Mechanism of a Coherent Air Core Forming from the Free-Surface Vortex in Hydraulic Intake Systems

The air-entraining vortex with a coherent air core is the most intense form of free-surface vortices in hydraulic intakes, causing the efficiency reduction and operation vibration of the hydraulic machinery. The quantitative relationship linking flow parameters to continuous air entrainment, and the influence of vortex–turbulence interactions upon vortex evolution, are yet to be fully elucidated. This gap is crucial for understanding vortex instability characteristics and improving vortex control strategies. Large eddy simulations are performed to reproduce air-entraining vortex phenomena in the hydraulic intake, and the air-water interface is captured using the coupled level-set and volume-of-fluid method. Parametric studies of the free-surface vortex by varying the intake flow rate and submergence depth are carried out, and influences of free-surface vortices on the intake flow uniformity are elucidated. The results show that the vortex strength must reach a threshold for air-entraining vortex formation, and air can only be continuously entrained into the intake system when the vortex intensity is no less than the threshold. The Froude number based on submergence depth is adopted as the characteristic parameter to unify the effects of flow parameters, and a quadratic polynomial correlation between this Froude number and the required threshold is proposed. Analysis of turbulent kinetic energy and vorticity distributions reveals that turbulent kinetic energy is highly coupled with the local vortex motion. The vortex-turbulence interaction plays a critical role in the formation of a coherent air core from free-surface vortices, and the turbulent kinetic energy transport equation is employed to analyze their mutual dynamics. The diffusion term of the transport equation affects the vortex core evolution from random vortices to a vortex pair and eventually to a single dominant vortex. Further analysis of the production terms show that interactions between streamwise/spanwise fluctuations and corresponding mean velocity gradients primarily contribute to the local turbulent kinetic energy enhancement.