Influence of the Semicircular Cycle in a Labyrinth Weir on the Discharge Coefficient

The labyrinth weir is an effective hydraulic structure, offering high discharge efficiency and economic advantages, making it a suitable option for dam construction or rehabilitation projects. Owing to its complex geometry, significant research efforts have been dedicated to enhancing its hydraulic performance. Since the beginning of this century, Computational Fluid Dynamics (CFD) has emerged as a vital approach, complementing traditional methods in the design of hydraulic structures. This study employs CFD ANSYS FLUENT to examine the discharge coefficient of a semicircular labyrinth weir, featuring a cyclic arrangement and a half-round crest profile. The numerical models and simulations address two-phase flow (air and water) under incompressible and free-surface conditions. The CFD ANSYS FLUENT approach used is multiphase flow modeling using the Volume of Fluid method to track the free water surface. For turbulence effects, it is complemented with the standard k-ε model and the Semi-Implicit Method for Pressure Linked Equations algorithm for pressure–velocity coupling. In addition, for boundary conditions, the flow velocity was defined as the inlet to the channel and atmospheric pressure as the outlet, and the walls of the channel and weir are considered solid, stationary, and non-sliding walls. The model was validated with experimental data reported in the literature. The results indicate that the semicircular labyrinth weir achieves greater discharge capacity when the headwater ratio HT/P increases for HT/P ≤ 0.25. A regression analysis mathematical model was also developed, using the HT/P ratio, to predict the discharge coefficient for 0.05 ≤ HT/P ≤ 1. Relative to other geometrical configurations, the semicircular labyrinth weir demonstrated a discharge capacity that was up to 88% higher than that of the trapezoidal labyrinth weir. Both weir and cycle efficiency were assessed, and maximum weir efficiency was observed when HT/P ≤ 0.1, while cycle efficiency peaked at HT/P ≤ 0.25. The geometric configuration under analysis demonstrated greater economic efficiency by providing a reduced total length and enhanced discharge capacity relative to trapezoidal designs, especially when the sidewall angle α is considered as α ≤ 12°. The study concludes by presenting a design sequence detailing the required concrete volume for construction, which is subsequently compared to the specifications of a trapezoidal labyrinth weir.