Streamwise Variations in Turbulence Statistics in Drag-Reducing Turbulent Boundary Layer of Viscoelastic Fluids

Direct numerical simulation (DNS) of a zero-pressure gradient drag-reducing turbulent boundary layer of viscoelastic fluids was performed at the different Weissenberg number We = 25, 50, 75, and 100 using the FENE-P model. The increase in We, i.e. the relaxation time leads to the larger maximum of trace of conformation tensor in upstream region, and to the larger maximum of drag reduction ratio DR in downstream region, in which the trace of conformation tensor decreases gradually in the streamwise direction, while the DR increases. The trace of conformation tensor is anticorrelated with DR, While the phase difference between DR and streamwise turbulence intensity becomes larger with the increase in We. Streamwise variations in DR, turbulence statistics and structures are so different between We = 25 and We = 50 to 100, and the difference is elucidated by using the active and hibernating turbulence mechanism of Xi and Graham (2010b) for the minimal channel flow. At We = 25, the locally high and low wall-shear stress regions show larger scale compared to Newtonian fluid. On the other hand, at We = 50, regions of active and hibernating turbulence become obscurer, while the mechanism itself is unchanged.