Bubble Count Rate Research Articles

Air–water flow characteristics in high-velocity free-surface flows with 50% void fraction

High-velocity free-surface flows are complex two-phase flows and limited information is available about the interactions between air and water for void fractions of about 50%. Herein a detailed experimental study was conducted in the intermediate flow region (C ∼ 50%) on a stepped spillway and the microscopic air–water flow characteristics were investigated. The results showed differences in water and droplet chord times with comparatively larger number of air chord times (0–2ms), and larger number of water chord times (2–6ms). A monotonic decrease of particle chord modes was observed with increasing bubble count rates. Several characteristic time scales were identified based upon inter-particle arrival time analyses of characteristic chord time classes as well as spectral analyses of the instantaneous void fraction signal. Chord times of 3–5ms appeared to be characteristic time scales of the intermediate flow region having similar time scales compared to the local correlation and integral turbulent time scales and to time scales associated with bubble break-up and turbulent velocity fluctuations. A further characteristic time scale of 100ms was identified in a frequency analysis of instantaneous void fraction. This time scale was of the same order of magnitude as free-surface auto-correlation time scales suggesting that the air–water flow structure was affected by the free-surface fluctuations.

Phase-detection measurements in free-surface turbulent shear flows

High-velocity self-aerated flows are described as 'white waters' because of the entrained air bubbles. The air entrainment induces a drastic change in the multiphase flow structure of the water column and this leads to significant bubble-turbulence interactions, turbulence modulation and associated mixing processes impacting on the bulk flow properties. In these high-velocity free-surface turbulent flows, the phase-detection needle probe is a most reliable instrumentation. The signal processing of a phase-detection probe is re-visited herein. It is shown that the processing may be performed on the raw probe signal as well as the thresholded data. The latter yields the time-averaged void fraction, the bubble count rate, the particle chord time distributions and the particle clustering properties within the particulate flow regions. The raw probe signal analysis gives further the auto-correlation time scale and the power spectrum density function. Finally dimensional considerations are developed with a focus on the physical modelling of free-surface flows in hydraulic structures. It is argued that the notion of scale effects must be defined in terms of some specific set of air–water flow properties within well-defined testing conditions, while a number of free-surface flow characteristics are more prone to scale effects than others, even in large-size physical facilities.

Aeration performances of a gabion stepped weir with and without capping

The stepped spillway design has been used for more than 3,300 years. A simple structure is the gabion stepped weir. A laboratory study was performed herein in a large size facility. Three gabion stepped weirs were tested with and without capping, as well as a flat impervious stepped configuration. For each configuration, detailed air–water flow measurements were conducted systematically for a range of discharges. The observations highlighted the seepage flow through the gabions and the interactions between seepage and overflow. The air–water flow properties showed that the air concentration, bubble count rate and specific interface data presented lower quantitative values in the gabion stepped weir, compared to those on the impervious stepped chute, while higher velocities were measured at the downstream end of the gabion stepped chute. The re-oxygenation rate was deduced from the integration of the mass transfer equation using air–water interfacial area and velocity measurements. The aeration performances of the gabion stepped weir were lesser than on the flat impervious stepped chute, but for the lowest discharge. For the two configurations with step capping, the resulting flow properties were close to those on the impervious stepped configuration.

Effects of Step Pool Porosity upon Flow Aeration and Energy Dissipation on Pooled Stepped Spillways

AbstractThe hydraulics of stepped spillways with flat steps has been studied for the last three decades, including for embankment dam slopes, but studies of alternative stepped designs are limited. In this study, a pooled stepped spillway was investigated in a relatively large-size facility, and three different pool wall porosities were tested. The flow patterns, the macro- and microscopic air-water flow properties, and the energy dissipation performances were recorded; the results were compared with the flat stepped spillway design for the same chute slope (θ=26.6°). The investigations highlighted a close agreement between air-water flow properties on the configurations in terms of void fraction, turbulence levels, bubble count rate, and chord sizes. The interfacial velocity distributions showed larger interfacial velocity on the pooled step configurations of approximately 5–10% linked with a reduced flow depth. On the porous pooled stepped spillways, the interfacial velocities within the cavity highligh...

Air entrainment and turbulent fluctuations in hydraulic jumps

A hydraulic jump is the sudden transition from a high-velocity impinging flow into a turbulent roller in an open channel. Substantial amounts of air are entrapped at the impingement point, and significant free-surface fluctuations take place above the roller. In the present study, some physical modelling was conducted in a relatively large sized facility. The flow conditions included a wide ranges of inflow Froude numbers and Reynolds numbers (3.8 < Fr1 < 10.0, 2.1 × 104 < Re < 1.6 × 105). The fluctuating features of free-surface and roller position were investigated non-intrusively with a series of acoustic displacement meters. The characteristic frequencies of the fluctuating motions were documented, and some major roller surface deformation patterns were revealed. The air-water flow properties were investigated with an intrusive phase-detection probe. The void fraction and bubble count rate data were documented in the jump roller, together with the interfacial velocity distributions. The rate of air entrainment was estimated based upon the void fraction and interfacial velocity distribution data. Some simultaneous measurements of instantaneous void fraction and free-surface fluctuations as well as longitudinal jump front oscillations were conducted. The relationship between the rate of air entrainment and turbulent fluctuations is discussed. Both the turbulent fluctuation and aeration properties are basic design parameters in urban water systems in which a hydraulic jump may take place. The present work provides relevant information for water systems including covered channels and partially-filled pipes.

Aeration, Flow Instabilities, and Residual Energy on Pooled Stepped Spillways of Embankment Dams

AbstractAir-water flow experiments were conducted on some flat and pooled stepped spillways with slopes of 8.9° and 26.6° in transition and skimming flows. The study comprised the observations of the flow patterns, characteristic air-water flow properties, and energy dissipation performances. The air-water flow properties showed some differences in terms of interfacial velocity, bubble count rate, and turbulence intensity between the stepped chutes for the two channel slopes. These differences were also reflected in the residual energy data, highlighting a better energy dissipation rate for the pooled stepped spillway with slope of 8.9°. However, the aerated flows on the pooled stepped spillways exhibited some hydrodynamic instabilities, and a safe operation must be tested in physical models. The flat stepped spillway appeared to be the preferable design in terms of energy dissipation and flow stability.

Scale effects affecting two-phase flow properties in hydraulic jump with small inflow Froude number

The transition from supercritical to subcritical flow is characterised by a strong dissipative mechanism, a hydraulic jump. Herein a comparative analysis of physical data is presented with a focus on a broad range of two-phase flow parameters. The results show that, for hydraulic jumps with Fr1=5.1, the void fraction data obtained with Re<4×104 could not be scaled up to Re=1×105. Most air–water flow properties measured with Reynolds numbers up to 1.25×105 could not be extrapolated to large-size prototype structures without significant scale effects in terms of bubble count rate, turbulence, bubble chord time distributions and bubble cluster characteristics. The findings have some implications of civil and sanitary engineering designs, because most hydraulic structures, storm water systems and water treatment facilities operate with Reynolds numbers larger than 106 to over 108.

A Two-Way Coupled Polydispersed Two-Fluid Model for the Simulation of Air Entrainment Beneath a Plunging Liquid Jet

Plunging liquid jets are commonly encountered in nature and are widely used in industrial applications (e.g., in waterfalls, waste-water treatment, the oxygenation of chemical liquids, etc.). Despite numerous experimental studies that have been devoted to this interesting problem, there have been very few two-phase flow simulations. The main difficulty is the lack of a quantitative subgrid model for the air entrainment process, which plays a critical role in this problem. In this paper, we present in detail a computational multiphase fluid dynamics (CMFD)-based approach for analyzing this problem. The main ingredients of this approach are a comprehensive subgrid air entrainment model that predicts both the rate and location of the air entrainment and a two-fluid transport model, in which bubbles of different sizes are modeled as a continuum fluid. Using this approach, a Reynolds-averaged Navier Stokes (RaNS) two-way coupled two-phase flow simulation of a plunging liquid jet with a diameter of 24 mm and a liquid jet velocity around 3.5 m/s was performed. We have analyzed the simulated void fraction and bubble count rate profiles at three different depths beneath the average free surface and compared them with experimental data in literature. We observed good agreement with data at all locations. In addition, some interesting phenomena on the different movements of bubbles with different sizes were observed and discussed.

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 × 10 4 < Re < 1.3 × 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.

Air–water flow properties in step cavity down a stepped chute

For the last three decades, the research into skimming flows down stepped chutes was driven by needs for better design guidelines. The skimming flow is characterised by some momentum transfer from the main stream to the recirculation zones in the shear layer developing downstream of each step edge. In the present study some physical modelling was conducted in a relatively large facility and detailed air–water flow measurements were conducted at several locations along a triangular cavity. The data implied some self-similarity of the main flow properties in the upper flow region, at step edges as well as at all locations along the step cavity. In the developing shear layer and cavity region (i.e. y/ h < 0.3), the air–water flow properties presented some specific features highlighting the development of the mixing layer downstream of the step edge and the strong interactions between cavity recirculation and mainstream skimming flows. Both void fraction and bubble count rate data showed a local maximum in the developing shear layer, although the local maximum void fraction was always located below the local maximum bubble count rate. The velocity profiles had the same shape as the classical mono-phase flow data. The air–water flow properties highlighted some intense turbulence in the mixing layer that would be associated with large shear stresses and bubble–turbulence interactions.

Two-phase flow measurements in turbulent hydraulic jumps

Hydraulic jumps are commonly experienced in industrial applications and manufacturing processes, as well in rivers and canals. The hydraulic jump is the sudden transition from a high-velocity open channel flow to a subcritical flow motion. Despite nearly two centuries of studies, there is still a lack of knowledge on the two-phase flow properties of the turbulent shear layer and the roller. New series of experimental measurements were conducted in hydraulic jumps with Froude numbers between 5 and 8.5, and inflow Reynolds numbers between 38,000 and 62,000. The two-phase flow measurements included some vertical profiles of void fraction, bubble count rate, interfacial velocity and bubble chords. In the air–water shear region, the void fraction and bubble count rate distributions exhibited marked peaks, with the maximum of void fraction always above the location of the maximum bubble count rate. The dimensionless turbulent diffusivity coefficient was estimated. The dimensionless distributions of interfacial velocity compared favourably with some wall-jet flow equations. The data analysis showed that the mean bubble chord in the turbulent shear layer was between 1 mm and 6 mm. The probability distribution functions (PDF) of bubble chord time illustrated a broad spectrum with predominance to small bubbles compared to the mean.

Experimental assessment of scale effects affecting two-phase flow properties in hydraulic jumps

A hydraulic jump is the rapid transition from a supercritical to subcritical free-surface flow. It is charac- terised by strong turbulence and air bubble entrainment. New air-water flow properties were measured in hydraulic jumps with partially developed inflow conditions. The data set together with the earlier data of Chanson (Air bubble entrainment in hydraulic jumps. Similitude and scale effects, 119 p, 2006) yielded similar experiments con- ducted with identical inflow Froude numbers Fr1 = 5 and 8.5, but Reynolds numbers between 24,000 and 98,000. The comparative results showed some drastic scale effects in the smaller hydraulic jumps in terms of void fraction, bubble count rate and bubble chord time distributions. The present comparative analysis demonstrated quantitatively that dynamic similarity of two-phase flows in hydraulic jumps cannot be achieved with a Froude similitude. In experimental facilities with Reynolds numbers up to 10 5 , some viscous scale effects were observed in terms of the rate of entrained air and air-water interfacial area.

Interfacial aeration and bubble count rate distributions in a supercritical flow past a backward-facing step

An example of high-velocity open channel flows is a supercritical flow past an abrupt drop. In such a geometry, the basic air–water flow properties were measured, including distributions of void fraction and bubble count rate, and local air and water chord size distributions, at and downstream of the backward-facing step. The bubble count rate distributions were compared with a conceptual model of streamwise distribution of air and water chords which yields a quasi-parabolic relationship between bubble count rate and void fraction. The proposed model was an attempt to explain the experimental relationship between bubble count rate and void fraction, rather a meticulous breakdown of the complex air–water structure.

Similitude and scale effects of air entrainment in hydraulic jumps

A hydraulic jump is characterized by some strong turbulence and air entrainment in the roller. New measurements were performed in two channels in which similar experiments with identical inflow Froude numbers and relative channel widths were conducted with a geometric scaling ratio of 2:1. Void fraction distributions showed the presence of an advection/diffusion shear layer in which the data followed an analytical solution of the diffusion equation for air bubbles. The data indicated some scale effects in the small channel in terms of void fraction and bubble count rate. Void fraction distributions implied comparatively greater detrainment at low Reynolds numbers yielding to lesser overall aeration of the jump roller. Dimensionless bubble count rates were significantly lower in the smaller channel especially in the mixing layer. The study is believed to be the first systematic investigation of scale effects affecting air entrainment in hydraulic jumps using an accurate air–water measurement technique.

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 time and length scale measurements in high-velocity open channel flows

In high-velocity open channel flows, the measurements of air-water flow properties are complicated by the strong interactions between the flow turbulence and the entrained air. In the present study, an advanced signal processing of traditional single- and dual-tip conductivity probe signals is developed to provide further details on the air-water turbulent level, time and length scales. The technique is applied to turbulent open channel flows on a stepped chute conducted in a large-size facility with flow Reynolds numbers ranging from 3.8 E+5 to 7.1 E+5. The air water flow properties presented some basic characteristics that were qualitatively and quantitatively similar to previous skimming flow studies. Some self-similar relationships were observed systematically at both macroscopic and microscopic levels. These included the distributions of void fraction, bubble count rate, interfacial velocity and turbulence level at a macroscopic scale, and the auto- and cross-correlation functions at the microscopic level. New correlation analyses yielded a characterisation of the large eddies advecting the bubbles. Basic results included the integral turbulent length and time scales. The turbulent length scales characterised some measure of the size of large vortical structures advecting air bubbles in the skimming flows, and the data were closely related to the characteristic air-water depth Y90. In the spray region, present results highlighted the existence of an upper spray region for C > 0.95 to 0.97 in which the distributions of droplet chord sizes and integral advection scales presented some marked differences with the rest of the flow.

Experimental analysis of Froude number effect on air entrainment in the hydraulic jump

A hydraulic jump is characterized by strong energy dissipation and mixing, large-scale turbulence, air entrainment, waves, and spray. Despite recent pertinent studies, the interaction between air bubbles diffusion and momentum transfer is not completely understood. The objective of this paper is to present experimental results from new measurements performed in a rectangular horizontal flume with partially developed inflow conditions. The vertical distributions of the void fraction and the air bubbles count rate were recorded for inflow Froude number Fr1 in the range from 5.2 to 14.3. Rapid detrainment process was observed near the jump toe, whereas the structure of the air diffusion layer was clearly observed over longer distances. These new data were compared with previous data generally collected at lower Froude numbers. The comparison demonstrated that, at a fixed distance from the jump toe, the maximum void fraction Cmax increases with the increasing Fr1. The vertical locations of the maximum void fraction and bubble count rate were consistent with previous studies. Finally, an empirical correlation between the upper boundary of the air diffusion layer and the distance from the impingement point was derived.

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.

Bubble entrainment, spray and splashing at hydraulic jumps

The sudden transition from a high-velocity, supercritical open channel flow into a slow-moving sub-critical flow is a hydraulic jump. Such a flow is characterised by a sudden rise of the free-surface, with some strong energy dissipation and air entrainment, waves and spray. New two-phase flow measurements were performed in the developing flow region using a large-size facility operating at large Reynolds numbers. The experimental results demonstrated the complexity of the flow with a developing mixing layer in which entrained bubbles are advected in a high shear stress flow. The relationship between bubble count rates and void fractions was non-unique in the shear zone, supporting earlier observations of some form of double diffusion process between momentum and air bubbles. In the upper region, the flow consisted primarily of water drops and packets surrounded by air. Visually significant pray and splashing were significant above the jump roller. The present study is the first comprehensive study detailing the two-phase flow properties of both the bubbly and spray regions of hydraulic jumps, a first step towards understanding the interactions between bubble entrainment and droplet ejection processes.

Air–Water Mass Transfer on a Stepped Waterway

Stepped waterways are commonly used as river training, debris dam structures, storm water systems and aeration cascades. The present study was focused on analysis of basic air-water flow properties on a low gradient stepped chute, combined with dissolved oxygen measurements. The oxygen aeration efficiency was found to be about 30% for 12 steps with a total drop in invert elevation of 1.4 m, nearly independently of the inflow conditions. Detailed air-water flow measurements, including void fraction, velocity, bubble count rate and interface area, were used to integrate the mass transfer equation and to estimate the aeration potential of the waterway. Direct comparisons with dissolved oxygen measurements showed good agreement between the two methods.