Effects of turbulence, resistivity and boundary conditions on helicoidal flow collimation: Consequences for the Von-Kármán-Sodium dynamo experiment

Abstract : We present hydrodynamic and magneto-hydrodynamic simulations of a liquid sodium flow using the compressible MHD code PLUTO to investigate the magnetic field regeneration in the Von-Kármán-Sodium dynamo experiment. The aim of the study is to analyze the influence of the fluid resistivity and turbulence level on the collimation by helicoidal motions of a remnant magnetic field. We use a simplified Cartesian geometry to represent the flow dynamics in the vicinity of one cavity of a multi-blades impeller inspired by those used in the Von-Kármán-Sodium (VKS) experiment. We perform numerical simulations with kinetic Reynolds numbers up to 1000 for magnetic Prandtl numbers between 30 and 0.1. Our study shows that perfect ferromagnetic walls favour enhanced collimation of flow and magnetic fields even if the turbulence degree of the model increases. More specifically, the location of the helicoidal coherent vortex in between the blades changes with the impinging velocity. It becomes closer to the upstream blade and the impeller base if the flow incident angle is analogous to the TM73 impeller configuration rotating in the unscooping direction. This result is also obtained at higher kinetic Reynolds numbers when the helicoidal vortex undergoes a precessing motion, leading to a reinforced effect in the vortex evolution and in the magnetic field collimation when using again perfect ferromagnetic boundary conditions. Configurations with different materials used for the impeller blades and the impeller base confirm a larger enhancement of the magnetic field when perfect ferromagnetic boundary conditions are used compared with the perfect conductor case, although smaller compared to a perfect ferromagnetic impeller, as it was observed in the VKS experiment. We further estimate the efficiency of a hypothetical dynamo loop occurring in the vicinity of the impeller and discuss the relevance of our findings in the context of mean field dynamo theory.