Hydraulic Performance of Variable-Tread Stepped Spillways: Froude Number Reduction and Energy Redistribution at the Stilling-Basin Inlet

Yataco Pastor L.A.; Castillo Alvarez Y.; Jiménez Borges R.; Aviles M.; Rodríguez-Abreo O.; Iturralde Carrera L.A.; González-Gutiérrez C.A.; Rodríguez-Reséndiz J. · Hydrology (2026) · DOI: 10.3390/hydrology13090250

Resumen

Transverse modification of step geometry has been repeatedly proposed as a means of increasing energy dissipation in stepped spillways, with numerically reported gains ranging from 5.6% to 34.7% for labyrinth configurations, in unresolved contradiction with air–water experimental evidence that detects no measurable difference. The objective of this study is threefold: to verify whether the transverse alternation of the tread length increases the net energy dissipation of the coupled chute–stilling basin system, to quantify its effect on the kinematic and energetic state of the flow delivered to the terminal energy dissipator, and to delimit its domain of applicability. That premise is subjected to verification through 38 three-dimensional Reynolds-averaged Navier–Stokes (RANS) simulations (k– (Formula presented.) shear-stress transport (SST) closure, homogeneous volume-of-fluid (VOF) formulation) performed in ANSYS CFX 2025 R2, comparing a three-section stepped spillway with a uniform rectilinear footprint against a configuration with transverse L– (Formula presented.) alternation, under 19 geometric–hydraulic combinations spanning the nappe, transition, and skimming flow regimes ((Formula presented.)). The model was verified through a mesh-convergence analysis of the uniform configuration (grid convergence index, GCI (Formula presented.), on the approach depth) and validated against a physical scale model (0.38% discrepancy, exceeding the propagated experimental uncertainty); a three-level mesh study of the variable-tread configuration shows that its toe-flow response develops as the transverse tread strips become resolved and is not yet mesh-independent at the finest level, which is stated as a limitation of the quantitative results. Because the homogeneous multiphase formulation does not include an air-entrainment submodel, all results correspond to the modeled non-aerated flow conditions. The results do not support the hypothesis of a net dissipative gain: the global energy balance of the two topologies is equivalent within the numerical resolution of the study (bias (Formula presented.) pp; root-mean-square error (RMSE) 0.26 pp), of the order of the discretization uncertainty of the study itself. The actual effect is a redistribution of the dissipative partition that conditions the flow delivered to the energy dissipator: the toe Froude number is reduced in all 19 paired cases (16.5–88.4%; mean: 34.1%). In nine scenarios the hydraulic jump is conditioned without being suppressed ((Formula presented.) from 3.95–4.57 to 1.19–3.71), the energy delivered to the stilling basin drops by 18.3–57.9%, and the residual energy decreases by up to 14.98%; under subcritical toe flow, the same thickening increases the delivered energy by 12.3–19.4% and penalizes the residual energy by up to 18.08%; in two intermediate-discharge scenarios the jump is suppressed, yielding no benefit whatsoever. The transition is expressed through a critical threshold, nominally (Formula presented.) within the observed separation interval (Formula presented.) : the thirteen resolvable scenarios preserve the predicted sign separation without exception. The variable footprint is not a dissipation intensifier but a chute–dissipator coupling element, applicable only to high relative discharges.

Instituciones: Universidad Nacional Mayor de San Marcos; Universidad Tecnológica del Perú