Liquid film flow is an important flow type in many applications of process engineering. For supporting experiments, theoretical and numerical investigations are required. The present state of the art is to model the liquid film flow with Navier--Stokes-based methods, whereas the lattice Boltzmann method is employed here. The final model has been developed within this treatise by means of a two-phase flow and a heat transfer model, and boundary and initial conditions. All these sub-models have been applied to simple test cases. It could be found that the two-phase model is capable of solving flow phenomena with a large density ratio which has been shown impressively in conjunction with wall boundary conditions. The heat transfer model was tested against spectral method results with a transient non-uniform flow field. It was possible to find optimal parameters for computation. The final model has been applied to steady-state film flow, and showed very good agreement to OpenFOAM simulations. Tests with transient film flow demonstrated that the model is also able to predict these flow phenomena. / Flüssigkeitsfilmströmungen kommen in vielen verfahrenstechnischen Prozessen zum Einsatz. Zur Unterstützung von Experimenten sind theoretische und numerische Untersuchungen nötig. Stand der Technik ist es, Navier--Stokes-basierte Modelle zu verwenden, wohingegen hier die Lattice-Boltzmann-Methode verwendet wird. Das finale Modell wurde unter Verwendung eines Zweiphasen- und eines Wärmeübertragungsmodell entwickelt und geeignete Rand- und Anfangsbedingungen formuliert. Alle Untermodelle wurden anhand einfacher Testfälle überprüft. Es konnte herausgefunden werden, dass das Zweiphasenmodell Strömungen großer Dichteunterschiede rechnen kann, was eindrucksvoll im Zusammenhang mit Wandrandbedingungen gezeigt wurde. Das Wärmeübertragungsmodell wurde gegen eine Spektrallösung anhand eines transienten und nichtuniformen Strömungsproblemes getestet. Stationäre Filmströmungen zeigten sehr gute Übereinstimmungen mit OpenFOAM-Lösungen und instationäre Berechungen bewiesen, dass das Model auch solche Strömungen abbilden kann.

This thesis presents an experimental study which investigates the behaviour of gas bubbles rising in a liquid metal and the related bubble-driven flow under the influence of external DC magnetic fields. The experimental configuration considered here concerns a cylindrical container filled with the eutectic alloy GaInSn. Argon gas bubbles are injected through a single orifice located at the container bottom in the centre of the circular cross-section. A homogeneous magnetic field was generated by a Helmholtz configuration of a pair of water-cooled copper coils. The magnetic field has been imposed either in vertical direction parallel to the main bubble motion or in horizontal direction, respectively. A vertical magnetic field stabilizes and damps the liquid metal flow effectively. The temporal variations of the fluid velocity with time become smaller with increasing magnetic induction. The velocity magnitudes are decreased, and the velocity distributions along the magnetic field lines are smoothed. The flow field keeps the axisymmetric distribution. A horizontal magnetic field destabilizes and enhances the flow within a range of moderate Hartmann numbers (100 < Ha < 400). The flow becomes non-axisymmetric due to the non-isotropic influence of the magnetic field. In the meridional plane parallel to the field lines, the flow changes its direction from a downward to an upward motion. Enhanced downward flows were observed in the meridional plane perpendicular to the field lines. The liquid velocity in both planes shows strong, periodic oscillations. The fluid motion is dominated by large-scale structures elongated along the magnetic field lines over the entire chord lengths of the circular cross-section.

Many fluid flow processes in nature and technology are characterized by the presence and coexistence of two ore more phases. These two- or multiphase flows are furthermore characterized by a greater complexity of possible flow phenomena and phase interactions then in single phase flows and therefore the numerical simulation of these multiphase flows is usually demanding a much higher numerical effort. The presented work summarizes the research and development work of the author and his research group on "Numerical Methods for Multiphase Flows" at the University of Technology, Chemnitz over the last years. This work was focussed on the development and application of numerical approaches for the prediction of disperse fluid-particle flows in the field of fluid mechanics and process technology. A main part of the work presented here is concerned with the modelling of different physical phenomena in fluid-particle flows under the paradigm of the Lagrangian treatment of the particle motion in the fluid. The Eulerian-Lagrangian approach has proved to be an especially well suited numerical approach for the simulation of disperse multiphase flows. On the other hand its application requires a large amount of (parallel) computational power and other computational ressources. The models described in this work give a mathematical description of the relevant forces and momentum acting on a single spherical particle in the fluid flow field, the particle-wall interaction and the particle erosion to the wall. Further models has been derived in order to take into account the influence of particle-particle collisions on the particle motion as well as the interaction of the fluid flow turbulence with the particle motion. For all these models the state-of-the-art from literature is comprehensively discussed. The main field of interest of the work presented here is in the area of development, implementation, investigation and comparative evaluation of parallelization methods for the Eulerian-Lagrangian approach for the simulation of disperse multiphase flows. Most of the priorly existing work of other authors is based on shared-memory approaches, quasi-serial or static domain decomposition approaches. These parallelization methods are mostly limited in theire applicability and scalability to parallel computer architectures with a limited degree of parallelism (a few number of very powerfull compute nodes) and to more or less homogeneous multiphase flows with uniform particle concentration distribution and minor complexity of phase interactions. This work now presents a novel parallelization method developed by the author, realizing a dynamic load balancing for the Lagrangian approach (DDD - Dynamic Domain Decomposition) and therefore leading to a substantial decrease in total computation time necessary for multiphase flow computations with the Eulerian-Lagrangian approach. Finally, the developed and entirely parallelized Eulerian-Lagrangian approach MISTRAL/PartFlow-3D offers the opportunity of efficient investigation of disperse multiphase flows with higher concentrations of the disperse phase and the resulting strong phase interaction phenomena (four-way coupling). / Viele der in Natur und Technik ablaufenden Strömungsvorgänge sind durch die Koexistenz zweier oder mehrerer Phasen gekennzeichnet. Diese sogenannten Zwei- oder Mehrphasensysteme zeichnen sich durch ein hohes Maß an Komplexität aus und erfordern oft einen sehr hohen rechentechnischen Aufwand zu deren numerischer Simulation. Die vorliegende Arbeit faßt langjährige Forschungs- und Entwicklungsarbeiten des Autors und seiner Forschungsgruppe "Numerische Methoden für Mehrphasenströmungen" an der TU Chemnitz zusammen, die sich mit der Entwicklung und Anwendung numerischer Berechnungsverfahren für disperse Fluid-Partikel-Strömungen auf dem Gebiet der Strömungs- und Verfahrenstechnik befassen. Ein wesentlicher Teil der Arbeit befaßt sich mit der Modellierung unterschiedlicher physikalischer Phänomene in Fluid-Partikel-Strömungen unter dem Paradigma der Lagrange'schen Betrachtungsweise der Partikelbewegung. Das Euler-Lagrange-Verfahren hat sich als besonders geeignetes Berechnungsverfahren für die numerische Simulation disperser Mehrphasenströmungen erwiesen, stellt jedoch in seiner Anwendung auch höchste Anforderungen an die Ressourcen der verwendeten (parallelen) Rechnerarchitekturen. Die näher ausgeführten mathematisch-physikalischen Modelle liefern eine Beschreibung der auf eine kugelförmige Einzelpartikel im Strömungsfeld wirkenden Kräfte und Momente, der Partikel-Wand-Wechselwirkung und der Partikelerosion. Weitere Teilmodelle dienen der Berücksichtigung von Partikel-Partikel-Stoßvorgängen und der Wechselwirkung zwischen Fluidturbulenz und Partikelbewegung. Der Schwerpunkt dieser Arbeit liegt im Weiteren in der Entwicklung, Untersuchung und vergleichenden Bewertung von Parallelisierungsverfahren für das Euler-Lagrange-Verfahren zur Berechnung von dispersen Mehrphasenströmungen. Zuvor von anderen Autoren entwickelte Parallelisierungsmethoden für das Lagrange'sche Berechnungsverfahren basieren im Wesentlichen auf Shared-Memory-Ansätzen, Quasi-Seriellen Verfahren oder statischer Gebietszerlegung (SDD) und sind somit in ihrer Einsetzbarkeit und Skalierbarkeit auf Rechnerarchitekturen mit relativ geringer Parallelität und auf weitgehend homogene Mehrphasenströmungen mit geringer Komplexität der Phasenwechselwirkungen beschränkt. In dieser Arbeit wird eine vom Autor entwickelte, neuartige Parallelisierungsmethode vorgestellt, die eine dynamische Lastverteilung für das Lagrange-Verfahren ermöglicht (DDD - Dynamic Domain Decomposition) und mit deren Hilfe eine deutliche Reduzierung der Gesamtausführungszeiten einer Mehrphasenströmungsberechnung mit dem Euler-Lagrange-Verfahren möglich ist. Im Ergebnis steht mit dem vom Autor und seiner Forschungsgruppe entwickelten vollständig parallelisierten Euler-Lagrange-Verfahren MISTRAL/PartFlow-3D ein numerisches Berechnungsverfahren zur Verfügung, mit dem disperse Mehrphasenströmungen mit höheren Konzentrationen der dispersen Phase und daraus resultierenden starken Phasenwechselwirkungen (Vier-Wege-Kopplung) effektiv untersucht werden können.

Gas injection into saturated porous media has a high practical relevance. It is applied in groundwater remediation (air sparging), in CO2 sequestration into saline aquifers, and in enhanced oil recovery of petroleum reservoirs. This wide range of application necessitates a comprehensive understanding of gas flow patterns that may develop within the porous media and required modeling of multi-phase flow. There is an ongoing controversy in literature, if continuum models are able to describe the complex flow pattern observed in heterogeneous porous media, especially the channelized stochastic flow pattern. Based on Selker’s stochastic hypothesis, a gas channel is caused by a Brownian-motion process during gas injection. Therefore, the pore-scale heterogeneity will determine the shape of the single stochastic gas channels. On the other hand there are many studies on air sparging, which are based on continuum modeling. Up to date it is not clear under which conditions a continuum model can describe the essential features of the complex gas flow pattern. The aim of this study is to investigate the gas flow pattern on bench-scale and field scale using the continuum model TOUGH2. Based on a comprehensive data set of bench-scale experiments and field-scale experiments, we conduct for the first time a systematic study and evaluate the prediction ability of the continuum model. A second focus of this study is the development of a “real world”-continuum model, since on all scales – pore-scale, bench scale, field scale – heterogeneity is a key driver for the stochastic gas flow pattern. Therefore, we use different geostatistical programs to include stochastic conditioned and unconditioned parameter fields. Our main conclusion from bench-scale experiments is that a continuum model, which is calibrated by different independent measurements, has excellent prediction ability for the average flow behavior (e.g. the gas volume-injection rate relation). Moreover, we investigate the impact of both weak and strong heterogeneous parameter fields (permeability and capillary pressure) on gas flow pattern. The results show that a continuum model with weak stochastic heterogeneity cannot represent the essential features of the experimental gas flow pattern (e.g., the single stochastic gas channels). Contrary, applying a strong heterogeneity the continuum model can represent the channelized flow. This observation supports Stauffer’s statement that a so-called subscale continuum model with strong heterogeneity is able to describe the channelized flow behavior. On the other hand, we compare the theoretical integral gas volumes with our experiments and found that strong heterogeneity always yields too large gas volumes. At field-scale the 3D continuum model is used to design and optimize the direct gas injection technology. The field-scale study is based on the working hypotheses that the key parameters are the same as at bench-scale. Therefore, we assume that grain size and injection rate will determine whether coherent channelized flow or incoherent bubbly flow will develop at field-scale. The results of four different injection regimes were compared with the data of the corresponding field experiments. The main conclusion is that because of the buoyancy driven gas flow the vertical permeability has a crucial impact. Hence, the vertical and horizontal permeability should be implemented independently in numerical modeling by conditioned parameter fields.

Gas injection into saturated porous media has a high practical relevance. It is applied in groundwater remediation (air sparging), in CO2 sequestration into saline aquifers, and in enhanced oil recovery of petroleum reservoirs. This wide range of application necessitates a comprehensive understanding of gas flow patterns that may develop within the porous media and required modeling of multi-phase flow. There is an ongoing controversy in literature, if continuum models are able to describe the complex flow pattern observed in heterogeneous porous media, especially the channelized stochastic flow pattern. Based on Selker’s stochastic hypothesis, a gas channel is caused by a Brownian-motion process during gas injection. Therefore, the pore-scale heterogeneity will determine the shape of the single stochastic gas channels. On the other hand there are many studies on air sparging, which are based on continuum modeling. Up to date it is not clear under which conditions a continuum model can describe the essential features of the complex gas flow pattern. The aim of this study is to investigate the gas flow pattern on bench-scale and field scale using the continuum model TOUGH2. Based on a comprehensive data set of bench-scale experiments and field-scale experiments, we conduct for the first time a systematic study and evaluate the prediction ability of the continuum model. A second focus of this study is the development of a “real world”-continuum model, since on all scales – pore-scale, bench scale, field scale – heterogeneity is a key driver for the stochastic gas flow pattern. Therefore, we use different geostatistical programs to include stochastic conditioned and unconditioned parameter fields. Our main conclusion from bench-scale experiments is that a continuum model, which is calibrated by different independent measurements, has excellent prediction ability for the average flow behavior (e.g. the gas volume-injection rate relation). Moreover, we investigate the impact of both weak and strong heterogeneous parameter fields (permeability and capillary pressure) on gas flow pattern. The results show that a continuum model with weak stochastic heterogeneity cannot represent the essential features of the experimental gas flow pattern (e.g., the single stochastic gas channels). Contrary, applying a strong heterogeneity the continuum model can represent the channelized flow. This observation supports Stauffer’s statement that a so-called subscale continuum model with strong heterogeneity is able to describe the channelized flow behavior. On the other hand, we compare the theoretical integral gas volumes with our experiments and found that strong heterogeneity always yields too large gas volumes. At field-scale the 3D continuum model is used to design and optimize the direct gas injection technology. The field-scale study is based on the working hypotheses that the key parameters are the same as at bench-scale. Therefore, we assume that grain size and injection rate will determine whether coherent channelized flow or incoherent bubbly flow will develop at field-scale. The results of four different injection regimes were compared with the data of the corresponding field experiments. The main conclusion is that because of the buoyancy driven gas flow the vertical permeability has a crucial impact. Hence, the vertical and horizontal permeability should be implemented independently in numerical modeling by conditioned parameter fields.

This thesis presents an experimental study which investigates the behaviour of gas bubbles rising in a liquid metal and the related bubble-driven flow under the influence of external DC magnetic fields. The experimental configuration considered here concerns a cylindrical container filled with the eutectic alloy GaInSn. Argon gas bubbles are injected through a single orifice located at the container bottom in the centre of the circular cross-section. A homogeneous magnetic field was generated by a Helmholtz configuration of a pair of water-cooled copper coils. The magnetic field has been imposed either in vertical direction parallel to the main bubble motion or in horizontal direction, respectively. A vertical magnetic field stabilizes and damps the liquid metal flow effectively. The temporal variations of the fluid velocity with time become smaller with increasing magnetic induction. The velocity magnitudes are decreased, and the velocity distributions along the magnetic field lines are smoothed. The flow field keeps the axisymmetric distribution. A horizontal magnetic field destabilizes and enhances the flow within a range of moderate Hartmann numbers (100 < Ha < 400). The flow becomes non-axisymmetric due to the non-isotropic influence of the magnetic field. In the meridional plane parallel to the field lines, the flow changes its direction from a downward to an upward motion. Enhanced downward flows were observed in the meridional plane perpendicular to the field lines. The liquid velocity in both planes shows strong, periodic oscillations. The fluid motion is dominated by large-scale structures elongated along the magnetic field lines over the entire chord lengths of the circular cross-section.

Non-isothermal compositional two-phase flow is considered to be one of the fundamental physical processes in the field of water resources research. The strong non-linearity and discontinuity emerging from phase transition phenomena pose a serious challenge for numerical modeling. Recently, Lauser et al.[1] has proposed a numerical scheme, namely the Nonlinear Complementary Problem (NCP), to handle this strong non-linearity. In this work, the NCP is implemented at both local and global levels of a Finite element algorithm. In the former case, the NCP is integrated into the local thermodynamic equilibrium calculation. While in the latter one, it is formulated as one of the governing equations. The two different formulations have been investigated through several well established benchmarks and analyzed for their efficiency and robustness. In the second part of the thesis, the presented numerical formulations are applied for application and process studies in the context of nuclear waste disposal in Switzerland. Application studies comprehend the coupling between multiphase transport model and complex bio-geo-chemical process to investigate the degradation of concrete material due to two major reactions: carbonation and Aggregate Silica Reaction(ASR). The chemical processes are simplified into a lookup table and cast into the transport model via source and sink term. The efficiency and robustness of the look-up table are further compared with a fully reactive transport model.

Many fluid flow processes in nature and technology are characterized by the presence and coexistence of two ore more phases. These two- or multiphase flows are furthermore characterized by a greater complexity of possible flow phenomena and phase interactions then in single phase flows and therefore the numerical simulation of these multiphase flows is usually demanding a much higher numerical effort. The presented work summarizes the research and development work of the author and his research group on "Numerical Methods for Multiphase Flows" at the University of Technology, Chemnitz over the last years. This work was focussed on the development and application of numerical approaches for the prediction of disperse fluid-particle flows in the field of fluid mechanics and process technology. A main part of the work presented here is concerned with the modelling of different physical phenomena in fluid-particle flows under the paradigm of the Lagrangian treatment of the particle motion in the fluid. The Eulerian-Lagrangian approach has proved to be an especially well suited numerical approach for the simulation of disperse multiphase flows. On the other hand its application requires a large amount of (parallel) computational power and other computational ressources. The models described in this work give a mathematical description of the relevant forces and momentum acting on a single spherical particle in the fluid flow field, the particle-wall interaction and the particle erosion to the wall. Further models has been derived in order to take into account the influence of particle-particle collisions on the particle motion as well as the interaction of the fluid flow turbulence with the particle motion. For all these models the state-of-the-art from literature is comprehensively discussed. The main field of interest of the work presented here is in the area of development, implementation, investigation and comparative evaluation of parallelization methods for the Eulerian-Lagrangian approach for the simulation of disperse multiphase flows. Most of the priorly existing work of other authors is based on shared-memory approaches, quasi-serial or static domain decomposition approaches. These parallelization methods are mostly limited in theire applicability and scalability to parallel computer architectures with a limited degree of parallelism (a few number of very powerfull compute nodes) and to more or less homogeneous multiphase flows with uniform particle concentration distribution and minor complexity of phase interactions. This work now presents a novel parallelization method developed by the author, realizing a dynamic load balancing for the Lagrangian approach (DDD - Dynamic Domain Decomposition) and therefore leading to a substantial decrease in total computation time necessary for multiphase flow computations with the Eulerian-Lagrangian approach. Finally, the developed and entirely parallelized Eulerian-Lagrangian approach MISTRAL/PartFlow-3D offers the opportunity of efficient investigation of disperse multiphase flows with higher concentrations of the disperse phase and the resulting strong phase interaction phenomena (four-way coupling). / Viele der in Natur und Technik ablaufenden Strömungsvorgänge sind durch die Koexistenz zweier oder mehrerer Phasen gekennzeichnet. Diese sogenannten Zwei- oder Mehrphasensysteme zeichnen sich durch ein hohes Maß an Komplexität aus und erfordern oft einen sehr hohen rechentechnischen Aufwand zu deren numerischer Simulation. Die vorliegende Arbeit faßt langjährige Forschungs- und Entwicklungsarbeiten des Autors und seiner Forschungsgruppe "Numerische Methoden für Mehrphasenströmungen" an der TU Chemnitz zusammen, die sich mit der Entwicklung und Anwendung numerischer Berechnungsverfahren für disperse Fluid-Partikel-Strömungen auf dem Gebiet der Strömungs- und Verfahrenstechnik befassen. Ein wesentlicher Teil der Arbeit befaßt sich mit der Modellierung unterschiedlicher physikalischer Phänomene in Fluid-Partikel-Strömungen unter dem Paradigma der Lagrange'schen Betrachtungsweise der Partikelbewegung. Das Euler-Lagrange-Verfahren hat sich als besonders geeignetes Berechnungsverfahren für die numerische Simulation disperser Mehrphasenströmungen erwiesen, stellt jedoch in seiner Anwendung auch höchste Anforderungen an die Ressourcen der verwendeten (parallelen) Rechnerarchitekturen. Die näher ausgeführten mathematisch-physikalischen Modelle liefern eine Beschreibung der auf eine kugelförmige Einzelpartikel im Strömungsfeld wirkenden Kräfte und Momente, der Partikel-Wand-Wechselwirkung und der Partikelerosion. Weitere Teilmodelle dienen der Berücksichtigung von Partikel-Partikel-Stoßvorgängen und der Wechselwirkung zwischen Fluidturbulenz und Partikelbewegung. Der Schwerpunkt dieser Arbeit liegt im Weiteren in der Entwicklung, Untersuchung und vergleichenden Bewertung von Parallelisierungsverfahren für das Euler-Lagrange-Verfahren zur Berechnung von dispersen Mehrphasenströmungen. Zuvor von anderen Autoren entwickelte Parallelisierungsmethoden für das Lagrange'sche Berechnungsverfahren basieren im Wesentlichen auf Shared-Memory-Ansätzen, Quasi-Seriellen Verfahren oder statischer Gebietszerlegung (SDD) und sind somit in ihrer Einsetzbarkeit und Skalierbarkeit auf Rechnerarchitekturen mit relativ geringer Parallelität und auf weitgehend homogene Mehrphasenströmungen mit geringer Komplexität der Phasenwechselwirkungen beschränkt. In dieser Arbeit wird eine vom Autor entwickelte, neuartige Parallelisierungsmethode vorgestellt, die eine dynamische Lastverteilung für das Lagrange-Verfahren ermöglicht (DDD - Dynamic Domain Decomposition) und mit deren Hilfe eine deutliche Reduzierung der Gesamtausführungszeiten einer Mehrphasenströmungsberechnung mit dem Euler-Lagrange-Verfahren möglich ist. Im Ergebnis steht mit dem vom Autor und seiner Forschungsgruppe entwickelten vollständig parallelisierten Euler-Lagrange-Verfahren MISTRAL/PartFlow-3D ein numerisches Berechnungsverfahren zur Verfügung, mit dem disperse Mehrphasenströmungen mit höheren Konzentrationen der dispersen Phase und daraus resultierenden starken Phasenwechselwirkungen (Vier-Wege-Kopplung) effektiv untersucht werden können.