Direct numerical simulation of Taylor–Couette flow with grooved walls: torque scaling and flow structure

Abstract

We present direct numerical simulations of Taylor–Couette flow with grooved walls at a fixed radius ratio ${\it\eta}=r_{i}/r_{o}=0.714$ with inner cylinder Reynolds number up to $Re_{i}=3.76\times 10^{4}$, corresponding to Taylor number up to $Ta=2.15\times 10^{9}$. The grooves are axisymmetric V-shaped obstacles attached to the wall with a tip angle of 90°. Results are compared to the smooth wall case in order to investigate the effects of grooves on Taylor–Couette flow. We focus on the effective scaling laws for the torque, flow structures, and boundary layers. It is found that, when the groove height is smaller than the boundary layer thickness, the torque is the same as that of the smooth wall cases. With increasing $Ta$, the boundary layer thickness becomes smaller than the groove height. Plumes are ejected from the tips of the grooves and secondary circulations between the latter are formed. This is associated with a sharp increase of the torque, and thus the effective scaling law for the torque versus $Ta$ becomes much steeper. Further increasing $Ta$ does not result in an additional slope increase. Instead, the effective scaling law saturates to the ‘ultimate’ regime effective exponents seen for smooth walls. It is found that even though after saturation the slope is the same as for the smooth wall case, the absolute value of torque is increased, and more so with the larger size of the grooves.