Acoustic modelling of exhaust devices with nonconforming finite element meshes and transfer matrices

[EN] Transfer matrices are commonly considered in the numerical modelling of the acoustic behaviour associated with exhaust devices in the breathing system of internal combustion engines, such as catalytic converters, particulate filters, perforated mufflers and charge air coolers. In a multidimensional finite element approach, a transfer matrix provides a relationship between the acoustic fields of the nodes located at both sides of a particular region. This approach can be useful, for example, when one-dimensional propagation takes place within the region substituted by the transfer matrix. As shown in recent investigations, the sound attenuation of catalytic converters can be properly predicted if the monolith is replaced by a plane wave four-pole matrix. The finite element discretization is retained for the inlet/outlet and tapered ducts, where multidimensional acoustic fields can exist. In this case, only plane waves are present within the capillary ducts, and three-dimensional propagation is possible in the rest of the catalyst subcomponents. Also, in the acoustic modelling of perforated mufflers using the finite element method, the central passage can be replaced by a transfer matrix relating the pressure difference between both sides of the perforated surface with the acoustic velocity through the perforations. The approaches in the literature that accommodate transfer matrices and finite element models consider conforming meshes at connecting interfaces, therefore leading to a straightforward evaluation of the coupling integrals. With a view to gaining flexibility during the mesh generation process, it is worth developing a more general procedure. This has to be valid for the connection of acoustic subdomains by transfer matrices when the discretizations are nonconforming at the connecting interfaces. In this work, an integration algorithm similar to those considered in the mortar finite element method, is implemented for nonmatching grids in combination with acoustic transfer matrices. A number of numerical test problems related to some relevant exhaust devices are then presented to assess the accuracy and convergence performance of the proposed procedure.Authors gratefully acknowledge the financial support of Ministerio de Ciencia e Innovacion and the European Regional Development Fund by means of the Projects DPI2007-62635 and DPI2010-15412.Denia, F.; Martínez-Casas, J.; Baeza, L.; Fuenmayor, F. (2012). Acoustic modelling of exhaust devices with nonconforming finite element meshes and transfer matrices. Applied Acoustics. 73(8):713-722. https://doi.org/10.1016/j.apacoust.2012.02.003S71372273

A finite element approach for the acoustic modelling of perforated dissipative mufflers with non-homogeneous properties

[EN] In this work, a finite element approach is presented for modeling sound propagation in perforated dissipative mufflers with non-homogeneous properties. The spatial variations of the acoustic properties can arise, for example, from uneven filling processes during manufacture and degradation associated with the flow of soot particles within the absorbent material. First, the finite element method is applied to the wave equation for a propagation medium with variable properties (outer chamber with absorbent material) and a homogeneous medium (central passage). For the case of a dissipative muffler, the characterization of the absorbent material is carried out by means of its equivalent complex density and speed of sound. To account for the spatial variations of these properties, a coordinate-dependent function is proposed for the filling density of the absorbent material. The coupling between the outer chamber and the central passage is achieved by using the acoustic impedance of the perforated central pipe, that relates the acoustic pressure jump and the normal velocity through the perforations. The acoustic impedance of the perforated central duct includes the influence of the absorbent material and therefore a spatial variation of the impedance is also taken into account. A detailed study is then presented to assess the influence of the heterogeneous properties and the perforated duct porosity on the acoustic attenuation performance of the muffler.The authors gratefully acknowledge the financial support of Ministerio de Ciencia e Innovacion and the European Regional Development Fund by means of the projects DPI2007-62635 and DPI2010-15412.Antebas, A.; Denia Guzmán, FD.; Pedrosa Sanchez, AM.; Fuenmayor Fernández, FJ. (2013). A finite element approach for the acoustic modelling of perforated dissipative mufflers with non-homogeneous properties. Mathematical and Computer Modelling. 57(7):1970-1978. https://doi.org/10.1016/j.mcm.2012.01.021S1970197857

Finite element based acoustic analysis of dissipative silencers with high temperature and thermal-induced heterogeneity

A mixed finite element model has been derived for the acoustic analysis of perforated dissipative silencers including several effects simultaneously: (1) High temperature and thermal gradients in the central duct and the outer absorbent material; (2) a perforated passage carrying non-uniform axial mean flow. For such a combination, the properties of sound propagation media and flow are inhomogeneous and vary with position. The material of the outer chamber can be modelled by its complex equivalent acoustic properties, which completely determine the propagation of sound waves in the air contained in the absorbent medium. Temperature gradients introduce variations in these properties that can be evaluated through a heterogeneous temperature-dependent resistivity in combination with material models obtained at room temperature. A pressure-based wave equation for stationary medium is then used with the equivalent density and speed of sound of the absorbent material varying as functions of the spatial coordinates. Regarding the central air passage, a wave equation in terms of acoustic velocity potential can be used to model the non-uniform moving medium since the presence of temperature variations introduce not only heterogeneous acoustic properties of the air but also a gradient in the mean flow velocity. The acoustic connection between the central passage and the outer chamber is given by the acoustic impedance of the perforated duct. This impedance depends on the heterogeneous properties of the absorbent material and the non-uniform mean flow, leading to a spatial variation of the acoustic coupling and also to additional convective terms in the governing equations. The results presented show the influence of temperature, thermal gradients and mean flow on the transmission loss of automotive silencers. It has been found that high temperature and thermal-induced heterogeneity can have a significant influence on the acoustic attenuation of an automotive silencer and so should be included in theoretical models. In some particular configurations it may be relatively accurate to approximate the temperature field by using a uniform profile with an average value, specially for low resistivity materials. It has been shown, however, that this is not always possible and attenuation overestimation is likely to be predicted, mainly for high radial thermal gradients and high material flow resistivities, if the temperature distribution is not taken into account.Authors gratefully acknowledge the financial support of Ministerio de Economía y Competitividad and the European Regional Development Fund (projects DPI2010-15412 and TRA2013-45596-C2-1-R), Generalitat Valenciana (project Prometeo/2012/023) and Universitat Politècnica de València (PAID-05-12, project SP20120452)

Point collocation scheme in silencers with temperature gradient and mean flow

This work presents a mathematical approach based on the point collocation technique to compute the transmission loss of perforated dissipative silencers with transversal 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 two-dimensional problem to extract the eigenvalues and associated eigenvectors for the silencer cross section. Mean flow as well as transversal temperature gradients and the corresponding thermal-induced material heterogeneities are included in the model. In addition, an axially uniform temperature field is taken into account, its value being the inlet/outlet average. A point collocation technique 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 favorably with a general three-dimensional finite element approach, offering a reduction in the computational effort.Ministerio de Economía y Competitividad and the European Regional Development Fund (project TRA2013-45596-C2-1- R), as well as Generalitat Valenciana (project Prometeo/2012/023)