Numerical investigation of velocity distribution and flow characteristics over modified steps of stepped spillway

Introduction: Stepped spillways are a common structure for energy dissipation by creating frictional resistance to flow through the steps. Based on the studies and depending on flow conditions, the flow over a stepped spillway is usually categorized into three regimes: nappe, transition, and skimming. The stepped spillway is often designed for skimming flows. There were different studies investigating various aspects of stepped spillways, but what is important in this type of spillway is increasing the effectiveness of steps in the rate of energy dissipation. This can be done by a new type of step structure (i.e., inclination angles on steps or using a sill on the edge of a step and cases like that) or geometric alteration and change of steps called labyrinth stepped spillways. Therefore, it is scientifically beneficial to modify the shape of the step of the stepped spillway to increase its collision and roll to achieve energy dissipation. The present study deals with the design of step modification by creating cubic elements on the steps in different arrangements and different hydraulic conditions. This has been considered to improve the performance of stepped spillways by increasing the energy dissipation. For this purpose, using FLOW-3D software, the influence of geometric appendance elements on the steps on the velocity distribution, pressure, the turbulent kinetic energy (TKE), and finally the flow resistance and the energy dissipation on modified spillways was investigated and compared with the flat stepped spillway.
Methodology: The physical model for verifying the numerical results was carried out in a rectangular flume with a length of 12 m, a width of 1.2 m, and a height of 0.8 m. The experiments were conducted on a stepped spillway with a slope of 26.60° and consisted of 10 steps with step length (l) and height (h) of 0.06 and 0.12 m, respectively. Stepped spillway models in numerical study include flat models and models with cubic elements placed on the steps in four arrangements of two side, zigzag, center, and hybrid AE elements and two heights of elements h/2 and h/4 (h step height). The commercially available CFD program FLOW-3D was used for the numerical simulations. The RNG k-ε turbulence model was employed for the turbulence calculations. To obtain mesh-independent results, three different mesh sizes were used, and the grid convergence index (GCI) methodology was employed to select the appropriate mesh. As a result, the mesh consisting of a containing block with a cell size of 1.3 cm and a nested block of 0.95 cm was selected. In the fluid domain, the boundary conditions were set according to the experimental conditions. In the upstream of the domain, a discharge flow rate (Q) definition was set. The downstream section was treated as an outflow (O) boundary condition. The bottom and the sides behave as rigid walls (W). For the upper boundary, the atmospheric pressure boundary, and at the inner boundary conditions, symmetry (S) was used.
Results and Discussion: The results showed that the appendance elements on the steps cause some fluctuations on the flow surface and increase the intensity of the current collision by deviating the flow from its parallel path. The result is reduced velocity by about 10%, an increase of 54% in TKE, and an increase of 6.42% in energy dissipation on modified models compared to the flat stepped model. There was no negative pressure on the horizontal plane of the steps, and the maximum pressure occurred in the middle of the steps and inclined to the end of the steps. The appendance elements reduce the negative pressure areas on the vertical surface of the steps and reduce the risk of cavitation. The hybrid element model performs best in other arrangements, and reducing the height of the elements improves their behavior.
Conclusion: According to the obtained results, it can be concluded that the appendance elements on the steps improved the hydraulic performance of stepped spillways by increasing the roughness of the steps, increasing energy dissipation, reducing the flow velocity over the spillway and reducing the risk of cavitation by reducing the negative pressure in the vertical plane of the steps. The use of cube-shaped elements on the steps and in the hybrid arrangement is suggested.