Labyrinth weirs represent a critical class of hydraulic structures engineered to manage upstream water levels, regulate discharge, and enhance flow capacity in open-channel systems, including irrigation canals, natural rivers, and spillways of dam reservoirs. These folded-crest weirs achieve superior hydraulic performance compared to linear weirs of equivalent crest length by increasing the effective wetted perimeter within a compact footprint, thereby promoting energy dissipation and reducing afflux under high-flow conditions.
A comprehensive numerical investigation was conducted using FLOW-3D, a commercial computational fluid dynamics (CFD) platform renowned for its volume-of-fluid (VOF) free-surface tracking and turbulence modeling capabilities. The study focused on both symmetric and asymmetric configurations of rectangular labyrinth weirs, enabling a direct comparison of geometric influences on hydraulic efficiency. Dimensional analysis, grounded in the Buckingham π theorem, identified the discharge coefficient (C_d) as the primary dependent variable, expressed as a function of three dimensionless groups: (1) the total head-to-weir height ratio (H_t/P), which encapsulates the relative submergence and driving hydraulic gradient; (2) the left-to-right cycle width ratio (W_L/W_R), which quantifies planform asymmetry and its impact on lateral flow contraction; and (3) the longitudinal weir ratio (B/W_avg), defined as the length of the sidewall crest segment divided by the mean cycle width, reflecting the degree of streamwise elongation and interference between adjacent cycles.
Physical validation was performed in a rectangular glass-walled flume measuring 8 m in length, 0.6 m in width, and 0.6 m in depth, ensuring fully developed turbulent flow and negligible sidewall effects for the tested geometries. Discharge was measured using calibrated sharp-crested weirs downstream, while piezometric heads were recorded with precision point gauges at multiple stations along the weir crest. The numerical domain replicated the experimental setup with high-fidelity unstructured meshes, incorporating renormalization group (RNG) k-ε turbulence closure and second-order discretization schemes to resolve complex three-dimensional separation zones, nappes, and air entrainment phenomena.
Comparative analysis revealed strong concordance between numerical predictions and laboratory measurements across the operational range of H_t/P from 0.15 to 0.55. For symmetric labyrinth weirs, experimentally derived C_d values exceeded CFD results by approximately 27%, a discrepancy attributable to minor scale effects, surface tension influences in the physical model, and slight under-prediction of nappe aeration in the numerical free-surface algorithm. Nonetheless, both approaches confirmed the characteristic non-linear increase in C_d with decreasing H_t/P, consistent with enhanced submergence and reduced crest interference at low heads.
A pivotal finding emerged from the asymmetric configurations: FLOW-3D simulations indicated that C_d for asymmetric labyrinth weirs surpassed that of symmetric counterparts by roughly 16% under identical approach conditions and cycle counts. This augmentation stems from the deliberate imbalance in cycle widths, which induces differential lateral contractions, promotes helical flow patterns, and mitigates vortex shedding at apex regions, thereby sustaining higher effective crest lengths and reducing form drag. Such geometric optimization underscores the potential for tailored asymmetry in field applications where space constraints or site-specific hydraulics preclude conventional symmetric layouts.
In summary, the integrated physical–numerical framework validates FLOW-3D as a robust tool for labyrinth weir design, while highlighting the superior discharge efficiency of asymmetric geometries. These insights inform hydraulic engineering practice by enabling precise prediction of stage–discharge relationships, minimizing upstream flooding risks, and optimizing spillway capacity without excessive structural footprints. Future research may extend the parameter space to oblique weir alignments, varying apex angles, and sediment-laden flows to further refine design guidelines.