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Deep axisymmetric cavities integrated into a chamber significantly influence acoustic wave propagation, notably by reducing the effective sound velocity. In our experimental configuration, the effective sound velocity is approximately one quarter of the sound velocity in air (c_e≈c_0/4). This substantial reduction suggests the possibility of introducing a mean flow exceeding c_e to investigate whether sound propagation against the flow can be blocked. However, previous attempts to achieve this effect were stopped by intense whistling instabilities occurring in empty cavities [1] and in cavities fitted with porous rings [2]. The present study investigates whether completely filling the cavities with porous material can mitigate or delay these instabilities while preserving the desired acoustic properties of the structure.Acoustic transmission and scattering measurements were performed on configurations comprising 30 cavities with porous treatments, under flow conditions up to M=0.35. Results demonstrate that no whistling occurs when cavities are fully filled with porous media. A pronounced asymmetry in sound propagation is observed between upstream and downstream directions. Nevertheless, at very low frequencies, transmission against the flow remains possible even at the highest Mach numbers tested.[1] Aurégan Y., and Golliard J., “Linear Aeroacoustics of Deep Cavities,” 30th AIAA/CEAS Aeroacoustics Conference (2024)[2] Golliard J. and Aurégan Y., “Transmission and amplification by deep periodic axisymmetric cavities with flow,” 32th AIAA/CEAS Aeroacoustics Conference (2026)