CONVECTION VELOCITY IN DRAG-REDUCED OSCILLATING PIPE FLOW

Direct Numerical Simulations (DNS) of turbulent pipe flow with periodic inflow/outflow boundary conditions at the ends of a 12 diameter long pipe domain are performed at Reynolds numbers=170, 360 and 720. We simulate standard pipe flow with motionless wall and pipe flow in which drag is reduced by oscillating the wall in the azimuthal direction. We present space-time correlations of the streamwise velocity with separation in the streamwise direction and examine the effect of periodic in-flow/out-flow. It is found that the turbulent fluctuations maintain significant correlation well beyond the time it takes to flow through the simulation domain, implying that streamwise periodicity is not a benign condition, at least for the 12 diameter domain length. We compute the convection velocity from the space-time correlation using the method of Wills (1964) and a new method obtained from the auto-correlations with pure spatial separation and pure time separation, quantities which are much less computationally demanding than the full space-time correlation. The new method uses the the values of the separation in space and time at which the respective correlations first cross zero. Fair agreement is found between the two methods, although the method of zeroes is sensitive to noise in the correlation functions. We also find that the temporal coherence of large-scale motions increases markedly in space and time in the frame of the convection velocity when the drag is reduced by wall oscillation.