Numerical simulation of the Tayler instability in liquid metals

Weber, Norbert; Galindo, Vladimir; Stefani, Frank; Weier, Tom; Wondrak, Thomas

doi:10.1088/1367-2630/15/4/043034

Cited by 59 publications

(95 citation statements)

References 37 publications

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“…7(c)). Note also that the disturbed potential at the interfaces is not constant as assumed previously 14 and its nonuniformity increases considerably with increasing current collectors aspect ratio (Figs. 7(b) and 7(c)).…”

Section: Exploring the Role Of Current Collectorsmentioning

confidence: 63%

“…As an improvement to Weber et al, 14 we include now also the current distribution in the current collectors. The total current density is…”

Section: Mathematical Modelmentioning

confidence: 99%

“…We apply an electrical current corresponding to Ha = 250 and vary the height H cc as well as the conductivity σ cc of the solid current collectors. Remember that the latter ones were not included by Weber et al 14 where the simplified condition ϕ = const was chosen as interface condition at top and bottom of the liquid metal column, and the currents in the current collectors were also ignored in the Biot-Savart law. From physical arguments, we anticipate that in long liquid metal columns, the effect of the detailed current distribution at the ends of the current collectors should be negligible, but that it might still be significant in shallow layers.…”

Section: Exploring the Role Of Current Collectorsmentioning

confidence: 99%

“…Similar to thermal convection, electro-vortex flows are often strongly time-dependent. Such simulation requires a much finer grid resolution than used for the TI by Weber et al 14 If we want to study the interaction of TI and electro-vortex flow, the latter should be rather weak to allow the TI to develop. Bearing these two things in mind, we choose the following simulation geometry: a relatively high liquid metal column (D = 1 m, H = 2.4 m) of aspect ratio 2.4 together with also high current collectors (H cc > 0.5 m).…”

Section: Exploring the Role Of The Feeding Linesmentioning

confidence: 99%

“…Here, a careful mixing of the alloy would be favourable, 11,12 e.g., by exploiting electro-vortex flow or thermal convection. 13 In a recent paper, 14 we made a first attempt to simulate the TI for realistic material parameters of liquid metals. Rather than applying the usual method of solving the coupled system of Navier-Stokes equation (NSE) for the velocity and induction equation for the magnetic field, we utilized an integro-differential equation approach in which the hydrodynamics is still simulated by the Navier-Stokes equation while the electromagnetic part is solved by applying a Poisson equation for the electric potential and the Biot-Savart law for the magnetic field.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2015

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The Tayler instability is a kink-type flow instability which occurs when the electrical current through a conducting fluid exceeds a certain critical value. Originally studied in the astrophysical context, the instability was recently shown to be also a limiting factor for the upward scalability of liquid metal batteries. In this paper, we continue our efforts to simulate this instability for liquid metals within the framework of an integro-differential equation approach. The original solver is enhanced by multi-domain support with Dirichlet-Neumann partitioning for the static boundaries.Particular focus is laid on the detailed influence of the axial electrical boundary conditions on the characteristic features of the Tayler instability, and, secondly, on the occurrence of electro-vortex flows and their relevance for liquid metal batteries.

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Section: Exploring the Role Of Current Collectorsmentioning

confidence: 63%

“…As an improvement to Weber et al, 14 we include now also the current distribution in the current collectors. The total current density is…”

Section: Mathematical Modelmentioning

confidence: 99%

Section: Exploring the Role Of Current Collectorsmentioning

confidence: 99%

Section: Exploring the Role Of The Feeding Linesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2015

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On the possibility of helicity oscillations in the saturation of the Tayler instability

Bonanno

Guarnieri

2017

Astron Nachr

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Recent numerical results of current-driven instabilities at low magnetic Prandtl number and high Hartmann number support the possibility of a saturation state characterized by helicity oscillations. We investigate the underlying mechanism by analyzing this possibility using a higher order Landau-Ginzburg effective Lagrangian for the weakly nonlinear amplitude dynamics, where the magnetic and velocity perturbations are linearly dependent. We find that, if the mirror symmetry between left-and right-handed modes is spontaneously broken, it is impossible to achieve an oscillating helical state. We argue that the result is likely to hold also for adding higher order terms and in the presence of an explicit symmetry breaking. We conclude that an oscillating saturating state for the Tayler instability is unlikely to depend on the interaction of chiral modes. KEYWORDS instabilities, magnetic fields, magnetohydrodynamics (MHD) INTRODUCTIONThe Tayler instability is the instability of a toroidal field in a stably stratified medium due to the presence of an electric current along the axis of symmetry (Tayler 1973). In its simplest realization, in cylindrical geometry with axial symmetry, it can be shown that a purely toroidal field B (r), where r is the cylindrical radius, is stable against axisymmetric perturbations if it satisfies the condition d(B ∕r)∕dr < 0, and to non-axisymmetric perturbations if d(r B 2 )∕dr ≤ 0. In recent times, this problem has attracted a considerable amount of analytical and numerical investigations (Bodo et al. 2013;Bonanno & Urpin 2011;Ibáñez-Mejía & Braithwaite 2015;Jouve et al. 2015) as well as experimental verification (Seilmayer et al. 2012), mainly for its relevance for our understanding of magnetism in stellar radiative regions (Braithwaite & Spruit 2015;Kitchatinov & Rüdiger 2008) but also for its implications in the tachocline stability problem and the solar dynamo (Bonanno 2013;Kitchatinov & Rüdiger 2007).In particular, it was noted in Bonanno & Urpin (2008) that the unstable modes are helical and, in the presence of a vertical component B z , also invariant under the symmetry transformation P LR z ∶ (m, ) → (−m, − ), with = B z ∕B and m the azimuthal wavenumber. This has led to the speculation that this instability can produce a magnetic -effect which, in turn, could produce a dynamo action (Rüdiger et al. 2012b; Spruit 2002). The effect of a finite Prandtl number has been investigated in cylindrical geometry (Rüdiger et al. 2012a), while the role played by a finite electrical resistivity in liquid conductor has been discussed in Weber et al. (2013). A recent work in this direction discussed the numerical evidence that the saturation state of the Tayler instability at low magnetic Prantdl number and high Hartmann number is characterized by helicity oscillations: a result of important consequences if confirmed .The aim of this paper is to extend the approach to the nonlinear saturation phase of the Tayler instability discussed in Bonanno et al. (2012) in order to account for additiona...

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Phase coherence and phase jumps in the Schwabe cycle

et al. 2020

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Guided by the working hypothesis that the Schwabe cycle of solar activity is synchronized by the 11.07‐year alignment cycle of the tidally dominant planets Venus, Earth, and Jupiter, we reconsider the phase diagrams of sediment accumulation rates in Lake Holzmaar and of methanesulfonate data in the Greenland ice core Greenland Ice Sheet Project 2 (GISP2), which are available for the period 10000–9000 cal. BP. As some half‐cycle phase jumps appearing in the output signals are, very likely, artifacts of applying a biologically substantiated transfer function, the underlying solar input signal with a dominant 11.04‐year periodicity can be considered to be mainly phase‐coherent over the 1,000‐year period in the early Holocene. For more recent times, we show that the reintroduction of a hypothesized “lost cycle” at the beginning of the Dalton minimum would lead to a real phase jump. Similarly, by analyzing various series of 14C and 10Be data and comparing them with Schove's historical cycle maxima, we support the existence of another “lost cycle” around 1565, also connected with a real phase jump. Viewed synoptically, our results lend greater plausibility to the starting hypothesis of a tidally synchronized solar cycle, which at times can undergo phase jumps, although the competing explanation in terms of a nonlinear solar dynamo with increased coherence cannot be completely ruled out.

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Numerical simulation of the Tayler instability in liquid metals

Cited by 59 publications

References 37 publications

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

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

On the possibility of helicity oscillations in the saturation of the Tayler instability

Phase coherence and phase jumps in the Schwabe cycle

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