  We have carried out axisymmetric numerical simulations of a spatially
developing hypersonic boundary layer over a sharp 7$^{\circ{}}$-half-angle cone
at $M_\infty=7.5$ inspired by the experimental investigations by Wagner (2015).
Simulations are first performed with impermeable (or solid) walls with a
one-time broadband pulse excitation applied upstream to determine the most
convectively-amplified frequencies resulting in the range 260kHz -- 400kHz,
consistent with experimental observations of second-mode instability waves.
Subsequently, we introduce harmonic disturbances via continuous periodic
suction and blowing at 270kHz and 350kHz. For each of these forcing frequencies
complex impedance boundary conditions (IBC), modeling the acoustic response of
two different carbon/carbon (C/C) ultrasonically absorptive porous surfaces,
are applied at the wall. The IBCs are derived as an output of a pore-scale
aeroacoustic analysis -- the inverse Helmholtz Solver (iHS) -- which is able to
return the broadband real and imaginary components of the surface-averaged
impedance. The introduction of the IBCs in all cases leads to a significant
attenuation of the harmonically-forced second-mode wave. In particular, we
observe a higher attenuation rate of the introduced waves with frequency of
350kHz in comparison with 270kHz, and, along with the iHS impedance results, we
establish that the C/C surfaces absorb acoustic energy more effectively at
higher frequencies.
