Showing papers in "Magnetohydrodynamics in 2017"

Metal pad roll instability in liquid metal batteries

Abstract: The increasing deployment of renewable energies requires three fundamental change to the electric grid: more transmission lines, a flexibilization of the demand and grid scale energy storage. Liquid metal batteries (LMBs) are considered these days as a promising means of stationary energy storage. Built as a stable density stratification of two liquid metals separated by a liquid salt, LMBs have three main advantages: a low price, a long life-time and extremely high current densities. In order to be cheap, LMBs have to be built large. However, battery currents of the order of kilo-amperes may lead to magnetohydrodynamic (MHD) instabilities, which – in the worst case – may short-circuit the thin electrolyte layer. The metal pad roll instability, as known from aluminium reduction cells, is considered as one of the most dangerous phenomena for LMBs. We develop a numerical model, combining fluid- and electrodynamics with the volume-of-fluid method, to simulate this instability in cylindrical LMBs. We explain the instability mechanism similar to that in aluminium reduction cells and give some first results, including growth rates and oscillation periods of the instability

The Tayler instability at low magnetic Prandtl numbers: Chiral symmetry breaking and synchronizable helicity oscillations

Abstract: The current-driven, kink-type Tayler instability (TI) is a key ingredient of the Tayler-Spruit dynamo model for the generation of stellar magnetic fields, but is also discussed as a mechanism that might hamper the up-scaling of liquid metal batteries. Under some circumstances, the TI involves a helical flow pattern which goes along with some alpha effect. Here we focus on the chiral symmetry breaking and the related impact on the alpha effect that would be needed to close the dynamo loop in the Tayler-Spruit model. For low magnetic Prandtl numbers, we observe intrinsic oscillations of the alpha effect. These oscillations serve then as the basis for a synchronized Tayler-Spruit dynamo model, which could possibly link the periodic tidal forces of planets with the oscillation periods of stellar dynamos.

Transitions in a magnetized quasi-laminar spherical Couette Flow

Abstract: First results of a new spherical Couette experiment are presented. The liquid metal flow in a spherical shell is exposed to a homogeneous axial magnetic field. For a Reynolds number Re=1000, we study the effect of increasing Hartmann number Ha. The resulting flow structures are inspected by ultrasound Doppler velocimetry. With a weak applied magnetic field, we observe an equatorially anti-symmetric jet instability with azimuthal wave number m=3. As the magnetic field strength increases, this instability vanishes. When the field is increased further, an equatorially symmetric return flow instability arises. Our observations are shown to be in good agreement with linear stability analysis and non-linear flow simulations.

Azimuthal Magnetorotational Instability at low and high magnetic Prandtl numbers

Abstract: Magnetorotational instability is considered to be one of the most powerful sources of turbulence in hydrodynamically stable quasi-Keplerian flows, such as those governing the accretion disk flows. Although the linear stability of these flows with an applied external magnetic field has been studied for decades, the influence of the instability on the outward angular momentum transport, necessary for the accretion of the disk, is still not well known. In this work, we model a Keplerian rotation with Taylor-Couette flow and imposed azimuthal magnetic field using both linear and nonlinear approaches. We present scalings of instability with Hartmann and Reynolds numbers via linear analysis and direct numerical simulations for two magnetic Prandtl numbers of 1.4 ·10−6 and 1. Inside the instability domains, modes with different axial wavenumbers dominate, resulting in sub-domains of instabilities which appear different for each Pm. Direct numerical simulations show the emergence of 1- and 2-frequency spatio-temporally oscillating structures for Pm = 1 close the onset of instability, as well as the significant enhancement of the angular momentum transport for Pm = 1, if compared to Pm = 1.4 ·10−6. Figs 7, Refs 11.

Nonmodal analysis of helical and azimuthal magnetorotational instabilities

Abstract: Helical and azimuthal magnetorotational instabilities operate in rotating magnetized flows with relatively steep negative or extremely steep positive shear. The corresponding lower and upper Liu limits of the shear, which determine the threshold of modal growth of these instabilities, are continuously connected when some axial electrical current is allowed to pass through the rotating fluid. We investigate the nonmodal dynamics of these instabilities arising from the non-normality of shear flow in the local approximation, generalizing the results of the modal approach. It is demonstrated that moderate transient/nonmodal amplification of both types of magnetorotational instability occurs within the Liu limits, where the system is stable according to modal analysis. We show that for the helical magnetorotational instability this magnetohydrodynamic behavior is closely connected with the nonmodal growth of the underlying purely hydrodynamic problem.

A homopolar disc dynamo experiment with liquid metal contacts

Abstract: We present experimental results of a homopolar disc dynamo constructed at CICATA-Queretaro in Mexico. The device consists of a flat, multi-arm spiral coil which is placed above a fast-spinning metal disc and connected to the latter by sliding liquid-metal electrical contacts. Theoretically, self-excitation of the magnetic field is expected at the critical magnetic Reynolds number Rm~45, which corresponds to a critical rotation rate of about 10 Hz. We measured the magnetic field above the disc and the voltage drop on the coil for the rotation rate up to 14 Hz, at which the liquid metal started to leak from the outer sliding contact. Instead of the steady magnetic field predicted by the theory we detected a strongly fluctuating magnetic field with a strength comparable to that of Earth's magnetic field which was accompanied by similar voltage fluctuations in the coil. These fluctuations seem to be caused by the intermittent electrical contact through the liquid metal. The experimental results suggest that the dynamo with the actual electrical resistance of liquid metal contacts could be excited at the rotation rate of around 21 Hz provided that the leakage of liquid metal is prevented.

Numerical calibration of a multicomponent local Lorentz force flowmeter

Abstract: Local Lorentz force velocimetry is a local velocity measurement technique for liquid metals. Due to the interaction between an electrically conducting liquid and an applied magnetic field, eddy currents and flow-braking Lorentz forces are induced in the fluid. Due to Newton’s third law, a force of the same magnitude acts on the source of the applied magnetic field, which is a permanent magnet in our case. The magnet is attached to a gauge that has been especially developed to record all three force and three torque components acting on the magnet. This new-generation local Lorentz force flowmeter (L2F2) has already been tested in a test stand for continuous casting with a 15mm cubic magnet providing an insight into the three-dimensional velocity distribution of the model melt GaInSn near the wide face of the mold. For better understanding of these results, especially regarding torque sensing, we propose dry experiments which consist in replacing a flowing liquid by a moving solid. Here, as the velocity field is fixed and steady, we are able to decrease considerably the variability and the noise of the measurements providing an accurate calibration of the system. In this paper, we present a numerical study of this dry calibration using a rotating disk made of aluminum and two different magnet systems that can be shifted along the rotation axis as well as in the radial direction.

Dynamics of a superparamagnetic microparticle chain in an oscillating magnetic field: Effects of field frequency

Abstract: Dynamics of an oscillating chain consisting of several magnetic microparticles and driven by oscillating magnetic fields with different frequencies are discussed. Because of a shorter driving time by the external field with a higher field frequency, the oscillating amplitude of the chain reduces. On the other hand, the higher field frequency leads to a faster local angular velocity. These two effects result in inconsistent behavior of the structural stability of the chain, so that the chain ruptures in a field of intermediate frequency. A dimensionless parameter of the reduced frequency is proposed to generally describe the monotonic decrease of the normalized amplitude. The phenomenon of trajectory shift triggered by the higher frequency field is also demonstrated.