Influence of backflow on skin friction in turbulent pipe flow

Abstract

A direct numerical simulation of a turbulent pipe flow (Re-tau = 544) is used to investigate the influence of the backflow on the vortical structures that contribute to the local skin friction. The backflow is a rare event with a probability density function (PDF) of less than 10(-3) . The backflow is found to extend up to y(+) approximate to 4 and is induced by the presence of a vortex in the buffer layer. The flow statistics are conditionally sampled under the condition of a negative streamwise velocity (u < 0) at y(+) = 3. The conditionally averaged < u'v'>(+) vertical bar(u<0) reaches its maximum at y(+) approximate to 27. The intensified conditionally averaged velocity fluctuations contribute to vertical and spanwise momentum transport around the backflow. The ensemble averaged < u'v'>+ and < u'w'> + reveal layered structures in the Q2 and Q4 events. A strong Q4 event appears above the backflow, flanked by two regions of Q2. The strong downwash of the flow along with the spanwise vortex induces the backflow. The upwash at upstream and downstream of the backflow enhances the movement of the low-speed flow in the streamwise and spanwise directions. The velocity-vorticity correlation reveals that the main contributions to C-f are the vorticity advection and vorticity stretching. The main contribution to the conditionally averaged C-f is the wall-normal gradient of the mean spanwise vorticity at the wall. The spanwise vorticity is positive above the backflow flanked by two regions of negative spanwise vorticity. The conditional PDF of the backflow under negative u(l)(+) at y(+) = 100 is more frequent than that under positive u(l)(+). Published by AIP Publishing.