Impact of Impellers on the Axisymmetric Magnetic Mode in the VKS2 Dynamo Experiment

In the von Kármán Sodium 2 (VKS2) successful dynamo experiment of September 2006, the observed magnetic field showed a strong axisymmetric component, implying that nonaxisymmetric components of the flow field were acting. By modeling the induction effect of the spiraling flow between the blades of the impellers in a kinematic dynamo code, we find that the axisymmetric magnetic mode is excited. The control parameters are the magnetic Reynolds number of the mean flow, the coefficient measuring the induction effect $\alpha$, and the type of boundary conditions. We show that using realistic values of $\alpha$, the observed critical magnetic Reynolds number, $R{m}^c\approx 32$, can be reached easily with ferromagnetic boundary conditions. We conjecture that the dynamo action achieved in this experiment may not be related to the turbulence in the bulk of the flow, but rather to the $\alpha$ effect induced by the impellers.

Figure 1

Geometry of the computational domain in a meridional plane. The axisymmetric meridional flow ($U_r,U_z$) is represented on the left with arrows. On the right the isovalues of $U_{\theta }$ are plotted. The radii $R_i$ and height $H$ as well as the conductivities ${\sigma }_i$ are defined in the text.

Figure 2

Sketch of the top impeller with eight radial blades attached to the disk. Because of the rotation of the disk (gray arrow on the top), radial helical vortices are produced between the blades (thick white arrows). An axisymmetric azimuthal field $(\mathbf{B}·{\mathbf{e}}_{\theta }){\mathbf{e}}_{\theta }$ (thin line) is distorted leading to eight magnetic loops.

Figure 3

Dynamo threshold $R{m}^c$ versus $-\alpha$, for (×, ▵) $m=0$, (□, ◊) $m=1$ and where (FM) and (I) indicate ferromagnetic and insulating boundary conditions, respectively.

Figure 4

Top: Geometry of the $m=0$ (FM) growing magnetic field for $R{m}^c=32$, $|\alpha |=2.2>|{\alpha }_c|=2.1$. The three cylinders are also represented. The lines correspond to the positive isovalues of $B_{\theta }$ and the arrows to the meridional field ($B_r,B_z$). Bottom: Isovalue of 25% of the maximum energy plotted in the 3D domain, together with some field lines.