Design of reactive rectangular expansion chambers for broadband acoustic attenuation performance based on optimal port location

Abstract

This paper analyses the transmission loss (TL) performance of rectangular expansion chambers having a single-inlet and single-outlet (SISO) or single-inlet and double-outlet (SIDO) by means of a 3-D semi-analytical formulation based on the modal expansion and the Green’s function approach. To this end, the acoustic field inside the rigid-wall rectangular chamber is obtained as the orthogonal modal solution of the 3-D homogeneous Helmholtz equation. The SISO/SIDO rectangular chamber system is characterised using the uniform piston-driven model in terms of the impedance matrix parameters (equivalently, the acoustic pressure response function) obtained by computing the average of the 3-D Green’s function over the surface area of the inlet/outlet ports modelled as rigid pistons oscillating with uniform velocity. The TL graphs computed using the 3-D semi-analytical formulation are found to be in an excellent agreement with those obtained from the 3-D FEA for SISO test cases, thereby validating the technique presented here. A parametric investigation is conducted to study the effect of arbitrary locations of the inlet/outlet ports on the chamber surface on the TL graph. This results in the formulation of guidelines towards designing the axially short and long SISO/SIDO rectangular chambers exhibiting a broadband TL performance in terms of optimal angular and axial location of ports on the appropriate acoustic pressure nodes. In addition, characteristic features of the TL spectrum of a general reciprocal and conservative single-inlet and multiple-outlet muffler system, such as (1) the effect of interchanging the position of inlet and outlet ports and (2) analysis of peaks and troughs, are proved analytically by means of the scattering matrix parameters. These features are corroborated through the analysis of the TL graphs (obtained using the 3-D semi-analytical formulation) of the SIDO rectangular chambers.