The effect of coherent structures on the secondary flow in a square duct

Abstract

The appearance of secondary flow of Prandtl’s second kind is a well-known phenomenon in fully developed turbulent rectangular duct flow. The intensity of the secondary flow is two orders of magnitude smaller than that of the mean streamwise velocity; however, it plays an important role in the crossstreamwise momentum, heat and mass transfer. Our recent study [1] revealed that the mean secondary flow is a statistical footprint of the turbulent flow structures, i.e. streamwise vortices and streaks which are observed in the nearwall region, whose cross-sectional positions are constrained by the presence of the side walls at marginal Reynolds number (approximately 1100, based on the bulk velocity and the duct half width, corresponding to a friction Reynolds number of about 80). In this marginal case, one low-speed streak associated with a pair of counter-rotating streamwise vortices can exist over each wall and they are self-sustained [2]. When considering the higher Reynolds numbers, the increment of duct width in wall unit allows the simultaneous presence of multiple low velocity streaks and pairs of streamwise vortices upon the wall.