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.

Conditional statistics of homogeneous isotropic turbulent flow is investigated by means of high-Reynolds number direct numerical simulations performed with 2048 3 collocation points. Eulerian as well as Lagrangian velocity increment statistics under several conditions are analyzed and compared. In agreement with experimental data longitudinal probability density functions P (δ || l u|ǫ l ) conditioned on a scale-averaged energy dissipation rate are close to Gaussian distributions over all scales within the inertial range of scales. Also transverse increments conditioned on either the dissipation rate or the square of the vorticity have quasi-Gaussian probability distribution functions (PDFs). Concerning Lagrangian statistics we found that conditioning on a trajectory averaged energy-dissipation rate ǫ τ significantly reduces the scale dependence of the increment PDFs P (δ τ u i |ǫ τ ). By means of dimensional arguments we propose a novel condition for Lagrangian increments which is shown to reduce even more the flatness of the corresponding PDFs and thus intermittency in the inertial range of scales. The conditioned Lagrangian PDF corresponding to the smallest increment considered is reasonably well described by the K41-prediction of the PDF of acceleration. Conditioned structure functions show approximately K41-scaling with a larger scaling range than the unconditioned ones.

No abstract

No abstract

No abstract