Multi‐Phase‐Multi‐Size‐Group Model for the Inclusion of Population Balances into the CFD Simulation of Gas‐Liquid Bubbly Flows

A CFD model for the simulation of gas‐liquid bubbly flow is developed. In the model, the multi‐phase flow is simulated by an Eulerian‐Eulerian approach using several phase definitions (from 3 to 10). The bubble size distribution is simulated by a solution of the discretized population balance equation with coalescence and break‐up of bubbles. The number of the discretized population balance equations in the model is larger than the number of the phases used in the flow field simulation. A desired accuracy in the simulation can be achieved by choosing a suitable number of phases as a compromise between accuracy and computational cost. With this model, more detailed flow hydrodynamics and bubble size distribution can be obtained. The model was tested with different operating conditions and for different numbers of dispersed phases in a bubble column, and was verified with a bubble size distribution obtained experimentally.     

Models for the Numerical Simulation of Bubble Columns: A Review

This work reviews the state‐of‐the‐art models for the simulation of bubble columns and focuses on methods coupled with computational fluid dynamics (CFD) where the potential and deficits of the models are evaluated. Particular attention is paid to different approaches in multiphase fluid dynamics including the population balance to determine bubble size distributions and the modeling of turbulence where the authors refer to numerous published examples. Additional models for reactive systems are presented as well as a special chapter regarding the extension of the models for the simulation of bubble columns with a present solid particle phase, i.e., slurry bubble columns.     

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     

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.     

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.     

CFD simulation of gas–liquid flow in a high-pressure bubble column with a modified population balance model

In this study, based on the Luo bubble coalescence model, a model correction factor C_e for pressures according to the literature experimental results was introduced in the bubble coalescence efficiency term. Then, a coupled modified population balance model (PBM) with computational fluid dynamics (CFD) was used to simulate a high-pressure bubble column. The simulation results with and without C_e were compared with the experimental data. The modified CFD-PBM coupled model was used to investigate its applicability to broader experimental conditions. These results showed that the modified CFD-PBM coupled model can predict the hydrodynamic behaviors under various operating conditions.     

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     

Gas-liquid flow and bubble size distribution in stirred tanks

This work is aimed at investigating the turbulent two-phase flow and the bubble size distribution (BSD) in aerated stirred tanks by experiments and computational fluid dynamics (CFD) modelling. The experimental data were collected using a two-phase particle image velocimetry technique and a digital image processing method based on a threshold criterion. With the former technique, the liquid and the gas phase ensemble-averaged mean and r.m.s. velocities are measured simultaneously, while with the latter the dimensions of the bubbles dispersed inside the liquid are evaluated. On the modelling side, a CFD approach, based on the solution of Reynolds average Navier-Stokes equations in an Eulerian framework for both phases, is adopted. As for the bubble dimensions modelling, besides the mono-dispersed assumption, a population balance method, named MUSIG, with bubble break-up and coalescence models is considered. The BSD and the axial and radial velocity of the gas and the liquid phase are presented and discussed. The outcomes of the computational work are evaluated on the basis of the experimental results.     

CFD‐Facilitated Flow Field Analysis of Bubble Columns with Concentric Plates for Biological Applications

As the hydrodynamic behavior in bubble columns is difficult to characterize, computational fluid dynamics (CFD) is a useful alternative tool for research and design. An experimental and computational analysis of the macromixing and gas holdup of a bubble column indicates that 3D simulations with CFD using an Eulerian‐Eulerian approximation yield results of the overall velocity field and gas holdup distribution that are suitable for engineering design purposes. Particularly, CFD simulations uncover that the inclusion of concentric solid plates into a bubbling column increase the gas holdup by 79 % and the mixing time by 48 % when compared with a column without plates operating at similar superficial gas velocities.     

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.     

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.     

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.     

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     

CFD modeling of slurry bubble column reactors for Fisher-Tropsch synthesis

Industrial bubble column reactors for Fischer-Tropsch (FT) synthesis include complex hydrodynamic, chemical and thermal interaction of three material phases: a population of gas bubbles of different sizes, a liquid phase and solid catalyst particles suspended in the liquid. In this paper, a CFD model of FT reactors has been developed, including variable gas bubble size, effects of the catalyst present in the liquid phase and chemical reactions, with the objective of predicting quantitative reactor performance information useful for design purposes. The model is based on a Eulerian multifluid formulation and includes two phases: liquid-catalyst slurry and syngas bubbles. The bubble size distribution is predicted using a Population Balance (PB) model. Experimentally observed strong influence of the catalyst particles concentration on the bubble size distribution is taken into account by including a catalyst particle induced modification of the turbulent dissipation rate in the liquid. A simple scaling modification to the dissipation rate is proposed to model this influence in the PB model. Additional mass conservation equations are introduced for chemical species associated with the gas and liquid phases. Heterogeneous and homogeneous reaction rates representing simplified FT synthesis are taken from the literature and incorporated in the model.Hydrodynamic effects have been validated against experimental results for laboratory scale bubble columns, including the influence of catalyst particles. Good agreement was observed on bubble size distribution and gas holdup for bubble columns operating in the bubble and churn turbulence regimes. Finally, the complete model including chemical species transport was applied to an industrial scale bubble column. Resulting hydrocarbon production rates were compared to predictions made by previously published one-dimensional semi-empirical models. As confirmed by the comparisons with available data, the modeling methodology proposed in this work represents the physics of FT reactors consistently, since the influence of chemical reactions, catalyst particles, bubble coalescence and breakup on the key bubble-fluid drag force and interfacial area effects are accounted for. However, heat transfer effects have not yet been considered. Inclusion of heat transfer should be the final step in the creation of a comprehensive FT CFD simulation methodology. A significant conclusion from the modeling results is that a highly localized FT reaction rate appears next to the gas injection region when the syngas flow rate is low. As the FT reaction is exothermal, it may lead to a highly concentrated heat release in the liquid. From the design perspective, the introduction of appropriate heat removal devices may be required.     

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.     

Drop breakage in a single-pass through vortex-based cavitation device: Experiments and modeling

Liquid–liquid emulsions are used in many sectors such as personal care, home care, and food products. There is an increasing need for developing compact and modular devices for producing emulsions with desired droplet size distribution (DSD). In this work, we have experimentally and computationally investigated an application of vortex-based hydrodynamic cavitation (HC) device for producing emulsions. The focus is on understanding drop breakage occurring in a single-pass through the considered HC device. The experiments were performed for generating oil-in-water emulsion containing 1%–20% rapeseed oil. The effect of pressure drop across the HC device in the range of 50–250 kPa on drop breakage was examined. DSD of emulsions produced through a single pass was measured using the focussed beam reflectance measurements. Comprehensive computational fluid dynamics (CFD) model based on the Eulerian approach was developed to simulate multiphase cavitating flow. Using the simulated flow, population balance model (PBM) with appropriate breakage kernels was solved to simulate droplet breakage in a vortex-based HC device. The device showed an excellent drop breakage efficiency (nearly 1% which is much higher than other commercial devices such as rotor–stators or sonolators) and was able to reduce mean drop size from 66 to ~15 μm in a single pass. The CFD and PBM models were able to simulate DSD. The presented models and results will be useful for researchers and engineers interested in developing compact devices for producing emulsions of desired DSD.     

CFD modeling of immiscible liquids turbulent dispersion in Kenics static mixers: Focusing on droplet behavior

The present study is concerned with the computational fluid dynamics(CFD) simulation of turbulent dispersion of immiscible liquids, namely, water–silicone oil and water–benzene through Kenics static mixers using the Eulerian–Eulerian and Eulerian–Lagrangian approaches of the ANSYS Fluent 16.0 software. To study the droplet size distribution(DSD), the Eulerian formulation incorporating a population balance model(PBM) was employed. For the Eulerian–Lagrangian approach, a discrete phase model(DPM) in conjunction with the Eulerian approach for continuous phase simulation was used to predict the residence time distribution(RTD) of droplets.In both approaches, a shear stress transport(SST) k-ω turbulence model was used. For validation purposes, the simulated results were compared with the experimental data and theoretical values for the Fanning friction factor, Sauter mean diameter and the mean residence time. The reliability of the computational model was further assessed by comparing the results with the available empirical correlations for Fanning friction factor and Sauter mean diameter. In addition, the influence of important geometrical and operational parameters, including the number of mixing elements and Weber number, was studied. It was found that the proposed models are capable of predicting the performance of the Kenics static mixer reasonably well.     

A unified theoretical model for breakup of bubbles and droplets in turbulent flows

Pressure has a significant effect on bubble breakup, and bubbles and droplets have very different breakup behaviors. This work aimed to propose a unified breakup model for both bubbles and droplets including the effect of pressure. A mechanism analysis was made on the internal flow through the bubble/droplet neck in the breakup process, and a mathematical model was obtained based on the Young–Laplace and Bernoulli equations. The internal flow behavior strongly depended on the pressure or gas density, and based on this mechanism, a unified breakup model was proposed for both bubbles and droplets. For the first time, this unified breakup model gave good predictions of both the effect of pressure or gas density on the bubble breakup rate and the different daughter size distributions of bubbles and droplets. The effect of the mother bubble/droplet diameter, turbulent energy dissipation rate and surface tension on the breakup rate, and daughter bubble/droplet size distribution was discussed. This bubble breakup model can be further used in a population balance model (PBM) to study the effect of pressure on the bubble size distribution and in a computational fluid dynamics‐population balance model (CFD‐PBM) coupled model to study the hydrodynamic behaviors of a bubble column at elevated pressures. © 2014 American Institute of Chemical Engineers AIChE J, 61: 1391–1403, 2015