When an electrically conducting fluid moves through a magnetic field, fluid mechanics and electromagnetism are coupled. This interaction is the object of magnetohydrodynamics, a discipline which covers a wide range of applications, from electromagnetic processing to plasma- and astro-physics. In this dissertation, the attention is restricted to turbulent liquid metal flows, typically encountered in steel and aluminium industries. Velocity measurements in such flows are extremely challenging because liquid metals are opaque, hot and often corrosive. Therefore, non-intrusive measurement devices are essential. One of them is the Lorentz force flowmeter. Its working principle is based on the generation of a force acting on a charge, which moves in a magnetic field. Recent studies have demonstrated that this technique can measure efficiently the mean velocity of a liquid metal. In the existing devices, however, the measurement depends on the electrical conductivity of the fluid. In this work, a novel version of this technique is developed in order to obtain measurements that are independent of the electrical conductivity. This is particularly appealing for metallurgical applications, where the conductivity often fluctuates in time and space. The study is entirely numerical and uses a flexible computational method, suitable for industrial flows. In this framework, the cost of numerical simulations increases drastically with the level of turbulence and the geometry complexity. Therefore, the simulations are commonly unresolved. Large eddy simulations are then very promising, since they introduce a subgrid model to mimic the dynamics of the unresolved turbulent eddies. The first part of this dissertation focuses on the quality and reliability of unresolved numerical simulations. The attention is drawn on the ambiguity that may arise when interpretating the results. Owing to coarse resolutions, numerical errors affect the performances of the discrete model, which in turn looses its physical meaning. In this work, a novel implementation of the turbulent strain rate appearing in the models is proposed. As opposed to its usual discretisation, the present strain rate is in accordance with the discrete equations of motion. Two types of flow are considered: decaying turbulence located far from boundaries, and turbulent flows between two parallel and infinite walls. Particular attention is given to the balance of resolved kinetic energy, in order to assess the role of the model. The second part of this dissertation deals with a novel version of Lorentz force flowmeters, consisting in one or two coils placed around a circular pipe. The forces acting on each coil are recorded in time as the liquid metal flows through the pipe. It is highlighted that the auto- or cross-correlation of these forces can be used to determine the flowrate. The reliability of the flowmeter is first investigated with a synthetic velocity profile associated to a single vortex ring, which is convected at a constant speed. This configuration is similar to the movement of a solid rod and enables a simple analysis of the flowmeter. Then, the flowmeter is applied to a realistic three-dimensional turbulent flow. In both cases, the influence of the geometrical parameters of the coils is systematically assessed.

When an electrically conducting fluid moves through a magnetic field, fluid mechanics and electromagnetism are coupled.<p>This interaction is the object of magnetohydrodynamics, a discipline which covers a wide range of applications, from electromagnetic processing to plasma- and astro-physics.<p><p>In this dissertation, the attention is restricted to turbulent liquid metal flows, typically encountered in steel and aluminium industries. Velocity measurements in such flows are extremely challenging because liquid metals are opaque, hot and often corrosive. Therefore, non-intrusive measurement devices are essential. One of them is the Lorentz force flowmeter. Its working principle is based on the generation of a force acting on a charge, which moves in a magnetic field. Recent studies have demonstrated that this technique can measure efficiently the mean velocity of a liquid metal. In the existing devices, however, the measurement depends on the electrical conductivity of the fluid. <p><p>In this work, a novel version of this technique is developed in order to obtain measurements that are independent of the electrical conductivity. This is particularly appealing for metallurgical applications, where the conductivity often fluctuates in time and space. The study is entirely numerical and uses a flexible computational method, suitable for industrial flows. In this framework, the cost of numerical simulations increases drastically with the level of turbulence and the geometry complexity. Therefore, the simulations are commonly unresolved. Large eddy simulations are then very promising, since they introduce a subgrid model to mimic the dynamics of the unresolved turbulent eddies. <p><p>The first part of this dissertation focuses on the quality and reliability of unresolved numerical simulations. The attention is drawn on the ambiguity that may arise when interpretating the results. Owing to coarse resolutions, numerical errors affect the performances of the discrete model, which in turn looses its physical meaning. In this work, a novel implementation of the turbulent strain rate appearing in the models is proposed. As opposed to its usual discretisation, the present strain rate is in accordance with the discrete equations of motion. Two types of flow are considered: decaying turbulence located far from boundaries, and turbulent flows between two parallel and infinite walls. Particular attention is given to the balance of resolved kinetic energy, in order to assess the role of the model.<p><p>The second part of this dissertation deals with a novel version of Lorentz force flowmeters, consisting in one or two coils placed around a circular pipe. The forces acting on each coil are recorded in time as the liquid metal flows through the pipe. It is highlighted that the auto- or cross-correlation of these forces can be used to determine the flowrate. The reliability of the flowmeter is first investigated with a synthetic velocity profile associated to a single vortex ring, which is convected at a constant speed. This configuration is similar to the movement of a solid rod and enables a simple analysis of the flowmeter. Then, the flowmeter is applied to a realistic three-dimensional turbulent flow. In both cases, the influence of the geometrical parameters of the coils is systematically assessed. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

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 &amp;lt; Ha &amp;lt; 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.

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 &amp;lt; Ha &amp;lt; 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.

In der vorliegenden Arbeit konnte gezeigt werden, dass die numerischen simulationen einer freien Rayleigh-Bénard-Konvektion und einer rein elektromagnetisch angetriebenen gezeiten-artigen Strömung in einem stehenden zylindrischen Volumen mit einem Seitenverhältnis Г = D/H = 1 und seitlich angelegten Magnetspulen eine gute Übereinstimmung mit entspre-chenden Experimenten aufweisen. Kombiniert man beide Mechanismen und moduliert die Lorentzkraft, so zeigen sich in den Frequenzspektren der Helizität in zwei Halbräumen des Volumens deutliche Maxima an der Modulationsfrequenz. Eine solche Helizitätssynchronisierung durch Gezeitenkräfte wird derzeit als mögliche Erklärung für die hohe Regularität des Sonnendynamos diskutiert. Des Weiteren wird die in freier Konvektion auftretende langsame azimutale Wanderung der Konvektionszelle unterdrückt. Der Schwingungswinkel der azimutalen Schwappbewegung nimmt dabei ab und die in der Strömung dominante Frequenz erhöht sich. Die durch die zwei unterschiedlichen Antriebsmechanismen erzeugten Strömungsstrukturen bleiben in der Strömung eigenständig erhalten und treten in gegenseitige Interaktion.:1. Einleitung 2. Grundlagen 2.1. Rayleigh-Bénard-Konvektion 2.2. MHD - Magnetohydrodynamik 2.3. Wichtige Aspekte des numerischen Modells 3. Modellerstellung 3.1. Geometrie 3.2. Numerisches Modell 3.2.1. Elektromagnetisches Modell in Opera 3.2.2. Modell der Strömungsberechnung in OpenFOAM 4. Ergebnisse 4.1. Ergebnisse der freien Rayleigh-Bénard-Konvektion 4.2. Ergebnisse der nichtmodulierten elektromagnetischen Strömungsanregung ohne Temperaturgradient 4.3. Ergebnisse der zeitmodulierten elektromagnetischen Strömungsanregung ohne Temperaturgradient 4.4. Ergebnisse der elektromagnetisch beeinflussten Rayleigh-Bénard-Konvektion 4.4.1. Auswirkung der elektromagnetischen Beeinflussung auf die Strömungsstruktur 4.4.2. Vergleich ausgewählter Ergebnisse der numerischen Untersuchung und des Experimentes 4.4.3. Auswirkung der elektromagnetischen Beeinflussung auf die Helizität 5. Zusammenfassung und Fazit