The flow dynamics in a short annulus with rotating end-walls

Abstract

The paper reports on the 3D direct numerical simulation (DNS) results of the flow in a short annulus of aspect ratios 3.8–4.8 and radius ratios 0.45, 0.5 with end-walls attached to a rotating inner cylinder. The research is focused on the bifurcation processes occurring in the local unsteady area, existing at very low Reynolds numbers (Re = 90–164) - this unsteady area is associated with the presence of the codimension-2 point occurring in this range of parameters. The study has revealed many interesting phenomena, e.g. the period-doubling, the homoclinic collision and the second modulated wave. New bifurcation lines have been determined. The DNS results are analyzed in the light of experimental data published so far. At higher Reynolds numbers the next unsteady area occurs, dynamical features of which have been studied in detail for Re up to 1000. The computations have also been performed for the configurations with cylinders rotating in the co- and counter-rotating systems with rotational rate Ωout/Ωin = ± 0.1 and ± 0.2, to determine the impact of these new boundary conditions on the bifurcation processes.