Jānis Priede

Helical magnetorotational instability in a Taylor-Couette flow with strongly reduced Ekman pumping

The magnetorotational instability (MRI) is thought to play a key role in the formation of stars and black holes by sustaining the turbulence in hydrodynamically stable Keplerian accretion disks. In previous experiments the MRI was observed in a liquid metal Taylor-Couette flow at moderate Reynolds numbers by applying a helical magnetic field. The observation of this helical MRI (HMRI) was interfered with a significant Ekman pumping driven by solid end caps that confined the instability only to a part of the Taylor-Couette cell. This paper describes the observation of the HMRI in an improved Taylor-Couette setup with the Ekman pumping significantly reduced by using split end caps. The HMRI, which now spreads over the whole height of the cell, appears much sharper and in better agreement with numerical predictions. By analyzing various parameter dependencies we conclude that the observed HMRI represents a self-sustained global instability rather than a noise-sustained convective one.

Linear stability of Hunt's flow

We analyse numerically the linear stability of the fully developed flow of a liquid metal in a square duct subject to a transverse magnetic field. The walls of the duct perpendicular to the magnetic field are perfectly conducting whereas the parallel ones are insulating. In a sufficiently strong magnetic field, the flow consists of two jets at the insulating walls and a near-stagnant core. We use a vector stream function formulation and Chebyshev collocation method to solve the eigenvalue problem for small-amplitude perturbations. Due to the two-fold reflection symmetry of the base flow the disturbances with four different parity combinations over the duct cross-section decouple from each other. Magnetic field renders the flow in a square duct linearly unstable at the Hartmann number Ha ≈ 5.7 with respect to a disturbance whose vorticity component along the magnetic field is even across the field and odd along it. For this mode, the minimum of the critical Reynolds number Re c ≈ 2018, based on the maximal velocity, is attained at Ha ≈ 10. Further increase of the magnetic field stabilizes this mode with Re c growing approximately as Ha. For Ha > 40, the spanwise parity of the most dangerous disturbance reverses across the magnetic field. At Ha ≈ 46 a new pair of most dangerous disturbances appears with the parity along the magnetic field being opposite to that of the previous two modes. The critical Reynolds number, which is very close for both of these modes, attains a minimum, Re c ≈ 1130, at Ha ≈ 70 and increases as Re c ≈ 91 Ha 1/2 for Ha » 1. The asymptotics of the critical wavenumber is k c ≈ 0.525Ha 1/2 while the critical phase velocity approaches 0.475 of the maximum jet velocity.

Contactless Electromagnetic Phase-Shift Flowmeter for Liquid Metals

We present a concept and test results of an eddy-current flowmeter for liquid metals. The flow rate is determined by applying a weak ac magnetic field to a liquid metal flow and measuring the flow-induced phase disturbance in the external electromagnetic field. The phase disturbance is found to be more robust than that of the amplitude used in conventional eddy-current flowmeters. The basic characteristics of this type of flowmeter are analysed using simple theoretical models, where the flow is approximated by a solid body motion. Design of such a flowmeter is presented and its test results are reported.

Single-magnet rotary flowmeter for liquid metals

We present a theory of single-magnet flowmeter for liquid metals and compare it with experimental results. The flowmeter consists of a freely rotating permanent magnet, which is magnetized perpendicularly to the axle it is mounted on. When such a magnet is placed close to a tube carrying liquid metal flow, it rotates so that the driving torque due to the eddy currents induced by the flow is balanced by the braking torque induced by the rotation itself. The equilibrium rotation rate, which varies directly with the flow velocity and inversely with the distance between the magnet and the tube, is affected neither by the electrical conductivity of the metal nor by the magnet strength. We obtain simple analytical solutions for the force and torque on slowly moving and rotating magnets due to eddy currents in a layer of infinite horizontal extent. The predicted equilibrium rotation rates qualitatively agree with the magnet rotation rate measured on a liquid sodium flow in stainless steel duct.

Absolute versus convective helical magnetorotational instability in a Taylor-Couette flow.

We analyze numerically the magnetorotational instability of a Taylor-Couette flow in a helical magnetic field [helical magnetorotational instability (HMRI)] using the inductionless approximation defined by a zero magnetic Prandtl number (Pr_{m}=0) . The Chebyshev collocation method is used to calculate the eigenvalue spectrum for small-amplitude perturbations. First, we carry out a detailed conventional linear stability analysis with respect to perturbations in the form of Fourier modes that corresponds to the convective instability which is not in general self-sustained. The helical magnetic field is found to extend the instability to a relatively narrow range beyond its purely hydrodynamic limit defined by the Rayleigh line. There is not only a lower critical threshold at which HMRI appears but also an upper one at which it disappears again. The latter distinguishes the HMRI from a magnetically modified Taylor vortex flow. Second, we find an absolute instability threshold as well. In the hydrodynamically unstable regime before the Rayleigh line, the threshold of absolute instability is just slightly above the convective one although the critical wavelength of the former is noticeably shorter than that of the latter. Beyond the Rayleigh line the lower threshold of absolute instability rises significantly above the corresponding convective one while the upper one descends significantly below its convective counterpart. As a result, the extension of the absolute HMRI beyond the Rayleigh line is considerably shorter than that of the convective instability. The absolute HMRI is supposed to be self-sustained and, thus, experimentally observable without any external excitation in a system of sufficiently large axial extension.

Force-free and contactless sensor for electromagnetic flowrate measurements

The magnetorotational instability (MRI) is considered to be one of the most powerful sources of turbulence in hydrodynamically stable quasi-Keplerian flows, such as those governing accretion disk flows. Although the linear stability of these flows with 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 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 (DNS) for the two magnetic Prandtl numbers of

The influence of current collectors on Tayler instability and electro-vortex flows in liquid metal batteries

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Linear stability of magnetohydrodynamic flow in a perfectly conducting rectangular duct

and

Inviscid helical magnetorotational instability in cylindrical Taylor-Couette flow.

1

Influence of growth parameters and melt convection on the solid-liquid interface during RF-floating zone crystal growth of intermetallic compounds

. Inside of the instability domains modes with different axial wavenumbers dominate, resulting in sub-domains of instabilities, which appear different for each