Stability assessment on sinusoidal roughness elements for crossflow-transition control

Abstract

In this work, we numerically investigate the effectiveness of sinusoidal roughness elements (SREs), which have been proposed by our group to delay crossflow boundary layer transition. First, an ideal control scenario was identified by several stability analysis solvers, and receptivity to stationary vortices behind conventional cylindrical discrete roughness elements (DREs) and SREs was simulated by means of direct numerical simulation (DNS). The critical heights of the two devices were next assessed with DNS. In a flow condition relevant to civil transport aircraft, it was found that the height of an SRE for control could be increased up to approximately 0.33 mm before flows became susceptible to tripping, whereas for a cylindrical DRE it was near to 0.13 mm. This finding illustrates that by the introduction of a high-initial amplitude subdominant vortex, SREs are better at suppressing amplification of the most dominant vortex. To investigate a predictive secondary N-factor (Ntr.) and associated instability mechanisms, we then carried out a bi-local analysis for flows past the critical SREs. The results revealed that there exist many unstable high-frequency secondary modes, Ntr. was approximately 8.4, and that the critical mode at the onset of transition belonged to a type-y mode at 275 kHz. This value of Ntr. was close to those reported by previous studies and also to that of the critical stationary mode at the primary stage.