Bubble mechanisms and characteristics at pore scale in a packed-bed reactor

An image processing technique was used to study dominant bubble mechanisms in a two-dimensional packed-bed at pore level under the bubbly flow regime. Bubble breakup and coalescence were identified as dominant mechanisms using a large number of image samples. Two types of coalescence mechanisms were identified that occur due to compression and deceleration associated with the bubbles and three breakup mechanisms were identified that are result of liquid shear force, bubble acceleration, and bubble impact. Data on various two-phase parameters, such as local void fraction, bubble velocity, size, number, and shape were obtained from the images. Results indicated that when a flow regime changed from bubbly to either trickling or pulsing flow, the number of average sized bubbles significantly decreased and the shape of the majority of the bubbles was no longer spherical. Although a mean bubble velocity of all sized bubbles was uniform for given gas and liquid superficial velocities, individual bubble velocities were quite different depending on the bubble location in the pore. The present bubble size distributions were compared with previous studies and the results on bubble size are in general agreement.     

Theoretical prediction of flow regime transition in bubble columns by the population balance model

Theoretical prediction of flow regime transition in bubble columns was studied based on the bubble size distribution by the population balance model (PBM). Models for bubble coalescence and breakup due to different mechanisms, including coalescence due to turbulent eddies, coalescence due to different bubble rise velocities, coalescence due to bubble wake entrainment, breakup due to eddy collision and breakup due to large bubble instability, were proposed. Simulation results showed that at relatively low superficial gas velocities, bubble coalescence and breakup were relatively weak and the bubble size was small and had a narrow distribution; with an increase in the superficial gas velocity, large bubbles began to form due to bubble coalescence, resulting in a much wider bubble size distribution. The regime transition was predicted to occur when the volume fraction of small bubbles sharply decreased. The predicted transition superficial gas velocity was about 4 cm/s for the air-water system, in accordance with the values obtained from experimental approaches.     

Experimental and modelling study of gas dispersion in a double turbine stirred tank

Gas dispersion in a double turbine stirred tank is experimentally characterised by measuring local gas holdups and local bubble size distributions throughout the tank, for three liquid media: tap water, aqueous sulphate solution and aqueous sulphate solution with PEG. For all these media, bubble coalescence generally prevails over breakage. Where average bubble size decreases, this can be attributed to the difference in slip velocity between different sized bubbles. Most of the coalescence takes place in the turbine discharge stream.A compartment model that takes into account the combined effect of bubble coalescence and breakage is used to simulate gas dispersion. The model predicts spatial distribution of gas holdup and of average bubble size, with average bubble size at the turbines as an input. Reasonable agreement between experiment and simulation is achieved with optimisation of two parameters, one affecting mainly the slip velocity, the other related mainly to the bubble coalescence/breakage balance. Different sets of parameters are required for each of the three liquid systems under study, but are independent of stirring/aeration conditions. The model only fails to simulate the smaller average bubble diameters at the bottom of the tank.     

网格和数值格式对TBPBM-CFD模型模拟鼓泡塔的影响

基于气泡动力学属性的现有认识,把气泡分成大、小气泡,首次建立了完整的双气泡相-群平衡模型(TBPBM)以预测气泡尺寸.通过编写用户自定义程序实现了TBPBM模型、Luo破碎模型以及Prince 聚并模型,并耦合TBPBM与CFD双流体模型对直径440 mm鼓泡塔进行数值模拟,详细考察了网格与数值格式对TBPBM-CFD模型模拟结果的影响.结果表明,网格与数值格式对各物理变量的模拟结果影响非常大,特别是网格和体积分数方程对流项离散格式的影响最为显著.随着计算精度的提高,湍流耗散率和整体气含率分布梯度增大,气泡平均直径减少,大气泡所占气相比率降低,液相速度及气含率径向分布与实验值更趋吻合.     

ABOUT BUBBLE BREAKUP MODELS TO PREDICT BUBBLE SIZE DISTRIBUTIONS IN HOMOGENEOUS FLOWS

We present results of a study of the equilibrium between coalescence and breakup of bubbles in homogeneous media with isotropic turbulence. The Boltzmann equation for the particle distribution function (pdf) was evaluated in steady state, using a multigroup approach. Binary bubble breakup was assumed. We used uniform function, delta function, and the model proposed by Luo and Svendsen (1996) for the bubble size distributions resulting from a breakup. The bubble breakup rate was calculated with Luo and Svendsen (1996) and Prince and Blanch (1990) models. Significant differences in bubble breakup rate, and therefore in bubble size distribution, are predicted by both models. The models were compared to the bubble size distributions measured by Boyd and Varley (1998) in air-water flow. The transient response of the bubble size distribution and interfacial area density was also analyzed. This work is of significance in the prediction of reaction rates when they are dependent on bubble size distribution.     

About bubble breakup models to predict bubble size distributions in homogeneous flows

We present results of a study of the equilibrium between coalescence and breakup of bubbles in homogeneous media with isotropic turbulence. The Boltzmann equation for the particle distribution function (pdf) was evaluated in steady state, using a multigroup approach. Binary bubble breakup was assumed. We used uniform function, delta function, and the model proposed by Luo and Svendsen (1996) for the bubble size distributions resulting from a breakup. The bubble breakup rate was calculated with Luo and Svendsen (1996) and Prince and Blanch (1990) models. Significant differences in bubble breakup rate, and therefore in bubble size distribution, are predicted by both models. The models were compared to the bubble size distributions measured by Boyd and Varley (1998) in air-water flow. The transient response of the bubble size distribution and interfacial area density was also analyzed. This work is of significance in the prediction of reaction rates when they are dependent on bubble size distribution.     

Computational modeling of microbubble coalescence and breakup using large eddy simulation and Lagrangian tracking

The flow of dispersed microbubbles was studied with an Eulerian–Lagrangian technique using large eddy simulation to predict the continuous liquid flow and Lagrangian tracking to compute bubble trajectories. The model fully accounts for bubble coalescence and breakup and was applied to horizontal and vertical channel flows. With low levels of turbulence, gravity in horizontal, and lift in vertical, channel flows govern the bubble spatial and collision distribution. When turbulence is sufficiently high to, at least partially, oppose bubble preferential concentration, more uniform collision and coalescence distributions are found, although these remain peaked near the wall in both configurations. Almost 100% coalescence efficiency was always found, due to bubbles colliding along similar trajectories, with breakup only recorded in a flow of low surface tension refrigerant R134a. Models like this can provide the required quantitative understanding of the microbubbles complex behavior, as well as supporting the development of more macroscopic modeling closures.     

Bubble size modeling approach for the simulation of bubble columns

The constant bubble size modeling approach (CBSM) and variable bubble size modeling approach (VBSM) are frequently employed in Eulerian–Eulerian simulation of bubble columns. However, the accuracy of CBSM is limited while the computational efficiency of VBSM needs to be improved. This work aims to develop method for bubble size modeling which has high computational efficiency and accuracy in the simulation of bubble columns. The distribution of bubble sizes is represented by a series of discrete points, and the percentage of bubbles with various sizes at gas inlet is determined by the results of computational fluid dynamics (CFD)–population balance model (PBM) simulations, whereas the influence of bubble coalescence and breakup is neglected. The simulated results of a 0.15 m diameter bubble column suggest that the developed method has high computational speed and can achieve similar accuracy as CFD–PBM modeling. Furthermore, the convergence issues caused by solving population balance equations are addressed.     

基于TFM-PBM耦合模型的离心泵内微气泡破碎合并的模拟研究

了解离心泵内微气泡的发生特性,对于优化现有基于旋转流场的微气泡发生装置的性能、提高工业废水废气的污染物去除率至关重要。在考虑气泡破碎合并的前提下,通过将双流体模型（TFM）与群体平衡模型（PBM）进行耦合,求解离心泵内气液两相旋转流场,研究了入口体积气含率（IGVF）、入口气泡尺寸对泵内气泡沿程尺寸变化、出口气泡尺寸分布的影响,并结合Luo等的破碎合并模型分析成因。结果表明,随IGVF增加,叶轮内气体聚集引起局部气含率陡升,气泡由破碎主导转变为合并主导,而后在蜗壳内气含率恢复正常,气泡又变为破碎主导,总体上出口气泡尺寸逐渐增大。另外,入口气泡尺寸对出口气泡尺寸的影响对IGVF敏感,当IGVF较低时,随入口气泡尺寸增大,出口气泡尺寸先增大后减小;而当IGVF较高时,由于泵内气体聚集,入口气泡尺寸的影响并不明显。     

二维鼓泡床内气泡尺寸分布的实验与CFD模拟

在有机玻璃制成的二维鼓泡床(0.20m×0.02m×2.00m)内,采用摄像法对空气－自来水的气液两相体系的气泡尺寸分布进行了考察。以商业计算流体力学软件ANSYS CFX 10.0为平台,在双流体模型的基础上,采用k-ε湍流模型和GRACE曳力模型对气液鼓泡床内流体动力学行为进行了多相流CFD数值模拟。结果表明 MUSIG(Multiple Size Group)模型实现了对多气泡体系内气泡尺寸分布特性的考察,气泡尺寸分布的模拟结果与实验结果吻合得较好,从而说明了考虑了气泡聚并破碎的MUSIG模型能很好地反映出鼓泡床内气泡尺寸分布特性。     

Bubble flow in trickle beds: investigations using resistive sensors

The local hydrodynamics of co-current gas-liquid down-flow through porous media are investigated in a quasi two-dimensional regular arrangement by means of a network of resistive sensors. The investigations are focused on a liquid continuous flow regime, the dispersed bubble flow, where the gas is divided into elongated bubbles. Due to the variation of the local flow channel orientation and the local void fraction, the average bubble velocity strongly depends on the local geometry. The flow is more coherent in vertical constrictions, compared to all other types of sites, this is probably due to bubble stagnation in the flow channel enlargements. At a given liquid superficial velocities and for sufficiently high superficial gas velocities, the average bubble size is independent of the gas flow rate; it is of the order of magnitude of the volume of the enlargements of the porous medium. The maximum bubble size is about three times its average size, corresponding thus to the coalescence of three average sized bubbles.     

Coalescence efficiency of bubbles in bubble columns

Bubble size distribution was modelled by employing the population balance equation (PBE). All three bubble coalescence mechanisms (turbulence, buoyancy and laminar shear) and the main bubble breakup mechanism (breakup due to turbulent eddies) were considered in the model. Local bubble size distributions at the top and bottom of the column were obtained by solving this PBE. The results were compared with the experimental data for seven independent multiphase systems (water/air, isomax diesel/air, kerosene/air and four other liquid mixture/air) at two diverse gas velocities. The experimental adjustable constant in the coalescence efficiency function was determined by fitting the population balance to the experimental bubble size distributions. An empirical correlation was proposed for the coalescence efficiency by the dimensional analysis, which includes Reynolds and Weber numbers. © 2011 Canadian Society for Chemical Engineering     

CFD simulation of bubble columns incorporating population balance modeling

A computational fluid dynamics (CFD)-code has been developed using finite volume method in Eulerian framework for the simulation of axisymmetric steady state flows in bubble columns. The population balance equation for bubble number density has been included in the CFD code. The fixed pivot method of Kumar and Ramkrishna [1996. On the solution of population balance equations by discretization—I. A fixed pivot technique. Chemical Engineering Science 51, 1311-1332] has been used to discretize the population balance equation. The turbulence in the liquid phase has been modeled by a k-ε model. The novel feature of the framework is that it includes the size-specific bubble velocities obtained by assuming mechanical equilibrium for each bubble and hence it is a generalized multi-fluid model. With appropriate closures for the drag and lift forces, it allows for different velocities for bubbles of different sizes and hence the proper spatial distributions of bubbles are predicted. Accordingly the proper distributions of gas hold-up, liquid circulation velocities and turbulence intensities in the column are predicted. A survey of the literature shows that the algebraic manipulations of either bubble coalescence or break-up rate were mainly guided by the need to obtain the equilibrium bubble size distributions in the column. The model of Prince and Blanch [1990. Bubble coalescence and break-up in air-sparged bubble columns. A.I.Ch.E. Journal 36, 1485-1499] is known to overpredict the bubble collision frequencies in bubble columns. It has been modified to incorporate the effect of gas phase dispersion number. The predictions of the model are in good agreement with the experimental data of Bhole et al. [2006. Laser Doppler anemometer measurements in bubble column: effect of sparger. Industrial & Engineering Chemistry Research 45, 9201-9207] obtained using Laser Doppler anemometry. Comparison of simulation results with the experimental measurements of Sanyal et al. [1999. Numerical simulation of gas-liquid dynamics in cylindrical bubble column reactors. Chemical Engineering Science 54, 5071-5083] and Olmos et al. [2001. Numerical simulation of multiphase flow in bubble column reactors: influence of bubble coalescence and breakup. Chemical Engineering Science 56, 6359-6365] also show a good agreement for liquid velocity and gas hold-up profiles.     

A unified theoretical model for breakup of bubbles and droplets in turbulent flows

Pressure has a significant effect on bubble breakup, and bubbles and droplets have very different breakup behaviors. This work aimed to propose a unified breakup model for both bubbles and droplets including the effect of pressure. A mechanism analysis was made on the internal flow through the bubble/droplet neck in the breakup process, and a mathematical model was obtained based on the Young–Laplace and Bernoulli equations. The internal flow behavior strongly depended on the pressure or gas density, and based on this mechanism, a unified breakup model was proposed for both bubbles and droplets. For the first time, this unified breakup model gave good predictions of both the effect of pressure or gas density on the bubble breakup rate and the different daughter size distributions of bubbles and droplets. The effect of the mother bubble/droplet diameter, turbulent energy dissipation rate and surface tension on the breakup rate, and daughter bubble/droplet size distribution was discussed. This bubble breakup model can be further used in a population balance model (PBM) to study the effect of pressure on the bubble size distribution and in a computational fluid dynamics‐population balance model (CFD‐PBM) coupled model to study the hydrodynamic behaviors of a bubble column at elevated pressures. © 2014 American Institute of Chemical Engineers AIChE J, 61: 1391–1403, 2015     

精馏塔板相界面积的粒数衡算模型

通过对气液湍流系统中气泡的动力学行为进行分析推导出气泡破碎速率与聚并速率的表达式,在此基础上建立了描述气泡分散特性的粒数衡算模型.求解粒数衡算方程可以计算精馏塔板上气泡的粒度分布以及气液相界面积,模拟计算的结果与实验测量的数据相当一致,证明可以利用粒数衡算模型较准确地预测气液湍流系统的分散性质.     

Population balance modelling of bubbling fluidized bed reactors—I. well-stirred dense phase

A detailed population balance model is presented for a fluidized bed reactor incorporating: the formation of bubbles at the grid plate, their rise with velocities governed by their sizes, random coalescence between bubbles, gas exchange between bubbles and the dense phase, and a first order chemical reaction in the dense phase under well-mixed conditions. Reaction conversion is calculated as a function of dimensionless parameters relating the rates of various competing processes such as coalescence, dense phase mixing, mass exchange between bubbles and dense phase and reaction rate. Comparison of conversions with those of Davidson et al. (1977) show significant variations indicating that the dynamics of bubble size distributions could have non-trivial effects on the extent of reaction. Fluctuations in bubble populations did not seem strong enough to translate to strong fluctuations in reaction conversion.     

Experimental measurement of bubble breakup in a jet bubbling reactor

The bubble breakups in a jet bubbling reactor are captured using a high-speed camera and the velocity field is measured by particle image velocimetry. Two typical breakup patterns, jet breakup and jet-vortex breakup are observed. The breakup time interval of the jet-vortex breakup is two orders of magnitude higher than the jet breakup. The probability of the jet-vortex breakup and the jet breakup accounting in the total breakup events increases and decreases with the jet velocity and the mother bubble size, respectively. The bubble breakup region increases with the jet velocity. The bubble breakup frequency increases with the turbulent dissipation rate and the mother bubble size. The average number of daughter bubbles increases with the Weber number. An L-shaped daughter bubble size distribution is observed. Empirical correlations are established for the bubble breakup frequency, the average number of daughter bubbles and daughter bubble size distribution, and fitted well with the experimental results.