Hydrodynamics of air–kerosene bubble column under elevated pressure in homogeneous flow regime

A multiphase computational fluid dynamics(CFD) model coupled with the population balance equation(PBE) was developed in a homogeneous air–kerosene bubble column under elevated pressure(P). The specific pressure drop(DP/L), gas holdup(a_G), and Sauter mean diameter(d_(32)) were experimentally measured in the bubble column with 1.8 m height and 0.1 m inner diameter, which was operated at a superficial gas velocity of 12.3 mm·s~(-1), and P = 1–35 bar(1 bar = 10~5 Pa). A modified drag coefficient model was proposed to consider the effect of bubble swarm and pressure on hydrodynamics of the bubble column.The Luo breakage model was modified to account for liquid density, viscosity, surface tension and gas density. The DP/L, a_G, and d_(32) obtained from the CFD model were compared with experimental data,and the gas density-dependent parameters of the CFD model were identified. With increasing P from 1 to 35 bar, the aGvaried from 5.4% to 7.2% and the d_(32) decreased from 2.3 to 1.5 mm. The CFD-PBE model is applicable to predict hydrodynamics of pressurized bubble columns for gas–organic liquid in the homogeneous regime.     

特征时间对剪切稀化流体气泡上浮特性的影响

非牛顿气液两相流广泛存在于工农业生产中,气泡和液相间的接触非常复杂,对相间的传递效率具有重要的影响。为了理解气泡在非牛顿流体中的运动特性,基于连续表面张力模型与Carreau本构模型,本文运用volume of fluid（VOF）法研究了单气泡在剪切稀化流体内自由上浮的运动特性。研究发现：气泡的动力学特性与液相的特征时间λ密切相关,液相的剪切稀化程度越强（流变指数n越小）或表面张力越小（Eo数越大）时,特征时间λ对气泡变形和尾涡的影响越大。在给定的剪切稀化程度和表面张力下,λ越大,气泡终端速度越大,其尾涡强度和尺度也越大,导致气泡周围液相高剪切速率区和低表观黏度区的范围越宽。此外,当液相的表面张力较小时,在气泡尾部出现了黏度盲区;并且随着λ的增大,黏度盲区逐渐脱离气泡尾部并破碎;黏度盲区的出现减小了气泡周围液相低表观黏度区的面积,增大了气泡上浮过程的摩擦阻力,降低了气泡的终端速度。     

Experimental and numerical investigations of scale-up effects on the hydrodynamics of slurry bubble columns

Experiments and simulations were conducted for bubble columns with diameter of 0.2 m(180 mm i.d.), 0.5 m(476 mm i.d.) and 0.8 m(760 mm i.d.) at high superficial gas velocities(0.12–0.62 m·s-1) and high solid concentrations(0–30 vol%). Radial profiles of time-averaged gas holdup, axial liquid velocity, and turbulent kinetic energy were measured by using in-house developed conductivity probes and Pavlov tubes. Effects of column diameter, superficial gas velocity, and solid concentration were investigated in a wide range of operating conditions. Experimental results indicated that the average gas holdup remarkably increases with superficial gas velocity, and the radial profiles of investigated flow properties become steeper at high superficial gas velocities. The axial liquid velocities significantly increase with the growth of the column size, whereas the gas holdup was slightly affected. The presence of solid in bubble columns would inhibit the breakage of bubbles, which results in an increase in bubble rise velocity and a decrease in gas holdup, but time-averaged axial liquid velocities remain almost the same as that of the hollow column. Furthermore, a 2-D axisymmetric k–ε model was used to simulate heterogeneous bubbly flow using commercial code FLUENT 6.2. The lateral lift force and the turbulent diffusion force were introduced for the determination of gas holdup profiles and the effects of solid concentration were considered as the variation of average bubble diameter in the model. Results predicted by the CFD simulation showed good agreement with experimental data.     

Use of models for lift, wall and turbulent dispersion forces acting on bubbles for poly-disperse flows

Closure laws are needed for the qualification of CFD codes for two-phase flows. In case of bubbly and slug flow, forces acting on the bubbles usually model the momentum transfer between the phases. Several models for such forces can be found in Literature. They show, that these forces depend on the liquid flow field as well as on the size and the shape of the bubbles. A validation of consistent sets of bubble force models for poly-disperse flows is given, basing on a detailed experimental database for vertical pipe flows, which contains data on the radial distribution of bubbles of different size as well as local bubble size distributions. A one-dimensional (1D) solver provides velocity profiles and bubble distributions in radial direction. It considers a large number of bubble size classes and is used for the comparison with the experiments. The simplified model was checked against the results of full 3D simulations done by the commercial code CFX-5.7 for simplified monodisperse cases. The effects of the number of bubbles classes as well as the effect of the lateral extension of the bubbles were analyzed. For the validation of bubble force models measured bubble size distributions were taken as an input for the calculation. On basis of the assumption of an equilibrium of the lateral bubble forces, radial volume fraction profiles were calculated separately for each bubble class. In the result of the validation of different models for the bubble forces, a set of Tomiyama lift and wall force, deformation force and Favre averaged turbulent dispersion force was found to provide the best agreement with the experimental data. Some discrepancies remain at high liquid superficial velocities.     

Bubble Behavior of a Large‐Scale Bubble Column with Elevated Pressure

Gas holdups and the rising velocity of large and small bubbles are measured using the dynamic gas disengagement approach in a pressured bubble column of 0.3 m in diameter and 6.6 m in height. The effects of superficial gas velocity, liquid surface tension, liquid viscosity, and system pressure on the gas holdups and the rising velocity of small and large bubbles are investigated. The holdup of large bubbles and the rising velocity of small bubbles increase with increasing liquid viscosity and liquid surface tension. Meanwhile, the holdup of small bubbles and the rising velocity of a swarm of large bubbles decrease. Moreover, the holdup of large bubbles and the rising velocity of a swarm of small bubbles decrease with increasing system pressure. A correlation for the holdup of small bubbles is obtained from experimental data.     

On the influence of the liquid physical properties on bubble volumes and generation times

This work presents both theoretical and experimental studies about the specific influence of viscosity, surface tension and density in the formation of a gas bubble. The theoretical model includes both bubble formation and free rising and extends some previous work. As the previous bibliography provides rather scattered data regarding the effect of the liquid properties on bubble generation times, the results can be considered a step forward in the understanding of the subject because they separately describe the influence of viscosity, surface tension and density. The model yields satisfactory results of bubble shapes and formation times when compared to the experimental high-speed video observations obtained using non-Newtonian solutions of carboxymetyl cellulose in water at different concentrations (0.4-1.6% w/w). The complete experimental study also includes a range of different gas flow rates (1-) and orifice diameters (1.5 and 2 mm).     

Influence of the lift force on the stability of a bubble column

This work investigates the role of the lift force for the stability of a homogeneous bubble column. Instabilities caused by the lift force may be one important reason for the transition from homogeneous to heterogeneous bubble column. On rising bubbles the lift force acts in a lateral direction, when gradients of the liquid velocity are present. Non-uniform liquid velocity fields may be induced if the gas fraction is not equally distributed, e.g. caused by local disturbances. This feedback mechanism is studied in the paper. It was found, that a positive lift coefficient (small bubbles) stabilizes the flow, while a negative coefficient (large bubbles) leads to unstable gas fraction distributions, and thus it favours the appearance of a heterogeneous bubble column regime. The turbulent dispersion force has always a stabilizing action, i.e., it partially compensates the destabilization induced by a negative lift coefficient. A stability analysis for a mono-dispersed system nevertheless showed, that influence of the lift force is much larger, compared to the influence of the turbulent dispersion force, if only bubble induced turbulence is considered. Thus, the stability condition is practically the positive sign of the lift force coefficient. The extension of the analysis to two bubbles classes, from which one being small enough to have a positive lift coefficient, results in a minimum fraction of small bubbles needed for stability. Finally a generalized criterion for N bubble classes and for a continuous bubble size distribution is given.     

Theoretical modelling of the effect of surface active species on the mass transfer rates in bubble column reactors

The complex composition of the liquid media in bubble column reactors makes their understanding and theoretical modelling challenging. In this work we have studied the effect of surface tension and contaminants, salts, on the mass transfer rates from a theoretical point of view, looking for a deeper understanding on the effect of surface active species which usually reduce surface tension and modify bubble surface behaviour. The specific contact area is obtained using a population balance where the effect of the presence of contaminants is addressed by the proper theoretical closures for bubble coalescence efficiency, for partially and fully immobile surfaces, and bubble break-up. Meanwhile, the contribution of contaminants to the liquid-film resistance is implemented as function of the coverage of the surface of the bubbles. It was found that the degree of bubble surface coverage not only affects bubble coalescence but also their break-up. The ion strength defines bubbles stability and the critical Weber number can be predicted as function of ion strength. Furthermore, the mass transfer rates are function of the surface coverage by the electrolytes. The model was able to predict k_La taking into account the fact that the concentration profiles surrounding individual bubbles are not completely developed due to the presence of other bubbles, in agreement with previous results from the literature.     

COMPREHENSIVE STUDY OF THE GAS HOLD UP AND BUBBLE SIZE DISTRIBUTION IN HIGHLY VISCOUS LIQUIDS I. GLYCEROL SOLUTIONS

The overall gas hold up, E_G, and bubble size distribution were separated into the particular gas hold up, E_GK, and Sauter diameter. d_SG. due to “small bubbles” as well as E_GG and d_SG, due to “intermediate to large bubbles.” Bubbles are defined to be “small” if they remain in the bubbling layer 15 seconds after the gas flow is turned off. The bubbles which leave the layer during this time are considered to be “intermediate to large bubbles.” The time dependences of E_G E_GK and E_GG, as well as of bubble size distribution after initiating the aeration of the liquid, is investigated. The steady state E_G, E_GK and E_GG, Sauter diameter and specific geometrical surface area of “small” and “intermediate to large” bubbles as well as of the entire bubble population were determined in bubble columns employing 50, 70, 90 and 95% glycerol solutions and perforated plates with different hole diameters (d_H = 0.5. 1.0 and 3.0 mm) respectively. In highly viscous media the “small” and “very large” bubble fractions are high. A comparison of the specific geometrical bubble surface areas with the corresponding volumetric mass transfer coefficients, k_La's, measured earlier indicate that the “small” bubbles do not contribute to k_La. The influence of the “small” bubbles on the fluiddynamics of the two phase system is discussed.     

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 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.     

Experimental Study on Bubble Rising and Descending Velocity Distribution in a Slurry Bubble Column Reactor

To determine bubble rising and descending velocity simultaneously, a BVW‐2 four‐channel conductivity probe bubble parameters apparatus and its analysis are used in gas‐liquid and gas‐liquid‐solid bubble columns. The column is 100 mm in internal diameter and 1500 mm in height. The solid particles used are glass beads with an average diameter of 17.82 μm, representing typical particle size for catalytic slurry reactors. The effects of superficial gas velocity (1.0 cm/s ≤ U_g ≤ 6.4 cm/s), solid holdup (0 % ≤ ?_s ≤ 30 %), and radial location (r/R = 0, 0.4, and 0.7) on bubble velocity distributions are determined. It is found that increasing U_g can increase the velocity of bubbles but do not exert much influence on bubble velocity distribution. Solid holdup mainly affects the distribution of bubble velocity while the radial direction affects bubble velocity distribution only slightly. The ratio of descending bubbles to rising bubbles increases from the bubble column center to the wall. It can be proved experimentally that large bubbles do not always rise faster than small bubbles at higher U_g (for example 6.4 cm/s).     

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).     

Analysis of deformation and internal flow patterns for rising single bubbles in different liquids

Gas–liquid multiphase flow is a significant phenomenon in chemical processes. The rising behaviors of single bubbles in the quiescent liquids have been investigated but the internal flow patterns and deformation rules of bubbles, which influence the mass transfer efficiency to a large extent, have received much less attention. In this paper, the volume of fluid method was used to calculate the bubble shapes, pressure, velocity distributions,and the flow patterns inside the bubbles. The rising behavior of the bubbles with four different initial diameters,i.e., 3 mm, 5 mm, 7 mm and 9 mm was investigated in four various liquids including water, 61.23% glycerol,86.73% glycerol and 100% glycerol. The results show that the liquid properties and bubble initial diameters have great impacts on bubble shapes. Moreover, flow patterns inside the bubbles with different initial diameters were analyzed and classified into three types under the condition of different bubble shapes. Three correlations for predicting the maximum internal circulation inside the bubbles in 86.73% glycerol were presented and the R-square values were all bigger than 0.98. Through analyzing the pressure and velocity distributions around the bubbles, four rules of bubble deformation were also obtained to explain and predict the shapes.     

Multiphase reacting flow studies of bubble column ozonation reactor for water remediation

A multiphase Volume‐of‐fluid (VOF) model was developed to gain further insights into the reactive flow parameters and electrical capacitance tomography (ECT) measurements on the remediation of hazardous organic pollutants. Low ozone bubble frequencies were obtained for high surface tension fluids, and the liquid viscosity affected the ozone bubbling frequency. The VOF model indicated that the increase of inlet gas velocity enriched the ozone bubble detachment and concomitantly generated larger ozone bubbles, decreasing the detoxification rates. VOF mappings and ECT visualizations of gas‐liquid unveiled preferential routes and highlighted the attenuation of the axisymmetric behavior of the ozonation bubble column under high‐interaction regimes.     

Behavior of a single coherent gas bubble chain and surrounding liquid jet flow structure

The motion of a single nitrogen gas bubble chain and the structure of water flow field surrounding the chain were experimentally studied. We developed a bubble generator that can control both the bubble diameter and the generation frequency independently. Experimental conditions of bubble Reynolds number and bubble distance divided by bubble diameter were from 300 to 650 and from 6.5 to 300, respectively. We discuss the interaction effects on the motion of each bubble rising in a chain, as compared to the effects of a single rising bubble. The bubble trajectories and the surrounding water flow fields in the state of bubbles rising in a chain were investigated using a high-speed digital video camera and an analog single-lens-reflex camera. We observed two important physical phenomena. First, bubbles passed through a nearly identical path in the case of low frequency of bubble production. On the contrary, at a height of approximately 50 mm from the nozzle, the bubbles in the case of high frequency deviated and scattered from this path due to bubble-bubble interaction. Second, with higher bubble production frequency, coherent bubble chain and the characteristic structure of the surrounding water flow called “liquid jet” were observed near the nozzle. The direction of liquid jet flow differed from the bubble trajectory. We theoretically investigated the relation of coherent bubble chain and liquid jet by applying the conservation of liquid momentum.     

Adhesion of solid particles to gas bubbles. Part 2: Experimental

In slurry bubble columns, the adhesion of solid catalyst particles to bubbles may significantly affect the G-L mass transfer and bubble size distribution. This feature may be exploited in design by modifying the hydrophilic or hydrophobic nature of the particles used. Previously we have proposed a generalised model, describing the adhesion of particles to G-L interface under stagnant conditions. In this work, we studied the adhesion of particles characterised by different degree of hydrophobicity and porosity: non-porous polystyrene and glass beads, unmodified and hydrophobised mesoporous silica, and activated carbon particles. Images recorded at high optical magnification show the particles adhering to gas bubbles individually or as aggregates. In aqueous media, higher liquid surface tension and particle surface hydrophobicity increase the adhesion strength and the tendency of particles to agglomerate, in agreement with the model. The adhesion of non-porous rough-surface particles to gas bubbles can be characterised by the receding contact angle. The advancing contact angle represents better the adhesion of the same particles to liquid droplets. We found that the “effective” contact angle of porous particles is much lower than an “intrinsic” contact angle calculated from the heat of immersion in water, or measured by sessile drop method. An equivalent contact angle derived from the Cassie rule explains the wetting behaviour of particles having the pores filled with liquid.     

PREDICTION OF VOID FRACTION AND VELOCITY PROFILES OF BUBBLY FLOWS IN VERTICAL PIPES

Adopting a similar approach to Beyerlein et al. (1985), void fraction distributions in turbulent two-phase bubbly air/water upflows and downflows in vertical pipes were analyzed using a simple transport model which was based on the assumptions that the lateral shear-induced lift force acting on bubbles (Thomas et al., 1983) is balanced by bubble dispersion, and that bubbles in the flow are conserved i.e. no bubble breakup or coalescence occurs. The model shows the importance of considering the lateral lift force experienced by bubbles as they move relative to the liquid phase in a non-uniform velocity field. This force causes the bubbles to accumulate near the wall forming a high concentration for upward flow, while the concentration increases toward the centre of the pipe for downward flow. The eddy diffusivity, as widely used in calculation of single-phase flow, can be extended to include the effect of pseudo-turbulence (Lance and Balaille, 1991) due to bubbles, and thus can be linked with the bubble dispersion coefficient. It is also demonstrated that the transverse or radial pressure gradient induced by the Reynolds stress exerts a lateral force on the bubbles, and thus affects their distribution in the flow. A comparison of the model predictions with experimental data from Serizawa et al. (1975) for upflows and Wang et al. (1987) for both upflows and downflows shows that our model predicts void fraction peaking near the wall for upflows and coring at the centre-line for downflows. Compared with similar investigations (e.g., Drew and Lahey, 1982; Lopez de Bertodano et al., 1990) of the same problem, our model approach appears to be simpler and more suitable for engineering calculations.     

Prediction of bubble diameter at detachment from a wall orifice in liquid cross-flow under reduced and normal gravity conditions

Bubble formation and detachment is an integral part of the two-phase flow science. The objective of the present work is to theoretically investigate the effects of liquid cross-flow velocity, gas flow rate embodied in the momentum flux force, and orifice diameter on bubble formation and detachment in a wall-bubble injection configuration. A two-dimensional one-stage theoretical model based on a global force balance on the bubble evolving from a wall orifice in a cross liquid flow is presented in this work. In this model, relevant forces acting on the evolving bubble are expressed in terms of the bubble center of mass coordinates and solved simultaneously. Relevant forces in low gravity included the momentum flux, shear-lift, surface tension, drag and inertia forces. Under normal gravity conditions, the buoyancy force, which is dominant under such conditions, can be added to the force balance. Two detachment criteria were applicable depending on the gas to liquid momentum force ratio. For low ratios, the time when the bubble acceleration in the direction of the detachment angle is greater or equal to zero is calculated from the bubble x and y coordinates. This time is taken as the time at which all the detaching forces that are acting on the bubble are greater or equal to the attaching forces. For high gas to liquid momentum force ratios, the time at which the y coordinate less the bubble radius equals zero is calculated. The bubble diameter is evaluated at this time as the diameter at detachment from the fact that the bubble volume is simply given by the product of the gas flow rate and time elapsed. Comparison of the model's predictions was also made with predictions from a two-dimensional normal gravity model based on Kumar-Kuloor formulation and such a comparison is presented in this work.     

Lightnin静态混合器内气泡分散流体动力学特性实验研究

以Lightnin静态混合器（LSM）内水-空气气液两相体系为研究对象,在连续相水表观速度U_L=0.071~0.127 m/s和离散相空气表观速度U_G=0.007~0.042 m/s的条件下,研究内径100 mm的LSM内气液两相湍流流动阻力与气泡分散水动力学行为。使用分辨率为1920×1080的高速相机Revealer-2F04M采集混合器内不同轴向窗口的气泡群演化过程。结果表明：当U_L<0.085 m/s和U_G=0.025~0.042 m/s时,LSM内的流型为泡状流。随着气泡群流经混合元件数的增加,气泡群的Sauter平均直径d₃₂逐渐减小。当液体表观速度U_L≤0.085 m/s时,Sauter平均直径d₃₂随气体表观速度的增加先减小后增大;U_G =0.028 m/s时d₃₂达到局部最小值,53%的气泡直径d_B/D₀在0.02~0.05范围内。Sauter平均直径、内径与无量纲停留时间τ之间的关系满足d₃₂/D₀=0.031τ^-0.14We^-0.41。平均气含率α的增大显著增加了单位体积内气泡数量密度,加剧气泡与元件表面碰撞频率,增大旋涡二次流强度,导致摩擦系数显著降低;采用Lockhart-Martinelli方法对实验数据回归,得到气液两相流压降预测常数C的关联式：C=5.26×10⁵U_G^-0.91/Re^0.74。