In this paper we present detailed Euler-Euler Large Eddy Simulations (LES) of dispersed bubbly flow in a rectangular bubble column. The motivation of this study is to investigate potential of this approach for the prediction of bubbly flows, in terms of mean quantities. The set of physical models describing the momentum exchange between the phases was chosen according to previous experiences of the authors. Experimental data, Euler-Lagrange LES and unsteady Euler-Euler Reynolds-Averaged Navier-Stokes model are used for comparison. It was found that the presented modelling combination provides good agreement with experimental data for the mean flow and liquid velocity fluctuations. The energy spectrum made from the resolved velocity from Euler-Euler LES is presented and discussed.

Multiphase flow denotes the simultaneous flow of two or more physically distinct and immiscible substances and it can be widely found in several engineering applications, for instance, power generation, chemical engineering and crude oil extraction and processing. In many of those applications, multiphase flows determine safety and efficiency aspects of processes and plants where they occur. Therefore, the measurement and imaging of multiphase flows has received much attention in recent years, largely driven by a need of many industry branches to accurately quantify, predict and control the flow of multiphase mixtures. Moreover, multiphase flow measurements also form the basis in which models and simulations can be developed and validated. In this work, the use of electrical impedance techniques for multiphase flow measurement has been investigated. Three different impedance sensor systems to quantify and monitor multiphase flows have been developed, implemented and metrologically evaluated. The first one is a complex permittivity needle probe which can detect the phases of a multiphase flow at its probe tip by simultaneous measurement of the electrical conductivity and permittivity at up to 20 kHz repetition rate. Two-dimensional images of the phase distribution in pipe cross section can be obtained by the newly developed capacitance wire-mesh sensor. The sensor is able to discriminate fluids with different relative permittivity (dielectric constant) values in a multiphase flow and achieves frame frequencies of up to 10 000 frames per second. The third sensor introduced in this thesis is a planar array sensor which can be employed to visualize fluid distributions along the surface of objects and near-wall flows. The planar sensor can be mounted onto the wall of pipes or vessels and thus has a minimal influence on the flow. It can be operated by a conductivity-based as well as permittivity-based electronics at imaging speeds of up to 10 000 frames/s. All three sensor modalities have been employed in different flow applications which are discussed in this thesis. The main contribution of this research work to the field of multiphase flow measurement technology is therefore the development, characterization and application of new sensors based on electrical impedance measurement. All sensors present high-speed capability and two of them allow for imaging phase fraction distributions. The sensors are furthermore very robust and can thus easily be employed in a number of multiphase flow applications in research and industry.

In this paper, a novel approach for tracking moving structures in multiphase flows over larger axial ranges is presented, which at the same time allows imaging the tracked structures and their environment. For this purpose, ultrafast electron beam X-ray computed tomography (UFXCT) is being extended by an image-based position control. Application is scanning and tracking of, for example, bubbles, particles, waves and other features of multiphase flows within vessels and pipes. Therefore, the scanner has to be automatically traversed with the moving structure basing on real-time scanning, image reconstruction and image data processing. In this paper, requirements and different strategies for reliable object tracking in dual image plane imaging mode are discussed. Promising tracking strategies have been numerically implemented and evaluated.

Inhalt der Arbeit sind theoretische und experimentelle Untersuchungen zum Einfluss akustischer Wellen auf das Verhalten mehrphasiger Strömungen in porösen Medien. Die Arbeit schlug mittels Frequenzanalyse Anregungsfrequenzen mit erhöhter Wahrscheinlichkeit den Strömungsvorgang positiv für die Erdölförderung zu beeinflussen. Die vorgeschlagenen Frequenzen erzielten auf verschiedenen Parametern erfolgreich eine positive Beeinflussung des Wasserdurchbruchspunktes, des Entölungsgrades und der relativen Permeabilität. Zur Erhöhung der Aussagekraft der Daten wurden Verfahren der multivariaten Statistik erfolgreich eingesetzt. Zudem wurden positive Rückkopplungseffekte mit dem Einsatz oberflächenaktiver Substanzen nachgewiesen. In einem abschließenden Schritt konnte die Wirkung des Verfahrens zudem durch Kombination mehrere Frequenzen optimiert werden. Diese von hoher Wichtigkeit geprägten Charakteristika zeigen klar das Potential des Verfahrens zum Einsatz als Verfahren der verbesserten Erdölförderung (EOR) auf.:1. Kurzfassung 5 2. Einleitung 6 2.1. Die primäre und sekundäre Förderphase 7 2.2. Tertiäre Fördermethoden 9 2.3. Akustische Verfahren 14 2.4. Aufgabenstellung 17 3. Grundlagen 18 3.1. Projektvorstellung 19 3.1.1. Vorstellung der Sonde 20 3.1.2. Eingrenzung der Laborparameter 22 3.2. Einordnung des Verfahrens in den Stand der Technik 23 3.2.1. Impuls- und Frequenzverfahren 23 3.2.2. Frequenzbereiche 25 3.3. Auswertemethoden 27 3.3.1. Frequenzanalysen 27 3.3.2. Flutversuche und relative Permeabilität 28 3.3.3. Imbibitionsversuche 32 3.4. Grundlagen der mathematischen Methoden 33 3.4.1. Fouriertransformation 34 3.4.2. Gradientenverfahren 34 3.4.3. Regressionsanalyse 37 4. Laborarbeiten 39 4.1. Versuchsaufbau 39 4.1.1. Flutanlage 39 4.1.2. Imbibitionsgefäße 42 4.2. Versuchsdurchführung 44 4.3. Der Versuchsplan der Flutexperimente 48 4.4. Voruntersuchungen 49 4.4.1. Gesteinsproben 49 4.4.2. Fluidproben 50 5. Datenauswertung 52 5.1. Frequenzanalyse 52 5.2. Flutversuche 55 5.2.1. Ergebnis der Regressionsanalyse 59 5.3. Imbibitionsversuche 61 5.4. Phänomenologische Untersuchungen 63 5.4.1. Injektivitätsveränderung 63 5.4.2. Instabile Emulsionsbildung 65 5.5. Weitergehende Forschungsansätze 67 5.5.1. Rückkopplungseffekte mit Tensiden 67 5.5.2. Bohrlochregeneration 69 6. Diskussion 71 7. Zusammenfassung 75

Gas migration in saturated argillaceous rock is studied in this work. Dependent on the pressure level the gas transport process is controlled by different mechanisms. Gas injection tests have been carried to investigate the gas transport process in low permeable argillaceous rock. We focus on the Opalinus Clay, which has been widely researched and is important for searching possible host rock of the radioactive waste disposal. Gas injection tests at different scales (laboratory, in-situ borehole and in-situ tunnel test) are intensively investigated in this work. The measurements of the tests are analysed and interpreted with numerical modelling method. A coupled multi-phase flow and mechanical model has been developed and implemented in the scientific computed codes OpenGeoSys (OGS). In the applied numerical model the relationship between capillary pressure and water saturation degree is described with van Genuchten model. The Darcy’s law is used for the phase flux, and the relative permeability of both water and gas phase is considered. The deformation process is calculated with elastic perfect-plastic model. The anisotropic hydraulic and mechanic behaviours of the Opalinus Clay are involved in the numerical model. The hydraulic anisotropy is controlled by the permeability tensor. The elastic deformation process is modelled by generalized Hooke’s law. The plastic behaviour is calculated with return mapping algorithm, and the anisotropy is considered with a so called microstructure tensor method. The permeability change during the gas injection is described using pressure dependent or deformation dependent approach. With considering the permeability evolution the measured data can be in the numerical model quantitatively represented, and test observations can be interpreted. Under laboratory condition it can be determined that the specimen permeability is reduced during compression. The significant permeability increase takes places when the gas injection pressure higher than the confining pressure. By the in-situ tests damage zone can be generated due to the drilling of boreholes and tunnel. The highly permeable areas dominate the hydraulic process. Fluid flows through the damaged zone into the not sealed section, e.g. the seismic observation boreholes by the in-situ borehole tests and the section out of the megapacker by the in-situ tunnel tests. In this work, the two phase flow controlled and pathway dilatancy controlled gas migration mechanisms are successfully simulated. The developed numerical model can be used to investigate the gas injection tests at different scales and conditions.

Measuring the liquid velocity and turbulence parameters in multiphase flows is a challenging task. In general, measurements based on optical methods are hindered by the presence of the gas phase. In the present work, it is shown that this leads to a sampling bias. Here, particle image velocimetry (PIV) is used to measure the liquid velocity and turbulence in a bubble column for different gas volume flow rates. As a result, passing bubbles lead to a significant sampling bias, which is evaluated by the mean liquid velocity and Reynolds stress tensor components. To overcome the sampling bias a window averaging procedure that waits a time depending on the locally distributed velocity information (hold processor) is derived. The procedure is demonstrated for an analytical test function. The PIV results obtained with the hold processor are reasonable for all values. By using the new procedure, reliable liquid velocity measurements in bubbly flows, which are vitally needed for CFD validation and modeling, are possible. In addition, the findings are general and can be applied to other flow situations and measuring techniques.

Es wurde ein neues Zweifluidmodell entwickelt, um Nichtgleichgewichtseffekte in kritischen und nahkritischen Ein-komponenten-Zweiphasenströmungen von anfänglich unter-kühlten oder siedenden Fluiden durch Rohre und Düsen zu untersuchen. Das vorgeschlagene Sechs-Gleichungsmodell besteht aus den phasenbezogenen Erhaltungsgleichungen für Masse und Impuls, der Bilanzgleichung für die thermische Energie der flüssigen Phase sowie einer zusätzlichen Transport-gleichung für die volumetrische Blasenanzahl. Zur Lösung des Systems aus partiellen Differentialgleichungen wird ein semi-implizites Finite-Differenzen-Zeitschrittverfahren angewendet. Die Schließung des Gleichungssystems wird durch Einbindung thermodynamischer Beziehungen und konstitutiver Gleichungen, die den strömungsformabhängigen Impuls-, Wärme- und Stofftransport beschreiben, erreicht. Für Strömungssysteme mit spontaner Entspannungsverdampfung aus dem rein flüssigen Zustand (Flashing) werden verschiedene Keimbildungsmodelle eingesetzt, die den Anfangszustand der verzögerten Dampfbildung beschreiben. Auf diese Weise werden thermodynamische Nichtgleichgewichtszustände als Folge von Zuständen mit für die Aktivierung von Keimstellen benötigtem Energieüberschuß, eingeschränkt vorhandener Phasengrenzfläche sowie begrenzter Wärmeübertragung zwischen den Phasen betrachtet. Abweichungen vom fluid-dynamischen Gleichgewicht (Phasenschlupf) ergeben sich aufgrund unterschiedlicher Trägheitseigenschaften und verschieden stark ausgeprägter mechanischer Kopplung zwischen den Phasen. Die mit diesem Modell erhaltenen numerischen Ergebnisse stimmen gut mit experimentellen Werten für Zweiphasen-strömungen mit unterschiedlichen Eintrittsbedingungen und Kanalgeometrien überein. / A new two-fluid flow model has been developed in order to examine non-equilibrium effects in critical and near-critical one-component two-phase flows of initially subcooled or saturated fluids through pipes and nozzles. The six-equation model proposed consists of the phasic conservation equations of mass and momentum, the liquid thermal energy, and of an additional transport equation for the bubble number density. To solve for the unknowns of the system of partial differential equations, a semi-implicit finite difference time-marching method is utilized. The closure of the set of equations is accomplished by thermodynamic relationships and additional constitutive equations describing momentum transport, interphase heat, and mass transfer which account for different flow regimes. For fluid flow systems undergoing a sudden change of phase from the pure liquid state (flashing), distinct nucleation models are included to describe the initial state of delayed vapor generation. In this way thermal non-equilibrium states are considered to be the consequence of excessive energy states required to activate nucleation sites, of restricted interfacial area and limited heat transfer between the phases. Deviation from fluid-dynamic equilibrium (phasic slip) results from different inertial properties and from distinct strength of mechanical coupling between the phases. The numerical results obtained with this model agree quite well with experimental data for two-phase flows with various inlet conditions and channel geometries.

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.

This thesis presents a numerical method for the phase-resolving simulation of rigid particles and deformable bubbles in viscous, magnetohydrodynamic flows. The presented approach features solid robustness and high numerical efficiency. The implementation is three-dimensional and fully parallel suiting the needs of modern high-performance computing. In addition to the steps towards magnetohydrodynamics, the thesis covers method development with respect to the immersed boundary method which can be summarized in simple words by From rigid spherical particles to deformable bubbles. The development comprises the extension of an existing immersed boundary method to non-spherical particles and very low particle-to-fluid density ratios. A detailed study is dedicated to the complex interaction of particle shape, wake and particle dynamics. Furthermore, the representation of deformable bubble shapes, i.e. the coupling of the bubble shape to the fluid loads, is accounted for. The topic of bubble interaction is surveyed including bubble collision and coalescence and a new coalescence model is introduced. The thesis contains applications of the method to simulations of the rise of a single bubble and a bubble chain in liquid metal with and without magnetic field highlighting the major effects of the field on the bubble dynamics and the flow field. The effect of bubble coalescence is quantified for two closely adjacent bubble chains. A framework for large-scale simulations with many bubbles is provided to study complex multiphase phenomena like bubble-turbulence interaction in an efficient manner.

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).