Martí Sánchez-Juny

Characterization of the nonaerated flow region in a stepped spillway by PIV

The development of the roller-compacted concrete (RCC) as a technique of constructing dams and the stepped surface that results from the construction procedure opened a renewed interest in stepped spillways. Previous research has focused on studying the air-water flow down the stepped chute with the objective of obtaining better design guidelines. The nonaerated flow region enlarges as the flow rate increases, and there is a lack of knowledge on the hydraulic performance of stepped spillways at high velocities that undermines its use in fear of cavitation damage. In the present, study the developing flow region in a stepped channel with a slope 1v:0.8h is characterized using a particle image velocimetry technique. An expression for the growth of the boundary layer thickness is proposed based on the streamwise distance from the channel crest and the roughness height. The local flow resistance coefficient is calculated by application of the von Karman integral momentum equation. The shear strain, vorticity, and swirling strength maps obtained from the mean velocity gradient tensor are presented. Also, the fluctuating velocity field is assessed. The turbulent kinetic energy map indicates the region near the pseudobottom (imaginary line joining two adjacent step edges) as the most active in terms of Reynolds stresses. The turbulence was found to be very intense with maximum levels of turbulence intensity from 0.40 to 0.65 measured near the pseudobottom. Finally, the quadrant analysis of the velocity fluctuations suggests the presence of strong outflows of fluid from the cavities as well as inflows into the cavities. It is conjectured that the mass transfer/exchange between cavities and main stream, play an important role in the high levels of turbulent energy observed.

Developing flow region and pressure fluctuations on steeply sloping stepped spillways.

The hydrodynamic pressure field is important for the design and safety of steeply sloping stepped spillways, which are typically designed for considerably lower maximum specific discharges than smooth spillways. The hydraulic performance of stepped spillways at high velocities may compromise its use due to major concern with safety against cavitation damage. Hydraulic model investigations were conducted in different large-size stepped chutes to characterize the nonaerated flow region which is potentially prone to cavitation damage and the pressure field acting on the step faces. The clear water depths and energy dissipation in the developing flow region are described in terms of integral measures of the turbulent boundary layer. Expressions for the location of and the flow depth at the inception point of air entrainment are derived. Pressure distributions on the horizontal and vertical faces of the step along the spillway are presented. Measurements indicated a different behavior of the pressure field in the aerated and nonaerated flow region. The mean and fluctuating pressure coefficients along the spillway are approximated by a regression function. The vertical face near the outer step edge close to the inception point of air entrainment is identified as a critical region for predicting cavitation inception in flow over stepped spillways. From the analysis of the pressure fluctuations in that region a maximum velocity of 15 m/s is proposed as a criterion to avoid extreme negative pressures in typical prototype steeply sloping stepped spillways, eventually leading to the occurrence of cavitation in the nonaerated flow.

Analysis of pressures on a stepped spillway

The pressure profiles on the horizontal and vertical step faces of a stepped spillway in the fully developed skimming flow region were measured. These observations allow to provide generalized equations that enable designers to analyze the amount and the location of negative pressures along the steps. The step locations subjected to negative pressure are also discussed including an analysis of the duration of the negative pressures. On the horizontal step faces, negative pressure were only observed on their upstream half for dimensionless discharges larger than dc/h = 1.3. On the vertical step faces, only the region close to the adjacent horizontal face was not subjected to negative pressure

Source term treatment of SWEs using the surface gradient upwind method

The Authors’ works, who have designed well-balanced 1D schemes for the Saint-Venant equations on irregular geometries, are of interest to develop efficient numerical methods. In recent years, most efforts have focused on improving the performance of 2D models, so that 1D schemes were forgotten to a certain degree, as evidenced by the large number of references of this discussion dealing with 2D models. However, 1D schemes, either by themselves or in combination with 2D schemes, still have advantages relative to lower computational cost and reduced information need. The Discussers would like to highlight two considerations: the first being related to the formulation, whereas the second to the verification.