Wake transitions behind a streamwise rotating disk

Direct numerical simulations are performed to investigate the wake transitions of the flow normal to a circular rotating disk. The diameter-thickness aspect ratio of the disk is chi = 50. The Reynolds number of the free stream is defined as Re-s = U infinity D/nu, with incoming flow velocity U-infinity, disk diameter D, and kinematic viscosity of the fluid nu. The rotational motion of the disk is described by the Reynolds number of rotation Re-r = omega Res, with non-dimensional rotation rate omega = 1/2wD/U-infinity, where w is the angular rotation speed of the disk. Extensive numerical simulations are performed in the parameter space 50 <= Re-s <= 250 and 0 <= Re-r <= 250, in which six flow regimes are identified as follows: the axisymmetric state, the low-speed steady rotation (LSR) state, the high-speed steady rotation (HSR) state, the low-speed unsteady rotation (LUR) state, the rotational vortex shedding state, and the chaotic state. Although plane symmetry exists in the wake when the disk is stationary, a small rotation will immediately destroy its symmetry. However, the vortex shedding frequencies and wake patterns of the stationary disk are inherited by the unsteady rotating cases at low Re-r. A flow rotation rate jump is observed at Re-s asymptotic to 125. The LUR state is intermediate between the LSR and HSR states. Due to the rotational motion, the wake of the disk enters the steady rotation state earlier at large Re-r, and is delayed into the vortex shedding state in the whole range of Re-r. In the steady rotation states (LSR and HSR), the steady flow rotation rate is linearly correlated with the disk rotation rate. It is found that the rotation of the disk can restrain the vortex shedding. The chaotic state can be regularized by the medium rotation speed of the disk.