Transition to turbulence in Hunt's flow in a moderate magnetic field. - In: epl, ISSN 1286-4854, Bd. 115 (2016), 4, S. 440012, insges. 6 S.
Pressure-driven magnetohydrodynamic duct flow in a transverse uniform magnetic field is studied by direct numerical simulation. The electric boundary conditions correspond to Hunt's flow with perfectly insulating walls parallel to the magnetic field (sidewalls) and perfectly conducting walls perpendicular to the magnetic field (Hartmann walls). The velocity distribution exhibits strong jets at the sidewalls, which are susceptible to instability even at low Reynolds numbers Re. We explore the onset of time-dependent flow and transition to states with evolved turbulence for a moderate Hartmann number Ha = 100. At low Re time-dependence appears in the form of elongated Ting-Walker vortices at the sidewalls of the duct, which, upon increasing Re, develop into more complex structures with higher energy and then the sidewall jets partially detach from the walls. At high values of Re jet detachments disappear and the flow consists of two turbulent jets and nearly laminar core. It is also demonstrated that, there is a range of Re, where Hunt's flow exhibits a pronounced hysteresis behavior, so that different unsteady states can be observed for the same flow parameters. In this range multiple states may develop and co-exist, depending on the initial conditions.
http://dx.doi.org/10.1209/0295-5075/115/44002
Global and local statistics in turbulent convection at low Prandtl numbers. - In: Journal of fluid mechanics, ISSN 1469-7645, Bd. 802 (2016), S. 147-173
http://dx.doi.org/10.1017/jfm.2016.457
Lorentz force transient response at finite magnetic reynolds numbers. - In: IEEE transactions on magnetics, ISSN 1941-0069, Bd. 52 (2016), 8, S. 6201611, insges. 11 S.
In this paper, we investigate the transient response of Lorentz force at finite magnetic Reynolds numbers Rm on an electrically conducting rectangular bar that is strongly accelerated in the presence of a localized magnetic field. This is done through numerical simulations utilizing a coupled finite-difference boundary element approach. The results show good qualitative agreement with existing experiments with a circular cylinder. The Lorentz force rise time is seen to be a linear function of Rm. The linear dependence of Lorentz force on Rm is found to be valid only for low values of Rm, after which the slope decays leading to an apparent saturation in the Lorentz force at sufficiently large values of Rm. Our results provide important information for the development of Lorentz force flow meters for transient flow applications. Index Terms: Lorentz force velocimetry (LFV), magnetic Reynolds number, transient response.
http://dx.doi.org/10.1109/TMAG.2016.2546229
Numerical simulations of magnetohydrodynamic flows driven by a moving permanent magnet. - In: Physical review fluids, ISSN 2469-990X, Bd. 1 (2016), 4, 043601, insges. 24 S.
We present results from numerical reconstructions of magnetic obstacle experiments performed in liquid metal flows. The experimental setup consists of an open rectangular container filled with a thin layer of liquid metal (GaInSn). A permanent magnet is installed on a rail beneath the container and is moved with a constant velocity U0, which in turn induces a flow inside the liquid metal due to Lorentz forces. The setup allows experiments in a parameter range that is accessible by direct numerical simulations (DNS). We present results from realizations with four different parameter sets, covering flows with stable stationary vortex structures in the reference system of the moving magnet as well as time-dependent flow regimes. Although the liquid metal layer is very thin, the flow shows a highly three-dimensional character in the near and in the far wake of the magnetic obstacle. We conclude that the streamline visualization in the experiment (using gas bubbles at the surface of the liquid metal layer) is insufficient to picture the flow structure occurring in the liquid metal. To underpin our conclusions, we introduce a modified numerical model which aims to mimic the movement of these gas bubbles. Although this model is a strong simplification of the highly complicated behavior of bubbles at a fluid-fluid interface, it captures the main effects and provides a good reproduction of the experimental results. Furthermore, transient effects are investigated when the flow is initiated, i.e., when the magnet approaches the container and crosses its front wall.We conclude that the process of vortex formation is accompanied by a decrease of the streamwise component of the Lorentz force compared to the time when the fluid is still quiescent. This decrease occurs only for flows with stable vortex structures, which might be of interest for practical applications like Lorentz force velocimetry. The Lorentz forces obtained from our DNS are in good agreement with the values measured in experiment.
http://dx.doi.org/10.1103/PhysRevFluids.1.043601
Magnetohydrodynamic duct and channel flows at finite magnetic Reynolds numbers. - Ilmenau : Universitätsbibliothek, 2016. - 1 Online-Ressource (vi, 119 Seiten)
Technische Universität Ilmenau, Dissertation 2016
Magnetohydrodynamische Kanalströmungen (MHD-KS) wurden bisher nur bei vernachlässigbar kleiner magnetischer Reynoldszahl $R_m$ untersucht. Bei endlichem $R_m$ wird das sekundäre Magnetfeld signifikant, was zu einer gekoppelten Entwicklung von Magnetfeld und leitfähiger Strömung führt. Die Charakterisierung solcher Strömungen ist essentiell für das Verständnis von wandbegrenzter MHD-Turbulenz und in Anwendungen wie z.B. elektromagnetischen Pumpen und der induktiven Strömungsmessung. Die Dissertation stellt ein Verfahren für die direkte numerische Simulation (DNS) von MHD-KS bei endlichem $R_m$ vor, welches dann auf drei Probleme angewendet wird. Am Anfang der Arbeit steht eine kurze Übersicht zur MHD und zum Stand des Wissens zu MHD-KS. Danach folgt eine Beschreibung des physikalischen Modells für die MHD-KS mit elektrisch isolierenden Wänden. Im Hauptteil der Arbeit wird ein hybrides Berechnungsverfahren entwickelt und implementiert, das auf finiten Differenzen sowie dem Randintegralverfahren basiert. Es dient zur Lösung der Induktionsgleichung mit Randbedingungen, die für einen stetigen Anschluss des Magnetfelds auf den Gebietsrändern zwischen Innen- und Außenraum sorgen. Eine detaillierte Verifikation des Codes wird durch Vergleich mit der quasistatischen Näherung vorgenommen. Anschließend wird das Zeitverhalten der Lorentzkraft bei beschleunigter Bewegung einer leitfähigen rechteckigen Stange in einem lokalisierten Magnetfeld untersucht. Die Zeitantwort der Lorentzkraft hängt linear von $R_m$ ab und stimmt gut mit Experimenten überein. Für große $R_m$ sind die Maximalwerte der Lorentzkraft umgekehrt proportional zu $R_m$. Im Weiteren wird das dynamische "Weglaufen" der Geschwindigkeit infolge von magnetischer Flussverdrängung in einer zweidimensionalen MHD-KS untersucht. Der Vergleich mit einem eindimensionalen Modell zeigt eine gute Übereinstimmung für das sogenannte Hartmann-Regime und den Bifurkationspunkt zum sogenannten Poiseuille-Regime, bei dem allerdings die Geschwindigkeit vom Modell überschätzt wird. Die Wellenlänge des Magnetfelds ist für den Bifurkationspunkt entscheidend. Abschließend wird die turbulente Hartmannströmung untersucht. Bei endlichem $R_m$ verschiebt sich die Relaminarisierung zu größeren Hartmannzahlen und es wird großskalige Turbulenz angeregt. Zwischen den Shercliff-Schichten und dem Strömungskern verringern sich die Reynoldsspannungen mit steigendem $R_m$, was zu höherer mittlerer Geschwindigkeit und flacheren Geschwindigkeitsprofilen führt.
http://nbn-resolving.de/urn:nbn:de:gbv:ilm1-2016000148
Transition to turbulence in Hunt's flow. - In: Proceedings of the 10th PAMIR International Conference on Fundamental and Applied MHD, (2016), S. 27-31
Transition in a pressure driven magnetohydrodynamic duct flow, subjected to a uniform transverse magnetic field is studied with direct numerical simulations. The electric boundary conditions correspond to a Hunt's flow regime, with perfectly insulating side walls and perfectly conducting Hartmann walls. The flow forms strong side wall jets at already moderate fields, represented here by Hartmann number Ha = 100. While increasing Reynolds number Re, various unsteady regimes are identified: Ting-Walker (TW) vortices at the side walls, elongated vortices, jet detachment and finally, fully turbulent side-wall jets. We have also found hysteresis behaviour in a broad range of Re.
Numerical simulation of jet flow in a straight duct under streamwise magnetic field. - In: Proceedings of the 10th PAMIR International Conference on Fundamental and Applied MHD, (2016), S. 229-233
The spatially evolving flow of a liquid-metal jet in a duct with streamwise uniform magnetic field is studied by direct numerical simulation. In contrast to the case of an imposed transverse field, only the turbulent fluctuations of the flow are affected in this setup. They tend to form structures elongated along the applied magnetic field. In that case turbulence becomes strongly anisotropic and, therefore, may completely change its properties. One interesting and important property is the flow stabilization, i.e. transition to turbulence can be largely delayed due to the stabilizing effect of the magnetic field. This occurs in the presence of moderate magnetic fields. In a strong magnetic field the flow becomes unsteady due to travelling waves that propagate along the field.
Magnetic obstacle: results from numerical reconstructions of experimental data. - In: Proceedings of the 10th PAMIR International Conference on Fundamental and Applied MHD, (2016), S. 574-578
We present results from numerical reconstructions of magnetic obstacle experiments in which a moving permanent magnet drives a free-surface flow in a container filled with liquid metal (GaInSn). The results cover different flow regimes, such as stationary (in the reference system of the moving magnet) so-called six vortex structures, as well as time-dependent flows. The numerical results show that - although the liquid metal layer is thin - the flow structure is highly three dimensional. We conclude that the experimental technique for streamline visualization (gas bubbles at the surface of the liquid metal) is insufficient to picture the occurring flow structure. To underpin our conclusion, we introduce a modified numerical model that aims to mimic the movement of the gas bubbles. The results of the modified model and the experiments are in excellent agreement. Furthermore, Lorentz forces obtained from simulations match well with those from the experiments.
Scaling of turbulent heat and momentum transfer for magnetoconvection in a vertical magnetic field. - In: Proceedings of the 10th PAMIR International Conference on Fundamental and Applied MHD, (2016), S. 532-536
Turbulent MHD channel flows under streamwise magnetic field. - In: Proceedings of the 10th PAMIR International Conference on Fundamental and Applied MHD, (2016), S. 238-242
A streamwise magnetic field leads to turbulent drag reduction in channel flow of a conducting liquid due to the selective Joule damping of certain flow structures. Near the walls, the turbulent mean velocity profile retains the logarithmic layer but the von Kármán constant decreases with increasing magnetic field strength. In the outer region, the flow is characterized by persistent streaky structures of large streamwise extent, which lead to a rather flat mean velocity profile. In addition, the streamwise velocity fluctuation profiles develop a pronounced second peak upon increasing the magnetic induction as well as a second logarithmic layer that increases in steepness.