On the role of resonance and thermoviscous losses in an implementation of “acoustic black hole” for sound absorption in air

In this work, we propose a mathematical model of a sound-absorbing structure for anechoic duct termination, commonly called the acoustic black hole. The structure consists of a set of rigid rings separated by narrow fluid-filled cavities. There are holes in the centers of the rings, whose radii smoothly vary along the structure. According to the previously published works, wave speed in this structure can theoretically decrease to zero value, which results in the reduction of the reflection coefficient. The proposed model is based on the linearized Navier–Stokes equations formulated in 2D axisymmetric cylindrical coordinates, which are solved numerically in the frequency domain employing the finite element method. This way, thermoviscous losses in the acoustic boundary layer adjacent to the fluid-solid interfaces, especially in the narrow cavities, are accounted for properly. The numerical results show that the absorption of acoustic energy in this structure is connected with resonances taking place in the cavities forming annular resonators, rather than with the acoustic wave slow-down. This effect has not been captured in the previously published models. It is shown that the geometrical details of the structure strongly influence its behavior, indicating the possibility of its optimization to serve as an efficient absorber of acoustic energy in a relatively wide frequency range.