CFD Simulations of a Bubble Column Operating in the Homogeneous and Heterogeneous Flow Regimes

Bubble columns are operated either in the homogeneous or heterogeneous flow regime. In the homogeneous flow regime, the bubbles are nearly uniform in size and shape. In the heterogeneous flow regime, a distribution of bubble sizes exists. In this paper, a CFD model is developed to describe the hydrodynamics of bubble columns operating in either of the two flow regimes. The heterogeneous flow regime is assumed to consist of two bubble classes: “small” and “large” bubbles. For the air‐water system, appropriate drag relations are suggested for these two bubble classes. Interactions between both bubble populations and the liquid are taken into account in terms of momentum exchange, or drag‐, coefficients, which differ for the “small” and “large” bubbles. Direct interactions between the large and small bubble phases are ignored. The turbulence in the liquid phase is described using the k‐ϵ model. For a 0.1 m diameter column operating with the air‐water system, CFD simulations have been carried out for superficial gas velocities, U, in the range 0.006–0.08 m/s, spanning both regimes. These simulations reveal some of the characteristic features of homogeneous and heterogeneous flow regimes, and of regime transition.     

Stability analysis of a bubble column

The aim of the paper is to study the transition between homogeneous and heterogeneous flows in bubble columns, by taking into account the destabilizing effects of both added mass force and deformation of the bubbles. The transition is expressed in terms of instability of a uniform bubbly flow. Special attention is paid to closure relations involving pressure terms at the gas–liquid interface. The models presented in this paper give instructive information on the transition between homogeneous and heterogeneous flows in bubble columns, highlighting the respective weight of physical phenomena, modeled in terms of closure relations introduced in the two-fluid model.     

Stability analysis of bubble columns: Predictions for regime transition

A criterion for the transition from the homogeneous to the heterogeneous regime in a bubble column is developed based on the theory of linear stability. Hydrodynamics of bubble column is described by two-fluid model incorporating the interphase forces like drag force and added mass force. Added mass force affects the hydrodynamics of gas-liquid flows significantly and is formulated by taking into account the bubble deformation. A proper understanding of the nature of gas-liquid interface (clean or contaminated) is desired for the reliable predictions of the added mass coefficient. Data from the literature on the transition in bubble columns is critically analyzed. A good agreement has been obtained between the experimental transition gas hold-up and the predictions of the same obtained by the theory developed in this work.     

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).     

Effect of interfacial forces and turbulence models on predicting flow pattern inside the bubble column

The numerical approaches have been used in many studies to predict the flow pattern inside the bubble column reactors because of the difficulties that are still found in designing and scaling-up the bubble columns. This review makes an effort to show suitable interfacial forces i.e., drag force, lift force, turbulent dispersion models and virtual mass and turbulence models such as standard k–ɛ model, Reynolds Stress Model, Large Eddy Simulation to predict flow pattern inside the bubble column using Eulerian–Eulerian. The effect of various interfacial forces and turbulence models on gas–liquid velocity and gas hold-up in bubble column is critically reviewed.     

基于气泡群相间作用力模型的加压鼓泡塔流体力学模拟

目前,多数文献报道了冷态加压湍动鼓泡塔内流动特征,并且通过实验数据回归相关经验关联式。然而,此类关联式适用范围有限,难以直接外推到工业鼓泡塔反应器条件。因此,在FLUENT平台上建立了基于气泡群相间作用力的、动态二维加压鼓泡塔计算流体力学模型。通过数值模拟考察了操作压力为0.5~2.0 MPa,表观气速为0.20~0.31 m·s^-1,内径0.3 m鼓泡塔内流场特性参数分布,并且与冷态实验数据进行比较。结果表明,采用修正后的气泡群曳力模型、径向力平衡模型以及壁面润滑力模型描述气泡群相间作用力,能够较为准确地反映平均气含率和气含率径向分布随操作压力和表观气速变化的规律。     

鼓泡塔反应器气液两相流CFD数值模拟

对圆柱形鼓泡塔反应器内的气液两相流动进行了三维瞬态数值模拟,模拟的表观气速范围为0.02～0.30 m•s^-1; 模拟采用了双流体模型,并耦合了气泡界面密度单方程模型预测气泡尺寸,该模型考虑了气泡聚并与破碎对气泡尺寸的影响。液相湍流采用考虑气相影响的修正k-ε模型,两相间的动量传输仅考虑曳力作用。模拟获得了轴向气/液相速度分布、气含率分布、湍流动能分布以及气泡表面面积密度等,对部分模拟结果与实验值进行了定量比较,结果表明模拟结果与实验结果吻合较好。     

CFD modeling of slurry bubble column reactors for Fisher-Tropsch synthesis

Industrial bubble column reactors for Fischer-Tropsch (FT) synthesis include complex hydrodynamic, chemical and thermal interaction of three material phases: a population of gas bubbles of different sizes, a liquid phase and solid catalyst particles suspended in the liquid. In this paper, a CFD model of FT reactors has been developed, including variable gas bubble size, effects of the catalyst present in the liquid phase and chemical reactions, with the objective of predicting quantitative reactor performance information useful for design purposes. The model is based on a Eulerian multifluid formulation and includes two phases: liquid-catalyst slurry and syngas bubbles. The bubble size distribution is predicted using a Population Balance (PB) model. Experimentally observed strong influence of the catalyst particles concentration on the bubble size distribution is taken into account by including a catalyst particle induced modification of the turbulent dissipation rate in the liquid. A simple scaling modification to the dissipation rate is proposed to model this influence in the PB model. Additional mass conservation equations are introduced for chemical species associated with the gas and liquid phases. Heterogeneous and homogeneous reaction rates representing simplified FT synthesis are taken from the literature and incorporated in the model.Hydrodynamic effects have been validated against experimental results for laboratory scale bubble columns, including the influence of catalyst particles. Good agreement was observed on bubble size distribution and gas holdup for bubble columns operating in the bubble and churn turbulence regimes. Finally, the complete model including chemical species transport was applied to an industrial scale bubble column. Resulting hydrocarbon production rates were compared to predictions made by previously published one-dimensional semi-empirical models. As confirmed by the comparisons with available data, the modeling methodology proposed in this work represents the physics of FT reactors consistently, since the influence of chemical reactions, catalyst particles, bubble coalescence and breakup on the key bubble-fluid drag force and interfacial area effects are accounted for. However, heat transfer effects have not yet been considered. Inclusion of heat transfer should be the final step in the creation of a comprehensive FT CFD simulation methodology. A significant conclusion from the modeling results is that a highly localized FT reaction rate appears next to the gas injection region when the syngas flow rate is low. As the FT reaction is exothermal, it may lead to a highly concentrated heat release in the liquid. From the design perspective, the introduction of appropriate heat removal devices may be required.     

A structured catalytic bubble column reactor: hydrodynamics and mixing studies

This paper reports the results of a comprehensive experimental study of the hydrodynamics and mixing in two bubble column reactors of 0.1 and 0.24 m in diameter with KATAPAK-S^® as packing material. Total gas hold up and axial dispersion coefficients were measured in the structured bubble columns and the values were compared with experimental results obtained in the same work with empty bubble columns. The results reveal that the gas hold up in structured bubble columns is practically the same as in empty bubble columns when compared at the same superficial gas velocity based on open area available for gas–liquid dispersion. The presence of the structured elements in the bubble column reactor reduces the liquid phase backmixing by one order of magnitude.     

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.     

Numerical investigation of the drag closure for bubbles in bubble swarms

The present paper describes an Euler–Lagrange model utilizing a drag closure derived from direct numerical simulations (front-tracking model) for (i) single isolated bubbles and (ii) bubbles rising in bubble swarms, expressed as a function of the local gas fraction. The model is applied to the prediction of an air/water system in a bubble column and for which experimental data is available. The effect of variation in size of the mapping window for the interphase coupling between the Eulerian and Lagrangian framework is investigated for both closure relations. It is found that the drag closure as a function of the local gas fraction is an improvement over the use of the drag closure for isolated single bubbles for the prediction of bubbly flow.     

Model validation for low and high superficial gas velocity bubble column flows

In the present work, gas-liquid flow dynamics in a bubble column are simulated with CFDLib using an Eulerian-Eulerian ensemble-averaging method in a two-dimensional Cartesian system. The two-phase flow simulations are compared to experimental measurements of a rectangular bubble column performed by Mudde et al. [1997. Role of coherent structures on Reynolds stresses in a 2-D bubble column. A.I.Ch.E. Journal 43, 913-926] and a cylindrical bubble column performed by Rampure et al. [2003. Modeling of gas-liquid/gas-liquid-solid flows in bubble columns: experiments and CFD simulations. The Canadian Journal of Chemical Engineering 81, 692-706] for low and high superficial gas velocities, respectively. The objectives are to obtain grid-independent numerical solutions using CFDLib to reconcile unphysical results observed using FLUENT with increasing grid resolutions [Law, D., Battaglia, F., Heindel, T.J., 2006. Numerical simulations of gas-liquid flow dynamics in bubble columns. In: Proceedings of the ASME Fluids Engineering Division, IMECE2006-13544, Chicago, IL], and to validate computational fluid dynamics (CFD) simulations with experimental data to demonstrate the use of numerical simulations as a viable design tool for gas-liquid bubble column flows. Numerical predictions are presented for the local time-averaged liquid velocity and gas fraction at various axial heights as a function of horizontal or radial position. The effects of grid resolution, bubble pressure (BP) model, and drag coefficient models on the numerical predictions are examined. The BP model is hypothesized to account for bubble stability, thus providing physical solutions.     

Experimental and numerical investigation of liquid circulation induced by a bubble plume in a baffled tank

Bubble induced liquid circulation is important in applications such as bubble columns and air-lift reactors. In this work, we describe an experimental and numerical investigation of liquid circulation induced by a bubble plume in a tank partitioned by a baffle. The baffle divides the tank into two compartments. Liquid can flow from one compartment to the other through openings at the top and the bottom of the baffle. Gas (air) was injected in the riser section in the form of bubbles at one corner of the tank. The temporal and spatial variation of velocity field in the liquid as a function of the gas flow rate was measured using particle image velocimetry (PIV). At a constant gas flow rate, the liquid flow field is unsteady due to the interaction with the bubbles. The time scales associated with the velocity-time series and the bubble plume thickness variation were calculated. The time averaged-velocity field was used to quantify the variation of the liquid circulation rate with gas flow rate. The turbulence in the liquid was measured in terms of turbulent intensities. These were calculated from the experimental data and were observed to be less than 3 cm/s. A 2-d Euler-Euler two-fluid model with buoyancy and drag as the interaction terms was used to simulate the flow. The parameters chosen for the simulations were selected from literature. It is shown that inclusion of turbulence model such as k-ε is necessary to capture the overall flow behavior. Good agreement was observed between experimentally obtained velocity profiles and the recirculation rates with the simulation results.     

Analogous description of the hydrodynamics of gas-solid fluidized beds and bubble columns

In this paper we stress analogies in the hydrodynamic behaviour of gassolid fluidized beds and bubble columns. Using published experimental data, it is demonstrated that the analogous hydrodynamic-behaviour is not only qualitative but also quantitative in nature. Specifically, we show the following.(1) The gas holdup in the homogeneous regimes of bubble columns and fluidized beds can be modelled in a unified way using V_slip = υ_∞(1 − ϵ_d)ⁿ⁻¹, where V_slip refers to the slip velocity between the dispersed (bubbles or particles) and continuous phases and ϵ_d the dispersed phase holdup. The Richardson-Zaki exponent n decreases with increasing gas density.(2) The transition from homogeneous to heterogeneous flow regimes in gasliquid bubble columns and gassolid fluid beds is delayed by increasing system pressure. Extrapolation of the influence of increased gas density allows us to consider liquidliquid dispersions and liquidsolid fluid beds as limiting cases.(3) In the heterogeneous flow regime of operation the classic two-phase theory of fluidized beds can be applied with profit to also describe the hydrodynamics of gasliquid bubble columns provided that the “dilute” phase is identified with the fast-rising large bubbles and the “dense” phase is identified with the liquid phase containing entrained “small” bubbles. Tentative analogies can also be drawn for the interphase mass transfer processes.(4) The “dense” phase backmixing can be modelled in a unified manner.(5) The two-phase theory can be extended to describe slurry reactors.It is argued that, because of cross-fertilization of concepts and information, appreciation of analogies can be invaluable tool in scaling up.     

鼓泡塔细胞反应器流体力学与传质特性

以超大规模细胞培养为目的,构建了与细胞培养体系十分接近的冷模实验体系,系统地研究了微载体(Cytodex I)、细胞保护剂(Pluronic F68)和消泡剂(Antifoam C)对鼓泡塔反应器中气、固、液三相流流体力学和氧传质特性的影响。在0.04～0.17cm/s 表观气速范围内采用 50 μm 孔径的烧结金属滤芯曝气时,在含有 0.5 和 1.0 g/L 的 Pluronic F68 的磷酸盐缓冲溶液冷模体系中,气含率与表观气速成线性增加关系,而气泡直径受表观气速影响较小;相同气速下的冷模体系与空气-水体系相比,气含率显著提高,气泡直径明显减小。在所研究的表观气速范围内微载体均可全悬浮,对气含率有一定增强,但微载体浓度为14%～20% 时对气泡大小几乎无影响。消泡剂用量在 1.60×10^-4时,可以有效抑制泡沫的形成。添加剂对液膜传质系数 k_L有较大负面作用,抵消了小气泡带来的传质面积增加,总的体积传质系数k_La 变化不大。Euler-Euler 多相流计算流体力学模型与拟稳态实验数据吻合较好,可用于指导反应器放...     

Calculation of flow fields in two and three-phase bubble columns considering mass transfer

The dimension of bubble column reactors is often based on empirical correlations. Very popular is the axial dispersion model. However, the applicability of these models is limited to the experimental conditions for which the dispersion coefficients are measured, because backmixing depends strongly on the columns dimension and the flow regime. This paper presents a numerical method for the calculation of the three-dimensional flow fields in bubble columns based on a multi-fluid model. Therefore, the local bubble size distribution is considered by a transport equation for the mean bubble volume, which is obtained from the population balance equation. For comparison with experimental results, the axial dispersion coefficients in the liquid and gas phase are calculated from the instationary, three-dimensional concentration fields of a tracer. The model is then extended to include mass transfer between the gas and liquid phase. Increasing mass transfer rates significantly influence the flow pattern. For several applications, a dispersed solid phase is added. For the calculation of three-phase gas-liquid-solid flow, the solid phase is considered numerically by an additional Eulerian phase.     

Numerical simulation of single bubble motion in ionic liquids

In this work a numerical simulation is studied to investigate the motion of single bubble in ionic liquids using an improved volume-of-fluid (VOF) method. In the improved method, besides the gravity and surface tension, a new drag force is added to the momentum equation in order to describe the gas–liquid interaction in the ionic liquids, which possess some special properties compared with the traditional solvents. The deformation, velocity and equivalent diameter of single bubble rising in three ionic liquids, i.e., bmimBF₄, bmimPF₆ and omimBF₄, are simulated and the calculation results agree well with the experimental data. Furthermore, the detailed velocity fields and pressure fields around the bubbles are predicted with the proposed numerical simulation model. This work is important for understanding the fluid dynamic performance of bubbles in ionic liquids, and could provide a useful tool for designing a bubble column with ionic liquids as its solvents.