Drag reduction in turbulent Taylor–Couette flow by axial oscillation of inner cylinder

Abstract

Drag reduction in turbulent Taylor–Couette flows by axial oscillation of inner cylinder is investigated by direct numerical simulation. In the present study, the reference friction Reynolds number is R e τ = 210 based on the friction velocity at the inner cylinder in the no control cases and the half gap width. We have obtained the effects of the oscillation period and the radius ratio of the inner to outer cylinders on the drag reduction rate. Our analysis shows that as the radius ratio is getting larger, the maximum drag reduction rate is decreased and the optimal oscillating period is increased. Under the condition of the short oscillating period, a larger radius ratio leads to a lower drag reduction rate. However, when the oscillating period becomes long, the larger radius ratio triggers a higher drag reduction rate. With the help of Fukagata–Iwamoto–Kasagi identity, the wall shear stress has been linked to turbulent motions at different scales. It is found that the long-period oscillations primarily reduce the wall friction drag induced by the large-scale Taylor vortices while the short-period oscillations mainly decrease wall shear stress originating from the small-scale velocity streaks. Visualizations of Taylor vortices and velocity streaks, premultiplied spectra, and the weighted Reynolds shear stress indicate that such different effects are related to the Stokes layer. A thick Stokes layer under the condition of large-period oscillations penetrates to the core region of the flow and the Taylor vortices whose center is located near the middle plane between the cylinders is thus attenuated effectively. On the contrary, the influence range of a thin Stokes layer caused by the short-period oscillation concentrates on the near-wall region, hence, the small-scale velocity streaks there are weakened greatly.