Direct numerical simulation of Taylor-Couette flow with vertical asymmetric rough walls

Abstract

Direct numerical simulations are performed to explore the effects of rotating direction of the vertical asymmetric rough wall on the transport properties of Taylor-Couette (TC) flow up to a Taylor number of $\textit{Ta} = 2.39 \times 10^7$. It is shown that compared to the smooth wall, the rough wall with vertical asymmetric strips can enhance the dimensionless torque \textit{Nu}$_\omega$, and more importantly, at high \textit{Ta} clockwise rotation of the inner rough wall (the fluid is sheared by the steeper slope side of the strips) results in a significantly bigger torque enhancement as compared to the counter-clockwise rotation (the fluid is sheared by the smaller slope side of the strips) due to the larger convective contribution to the angular velocity flux, although the rotating direction has a negligible effect on the torque at low \textit{Ta}. The larger torque enhancement caused by the clockwise rotation of vertical asymmetric rough wall at high \textit{Ta} is then explained by the stronger coupling between the rough wall and the bulk due to the larger biased azimuthal velocity towards the rough wall at the mid-gap of TC system, the increased intensity of turbulence manifesting by larger Reynolds stress and thinner boundary layer, and the more significant contribution of the pressure force on the surface of rough wall to the torque.