Enhancing Energy Dissipation in Piano Key Weirs Using Curved Inlet and Outlet Keys

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Abstract
Piano key weirs (PKWs) provide high discharge efficiency within a limited footprint, but the influence of inlet- and outlet-key shapes on their energy dissipation has received limited attention. This study investigates the effects of curved inlet- and outlet-key geometries on PKW energy dissipation using 102 free-flow experimental runs. Nine configurations are tested: a linear reference (M1) and C-shaped, inverted C-shaped, S-shaped, and inverted S-shaped modifications applied separately to the inlet and outlet keys. A FLOW-3D HYDRO model is validated against the measurements, reproducing the total head with R2 = 0.997 and RMSE = 0.0013 m and the relative energy loss within ±15% (MAPE = 6.70%), and is then used to evaluate a combined configuration (M10) with C-shaped inlet and outlet keys. Experimental results show that the relative energy loss decreases with increasing total head ratio, from approximately 71–74% at low heads to 46–52% at higher heads. At HT/P = 0.18, the C-shaped inlet (M4) and outlet (M5) increase the relative energy loss by 12.80% and 8.27%, respectively, relative to M1. Compared with the numerically simulated M1, M10 is predicted to increase the relative energy loss by 5.86%, 9.64%, and 14.61% at HT/P = 0.08, 0.12, and 0.18, respectively. A logarithmic relationship fitted to 11 numerical runs is provided for estimating the relative energy loss of M10 within HT/P = 0.075–0.266. The results show that PKW energy dissipation depends strongly on curvature shape, orientation, and key location.

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