Critical roughness heights of turbulent transition on a swept laminar-flow wing

In the three-dimensional boundary layer on swept wing, an unstable mode called the crossflow vortex grows and causes a multistep turbulent transition via the receptivity stage and the secondary instability of the crossflow vortices. It is well known that, in the presence of crossflow instability, the unstable mode grows from disturbance and results in transition to turbulence due to nonlinear secondary instability. The present study has focused on rather larger discrete roughness element that may induce the forced transition which corresponds to immediately breakdown to turbulence after the roughness element without the crossflow vortex. A laminar flow airfoil of NLF (2)-0415 was analyzed by means of direct numerical simulation (DNS) and nonlinear parabolized stability equations (NPSE) to examine the entire airfoil. We varied the roughness height and investigated the critical roughness height of the onset of the forced transition. In addition to this first criticality, we determine the critical value, above which the forced transition occurs. For both the criticalities, those roughness Reynolds numbers Rekk were also defined. As for the minimal roughness of Rekk < 0.015, no saturation of the disturbance amplitude as well as the natural transition within the chord length was observed by NPSE-DNS analysis.