Numerical simulation of the Von-Kármán-Sodium dynamo experiment

Abstract : We present hydrodynamic and magnetohydrodynamic (MHD) simulations of liquid sodium 1 flows in the Von-Kármán-Sodium (VKS) setup. The counter-rotating impellers made of 2 soft iron that were used in the successful 2006 experiment are realistically represented 3 by means of a pseudo-penalty method. Hydrodynamic simulations are performed at high 4 kinetic Reynolds numbers using a Large Eddy Simulation technique. The results compare 5 well with the experimental data: the flow is laminar and steady or slightly fluctuating at 6 small angular frequencies; small scales fill the bulk and a Kolmogorov-like spectrum is 7 obtained at large angular frequencies. Near the tips of the blades the flow is expelled and 8 takes the form of intense helical vortices. The equatorial shear layer acquires a wavy shape 9 due to three coherent co-rotating radial vortices as observed in hydrodynamic experi-10 ments. MHD computations are performed: at fixed kinetic Reynolds number, increasing 11 the magnetic permeability of the impellers reduces the critical magnetic Reynolds num-12 ber for dynamo action; at fixed magnetic permeability, increasing the kinetic Reynolds 13 number also decreases the dynamo threshold. Our results support the conjecture that the 14 critical magnetic Reynolds number tends to a constant as the kinetic Reynolds number 15 tends to infinity. The resulting dynamo is a mostly axisymmetric axial dipole with an az-16 imuthal component concentrated near the impellers as observed in the VKS experiment.
Type de document :
Pré-publication, Document de travail
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Contributeur : Jean-Luc Guermond <>
Soumis le : lundi 21 août 2017 - 18:08:26
Dernière modification le : jeudi 11 janvier 2018 - 06:25:47


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  • HAL Id : hal-01575765, version 1


C Nore, D Castanon Quiroz, L Cappanera, J.-L Guermond. Numerical simulation of the Von-Kármán-Sodium dynamo experiment. 2017. 〈hal-01575765〉



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