Direct Numerical Simulations of Local and Global Torque in Taylor-Couette Flow up to Re=30.000

TL;DR

This study uses direct numerical simulations to analyze how local and global torques behave in turbulent Taylor-Couette flow up to Re=30,000, revealing the influence of rotation, vortex structures, and boundary layers on torque dynamics.

Contribution

It provides new insights into the relationship between local transport, vortex structures, and torque scaling in turbulent Taylor-Couette flow at high Reynolds numbers.

Findings

Torque maximum occurs at moderate counter-rotation for Re_S>=2x10^4.

Fluctuation enhancement observed in the outer region during strong counter-rotation.

Boundary-layer thickness correlates with torque variations.

Abstract

The torque in turbulent Taylor-Couette flows for shear Reynolds numbers Re_S up to 3x10^4 at various mean rotations is studied by means of direct numerical simulations for a radius ratio of \eta=0.71. Convergence of simulations is tested using three criteria of which the agreement of dissipation values estimated from the torque and from the volume dissipation rate turns out to be most demanding. We evaluate the influence of Taylor vortex heights on the torque for a stationary outer cylinder and select a value of the aspect ratio of \Gamma=2, close to the torque maximum. The connection between the torque and the transverse current J^\omega of azimuthal motion which can be computed from the velocity field enables us to investigate the local transport resulting in the torque. The typical spatial distribution of the individual convective and viscous contributions to the local current is analysed for a turbulent flow case. To characterise the turbulent statistics of the transport, PDF's of local current fluctuations are compared to experimental wall shear stress measurements. PDF's of instantaneous torques reveal a fluctuation enhancement in the outer region for strong counter-rotation. Moreover, we find for simulations realising the same shear Re_S>=2x10^4 the formation of a torque maximum for moderate counter-rotation with angular velocities \omega_o\approx-0.4\omega_i. In contrast, for Re_S<=4x10^3 the torque features a maximum for a stationary outer cylinder. In addition, the effective torque scaling exponent is shown to also depend on the mean rotation state. Finally, we evaluate a close connection between boundary-layer thicknesses and the torque.