Numerical study of the behavior of rectangular acoustic black holes for sound absorption in air

In this work, the behavior of acoustic black holes (ABHs) serving as an anechoic termination of air-filled waveguides with a rectangular cross-section is numerically studied. These ABHs consist of a set of rigid ribs separated by narrow slits, whose height smoothly varies along the structure and whose aim is to slow-down the impinging acoustic wave and cause its absorption. For the purpose of this study, a 2D mathematical model based on linearized Navier-Stokes equations and employing the finite element method has been proposed, which allows for an accurate capturing the thermoviscous losses in the acoustic boundary layer adjacent to the solid-fluid interfaces, as well as the effects connected with geometrical details of the ABHs' inner structure. The numerical results show that in rectangular ABHs with a fine internal structure, the acoustic wave slow-down plays a significant role and that absorption properties are strongly dependent on their inner structure details. Simplified 1D mathematical models of rectangular ABHs based on the Riccati equation or transfer matrix method have also been proposed. These simplified models are computationally highly efficient, as it has been demonstrated, they provide accurate results, especially in the case of ABHs with a fine internal structure, which feature superior acoustic energy absorbing properties.