Studying strongly turbulent flows is still a major challenge in fluid dynamics. It is highly desirable to have comparable experiments to obtain a better understanding of the mechanisms generating turbulence. The von Kármán flow apparatus is one of those experiments that has been used in various turbulence studies by different experimental groups over the last two decades. The von Kármán flow apparatus produces a highly turbulent flow inside a cylinder vessel driven by two counterrotating impellers. The studies cover a broad range of physical systems including incompressible flows, especially water and air, magnetohydrodynamic systems using liquid metal for understanding the important topic of the dynamo instability, particle tracking to study Lagrangian type turbulence and recently quantum turbulence in super-fluid helium. Therefore, accompanying numerical studies of the von Kármán flow that compare quantitatively data with those from experiments are of high importance for understanding the mechanism producing the characteristic flow patterns. We present a direct numerical simulation (DNS) version the von Kármán flow, forced by two rotating impellers. The cylinder geometry and the rotating objects are modelled via a penalization method and implemented in a massive parallel pseudo-spectral Navier-Stokes solver. From the wide range of different impellers used in von Kármán water and sodium experiments we choose a special configuration (TM28), in order to compare our simulations with the according set of well documented water experiments.Though this configuration is different from the one in the final VKS experiment (TM73), using our method it is quite easy to change the impeller shape to the one actually used in VKS. The decomposition into poloidal and toroidal components and the mean velocity field from our simulations are in good agreement with experimental results. In addition, we analysed the flow structure close to the impeller blades, a region hardly accessible to experiments. Depending on the blade geometry different vortex topologies are found. The very promising results imply that our numerical modelling could also be applied to other physical systems and configurations driven by the von Kármán flow.

We present results from consistent dynamo simulations, where the electrically conducting and incompressible flow inside a cylinder vessel is forced by moving impellers numerically implemented by a penalization method. The numerical scheme models jumps of magnetic permeability for the solid impellers, resembling various configurations tested experimentally in the von-Karman Sodium experiment. The most striking experimental observations are reproduced in our set of simulations. In particular, we report on the existence of a time averaged axisymmetric dynamo mode, selfconsistently generated when the magnetic permeability of the impellers exceeds a threshold. We describe a possible scenario involving both the turbulent flow in the vicinity of the impellers and the high magnetic permeability of the impellers.PACS numbers: 47.27.E-,47.11. Kb,47.27.ek, Introduction: Nearly a century ago, Larmor suggested that the dynamo effect, an instability converting kinetic energy into magnetic energy, could be at the origin of most astrophysical magnetic fields. The experimental observation of the dynamo instability has been a long quest requiring careful flow optimization, and has only been achieved in the Riga [1], Karlsruhe [2] and von Kármán sodium (VKS) [3] experiments. While the behavior of the two former experiments could be explained from computations using simplified flows, this is not the case for the VKS experiment -in which a strongly turbulent liquid sodium flow is driven by the counter-rotation of impellers fitted with blades in a cylindrical vessel. Two major puzzles in the understanding of the dynamo mechanism are still unanswered: (i) the dynamo instability was only observed in the presence of impellers having high magnetic permeability [4] and (ii) the time-averaged dynamo magnetic field in the saturated regime has an axial dipolar structure [5], while an equatorial dynamo dipole is expected from computations in the growing phase of the instability using the time-averaged axisymmetric flow [6].