Transition of flow between eccentrically rotating double cylinders

We report on the drag force acting on a mixing rod which rotates at the same rate as its orbital motion in a circular container. To gain insights into the mechanism of the drag increase owing to the wake development, we perform a series of numerical simulations in which the Reynolds number, the radius of a rod, and its orbit are parameterized. The flow transition can be realized by increasing the Reynolds number but strongly depends on the system geometries. To account for this transition, the gap Reynolds number is introduced herein; we find that the drag increase and the onset of vortex shedding can be well-scaled by the gap Reynolds number. We further demonstrate that the number of azimuthal waves is relevant to the eccentricity. The current findings, albeit empirical, suggest that the sidewall confinement can efficiently lead to a delay of flow transition and open a new venue for controlling the fluid–structure interaction in mixing processes.