Application of extended quadrature method of moments for simulation of bubbly flow and mass transfer in gas‐liquid stirred tanks

In the present paper, two gas‐liquid stirred tanks, one agitated by a radial impeller and another by an axial impeller, are modelled using the open‐source computational fluid dynamic (CFD) package OpenFOAM (open source field operation and manipulation). The combined effect of the bubble break‐up and coalescence in the tank is considered by a population balance model (PBM) called extended quadrature method of moments (EQMOM). The three‐dimensional simulation is made using a multiple reference frame (MRF), a well‐established method for the modelling of mixers. Dispersed gas and bubble dynamics in the turbulent flow are modelled using the Eulerian‐Eulerian approach (E‐E) with mixture k‐epsilon turbulent model and the modified Tomiyama drag coefficient for the momentum exchange. The model is developed to predict the spatial distribution of gas phase fraction, Sauter mean bubble diameter (), number density function (NDF), dissolved oxygen (DO) evolution, and flow structure. The numerical results are compared with experimental data and a fair agreement is achieved. The results of the axial impeller are discussed based on four impeller rotational speeds with different volumetric mass transfer coefficients.     

Numerical Investigation of the Effect of Impeller Design Parameters on the Performance of a Multiphase Baffle‐Stirred Reactor

The turbulent gas‐liquid flow field in an industrial 100‐m³ stirred tank was calculated by using computational fluid dynamics based on the finite‐volume method. Turbulent effects were modeled with the shear stress transport model, and gas‐liquid bubbly flow was modeled with the Eulerian‐Eulerian approach using the Grace correlation for the drag force interphase momentum transfer. The relative motion between the rotating impeller and the stationary baffled tank was considered by using a multiple frames of reference algorithm. The effects of Rushton and pitched‐blade impeller design parameters such as blade geometry, location, and pumping direction on the mixing performance were investigated. It was found that a combination of Rushton turbines with up‐pumping pitched‐blade turbines provides the best mixing performance in terms of gas holdup and interfacial area density. The approach outlined in this work is useful for performance optimization of biotechnology reactors, as typically found in fermentation processes.     

Experimental and numerical study of gas hold-up in surface aerated stirred tanks

Although the distribution of gas hold-up in stirred tanks is a key factor to their design and operation, systematic experimental data on local gas hold-up of surface-aerated stirred tanks are not available in open literature. In this work, turbulent two-phase flow in a surface aeration stirred tank with a diameter of 0.380 m was investigated experimentally and numerically. The gas hold-up was measured with a conductance probe at various operating conditions. A surface baffle to improve the efficiency of surface aeration of a Rushton disk turbine was designed and tested. The experimental data suggest that the gas hold-up distribution in the surface aeration tank is very non-uniform, and the surface baffle improves the aeration rate particularly at a high agitation speed. A three-dimensional in-house computational fluid dynamic (CFD) two-fluid model with the standard k?A_p turbulence model was used to predict the gas-liquid flow, and the impeller region was handled using the improved inner-outer iterative procedure. Based on Kolmogoroff's theory of isotropic turbulence, a constitutive equation for surface aeration strength was proposed. The numerical prediction, in combination with the measurements, gives insight to the surface aeration performance of stirred tanks. It was found that the simulation reasonably predicted the gas hold-up distribution in the upper tank, but underestimated it in the region below the stirrer.     

Mass transfer in sparged and stirred reactors: influence of carbon particles and electrolyte

Mass transfer in multiphase systems is one of the most studied topics in chemical engineering. However, in three-phase systems containing small particles, the mechanisms playing a role in the increased rate of mass transfer compared to two-phase systems without particles, are still not clear. Therefore, mass transfer measurements were carried out in a 2D slurry bubble column reactor , a stirred tank reactor with a flat gas-liquid interface, and in a stirred tank reactor with a gas inducing impeller. The rate of mass transfer in these reactors was investigated with various concentrations of active carbon particles (average particle size of ), with electrolyte (sodium gluconate), and with combinations of these. In the bubble column, high-speed video recordings were captured from which the bubble size distribution and the specific bubble area were determined. In this way, the specific mass transfer area a_gl was determined separately from the mass transfer coefficient k_l. Mechanisms proposed in literature to describe mass transfer and mass transfer enhancement in stirred tank reactors and bubble columns are compared. It is shown that the increased rates of mass transfer in the 2D bubble column and in the stirred tank reactor with the gas inducing impeller are completely caused by an increased gas-liquid interfacial area upon addition of carbon particles and electrolyte. It is suggested that an increased level of turbulence at the gas-liquid interface caused by carbon particles accounts for a smaller effective boundary layer thickness and an enhancement of mass transfer in the flat gas-liquid surface stirred tank reactor. However, for the carbon particles used in this study, it is rather unlikely that mass transfer enhancement takes place due to the well-known shuttle or grazing effect.     

Investigations on hydrodynamics and mass transfer in gas–liquid stirred reactor using computational fluid dynamics

In this work, the hydrodynamics and mass transfer in a gas–liquid dual turbine stirred tank reactor are investigated using multiphase computational fluid dynamics coupled with population balance method (CFD–PBM). A steady state method of multiple frame of reference (MFR) approach is used to model the impeller and tank regions. The population balance for bubbles is considered using both homogeneous and inhomogeneous polydispersed flow (MUSIG) equations to account for bubble size distribution due to breakup and coalescence of bubbles. The gas–liquid mass transfer is implemented simultaneously along with the hydrodynamic simulation and the mass transfer coefficient is obtained theoretically using the equation based on the various approaches like penetration theory, slip velocity, eddy cell model and rigid based model. The CFD model predictions of local hydrodynamic parameters such as gas holdup, Sauter mean bubble diameter and interfacial area as well as averaged quantities of hydrodynamic and mass transfer parameters for different mass transfer theoretical models are compared with the reported experimental data of [Alves et al., 2002a] and [Alves et al., 2002b] . The predicted hydrodynamic and mass transfer parameters are in reasonable agreement with the experimental data.     

Theoretical prediction of gas-liquid mass transfer coefficient, specific area and hold-up in sparged stirred tanks

A prediction method for calculating the volumetric mass transfer coefficient, k_La, in gas-liquid sparged stirred tanks is proposed. A theoretical equation based on Hibie's penetration theory and the isotropic turbulence theory of Kolmogoroff is used for k_L determination. The values of the interfacial area have been calculated from a hold-up theoretical equation and the mean size of the gas bubble. Both Ostwald-De Waele and Casson models are used to describe the rheological properties of the fluid. The model predicts the mass transfer coefficient and the interfacial area values in stirred tank reactors, analysing the influence of different variables. The values of the volumetric mass transfer coefficient can be calculated for different geometries of the reactor, different physicochemical properties of the liquid and under different operational conditions. The capability of prediction has been examined using experimental data available in the literature for Newtonian and non-Newtonian fluids, for very different vessel sizes, different numbers and types of stirrers and a wide range of operational conditions, with very good results.     

Numerical simulations of gas-liquid mass transfer in bubble columns with a CFD-PBM coupled model

Gas-liquid mass transfer in a bubble column in both the homogeneous and heterogeneous flow regimes was studied by numerical simulations with a CFD-PBM (computation fluid dynamics-population balance model) coupled model and a gas-liquid mass transfer model. In the CFD-PBM coupled model, the gas-liquid interfacial area a is calculated from the gas holdup and bubble size distribution. In this work, multiple mechanisms for bubble coalescence, including coalescence due to turbulent eddies, different bubble rise velocities and bubble wake entrainment, and for bubble breakup due to eddy collision and instability of large bubbles were considered. Previous studies show that these considerations are crucial for proper predictions of both the homogenous and the heterogeneous flow regimes. Many parameters may affect the mass transfer coefficient, including the bubble size distribution, bubble slip velocity, turbulent energy dissipation rate and bubble coalescence and breakup. These complex factors were quantitatively counted in the CFD-PBM coupled model. For the mass transfer coefficient k_l, two typical models were compared, namely the eddy cell model in which k_l depends on the turbulent energy dissipation rate, and the slip penetration model in which k_l depends on the bubble size and bubble slip velocity. Reasonable predictions of k_la were obtained with both models in a wide range of superficial gas velocity, with only a slight modification of the model constants. The simulation results show that CFD-PBM coupled model is an efficient method for predicting the hydrodynamics, bubble size distribution, interfacial area and gas-liquid mass transfer rate in a bubble column.     

双层涡轮桨搅拌反应器内混合时间的大涡模拟

采用计算流体力学(CFD)方法对直径为0.476m双层涡轮桨搅拌反应器内的流动及混合进行了数值模拟,并实验测试了混合过程。利用大涡模拟(LES)及Smagorinsky-Lilly亚格子模型求解湍流流动与示踪剂传递过程,桨叶区域采用滑移网格技术。研究结果表明,大涡模拟得到的示踪剂响应曲线和混合时间与实验结果吻合良好,其预测精度明显优于基于雷诺平均(Reynolds-averaged Navier-Stokes,RANS)的标准k-ε模型的模拟结果。大涡模拟是研究搅拌反应器内非稳态及周期性湍流流动的有效方法。     

搅拌反应器内气液两相流的CFD研究进展

搅拌式气液反应器因其操作灵活、适用性强等优点,在过程工业中应用广泛.综述了采用计算流体力学CFD技术对搅拌反应器内气液两相流动行为的数值模拟研究.Euler-Euler双流体模型作为主要方法用于描述气液两相流动,在其基础上耦合相对简单的气泡数密度函数模型或复杂的群体平衡模型,可较为准确地预测搅拌反应器内气泡尺寸和局部气含率及其分布规律.CFD模拟结果可用以分析和评价不同搅拌桨叶、搅拌桨组合和气体分布器的气液分散性能,对气液反应器的结构优化和过程强化提供了有效手段.     

Experimental determination and numerical simulation of mixing time in a gas-liquid stirred tank

In this work, mixing experiments and numerical simulations of flow and macro-mixing were carried out in a 0.24 m i.d. gas-liquid stirred tank agitated by a Rushton turbine. The conductivity technique was used to measure the mixing time. A two-phase CFD (computational fluid dynamics) model was developed to calculate the flow field, k and ε distributions and holdup. Comparison between the predictions and the reported experimental data [Lu, W.M., Ju, S.J., 1987. Local gas holdup, mean liquid velocity and turbulence in an aerated stirred tank using hot-film anemometry. Chemical Engineering Journal 35 (1), 9-17] of flow field and holdup at same conditions were investigated and good agreements have been got. As the complexity of gas-liquid systems, there was still no report on the prediction of mixing time through CFD models in a gas-liquid stirred tank. In this paper, the two-phase CFD model was extended for the prediction of the mixing time in the gas-liquid stirred tank for the first time. The effects of operating parameters such as impeller speed, gas flow rate and feed position on the mixing time were compared. Good agreements between the simulations and experimental values of the mixing time have also been achieved.     

Solid-liquid mass transfer analysis in a multi-phase tank reactor containing submerged coated inclined-plates: A computational fluid dynamics approach

Although there is a voluminous literature on the estimation of interphase transport parameters in conventional slurry bubble column reactors, these correlations are inadequate in photoreactors equipped with specialized internals to facilitate light harvesting efficiency of the photocatalyst. This is particularly germane to the present externally illuminated bubble column reactor containing titania-coated plates immersed in the liquid column at different angles of inclination. Thus, a computational fluid dynamics (CFD) procedure utilizing the Eulerian-Eulerian approach has been used to solve the governing differential equations for the solid liquid mass transport problem based on the standard k-ε model incorporating additional terms that take account of the interfacial turbulent momentum transfer. Mass transfer from the surface of the coated-quartz plates to the liquid phase was modeled using the Launder-Spalding wall functions. The plates were coated with benzoic acid as solid substrate with water and air as the liquid and gas phases, respectively. The increase in mass transfer due to reduction of the boundary layer thickness during air-induced liquid recirculation on either side of the submerged inclined plates was correlated with difference between turbulent and molecular Schmidt numbers via an adjustable parameter, A. CFD simulation using the Launder-Spalding wall function (with A=1.08) gave better agreement with experimental transient concentration profiles than calculations based on FLUENT's enhanced wall function for the plate orientations (θ=0^°, 22.5^°, and 45^°) studied. The solid-to-liquid mass transfer was higher on the lower-side of the plate than the upper-side. In particular, mass transfer coefficient was higher with the inclined plate than with the vertical or horizontal orientation suggesting an added advantage for the application of the system as a solar photoreactor.     

Practical validation of the two-fluid model applied to dense gas-solid flows in fluidized beds

This paper discusses the simulation of bubbling gas-solid flows by using the Eulerian two-fluid approach. Predictions of particle motion, bed expansion, bubble size and bubble velocity in bubbling beds containing Geldart B particles are compared with experimental results and correlations found in the literature. In addition, gas mixing in a bed of Geldart A particles is investigated.An in-house code has been developed based on the finite-volume method and the time-splitting approach using a staggered grid arrangement. The velocities in both phases are obtained by solving the 2D Reynolds-averaged Navier/Stokes equations using a partial elimination algorithm (PEA) and a coupled solver. The k-ε turbulence model is used to describe the turbulent quantities in the continuous phase.In general, the model predictions are in good agreement with experimental data found in the literature. Most important observations are: the level of the restitution coefficient was found to be crucial in order to obtain successful results from 2D axisymmetric simulations of a system containing Geldart B particles. Bubble size and bubble rise velocities are not as sensitive to the restitution coefficient. The turbulence model is of outmost importance concerning gas mixing in a fluidized bed of Geldart A particles.From these numerical analyzes an optimized granular flow two-fluid model can be designed for the purpose of simulating reactive systems in fluidized bed reactors.     

The confined impeller stirred tank (CIST): A bench scale testing device for specification of local mixing conditions required in large scale vessels

A new stirred tank geometry, the confined impeller stirred tank (CIST), was designed to provide repeatable testing of the effect of mixing on the performance of chemical additives at the bench scale. The CIST (T = 0.076 m, H = 3T) is filled with five or six impellers. Three impeller geometries were tested: A310, Rushton and Intermig. This paper presents the following hydrodynamic characteristics of the CIST: power number, flow number, momentum number, velocity profiles at different locations in the tank and the transition point from fully turbulent to transitional flow. Based on the scaled velocity profiles, the CIST was able to keep the flow turbulent at Re < 2000 for Rushton turbines and 3200 for Intermigs. The ratio ?_max/?_average was lower for the CIST than for a conventional stirred tank, indicating that the energy dissipation is more uniformly distributed in the CIST. The CIST consistently maintains turbulent flow down to a Reynolds number 10× smaller than that needed in a conventional stirred tank.     

Simultaneous measurement of flow pattern and mass transfer coefficient in bubble columns

Mass transfer studies were carried out in a bubble column using the chemical method. Catalytic oxidation of sodium sulfite was chosen for the studies and the corresponding specific rates of oxidation were obtained using a stirred cell. Laser Doppler anemometer (LDA) was used to measure the instantaneous velocities in the same stirred cell as well as in bubble columns (100 and i.d.). An efficient algorithm based on the multiresolution analysis of the velocity-time data using wavelets was used for the isolation of data belonging to the gas and liquid phases. Eddy isolation model was used for the characterization of the eddy motion including the estimation of the energy dissipation rate. Using the knowledge of eddy motion, a methodology was developed for the prediction of true mass transfer coefficient (k_L) in a stirred cell as well as in bubble columns. The predicted values of k_L have been compared with the experimental values obtained by the chemical method.     

基于离散颗粒法模拟搅拌釜气含率分布

The discrete particle method was used to simulate the distribution of gas holdup in a gas-liquid standard Rushton stirred tank. The gas phase was treated as a large number of bubbles and their trajectories were tracked with the results of motion equations. The two-way approach was performed to couple the interphase momentum exchange. The turbulent dispersion of bubbles with a size distribution was modeled using a stochastic tracking model, and the added mass force was involved to account for the effect of bubble acceleration on the surrounding fluid. The predicted gas holdup distribution showed that this method could give reasonable prediction comparable to the reported experimental data when the effect of turbulence was took into account in modification for drag coefficient.     

Physical explanation of the empirical coefficients of gas-liquid mass transfer equations

Equipment design and scale up is one of the biggest problems that chemical engineers face. A lot of research has been done at laboratory and pilot plant scale. However, experimental data are, many times, useless in equipment scale up because they overlook the processes involving bubbles. Therefore, a new approach considering the hydrodynamics of the bubbles is proposed to explain and understand the mass transfer rates. Semi-theoretical equations have been developed for bubble columns and stirred tanks based on hydrodynamic considerations of the flow, the bubbles and dispersions in the tank. These equations are able to explain the physical meaning, identify the effect of the scale on mass transfer rates and even predict the coefficients of the empirical correlations for k_La based on the hydrodynamic processes that bubbles experience. It can be concluded that the proportional constant of the correlations for k_La depends on the bubble size, on the physical and transport properties and on the size of the tank because it affects the mixing. Meanwhile, the exponents related to the power input and the superficial gas velocity depend on bubble break up and coalescence, and the dispersions generated. In the case of stirred tanks, the physical effect of the impeller on the bubbles also plays an important role on the exponents.     

Numerical Simulation of Gas‐Liquid Flow in a Stirred Tank with Swirl Modification

Although the standard k‐? model is most frequently used for turbulence modeling, it often leads to poor results for strongly swirling flows involved in stirred tanks and other processing devices. In this work, a swirling number, R_S, is introduced to modify the standard k‐? model. A Eulerian‐Eulerian model is employed to describe the gas‐liquid, two‐phase flow in a baffled stirred tank with a Rushton impeller. The momentum and the continuity equations are discretized using the finite difference method and solved by the SIMPLE algorithm. The inner‐outer iterative algorithm is used to account for the interaction between the rotating impeller and the static baffles. The predictions, both with and without R_S corrections, are compared with the literature data, which illustrates that the swirling modification could improve the numerical simulation of gas‐liquid turbulent flow in stirred tanks.     

Probability density functions for bubble size distribution in air–water systems in stirred tanks

Bubble size distribution (BSD) is relevant to the design of gas–liquid systems, as it determines the interfacial area available in heat and mass transfer processes. Although data on BSD in stirred aerated tanks are available, a systematic comparison of alternative modeling functions for these data is lacking. In this work, BSDs obtained in air–water dispersions in a stirred aerated tank with a Rushton turbine and BSDs available in the literature for similar systems were modeled by 14 empirical probability density functions (PDFs). It was found that both the distribution of Nukiyama–Tanasawa with three adjustable parameters and the Rosin–Rammler distribution with two adjustable parameters reasonably fit original and literature BSDs. It is also concluded that it is possible to correlate the PDF parameters with the power dissipated by the agitator in the liquid phase, allowing the BSD to be modeled with only two parameters in a range of dissipated power from 0.5 to 2.3?kW/m³. BSDs thus modeled provide good predictions of average bubble size.     

Gas-phase properties in stirred tank bioreactors

Bubble properties in stirred tank bioreactors equipped with standard radial flow Rushton turbines have been investigated. Bubble velocity patterns within a stirred tank reactor were derived from measured local bubble velocity distributions. Local information on specific interfacial areas, bubble number densities and bubble diameters together with local gas hold-ups, measured in a model medium at gas flow rates which are employed in practice, is presented. All measurements were performed with two new ultrasound pulse techniques which can be used in model as well as during real cultivation processes.