Fan noise propagating within ducts is typically broadband in nature. Conventional silencers often fail to achieve effective broadband noise insulation, presenting a persistent challenge in engineering applications. The rainbow trapping effect offers an innovative solution to this problem. This paper proposes a ventilated silencer based on the rainbow trapping effect, which provides broadband capability of noise attenuation without altering the duct inner diameter. The original rainbow trapping structure is transformed into a fan shaped configuration, mounted by circular arrays and filled with porous materials to form a silencer suitable for duct applications. To analyze the performance of this silencer, a comprehensive finite element model is developed, which is validated through impedance tube experiments. The results reveal that sound waves with different frequencies could be captured by branch cavities with varying depths, and the acoustic energy will be subsequently dissipated by the filled porous materials. Both impedance tube experimental and simulation results demonstrate the broadband performance of the proposed silencer, specifically achieving a sound transmission loss exceeding 10 dB above 257 Hz, representing 90% acoustic energy insulation. Fan tests demonstrated that the average overall sound pressure level is reduced by 4.8 dB after installing the silencer. Parametric analysis indicates that this silencer can achieve excellent broadband performance without requiring complicated design and manufacturing processes. This work presents a promising approach for duct and fan noise control applications.
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