Wave propagation in aeroacoustic permeable materials with active momentum sources

This work investigates acoustic wave propagation in permeable materials in which a background velocity field is generated by either a macroscopic static pressure gradient, spinning solid cylinders, or both. Linearisation of the Fourier-Navier-Stokes system yields transport equations in permanent and dynamic regimes. In the latter, the background velocity field generated in permanent regime affects the dynamic velocity and temperature fields through convective terms. The use of the two-scale homogenisation method yields, for small Mach numbers, linear boundary-value transport problems for the permanent and dynamic physical variables. Theoretical analyses show that the dynamic convection strongly alters the effective properties of the media and leads to a reduced or even negative real part of the dynamic conductivity, whereas the effective compressibility remains classical. Moreover, the derived macroscopic description evidences non-reciprocal acoustic wave propagation in the studied media. Numerical examples illustrate the key features of the effective properties when in presence of two background velocity fields, further showing their effect on the effective speed of sound and wave number. This work offers new perspectives on the low-frequency control of acoustic waves by permeable media with active momentum sources.