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The roughness Froude number is a relatively new dimensionless parameter that began appearing in the hydraulic engineering literature in the late 1970s, first for the analysis of aeration inception in smooth chutes, and then later in connection with stepped chutes. This article reviews its foundations, historical development, alternative forms, present-day applications, and physical significance, which has received little attention previously. In addition to its empirically demonstrated connection to aeration inception, this paper shows that one form of a roughness Froude number has a strong relation to the transition between nappe and skimming flow regimes of stepped chutes, while another combines the dimensionless flow friction factor and the relative submergence of roughness elements. [ABSTRACT FROM AUTHOR]

The energy dissipation in plunge pools is often related to air entrainment in the plunging jet. Recent experimental work showed that the void fractions below the impinging jet are significantly smaller than outside the jet impact. This was attributed to the compression of the entrained air bubbles. In this paper, the thermodynamics of air bubble compression is introduced as a novel energy dissipation mechanism in civil engineering hydraulics. For the analysis of reported experimental data, isothermal conditions were applied as a lower bound approximation. It was found that the energy dissipation rates range from 2.7–9.7% for a jet velocity of 10 m s−2 and void fractions of 0.11 and 0.31, to 15.9–36.0% for a jet velocity of 24.5 m s−1 and void fractions of 0.35–0.55. The results may explain the difference between energy dissipation rates in plunge pools at model and full scale. [ABSTRACT FROM AUTHOR]

A numerical model, based on the open source code OpenFOAM, was developed to predict jet regimes and total dissolved gas downstream of spillways. The model utilizes the volume of fluid method to track the interface between air and water. A detached eddy simulation model is used for turbulence closure. Transport and dissolution of bubbles are predicted using an Eulerian approach. A bubble number density equation was implemented to predict bubble size changes caused by dissolution and compression. Total dissolved gas was computed using a transport equation that includes the mass transfer between bubbles and water. The model simultaneously captured spillway jet regimes and distribution of total dissolved gas in a spillway sectional model of McNary Dam. Model parameters, gas volume fraction and bubble size at the entrainment region, were calibrated to match total dissolved gas measured in the field under different dam operations. [ABSTRACT FROM AUTHOR]

Optical flow estimation is known from Computer Vision where it is used to determine obstacle movements through a sequence of images following an assumption of brightness conservation. This paper presents the first study on application of the optical flow method to aerated stepped spillway flows. For this purpose, the flow is captured with a high-speed camera and illuminated with a synchronized LED light source. The flow velocities, obtained using a basic Horn-Schunck method for estimation of the optical flow coupled with an image pyramid multi-resolution approach for image filtering, compare well with data from intrusive conductivity probe measurements. Application of the Horn-Schunck method yields densely populated flow field data sets with velocity information for every pixel. It is found that the image pyramid approach has the most significant effect on the accuracy compared to other image processing techniques. However, the final results show some dependency on the pixel intensity distribution, with better accuracy found for grey values between 100 and 150. [ABSTRACT FROM AUTHOR]

Stepped chutes effectively dissipate the energy of supercritical flow of steep channels. In general, stepped chute flows are characterized by self-aeration. For their hydraulic design, it is important to know the aerated flow depth, the aerated flow velocity, the air concentration, and the specific energy. Herein, quasi-uniform aerated skimming flow is systematically investigated over a range of chute angles from 19° to 55° for a wide range of step heights and discharges. Air concentration and aerated flow velocity profiles are presented, and the depth-averaged air concentration and the friction factor are determined. The specific energy is determined based on the aerated flow characteristics, revealing the effects of chute angle and step height on the specific energy of aerated skimming flow. This quantity was compared with the conventional specific energy of clear-water flows. [ABSTRACT FROM AUTHOR]