Optimal shaping of acoustic black holes for sound absorption in air

This article presents a systematic numerical study of the absorbing properties of acoustic black holes (ABHs) serving as an anechoic termination of waveguides. The study focuses on the sensitivity of ABHs’ absorbing performance to their profile and internal-structure parameters. The article compares numerical predictions from 1D model based on the Riccati equation with a detailed 2D model based on the linearized Navier-Stokes equations and the finite element method, finding good agreement among all results, especially for ABHs with fine internal structures. The mean value of the reflection coefficient modulus is used to quantify the ABH’s absorbing performance, and the article introduces the use of power-law functions and cubic splines to define the ABH’s shape function. An evolutionary algorithm is employed to optimize the ABH’s profile, resulting in improved absorbing performance. The numerical results suggest that the optimum shape is simple and more-or-less insensitive to other geometrical and internal-structure parameters.