Bubble size modeling approach for the simulation of bubble columns

The constant bubble size modeling approach (CBSM) and variable bubble size modeling approach (VBSM) are frequently employed in Eulerian–Eulerian simulation of bubble columns. However, the accuracy of CBSM is limited while the computational efficiency of VBSM needs to be improved. This work aims to develop method for bubble size modeling which has high computational efficiency and accuracy in the simulation of bubble columns. The distribution of bubble sizes is represented by a series of discrete points, and the percentage of bubbles with various sizes at gas inlet is determined by the results of computational fluid dynamics (CFD)–population balance model (PBM) simulations, whereas the influence of bubble coalescence and breakup is neglected. The simulated results of a 0.15 m diameter bubble column suggest that the developed method has high computational speed and can achieve similar accuracy as CFD–PBM modeling. Furthermore, the convergence issues caused by solving population balance equations are addressed.     

Three‐dimensional CFD‐PBM coupled model of the temperature fields in fluidized‐bed polymerization reactors

A three‐dimensional (3‐D) computational fluid dynamics model, coupled with population balance (CFD‐PBM), was developed to describe the gas–solid two‐phase flow in fluidized‐bed polymerization reactors. The model considered the Eulerian–Eulerian two‐fluid model, the kinetic theory of granular flow, the population balance, and heat exchange equations. First, the model was validated by comparing simulation results with the classical calculated data. The entire temperature fields in the reactor were also obtained numerically. Furthermore, two case studies, involving constant solid particle size and constant polymerization heat or evolving particle‐size distribution, polymerization kinetics, and polymerization heat, were designed to identify the model. The results showed that the calculated results in the second case were in good agreement with the reality. Finally, the model of the second case was used to investigate the influences of operational conditions on the temperature field. © 2011 American Institute of Chemical Engineers AIChE J, 2011     

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.     

Populationsbilanzmodellierung mit einem Mehrphasen‐CFD‐Code und vergleichende Visualisierung

The Euler‐Euler multiphase approach multiphaseEulerFoam is extended by implementation of several population balance models to describe the variation of the dispersed phase bubble size. The different models are compared with each other and with experimental data. A new approach is developed, which allows, in addition to the representation of the bubble size, an accurate visualization of the bubble shape based on the Eötvös and Reynolds number as well as position probability and number of bubbles and therefore simplifies the comparison between simulation and experiment.     

Bubble Size Distribution in Oil‐Based Bubble Columns

A practical population balance model was used to evaluate the bubble size distribution in a bubble column. In addition, the bubble size distribution in the bubble column was measured at different gas velocities by photography and analysis of the pictures. Four types of liquid, i.e., water and three petroleum‐based liquids, were used in the experiments. The gas phase was air. It was found that the existing models in the literature are not able to satisfactorily predict the experimentally measured bubble size distribution. The model can be corrected by applying a correction factor to the energy dissipation rate. The corrected model fits the experimental bubble size distribution considerably better than the existing models. The variation of this correction factor is reported for different systems at different gas velocities.     

Simulation of a Bubble Column by Computational Fluid Dynamics and Population Balance Equation Using the Cell Average Method

An axisymmetric computational fluid dynamics (CFD) simulation coupled with a population balance equation (PBE) has been applied in simulating the gas‐liquid flow in a bubble column with an in‐house code. The novel feature of this simulation is the application of the cell average method in a CFD‐PBE coupled model for the first time. The predicted results by this method are compared with those by the traditional fixed pivot method and experimental data. For both methods, the simulated results are in reasonable agreement with the reported experimentally measured values. However, the bubble size distributions determined by the cell average method are slightly better than those found by means of the fixed pivot method, i.e., the latter provides a smaller peak value and a wider bubble size distribution, and the probability density function of large bubbles is higher.     

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.     

Bubble size distribution modeling in stirred gas–liquid reactors with QMOM augmented by a new correction algorithm

Local gas hold‐up and bubbles size distributions have been modeled and validated against experimental data in a stirred gas–liquid reactor, considering two different spargers. An Eulerian multifluid approach coupled with a population balance model (PBM) has been employed to describe the evolution of the bubble size distribution due to break‐up and coalescence. The PBM has been solved by resorting to the quadrature method of moments, implemented through user defined functions in the commercial computational fluid dynamics code Fluent v. 6.2. To overcome divergence issues caused by moments corruption, due to numerical problems, a correction scheme for the moments has been implemented; simulation results prove that it plays a crucial role for the stability and the accuracy of the overall approach. Very good agreements between experimental data and simulations predictions are obtained, for a unique set of break‐up and coalescence kinetic constants, in a wide range of operating conditions. © 2009 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     

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.     

A CFD‐PBM‐PMLM integrated model for the gas–solid flow fields in fluidized bed polymerization reactors

Although the use of computational fluid dynamics (CFD) model coupled with population balance (CFD‐PBM) is becoming a common approach for simulating gas–solid flows in polydisperse fluidized bed polymerization reactors, a number of issues still remain. One major issue is the absence of modeling the growth of a single polymeric particle. In this work a polymeric multilayer model (PMLM) was applied to describe the growth of a single particle under the intraparticle transfer limitations. The PMLM was solved together with a PBM (i.e. PBM‐PMLM) to predict the dynamic evolution of particle size distribution (PSD). In addition, a CFD model based on the Eulerian‐Eulerian two‐fluid model, coupled with PBM‐PMLM (CFD‐PBM‐PMLM), has been implemented to describe the gas–solid flow field in fluidized bed polymerization reactors. The CFD‐PBM‐PMLM model has been validated by comparing simulation results with some classical experimental data. Five cases including fluid dynamics coupled purely continuous PSD, pure particle growth, pure particle aggregation, pure particle breakage, and flow dynamics coupled with all the above factors were carried out to examine the model. The results showed that the CFD‐PBM‐PMLM model describes well the behavior of the gas–solid flow fields in polydisperse fluidized bed polymerization reactors. The results also showed that the intraparticle mass transfer limitation is an important factor in affecting the reactor flow fields. © 2011 American Institute of Chemical Engineers AIChE J, 58: 1717–1732, 2012     

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

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

鼓泡床中的气泡尺寸分布

根据气泡聚并和破裂速率模型,提出一个描述鼓泡床中气泡尺寸分布的总体平衡(Population Balance)模型。该模型可预计鼓泡床中气泡尺寸分布随床高的变化。对空气-水体系的模拟结果与实测结果吻合较好。     

Numerical Simulation of Absorbing CO2 with Ionic Liquids

Although separating CO₂ from flue gas with ionic liquids has been regarded as a new and effective method, the mass transfer properties of CO₂ absorption in these solvents have not been researched. In this paper, a coupled computational fluid dynamic (CFD) model and population balance model (PBM) was applied to study the mass transfer properties for capturing CO₂ with ionic liquids solvents. The numerical simulation was performed using the Fluent code. Considering the unique properties of ionic liquids, the Eulerian‐Eulerian two‐flow model with a new drag coefficient correlation was employed for the gas‐liquid fluid dynamic simulation. The gas holdup, interfacial area, and bubble size distribution in the bubble column reactor were predicted. The mass transfer coefficients were estimated with Higbie's penetration model. Furthermore, the velocity field and pressure field in the reactor were also predicted in this paper.     

Gas phase hydrodynamics in a surface-aerated tank with a long-short blades agitator

This work aims to study the gas phase hydrodynamics in a stirred tank with a surface-aerated long-short blades agitator by the Eulerian–Eulerian approach coupled with population balance model. Predicted local gas holdup and bubble size distribution agree well with those measured by a conductivity probe technique. The predictions demonstrate that the pressure depression in the center is the main driving force for gas suction and the downward flow carries the bubbles down to redistribute in the whole tank. The gas phase has higher gas holdup with large bubble size in the upper part and lower gas holdup but with small bubble size in the lower part of the tank. The predicted liquid-phase mass transfer coefficients agree well with our previous experimental results and just depend on the power consumption per unit volume when the aspect ratio of the liquid height to the tank diameter varies from 1.1 to 2.0.     

Comparison of Eulerian QBMM and classical Eulerian–Eulerian method for the simulation of polydisperse bubbly flows

The spatial gas distribution of poly-disperse bubbly flows depends greatly on the bubble size. To reflect the resulting polycelerity, more than two momentum balance equations (typically for the gas and liquid phases) have to be considered, as done in the multifluid approach. The inhomogeneous multiple-size group model follows this approach, also combined with a population balance model. As an alternative, in a previous work, an Eulerian quadrature-based moments method (E-QBMM) was implemented in OpenFOAM; however, only the drag force was included. In this work, different nondrag forces (lift, wall lubrication, and turbulent dispersion) are added to enable more complex test cases to be simulated. Simulation results obtained using E-QBMM are compared with the classical E–E method and validated against experimental data for different test cases. The results show that there is good agreement between E-QBMM and E–E methods for mono-disperse cases, but E-QBMM can better simulate the separation and segregation of small and large bubbles.     

Flow Characteristics in a Honeycomb Structure to Design Nanobubble Generating Apparatus

A nanobubble generator with honeycomb structures producing a large amount of water including large nanobubble density in a short time is described. The nanobubble-generating performance is investigated for large and small apparatus having different honeycomb cell dimensions by applying computational fluid dynamics (CFD) coupled with a population balance model (PBM). The CFD simulation shows that a significant pressure drop and shear stress occur in the bubbly flow in the honeycomb cell. The numerical model is based on the Eulerian multiphase model and the PBM is used to calculate the bubble size distribution. The obtained CFD-PBM results are compared with the experimental results for large and small apparatus. Bubble size distributions in the honeycomb structure under different inlet absolute pressure can be predicted by the PBM. The maximum shear stress is determined as the main controlling factor for nanobubble generation.     

Numerical and Experimental Study of Catalyst Loading and Body Effects on a Gas‐Liquid Trickle‐Flow Bed

The influence of tortuosity and fluid volume fractions on trickle‐flow bed performance was analyzed. Hydrodynamics of the gas‐liquid downward flow through trickle beds, filled with industrial trilobe catalysts, were investigated experimentally and numerically. The pressure drop and liquid holdup were measured at different gas and liquid velocities and in two different loading methods, namely, sock and dense catalyst loading. The effect of sharp corners on hydrodynamic parameters was considered in a bed with rectangular cross section. The reactor was simulated, considering a three‐phase model, appropriate porosity function, and interfacial forces based on the Eulerian‐Eulerian approach. Computational fluid dynamics (CFD) simulation results for pressure drop and liquid holdup agreed well with experimental data. Finally, the velocity distribution in two types of loading and the effect of bed geometry in CFD results demonstrated that pressure drop and liquid holdup were reduced compared to a cylindrical one due to high voidage at sharp corners.