Performance and Design of a Stepped Spillway Aerator

Stepped spillways are frequently limited to specific discharges under around 30 m2/s due to concerns about potential cavitation damages. A small air concentration can prevent such damages and the design of bottom aerators is well established for smooth chutes. The purpose of this study is to systematically investigate the performance of a deflector aerator at the beginning of stepped chutes. Six parameters (chute angle, step height, approach flow depth, approach flow Froude number, deflector angle and deflector height) are varied in a physical model. The spatial air concentration distribution downstream of the aerator, the cavity sub-pressure, water discharge and air discharges are measured. The results describe the commonly used air entrainment coefficient, the jet length, as well as the average and bottom air concentration development to design an aerator. The lowest bottom air concentration measured in all tests is higher than the air concentration recommended in literature to protect against cavitation damages. And, unlike smooth chutes, there appears to be no significant air detrainment downstream of the jet impact. One deflector aerator seems therefore sufficient to provide protection of a stepped spillway.

Numerical Analysis of Pressure Profiles and Energy Dissipation across Stepped Spillways Having Curved Risers

In this study, curved risers stepped spillways models based on the increasing angle of suspension were tested to check for improvement in energy dissipation and pressure distributions. Four fourteen-steps stepped spillway models with a slope 1:0.84 were selected, using Froude’s number non-dimensional similarity. The risers of steps were made curved, based on three angles of suspensions, i.e., 30°, 60°, and 90°. The simulations were performed by FLOW 3D software and by the turbulence model Renormalization Group (RNG) for discharges between 0.020 and 0.068 m3/s followed by the model calibration. The 3D Reynolds-averaged Navier–Stokes equations were solved, which included sub-grid models for air entrainment, density evaluation, and drift–flux, to capture free-surface flow over the stepped spillway. It was estimated that curving the risers increases the energy dissipation up to three percent for lower flow rates, whereas it has no significant impact on energy dissipation for higher flow rates. It was found that in simply stepped spillway lower steps dissipate more energy as compared to curved risers stepped where energy dissipation is shifted to higher steps. On the other hand, curved risers stepped spillways showed lower values of negative pressures as compared to the simply stepped spillway. It was seen that a higher energy dissipating step as experienced more negative pressures as compared to the lower energy dissipating step.

Analysis of Energy Dissipation of Interval-Pooled Stepped Spillways

The water flow characteristics over an interval-pooled stepped spillway are investigated by combining the renormalization group (RNG) k-ε turbulence model with the volume of fluid (VOF) interface capture technique in the present study. The results show that the energy dissipation performance of the interval-pooled stepped spillway was generally better than that of the pooled, stepped spillways and the traditional flat-panel stepped spillway. The omega vortex intensity identification method is introduced to evaluate the energy dissipation. Due to the formation of “pseudo-weir”, the energy dissipation did not increase with the growth of the pool’s height. In addition, the average vortex intensity can characterize the dissipation rate to some extent.

Energy dissipation performance of the trapezoidal stepped spillway

Stepped spillways are a more effective type of spillway in energy dissipation than conventional chute channels. Therefore, the dimensions of the energy breaker at the downstream of the stepped spillways are lower. It is an alternative especially for the downstream pool that cannot be built in sufficient length due to the terrain conditions. In this study, the energy dissipation performance of the trapezoidal stepped spillways was investigated numerically by using Flow3D software. Four different models and three different discharges were utilized for this aim. According to the results, the trapezoidal stepped spillway is more effective up to 30% than classical stepped spillways in energy dissipation. The depth of the trapezoidal step and the bottom base length of the trapezoid significantly affected the energy dissipation rate for the trapezoidal stepped spillway.

Genetic algorithms for optimizing stepped spillways to maximize energy dissipation

Stepped spillways are important water-management structures that are used for energy dissipation. Use of these spillways has increased in recent decades, they can reduce construction time and they are effective for reducing the flow's downstream kinetic energy. In this study, the width and height of the steps as well as the slope and height of the overflow spillway were considered as variables. Due to the large number of variables, non-linearity of the objective function and constraints, and the lack of an explicit relationship between decision variables, a genetic algorithm (GA) was used. A stepped spillway with optimal dimensions was proposed as a replacement of the smooth spillway of Sarogh Dam located in West Azerbaijan province, Iran. The proposed steps increase energy dissipation; for constant discharge and varying slopes, the changes in the optimal height of the steps were insignificant. Sensitivity analysis using the objective function showed that the relative energy dissipation for a constant discharge is independent of the optimal height of the steps and decreases with increasing spillway slope. In addition, for fixed slopes, increasing the flow rate leads to a decrease in relative energy dissipation and an increase in the optimal height of the steps.

Predicting the Flow Velocity at the Toe of a Labyrinth Stepped Spillway

The velocity at the toe of a spillway is a major variable when designing a stilling basin. Reducing this velocity leads to reduce the size of the basin as well as the required appurtenances which needs for dissipating the surplus kinetic energy of the flow. If the spillway chute is able to dissipate more kinetic energy, then the resulting flow velocity at the toe of spillway will be reduced. Typically, stepped spillway is able to dissipate more kinetic energy than that of a smooth surface. In the present study, the typical uniform shape of the steps has been modified to a labyrinth shape. It is postulated that a labyrinth shape can increase the dissipation of kinetic energy through increasing the overlap between the forests of nappe will circulating the flow that in turns leading to further turbulence. This action can reduce the jet velocities near the surfaces, thus minimizing cavitation. At the same time the increasing of circulation regions will maximize the opportunity for air entrainment which also helps to dissipate more kinetic energy. The undertaken physical models were consisted of three labyrinth stepped spillways with magnification ratios (width of labyrinth to width of conventional step) WL/W are 1.1, 1.2, and 1.3 as well as testing a conventional stepped spillway (WL/W=1). It is concluded that the spillway chute coefficient is directly proportional to the labyrinth ratio and its value decreases as this ratio increases.

Multi-objective optimization of stepped spillway and stilling basin dimensions

In the present paper, an optimization procedure is proposed for stepped spillway design dimensions, which leads to maximum energy dissipation rate and minimum construction cost considering independently the chute cost and stilling basin cost. Three independent objective functions are thus simultaneously satisfied. The procedure involves four main tools: The multi-objective particle swarm optimization method (MOPSO) to find Pareto solutions in one run, the K-means clustering algorithm to reduce the size of the obtained non-dominated solutions, the pseudo-weight vector approach (PWV) to facilitate the decision making and to select some adequate solutions, and finally, CFD simulations to analyze the retained optimal solutions. The suitability of the proposed procedure is tested through an example of application. As results, a set of twenty solutions with different satisfaction levels are found and compared to existing solutions. A multi-objective optimization problem may have many different solutions, the originality of the present work lies in the proposed procedure which explores several possible ones and reduces their number to give help for the decision making. Furthermore, an approximate expression of spillway total cost is also derived as a function of flow energy dissipation rate.