Three-dimensional acoustic analysis of lined rectangular ducts and plenum chambers

Abstract

Dissipative silencers are generally used in HVAC systems or intake/exhaust system of vehicles by utilizing the visco-thermal loss of sound along the passage of porous materials. In this thesis, transmission loss or transfer matrix of the three typical dissipative silencers, such as lined duct, lined rectangular plenum chamber, and rectangular splitter silencer, are developed. Firstly, in order to investigate the acoustic property of lined ducts, the propagation constants of sound in lined ducts are calculated in both locally-and bulk-reacting liner. Their transmission losses are also predicted using the mode-matching technique, boundary element method, and ray model. The acoustic performance of a fully lined rectangular plenum chamber having inlet and outlet ports at arbitrary locations is predicted. Because no exact analytic solution exists for this reactive-resistive silencer configuration, numerical methods are only available for a three-dimensional analysis. The lined plenum chamber is modeled as a piston-driven rectangular tube without a mean flow and the acoustic pressure in the lined chamber is obtained by superposing the acoustic pressures due to each harmonically fluctuating piston. Air pore and skeleton material of the porous liner is reduced to an equivalent medium; thus, its acoustic characteristic is given by bulk-reacting liner properties. A single weak variational statement, which satisfies the conditions of the oscillating piston and all necessary boundary conditions, is developed. The Rayleigh-Ritz method is employed as the numerical scheme for the derived variational statement. Using a transfer matrix and measured material properties, all possible types of lined plenum chambers are tested. Computed results are compared with the predicted transmission loss by the locally-reacting liner model and experimental results. Good agreement is observed between measured and predicted TL by the Rayleigh-Ritz method employing the bulk-reacting liner model....