Crossflow instability analysis of boundary layer on a yawed cone

The crossflow instability is one of the main transition mechanisms in complex three-dimensional boundary layers, yet is still far from being fully understood. In the present study, the two-dimensional global stability analysis (BiGlobal) and plane-marching parabolized stability equations (PSE3D) were employed for the crossflow instability in the boundary layer of a sharp cone at 6° angle of attack under the Mach 6 wind tunnel experimental conditions. The results were compared with those of the one-dimensional stability analysis (LST) and direct numerical simulation (DNS). It is shown that the crossflow mode is mainly distributed on the leeward side, yet can still remarkably affect the windward side as its amplitude increases downstream. The most unstable travelling crossflow mode is more amplified and has a smaller wave angle than the stationary crossflow mode. PSE3D obtains a slightly lower N factor than that obtained by BiGlobal, while the two have similar peak frequencies, indicating that the non-parallel effect weakens the growth of crossflow disturbance, without changing the peak frequency of disturbance. The N factor obtained by LST is significantly larger than those from global stability analyses, reflecting the difference in the definition of the growth rate between those two methods as well as the influence of three-dimensional effects. Therefore, different stability analysis methods have a significant impact on determining the transition N factor.