Jorge Matos

Water-related challenges represent one of the most pressing global concerns of the 21st century

Over the past decades, significant advances have been achieved in hydraulic structures for dams, namely in water release structures such as spillway weirs, chutes, and energy dissipators. This editorial presents a brief overview of the eleven papers in this Special Issue, Advances in Spillway Hydraulics: From Theory to Practice, and frames them in current research trends. This Special Issue explores the following topics: spillway inlet structures, spillway transport structures, and spillway outlet structures. For the first topic of spillway inlet structures, this collection includes one paper on the hydrodynamics and free-flow characteristics of piano key weirs with different plan shapes and another that presents a theoretical model for the flow at an ogee crest axis for a wide range of head ratios. Most of the contributions address the second topic of spillway transport structures as follows: a physical modeling of a beveled-face stepped chute; the description and recent developments of the generalized, energy-based, water surface profile calculation tool SpillwayPro; an application of the SPH method on non-aerated flow over smooth and stepped converging spillways; a physical model study of the effect of stepped chute slope reduction on the bottom-pressure development; an assessment of a spillway offset aerator with a comparison of the two-phase volume of fluid and complete two-phase Euler models included in the OpenFOAM^® toolbox; an evaluation of the performance and design of a stepped spillway aerator based on a physical model study. For the third topic of spillway outlet structures, physical model studies are presented on air–water flow in rectangular free-falling jets, the performance of a plain stilling basin downstream of 30° and 50° inclined smooth and stepped chutes, and scour protection for piano key weirs with apron and cutoff wall. Finally, we include a brief discussion about some research challenges and practice-oriented questions.

Energy dissipators, such as stilling basins, are usually required at the toe of stepped chutes to achieve adequate and safe operation of the spillway. Stepped chute hydraulics has been extensively studied in last several decades, however, only limited knowledge is available on the stilling basin performance below stepped chutes. In particular, the effect of the chute slope remains unknown, despite being a central design issue. Therefore, an experimental campaign was performed using a 30° or 50° inclined smooth or stepped chute with an adjacent conventional plain stilling basin. The experimental results indicated that, within the stilling basin, the surface characteristics and the roller as well as hydraulic jump lengths are practically independent of the chute slope. This further strengthens the previous findings that stepped chutes require 17% longer dimensionless jump lengths and consequently stilling basin lengths. The experimental results also confirmed that stepped chutes generated increased extreme and fluctuating bottom pressure characteristics at the stilling basin entrance area. With increasing chute slope, the latter were found to significantly magnify. However, such increased magnitudes were not expected to provoke cavitation damage as stepped chute inflows induced bottom aeration at the basin entrance, irrespective of the chute slope.

In recent decades, stepped chutes followed by a stilling basin became a standard for spillways of dams. The comprehensive knowledge of stepped chute approach flows on internal air–water flow properties of the hydraulic jump is still too limited for an appropriate design of stilling basins. Therefore, an experimental campaign was performed on a large-scale physical model of a plain stilling basin preceded by a 30° sloping smooth or stepped chute. Stepped chute approach flows induce lower deaeration rates along the jump roller as compared to smooth chute approach flows, indicating longer dimensionless jump lengths, normalized by the tailwater depth. Pronounced bottom air concentrations were observed within the first 40% of the jump length in the stilling basin downstream of the stepped chute. Thus, despite the significantly higher pressure fluctuations, this zone seems better protected against cavitation damage than in stilling basins following a smooth chute.

Three-dimensional (3D) simulations using the smoothed particle hydrodynamics (SPH) method were performed for smooth and stepped spillways with converging walls, in order to evaluate the influence of the wall deflection and the step macro-roughness on the main non-aerated flow properties. The simulations encompassed a 1V:2H sloping spillway, wall convergence angles of 9.9° and 19.3°, and discharges corresponding to skimming flow regime, in the stepped chute. The overall development of the experimental data on flow depths, velocity profiles, and standing wave widths was generally well predicted by the numerical simulations. However, larger deviations in flow depths and velocities were observed close to the upstream end of the chute and close to the pseudo-bottom of the stepped invert, respectively. The results showed that the height and width of the standing waves were significantly influenced by the wall convergence angle and by the macro-roughness of the invert, increasing with a larger wall deflection, and attenuated on the stepped chute. The numerical velocity and vorticity fields, along with the 3D recirculating vortices on the stepped invert, were in line with recent findings on constant width chutes.

The lack of sidewalls in a spillway leads to lateral expansion of the flow and, consequently, a non-uniform transversal flow rate distribution along the chute. The present work shows the velocity field measured in a physical model of a 1 V:0.8 H steeply sloping stepped spillway without sidewalls. An application of a Bubble Image Velocimetry (BIV) technique in the self-aerated region is shown, using air bubbles entrained into the flow downstream of the inception point as tracers. The results indicate that, for small dimensionless discharges and sufficiently downstream of the point of inception, the free-surface velocity compares relatively well with the corresponding air–water interfacial velocity previously obtained with a double-tip fiber optical probe in the same facility. In turn, the velocity profiles along the normal to the pseudo-bottom, far downstream of the inception point, are reasonably in agreement with the air–water interfacial velocity profiles in the inner part of the skimming flow, with the largest differences being verified in the upper skimming flow region near the free-surface.

Stepped spillways have been increasingly used to handle flood releases from large dams associated with hydropower plants, and it is important to evaluate the fluctuating pressure field on the steps. Hydraulic model investigations were conducted on three 53° (1V:0.75H) sloping and relatively large-stepped chutes to characterize the mean, fluctuating, and extreme pressures acting on the most critical regions of the step faces, near their outer edges. The pressure development along the chutes is presented, generally indicating an increase of the modulus of pressure coefficients up to the vicinity of the point of inception of air entrainment, and a decrease further downstream. The extreme pressure coefficients along the spillway are fitted by an empirical formula, and the critical conditions potentially leading to cavitation on prototypes are calculated. The correlation between the cavitation index and the friction factor is also applied for predicting the onset of cavitation on prototypes, and the results are compared with the pressure data-based method. Generally, the results obtained from those methods yield typical values for the cavitation index in the vicinity of the point of inception, varying approximately from 0.8 to 0.6, respectively. In light of these results, maximum unit discharges of about 15–20 m²/s are considered advisable on 53° sloping large-stepped spillways without artificial aeration, for step heights ranging from 0.6 to 1.2 m. For much higher unit discharges, a considerable reach of the spillway may potentially be prone to the risk of cavitation damage.

Fluctuating bottom-pressures on stepped chutes are relevant for the spillway design. An abrupt slope reduction causes a local alteration of the bottom-pressure development. Little information is available regarding the air–water flow properties near an abrupt slope reduction on stepped chutes, particularly on the local pressure evolution. Nevertheless, the option of providing a chute slope reduction may be of interest in spillway layout. The experiments presented herein include pressure distributions on both vertical and horizontal step faces, subsequent to an abrupt slope reduction on stepped chutes. A relatively large-scale physical model including abrupt slope reductions from 50° to 18.6° and from 50° to 30° was used, operated with skimming flow. The data indicate a substantial influence of the tested slope reductions on the bottom-pressure development. In the vicinity of the slope reduction, the mean pressure head near the edge of the horizontal step face reached 0.4 to 0.6 times the velocity head upstream of the slope reduction, for critical flow depths normalized by the step height ranging between 2.6 and 4.6.