Direct numerical simulation of the axial dipolar dynamo in the Von Kármán Sodium experiment

Nore, Caroline; Quiroz, Daniel Castanon; Cappanera, Loïc; Guermond, Jean‐Luc

doi:10.1209/0295-5075/114/65002

Cited by 16 publications

(19 citation statements)

References 29 publications

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“…Dynamo action is obtained with a magnetic field that is mainly axisymmetric and similar to the one observed in the experiment. Some of these results were announced in Nore, C. et al (2016), but in the present paper we go well beyond the range of kinetic Reynolds numbers attained in the above reference. Our main result is that the critical magnetic Reynolds number decreases as the kinetic Reynolds number increases and this number seems to converge to a constant at very large kinetic Reynolds numbers.…”

Section: Introductionsupporting

confidence: 66%

“…We have shown in Nore, C. et al (2016) that two distinct dynamo families compete at small Reynolds numbers (typically for R e < 700) and that these two families merge at larger kinetic Reynolds numbers. In the first family, the magnetic field is essentially supported on the even Fourier modes, whereas in the second family the magnetic field is essentially supported on the odd modes; these are called the 0-family and the 1-family in Nore, C. et al (2016), respectively. In the entire section we focus on R e ≥ 1.5×10 3 ; hence all the Fourier modes of the magnetic field are coupled and vary in time with the same (growth or decay) rate in the linear dynamo regime.…”

Section: Summary Of Our Previous Resultsmentioning

confidence: 85%

“…SFEMaNS has been thoroughly validated on numerous manufactured solutions and against other MHD codes (see e.g. Guermond et al (2009); Giesecke et al (2012); Nore et al (2016)). The reader who is familiar with the numerical details or is not interested in such details is now invited to jump to section 3.…”

Section: Sfemansmentioning

confidence: 99%

“…We also fix the Reynolds number to R e = 1.5×10 3 . Figures 14(a-e) The computations reported in figure 14a have been done with H 0 = 10 −3 (e z + e x ) plus a random noise of amplitude 5×10 −5 on all the Fourier modes m ≥ 1 of H 0 as in Nore, C. et al (2016). But since it turned out that this type of perturbation was a bit too large to yield a very accurate estimate of the threshold over reasonable integration times, the is estimated to be R c m = 170 ± 5.…”

Section: Influence Of the Magnetic Permeabilitymentioning

confidence: 99%

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Numerical simulation of the von Kármán sodium dynamo experiment

et al. 2018

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We present hydrodynamic and magnetohydrodynamic (MHD) simulations of liquid sodium flows in the von Kármán sodium (VKS) set-up. The counter-rotating impellers made of soft iron that were used in the successful 2006 experiment are represented by means of a pseudo-penalty method. Hydrodynamic simulations are performed at high kinetic Reynolds numbers using a large eddy simulation technique. The results compare well with the experimental data: the flow is laminar and steady or slightly fluctuating at small angular frequencies; small scales fill the bulk and a Kolmogorov-like spectrum is obtained at large angular frequencies. Near the tips of the blades the flow is expelled and takes the form of intense helical vortices. The equatorial shear layer acquires a wavy shape due to three coherent co-rotating radial vortices as observed in hydrodynamic experiments. MHD computations are performed: at fixed kinetic Reynolds number, increasing the magnetic permeability of the impellers reduces the critical magnetic Reynolds number for dynamo action; at fixed magnetic permeability, increasing the kinetic Reynolds number also decreases the dynamo threshold. Our results support the conjecture that the critical magnetic Reynolds number tends to a constant as the kinetic Reynolds number tends to infinity. The resulting dynamo is a mostly axisymmetric axial dipole with an azimuthal component concentrated near the impellers as observed in the VKS experiment. A speculative mechanism for dynamo action in the VKS experiment is proposed.

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Section: Introductionsupporting

confidence: 66%

Section: Summary Of Our Previous Resultsmentioning

confidence: 85%

Section: Sfemansmentioning

confidence: 99%

Section: Influence Of the Magnetic Permeabilitymentioning

confidence: 99%

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Numerical simulation of the von Kármán sodium dynamo experiment

et al. 2018

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“…This can be understood from the flow behind the impellers, where a strong shear layer produces a strong ω-effect (this shear layer is not present in Ref. [19]), and from continuity conditions of the electromagnetic fields leading to magnetic field line refraction at high µ r [8,15,19]. A second observation is that, slightly above the impeller, the strong shear layer above the blades (of opposite sign as compared to behind the disk) leads to an H φ component with the opposite sign of that behind the impeller.…”

Section: The Magnetic Energy Is Defined Asmentioning

confidence: 99%

Dynamo Enhancement and Mode Selection Triggered by High Magnetic Permeability

et al. 2017

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We present results from consistent dynamo simulations, where the electrically conducting and incompressible flow inside a cylinder vessel is forced by moving impellers numerically implemented by a penalization method. The numerical scheme models jumps of magnetic permeability for the solid impellers, resembling various configurations tested experimentally in the von-Karman Sodium experiment. The most striking experimental observations are reproduced in our set of simulations. In particular, we report on the existence of a time averaged axisymmetric dynamo mode, selfconsistently generated when the magnetic permeability of the impellers exceeds a threshold. We describe a possible scenario involving both the turbulent flow in the vicinity of the impellers and the high magnetic permeability of the impellers.PACS numbers: 47.27.E-,47.11. Kb,47.27.ek, Introduction: Nearly a century ago, Larmor suggested that the dynamo effect, an instability converting kinetic energy into magnetic energy, could be at the origin of most astrophysical magnetic fields. The experimental observation of the dynamo instability has been a long quest requiring careful flow optimization, and has only been achieved in the Riga [1], Karlsruhe [2] and von Kármán sodium (VKS) [3] experiments. While the behavior of the two former experiments could be explained from computations using simplified flows, this is not the case for the VKS experiment -in which a strongly turbulent liquid sodium flow is driven by the counter-rotation of impellers fitted with blades in a cylindrical vessel. Two major puzzles in the understanding of the dynamo mechanism are still unanswered: (i) the dynamo instability was only observed in the presence of impellers having high magnetic permeability [4] and (ii) the time-averaged dynamo magnetic field in the saturated regime has an axial dipolar structure [5], while an equatorial dynamo dipole is expected from computations in the growing phase of the instability using the time-averaged axisymmetric flow [6].

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Laboratory Experiments and Numerical Simulations on Magnetic Instabilities

Stefani

Gellert

Kasprzyk

et al. 2018

Magnetic Fields in the Solar System

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Magnetic fields of planets, stars and galaxies are generated by selfexcitation in moving electrically conducting fluids. Once produced, magnetic fields can play an active role in cosmic structure formation by destabilizing rotational flows that would be otherwise hydrodynamically stable. For a long time, both hydromagnetic dynamo action as well as magnetically triggered flow instabilities had been the subject of purely theoretical research. Meanwhile, however, the dynamo effect has been observed in large-scale liquid sodium experiments in Riga, Karlsruhe and Cadarache. In this paper, we summarize the results of some smaller liquid metal experiments devoted to various magnetic instabilities such as the helical and the azimuthal magnetorotational instability, the Tayler instability, and the different instabilities that appear in a magnetized spherical Couette flow. We conclude with an outlook on a large scale Tayler-Couette experiment using liquid sodium, and on the prospects to observe magnetically triggered instabilities of flows with positive shear.

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Direct numerical simulation of the axial dipolar dynamo in the Von Kármán Sodium experiment

Cited by 16 publications

References 29 publications

Numerical simulation of the von Kármán sodium dynamo experiment

Numerical simulation of the von Kármán sodium dynamo experiment

Dynamo Enhancement and Mode Selection Triggered by High Magnetic Permeability

Laboratory Experiments and Numerical Simulations on Magnetic Instabilities

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