Numerical Investigation of Open and Closed Von Kármán Flow

Direct numerical simulations of flow between two counter-rotating coaxial disks with and without cylindrical side walls are carried out to investigate the developed turbulent swirling flow. The developed von K\'{a}rm\'{a}n flow when enclosed within a cylinder is defined as the closed von K\'{a}rm\'{a}n flow and without cylindrical side walls as open von K\'{a}rm\'{a}n flow. The validation study carried out for the smooth flat disks for high radius to height ratio, shows good comparison with the results reported in Gauthier \textit{et al.}\footnote{G. Gauthier et al., \textbf{J.Fluid Mech.} 121, 473, (2002)}. For high value of Reynolds number of the top disk, ($Re_t$), the flow shows the formation of negative spirals extending from the periphery of the disks to the center. On increasing the value of $Re_t$, only positive spirals are observed. From the radial, tangential and axial components of velocity field, high radial and axial bulk flow is noticed for open von K\'{a}rm\'{a}n flow. The vortex extraction method of Q-criteria shows strong and stable vortical structures formed at intermediate times, existing up to later times. The impact of coherent structures on the turbulent kinetic energy budget is ascertained. Grid convergence study is performed using three refined grids.