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.

中文翻译：

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圆形钢琴键入口竖井溢洪道流场数值模拟

竖井溢洪道通常设置有足够的淹没度，以避免空气夹带和涡流。但是，如果无法满足所需的进场流量条件，也可以为此目的考虑其他结构方法。优化入口形状，例如通过在轴溢洪道上安装圆形钢琴键 (CPK) 入口，是减少空气夹带和旋流强度的经济方法。在这项研究中，进行了数值模拟以研究带有 CPK 入口的竖井溢洪道周围的流场。研究了 CPK 入口在孔口控制流量（液压系统运行的不利流动条件）下提高简单竖井溢洪道性能的效果。鉴于其特殊的配置，CPK 入口降低了涡流强度并显着增加了通过轴的流量排放。有限体积法用于求解圆柱坐标系中的运动控制微分方程。在无水表面上施加两相空气 - 水流以及标准k – ε湍流模型。还研究了不同 CPK 几何形状对流动水力特性的影响。结果表明，与简单竖井甚至牵牛花溢洪道相比，CPK进水口显着增加了流量，降低了湍流强度。为了最大限度地提高垂直竖井溢洪道的效率，导出了 CPK 入口的最佳几何形状。