A virtual Herschel-Quincke tube using slow sound

Abstract

While an acoustic wave propagates along a duct, of which the wall is treated with either dissipative or a reactive material, the phase speed can be slowed down because of wave dispersion. It has been thought that such slow sound can be used for a novel control method to reduce the in-duct noise at low to medium frequencies generated from a fluid machinery system. In this work, the Herschel-Quincke tube (hereafter, H-Q tube), which exploits the path length difference of two parallel ducts, is modified to demonstrate the application potential of the slow sound. A test rig is designed to create the two different phase speeds by arranging the two parallel, equal-length ducts inside a main duct, one of them is hard-walled and the other one lined with a periodic array of resonators. This slow sound H-Q device is then modelled by both analytical and numerical methods assuming a plane wave incidence. Also, an experiment is conducted to measure the transmission loss. The result reveals a low frequency peak (TL~30 dB) in the range of 200-400 Hz, which occurs far below the lowest resonance of the resonator. At the original resonance frequency of 691 Hz, a small attenuation (TL~6 dB) is obtained due to the fact that one duct is subject to a high loss, and the other is without appreciable loss. The result clearly demonstrates the potential of applying slow sound device to overcome the spatial limitation of the classical H-Q tube.