Bubble Swarm Research Articles

Statistical method to calculate local interfacial variables in two-phase bubbly flows using intrusive crossing probes

This paper presents a statistical method to calculate local interfacial variables in two-phase gas–liquid bubbly flows from data taken with double-sensor intrusive probes. Firstly, one derives the geometrical relationship existing between the apparent and actual bubble velocity for a single spherical bubble flowing in a multidimensional flow field. The apparent variables are obtained from the experimental data when one assumes that the bubble trajectory is aligned with the probe axis. A similar relationship exists for the intersected chord length and bubble diameter. Then, the analysis is extended to a swarm of bubbles. The ratio between the apparent to the actual bubble velocity and the intersected chord length to the bubble diameter appear now as probability density functions. The experimental data were taken for air–water bubbly flow regime in a vertical round pipe with a double tip electrical probe. Processing the phase density function generated by the bubble events, one determines distribution function of the bubble velocity and intersected chord length, termed the apparent distributions. The variables of interest, actual bubble velocity and diameter, come out of the solution of a linear system of equations relating the probability function of the measured and estimated bubble velocity and bubble size ratio. The probability density function of the actual bubble velocity and bubble diameter, plus the bubble frequency, add up to various interfacial properties calculated with this technique: the void fraction, the bubble velocity, the bubble size, the interfacial area density and the interface velocity fluctuation intensity. To validate the method, the paper compares local and area averaged quantities with previously published results, volumetric measurements and extensively used correlation.

A Scale-Up Strategy for a Commercial Scale Bubble Column Slurry Reactor for Fischer-Tropsch Synthesis

Bubble column reactors are finding increasing use in industrial practice; this reactor technology figures prominently in processes for converting natural gas to liquid fuels and light olefins using Fischer-Tropsch synthesis. There are considerable reactor design and scale-up problems associated with the Fischer-Tropsch bubble column slurry reactor. Firstly, large gas throughputs are involved, necessitating the use of large diameter reactors, typically 5-8 m, often in parallel. Secondly, the process operates under high-pressure conditions, typically 40 bar. Thirdly, in order to obtain high conversion levels, large reactor heights, typically 30-40 m tall, are required along with the use of highly concentrated slurries, approaching 40 vol%. Finally, the process is exothermic in nature, requiring heat removal by means of cooling tubes inserted in the reactor. Successful commercialisation of this technology is crucially dependent on the proper understanding of the scaling-up principles of bubble columns for the above mentioned conditions which fall outside the purview of most published theory and correlations. In order to develop the proper scale-up rules for the bubble column slurry reactor we have undertaken a comprehensive program of investigation of the hydrodynamics (gas holdup, radial distribution of liquid velocities, backmixing of the liquid) in columns of diameters 0. 05, 0. 1, 0. 15, 0. 174, 0. 19, 0. 38 and 0. 63 m. A variety of liquids (water, tetradecane, paraffin oil, Tellus oil) were used as the liquid phase. Silica particles in concentrations up to about 40 vol% were added to paraffin oil in order to study slurry hydrodynamics. One column of 0. 15 m diameter was operated at pressures ranging from 0. 1 to 1. 3 MPa with the air-water system and the gas holdup and gas-liquid mass transfer were measured. Additionally, video imaging studies in a rectangular two-dimensional column were carried out to study the rise characteristics of single bubbles, bubble-bubble interactions and coalescence-breakup phenomena. Our experiments show that the hydrodynamics is significantly affected by column diameter, elevated system pressures, concentration of the slurry. These effects are not adequately described by published literature correlations. The extrapolation of data obtained in laboratory cold flow units to the commercial scale reactors requires a systematic approach based on the understanding of the scaling principles of bubble dynamics and of the behaviour of two-phase dispersions in large scale columns. We develop a multi-tiered approach to bubble column reactor scale-up, relying on a combination of experiments, backed by Computational Fluid Dynamics (CFD) simulations for physical understanding. This approach consists of the following steps:- description of single bubble morphology and rise dynamics; here both experiments and Volume of Fluid (VOF) simulations are used;- modelling of bubble-bubble interactions;- description of the behaviour of bubble swarms and of the development of the proper interfacial momentum exchange relations between the bubbles and the liquid;- CFD simulations in the Eulerian framework for extrapolation of laboratory scale information to large scale commercial reactors.

Effects of Equipment Dimensions on Circulation Flow Rates of Liquid and Gas in Bubble Column with Draft Tube.

For a bubble column with draft tube sparging gas into the annulus, the effects of equipment dimensions and liquid properties on the circulation flow rates of liquid and gas are experimentally studied. The gas circulation flow rate is estimated by comparing gas holdup in the downcomer with that in a gas-liquid cocurrent downflow bubble column. The liquid circulation flow rate becomes higher as the distance between the upper end of draft tube and the liquid surface at aeration lengthens, and it remains unchanged when the distance is beyond double the column diameter. It increases with increasing draft tube diameter and with increasing bubble size. The gas circulation flow rate is strongly governed by the liquid circulation flow rate. The driving force for gas circulation is the difference between the descending velocity of liquid and the rising velocity of bubble swarm in the downcomer. Based on the energy balance, an empirical equation of the loss coefficient in the zone above the upper end of the draft tube is obtained. The circulation flow rates of liquid and gas calculated by using the energy balance and correlations, agree with the measured data within an error of ±30%.

Experimental and numerical studies of the hydrodynamics in a bubble column

The hydrodynamics in a bubble column of 140 mm diameter and a height of 650 mm was analysed using a phase-Doppler anemometer (PDA). In order to allow the application of PDA, the bubble column was aerated with relatively fine bubbles with a size spectrum between about 0.3 and 1.5 mm. The gas hold-up was varied in the range between 0.5 and 3%. The measurement of the liquid velocities in the bubble swarm was done by adding fluorescing seed particles. Moreover, the Euler/Lagrange approach was extended to allow time-dependent calculations of the flow evolving in a bubble column based on the Reynolds-averaged Navier–Stokes equations together with the k– ε turbulence model which was extended to account for turbulence modification by the bubbles. The coupling between the phases was considered through momentum source terms and source terms in the k- and ε-equation which also include the effect of wake-generated turbulence. The bubble motion was calculated by solving an equation of motion taking into account drag force, added mass, buoyancy and gravity, and the transverse lift force. In order to identify the relative importance of the different physical phenomena involved in the model, a detailed parametric study was performed and the numerical results were compared with the measurements for validation.

A study on coalescence and breakage mechanisms in three different bubble columns

A study of the interfacial mechanisms focusing on the coalescence and breakage is carried out in the framework of a BRITE-EURAM project named ADMIRE. The main objective of this study is to develop a new methodology to analyse breakage and coalescence phenomena in bubble columns. For this purpose both detailed measurements of the bubble-size distribution and the development of population balance equation (PBE) model were carried out. An elaborate database is established which describes the evolution of the bubble-size distribution in three different columns at EniChem, Politecnico di Milano and DSM. The database contains a unique set of bubble-size distribution measurements: not only the evolution of this distribution as a function of height in the column has been investigated but also the influence of gas superficial velocity and different hydrodynamic configurations have been studied. The distribution curves were obtained by analysing a large amount of bubbles with a measurement based on a new image analysis technique. The experimental measurements showed a consistent trend on the three sites and the influence of the bubble size on breakage and coalescence rates has clearly been observed. Simultaneously, a novel model that describes bubble–bubble interactions was developed. The advantage of this new model with respect to models published in literature is that the physics of free rising bubbles (e.g. wake interactions, bubble swarm velocity and the shape of the bubbles) are also taken into account. Moreover, this model is especially tailored for bubble columns where the physics of the interfacial mechanisms is thought to play a major role. For this reason this model distinguishes itself from general-purpose models which usually describe less accurately the phenomena taking place in such particular systems. The validation of the model using the experimental data is satisfactory.

Influence of scale on the hydrodynamics of bubble columns operating in the churn-turbulent regime: experiments vs. Eulerian simulations

The radial distribution of the liquid velocities, along with the liquid-phase axial dispersion coefficients, have been measured for the air–water system in bubble columns of 0.174, 0.38 and 0.63 m diameter. The experimental results emphasise the significant influence of the column diameter on the hydrodynamics, especially in the churn-turbulent regime. Computational fluid dynamics (CFD) is used to model the influence of column diameter on the hydrodynamics. The bubble column is considered to be made up of three phases: (1) liquid, (2) “small” bubbles and (3) “large” bubbles and the Eulerian description is used for each of these phases. Interactions between the gas phases and the liquid are taken into account in terms of momentum exchange, or drag, coefficients, which differ for these two gas phases. The drag coefficient between the small bubbles is estimated using the Harmathy correlation ( A.I.Ch.E. Journal 6 (1960) 281–288). The drag relation for interactions between the large bubbles and the liquid, is developed from analysis of an extensive data base on large bubble swarm velocities measured in columns of 0.051, 0.1, 0.174, 0.19, 0.38 and 0.63 m diameter using a variety of liquids (water, paraffin oil, tetradecane). The interactions between the large and small bubble phases are ignored. The turbulence in the liquid phase is described using the k– ε model. The three-phase description of bubble columns was implemented within the Eulerian framework of a commercial code CFX 4.1c of AEA Technology, Harwell, UK. Comparison of the experimental measurements with the Eulerian simulations show good agreement and it is concluded that the three-phase Eulerian simulation approach developed here could be a powerful design and scale-up tool.

Large-Scale Simulations of Bubble-Induced Convection in a Liquid Layer

The flow pattern induced by a swarm of bubbles rising in a liquid layer is studied numerically. The fluid motion is described by spatially filtered Navier-Stokes equations forced by the presence of the bubbles. When the volume fraction and the residence time of the bubbles increase, a Rayleigh-Taylor-type instability develops. After transient stages, the flow reaches an equilibrium state made of counterrotating cellular structures. The simulations suggest that no wavelength selection mechanism exists in the present situation, making a striking difference with thermal convection.

Rise velocity of a swarm of large gas bubbles in liquids

This paper develops a procedure for estimation of the rise velocity of a swarm of large gas bubbles in a bubble column operating in the churn-turbulent flow regime. The large bubble swarm velocity is estimated by introducing two correction factors into the classical Davies–Taylor (1950) relation for rise of a single spherical cap bubble in a liquid V b=0.71 gd b ( SF) ( AF). The scale correction factor (SF) accounts for the influence of the column diameter. This correction is given by the Collins relation ( J. Fluid Mech., 28, 97–112, 1967) and is a function of the ratio of the bubble diameter d b to the column diameter D T . Volume-of-fluid simulations confirm the validity of the Davies–Taylor–Collins relations for a variety of liquid properties. The acceleration factor (AF) accounts for the increase in the rise velocity of a bubble because of its interaction with the wake of a bubble preceding it. By analysis of video recordings of the interactions between two bubbles, both in-line and off-line, it is found that the acceleration factor AF increases linearly as the vertical distance of separation between the two bubbles decreases. Increasing liquid viscosity reduces this wake acceleration effect. With the aid of an extensive data set on the large bubble swarm velocity in columns of 0.051, 0.1, 0.174, 0.19, 0.38 and 0.63 m in diameter a correlation is developed for the acceleration factor. The large bubble swarm velocity is found to be three to six times higher than that of a single isolated bubble.

Behavior of Coal Particles in Column Flotation.

The behavior of Datong coal particles in a flotation column was investigated in a batchwise operation using a gas distributor evolving uniform bubbles by varying the superficial gas velocity and column height. The value of superficial gas velocity was controlled at 0.66 or 1.99 cm s–1.The time course of ash content in floats was measured when column height was 1.85 m. The ash content in clean coal was larger for higher superficial gas velocity. The hydrophobicity of coal particles recovered from the top of the column was evaluated by means of a film flotation method. Hydrophilic particles having the critical wetting surface tension of particles, γc, greater than 60 mN m–1 floated well for higher superficial gas velocity. The weight percent of fractions having γc above 60 mN m–1 was 29.5, 31.9 and 40.5% for 0.25, 2.00 and 4.25 min, respectively. These values increased with sampling time, and were much greater than those for the lower superficial gas velocity. At lower superficial gas velocity, the hydrophobic coal particles seem to be selectively floated by colliding and attaching to the bubble surfaces. On the other hand, at higher superficial gas velocity, hydrophilic particles that are difficult to attach to bubbles seem to be entrained in the turbulent wake of bubble swarms and float.The grade of clean coal was better for the lower superficial gas velocity, however, carbonaceous materials recovery was lower than that for higher superficial gas velocity. Carbonaceous materials recovery was improved by increasing the recovery zone height.

Rising velocity of a swarm of spherical bubbles in power law fluids at high reynolds numbers

AbstractIn this work, a theoretical scheme for estimating the rise velocity of a swarm of spherical bubbles through quiescent power law liquids at high Reynolds number is developed. The inter‐bubble interactions have been accounted for by the use of a cell model. The effect of the power law index and the volume fraction of the gas on the rise velocity is elucidated. Depending upon the degree of shearthinning behaviour and the gas fraction, the swarm may rise slower or faster than a single bubble. This behaviour has been explained qualitatively in terms of two competing mechanisms.

Influence of elevated pressure on the stability of bubbly flows

The effect of elevated pressure on the stability of the homogeneous bubbly flow regime in a gas-liquid bubble column is examined. Experiments were performed in a 0.15 m diameter bubble column operated at pressures in the range 0.1–1.3 MPa with nitrogen as the gas phase and water as the liquid phase. The transition from homogeneous to heterogeneous flow regime was determined by two procedures. The first procedure involved visual examination of the swarm velocity vs gas velocity curve to determine the transition point. In the second procedure the transient pressure signals were monitored by high-frequency pressure transducers and the instability point determined by analysis of the chaotic features. The two major findings of the work were: (a) increased system pressure reduces the bubble swarm velocity of the homogeneous dispersion, (b) increased system pressure results in a significant increase in the gas holdup at the instability point. The stability theory of Batchelor (1988, J. Fluid Mech.193, 75–110) and Lammers and Biesheuvel (1996, J. Fluid Mech.328, 67–93) has been used to provide theoretical support to these observations.

Bubble swarm velocity in a column: a two-dimensional approach

The average gas velocity, u g , is widely used as a measure of bubble swarm velocity in a column. However, it is only correct in the ideal case: i.e. uniform distribution of uni-sized bubbles. Under real conditions, i.e. a non-uniform distribution of multi-sized bubbles, the hindered velocity, u h , obtained by interpolating the interface rise velocity, was identified with the real bubble swarm velocity by the authors (Shen and Finch, 1996, Chem. Engng Sci. 51, 3665–3674). The ideal case is akin to a one-dimensional domain. In the two-dimensional domain, with a knowledge of the radial gas holdup profile and liquid circulation velocity over the cross section of the column, u h was simulated using the model of Richardson and Zaki with the coefficient m c describing the system characteristics. The observation that u h ≤ u g was mathematically proved by an inequality assuming a parabolic gas holdup profile of order n = 2.

PREDICTION OF GAS-PHASE HOLDUP IN A BUBBLE COLUMN

Hydrodynamic properties of bubble columns play a significant role in many chemical and biochemical processes. Recent theoretical and experimental work conducted by Krishna et al. (1991, 1994), and Wilkinson et al. (1992) have been examined in conjunction with a bubble column and data for the air-water system operating at ambient conditions. The bubble column is 0.108 m in internal diameter, has a 1.70 m tall test section, and is equipped with a perforated plate distributor having 91 holes of 0.8 mm diameter. The data are taken for five values of the slumped water column height in range from 0.79 to 1.15 m, and for superficial air velocities up to about 0.4 m/s. The data accord to the qualitative aspects of Krishna et al. model but lead to different values of the bubble swarm rise velocity, and superficial transition air velocity characterizing the transition from homogeneous bubbly flow regime to heterogeneous churn-turbulent flow regime. The quantitative reproduction by the model expressions of these recent works of the experimental data is poor. This may be partly attributed to the geometry of the column, diameter and distributor design. The qualitative features of Krishna et al. model for the two regimes are confirmed by the present data. For quantitative predictions of gas-phase holdup, a new model is proposed in which the large bubble flow in the churn-turbulent regime is formulated following the drift-flux theory. The proposed theory and experimental data are in good agreement.

Prediction of the bubble-hole size of a cap bubble in a bubble swarm

A phenomenological, semi-theoretical model is proposed for predicting the size or thickness of the bubble-depleted region, or ‘bubble hole’, in the frontal vicinity of a larg cap bubble rising through a swarm of otherwise uniformly dispersed small bubbles. The model lays its theoretical basis on the axial pressure distribution in the very front of the cap nose which modifies the hydrostatic pressure gradient in the absence of the cap. The consequence of this pressure modification is interpreted as a local variation/increase in the effective buoyancy acting on the swarm bubbles being overtaken by the cap; the bubble rise velocity increases as the vertical distance between the bubble and the cap decreases and, under sufficient pressure gradient, it reaches the cap rise velocity. The bubble-hole thickness is estimated in essence as the bubble-cap distance along the cap central axis in this limiting state. Experments are conducted in a two-dimensional column to measure the hole size over a wide range of swarm gas holdups. Different liquids, including sodium sulfite and glycerin solutions, are used; the former as an electrolyte solution favors the formation and prevalence of smaller bubbles, thus for examining the bubble-size effect; the latter leads to a smaller increase in the local pressure gradient due to viscous action. The present model is found to be only capable of predicting the qualitative trends exhibited by the experimental data but to severely underestimate the extent of the bubble hole.

Development of a Particle‐Bubble Collision Model for Flotation columns

AbstractParticle‐bubble collisions in bubble swarm systems have been modelled based on previous work on single bubble systems and bubbly flow characterization. This approach relates the overall collision probability to bubble and particle sizes, gas holdup, column height, and other operating parameters, thus providing a theoretical basis for column design and analysis of particle collection in flotation columns. The simulated results indicate that the existing collision models based on single bubble systems cannot be accurately applied to actual flotation columns for analysis of the particle‐bubble collision process. This is mainly due to the effect of gas holdup, bubble interaction, and multi‐layers of bubbles in a swarm. For column flotation of fine particles under normal operating conditions, a recovery zone of about 10 meters is sufficient to ensure that the collision probability approaches unity. For bigger particles, higher gas holdups, and smaller bubble sizes, much shorter recovery zone heights can be used to achieve the same high collision probability.

Bubble swarm velocity in a column

In an air-water-only system under batch operation, a bubble interface was created in a laboratory column by introducing a step change in gas flow, and the rise velocity of this interface, u in, was measured using a novel method based on electrical conductivity with a custom-designed fast-response conductivity meter. The u in was plotted against J g2 J g1 , where J g1 and J g2 are the superficial gas velocities before and after the step change, respectively. The velocity of the undisturbed system was estimated by interpolation at J g2 J g1 = 1 . This velocity was referred to as the hindered velocity, u h . The local average gas velocity, u g, loc (= J g loc ε g, loc ) [corrected from the average gas velocity ( = J g ε g ) to account for the local pressure], was different from u h . It is argued that u h is the real bubble swarm velocity and u g, loc is the bubble swarm velocity for the ideal case of uniform bubble size. Unlike u g, loc , the u h was constant along the column, a result supported by theoretical momentum analysis. The u h is proposed as the key characteristic swarm velocity of the system.

Effect of fine solids and frother on gas hold-up and liquid mixing in a flotation column

The effect of fine solids and frother addition on gas hold-up and average bubble rise velocity in bubble swarm, and liquid phase mixing intensity has been studied in a 0.06 m flotation column. The variables studied were frother (pine oil) addition, feed solid concentration, gas and slurry velocities. The gas hold-up was estimated from the static pressure method, while the liquid phase mixing intensities were estimated using the pulse technique. In comparison with our previous air-water study [1], frother addition has a drastic effect on bubble characteristics, while the effect of solids is negligible except at low gas velocities for which complete suspension of solids from the gas distributor were not observed. The presence of small quantities of solids on the gas distributor resulted in bubble coalescence even in the presence of frother. In general, frother addition resulted in an increase in the liquid mixing intensity while the presence of solids had the opposite effect. Our results indicate that in the presence of frother, the bubbly flow regime is maintained over a wider gas velocity range.

Further remarks on the drag of a swarm of bubbles

In this note, the influence of the geometrical arrangement of bubbles on the drag of bubble swarms has been ascertained by carrying out detailed comparisons between various estimates of drag available in the literature. Likewise, the predictions based on the two commonly used cell (free surface and zero vorticity) models have been contrasted with each other. A simple method for estimating the free rise velocity of bubble swarms is outlined.

The extent of the bubble-depleted region in the frontal vicinity of a large cap bubble rising in a bubble swarm

The study concerns the visual observation of the formation of the bubble-depleted region in the frontal vicinity of a large bubble injected in a swarm of otherwise uniformly dispersed small bubbles. For this purpose, experiments are conducted exclusively in a two-dimensional column to ensure the distinct appearance of a single cap throughout its rise in the swarm over a wide range of gas hold-ups. Other parameters, including physical properties of the gas and liquid phases and sizes of the two classes of bubbles, are either fixed or of limited ranges. The specific focus is on the measurement of the size of the bubble-depleted region

Drag Coefficients of Bubbles. 2nd Report. Drag Coefficient for a Swarm of Bubbles and its Applicability to Transient Flow.

In the previous report, we proposed constitutive equations for a drag coefficient, CD, of a single bubble in a stagnant liquid. Applicability of the proposed CD to transient flow was examined in this report based on the relaxation time required for a stationary bubble to reach the terminal condition. As a result, it was confirmed that the bubble will reach the terminal condition after traveling a distance almost equal to 2d where d is the bubble diameter. Hence, we can apply the proposed CD to transient flow provided that the whole flow field does not change much while the bubble moves the distance about 2d. Then, the proposed CD was modified so as to be applicable to a swarm of bubbles. The modification was carried out using an empirical correlation for drift velocity of the swarm and balance of forces acting on a bubble in the swarm. Comparisons between measured and calculated transient bubble-induced natural circulation were conducted to verify the modified CD. The calculation was carried out using a two-fluid model with the modified CD. It was confirmed that the modified CD can give good predictions.