Multiple Size Group Model Research Articles

Study on characteristics of gas–liquid two-phase flow in pump as turbine using multiple-size group model

The multi-size group (MUSIG) model is employed in this paper to simulate the gas–liquid two-phase flow in pump as turbine (PAT) since the traditional Eulerian–Eulerian two-fluid model is unable to take into account the phenomena of breakup and coalescence of bubbles. First, the simulation of gas–liquid two-phase flow in a square column is compared with the experiment to verify the accuracy of the MUSIG model. Then, the results of gas–liquid two-phase flow in PAT simulated by the MUSIG model are compared with those by the conventional uniform bubble (UB) model and find that the MUSIG model is more favorable to capture the flow pattern at high gas content compared to the UB model. Based on the MUSIG model, the internal flow characteristics, pressure fluctuation, and bubble size distribution of the PAT are analyzed. The rotation of the blades breaks a part of big bubbles into small bubbles in the volute, resulting in a smaller diameter of the bubbles entering the impeller. As the gas content increases, the number and size of vortices in the impeller flow channel increase. The vortex is formed at locations where the gas phase distribution in the impeller flow channel is concentrated. The outlet of the impeller is more prone to bubble consolidation under high gas content conditions. In conclusion, the MUSIG model can well predict the complex flow characteristics of gas–liquid two-phase inside the PAT and identify the key influencing factors of energy acquisition, which can provide support for improving the performance of the PAT design.

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.

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.

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.

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.

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.

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.

Numerical Study of Bubble Coalescence and Breakup in the Reactor Fuel Channel with a Vaned Grid

The characteristics of bubbles of different sizes in fuel assembly are vital to two-phase flow resistance and heat transfer capacity. However, due to the swirl flow caused by the mixing vane, bubbles can crowd at the heated surface, which may anticipate the occurrence of departure from nucleation boiling. In the current work, the adiabatic two-phase flow in a simplified fuel assembly was analyzed by using the Eulerian two-fluid model and the MUSIG (MUltiple SIze Group) model. This computational domain consists of two coolant channels and two sets of vaned spacers, with three sets of periodic boundary conditions at the side faces of the domain. The distributions of vapor phase and bubble diameters were obtained, based on which the effects of mixing vanes on the bubble characteristics were analyzed. Vapor phase crowded at the rod surface in the higher inlet vapor fraction case, but crowded in the channel center in the lower inlet vapor fraction cases. This work can be used as a reference for the design of mixing vanes to avoid the anticipation of departure of nucleation boiling that may be caused by unreasonable design.

Computational fluid dynamics on the hydrodynamic characteristics of the conical cap tray

This paper addresses an investigation on the hydrodynamic behavior of a new type of cap trays called conical cap tray (ConCap tray). A 3-D computational fluid dynamics model was developed to predict the hydrodynamics of the ConCap tray which is operated in the spray regime. The model considers two phase flow of gas and liquid in a VOF-like code framework. The homogeneous multiple size group model (MUSIG model) and shear stress transport (SST) turbulence model were implemented. Detailed insights into the hydrodynamic behavior of the inside of the cones were obtained. The relation between velocity, pressure and cross section area of the flow inside the cone also was formulated. The computational fluid dynamic (CFD) results show that the pressure variation in the cones forces the liquid on the tray to be highly turbulent, which leads to deform the interface to break up. Effect of different riser heights was also studied by CFD simulations. The results show that the riser height has a significant role in the hydrodynamics of the tray, especially in uniform gas distribution in the tray and reducing weeping rates.

Numerical modelling of air–nanofluid bubbly flows in a vertical tube using the MUltiple-SIze-Group (MUSIG) model

The MUltiple-SIze-Group (MUSIG) model was used in this study to simulate bubbly flows of air–water and air–nanofluid in a vertical tube. Flow parameters including the void fraction, gas velocity, interfacial area concentration and Sauter mean bubble diameter were predicted and compared against the experimental data available in the literature. The model agreed well with the experimental data of air–water bubbly flow, but exhibited notable discrepancies from the data of air–nanofluid bubbly flow. With the aim to improve the MUSIG model for an effective modelling of air–nanofluid bubbly flows, some latest experimental and theoretical research outcomes were summarised and analysed. It was proposed that the key job when modelling bubbly flows of nanofluids using the MUSIG model is to address the spontaneous assembly of nanoparticles at bubble surfaces and its effects on the interfacial forces and bubble coalescence process.

Modeling of bubble behaviors and size distribution in a slab continuous casting mold

Population balance equations combined with Eulerian–Eulerian two-phase model are employed to predict the polydispersed bubbly flow inside the slab continuous-casting mold. The class method, realized by the MUltiple-SIze- Group (MUSIG) model, alongside with suitable bubble breakage and coalescence kernels is adopted. A two-way momentum transfer mechanism model combines the bubble induced turbulence model and various interfacial forces including drag, lift, virtual mass, wall lubrication, and turbulent dispersion are incorporated in the model. A 1/4th scaled water model of the slab continuous-casting mold was built to measure and investigate the bubble behavior and size distribution. A high speed video system was used to visualize the bubble behavior, and a digital image processing technique was used to measure the mean bubble diameter along the width of the mold. Predictions by previous mono-size model and MUSIG model are compared and validated against experimental data obtained from the water model. Effects of the water flow rate and gas flow rate on the mean bubble size were also investigated. Close agreements by MUSIG model were achieved for the gas volume fraction, liquid flow pattern, bubble breakage and coalescence, and local bubble Sauter mean diameter against observations and measurements of water model experiments.

Modelling of Bubble Aggregation, Breakage and Transport in Slab Continuous Casting Mold

The bubble-liquid flow, especially the aggregation and breakage behavior, plays a significant role in the slab continuous casting process. A 1/4th water model was employed to investigate the two-phase flow characteristics and the bubble size distribution. A mathematical model based on the Euler-Euler approach was developed to analyze the bubble aggregation and breakage in the bubbly flow. The population balance model (PBM) was applied to calculate bubble size distribution, and the simulation was implemented through the MUSIG (multiple size group) model. The numerical predictions were verified by the water model experiment. The results show that the PBM is a useful approach for analyzing bubble size distribution and can be taken into industrial applications of gas-liquid two phase flow inside the continuous casting mold. The ratio of big bubbles and bubble mean diameter in the upper recirculation zone are found to decrease with the increment of water flow rate and increase with the increment of gas flow rate. The bubble aggregation and breakage behavior, bubble size distribution and the effect of gas bubbles on flow field in the continuous casting mold are revealed. The numerical results are compared with the experiment and they show good agreement.

Impact of bubble coalescence on separation performance of a degassing hydrocyclone

The physical separation of liquid–gas flows is an integral part of many industrial processes. A hydrocyclone is an important item of separation equipment and is widely used in many processes for liquid–gas separation. In this study, the multiple size group model was firstly used to study the separation performance with bubble coalescence and break-up in a degassing hydrocyclone. The separation efficiency for 30-μm bubbles increases from 29.67% to 99.53% when the bubble diameter changes from 30μm to 100μm. The gas concentration changes more quickly at the center of the hydrocyclone, while the range of bubble sizes that coalesced increases. The break-up and coalescence of larger bubbles lead to a pressure increase in specific domains that also contributes to the liquid flow. Transient analysis allows us to determine the relationship between the flow pattern and time. The maximum bubble diameter is one of the most important factors affecting bubble separation in a hydrocyclone and is essential to the analysis and design of a degassing hydrocyclone.

Multiple Size Group Modeling of Polydispersed Bubbly Flow in the Mold: An Analysis of Turbulence and Interfacial Force Models

An inhomogeneous Multiple Size Group (MUSIG) model based on the Eulerian–Eulerian approach has been developed to describe the polydispersed bubbly flow inside the continuous-casting mold. A laboratory scale mold has been simulated using four different turbulence closure models (modified k − ɛ, RNG k − ɛ, k − ω, and SST) with the purpose of critically comparing their predictions of bubble Sauter mean diameter distribution with previous experimental data. Furthermore, the influences of all the interfacial momentum transfer terms including drag force, lift force, virtual mass force, wall lubrication force, and turbulent dispersion force are investigated. The breakup and coalescence effects of the bubbles are modeled according to the bubble breakup by the impact of turbulent eddies while for bubble coalescence by the random collisions driven by turbulence and wake entrainment. It has been found that the modified k − ɛ model shows better agreement than other models in predicting the bubble Sauter mean diameter profiles. Further, simulations have also been performed to understand the sensitivity of different interfacial forces. The appropriate drag force coefficient, lift force coefficient, virtual mass force coefficient, and turbulent dispersion force coefficient are chosen in accordance with measurements of water model experiments. However, the wall lubrication force does not have much effect on the current polydispersed bubbly flow system. Finally, the MUSIG model is then used to estimate the argon bubble diameter in the molten steel of the mold. The argon bubble Sauter mean diameter generated in molten steel is predicted to be larger than air bubbles in water for the similar conditions.

Population Balance Modeling of Polydispersed Bubbly Flow in Continuous-Casting Using Multiple-Size-Group Approach

A population balance model based on the multiple-size-group (MUSIG) approach has been developed to investigate the polydispersed bubbly flow inside the slab continuous-casting mold and bubble behavior including volume fraction, breakup, coalescence, and size distribution. The Eulerian–Eulerian approach is used to describe the equations of motion of the two-phase flow. All the non-drag forces (lift force, virtual mass force, wall lubrication force, and turbulent dispersion force) and drag force are incorporated in this model. Sato and Sekiguchi model is used to account for the bubble-induced turbulence. Luo and Svendsen model and Prince and Blanch model are used to describe the bubbles breakup and coalescence behavior, respectively. A 1/4th water model of the slab continuous-casting mold was applied to investigate the distribution and size of bubbles by injecting air through a circumferential inlet chamber which was made of the specially-coated samples of mullite porous brick, which is used for the actual upper nozzle. Against experimental data, numerical results showed good agreement for the gas volume fraction and local bubble Sauter mean diameter. The bubble Sauter mean diameter in the upper recirculation zone decreases with increasing water flow rate and increases with increasing gas flow rate. The distribution of bubble Sauter mean diameter along the width direction of the upper mold increases first, and then gradually decreases from the SEN to the narrow wall. Close agreements between the predictions and measurements demonstrate the capability of the MUSIG model in modeling bubbly flow inside the continuous-casting mold.

Application of a new concept for multi-scale interfacial structures to the dam-break case with an obstacle

New results of a generalized concept developed for the simulation of two-phase flows with multi-scale interfacial structures are presented in this paper. By extending the inhomogeneus Multiple Size Group-model, the concept enables transitions between dispersed and continuous gas morphologies, including the appearance and evanescence of one of these particular gas phases. Adequate interfacial transfer formulations, which are consistent with such an approach, are introduced for interfacial area density and drag. A new drag-formulation considers shear stresses occurring within the free surface area.The application of the concept to a collapsing water column demonstrates the breakup of continuous gas into a polydispersed phase forming different bubble sizes underneath the free surface. Thus, both resolved free surface structures as well as the entrainment of bubbles and their coalescence and breakup underneath the surface can be described in the same time. The simulations have been performed with the CFD-code CFX 14.0 and will be compared with experimental images.The paper will further investigate the possible improvement of such free surface simulations by including sub-grid information about small waves and instabilities at the free surface. A comparison of the results will be used for a discussion of possible new mass transfer models between filtered free surface areas and dispersed bubble size groups as part of the future work.

Numerical Prediction for Subcooled Boiling Flow of Liquid Nitrogen in a Vertical Tube with MUSIG Model

Multiple size group (MUSIG) model combined with a three-dimensional two-fluid model were employed to predict subcooled boiling flow of liquid nitrogen in a vertical upward tube. Based on the mechanism of boiling heat transfer, some important bubble model parameters were amended to be applicable to the modeling of liquid nitrogen. The distribution of different discrete bubble classes was demonstrated numerically and the distribution patterns of void fraction in the wall-heated tube were analyzed. It was found that the average void fraction increases nonlinearly along the axial direction with wall heat flux and it decreases with inlet mass flow rate and subcooled temperature. The local void fraction exhibited a U-shape distribution in the radial direction. The partition of the wall heat flux along the tube was obtained. The results showed that heat flux consumed on evaporation is the leading part of surface heat transfer at the rear region of subcooled boiling. The turning point in the pressure drop curve reflects the instability of bubbly flow. Good agreement was achieved on the local heat transfer coefficient against experimental measurements, which demonstrated the accuracy of the numerical model.