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。     

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-PBM simulation of the column flotation unit of FCMC: Importance of gas–liquid interphase forces models

The cyclonic micro-bubble flotation column (FCMC) is an efficient flotation device for the separation of fine minerals, but its mechanisms are rarely studied using computational fluid dynamics (CFD). This paper reports the air–water two-phase computational fluid dynamics-population balance model (CFD-PBM) simulations for the column flotation unit of an FCMC. The shear stress transport (SST) k-ω model with curvature correction (CC) is used to simulate turbulence effects. Then, the interphase forces models considering bubble size distribution are selected according to the experimental data in a bubble column, which is in analogy to the column flotation unit of the FCMC. Finally, the optimal combination of interphase forces models (i.e., the Ishii–Zuber drag force model, the Hosokawa–Frank wall lubrication force model, and the Lopez de Bertodano turbulent dispersion force model) is applied to simulate an FCMC with a superficial gas velocity of 0.0144 m/s. The results show that the CFD-PBM simulation can achieve a relative error of 9.09% for gas volume fraction and −5.45% for bubble rising velocity, indicating the reliability of the selected combination of interphase forces models.     

Numerical simulation of bubble columns flows: effect of different breakup and coalescence closures

Two-dimensional axisymmetric Eulerian/Eulerian simulations of two-phase (gas/liquid) transient flow were performed using a multiphase flow algorithm based on the finite-volume method. These numerical simulations cover laboratory scale bubble columns of different diameters, operated over a range of superficial gas velocities ranging from the bubbly to the churn turbulent regime. The bubble population balance equation (BPBE) is implemented in the two-fluid model that accounts for the drag force and employs the modified k-ε turbulence model in the liquid phase. Several available bubble breakup and coalescence closures are tested. Quantitative agreements between the experimental data and simulations are obtained for the time-averaged axial liquid velocity profiles, as well as for the kinetic energy profiles, only when model predicted breakup rate is increased by a factor of ten to match the coalescence rate. The calculated time-averaged gas holdup profiles deviate in shape from the measured ones and suggest that full three-dimensional simulation is needed. Implementation of BPBE leads to better agreement with data, especially in the churn-turbulent flow regime, compared to the simulation based on an estimated constant mean bubble diameter. Differences in the predicted interfacial area density, with and without BPBE implementation, are significant. The choice of bubble breakup and coalescence closure does not have a significant impact on the simulated results as long as the magnitude of breakup is increased tenfold.     

Hydrodynamics and simulation of air–water homogeneous bubble column under elevated pressure

A gas–liquid Eulerian computational fluid dynamics (CFD) model coupled with a population balance equation (PBE) was presented to investigate hydrodynamics of an air–water bubble column (1.8 m in height and 0.1 m in inner diameter) under elevated pressure in terms of pressure drop, gas holdup, mean bubble size, and bubble surface area. The CFD-PBE model was modified with three pressure correction factors to predict both the total gas holdup and the mean bubble size in the homogeneous bubbly flow regime. The three correction factors were optimized compared to experimental data. Increasing the pressure led to increasing the density, reducing the bubble size, and increasing the gas holdup. The bubble size distribution moved toward a smaller bubble size, as the pressure increased. The modified CFD-PBE model validated with experimental data and empirical models represented well hydrodynamics of the bubble column at P = 0.1, 1.5, and 3.5 MPa.     

矩形鼓泡塔流体动力学数值模拟

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。文中应用CFX4.4商业软件,采用k-ε模型中气泡诱发湍流模型,对较高鼓泡塔中湍流弥散力影响和Tomiyama模型的作用进行了数值模拟。研究发现,目前通用的湍流弥散力对所研究的气泡流体动力学影响很小,引入带有气泡诱发湍流模型的Tomiyama模型能获得较好的速度分布。在这种情况下,Pfleger&Becker的模型要优于Troshko&Hassan模型,原因在于后者高估气泡诱发湍流时间尺度。     

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。     

CFD simulations of hydrodynamic/thermal coupling phenomena in a bubble column with internals

CFD simulations have been carried out in a full three‐dimensional, unsteady, Eulerian framework to simulate hydrodynamic/thermal coupling in a bubble column with internals. A first part of the study, dedicated to the hydrodynamic/thermal coupling in liquid single‐phase flows, showed that assuming constant wall temperature on the internals constitutes a reasonable approximation in lieu of comprehensive simulations encompassing shell flow and coolant flow together. A second part dealing with the hydrodynamics of gas–liquid flows in a bubble column with internals showed that a RNG k–ε turbulence model formulation accounting for gas‐induced turbulence was a relevant choice. The last part used these conclusions to build a hydrodynamic/thermal coupling model of a gas–liquid flow in a bubble column with internals. With a per‐phase RNG k–ε turbulence model and assuming constant wall temperature, it was possible to simulate heat transfer phenomena consistent with experimentally measured heat transfer coefficients. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

CFD analysis of two‐phase turbulent flow in internal airlift reactors

The hydrodynamic performance of three internal airlift reactor configurations was studied by the Eulerian–Eulerian k–ε model for a two‐phase turbulent flow. Comparative evaluation of different drag and lift force coefficient models in terms of liquid velocity in the riser and downcomer and gas holdup in the riser was highlighted. Drag correlations as a function of Eötvös number performed better results in comparison to the drag expressions related to Reynolds number. However, the drag correlation as a function of both Reynolds and Eötvös numbers fitted well with experimental results for the riser gas holdup and downcomer liquid velocity in configurations I and II. Positive lift coefficients increase the liquid velocity and decrease the riser gas holdup, while opposite results were obtained for negative values. By studying the effects of bubble size and their shape, the smaller bubbles provide a lower liquid velocity and a gas holdup. The effects of bubble‐induced turbulence and other non‐drag closure models such as turbulent dispersion and added mass forces were analysed. The gas velocity and gas holdup distributions, liquid velocity in the riser and downcomer, vectors of velocity magnitude and streamlines for liquid phase, the dynamics of gas holdup distribution and turbulent viscosity at different superficial gas velocities for different reactor configurations were computed. The effects of various geometrical parameters such as the draft tube clearance and the ratio of the riser to the downcomer cross‐sectional area on liquid velocities in the riser and the downcomer, the gas velocity and the gas holdup were explored. © 2011 Canadian Society for Chemical Engineering     

Numerical simulation of turbulent gas–particle flow in a 90° bend: Eulerian–Eulerian approach

A numerical investigation into the physical characteristics of dilute gas–particle flows over a square-sectioned 90° bend is reported. The modified Eulerian two-fluid model is employed to predict the gas–particle flows. The computational results using both the methods are compared with the LDV results of Kliafas and Holt, wherein particles with corresponding diameter of 50 μm are simulated with a flow Reynolds number of 3.47 × 10⁵. RNG-based κ–? model is used as the turbulent closure, wherein additional transport equations are solved to account for the combined gas–particle interactions and turbulence kinetic energy of the particle phase turbulence. Moreover, using the current turbulence modelling formulation, a better understanding of the particle and the combined gas–particle turbulent interaction has been shown. The Eulerian–Eulerian model used in the current study was found to yield good agreement with the measured values.     

Quantifying sub-grid scale (SGS) turbulent dispersion force and its effect using one-equation SGS large eddy simulation (LES) model in a gas–liquid and a liquid–liquid system

The one-equation SGS LES model has shown promise in revealing flow details as compared to the Dynamic model, with the additional benefit of providing information on the modelled SGS-turbulent kinetic energy (Niceno et al., 2008). This information on SGS-turbulent kinetic energy (SGS-TKE) offers the possibility to more accurately model the physical phenomena at the sub-grid level, especially the modelling of the SGS-turbulent dispersion force (SGS-TDF). The use of SGS-TDF force has the potential to account for the dispersion of particles by sub-grid scale eddies in an LES framework, and through its use, one expects to overcome the conceptual drawback faced by Eulerian–Eulerian LES models. But, no work has ever been carried out to study this aspect. Niceno et al. (2008) could not study the impact of SGS-TDF effect as their grid size was comparable to the dispersed bubble diameter. A proper extension of research ahead would be to quantify the effect of sub-grid scale turbulent dispersion force for different particle systems, where the particle sizes would be smaller than filter-size. This work attempts to apply the concept developed by Lopez de Bertodano (1991) to approximate the turbulent diffusion of the particles by the sub-grid scale liquid eddies. This numerical experimentation has been done for a gas–liquid bubble column system (Tabib et al., 2008) and a liquid–liquid solvent extraction pump-mixer system ( [Tabib et al., 2010] and [28] ). In liquid–liquid extraction system, the organic droplet size is around 0.5 mm, and in bubble columns, the bubble size is around 3–5 mm. The simulations were run with mesh size coarser than droplet size in pump-mixer, and for bubble column, two simulations were run with mesh size finer and coarser than bubble diameter. The magnitude of SGS-TDF values in all the cases were compared with magnitude of other interfacial forces (like drag force, lift force, resolved turbulent dispersion force, force due to momentum advection and pressure). The results show that the relative magnitude of SGS-TDF as compared to other forces were higher for the pump-mixer than for the coarser and finer mesh bubble column simulations. This was because in the pump-mixer, the ratio of “dispersed phase particle diameter to the grid-size” was smaller than that for the bubble column runs. Also, the inclusion of SGS-TDF affected the radial hold-up, even though the magnitudes of these SGS-TDF forces appeared to be small. These results confirms that (a) the inclusion of SGS-TDF will have more pronounced effect for those Eulerian–Eulerian LES simulation where grid-size happens to be more than the particle size, and (b) that the SGS-TDF in combination with one-equation-SGS-TKE LES model serves as a tool to overcome a conceptual drawback of Eulerian–Eulerian LES model.     

Numerical simulation of two-phase flow with bubble break-up and coalescence coupled with population balance modeling

A computational fluid dynamic (CFD) model was developed with an improved source term based on previous work by Hagesaether et al. [1] for bubble break up and bubble coalescence to carry out numerical prediction of number density of different bubble class in turbulent dispersed flow. The numerical prediction was based on two fluid models, using the Eulerian–Eulerian approach where the liquid phase was treated as a continuum and the gas phase (bubbles) was considered as a dispersed phase. Bubble–bubble interactions, such as breakage due to turbulence and coalescence due to the combined effect of turbulence and laminar shear were considered. The result shows that the radial distributions of number densities of lower bubble classes are more than its higher counterpart. The result also shows that the Sauter mean diameter increases with the increase of height up to 1 m and then become steady. Simulated results are found to be in good agreement with the experimental data.     

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.     

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.     

Computational flow modelling and design of bubble column reactors

The present design practice of the bubble column reactors is still closer to an art than science because of the complexity of the fluid mechanics. In view of this, there have been continuous attempts to understand the complex three-dimensional turbulent two-phase flow. The present paper reviews the modelling efforts on the flow patterns published in the last 30 years with relatively more focus on the last 10 years. Over this period, there have been sustained efforts to improve our understanding of the governing equations of the change (equations of continuity and motion) for two-phase flows. Both Eulerian and Lagrangian approaches have been extensively used. The development has been mainly on three fronts: (i) formulation of interfacial forces (ii) closure problem for the eddy viscosity and (iii) modelling of the correlations arising out of Reynolds averaging procedure.As regards to interface force terms, the published literature has been critically analysed. The present status of our understanding of the drag force, virtual mass force and lift force has been presented. The physical significance of the various formulations has been brought out. The mechanism of the energy transfer from gas to liquid phase has been explained. The developments in closure problem have been most dramatic. The progress of the past 30 years has been reviewed with a focus on the past 10 years. The published literature has been critically analysed and chronology of development has been presented. The effort has been concentrated on cylindrical bubble columns where results on flow pattern could be extended to the design. The studies on transient flow pattern in two-dimensional columns have not been covered because the subject is still under development and the results cannot be extended to the design objective. The closure problem is intimately linked with the physics of turbulence.An attempt has been made to develop a complete correspondence between an operation of real column and the model simulation. Attention has been focused on the cylindrical bubble columns because of their widespread applications in the industry. The effects of the superficial gas velocity, column diameter and bubble slip velocity on the flow pattern have been examined. Extensive comparison has been presented between the predicted and the experimental velocity profiles.For the design of the bubble columns, the knowledge of various design parameters (such as pressure drop, rate of mixing, residence time distribution of both the phases, heat and mass transfer coefficients) is needed. For the estimation of these parameters, the prevailing procedures are largely empirical. The fundamental basis for the estimations is possible through the understanding of the detailed macro- and micro-flow patterns. This basic direction has been the subject of several publications, particularly during the last 5 years. All these studies have been critically analysed in the present review paper. A coherent and holistic approach has been presented on the modelling of fluid mechanics and design of bubble column reactors.Recommendations have been made for the future research in this area.     

Prediction of gas–liquid interfacial area in valve trays

An accurate prediction of gas–liquid interfacial area is very important for the design and optimization of column trays. However, the difference of the gas–liquid flow regimes operating at different scale trays significantly affect the interfacial area calculation. Therefore, in this study, an interfacial area model operating at small column was established using the Kolmogorov's isotropic turbulence hypothesis. According to the analyzes of the gas–liquid flow phenomena of different scale columns, an assumption that the similarity principle of flow characteristics of gas–liquid in full contact was proposed. Moreover, a new model that can be used to predict the gas–liquid interfacial area of a large column with exiting the nonideal flow was obtained through the extension of the small tray interfacial area model based on this principle. Finally, the new model was tested by comparisons with the experimental results of references. The prediction accuracy significantly improved with the maximum deviation of approximately 40%. © 2015 American Institute of Chemical Engineers AIChE J, 62: 905–915, 2016     

Phase distribution in dispersed liquid–liquid flow in vertical pipe: Mean and turbulent contributions of interfacial force

We applied an Eulerian–Eulerian two‐fluid model on an upward dispersed oil–water flow in vertical pipe with 80 mm diameter and 2.5 m length. The numerical profiles of the radial distribution of the oil drops at 1.5 m from the inflow are compared to the experimental data of Lucas and Panagiotopoulos (Flow Meas Instrum. 2009;20:127–135) This article analyzes the roles of turbulence and interfacial forces on the phase distribution phenomenon. In liquid–liquid flow the relative velocity is low and the distribution of the dispersed phase is mainly governed by the turbulence. This work highlights the important role of the turbulent contribution obtained by averaging the added mass force on the radial distribution profiles of the oil drops. The numerical results present improved profiles of the dispersed phase comparing to the experimental data when this turbulent contribution is taken into account in the momentum balance. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4214–4223, 2017     

Simulations of Gas Distributors in the Design of Shallow Bubble Column Reactors

Computational fluid dynamics (CFD) was used to simulate the effect of sparger construction in gas holdup and liquid axial velocity in a shallow bubble column reactor for the air‐water system. Model parameters were evaluated in 2‐ and 3‐D simulations by using a two‐fluid model and the standard k‐? turbulence model. The Eulerian‐Eulerian approach was employed to predict the height of column that is affected by the sparger. It was found that increasing the number of orifices in the sparger increases the total gas holdup. Moreover, each orifice causes an increase in the circulation and mixing of liquid in the column. The results of the simulations follow the trends observed in the findings of Dhotre and Joshi [1].