Magnetohydrodynamics measurements in the von Kármán sodium experiment

Bourgoin, Mickaël; Marié, Louis; Pétrélis, François; Gasquet, C.; Guigon, A.; Luciani, J.-B.; Moulin, Marc; Namer, F.; Burguete, Javier; Chiffaudel, Arnaud; Daviaud, François; Fauve, S.; Odier, Philippe; Pinton, Jean‐François

doi:10.1063/1.1497376

Cited by 100 publications

(165 citation statements)

References 27 publications

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“…The first process is easily modeled in an axisymmetric system: toroidal differential rotation of a highly-conducting fluid sweeps the pre-existing poloidal field in the toroidal direction creating toroidal field. This phenomenon, known as the ω-effect, is efficient at producing magnetic field and has been observed experimentally [2,3,4]. The second ingredient to the model is more subtle, as toroidal currents must be generated to reinforce the original axisymmetric poloidal field.…”

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Observation of a Turbulence-Induced Large Scale Magnetic Field

et al. 2006

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An axisymmetric magnetic field is applied to a spherical, turbulent flow of liquid sodium. An induced magnetic dipole moment is measured which cannot be generated by the interaction of the axisymmetric mean flow with the applied field, indicating the presence of a turbulent electromotive force. It is shown that the induced dipole moment should vanish for any axisymmetric laminar flow. Also observed is the production of toroidal magnetic field from applied poloidal magnetic field (the ω-effect). Its potential role in the production of the induced dipole is discussed. Many stars and planets generate their own nearlyaxisymmetric magnetic fields. Understanding the mechanism by which these fields are generated is a problem of fundamental importance to astrophysics. These dynamos are sometimes modeled using two components: a process which generates toroidal magnetic field from poloidal field and a feedback mechanism which reinforces the poloidal field [1]. The first process is easily modeled in an axisymmetric system: toroidal differential rotation of a highly-conducting fluid sweeps the pre-existing poloidal field in the toroidal direction creating toroidal field. This phenomenon, known as the ω-effect, is efficient at producing magnetic field and has been observed experimentally [2,3,4]. The second ingredient to the model is more subtle, as toroidal currents must be generated to reinforce the original axisymmetric poloidal field. Cowling's theorem [5] excludes the possibility of an axisymmetric flow generating such currents so some symmetry-breaking mechanism is required.The usual mechanism invoked [6] is a turbulent electromotive force (EMF), E = ṽ ×b , whereby small scale fluctuations in the velocity and magnetic fields break the symmetry and interact coherently to generate the large scale magnetic field. This EMF is sometimes expanded [7] in terms of transport coefficients about the mean magnetic field: E = αB + β∇ × B + γ × B; α is characterized by helicity in the turbulence, β by enhanced diffusion and γ by a gradient in the intensity of the turbulence. α is of particular interest as it results in current flowing parallel to a magnetic field, and when coupled with the ω-effect can generate the toroidal currents needed to reinforce the poloidal field. Experimental evidence for mean-field EMFs (such as the α-effect) in turbulent flows has been scarce. Three experiments, relying on a laminar α-effect, have generated an EMF [8] and dynamo action [9,10], but heavilyconstrained flow geometries were used to produce the needed helicity; the role of turbulence was ambiguous. Experiments with unconstrained flows have provided evidence for turbulent EMFs, though not the turbulent α- effect. Reighard and Brown [11] have attributed a measured reduction in the conductivity of a turbulent flow of sodium to the β-effect. Pétrélis et al. have observed [12] distortion of a magnetic field similar to an α-effect (currents generated in the direction of an applied magnetic field) and postulate that turbulence may be responsible for...

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Observation of a Turbulence-Induced Large Scale Magnetic Field

et al. 2006

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“…Induced magnetic fields orthogonal to the applied ones have also been observed in flows of liquid metals: generation of a toroidal field from an axial one by differential rotation (the ''! effect'') [3][4][5], and generation of an electric current parallel to the applied magnetic field (the '' effect'') [6]. These induction effects are the key mechanisms of most astrophysical and geophysical dynamo models [7][8][9][10], as well as in the recent experimental observations of self-generation of a magnetic field by a flow of liquid sodium [11].…”

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“…1). The sodium flow is operated in a loop that has been described elsewhere together with the details of the experimental setup [5]. In this study, the flow is driven by rotating one of the two disks of radius R located at position (1) or (2) in a cylindrical vessel, 410 mm in inner diameter and 400 mm in length.…”

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Nonlinear Magnetic Induction by Helical Motion in a Liquid Sodium Turbulent Flow

et al. 2003

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We report an experimental study of the magnetic fieldB B induced by a turbulent swirling flow of liquid sodium submitted to a transverse magnetic fieldB B 0 . We show that the induced field can behave nonlinearly as a function of the magnetic Reynolds number, R m . At low R m , the induced mean field along the axis of the flow, hB x i, and the one parallel toB B 0 , hB y i, first behave like R 2 m , whereas the third component, hB z i, is linear in R m . The sign of hB x i is determined by the flow helicity. At higher R m ,B B strongly depends on the local geometry of the mean flow: hB x i decreases to zero in the core of the swirling flow but remains finite outside. We compare the experimental results with the computed magnetic induction due to the mean flow alone.

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“…The flow needs to be highly turbulent in order for nonlinearities to develop in the magnetic induction. Numerous experimental [25,26] or numerical [27,28] studies have then been dedicated to magneto-hydrodynamics turbulence in the Von Kármán geometry. In the latter work, the flow has been optimized using a water model experiment, varying the driving impeller configuration, well described in [21].…”

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Turbulence modeling of the Von Kármán flow: Viscous and inertial stirrings

Poncet

Schiestel

Monchaux

2008

International Journal of Heat and Fluid Flow

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The present work considers the turbulent Von Kármán flow generated by two counter-rotating smooth flat (viscous stirring) or bladed (inertial stirring) disks.Numerical predictions based on one-point statistical modeling using a low Reynolds number second-order full stress transport closure (RSM model) are compared to velocity measurements performed at CEA (Commissariatà l'Énergie Atomique, France). The main and significant novelty of this paper is the use of a drag force in the momentum equations to reproduce the effects of inertial stirring instead of modelling the blades themselves. The influences of the rotational Reynolds number, the aspect ratio of the cavity, the rotating disk speed ratio and of the presence or not of impellers are investigated to get a precise knowledge of both the dynamics and the turbulence properties in the Von Kármán configuration. In particular, we highlighted the transition between the merged and separated boundary layer regimes and the one between the Batchelor [1] and the Stewartson [2] flow structures in the smooth disk case. We determined also the transition between the one cell and the 2 two cell regimes for both viscous and inertial stirrings.

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Magnetohydrodynamics measurements in the von Kármán sodium experiment

Cited by 100 publications

References 27 publications

Observation of a Turbulence-Induced Large Scale Magnetic Field

Observation of a Turbulence-Induced Large Scale Magnetic Field

Nonlinear Magnetic Induction by Helical Motion in a Liquid Sodium Turbulent Flow

Turbulence modeling of the Von Kármán flow: Viscous and inertial stirrings

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