Numerical study of impeller-driven von Kármán flows via a volume penalization method

Abstract

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 counter-rotating 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.

Keywords

• von Kármán flow
• turbulence
• moving boundaries
• volume penalization
• pseudospectral method
• 47.27.E-