The Point-Matching Method on Dissipative Silencers of Arbitrary Cross-Section

Glav, Ragnar

doi:10.1006/jsvi.1996.0009

Cited by 41 publications

(17 citation statements)

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“…Here, the acoustic fields adopt a modal representation [4,6,7,13,14]. The acoustic pressure in a particular region (inlet/outlet ducts and chamber) can be written in terms of a modal expansion, containing incident as well as the reflected waves.…”

Section: Pressure and Velocity Fieldsmentioning

confidence: 99%

“…To match the transversal solution with the axially propagating waves, the point collocation technique takes into account the compatibility conditions of the pressure and axial acoustic velocity at the silencer geometric discontinuities. Although this approach delivers a considerable reduction in the computational effort compared to the full three-dimensional FEM, attention has to be paid to some numerical issues, such as those found in the point collocation approach [4,13,14], where predictions exhibit a high sensitivity to silencer geometry and also the collocation grid.…”

Section: Introductionmentioning

confidence: 99%

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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: Pressure and Velocity Fieldsmentioning

confidence: 99%

Section: Introductionmentioning

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

View full text Add to dashboard Cite

show abstract

“…Both studies do, however, omit the effects of a perforate and, more importantly, neither progress to predicting the silencer transmission loss. A number of alternative numerical eigenvalue formulations have also been sought for elliptical crosssections, examples include the Rayleigh Ritz approach of Cummings 7 and the point matching technique of Glav 8 . These alternative formulations do, however, compromise, to some extent, the versatility and robustness of the FEM; the analysis of Cummings is restricted to the fundamental mode only, the method of Glav is very sensitive to silencer geometry and the collocation grid chosen.…”

Section: Introductionmentioning

confidence: 99%

Transmission loss predictions for dissipative silencers of arbitrary cross section in the presence of mean flow

Kirby¹

2003

The Journal of the Acoustical Society of America

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A numerical technique is developed for the analysis of dissipative silencers of arbitrary, but axially uniform, cross section. Mean gas flow is included in a central airway which is separated from a bulk reacting porous material by a concentric perforate screen. The analysis begins by employing the finite element method to extract the eigenvalues and associated eigenvectors for a silencer of infinite length. Point collocation is then used to match the expanded acoustic pressure and velocity fields in the silencer chamber to those in the inlet and outlet pipes.Transmission loss predictions are compared with experimental measurements taken for two automotive dissipative silencers with elliptical cross sections.Good agreement between prediction and experiment is observed both without mean flow and for a mean flow Mach number of 0.15. It is demonstrated also that the technique presented offers a considerable reduction in computational expenditure when compared to a three dimensional finite element analysis.3

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“…and R jm is given by (8). Note that, the explicit form for R jm for this problem is given in equation (33).…”

Section: A Simple Dissipative Silencermentioning

confidence: 99%

Mode-matching without root-finding: Application to a dissipative silencer

Lawrie

Kirby

2006

The Journal of the Acoustical Society of America

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This article presents an analytic mode-matching approach suitable for modelling the propagation of sound in a two-dimensional, three-part, ducting system. The approach avoids the need to the find roots of the characteristic equation for the middle section of the duct (the component) and is readily applicable to a broad class of problems. It is demonstrated that the system of equations, derived via analytic mode-matching, exhibits certain features which ensure that they can be re-cast into a form that is independent of the roots of the characteristic equation for the component. The precise details of the component are irrelevant to the procedure; it is required only that there exists an orthogonality relation, or similar, for the eigenmodes corresponding to the propagating wave-forms in this region.The method is applied here to a simple problem involving acoustic transmission through a dissipative silencer of the type commonly found in heating ventilation and air-conditioning (HVAC) ducts. With reference to this example, the silencer transmission loss is computed, and the power balance for the silencer is investigated and is shown to be an identity that is necessarily satisfied by the system of equations, regardless of the level of truncation. * Portions of this work were presented in "On analysing a dissipative silencer: a mode-matching ap-

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The Point-Matching Method on Dissipative Silencers of Arbitrary Cross-Section

Cited by 41 publications

References 0 publications

Point collocation scheme in silencers with temperature gradient and mean flow

Point collocation scheme in silencers with temperature gradient and mean flow

Transmission loss predictions for dissipative silencers of arbitrary cross section in the presence of mean flow

Mode-matching without root-finding: Application to a dissipative silencer

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