CFD simulation of bubbly flows: Random dispersion model

Three-dimensional CFD simulations of two-phase flow in a vertical pipe, a square cross-sectional bubble column and a large-scale plume are presented. A random dispersion model (RDM) is used to generate an instantaneous turbulent fluctuating velocity field by assuming that it is comprised of eddies, lifetimes and length-scales of which can be deduced from local mean flow properties. The RDM is used to describe turbulent dispersion of bubbles, and is validated here against the experimental data, and compared with predictions obtained by imposing an empirical turbulent dispersion force (TDF), but without introducing adjustable coefficients. The strictly mechanistic approach to bubble dispersion can offer better opportunities for the development of trustworthy, two-phase flow models.     

On the development of flow pattern in a bubble column reactor: Experiments and CFD

A comprehensive analysis of the development of flow pattern in a bubble column reactor is presented here through extensive LDA measurements and CFD predictions. In the LDA measurements, the simultaneous measurements of 2D velocity-time data were carried out at several radial locations and many axial cross-sections of the column for two different spargers. The profiles of mean axial liquid velocity, fractional gas hold-up and bubble slip velocity showed excellent agreement between the predictions and the experimentally measured values. The experimental results showed that the mean tangential velocity varies systematically in the radial as well as along the axial co-ordinates. The turbulence parameters viz. turbulent kinetic energy, energy dissipation rate and eddy diffusivity were also analysed. The estimated values of local energy dissipation rate obtained using eddy isolation model were used for establishing the energy balance in the column. The experimental data were used for the estimation of normal and shear stress profiles. For the case of single point sparger, just above the sparger region, the bubble plume was seen to have a strong tangential component of motion thereby yielding higher gas hold-up slightly away from the centre. This visual observation was well captured in profiles of all the hydrodynamic parameters obtained from the experimental data. CFD simulations of the mean velocities, gas hold-up and turbulent kinetic energy compared well with the experimental results.     

Influence of the lift force closures on the numerical simulation of bubble plumes in a rectangular bubble column

Numerical Eulerian-Eulerian simulations of the unsteady gas-liquid flow in a centrally aerated two-dimensional bubble column were carried out in order to understand the effect of different formulations of the lift force coefficient (C_L) on the computational results. Three different values of the superficial gas velocity (U_G=2.4, 12.0 and 21.3 mm s⁻¹) that ensure the existence of different flow regimes were experimentally and computationally studied. The validation of the simulated results was based on visual observations and measurements of the global gas hold-up (ε_G) and the plume oscillation period (POP). The results presented reveal that, at U_G=12.0 and 21.3 mm s⁻¹, using C_L<0 results in under- and over-estimation of the ε_G and POP, respectively. On the other hand, taking C_L>0 does not affect the POP while it leads to increasingly higher ε_G values, which are different from those experimentally reported. At U_G=2.4 mm s⁻¹, the effect of the lift force is not so evident, although it slightly improves the prediction of experimental values. Particularly interesting is the case of C_L>0.4 at U_G=21.3 mm s⁻¹, producing a non-symmetric bubble plume oscillation. Since using Tomiyama's lift coefficient correlation does not improve the results, including the lift force into the simulation of bubble plumes is not recommended.     

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.     

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.     

Role of hydrodynamic flow parameters in lipase deactivation in bubble column reactor

The dynamic environment within the bioreactor and in the purification equipment is known to affect the activity and yield of enzyme production. In the present work, the effect of hydrodynamic flow parameters and τ_N,max) and interfacial flow parameters ( and ) on the activity of lipase has been comprehensively investigated in bubble column reactors. Lipase solution was subjected to hydrodynamic flow parameters in 0.15 and 0.385 m i.d. bubble column reactors over a wide range of superficial gas velocity (0.01<V_G<0.4-). The flow parameters were estimated using an in-house CFD simulation code based on k-ε approach. The extent of lipase deactivation in both the columns was found to increase with an increase in hydrodynamic and interfacial flow parameters. However, at equal value of any of these parameters, the extent of deactivation was different in the two columns. The rate of deactivation was found to follow first order kinetics. An attempt has been made to develop rational correlations for the extent of deactivation as well as for the deactivation constant. The rate of deactivation was found to be depending on the average turbulent normal stress and interfacial flow parameters such as bubble diameter and bubble rise velocity.     

CFD simulations of bubble column reactors: 1D, 2D and 3D approach

CFD simulations have been carried out for the predictions of flow pattern in bubble column reactors using 1D, 2D and 3D k-ε models. An attempt has been made to develop a complete correspondence between the operation of a real column and the simulation. Attention has been focused on the cylindrical bubble columns because of their widespread applications in the industry. All the models showed good agreement with the experimental data for axial liquid velocity and the fractional gas hold-up profiles. However, as regards to eddy diffusivity, only the 3D model predictions agree closely with the experimental data.The CFD model has been extended for the estimation of an axial dispersion coefficient (D_L) using 1D, 2D and 3D models. Excellent agreement was found only between the experimental values and the 3D predictions. The 1D and 2D simulations, however, yielded D_L values, which were lower by 25-50%. For this, a mechanistic explanation has been provided.     

Multi-scale analysis of gas–liquid interaction and CFD simulation of gas–liquid flow in bubble columns

The ratio of effective drag coefficient to bubble diameter is of critical importance for CFD simulation of gas–liquid flow in bubble columns. In this study, a novel model is proposed to calculate the ratio on the basis of the Dual-Bubble-Size (DBS) model. The motivation of the study is that a stability condition reflecting the compromise between different dominant mechanisms can serve for a closure in addition to mass and momentum conservative constraints, and the interphase momentum transfer should be related to different paths of energy dissipation. With the DBS model, we can first offer a physical interpretation on macro-scale regime transition via the shift of global minimum point of micro-scale energy dissipation from one potential trough to the other. Then the proposed drag model is integrated into a CFD simulation. Prior to this integration, we investigate the respective effects of bubble diameter and correction factor and found that the effect of bubble diameter is limited, whereas the correction factor due to the bubble swarm effect is eminent and appropriate correction factor has to be selected for different correlations of standard drag efficient to be in accord with experiments. By contrast, the DBS drag model can well predict the radial gas holdup distribution, the total gas holdup as well as the two-phase flow field without the need to adjust model parameters, showing its great potential and advantage in understanding the complex nature of multi-scale structure of gas–liquid flow in bubble columns.     

CFD modeling of gas dispersion and bubble size in a double turbine stirred tank

In the present paper, gas dispersion in a double turbine baffled stirred tank is modeled using a commercial computational fluid dynamics (CFD) code FLUENT 6.1 (Fluent Inc., USA). A bubble number density equation is implemented in order to account for the combined effect of bubble break-up and coalescence in the tank. In the proposed work, the impellers are explicitly described in three dimensions using multiple reference frame model. Dispersed gas and bubbles dynamics in the turbulent water are modeled using an Eulerian-Eulerian approach with dispersed k-ε turbulent model and modified standard drag coefficient for the momentum exchange. The model predicts spatial distribution of gas holdup, average local bubble size and flow structure. The results are compared with experimental and numerical finding reported in the literature and good agreement between the present model and measurements of Alves et al. [Gas liquid mass transfer coefficient in stirred tanks interpreted through bubble contamination kinetics. Chemical Engineering Science, 2002, 57, 487-496] is achieved.     

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.     

CFD Simulation of Liquid Film Flow on Inclined Plates

A two‐phase flow CFD model using the volume of fluid (VOF) method is presented for predicting the hydrodynamics of falling film flow on inclined plates, corresponding to the surface texture of structured packing. Using the proposed CFD model the influence of the solid surface microstructure, liquid properties and gas flow rate on the flow behavior was investigated. From the simulated results it was shown that under the condition of no gas flow the liquid flow patterns are dependent on the microstructure of the plates, and proper microstructuring of the solid surface will improve the formation of a continuous liquid film. It was also found that liquid properties, especially surface tension, play an important role in determining the thin‐film pattern. However, there are very different liquid film patterns under the action of gas flow. Thinner liquid films break easily, but thicker liquid films can remain continuous even at higher gas flow rates, which demonstrates that all factors affecting the liquid film thickness will affect the liquid film patterns under conditions of counter‐current two‐phase flow.     

CFD Simulations of a Bubble Column Operating in the Homogeneous and Heterogeneous Flow Regimes

Bubble columns are operated either in the homogeneous or heterogeneous flow regime. In the homogeneous flow regime, the bubbles are nearly uniform in size and shape. In the heterogeneous flow regime, a distribution of bubble sizes exists. In this paper, a CFD model is developed to describe the hydrodynamics of bubble columns operating in either of the two flow regimes. The heterogeneous flow regime is assumed to consist of two bubble classes: “small” and “large” bubbles. For the air‐water system, appropriate drag relations are suggested for these two bubble classes. Interactions between both bubble populations and the liquid are taken into account in terms of momentum exchange, or drag‐, coefficients, which differ for the “small” and “large” bubbles. Direct interactions between the large and small bubble phases are ignored. The turbulence in the liquid phase is described using the k‐ϵ model. For a 0.1 m diameter column operating with the air‐water system, CFD simulations have been carried out for superficial gas velocities, U, in the range 0.006–0.08 m/s, spanning both regimes. These simulations reveal some of the characteristic features of homogeneous and heterogeneous flow regimes, and of regime transition.     

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。     

含垂直列管束内构件鼓泡塔的CFD模拟

针对含有密集垂直列管束内构件的气液鼓泡塔,在两相Euler二维轴对称k-ε模型中,分别考虑气相和液相受到的列管阻力。通过引入相应的动量源、湍动源以及耗散源建立带列管内构件的鼓泡塔二维CFD模型。模型能清晰、准确地描述带列管束鼓泡塔中气液流动的特征:"烟囱效应"以及分布器影响区延长。计算得到的气含率以及液速的二维分布在宽泛的表观气速(0.12～0.62 m·s^-1)范围内与实验值相符。     

CFD simulation of gas-liquid contacting in tubular reactors

Gas-liquid contacting in tubular reactors was simulated using an Eulerian-Eulerian CFD approach in which accurate interphase momentum closure relations are incorporated, bubble-induced turbulence is accounted for, and population balance equations are used to describe bubble breakage and coalescence. The ability of two breakup kernels (Luo, H., Svendsen, H.F., 1996. Theoretical model for drop and bubble breakup in turbulent dispersions. A.I.Ch.E. Journal 42, 1225-1233; Lehr, F., Millies, M., Mewes, D., 2002. Bubble size distributions and flow fields in bubble columns. A.I.Ch.E. Journal 48, 2426-2443) and three coalescence kernels (Prince, M.J., Blanch, H.W., 1990. Bubble coalescence and breakup in air sparged bubble columns. A.I.Ch.E. Journal 36, 1485-1499; Luo, H., 1993. Coalescence, breakup and liquid recirculation in bubble column reactors. Ph.D. Thesis, Norwegian University of Science and Technology, Trondheim; Lehr, F., Millies, M., Mewes, D., 2002. Bubble size distributions and flow fields in bubble columns. A.I.Ch.E. Journal 48, 2426-2443) to accurately predict several flow parameters in pipe flow was tested.Good agreement between simulation and experimental results (radial profiles of gas holdup, turbulence intensity, and local Sauter bubble diameter) was achieved without the use of empirically derived relationships (such as Drift flux) by adjusting a single parameter which accounts for the deviation in the coalescence behaviour of tap water from that of pure water. The approach adopted in this investigation may thus be applicable to more complex hydrodynamic situations such as those encountered in mechanically agitated tanks and the need for extensive experimental testing may be replaced by single measurement of the effect interfacial properties have on coalescence rates.     

Prediction of bubble behaviour in fluidised beds based on solid motion and flow structure

It has been demonstrated that the non-intrusive positron emission particle tracking (PEPT) could be a potential technique for observing bubble flow pattern, measuring bubble size and rise velocity in bubbling fluidised beds according to the solid motion in bubble and its wake. The results indicate that the behaviour of air bubbles varies greatly with the bed materials and superficial gas velocity. Three types of bubbling patterns (namely A, B and C) have been reported in this study, in which the pattern C is observed when the polyethylene fluidised bed is operated at the superficial gas velocity (U − U_mf) of 0.25–0.5 m/s and the ratio of bed height to bed diameter is unity. After the comparison of the results measured by the PEPT technique with the values calculated by using a number of empirical correlations, two modified correlations are recommended to calculate the bubble size based on the PEPT data.     

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 acoustic cavitation in a crude oil upgrading sonoreactor and prediction of collapse temperature and pressure of a cavitation bubble

In acoustic cavitation, high pressure and temperature are generated due to cavitation bubble collapse in the liquid bulk around the bubble which causes physical and chemical changes in the liquid. In this study, pressure distribution in water caused by ultrasonic wave propagation in a sonoreactor was investigated. Active cavitation zones were determined by calculating acoustic pressure threshold for cavitation inception and compared with experimental results. Collapse pressure and temperature were predicted 3000 atm and 3200 K, respectively, for crude oil at temperature of 25 °C by evaluating cavitation bubble dynamics in the exerted acoustic field. As a consequence, the huge amounts of energy generated by this phenomenon can be applied for changes in oil properties and crude oil upgrading.