Determination of a Power Transfer Matrix via a Boundary Element Method Determined Scattering Matrix

The transfer matrix approach is commonly used to simulate mufflers below the plane wave cutoff frequency. Transfer matrices have been developed for common muffler elements and models can be solved in seconds. In this paper, a similar power transfer matrix method is detailed which is applicable to systems above the cutoff frequency. To determine the 2X2 power transfer matrix, a scattering matrix calculated using the boundary element method is reduced to the power transfer matrix. The procedure for doing so is outlined. Although the reduction from the full scattering matrix to the 1-D power transfer matrix provides only an approximation, it works seamlessly with other 1-D analysis tools and first-mode analytical solutions for a cascaded exhaust design. Several examples are provided to validate and demonstrate the proposed method.