Thermal convection experiments in liquid metal flows with and without magnetic field

The interaction of electrically conducting fluid flows with magnetic fields appears in numerous natural phenomena and technical applications. Since the relevant fluids – such as liquid metals and plasmas – are generally very hot, the flows are often accompanied or even driven by thermal convection. The study of this so-called magnetoconvection is thus of interest for a number of physical systems. Two aspects are investigated in this thesis. The first concerns the case when an imposed magnetic field does not alter the fluid flow. The second case explores the changes of the flow structure and global transport properties in the presence of strong magnetic fields. The first point is relevant for inductive measurement techniques, which are required to probe the flow without disturbing it. Here, the size of the fluid volume affected by a localised magnetic field is of major importance. This topic is investigated theoretically by deriving an algorithm to calculate the penetration depth of the magnetic field into the medium. This allows the prediction of a magnetic field strength, above which a flow is significantly disturbed. The theoretical results are verified for the measurement method of local Lorentz force velocimetry which is applied to a vertical convection flow. The second point is investigated experimentally for a Rayleigh-Bénard convection system that is subject to a homogeneous vertical magnetic field. The set-up consists of a cylindrical cell of aspect ratio one. The large-scale flow structure is monitored using temperature measurements and ultrasound Doppler velocimetry. The evolution of the flow with increasing magnetic field strength is classified into different regimes and compared with theoretical predictions, and numerical simulations. Global transport properties of the flow concerning its momentum, and the heat passing through the fluid are analysed and their behaviour is interpreted in light of the aforementioned flow regimes. Additionally, a new theoretical model is developed to predict the turbulent heat and momentum transfer in the fluid by extending the Grossmann-Lohse theory for the classical Rayleigh-Bénard convection setting by the effects of a vertical magnetic field. Experimental data of the present study and from literature are used to verify and enhance the model, and to identify relevant physical mechanisms responsible for the observed results.Die Wechselwirkung zwischen elektrisch leitfähigen Fluiden und Magnetfeldern tritt in zahlreichen natürlichen Phänomenen und technischen Anwendungen auf. Weil die dabei relevanten Medien - meist Flüssigmetalle oder Plasmen - im Allgemeinen sehr heiß sind, werden die Strömungen meist von thermischer Konvektion begleitet oder werden sogar von dieser getrieben. Das Phänomen der sogenannten Magnetokonvektion ist damit von Interesse für eine große Anzahl physikalischer Systeme. Die vorliegende Arbeit untersucht hierbei zwei Aspekte. Zum einen wird der Fall betrachtet, wenn ein aufgeprägtes Magnetfeld das Strömungsfeld nicht verändert. Zum anderen werden die Modifizierungen von Strömungsstruktur und globalen Transporteigenschaften durch starke Magnetfelder untersucht. Der erste Fall ist wichtig für induktive Messtechniken, welche die Bewegung eines Mediums untersuchen müssen, ohne dieses dabei zu stören. Die Größe des Fluidvolumens, welches von einem örtlich begrenzten Magnetfeld beeinflusst wird, ist hier ein äußerst wichtiger Faktor. Dieses Thema wird untersucht, indem die Eindringtiefe des Magnetfeldes in das Medium theoretisch hergeleitet wird. Das erlaubt die Vorhersage einer Magnetfeldstärke, oberhalb derer eine Strömung maßgeblich gestört wird. Die theoretischen Ergebnisse werden mittels experimenteller Messungen überprüft. Dazu wird die Messmethode der lokalen Lorentzkraft-Anemometrie auf eine vertikale Konvektionsströmung angewandt. Für den zweiten Fall wird das System der Rayleigh-Bénard Konvektion unter einem homogenen, vertikalen Magnetfeld experimentell untersucht. Der Aufbau besteht aus einer zylindrischen Zelle mit einem Aspektverhältnis von eins. Die großskalige Struktur der Strömung wird mittels Temperaturmessungen und Ultraschall Doppler Anemometrie überwacht. Die Entwicklung der Strömung mit ansteigender Magnetfeldstärke kann in verschiedene Regime kategorisiert und mit theoretischen Vorhersagen sowie numerischen Simulationen verglichen werden. Globale Transporteigenschaften des Systems bezüglich Impuls und übertragener Wärme werden analysiert und ihr Verhalten anhand der zuvor gefundenen Strömungsregime interpretiert. Zusätzlich wird ein theoretisches Modell entwickelt um den turbulenten Wärme- und Impulstransport vorherzusagen. Dazu wird die Großmann-Lohse Theorie für klassische Rayleigh-Bénard Konvektion durch den Effekt eines vertikalen Magnetfeldes erweitert. Die experimentellen Daten aus der vorliegenden Arbeit und aus der Literatur werden genutzt, um dieses Modell zu verifizieren und zu optimieren. Dabei werden physikalische Prozesse identifiziert, welche maßgeblich zu den beobachteten Ergebnissen beitragen

Collapse of Coherent Large Scale Flow in Strongly Turbulent Liquid Metal Convection

The large-scale flow structure and the turbulent transfer of heat and momentum are directly measured in highly turbulent liquid metal convection experiments for Rayleigh numbers varied between $4 \times 10^5$ and $\leq 5 \times 10^9$ and Prandtl numbers of $0.025~\leq~Pr~\leq ~0.033$. Our measurements are performed in two cylindrical samples of aspect ratios $\Gamma =$ diameter/height $= 0.5$ and 1 filled with the eutectic alloy GaInSn. The reconstruction of the three-dimensional flow pattern by 17 ultrasound Doppler velocimetry sensors detecting the velocity profiles along their beamlines in different planes reveals a clear breakdown of coherence of the large-scale circulation for $\Gamma = 0.5$. As a consequence, the scaling laws for heat and momentum transfer inherit a dependence on the aspect ratio. We show that this breakdown of coherence is accompanied with a reduction of the Reynolds number $Re$. The scaling exponent $\beta$ of the power law $Nu\propto Ra^{\beta}$ crosses \FIN{eventually} over from $\beta=0.221$ to 0.124 when the liquid metal flow at $\Gamma=0.5$ reaches $Ra\gtrsim 2\times 10^8$ and the coherent large-scale flow is completely collapsed.Comment: 4 pages, 5 figures, 1 supplementary with 1 figure and 4 tables, 1 movi

Refined mean field model of heat and momentum transfer in magnetoconvection

International audienceIn this article, the theoretical model on heat and momentum transfer for Rayleigh-Bénard convection in a vertical magnetic field by Zürner et al. (Phys. Rev. E 94, 043108 (2016)) is revisited. Using new data from recent experimental and numerical studies the model is simplified and extended to the full range of Hartmann numbers, reproducing the results of the Grossmann-Lohse theory in the limit of vanishing magnetic fields. The revised model is compared to experimental results in liquid metal magnetoconvection and shows that the heat transport is described satisfactorily. The momentum transport, represented by the Reynolds number, agrees less well which reveals some shortcomings in the theoretical treatment of magnetoconvection

Size-independent phase distinction in dispersed two-phase flows

In the study of dispersed two phase flows, having access to the velocities of both phases is necessary to fully understand and study the behaviour of these complex systems. While all data can be obtained in numerical simulations, this can prove more difficult to perform with experimental measurements. In this article, a new method to separate inertial particles from tracers in a two-dimensional laser sheet is described. By using a two camera acquisition system in conjunction with an optical filter, the two phases can successfully be segregated, without relying on an apparent size or intensity difference between inertial particles and tracers. This allows for the velocities and positions of the particles to be measured in conjunction with the velocity field of the carrying phase. A series of tests are performed on the method. In addition to ensuring that the method functions in a satisfactory manner, these tests give indications on how to use the method properly. As an example, measurement results of ceramic particles settling in still water are presented

Low Prandtl Number Rayleigh-Bénard Convection in a Vertical Magnetic Field

Lecture (Conference) 11th PAMIR International Conference- Fundamental and Applied MHD July 1-5, 2019, Reims, EVEM France We are investigating turbulent Rayleigh-Bénard convection in liquid metal under the influence of a vertical magnetic field. Utilizing a combination of thermocouple (TC) and ultrasound-Doppler-velocimetry (UDV) measurements gives us the possibility to directly determine the temperature and velocity field, respectively. Further this gives us the possibility to observe changes in the large-scale flow structure. By applying magnetic fields to the liquid metal convection, we quantified changes of heat and momentum transport in the liquid metal alloy GaInSn. The experimental results of our setup agree well with theory findings and direct numerical simulations of the dynamics in our convection cell. The requirement of large computing power at these parameters makes it hard to simulate long-term dynamics with time scales from minutes to several hours. Thus to investigate slow developing dynamics like sloshing, rotation, or deformation of the large- scale flow structure model experiments are indispensable. We demonstrate the suppression of the convective flow by a vertical magnetic field in a cylindrical cell of aspect ratio 1. In this setup Rayleigh numbers up to 6·107 are investigated. The flow structure at low Hartmann numbers is a single roll large scale circulation (LSC). Increasing the Hartmann number leads to a transition from the single-roll LSC into a cell structure. An even stronger magnetic field supresses the flow in the center of the cell completely and expels the flow to the side walls. Even above the critical Hartmann numbers corresponding to the Chandrasekhar limit for the onset of magnetoconvection in a fluid layer without lateral boundaries we still observe remarkable flows near the side walls. The destabilising effect of the non-conducting side walls was predicted by theory and simulations, and is here for the first time experimentally confirmed.Support by Deutsche Forschungsgemeinschaft with grants VO 2332/1-1 and SCHU 1410/29-

Rayleigh-Bénard Convection in Liquid metal under Influence of Vertical Magnetic Fields

Conference (Lecture): American Physics Society (APS) DFD meeting 2019 Seattle In the presented Rayleigh-Bénard convection experiments the turbulent 3d- flow of the liquid gallium-indium-tin alloy is investigated by use of ultrasound Doppler velocimetry, temperature and contactless inductive flow tomography measurements. We reconstruct for the first time near-wall as well as bulk flow, momentum and heat transport as well as long-term behaviour of the large-scale liquid metal flow at a low Prandtl number of 0.029 and high Rayleigh numbers up to 6 · 10e7. Also the influence of a strong magnetic field on the turbulent liquid metal is investigated. The results of the experiments are compared to direct numerical simulations and other experiments. These are also considered for the interpretation of the measured turbulence statistics. Our experiments aim to provide a deeper understanding of the turbulent convection and its interaction with magnetic fields in turbulent low Prandtl number flows as those in molten steel, aluminium or geo- and astrophysical flows.Supported by Deutsche Forschungsgemeinschaft with grants VO 2332/1-1 and SCHU 1410/29-

Data publication: Collapse of Coherent Large Scale Flow in Strongly Turbulent Liquid Metal Convection

Rawdata on which the publication is based on. .BDD binary files for Ultrasound measurements. .dat: direct temperature measurement data