Numerical modelling of flow field at shaft spillways with circular piano-key inlets

Shaft spillways are commonly provided with adequate submergence to avoid air entrainment and swirling flows. However, other structural approaches can also be considered for this purpose if the required approach flow conditions cannot be met. Optimising the inlet shape, for example by installing a circular piano-key (CPK) inlet over the shaft spillway, is an economic way of reducing air entrainment and the swirling flow strength. In this study, numerical modelling was performed to investigate the flow field around a shaft spillway with a CPK inlet. The effects of the CPK inlet in increasing the performance of a simple shaft spillway under orifice control flow – an unfavourable flow condition for the operation of hydraulic systems – was examined. Given its special configuration, a CPK inlet reduces the swirling flow strength and significantly increases flow discharge through the shaft. The finite-volume method was used to solve the governing differential equations of motion in a cylindrical coordinate system. A two-phase air–water flow was applied on the water free surface along with a standard k–ε turbulence model. The effects of different CPK geometries on the hydraulic characteristics of flow were also investigated. The results showed that CPK inlets significantly increase the flow discharge and reduce the turbulent flow intensity compared with a simple shaft or even a morning glory spillway. To maximise the efficiency of vertical shaft spillways, optimal geometries of the CPK inlets were derived.