Hypersonic boundary-layer receptivity is investigated using direct numerical simulation for Mach 6 flow over a 0.79 mm nose radius, 5° half-angle cone to slow acoustic waves. Two ways of exciting the second mode are discovered: For a low-frequency forcing (region I where f < 370 kHz), the first mode is initially excited and subsequently evolves into the second mode, whereas for a high-frequency forcing (region II where f 370 kHz), the second mode is excited through the disturbances in the entropy layer. The receptivity mechanisms corresponding to the first and second modes are consistent with those of a previously investigated large bluntness cone. The receptivity coefficient shows a dramatical decrease with the frequency for disturbances in region I while a slight increase for disturbances in region II. The results show that the correlation between the receptivity coefficient of the first mode and the frequency proposed for large bluntness cones also applies to the current case. Furthermore, with receptivity and the measured freestream noise spectra taken into account, it is found that at the measured transition location, the disturbance predicted by the traditional eN method is no longer the most amplified disturbance, since the disturbances with lower frequencies can acquire larger amplitudes due to their large receptivity coefficients despite their smaller growth rates.

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