Turbulent boundary layers altered by passively rotating discs

Abstract

Turbulent boundary layers characterised by friction Reynolds numbers in the range (Formula presented) 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 Elnahhas & Johnson (2022) J. Fluid Mech. 940, 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. The velocity covariances are enhanced in the proximity of adjacent discs, in line with the roughness effect in that region. The Reynolds-shear-stress term in the Elnahhas–Johnson identity is thereby globally enhanced. Nonetheless, the near-wall one-point and two-point covariances of the velocity fluctuations and the Reynolds shear stresses are reduced in magnitude and spatial coherence. This result is the first experimental evidence confirming that the attenuation of the Reynolds shear stresses is the central drag-reducing mechanism behind the rotating-disc flow.