The Transfer Matrix for a Dissipative Silencer of Arbitrary Cross-Section

Glav, Ragnar

doi:10.1006/jsvi.2000.2994

Cited by 21 publications

(14 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…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%

See 1 more Smart Citation

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

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.

show abstract

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

“…However, the number of degrees of freedom in the problem grows rapidly as silencer dimensions and excitation frequency increases and, even for a relatively small automotive silencer, the subsequent CPU expenditure quickly becomes prohibitive (see Kirby [3]). An analytic approach is arguably preferable to a numerical one and, for automotive silencers, the mode matching approach of Cummings and Chang [4], and later Glav [5], have been shown to work well, although only in the case of zero mean flow. Analytic matching of the continuity conditions over the inlet/outlet planes of the silencer does, however, demand that a sufficient number of roots to the dispersion relation have been found in order to achieve a converged solution for the problem.…”

Section: Introductionmentioning

confidence: 99%

A point collocation approach to modelling large dissipative silencers

Kirby

Lawrie

2005

Journal of Sound and Vibration

View full text Add to dashboard Cite

A numerical matching technique known as point collocation is used to model mathematically large dissipative splitter silencers of a type commonly found in HVAC ducts. Transmission loss predictions obtained using point collocation are compared with exact analytic mode matching predictions in the absence of mean flow. Over the frequency range in which analytic mode matching predictions are available, excellent agreement with point collocation transmission loss predictions is observed for a range of large splitter silencers. The validity of using point collocation to tackle large dissipative silencers is established, as is the computational efficiency of the method and its suitability for tackling dissipative silencers of arbitrary, but axially uniform, cross sections.3

show abstract

“…Cummings and Chang (1988) developed a modal method for analyzing a dissipative flow duct silencer of finite length with internal mean flow in the absorbent material. Glav (2000) extended his previous work (null-field and mode-matching) to dissipative silencers of finite length with arbitrary cross-sectional areas using a transfer matrix method. Concerning the volume modulus, Peat (1991) used a transfer matrix in evaluating the acoustical performance for an absorbing silencer element.…”

Section: Introductionmentioning

confidence: 87%

Optimization Design of Hybrid Mufflers on Broadband Frequencies Using the Genetic Algorithm

Chiu¹

2011

Archives of Acoustics

View full text Add to dashboard Cite

Recently, there has been research on high frequency dissipative mufflers. However, research on shape optimization of hybrid mufflers that reduce broadband noise within a constrained space is sparse. In this paper, a hybrid muffler composed of a dissipative muffler and a reactive muffler within a constrained space is assessed. Using the eigenvalues and eigenfunctions, a coupling wave equation for the perforated dissipative chamber is simplified into a four-pole matrix form. To efficiently find the optimal shape within a constrained space, a four-pole matrix system used to evaluate the acoustical performance of the sound transmission loss (STL) is evaluated using a genetic algorithm (GA).A numerical case for eliminating a broadband venting noise is also introduced. To verify the reliability of a GA optimization, optimal noise abatements for two pure tones (500 Hz and 800 Hz) are exemplified. Before the GA operation can be carried out, the accuracy of the mathematical models has been checked using experimental data. Results indicate that the maximal STL is precisely located at the desired target tone. The optimal result of case studies for eliminating broadband noise also reveals that the overall sound power level (SWL) of the hybrid muffler can be reduced from 138.9 dB(A) to 84.5 dB(A), which is superior to other mufflers (a one-chamber dissipative and a one-chamber reactive muffler). Consequently, a successful approach used for the optimal design of the hybrid mufflers within a constrained space has been demonstrated.

show abstract

The Transfer Matrix for a Dissipative Silencer of Arbitrary Cross-Section

Cited by 21 publications

References 17 publications

Point collocation scheme in silencers with temperature gradient and mean flow

Point collocation scheme in silencers with temperature gradient and mean flow

A point collocation approach to modelling large dissipative silencers

Optimization Design of Hybrid Mufflers on Broadband Frequencies Using the Genetic Algorithm

Contact Info

Product

Resources

About