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An experimental study on a large model flume using fiber-optical instrumentation indicated that the onset of skimming flow is a function of critical depth, chute angle, and step height. Uniform mixture depths that determine the height of chute sidewalls and uniform equivalent clear water depths are described in terms of a roughness Froude number containing unit discharge, chute angle and step height. The spillway length needed to attain uniform flow is expressed as a function of critical depth and chute angle. The flow resistance of stepped spillways is significantly larger than for smooth chutes due to the macro roughness of the steps. The friction factor for uniform aerated flow is of the order of 0.1 for typical gravity dam and embankment dam slopes, whereas the effect of relative roughness is rather small. The energy dissipation characteristics of stepped spillways and the design of training walls are also discussed. The paper aims to focus on significant findings of a research program and develops design guidance to lessen the need for individual physical model studies. A design example is further presented. DOI: 10.1061/(ASCE)0733-9429(2003)129:9(671) CE Database subject headings: Spillways; Two phase flow; Cascades; Aeration; Dam design; Energy dissipation; Friction factors.

An experimental study on a large model flume with fiber-optical instrumentation indicated that minimum Reynolds and Weber numbers of about [10.sup.5] 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. DOI: 10.1061/(ASCE)0733-9429(2003)129:9(661) CE Database subject headings: Two phase flow; Flow characteristics; Spillways; Scale effect.

This article presents a discussion of the authors regarding hydraulic models. The focus of the article is a model of skimming flow on stepped spillway, which had been presented by Geoffrey Pegram, Andrew Officer, and Samuel Mottram.

This article critically analyses and evaluates the research study on the two-phase cascade flow in a flume model reported earlier in the journal by M.R. Chamani and N. Rajaratnam. The analysis covers a wide range of cognate topics including skimming flow characteristics, free-surface aeration process, air concentration distribution, and energy dissipation.

Numerical models are used increasingly to tackle aerated flows for example in spillway design. However, these models are usually empirical and often lack thorough calibration. Herein a mixture model is calibrated with experimental data on uniform aerated flow from literature. A commercial code was used to solve the mixture Reynolds-averaged Navier–Stokes equations. Air entrainment was modelled with a turbulent kinetic energy based sub-grid model. The effects of drag, swarm correction and bubble diameter were evaluated with different models for sub-grid scale air-transport. Employing dynamic bubble size calculation and swarm correction resulted in ∼10% typical error in the simulated mixture flow depth and concentration profile for chute slopes from 7.5° to 75° and unit discharges from 0.20 to 0.51 m2 s−1. The obtained calibration parameters are independent of mean air concentration over a wide range of parameters; thereby providing a basis for air entrainment simulations of more complex flows. [ABSTRACT FROM AUTHOR]