Physical aspects of Tollmien–Schlichting wave acoustic receptivity due to sharp-edged rectangular bumps and gaps investigated via subsonic high-fidelity simulations

The acoustic receptivity of Tollmien–Schlichting (TS) waves due to two-dimensional sharp-edged rectangular bumps and gaps in a compressible boundary layer was investigated by direct numerical simulations. The conclusions were based on a new procedure proposed for obtaining the receptivity amplitudes which appeared to be more robust and accurate than previous ones. The procedure is particularly important for the correct evaluation of the receptivity of gaps. The receptivity amplitudes for gaps were smaller than those for bumps, except for the nominally zero height/depth roughness element, where, consistent with a linear behaviour, they had the same absolute value. The procedure also revealed in detail the behaviour in the region downstream of the roughness element where the TS wave is formed (the formation region). This region extends for approximately $50\delta ^*_{b}$ , regardless of bump height or gap depth. For bumps, the receptivity scaled superlinearly with bump height while for the gaps it scaled sublinear with depth. This behaviour is associated with the different velocity profiles caused by bumps and gaps in the formation region. We also discussed issues regarding comparison with experiments. Investigation of the effect of compressibility confirmed that, in the subsonic regime, the receptivity reduces with Mach number. Finally, we addressed the receptivity scaling with the acoustic wave amplitude. It was found that the receptivity scales linearly with the acoustic wave amplitude in a range for which experiments available in the literature indicated a superlinearly scaling. Reasons for these conflicting results are discussed.