Air Bubble Entrainment in Hydraulic Jumps: Physical Modelling and Scale Effects

A hydraulic jump is characterised by strong energy dissipation and air entrainment. In the present study, new air-water flow measurements were performed in hydraulic jumps with partially-developed flow conditions in relatively large-size facilities with phase-detection probes. The experiments were conducted with identical Froude numbers, but a range of Reynolds numbers and relative channel widths. The results showed drastic scale effects at small Reynolds numbers in terms of void fraction and bubble count rate distributions. The void fraction distributions implied comparatively greater detrainment at low Reynolds numbers leading to a lesser overall aeration of the jump roller, while dimensionless bubble count rates were drastically lower especially in the mixing layer. The experimental results suggested also that the relative channel width had little effect on the air-water flow properties for identical inflow Froude and Reynolds numbers.

Dynamic Similarity and Scale Effects Affecting Air Bubble Entrainment in Hydraulic Jumps

In an open channel, the transition from super- to sub-critical flow is a flow singularity (the hydraulic jump) characterised by a sharp rise in free-surface elevation, strong turbulence and air entrainment in the roller. A key feature of the hydraulic jump flow is the strong free-surface aeration and air-water flow turbulence. In the present study, similar experiments were conducted with identical inflow Froude numbers Fr1 using a geometric scaling ratio of 2:1. The results of the Froude-similar experiments showed some drastic scale effects in the smaller hydraulic jumps in terms of void fraction, bubble count rate and bubble chord time distributions. Void fraction distributions implied comparatively greater detrainment at low Reynolds numbers yielding some lesser aeration of the jump roller. The dimensionless bubble count rates were significantly lower in the smaller channel, especially in the mixing layer. The bubble chord time distributions were quantitatively close in both channels, and they were not scaled according to a Froude similitude. Simply the hydraulic jump remains a fascinating two-phase flow motion that is still poorly understood.

Measuring the interaction forces between protein inclusion bodies and an air bubble using an atomic force microscope

Interaction forces between protein inclusion bodies and an air bubble have been quantified using an atomic force microscope (AFM). The inclusion bodies were attached to the AFM tip by covalent bonds. Interaction forces measured in various buffer concentrations varied from 9.7 nN to 25.3 nN (+/- 4-11%) depending on pH. Hydrophobic forces provide a stronger contribution to overall interaction force than electrostatic double layer forces. It also appears that the ionic strength affects the interaction force in a complex way that cannot be directly predicted by DLVO theory. The effects of pH are significantly stronger for the inclusion body compared to the air bubble. This study provides fundamental information that will subsequently facilitate the rational design of flotation recovery system for inclusion bodies. It has also demonstrated the potential of AFM to facilitate the design of such processes from a practical viewpoint.

What is the shape of an air bubble on a liquid surface?

We have calculated the equilibrium shape of the axially symmetric meniscus along which a spherical bubble contacts a flat liquid surface by analytically integrating the Young-Laplace equation in the presence of gravity, in the limit of large Bond numbers. This method has the advantage that it provides semianalytical expressions for key geometrical properties of the bubble in terms of the Bond number. Results are in good overall agreement with experimental data and are consistent with fully numerical (Surface Evolver) calculations. In particular, we are able to describe how the bubble shape changes from hemispherical, with a flat, shallow bottom, to lenticular, with a deeper, curved bottom, as the Bond number is decreased.

What is the shape of an air bubble on a liquid surface?

We have calculated the equilibrium shape of the axially symmetric meniscus along which a spherical bubble contacts a flat liquid surface, by analytically integrating the Young-Laplace equation in the presence of gravity, in the limit of large Bond numbers. This method has the advantage that it provides semi-analytical expressions for key geometrical properties of the bubble in terms of the Bond number. Results are in good overall agreement with experimental data and are consistent with fully numerical (Surface Evolver) calculations. In particular, we are able to describe how the bubble shape changes from hemispherical, with a shallow flat bottom, to lenticular, with a deeper, curved bottom, as the Bond number is decreased.

Bubbly Flow Structure in Hydraulic Jump

In an open channel, a hydraulic jump is the rapid transition from super- to sub-critical flow associated with strong turbulence and air bubble entrainment in the mixing layer. New experiments were performed at relatively large Reynolds numbers using phase-detection probes. Some new signal analysis provided characteristic air-water time and length scales of the vortical structures advecting the air bubbles in the developing shear flow. An analysis of the longitudinal air-water flow structure suggested little bubble clustering in the mixing layer, although an interparticle arrival time analysis showed some preferential bubble clustering for small bubbles with chord times below 3 ms. Correlation analyses yielded longitudinal air-water time scales Txx*V1/d1 of about 0.8 in average. The transverse integral length scale Z/d1 of the eddies advecting entrained bubbles was typically between 0.25 and 0.4, irrespective of the inflow conditions within the range of the investigations. Overall the findings highlighted the complicated nature of the air-water flow

Turbulence in Hydraulic Jumps: Experimental Measurements

A hydraulic jump is the transition from a supercritical open channel flow to a subcritical regime. It is characterised by a highly turbulent flow with macro-scale vortices, some kinetic energy dissipation and a bubbly two-phase flow structure. New air-water flow measurements were performed in hydraulic jump flows for a range of inflow Froude numbers. The experiments were conducted in a large-size facility using two types of phase-detection intrusive probes: i.e., single-tip and double-tip conductivity probes. These were complemented by some measurements of free-surface fluctuations using ultrasonic displacement meters. The present study was focused on the turbulence characteristics of hydraulic jumps with partially-developed inflow conditions. The void fraction measurements showed the presence of an advective diffusion shear layer in which the void fractions profiles matched closely an analytical solution of the advective diffusion equation for air bubbles. The present results highlighted some influence of the inflow Froude number onto the air bubble entrainment process. At the largest Froude numbers, the advected air bubbles were more thoroughly dispersed vertically, and larger amount of air bubbles were detected in the turbulent shear layer. In the air-water mixing layer, the maximum void fraction and bubble count rate data showed some longitudinal decay function in the flow direction. Such trends were previously reported in the literature. The measurements of interfacial velocity and turbulence level distributions provided new information on the turbulent velocity field in the highly-aerated shear region. The present data suggested some longitudinal decay of the turbulence intensity. The velocity profiles tended to follow a wall jet flow pattern. The air–water turbulent time and length scales were deduced from some auto- and cross-correlation analyses based upon the method of CHANSON (2006,2007). The results provided the integral turbulent time and length scales of the eddy structures advecting the air bubbles in the developing shear layer. The experimental data showed that the auto-correlation time scale Txx was larger than the transverse cross-correlation time scale Txz. The integral turbulence length scale Lxz was a function of the inflow conditions, of the streamwise position (x-x1)/d1 and vertical elevation y/d1. Herein the dimensionless integral turbulent length scale Lxz/d1 was closely related to the inflow depth: i.e., Lxz/d1 = 0.2 to 0.8, with Lxz increasing towards the free-surface. The free-surface fluctuations measurements showed large turbulent fluctuations that reflected the dynamic, unsteady structure of the hydraulic jumps. A linear relationship was found between the normalized maximum free-surface fluctuation and the inflow Froude number.

Clustering Process Analysis in a Large-Size Dropshaft and in a Hydraulic Jump

Recent efforts in the characterization of air-water flows properties have included some clustering process analysis. A cluster of bubbles is defined as a group of two or more bubbles, with a distinct separation from other bubbles before and after the cluster. The present paper compares the results of clustering processes two hydraulic structures. That is, a large-size dropshaft and a hydraulic jump in a rectangular horizontal channel. The comparison highlighted some significant differences in clustering production and structures. Both dropshaft and hydraulic jump flows are complex turbulent shear flows, and some clustering index may provide some measure of the bubble-turbulence interactions and associated energy dissipation.

Experimental investigation of gravitational gas separation in an inclined annular channel

The oil industry uses gas separators in production wells as the free gas present in the suction of the pump reduces the pumping efficiency and pump lifetime. Therefore, free gas is one of the most important variables in the design of pumping systems. However, in the literature there is little information on these separators. It is the case of the inverted-shroud gravitational gas separator. It has an annular geometry due to the installation of a cylindrical container in between the well casing and pioduction pipe (tubing). The purpose of the present study is to understand the phenomenology and behavior of inverted-shroud separator. Experimental tests were performed in a 10.5-m-length inclinable glass tube with air and water as working fluids. The water flow rate was in the range of 8.265-26.117 l/min and the average inlet air mass flow rate was 1.1041 kg/h, with inclination angles of 15 degrees, 30 degrees, 45 degrees, 60 degrees, 75 degrees, 80 degrees and 85 degrees. One of the findings is that the length between the inner annular level and production pipe inlet is one of the most important design parameters and based on that a new criterion for total gas separation is proposed. We also found that the phenomenology of the studied separator is not directly dependent on the gas flow rate, but on the average velocity of the free surface flow generated inside the separator. Maps of efficiency of gas separation were plotted and showed that liquid flow rate, inclination angle and pressure difference between casing and production pipe outlet are the main variables related to the gas separation phenomenon. The new data can be used for the development of design tools aiming to the optimized project of the pumping system for oil production in directional wells. (C) 2012 Elsevier Inc. All rights reserved.

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 rectangular horizontal flume with partially-developed inflow conditions. The vertical distributions of void fraction and 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 provided.

Air-water flows down stepped chutes: turbulence and flow structure observations

Interactions between turbulent waters and atmosphere may lead to strong air-water mixing. This experimental study is focused on the flow down a staircase channel characterised by very strong flow aeration and turbulence. Interfacial aeration is characterised by strong air-water mixing extending down to the invert. The size of entrained bubbles and droplets extends over several orders of magnitude, and a significant number of bubble/droplet clusters was observed. Velocity and turbulence intensity measurements suggest high levels of turbulence across the entire air-water flow. The increase in turbulence levels, compared to single-phase flow situations, is proportional to the number of entrained particles. (C) 2002 Elsevier Science Ltd. All rights reserved.

Vacuum-induced bubble formation in liquid-tempered chocolate

Bubble inclusion is one of the fastest growing operations practiced in the food industry. A variety of aerated foods is currently available in supermarkets, and newer products are emerging all the time. This paper aims to combine knowledge on chocolate aeration with studies performed on bubble formation and dispersion characteristics. More specifically, we have investigated bubble formation induced by applying vacuum. Experimental methods to determine gas hold-up (volume fraction of air), bubble section distributions along specific planes, and chocolate rheological properties are presented. This study concludes that decreasing pressures elevate gas hold-up values due to an increase in the number of bubble nuclei being formed and release of a greater volume of dissolved gases. Furthermore, bubbles are observed to be larger at lower pressures for a set amount of gas because the internal pressure needs to be in equilibrium with the surrounding pressures. Temperature-induced changes to the properties of the chocolate have less of an effect on bubble formation. On the other hand, when different fats and emulsifiers are added to a standard chocolate recipe, milk fat was found to increase, significantly, the gas hold-up values and the mean bubble-section diameters. It is hypothesized that this behavior is related to the way milk fats, which contain different fatty acids to cocoa butter, crystallize and influence the setting properties of the final product. It is highlighted that apparent viscosity values at low shear rate, as well as setting behavior, play an important role in terms of bubble formation and entrainment.

Free-Surface Aeration and Momentum Exchange at a Bottom Outlet

This study aims to provide some new understanding of the air-water flow properties in high-velocity water jets discharging past an abrupt drop. Such a setup has been little studied to date despite the relevance to bottom outlets. Downstream of the step brink, the free-jet entrains air at both upper and lower air-water interfaces, as well as along the sides. An air-water shear layer develops at the lower nappe interface. At the lower nappe, the velocity redistribution was successfully modelled and the velocity field was found to be similar to that in two-dimensional wake flow. The results highlighted further two distinct flow regions. Close to the brink (Wex < 5000), the flow was dominated by momentum transfer. Further downstream (Wex > 5000), a strong competition between air bubble diffusion and momentum exchanges took place.

Two fluid numerical model for coastal applications

Wave breaking is an important coastal process, influencing hydro-morphodynamic processes such as turbulence generation and wave energy dissipation, run-up on the beach and overtopping of coastal defence structures. During breaking, waves are complex mixtures of air and water (“white water”) whose properties affect velocity and pressure fields in the vicinity of the free surface and, depending on the breaker characteristics, different mechanisms for air entrainment are usually observed. Several laboratory experiments have been performed to investigate the role of air bubbles in the wave breaking process (Chanson & Cummings, 1994, among others) and in wave loading on vertical wall (Oumeraci et al., 2001; Peregrine et al., 2006, among others), showing that the air phase is not negligible since the turbulent energy dissipation involves air-water mixture. The recent advancement of numerical models has given valuable insights in the knowledge of wave transformation and interaction with coastal structures. Among these models, some solve the RANS equations coupled with a free-surface tracking algorithm and describe velocity, pressure, turbulence and vorticity fields (Lara et al. 2006 a-b, Clementi et al., 2007). The single-phase numerical model, in which the constitutive equations are solved only for the liquid phase, neglects effects induced by air movement and trapped air bubbles in water. Numerical approximations at the free surface may induce errors in predicting breaking point and wave height and moreover, entrapped air bubbles and water splash in air are not properly represented. The aim of the present thesis is to develop a new two-phase model called COBRAS2 (stands for Cornell Breaking waves And Structures 2 phases), that is the enhancement of the single-phase code COBRAS0, originally developed at Cornell University (Lin & Liu, 1998). In the first part of the work, both fluids are considered as incompressible, while the second part will treat air compressibility modelling. The mathematical formulation and the numerical resolution of the governing equations of COBRAS2 are derived and some model-experiment comparisons are shown. In particular, validation tests are performed in order to prove model stability and accuracy. The simulation of the rising of a large air bubble in an otherwise quiescent water pool reveals the model capability to reproduce the process physics in a realistic way. Analytical solutions for stationary and internal waves are compared with corresponding numerical results, in order to test processes involving wide range of density difference. Waves induced by dam-break in different scenarios (on dry and wet beds, as well as on a ramp) are studied, focusing on the role of air as the medium in which the water wave propagates and on the numerical representation of bubble dynamics. Simulations of solitary and regular waves, characterized by both spilling and plunging breakers, are analyzed with comparisons with experimental data and other numerical model in order to investigate air influence on wave breaking mechanisms and underline model capability and accuracy. Finally, modelling of air compressibility is included in the new developed model and is validated, revealing an accurate reproduction of processes. Some preliminary tests on wave impact on vertical walls are performed: since air flow modelling allows to have a more realistic reproduction of breaking wave propagation, the dependence of wave breaker shapes and aeration characteristics on impact pressure values is studied and, on the basis of a qualitative comparison with experimental observations, the numerical simulations achieve good results.

Air bells of water spiders are an extended phenotype modified in response to gas composition

The water spider Argyroneta aquatica (Clerck) is the only spider that spends its whole life under water. Water spiders keep an air bubble around their body for breathing and build under-water air bells, which they use for shelter and raising offspring, digesting and consuming prey, moulting, depositing eggs and sperm, and copulating. It is unclear whether these bells are an important oxygen reservoir for breathing under water, or whether they serve mainly to create water-free space for feeding and reproduction. In this study, we manipulated the composition of the gas inside the bell of female water spiders to test whether they monitor the quality of this gas, and replenish oxygen if required. We exchanged the entire gas in the bell either with pure O(2), pure CO(2), or with ambient air as control, and monitored behavioural responses. The test spiders surfaced and replenished air more often in the CO(2) treatment than in the O(2) treatment, and they increased bell building behaviour. In addition to active oxygen regulation, they monitored and adjusted the bells by adding silk. These results show that water spiders use the air bell as an oxygen reservoir, and that it functions as an external lung, which renders it essential for living under water permanently. A. aquatica is the only animal that collects, transports, and stores air, and monitors its property for breathing, which is an adaptive response of a terrestrial animal to the colonization of an aquatic habitat. J. Exp. Zool. 307A:549-555, 2007. (c) 2007 Wiley-Liss, Inc.