INVISCID LIQUID CIRCULATION IN BUBBLE COLUMNS

For circulation in axi-symmetric (cylindrical) bubble columns, the recently developed mathematical model^25,26 has been used along with the criterion of minimum circulation strength to determine the height of each circulation cell in a tall column. This is then used to derive a theoretical expression, first of its kind, for gas hold-up inside a bubble column. The predictions of this equation as well as the equation derived here for axial liquid velocity at column axis have been compared with available data and the comparison is found to be excellent for both the variables. An explicit relation is derived for the average liquid circulation velocity. The model is also used to derive an expression for liquid axial dispersion coefficient which compares almost exactly with Deckwer et al.'s⁴ correlation.

For circulation in two-dimensional bubble columns a new mathematical model is developed. The predictions of bubble envelope shape and bubble envelope area compare well with published data. The predictions of number of circulation cells in the horizontal direction also compare well with published data.     

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。     

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.     

基于EMMS方法的鼓泡塔反应器CFD及群平衡模拟

能量最小多尺度（energy-minimization multi-scale,EMMS）方法已经被应用于气液体系中群平衡（population balance model,PBM）模型的改进。EMMS模型可计算气泡破碎聚并过程的能量,进而获得聚并速率的修正因子。应用这一模型对高气速鼓泡塔进行了模拟计算,并进一步对比了均一尺径模型、CFD-PBM模型以及CFD-PBM-EMMS模型的模拟结果与实验数据。结果表明,在高表观气速条件下,基于EMMS方法的群平衡模型可以更加准确地预测鼓泡塔中不同高度的气泡尺径分布和轴向液速,同时提高了对整体气含率和局部气含率的模拟准确性。在表观气速为0.16 m·s^-1和0.25 m·s^-1时,CFD-PBM-EMMS模型对气泡尺径分布的预测精度更高,同时整体气含率模拟的相对误差下降为5%和15%,局部气含率模拟平均相对误差下降为8%和17%。     

Liquid phase mixing in bubble columns with Newtonian and non-Newtonian fluids

A hydrodynamic model for the liquid phase in bubble columns is developed. The proposed model for fully developed turbulent Newtonian and non-Newtonian fluids is based on an energy balance and the mixing length theory. The predictions of the model are in reasonably good agreement with data on liquid velocity at the column axis and the axial dispersion coefficient. The liquid velocity data in an inverted conical bottom gas—liquid column contactor have also been measured. They are correlated by the proposed model reasonably well.     

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.     

Local hydrodynamics of gas–liquid-nanoparticles three-phase fluidization

The laser Doppler anemometer (LDA) and conductivity probes were used for measuring the local hydrodynamic performances such as gas holdup and liquid velocity in a lab-scale gas–liquid–TiO₂ nanoparticles three-phase bubble column. Effects of operating parameters on the local gas holdup and liquid velocity were investigated systematically. Experimental results showed that local averaged axial liquid velocity and local averaged gas holdup increased with increasing superficial gas velocity but decreased with increasing TiO₂ nanoparticles loading and the axial distance from the bottom of the bubble column. A three-dimensional computational fluid dynamic (CFD) model was developed in this paper to simulate the structure of gas–liquid–TiO₂ nanoparticles three-phase flow in the bubble column. The time-averaged and time-dependent predictions were compared with experimental data for model validation. A successful prediction of instantaneous local gas holdup, gas velocity, and liquid velocity were also presented.     

基于径向力平衡的鼓泡塔二维流体力学模型

提出了一种鼓泡塔二维轴对称流体力学模型,模型中将气泡所受的升力以及湍动扩散力作为形成塔内气含率稳定分布的主要机制.采用Fluent 6.3流体力学软件求解模型,能得到稳定的二维流场,气含率与液速分布与实验值吻合良好,模型能准确反映表观气速(0.12～0.62 m·s^-1)以及塔径(ø200 mm、ø500 mm、ø800 mm)对流型的影响.利用该模型对更大直径鼓泡塔的流动参数进行了预测,结果与文献给出的经验关联式相符.     

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.     

Turbulent circulation in bubble columns from eddy viscosity distributions of single-phase pipe flow

The exact prediction of the flow structure in bubble columns is important for their design and scale-up. This paper proposes a theoretical model for the liquid circulation on the basis of Reynolds equation of motion and the eddy viscosity distribution of single phase pipe flow, and presents a derivation of an analytical equation for the axial liquid velocity profiles that is fast and easy to use. The model shows a strong analogy for the eddy viscosity between multiphase and single-phase systems, and how both eddy and molecular viscosities affect the flow. The velocity profiles calculated from the model are shown to agree well with reported experimental data for both low and high viscosity fluids.     

Axial dispersion in a rectangular bubble column

This paper presents the results of an experimental study on the gas holdup and the liquid phase axial dispersion coefficient in a narrow packed and unpacked rectangular bubble column. In both cases the gas and liquid flow rates were varied and the data were obtained by employing standard tracer technique. The gas holdup and the axial dispersion coefficient for both the packed and unpacked columns were found to be dependent on the gas and liquid flow rates. For given gas and liquid velocities and a given packing size in the case of the packed column, the rectangular column gave significantly higher dispersion coefficients than a cylindrical column of the equivalent cross sectional area. This result agrees very well with the one predicted by the velocity distribution model. The correlations for the Peclet number, the axial dispersion coefficient, and the fluid holdup for both the unpacked and packed bubble columns are presented.     

CIRCULATION IN LARGE SCALE JET BUBBLE COLUMNS

A hydrodynamic study in a gas-liquid jet bubble column was undertaken in a column with a 122 cm diameter cylindrical section and a conical bottom section approximately 180cm in height. Due to the jetting action in the cone, the circulation patterns are different from those in cylindrical bubble columns. In order to examine this difference in flow pattern, circulation velocity measurements were undertaken (for V₅ = 0.39-2.73 cm/s and V, = 0-0.044 cm/s) using the Pavlov tube technique. These measurements should be helpful in understanding other design parameters (such as mixing, phase distribution, transport coefficients, etc.). Pressure drops were also measured at nine axial taps and using these values, sectional average gas holdup values were calculated. The study was centered on the conical section; the cylindrical bubble column was assumed to be the limiting case for the interpretation of the data. Using the experimental observations, the height of the jet effective region was approximated by two different methods. A simple empirical correlation to find the centerline velocity is proposed.     

Design and selection of sparger for bubble column reactor. Part II: Optimum sparger type and design

Bubble columns are widely used for conducting gas–liquid and gas–liquid–solid mass transfer/chemical reactions. Sparger is the most important accessory because it decides the bubble size/rise velocity distribution. These, in turn, govern the radial and axial hold-up profiles, the liquid phase flow pattern and hence the performance of bubble columns. In particular, the sparger design is critical if the aspect ratio is low and the sparger design dominates the performance of the bubble column. However, systematic procedure for the selection of sparger design and type are not available in the published literature. This is the specific objective of the present work. In Part I, the performance of different spargers, including the newly developed wheel type of sparger is discussed. Thus the important considerations required for the sparger design are highlighted. The bubble column used in the manufacture of hydrogen peroxide has been considered as a case for illustration.     

Comparison of Hydrodynamics and Mass Transfer in Airlift and Bubble Column Reactors Using CFD

Computational Fluid Dynamics (CFD) is used to compare the hydrodynamics and mass transfer of an internal airlift reactor with that of a bubble column reactor, operating with an air/water system in the homogeneous bubble flow regime. The liquid circulation velocities are significantly higher in the airlift configuration than in bubble columns, leading to significantly lower gas holdups. Within the riser of the airlift, the gas and liquid phases are virtually in plug flow, whereas in bubble columns the gas and liquid phases follow parabolic velocity distributions. When compared at the same superficial gas velocity, the volumetric mass transfer coefficient, k_La, for an airlift is significantly lower than that for a bubble column. However, when the results are compared at the same values of gas holdup, the values of k_La are practically identical.     

Axial mixing in a novel pilot scale gas–liquid reciprocating plate column

Axial mixing in a novel pilot scale landau reciprocating plate column (LRPC) has been investigated for counter-current gas–liquid contacting over a wide range of operating conditions. The experimental results obtained using the dynamic response method were analysed using both the dispersion and compartment models under different boundary conditions and using both the method of moments and the direct time domain parameter estimation techniques. Based on the results, it was identified that axial mixing in this column can be best described using the back flow and the dispersion models solved with “closed–closed” boundary conditions. A general correlation describing the effect of operating parameters on the extent of axial mixing was developed with a mean absolute relative residuals of 6.8%. Similar to other RPC designs, axial mixing in LRPC increases with increasing both phase flows and plates oscillatory velocity. Values of axial dispersion coefficient in this work ranged from 10⁻⁴ to over 3 × 10⁻³ m²/s, which are comparable or less than those in other RPC designs under similar phase velocities and oscillatory conditions, but an almost order of magnitude lower than those measured in bubble columns under similar operating flow rates.     

湍动浆态床流体力学研究(Ⅴ)-带多层水平网格的浆态床流体力学模型

水平布置的多层筛网是最简单的阻尼型内构件,用于改善流动分布。在安装多层筛网的?500×5000鼓泡塔冷模装置中进行了流速分布与气含率分布测定。实验表明,网格型内构件可以有效抑制塔中心区过快上升的流速,改善其分布。网孔越小,流动阻尼效果越明显,同时平均气含率也会有所增大。提出了与列管内构件相似的一维流体力学模型,将网格内构件对流体的阻尼效果作为体积源来考虑,湍流耗散方程中的参数值c3=1.0,c4=1.3与列管束内构件略有不同。模型计算与实验数据符合良好,能够定量描述网格型阻尼内构件对流场的影响。     

Studies on hydrodynamics of turbulent slurry bubble column (Ⅴ)：Modeling of the bubble column with multi-layer screens

水平布置的多层筛网是最简单的阻尼型内构件,用于改善流动分布。在安装多层筛网的?500×5000鼓泡塔冷模装置中进行了流速分布与气含率分布测定。实验表明,网格型内构件可以有效抑制塔中心区过快上升的流速,改善其分布。网孔越小,流动阻尼效果越明显,同时平均气含率也会有所增大。提出了与列管内构件相似的一维流体力学模型,将网格内构件对流体的阻尼效果作为体积源来考虑,湍流耗散方程中的参数值c3=1.0,c4=1.3与列管束内构件略有不同。模型计算与实验数据符合良好,能够定量描述网格型阻尼内构件对流场的影响。     

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.     

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.     

On the development of flow pattern in a bubble column reactor: Experiments and CFD

A comprehensive analysis of the development of flow pattern in a bubble column reactor is presented here through extensive LDA measurements and CFD predictions. In the LDA measurements, the simultaneous measurements of 2D velocity-time data were carried out at several radial locations and many axial cross-sections of the column for two different spargers. The profiles of mean axial liquid velocity, fractional gas hold-up and bubble slip velocity showed excellent agreement between the predictions and the experimentally measured values. The experimental results showed that the mean tangential velocity varies systematically in the radial as well as along the axial co-ordinates. The turbulence parameters viz. turbulent kinetic energy, energy dissipation rate and eddy diffusivity were also analysed. The estimated values of local energy dissipation rate obtained using eddy isolation model were used for establishing the energy balance in the column. The experimental data were used for the estimation of normal and shear stress profiles. For the case of single point sparger, just above the sparger region, the bubble plume was seen to have a strong tangential component of motion thereby yielding higher gas hold-up slightly away from the centre. This visual observation was well captured in profiles of all the hydrodynamic parameters obtained from the experimental data. CFD simulations of the mean velocities, gas hold-up and turbulent kinetic energy compared well with the experimental results.