Ambivalent effects of added layers on steady kinematic dynamos in cylindrical geometry: application to the VKS experiment

Stefani, Frank; Xu, Mingtian; Gerbeth, Günter; Ravelet, Florent; Chiffaudel, Arnaud; Daviaud, François; Léorat, J.

doi:10.1016/j.euromechflu.2006.02.002

Cited by 53 publications

(89 citation statements)

References 28 publications

(77 reference statements)

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“…[33] allows a description of the amplitude of the magnetic vector potential by an equation similar to Eq. (10). A parametric resonance (also called swing excitation) is observed when the frequency of the perturbing velocity pattern is twice the natural frequency of the dynamo.…”

Section: -11mentioning

confidence: 99%

“…In an idealizing model the mean axisymmetric flow between counter-rotating impellers comprises two toroidal and two poloidal eddies (so-called s2t2 topology), and it is well known that this flow is able to drive a dynamo [5,6]. Various attempts in different geometries have been made (numerically as well as experimentally) in order to examine dynamo action driven by such a flow [4,[7][8][9][10][11][12][13][14][15][16][17][18][19][20]. However, so far, experimental dynamo action driven by a von Kármán-like flow is obtained only at the VKS facility and only when at least one of the flow-driving impellers is made of soft iron with a large relative permeability.…”

Section: Introductionmentioning

confidence: 99%

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Impact of time-dependent nonaxisymmetric velocity perturbations on dynamo action of von Kármán-like flows

2012

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We present numerical simulations of the kinematic induction equation in order to examine the dynamo efficiency of an axisymmetric von Kármán-like flow subject to time-dependent nonaxisymmetric velocity perturbations. The numerical model is based on the setup of the French von Kármán-sodium dynamo (VKS) and on the flow measurements from a water experiment conducted at the University of Navarra in Pamplona, Spain. The principal experimental observations that are modeled in our simulations are nonaxisymmetric vortexlike structures which perform an azimuthal drift motion in the equatorial plane. Our simulations show that the interactions of these periodic flow perturbations with the fundamental drift of the magnetic eigenmode (including the special case of nondrifting fields) essentially determine the temporal behavior of the dynamo state. We find two distinct regimes of dynamo action that depend on the (prescribed) drift frequency of an (m = 2) vortexlike flow perturbation. For comparatively slowly drifting vortices we observe a narrow window with enhanced growth rates and a drift of the magnetic eigenmode that is synchronized with the perturbation drift. The resonance-like enhancement of the growth rates takes place when the vortex drift frequency roughly equals the drift frequency of the magnetic eigenmode in the unperturbed system. Outside of this small window, the field generation is hampered compared to the unperturbed case, and the field amplitude of the magnetic eigenmode is modulated with approximately twice the vortex drift frequency. The abrupt transition between the resonant regime and the modulated regime is identified as a spectral exceptional point where eigenvalues (growth rates and frequencies) and eigenfunctions of two previously independent modes collapse. In the actual configuration the drift frequencies of the velocity perturbations that are observed in the water experiment are much larger than the fundamental drift frequency of the magnetic eigenmode that is obtained from our numerical simulations. Hence, we conclude that the fulfillment of the resonance condition might be unlikely in present day dynamo experiments. However, a possibility to increase the dynamo efficiency in the VKS experiment might be realized by an application of holes or fingers on the outer boundary in the equatorial plane. These mechanical distortions provoke an anchorage of the vortices at fixed positions thus allowing an adjustment of the temporal behavior of the nonaxisymmetric flow perturbations.

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Section: -11mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Impact of time-dependent nonaxisymmetric velocity perturbations on dynamo action of von Kármán-like flows

2012

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“…In the present experiment, fluctuations enter both multiplicatively, because of the turbulent velocity, and additively, due to the interaction of the velocity field with the ambient magnetic field. Finally, we note that both R c m and R 0 m are smaller than the thresholds computed with kinematic dynamo codes taking into account only the mean flow, that are in the range R c m = 43 to 150 depending on different boundary conditions on the disks and on configurations of the flow behind them [14,20].…”

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confidence: 99%

“…It has been also shown that in the case of a Ponomarenko or G. O. Roberts flows, the addition of an external wall of high permeability can decrease the dynamo threshold [19]. Finally, recent kinematic simulations of the VKS mean flow have shown that different ways of taking into account the sodium behind the disks lead to an increase of the dynamo threshold ranging from 12 % to 150 % [20]. We thought that using iron disks could screen magnetic effects in the bulk of the flow from the region behind the disks, although the actual behavior may be more complex.…”

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confidence: 99%

Generation of a Magnetic Field by Dynamo Action in a Turbulent Flow of Liquid Sodium

et al. 2007

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We report the observation of dynamo action in the VKS experiment, i.e., the generation of magnetic field by a strongly turbulent swirling flow of liquid sodium. Both mean and fluctuating parts of the field are studied. The dynamo threshold corresponds to a magnetic Reynolds number Rm ∼ 30. A mean magnetic field of order 40 G is observed 30 % above threshold at the flow lateral boundary. The rms fluctuations are larger than the corresponding mean value for two of the components. The scaling of the mean square magnetic field is compared to a prediction previously made for high Reynolds number flows.

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“…Previous numerical studies [13,14] compared the threshold values in configurations including and excluding the effect of fluid behind the disks. We reproduce here a similar behaviour of the threshold: using insulating boundary conditions directly on the disks yields a threshold value Rm c = 63.…”

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Effect of magnetic boundary conditions on the dynamo threshold of von Kármán swirling flows

et al. 2008

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Abstract. -We study the effect of different boundary conditions on the kinematic dynamo threshold of von Kármán type swirling flows in a cylindrical geometry. Using an analytical test flow, we model different boundary conditions: insulating walls all over the flow, effect of sodium at rest on the cylinder side boundary, effect of sodium behind the impellers, effect of impellers or side wall made of a high magnetic permeability material. We find that using high magnetic permeability boundary conditions decreases the dynamo threshold, the minimum being achieved when they are implemented all over the flow.Dynamo action, i.e., self-generation of magnetic field by the flow of an electrically conducting fluid, is at the origin of planetary, stellar and galactic fields [1]. Fluid dynamos have been observed only recently in laboratory experiments in Karlsruhe [2] and Riga [3] by geometrically constraining the flow lines in order to mimic laminar flows that were known analytically for their dynamo efficiency [4]. More recently, the VKS experiment displayed self-generation in a less constrained geometry, e.g. a von Kármán swirling flow generated between two counterrotating impellers in a cylinder [5]. However, until now, dynamo action in the VKS geometry has been found only when the impellers are made of soft iron. It is thus of primary importance to understand how the dynamo problem is modified by the presence of magnetic material at the flow boundaries. We address this problem here using a kinematic dynamo code in a cylindrical geometry. Two important approximations are made to simplify the study. First, an analytic test flow that mimics the geometry of the mean flow of the VKS experiment is considered. Second, the magnetic boundary conditions are taken in the limit of infinite magnetic permeability of the boundaries compared to the one of the fluid. This seems a reasonable approximation for soft iron compared to liquid sodium. Our main result is that the critical magnetic Reynolds number, Rm c , for dynamo generation is significantly decreased with boundaries of high magnetic permeability all over the flow.The VKS experimental set-up is sketched in Figure 1. A turbulent von Kármán flow of liquid sodium is generated by two counter-rotating impellers (rotation frequencies F 1 and F 2 ). The impellers are made of iron disks of radius 154 mm, fitted with 8 iron blades of height 41.2 mm, and are placed 371 mm apart in an inner cylinder of radius 206 mm and length 524 mm. It is surrounded by sodium at rest in another concentric cylindrical vessel, 578 mm in inner diameter. This has been shown to decrease the dynamo threshold in kinematic computations based on the mean flow velocity [6]. When the impellers are operated at equal and opposite rotation rates F , a statistically stationary magnetic field is generated above a magnetic Reynolds number R m ∼ 30 [5]. The large scale field involves an azimuthal component and a poloidal one which is dominated by an axial dipole. This geometry has been understood with a simple α − ω dy...

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Ambivalent effects of added layers on steady kinematic dynamos in cylindrical geometry: application to the VKS experiment

Abstract: International audienc

Cited by 53 publications

References 28 publications

Impact of time-dependent nonaxisymmetric velocity perturbations on dynamo action of von Kármán-like flows

Impact of time-dependent nonaxisymmetric velocity perturbations on dynamo action of von Kármán-like flows

Generation of a Magnetic Field by Dynamo Action in a Turbulent Flow of Liquid Sodium

Effect of magnetic boundary conditions on the dynamo threshold of von Kármán swirling flows

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