Analytic mode matching for a circular dissipative silencer containing mean flow and a perforated pipe

An analytic mode matching scheme that includes higher order modes is developed for a straight-through circular dissipative silencer. Uniform mean flow is added to the central airway and a concentric perforated screen separates the mean flow from a bulk reacting porous material. Transmission loss predictions are compared with experimental measurements and good agreement is demonstrated for three different silencers. Furthermore, it is demonstrated that, when mean flow is present, the axial kinematic matching condition should equate to that chosen for the radial kinematic boundary condition over the interface between the airway and the material. Accordingly, if the radial matching conditions are continuity of pressure and displacement, then the axial matching conditions should also be continuity of pressure and displacement, rather than pressure and velocity as previously thought. When a perforated screen is present the radial pressure condition changes, but the radial kinematic condition should always remain equivalent to that chosen for the axial kinematic matching condition; here, results indicate that continuity of displacement should be retained when a perforated screen is present

Numerical mode matching in dissipative silencers with temperature gradients and mean flow

This work presents a mathematical approach based on the mode matching method to compute the transmission loss of perforated dissipative silencers with temperature gradients and mean flow. Three-dimensional wave propagation is considered in silencer geometries with arbitrary, but axially uniform, cross section. To reduce the computational requirements of a full multidimensional finite element calculation, a method is developed combining axial and transversal solutions of the wave equation. First, the finite element method is employed in a twodimensional problem to extract the eigenvalues and associated eigenvectors for the silencer cross section. Mean flow as well as radial temperature gradients and the corresponding thermal-induced material heterogeneities are included in the model. Assuming a low acoustic influence of axial gradients (compared to radial variations), an axially uniform temperature field is taken into account, its value being the inlet/outlet average. A weighted residual approach is then used to match the acoustic fields (pressure and axial acoustic velocity) at the geometric discontinuities between the silencer chamber and the inlet and outlet pipes. Transmission loss predictions are compared favourably with a general three-dimensional finite element approach, offering a reduction in the computational effort

Sound attenuation in partially-filled perforated dissipative mufflers with extended inlet/outlet

The current study considers the acoustic characteristics of partially-filled perforated dissipative circular mufflers with extended inlet/outlet. In addition to the finite element method (FEM), a two-dimensional (2-D) axisymmetric analytical approach is developed that matches the acoustic field across the discontinuities by applying the continuity conditions of the acoustic pressure and velocity. The complex characteristic impedance, wavenumber and perforation impedance are taken into account to evaluate the axial wavenumber in the absorbing fiber and in the central perforated pipe. In addition, experimental work is considered for validation purposes. Several effects regarding the extended inlet/outlet ducts and the fiber properties are presented and discussed

Multidimensional acoustic modelling of catalytic converters

In this work the finite element method is applied to predict the acoustic behaviour of catalytic converters. Two different modelling techniques are considered and compared for the monolith: (1) First, the procedure described in previous works, in which the wave propagation in the monolithic catalytic converter is assumed to be analogous to the propagation in an equivalent fluid, characterized by its complex and frequency dependent impedance and wave number. In this case, the finite element model leads to the calculation of the three-dimensional acoustic field inside the complete catalytic converter, including the inlet/outlet ducts and the monolith. Therefore, this first approach allows the consideration of higher order modes inside all the catalyst components; (2) On the other hand, a coupling technique is applied in which the monolith is replaced by a plane wave transfer matrix, that is, only one-dimensional acoustic behaviour is allowed for the capillary ducts, while three-dimensional acoustic waves can still be present in the inlet/outlet ducts. The results provided by both approaches are compared with experimental measurements for a selected configuration, showing that the latter technique exhibits a better agreement. In addition, the effect of several parameters on the acoustic behaviour of the catalyst is investigated