Three-dimensional swirling flow with a precessing vortex breakdown in a rotor-stator cylinder

Time-dependent swirling flows are studied inside an enclosed cylindrical rotor-stator cavity with aspect ratio H/R=4, larger than those usually considered in the literature. The study is carried out by a numerical resolution of the 3D Navier–Stokes equations, based on high-order spectral approximations. The bifurcation to the oscillatory regime is axisymmetric at Re=3700. The transition to a three-dimensional flow associated with a vortex breakdown is investigated and is shown to be brought about the centrifugal instability originated from the vertical sidewall layer. At Re=6500, the time-dependent flow is three dimensional. A modulated rotating wave with azimuthal wave number k=8 arises first in the vertical layer. The vortex breakdown evolves from an axisymmetric bubble to an S-shape type and gyrates around the axis (Ωt=1500) inducing a new time-dependent regime. This precession motion is associated to an antisymmetric k=1 mode of an instability.