Numerical investigation of air-entrainment in skimming flow over stepped spillways

As a widely used flood energy dissipator, the stepped spillway can significantly dissipate the kinetic or hydraulic energy due to the air-entrainment in skimming flow over the steps. The free-surface aeration involves the sharp deformation of the free surface and the complex turbulent shear flows. In this study, the volume of fluid （VOF）, mixture, and Eulerian methods are utilized to simulate the air-entrainment by coupling with the Reynolds-averaged Navier-Stokes/large eddy simulation （RANS/LES） turbulence models. The free surface deformation, air volume fraction, pressure, and velocity are compared for the three different numerical methods. Only the Eulerian＋RANS method fails to capture the free-surface aeration. The air volume fraction predicted by the VOF＋LES method best matches the experimental measurement, while the mixture＋LES method predicts the inception point of the air entrainment more accurately.

Numerical Simulation of Flow over Stepped Spillways with Varying Step-Angle

In the present study,the flow over the stepped spillway was numerically investigated by using Flow3D model.The effect of step angle on different properties of Nappe flow regime such as the water surface profile,location of free-surface aeration inception,Froude number at the spillway’s toe,and pressure,flow velocity,air concentration and cavitation index were evaluated.The realizable k–εwas applied as the turbulence model,and Volume of Fluid(VOF)model was used to determine the free surface flow profiles of the spillway.The model was verified using experimental data.In order to investigate the different characteristics of Nappe flow regime,17 numerical runs was designed,in which,four step angles,four flow discharge were considered to investigate the flow characteristics over the stepped spillway.The results indicated that the numerical model is well suited with the experimental data over the stepped spillway(RMSE=0.147 and ARE=6.9%).In addition,with increasing the step angles,the aeration inception point is generally moved downstream.By increasing the step angles from zero to 10 degrees,the Froude number does not change significantly,however,at the angle of 15 degrees,the Froude number decreases by about 42 percent.

THREE-DIMENSIONAL TURBULENCE NUMERICAL SIMULATION OF A STEPPED SPILLWAY OVERFLOW

In this paper, the k ε turbulence model is used to simulate the three dimensional turbulence flow over the stepped spillway at the Yubeishan reservoir. In order to solve the curved free water surface and to handle the complex boundary conditions, the fractional Volume Of Fluid (VOF) model that is applicable to the solution of the stratified two phase flow is introduced along with k ε turbulence model and the unstructured grid is used for the discretization of the irregular simulation domain. By these methods, the turbulence flow field of the stepped spillway is simulated successfully. The location of the free surface along the spillway, the magnitude and distribution of the velocity, the pressure on the step surface, the turbulence kinetic energy and turbulence dissipation rate are obtained by simulation. The changes and distributions of these characteristics along the width of the spillway are also obtained. The energy dissipation ratio of the stepped spillway is calculated according to the upstream and downstream water depth and velocities

THREE-DIMENSIONAL TURBULENCE NUMERICAL SIMULATION OF A STEPPED SPILLWAY OVERFLOW

In this paper, the k-ε two-equation turbulence model was used to simulatethe three-dimensional turbulent flow of the stepped spillway at the Yubeishan reservoir. In order tosolve the curved free water surface and to handle the complex boundary conditions, the fractionalVolume Of Fluid (VOF) model that is applicable to the solution of the stratified two-phase flow wasintorduced to the k-ε turbulence model and the unstructured grid was used for the discretization ofthe irregular simulation domain. By these methods, the turbulent flow field of the stepped spillwaywas simulated successfully. The location of the free surface along the spillway, the magnitude anddistribution of the velocity, the pressure distribution on the step surface, the turbulence kineticenergy and turbulence dissipation rate were obtained by simulation. The changes and distributions ofthese characteristics along the width of the spillway were also obtained. The energy dissipationratio of the stepped spillway was calculated according to the upstream and downstream water depthand velocities.

INFLUENCING FACTORS FOR THE ENERGY DISSIPATION RATIO OF STEPPED SPILLWAYS

In order to search for the measure to increase the energy dissipation ratio of stepped spillways, some main influencing factors for the energy dissipation ratio of stepped spillways, such as unit discharge, dam slope, height of step and so on, were studied. The results show that the energy dissipation ratio decreases with the increase in the unit discharge and increases as the slope becomes gentle. The effects of step height on the energy dissipation ratio are closely related to unit discharge. If the unit discharge is smaller, the change of energy dissipation ratio with step height becomes greater. While, if the unit discharge is greater, the influence of step height on energy dissipation ratio is very little. According to the distributions of the turbulence kinetic energy and turbulence dissipation rate obtained by numerical simulation, the basic reason of the decrease of energy dissipation ratio with the increase in the unit discharge was discussed and some specific measures to increase the energy dissipation ratio were suggested.

Inception point of air entrainment over stepped spillways

The location of the inception point of the air entrainment directly affects the energy dissipation ratio, the cavitation damage control, and the training wall height designs for a stepped spillway and a stilling basin. In this paper, the boundary layer theory of plates is used to predict the location of the inception point of the air entrainment over the stepped spillways by assuming the steps on the spillways as a kind of roughness. An empirical formula is presented based on the physical model experiments, with the maximum error less than 1% except at one point where the error is 1.6%, as compared to the experimental data. Meanwhile, it is shown that the location of the inception point of the air entrainment for the stepped spillway is much nearer to the top of the spillway than that for a smooth spillways, which explains why the high ratio of the energy dissipation is provided for the stepped spillway.

Energy dissipation on stepped spillways and hydraulic challenges—Prototype and laboratory experiences

Stepped cascades, chutes and spillways have been in use for more than three millennia. With the introduction of new construction materials and techniques, the staircase chute design has regained some interest within the last forty years. The stepped invert increases significantly the energy dissipation occurring above the steep chute and reduces the size of the required downstream stilling structure. The application of stepped chutes further encompasses in-stream re-aeration and water treatment plant cascades, to enhance the air-water transfer of atmospheric gases and of volatile organic components. However, the engineering design of stepped spillways is not simple because of the hydrodynamic challenges, with several markedly different flow regimes, some complicated two-phase air-water fluid dynamics and massive rate of energy dissipation above the stepped chute. Simply, the technical challenges in the hydraulic design of stepped spillways are massive. This review paper examines the hydraulic characteristics of stepped chute flows and develops a reflection on nearly three decades of active hydraulic research, including recent field measurements during major flood events. The author aims to share his passion for the complicated hydraulic engineering, as well as some advice for engineering professionals and researchers.

The effects of step inclination and air injection on the water flow in a stepped spillway:A numerical study

In this work, we perform a numerical study of a water flow over a stepped spillway. This flow is described by the Reynolds averaged Navier-Stokes equation （RANS） associated with the turbulence k - model. These equations are solved using a commercial software based on the finite volume scheme and an unstructured mesh. The air-water flow was modeled using volume of fluid （VOF） and multiphasic methods. The characteristics of the profile, etc.. We analyze the effects on the flow structure of the flow were investigated including the total pressure, the velocity steps and countermarch inclination, the air injection through the countermarch into the water flow and the dynamics water discharges. Results show that the inclination of the countermarch relative to the vertical and the air injection into the water flow increase the total pressure in the neighbourhood of the steps.

3D NUMERICAL SIMULATION ON WATER AND AIR TWO-PHASE FLOWS OF THE STEPS AND FLARING GATE PIER

A new-style flood discharging dam, which consolidates the flaring gate pier and the stepped spillway for discharging the flood through the dam surface, had been applied in China. The theoretical study on it is in a beginning stage at present. The three-dimensional numerical simulation has not been reported. In this paper, the 3D numerical calculation on the two-phase flow of water and air with discharge per unit width 195m~ 3 /s· m is presented . The results indicate that there is negative pressure on the juncture of the spillway surface and the first step. There forms obvious longitudinal and transverse eddies on the steps and the velocity decreases obviously compared with the smooth spillway. The figures of the velocity distributions and the water-air two-phase flows are plotted. The results calculated on the pressure are in agreement with the experimental data. Based on the position of the negative pressure obtained from calculation, measurement points of pressure are arranged in physical model. The experimental results validate the existence of the negative pressure. Being an applied and trial study, the results obtained are of theoretical and practical significance.

Air entrainment of hydraulic jump aeration basin

In order to avoid the cavitation damage and the decrease of the energy dissipation of the stepped spillways with a large unit discharge, the air entrainments of the hydraulic jump aeration basin （HJAB） are theoretically and experimentally investigated for the hydraulic-jump-stepped spillway developed by the authors. It is shown that the submerged degree of the hydraulic jump and the air concentration in the measuring section are all functions of the dimensionless discharge, the length and the end sill height of the H JAB. The submerged degree odecreases with the increase of the dimensionless discharge or the dimensionless length of the H JAB, but increases with the increase of the dimensionless height of the end sill of the HJAB. The flow regimes near the critical hydraulic jump, namely, at or= 1.0, have the best effect of the air entrainment for the flow at the measuring section and then that of the stepped spillway.