The Impedance of Perforated Plates Subjected to Grazing Gas Flow and Backed by Porous Media

Kirby, Ray; Cummings, A.

doi:10.1006/jsvi.1998.1811

Cited by 133 publications

(95 citation statements)

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“…The concept of transmission impedance is typically used as a macroscopic model for microscopic features. For instance, a perforated metallic plate is often modeled as a mass-damping system, in which semi-empirical formulas for the mass and damping coefficients can be deduced from experiments [9]. The reactive part of the perforation impedance can be established by homogenization of the inviscid equations [10].…”

Section: Linear Acoustics In the Presence Of Impedance Surfacesmentioning

confidence: 99%

A Nitsche-type method for Helmholtz equation with an embedded acoustically permeable interface

Yedeg

Wadbro

Hansbo

et al. 2016

Computer Methods in Applied Mechanics and Engineering

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We propose a new finite element method for Helmholtz equation in the situation where an acoustically permeable interface is embedded in the computational domain. A variant of Nitsche's method, different from the standard one, weakly enforces the impedance conditions for transmission through the interface. As opposed to a standard finite-element discretization of the problem, our method seamlessly handles a complex-valued impedance function Z that is allowed to vanish. In the case of a vanishing impedance, the proposed method reduces to the classic Nitsche method to weakly enforce continuity over the interface. We show stability of the method, in terms of a discrete Gårding inequality, for a quite general class of surface impedance functions, provided that possible surface waves are sufficiently resolved by the mesh. Moreover, we prove an a priori error estimate under the assumption that the absolute value of the impedance is bounded away from zero almost everywhere. Numerical experiments illustrate the performance of the method for a number of test cases in 2D and 3D with different interface conditions.

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Section: Linear Acoustics In the Presence Of Impedance Surfacesmentioning

confidence: 99%

A Nitsche-type method for Helmholtz equation with an embedded acoustically permeable interface

Yedeg

Wadbro

Hansbo

et al. 2016

Computer Methods in Applied Mechanics and Engineering

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“…Both issues have been dealt with in the literature and a comprehensive review lies beyond the scope of this work. A number of references can be found regarding the acoustic behaviour of perforated ducts with grazing mean flow [20,33,39,41,47,48]. Good correlation with experimental results has been found in earlier studies [34] considering the model of Lee and Ih [47], which will be used in the current investigation.…”

Section: Non-uniform Acoustic Impedance Of the Perforated Surfacementioning

confidence: 55%

“…This impedance is defined as the ratio of the pressure difference to the normal acoustic velocity Un [33] a m p n P P Z U − =  (30) and depends, among others, on frequency, hole diameter, thickness, porosity, properties of the absorbent material and mean flow [39][40][41] (see details in section 3.2.). Eq.…”

Section: Acoustic Coupling At the Perforated Surfacementioning

confidence: 99%

“…(47)- (50), however, do not include the effect of the absorbent material on the acoustic impedance of the perforated duct. This influence has received attention in several works [39][40][41]. In reference [39], the effect of a fibrous material on the impedance of the perforated surface was measured and the authors suggested adding a correction to the impedance obtained in the absence of material.…”

Section: Non-uniform Acoustic Impedance Of the Perforated Surfacementioning

confidence: 99%

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

Denia

Sánchez-Orgaz

Martínez‐Casas

et al. 2015

Finite Elements in Analysis and Design

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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.

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“…Kirby and Cummings [8] have presented data for the acoustic impedance of multiply perforated plates exposed to fully developed grazing gas flow in a duct, both with and without a backing layer of porous material. Cummings and Astley [9] have described a FE formulation for sound attenuation in ''bar-silencers'', consisting of rectangular prisms of sound-absorbing material placed in a rectangular lattice arrangement within a rigid-walled duct.…”

Section: Introductionmentioning

confidence: 99%

The insertion loss of perforated porous plates in a duct without and with mean air flow

Aygun

Attenborough

2008

Applied Acoustics

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Measurements of the acoustic insertion loss of poroelastic plates with different perforation ratios, mounted transversely across a flow duct, without and with flow have been made at various locations in the duct. For the lower perforation ratio the insertion loss is found to be approximately 3 dB higher with air flow than without over the frequency range of the measurements. A parallel impedance model has been formulated to predict the effects of perforation on the insertion loss without flow. Measurements and predictions without flow have been found to be in reasonable agreement.

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The Impedance of Perforated Plates Subjected to Grazing Gas Flow and Backed by Porous Media

Cited by 133 publications

References 0 publications

A Nitsche-type method for Helmholtz equation with an embedded acoustically permeable interface

A Nitsche-type method for Helmholtz equation with an embedded acoustically permeable interface

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

The insertion loss of perforated porous plates in a duct without and with mean air flow

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