Hydrodynamics and Free-Flow Characteristics of Piano Key Weirs with Different Plan Shapes

Abstract

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 (Ho/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 Ho/P values (Ho/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 Ho/P, B/w, and A/w. According to the obtained results, while the discharge coefficient is a decreasing function of A/w in Ho/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 (Ho/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 Ho/P > 0.5), the efficiency a rectangular PKW exceeds that of the other shapes.

Advances in Spillway Hydraulics: From Theory to Practice

“…A collection of eleven papers were included in this Special Issue addressing spillway hydraulics, embracing the following main elements: spillway inlet structures, spillway transport structures, and spillway outlet structures. For the first topic, spillway inlet structures, discharge efficiency, and flow conditions are experimentally studied for PK weir with different plan shapes (i.e., triangular, trapezoidal, and rectangular), considering a large range of parameter values (Sangsefidi et al [6]). In turn, Stilmant et al [14] derive a purely theoretical model, validated against experimental data for a broad range of upstream heads, to compute the discharge coefficient with an ogee crest, which does not depend on empirical coefficients.…”

“…Sangsefidi et al [6] complement the rich literature, e.g., [7][8][9][10][11], on the innovative piano key weir, an improved type of nonlinear weir with high discharge capacity which can be placed atop gravity dams, first proposed by Lempérière and Ouamane in 2003 [12]. Based on physical model tests, they analyze discharge efficiency and detail flow conditions for triangular, trapezoidal, and classical rectangular piano key weirs considering a large range of parameter values.…”

Laboratory Study of the Hydraulic Performance of the A-Type Triangular Piano Key Weir

“…Main geometrical parameters of the PKW are in Figure 2. In this figure, P = weir height, B = weir length, B o = upstream overhang length, B i = downstream overhang length, B b = weir base width, and t = wall thickness [5]. To the best of our knowledge, hardly any research and no standard design method exist for TPKW, although a large number of studies were conducted on other types of PKW.…”