An experimental study of the transition to turbulence in a confined quasi-two-dimensional magnetohydrodynamic flow is presented. A pair of counterrotating vortice is electrically driven in the center of a thin horizontal liquid metal layer, enclosed in a cylindrical container and subject to a homogeneous vertical magnetic field. When the forcing is increased, the pair is displaced away from the center. Boundary layer separations from the circular wall appear that trigger a sequence of supercritical bifurcations. These are singled out in numerical calculations based on our previously developed shallow water model as well as in the experiment, and these bifurcations are shown to resemble those observed in flows past a cylindrical obstacle. For the highest forcing, the flow then ends up in a turbulent regime where the dissipation increases drastically, which we could relate to a possible transition from a laminar to a turbulent Hartmann boundary layer. Finally we show the first experimental evidence of a transition to three-dimensionality in liquid metal magnetohydrodynamics (MHD) by comparing velocity measurements on either horizontal sides of the layer as we find that columnar vortice wobble for a high enough forcing.

Zusammenfassung Der Beitrag beschreibt den experimentellen Aufbau und die ersten Messergebnisse einer neuen Durchflussmesstechnik für schwach leitfähige Fluide mittels Lorentzkraft-Anemometrie, einem berührungslosen Messverfahren, welches schon erfolgreich für gut leitfähige Fluide wie Metallschmelzen eingesetzt wurde. Potentielle Anwendungen sind heiße und chemisch aggressive sowie nicht transparente Flüssigkeiten, da hier verfügbare Durchflussmesstechniken nur bedingt anwendbar sind.

Lorentz Force Velocimetry is a contactless method for the flow rate measurement of electrically conducting fluids. This method is based on the interaction of the fluid flow with the transversal permanent magnetic field. The equal electromagnetic force acts on the fluid and on the magnet system. The flow rate can be determined by measuring of this electromagnetic force. The magnet system has been optimized to achieve maximal sensitivity at a given magnet system weight. The sensitivity was defined as the ratio between the Lorentz force and the magnet system weight. The numerical model was developed using COMSOL Multiphysics. Validation and verification of the numerical model has been performed. The magnet system was optimized using the optimization toolbox in MATLAB.

We show that the performances of flowmeters based on the measurement of Lorentz force in duct flows can be sufficiently optimized to be applied to fluids of low electrical conductivity. The main technological challenge is to design a system with permanent magnets generating a strong enough field for the Lorentz force generated when a fluid of low conductivity passes through it to be reliably measured. To achieve this, we optimize the design of a magnet system based on Halbach arrays placed on either side of the duct. In the process, we show that the fluid flow can be approximated as a moving solid bar with practically no impact on the optimization result and devise a rather general iterative optimization procedure, which incurs drastically less computational cost than a direct procedure of equivalent precision. We show that both the Lorentz force and the efficiency of the system (defined as the ratio of the Lorentz force to the weight of the system) can be increased several fold by using Halbach arrays made of three, five, seven or nine magnets on either side of the duct but that this improvement comes at a cost in terms of the precision required to position the system.

Zusammenfassung In der Metallurgiebranche fehlen derzeit geeignete Verfahren zur präzisen Erfassung, Regelung und Dosierung der zwischen den einzelnen Produktionsstufen übertragenen Mengen an Metallschmelze. Durch den Einsatz des patentierten Verfahrens der Lorentzkraft-Anemometrie, bei dem der direkte Kontakt zur heißen Metallschmelze nicht erforderlich ist, lässt sich diese Aufgabe lösen und somit ein nachhaltiger Beitrag zu zukünftig energie- und kostenoptimierter Produktion leisten. Im vorliegenden Artikel werden das Prinzip des Verfahrens erläutert und die wissenschaftlich-technischen Wege zur Entwicklung, Prüfung und Kalibierung von entsprechenden Lorentzkraft-Anemometern vorgestellt. Desweiteren werden Beispiele aktueller Anwendungen der Lorentzkraft-Anemometrie in der Praxis diskutiert.