Secondary flow in a laminar boundary layer developing over convergent-divergent riblets

Convergent-divergent (C-D) riblets are a type of bio-inspired surface pattern. They are known to induce secondary flow in a boundary layer that may point to their potential for surface friction drag reduction and flow separation control. In this paper, a systematic investigation of the effect of riblet height, wavelength and yaw angle on the secondary flow in a flat-plate laminar boundary layer developing over a C-D riblet section is undertaken. The large-scale secondary flow in the cross-stream plane belongs to Prandtl’s first kind, and is induced by the spanwise velocity generated by the yawed riblet passages. The exact structure of this secondary flow depends on the relative size of riblet height and wavelength to the local boundary layer thickness, and three different patterns are observed within the range of parameters examined. As the wavelength increases, the strength of the secondary flow increases firstly and then levels off at large wavelengths, whereas the average strength per unit area exhibits a peak around a ratio between wavelength and local boundary layer thickness of 1. As the yaw angle increases from 20o to 70o, the strength of the secondary flow exhibits a parabolic trend and achieves a maximum around a yaw angle of 45o. The findings from this work can be used to inform the choice of riblet geometry for maximizing the strength of the secondary flow in a given boundary layer flow.