Turbulence, dynamic similarity and scale effects in high-velocity free-surface flows above a stepped chute

Abstract

In high-velocity free-surface flows, air entrainment is common through the interface, and intense interactions take place between turbulent structures and entrained bubbles. Two-phase flow properties were measured herein in high-velocity open channel flows above a stepped chute. Detailed turbulence measurements were conducted in a large-size facility, and a comparative analysis was applied to test the validity of the Froude and Reynolds similarities. The results showed consistently that the Froude similitude was not satisfied using a 2:1 geometric scaling ratio. Lesser number of entrained bubbles and comparatively greater bubble sizes were observed at the smaller Reynolds numbers, as well as lower turbulence levels and larger turbulent length and time scales. The results implied that small-size models did underestimate the rate of energy dissipation and the aeration efficiency of prototype stepped spillways for similar flow conditions. Similarly a Reynolds similitude was tested. The results showed also some significant scale effects. However a number of self-similar relationships remained invariant under changes of scale and confirmed the analysis of Chanson and Carosi (Exp Fluids 42:385-401, 2007). The finding is significant because self-similarity may provide a picture general enough to be used to characterise the airwater flow field in large prototype channels. Cross-correlation time scale ( List of symbols

Air–water flow measurements in a flat slope pooled stepped waterway

“…On the flat stepped chute, the turbulence level distributions were qualitatively and quantitatively comparable to earlier findings on flat stepped spillways with maximum values of up to 150% in the intermediate flow region (Carosi andChanson 2008, Felder andChanson 2009). Some typical distributions of turbulence intensity Tu are illustrated in Figure 7 for all experimental configurations.…”

Analysis of nonuniform aerated skimming flows on stepped channels

“…For R ≥ 4×10 4 at a given section of H s /d c (Fig.1) in the nonuniform flow region, a Froude similitude with Eq. (1) may be applied specifically for the magnitude and distribution of C and u/u 0.9 (Takahashi and Ohtsu 2013) except in terms of turbulent properties and bubble sizes (Pfister andChanson 2012, Felder andChanson 2009a). Thus, experimental data were collected in the range of 4×10 4 ≤ R ≤ 9×10 4 to satisfy these limits.…”

Flow aeration, cavity processes and energy dissipation on flat and pooled stepped spillways for embankments

“…In a free-surface skimming flow down a stepped spillway, a dimensional analysis gives a series of dimensionless relationships between the two-phase flow properties at a dimensionless location along the chute and the channel characteristics, inflow properties and fluid properties (Chanson 2004, Chanson and Gonzalez 2005, Felder and Chanson 2009b): …”