Optimizing the performance of a side-branch array duct muffler

Recent studies of the authors show that muffler formed by putting together narrow side-branches in array form can offer strong and broadband sound attenuation in low Mach number flow ducts. It is also found that such muffler with the increasing branch length in the direction of duct flow has stronger resilience to flow excitation and thus can maintain its sound attenuation performance unless the duct flow is high. However, the arrangement of the branch length has not been optimized. Numerical investigation is carried out using finite-element computation in the present study to further understand how the branch length variation is affecting the overall sound attenuation of the side-branch array muffler. For simplicity, a branch length variation is assumed to follow a power law of the branch order. A power law index of 1 represents linear variation. It is found that for a muffler with 11 side-branches, the index for minimum transmission is about 1.5, but that for maximum particle kinetic energy is around 1.38. In term of noise attenuation spectrum, the muffler with index 1 and 3 give very strong attenuation at particular frequencies, while that with index 1.5 gives a more uniform attenuation within the operation frequency range.