Numerical investigation of flow characteristics and energy dissipation over piano key and trapezoidal labyrinth weirs under free-flow conditions

Piano Key (PK) and trapezoidal labyrinth (TL) weirs are nonlinear control structures suitable for narrow channels with high discharge by expanding the crest length of the overflow. In open channels, high discharge flows can increase flow velocity and erode the downstream riverbed. This study investigates the discharge performance, flow characteristics, and energy dissipation over PK and TL weirs under free-flow conditions using the FLOW-3D software. The FLOW-3D model was validated by comparing the experimental data of two heights of type-A PK weirs with the numerical simulation. A good agreement was found between experimental and numerical results, with Mean-Absolute-Percentage-Error ( MAPE ) values for two PK weirs of 2.24% and 5.78%, which indicate an acceptable precision to simulate the flow over weirs. After this step, two scenarios were presented. In the first scenario, the geometric properties of the two PK weir heights were modified to achieve the optimum hydraulic and best economic designs based on previous recommended geometric parameters, then compared to the same-height TL and linear weirs. In the second scenario, the best economic PK weir was compared to TL weirs with three sidewall angles of 12, 20, and 30°. Overall, sixty-six and twelve simulations were run for the first and second scenarios, respectively. Results demonstrated that linear weirs had the lowest discharge and energy performance compared to PK and TL weirs. In terms of discharge performance, PK weirs are preferred over TL weirs at lower headwater ratios ( H/P ≤ 0.20), while TL weirs with smaller angles ( α ≤ 12°) are recommended at higher ratios ( H : upstream head above weir crest, P : weir height). Energy dissipation rates of TL weirs increase as the sidewall angle increases; thus, TL weirs with larger angles ( α > 12°) are recommended over PK weirs. Increasing the weir height by 1.66 times enhances the energy dissipation rate by 24% for all weir types. Finally, PK and TL weirs gain a new performance as energy dissipators since they dissipate energy close to the maximum limit.