Two-Phase Flow Characteristics of Stepped Spillways

An experimental study on a large model flume with fiber-optical instrumentation indicated that minimum Reynolds and Weber numbers of about 105 and 100, respectively, are required for viscosity and surface tension effects to become negligible compared to gravitational and inertial forces expressed by Froude similitude. Both the location of and the flow depth at the inception point of air entrainment can be expressed as functions of a so-called roughness Froude number containing the unit discharge, step height and chute angle. The depth-averaged air concentration is found to depend only on a normalized vertical distance from the spillway crest and the chute angle for chute slopes ranging from embankment to gravity dam spillways. Air concentration profiles can be expressed by an air bubble diffusion model. The pseudobottom air concentration allows the assessment of the cavitation risk of stepped chutes and is approximated by a regression function. Finally, a new velocity distribution function is presented consisting of a power law up to 80% of the characteristic nondimensional mixture depth, and a constant value above.