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.

Supernovae are known to be the dominant energy source for driving turbulence in the interstellar medium. Yet, their effect on magnetic field amplification in spiral galaxies is still poorly understood. Analytical models based on the uncorrelated-ensemble approach predicted that any created field will be expelled from the disk before a significant amplification can occur. By means of direct simulations of supernova-driven turbulence, we demonstrate that this is not the case. Accounting for vertical stratification and galactic differential rotation, we find an exponential amplification of the mean field on timescales of 100Myr. The self-consistent numerical verification of such a “fast dynamo” is highly beneficial in explaining the observed strong magnetic fields in young galaxies. We, furthermore, highlight the importance of rotation in the generation of helicity by showing that a similar mechanism based on Cartesian shear does not lead to a sustained amplification of the mean magnetic field. This finding impressively confirms the classical picture of a dynamo based on cyclonic turbulence. / Supernovae sind bekanntermaßen die dominante treibende Energiequelle für Turbulenz im interstellaren Medium. Dennoch ist ihre Auswirkung auf die Verstärkung von Magnetfeldern in Spiralgalaxien weitestgehend unverstanden. Analytische Modelle, die auf der Annahme eines unkorrelierten Ensembles beruhen, sagen voraus, dass das erzeugte Feld aus der galaktischen Scheibe herausgedrängt wird bevor eine substantielle Verstärkung erfolgen kann. Mithilfe numerischer Simulationen supernovagetriebener Turbulenz zeigen wir, dass dies nicht der Fall ist. Unter Berücksichtigung einer vertikalen Schichtung und differentieller galaktischer Rotation beobachten wir eine exponentielle Verstärkung des mittleren Magnetfeldes auf einer Zeitskala von 100 Mio. Jahren. Diese selbstkonsistente numerische Bestätigung eines “schnellen Dynamos” erlaubt es, die beobachteten starken Magnetfelder in jungen Galaxien zu erklären. Darüberhinaus stellen wir die Wichtigkeit der Rotation bei der Erzeugung von Helizität heraus, indem wir zeigen, dass ein ähnlicher Effekt basierend auf kartesischer Scherung nicht zu einer Verstärkung des mittleren Magnetfeldes führt. Dies bestätigt eindrucksvoll das klassische Bild zyklonischer Turbulenz.

Observations show that Coronal Mass Ejections (CMEs) are associated with twisted magnetic flux configurations. Conventionally, CMEs are modeled by shearing and twisting the footpoints of a certain distribution of magnetic flux at the solar surface and letting it evolve at the surface. Of course, the surface velocities and magnetic field patterns should ultimately be obtained from realistic simulations of the solar convection zone where the field is generated by dynamo action. Therefore, a unified treatment of the convection zone and the CMEs is needed. Numerical simulations of turbulent dynamos show that the amplification of magnetic fields can be catastrophically quenched at magnetic Reynolds numbers typical of the interior of the Sun. A strong flux of magnetic helicity leaving the dynamo domain can alleviate this quenching. In this sense, a realistic (magnetic) boundary condition is an important ingredient of a successful solar dynamo model. Using a two-layer model developed in this thesis, we combine a dynamo-active region with a magnetically inert but highly conducting upper layer which models the solar corona. In four steps we improve this setup from a forced to a convectively driven dynamo and from an isothermal to a polytropic stratified corona. The simulations show magnetic fields that emerge at the surface of the dynamo region and are ejected into the coronal part of the domain. Their morphological form allows us to associate these events with CMEs. Magnetic helicity is found to change sign in the corona to become consistent with recent helicity measurements in the solar wind. Our convection-driven dynamo model with a coronal envelope has a solar-like differential rotation with radial (spoke-like) contours of constant rotation rate, together with a solar-like meridional circulation and a near-surface shear layer. The spoke-like rotation profile is due to latitudinal entropy gradient which violates the Taylor--Proudman balance through the baroclinic term. We find mean magnetic fields that migrate equatorward in models both with and without the coronal layer. One remarkable result is that the dynamo action benefits substantially from the presence of a corona becoming stronger and more realistic. The two-layer model represents a new approach to describe the generation of coronal mass ejections in a self-consistent manner. On the other hand, it has important implications for solar dynamo models as it admits many magnetic features observed in the Sun. / <p>At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 5: Manuscript; Paper 6: Manuscript.</p>

Plasma flow physics in magnetic nozzles must be clearly understood for optimal design of plasma propulsion devices. Toward that end, in this thesis we: i) perform an extensive literature survey of magnetic nozzle physics, ii) assess the validity of magnetohydrodynamics for studying magnetic nozzle physics, and iii) illustrate the effects of the Hall term in simple flows as well as in magnetic nozzle configurations through numerical experiments with the Magneto-Gas Kinetic Method (MGKM). The crucial steps necessary for thrust generation in magnetic nozzles are energy conversion, plasma detachment, and momentum transfer. These three physical phenomena must be understood to optimize magnetic nozzle design. The operating dimensionless parameter ranges of six prominent experiments are considered and the corresponding mechanisms are discussed. An order of magnitude analysis of the governing equations reveal: i) most magnetic nozzles under consideration operate at the edge of the continuum regime rendering continuum-based description and computation valid; ii) in the context of MHD framework, the generalized Ohm’s law must be used to capture all of the relevant physics. This work also continues the development of the Magneto Gas Kinetic Method (MGKM) computational tool. Validation of the solver is performed in shock-tube and Hartmann channel flows in the Hall physics regime. Comparison with theory and available data is made whenever possible. Novel numerical experiments of magnetic nozzle plasma jets in the Hall regime are performed, confirming the theoretically predicted azimuthal rotation of the plasma jet due to Hall physics. The primary conclusion from this work is that the addition of the Hall effect generates helical structures in magnetic nozzle plasma flows. Preliminary results are encouraging for future magnetic nozzle studies and further challenges are identified.

Control of bulk melt crystal growth techniques is desirable for producing semiconductors with the highest purity and ternary alloys with tunable electrical properties. Because these molten materials are electrically conducting, external magnetic fields are often employed to regulate the flow in the melt. However, complicated by the coupled flow, thermal, electromagnetic and chemical physics, such magnetic control is typically empirical or even an educated guess. Two magnetic flow control mechanisms: flow damping by steady magnetic fields, and flow stirring by alternating magnetic fields, are investigated numerically. Magnetic damping during optically-heated float-zone crystal growth is modeled using a spectral collocation method. The Marangoni convection at the free melt-gas interface is suppressed by applying a steady magnetic field, measured by the Hartmann number Ha. Using normal mode linear stability analyses, suppression of detrimental flow instabilities is quantitatively determined in a range applicable to experiments (up to Ha = 300 for Pr = 0.02, and up to Ha = 500 for Pr = 0.001). The hydrodynamic flow instability for small Prandtl number P r float-zone is confirmed by energy analyses. Rotating magnetic field stirring during confined crystal growth in an ampoule is also modeled. Decoupled from the flow field at small magnetic Reynolds number, the electromagnetic field is solved in a finite element solver. At low AC frequencies, the force is only in the azimuthal direction but penetrates deep into the melt. In contrast, the magnetic shielding effect is observed at high alternating current (AC) frequencies, where the external magnetic field penetrates only by a skin depth into the electrically conducting media within the short AC cycle. As a result, the electromagnetic body force is primarily confined to the ampoule surface. At these high AC frequencies the magnetic flux lines are drastically distorted within the melt. The body force is fully three-dimensional and is much stronger than at low AC frequencies, but is confined to near the ampoule surface due to the magnetic shielding effect. These models promote fundamental understanding of flow dynamics regulated by electromagnetic body forces. They provide quantitative guidance for crystal growth to minimize trial and error experimentation that is slow and expensive.

This thesis describes work on building numerical models of the Earth's magnetosphere using magnetohydrodynamics (MHD) and other related modeling methods. For many years, models that solve the MHD equations have been the main tool for improving our theoretical understanding of the large-scale dynamics of the Earth's magnetosphere. While the MHD models have been very successful in capturing many large-scale features, they fail to adequately represent the important drift physics in the inner magnetosphere. Consequently, the ring current, which contains most of the particle energy in the inner magnetosphere, is not realistically represented in MHD models. In this thesis, Chapter 2 and 3 will describe in detail our effort to couple the OpenGGCM (Open Geospace General Circulation Model), one of the major MHD models, to the Rice Convection Model (RCM), an inner magnetosphere ring current model, with the goal of including energy dependent drift physics into the MHD model. In Chapter 4, we will describe an initial attempt to use a direct-integration method to calculate Birkeland currents in the MHD code. Another focus of the thesis work, presented in Chapter 5, addresses a longstanding problem on how a geomagnetic substorm can occur within the closed field line region of the tail. We find a scenario of a bubble-blob pair formation in an OpenGGCM simulation just before the expansion phase of the substorm begins and the subsequent separation of the bubble and the blob decreases the normal component of the magnetic field until finally an X-line occurs. Thus the formation of the bubble-blob pair may play an important role in changing the magnetospheric configuration from a stretched field to the X-line formation that is believed to be the major signature of a substorm.

Untersuchung konvektiver Transportprozesse innerhalb einer auf der Lorentz-Kraft basierenden Strömung während der elektrolytischen Abscheidung.

This study uses the Magnetohydrodynamics (MHD) method to simulate unsteady two-dimensional transport variables in argon (Ar) plasma, under low pressure, high density, and weak ionization between two infinite planar electrodes suddenly biased by a negative voltage. Plasma has been widely used in materials processing, thin film manufacturing, light source, nuclear fusion, and etching, etc. Properties of plasmas are also becoming important area for research in physics, chemistry, photonics, aerospace, engineering science and technology. Studying transport processes of plasmas therefore is important. This research consider by electric fields and magnetic fields, viscous, momentum exchange collisions between electrons ions and neutral particles. The computed results in this work quantitatively show density, velocity, electric potential, temperature, magnetic field, viscosity, thermal conductivity of the electrons ions and neutral particles across the sheath to the surfaces suddenly biased by a DC negative voltage. And increase of the boundary layer and sheath thickness. We can compare the theory and the simulation to know the behavior of the plasma near a surface.

The exact mechanisms responsible for heating the solar atmosphere in regions such as the chromosphere (partially ionized) and the corona (fully ionized) remain quantitatively unknown. This thesis demonstrates that the ions can be heated by Alfven waves with low frequencies in fully and partially ionized low beta plasmas, which is contrary to the customary expectation. For the partially ionized case, we find the heating process to be less efficient than the scenario with no ion-neutral collisions, and that the heating efficiency depends on the ratio of ion-neutral collision frequency to the ion gyrofrequency. For Alfven waves propagating obliquely to the background magnetic field in fully ionized plasmas, we find the heating process to be more efficient than the situation with Alfven waves propagating along the background magnetic field. Furthermore, the simulation results show the parallel kinetic temperature can become even larger than the perpendicular component for the case of obliquely propagating Alfven waves.

The Magnetorotational Instability (MRI) is believed to be the primary mechanism for angular momentum transfer in astrophysical accretion disks. This instability, which exists in ionized disks in the presence of weak magnetic fields, can either transfer angular momentum directly, or give rise to anomalous viscosity via non-linear turbulence. While many previous analytical treatments are concerned with the local theory of the MRI, when the length scale of rotation shear is comparable to the length scale of the most unstable modes, a global analysis is necessary. In this dissertation we investigate the global theory of the linear MRI. In particular, we show how rotation shear can localize global modes and how the global growth rates can differ signicantly from the local approximation in certain cases. Changes in the equilibrium density are considered. In addition, the effects of Hall Magnetohydrodynamics on the MRI are studied in both the local and global cases. / text