Characterizing the turbulent drag properties of rough surfaces with a Taylor--Couette setup

Wall-roughness induces extra drag in wall-bounded turbulent flows. Mapping any given roughness geometry to its fluid dynamic behaviour has been hampered by the lack of accurate and direct measurements of skin-friction drag. Here the Taylor-Couette (TC) system provides an opportunity as it is a closed system and allows to directly and reliably measure the skin-friction. However, the wall-curvature potentially complicates the connection between the wall friction and the wall roughness characteristics. Here we investigate the effects of a hydrodynamically fully rough surface on highly turbulent, inner cylinder rotating, TC flow. We find that the effects of a hydrodynamically fully rough surface on TC turbulence, where the roughness height k is three orders of magnitude smaller than the Obukhov curvature length Lc (which characterizes the effects of curvature on the turbulent flow, see Berghout et al. arXiv: 2003.03294, 2020), are similar to those effects of a fully rough surface on a flat plate turbulent boundary layer (BL). Hence, the value of the equivalent sand grain height ks, that characterizes the drag properties of a rough surface, is similar to those found for comparable sandpaper surfaces in a flat plate BL. Next, we obtain the dependence of the torque (skin-friction drag) on the Reynolds number for given wall roughness, characterized by ks, and find agreement with the experimental results within 5 percent. Our findings demonstrate that global torque measurements in the TC facility are well suited to reliably deduce wall drag properties for any rough surface.