Wake transitions behind a streamwise rotating disk

Abstract

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 $Re_s=U_\infty D/\nu$ , with incoming flow velocity $U_\infty$ , disk diameter $D$ , and kinematic viscosity of the fluid $\nu$ . The rotational motion of the disk is described by the Reynolds number of rotation $Re_r=\varOmega Re_s$ , with non-dimensional rotation rate $\varOmega =\frac {1}{2}\omega D/U_\infty$ , where $\omega$ is the angular rotation speed of the disk. Extensive numerical simulations are performed in the parameter space $50 \leqslant Re_s \leqslant 250$ and $0 \leqslant Re_r \leqslant 250$ , 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 $Re_s\approx 125$ . 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.