Virtual Herschel-Quincke tube using the multiple small resonators and acoustic metamaterials

Abstract

This study is on the practical application of the acoustic metamaterials to the design of a silencer with high acoustic and geometric efficiencies, and negligible pressure drop. The object is to achieve broadband and low-frequency attenuation simultaneously by combining the effects of resonance, periodicity, phase difference, and impedance mismatch. An array of multiple small resonators, which is periodically applied to the wall of a duct, invokes the dispersion of sound propagating in the duct. This phenomenon is implemented to construct a virtual Herschel-Quincke (HQ) tube system. The main duct is split into two parallel ducts of the same length: a rigid duct and a duct with a wall covered by the periodic resonators. For a modelling of sound propagation in a dispersive duct, the phase speed of sound is analytically derived in the presence of a mean flow. Also, the attenuation conditions of the virtual HQ tube are proposed to establish a guideline in selecting the proper design parameters for achieving the required transmission loss (TL) in the desired frequency range. The predicted TL spectra are compared with the test results, for a virtual HQ tube system with 9 identical quarter-wavelength tube resonators, and they generally agree well. With increasing flow speed, the amount of attenuation decreases a bit, but the general spectral characteristics are maintained for |M|≤0.1. Based on the same principle, the acoustic metamaterials (AMM) are applied to the practical silencer design to achieve the wide-band sound reduction at low- to mid-frequencies for a given small space. A virtual HQ tube having 26 cells of AMM is tested, of which a cell is composed of 3 types of quarter-wavelength tube resonators. The experiment well validates the predicted TL. The results show that TL is at least 5 dB for a wide frequency range of 230–1000 Hz. The additional volume due to the attachment of the AMM layer is only 40%, while the TL is far larger than that of the simple expansion chamber or the dissipative silencer having the same excess volume.