Bubble size effect on low liquid input drift-flux parameters

We investigated the effect of bubble size on the drift-flux parameters at low liquid flow conditions by measuring the radial profiles of void fraction and phase velocities in a vertical bubbly pipe flow of diameter and height . To study the effect of the bubble size we used two different types of bubble inlets. We measured the local bubble fraction and velocity U_g by using single and four-point-optical fibre probes, and we used Laser Doppler Anemometry to determine the liquid velocity U_l. The distribution parameter C₀ and the weighted mean drift velocity |U_drift| were directly computed from the local measurements at a height on our experimental set-up. Both parameters were influenced by the bubble size. Provided no liquid flow reversal occurred at the near wall region, the distribution parameter reached a below unity minimum plateau value of C₀=0.95 for wall peaking void fraction profiles. At low liquid input conditions both the liquid input and bubble size had an influence on the distribution parameter. Extreme values such as C₀>2 were measured. From these measurements we developed models for the drift-flux parameters to take into account the effect of bubble size and input-flow conditions for our intermediate pipe diameter value. These models were tested and validated with separately collected experimental data.     

Flow patterns in the wake of a Taylor bubble rising through vertical columns of stagnant and flowing Newtonian liquids: An experimental study

The flow in the wake and near-wake regions of individual Taylor bubbles rising through stagnant and co-current vertical columns of Newtonian liquids was studied, employing simultaneously particle image velocimetry (PIV) and pulsed shadowgraphy techniques (PST). Experiments were made with water and aqueous glycerol solutions covering a wide range of viscosities , in an acrylic column of 32 mm ID.Different wake structures (laminar, transitional and turbulent) are identified, in both stagnant and co-current flow conditions. In stagnant liquids, the wake flow pattern is only dependent on the dimensionless group N_f. The different types of wakes obtained are in accordance with the critical N_f numbers proposed in previous works. For co-current flow conditions, the flow patterns in the wake depend on the Reynolds number based on the relative (to the bubble) average velocity of the upward liquid flow, the laminar-transitional and transitional-turbulent limits being for the first time experimentally determined.The wake flow patterns are quantified by means of instantaneous and average flow fields. Values for the wake length and wake volume are also presented and compare well with correlations found in literature. Study of the flow in the near-wake zone enabled determination of the distance needed to recover the undisturbed liquid velocity profile.The detailed study of the flow in the wake and near-wake regions is an important contribution to better understanding the interaction and coalescence mechanisms between Taylor bubbles.The data reported are relevant to the validation of numerical simulation codes in the vertical slug flow regime.     

Hydrodynamics and steel tube wastage in a fluidized bed at elevated temperature

Hydrodynamic measurements were made in a bubbling fluidized bed operated at 550°C at three different excess gas velocities (0.15, 0.40 and ). The bed has a cross-sectional area of with an immersed tube bank consisting of 59 horizontal stainless steel tubes (AISI 304L), 21 of which are exchangeable, thus allowing erosion studies. Capacitance probe analysis was used to determine the mean bubble rise velocity, the mean bubble frequency, the mean pierced bubble length, the mean bubble volume fraction and the mean visible bubble flow rate. Tube wastage was calculated from roundness profiles obtained by stylus profilometry.A redistribution of the bubble flow towards the center of the bed occurs when the excess gas velocity is increased. Measurements along a target tube, situated next to the capacitance probe, usually show greater material wastage at the central part of the tube, since the mean bubble rise velocity and the mean visible bubble flow rate are higher there. It is suggested that the greater material degradation is also an effect of the through-flow of a particle-transporting gas stream in the bubbles. With increasing height above the distributor plate the circumferential wastage profiles for the lowest excess gas velocity show a gradual change from an erosion pattern with one maximum (Type B behavior) to a pattern with two maxima (Type A behavior). Power spectral density distributions of the fluctuating pressure signals show that this is a result of the formation of larger bubbles, when the fluidization regime is changed in the upper part of the bed. At the highest excess gas velocity the bubble flow becomes more constrained due to a more rapid coalescence of the bubbles and the tubes show Type A wastage profiles throughout the bed.     

On the formation of Taylor bubbles in small tubes

The formation of Taylor bubbles and resulting bubble lengths were studied in a ID vertical tube for air-water and air-octane systems. In the co-flow tube/nozzle arrangement two nozzle sizes were used as gas inlets. Superficial velocities varied between 0.001- for the liquid and 0.002- for the gas. Three different mechanisms of initial bubble formation were observed. Of the three mechanisms, mechanism 3 is periodic (with period consisting of a bubble and a liquid slug), reproducible and can be simply modelled. After initial bubble formation further modifications may occur in the formed bubble size by coalescence or pairing. Bubble pairing is encouraged by smaller nozzles and liquid flow rates, while coalescence is observed only for cases where non-Taylor bubbles form initially.Two simple models have been proposed, the first predicts the size of the Taylor bubbles formed by mechanism 3 while the second attempts to predict the condition for bubble pairing to occur. Reasonable agreement with experimental results validates the predictions of the first model for a strong dependence of the volume of Taylor bubbles formed on the gas and liquid flow rates, a moderate dependence on nozzle diameter and a weak dependence (if at all) on the surface tension of the liquid used. Mismatch with the experimental results is caused (at least in part) by the experimental setup where there was no perfect axial alignment of the gas inlet. The experiments also suffered from problems at the outlet at low flow rates where smooth bubble disengagement could not be ensured for long Taylor bubbles. The second model for pairing predicts its occurrence for concentric tube/nozzle arrangements as a function of flow rates and channel diameters. The model over-predicted the range of liquid flow rates at which pairing was observed experimentally, but it captured the form of the boundary between different bubble volume modification mechanisms when represented on superficial velocity graphs.     

Analytical and numerical evaluation of two-fluid model solutions for laminar fully developed bubbly two-phase flows

An analysis of the two-fluid model in the case of vertical fully developed laminar bubbly flows is conducted. Firstly the phase distribution in the central region of the pipe (where wall effects vanish) is considered. From the model equations an intrinsic length scale L is deduced such that the scaled system reduces to a single equation without parameters. With the aid of this equation some generic properties of the solutions of the model for pipes with diameter greater than about 20L (the usual case, since L is of the order of the bubble radius) are found. We prove that in all physically meaningful solutions an (almost) exact compensation of the applied pressure gradient with the hydrostatic force occurs (with ρ_eff the effective density and the gravity). This compensation implies flat void fraction and velocity profiles in the central region not affected by the wall, even when no turbulence effects are accounted for.We then turn to consider the complete problem with a numerical approach, with the effect of the wall dealt via wall forces. The previous mathematical results are confirmed and the near-wall phase distributions and velocity profiles are found. With the numerical code it is also possible to investigate the regime in which the pressure gradient is greater than the weight of the pure liquid, in which case a region of strictly zero void fraction develops surrounding the axis of the pipe (in upward flow of bubbles).Finally, the same code is used to study the effect of reducing the gravity. As decreases, so does the relative velocity between the phases, making the lift force increasingly dominant. This produces, in upward bubbly flows, narrower and sharper void fraction peaks that also appear closer to the wall.     

Physical modelling and similitude of air bubble entrainment at vertical circular plunging jets

When a plunging jet impinges into a pool of liquid, air bubble entrainment takes place if the inflow velocity exceeds a threshold velocity. This study investigates air entrainment and bubble dispersion in the developing flow region of vertical circular plunging jets. Three scale models were used and detailed air-water measurements (void fraction, bubble count rate, bubble sizes) were performed systematically for identical inflow Froude numbers. The results highlight that the modelling of plunging jet based upon a Froude similitude is affected by significant scale effects when the approach flow conditions satisfied We₁<1E+3, while some lesser scale effect was noticed for V₁/u_r<10 and We₁>1E+3. Bubble chord time measurements showed pseudo-chord sizes of entrained bubbles ranging from less than to more than with an average pseudo-chord size were between 4 and . However, bubble size data could not be scaled properly.     

Evolution of hydrodynamic and statistical parameters of gas-liquid slug flow along inclined pipes

The development of slug flow along two long inclined pipes (2-90° from the horizontal) with internal diameters of 0.024 and was measured by three optical fiber probes. The probes were located in a measurement module at axial distances of between the fiber tips. To measure the evolution of slug flow, the module was placed at different positions along the pipe. Instantaneous elongated bubble velocities and corresponding elongated bubble and liquid slug lengths were determined by processing the optical probe signals. The evolution of the liquid slug and elongated bubble length distributions along the pipes is characterized by a gradual growth of the mean and mode values. The growth rate decreases with decreasing inclination. Mean elongated bubble lengths have a minimum at about 60°, while mean liquid slug lengths decrease slowly with decreasing inclination angle. The coalescence rate, defined as the decrease in the ensemble size, becomes almost negligible at x/D>60, independent of pipe diameter, flow rates and inclination angle. The slug frequency has a maximum at about 60° inclination.     

Effect of gas expansion on the velocity of individual Taylor bubbles rising in vertical columns with water: Experimental studies at atmospheric pressure and under vacuum

This study was designed to determine the effect of gas expansion on the velocity of Taylor bubbles rising individually in a vertical column of water. This experimental study was conducted at atmospheric pressure or under vacuum (33.3 and ) using three different acrylic columns with internal diameters of 0.022, 0.032, and 0.052 m, and more than 4.0 m high. A non-intrusive optical method was used to measure velocity and length of Taylor bubbles at five different locations along the columns. The operating conditions used correspond to inertial controlled regime.In experiments performed under vacuum, there is considerable gas expansion during the rise of Taylor bubbles, particularly when they approach the liquid free surface where the pressure drop (due to the hydrostatic pressure) is of the order of magnitude of the absolute pressure. The liquid ahead of the bubble is displaced upward by an amount proportional to the gas expansion resulting in increased bubble velocity. The calculated Reynolds number suggests a laminar regime in the liquid ahead of the bubble. However, the experimentally determined velocity coefficient C for each column was much smaller than 2, which would be expected for laminar flow. The value of C obtained ranges from 1.13±0.09, for the narrowest column, to 1.40±0.24, for the widest column. This suggests that a fully developed laminar flow in the liquid ahead of the bubble is never achieved due to continuous bubble expansion at a variable rate, regardless of column height.The velocity coefficient C can be used to calculate the contribution of liquid motion to bubble velocity. Subtracting this contribution from the measured bubble velocity defines a constant value which is nearly identical to the bubble rise velocity measured in the same column operated as a constant volume system (two ends closed) where gas expansion is absent.     

On the effect of liquid temperature upon bubble coalescence

An experimental study concerning the influence of liquid temperature on bubble coalescence is presented. Bubble collisions in two different liquids (water and ethanol) were analysed at four distinct temperatures , using air as the dispersed phase in all cases. A quantitative criterion was developed to compute the critical velocity for bubble coalescence based on the relative velocities and the outcome (coalescence or bouncing) of the recorded collisions. The critical velocity, and consequently bubble coalescence, was shown to increase as the liquid temperature was raised, an effect whose intensity depended on the kind of liquid employed. Using some simplifying assumptions, a comparison between the experimentally observed trends and the predictions of literature models for the film drainage was drawn. The experimental data were used together with available literature data in the development of a dimensionless correlation for predicting the critical velocity as a function of the liquid properties.     

CFD simulations of mass transfer from Taylor bubbles rising in circular capillaries

Computational Fluid Dynamics (CFD) is used to investigate mass transfer from Taylor bubbles to the liquid phase in circular capillaries. The liquid phase volumetric mass transfer coefficient k_La was determined from CFD simulations of Taylor bubbles in upflow, using periodic boundary conditions. The separate influences of the bubble rise velocity, unit cell length, film thickness, film length, and liquid diffusivity on k_La were investigated for capillaries of 1.5, 2 and diameter. The mass transfer from the Taylor bubble is the sum of the contributions of the two bubble caps, and the film surrounding the bubble. The Higbie penetration model is used to describe the mass transfer from the two hemispherical caps. The unsteady-state diffusion model of Pigford is used to describe the mass transfer to the downward flowing liquid film. The developed model for k_La is in good agreement with the CFD simulated values, and provides a practical method for estimating mass transfer coefficients in monolith reactors.     

Effect of inclination on circumferential film thickness variation in annular gas/liquid flow

Time-varying, circumferentially local liquid film thickness data have been collected on a 38 mm internal diameter pipe at inclinations of 0^°, 30^°, 45^°, 60^° and 85^° from the horizontal using flush-mounted and parallel wire conductance probes. Analysis of these data permits time-averaged thicknesses, probability density functions, and power spectral densities to be determined. Results show that the distribution of the liquid film is not symmetrical with thicker films on the lower part of the pipe, which are dominated by large disturbance waves. Moreover, as the inclination angle deviates from horizontal, the film thickness distribution becomes systematically less asymmetric. The probability density functions show a strong narrow peak where the liquid film is less disturbed by the presence of waves. The power spectra show that a large portion of wave energy at the bottom is carried by waves of frequency . There is no influence of liquid velocity on the shape of the spectra. However, the dominant frequency appears to decrease with increasing liquid flow rate. The frequency of the disturbance waves at the bottom decreases with increasing inclination. Moreover, the spectra tend to flatten out with increasing inclination, due to the more uniform distribution of energy among waves of a broad frequency range.     

Liquid mixing in gas-liquid two-phase flow by meandering microchannels

The influence of the channel radius on the mass transfer in rectangular meandering microchannels (width and height of ) has been investigated for gas-liquid flow. Laser induced velocimetry measurements have been compared with theoretical results. The symmetrical velocity profile, known from the straight channel, was found to change to an asymmetrical one for the meandering channel configuration. The changes in the secondary velocity profile lead to an enhanced radial mass transfer inside the liquid slug, resulting in a reduced mixing length. In the investigated experimental range (superficial gas velocity and superficial liquid velocity ) the mixing time was reduced eightfold solely due to changes in channel geometry. An experimental study on the liquid slug lengths, the pressure drop and their relation to the mass transfer have also been performed. Experimental results were validated by a simulation done in Comsol Multiphysics^®. To obtain information for higher velocity rates, simulations were performed up to . These velocity variations in the simulation indicate the occurrence of a different flow pattern for high velocities, leading to further mass transfer intensification.     

Modeling of bubble coalescence in bubbly co-current flows restricted by confined geometry

Principles of kinetic theory are used to model the coalescence of bubbles in horizontal and vertical upflows where bubble movements are restricted by channel geometry. There are four critical variables that determine the rate at which a swarm of small bubbles will coalesce: the initial bubble population, the average initial bubble diameter, the average relative velocity of the bubbles, and the efficiency of bubble collisions. A model based on dimensional considerations is proposed to predict bubble size as a function of flow position. This model agrees well with experimental results for air/water and air/water/glycerin systems performed in a rectangular channel with an aspect ratio of 12.5 and a cross-sectional area of under both vertical and horizontal orientations.     

Influence of the lift force in direct numerical simulation of upward/downward turbulent channel flow laden with surfactant contaminated microbubbles

In this work, we employ direct numerical simulation of turbulence one-way coupled to Lagrangian tracking to investigate microbubble distribution in upward and downward channel flow. We consider a closed channel flow at Re_τ=150 and a dispersion of microbubbles characterized by a diameter of . Bubbles are assumed contaminated by surfactants (i.e., no-slip condition at bubble surface) and are subject to drag, gravity, pressure gradient forces, Basset history force and aerodynamic lift.Our results confirm previous findings and show that microbubble dispersion in the wall region is dominated by the action of gravity combined with the lift force. Specifically, in upward flow, bubble rising velocity in the wall region generates a lift force which pushes bubbles to the wall. In downward flow, bubble rising velocity against the fluid generates a lift force which prevents microbubbles from reaching the viscous sublayer.In the wall region, we observe bubble preferential segregation in high-speed regions in the downflow case, and non-preferential distribution in the upflow case. This phenomenon is related to the effect of the lift force. Compared to experiments, the current lift force model produces larger consequences, this effect being overemphasized in the upflow case in which a large number of bubbles is segregated near the wall. In this case, the resulting bubble wall-peak of concentration outranges experimental results.These results, so deeply related to the lift force, underline the crucial role of current understanding of the fluid forces acting on bubbles and help to formulate questions about available force models, bubble-bubble interactions and two-way coupling which can be crucial for accurate predictions in the region very near the wall.     

Bubble-wall interactions in a vertical gas-liquid flow: Bouncing, sliding and bubble deformations

The paper presents the results of a study on the motion of single (individual) bubbles rising in upward shear liquid flow in the vicinity of a vertical wall. Bubbles were found to slide along the wall when their diameter is small. Bubbles could also experience multiple collisions with the wall at certain experimental parameters (geometry of a channel, range of superficial liquid velocity, bubble size, etc). The latter was theoretically predicted by solving the equation of the bubble motion for the lateral direction in the boundary layer of the channel. For this, constitutive models available in the literature for the interfacial forces acting on a bubble in the vicinity of the wall were used. A simplified 1D model predicting bubble lateral displacement near the wall and taking into account the balance of drag and non-drag forces acting on a bubble was proposed. The numerical results were verified against the experimental ones obtained by non-intrusive high-speed video observations and subsequent image processing.The experiments on the bubble motion were conducted in a vertical acrylic duct having a square cross-section of and a height of approximately 1.3 m. Desalinated water and air both taken at room temperature were used in the experiments. All measurements on the bubble motion were performed at channel heights between 0.8 and 1 m above the gas injection point.     

Coalescence during bubble formation at two neighbouring pores: An experimental study in microscopic scale

This work studies the effect of the liquid properties and the operating conditions on the interactions between under-formation bubbles in a cell equipped with two adjacent micro-tubes (i.d. ) for the gas injection, placed 210, 700 and apart. This set-up simulates, though in a simplified manner, the operation of the porous sparger in a bubble column, and it is used to study the bubble interactions observed on the sparger surface. Various liquids covering a wide range of surface tension and viscosity values are employed, while the gas phase is atmospheric air. A fast video recording technique is used both for the visual observations of the phenomena occurring onto the tubes and for the bubble size measurements. The experiments reveal that the interactions between under-formation bubbles as well as the coalescence time depend strongly on the liquid properties, the distance between the tubes and the gas flow rate. Two correlations, which can be found helpful for the bubble column design, have also been formulated and are in good agreement with the available experimental data.     

Oxygen transfer prediction in aeration tanks using CFD

In order to optimize aeration in the activated sludge processes, an experimentally validated numerical tool, based on computational fluid dynamics and able to predict flow and oxygen transfer characteristics in aeration tanks equipped with fine bubble diffusers and axial slow speed mixers, is proposed. For four different aeration tanks (1;1493;8191 and ), this tool allows to precisely reproduce experimental results in terms of axial liquid velocities, local gas hold-ups. Predicted oxygen transfer coefficients are within ±5% of experimental results for different operating conditions (varying pumping flow rates of the mixers and air flow rates). The actual bubble size must be known with precision in order to have a reliable estimation of the oxygen transfer coefficients.     

Modelling the effect of liquid motion on bubble nucleation during beer dispense

Beer dispense involves ejecting supersaturated beer under gas pressure, from a nozzle into a receiving vessel. Bubble nucleation therefore occurs in a flowing liquid. This situation is encountered in other processes, but is not accounted for in current nucleation models. An experimental system was developed to measure bubble production rates and sizes in laboratory scale beer dispense. Experimental results indicate that bubble nucleation is affected by both liquid flow rate and dissolved gas composition. Pre-existing gas nuclei models have been adapted using bubble and droplet detachment models to include the effect of liquid motion and gas composition. The adapted nucleation models were compared to the experimental results. Predicted bubble detachment radii and overall nucleation rates were affected by liquid flow rate, direction of liquid flow, dissolved gas composition, the contact radius and the level of contact angle hysteresis. Accurate predictions were achieved for different surface orientations and liquid flow directions. Accurate predictions occurred at hysteresis levels of 3.5°, 7.5° and 20° for liquid flow rates of 0.6, 2.2 and , respectively. It is clear that the predicted overall nucleation rate however, also depended on the number of nucleation sites and how many of these were active; although values for these parameters were not experimentally determined in this case. Further understanding of the exact number and size of nucleation sites available and the contact angle for the particular combination of liquid and solid used is required to improve the fit of the model to the experimental data.     

Validation of bubble breakage, coalescence and mass transfer models for gas-liquid dispersion in agitated vessel

Bubble breakage and coalescence phenomena and multicomponent gas-liquid mass transfer were studied in a Rushton turbine agitated vessel. Local bubble size distributions (BSD) were measured from air-tap water system at several agitation conditions with capillary suction probe (CSP) technique. The CSP was compared to the digital imaging (DI) and phase Doppler anemometry (PDA) techniques in a stirred vessel. The volumetric BSDs between the CSP and DI were in agreement, but number BSDs showed notable deviation. The limitations of measurement techniques seem to be the main reason.A multiblock stirred tank model with discretized population balances for bubbles and two-film Maxwell-Stefan multicomponent mass transfer between gas and liquid was created for the agitated vessel. The model considers local mass transfer conditions in the vessel and is simple enough for the mathematical optimization of unknown model parameters. Unknown parameters in the mechanistic bubble breakage and coalescence models were fitted against measured local BSDs. After this, a parameter in the liquid film mass transfer correlation was adjusted against absorption and desorption experiments of oxygen. Local gas-liquid mass transfer areas were calculated from the population balance model. The simulations with the validated models show good agreement against experiments. On the other hand, the fitted parameters deviate from the theoretical values, which emphasizes the need of model validation against accurate experiments. Due to their fundamental character and the validation process, the fitted models seem to be useful tools for the design and scale-up of agitated gas-liquid reactors.     

Numerical and experimental investigations of gas-liquid dispersion in an ejector

The effects of the ejector geometry (nozzle diameter and mixing chamber) and the operating conditions (liquid circulating rate, liquid level in column) on the hydraulic characteristics in a rectangular bubble column with a horizontal flow ejector were determined. The gas phase holdup increases with increasing liquid circulating rate but decreases with increasing liquid level in the column. In the multiphase CFD simulation with the mixture model and the experiments, the gas suction rate increases with increasing liquid circulating rate. However, the gas suction rate decreases with increasing the liquid level in the column and nozzle diameter. The predicted values from the CFD simulation are well accord to the experimental data.