Turbulent boundary layers altered by passively rotating discs

Abstract

Turbulent boundary layers characterised by friction Reynolds numbers in the range $Re_τ = 880 - 1460$ and flowing over flush-mounted passively rotating discs are investigated in a wind tunnel with the purpose of reducing the skin-friction drag. The test surface is composed of thirty-two rotating discs arranged in a staggered configuration and supported by bearings mounted in cylindrical cavities. As the discs are half covered by thin rigid plates, a steady rotation of the discs is sustained via the asymmetric distribution of the wall-shear stress exerted by the wall turbulence on the exposed halves of the discs. Direct force measurements reveal that the drag increases with respect to a flat-plate case because of the flow interaction with the disc housings and the covering plates. The effect of the disc motion is isolated and a 3\% drag reduction is measured with respect to the flow over stationary discs. The skin-friction identity by \cite{Elnahhas_Johnson_2022} (\emph{J. Fluid Mech.}, vol. 940, 2022), extended herein to include the disc-flow effects, is utilised for the first time to analyse experimental data. This direct slip effect, quantified by using the measured disc angular velocities in the Elnahhas-Johnson identity, is negligible. Measurements obtained by particle image velocimetry disclose that a roughness mean-flow effect occurs between adjacent discs because of the clearance gaps around the discs and that a downwash secondary flow exists near the covering plates, analogous to flows over streamwise-elongated rectangular roughness elements. This downwash velocity is streamwise modulated because of the spanwise disc motion and alters the wall-normal transport term in the Elnahhas-Johnson identity, thus reducing the drag locally.