Many flow regimes in Nuclear Reactor Safety Research are characterized by multiphase flows, with one phase being a continuous liquid and the other phase consisting of gas or vapour of the liquid phase. In dependence on the void fraction of the gaseous phase the flow regimes e.g. in vertical pipes are varying from bubbly flows with low and higher volume fraction of bubbles to slug flow, churn turbulent flow, annular flow and finally to droplet flow. In the regime of bubbly and slug flow the multiphase flow shows a spectrum of different bubble sizes. While disperse bubbly flows with low gas volume fraction are mostly mono-disperse, an increase of the gas volume fraction leads to a broader bubble size distribution due to breakup and coalescence of bubbles. Bubbles of different sizes are subject to lateral migration due to forces acting in lateral direction different from the main drag force direction. The bubble lift force was found to change the sign dependent on the bubble size. Consequently this lateral migration leads to a de-mixing of small and large bubbles and to further coalescence of large bubbles migrating towards the pipe center into even larger Taylor bubbles or slugs. An adequate modeling has to consider all these phenomena. A Multi Bubble Size Class Test Solver has been developed to investigate these effects and test the influence of different model approaches. Basing on the results of these investigations a generalized inhomogeneous Multiple Size Group (MUSIG) Model based on the Eulerian modeling framework has been proposed and was finally implemented into the CFD code CFX. Within this model the dispersed gaseous phase is divided into N inhomogeneous velocity groups (phases) and each of these groups is subdivided into Mj bubble size classes. Bubble breakup and coalescence processes between all bubble size classes Mj are taken into account by appropriate models. The inhomogeneous MUSIG model has been validated against experimental data from the TOPFLOW test facility.

Many flow regimes in Nuclear Reactor Safety Research are characterized by multiphase flows, with one phase being a continuous liquid and the other phase consisting of gas or vapour of the liquid phase. In dependence on the void fraction of the gaseous phase the flow regimes e.g. in vertical pipes are varying from bubbly flows with low and higher volume fraction of bubbles to slug flow, churn turbulent flow, annular flow and finally to droplet flow. In the regime of bubbly and slug flow the multiphase flow shows a spectrum of different bubble sizes. While disperse bubbly flows with low gas volume fraction are mostly mono-disperse, an increase of the gas volume fraction leads to a broader bubble size distribution due to breakup and coalescence of bubbles. Bubbles of different sizes are subject to lateral migration due to forces acting in lateral direction different from the main drag force direction. The bubble lift force was found to change the sign dependent on the bubble size. Consequently this lateral migration leads to a de-mixing of small and large bubbles and to further coalescence of large bubbles migrating towards the pipe center into even larger Taylor bubbles or slugs. An adequate modeling has to consider all these phenomena. A Multi Bubble Size Class Test Solver has been developed to investigate these effects and test the influence of different model approaches. Basing on the results of these investigations a generalized inhomogeneous Multiple Size Group (MUSIG) Model based on the Eulerian modeling framework has been proposed and was finally implemented into the CFD code CFX. Within this model the dispersed gaseous phase is divided into N inhomogeneous velocity groups (phases) and each of these groups is subdivided into Mj bubble size classes. Bubble breakup and coalescence processes between all bubble size classes Mj are taken into account by appropriate models. The inhomogeneous MUSIG model has been validated against experimental data from the TOPFLOW test facility.

To simulate dispersed two-phase flows CFD tools for predicting the local particle number density and the size distribution are required. These quantities do not only have a significant effect on rates of mixing, heterogeneous chemical reaction rates or interfacial heat and mass transfers, but also a direct relevance to the hydrodynamics of the total system, such as the flow pattern and flow regime. The Multiple Size Group (MUSIG) model available in the commercial codes CFX-4 and CFX-5 was developed for this purpose. Mathematically, this model is based on the population balance method and the two-fluid modeling approach. The dispersed phase is divided into N size classes. In order to reduce the computational cost, all size groups are assumed to share the same velocity field. This model allows to use a sufficient number of particle size groups required for the coalescence and breakup calculation. Nevertheless, the assumption also restricts its applicability to homogeneous dispersed flows. We refer to the CFX MUSIG model mentioned above as the homogeneous model, which fails to predict the correct phase distribution when heterogeneous particle motion becomes important. In many flows the non-drag forces play an essential role with respect to the bubble motion. Especially, the lift force acting on large deformed bubbles, which is dominated by the asymmetrical wake, has a direction opposite to the shear induced lift force on a small bubble. This bubble separation cannot be predicted by the homogeneous MUSIG model. In order to overcome this shortcoming we developed an efficient inhomogeneous MUSIG model in cooperation with ANSYS CFX. A novel multiple velocity multiple size group model, which incorporates the population balance equation into the multi-fluid modeling framework, was proposed. The validation of this new model is discussed in this report.

Turbulence dispersion is a phenomenon of practical importance in many multiphase flow systems. It has a strong effect on the distribution of the dispersed phase. Physically, this phenomenon is a result of interactions between individual particles of the dispersed phase and the continuous phase turbulence eddies. In a Lagrangian simulation, a particle-eddy interaction sub-model can be introduced and the effect of turbulence dispersion is automatically accounted for during particle tracking. Nevertheless, tracking of particleturbulence interaction is extremely expensive for the small time steps required. For this reason, the Lagrangian method is restricted to small-scale dilute flow problems. In contrast, the Eulerian approach based on the continuum modeling of the dispersed phase is more efficient for densely laden flows. In the Eulerian frame, the effect of turbulence dispersion appears as a turbulent diffusion term in the scalar transport equations and the so-called turbulent dispersion force in the momentum equations. The former vanishes if the Favre (mass-weighted) averaged velocity is adopted for the transport equation system. The latter is actually the total account of the turbulence effect on the interfacial forces. In many cases, only the fluctuating effect of the drag force is important. Therefore, many models available in the literature only consider the drag contribution. A new, more general derivation of the FAD (Favre Averaged Drag) model in the multi-fluid modeling framework is presented and validated in this report.

To simulate dispersed two-phase flows CFD tools for predicting the local particle number density and the size distribution are required. These quantities do not only have a significant effect on rates of mixing, heterogeneous chemical reaction rates or interfacial heat and mass transfers, but also a direct relevance to the hydrodynamics of the total system, such as the flow pattern and flow regime. The Multiple Size Group (MUSIG) model available in the commercial codes CFX-4 and CFX-5 was developed for this purpose. Mathematically, this model is based on the population balance method and the two-fluid modeling approach. The dispersed phase is divided into N size classes. In order to reduce the computational cost, all size groups are assumed to share the same velocity field. This model allows to use a sufficient number of particle size groups required for the coalescence and breakup calculation. Nevertheless, the assumption also restricts its applicability to homogeneous dispersed flows. We refer to the CFX MUSIG model mentioned above as the homogeneous model, which fails to predict the correct phase distribution when heterogeneous particle motion becomes important. In many flows the non-drag forces play an essential role with respect to the bubble motion. Especially, the lift force acting on large deformed bubbles, which is dominated by the asymmetrical wake, has a direction opposite to the shear induced lift force on a small bubble. This bubble separation cannot be predicted by the homogeneous MUSIG model. In order to overcome this shortcoming we developed an efficient inhomogeneous MUSIG model in cooperation with ANSYS CFX. A novel multiple velocity multiple size group model, which incorporates the population balance equation into the multi-fluid modeling framework, was proposed. The validation of this new model is discussed in this report.

Turbulence dispersion is a phenomenon of practical importance in many multiphase flow systems. It has a strong effect on the distribution of the dispersed phase. Physically, this phenomenon is a result of interactions between individual particles of the dispersed phase and the continuous phase turbulence eddies. In a Lagrangian simulation, a particle-eddy interaction sub-model can be introduced and the effect of turbulence dispersion is automatically accounted for during particle tracking. Nevertheless, tracking of particleturbulence interaction is extremely expensive for the small time steps required. For this reason, the Lagrangian method is restricted to small-scale dilute flow problems. In contrast, the Eulerian approach based on the continuum modeling of the dispersed phase is more efficient for densely laden flows. In the Eulerian frame, the effect of turbulence dispersion appears as a turbulent diffusion term in the scalar transport equations and the so-called turbulent dispersion force in the momentum equations. The former vanishes if the Favre (mass-weighted) averaged velocity is adopted for the transport equation system. The latter is actually the total account of the turbulence effect on the interfacial forces. In many cases, only the fluctuating effect of the drag force is important. Therefore, many models available in the literature only consider the drag contribution. A new, more general derivation of the FAD (Favre Averaged Drag) model in the multi-fluid modeling framework is presented and validated in this report.

Experimente mit neuartigen Messverfahren lieferten Daten über die Struktur von transienten Flüssig-keits-Gas-Strömungen für die Entwicklung und Validierung von mikroskopischen, d.h. geometrieunabhängigen Konstitutivbeziehungen zur Beschreibung des Impulsaustauschs zwischen Flüssig-phase und Gasblasen sowie zur Quantifizierung der Häufigkeit von Blasenkoaleszenz und -zerfall. Hierzu wurde eine vertikale Testsektion der Zweiphasentestschleife MTLoop in Rossendorf genutzt, wobei erstmals Gittersensoren mit einer Auflösung von 2-3 mm bei einer Messfrequenz von bis zu 10 kHz angewandt wurden. Dabei wurde die Evolution von Gasgehalts-, Geschwindigkeits- und Bla-sengrößenverteilungen entlang des Strömungsweges und bei schnellen Übergangsprozessen aufge-nommen und so die für die Modellbildung erforderlichen Daten bereitgestellt. Für den Test der Mo-dellbeziehungen wurde ein vereinfachtes Verfahren zur Lösung der Strömungsgleichungen entlang des Strömungswegs erstellt. Es basiert auf der Betrachtung einer größeren Anzahl von Blasengrö-ßenklassen. Die erhaltenen numerische Lösungen haben erstmals gezeigt, dass der bei Erhöhung der Gasvolumenstromdichte stattfindende Übergang von einer Blasenströmung mit Randmaximum zu einem Profil mit Zentrumsmaximum und anschließend zu einer Pfropfenströmung ausgehend von einem einheitlichen Satz physikalisch begründeter und geometrieunabhängiger Konstitutivgleichun-gen modelliert werden kann. Die Modellbeziehungen haben sich in einem abgegrenzten Gebiet der Volumenstromdichten als generalisierungsfähig erwiesen und sind für den Einbau in CFD-Modelle geeignet. Weiterhin wurden Arbeiten zur Kondensation durchgeführt, die direkten Bezug zu den Kon-densationsmodellen haben, die in Thermohydraulik-Codes enthalten sind. Die Untersuchung liefert darüber hinaus experimentelle Daten für die Modellvalidierung hinsichtlich des Verhaltens und des Einflusses nichtkondensierbarer Gase. Hierfür wurden spezielle Sonden für die Bestimmung der Konzentration und für die Lokalisierung von Pfropfen nichtkondensierbarer Gase entwickelt und bei transienten Kondensationsversuchen in einem leicht geneigten Wärmeübertragerrohr eingesetzt.

Experimente mit neuartigen Messverfahren lieferten Daten über die Struktur von transienten Flüssig-keits-Gas-Strömungen für die Entwicklung und Validierung von mikroskopischen, d.h. geometrieunabhängigen Konstitutivbeziehungen zur Beschreibung des Impulsaustauschs zwischen Flüssig-phase und Gasblasen sowie zur Quantifizierung der Häufigkeit von Blasenkoaleszenz und -zerfall. Hierzu wurde eine vertikale Testsektion der Zweiphasentestschleife MTLoop in Rossendorf genutzt, wobei erstmals Gittersensoren mit einer Auflösung von 2-3 mm bei einer Messfrequenz von bis zu 10 kHz angewandt wurden. Dabei wurde die Evolution von Gasgehalts-, Geschwindigkeits- und Bla-sengrößenverteilungen entlang des Strömungsweges und bei schnellen Übergangsprozessen aufge-nommen und so die für die Modellbildung erforderlichen Daten bereitgestellt. Für den Test der Mo-dellbeziehungen wurde ein vereinfachtes Verfahren zur Lösung der Strömungsgleichungen entlang des Strömungswegs erstellt. Es basiert auf der Betrachtung einer größeren Anzahl von Blasengrö-ßenklassen. Die erhaltenen numerische Lösungen haben erstmals gezeigt, dass der bei Erhöhung der Gasvolumenstromdichte stattfindende Übergang von einer Blasenströmung mit Randmaximum zu einem Profil mit Zentrumsmaximum und anschließend zu einer Pfropfenströmung ausgehend von einem einheitlichen Satz physikalisch begründeter und geometrieunabhängiger Konstitutivgleichun-gen modelliert werden kann. Die Modellbeziehungen haben sich in einem abgegrenzten Gebiet der Volumenstromdichten als generalisierungsfähig erwiesen und sind für den Einbau in CFD-Modelle geeignet. Weiterhin wurden Arbeiten zur Kondensation durchgeführt, die direkten Bezug zu den Kon-densationsmodellen haben, die in Thermohydraulik-Codes enthalten sind. Die Untersuchung liefert darüber hinaus experimentelle Daten für die Modellvalidierung hinsichtlich des Verhaltens und des Einflusses nichtkondensierbarer Gase. Hierfür wurden spezielle Sonden für die Bestimmung der Konzentration und für die Lokalisierung von Pfropfen nichtkondensierbarer Gase entwickelt und bei transienten Kondensationsversuchen in einem leicht geneigten Wärmeübertragerrohr eingesetzt.

This paper describes the modelling of bubbly flow in a bubble column considering non-drag forces, polydispersity and bubble induced turbulence using the Eulerian two-fluid approach. The set of used closure models describing the momentum exchange between the phases was chosen on basis of broad experiences in modelling bubbly flows at the Helmholtz-Zentrum Dresden-Rossendorf. Polydispersity is modeled using the inhomogeneous multiple size group (iMUSIG) model, which was developed by ANSYS/CFX and Helmholtz-Zentrum Dresden-Rossendorf. Through the importance of a comprehensive turbulence modeling for coalescence and break-up models, bubble induced turbulence models are investigated. A baseline has been used which was chosen on the basis of our previous work without any adjustments. Several variants taken from the literature are shown for comparison. Transient CFD simulations are compared with the experimental measurements and Large Eddy Simulations of Akbar et al. (2012).

This paper describes the modelling of bubbly flow in a bubble column considering non-drag forces, polydispersity and bubble induced turbulence using the Eulerian two-fluid approach. The set of used closure models describing the momentum exchange between the phases was chosen on basis of broad experiences in modelling bubbly flows at the Helmholtz-Zentrum Dresden-Rossendorf. Polydispersity is modeled using the inhomogeneous multiple size group (iMUSIG) model, which was developed by ANSYS/CFX and Helmholtz-Zentrum Dresden-Rossendorf. Through the importance of a comprehensive turbulence modeling for coalescence and break-up models, bubble induced turbulence models are investigated. A baseline has been used which was chosen on the basis of our previous work without any adjustments. Several variants taken from the literature are shown for comparison. Transient CFD simulations are compared with the experimental measurements and Large Eddy Simulations of Akbar et al. (2012).