Response of supersonic flow over blunted plates to free stream disturbances

This study investigates the response of a Mach 4 flow over blunted plates to free stream disturbances using the linearised Navier–Stokes equations. Six nose radii, ranging from 0.1 to 2 mm, are considered. The free stream conditions match those of the experiments by Lysenko ( J. Appl. Mech. Tech. Phys. vol. 31, 1990, pp. 868–873), in which the critical nose radius for transition reversal was found to be approximately 0.5 mm. The current study finds that increasing the nose radius strengthens low-frequency streamwise streaks while stabilising the oblique first mode. This leads to a shift in the dominant instability inside the boundary layer from the oblique first mode to streamwise streaks. For slow acoustic waves, the changeover nose radius is 0.7 mm. For entropy waves, vorticity waves and optimal free stream forcing obtained from resolvent analysis, the changeover nose radius is 0.2 mm. The results reproduce the transition reversal observed in the experiments and suggest that it can occur regardless of the type of free stream disturbances. The streak enhancement is attributed to the increasing magnitude of velocity perturbations near the stagnation line as the nose radius increases. Streamwise vortex-like disturbances of inviscid nature at the stagnation line generate streamwise streaks downstream via the lift-up mechanism. For the most amplified streaks, the ratio of the local boundary-layer thickness to the spanwise wavelength approaches a constant value downstream. This ratio is found to be independent of the nose radius and the type of free stream forcing. For slow acoustic disturbances, the streak strength is found to be insensitive to the angle of incidence.