Influence of Inlet- and Outlet-Key Configurations on the Discharge Coefficient and Crest Discharge Distribution of Type-A Piano Key Weirs

Abstract

Piano key weirs (PKWs) increase the effective crest length and provide high discharge capacity within limited spillway widths; however, their hydraulic efficiency depends on key geometry. Addressing the limited understanding of key-curvature effects, this study systematically investigates the influence of inlet- and outlet-key curvature on the discharge coefficient (Cd) and crest-wise discharge distribution of type-A PKWs. Nine configurations are examined experimentally in a flume at the Hydraulics Research Institute, Egypt. These include a reference model with linear inlet and outlet keys and modified geometries incorporating C- and S-shaped keys in both normal and inverted forms. Experiments are conducted under free-flow conditions for total-head ratios HT/P up to 0.23, where HT is the total upstream head above the crest and P is the PKW height. A three-dimensional numerical model using FLOW-3D HYDRO is validated against these experimental data and subsequently extended to HT/P ≈ 0.50–0.60. All reported results and conclusions are based on the numerical simulations over the full investigated range. Results show that Cd increases to a peak near HT/P ≈ 0.08 and then decreases gradually for all configurations. Both inlet- and outlet-key curvature influence hydraulic performance by modifying flow guidance and redistribution along the crest. However, only the inverted C-shaped inlet configuration (M2) improves efficiency, increasing Cd by about 5.46% on average over the investigated head range and enhancing the total discharge by approximately 4.36% at HT/P ≈ 0.12 relative to the reference case. Discharge-distribution analysis indicates that this improvement results from inlet feeding and efficient flow conveyance along the sidewall crest. A predictive relation is developed for the optimal configuration to support hydraulic design.