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

Denia, F.D.; Martínez‐Casas, José; Baeza, Luis; Fuenmayor, F. J.

doi:10.1016/j.apacoust.2012.02.003

Cited by 16 publications

(30 citation statements)

References 23 publications

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“…(14) and (15) correspond to the FE load vectors. These involve similar shape functions N = N * for conforming discretizations, while different interpolation functions should be considered for non-conforming meshes [27], N * being those associated with region SM in Eq. (14) and with region SA in Eq.…”

Section: Wavenumbers and Pressure Modes: Transversal Eigenvalue Problemmentioning

confidence: 99%

Point collocation scheme in silencers with temperature gradient and mean flow

Denia

Sánchez-Orgaz

Baeza

et al. 2016

Journal of Computational and Applied Mathematics

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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.

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Section: Wavenumbers and Pressure Modes: Transversal Eigenvalue Problemmentioning

confidence: 99%

Point collocation scheme in silencers with temperature gradient and mean flow

Denia

Sánchez-Orgaz

Baeza

et al. 2016

Journal of Computational and Applied Mathematics

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“…The FEM is to solve the acoustic FE equations and get the sound pressure at every point under specific boundary conditions. The perforated elements can be expressed by acoustic transfer relation admittance calculated based on appropriate impedance model [16], which normally work very well under conditions that they are intended for. The viscous losses are considered in the real part of the impedance model.…”

Section: Comparison Between 1d Tmm and Fem Based On Test Resultsmentioning

confidence: 99%

Comparison of 1D transfer matrix method and finite element method with tests for acoustic performance of multi-chamber perforated resonator

2016

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“…Therefore, not only noise attenuation due to silencers, but also the influence of catalytic converters and filters, should be considered in the development of analytical and numerical tools for predicting the acoustic behaviour of the complete exhaust system. For this reason, a number of publications can be found associated with the acoustic modelling of these devices [2][3][4][5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

“…The traditional plane wave models [14][15][16] have important limitations and are only applicable in the low frequency range and for relatively small cross-sectional ducts [16]. For these reasons, and in order to have higher accuracy in the analysis, a number of multidimensional numerical models [7,8,17] and analytical approaches [5,6,9] have been developed in the last decades, the latter providing a lower computational effort. Multidimensional schemes can be subdivided into two large groups.…”

Section: Introductionmentioning

confidence: 99%

“…To do so, it is assumed that the monolith resembles, acoustically speaking, a sound absorbent material with homogeneous and isotropic behaviour, defined by complex and frequency-dependent equivalent properties, such as the density and speed of sound [18]. Secondly, the more realistic 3D cavities/1D monolith technique, which retains multidimensional propagation in the expansion chambers and inlet/outlet ducts, but assumes one-dimensional acoustic behaviour within the capillaries and thus ignores any possible three-dimensionality of the sound field within the monolith [4][5][6][7][8][9]17]. From a mathematical point of view, this second approach therefore allows the replacement of the ceramic monolith by a plane wave fourpole transfer matrix and only the presence of plane waves in the monolith occurs, which seems more consistent with the one-dimensional characteristics of the capillary tubes integrating the CC.…”

Section: Introductionmentioning

confidence: 99%

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Computational performance of analytical methods for the acoustic modelling of automotive exhaust devices incorporating monoliths

Denia

Martnez-Casas

Carballeira

et al. 2018

Journal of Computational and Applied Mathematics

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The acoustic modelling of automotive exhaust devices, such as catalytic converters (CC) and diesel particulate filters (DPF), usually requires the use of multidimensional analytical and numerical techniques. The presence of higher order modes and three-dimensional waves in the expansion and contraction subdomains, as well as sound propagation within the monolith capillary ducts, can be considered through the finite element method (FEM), although this approach is traditionally thought to be very time consuming. With a view to overcome this limitation and to reduce the computational effort of the FEM, alternative modelling techniques are presented in the current work to speed up transmission loss calculations in exhaust devices incorporating monoliths. These approaches are based on the point collocation technique and the mode matching method. As shown in earlier studies, the sound attenuation of an exhaust device incorporating a monolith can be properly predicted if the latter is replaced by a plane wave four-pole transfer matrix providing a relationship between the acoustic fields at both sides of the monolithic region. Therefore, this work combines the presence of multidimensional higher order modes in the expansion and contraction regions with one-dimensional wave propagation within the capillary ducts of the central monolith. The point collocation technique and the mode matching method are applied to the compatibility conditions of the acoustic fields at all the subdomain interfaces to couple the solutions of the wave equation in the corresponding exhaust device subcomponents. For the particular case of rigid circular ducts, Bessel functions are considered as transversal pressure modes. The computational efficiency and accuracy of the results associated with the two analytical modelling techniques presented here are assessed, including the effect of the number of modes and collocation points, as well as their location. All the analytical approaches proposed in this work provide accurate predictions of the device attenuation performance and outperform the computational expenditure of a FE computation. Some differences are found, however, among the various analytical schemes in terms of computational speed and solution accuracy. From the results presented here, the mode matching method is the most efficient technique for the particular configurations under study, mainly due to the possibility of exploiting the orthogonality properties of the transverse pressure modes.

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

Cited by 16 publications

References 23 publications

Point collocation scheme in silencers with temperature gradient and mean flow

Point collocation scheme in silencers with temperature gradient and mean flow

Comparison of 1D transfer matrix method and finite element method with tests for acoustic performance of multi-chamber perforated resonator

Computational performance of analytical methods for the acoustic modelling of automotive exhaust devices incorporating monoliths

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