This paper focuses on Piano Key Weirs (PKWs) as an effective solution for improving the discharge capacity of spillway systems. The flow behavior in inlet and outlet keys is experimentally studied to analyze the discharge capacity of PKWs with different plan shapes (i.e., rectangular, trapezoidal, and triangular). The results show that in outlet keys, the flow aeration regimes extend to higher values of headwater ratios (H_o/P) by increasing the length magnification ratio (B/w) and apex width ratio (A/w). In addition, the local submergence length is a decreasing function of A/w, especially in high flow heads. While the total interference length enlarges by reducing A/w in lower H_o/P values (H_o/P < 0.5), a reverse trend is observed in higher headwater ratios. PKW performance may also be impacted by the flow contraction and recirculation zone in inlet keys, which intensify in higher values of H_o/P, B/w, and A/w. According to the obtained results, while the discharge coefficient is a decreasing function of A/w in H_o/P > 0.4, it may have a reverse trend in lower head conditions. In addition, a trapezoidal PKW has the highest discharge efficiency in a wide range of the studied domain (H_o/P > 0.25 and B/w ≥ 2). It can improve the discharge efficiency by around 5%, while its body volume is almost 7% smaller than the traditional rectangular PKW. However, for low-length and high-head conditions (B/w = 1 and H_o/P > 0.5), the efficiency a rectangular PKW exceeds that of the other shapes.

中文翻译：

---

不同平面形状钢琴键堰的流体动力学和自由流动特性

本文重点介绍钢琴键堰 (PKW) 作为提高溢洪道系统排放能力的有效解决方案。实验研究了入口和出口键的流动行为，以分析具有不同平面形状（即矩形、梯形和三角形）的 PKW 的排放能力。结果表明，在出口键中，通过增加长度放大比 ( B / w ) 和顶点宽度比 ( A / w ) ，流动曝气机制扩展到更高的水源比 ( H _o / P )。此外，局部淹没长度是A / w的递减函数，尤其是在高流量扬程中。虽然在较低的H _o / P值 ( H _o / P < 0.5) 中通过降低A / w 会增加总干扰长度，但在较高的水源比率中观察到相反的趋势。PKW 性能也可能受到入口键中的流动收缩和再循环区的影响，这在H _o / P、B / w和A / w值较高时会加剧。根据所获得的结果，而排放系数的递减函数甲/瓦特在H _o / P > 0.4，在低水头条件下可能有反向趋势。此外，梯形 PKW 在广泛的研究范围内具有最高的放电效率（H _o / P > 0.25 和B / w ≥ 2）。它可以将放电效率提高5%左右，而其体积比传统的矩形PKW小了近7%。然而，对于低长度和高水头条件（B / w = 1 和H _o / P > 0.5），矩形 PKW 的效率超过其他形状。