Liquid Flow In Bubble Column Research Articles

Drag models coupled with CFD–PBM method for simulation in bubble columns

AbstractIn this study, three‐dimensional numerical simulation of gas–liquid flow in bubble columns was realized by using the computation fluid dynamics (CFD)–population balance model (PBM). The new drag model improves the stability‐constrained multi‐fluid (SCMF‐C) model because of the consideration of the wake accelerating and the hindering effects for calculating the drag correction factor. The gas holdup, axial liquid velocity, and bubble size distribution (BSD) predicted by four drag models at 0.02 and 0.1 m/s were compared. The results revealed that the proposed drag model can provide excellent predictions for both bubbly and heterogeneous flows. Because the wake accelerating and the hindering effects were considered, reliable predictions were achieved for the gas holdup, and the problem of uniform gas holdup distribution was mitigated. Therefore, the SCMF‐C model can be extended for nonuniform BSD. The gas holdup and liquid velocity increased, and the nonuniformity of radial results became pronounced at 0.1 m/s. The profiles of four drag models were similar at a low height, whereas the difference between the simulations of the four models became obvious with the variation of heights. The results of the four models were accurate, and the BSD was wide at 0.1 m/s. Subsequently, the feasibility of the four drag models was evaluated at 0.2 and 0.4 m/s. The results of the comparison revealed that the proposed drag model exhibited excellent feasibility at higher gas velocities and was powerful for the simulation of bubble columns.

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 of the bubble column. The values simulated by optimized CFD model were in agreement with experimental data, and the errors were within ± 20%. In addition, the axial velocity, turbulent kinetic energy, bubble size distribution, and the dynamic characteristic of bubble plume were analyzed at different superficial gas velocities. This research work could provide a theoretical basis for the extension of the CFD–PBM coupled model to other multiphase reactors..

Exploration on the stability conditions in bubble columns by noncooperative game theory

• Different pathways of compromise of dominant mechanisms in bubbly flow. • Formulation of different stability conditions for gas–iquid bubbly flow. • Game theory and non-inferior solution to unravel the compromising mechanisms. • Understand regime transition and structure of bubble classes via stability condition. The energy-minimization multiscale (EMMS) model, originally proposed for gas–solid fluidization, features a stability condition to close the simplified conservation equations. It was put forward to physically reflect the compromise of two dominant mechanisms, i.e. , the particle-dominated with minimal potential energy of particles, and the gas-dominated with the least resistance for gas to penetrate through the particle bed. The stability condition was then formulated as the minimization of the ratio of these two physical quantities. Analogously, the EMMS approach was later extended to the gas–liquid flow in bubble columns, termed dual-bubble-size model. It considers the compromise of two dominant mechanisms, i.e ., the liquid-dominated regime with small bubbles, and the gas-dominated regime with large bubbles. The stability condition was then formulated as the minimization of the sum of these two physical quantities. Obviously, the two stability conditions were expressed in different manner, though gas–solid and gas–liquid systems bear some analogy. In addition, both the conditions transform the original multi-objective variational problem into a single-objective problem. The mathematical formulation of stability condition remains therefore an open question. This study utilizes noncooperative game theory and noninferior solutions to directly solve the multi-objective variational problem, aiming to explore the different pathways of compromise of dominant mechanisms. The results show that only keeping the single dominant mechanism cannot capture the jump change of gas holdup, which is associated with flow regime transition. Hybrid of dominant mechanisms, noninferior solutions and noncooperative game theory can predict the flow regime transition. However, the game between the two mechanisms makes the two-bubble structure degenerate and reduce to the single-bubble structure. The game of the three mechanisms restores the two-bubble structure. The exploration on the formulation of stability conditions may help to understand the roles and interactions of different dominant mechanisms in the origin of complexity in multiphase flow systems.

Dynamics of gas–liquid flow in a cylindrical bubble column: Comparison of electrical resistance tomography and voidage probe measurements

Gas–liquid flow in bubble columns is inherently unsteady, and dynamics of such flow is known to influence local mixing, mass and heat transport and therefore, the performance of bubble column reactors. The present work is carried out to verify dynamics of gas–liquid flow measured using time-resolved Electrical Resistance Tomography (ERT) with the measurements performed using in-house developed voidage probes. Experiments were performed in a cylindrical bubble column under dilute to dense conditions (superficial gas velocity (UG) in the range of 1–40cm/s). The instantaneous and time-averaged gas volume fraction distribution was measured using the ERT and voidage probes for uniform and local spargers. The time-averaged gas volume fraction measured using both the techniques was found in a quantitative agreement for all UG and sparger configurations considered in the present work. The low-frequency oscillations (<1Hz) generated by meandering motion of bubble plume and high-frequency oscillations (1–10Hz) generated by bubble-scale processes, measured using the ERT and voidage probes were in a satisfactory agreement. The results reported in the present work will help to benchmark the ERT to infer the dynamics of gas–liquid flow and to validate the dynamic characteristics predicted using CFD models under dense flow conditions.

Experimental characterization of dense gas–liquid flow in a bubble column using voidage probes

Gas–liquid flow in bubble columns under dilute flow condition has been investigated widely. In the present work, we have characterized gas–liquid flow in a pseudo 2D bubble column for a wide range of superficial gas velocities (UG=1–30cm·s-1) that cover dilute to dense flow conditions. In-house developed voidage probes were used to measure local gas volume fraction fluctuations, which in turn were used to characterize dynamics of column-scale re-circulatory flow and bubble-scale flow processes, under dilute-to-dense conditions. Importantly, the spatial distribution of internal composition of gas volume fraction, i.e. gas volume fraction contained in different bubble size groups, was measured. Further, the spatial distribution of chord length and bubble size was measured for a wide range of UG. With increase in UG, the low frequency oscillations caused by meandering bubble plume at lower UG were found to diminish and the fluctuations caused by bubble swarms were found to dominate under the dense flow conditions. Using the time spent by the probe in each bubble, the bubble population was classified into different size groups and the gas volume fraction for each size group was measured. Under dense flow conditions, small bubbles were seen to accumulate near column walls, as exhibited by wall peaking in gas volume fraction profiles and that large bubbles were found to flow through the column centre. The results presented in this work are important to improve the understanding of dense gas–liquid flow and also for rigorous validation of CFD models.

Implementation of an improved bubble breakup model for TFM-PBM simulations of gas–liquid flows in bubble columns

An improved bubble coalescence and breakup model was implemented in the inhomogeneous TFM-PBM model for buoyancy-driven gas–liquid bubbly flows. The bubble coalescence was modeled by considering bubble collisions induced by turbulent fluctuations, buoyancy driven, wake entrainment, and viscous shear, and the liquid film drainage model was used for the description of the coalescence efficiency of collisions. The bubble breakup was analyzed in terms of bubble interactions with turbulent eddies which coupled the restriction of surface energy with the capillary pressure. A generic TFM-PBM model was developed and applied for the simulations of bubble columns operated in different flow regimes. The evolutions of the bubble size distributions were simulated and validated for literature data of a D=0.14m cylindrical bubble column at gas superficial velocities 0.03 and 0.45m/s, respectively. Furthermore, a well documented D=0.44m bubble column was simulated, and the predicted distributions of the gas holdup and liquid velocity were compared with the experimental measurements of Chen et al. (1998). The model showed the capacity of describing the gas–liquid fluid dynamics of bubble columns operated in both bubbly and churn-turbulent flow regimes.

Stability-constrained multi-fluid CFD models for gas–liquid flow in bubble columns

We have proposed a Dual-Bubble-Size (DBS) model featuring a stability condition describing the compromise of two dominant mechanisms, and then a stability-constrained multi-fluid model (SCMF-A) integrating the DBS model into CFD simulation. This work further validates the model and extends to much higher flow rate, and then tentatively proposes a new model termed SCMF-B. It solves the conservative equations for a dense phase composed of small bubbles and liquid and a dilute phase involving large bubbles. The DBS model supplies the structure parameters of the two bubble classes such as the gas volume fraction of small bubbles, the ratio of drag coefficient to bubble diameter for large bubbles and the superficial gas velocity of large bubbles to close the SCMF-B model. A thorough comparison indicates that without any fitting parameters, the SCMF models are superior to the two-fluid model (TFM) with empirical drag correlations in the prediction of overall gas holdup, radial profile of gas holdup and liquid flow field over a wide range of operating gas velocities. By comparison, each SCMF model has its strength and weakness at different flow conditions. SCMF-B can better reproduce the plateau of overall gas holdup as a function of gas flow rate, and the relative error of radial profile of gas holdup is the smallest among all the models at relatively higher flow rate. SCMF-A is better for the lower and much higher gas flow rates. We also design a special and step-by-step strategy to ascertain the evolution from SCMF-A to SCMF-B. We find that the physical properties, flow rate and drag coefficient of different bubble classes have respective functions in the model evolution and only their synergistic effects could generate reasonable prediction. This suggests that the definition of two “fluids” in the SCMF-B in terms of the differences in dense and dilute phases, rather than the thermal physical properties, is reasonable only when all the above “external” and “internal” factors are taken into account.

Large Eddy Simulation of the Gas–Liquid Flow in a Cylindrical Cross-Sectioned Bubble Column

This paper is concerned with the numerical study of gas–liquid flow in bubble columns by large eddy simulations (LES). The Euler–Euler approach is used to describe the equations of motion of the two-phase flow. The mean velocities and the fluctuating velocities are obtained. It is found that, when the drag, lift and virtual mass forces are used, the computed results in agreement with experimental transient behavior can be captured.

In-Depth Exploration of the Dual-Bubble-Size Model for Bubble Columns

The Dual-Bubble-Size (DBS) model is an extension of the Energy-Minimization Multi-Scale (EMMS) model, which was originally proposed for gas–solid fluidization to gas–liquid systems. This model is featured by a stability condition in addition to conservative equations for two bubble classes. The stability condition is mathematically formulated as a minimization tendency of microscale energy dissipation and physically reflects the compromise between different dominant mechanisms. This work attempts to use the Simulated Annealing (SA) method to solve the nonlinear optimization problem of the model. It is found that the SA method could greatly reduce the computational cost while capturing the jump change of gas holdup more accurately for the DBS model. The jump change reflects the transition from homogeneous and transitional regimes to heterogeneous regime, and essentially arises from the inflection of the trajectory of global minimum point within the space of the three structure parameters. The DBS model then is extended to Triple-Bubble-Size (TBS) and Multiple-Bubble-Size (MBS) models by introducing three or more bubble classes. We find that the TBS and MBS model prediction is reduced to that of DBS model and the two characteristic bubble classes are distinct in the calculation, even though the gas is resolved into three or more bubble classes. This implies that gas–liquid flow in bubble columns are essentially dominated by two bubble classes rather than multiple bubble classes, and the DBS model may be an intrinsic model for reflecting the compromising mechanisms in the system and thereby describing the system evolution and gas–liquid interaction. Its integration with computational fluid dynamics (CFD) simulation may offer a more reasonable way to model the complex gas–liquid flow in bubble columns.

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 Simulation of Bubble Columns: Modeling of Nonuniform Gas Distribution at Sparger

Most laboratory bubble columns are equipped with sieve plate spargers. The sieve plate spargers are known to lead to nonuniform gas distribution. It is important to account for such nonuniform gas distribution at the sparger in the computational model before experimental data collected from such columns are used to fit the model parameters. In this article, such an attempt is made. A detailed, 3D CFD model was developed to simulate unsteady gas−liquid flows in bubble columns with sieve plate spargers. The sensitivity of the nonuniformity of gas distribution at the sparger with sparger resistance was examined. The model predictions were compared with the experimental data. The developed model and presented results will be useful for simulating industrial bubble columns.

Eulerian–Lagrangian simulations of unsteady gas–liquid flows in bubble columns

We studied the dynamics of gas–liquid flows in a rectangular bubble column using Eulerian–Lagrangian simulations. Three-dimensional, unsteady simulations were performed to simulate the dynamic characteristics of the oscillating bubble plume. The effect of superficial gas velocity and aerated liquid height-to-column width ( H/ W) ratio on the dynamic and time-averaged flow properties was studied and the simulated results were validated using wall pressure and voidage fluctuation measurements. The effect of lift force and numerical diffusion on the dynamic and time-averaged properties is discussed in detail. Further, the results obtained using the Eulerian–Lagrangian simulations were compared with the Eulerian–Eulerian simulations. The bubble scale information, which is otherwise lost in the Eulerian–Eulerian simulations, was validated using the voidage fluctuation measurements. Such experimentally validated Eulerian–Lagrangian models will be useful for the simulation of mass transfer and reactions in bubble columns.

Characterization of dynamics of gas–liquid flows in rectangular bubble columns

AbstractGas–liquid flow in bubble columns is inherently unsteady. The unsteady fluid dynamics influences mixing and other transport processes occurring in bubble column reactors. In this work, we have characterized dynamics of gas–liquid flows in rectangular bubble columns using wall pressure and voidage fluctuations. The low‐frequency oscillations caused by meandering bubble plume were characterized using the plume oscillation period. Experiments were carried out to study the influence of superficial gas velocity, sparger configuration, and liquid height‐to‐width (H/W) ratio on the low‐frequency oscillations. The dimensional analysis based on analogy between buoyancy‐driven thermal and bubbly flows was carried out to relate low‐frequency oscillations to various design and operating parameters. This analysis was able to correlate present as well as previously published experimental data. We have further demonstrated the importance of establishing such a quantitative relationship for validation of computational fluid dynamics (CFD)–based models by carrying out CFD simulations of gas–liquid flow in rectangular bubble columns. The importance of bubble‐scale information obtained using conductivity probes in validating Eulerian–Lagrangian models is also demonstrated. © 2004 American Institute of Chemical Engineers AIChE J, 50: 2394–2407, 2004

Two-Dimensional CFD Model for the Prediction of Flow Pattern, Pressure Drop and Heat Transfer Coefficient in Bubble Column Reactors

In this paper, a CFD model has been developed for the prediction of flow pattern and eddy diffusivity profiles in bubble columns. A low Reynolds number k–ɛ model has been incorporated for the near-wall region. Simulations have been carried out for a wide range of superficial gas velocity (VG), column diameter (D), column height (HD) and the nature of the gas–liquid system. The model predictions have been compared with all the experimental data available in the literature. Complete energy balance has been established in all the cases. The validated CFD model has been extended for the prediction of pressure drop and heat transfer for two-phase gas–liquid flows in bubble columns. The predicted values of the two-phase friction multiplier and heat transfer coefficient were in good agreement with the experimental data.

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.

Effect of bubble deformation on stability and mixing in bubble columns

The paper deals with hydrodynamics in bubble columns. The objective of the paper is to study stability and mixing in a bubble column. The modeling of parameters such as stationary drag and added mass is addressed. In addition, the effect of bubble deformation in terms of eccentricity is highlighted. In a previous paper, the transition between homogeneous and heterogeneous regimes in bubble column without liquid flow has been shown to be driven by the deformation of the bubbles associated to drag and added mass. In the present paper, this work is generalized to bubble column with liquid flow and to the transition from bubble flow to slug flow in a vertical pipe. Numerical simulations of gas–liquid reactors are presented. The numerical simulations are validated in the case of gas plume after the Becker et al. data (Becker, S., Sokolichin, A., & Eigenberg, G. (1994) Gas–liquid flow in bubble columns and loop reactors: Part II. Comparison of detailed experiments and flow simulations. Chemical Engineering Science, 49 (24B), 5747–5762. The numerical simulations are finally applied to a bubble column. The simulations of residence time distribution coupled to transient hydrodynamics are shown to be very sensitive to the modeling of interfacial transfer of momentum from the bubbles to the liquid in terms of drag and added mass, including the effect of bubble deformation.

A low Reynolds number k– ε model for the prediction of flow pattern and pressure drop in bubble column reactors

A low Reynolds number k– ε CFD model has been used for the description of flow pattern near the wall. An excellent agreement has been shown between the predicted and experimental hold-up and velocity profiles over a wide range of superficial gas velocity ( V G ), column diameter ( D), column height ( H D ) and the nature of gas–liquid system (bubble diameter and their rise velocity). The CFD model has been extended for the prediction of pressure drop for two-phase gas–liquid flows in bubble columns. A comparison has been presented between the predicted and the experimental data over a wide range of superficial gas and liquid velocities and for three gas–liquid systems.

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.

Dynamics of gas-liquid flows in bubble column reactors

Wall pressure fluctuations were measured in bubble columns at different locations and for different gas velocities and height to diameter ratios. Non-linear analysis of the acquired data of pressure fluctuations was carried out to quantify dynamic characteristics. A bubble–bubble interaction model was developed to simulate voidage fluctuations in bubble columns. Dynamic characteristics of the simulated voidage fluctuations were compared with those of measured pressure fluctuations. The data and analysis will be useful to validate full transient CFD simulations of gas–liquid flow in bubble columns.

NUMERICAL PREDICTION OF TWO-PHASE FLOW IN BUBBLE COLUMNS

A numerical model is described for the prediction of turbulent continuum equations for two-phase gas–liquid flows in bubble columns. The mathematical formulation is based on the solution of each phase. The two-phase model incorporates interfacial models of momentum transfer to account for the effects of virtual mass, lift, drag and pressure discontinuities at the gas–liquid interface. Turbulence is represented by means of a two-equation k–ϵ model modified to account for bubble-induced turbulence production. The numerical discretization is based on a staggered finite-volume approach, and the coupled equations are solved in a segregated manner using the IPSA method. The model is implemented generally in the multipurpose PHOENICS computer code, although the present appllications are restricted to two-dimensional flows. The model is applied to simulate two bubble column geometries and the predictions are compared with the measured circulation patterns and void fraction distributions.