Drag Reduction Effect of Turbulent Flow by Synchronized Wall-Oscillation in Annular Pipe

Direct numerical simulations of the concentric annular turbulent pipe flow are performed to investigate the skin-friction drag reduction effect by the wall oscillation control technique. The oscillation on the inner and outer walls is synchronized, and the control effect is investigated for different radius ratios. While drag reduction by wall oscillation has been extensively studied in canonical wall-bounded flows such as plane channels and circular pipes, its effects in geometrically non-uniform configurations, such as the annular pipe, remain less understood. Curvature and frictional asymmetry give rise to characteristic flow responses. The simulations demonstrate that the friction drag decreases owing to the wall oscillation. The maximum drag reduction rate is $$R_D \approx 0.5$$ at the optimal period of $$T^+ \approx 150$$ . An identity equation for the skin-friction coefficient of the annular pipe flow is derived, and the contribution from turbulence is quantitatively discussed. Scaling methods for the drag reduction rate are applied: 1) increment of the mean velocity and 2) based on the Stokes problem. Both scaling methods appropriately describe the drag-reduction behavior in the drag-reduction regime at $$T^+ \lessapprox 150$$ .