Multiple Size Group Model Research Articles

CFD modeling of hydrodynamic characteristics of a gas–liquid two-phase stirred tank

A three-dimensional CFD model was developed in this work to simulate hydrodynamic characteristics of a gas–liquid two-phase stirred tank with two six-bladed turbines and four baffles, coupling of the Multiple Size Group model to determine bubble size distribution. Important hydrodynamic parameters of the multi-phase system such as volume-averaged overall and time-averaged local gas holdups and axial liquid velocities along time and transversal courses were simulated and analyzed in detail, under varied operating conditions (inlet air flow rate and impeller rotation speed). Model predictions of local transient gas holdup and liquid velocity distributions on vertical and horizontal sections of the tank were also carried out. The overall flow patterns were discussed in detail to assess the mixing. Bubble size distributions were further predicted to reveal the unique properties of gas phase. Experimental measurements of overall gas holdups and local axial liquid velocities were used to validate the developed model.

Numerical Simulation of Bubble Column Flows in Churn-Turbulent Regime: Comparison of Bubble Size Models

Numerical simulations of cylindrical bubble column operating in the churn-turbulent regime have been simulated using Euler–Euler approach incorporated with the RNG k–ε model for liquid turbulence. Single-size bubble model, double-size bubble model, and the multiple size group model (MUSIG), including the homogeneous and inhomogeneous discrete methods, are employed in the simulations. Mass conserved formulations of breakup and coalescence rates were used in the computation of bubble size distributions. The Schiller–Naumann drag force was used in the single-size model, and the Ishii–Zuber drag force was used for the MUSIG simulations. For the double-size bubble model, an empirical drag formulation was adapted. The simulation results of time-averaged axial velocity and gas holdup obtained with the three models were compared with reported experimental data in the literature. The results showed that only MUSIG models with lift force can reproduce the measured radial distribution of gas holdup in the fully developed flow regime and that the inhomogeneous MUSIG model performs a little better than other models in the prediction of axial liquid velocity. The RNG k–ε model was used in all simulations, and the results confirmed that this version of k–ε model did yield relatively high turbulence dissipation rates and high bubble breakup rates and, thus, resulted in a rational bubble size distribution. The ad hoc manipulation of the breakup rates was avoided. The simulation results indicated profound mutual effects of drag force, mean bubble sizes, and turbulence characteristics. An increase in drag force yielded a decrease in the relative velocity between phases, the later could result in decreases in k and ε. A large Sauter diameter results from a low bubble breakup rate which was directly connected to the dissipation rates of turbulence. The change of Sauter diameter, in turn, influenced the drag force.

A combined CFD modeling with population balance equation to predict pressure drop in venturi scrubbers

A venturi scrubber is one of the most important devices for air pollution control. Although there are different models for predicting the pressure drop in venturi scrubbers, most of them have some defects and cannot predict the pressure drop correctly. In this study, for the first time, an Eulerian–Eulerian computational fluid dynamics (CFD) model is combined with a population balance equation to predict the pressure drop in venturi scrubbers. This simulation takes into account a multiple size group model for droplet dispersion and droplet size distribution, which is based on a population balance equation. Flow field has been calculated by solving the time averaged continuity and Navier–Stokes equations along with the standard k–e turbulence model. The equations included drag, turbulent dispersion, and buoyancy forces. The calculated pressure drop with and without considering the population balance equation was compared with the experimental data to evaluate the accuracy of the CFD modeling. The size distribution of droplets in the venturi scrubber was studied at different points for different liquid to gas ratios and throat gas velocities. The results show that the maximum break-up of droplets happens at the liquid injection point. Finally, the effects of nozzle diameter and nozzle arrangement on pressure drop in venturi scrubbers were investigated.

Coupling of Wall Boiling with Discrete Population Balance Model

A coupling between a polydisperse population balance method (Multiple Size Group Model – MUSIG) and the RPI wall boiling model for nucleate subcooled boiling has been implemented in ANSYS CFX. It allows more accurate prediction of the interfacial area density for mass, momentum and energy transfer between phases in comparison to the usual local-monodisperse bubble size assumption and underlying bulk bubble diameter correlations as they are commonly used in boiling flow applications like e.g. the prediction of subcooled nucleate boiling in rod bundles and fuel assemblies of PWR. The paper outlines the methodology of the coupled CFD model, which automatically avoids possible inconsistencies in the model formulation for the heated wall, when the generated steam bubbles on the heater surface are injected exactly in the bubble size class corresponding to the predicted bubble departure diameter. The coupling of the RPI wall boiling model and the MUSIG model has been implemented for both homogenous/inhomogeneous variants of the MUSIG model. The paper presents the validation of the coupled modeling approach for the well known test case of nucleate subcooled boiling of R113 refrigerant in a circular annulus with inner heated rod based on the experiments of Roy et al. [1]. ANSYS CFX results with the newly implemented approach as well as comparison to data and locally-monodisperse simulations are provided.

On the Prediction of Bubble Size Distribution and Void Fraction in Vertical Gas-Liquid Flows

Two-fluid modeling approach is considered as one of the most practical and accurate macroscopic formulation of handling bubbly flow systems. Nevertheless, in order to rigorously account for bubble-bubble interactions, the population balance equation (PBE) must be solved alongside with the continuity and momentum balance equations. Class method typified by the MUltiple SIze Group (MUSIG) model appears to be one of the most direct methods to solve the PBE using a finite series of discrete classes. In this paper, an alternative approach based on the direct quadrature method of moments (DQMOM) is investigated. In contrast to MUSIG model which requires a large number of classes to resolve the bubble distribution, the main advantage of DQMOM is that the number of moments to be solved is generally very small. Validation and assessment of the two population balance models are carried out against measurements of vertical bubbly flows for a range of flow conditions. Based on the present study, preliminary computed results have been found to compare very well against the experimental data as well as the numerical results predicted through the MUSIG model.

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The current paper presents the prediction results of a bubbly flow under plunging jet conditions using multiphase mono- and poly-dispersed approaches. The models consider interfacial momentum transfer terms arising from drag, lift, and turbulent dispersion force for the different bubble sizes. The turbulence is modeled by an extended k–ɛ model which accounts for bubble induced turbulence. Furthermore in case of a poly-dispersed air–water flow the bubble size distribution, bubble break-up and coalescence processes as well as different gas velocities in dependency on the bubble diameter are taken into account using the Inhomogeneous MUSIG model. This model is a generalized inhomogeneous multiple size group model based on the Eulerian modeling framework which was developed in the framework of a cooperative work between ANSYS-CFX and Forschungszentrum Dresden-Rossendorf (FZD). The latter is now implemented into the CFD code CFX.According to the correlation on the lateral lift force obtained by Tomiyama (1998); this force changes its sign in dependence on the bubble size. Consequently the entrained small bubbles are trapped below the jet. They can escape from the bubble plume only by turbulent fluctuations or by coalescence. If the size of the bubbles generated by coalescence exceeds the size at which the lift force changes its sign these large bubbles go out from the plume and rise to the surface.A turbulent model based on an additional source term for turbulence kinetic energy and turbulence eddy dissipation equation is compared to the common concept for modeling the turbulence quantities proposed by Sato et al. (1981). It has been found that the large bubble distribution is slightly affected by the turbulence modeling which affects particularly the bubble coalescence and break-up process.

Numerical study of a bubble plume generated by bubble entrainment from an impinging jet

The current paper presents the prediction results of a bubbly flow under plunging jet conditions using multiphase mono- and poly-dispersed approaches. The models consider interfacial momentum transfer terms arising from drag, lift, and turbulent dispersion force for the different bubble sizes. The turbulence is modeled by an extended k– ɛ model which accounts for bubble induced turbulence. Furthermore in case of a poly-dispersed air–water flow the bubble size distribution, bubble break-up and coalescence processes as well as different gas velocities in dependency on the bubble diameter are taken into account using the Inhomogeneous MUSIG model. This model is a generalized inhomogeneous multiple size group model based on the Eulerian modeling framework which was developed in the framework of a cooperative work between ANSYS-CFX and Forschungszentrum Dresden-Rossendorf (FZD). The latter is now implemented into the CFD code CFX. According to the correlation on the lateral lift force obtained by Tomiyama (1998); this force changes its sign in dependence on the bubble size. Consequently the entrained small bubbles are trapped below the jet. They can escape from the bubble plume only by turbulent fluctuations or by coalescence. If the size of the bubbles generated by coalescence exceeds the size at which the lift force changes its sign these large bubbles go out from the plume and rise to the surface. A turbulent model based on an additional source term for turbulence kinetic energy and turbulence eddy dissipation equation is compared to the common concept for modeling the turbulence quantities proposed by Sato et al. (1981). It has been found that the large bubble distribution is slightly affected by the turbulence modeling which affects particularly the bubble coalescence and break-up process.

Modeling Vertical Subcooled Boiling Flows at Low Pressures

Abstract An improved wall heat flux partitioning model at the heated surface was developed by Yeoh et al. This model, coupled with a three-dimensional two-fluid model and Multiple Size Group model, has led to satisfactory agreement being achieved between the model predictions and experimental measurements. Nevertheless, one shortcoming is the reliance on empirical correlations for the active nucleation site density in the wall heat flux partitioning model. This discrepancy brings about uncertainties, especially in appropriately evaluating the vapor generation rate, which greatly influences the model prediction on the axial and radial void fraction profiles within the bulk fluid flow. By considering the fractal model with the aforementioned subcooled boiling flow model in the absence of empirical correlations for the active nucleation site density, a comprehensive mechanistic model to predict vertically oriented subcooled boiling flows is developed. The proposed model is assessed against the experimental data of axial measurements of Zeitoun and Shoukri and the radial measurements of Yun et al. and Lee et al. for vertical subcooled boiling flows within annular channels. Improved model predictions are obtained when the model is compared against typically applied empirical correlations for active nucleation site density. Discussions on the agreement of other two-phase flow parameters are also presented.

CFD modelling of phenol biodegradation by immobilized Candida tropicalis in a gas–liquid–solid three-phase bubble column

A three-dimensional transient model, combining three-phase fluid flow, interphase mass transfer and intrinsic bioreaction kinetics, was developed to simulate the dynamic behaviors of batch phenol biodegradation by immobilized Candida tropicalis in a gas–liquid–solid three-phase bubble column (BC). A computational fluid dynamics (CFD) method was used, with a multiple size group model adopted to determine the bubble size distribution, based on a previous three-phase BC hydrodynamic CFD model [1]. Current simulation results of phenol and oxygen concentration changes in the liquid phase were validated by corresponding experimental measurements under various operating conditions. Furthermore, local transient batch phenol biodegradation characteristics such as the oxygen concentration profiles in the gas, liquid and solid phases, the phenol concentration profiles in the liquid and solid phases, and the cell concentration profile in the solid phase were predicted. Comparisons between species interphase mass transfer and bioreaction rates were carried out to identify the rate-limiting step in the immobilized batch phenol biodegradation processes.

Numerical simulation of micro-bubble drag reduction using population balance model

The phenomenon of drag reduction by the injection of micro-bubbles into turbulent boundary layer has been investigated using an Eulerian–Eulerian two-fluid model. Multiple-size group (MUSIG) based on population balance models, which resolve a wide range of bubble sizes taking into account the bubble break-up and coalescence have been used for this purpose. The simulated results are compared against the experimental findings of Madavan et al. [1984. Reduction of turbulent skin friction by micro-bubbles. Physics of Fluids 27, 356–363] and also other numerical studies explaining the sophisticated phenomena of drag reduction. For the two Reynolds number cases considered, the buoyancy with the plate on the bottom configuration is investigated, as from the experiments it is seen that buoyancy seem to play a role in the drag reduction. Numerical model employed in the investigation comprises of a micro-bubble laden flow wherein two independent sets of Reynolds averaged Navier–Stokes (RANS) transport equations were used to describe both the phases of the flow. The shear stress transport (SST) turbulence model is used as the turbulent closure for the primary phase and a zero equation turbulence model is used for the micro-bubbles. Change in the mean streamwise velocity profiles, void fraction, turbulence modification and other results are presented and discussed with corresponding change in the gas injection rates. The complex mechanism of drag reduction are scrutinised and explained in context to our numerical findings. Special attentions have been also devoted to divulge the effect of bubble coalescence and break-up caused by random collision and turbulent impact. Numerical results showed good agreement for the skin-friction coefficients against experimental data throughout various air injection rates. The MUSIG model was found to be one of the best candidates to resolve the bubble dynamics in micro-bubble-induced drag reduction problems.

Numerical Simulation of Gas Dispersion in an Aerated Stirred Reactor with Multiple Impellers

The flow field and void fraction distribution in an aerated tank of 0.45 m diameter with a three-impeller agitator have been numerically simulated and validated against prior experimental data. An asymmetric deep hollow-blade disk turbine (BT-6) was used as bottom impeller to disperse the incoming gas, with two up-pumping, four-blade, Maxflo (MFU) hydrofoils above to ensure effective axial mixing from top to bottom of the tank. The standard Eulerian−Eulerian formulation of the k−e turbulence model with multiple frames of reference (MFR) was used in the simulation. A population balance model (PBM) combined with a multiple size group (MUSIG) model has been implemented using the commercial CFX code. Bubble breakup and coalescence have been modeled fundamentally using isotropic turbulence theory. An alternative approach was provided by an Euler−Euler computation assuming a constant single average bubble diameter (SABD), set to 4 mm. These SABD results were compared with those predicted by the MUSIG model and ...

Population balance models for subcooled boiling flows

PurposeThis study aims to examine both the population balance approach based on the MUltiple SIze Group (MUSIG) model and the average bubble number density transport equation (ABND) model for 3D, low pressure, gas‐liquid, subcooled boiling, vertical flows. The purpose is to assess the ability of both models to predict the radial profile of void fraction, bubble Sauter mean diameter and interfacial area concentration which characterise subcooled boiling.Design/methodology/approachImprovement in the ABND model to simulate gas‐liquid bubbly flows with heat transfer was achieved by combining the condensation expression with the gaseous mass transport equation within the CFD commercial code CFX4.4.FindingsOverall, both the ABND model and the MUSIG model provided good results in terms of the above‐mentioned criteria when compared against experimental measurements. However, the ABND model was found to have limitations in predicting high‐subcooled boiling flows due to the lack of bubble size resolution to adequately capture the effect of condensation over a range of bubbles sizes.Originality/valueIt is shown that the ABND model provides an economic alternative to the MUSIG model in terms of complexity and computational time, as long as one is aware of the limitations in simulating high‐subcooling flow regimes.

Fundamental consideration of wall heat partition of vertical subcooled boiling flows

Improved wall heat flux partitioning accounting sliding bubbles and a mechanistic model that incorporates the fundamental consideration of bubble frequency during low-pressure subcooled flow boiling is presented. A model considering the forces acting on departing bubbles at the heated surface is employed. Coupled with a three-dimensional two-fluid and population balance equations based on the modified MUSIG (MUltiple-SIze-Group) model, the behavior of an upward forced convective subcooled boiling flows in a vertical annular channel is simulated. Comparison of model predictions against local and axial measurements (heat fluxes ranged from 152.9 to 705.0kW/m2) is made for the void fraction, Sauter mean bubble diameter and interfacial area concentration covering a range of different mass and heat fluxes and inlet subcoolings. Good agreement is achieved between the predicted and measured profiles. Reasonable agreement with recent experimental measurements is also attained for the predicted growth and waiting times of bubble frequency at particular local wall superheat and subcooling temperatures.

The inhomogeneous MUSIG model for the simulation of polydispersed flows

A generalized inhomogeneous multiple size group (MUSIG) model based on the Eulerian modeling framework was developed in close cooperation of ANSYS-CFX and Forschungszentrum Dresden-Rossendorf and implemented into the CFD code CFX. The model enables the subdivision of the dispersed phase into a number of size groups regarding the mass balance as well as regarding the momentum balance. In this work, the special case of polydispersed bubbly flow is considered. By simulating such flows, the mass exchanged between bubble size classes by bubble coalescence and bubble fragmentation, as well as the momentum transfer between the bubbles and the surrounding liquid due to bubble size dependent interfacial forces have to be considered. Particularly the lift force has been proven to play an important role in establishing a certain bubble size distribution dependent flow regime. In a previous study [Krepper, E., Lucas, D., Prasser, H.-M., 2005. On the modeling of bubbly flow in vertical pipes. Nucl. Eng. Des. 235, 597–611] the application of such effects were considered and justified and a general outline of such a model concept was given. In this paper the model and its validation for several vertical pipe flow situations is presented. The experimental data were obtained from the TOPFLOW test facility at the Forschungszentrum Dresden-Rossendorf (FZD). The wire-mesh technology measuring local gas volume fractions, bubble size distributions and velocities of gas and liquid phases were employed. The inhomogeneous MUSIG model approach was shown as capable of describing bubbly flows with higher gas content. Particularly the separation phenomenon of small and large bubbles is well described. This separation has been proven as a key phenomenon in the establishment of the corresponding flow regime. Weaknesses in this approach can be attributed to the characterization of bubble coalescence and bubble fragmentation, which must be further investigated.

Local hydrodynamics modeling of a gas–liquid–solid three‐phase bubble column

AbstractA three‐dimensional (3D) transient model was developed to simulate the local hydrodynamics of a gas–liquid–solid three‐phase bubble column using the computational fluid dynamic method, where the multiple size group model was adopted to determine the size distribution of the gas bubbles. Model simulation results, such as the local time‐averaged gas holdups and axial liquid velocities, were validated by experimental measurements under varied operating conditions, e.g., superficial gas velocities and initial solid loadings at different locations in the three‐phase bubble column. Furthermore, the local transient hydrodynamic characteristics, such as gas holdups, liquid velocities, and solid holdups, as well as gas bubble size distribution were predicted reasonably by the developed model for the dynamic behaviors of the three‐phase bubble column. © 2007 American Institute of Chemical Engineers AIChE J, 2007

On the numerical study of isothermal vertical bubbly flow using two population balance approaches

Two population balance approaches based on the MUltiple-SIze-Group (MUSIG) model and one-group average bubble number density (ABND) model for handling the bubble size distribution of gas–liquid bubbly flows under isothermal conditions are assessed. Three forms of coalescence and breakage mechanisms by Wu et al. [1998. One-group interfacial area transport in vertical bubbly flow. International Journal of Heat Mass Transfer 41, 1103–1112], Hibiki and Ishii [2002. Development of one-group interfacial area transport equation in bubbly flow systems. International Journal of Heat Mass Transfer 45, 2351–2372] and Yao and Morel [2004. Volumetric interfacial area prediction in upwards bubbly two-phase flow. International Journal of Heat Mass Transfer 47, 307–328] are incorporated in the ABND model. To examine the relative merits of both approaches, local radial distributions of five primitive variables in bubbly flows: void fraction, Sauter mean bubble diameter, interfacial area concentration, and gas and liquid velocities, are compared against the experimental data of Liu and Bankoff [1993a. Structure of air–water bubbly flow in a vertical pipe—I. Liquid mean velocity and turbulence measurements. International Journal of Heat Mass Transfer 36, 1049–1060; 1993b. Structure of air–water bubbly flow in a vertical pipe—II. Void fraction, bubble velocity and bubble size distribution. International Journal of Heat Mass Transfer 36, 1061–1072] and Hibiki et al. [2001. Axial interfacial area transport of vertical bubble flows. International Journal of Heat Mass Transfer 44, 1869–1888]. In general, both of the ABND model and MUSIG model predictions yield close agreement with experimental results. To account for the range of different bubble sizes in the gas–liquid bubbly flows, the resolution required is achieved through the application of the MUSIG model. Nevertheless, computational times increase by a factor of two when compared to applying the simpler ABND model. To further exploit the models’ capabilities, investigations are carried out by extending the two population approaches beyond the bubbly flow regime of higher void fraction, particularly in the transition regime. The numerical results are found to be grossly over-predicted, which expose the inherent limitations of the models. It is known that bubbles in this regime are generally highly distorted and closely packed instead of spherical shape and allowed to move freely in bubbly flow regime.

Two-fluid and population balance models for subcooled boiling flow

Population balance equations combined with a three-dimensional two-fluid model are employed to predict subcooled boiling flow at low pressure in a vertical annular channel. The MUSIG (MUltiple-SIze-Group) model implemented in the computer code CFX4.4 is further developed to accommodate the wall nucleation at the heated wall and condensation in the subcooled boiling regime. Comparison of model predictions against local measurements is made for the void fraction, bubble Sauter mean diameter and gas and liquid velocities covering a range of different mass and heat fluxes and inlet subcooling temperatures. Additional comparison using empirical relationships for the active nucelation site density and local bubble diameter is also investigated. Good agreement is achieved with the local radial void fraction, bubble Sauter diameter and liquid velocity profiles against measurements. However, significant weakness of the model is evidenced in the prediction of the vapour velocity. Work is in progress to circumvent the deficiency through the consideration of additional momentum equations or developing an algebraic slip model to account for bubble separation.

On Population Balance Approach for Subcooled Boiling Flow Prediction

The capability of using the population balance approach combined with a three-dimensional two-fluid model for predicting subcooled boiling flow is investigated. Experiments were conducted to study the local flow characteristics of subcooled boiling flow and to provide measured local two-phase flow parameters. Calculations were performed using the newly developed population balance boiling model to study the effects of various factors on numerical predication of local two-phase flow parameters in the subcooled boiling regime. Comparison of model predictions against local measurements was made for the radial distribution of the bubble Sauter diameter and void fraction covering a range of different mass and heat fluxes and inlet subcooling temperatures. Additional comparison using recent active nucleation site density models and empirical relationships to determine the local bubble diameter adopted by other researchers was also investigated. Overall, good agreement was achieved between predictions and measurements using the newly formulated population balance approach based on the modified MUSIG (multiple-size-group) model for subcooled boiling and two-fluid model.

Thermal‐hydrodynamic modeling of bubbly flows with heat and mass transfer

AbstractA three‐dimensional (3‐D) two‐fluid model coupled with the population balance equation is used to predict bubbly flows with the presence of heat and mass transfer processes, particularly on subcooled boiling flows at low pressures. To account for the nonuniform bubble distribution in the bulk liquid at subcooled conditions, the CFX MUSIG (MUltiple‐Size Group) model is further developed by incorporating the wall nucleation at the heated wall and condensation in the flow regime. Model predictions, covering a wide range of different mass and heat fluxes and inlet subcooling temperatures, are compared against local and axial measurements. For the local case, the bubble size predictions include the comparison of the empirical bubble diameter relationships adopted in the CFX boiling model. The study shows that good agreement is better achieved by the present model with respect to the radial distributions of the bubble Sauter diameter, void fraction, interfacial area concentration, and liquid velocity profiles. However, significant weakness prevails over the vapor velocity distribution. Work is in progress to circumvent the deficiency by considering additional momentum equations or developing an algebraic slip model to account for bubble separation. For the axial case, good agreement is also achieved for the axial distributions of the mean bubble Sauter diameter, void fraction, and interfacial area concentration profiles. Here, the model correctly represents the plateau at the initial boiling stages at upstream, typically found in low‐pressure subcooled boiling flows, followed by the significant increase of the void fraction at downstream. © 2004 American Institute of Chemical Engineers AIChE J, 51: 8–27, 2005

Population balance modelling for bubbly flows with heat and mass transfer

Population balance equations combined with a three-dimensional two-fluid model are employed to predict bubbly flows with the presence of heat and mass transfer processes. Subcooled boiling flow belongs to this specific category of bubbly flows is considered. The MUSIG (MUltiple-SIze-Group) model implemented in CFX4.4 is further developed to account for the wall nucleation and condensation in the subcooled boiling regime. Comparison of model predictions against local measurements near the test channel exit is made for the radial distribution of the bubble Sauter diameter, void fraction, interfacial area concentration and gas and liquid velocities covering a range of different mass and heat fluxes and inlet subcooling temperatures. Additional comparison was also performed against existing boiling model in CFX4.4 and the modified model developed in our previous work (Int. J. Heat Mass Transfer 45 (2002) 1197). Good agreement is better achieved with the local radial bubble Sauter diameter, void fraction, interfacial area concentration and liquid velocity profiles against measurements using the newly formulated MUSIG boiling model over the simpler boiling models. However, significant weakness of the model is still evidenced in the prediction of the vapour velocity. Work is in progress to circumvent the deficiency of the model by the consideration of additional momentum equations or an algebraic slip model to account for bubble separation.