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

Abstract

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.

Advanced numerical techniques for the acoustic modelling of materials and noise control devices in the exhaust system of internal combustion engines

“…The physical and chemical properties of various materials and their relative durability in simulated automotive silencer operations are described by Huff [88]. Despite the improvements of the material properties and the increasing interest not only in reducing the noise levels under the legal limits, but also in the sound quality, having promoted use of the absorbent materials as a part of the silencers over recent decades [47,65,100,138,155,159,160], recent studies [5,8,64,182] have raised an interesting trend that promotes the search of less polluting alternatives.…”

“…The wavenumber k m and the characteristic impedance Z m of the equivalent fluid are also complex [10,57,134]. This model can be used for a number of fibrous materials used by industry in the manufacturing process of silencers [65,138,149,155,156,180]. The second model, also known as the poroelastic approach, is based on Biot's theories [32,33] and was adapted by Allard et al [11] to the acoustic problem.…”

“…In this section, the transmission loss of reactive and dissipative silencers is computed in order to show the basic sound attenuation characteristics. Both types of silencer has been widely studied in the literature [46,56,65,105,126,158]. Particularly, the dissipative configuration have been profusely studied from a multidimensional point of view in subsequent chapters.…”

“…The presence of high temperature and strong thermal gradients in dissipative silencers modifies their acoustic attenuation performance. Therefore, it is important to consider them in order to assess the silencer attenuation [65].…”

“…The temperature distribution within the silencer, causative of the variation of the properties of the different propagation media [65,127,167], is modelled according to the silencer region under analysis. In this case, an axisymmetric configuration, as shown in Figure 3.3, is considered for computational purposes:…”