Investigation and parameterization of transition shielding in roughness-disturbed boundary layer with direct numerical simulations

Roughness-induced transition control is a key technology for aircraft design, and associated research is useful in practical applications as well as for understanding the mechanism of the roughness-induced transition. One practical approach involves the “shielding effect,” whereby the roughness-induced transition is shielded by smaller pockets of surrounding roughness. In this paper, we investigate the shielding effect of a two-dimensional downstream strip in the boundary layer disturbed by discrete smooth-edged roughness and focus on the shielding strip height kss and the distance between the two areas of roughness xss. Our results indicate that downstream shielding delays the transition by weakening the strongest streamwise vortices in the middle of the wake, thus inhibiting the “lift-up” effect that induces growth in the disturbance. The main mechanisms for reducing the streamwise vorticity are (a) enhanced dissipation of the streamwise vorticity and (b) conversion of streamwise vorticity into more stable spanwise vorticity. The strip suppresses the separation zone behind the roughness, thus affecting the receptivity process and reducing the initial disturbance. However, the strip strengthens other streamwise vortices in the wake. When kss exceeds a critical value, vortices closer to the wall will induce stronger lift-up than those in the middle of the wake, resulting in an earlier transition. Analysis of xss shows a simpler trend, whereby the onset position of the transition moves upstream as xss increases. This is because the shielding strip weakens the streamwise vortices earlier and the separation zone becomes smaller as the strip moves closer to the discrete roughness patch.