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 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.

Mean-field model of the von Kármán sodium dynamo experiment using soft iron impellers

“…This conundrum cannot be unequivocally resolved num erically either, yet, since sim ulating num erically the w hole C adarache experim ent, including the rotating im pellers, is not feasible w ith the num erical tools currently available. Som e team s are w orking in this direction, though [5], in cluding ours, and it is reasonable to think that num erical sim ulations o f the VKS experim ent at m oderate kinetic and m agnetic Reynolds num bers could be done in the near future.…”

“…In the following, in an effort to minimize the number of modeling parameters, we neglect the P effect and assume that a is diagonal. The components of the tensor a can be estimated by evaluating the interaction between the mean-field B and the jets trapped between the blades, which we assume to flow outward in the radial direction (see [5,12]). As explained in Fig.…”

Effects of turbulence, resistivity and boundary conditions on helicoidal flow collimation: Consequences for the Von-Kármán-Sodium dynamo experiment

“…HD simulations performed with different R e and Γ values show a radial helicoidal vortex generated by the impinging flow at the impeller as evidenced in F. Ravelet [2012] and S. Kreuzahler [2014]. The [KE] grows from 4 · 10 5 to 6.5 · 10 5 J as R e increases from 200 to 1000, while the [KH] oscillates around values close to 220 ms −2 , pointing out that the vortex becomes more and more concentrated (Figure 2A and B).…”

Direct numerical simulation of the axial dipolar dynamo in the Von Kármán Sodium experiment

“…The fluid is liquid sodium heated at 120 • C. The set-up uses two concentric cylindrical containers: one of radius R cyl = 206 mm (with a very small thickness) and another thick one, made of copper, of inner and outer ,ah e i g h t of 41 mm and a thickness of 5 mm. The distance between the inner faces of the disks is set to 370 mm such that the aspect ratio of the fluid is 370/206 = 1.8a si nt h eT M 7 3 configuration used in [3] and the TM28 configuration that has been numerically studied in [5] with a penalty method similar to the one used in the present study. The liquid sodium in the inner cylinder is pushed by the convex side of the blades (called the unscooping sense of rotation or (+) sense).…”