A study on the acoustic propagation characteristics of circular expanding ducts using the finite element method

A circular expanding duct features an increasing cross-sectional area that tends to excite higher-order modes at low frequencies, thereby affecting the performance of acoustic devices. Studying the acoustic propagation characteristics of circularly expanding ducts is thus crucial for optimal design and noise control. Traditional prediction methods do not adequately account for three-dimensional wave effects inside a duct. This study investigates the sound attenuation performance of various circular expanding ducts in the frequency range of 10–2500 Hz using the three-dimensional finite element method in combination with acoustic theory. The results show that the geometric expansion of the duct changes the wavefront shapes of transmitted sound waves, causing varying degrees of wavefront distortion. Behind the expanding region, these distorted wavefronts interfere with each other to varying extents, affecting the transmission loss (TL) of the duct. When the length of the expanding section is shorter, the average attenuation is generally higher. However, at specific frequencies (e.g., 2100 Hz), a longer expanding section may enhance sound attenuation by exciting more resonant modes. As the expansion ratio of the cross-sectional area increases, wavefront distortion and modal resonance become more pronounced, leading to increased average attenuation and the appearance of more peaks in the TL curve. In addition, the incidence of higher-order modes induces complex modal coupling and interference, significantly reducing the average sound attenuation of the duct. This study provides theoretical foundations and reference values for optimizing the design of circular expanding ducts to improve acoustic performance.