Gas entrainment by a liquid film falling around a stationary Taylor bubble in a vertical tube

Gas entrainment by a liquid film falling around a stationary Taylor bubble in a 0.1 m diameter vertical tube is studied experimentally with the purpose of validating a model formulated in an earlier phase of our research. According to this model for a fixed liquid velocity the gas entrainment should be proportional to the waviness of the film (its intermittency) and the wave height and inversely proportional to the film thickness. For Taylor bubble lengths ranging from 1D to 15D these film parameters have been measured with a Laser Induced Fluorescence technique. The gas entrainment has been determined from the net gas flux into the liquid column underneath the Taylor bubble by using data on gas re-coalescence into the rear of the Taylor bubble. These data are available for lengths ranging from 4.5D to 9D. The model results with the measured film characteristics compare well with the observed gas entrainment. The fact that the net gas flux becomes constant for long Taylor bubbles, whereas the wave height still increases, warrants further study.     

A numerical study of weak shock wave propagation in a reactive bubbly liquid

A numerical study is presented on the response of a weakly shock compressed liquid column that contains reactive gas bubbles. Both the liquid and gas are considered compressible. Compressibility of the liquid allows calculation of shock and rarefaction waves in the pure liquid as well as in the gas/liquid mixture. A microscopic model for local bubble collapse is coupled with a macroscopic model of wave propagation through the gas/liquid mixture. In the particular cases presented here, the characteristic times of propagation of the shock wave and bubble collapse are of the same order of magnitude. Consequently, the coupling between various phenomena is very strong. The present model based on fundamental principles of two-phase fluid mechanics takes into account the coupling of localized bubble oscillations. This model is composed of a microscopic one in the scale of a bubble size, and a macroscopic one which is based on the mixture theory. The liquid under study is water, and the gas is a reactive mixture of argon, hydrogen and oxygen. Received 18 December 1995 / Accepted 2 June 1996     

SVR-based prediction of point gas hold-up for bubble column reactor through recurrence quantification analysis of LDA time-series

Recurrence quantification analysis (RQA) has emerged as a useful tool for detecting singularities in non-stationary time-series data. In this paper, we use RQA to analyze the velocity–time data acquired using laser doppler anemometry (LDA) signals in a bubble column reactor for Single point and Multipoint point spargers. The recurring dynamical states within the velocity–time-series occurring due to the bubble and the liquid passage at the point of measurement, are quantified by RQA features (namely % Recurrence, % Determinism, % Laminarity and Entropy), which in turn are regressed using support vector regression (SVR) to predict the point gas hold-up values. It has been shown that SVR-based model for the bubble column reactor can be potentially useful for online prediction and monitoring of the point gas hold-up for different sparging conditions.     

Eulerian–Lagrangian 3-D simulations of unsteady two-phase gas–liquid flow in a rectangular column by considering bubble interactions

This work discusses the development of a three-dimensional Eulerian–Lagrangian CFD model for a gas–liquid flow in a rectangular column. The model resolves the time-dependent, three-dimensional motion of small gas bubbles in a liquid to simulate the dynamic characteristics of the oscillating bubble plume. Our model incorporates drag, gravity, buoyancy, lift, pressure gradient and virtual mass forces acting on a bubble rising in a liquid, and accounts for two-way momentum coupling between the phases. We use MUSIG model that provides a framework in which the population balance method together with the break up and coalescence models can be incorporated into three-dimensional CFD calculations. We use turbulent flow to describe liquid flow field. The standard κ–ε of turbulence is selected for calculating the properties of turbulent flow. The effect of aspect ratio of the column on the flow pattern, liquid velocity and gas hold-up profiles is discussed.     

The effect of aspect ratio in counter-current gas-liquid bubble columns: Experimental results and gas holdup correlations

It is generally admitted that the gas holdup is independent of the column dimensions and gas sparger design if three criteria are satisfied: the diameter of the bubble column is larger than 0.15 m, gas sparger openings are larger than 1–2 mm and the aspect ratio is larger than 5. This paper contributes to the existing discussion; in particular, the effect of the aspect ratio (within the range 1–15) in a counter-current gas-liquid bubble column has been experimentally studied and a new gas holdup correlation to estimate the influence of aspect ratio, operation mode and working fluid on the gas holdup has been proposed. The bubble column, equipped with a spider gas sparger, is 5.3 m in height, has an inner diameter of 0.24 m; gas superficial velocities in the range of 0.004–0.23 m/s have been considered, and, for the runs with water moving counter-currently to the gas phase, the liquid has been recirculated at a superficial velocity of −0.0846 m/s. Filtered air has been used as the gaseous phase in all the experiments, while the liquid phase has included tap water and different aqueous solutions of sodium chloride as electrolyte. Gas holdup measurements have been used to investigate the flow regime transitions and the global bubble column hydrodynamics. The counter-current mode has turned out to increase the gas holdup and destabilize the homogeneous flow regime; the presence of electrolytes has resulted in increasing the gas holdup and stabilizing the homogeneous flow regime; the aspect ratio, up to a critical value, has turned out to decrease the gas holdup and destabilize the homogeneous flow regime. The critical value of the aspect ratio ranged between 5 and 10, depending on the bubble column operation (i.e., batch or counter-current modes) and liquid phase properties. Since no correlation has been found in the literature that can correctly predict the gas holdup under the investigated conditions, a new scheme of gas holdup correlation has been proposed. Starting from considerations concerning the flow regime transition, corrective parameters are included in the gas holdup correlation to account for the effect of the changes introduced by the aspect ratio, operation mode and working fluid. The proposed correlation has been found to predict fairly well the present experimental data as well as previously published gas holdup data.     

Development of co-current air–water flow in a vertical pipe

Measurements of the cross-sectional distribution of the gas fraction and bubble size distributions were conducted in a vertical pipe with an inner diameter of 51.2 mm and a length of about 3 m for air/water bubbly and slug flow regimes. The use of a wire-mesh sensor obtained a high resolution of the gas fraction data in space as well as in time. From this data, time averaged values for the two-dimensional gas fraction profiles were decomposed into a large number of bubble size classes. This allowed the extraction of the radial gas fraction profiles for a given range of bubble sizes as well as data for local bubble size distributions. The structure of the flow can be characterized by such data. The measurements were performed for up to 10 different inlet lengths and for about 100 combinations of gas and liquid volume flow rates. The data is very useful for the development and validation of meso-scale models to account for the forces acting on a bubble in a shear liquid flow and models for bubble coalescence and break-up. Such models are necessary for the validation of CFD codes for the simulation of bubbly flows.     

Experimental investigation of the influence of column scale,gas density and liquid properties on gas holdup in bubble columns

Measurements of gas holdups in bubble columns of 0.16, 0.30 and 0.33 m diameter were carried out. These columns were operated in co-current flow of gas and liquid phases and in semibatch mode. The column of 0.33 m diameter was operated at elevated pressures of up to 3.6 MPa. Nitrogen was employed as the gas phase and deionized water, aqueous solutions of ethanol and acetone and pure acetone and cumene as the liquid phase. The effects of differing liquid properties, gas density (due to elevated pressure), temperature, column diameter and superficial liquid velocity on gas holdup were studied. The gas holdup measurements were utilized by differential pressure measurements at different positions along the height of the bubble columns which allowed for the identification of axial gas holdup profiles. A decrease of gas holdup with increasing column diameter and an increase of gas holdup with increasing pressure was observed. The effect of a slightly decreasing gas holdup with increasing liquid velocity was found to exist at smaller column diameters. The use of organic solvents as the liquid phase resulted in a significant increase in gas holdup compared to deionized water. It is found that published gas holdup models are mostly unable to predict the results obtained in this study.     

Experimental and numerical investigation a bubble-driven laminar flow in a axisymmetric vessel

Measurements have been obtained, by laser-Doppler anemometry (LDA), of the axisymetric, recirculating liquid flow caused by a column of air bubbles ($\text{5–6}\text{1}\text{2}\text{mm dia.}$) rising through caster oil in a cylindrical enclosure (100 mm dia.). The liquid velocities correspond to creeping flow. Axial and radial liquid velocity profiles are reported at eight axial stations and, close to within the bubble column, as a function of time. The maximum liquid velocity found outside the bubble column is about 0.5 of that of the bubbles and a very rapid radical decay from this value is noted. The temporal variation of the velocity field, due to the passage of the air bubbles, is undetectable at radial locations greater than about $\text{1}\text{1}\text{2}$ bubble radii from the centreline.The variation of bubble velocity with axial distance was aise measured by LDA for liquid height to enclosure diámeter ratios of 0.98 and 2.78. The maximum bubble velocities were about 0.1–0.2 higher than the Strokes law terminal velocity. The increase is due to the convection of the bubble column by the liquid flow. The maximum bubble velocity is established within approximately three bubble diameters of the air inlet.The motion of the liquid has been calculated by the numerical solution of the steady form of the equations of motion, with the inner boundary of the area of integration lying 1.3 bubble radii from the centerline. The boundary conditions at this surface are assumed to be steady and are taken from measurements of the time-averaged velocity components. The assumption of steady flow at this boundary is supported by experimental observation and results in calculations which are generally in close agreement with the measurements. Discrepancies are confined to the immediate vicinity of the bubble column near to the top and bottom of the enclosure. These are ascribed to a combination of small asymmetries in the experiment and inadequate numerical resolution in these regions.     

Dynamic detachment of a gas bubble from a solid flat substrate performing normal harmonic vibrations

This paper presents an investigation of the detachment of a bubble from a solid flat substrate according to a dynamic scenario, i. e., due to strong vibrations of the surface shape of the bubble caused by normal nonacoustic harmonic vibrations of the substrate. The Layzer’s model based on an analysis of single-mode solutions near the bubble top was used to study its detachment in microgravity, where the dynamics of the bubble surface is due to competition between liquid inertia forces and surface tension forces. Detachment of the bubble from the substrate was determined from the condition of its elongation during vibrations by a magnitude comparable to the radius of the bubble in equilibrium. The dependence of the vibration intensity required for the detachment of the bubble on the problem parameters was determined using a number of empirical assumptions. The volume of the detached bubbles was estimated.     

Enhancement of channel wall vibration due to acoustic excitation of an internal bubbly flow

The effect of an internal turbulent bubbly flow on vibrations of a channel wall is investigated experimentally and theoretically. Our objective is to determine the spectrum and attenuation rate of sound propagating through a bubbly liquid flow in a channel, and connect these features with the vibrations of the channel wall and associated pressure fluctuations. Vibrations of an isolated channel wall and associated wall pressure fluctuations are measured using several accelerometers and pressure transducers at various gas void fractions and characteristic bubble diameters. A waveguide-theory-based model, consisting of a solution to the three-dimensional Helmholtz equation in an infinitely long channel with the effective physical properties of a bubbly liquid is developed to predict the spectral frequencies of the wall vibrations and pressure fluctuations, the corresponding attenuation coefficients and propagation phase speeds. Results show that the presence of bubbles substantially enhances the power spectral density of the channel wall vibrations and wall pressure fluctuations in the 250–1200 Hz range by up to 27 and 26 dB, respectively, and increases their overall rms values by up to 14.1 and 12.7 times, respectively. In the same frequency range, both vibrations and spectral frequencies increase substantially with increasing void fraction and slightly with increasing bubble diameter. Several weaker spectral peaks above that range are also observed. Trends of the frequency and attenuation coefficients of spectral peaks, as well as the phase velocities are well predicted by the model. This agreement confirms that the origin of enhanced vibrations and pressure fluctuations is the excitation of streamwise propagating pressure waves, which are created by the initial acoustic energy generated during bubble formation.     

Effects of particle size and concentration on bubble coalescence and froth formation in a slurry bubble column

A new approach for simulating the formation of a froth layer in a slurry bubble column is proposed. Froth is considered a separate phase, comprised of a mixture of gas, liquid, and solid. The simulation was carried out using commercial flow simulation software (FIRE v2014) for particle sizes of 60–150 μm at solid concentrations of 0–40 vol%, and superficial gas velocities of 0.02–0.034 m/s in a slurry bubble column with a hydraulic diameter of 0.2 m and height of 1.2 m. Modelling calculations were conducted using a Eulerian–Eulerian multiphase approach with k–ε turbulence. The population balance equations for bubble breakup, bubble coalescence rate, and the interfacial exchange of mass and momentum were included in the computational fluid dynamics code by writing subroutines in Fortran to track the number density of different bubble sizes. Flow structure, radial gas holdup, and Sauter mean bubble diameter distributions at different column heights were predicted in the pulp zone, while froth volume fraction and density were predicted in the froth zone. The model was validated using available experimental data, and the predicted and experimental results showed reasonable agreement. To demonstrate the effect of increasing solid concentration on the coalescence rate, a solid-effect multiplier in the coalescence efficiency equation was used. The solid-effect multiplier decreased with increasing slurry concentration, causing an increase in bubble coalescence efficiency. A slight decrease in the coalescence efficiency was also observed owing to increasing particle size, which led to a decrease in Sauter mean bubble diameter. The froth volume fraction increased with solid concentration. These results provide an improved understanding of the dynamics of slurry bubble reactors in the presence of hydrophilic particles.     

Estimating gas holdup via pressure difference measurements in a cocurrent bubble column

Estimating gas holdup via pressure difference measurements is a simple and low-cost non-invasive technique to study gas holdup in bubble columns. It is usually used in a manner where the wall shear stress effect is neglected, termed Method II in this paper. In cocurrent bubble columns, when the liquid velocity is high or the fluid is highly viscous, wall shear stress may be significant and Method II may result in substantial error. Directly including the wall shear stress term in the determination of gas holdup (Method I) requires knowledge of two-phase wall shear stress models and usually requires the solution of non-linear equations. A new gas holdup estimation method (Method III) via differential pressure measurements for cocurrent bubble columns is proposed in this paper. This method considers the wall shear stress influences on gas holdup values without calculating the wall shear stress. A detailed analysis shows that Method III always results in a smaller gas holdup error than Method II, and in many cases, the error is significantly smaller than that of Method II. The applicability of Method III in measuring gas holdup in a cocurrent air–water–fiber bubble column is examined. Analysis based on experimental data shows that with Method III, accurate gas holdup measurements can be obtained, while measurement error is significant when Method II is used for some operational conditions.     

Oscillations of a gas bubble in a non-Newtonian liquid under the action of an acoustic field

The evolution of the radius of a spherical cavitation bubble in an incompressible non-Newtonian liquid under the action of an external acoustic field is investigated. Non-Newtonian liquids having relaxation properties and also pseudoplastic and dilatant liquids with powerlaw equation of state are studied. The equations for the oscillation of the gas bubble are derived, the stability of its radial oscillation and its spherical form are investigated, and formulas are given for the characteristic frequency of oscillations of the cavitation hollow in a relaxing liquid. The equations are integrated numerically. It is shown that in a relaxing non-Newtonian liquid the viscosity may lead to the instability of the radial oscillations and the spherical form of the bubble. The results obtained here are compared with the behavior of a gas bubble in a Newtonian liquid.     

Local gas and liquid phase velocity measurement in a miniature stirred vessel using PIV combined with a new image processing algorithm

A method which combines standard two-dimensional particle image velocimetry (PIV) with a new image processing algorithm has been developed to measure the average local gas bubble velocities, as well as the local velocities of the liquid phase, within small stirred vessel reactors. The technique was applied to measurements in a gas–liquid high throughput experimentation (HTE) vessel of 45 mm diameter, but it is equally suited to measurements in larger scale reactors. For the measurement of liquid velocities, 3 μm latex seeding particles were used. For gas velocity measurements, a separate experiment was conducted which involved doping the liquid phase with fluorescent Rhodamine dye to allow the gas–liquid interfaces to be identified. The analysis of raw PIV images enabled the detection of bubbles within the laser plane, their differentiation from obscuring bubbles in front of the laser plane, and their use in lieu of tracer particles for gas velocity analysis using cross-correlation methods. The accuracy of the technique was verified by measuring the velocity of a bubble rising in a vertical glass column. The new method enabled detailed velocity fields of both phases to be obtained in an air–water system. The overall flow patterns obtained showed a good qualitative agreement with previous work in large scale vessels. The downward liquid velocities above the impeller were greatly reduced by the addition of the gas, and significant differences between the flow patterns of the two-phases were observed.     

Disengagement of the gas phase in bubble columns

The technique of gas disengagement is popularly used to assess the bubble size distribution in bubble columns. The technique involves the dynamic measurement of dispersion height when the gas supply is stopped. In this paper a mathematical model has been proposed for the process of dynamic gas disengagement. It has been shown that the initial faster disengagement is due to the presence of internal liquid circulation and not due to the presence of very large bubbles. Further, slower disengagement has been attributed to the transition from heterogeneous dispersion to homogeneous dispersion. The new model also explains the effects of superficial gas velocity, column diameter, column height and liquid phase physical properties on the gas disengagement.     

NUMERICAL PREDICTION OF TWO-PHASE FLOW IN BUBBLE COLUMNS

A numerical model is described for the prediction of turbulent continuum equations for two-phase gas–liquid flows in bubble columns. The mathematical formulation is based on the solution of each phase. The two-phase model incorporates interfacial models of momentum transfer to account for the effects of virtual mass, lift, drag and pressure discontinuities at the gas–liquid interface. Turbulence is represented by means of a two-equation k–ϵ model modified to account for bubble-induced turbulence production. The numerical discretization is based on a staggered finite-volume approach, and the coupled equations are solved in a segregated manner using the IPSA method. The model is implemented generally in the multipurpose PHOENICS computer code, although the present appllications are restricted to two-dimensional flows. The model is applied to simulate two bubble column geometries and the predictions are compared with the measured circulation patterns and void fraction distributions.     

An advanced LIF-PLV system for analysing the hydrodynamics in a laboratory bubble column at higher void fractions

Bubble columns are widely used in the chemical industry and biotechnology. Flow and turbulence in such an apparatus are induced by the bubble rise, and the bubble behaviour is strongly affected by swarm effects (i.e. the interaction between bubbles). For analysing the bubble swarm behaviour and simultaneously evaluating the flow structure and bubble-induced turbulence, a bubble column of 140 mm diameter and a height of 650 mm or 1,400 mm (initial water level) were considered. The bubble column was aerated with relatively fine bubbles having a mean size between about 0.5 and 4.0 mm. The gas hold-up was varied in the range between 0.5 and 19%. A two-phase pulsed-light velocimetry (PLV) system was developed to evaluate instantaneous flow fields of both rising bubbles and the continuous phase. The measurement of the liquid velocities in the bubble swarm was achieved by adding fluorescing seed particles. Images of bubbles and fluorescing tracer particles were acquired by two CCD cameras. Hence, the images from tracers and bubbles were easily separated by optical interference filters with a bandwidth corresponding to the emitting wavelength of the fluorescing tracer particles and the wavelength of the applied Nd-YAG pulsed laser, respectively. To improve the phase separation of the system, the CCD cameras were additionally placed in a non-perpendicular arrangement with respect to the light sheet. The acquired images were evaluated with the minimum-quadratic-difference algorithm. The potential of this technique for the analysis of bubbly flows with higher void fraction was explored. In order to obtain averaged velocity maps of bubble and fluid within the entire column, about 1,000 image pairs were recorded and evaluated for each phase. In addition, turbulence intensities of the fluid were deduced from the measurements. The turbulence properties were used to characterise bubble-induced turbulence for various bubble mean diameters and gas hold-ups. Moreover, the determination of the average bubble slip velocity within the bubble swarm was possible.     

Effects of hydrophilic particles on bubbly flow in slurry bubble column

To investigate the effects of hydrophilic particles on slurry bubble flows in a bubble column, distributions of the local gas holdup and the bubble frequency are measured using an electric conductivity probe. Particles are made of silica and their diameter is 100 μm. The particle volumetric concentration C_S is varied from 0 to 0.40. The measured data imply that the presence of particles promotes bubble coalescence. The film drainage time for two coalescing bubbles in a quasi two-dimensional bubble flow in a small vessel is also measured to quantitatively evaluate the particle effect on coalescence. A particle-effect multiplier is introduced into a coalescence efficiency model by taking into account the data of film drainage time and is implemented into a multi-fluid model. The main conclusions obtained are as follows: (1) the local gas holdup and bubble frequency in slurry bubble flows decrease with increasing the particle concentration, (2) the hydrophilic particles enhance bubble coalescence and the enhancement saturates at C_S ≃ 0.45, (3) the particle effect on coalescence is well accounted for by introducing the particle-effect multiplier to the film drainage time, and (4) the multi-fluid model can give good predictions for the distribution of the local gas holdup in the slurry bubble column.     

Three-dimensional CFD simulation of bubble–melt two-phase flow with air injecting and melt stirring

This paper reports on progress in developing CFD simulations of gas bubble–metallic melt turbulent flows induced by a pitched-blade impeller with an inclined shaft. Foaming process of aluminum foams, in which air is injected into molten aluminum composites and the melt is mechanical stirred by the impeller, has been investigated. A two-fluid model, incorporated with the Multiple Reference Frames (MRF) method is used to predict the three-dimensional gas–liquid flow in the foaming tank, in which a stirring shaft is positioned inclined into the melt. Locally average bubble size is also predicted by additively solving a transport equation for the bubble number density function, which accounts for effects of bubble breakup and coalescence phenomena. The computed bubble sizes are compared with experimental data from our water model measurement and reasonable agreements are obtained. Further, simulated results show that the volume averaged total and local gas fractions are generally increased with rising impeller speed and gas flow rate. The local averaged bubble size increases with increasing gas flow rate and orifice diameter and decreasing liquid viscosity, and decreases also with rising rotation speed of the impeller.