A homogenization method used to predict the performance of silencers containing parallel splitters

Abstract

An analytical model based on a homogenization process is used to predict and understand the behavior of finite length splitter/baffle-type silencers inserted axially into a rigid rectangular duct. Such silencers consist of a succession of parallel baffles made of porous material and airways inserted axially into a rigid duct. The pore network of the porous material in the baffle and the larger pores due to the airway can be considered as a double porosity (DP) medium with well-separated pore sizes. This scale separation leads by homogenization to the DP model, widely used in the porous material community. This alternative approach based on a homogenization process sheds physical insight into the attenuation mechanisms taking place in the silencer. Numerical comparisons with a reference method are used to show that the theory provides good results as long as the pressure wave in the silencer airways propagates as a plane wave parallel to the duct axis. The explicit expression of the axial wavenumber in the DP medium is used to derive an explicit expression for the optimal resistivity value of the porous material, ensuring the best dissipation for a given silencer geometry.

Sound attenuation optimization using metaporous materials tuned on exceptional points

“…For some other applications, porous materials are often used [8][9][10][11][12][13] to reduce the noise emission, e.g., in the ventilation systems and the Auxiliary Power Units (APU) of aircrafts. Porous materials generally offer a wider absorption/attenuation band 14 and the recent progresses of metallic foam open the door for porous materials solution in an aggressive environment.…”

Additional Sound Absorption Within a Poroelastic Lamella Network Under Oblique Incidence

“…In comparison with the homogeneous layer at normal incidence (see Figure 6), the sound absorption coefficient is slightly lower for the lamella network since the fraction of porous material is smaller. It is noteworthy that this can be avoided by tuning the resistivity, as in [5,39] to obtain the DP pressure diffusion effect [4]. Figure 5(a) shows the effect of the inclination angle θ for an azimuthal angle φ of 0 degrees.…”

“…For instance, rigid splitters [17] can be replaced by air gaps, leading to a horizontal lamella network of different sizes that can be excited at all incidence angles and be tuned at different frequencies to enlarge the frequency range of the additional absorption. The network should also be designed by optimizing its properties involved in double porosity dissipation [39] with air gap size, periodicity and material resistivity or by applying critical coupling [20] to the bending mode to obtain maximum sound absorption.…”

A transverse isotropic equivalent fluid model combining both limp and rigid frame behaviors for fibrous materials

“…In a second part of the paper, some experimental results are shown. Two specific scenarios are investigated: one concerns the sound absorption properties at normal incidence, the other one is related to the transmission loss for dissipative silencers whose dimensions are very similar to recent applications already published by the present authors 31,32 . Results are discussed and compared with numerical simulations.…”

“…in the transverse direction and the classical rigid frame equivalent density in the plane of isotropy ρ I eq . In the low frequency limit 32 , the rigid frame model density is dominated by its imaginary part and ρ I eq ∼ iσ I /ω while the limp effective density tends to a real-valued constant equal to the total apparent mass of the equivalent fluid limp medium as ρ T ≈ ρ 1 + φρ f which can reach a high value depending on the frame added mass.…”