The low-noise commercial aircraft necessitates the meticulous design of acoustic liners within engine nacelles. Acoustic liners, due to their porous wall nature, can substantially affect near-wall turbulent structures, thereby inducing various propagating waves with regular wave number and frequency. In this study, direct numerical simulations (DNS) of channel flow bounded by solid and porous walls were conducted at bulk Mach numbers of $M_b=0.2$, 0.5, and 0.8, where time-domain impedance boundary conditions (TDIBC) were employed to model the porous-wall effects. Longitudinal and oblique acoustic waves within the channel flow were accurately captured under porous wall constraints. The wavenumber-frequency relationships for all reflected waves and surface waves subjected to the specified TDIBC were theoretically developed, inspired by the work of Rienstra and Hirschberg [An Introduction to Acoustics (Technische Universiteit Eindhoven, Netherlands, 2004)]. The accuracy of these theoretical predictions was further validated through high-fidelity DNS results. Compared to the solid wall, it has been observed that the porous wall induces a phase offset in waves reflected from impedance walls and the characteristic wave-number-frequency relationship for surface acoustic waves has been confirmed by DNS. Furthermore, the wavenumber spectrum on the wall was explored, revealing the presence of supersonic ridges distributed along a series of concentric ellipses, but with modified wavenumber relationships. These features stem from the propagation characteristics of reflected waves within the channel flow.

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• Aeroacoustics
• Channel flow
• Compressible turbulence
• Porous media