Acoustic length correction of duct extension into a cylindrical chamber

The one-dimensional (1D) analytical model for the accurate acoustic performance prediction of silencers and resonators with duct extensions require the introduction of acoustic length corrections in order to account for the multidimensional effects at junctions. In the present study, a two-dimensional (2D) axisymmetric analytical approach, and three-dimensional (3D) finite element method (FEM) are developed to determine the acoustic length correction of duct extension into cylindrical chamber. The effect of chamber geometry on the acoustic length correction is examined and an approximate expression for the acoustic length correction is provided. The corrected 1D analytical approach with acoustic length correction is then used to predict transmission loss of Helmholtz resonator with neck extension and expansion chamber with extended inlet/outlet. The 1D analytical solutions of transmission loss are compared with FEM predictions and experimental results.