Physical Modelling, Scale Effects, and Self-Similarity of Stepped Spillway Flows

Abstract

Stepped spillway flows are characterised by significant turbulent dissipation on the chute associated with strong free-surface aeration. Herein the validity of the Froude similitude is tested by re-analysing three experimental data sets corresponding to moderate slopes typical of embankment dams and storm waterways ( = 3.4 to 22°). The measurements included distributions of void fraction, bubble count rate, interfacial velocity, turbulence intensity, bubble chord sizes, and integral turbulent length and time scales which were scaled with a 2:1 undistorted geometric scaling ratio. The criterion selection for scale effects is a critical issue. Major differences (i.e. scale effects) were observed in terms of bubble count rates, bubble chord sizes, turbulence levels and integral turbulent length scales although little scale effects were seen in terms of void fraction and velocity distributions. The findings suggested that most physical results, including the rate of energy dissipation and re-aeration, cannot be extrapolated to prototype flow conditions without significant scale effects. A complementary approach may be based upon self-similarity, since self-similar relationships were observed systematically at both macroscopic and microscopic levels. Keywords : Stepped spillways, Air-water flow properties, Physical modelling, Scale effects, Self-similarity, Froude similitude. INTRODUCTIONStepped spillways are typically designed to increase the rate of energy dissipation on the (stepped) chute and to reduce the size of the downstream energy dissipator. At large discharges, skimming flows on stepped spillways are characterised by a significant rate of turbulent dissipation associated with strong free-surface aeration (Fig. 1). Although research in the hydraulics of stepped spillways has been very active during the last three decades (Chanson 1995,2001, Matos and Chanson 2006, the fundamental issues of dynamic similarity and scale effects were rarely discussed. How confidently can we extrapolate laboratory results to prototype spillways ? Detailed air-water flow measurements are re-analysed systematically. The data were recorded in three large-size stepped chute facilities with slopes = 3.4º, 16º and 22º, and step heights h = 0.05 m to 0.143 m. Detailed turbulence data were collected in the large-size channels with a stepped invert, including turbulence levels and turbulent time and length scales. The results are used to test the validity of the Froude similarity and to assess the scale effects and the experimental distortion to prototype stepped spillways.

Artificial aeration of stepped spillways by crest piers and flares for the mitigation of cavitation damage

“…The Type B stepped spillway model was designed with a scale of 1:50, which exceeds the recommendations of the previously mentioned researchers. Although the small scale induced aeration scale effects, the air concentration was accurately scaled and captured, as it conformed to the law of self-similarity (Chanson & Carosi 2007;Chanson 2008;Felder & Chanson 2017). The phenomenon of self-similarity is defined as the spatial distribution of properties at various instances of time and spatial locations to be obtained from one another by a similarity transformation.…”