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Pool scrubbing refers to the process of retention of harmful particles or gaseous components by bubbling in liquid media, which is characterized with high injection velocity and complex bubble dynamics. A comparative study of bubble breakup and coalescence models is performed to investigate the bubble size evolution in a pool-scrubbing column. The bubble size distributions along the column height are obtained by using a CFD (Computational Fluid Dynamics) – PBM (population balance model) coupled method, where the flow field is described by a two-fluid model while bubble size change by the discrete PBM. Various combinations of bubble breakup and coalescence models are investigated, and the bubble size distribution and Sauter mean diameter are compared with the literature data. The results show that under the pool-scrubbing conditions, bubble breakup is dominant compared to coalescence and bubble size decreases continuously, especially in the injection zone. The breakup rate predicted by three breakup models available in the official release of OpenFOAM foundation is found to differ by several orders of magnitudes, and their daughter size distributions are completely different as well. Some model combinations are able to predict the bubble size more satisfactorily, but there are still biases. For example, the fraction of bubbles is either overestimated or underestimated in certain size ranges compared to the experimental values. Proper description of the breakup rate and daughter bubble size distribution needs further efforts. Additionally, the mechanism governing the breakup is investigated by implementing the breakup model of Liao, which accounts for the effects of turbulence fluctuation, velocity shear in the bulk and eddies as well as interfacial friction. It revealed that both turbulence and interfacial friction contribute to bubble breakup in the pool scrubbing column, and the calibration of each mechanism under different conditions is necessary for future study.

The role of pool scrubbing in attenuating radioactivity release after severe accidents has been explored extensively. It is known that the scrubbing efficiency is largely determined by the hydrodynamic phenomenology in pools. The aerosol gas forms large globules at the nozzle exit, which subsequently break up to a swarm of stable bubbles, where the change of bubble size can reach over two orders. Furthermore, with the increase of flow rates, the injection regime changes from globule to jet characterized by a continuous gas structure. The flow field in the pool can be divided into injection and rise (swarm) two zones according to the gas-liquid interface morphology. In different zones, the scrubbing is governed by different mechanisms such as inertial impact, diffusion and gravity, and bubble shape, size and velocity in addition to particle size are major influential parameters. So far, numerical analysis of pool scrubbing is routinely based on system codes, which rely on empirical correlations for the determination of these parameters. More recently, owing to the increasing availability of computational resources, the knowledge is improved through three-dimensional computational fluid hydrodynamics simulations. Nevertheless, the morphology and regime change represents still a challenge. The conventional two-fluid model is generally effective for bubble size smaller than the cell size, while interface-tracking (capturing) methods demands dozens of cells per bubble size. The present work aims to capture the complex hydrodynamic process in the pool scrubbing with a hybrid multi-field two-fluid model. By comparing with experimental data, the results are shown to be promising.

Pool scrubbing is often used for removing harmful aerosol particles by injecting the gas mixture into a liquid pool [1], where hydrodynamics affects the decontamination factor significantly. The poolscrubbing bubble column is characterized by a large nozzle and high injection flow rates, which lead to large gas structures in the injection zone. As they rise up, these globules break up and form a swarm of small bubbles. The wide range of bubble size and shape poses a challenge for both two-fluid model (TFM) and interface-tracking approaches [2]. In this work, we apply the hybrid multi-field two-fluid model MultiMorph [3] to simulate a rectangular pool-scrubbing bubble column. The MultiMorph model considers the interaction between the gas and liquid according to the scale of the interfaces, applying a VOF-like treatment at the largescale interfaces and the conventional TFM to the small-scale ones. In this way, the description of the topology changes and regime transition is realized with the same set of equations. In the simulation, both the gas and liquid can be treated as either dispersed or continuous phases depending on the ratio between the particle (droplet or bubble in this work) size and the local cell size. The capability of the model is validated by comparing with experimental data from reference [4] as well as results obtained with the VOF and TFM, respectively. The MultiMorph model turns out to show significantly improved agreement with experimental data.

The phenomenon of buoyancy-driven bubbles near a fluid‒solid interface is common in both natural settings and industrial processes, such as oil and gas exploration and production. The intricate dynamics of bubbles are profoundly shaped by their interactions with adjacent solid walls. In this study, a direct numerical simulation of bubbles rising near a wall is conducted using the volume of fluid method. The motion behavior and wake vortex structure of bubbles with three types of migration trajectories (linear, zigzag, and spiral) are analyzed. The influences of the initial shape and wall distance of the bubbles on their motion trajectory, rising velocity, and wake structure is investigated. The results show that the presence of a nearby wall obstructs the diffusion of eddies across a bubble surface, and the repulsive force induced by the wall increases as the distance between the bubble and the wall decreases. Remarkably, at a dimensionless wall distance of 0.6, a change in the lateral lift direction triggers a collision between a zigzagging bubble and the wall, consequently setting the bubble into a bouncing motion mode. In the case of spiral-moving bubbles, proximity to the wall enhances the likelihood of oscillations within the bubble's migration trajectory along the x-y plane while maintaining stability along the z-y plane. While variations in the initial aspect ratio of bubbles have marginal impacts on the migration paths of linear and zigzagging bubbles, the initial shape affects the migration trajectory of spiral bubbles to some extent. The bubble migration trajectory first experiences oscillations when the initial deformation reaches its maximum.

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Because of its high interfacial area density and mixing efficiency bubbly flow are utilized in diverse technical applications to enhance the interfacial mass and heat transfer rate. However, due to the superposition of complex shape variation as well as bubble-bubble interaction, many aspects concerning the effect of bubbles on the bulk flow remain unclear, and bubble-induced turbulence (BIT) is one of them. In the past great effort has been made towards the BIT modelling in the framework of two-equation turbulence models, but the understanding of physics is still far from satisfactory. This work revisits the model proposed by Ma et al. [Phys. Rev. Fluids 2, 034301 (2017)], which considers the BIT with an additional source term in the k- and epsilon" (or omega)- equation, respectively, and has been widely adopted in the simulations of bubbly flows. Recent experiments show that contamination of the carrier phase plays a considerable role in BIT: although the bubbles rise slower with adding surfactants, the BIT increases. This trend cannot be reproduced by any current BIT models, including Ma et al. (2017). We have further investigated the reason for this and discuss the new possibility for the prefactor in the source term of the "epsilon-equation that may improve the results.

Due to its relevance for the safety analysis of pressurized water reactors, many research activities on flashing flows in pipes and nozzles arose from the mid of last century. Most of them have focused on the mass flow rate and pressure or temperature fluctuation by means of experiments and system codes. With the increase in computer speed, computational fluid dynamics is used more and more in the investigation of flashing flows, which has the advantage of providing further insights regarding the internal flow structure as well as its evolution. Various mixture or two-fluid models have been proposed in the literature. However, knowledge on the non-equilibrium effects, interphase transfer as well as interfacial area under different flashing conditions is still insufficient, and a general and precise definition of the problem remains a challenge. In this work, the two-fluid model is adopted to simulate various nuclear flashing scenarios (pipe blowdown, nozzle flashing flow, steam-generator leakage, flashing-induced instability, pressure release). It is shown that the thermal phase-change model is superior to pressure phase-change, relaxation and equilibrium models. Nevertheless, efforts are required to improve the interphase heat-transfer model. Furthermore, since flashing is often accompanied with high void fraction and broad bubble size range, a poly-disperse two-fluid model is recommended, and further research is needed to account for the effect of phase change on bubble coalescence and breakup. In addition, during flashing the flow pattern may change from single phase to bubbly flow, churn flow, annular flow, and even mist flow. The rapid change of interfacial topology as well as its influence on the applicability of closure models needs to be considered.

In the present work, the two-fluid model (TFM) is coupled with the population balance model (PBM) to trace the spatial and temporal change of bubble size and interfacial area concentration (IAC) in flashing flows. The model is first validated for bubble growing in stagnant superheated liquid, and satisfactory predictions of the bubble size under low and moderate superheat are obtained. It is then applied to flashing pipe flows, which are characterized by low superheat and high turbulence intensities. The results show that in these cases, coalescence and breakup are important phenomena changing the bubble size distribution in addition to growth. The neglect of their contribution leads to a significant under-prediction of the bubble size and consequently over-prediction of IAC. In addition, choosing an appropriate closure for interfacial heat transfer coefficient (HTC) is another key point in flashing simulation. In high-Reynolds cases (e.g. Re > 10^6), the enhancement due to turbulence is nonnegligible.

The removal of aerosols, vapor as well as soluble gases by injecting the mixture into a water pool is referred to as pool scrubbing, which is known to be an effective means for mitigating the source term during severe nuclear accidents. The pool hydrodynamics and bubble dynamics has a significant effect on the retention efficiency, which is however still far from being understood due to the complexity of the process. One-dimensional system or lumped parameter codes are routinely used for the calculation of the decontamination factor, which describes the particle removal capability of a pool scrubbing process. These codes rely on a number of empirical correlations, e.g. for the determination of bubble size and shape, which are correlated with some global and geometrical parameters such as nozzle diameter, submergence and injection velocity. Because of limited data and knowledge, the validity of these correlations is largely limited. Computational Fluid Dynamics (CFD) has the advantage of resolving local flow field and phenomena and is able to provide more insights in the bubble dynamics. In the frame of IPRESCA project, HZDR is participating in the work package 3.1 “bubble dynamics -CFD”. The main activities include three types of CFD simulations, respectively using: a) two-fluid model, where both mono-disperse and poly-disperse approaches are investigated, b) VOF interface-tracking method, and c) hybrid method, which incorporates the two-fluid and VOF models in one framework. The results shown possibilities and challenges of CFD in applying to pool scrubbing, and further efforts are needed.

The role of pool scrubbing in attenuating radioactivity release after severe accidents has been explored extensively. It is known that the scrubbing efficiency is largely determined by the hydrodynamic phenomenology in pools. The aerosol gas forms large globules at the nozzle exit, which subsequently break up to a swarm of stable bubbles, where the change of bubble size can reach over two orders. Furthermore, with the increase of flow rates, the injection regime changes from globule to jet characterized by a continuous gas structure. The flow field in the pool can be divided into injection and rise (swarm) two zones according to the gas-liquid interface morphology. In different zones, the scrubbing is governed by different mechanisms such as inertial impact, diffusion and gravity, and bubble shape, size and velocity in addition to particle size are major influential parameters. So far, numerical analysis of pool scrubbing is routinely based on system codes, which rely on empirical correlations for the determination of these parameters. More recently, owing to the increasing availability of computational resources, the knowledge is improved through three-dimensional computational fluid hydrodynamics simulations. Nevertheless, the morphology and regime change represents still a challenge. The conventional two-fluid model is generally effective for bubble size smaller than the cell size, while interface-tracking (capturing) methods demands dozens of cells per bubble size. The present work aims to capture the complex hydrodynamic process in the pool scrubbing with a hybrid multi-field two-fluid model. By comparing with experimental data, the results are shown to be promising.

Understanding bubble coalescence in slurry columns and how it is affected by the presence of particles is of great significance to a variety of engineering applications. Despite decades of research, high-resolution data on the film drainage process in a bubble column are scarce, which prevents a precise description of the phenomenon and the derivation of reliable models for further analyses. The existing work on bubble coalescence in the presence of particles either focuses on experimental or analytical studies under nearly hydrostatic conditions with very low approach velocity (up to 0.1 mm/s), or is limited to a mesoscopic scale, for example, by acquiring void fraction and bubble size distribution changes in the column. The present work aims to fill the gap in-between and provide insights into the film drainage process at the microscopic scale under bubble column hydrodynamic conditions. By coupling the volume-of-fluid (VOF) and multiphase particle-in-cell (MP-PIC) methods with a chimera mesh approach in OpenFOAM, a high resolution of the interface and fluid flow field is realized and meaningful results on the effect of particles are achieved. In the investigated parameter range and condition, the presence of particles in the liquid is shown to affect majorly the film drainage process, while have negligible effects on the bubble rise and approach velocity. The influence of particle number concentration is found to be complex and multimodal in co-axial coalescence. At sufficiently low concentration, particles are pushed out from the film and do not alter the drainage and coalescence rate noticeably. As the concentration increases, first a physical blocking effect then a slight promotion because of the drainage changing from axisymmetry to asymmetry is observed. The drainage process is greatly retarded by a conjunct motion, where the bubbles rotate along the colliding interfaces. Furthermore, no dimple formation is observed at high concentrations, which is typical a

Due to its relevance for the safety analysis of pressurized water reactors, many research activities on flashing flows in pipes and nozzles arose from the mid of last century. Most of them have focused on the mass flow rate and pressure or temperature fluctuation by means of experiments and system codes. With the increase in computer speed, computational fluid dynamics is used more and more in the investigation of flashing flows, which has the advantage of providing further insights regarding the internal flow structure as well as its evolution. Various mixture or two-fluid models have been proposed in the literature. However, knowledge on the non-equilibrium effects, interphase transfer as well as interfacial area under different flashing conditions is still insufficient, and a general and precise definition of the problem remains a challenge. In this work, the two-fluid model is adopted to simulate various nuclear flashing scenarios (pipe blowdown, nozzle flashing flow, steam-generator leakage, flashing-induced instability, pressure release). It is shown that the thermal phase-change model is superior to pressure phase-change, relaxation and equilibrium models. Nevertheless, efforts are required to improve the interphase heat-transfer model. Furthermore, since flashing is often accompanied with high void fraction and broad bubble size range, a poly-disperse two-fluid model is recommended, and further research is needed to account for the effect of phase change on bubble coalescence and breakup. In addition, during flashing the flow pattern may change from single phase to bubbly flow, churn flow, annular flow, and even mist flow. The rapid change of interfacial topology as well as its influence on the applicability of closure models needs to be considered.

The role of pool scrubbing in attenuating radioactivity release after severe accidents has been explored extensively. It is known that the scrubbing efficiency is largely determined by the hydrodynamic phenomenology in pools. The aerosol gas forms large globules at the nozzle exit, which subsequently break up to a swarm of stable bubbles, where the change of bubble size can reach over two orders. Furthermore, with the increase of flow rates, the injection regime changes from globule to jet characterized by a continuous gas structure. The flow field in the pool can be divided into injection and rise (swarm) two zones according to the gas-liquid interface morphology. In different zones, the scrubbing is governed by different mechanisms such as inertial impact, diffusion and gravity, and bubble shape, size and velocity in addition to particle size are major influential parameters. So far, numerical analysis of pool scrubbing is routinely based on system codes, which rely on empirical correlations for the determination of these parameters. More recently, owing to the increasing availability of computational resources, the knowledge is improved through three-dimensional computational fluid hydrodynamics simulations. Nevertheless, the morphology and regime change represents still a challenge. The conventional two-fluid model is generally effective for bubble size smaller than the cell size, while interface-tracking (capturing) methods demands dozens of cells per bubble size. The present work aims to capture the complex hydrodynamic process in the pool scrubbing with a hybrid multi-field two-fluid model. By comparing with experimental data, the results are shown to be promising.

Pool scrubbing is a widely used technique for retaining aerosol particles. It is characterized by high gas injection flow rates and substantial topological changes in different zones within the scrubber. The scrubbing process is generally divided into injection and swarm zones based on the evolution of the gas-liquid interface topology, and different mechanisms prevail in each zone. The disintegration of large globules in the injection zone forms a swarm of stable bubbles that significantly affect the retention efficiency since scrubbing largely depends on bubble size and velocity. However, the characteristics of the pool scrubbing process, such as high momentum, a wide range of bubble sizes, and complex interactions, make numerical simulations difficult. Turbulence is a key factor affecting bubble breakup, and estimating turbulence parameters properly is essential. In bubble columns, the effect of bubble-induced turbulence is dominant compared to turbulent pipe flows. However, the contribution of shear-induced turbulence is also significant due to circulation and strong oscillation formed in the pool by high-velocity gas injection. Modeling turbulence considering both shear and bubble-induced turbulence is still challenging in multiphase simulations. In this work, two turbulence models (mixtureKEpsilon and k-omega SST) that include the bubble-induced effects in OpenFOAM are evaluated for a pool scrubbing experiment from the literature. Using the two-equation models for turbulence is the widely accepted method in numerical simulations, making the accurate estimation of the turbulence boundary conditions critical. However, most of the correlations developed to estimate the turbulence boundary conditions are for fully developed pipe flow, making it harder to use them for bubble column simulations. Therefore, special attention is paid to characterizing turbulence intensity in a bubble column and estimating inlet boundary conditions for turbulence parameters s

Two-phase flows generally occur with various flow regimes, even in fixed geometries. The transition from one regime to another requires careful numerical modeling. In vane-type gas-liquid separators, the transition from bubbly flow to stratified flow is the dominating phenomena. This paper describes the application of a morphology adaptive hybrid multi-field model (OpenFOAM-Hybrid) to predict the complex flow in such vane-type separator, covering different regimes and the corresponding transitions. By means of OpenFOAM-Hybrid, the coexistence of dispersed bubbles and continuous gas core is modelled simultaneously with the same set of equations. The key issue here is the definition of a morphology transition criterion describing the formation of continuous gas out of dispersed gas. Such a transition criterion, based on the local volume fractions of the dispersed and the continuous gas phase, is proposed. It combines coalescence and absorption transfer processes. This model is added to OpenFOAM-Hybrid and validated by predicting both gas bubbles and a continuous gas core as well as transitional regimes in the vane-type separator. The gas core morphology evolution is investigated in detail. OpenFOAM-Hybrid is capable of capturing the gas core dynamics in the vane-type separator and thus proves to be a reliable predictive tool.

Pressure relief by blowdown is one of the most important measures to prevent excessive pressures in the primary circuit or containment in the event of severe nuclear accidents. Pool scrubbing can significantly reduce the release of radioactive materials, e.g. aerosols, to the environment during the pressure relief. The decontamination factor indicating the particle retention efficiency depends, among other factors, on the hydrodynamic conditions of the gas-liquid two-phase flow inside the pool. In the present work, the hydrodynamics in two typical pool scrubbing experiments is investigated with the two-fluid bubbly flow model, and the influence of some key factors including bubble diameter, nozzle submergence as well as interaction models is analysed. One case is a rectangular pool and the other is a cylindrical column, and their injection Weber number is around 2×103 and 4×105, respectively. The numerical results show that the void fraction and velocity field expand from the central region where the nozzle is located to the whole cross section, as the distance from the nozzle exit increases. The profile as well as its development depends largely on the bubble size and the interaction force model. It reveals that in the monodisperse simulation the tuning of bubble diameter is necessary for achieving good agreement, which is however awkward for high velocity gas injection. More information is required for properly describing the bubble size distribution as well as its evolution in pool scrubbing conditions. Furthermore, the experimental data show clear drag reduction in the bubble swarm generated by the gas jet, and further investigations on the mechanism and model improvement have to be done.

Flashing-induced instability (FII) has a significant impact on the safe operation of a natural cir-culation circuit, a phenomenon frequently encountered in the cooling systems of advanced light water reactors. While one-dimensional system codes are commonly used for engineering design and safety analysis of FII, there is a strong academic interest in understanding the underlying physical mechanisms. To address this, high-resolution computational fluid dynamics (CFD) simulations serve as a valuable tool. However, the current state of CFD modeling for phase change two-phase flows, particularly high transient fluctuating flashing flows, is still in its early stages of development. In this study, we establish a CFD model that focuses on interphase heat transfer to analyze FII. By incorporating experimental data from the literature, we investigate the transient flow field and thermodynamic behavior in the riser of the GENEVA test facility. The study provides valuable insights into the non-equilibrium and interfacial transfer phenom-ena during the phase change as well as the effect of high-frequency fluctuation. Additionally, we discuss in detail the challenges associated with FII modeling and the limitations of the current model. We also provide suggestions for potential improvements in future numerical studies.

Flashing flows of initially sub-cooled water in a converging–diverging nozzle is investigated numerically in the framework of the two-fluid model (TFM). The thermal non-equilibrium effect of phase change is considered by an interfacial heat transfer model, while the pressure jump across the interface is ignored. The bubble size distribution induced by nucleation, bubble growth/shrinkage, coalescence, and breakup is described based on the interfacial area transport equation (IATE) and constant bubble number density model (CBND), respectively. The results are compared with the experimental data. Satisfactory prediction of the axial pressure distribution along the nozzle as well as the flashing inception, is achieved by the TFM-IATE coupling method. It was also found that the vapor production in the diverging section was overpredicted, and the radial gas volume fraction distribution deviated from the experiment. The radial diameter profiles exhibit opposite patterns at the nozzle throat and near the outlet, and similar trends can be observed for the superheated degree. A poly-disperse method is suggested to be introduced to describe the evolution of interfacial area concentration.

Heat transfer on a vapor bubble rising in superheated liquid is investigated by direct numerical simulation. The vapor-liquid system is described by the one-fluid formulation with the level set method capturing the interface. The proportional-integral-derivative controller is employed to keep the bubble’s location fixed and evaluate interfacial forces. The heat transfer performance featured by the Nusselt number is evaluated based on the energy balance. Simulations are carried out for the bubble Reynolds number ranging from 20 to 500 and Morton number from 1.10×10-10 to 3.80×10-4. The aim of this paper is to shed some light on the effect of bubble deformation and oscillation on interfacial heat transfer. The results show that the front part of the bubble contributes to the majority of the interfacial heat transfer, while the rear part mainly affects the oscillation amplitude of the total heat transfer. The interface stretch during bubble oscillation is considered as a key mechanism in enhancing the instantaneous Nusselt number. The potential flow solution of the averaged Nusselt number is corrected by considering the influence of the aspect ratio. This research provides additional insights into the mechanism of interfacial heat transfer and the results apply equally to interfacial mass transfer.

In the present work, the two-fluid model (TFM) is coupled with the population balance model (PBM) to trace the spatial and temporal change of bubble size and interfacial area concentration (IAC) in flashing flows. The model is first validated for bubble growing in stagnant superheated liquid, and satisfactory predictions of the bubble size under low and moderate superheat are obtained. It is then applied to flashing pipe flows, which are characterized by low superheat and high turbulence intensities. The results show that in these cases, coalescence and breakup are important phenomena changing the bubble size distribution in addition to growth. The neglect of their contribution leads to a significant under-prediction of the bubble size and consequently over-prediction of IAC. In addition, choosing an appropriate closure for interfacial heat transfer coefficient (HTC) is another key point in flashing simulation. In high-Reynolds cases (e.g. Re > 10^6), the enhancement due to turbulence is nonnegligible.

In order to clarify the migration mechanism and wake behavior of a single bubble rising near a vertical wall, three-dimensional direct numerical simulations are implemented based on the open-source software Basilisk and various types of migration paths like linear, zigzag and spiral are investigated. The volume of fluid (VOF) method is used to capture the bubble interface at a small scale, while the gas-liquid interface and high-velocity-gradient regions in the flow field are encrypted with the adaptive mesh refinement technology. The results show that the vertical wall has an obstructive effect on the diffusion of the vortex boundary layer on the surface of the bubble migrating in a straight line, and the resulting reaction force tends to push the bubbles away from the wall surface. For the zigzag or spiral movement of a bubble in the x-y plane, the perpendicular wall is an unstable factor, but on the contrary, the motion in the z-y plane is stabilized.

The recent experimental results of Ma et al. [1] reveal that with increasing concentration of surfactants, the generated bubble-induced turbulence (BIT) increases as well, although the bubbles rise slower. We show that this phenomenon has not be considered so far in the standard Reynolds-averaged Navier-Stokes (RANS) modelling for BIT, using the ansatz with source terms added to the transport equation of turbulent kinetic energy and dissipation, respectively. Some problematic issues related to the common concepts for closure of the liquid phase turbulence kinetic energy equation are also discussed. Furthermore, we demonstrated this issue by simulating the experiments using two-fluid approach.

Due to its relevance for the safety analysis of pressurized water reactors, many research activities on flashing flows in pipes and nozzles arose from the mid of last century. Most of them have focused on the mass flow rate and pressure or temperature fluctuation by means of experiments and system codes. Owing to the increase in computer speed and progress in numerical algorithm, CFD is used more and more in the investigation of flashing flows, which has the advantage of providing further insights regarding the internal flow structure as well as its evolution. Various mixture or two-fluid models have been proposed in the literature. However, knowledge on local non-equilibrium effects, interphase transfer as well as interfacial area under different flashing conditions is still insufficient; a general and precise definition of the problem remains a challenge. In this lecture, two-fluid modelling of various nuclear flashing scenarios such as pipe blowdown, nozzle flow, steam-generator leakage, flashing-induced instability and pressure release will be presented. The performance of different mass transfer models including thermal phase-change, pressure phase-change, relaxation and equilibrium models will be compared. Challenges related to interfacial heat transfer, bubble poly-dispersity as well as flow regime transition will be discussed.

The role of pool scrubbing in attenuating radioactivity release after severe accidents has been explored extensively. It is known that the scrubbing efficiency is largely determined by the hydrodynamic phenomenology in pools. The aerosol gas forms large globules at the nozzle exit, which subsequently break up to a swarm of stable bubbles, where the change of bubble size can reach over two orders. Furthermore, with the increase of flow rates, the injection regime changes from globule to jet characterized by a continuous gas structure. The flow field in the pool can be divided into injection and rise (swarm) two zones according to the gas-liquid interface morphology. In different zones, the scrubbing is governed by different mechanisms such as inertial impact, diffusion and gravity, and bubble shape, size and velocity in addition to particle size are major influential parameters. So far, numerical analysis of pool scrubbing is routinely based on system codes, which rely on empirical correlations for the determination of these parameters. More recently, owing to the increasing availability of computational resources, the knowledge is improved through three-dimensional computational fluid hydrodynamics simulations. Nevertheless, the morphology and regime change represents still a challenge. The conventional two-fluid model is generally effective for bubble size smaller than the cell size, while interface-tracking (capturing) methods demands dozens of cells per bubble size. The present work aims to capture the complex hydrodynamic process in the pool scrubbing with a hybrid multi-field two-fluid model. By comparing with experimental data, the results are shown to be promising.

The retention of fission products in the form of aerosols and volatile species of iodine by bubbling them into liquid solution is known as pool scrubbing. It occurs frequently during accident scenarios such as SGTR (Steam Generator Tube Rupture), core meltdown and in BWR (boiling water reactor) suppression pool and FCVS (filtered containment venting system). Pool scrubbing is featured by complex hydrodynamics. The flow regime can be divided into injection, transition and bubble rise three zones. In each zone, different phenomena or mechanisms control the scrubbing of particles, e.g. globule breakup in the injection and transition zone, and swarm effect in the rise zone. Pool scrubbing codes were mostly developed in the 1980’s and 1990’s such as SUPRA, SPRAC and BUSCA, which have been widely used in the nuclear safety analysis. One major weakness of the lumped parameter codes is that they rely on various empirical correlations and assumptions, whose validity range is often limited. For example, the globule size in the jet regime and the rise velocity of large bubbles are found to be underestimated. CFD (computational fluid dynamics) has the advantage of resolving the gas-liquid interface and flow field inside the pool, capturing the coalescence and breakup of bubbles locally and physically. In the frame of IPRESCA project, several CFD studies on pool scrubbing have been published, using both VOF and two-fluid approaches. For three-dimensional large-scale pool simulations, the interface-tracking method is mainly restricted by high computational load and insufficient mesh resolution, while two-fluid method by the limitations in closure models. Reliable modelling of the processes, e.g. globule breakup in high-velocity injection zone, multiphase turbulence, interphase heat transfer, particle removal as well as bubble burst and entrainment at the free surface, remains a challenge.

Pool scrubbing is a widely used technique for retaining aerosol particles. It is characterized by high gas injection flow rates and substantial topological changes in different zones within the scrubber. The scrubbing process is generally divided into injection and swarm zones based on the evolution of the gas-liquid interface topology, and different mechanisms prevail in each zone. The disintegration of large globules in the injection zone forms a swarm of stable bubbles that significantly affect the retention efficiency since scrubbing largely depends on bubble size and velocity. However, the characteristics of the pool scrubbing process, such as high momentum, a wide range of bubble sizes, and complex interactions, make numerical simulations difficult. Turbulence is a key factor affecting bubble breakup, and estimating turbulence parameters properly is essential. In bubble columns, the effect of bubble-induced turbulence is dominant compared to turbulent pipe flows. However, the contribution of shear-induced turbulence is also significant due to circulation and strong oscillation formed in the pool by high-velocity gas injection. Modeling turbulence considering both shear and bubble-induced turbulence is still challenging in multiphase simulations. In this work, two turbulence models (mixtureKEpsilon and k-omega SST) that include the bubble-induced effects in OpenFOAM are evaluated for a pool scrubbing experiment from the literature. Using the two-equation models for turbulence is the widely accepted method in numerical simulations, making the accurate estimation of the turbulence boundary conditions critical. However, most of the correlations developed to estimate the turbulence boundary conditions are for fully developed pipe flow, making it harder to use them for bubble column simulations. Therefore, special attention is paid to characterizing turbulence intensity in a bubble column and estimating inlet boundary conditions for turbulence parameters s

Due to its relevance for the safety analysis of pressurized water reactors, many research activities on flashing flows in pipes and nozzles arose from the mid of last century. Most of them have focused on the mass flow rate and pressure or temperature fluctuation by means of experiments and system codes. With the increase in computer speed, computational fluid dynamics is used more and more in the investigation of flashing flows, which has the advantage of providing further insights regarding the internal flow structure as well as its evolution. Various mixture or two-fluid models have been proposed in the literature. However, knowledge on the non-equilibrium effects, interphase transfer as well as interfacial area under different flashing conditions is still insufficient, and a general and precise definition of the problem remains a challenge. In this work, the two-fluid model is adopted to simulate various nuclear flashing scenarios (pipe blowdown, nozzle flashing flow, steam-generator leakage, flashing-induced instability, pressure release). It is shown that the thermal phase-change model is superior to pressure phase-change, relaxation and equilibrium models. Nevertheless, efforts are required to improve the interphase heat-transfer model. Furthermore, since flashing is often accompanied with high void fraction and broad bubble size range, a poly-disperse two-fluid model is recommended, and further research is needed to account for the effect of phase change on bubble coalescence and breakup. In addition, during flashing the flow pattern may change from single phase to bubbly flow, churn flow, annular flow, and even mist flow. The rapid change of interfacial topology as well as its influence on the applicability of closure models needs to be considered.

Understanding bubble coalescence in slurry columns and how it is affected by the presence of particles is of great significance to a variety of engineering applications. Despite decades of research, high-resolution data on the film drainage process in a bubble column are scarce, which prevents a precise description of the phenomenon and the derivation of reliable models for further analyses. The existing work on bubble coalescence in the presence of particles either focuses on experimental or analytical studies under nearly hydrostatic conditions with very low approach velocity (up to 0.1 mm/s), or is limited to a mesoscopic scale, for example, by acquiring void fraction and bubble size distribution changes in the column. The present work aims to fill the gap in-between and provide insights into the film drainage process at the microscopic scale under bubble column hydrodynamic conditions. By coupling the volume-of-fluid (VOF) and multiphase particle-in-cell (MP-PIC) methods with a chimera mesh approach in OpenFOAM, a high resolution of the interface and fluid flow field is realized and meaningful results on the effect of particles are achieved. In the investigated parameter range and condition, the presence of particles in the liquid is shown to affect majorly the film drainage process, while have negligible effects on the bubble rise and approach velocity. The influence of particle number concentration is found to be complex and multimodal in co-axial coalescence. At sufficiently low concentration, particles are pushed out from the film and do not alter the drainage and coalescence rate noticeably. As the concentration increases, first a physical blocking effect then a slight promotion because of the drainage changing from axisymmetry to asymmetry is observed. The drainage process is greatly retarded by a conjunct motion, where the bubbles rotate along the colliding interfaces. Furthermore, no dimple formation is observed at high concentrations, which is typical a

The removal of aerosols, vapor as well as soluble gases by injecting the mixture into a water pool is referred to as pool scrubbing, which is known to be an effective means for mitigating the source term during severe nuclear accidents. The pool hydrodynamics and bubble dynamics has a significant effect on the retention efficiency, which is however still far from being understood due to the complexity of the process. One-dimensional system or lumped parameter codes are routinely used for the calculation of the decontamination factor, which describes the particle removal capability of a pool scrubbing process. These codes rely on a number of empirical correlations, e.g. for the determination of bubble size and shape, which are correlated with some global and geometrical parameters such as nozzle diameter, submergence and injection velocity. Because of limited data and knowledge, the validity of these correlations is largely limited. Computational Fluid Dynamics (CFD) has the advantage of resolving local flow field and phenomena and is able to provide more insights in the bubble dynamics. In the frame of IPRESCA project, HZDR is participating in the work package 3.1 “bubble dynamics -CFD”. The main activities include three types of CFD simulations, respectively using: a) two-fluid model, where both mono-disperse and poly-disperse approaches are investigated, b) VOF interface-tracking method, and c) hybrid method, which incorporates the two-fluid and VOF models in one framework. The results shown possibilities and challenges of CFD in applying to pool scrubbing, and further efforts are needed.

The retention of fission products in the form of aerosols and volatile species of iodine by bubbling them into liquid solution is known as pool scrubbing. It occurs frequently during accident scenarios such as SGTR (Steam Generator Tube Rupture), core meltdown and in BWR (boiling water reactor) suppression pool and FCVS (filtered containment venting system). Pool scrubbing is featured by complex hydrodynamics. The flow regime can be divided into injection, transition and bubble rise three zones. In each zone, different phenomena or mechanisms control the scrubbing of particles, e.g. globule breakup in the injection and transition zone, and swarm effect in the rise zone. Pool scrubbing codes were mostly developed in the 1980’s and 1990’s such as SUPRA, SPRAC and BUSCA, which have been widely used in the nuclear safety analysis. One major weakness of the lumped parameter codes is that they rely on various empirical correlations and assumptions, whose validity range is often limited. For example, the globule size in the jet regime and the rise velocity of large bubbles are found to be underestimated. CFD (computational fluid dynamics) has the advantage of resolving the gas-liquid interface and flow field inside the pool, capturing the coalescence and breakup of bubbles locally and physically. In the frame of IPRESCA project, several CFD studies on pool scrubbing have been published, using both VOF and two-fluid approaches. For three-dimensional large-scale pool simulations, the interface-tracking method is mainly restricted by high computational load and insufficient mesh resolution, while two-fluid method by the limitations in closure models. Reliable modelling of the processes, e.g. globule breakup in high-velocity injection zone, multiphase turbulence, interphase heat transfer, particle removal as well as bubble burst and entrainment at the free surface, remains a challenge.

The role of pool scrubbing in attenuating radioactivity release after severe accidents has been explored extensively. It is known that the scrubbing efficiency is largely determined by the hydrodynamic phenomenology in pools. The aerosol gas forms large globules at the nozzle exit, which subsequently break up to a swarm of stable bubbles, where the change of bubble size can reach over two orders. Furthermore, with the increase of flow rates, the injection regime changes from globule to jet characterized by a continuous gas structure. The flow field in the pool can be divided into injection and rise (swarm) two zones according to the gas-liquid interface morphology. In different zones, the scrubbing is governed by different mechanisms such as inertial impact, diffusion and gravity, and bubble shape, size and velocity in addition to particle size are major influential parameters. So far, numerical analysis of pool scrubbing is routinely based on system codes, which rely on empirical correlations for the determination of these parameters. More recently, owing to the increasing availability of computational resources, the knowledge is improved through three-dimensional computational fluid hydrodynamics simulations. Nevertheless, the morphology and regime change represents still a challenge. The conventional two-fluid model is generally effective for bubble size smaller than the cell size, while interface-tracking (capturing) methods demands dozens of cells per bubble size. The present work aims to capture the complex hydrodynamic process in the pool scrubbing with a hybrid multi-field two-fluid model. By comparing with experimental data, the results are shown to be promising.

Pool scrubbing with bubble swarm generated by gas jet is an effective technique for aerosol retention at severe accidents, owing to large interfacial area and long residence time. Correct understanding of the process and thus enhancing its efficiency relies on analysis of the hydrodynamic behaviour of the gas, since it affects particle removal mechanisms directly. The objective of the present work is to explore the gas jet structure in detail by means of VOF interface-capturing method and additional techniques for tracking bubble characteristics and trajectories. The main findings are: a) The breakup of globules in the injection zone becomes significant at high gas flow rates and has a great contribution in particle removal; b) The increase of bubble size and velocity with the injection velocity will promote the inertial and centrifugal deposition of aerosol particles; c) However, the coalescence probability of rising bubbles is found to increase with the gas flow rate, which may influence particle retention by re-enclosing particles from liquid film and reducing surface area; d) Furthermore, the reduction in bubble residence time as they rise through the pool is unfavourable for particle removal. Nevertheless, liquid recirculation originated from violent interaction between the gas jet and the pool surface as well as swarm effects helps to prolong the residence of bubbles. The effect of gas flow rates on the decontamination factor is found to be associated with a variety of gas-liquid hydrodynamic phenomena. The proposed numerical approach is capable of acquiring detailed local information that is required for model development. Both the time-averaged spatial distribution of void fraction and the instantaneous size/rise velocity of individual bubbles obtained from the simulation conform to the experimental data. In the next step it will be extended to include aerosol particles.

Pool scrubbing with bubble swarm generated by gas jet is an effective technique for aerosol retention at severe accidents, owing to large interfacial area and long residence time. Correct understanding of the process and thus enhancing its efficiency relies on analysis of the hydrodynamic behaviour of the gas, since it affects particle removal mechanisms directly. The objective of the present work is to explore the gas jet structure in detail by means of VOF interface-capturing method and additional techniques for tracking bubble characteristics and trajectories. The main findings are: a) The breakup of globules in the injection zone becomes significant at high gas flow rates and has a great contribution in particle removal; b) The increase of bubble size and velocity with the injection velocity will promote the inertial and centrifugal deposition of aerosol particles; c) However, the coalescence probability of rising bubbles is found to increase with the gas flow rate, which may influence particle retention by re-enclosing particles from liquid film and reducing surface area; d) Furthermore, the reduction in bubble residence time as they rise through the pool is unfavourable for particle removal. Nevertheless, liquid recirculation originated from violent interaction between the gas jet and the pool surface as well as swarm effects helps to prolong the residence of bubbles. The effect of gas flow rates on the decontamination factor is found to be associated with a variety of gas-liquid hydrodynamic phenomena. The proposed numerical approach is capable of acquiring detailed local information that is required for model development. Both the time-averaged spatial distribution of void fraction and the instantaneous size/rise velocity of individual bubbles obtained from the simulation conform to the experimental data. In the next step it will be extended to include aerosol particles.

Bubbly flow still represents a challenge for large-scale numerical simulation. Among many others the understanding and modelling of bubble-induced turbulence (BIT) are far from being satisfactory even though continuous efforts have been made. In particular, the buoyancy of the bubbles generally introduces turbulence anisotropy in the flow, which can not be captured by the standard eddy viscosity models with specific source terms representing BIT. Recently, on the basis of bubble-resolving Direct Numerical Simulations data, a new Reynolds-stress model considering BIT were developed by Ma et al. (J. Fluid Mech., vol. 883, 2020, A9) within the Euler–Euler framework. The objective of the present work is to assess this model and compare its performance with other standard Reynolds-stress models using a systematic test strategy. We select the experimental data in the BIT dominated range and find that the new model leads to major improvements in the prediction of full Reynolds-stress components.

The separation efficiency of a vane-type separator is greatly affected by swirl instability. The separator consists of a swirling vane, a recovery vane and a main pipe. Driven by centrifugal force, the bubbly flow tends to develop into stratified flow with a continuous gas core floating in the central axis of the separator and facilitating the separation. Yet, the straight gas core can turn into a double helix under some circumstances for example if the pressure difference across the orifices of recovery vane falls below the critical value, and swirl instability occurs. In order to reveal the underlying mechanism, a device with adjustable operating pres-sure was introduced to reproduce the dynamic process of gas core transform between stable and unstable. With the increase of pressure difference, the gas core morphology near the recovery vane will turn from double-helix to straight-line within several seconds. The whole process was investigated further by using the tomographic particle image velocimetry. Results show that the development of vorticity structures in the swirl flow gives rise to the evolution of gas core morphology and keeps it stable. Furthermore, the direction of axial velocity, which becomes negative by low pressure differences, is found to be crucial in controlling the formation of inner forced vortex and hence leading to the occurrence of swirl instability. In addition, the magnitude of positive axial velocity is identified to be of great significance in vorticity enhancement.

Single bubble rising in the close vicinity of a vertical wall is one of the focuses in the field of gas-liquid two-phase flow. In this work, three-dimensional direct numerical simulation based on volume of fluid (VOF) and adaptive mesh refinement method is performed to investigate the bubble rising and wake structures near a vertical wall. The bubble migration trajectory, deformation, velocity and wake structures were analyzed under various Galileo numbers and initial wall distances. Bubbles with a Galileo number of 8.8 significantly migrate away from the wall, which is driven by the repulsive force as a result of the suppression of the vortex diffusion on the bubble surface. As the Galileo number increases, the asymmetry of the shedding vortex tends to play a vital role on the repulsive force, which is exacerbated by the presence of the vertical wall. A periodic shedding of the vortex appears behind the bubble when the Galileo number reaches at 95. Meanwhile, the bubble trajectory changes from rectilinear to spiral along with a periodic oscillation. Due to the interaction between the vertical wall and the bubble wake, a transition from a rectilinear rising path to a spiral rising path is more likely to occur compared to that without a vertical wall. The presence of a vertical wall contributes to bubble-rising oscillations. A decrease of the bubble terminal velocity due to viscous effect near the vertical wall is observed for bubbles at low Galileo numbers. However, the viscous effect is less pronounced as the Galileo number increases.

Polydispersity is a challenging feature of many industrial and environmental multiphase flows, influencing all related transfer and transport processes. Besides their size, the fluid or solid particles may be distributed with respect to other properties such as their velocity or shape. Here, a population balance model based on the method of classes is combined with a multifluid solver within the open source Computational Fluid Dynamics library OpenFOAM. The model allows for tracking the evolution of one or more size-conditioned secondary properties. It is applied to two different problems, the first being bubbly flow of air and water in a vertical pipe, where considering the velocity as a secondary property allows to resolve the size-dependent radial segregation. The second application is the gas phase synthesis of titania powder, where non-spherical particle aggregates appear whose shape is modeled through a collision diameter, leading to an improved prediction of the size distribution.

There has been considerable discussion in recent years concerning whether a log-law exists for wall-bounded, turbulent bubbly flows. Previous studies have argued for the existence of such a log-law, with a modified von K´arm´an constant, and this is used in various modelling studies. We provide a critique of this idea, and present several theoretical reasons why a log-law need not be expected in general for wall-bounded, turbulent bubbly flows. We then demonstrate using recent data from interface-resolving Direct Numerical Simulations that when the bubbles make a significant contribution to the channel flow dynamics, the mean flow profile of the fluid can deviate significantly from the log-law behaviour that approximately holds for the single-phase case. The departures are not surprising and the basic reason for them is simple, namely that for bubbly flows, the mean flow is affected by a number of additional dynamical parameters, such as the void fraction, that do not play a role for the single-phase case. As a result, the inner/outer asymptotic regimes that form the basis of the derivation of the loglaw for single-phase flow do not exist in general for bubbly turbulent flows. Nevertheless, we do find that for some cases, the bubbles do not cause significant departures from the unladen log-law behaviour. Moreover, we show that if departures occur these cannot be understood simply in terms of the averaged void fraction, but that more subtle effects such as the bubble Reynolds number and the competition between the wall-induced turbulence and the bubble-induced turbulence must play a role.

There has been considerable discussion in recent years concerning whether a log-law exists for wall-bounded, turbulent bubbly flows. Previous studies have argued for the existence of such a log-law, with a modified von K´arm´an constant, and this is used in various modelling studies. We provide a critique of this idea, and present several theoretical reasons why a log-law need not be expected in general for wall-bounded, turbulent bubbly flows. We then demonstrate using recent data from interface-resolving Direct Numerical Simulations that when the bubbles make a significant contribution to the channel flow dynamics, the mean flow profile of the fluid can deviate significantly from the log-law behaviour that approximately holds for the single-phase case. The departures are not surprising and the basic reason for them is simple, namely that for bubbly flows, the mean flow is affected by a number of additional dynamical parameters, such as the void fraction, that do not play a role for the single-phase case. As a result, the inner/outer asymptotic regimes that form the basis of the derivation of the loglaw for single-phase flow do not exist in general for bubbly turbulent flows. Nevertheless, we do find that for some cases, the bubbles do not cause significant departures from the unladen log-law behaviour. Moreover, we show that if departures occur these cannot be understood simply in terms of the averaged void fraction, but that more subtle effects such as the bubble Reynolds number and the competition between the wall-induced turbulence and the bubble-induced turbulence must play a role.

Two-equation turbulence models based on the Boussinesq eddy viscosity hypothesis that have been used in the vast majority of previous simulation studies on bubbly pipe flows contain a term which renders the radial pressure distribution non-constant. In single phase simulations this effect is invariably absorbed in the definition of a modified pressure, from which the real pressure may be recovered if necessary. For bubbly multiphase flows however, this is not possible since the bubbles experience a force which depends, of course, on the real pressure rather than the modified one. As it turns out, most software codes by default rely on the approximation of neglecting the difference between modified and real pressure for bubbly flows. The purpose of the present study is to assess the influence of this approximation on the final simulations results. Fortunately it turns out that at least for the conditions considered in this study, the error is small.

Two-equation turbulence models based on the Boussinesq eddy viscosity hypothesis that have been used in the vast majority of previous simulation studies on bubbly pipe flows contain a term which renders the radial pressure distribution non-constant. In single phase simulations this effect is invariably absorbed in the definition of a modified pressure, from which the real pressure may be recovered if necessary. For bubbly multiphase flows however, this is not possible since the bubbles experience a force which depends, of course, on the real pressure rather than the modified one. As it turns out, most software codes by default rely on the approximation of neglecting the difference between modified and real pressure for bubbly flows. The purpose of the present study is to assess the influence of this approximation on the final simulations results. Fortunately it turns out that at least for the conditions considered in this study, the error is small.

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 transient 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.

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 transient 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.

The flashing flow is an relevant multiphase phenomenon in many technical applications including nuclear safety analysis, which has been the subject of intense research. Numerical studies have evolved from one-dimensional to multi-dimensional. A variety of methods have been proposed, while a broad consensus was not exiting. The present work aims to present an overview of available models as well their assumptions and limitations by conducting a literature survey. The final focus was put on recent computational fluid dynamics simulations. Some consensus on modelling interfacial slip, phase change mechanism and bubble size is identified. Since flashing scenarios often accompanying with high void fraction and broad bubble size range, a poly-disperse two-fluid model is recommended. Thermal phase change model is superior to pressure phase change, relaxation and equilibrium models for practical flashing problems. Major challenges include improving closure models for interphase transfer, bubble dynamics processes, interfacial area as well two-phase turbulence. For this purpose, high-resolution high quality experimental data are important, which are lacking in many cases. Considering that heterogeneous gas structures often exist in flashing flows, multi-field approaches able to handle different shapes of gas-liquid interface are recommended.

The flashing flow is an relevant multiphase phenomenon in many technical applications including nuclear safety analysis, which has been the subject of intense research. Numerical studies have evolved from one-dimensional to multi-dimensional. A variety of methods have been proposed, while a broad consensus was not exiting. The present work aims to present an overview of available models as well their assumptions and limitations by conducting a literature survey. The final focus was put on recent computational fluid dynamics simulations. Some consensus on modelling interfacial slip, phase change mechanism and bubble size is identified. Since flashing scenarios often accompanying with high void fraction and broad bubble size range, a poly-disperse two-fluid model is recommended. Thermal phase change model is superior to pressure phase change, relaxation and equilibrium models for practical flashing problems. Major challenges include improving closure models for interphase transfer, bubble dynamics processes, interfacial area as well two-phase turbulence. For this purpose, high-resolution high quality experimental data are important, which are lacking in many cases. Considering that heterogeneous gas structures often exist in flashing flows, multi-field approaches able to handle different shapes of gas-liquid interface are recommended.

The accuracy of gas-liquid flow modelling strongly depends on an appropriate modelling of interfacial forces. Among those, the drag is dominating. Most drag models reported in the literature have been derived and validated for laminar or low-turbulence flow conditions only. In this study, we evaluated different drag models from the literature for a highly turbulent gas-liquid flow around an obstacle in a pipe that produces a pronounced vortex region. We compared void fraction, as well as gas and liquid velocity profiles with experimental data obtained by means of Ultrafast X-ray Computed Tomography. We found that all the models except Bakker and Feng, predict the void fraction well compared to experimental data upstream of the obstacle, that is, for a developed two-phase pipe flow with axial symmetry. However, the void fraction downstream is grossly overestimated by all of the models. Based on the results, a hybrid drag model is proposed, which improves void fraction predictions considerably.

Flashing is frequently encountered in nuclear power systems for example as leakage occurring on the steam generator (SG) heat transfer tubes. Pressurized primary coolant flows rapidly through the crack and flashes into vapor. The pressure relief rate and loss rate of coolant, which affects largely the safety of fission reactors, are determined by the flashing phase change process. Information about the flashing phenomenon is of significance for the leakage online monitoring system, which ensures the normal operation of steam generator (SG) and safety of the reactor when tube rupture accidents occur. In this research, steady-state and transient 3D flashing flow inside a short micro-crack channel in the heat transfer tube wall of SG have been studied using FLUENT. The cavitation model and evaporation-condensation model, in combination with both the mixture two-phase flow and the Eulerian two-fluid model, are adopted to simulate the flashing phenomenon. The real geometry and operating conditions of AP1000 nuclear system are adopted to reflect the reality leakage phenomenon in SG. Two types of micro-crack shape including axial crack and circumferential crack, which both can happen in the reality, are considered. The CFD results gained from five different models have been compared with experimental data, and good agreement is demonstrated. The model comparison shows that the evaporation-condensation model behaves superior to the cavitation model in simulating the flashing phenomenon. Finally, the leakage rates are gained under different crack shapes, sub-cooling degrees and backpressures with the most accuracy scheme. In addition, two-phase choking flow phenomenon is simulated by changing backpressure of cracked tubes. The simulation results in this research could be good reference for leakage prediction of micro-crack in SG to improve the operation performance of SG and safety of the whole nuclear power system.

Eulerian-Eulerian computational fluid dynamic (CFD) models allow the prediction of complex and large-scale industrial multiphase gas-liquid bubbly flows with a relatively limited computational load. However, the interfacial transfer processes are entirely modelled, with closure relations that often dictate the accuracy of the entire model. Numerous sets of closures have been developed, often optimized over few experimental data sets and achieving remarkable accuracy that, however, becomes difficult to replicate outside of the range of the selected data. This makes a reliable comparison of available model capabilities difficult and obstructs their further development. In this paper, the CFD models developed at the University of Leeds and the Helmholtz-Zentrum Dresden-Rossendorf are benchmarked against a large database of bubbly flows in vertical pipes. The research groups adopt a similar modelling strategy, aimed at identifying a single universal set of widely applicable closures. The main focus of the paper is interfacial momentum transfer, which essentially governs the void fraction distribution in the flow, and turbulence modelling closures. To focus on these aspects, the validation database is limited to experiments with a monodispersed bubble diameter distribution. Overall, the models prove to be reliable and robust and can be applied with confidence over the range of parameters tested. Areas are identified where further development is needed, such as the modelling of bubble-induced turbulence and the near-wall region. A benchmark is also established and is available for the testing of other models. Similar exercises are encouraged to support the confident application of multiphase CFD models, together with the definition of a set of experiments accepted community-wide for model benchmarking.

Flashing is frequently encountered in nuclear power systems for example as leakage occurring on the steam generator (SG) heat transfer tubes. Pressurized primary coolant flows rapidly through the crack and flashes into vapor. The pressure relief rate and loss rate of coolant, which affects largely the safety of fission reactors, are determined by the flashing phase change process. Information about the flashing phenomenon is of significance for the leakage online monitoring system, which ensures the normal operation of steam generator (SG) and safety of the reactor when tube rupture accidents occur. In this research, steady-state and transient 3D flashing flow inside a short micro-crack channel in the heat transfer tube wall of SG have been studied using FLUENT. The cavitation model and evaporation-condensation model, in combination with both the mixture two-phase flow and the Eulerian two-fluid model, are adopted to simulate the flashing phenomenon. The real geometry and operating conditions of AP1000 nuclear system are adopted to reflect the reality leakage phenomenon in SG. Two types of micro-crack shape including axial crack and circumferential crack, which both can happen in the reality, are considered. The CFD results gained from five different models have been compared with experimental data, and good agreement is demonstrated. The model comparison shows that the evaporation-condensation model behaves superior to the cavitation model in simulating the flashing phenomenon. Finally, the leakage rates are gained under different crack shapes, sub-cooling degrees and backpressures with the most accuracy scheme. In addition, two-phase choking flow phenomenon is simulated by changing backpressure of cracked tubes. The simulation results in this research could be good reference for leakage prediction of micro-crack in SG to improve the operation performance of SG and safety of the whole nuclear power system.

The stability condition for solving the population balance equation (PBE) involving bubble growth and shrinkage within the Eulerian framework is proposed. The particle flux weighted average Courant number, CCFL, which reflects the propagation of particle state of the entire size classes on internal coordinates is first derived. Stability conditions of internal convection for PISO and PIMPLE algorithms are obtained by evaluating a series of tests concerning the constant bubble growth. The proposed stability conditions are then applied to simulate two kinds of laboratory experiments, i.e. the bubble growth in stagnant liquid and condensing steam-water pipe flows. The results show that the stable PBE solutions hold for the cases using either PISO or PIMPLE algorithms combined with the corresponding stability condition. Meanwhile, the conservation of the zeroth and first moments of the number density function can be guaranteed when the stability condition is satisfied. In addition, the effect of heat transfer coefficient correlations is also discussed.