Year of Publication


Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation




Mechanical Engineering

First Advisor

Dr. Tingwen Wu


Large silencers used in the power generation industry usually have a very large cross section at the inlet and outlet. Higher-order modes will populate the inlet and outlet even at very low frequencies. Although the silencer itself is often modeled by a three-dimensional analysis tool such as the boundary element method (BEM) or finite element method (FEM), a direct computation of the transmission loss (TL) from the BEM or FEM model can be challenging without incorporating certain forms of modal expansion.

A so-called “impedance-to-scattering matrix method” is proposed to extract the modes at the inlet and outlet from the BEM impedance matrix based on the point collocation method. The BEM impedance matrix relates the sound pressures at the inlet and outlet to the corresponding particle velocities, while the scattering matrix relates the modes at the inlet and outlet. Normally there are more boundary elements than the total number of modes at the inlet and outlet, and a least-squares procedure is used to condense the element-based impedance matrix to the mode-based scattering matrix. The TL computation will follow if a certain form of the incident wave is assumed and the outlet is non-reflective. Several commonly used inlet/outlet configurations are considered in this dissertation, which include axisymmetric, non-axisymmetric circular, and rectangular inlet/outlet shapes. In addition to the single inlet and outlet silencers, large multi-inlet and multi-outlet silencers are also investigated.

Besides the collocation-based impedance-to-scattering matrix method, an integral-based impedance-to-scattering matrix method based on the reciprocal identity is also proposed for large silencer analysis. Although it may be more time-consuming to perform the additional numerical integration, an integral-based method is free of any uncertainties associated with collocation points. The computational efficiency, accuracy and stability are compared between two proposed methods.

One bonus effect of producing the scattering matrix is that it can also be used to combine subsystems in series connection. The Redheffer’s star product is introduced to combine scattering matrices of subsystems.

In the design stage, rapid assessment of the silencer performance is always preferred. However, the existing analytical approaches are only suitable for simple dissipative silencers such as straight lined ducts. A two-dimensional first-mode semi-analytical solution is developed to quickly evaluate the performance of tuned dissipative silencers below the cut-off frequency. The semi-analytical solution can also serve as a validation tool for the BEM.

Digital Object Identifier (DOI)