Study of ﬂ ow over piano key weir of different plan shapes with free and partially submerged outlet conditions

Piano key weirs are being increasingly used for better ﬂ ood passage downstream, both as a new structure or on top of hydraulic structures like a dam, to increase their discharging capacity as well as reservoir storage. Much research has been done on rectangular plan-form, while other plan-forms warrant attention. The present study focuses on two different plan geometries of PKW, i.e., rectangular (RPKW) and trapezoidal with angle α equal to 9 degrees (TPKW9) for their head-discharge relation in a wide channel of 0.984 m width under free- ﬂ ow condition. Since the role of CFD is increasingly becoming prominent in present times, a numerical study using ANSYS-FLUENT was also carried out to ascertain its relevance in predicting ﬂ ows around complex structures like PKW. Further, the tailgate was closed to render the PKW ’ s outlet from partial to fully submerged conditions. The effect of these submerged outlets was studied for any changes in the discharging capacity of the PKW. The study shows RPKW to be more hydraulically ef ﬁ cient than TPKW9 for the model geometry. Further, the study ﬁ nds that under partial to full submergence of PKW outlets, both PKW units ’ discharging capability remains unchanged.

Moreover, augmenting the discharges of already constructed gates and spillways also has to be investigated to extend the life and reduce the risk factor of overtopping such hydraulic structures. A weir's self-cleaning ability is also an essential factor to be considered while evaluating its life.
Studies to achieve all such favorable outcomes have been carried out in the past, leading to different weirs' evolution.
Experimental and numerical studies on labyrinth weirs continue to better understand the flow around these structures (Daneshfaraz et al. ; Ghaderi et al. a). Labyrinth weirs were also studied for their different plan geometries (Ghaderi et al. b) and their use as a side weir ( Researchers have tried to find and refine empirical equations that can be used to find the discharging capacity of PKW. Submergence of a weir is defined when the tailwater exceeds a specific limit above the weir's crest to increase the upstream head for a given discharge. Submergence

Experimental setup
The PK weir testing was conducted in a laboratory flume  and their average was taken as the crest head for further analysis and study purposes.
The entire setup rested upon an underground sump from where water was circulated in the channel. The experiment was run for free overflow and partial closure of gates to produce partial to complete submergence of outlets of PKW. The head was measured from the well installed near the linear weir, and the discharge was then read from the graph available in the Hydraulics lab of IIT (BHU), Varanasi. The discharge was varied from as low as 3 L/s to 40 L/s.

Numerical setup
Numerical simulations were performed on the ANSYS- The same meshing technique was adopted for the two geometries to ensure a standard reference. The top and outlet were specified as 'pressure outlets,' while the inlet was specified as 'velocity inlet.' Both sides of the channel were taken as 'symmetry,' while the bottom and PKW were treated as 'walls.' The numerical study was carried out for four discharges (6.67, 12, 20 and 29 L/s) in free-flow conditions.
Each of these discharges was selected as they mark a change in the nappe flow over the PKW.
The flow over PKW has been categorized as a transition from a clinging nappe to leaping and then to a springing

RESULTS AND CONCLUSIONS
Discharge-head relationship of PKW models Discharge (Q) vs. head at the crest (h) for RPKW has been plotted in Figure 2 A comparison of the RPKW and TPKW9 discharge-head relationship has been plotted in Figure 2(c). The results show RPKW to be more hydraulically efficient than TPKW9 for the same number of cycles and upstream-downstream distance (B) and the same channel width.
The efficiency of an RPKW and TPKW9 has also been compared with a linear weir. The comparison has been shown in Figure 3(a) and 3(b), for RPKW and TPKW9 respectively. PKWs, at higher heads, tend to behave like a linear weir. Hence, the increased discharge ratio 'r', which is the ratio of the discharge through PKW(Q PKW ) as compared to a linear weir with the same width W(Q W ), further illustrates the superiority of PKWs (Ribeiro et al. ).
Since our experimental model, the H/P ratio is much smaller; we can see the high hydraulic advantage of PKWs compared to the linear weir.
Observations under partial to full submergence of the outlet of PKW  The outlets of PKW were partially to fully submerged by closing the tailgates, and patterns emerging from this closure were studied. The study showed that partial to full outlet submergence had a negligible effect on the head measured at the crest of PKW within the experimental limits of the h/P ratio.

CONCLUSIONS
Head over the crest of PKW increased only after full submergence of outlets of PKW and downstream water level being higher than the height of PKW (P). The present study hopes to contribute to the literature on developing and refining discharge-head empirical equations for RPKW & TPKW.
Sediment passage in the upstream and scour formation in the downstream need to be studied for different plan geometries of PKW. Energy dissipation is another area that demands attention for these PKW geometries. A combination of experimental and numerical studies will lead to a better understanding of these grey areas in the future.