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.     

Bubble sizes in agitated solvent/reactant mixtures used in heterogeneous catalytic hydrogenation of 2-butyne-1,4-diol

Catalytic hydrogenations reactions are frequently conducted in “dead-end” multiphase stirred reactors with the reactant dissolved either in an alcohol, or in water or a mixture of the two. In such systems, the rate of gas-liquid mass transfer, which depends on bubble size, may well be the overall rate-limiting step. However, a study of bubble sizes across the whole range of solvent compositions from entirely water to entirely organic has not been reported. Here, for the first time, a systematic investigation has been made in a 3 L, closed vessel simulating a “dead-end” reactor containing 1% by volume of air which is dispersed by a Rushton turbine in water, isopropanol (IPA) and mixtures of the two, with and without 2-butyne-1,4-diol simulating a reactant. Mean specific energy dissipation rates, , up to have been used and bubbles size distributions and mean size were measured using a video-microscope-computer technique. In the single component solvents (water, ; IPA, though the interfacial tensions are very different, irregular, relatively large bubbles of similar sizes were observed ( in IPA, and in water) with a wide size distribution. In the mixed aqueous/organic solvents, and especially at the lower concentrations of IPA (1%, 5%, 10%), the bubbles were spherical, much smaller (d₃₂ from 50 to ) with a narrow size distribution. The addition of the reactant (0.2 M 2-butyne-1,4-diol) to the mixed solvents had little effect on the mean size, shape or distribution. However, addition to water (thus producing a mixed aqueous/organic liquid phase) led to small spherical bubbles of narrow size distribution. Neither Weber number nor surface tension was suitable for correlating bubble sizes since σ decreased steadily from pure water to IPA whilst bubble size passed through a minimum at around 5% IPA. For any particular fluid composition, the functionality between d₃₂ and was similar, i.e. . The above observations are explained in terms of the polarisation of bubble surfaces in miscible mixed aqueous/organic liquids caused by preferential directional adsorption at low concentrations of the organic component with its hydrophilic part directed into the aqueous phase and its hydrophobic part into the gas phase. As a result, coalescence is heavily suppressed in the low-concentration miscible alcohol (or diol)/aqueous systems whilst strong coalescence dominates bubble sizes in water and the alcohol and at high concentrations of the latter.     

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.     

Chaos in bubbling—nonlinear analysis and modelling

In the present paper, nonlinear features and analytical results for the chaotic bubbling from a submerged orifice are described. A chain of air bubbles was produced from the single orifice of in diameter and micro-convection induced by the bubble generation was recorded using hot-probe anemometer located close to the orifice. The air flow rate was varied widely from q=100 to and the aspects of bubbling were observed by high-speed video. The nonlinear analysis is performed for the time series data of hot-probe anemometer especially in the range of q=435-. The calculated largest Lyapunov exponent shows that with increase of air volume flow rate, the time period for the process of liquid flow to lose stability becomes shorter and at high air flow rate such as , it is shorter than the time period between subsequent bubbles. To explain such chaotic behaviors of bubbling, a simple model has been proposed. The model simulates the process of interaction between the elastic bubble wall and liquid. Simulation results compared well with the analytical results of experimental data. Summarizing, it is concluded that one of the reasons for chaos appearance is the nonlinear character of interaction between an elastic bubble wall and the liquid stream.     

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.     

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.     

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.     

Axial dispersion of particles in a slugging column—the role of the laminar wake of the bubbles

Axial solid dispersion promoted by Taylor bubbles in a batch liquid column was studied. A mechanistic model was developed to predict the axial solid dispersion. The model is based on the upward transport of particles inside closed wakes of non-interacting Taylor bubbles. The model predictions are compared with experimental data. The experimental data were obtained in a test tube of internal diameter. The particle volumetric distribution was measured by several differential pressure transducers placed along the column. Two classes of glass beads, mean diameter 180 and , were suspended in aqueous glycerol solutions, with glycerol percentage ranging from 40% (v/v) to 100% (v/v). The amount of particles in the column was such that the volumetric particle fractions were 0.1, 0.2 and 0.3, supposing homogeneous liquid-solid suspension. The air flow rate ranged from 90×10⁻⁶ to at PTN conditions. The obtained experimental data are in good agreement with the model predictions for laminar wakes, i.e., closed wakes with internal recirculation and without vortex shedding. The experimental data show a higher upward particle transport for wakes in the transition laminar-turbulent regime; closed wakes with internal recirculation and vortex shedding. The upward particle transport is higher for increasing air flow rate, decreasing particle diameter and increasing amount of particles in the column.     

Flow regimes and gas holdup in paper pulp-water-gas three-phase slurry flow

Hydrodynamic flow characteristics of solid-liquid-gas slurry made by intimately mixing fibrous paper pulp with water and air were investigated in a short, vertical circular column. The pulp consistency (weight fraction of pulp in the pulp-water mixture) was varied in the low consistency range of 0.0-1.5%. The test section was long, with inner diameter. Mixing of the slurry prior to entering the test section was done using a patented mixer with controlled cavitation that generated finely dispersed micro-bubbles.Flow structures, gas holdup, and the geometric and population characteristics of gas bubbles in the gas-pulp-liquid three-phase flow were experimentally investigated, using visual observation, Gamma-ray densitometry, and flash X-ray photography. Superficial velocities of the gas and liquid/pulp mixture covered the ranges 0- and 21-, respectively.Five distinct flow regimes could be visually identified. These included dispersed bubbly, characterized by isolated micro-bubbles entrapped in fiber networks; layered bubbly, characterized by bubbles rising in a low consistency annular zone near the channel wall; plug; churn-turbulent; and slug. The dispersed and layered bubbly regimes could be maintained only at very low gas superficial velocities or gas holdups. Flow regime maps were constructed using phasic superficial velocities as coordinates, and the regime transition lines were found to be sensitive to consistency.The cross section-average gas holdup data showed that both the dispersed and the layered bubbly regimes could best be represented by the homogeneous mixture model. The drift flux model could best be applied to the reminder of the data when the plug and churn-turbulent flow regimes were treated together, and the slug flow was treated separately. The drift flux parameters depended on the pulp consistency.     

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.     

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.     

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.