Low-frequency non-reciprocal sound propagation features in thermoacoustic waveguide

Thermoacoustic waveguides are systems of hollow tubes and thermally graded porous segments that can operate as active materials where acoustic waves receive energy from an external heat source. This work demonstrates that by adjusting the pore geometry several unique low-frequency propagation features arise from the complex-valued band structure of periodic thermoacoustic waveguides that reflect into the acoustic pressure field within finite-length systems. Numerical methods have been employed to model waveguides with porous segments constituted by cylindrical inclusions (parallel pins). In periodic structures, a critical frequency emerges where the sign of the refractive index in one direction of propagation changes, thus zero- and negative-unidirectional refractive index, unidirectional energy transport, and amplification/attenuation crossover effects may take place. On the other hand, the study of the acoustic pressure field shows that, for wave packets with either direction of propagation, finite-length waveguides may behave as active acoustic metamaterials with zero- or negative-refractive index. The acoustic pressure field in the waveguide, generated by an upstream source, may exhibit increasing amplitude and phase recovery farther away from the source, mimicking the field created by a downstream source, propagating upstream in a non-active medium.