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.     

Compressibility induced bubble size variation in bubble column reactors: Simulations by the CFD–PBE

Bubble column reactors can be simulated by the two fluid model (TFM) coupled with the population balance equation (PBE). For the large industrial bubble columns, the compressibility due to the pressure difference may introduce notable bubble size variation. In order to address the compressibility effect, the PBE should be reformulated and coupled with the compressible TFM. In this work, the PBE with a compressibility term was formulated from single bubble dynamics, the mean Sauter diameters predicted by the compressible TFM coupled with the PBE were compared with the analytical solutions obtained by the ideal gas law. It was proven that the mesoscale formulations presented in this work were physically consistent with the macroscale modeling. It can be used to simulate large industrial plants when the compressibility induced bubble size variation is important.     

Experimental Determination and Modeling of Bubble Size Distributions in Bubble Columns

Using a five point conductivity technique local values of bubble size,bubble velocity and gas fractionhave been experimentally determined in a 288 mmID and 4.3 m high bubble column as a function of axial andradial position for the air/water and CO_2/N_2/aqueous MDEA systems.The experimental results are comparedwith predictions from a fundamental two-fluid model.The implementation of a non-steady lateral drag term inthe two-fluid model has been shown.In addition to improving the physical realism of the model,it is found togive slight improvements in the predictions of the distributions of local bubble size.Predictions of bubble size arefound in reasonable agreement with experimental values in the heterogeous flow regime,whereas they are stil1found to be unreliable at low gas velocities.Local void predictions are found in reasonable agreement with experi-mental values,but deviations occur in the homogeneous flow regime towards the wall.This is attributed to defi-ciencies in the simplified bubble size mode     

Numerical simulation of gas–liquid flow in the bubble column using Wray–Agarwal turbulence model coupled with population balance model

In this paper, an improved computational fluid dynamic(CFD) model for gas–liquid flow in bubble column was developed using the one-equation Wary–Agarwal(WA) turbulence model coupled with the population balance model(PBM). Through 18 orthogonal test cases, the optimal combination of interfacial force models, including drag force, lift force, turbulent dispersion force. The modified wall lubrication force model was proposed to improve the predictive ability for hydrodynamic behavior near the wall ...     

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.     

Two-area model for bubble distribution in a turbulent fluidized bed of fine particles

The flow behavior of gas and solid was investigated in FCC simulator of φ710×4000/φ870×11000mm.The axial and radial distributions were detected with matrix fiber-opticprobes.It was found that the distribution of bubble diameter in the turbulent region of the fluidizedbed of fine particles was different from the results reported for lab-scale experiments.Radially therewere three areas,i.e.,the central(r/R=0-0.4),the intermittent or stable(r/R=0.4-0.8)and thenear wall(r/R=0.8-1.0)areas respectively.It was noticed that bubbles were almost non-existing atthe near wall area.Hence,according to the coalescence and splitting theory of bubbles,a two-areamodel of bubble diameter distribution was proposed and a dimensionless parameter(γ_M)regarded asan index for'quality'of fluidization was deduced.     

Size distribution of droplets above a rotating stream tray and model of droplet motion therein

Droplet size distributions have been investigated with a two-probe system above a rotatingstream tray of 300 mm diameter.The measured distributions are found to follow the upper limitedlognormal distribution with three parameters dependent primarily on gas hole F-factor.A probabilitymethod is used to describe the initial state of the droplet population above the tray,and a model fordroplet motion is presented.The results computed with model agree well with experimental data.     

Large eddy simulation of the Gas–Liquid flow in a square cross-sectioned bubble column

In this work the use of large eddy simulations (LES) in numerical simulations of the gas–liquid flow in bubble columns is studied. The Euler–Euler approach is used to describe the equations of motion of the two-phase flow. It is found that, when the drag, lift and virtual mass forces are used, the transient behaviour that was observed in experiments can be captured. Good quantitative agreement with experimental data is obtained both for the mean velocities and the fluctuating velocities. The LES shows better agreement with the experimental data than simulations using the k–ε model.     

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.     

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.     

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.     

Small bubble formation via a coalescence dependent break-up mechanism

A mechanism has been elucidated for the coalescence-mediated break-up of bubbles in gas-liquid systems. Images taken from dynamic systems (a coalescence cell and laboratory-scale bubble columns) show that in some instances the coalescence of two bubbles is accompanied by the formation of a much smaller daughter bubble. Following the coalescence process an annular wave is formed due to the very rapid expansion of the hole following the instant of film rupture. As the wave moves along the length of the bubble, away from the point of rupture it causes a rippling effect which distorts the newly coalesced bubble and may result in the formation of an unstable extension. Instabilities due to the annular wave pinch off a portion of this extension, resulting in the generation of a small daughter bubble. In coalescence dominated systems the process results in the generation of significant numbers of bubbles much smaller (100- diameter) than the Sauter mean diameter (3-).     

Numerical simulation of the gas–liquid flow in a laboratory scale bubble column: Influence of bubble size distribution and non-drag forces

In the present work, a computational model based on an Eulerian–Eulerian approach was used for the simulation of the transient two-phase flow in a rectangular partially aerated bubble column. Superficial gas velocities (U_G) ranging from 0.24 to 2.30 cm/s were used throughout both the experiments and the simulations. The calculated results were verified by comparing them with experimental data including measurements of gas hold-up, plume oscillation period (POP) and Sauter mean bubble diameter. The study shows the effect of mesh refinement, time-step and physical model selection, the latter regarding the role of bubble size distribution and non-drag forces, on the computational results. According to the results presented here, the representation of bubble populations using multiple size groups (MUSIG model) instead of a single group improves the prediction of the experimental parameters under study. Additionally, the results obtained after including the virtual mass force term do not differ considerably from those obtained including only the drag force. On the contrary, as a consequence of introducing the lift force term into the model, the gas hold-up is overestimated and a non-symmetric bubble plume oscillation appears, a fact that is not experimentally observed.     

Computational study of bubble coalescence/break-up behaviors and bubble size distribution in a 3-D pressurized bubbling gas-solid fluidized bed of Geldart A particles

A computational study was carried out on bubble dynamic behaviors and bubble size distributions in a pressurized lab-scale gas-solid fluidized bed of Geldart A particles. High-resolution 3-D numerical simulations were performed using the two-fluid model based on the kinetic theory of granular flow. A fine-grid, which is in the range of 3–4 particle diameters, was utilized in order to capture bubble structures explicitly without breaking down the continuum assumption for the solid phase. A novel bubble tracking scheme was developed in combination with a 3-D detection and tracking algorithm (MS3DATA) and applied to detect the bubble statistics, such as bubble size, location in each time frame and relative position between two adjacent time frames, from numerical simulations. The spatial coordinates and corresponding void fraction data were sampled at 100 Hz for data analyzing. The bubble coalescence/break-up frequencies and the daughter bubble size distribution were evaluated by using the new bubble tracking algorithm. The results showed that the bubble size distributed non-uniformly over cross-sections in the bed. The equilibrium bubble diameter due to bubble break-up and coalescence dynamics can be obtained, and the bubble rise velocity follows Davidson’s correlation closely. Good agreements were obtained between the computed results and that predicted by using the bubble break-up model proposed in our previous work. The computational bubble tracking method showed the potential of analyzing bubble motions and the coalescence and break-up characteristics based on time series data sets of void fraction maps obtained numerically and experimentally.     

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.     

Coalescence during bubble formation at two neighbouring pores: An experimental study in microscopic scale

This work studies the effect of the liquid properties and the operating conditions on the interactions between under-formation bubbles in a cell equipped with two adjacent micro-tubes (i.d. ) for the gas injection, placed 210, 700 and apart. This set-up simulates, though in a simplified manner, the operation of the porous sparger in a bubble column, and it is used to study the bubble interactions observed on the sparger surface. Various liquids covering a wide range of surface tension and viscosity values are employed, while the gas phase is atmospheric air. A fast video recording technique is used both for the visual observations of the phenomena occurring onto the tubes and for the bubble size measurements. The experiments reveal that the interactions between under-formation bubbles as well as the coalescence time depend strongly on the liquid properties, the distance between the tubes and the gas flow rate. Two correlations, which can be found helpful for the bubble column design, have also been formulated and are in good agreement with the available experimental data.     

On the effect of liquid temperature upon bubble coalescence

An experimental study concerning the influence of liquid temperature on bubble coalescence is presented. Bubble collisions in two different liquids (water and ethanol) were analysed at four distinct temperatures , using air as the dispersed phase in all cases. A quantitative criterion was developed to compute the critical velocity for bubble coalescence based on the relative velocities and the outcome (coalescence or bouncing) of the recorded collisions. The critical velocity, and consequently bubble coalescence, was shown to increase as the liquid temperature was raised, an effect whose intensity depended on the kind of liquid employed. Using some simplifying assumptions, a comparison between the experimentally observed trends and the predictions of literature models for the film drainage was drawn. The experimental data were used together with available literature data in the development of a dimensionless correlation for predicting the critical velocity as a function of the liquid properties.     

CFD simulation of effects of the configuration of gas distributors on gas-liquid flow and mixing in a bubble column

Numerical simulations of gas-liquid flow in a cylindrical bubble column of 400 mm in diameter at the superficial gas velocity were conducted to investigate effects of the configuration of gas distributors on hydrodynamic behaviour, gas hold-up and mixing characteristics. Eight different gas distributors were adopted in the simulation. The simulation results clearly show that the configuration of gas distributor have an important impact on liquid velocity and local gas hold-up in the vicinity of the gas distributor. Comparisons of the overall gas holdup and mixing time among different gas distributors have demonstrated that none of the adopted gas distributors was able to produce the highest interfacial area and also yield the shortest mixing time. The CFD modelling results reveal that an increase in the number of gas sparging pipes used in gas distributors is beneficial in improving the gas hold-up but is disadvantageous in reducing bubble size due to a decrease in turbulent kinetic dissipation. It has been demonstrated from the simulations that the appearance of asymmetrical flow patterns in the bubble column and the adoption of smaller gas sparging pipes for gas distributors are effective in improving the mixing characteristics.     

Modeling of bubble coalescence in bubbly co-current flows restricted by confined geometry

Principles of kinetic theory are used to model the coalescence of bubbles in horizontal and vertical upflows where bubble movements are restricted by channel geometry. There are four critical variables that determine the rate at which a swarm of small bubbles will coalesce: the initial bubble population, the average initial bubble diameter, the average relative velocity of the bubbles, and the efficiency of bubble collisions. A model based on dimensional considerations is proposed to predict bubble size as a function of flow position. This model agrees well with experimental results for air/water and air/water/glycerin systems performed in a rectangular channel with an aspect ratio of 12.5 and a cross-sectional area of under both vertical and horizontal orientations.