A coupled approach for predicting transmission loss of silencers with consideration of three-dimensional wave effects in inlet and outlet ducts

A coupled approach combining finite element method and duct mode expansion is proposed to determine the transmission loss of large silencers with consideration of three-dimensional wave effects in inlet and outlet ducts in the presence of flow. The finite element formula is established for the linearized potential equation (LPE), and the acoustic variables in the boundary integrals on the inlet and outlet surfaces are expressed analytically in terms of mode expansion. Since the introduced modal amplitude coefficients add unknown variables, the intrinsic functions are used as weighted functions to construct integral equations on the inlet and outlet surfaces to form a closed set of equations. Expressions of incident and transmitted sound powers are derived, and the transmission loss of silencer may be determined for any-giving mode incidence. For the symmetric silencers, specific combinations of acoustic modes are presented to improve the stability and efficiency of the approach. The dissipative and reactive silencers with rectangular and circular cross-sectional inlet and outlet ducts are examined, good agreements between predictions and benchmark data verified the present approach. Effects of Mach numbers and geometric parameters, flow fields and acoustic excitations on the acoustic attenuation behavior of the silencers as well as transmission loss predictions from different strategies are discussed.