Simple Model for Predicting the Insertion Loss of a Straight Tube Silencer

The simplest model for predicting the insertion loss of straight ventilation silencers is Piening's model. However, it can be applied only below the cut-off frequency, which is, for typical silencers, between 160 and 2000 Hz. Above the cut-off frequency, Piening's model overestimates strongly the insertion loss. The purpose of this study was to introduce a simple high-frequency extension to Piening's model. The model was based on the presumption that the wall of the silencer is highly absorbing so that plane wave is the dominating waveform in the silencer at high frequencies. The cross-sectional area of the duct was divided into the absorption and the transmission band. The absorption band locates close to the absorbing walls and the transmission band in the middle of the silencer. The thickness of the absorption band is approximately a half wavelength. At low frequencies, the absorption band covers the whole cross-section of the silencer. Above the limit frequency, the thickness of absorption band decreases with increasing frequency so that at high frequencies only small part of cross-section belongs to absorption band. This explains why the insertion loss of silencers decreases strongly above the cut-off frequency. Two specimens were measured in the laboratory according to ISO 7235. The predicted insertion loss was close to the measured insertion loss except below the limit frequency where the model underestimated the insertion loss by 10 dB for both specimens. The existence of absorption and transmission bands could be proved by radial sound level measurements inside the silencer.