Study On Wideband Transmission Loss Predictive Method For Silencing Devices

Pipe silencing devices are widely used in the field of noise control engineering.Transmission loss(TL)is commonly used to measure noise attenuation performance of pipe silencing devices.Therefore,it is important and valuable to investigate the accurate and efficient wide-band frequency TL computational methods.In order to improve computation efficiency,a hybrid technique combining the analytical approach and numerical method is proposed by consideration of the characteristics of pipe silencing system in the paper.To overcome the limitations of traditional TL calculation and consider the effect of higher order modes in the inlet and outlet pipes on TL of pipe silencing devices,the wide-band frequency computational methods are investigated in detail.The pipe silencing devices in practical engineering may always be divided into the reguralr components and complex irregular substructures.To utilize the merits of such characteristics,a hybrid method based on the substructuring impedance matrix approach is proposed and studied to calculate TL in the paper.The whole structure is divided into several substructures and a suitable method for each substructure is adopted to calculate the impedance matrix according to the cross-section shape and complexity of the substructure.In the paper,mixed-body boundary element method(MBEM)is used to calculate the impedance matrix of the complex substructures,and point collocation approach is employed for the substructures with axially uniform cross-section.Both analytical and numerical point collocation methods are illustrated in the paper.For the independent simple structures used in the silencing system,the numerical mode matching method is applied to calculate the impedance matrix.Finally,all the impedance matrices are connected together and the impedance matrix relationship of the whole structure can be obtained.The application details are introduced in the paper and the calculation accuracy and efficiency are analyzed by comparing with traditional BEM.For large dimension structures,the traditional BEM-based method will require large storage space and long computation time.A fast multipole mixed-body boundary element method(FMMBEM)is proposed in the paper by combining the MBEM with the fast multipole algorithm(FMA).Furthermore,the FMMBEM is combined with mode matching method for TL calculation of a pipe silencing system.The traditional TL calculation method is based on the plane wave propagation assumption in the inlet and outlet pipes.However,the method is no longer applicable if higher order modes exist in the inlet and outlet pipes.The present study develops four methodologies for the wide-band frequency TL calculation of pipe silencing devices with any-shaped cross-section inlet/outlet.The first approach is based on the scattering matrix theory.After the impedance matrix of the structure has been obtained,the acoustic variables are expressed analytically by mode expansion.Then the impedance matrix is transferred to scattering matrix.By solving the linear equations,the unknown mode amplitudes can be obtained and the TL is calculated by the acoustic power of inlet and outlet.The second approach is based on the acoustic reciprocal identity and each reciprocal identity couples two different acoustic fields on the same silencer.The first sound field employs the analytical modal expansion in the inlet and outlet,while the second sound field is the boundary element solution associated with a random boundary condition set.In the paper,the impedance matrix is used to provide the solution.Again,by solving the linear equations,the unknown modal amplitudes may be obtained and then the TL can be calculated.The third approach named hybrid finite element-mode matching method is presented in the paper.The acoustic variables on the inlet and outlet are expressed analytically and then combined with the FEM formulation.For the sound pressure on the inlet and outlet,the eigen-function of the cross-section is adopted as weighting function and integration is execrated at inlet and outlet area.The unknown modal amplitudes are then obtained by solving the linear equations considering the corresponding boundary conditions.Finally,the TL is calculated using the acoustic power of inlet and outlet.The fourth method is a direct energy superposition method.The boundary element method is employed to calculate the acoustic power of inlet and outlet respectively after acoustic wave decomposition technique is applied to every element at the inlet and outlet.The TL is calculated by superposing the acoustic power of every element at inlet and outlet respectively.Furthermore,the application range and advantages of the direct methodology are analyzed.Finally,based on the two-load method,the transmission loss measurement is executed by using the impedance tube setup.Three silencers are designed and the transmission loss measurement results are employed to verify the previous hybrid method.The calculation results agree well with experimental data.