TY - JOUR
T1 - Direct numerical simulation of Taylor–Couette flow with grooved walls: torque scaling and flow structure
AU - Zhu, Xiaojue
AU - Ostilla-Mónico, Rodolfo
AU - Verzicco, Roberto
AU - Lohse, Detlef
PY - 2016
Y1 - 2016
N2 - We present direct numerical simulations of Taylor–Couette flow with grooved walls at a fixed radius ratio ${\it\eta}=r_{i}/r_{o}=0.714$η=ri/ro=0.714 with inner cylinder Reynolds number up to $Re_{i}=3.76\times 10^{4}$Rei=3.76×104, corresponding to Taylor number up to $Ta=2.15\times 10^{9}$Ta=2.15×109. 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 $Ta$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 $Ta$Ta becomes much steeper. Further increasing $Ta$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.
AB - We present direct numerical simulations of Taylor–Couette flow with grooved walls at a fixed radius ratio ${\it\eta}=r_{i}/r_{o}=0.714$η=ri/ro=0.714 with inner cylinder Reynolds number up to $Re_{i}=3.76\times 10^{4}$Rei=3.76×104, corresponding to Taylor number up to $Ta=2.15\times 10^{9}$Ta=2.15×109. 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 $Ta$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 $Ta$Ta becomes much steeper. Further increasing $Ta$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.
KW - Plumes/thermals
KW - Taylor–Couette flow
KW - Turbulence simulation
U2 - 10.1017/jfm.2016.179
DO - 10.1017/jfm.2016.179
M3 - Article
VL - 794
SP - 746
EP - 774
JO - Journal of fluid mechanics
JF - Journal of fluid mechanics
SN - 0022-1120
ER -