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.     

Linear stability analysis of a two-fluid model for air-water bubble columns

Linear stability analysis is performed for the two-dimensional, two-fluid model for gas-liquid flow applied in our previous computational study of bubble columns [Monahan, S.M., Vitankar, V.S., Fox, R.O., 2005. CFD predictions for flow-regime transitions in bubble columns. A.I.Ch.E. Journal 51, 1897-1923]. The growth rate and the velocity of propagation for a small-amplitude disturbance wave are shown to be highly dependent on the wave number, the direction of propagation, and the two-fluid model parameters. Two types of vertical instabilities are identified: one corresponding to the classical analysis of Jackson [1963. The mechanics of fluidized beds. I: the stability of the state of uniform fluidization. Transactions of the Institution of Chemical Engineers 41, 13-21] for the one-dimensional model, and the other due to a second pair of roots to the characteristic equation of the linearized two-dimensional model. Numerical simulations keeping one type or the other of the roots stable (or unstable) show distinctly different dynamics and suggest that large-scale instabilities seen experimentally may be associated with the second type of instability. The latter leads to instability in the horizontal velocities and is associated with a positive lift coefficient in flows without mean shear in the presence of isotropic bubble-bubble interactions (i.e., “bubble pressure”). This instability is thus different than previously reported instabilities due to negative lift or cooperative/hindered rise.     

Effect of bubble deformation on stability and mixing in bubble columns

The paper deals with hydrodynamics in bubble columns. The objective of the paper is to study stability and mixing in a bubble column. The modeling of parameters such as stationary drag and added mass is addressed. In addition, the effect of bubble deformation in terms of eccentricity is highlighted. In a previous paper, the transition between homogeneous and heterogeneous regimes in bubble column without liquid flow has been shown to be driven by the deformation of the bubbles associated to drag and added mass. In the present paper, this work is generalized to bubble column with liquid flow and to the transition from bubble flow to slug flow in a vertical pipe. Numerical simulations of gas-liquid reactors are presented. The numerical simulations are validated in the case of gas plume after the Becker et al. data (Becker, S., Sokolichin, A., & Eigenberg, G. (1994) Gas-liquid flow in bubble columns and loop reactors: Part II. Comparison of detailed experiments and flow simulations. Chemical Engineering Science, 49 (24B), 5747-5762. The numerical simulations are finally applied to a bubble column. The simulations of residence time distribution coupled to transient hydrodynamics are shown to be very sensitive to the modeling of interfacial transfer of momentum from the bubbles to the liquid in terms of drag and added mass, including the effect of bubble deformation.     

CFD simulation of mixing in tall gas-liquid stirred vessel: Role of local flow patterns

In this work, we have used the computational fluid dynamics (CFD)-based models to investigate the gas-liquid flows generated by three down-pumping pitched blade turbines. A two-fluid model along with the standard k-ε turbulence model was used to simulate the dispersed gas-liquid flow in a stirred vessel. Appropriate drag corrections to account for bulk turbulence [Khopkar and Ranade, 2005. CFD simulation of gas-liquid flow in a stirred vessel: VC, S33 and L33 flow regimes. A.I.Ch.E. Journal, accepted for publication] were developed to correctly simulate different flow regimes. The computational snapshot approach was used to simulate impeller rotation and was implemented in the commercial CFD code, FLUENT4.5 (of Fluent. Inc., USA). The computational model has successfully captured the flow regimes as observed during experiments. The particle trajectory simulations were then carried out to examine the influence of the different flow regimes on the circulation time distribution. The model predictions were verified by comparing the predicted results with the experimental data of [Shewale and Pandit, 2006. Studies in multiple impeller agitated gas-liquid contactors. Chemical Engineering Science 61, 489-504]. The computational model and results discussed in this study would be useful for explaining the implications local flow patterns on the mixing process and extending the applications of CFD models for simulating large multiphase stirred reactors.     

On the numerical study of isothermal vertical bubbly flow using two population balance approaches

Two population balance approaches based on the MUltiple-SIze-Group (MUSIG) model and one-group average bubble number density (ABND) model for handling the bubble size distribution of gas-liquid bubbly flows under isothermal conditions are assessed. Three forms of coalescence and breakage mechanisms by Wu et al. [1998. One-group interfacial area transport in vertical bubbly flow. International Journal of Heat Mass Transfer 41, 1103-1112], Hibiki and Ishii [2002. Development of one-group interfacial area transport equation in bubbly flow systems. International Journal of Heat Mass Transfer 45, 2351-2372] and Yao and Morel [2004. Volumetric interfacial area prediction in upwards bubbly two-phase flow. International Journal of Heat Mass Transfer 47, 307-328] are incorporated in the ABND model. To examine the relative merits of both approaches, local radial distributions of five primitive variables in bubbly flows: void fraction, Sauter mean bubble diameter, interfacial area concentration, and gas and liquid velocities, are compared against the experimental data of Liu and Bankoff [1993a. Structure of air-water bubbly flow in a vertical pipe—I. Liquid mean velocity and turbulence measurements. International Journal of Heat Mass Transfer 36, 1049-1060; 1993b. Structure of air-water bubbly flow in a vertical pipe—II. Void fraction, bubble velocity and bubble size distribution. International Journal of Heat Mass Transfer 36, 1061-1072] and Hibiki et al. [2001. Axial interfacial area transport of vertical bubble flows. International Journal of Heat Mass Transfer 44, 1869-1888]. In general, both of the ABND model and MUSIG model predictions yield close agreement with experimental results. To account for the range of different bubble sizes in the gas-liquid bubbly flows, the resolution required is achieved through the application of the MUSIG model. Nevertheless, computational times increase by a factor of two when compared to applying the simpler ABND model. To further exploit the models’ capabilities, investigations are carried out by extending the two population approaches beyond the bubbly flow regime of higher void fraction, particularly in the transition regime. The numerical results are found to be grossly over-predicted, which expose the inherent limitations of the models. It is known that bubbles in this regime are generally highly distorted and closely packed instead of spherical shape and allowed to move freely in bubbly flow regime.     

CFD simulation of gas-liquid flows in stirred vessel equipped with dual rushton turbines: influence of parallel, merging and diverging flow configurations

Computational fluid dynamics (CFD) was used to investigate the influence of parallel, merging and diverging flow configurations on the gas dispersion operation in stirred vessel. The simulation was based on the two-fluid model along with the standard k-ε turbulence model along with an appropriate drag correction to account for bulk turbulence [Khopkar, A.R., Ranade, V.V., 2006. CFD simulation of gas-liquid stirred vessel: VC, S33 and L33 flow regimes. A.I.Ch.E. Journal 52, 1654-1671]. The model predictions were compared with the published experimental data of Bombac, Zun [2000. Gas-filled cavity structures and local void fraction distribution in vessel with dual-impellers. Chemical Engineering Science 55, 2995-3001] for parallel flow configuration. The predicted results show reasonably good agreement with the experimental data. The computational model was then used to simulate the gas-liquid flows for the other two flow configurations. The results of this work provide ‘a priory’ information on the implications of flow configuration on the vessel performance.     

Numerical simulation of the dynamic flow behavior in a bubble column: A study of closures for turbulence and interface forces

Numerical simulations of the bubbly flow in two square cross-sectioned bubble columns were conducted with the commercial CFD package CFX-4.4. The effect of the model constant used in the sub-grid scale (SGS) model, C_S, as well as the interfacial closures for the drag, lift and virtual mass forces were investigated. Furthermore, the performance of three models [Pfleger, D., Becker, S., 2001. Modeling and simulation of the dynamic flow behavior in a bubble column. Chemical Engineering Science, 56, 1737-1747; Sato, Y., Sekoguchi, K.,1975. Liquid velocity distribution in two-phase bubble flow. International Journal of Multiphase Flow 2, 79-95; Troshko, A.A., Hassan, Y.A., 2001. A two-equation turbulence model of turbulent bubbly flows. International Journal of Multiphase Flow 27, 1965-2000] to account for the bubble-induced turbulence in the k-ε model was assessed. All simulation results were compared with experimental data for the mean and fluctuating liquid and gas velocities. It is shown that the simulation results with C_S=0.08 and 0.10 agree well with the measurements. When C_S is increased, the effective viscosity increases and subsequently the bubble plume becomes less dynamic. All three bubble-induced turbulence models could produce good solutions for the time-averaged velocity. The models of Troshko and Hassan and Pfleger and Becker reproduce the dynamics of the bubbly flow in a more accurate way than the model of Sato and Sekoguchi. Based on the comparison of the results obtained for two columns with different aspect ratio (H/D=3 and H/D=6), it was found that the model of Pfleger and Becker performs better than the model of Troshko and Hassan, while the model of Sato and Sekoguchi performs the worst. It was observed that the interfacial closure model proposed by Tomiyama [2004. Drag, lift and virtual mass forces acting on a single bubble. Third International Symposium on Two-Phase Flow Modeling and Experimentation, Pisa, Italy, 22-24 September] performs better for the taller column. With the drag coefficient proposed by Tomiyama, the predicted slip velocity agrees well with the experimental data in both columns. The virtual mass force has a small influence on the investigated bubbly flow characteristics. However, the lift force strongly influences the bubble plume dynamics and consequently determines the shape of the vertical velocity profile. In a taller column, the lift coefficient following from the model of Tomiyama produces the best results.     

CFD simulation of hydrodynamics of gas-liquid-solid fluidised bed reactor

A three dimensional transient model is developed to simulate the local hydrodynamics of a gas-liquid-solid three-phase fluidised bed reactor using the computational fluid dynamics (CFD) method. The CFD simulation predictions are compared with the experimental data of Kiared et al. [1999. Mean and turbulent particle velocity in the fully developed region of a three-phase fluidized bed. Chemical Engineering & Technology 22, 683-689] for solid phase hydrodynamics in terms of mean and turbulent velocities and with the results of Yu and Kim [1988. Bubble characteristics in the racial direction of three-phase fludised beds. A.I.Ch.E. Journal 34, 2069-2072; 2001. Bubble-wake model for radial velocity profiles of liquid and solid phases in three-phase fluidised beds. Industrial and Engineering Chemistry Research 40, 4463-4469] for the gas and liquid phase hydrodynamics in terms of phase velocities and holdup. The flow field predicted by CFD simulation shows a good agreement with the experimental data. From the validated CFD model, the computation of the solid mass balance and various energy flows in fluidised bed reactors are carried out. The influence of different interphase drag models for gas-liquid interaction on gas holdup are studied in this work.     

Computational fluid dynamics (CFD) modeling of spouted bed: Assessment of drag coefficient correlations

In the computational fluid dynamics (CFD) modeling of gas-solids two-phase flows, drag force is the only accelerating force acting on particles and thus plays an important role in coupling two phases. To understand the influence of drag models on the CFD modeling of spouted beds, several widely used drag models available in literature were reviewed and the resulting hydrodynamics by incorporating some of them into the CFD simulations of spouted beds were compared. The results obtained by the different drag models were verified using experimental data of He et al. [He, Y.L., Lim, C.J., Grace, J.R., Zhu, J.X., Qin, S.Z., 1994a. Measurements of voidage profiles in spouted beds. Canadian Journal of Chemical Engineering 72 (4), 229-234; He, Y.L., Qin, S.Z., Lim, C.J., Grace, J.R., 1994b. Particle velocity profiles and solid flow patterns in spouted beds. Canadian Journal of Chemical Engineering 72 (8), 561-568.] The quantitative analyses showed that the different drag models led to significant differences in dense phase simulations. Among the different drag models discussed, the Gidaspow (1994. Multiphase Flow and Fluidization, Academic Press, San Diego.) model gave the best agreement with experimental observation both qualitatively and quantitatively. The present investigation showed that drag models had critical and subtle impacts on the CFD predictions of dense gas-solids two-phase systems such as encountered in spouted beds.     

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.     

Dynamics of gas–liquid flow in a rectangular bubble column: experiments and single/multi-group CFD simulations

Several flow processes influence overall dynamics of gas–liquid flow and hence mixing and transport processes in bubble columns. In the present work, we have experimentally as well as computationally studied the effect of gas velocity, sparger design and coalescence suppressing additives on dynamics of gas–liquid flow in a rectangular bubble column. Wall pressure fluctuations were measured to characterize the low frequency oscillations of the meandering bubble plume. Bubble size distribution measurements were carried out using high-speed digital camera. Dispersed gas–liquid flow in bubble column was modelled using Eulerian–Eulerian approach. Bubble population was represented in the model with a single group or multiple groups. Bubble coalescence and break-up processes were included in the multi-group simulations via a suitable population balance framework. Effect of superficial gas velocity and sparger configurations was studied using single-group simulations. Model predictions were verified by comparison with the experimental data. Role of bubble size in determining plume oscillation period was studied. Multi-group simulations were carried out to examine evolution of bubble size distribution. An attempt is made to understand the relationship between local and global (over all the dispersion volume) bubble size distribution. The models and results reported here would be useful to develop and to extend the applications of multi-group CFD models.     

鼓泡塔出口边界条件的数值模拟

鼓泡塔反应器内流体动力学特性预测对于鼓泡塔的设计和发展具有重要意义。应用CFX4.4商业软件,分别采用"压力"和"开口"出口边界,数值模拟研究出口边界条件对鼓泡塔里气液泡状流动结果的影响。结果表明,当出口应用"开口"边界条件,自由表面是一个动态表面,CFX可以捕捉塔顶部整个自由表面特性。由"压力"出口边界和"开口"出口边界条件求得的数值结果差异很小。     

CHARACTERIZATION OF GAS-LIQUID FLOWS IN RECTANGULAR BUBBLE COLUMNS USING CONDUCTIVITY PROBES

Unsteady gas-liquid flows in bubble columns are comprised of various flow processes occurring with varying length and time scales and govern mixing and transport processes. In the present work, we have characterized dynamic and time-averaged properties of gas-liquid flows in rectangular bubble columns using conductivity probes. The development of a single-tip conductivity probe, data processing methodology, and photographic validation procedure is discussed in detail. The effect of superficial gas velocity and aerated liquid height-to-width (H/W) ratio on voidage fluctuations and time-averaged gas holdup was investigated. The experimental data presented here can help in understanding the dynamics of various flow processes and validating computational fluid dynamics based models.     

INFLUENCE OF DIFFERENT CLOSURES ON THE HYDRODYNAMICS OF BUBBLE COLUMN FLOWS

Computational fluid dynamic (CFD) simulations are performed for two-dimensional bubble columns to examine the effect of different interfacial force closures on the computed liquid velocity and gas holdup profiles. In this regard, six different drag closure relationships and three different virtual mass formulations are incorporated in the framework of the Los Alamos National Laboratory's code CFDLIB. The Eulerian-Eulerian two-fluid model is used. The results are compared with the experimental results of Mudde et al. (1997), the gas holdup correlation of Anabtawi et al., (2003), and CFD simulations of Pan et al. (2000). With the exception of one, all the correlations studied give good agreement (within engineering accuracy) between the computed results and the experimental data.     

二维鼓泡床内气液流动特性实验与数值模拟

采用高速摄像法测量了0.20 m×0.02 m×2.00 m拟二维床内气泡尺寸分布和流型等变化规律,结果表明,随着表观气速的增大,鼓泡床内依次呈现均匀鼓泡区、过渡区和湍动区3种形式,以气泡个数概率表示的气泡尺寸分布呈对数正态分布。以计算流体力学软件ANSYS CFX 10.0为平台,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展开了数值模拟,其结果与实验值比较吻合。研究表明,从多相流理论出发的计算流体力学模拟方法可以用来预报鼓泡床内流型过渡等流体动力学特性。     

Modeling of the evolution with length of bubble size distributions in bubble columns

Many of the existing methods, for the determination of the specific interfacial area in bubble columns, consider the column in a dynamic equilibrium between bubble coalescence and breaking-up. The aim of this work is to study if this consideration can be considered true for low superficial gas velocities. Two existing models have been chosen from literature in order to predict the break-up [Wang, T., Wang, J., Jin, Y., 2003. A novel theoretical breakup kernel function for bubbles/droplets in a turbulent flow. Chemical Engineering Science 58, 4629-4637] and the coalescence [Lehr, F., Millies, M., Mewes, D., 2002. Bubble size distributions and flow fields in bubble columns. A.I.Ch.E. Journal 48, 2426] rates. In order to confirm the validity of the models, predictions were compared with experimental results obtained by image analysis. Several simulations were performed for different superficial gas velocities and initial bubble size distributions. The column length needed to reach dynamic equilibrium was calculated for each simulation. The results show that the necessary length to reach the dynamic equilibrium does not depend on the shape of the initial distribution, but essentially on its Sauter mean diameter. The necessary length to reach the dynamic equilibrium is very important for low superficial gas velocities. The assumption that the entire column is in dynamic equilibrium is in general not valid. Therefore, the initial Sauter mean diameter and the total column length are important parameters for the determination of the specific interfacial area.     

A second-order moment method of dense gas-solid flow for bubbling fluidization

A gas-solid two-fluid model with the second-order moment method is presented to close the set of equations applied to fluidization. With the kinetic theory of granular flow, transport equations for the velocity moments are derived for the particle phase. Closure equations for the third-order moments of velocity and for the fluid-particle velocity correlation are presented. The former is based on a modified model with the contribution of the increase of the binary collision probability, and the latter uses an algebraic model proposed by Koch and Sangani [1999. Particle pressure and marginal stability limits for a homogeneous monodisperse gas-fluidized bed: kinetic theory and numerical simulations. Journal of Fluid Mechanics 400, 229-263]. Boundary conditions for the set of equations describing flow of particles proposed by Strumendo and Canu [2002. Method of moments for the dilute granular flow of inelastic spheres. Physical Review E 66, 041304/1-041304/20] are modified with the consideration of the momentum exchange by collisions between the wall and particles. Flow behavior of gas and particles is performed by means of gas-solid two-fluid model with the second-order moment model of particles in the bubbling fluidized bed. The distributions of velocity and moments of particles are predicted in the bubbling fluidized bed. Predictions are compared with experimental data measured by Muller et al. [2008. Granular temperature: comparison of magnetic resonance measurements with discrete element model simulations. Powder Technology 184, 241-253] and Yuu et al. [2000. Numerical simulation of air and particle motions in bubbling fluidized bed of small particles. Powder Technology 110, 158-168]. in the bubbling fluidized beds. The simulated second-order moment in the vertical direction is 1.1-2.5 [Muller, C.R., Holland, D.J., Sedeman, A.J., Scott, S.A., Dennis, J.S., Gladden, L.F., 2008. Granular temperature: comparison of magnetic resonance measurements with discrete element model simulations. Powder Technology 184, 241-253] and 1.1-4.0 [Yuu, S., Umekage, T., Johno, Y., 2000. Numerical simulation of air and particle motions in bubbling fluidized bed of small particles. Powder Technology 110, 158-168] times larger than that in the lateral direction because of higher velocity fluctuations for particles in the bubble fluidized bed. The bubblelike Reynolds normal stresses per unit bulk density used by Gidaspow et al. [2004. Hydrodynamics of fluidization using kinetic theory: an emerging paradigm 2002 Flour-Daniel lecture. Powder Technology 148, 123-141.] are computed from the simulated hydrodynamic velocities. The predictions are in agreement with experimental second-order moments measured by Muller et al. [2008. Granular temperature: comparison of magnetic resonance measurements with discrete element model simulations. Powder Technology 184, 241-253] and fluctuating velocity of particles measured by Yuu et al. [2000. Numerical simulation of air and particle motions in bubbling fluidized bed of small particles. Powder Technology 110, 158-168].