Explicit equations for critical depth in open channels with complex compound cross sections. A discussion

In open channel hydraulics, the notion of critical flow conditions and critical depth are not restricted to open channel flows with hydrostatic pressure distributions. This contribution shows an extension of the concept of critical flow conditions linked with the minimum specific energy, as introduced by Bakhmeteff [1] and extended by Liggett [9] and Chanson [5]. It demonstrated that the critical depth may be defined more broadly including when the pressure field is not hydrostatic

Air Bubble Entrainment in Open Channels: Flow Structure and Bubble Size Distributions

At spillways and sewers, high-velocity open channel flows are characterised by free-surface aeration (i.e. 'white waters'). The air-water flow comprises a region of low-air-content (i.e. C < 0.3 to 0.4) with a bubbly flow structure, and a high-air-content region above characterised by air-water projections and foam structures. New experiments were performed in a 25-m long channel with a 4-degree slope. Measured air-water flow properties and bubble chord length distributions are described. The analysis of the new data provides information on the air concentration distributions, the distributions of mean air-water velocities and the bubble chord length distributions. The results indicate a broad spectrum of chord length sizes extending over several orders of magnitude. The cumulative distributions of chord lengths follow approximately a Log-Normal distribution while the bubble frequency distributions is related to the void fraction by a parabolic law

Free-surface fluctuations in hydraulic jumps: Experimental observations

A hydraulic jump is the rapid and sudden transition from a high-velocity supercritical open channel flow to a subcritical flow. It is characterised by the dynamic interactions of the large-scale eddies with the free-surface. New series of experimental measurements were conducted in hydraulic jumps with Froude numbers between 3.1 and 8.5 to investigate these interactions. The dynamic free surface measurements were performed with a non-intrusive technique while the two-phase flow properties were recorded with a phase-detection probe. The shape of the mean free surface profile was well defined and the turbulent fluctuation profiles highlighted a distinct peak of turbulent intensity in the first part of the jump roller, with free-surface fluctuation levels increasing with increasing Froude number. The dominant free-surface fluctuation frequencies were typically between 1 and 4 Hz. A comparison between the acoustic sensor signals and conductivity probe data suggested that the air-water "free-surface" detected by the acoustic sensor corresponded to about the boundary between the turbulent shear layer and the upper free-surface layer. Simultaneous measurements of free surface and bubbly flow fluctuations for Fr = 5.1 indicated that the frequency ranges of both sensors were similar (F < 5 Hz) whatever the position downstream of the toe. The present results highlighted that the dynamic free-surface measurements can be conducted successfully using acoustic displacement meters, and the time-averaged depth measurements was a physical measure of the free-surface location in hydraulic jumps

Self-Aeration and Turbulence in a Stepped Channel: Influence of Cavity Surface Roughness

The strong interactions between free-surface flows and atmospheric surroundings may lead to substantial air-water mixing with void fractions ranging from zero in clear-water to 100%. In this study, the air-water flow properties were studied in a large stepped water channel operating at large Reynolds numbers. Interactions between free-surface and cavity recirculation were systematically investigated in the skimming flow regime. Some surface roughness was introduced on the cavity walls and identical experiments were performed with several configurations. Basic results demonstrated some influence of step surface roughness on the flow properties leading to some counter-intuitive finding. The presence of cavity roughness was associated with higher flow velocities and comparatively lower turbulence levels. Distributions of bubble/droplet chords spanned over several orders of magnitude without significant influence of the cavity roughness. The distributions of turbulence levels and bubble count rates showed some correlation and highlighted strong interactions between entrained particles (bubbles, drops) and the flow turbulence

Advanced Post-Processing and Correlation Analyses in High-Velocity Air-Water Flows

The interest in air-water flows has not diminished in recent years, but it is accompanied by frequent citations of early, sometimes outdated articles. A basic issue is the inadequate, incomplete interpretation of air-water flow instrumentation by hydraulic engineers and researchers. This article comments on high-velocity air-water flow measurements by means of intrusive phase detection probes. This article focus on the bubbly flow structure of high-velocity air-water flow based upon measurements by means of intrusive phase detection probes. It is shown that some advanced post-processing techniques may yields expanded information on the air-water turbulent flow properties and bubbly flow structures. The outcomes demonstrate simple techniques in high-velocity air-water flow analysis

Bubbly flow measurements in hydraulic jumps with small inflow Froude numbers

The transition from supercritical to subcritical open channel flow is characterised by a strong dissipative mechanism called a hydraulic jump. A hydraulic jump is turbulent and associated with the development of large-scale turbulence and air entrainment. In the present study, some new physical experiments were conducted to characterise the bubbly flow region of hydraulic jumps with relatively small Froude numbers (2.4 < Fr(1) < 5.1) and relatively large Reynolds numbers (6.6 x 10(4) < Re < 1.3 x 10(5)). The shape of the time-averaged free-surface profiles was well defined and the longitudinal profiles were in agreement with visual observations. The turbulent free-surface fluctuation profiles exhibited a peak of maximum intensity in the first half of the hydraulic jump roller, and the fluctuations exhibited some characteristic frequencies typically below 3 Hz. The air-water flow properties showed two characteristic regions: the shear layer region in the lower part of the flow and an upper free-surface region above. The air-water shear layer region was characterised by local maxima in terms of void fraction and bubble count rate. Other air-water flow characteristics were documented including the distributions of interfacial velocity and turbulence intensity. The probability distribution functions (PDF) of bubble chord time showed that the bubble chord times exhibited a broad spectrum, with a majority of bubble chord times between 0.5 and 2 ms. An analysis of the longitudinal air-water structure highlighted a significant proportion of bubbles travelling within a cluster structure. (C) 2011 Elsevier Ltd. All rights reserved

Surface Waves and Roughness in Self-Aerated Supercritical Flow

In high-velocity open channel flows, free-surface aeration is commonly observed. The effects of surface waves on the air-water flow properties are tested herein. The study simulates the air-water flow past a fixed-location phase-detection probe by introducing random fluctuations of the flow depth. The present model yields results that are close to experimental observations in terms of void fraction, bubble count rate and bubble/droplet chord size distributions. The results show that the surface waves have relatively little impact on the void fraction profiles, but that the bubble count rate profiles and the distributions of bubble and chord sizes are affected by the presence of surface waves

Turbulent length-time scales distributions in hydraulic jumps

Air–water flow measurements were performed in hydraulic jump flows for a range of inflow Froude numbers. The experiments were conducted in a large-sized facility using phase-detection intrusive probes. The void fraction measurements showed the presence of an advective diffusion shear layer where the air concentration vertical distributions were successfully compared with an analytical solution of the advective diffusion equation for air bubbles. In the air–water shear layer, a new empirical relationship between the maximum air concentration decay as a function of both the distance from the jump toe and the inflow Froude number was derived. Air–water turbulent time and length scales were deduced from auto- and cross-correlation analyses based on the method of Chanson (2007). The result provided some characteristic transverse time and length scales of the eddy structures advecting the air bubbles in the developing shear layer. The turbulence time scale data showed an increase with the relative elevation above the bed, as well as some decrease with increasing distance from the toe. The dimensionless integral turbulent length scale Lxz/d1 was closely related to the inflow depth

Should Field Works Be Compulsory in Hydraulic Engineering Courses ?

Engineering graduates should be familiar with real-world problems, practical applications and relevant solutions. Hydraulic engineers are no exception, but the teaching of open channel hydraulics is a major challenge. In open channel flows, the free surface rises and falls in response to perturbations to the flow (e.g., changes in channel slope or width). Field studies complement traditional lectures and laboratory work. Student fieldwork was introduced systematically in a series of hydraulic engineering subjects within undergraduate civil and environmental engineering curricula. Anonymous student feedback demonstrated a strong student interest for the fieldwork. This was associated with greater motivation for the course, leading in turn to lower failure rates. Feedback from former students indicated that fieldwork experience was an important component of their studies and helped their professional development. Employers testified that fieldwork are an essential component of a hydraulic engineering course and that it should be a requirement in all civil/environmental engineering curricula. This pedagogical experience demonstrated the very-significant role of fieldwork in the teaching of hydraulic engineering. Lecturers and professionals should not be complacent with university hierarchy and administration clerks intent on cutting costs by eliminating field studies. Although the preparation of fieldwork with large class sizes is a major effort, the outcome is very rewarding for the students and the lecturer. Yes, fieldwork should be definitely compulsory in each and every hydraulic engineering course