Wideband reduction of both sound reflection and transmission using compact non-intrusive liners remains a challenging issue for duct noise control applications. This work focuses on the acoustical performance limitations of cylindrical silencers made up of annular ring resonators with axial gradient of their cavity depths. It is shown from theoretical, numerical and experimental studies that a sub-wavelength silencer with optimized acoustic black hole (ABH) properties can be designed through which incident sound waves are retarded and fully dissipated within the activated resonant cavities. Such ABH-type silencer requires a suitable interplay between the wall impedance axial variations and the visco-thermal losses within the cavities. Key parameters that influence this balance are the axial growth of cavity depths and the wall porosity. A causal-based criterion has been proposed that maximizes the total integrated dissipated power, thereby leading to the optimal value of the wall porosity and to the ultimate bandwidth-to-length ratio that can be achieved by an ABH-type silencer given a target dissipation value. A space-frequency region has been numerically and experimentally identified over which the ABH effect is prominent. The causal-based criterion has been extended to account for the low-frequency ultimate performance of ABH silencers with coiled cavities and for the effects of a low-speed grazing flow.
This work is part of the project TED2021-130103B-I00, funded by MCIN/AEI/10.13039/501100011033 and the European Union “NextGenerationEU”/PRTR. It has also received support from the French government under the France 2030 investment plan, as part of the Initiative d'Excellence d'Aix-Marseille Université - A*MIDEX (AMX-19-IET-010).