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.     

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 in the sparger region of bubble columns

It is well known that the gas distributor can play an important role on the evolution of the bubble size distribution (BSD) in gas-liquid reactors, strippers and absorbers. Therefore, the main subject of the present work was to study the influence of sparger design and process parameters on the BSD in the sparger region of the considered apparatus. For this purpose, both detailed measurements and prediction of the size of bubbles produced at the sparger were carried out in three different experimental apparatuses.The unique set of BSD curves were obtained by analyzing a large amount of bubbles with a measurement based on image analysis technique.Additionally, Colella's model of BSD evolution in bubble columns was further developed by implementing a detailed physical model for predicting the initial BSD at the sparger where the model input is only based on design/process parameters. A validation of the model was carried out using data from two different columns. The comparison between calculated and experimental BSD shows good agreement.     

Theoretical prediction of flow regime transition in bubble columns by the population balance model

Theoretical prediction of flow regime transition in bubble columns was studied based on the bubble size distribution by the population balance model (PBM). Models for bubble coalescence and breakup due to different mechanisms, including coalescence due to turbulent eddies, coalescence due to different bubble rise velocities, coalescence due to bubble wake entrainment, breakup due to eddy collision and breakup due to large bubble instability, were proposed. Simulation results showed that at relatively low superficial gas velocities, bubble coalescence and breakup were relatively weak and the bubble size was small and had a narrow distribution; with an increase in the superficial gas velocity, large bubbles began to form due to bubble coalescence, resulting in a much wider bubble size distribution. The regime transition was predicted to occur when the volume fraction of small bubbles sharply decreased. The predicted transition superficial gas velocity was about 4 cm/s for the air-water system, in accordance with the values obtained from experimental approaches.     

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.     

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.     

CFD-PBE simulation of a bubble column in OpenFOAM

A general CFD-PBE (computational fluid dynamics-population balance equation) solver for gas–liquid poly-dispersed flows of both low and high gas volume fractions is developed in OpenFOAM (open-source field operation and manipulation) in this work. Implementation of this solver in OpenFOAM is illustrated in detail. The PBE is solved with the cell average technique. The coupling between pressure and velocity is dealt with the transient PIMPLE algorithm, which is a merged PISO-SIMPLE (pressure implicit split operator-semi-implicit method for pressure-linked equations) algorithm. Results show generally good agreement with the published experimental data, whereas the modeling precision could be improved further with more sophisticated closure models for interfacial forces, the models for the bubble-induced turbulence and those for bubble coalescence and breakage. The results also indicate that the PBE could be solved out the PIMPLE loop to save much computation time while still preserving the time information on variables. This is important for CFD-PBE modeling of many actual gas–liquid problems, which are commonly high-turbulent flows with intrinsic transient and 3D characteristics.     

Three-dimensional mathematical modeling of dispersed two-phase flow using class method of population balance in bubble columns

Computational fluid dynamics (CFD) simulations of bubble columns have received recently much attention and several multiphase models have been developed, tested, and validated through comparison with experimental data. In this work, we propose a model for two-phase flows at high phase fractions. The inter-phase forces (drag, lift and virtual mass) with different closure terms are used and coupled with a classes method (CM) for population balance. This in order to predict bubble’s size distribution in the column which results of break-up and coalescence of bubbles. Since these mechanisms result greatly of turbulence, a dispersed k– turbulent model is used.The results are compared to experimental data available from the literature using a mean bubble diameter approach and CM approach and the appropriate formulations for inter-phase forces in order to predict the flow are highlighted.The above models are implemented using the open source package OpenFoam.     

Model based on population balance for the simulation of bubble columns using methods of the least-square type

A novel model is presented which uses mass and momentum equations based on population balances to describe the dispersed phase of bubble columns. A set of integro-differential non-linear equations constitutes the model, which can be solved directly using the least-squares methods. The implementation for these is presented.The model presents a degree of flexibility, as different density functions (number, mass and volume) and different internal coordinates (bubble diameter, volume and mass) can be used.A simplified 1D model of a bubble column is solved using the least-squares spectral element method. The results obtained for two different gas volume fluxes at the inlet are compared with experiments by several authors. The simulations show good agreement with the measured data.     

Bubble size distribution in bubble columns

The bubble size distributions are measured for the air-water system as a function of air velocity at room temperature in two bubble columns. High speed cinephotography and fiber optic probe techniques are used to measure the bubble size. Our limited measurements suggest that the bubble size may be independent of gas velocity in the range 3.6 to 9.2 cm/s and may be dependent on column diameter with smaller bubbles for narrower columns. The bubble size appears to be smaller at the column wall than at distances away from the wall.     

Population balance modeling of bubble size distributions in a direct-contact evaporator using a sparger model

The study of bubble size distributions in direct-contact evaporators was addressed both theoretically and experimentally. Recently developed models for calculating bubble coalescence and breakage frequencies in isothermal bubble columns were adapted to the population balance equation using the bubble mass as the internal coordinate which was discretized using an expansion of the number density function by impulse functions. A sparger model was developed based on experimental data for a non-coalescing system and using bubble formation models for isothermal and non-isothermal conditions. Bubble size distributions in a direct-contact evaporator operating in the quasi-steady-state regime for four different gas superficial velocities, including the homogeneous and heterogeneous regimes, together with the sparger model, were used for estimating the three empirical parameters from the population balance model, which were observed to be functions of the gas superficial velocity. In all cases considered, the population balance model fitted the experimental data rather well and the regressed parameters exhibit the physically expected behavior with changes in the gas superficial velocity.     

Bubble characteristics in shallow bubble column reactors

The bubble characteristics have been investigated in an air–water bubble column with shallow bed heights. The effect of bed height, location and the presence of solids on the bubble size, bubble rise velocity and overall and sectional gas holdup are studied over a range of superficial gas velocities. Optimal shallow bed operation relies on the combined entrance and exit effects at the distributor and the liquid bed surface. The gas holdup is found to decrease with an increase in H/D ratio but the effect is diminishing at high H/D ratios. A H/D ratio of 2–4 is found to be suitable for shallow bed operation. The presence of solids causes the formation of larger bubbles at the distributor and the effect is diminishing as the gas velocity is increased.     

Modelling local bubble size distributions in agitated vessels

Photography and capillary suction probe were used to measure local bubble size distributions (BSDs) from Rushton turbine agitated (14/200 L) air-tap water and CO₂-n-butanol dispersions. A multiblock stirred tank model with population balances (PBs) for bubbles was created to describe local BSDs in agitated vessels. Unknown parameters in breakage and coalescence models were adjusted by comparing the predicted and measured local BSDs. The BSDs from both investigated systems and varying vessel-operating conditions were included simultaneously to the fitting. The adjusted models were incorporated to MUSIG PB model in CFX-5.7 and tested for the laboratory stirred tanks. The multiblock model showed to be an optimal trade-off between the accuracy and CPU time for the investigation of gas-liquid hydrodynamics and validation of closure models. As a result of fitting, the adjusted model seems to describe local BSDs more accurately in agitated vessels than the model of Lehr et al. [2002. Bubble-size distributions and flow fields in bubble columns. A.I.Ch.E. Journal 48, 2426-2443], which has been successful in bubble column studies. This shows that phenomenological breakage and coalescence closures need experimental validation for various flow environments.     

Numerical Simulation of Interfacial Closures for 3D Bubble Column Flows

Numerical investigation of flow hydrodynamics in a square cross‐sectioned bubble column was conducted in a transient Euler‐Euler environment by applying the simulation tool Ansys CFX 14.0. The influence of the drag coefficient (C_D) was investigated and the results were also compared with drag force models. Furthermore, three different lift force models and a defined lift coefficient were studied. All results were compared with the available experimental data. All simulations were carried out for a single‐hole sparger with given aspect ratio (H/D) and superficial gas velocity.     

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

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

Effect of antifoam agents on bubble characteristics in bubble columns based on acoustic sound measurements

In this paper, the effect of antifoam agents on bubble characteristics in bubble columns is studied. Specifically, the bubble characteristics of air in tap water are compared to those of air in 5% and 10% antifoam solutions. Bubble characteristics such as gas holdup, bubble diameter, bubble-size distribution, and damping ratio were investigated at various superficial gas velocities. These properties were deduced from the acoustic sound measurement. The study revealed that the addition of antifoam chemicals reduces the overall gas holdup and increases the average bubble diameter. The bubble-size distribution in tap water is found to be homogeneous while in antifoam solutions to be heterogeneous. It is also found that at low gas velocities the damping ratio for antifoam solutions is higher than that for tap water, while at high gas velocities the damping ratio is not affected. The results affirm that acoustic probes are excellent measuring tools over classical tools at moderate gas velocities.     

Numerical and technological properties of bubble column bioreactors for aerobic processes

This paper describes the method of modelling and numerical simulation of bubble column bioreactors in which the process of aerobic biodegradation of carbonaceous substrate occurs. Such bioreactors belong to systems with distributed state variables. Determining steady states of such objects results in solving non-linear boundary-value problems.The bioreactors with axial dispersion and piston flow with biomass recirculation were analysed. The effectiveness of selected algorithms used to determine the steady states of such bioreactors were compared; the numerical properties of mathematical models of analysed bioreactors were specified, the branches of steady states in bioreactors with axial dispersion and piston flow were determined and the application areas of such bioreactors were defined.     

A novel approach for estimating the average bubble size for foams flowing in vertical columns

Bubbles in flowing foams deform, coalesce, and rupture. The bubble size, however, determines to a great extent the functionality and mechanical properties of the foam. Often it is not possible to measure directly the bubble size in a flowing foam, either because the system or the foam itself is not transparent. In order to determine the average bubble size in a flowing foam, a novel approach to estimate the average bubble size was developed, based upon the overflowing foam liquid content and conductivity measurements.A flowing foam column with variable orifice diameters was designed and experiments were performed with different gas flowrates, orifice diameters and surfactant (Sodium dodecyl sulphate) concentrations. Image analysis was used to measure directly the bubble size in the foam. When progressively smaller orifices were inserted, more coalescence was observed, as well as a decrease in the overflowing liquid content and the foam conductivity. Estimating the bubble size from these measurements showed close agreement with the directly measured bubble sizes.     

二维鼓泡床内气泡尺寸分布的实验与CFD模拟

在有机玻璃制成的二维鼓泡床(0.20m×0.02m×2.00m)内,采用摄像法对空气－自来水的气液两相体系的气泡尺寸分布进行了考察。以商业计算流体力学软件ANSYS CFX 10.0为平台,在双流体模型的基础上,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进行了多相流CFD数值模拟。结果表明 MUSIG(Multiple Size Group)模型实现了对多气泡体系内气泡尺寸分布特性的考察,气泡尺寸分布的模拟结果与实验结果吻合得较好,从而说明了考虑了气泡聚并破碎的MUSIG模型能很好地反映出鼓泡床内气泡尺寸分布特性。