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

TL;DR

This study uses a Taylor-Couette setup to accurately measure the skin-friction drag of rough surfaces in turbulent flow, revealing that roughness effects are similar to those on flat plates and enabling reliable drag property characterization.

Contribution

It demonstrates that Taylor-Couette experiments can directly and reliably measure the skin-friction drag of rough surfaces, linking roughness characteristics to turbulent flow behavior.

Findings

Roughness effects in TC flow resemble those on flat plate boundary layers.

The equivalent sand grain height ks correlates with flat surface measurements.

Torque measurements agree within 5% with theoretical predictions.

Abstract

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.