We present and discuss the results of a comprehensive study addressing the non-aerated region of the skimming flow in steep stepped spillways. Although flows in stepped spillways are usually characterized by high air concentrations concomitant with high rates of energy dissipation, the non-aerated region becomes important in small dams and/or spillways with high specific discharges. A relatively large physical model of such spillway was used to acquire data on flow velocities and water levels and, then, well-resolved numerical simulations were performed with a commercial code to reproduce those experimental conditions. The numerical runs benefited from the ability of using multi-block grids in a Cartesian coordinate system, from capturing the free surface with the TruVOF method embedded in the code, and from the use of two turbulence models: the ${k{-}\varepsilon}$ and the RNG ${k{-}\varepsilon}$ models. Numerical results are in good agreement with the experimental data corresponding to three volumetric flow rates in terms of the time-averaged velocities measured at diverse steps in the spillway, and they are in very satisfactory agreement for water levels along the spillway. In addition, the numerical results provide information on the turbulence statistics of the flow. This work also discusses important aspects of the flow, such as the values of the exponents of the power-law velocity profiles, and the characteristics of the development of the boundary layer in the spillway.

Traditionally, research on stepped spillway hydraulics has been focused on the air-water flow region but for the hydraulic design of small embankment dams experiencing relatively large overtopping flows, the nonaerated region can be very important. Empirical formulas are presented for predicting skimming flow properties upstream of the point of inception of air entrainment for 1V:2H sloping stepped spillways, and the location and flow depth at the point of inception. Particular emphasis is placed on the clear-water depth, velocity distribution, and the energy dissipation characteristics in the developing nonaerated flow region. The velocity distribution is well described by a power law. The normalized clear-water depth and the normalized specific energy varied with the relative distance along the spillway and the effect of the normalized critical depth was negligible. Finally, the rate of energy dissipation was small, which has direct implications for the design of the downstream energy dissipator.

The nonaerated region may occupy a large portion of the skimming flow in steep, stepped spillways, particularly for relatively high unit flow rates. In spite of the numerous contributions on the hydraulic properties at both the inception point of air entrainment and the aerated region, much less is known regarding the flow in the nonaerated region. In this paper, new empirical evidence, based on an extensive data set obtained during several years in a large-scale facility, sheds light on the features of the nonaerated-flow region. Diverse ways to locate and estimate the main hydraulic properties at the inception point are first discussed and compared. Then, expressions capable of characterizing the main flow variables along the nonaerated region are presented, namely, the boundary-layer development, the velocity distribution, the equivalent clear-water depth, the characteristic depth taking into account the free-surface unsteadiness due to turbulence, and the energy dissipation. The energy dissipa...

We discuss, apply and validate several physics-based criteria for air entrainment into flows on steep stepped spillways, using laboratory observations and numerical results published elsewhere. To the best of our knowledge, this is the first time a validation of these criteria is undertaken for any chute flow in general, and for the skimming flow in steep stepped spillways in particular. To undertake the validation, we employed experimental and numerical data covering a considerable range of volume flow rates and step heights. We observed an overall good performance of most of the criteria, especially taking into account the intrinsic difficulties in defining the time-averaged location and depth of the inception point of air entrainment experimentally. Finally, we present two novel non-dimensional numbers designed to facilitate the physical interpretation of the location of the inception point of air entrainment.