Effects of turbulence, resistivity and boundary conditions on helicoidal flow collimation: consequences for the Von-K\'arm\'an-Sodium dynamo experiment

TL;DR

This study uses simulations to explore how turbulence, resistivity, and boundary conditions influence magnetic field collimation in the Von-Karman-Sodium dynamo experiment, highlighting the role of ferromagnetic walls and vortex dynamics.

Contribution

It provides new insights into the effects of boundary conditions and turbulence on magnetic field collimation in liquid sodium flows relevant to dynamo experiments.

Findings

Ferromagnetic walls enhance magnetic and flow collimation.

Vortex position shifts with impeller velocity and flow angle.

Precessing vortices reinforce magnetic field collimation.

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-Karman-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-Karman-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. The location of the helicoidal coherent vortex in between the blades changes with the impinging velocity. It becomes closer to the upstream blade and 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. We 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.