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ABSTRACT:The development of the roller compacted concrete as a technique of constructing dams and the stepped surface that results from the construction procedure opened a renewal interest in stepped spillways.Previous research has focused in studying the air-water flow down the stepped chute with objective of obtaining better design guidelines. The non aerated 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's 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 pseudo-bottom (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 pseudo-bottom. 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.

En el presente artículo se presenta un conjunto de criterios para el diseño de aliviaderos escalonados con pendientes típicas de presas de hormigón compactado con rodillo. El texto se basa en Informa­ción recogida en la bibliografía e incorpora los resultados del trabajo de Investigación desarrollado en Amador (2005). Se aborda el diseño de la cresta, la selección del ancho del aliviadero y la geometría de los peldaños. Se proponen criterios para determinar el tipo de flujo existente sobre la estructura y, en el caso del flujo rasante, se presentan expresiones que permiten obtener las principales caracterís­ticas del flujo a lo largo de la rápida. Con ha.se en los resultados del análisis del campo de presiones se proponen un conjunto de ecuaciones para estimar las solicitaciones que el vertido ejerce sobre los peldaños a lo largo del aliviadero. Finalmente se hacen algunas consideraciones sobre los aspectos constructivos de los aliviaderos escalonados.

Numerical simulation of water flow over the stepped spillway is conducted using Mixture multiphase flow model. Different turbulence models are chosen to enclose the controlling equations. The turbulence models investigated are realizable k-ε model, SST k-ω model, v 2 -f model and LES model. The computational results by the four turbulence models are compared with experimental ones in the following aspects: mean velocity, the spanwise vorticity and the growth of the turbulent boundary layer thickness in the streamwise direction. It is found from the comparison that the realizable k-ε model, in which the rotation tensor is included, shows good performance for simulation of flows involving rotation, boundary layer and recirculation. The realizable k-ε model is the most efficient in simulating flow over stepped spillways. Further, the characteristics of water flow on the stepped spillway are studied in terms of the mean velocity profile normal to the pseudo-bottom and the pressure field on the steps based on the simulation results using realizable k-ε model. stepped spillway, turbulence model, numerical simulation, boundary layerAs an important energy dissipation structure, stepped spillways are widely used in recent years due to the development of roller-compacted concrete (RCC) technique. When the water skims over the steps, steady vortices appear in triangular zone formed by the step faces and the pseudo-bottom, and air entrainment occurs due to high turbulence. Momentum exchange exists between the recirculating fluid trapped on the steps and the upper skimming flows.It can be tracked back to the 1970s the first studies that payed attention to the hydraulic design of stepped spillway [1] . In the following 30 years, very active experimental research has been done on the air-water flow characteristics over stepped spillways, such as flow patterns, inception of air entrainment, air concentration, velocity field, pressure field and energy dissipation [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] . The complexity of the flow structure and the investigation on scale effects has caused uncertainties in transposing the experimental results to prototype. The minimum Reynolds and Weber numbers required to minimize scale effects in physical modeling of air-water two-phase flows on stepped spillways were given by Boes and Hager [16] . With the development of computational fluid dynamics (CFD), complex multiphase flows can be simulated numerically and the results are reliable and integrated. The flow over stepped spillways was simulated using the VOF (Volume of Fluid) method in conjunction with standard k-ε turbulence model by Chen et al. [17] . Cheng et al. [18,19] used the VOF and Mixture models respectively to simulate flow over stepped spillways and reported that the Mixture model has an obvious advantage over the VOF model. The steps behave as macroroughness and the flow is highly turbulent, therefore the definition of a correct turbulence model is fundamental to get reliable results. In this paper, the Mix

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