Determining the optimal design characteristics of trapezoidal piano key weirs for improved water discharge
As extreme flood events become more frequent and severe, improving the discharge performance of weirs has emerged as a key hydraulic engineering objective. This study evaluates the influence of geometric design parameters and flow characteristics on the discharge capacity of trapezoidal piano key weirs (TPKWs). To analyze major design effects, nine models were simulated by varying width ratios (1.25, 1.75, and 2.25) and sidewall angles (+ 2°, + 4°, and − 2°). The numerical model was validated using laboratory experiments, achieving an RMSE of 0.0137 and a MAPE of 3.18%, confirming its predictive reliability. As auxiliary parameters, square (Sq) and newly proposed triangular (Tri) parapets were applied to the two highest-performing base geometries to assess additional performance enhancement. Computational fluid dynamics (CFD) simulations were used to analyze three-dimensional flow structures, including streamline redistribution, velocity reduction, and nappe interference. The results showed that modifying the width ratio and sidewall angle increased discharge efficiency by up to approximately 20%. Furthermore, the Tri-parapet configuration yielded up to 72.3% improvement in discharge efficiency relative to the reference geometry at the lowest head ratio (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${H}_{t}/P$$\end{document} = 0.07), with the gain decreasing to 4.9% at the highest head (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${H}_{t}/P$$\end{document} = 0.73). These findings provide a physically based explanation of how geometric parameters control crest utilization and overflow behavior, and they offer practical insights for optimizing PKW designs for dam rehabilitation and flood-routing enhancement.