On the stability characteristics of a hypersonic boundary-layer flow over parametrised sinusoidal surface roughness

Abstract

The stability characteristics of a Mach boundary-layer flow over a flat plate with parametrised two-dimensional sinusoidal surface roughness are investigated. The investigation involves varying the roughness height from to of the boundary-layer thickness and exploring wavelengths ranging between and times the dominant second-mode wavelength in the region. The introduction of surface roughness leads to notable variations in the mean flow, resulting in separation behind the roughness elements and the propagation of local compression and expansion waves into the free stream. Stability investigations involved the utilisation of wave packet tracking in a linear disturbance simulation (LDS) framework and linear stability theory. The findings revealed significant effects on Mack modes including a reduction in frequency corresponding to maximum amplification with increased roughness height. Proper scaling of the dominant wavelength facilitates a collapse of the growth rate data. In contrast to the commonly reported stabilisation effects for roughness wavelengths significantly larger than the instability mode's wavelength, the findings primarily revealed destabilisation compared with the smooth-wall case, except for cases with very small roughness wavelengths and large amplitudes approaching the threshold of being classified as porous media. The LDS findings depicted lobed wall pressure amplitude plots, indicating potential undiscovered instability mechanisms or differences compared with the smooth wall. A detailed stability analysis elucidates these LDS findings, establishing a connection between the lobed amplitude structures and substantial changes in local stability characteristics, along with the emergence of Mack's first, second and third modes.