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

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.

arXiv comment18 pages, 13 figures

References in corpus (13)

• Large scale dynamics in turbulent Rayleigh-Benard convection
• High Reynolds number Taylor-Couette turbulence
• Multiple states in highly turbulent Taylor-Couette flow
• Optimal Taylor-Couette turbulence
• The Twente turbulent Taylor-Couette (T3C) facility: Strongly turbulent (multiphase) flow between two independently rotating cylinders
• The near-wall region of highly turbulent Taylor-Couette flow
• Wall roughness induces asymptotic ultimate turbulence
• Velocity profiles in strongly turbulent Taylor-Couette flow
• Disentangling the origins of torque enhancement through wall roughness in Taylor-Couette turbulence
• Direct numerical simulations of Taylor--Couette turbulence: the effect of sand grain roughness
• Taylor-Couette turbulence at radius ratio $\eta =0.5$: scaling, flow structures and plumes
• Controlling secondary flow in Taylor-Couette turbulence through spanwise-varying roughness
• Calculation of the mean velocity profile for strongly turbulent Taylor--Couette flow and arbitrary radius ratios