Analysis of nonuniform aerated skimming flows on stepped channels

Takahashi, Masayuki; Ohtsu, Iwao

doi:10.14264/uql.2014.18

Cited by 3 publications

(2 citation statements)

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“…When the boundary layer outer edge is close to the free-surface, the turbulent shear stress next to the free-surface is large enough to overcome both the surface tension and buoyancy effects and free-surface aeration occurs (Ervine and Falvey 1987, Chanson inception point showed intense free-surface aeration in this very rapidly-varied flow region: "at the point of inception [...] the mean concentration is approximately 0.2" (Matos 2000). The finding was confirmed experimentally for a range of slopes (Boes 2000, Chanson and Toombes 2002, Bung 2011, Meireles et al 2012, Takahashi and Ohtsu 2014.…”

Section: Introductionsupporting

confidence: 53%

Self-aeration in the rapidly- and gradually-varying flow regions of steep smooth and stepped spillways

Zhang

Chanson

2015

Environ Fluid Mech

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In high-velocity chute flows, free-surface aeration is often observed. The phenomenon is called self-aeration or white waters. When the turbulent shear stresses next to the free-surface are large enough, air bubbles are entrained throughout the entire air-water column. A rapidly-varied flow region is observed immediately downstream of the inception point of free-surface aeration. An analytical solution of the air diffusion equation is proposed and the results compare well with new experimental data. Both experiments and theory indicate that the flow bulking spans over approximately 3 to 4 step cavities downstream of the inception point of free-surface aeration on a stepped chute. Further downstream the void fraction distributions follow closely earlier solutions of the air diffusion equation. The application of the diffusion equation solution to prototype and laboratory data shows air bubble diffusivities typically larger than the momentum transfer coefficient. The result highlights however a marked decrease in the ratio of air bubble diffusivity to eddy viscosity with increasing Reynolds number. The finding might indicate some limitation of laboratory investigations of air bubble diffusion process in self-aerated flows and of their extrapolation to full-scale prototype applications.

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