Energy Dissipation of Rectangular and Trapezoidal Piano Key Weir

Piano key weirs are a kind of non-linear weirs, initially introduced by Hydrocoop (Blanc and Lempérière, 2001). Piano key weirs (PKWs) include inlet and outlet keys as well as an inclined surface. They are also a part of the crest, extending beyond the weir base and, thus, creating bulges upstream and downstream (Eslinger and Crookston, 2020). Due to their high compatibility with the site and their economic and hydraulic performance, PKWs have been used in more than 34 structures in North America, Europe, Asia, and Australia on gravity dams (e.g., Malarce Dam, France), embankment dams (e.g. Lake Peachtree Dam, GA, USA), and river structures (e.g. Dakmi 2 and Van Phong Barrage, Vietnam).
There is a wide range of studies addressing the discharge coefficient of PKWs, but the energy dissipation of rectangular, and trapezoidal PKWs has not been compared so far. Hence, it seems necessary to evaluate the energy dissipation of these three plans.

Tests were conducted in the hydraulic lab of Tarbiat Modares University, Tehran to assess the energy dissipation and flow properties downstream of rectangular and trapezoidal PKWs. Tests were performed using a 10×0.75×10 m flume (Fig. 1). The water was provided by an underground sump. PK weir was installed and sealed at 4 m away from the flume inlet, so the minimum flow turbulence was achieved. The discharge flow was adjusted by changing the speed of the pumps using a control panel. The upstream and downstream flow depths were measured at 4P (Crookston, 2010) and 10P (Eslinger and Crookston, 2010) away from the weir upstream and downstream, respectively, using digital point gage with an accuracy of ±0.1 mm. The weir specifications are listed in Table 1. Experiments were conducted for various discharges and approach flow depths.

The flow field upstream of PKWs was almost uniform and no turbulence was observed on the water surface. The flow deviated near the PKW with streamlines along inlet and outlet keys and over the weir walls. Flow deviation led to an increased unit discharge in the outlet keys. Meanwhile, the local velocity was increased, leading to a positive acceleration. The observations showed that this was accompanied by water level decline and increased downstream turbulence. The upper front of the PKW and the upstream overhang length contributed to energy dissipation.
The flow jet passing over the crest was accompanied by the interaction of three colliding jets. The interaction was the result of the collision between the flow nappies from lateral crests and the flow in the outlet keys (Fig. 4). The resulting interactions led to significant turbulence, and expansion of flow at the downstream. As the head increased, the outlet key discharge (in the space between two side walls of the PKW outlet key) were increased, and energy dissipation was limited.
Fig. 5 shows variations of the energy dissipation for rectangular and trapezoidal PKWs. The relative energy dissipation by the trapezoidal PKW was more than that of rectangular PKW, by average of abbot 3%. Fig. 6 shows the residual energy of the PKW versus discharge for rectangular and trapezoidal PKWs. It is clear that as the discharge increased, E1/E2 increased. Furthermore, the ascending rate of E1/E2 was higher for lower discharges. This is due to the local submersion upstream of the weir at high discharge.

Energy dissipation of trapezoidal PKWs are higher than rectangular PKWs.
The average discharge coefficient for trapezoidal PKWs is higher than rectangular PKW.
The flow characteristics is different for rectangular and trapezoidal PKWs. For Ht/P≤0.15, no aeration is occurred. For 0.15<Ht/P<0.45, a week hydraulic jump is formed at the end of the weir outlet keys. New equation was obtained for estimation of energy dissipation.