  We present magneto-hydrodynamic simulations of liquid sodium flow with the
PLUTO compressible MHD code. We investigate the influence of the remnant
magnetic field orientation and intensity, impinging velocity field due to Ekman
pumping as well as the impeller dimensions on the magnetic field collimation by
helical flows in between the impeller blades. For a simplified cartesian
geometry we model the flow dynamics of a multi-blades impeller inspired by the
Von-Karman-Sodium (VKS) experiment. The study shows that a remnant magnetic
field oriented in the toroidal direction is the less efficient configuration to
collimate the magnetic field, although if the radial or vertical components are
not negligible the collimation is significantly improved. If the intensity of
the remnant magnetic field increases the system magnetic energy is larger but
the magnetic field collimation efficiency is the same, so the gain of magnetic
energy is smaller as the remnant magnetic field intensity increases. The
magnetic field collimation is modified if the impinging velocity field changes:
the collimation is weaker if the impinging velocity increases from Gamma=0.8 to
0.9, slightly larger if the impinging velocity decreases from Gamma=0.8 to 0.7.
The analysis of the impeller dimensions points out that the most efficient
configuration to collimate the magnetic field requires a ratio between impeller
blade height and base longitude between 0.375 - 0.5. The largest enhancement of
the hypothetical alpha^2 dynamo loop, compared to the hypothetical Omega-alpha
dynamo loop, is observed for the model that mimics TM 73 impeller configuration
rotating in the unscooping direction with a remnant magnetic field of 10^-3 T
orientated in the radial or vertical direction. The optimization trends
obtained in the parametric analysis are also confirmed in simulations with
higher resolution and turbulence degree.
