Rough wall turbulent Taylor-Couette flow: the effect of the rib height

TL;DR

This paper investigates how the height and number of transverse ribs on the walls affect turbulent Taylor-Couette flow, revealing a scaling law for torque enhancement and the persistence of vortices despite roughness.

Contribution

It provides empirical scaling relations for torque increase due to wall rib roughness and demonstrates the persistence of turbulent vortices in rough wall regimes.

Findings

Torque scaling with rib height and number of ribs as $N_r h^{1.71}$

Pressure forces on ribs dominate torque contribution

Turbulent Taylor vortices persist despite wall roughness

Abstract

In this study, we combine experiments and direct numerical simulations to investigate the effects of the height of transverse ribs at the walls on both global and local flow properties in turbulent Taylor-Couette flow. We create rib roughness by attaching up to 6 axial obstacles to the surfaces of the cylinders over an extensive range of rib heights, up to blockages of 25% of the gap width. In the asymptotic ultimate regime, where the transport is independent of viscosity, we emperically find that the prefactor of the $Nu_{\omega} \propto Ta^{1/2}$ scaling (corresponding to the drag coefficient $C_f(Re)$ being constant) scales with the number of ribs $N_r$ and by the rib height $h^{1.71}$. The physical mechanism behind this is that the dominant contribution to the torque originates from the pressure forces acting on the rib which scale with rib height. The measured scaling relation of $N_r h^{1.71}$ is slightly smaller than the expected $N_r h^2$ scaling, presumably because the ribs cannot be regarded as completely isolated but interact. In the counter-rotating regime with smooth walls, the momentum transport is increased by turbulent Taylor vortices. We find that also in the presence of transverse ribs these vortices persist. In the counter-rotating regime, even for large roughness heights, the momentum transport is enhanced by these vortices.