drift-flux, to capture self-aerated free-surface flow over the spillway. The pressure on the vertical step faces was compared with laboratory data. In addition, the air–water two-phase flow characteristics and prototype step failure of the simulated prototype spillway were analyzed based on the numerical results of velocity, pressure, and air concentration. Moreover, an optimized bottom-aeration was further studied. The results reveal that the involved models can predict the air concentration near the steps. The cavitation index at the stepped surface is below the threshold value, and the air concentration is insufficient under high unit discharges. Moreover, with the proposed optimization of the aerator air entrainment can be improved and thereby cavitation erosion risk can be reduced.