A space-folded metamaterial muffler (SMM) for pipe noise attenuation was proposed in this paper, and an improved space-folded metamaterial muffler (ISMM) was formed by arranging wire meshes at the branch inlet. Under the absence of flow and grazing flow, analytical models of SMM and ISMM were developed based on the wave expansion method and Green's function, and correspondingly, the computational fluid dynamics - linear Navier-Stokes (CFD-LNS) numerical models were established. The acoustic characteristics of responsive space (RS) were described through the complex frequency plane. The transmission coefficient of SMM was obtained and verified by sound transmission loss experiments. The results indicate that due to the thermal-viscous effects, the minimum transmission coefficient of RS cannot reach 0. Therefore, the thermal-viscous effect is one of the critical factors. By the parameter retrieving method, it is clarified that the SMM is a single-negative acoustic metamaterial. The effect of the grazing velocity on the transmission coefficient and impedance was revealed quantitatively. The grazing velocity is positively correlated with impedance at the side branch inlet and negatively correlated with total impedance. Therefore, an increase in the grazing velocity will weaken the muffler performance. Since the CFD-LNS model cannot characterize aerodynamic noise, a computational aeroacoustics (CAA) model was established for SMM and ISMM. Numerical results show that the velocity and vorticity at the side branch inlet significantly decrease due to the wire mesh. When Ma is 0.1, 0.05, and 0.01, ISMM reduces aerodynamic noise by 6.11 dB, 9.19 dB, and 2.76 dB, respectively, compared to SMM. Therefore, ISMM has better aerodynamic noise suppression capability. Finally, noise reduction experiments of the ISMM under the grazing flow were performed in an anechoic chamber, and the effectiveness of the ISMM in practical applications was verified by acoustic imaging and spectrogram results.
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