Abstract
In this work, a computationally efficient numerical technique based on the mode matching method is presented to model and analyse the acoustic behaviour of dissipative silencers. Three-dimensional wave propagation and temperature gradients are considered in the absorbent material while a perforated duct separates the dissipative region and the central passage. The use of a full multidimensional finite element formulation is computationally expensive in configurations with arbitrary geometry and complex thermal gradients. To avoid this drawback, a technique is proposed combining axial and transversal solutions of the wave equation in the different ducts. The latter are obtained through a two-dimensional finite element approach that allows the computation of the eigenvalues and eigenvectors associated with the transversal section, including radial temperature gradients and the corresponding thermal-induced heterogeneities of the absorbent material properties. Due to the reduced acoustic impact of axial gradients compared to radial variations, an axially uniform temperature field is assumed, its value being the inlet/outlet average. Then, the compatibility equations of the acoustic field (pressure and axial acoustic velocity) at the geometric discontinuities together with the mode matching method are used to obtain the wave propagation coefficients in the different regions of the silencer, such as the central chamber and the inlet/outlet pipes. This methodology is compared with the results given by full three-dimensional finite element computations including axial and radial temperature gradients, showing a good agreement with lower computational requirements.
