Disentangling the origins of torque enhancement through wall roughness in Taylor-Couette turbulence

TL;DR

This study uses direct numerical simulations to analyze how wall roughness affects torque scaling and flow dynamics in turbulent Taylor-Couette flow, revealing that roughness enhances the effective scaling exponent and shifts dissipation towards the bulk.

Contribution

It demonstrates that wall roughness alters the torque scaling and flow dissipation mechanisms, providing new insights into turbulence behavior in Taylor-Couette systems with rough surfaces.

Findings

Rough wall torque scales as $Nu_r hicksim Ta_r^{0.47}$, close to the ultimate regime.

Smooth wall torque follows $Nu_s hicksim Ta_s^{0.38}$, consistent with smooth-wall cases.

Roughness shifts dissipation from the wall to the bulk, increasing the effective scaling exponent.

Abstract

Direct numerical simulations (DNSs) are performed to analyze the global transport properties of turbulent Taylor-Couette flow with inner rough wall up to Taylor number $Ta=10^{10}$. The dimensionless torque $Nu_\omega$ shows an effective scaling of $Nu_\omega \propto Ta^{0.42\pm0.01}$, which is steeper than the ultimate regime effective scaling $Nu_\omega \propto Ta^{0.38}$ seen for smooth inner and outer walls. It is found that at the inner rough wall, the dominant contribution to the torque comes from the pressure forces on the radial faces of the rough elements; while viscous shear stresses on the rough surfaces contribute little to $Nu_\omega$. Thus, the log layer close to the rough wall depends on the roughness length scale, rather than on the viscous length scale. We then separate the torque contributed from the smooth inner wall and the rough outer wall. It is found that the smooth wall torque scaling follows $Nu_s \propto Ta_s^{0.38\pm0.01}$, in excellent agreement with the case where both walls are smooth. In contrast, the rough wall torque scaling follows $Nu_r \propto Ta_r^{0.47\pm0.03}$, very close to the pure ultimate regime scaling $Nu_\omega \propto Ta^{1/2}$. The energy dissipation rate at the wall of inner rough cylinder decreases significantly as a consequence of the wall shear stress reduction caused by the flow separation at the rough elements. On the other hand, the latter shed vortices in the bulk that are transported towards the outer cylinder and dissipated. Compared to the purely smooth case, the inner wall roughness renders the system more bulk dominated and thus increases the effective scaling exponent.