Abstract
As with most high-velocity free-surface flows, stepped spillway flows become self-aerated when the drop height exceeds a critical value. Due to the step-induced macro-roughness, the flow field becomes more turbulent than on a similar smooth-invert chute. For this reason, cascades are oftentimes used as re-aeration structures in wastewater treatment. However, for stepped spillways as flood release structures downstream of deoxygenated reservoirs, gas transfer is also of crucial significance to meet ecological requirements. Prediction of mass transfer velocities becomes challenging, as the flow regime differs from typical previously studied flow conditions. In this paper, detailed air-water flow measurements are conducted on stepped spillway models with different geometry, with the aim to estimate the specific air-water interface. Re-aeration performances are determined by applying the absorption method. In contrast to earlier studies, the aerated water body is considered a continuous mixture up to a level where 75% air concentration is reached. Above this level, a homogenous surface wave field is considered, which is found to significantly affect the total air-water interface available for mass transfer. Geometrical characteristics of these surface waves are obtained from high-speed camera investigations. The results show that both the mean air concentration and the mean flow velocity have influence on the mass transfer. Finally, an empirical relationship for the mass transfer on stepped spillway models is proposed.
Highlights
Stepped spillways and cascades are known to be effective energy dissipaters downstream of reservoirs due to the increased flow resistance created by the steps [1]
Oxygen transfer is of high interest as water in reservoirs often suffer from deoxygenation, there being a level of dissolved oxygen (DO) content required to keep good ecological conditions in downstream rivers and streams
The specific air-water interface according to Equation (7) has been determined between the inception pointair-water of self-aeration and the quasi-uniform flow region
Summary
Stepped spillways and cascades are known to be effective energy dissipaters downstream of reservoirs due to the increased flow resistance created by the steps [1]. Once the self-aeration has been triggered, the water surface becomes more and more disturbed, and bubbles, entrained in water, as well as droplets, ejected to the air, are transported along the chute. This involves a significant specific air-water interface across which gas transfer can take place. Gas transfer between water and air is driven by an existing concentration gradient grad (Cgas ). May be described by Fick’s 1st law, according to which the diffusive flux Igas (in mg/(m2 s)) is proportional to this gradient and directed from high concentrations to low concentrations: Igas = − Dgas × grad Cgas , (1). For the one-dimensional diffusion perpendicular to the air-water interface, Equation (2) becomes ∂2 Cgas Considering mass conservation and assuming an isotropic diffusivity, a diffusion equation is found as ∂Cgas
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