Direct numerical simulations of a turbulent channel flow developing over convergent-divergent riblets

Direct numerical simulations of a turbulent channel flow developing over convergent-divergent (C-D) riblets at a Reynolds number of Reb = 2800 are presented. It is found that, with a fixed normalized riblet height of h+ = 5, as the ratio of the riblet spacing and the height, s/h, increases from 2 to 10, the strength of the large-scale secondary flow motion Gamma generated by the C-D riblets peaks around s/h = 4 when the C-D riblets behavior lies between d- and k-type roughness. Compared to the baseline case with smooth walls, the turbulent activities and energy level increase significantly and peak at s/h = 4 when Gamma is the highest. It is shown that while the intense local turbulent kinetic energy (TKE) production occurring in the diverging region is caused by the high local velocity gradient due to the downwelling of the secondary flow, the strong local TKE production occurring in the converging region is caused by the high turbulent shear stress associated with upwelling. Furthermore, the TKE transport characteristics are significantly altered by the secondary flow motion, especially over the converging and diverging regions. The secondary flow is not caused by the local imbalance between turbulent kinetic energy production and dissipation but by the yawed riblets. It is then more appropriate to classify this flow as a Prandtl's secondary flow of the first kind, also known as the geometry-driven secondary flow. Finally, in comparison with the baseline case, the drag increases for all the riblet cases examined, and a direct correlation between the amount of drag and intensity of the secondary flow exists, both peaking at s/h = 4