Mitigating the propagation of low frequency noise sources in ducted flows represents a challenging task since wall treatments have often a limited area and thickness. Loading the periphery of a duct with a periodic distribution of side-branch Helmholtz resonators broadens the bandwidth of the noise attenuated with respect to a single resonator and generates stop bands that inhibit wave propagation. However, significant flow pressure drop may occur along the duct axis that could be reduced using micro-perforated patches at the duct-neck junctions. In this study, a transfer matrix formulation is derived to determine the sound attenuation properties of a periodic distribution of MPPs backed by Helmholtz resonators along the walls of a duct in the plane wave regime. In the no-flow case, it is shown that an optimal choice of the MPP parameters and resonators separation distance lowers the frequencies of maximal attenuation while maintaining broad stopping bands. As observed in the no-flow and low-speed flow cases, these frequencies can be further decreased by coiling the acoustic path length in the resonators cavity, albeit at the expense of narrower bands of low pressure transmission. The achieved effective wall impedances are compared against Cremer optimal impedance at the first attenuation peak.
Asymptotic modeling of Helmholtz resonators including thermoviscous effects
