Determination of the complex acoustic scattering matrix of a right-angled duct

Abstract

A method for determining the complete higher-order scattering matrix of an acoustic discontinuity is developed. The method is demonstrated for a right-angled waveguide bend, and the magnitude and phase of the reflection and transmission coefficients are extracted precisely. The procedure is straightforward and based on the solutions to the Helmholtz equation by the finite element method (FEM). The consistency of the scattering coefficients found by this method is verified by their properties of symmetry, and their accuracy is established by the conservation of energy. The reliability of the new technique is further proved by means of an arbitrary sound source and by comparing the direct FEM response to the reflection matrix calculation. Some features of the scattering matrix as a function of frequency are surprising, such as the steps and reversion of the phase evolution or the complete loss of transmission of the incoming wave. The methodology detailed in this paper can be extended to other multiport junctions, such as T-junctions or size discontinuities in ducts.

Sub-chamber optimization for silencer design

“…Coupling effect between two sub-chambers C 1 and C 2 . silencer outlet, a perfectly matched layer (PML) is introduced to describe the anechoic condition, which only allows outgoing waves with no spurious reflections [25].…”

Going round the bend: reflection and transmission of long waves by waveguide corners and labyrinths

“…For 90∘ and 180∘ bends, see [11]. For 90∘ bends, there are later papers in which finite-element methods are used [12,13]. For some other geometries, see [14–16].…”

Modal analysis of the scattering coefficients of an open cavity in a waveguide

“…To accommodate cross modes in a duct with scatterers, the wave matching technique [2,3] is used. The finite element and boundary element methods, are used to determine the scattering coefficients when the geometries of the ducts and scatterers are complicated [4,5]. While these wave matching and numerical methods are capable of producing accurate coefficients, they are less useful in directly delivering the physical insight into the peaks and valleys in the coefficient curves.…”