On the drag force of bubbles in bubble swarms at intermediate and high Reynolds numbers

An accurate and fast simulation of large-scale gas/liquid contact apparatusses, such as bubble columns, is essential for the optimization and further development of many (bio)chemical and metallurgical processes. Since it is not feasible to simulate an entire industrial-scale bubble column in full detail from first principles (direct numerical simulations), higher-level models rely on algebraic closure relations to account for the most important physical phenomena prevailing at the smallest length and time scales, while keeping computational demands low. The most important closure for describing rising bubbles in a liquid is the closure for the drag force, since it dominates the terminal rise velocity of the bubbles.Due to the very high gas loadings used in many industrial processes, bubble–bubble (or ‘swarm’) interactions need to be accounted for in the drag closure. An advanced front-tracking model was employed, which can simulate bubble swarms up to 50% gas hold-up without the problem of (numerical) coalescence. The influence of the gas hold-up for mono-disperse bubble swarms with different bubble diameters (i.e. Eötvös numbers) was quantified in a single drag correlation valid for the intermediate to high Reynolds numbers regime . Also the physical properties of the liquid phase were varied, but the simulation results revealed that the drag force coefficient was independent of the Morton number. The newly developed correlation has been implemented in a larger-scale model, and the effect of the new drag closure on the hydrodynamics in a bubble column is investigated in a separate paper (Lau et al., this issue).     

Numerical simulations of bubble formation on submerged orifices: Period-1 and period-2 bubbling regimes

The process of bubble formation is involved in several gas-liquid reactors and process equipment. It is therefore important to understand the dynamics of bubble formation and to develop computational models for the accurate prediction of the bubble formation dynamics in different bubbling regimes. This work reports the numerical investigations of bubble formation on submerged orifices under constant inflow conditions. Numerical simulations of bubble formation at high gas flow rates, where the bubble formation is dominated by inertial forces, were carried out using the combined level set and volume-of-fluid (CLSVOF) method and the predictions were experimentally validated. Effects of gas flow rate and orifice diameter on the bubbling regimes and in particular, on the transition from period-1 to period-2 bubbling regime (with pairing or coalescence at the orifice) were investigated. Using the simulation data on the transition of bubble formation regimes, the bubble formation regime map constructed using Froude and Bond numbers is presented.     

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.     

Role of hydrodynamic flow parameters in lipase deactivation in bubble column reactor

The dynamic environment within the bioreactor and in the purification equipment is known to affect the activity and yield of enzyme production. In the present work, the effect of hydrodynamic flow parameters and τ_N,max) and interfacial flow parameters ( and ) on the activity of lipase has been comprehensively investigated in bubble column reactors. Lipase solution was subjected to hydrodynamic flow parameters in 0.15 and 0.385 m i.d. bubble column reactors over a wide range of superficial gas velocity (0.01<V_G<0.4-). The flow parameters were estimated using an in-house CFD simulation code based on k-ε approach. The extent of lipase deactivation in both the columns was found to increase with an increase in hydrodynamic and interfacial flow parameters. However, at equal value of any of these parameters, the extent of deactivation was different in the two columns. The rate of deactivation was found to follow first order kinetics. An attempt has been made to develop rational correlations for the extent of deactivation as well as for the deactivation constant. The rate of deactivation was found to be depending on the average turbulent normal stress and interfacial flow parameters such as bubble diameter and bubble rise velocity.     

The bubbling behavior of cohesive particles in the 2D fluidized beds

The present work focuses on a fully statistical analysis of bubbling behavior in the two-dimensional (2D) fluidized beds with cohesive particles. Various significant bubble properties such as bubble size, rising velocity, aspect ratio, bed expansion and bubble hold-up, etc., were investigated. An equation for bubble diameter is developed, , and the observed bubbles are generally smaller than the ones generated in the beds with A or B type powders. Both the average bubble size and rising velocity initially increase with the elevation above the distributor and keep constant beyond certain heights. The bubbles exhibit oblong with the most density aspect ratio (β) equal to 0.7. In addition, the bubble rising velocity coefficient ranges from 0.8 to 1.5. Two core-annular flows form in the large diameter, shallow fluidized bed used in this experiment.     

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.     

Effect of contaminants on mass transfer coefficients in bubble column and airlift contactors

In this work, the effects of surface-active contaminants on mass transfer coefficients k_La and k_L were studied in two different bubble contactors. The oxygen transfer coefficient, k_L, was obtained from the volumetric oxygen transfer coefficient, k_La, since the specific interfacial area, a, could be determined from the fractional gas holdup, ε, and the average bubble diameter, d₃₂. Water at different heights and antifoam solutions of 0.5- were used as working media, under varying gas sparging conditions, in small-scale bubble column and rectangular airlift contactors of 6.7 and capacity, respectively. Both the antifoam concentration and the bubble residence time were shown to control k_La and k_L values over a span of almost 400%. A theoretical interpretation is proposed based on modelling the kinetics of single bubble contamination, followed by sudden surface transition from mobile to rigid condition, in accordance with the stagnant cap model. Model results match experimental k_L data within ±30%.     

The effect of bubble column diameter on gas holdup in fiber suspensions

Three bubble column diameters (D=10.2, 15.2, and 32.1 cm) are employed to study the scale-up effect on gas holdup in air-water and air-water-cellulose fiber (hardwood, softwood, and BCTMP) systems. The effect of column diameter depends on flow regime and fiber mass fraction. When , gas holdup decreases with increasing column diameter for the transitional and heterogeneous flow regime, and column diameter effects are negligible in the homogeneous flow regime. When , gas holdup is only affected by column diameter in the transitional flow regime for an air-water system and low fiber mass fraction suspensions (C?0.25%); column diameter effects disappear at medium fiber mass fractions (e.g., C=0.8%) but are significant at high fiber mass fractions (e.g., C=1.4%).     

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.     

Spargers for controlled bubble size by means of the multiple slot disperser (MSD)

Sparging technology is crucial in the dispersion of gases in liquids. In this work, it was demonstrated that an effective, controllable sparger can be made by assembling an array of flat parallel slot-nozzles which may offer new options for sparger design and operation. To illustrate the technique, a compact, ‘multiple slot disperser’ (MSD) having a slot width of and a total slot length of 1.26 m was assembled from a series of 5-mm-thick graphite plates. In water containing a low concentration of frother, a dense three-dimensional bubble plume was produced. The MSD generated consistently narrow bubble size distributions with well-defined median bubble diameters in the range 2.6-3.1 mm, equivalent to a range of gas flow rate from 11 to 26 std l/min. The bubble sizes were readily predictable from established single slot bubble size correlations. The method of construction also allows for simple maintenance, repair and replacement of individual components as needed.     

Measurement of local specific interfacial area in bubble columns via a non-isokinetic withdrawal method coupled to electro-optical detector

Precise measurement of gas-liquid interfacial surface area is essential to reactor design and operation. Mass transfer from the gas phase to the liquid phase is often a key feature that controls the overall process. Measurement of gas-liquid interfacial area is often made through a separate measurement of the gas holdup and bubble size with complex and/or sophisticated methods. In this work, an inexpensive method is presented for the simultaneous determination of both local gas holdup and bubble diameter. The method is based on the withdrawal of the air-liquid dispersion under non-isokinetic conditions and on bubble counting via a simple optical device. The method was calibrated in a bubble column with several withdrawal pressures using coalescing and non-coalescing media. During the same calibration experiment, gas holdup was also measured manometrically and individual bubble diameters were measured by a photographic method. With a vacuum pressure of 3 kPa, local interfacial area measured with the withdrawal method produced a relative error below 13%, compared to the manometric/photographic method. The method was then used to characterize local specific interfacial area in a bubble column under several operating conditions with coalescing and non-coalescing media. In coalescing media and with superficial gas velocities (v_g) from 0.25 to 3.5 cm/s, the average interfacial area ranged from 17 to . With non-coalescing media the average interfacial area ranged from 40 to . Under the test condition it was observed that gas holdup is a parameter that has a greater distribution (standard deviation from 30% to 70%) than the volume-mean bubble diameter (standard deviation from 6% to 12%). It is shown that a model previously developed for characterizing gas holdup homogeneity is also suitable for characterizing interfacial area homogeneity.     

Gas back-mixing studies in membrane assisted bubbling fluidized beds

Fluidized beds employing fine powders are finding increased application in the chemical and petrochemical industry because of their excellent mass and heat transfer characteristics. However, in fluidized bed chemical reactors axial gas back mixing can strongly decrease the conversion and selectivity. By insertion of membranes in fluidized beds large improvements in conversion and selectivity can be achieved, firstly by optimizing axial concentration profiles via distributive feeding of one of the reactants or selective withdrawal of one of the products, and secondly, by decreasing the effective axial dispersion via compartmentalization of the fluidized bed. Moreover, insertion of membrane bundles in a suitable configuration impedes bubble growth, thereby reducing reactant by-pass via rapidly rising large bubbles. In this work the influence of the presence and configuration of membrane bundles and the effect of gas addition via the membranes on the effective axial dispersion was studied experimentally.Steady state concentration profiles were measured where a CO₂-tracer was injected at different locations through a probe (point injection) or via the membranes (line injection) into a square fluidized bed containing glass particles (75-, 2550 kg/m³) fluidized with nitrogen distributed via a porous plate. Different bed configurations, viz. without internals, with vertical or horizontal membrane bundles were investigated and the effects of overall fluidization velocity and gas flow ratio of gas fed through the membrane bundles and the porous plate distributor were studied.Experimental results revealed that the insertion of vertical and horizontal membrane bundles decreases the effective axial dispersion considerably compared to a bed without internals. The point injection experiments indicated the importance of a non-uniform lateral emulsion phase velocity profile. The line injection experiments clearly pointed out the importance of bubble-to-emulsion phase mass transfer limitations. Gas addition through the membrane bundles decreases the effective axial gas dispersion enormously by almost annihilating the solids down flow along the walls and by decreasing the average bubble size and bubble fraction.     

Hydrodynamics and mass transfer in an upward venturi/bubble column combination

The hydrodynamics and mass transfer characteristics of a venturi/bubble column combination were studied at high liquid superficial velocities of up to 0.35 m/s. The gas hold-up was increased by 50% to 150% and the overall volumetric mass transfer coefficient was tripled when the venturi was used as “gas distributor” instead of a porous distributor. A correlation of the overall volumetric mass transfer coefficient (K_La) with the gas hold-up, valid for gas hold-ups as high as 0.3, was proposed for the cylindrical bubble column section. The energy consumption per mole of oxygen transferred was lower than with most distributors and the oxygen transfer rate per unit of reactor volume was higher than in a bubble column with a porous distributor. The venturi/bubble column combination is a compact and efficient system which does not have the operating problems of systems which require internals.     

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.     

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.     

Mass transfer in sparged and stirred reactors: influence of carbon particles and electrolyte

Mass transfer in multiphase systems is one of the most studied topics in chemical engineering. However, in three-phase systems containing small particles, the mechanisms playing a role in the increased rate of mass transfer compared to two-phase systems without particles, are still not clear. Therefore, mass transfer measurements were carried out in a 2D slurry bubble column reactor , a stirred tank reactor with a flat gas-liquid interface, and in a stirred tank reactor with a gas inducing impeller. The rate of mass transfer in these reactors was investigated with various concentrations of active carbon particles (average particle size of ), with electrolyte (sodium gluconate), and with combinations of these. In the bubble column, high-speed video recordings were captured from which the bubble size distribution and the specific bubble area were determined. In this way, the specific mass transfer area a_gl was determined separately from the mass transfer coefficient k_l. Mechanisms proposed in literature to describe mass transfer and mass transfer enhancement in stirred tank reactors and bubble columns are compared. It is shown that the increased rates of mass transfer in the 2D bubble column and in the stirred tank reactor with the gas inducing impeller are completely caused by an increased gas-liquid interfacial area upon addition of carbon particles and electrolyte. It is suggested that an increased level of turbulence at the gas-liquid interface caused by carbon particles accounts for a smaller effective boundary layer thickness and an enhancement of mass transfer in the flat gas-liquid surface stirred tank reactor. However, for the carbon particles used in this study, it is rather unlikely that mass transfer enhancement takes place due to the well-known shuttle or grazing effect.     

Gas hold-up, mixing time and gas-liquid volumetric mass transfer coefficient of various multiple-impeller configurations: Rushton turbine, pitched blade and techmix impeller and their combinations

Gas hold-up, mixing intensity of dispersion characterised by exchange flows between adjacent impellers and a volumetric mass transfer coefficient are presented for 18 impeller configurations in triple-impeller vessel of inner diameter . Rushton Turbines, six Pitched Blade impellers pumping down and hydrofoil impellers Techmix 335 (Techmix co., Czech republic) pumping up or down and their combinations were used. aqueous solution was used as a liquid phase, which represents non-coalescent batches. Gas hold-ups and volumetric mass transfer coefficients are presented for individual configurations as functions of specific power dissipated and superficial gas velocity. The regression of the mass transfer coefficients shows large standard deviation (30%). The power number included to the regression to express the impeller configuration effect did not improve the standard deviation significantly (23%). The impeller configurations with low power number (less than unity) provide higher dispersion mixing intensities, while the impeller configurations with high power number provide better mass transfer performance.     

Effect of fiber length distribution on gas holdup in a cocurrent air-water-fiber bubble column

An experimental investigation is reported on the effect of fiber length distribution on gas holdup in a cocurrent air-water-fiber bubble column. Different combinations of 1 and 3 mm Rayon fibers are used to simulate different fiber length distributions. At a constant total fiber mass fraction, gas holdup generally decreases with increasing mass fraction of the 3 mm Rayon fiber while other conditions remain constant. Crowding factors estimated using four different methods (N_c=N_c,A, , N_c,L, and N_c,M) and the parameters and are tested on their performance to quantify the overall effects of fiber mass fraction and fiber length and its distribution on gas holdup. and provide the best characterization of the fiber effects on gas holdup in the cocurrent air-water-fiber bubble column. The crowding factor estimated using the model-based average fiber length (N_c,M) also provides a good characterization and is better than the other crowding factor definitions.