Multiple Size Group Research Articles

Investigation of Wall Boiling Closure, Momentum Closure and Population Balance Models for Refrigerant Gas–Liquid Subcooled Boiling Flow in a Vertical Pipe Using a Two-Fluid Eulerian CFD Model

The precise design of heat exchangers in automobile air conditioning systems for more sustainable electric vehicles requires an enhanced assessment of CFD mechanistic models for the subcooled boiling flow of pure eco-friendly refrigerant. Computational Multiphase Flow Dynamics (CMFDs) relies on two-phase closure models to accurately depict the complex physical phenomena involved in flow boiling. This paper thoroughly examines two-phase CMFD flow boiling, incorporating sensitivity analyses of critical parameters such as boiling closures, momentum closures, and population balance models. Three datasets from the DEBORA experiment, involving vertical pipes with subcooled boiling flow of refrigerant at three different pressures and varying levels of inlet liquid subcooling, are used for comparison with CFD simulations. This study integrates nucleate site density and bubble departure diameter models to enhance wall boiling model accuracy. It aims to investigate various interfacial forces and examines the S-Gamma and Adaptive Multiple Size-Group (A-MuSiG) size distribution methods for their roles in bubble break up and coalescence. These proposed approaches demonstrate their efficacy, contributing to a deeper understanding of flow boiling phenomena and the development of more accurate models. This investigation offers valuable insights into selecting the most appropriate sub-closure models for both boiling closure and momentum closure in simulating boiling flows.

Modeling and simulation of bubble condensation using polydisperse approach with bubble collapse model

An accurate modeling of the bubble condensation phenomena in sub-cooled water is developed in this work, using a two-fluid model with one disperse phase and one Interfacial Area Transport Equation (IATE). For this, the aspects of some models are investigated, such as the choice of population balance models, Nusselt closure model and bubble collapse model in IATE. The standard method of moments is formulated using two different bubble size distribution functions among all, namely Dirac and quadratic laws. Therefore, different models for mass and energy interfacial transfers, interfacial forces and source terms of the IATE are developed using both functions. While limited differences are noticeable for the mass and energy transfers obtained by both functions, the results are largely improved using quadratic function for the drag force term and for the IATE source terms. Moreover, the simulations results show that the widely used Ranz-Marshall correlation clearly underestimates the condensation rate. However, this work shows that Chen–Mayinger correlation is relevant to simulate this type of flow, regardless the distribution function. Afterwards, a model is introduced to take into account the effect of bubble collapse by condensation in the IATE. The numerical results obtained using the quadratic function, the collapse model in the IATE and the Chen–Mayinger correlation are comparable to those obtained by the inhomogeneous MUltiple Size Group (iMUSIG) approach, while being less time-consuming.

Mathematical modeling of the effect of SEN outport shape on the bubble size distribution in a wide slab caster mold

Herein, the effects of outport shapes of the submerged entry nozzle (SEN) on the size distribution of argon bubbles were studied in a wide slab caster mold by the mathematical modeling. The Eulerian–Eulerian model coupled with Multiple-Size-Group (MUSIG) approach were used to solve equations of the two phase flow and polydispersed bubbly flow in the mold, respectively. The effect of the SEN outport angle and shape on the distribution of the molten steel flow, argon gas volume fraction, and argon bubble size were investigated. The outport shapes of the SEN included large rectangular, small rectangular, square, trapezoid, and runway. Results showed that the speed of molten steel increased within the range of 260 mm from the SEN, and decreased within the range of 550 mm from the narrow face with the outport angle of SEN increased from 20° to 45°. The bubble diameter was 5.7 mm at 255 mm distance from the SEN along the mold width at different outport angles. The average speed of molten steel at the outport of SEN decreased from 0.91 to 0.72 m/s with the outport shape changed from small rectangular to runway, trapezoid, square and large rectangular. The average diameter of bubbles was approximate 5.2 mm at the outport for the five types of nozzles, and increased from 3.2 to 3.45 mm inside the mold with the outport shape changed from the runway to square, trapezoid, large rectangular and small rectangular, indicating the rate of bubble breakup was larger with the runway and square SEN casting.

Simulation of the Axial-Flow Centrifugal Bubble Separator for Liquid-Fueled Molten Salt Reactors Using Eulerian Two-Fluid Model

The axial-flow centrifugal bubble separator designed for the gaseous fission product removal system in liquid-fueled molten salt reactors is simulated using the Eulerian two-fluid model coupled with the Adaptive Multiple Size Group method to account for the significant coalescence and breakup in the bubble separator. The behavior of the gas core in the bubble separator is mimicked by the symmetric interfacial area concentration model. The separator efficiency, local velocity, and pressure profiles at various conditions are compared with experimental data. Good agreement is found between the experiment and the simulation for the separator efficiency. With the coalescence and breakup being accounted for, the effect of the inlet void fraction on the separator efficiency is correctly captured. For the local pressure and velocity profiles, the agreement is only quantitative due to the simplifications on the geometry and potential limitations of the current computational fluid dynamics models. As good agreement is found for the separator efficiency, the sensitivity study is performed for various operational and design parameters with further simplified two-dimensional axisymmetric simulation.

Numerical study on gas–liquid two phase flow characteristic of multistage electrical submersible pump by using a novel multiple-size group (MUSIG) model

Electrical submersible pumps (ESPs) face enormous challenges in the petroleum industry while handling gas–liquid two-phase flow. The major difficulty is caused by the accumulation of gas bubbles inside ESP-impellers, which results in mild to severe degradation in pump performance. Therefore, to analyze the influence of gas entrainment and bubble size, a combination of experimental and numerical analysis is performed on a five-stage mixed-flow ESP in the present study. The experiments are first conducted to analyze the performance of ESP under pure water conditions at different rotating speeds, followed by the gas–liquid two-phase flow experiments that are performed at constant rotating speed (1475 r/min) and for a wide range of inlet gas void fractions (IGVFs). For numerical calculations, a novel multiple-size group (MUSIG) model is applied in ANSYS CFX to analyze the performance and different flow patterns in ESP in different IGVFs and understand the coalescence and breakup phenomena of gas bubbles in the impeller flow passage. The simulation results from the MUSIG model are compared with the Euler–Euler two-fluid model and test results. The MUSIG model can more accurately predict the changes in the performance and internal flow-field of ESP under two-phase flow conditions. Moreover, when the MUSIG model is used to calculate the two-phase flow of the ESP, the first-stage impeller has a higher head than other stages because the flow inside the second and other stages is affected by the disoriented flow coming from the first-stage diffuser and other return channels. Furthermore, this study gives an insight into the comprehensive application of the novel MUSIG model for complex turbo-machine designs such as ESP.

Numerical simulation of multi-size bubbly flow in a continuous casting mold using an inhomogeneous multiple size group model

Multi-size bubbly flow in a one-quarter-scale water model of a continuous casting mold was simulated using the inhomogeneous multiple size group (IMUSIG) model. The Sauter mean bubble diameter, gas volume fraction, interfacial area density, turbulence kinetic energy, and velocity field predicted by the IMUSIG and multiple size group (MUSIG) models were compared. The IMUSIG model separated the motions of the small and large bubbles on the basis of two velocity groups, and both models adopted 15 size groups. The results showed that the IMUSIG model better reflected the bubble size distribution near the nozzle. Small bubbles were further transported by the jet flow, which enlarged the bubble cluster range and decreased the gas volume fraction and interfacial area density in the upper part of the submerged entry nozzle, likely diminishing the coalescence rate in this region; consequently, the overestimation of Sauter mean bubble diameter outside the nozzle was corrected. The liquid-phase flow fields predicted by the IMUSIG and MUSIG models were very similar, and the IMUSIG-predicted magnitudes of velocity and turbulence kinetic energy were only slightly lower than the MUSIG predictions; this slight difference is attributable to the expanded bubble cluster range and higher interfacial area density, which weakened the upper recirculation in the IMUSIG model.

Experiments and fully transient coupled CFD-PBM 3D flow simulations of disperse liquid-liquid flow in a baffled stirred tank

Liquid-liquid disperse multiphase flow in a baffled tank stirred by a Rushton turbine is investigated by experiments and 3D simulations for different impeller speeds and volume fractions. Droplet size distributions are experimentally measured with an inline shadowgraphic probe and compared with fully transient coupled CFD-PBM simulations using the Eulerian multi-fluid framework, the inhomogeneous Multiple Size Group approach and a statistical turbulence model. The simulation model is assessed by a variation of size class and velocity group numbers, grid resolution and simulation domain extent. The model parameters for the breakup and coalescence kernels are fitted to match the measured droplet size distribution at a selected operation point. A subsequent application to different operation points shows that experimental droplet size trends are captured, albeit aside from the fitting point, deviations to data increase. The resulting droplet size distribution is analyzed by an assessment of the turbulent mixing, breakup and coalescence time scales.

Numerical simulation of multi-size bubbly flow in a continuous casting mold using population balance model

A population balance model based on the multiple-size-group (MUSIG) approach was developed to investigate the multi-size bubbly flow in a slab continuous casting mold. Firstly, effects of the bubble size group number, the initial bubble diameter, and the calibration factors for breakage and coalescence in MUSIG model on the multi-size bubbly flow were discussed in detail. Then, effects of both the water and gas flow rates on the bubble size distribution, the gas volume fraction, and the turbulence intensity of liquid phase were investigated. A relatively high water flow rate intensified the turbulence in the upper recirculation region of the mold and also eased the turbulence near the submerged entry nozzle (SEN) by promoting the breakage and horizontal transportation of bubbles; thus, an appropriate water flow rate is essential for better stability with a lower turbulence intensity near the SEN to prevent exposed slag eye formation and slag entrainment. With increase in the gas flow rate, the mean bubble diameter and gas volume fraction increased significantly, the turbulence near the SEN was also significantly increased, but this effect was much weaker in the region away from the SEN.

Numerical simulation of gravity-driven mono- and polydisperse bubbly flows in a three-dimensional column in the framework of the Euler-Euler approach

The paper presents a comparison of the results of numerical modeling of the three-dimensional flow of mono- and polydisperse media in a rectangular bubble column reactor. The mathematical model used in the paper is based on the Euler – Euler description of a multiphase medium taking into account interphase momentum transfer, turbulence modeling of the carrier phase with bubble induced turbulence and polydispersity in the framework of the inhomogeneous multiple-size group (MUSIG) model. The comparison is carried out of the mono- and polydisperse approaches under the conditions studied for simplified and full formulations. Numerical results are compared with the available experimental data and simulations of other authors.

CFD simulation of bubbly flow around an obstacle in a vertical pipe with a focus on breakup and coalescence modelling

In the present study, we assessed the capabilities of Eulerian-Eulerian CFD two-phase flow simulation with the homogeneous Multiple Size Group Model (MUSIG) and consideration of breakup and coalescence under three-dimensional flow conditions. We compared void fraction, bubble size and bubble velocity distributions against experimental data from vertical gas-disperse two-phase flow in a pipe with a flow obstruction. The simulation results generally agree well upstream the obstacle, where we have a typically developed pipe flow. Downstream of the obstacle void fraction is overpredicted while bubble velocity is underpredicted. The bubble size distribution has no clear trend. With higher liquid velocities, the deviations increase. As a conclusion, the simulation has difficulties to balance the gas fraction in the strong vortex in the shadow of the obstacle. Here further model improvement is needed.

Multi-fluid modelling of bubbly channel flows with an adaptive multi-group population balance method

Mass, momentum, and energy transfer in bubbly flows strongly depends on the bubble’s size distribution, which determines the contact area between the interacting phases. Characterization of bubble sizes in polydisperse flows requires empirical modelling of sub-grid physical mechanisms such as break-up and coalescence. In the present work an adaptive multiple size-group (A-MuSiG) method is incorporated into the Eulerian multiphase solver available in Simcenter STAR-CCM+ in order to model polydisperse bubbly flows in horizontal and vertical channels. The disperse phasespace is discretized into multiple size-groups each represented by its own size, number-density, and velocity field. The diameter of the bubbles in each of the size-groups varies in time and space, dynamically adapting to the local flow conditions. The interphase momentum transfer between the continuous phase and polydisperse bubbles is modelled through drag, virtual mass, turbulent dispersion, and lift forces. For modelling sub-grid bubble break-up and coalescence processes, different phenomenological kernels are evaluated. The empirical parameters of the adopted kernels are calibrated in two steps. The initial stage of the analysis considers experimental channel flows at low Reynolds number and zero-gravity conditions, under which the bubble size distribution is solely dependent on coalescence. As part of the second phase of the evaluation, additional parametric simulations in turbulent channel flows are performed in order to calibrate the break-up models, assuming the coalescence scaling constants derived in the previous step. The obtained results demonstrate that in flows with high turbulent mixing the ensuing bubble dynamics are strongly coupled to the internal properties of the population, which in turn influence the developing multiphase interactions in a transient manner.

A model of breakup of a rising bubble in a turbulent flow

Breakup of a bubble, rising under gravity in a turbulent flow, is analyzed. A model developed represents the critical Weber number of a bubble, indicating bubble breakup conditions, as a function of deformation caused by bubble rising. An ellipsoidal bubble shape is assumed. A simplified model of bubble deformation allows to obtain an analytical expression for the critical Weber number. An equation for the sepcific breakup rate of a rising bubble is also suggested and, then, validated against experimental data. The model developed is incorporated into the developer’s version of the adaptive multiple size-group (A-MuSiG) method of the Simcenter STAR-CCM+® CFD code. A good agreement of computed data vs. experimental results is demonstrated for a bubbly flow in a horizontal pipe without tuning any adjustable parameters.

Bubble behavior in the slab continuous casting mold: Physical and mathematical model

A two phase population balance is used to predict the polydispersed bubble flow and size distribution in a slab continuous casting mold and Submerged Entry Nozzle (SEN) system. Multiple Size Group (MUSIG) with a suitable breakage and coalescence model (Ansys CFX) was adopted to account for the polydispersed gas flow. Initial bubble size distribution as determined for two industrial refractories have been taken in consideration. A two way coupling model including the effect of the drag force and non-drag forces such as virtual mass force and turbulent dispersion force was considered. The results are compared with gas distribution in a 1:1 scale water — air mold model running under conditions of fluidynamic similarity to validate the model. The simulations have then been extended to describe the actual steel — argon flow, considering a thermal expansion factor for argon bubbles. The effect of gas distribution on the flow field of liquid inside the mold and other metallurgical aspects are discussed.

Numerical simulation research of subcooled flow boiling based on MUSIG model under low pressure

Subcooled boiling heat transfer is widely used in modern high-power and high-load internal combustion engines (ICEs) because of its efficient heat transfer characteristics. In the present work, a numerical simulation of subcooled boiling under low-pressure conditions is performed on CFX with a user-defined program. Lee’s subcooled boiling experiment results are used for calculations. The bubble departure diameter is simulated by Du’s model. In order to apply the simulation method to engine cooling system with complex channel, the Favre Averaged Drag Model and Tomiyama Lift Force Model are used which makes up for shortcomings of the experience factor needed to be adjusted. The Multiple Size Group (MUSIG) model considering the effects of vapor bubbles coalescence and breakup is used to describe the different sizes of bubbles in the liquid phase. A qualitatively good agreement with the experimental data is achieved without changing model parameters, which lays a good foundation for the application of the simulation method in an engine cooling system.

CFD modelling of turbulent liquid–liquid dispersion in a static mixer

Emulsification process in high-efficiency vortex (HEV) mixer is studied numerically. The two-phase flow is modelled using a multi-phase Eulerian approach, while the droplets size distribution is calculated by our recently-developed adaptive multiple size-group (A-MuSiG) method. The CFD allows for a more detailed analysis of the emulsification process: the baffles, installed at the mixer's walls, generate large-scale longitudinal vortices enhancing mixing in the transversal plane; most of the breakup occurs near the wall, while the vortices ensure transport of the disperse phase to and out of the wall. Intensity of the turbulence and the droplets size distribution were found to be in good agreement with the experimental data.

Update to the MUSIG model in ANSYS CFX for reliable modelling of bubble coalescence and breakup

The MUSIG (Multiple Size Group) model in the commercial CFD code ANSYS CFX is a population balance approach for describing binary bubble coalescence and breakup events. It is widely used in the simulation of poly-dispersed bubbly flows. The purpose of this work is to identify the internal inconsistencies in the discrete method that is applied for the solution of the population balance equation in MUSIG, and to propose an internally consistent one for discretising the source and sink terms that result from bubble coalescence and breakup. The new formulation is superior to the existing ones in preserving both mass and number density of bubbles, allowing arbitrary discretisation schemes and is free of costly numerical integrations. The numerical results on the evolution of bubble size distributions in bubbly flows reveal that the inconsistency in the original MUSIG regarding bubble breakup is non-negligible for both academic and practical cases. The discussion on the effect of internal inconsistency as well as updates to the model presented in this work are necessary and important for calibration of bubble coalescence and breakup models using the MUSIG approach.

Polydisperse bubble flows: a study of the bubble cloud evolution by CFD methods

The evolution of a polydisperse bubble cloud is analyzed by means of computational fluid dynamics. Gravity-driven bubble flows in a column with a circular cross-section as well as a downward flow in a long vertical pipe are numerically investigated. A method employed in the simulations is based on the Euler-Euler description of the multiphase medium. An inhomogeneous multiple-size group (MUSIG) model is used to describe the bubble size distribution. The formulated approach provides detailed description of the bubble flow structure including variation of the bubble size distribution.

CFD investigation of sub-cooled boiling flow using a mechanistic wall heat partitioning approach with Wet-Steam properties

In this paper, the mechanistic wall heat partitioning approach was used to capture the complex heat and mass transfer in sub-cooled boiling flows. In order to accommodate the changes of local variables to be relevant to the physical properties of sub-cooled fluids, the Wet-Steam (IAPWS-IF97) is used as the working fluid. Currently, the approach is evaluated based on the bubble sliding along the wall before lifting-off, which is usually found in the flow boiling situations. In the simulation, the closure mechanistic models, including the fractal analysis, the force balance and the mechanistic frequency, were coupled with the Eulerian–Eulerian two-fluid framework, while the Shear Stress Transport model was used as a turbulent modelling closure. The Multiple Size Group model was introduced to handle the bubble interactions and predict the bubble size distribution. Moreover, the effect of adopting the sub-cooled liquid properties into the modelling was investigated and compared with the experiments over a wide range of flow conditions. Specifically, the predicted void fraction and the sub-cooling temperature near the heated wall were precisely compared with the cases of using the constant-property liquid. Overall, the satisfactory agreements were found between the experiments and the predictions of the liquid temperature, void fraction, interfacial area concentration, Sauter mean diameter and bubble and liquid velocities with the exception of the case of high heat and mass fluxes. To enhance the current prediction accuracy for a situation of having a high superheating temperature, more bubble interactions on the boiling wall, such as merging of the bubbles while sliding, need to be considered. Furthermore, to assess the model capability, this mechanistic approach will be introduced to elucidate the sub-cooled boiling flow in situations of using different fluids in the near future.

Population balance modeling for air–water bubbly flow in a vertical U-bend

Bubbly flow in U-bend is widely encountered in two-phase flow systems because of its compactness and high heat transfer coefficient. The modeling of phase distributions, velocity fields, and interfacial area concentration in the U-bend is crucial for the analysis of mass, momentum, and energy transportation processes in the equipment. However, this subject has not received enough attention yet. In this paper, the combination of population balance model and two-fluid model was used in the simulation of air–water bubbly flow in a U-bend with 24 mm inner diameter and 96 mm curvature. The homogeneous multiple size group model was used to solve the population balance equation and reconstruct the bubble size distribution function. The phase distribution at 0°, 90°, and 180° was predicted and the results showed that the superficial velocities of gas and liquid phase were the control parameters. Under higher gas superficial velocity, the buoyant force is dominant and makes the bubbles concentrate on the outer side of the tube wall; while under lower gas superficial velocity, the centrifugal force is dominant and makes the bubbles concentrate on the inner side of the tube wall. These results met well with the experimental results of Usui.

The Implementation of an Activated Temperature-Dependent Wall Boiling Model in an Eulerian-Eulerian Computational Fluid Dynamics Approach for Predicting the Wall Boiling Process

In this work, we report on the development of a time-averaged Eulerian multiphase approach applied in the wall boiling process especially in the forced convective boiling process. Recently, in order to obtain accurate bubble dynamics and reduce case dependency, a single bubble model for nucleate boiling based on known published models was developed. The model considers geometry change and dynamic contact and inclination angles during bubble growth. The model has good agreement with experiments. However, the predicted bubble dynamics is dependent on the wall superheat (cavity activation temperature). This single bubble model requires an update of the current nucleation site activation and heat flux partitioning models in time-averaged Eulerian multiphase approaches. In this work, we will introduce this implementation in detail. Further, with help of the MUSIG (MUltiple SIze Group) model and a breakup and coalescence model, the time-averaged Eulerian approach could simulate the bubble size distribution in a heated pipe. With the necessary calibration of the nucleation site density, the comparisons between the calculation results and Bartolomei et al.’s experiments demonstrate the success of the implementation and the accuracy of this approach.