Introduction
Spillways and gates serve as flow measurement and water level control structures in both natural and artificial irrigation channels. Ogee spillways, in particular, not only regulate reservoir levels but are also widely used for power generation, irrigation, and flood control. A ogee spillway allows excess reservoir water to flow downstream. However, due to high-velocity flow at the downstream of these structures, hydraulic jumps commonly occur, characterized by sudden transitions from supercritical to subcritical flow, turbulent air entrainment, and energy dissipation.
Combined spillway-gate or spillway-culvert systems are designed to enhance hydraulic efficiency and sediment flushing by separating the ogee from the channel bed via gates or culverts. These configurations typically pass higher discharge than simple weirs due to dual flow paths—over the spillway and under the gate. The interaction of these flows significantly increases downstream energy dissipation, reducing scouring risks.
Numerous studies have examined the hydraulic performance of various geometries, including sharp-ogeeed, inclined, rectangular, and cylindrical weirs. Research highlights how geometric parameters like gate opening, spillway height, and flow head affect discharge and flow characteristics. Modern research increasingly relies on numerical and experimental methods to investigate hydraulic jumps and two-phase (air-water) flow behavior in such systems, ensuring safe and efficient hydraulic structure designs.
Methodology
A three-dimensional Computational Fluid Dynamics (CFD) model was developed using FLOW-3D software to simulate flow behavior in a composite hydraulic structure consisting of a ogee ogee spillway integrated with a culvert under free-flow conditions. The FLOW-3D code solves Reynolds-Averaged Navier-Stokes (RANS) equations using the finite volume method, incorporating VOF and FAVOR techniques for tracking free surfaces and representing solid boundaries, respectively. Turbulence was modeled using four approaches: standard k-ε, RNG, LES, and k-ω, with calibration based on experimental data from Toozandehjani & Kashefipour (2012, 2013). The physical model consisted of a 12-meter-long rectangular flume. For numerical efficiency, the model domain was shortened to 5 meters.
Experimental results identified a 45° outlet angle as optimal for energy dissipation. Numerical simulations evaluated the performance of different turbulence models, showing that k-ω achieved the best agreement with experimental data, with R² = 0.97 and RMSE = 0.0112. Mesh independence analysis confirmed that a cell size of 0.0007 m provided stable velocity profiles. Simulations also investigated the influence of culvert elevation within the spillway body across four configurations. The model reached steady-state flow after 72 seconds, validating its temporal convergence.
Finally, variations in culvert positioning significantly affected flow patterns and energy dissipation. This study highlights the effectiveness of FLOW-3D in simulating complex free-surface flows and optimizing hydraulic structure designs through combined experimental and numerical analysis.
Results and Discussion
This study numerically investigates flow behavior in a ogee overflow spillway equipped with culverts under free flow conditions, focusing on velocity patterns, Froude number variations, and total energy loss.
Velocity Distribution:

Two-dimensional velocity vectors and vertical velocity profiles before and after the hydraulic jump were analyzed for minimum and maximum discharges. Vortex formation and air–water mixing were observed in the hydraulic jump region, particularly when culverts were present. Two primary vortices were identified: one near the culvert outlet close to the bed and another above the jet stream. Unlike the classical hydraulic jump, the velocity profiles with culverts showed the maximum velocity occurring above the bed, indicating altered jet behavior due to culvert interactions. When culverts were placed at 50% and 75% of the spillway height, the surface jet velocity was higher than the culvert jet, causing more concentrated downstream flow. Dual-culvert configurations reduced peak velocity by 40% and shifted its location 14% higher compared to the spillway without culverts.
Froude Number Analysis:

The longitudinal profile of the Froude number showed that culvert placement significantly influenced flow regimes. For low discharge, the flow remained subcritical longer when culverts were elevated (e.g., at 75% height). Dual-culvert setups caused submerged hydraulic jumps near the toe of the spillway. At high discharges, subcritical flow extended further downstream across all culvert placements. The greatest Froude number reduction occurred when culverts were placed at the base or used in pairs, reducing subcritical zones by up to 25% of the spillway slope.
Energy Loss:

Energy loss contours indicated that the presence of culverts shifted energy dissipation toward the spillway body, weakening the hydraulic jump and reducing its length. At low discharges, energy loss was more pronounced due to the dominant culvert flow. As discharge increased, energy losses decreased due to reduced upstream-downstream water level differences. Culvert-spillway systems also reduced the secondary depth of hydraulic jumps, further enhancing energy dissipation efficiency.
Conclusion
The hydrodynamics of flow downstream of ogee spillway–culvert structures were investigated numerically using a series of laboratory-based studies under various culvert placement scenarios. The hydraulic assessment of the proposed spillway–culvert configuration under free flow conditions indicated that the structure possesses a higher discharge capacity compared to a conventional ogee spillway. Variations in turbulent kinetic energy at different flow rates revealed that the location of maximum energy dissipation shifts toward the toe of the spillway as the culvert is positioned closer to it. This shift in energy dissipation results in a reduced energy loss rate, thereby increasing the potential for erosion. It was also found that, at peak discharges, the formation of dual vortices in the dual-culvert configuration enhances energy dissipation, making the proposed structure more effective and potentially suitable as a fish passage route.