Rainbow trapping filters (RTFs) have been so far investigated to achieve broadband unit sound absorption in closed-end duct terminations. However, opened RTFs have been scarcely explored to realize broadband low-frequency dissipation of sound waves while being traversed by a low speed flow. To bridge the gap, we propose a RTF composed of coiled cavities whose inner radius follows a flow-compliant converging profile, referred to as a converging coiled CCRTF silencer. An effective medium approach and the transfer matrix method (TMM) showed the ability of such devices to produce slow sound, impedance matching and minute sound reflection and transmission over a wide bandwidth, confirmed by finite element simulations and scattering matrix measurements without flow. A causal analysis revealed that a large density of wall resonators enhances the silencer performance while its bandwidth is driven by the coiling factor, convergent contraction ratio and cavities axial growth. Particle swarm optimization of these parameters led to a sub-wavelength CCRTF silencer with near-unit dissipation over 3.5 octaves from 200 Hz upwards. Extended TMM and aeroacoustic measurements showed resilience of the CCRTF performance under upstream or downstream propagation conditions for outlet Mach numbers below 0.16, thereby opening up applications like the design of silent convergent nozzles.
Acknowledgments
This work is part of the project TED2021-130103B-I00, funded by MCIN/AEI/10.13039/501100011033 and the European Union “Next Generation EU”/PRTR, and the project PID2022-139414OB-I00, funded by MCIN/AEI/10.13039/501100011033/ and by "ERDF A way of making Europe". 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-22-RE-AB-157). The authors are grateful to E. Bertrand, M. Amielh and D. Mazzoni for their technical and experimental support during the aero-acoustic testings at IRPHE CNRS Laboratory.
