Microstructure based model for sound absorption predictions of perforated closed-cell metallic foams

Abstract

To cite this version: Camille Perrot Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallée, France e-mail: camille.perrot@univ-paris-est.frClosed-cell metallic foams are known for their rigidity, their lightness, their thermal conductivity as well as their low production cost compared to open-cell metallic foams. Yet, they are also poor sound absorbers. A method to enhance their sound absorption is to perforate them. This method has shown good preliminary results but has not yet been analyzed from a microstructural point of view. The objective of this work is to better understand how perforations modify the sound absorption of closed-cell metallic foams. First, a simple twodimensional (2D) microstructural model of the perforated closed-cell metallic foam is proposed and solved through numerical homogenization. A rough three-dimensional (3D) correction of the 2D results is then given from the standpoint of straightforward examination of the analytical slits/cylinders macroscopic parameters. The results show that the diameter of both the perforation and the pore appear as the main controlling parameters of the sound absorption behavior. An experimental comparison demonstrates that the 2D proposed microstructural numerical model combined with a 3D analytical correction factor yields realistic trends for optimization purposes.

Acoustical properties of double porosity granular materials

“…38 Other possible geometries for modelling foams are the Weaire-Phelan foam, 38 array of cylinders arranged in a hexagonal lattice, 39 and array of spherical voids connected by cylindrical pores. 40 The Weaire-Phelan foam has eight cells in the REV. This low symmetry limits its use.…”

Computation of acoustic absorption in media composed of packed microtubes exhibiting surface irregularity

“…8). This decrease in permeability serves to explain the overall poor absorption of Array 2-less flow in the tubes leads to less opportunity for energy dissipation due to thermo-viscous losses (Chevillotte et al, 2010), a physical argument that is supported by the permeability and absorption observation previously observed.…”

“…Note that in region S 2 we have observed that resonance peaks shift to higher frequencies; however, the observed frequency shifts are much smaller in magnitude. Chevillotte et al (2010) cite that large pores increase tortuosity and therefore the absorption maximum shifts toward lower frequencies. For a fixed ' R and increasing A R (analogous to increasing the pore size) we observe the same trend for the maximum absorption peak in the region S 1 , but not for the complete parametric range ' R 2 25 lm; 500 lm ½ and A R 2 1 lm; 65 lm ½ .…”

“…This procedure, known as the multi-scale asymptotic method (MAM) (Sanchez-Palencia, 1980;Auriault et al, 1985;Zhou and Sheng, 1989;Lafarge et al, 1997;Boutin et al, 1998), allows the computation of the frequency-dependent acoustic parameters for the microstructure. Acoustics in irregular pore geometries have been considered in Zhou and Sheng (1989); Russ and Sapoval (2002); Cortis et al (2003); Felix et al (2007); Felix et al (2009), with specific applications to periodic porous media by Cortis et al (2003); Zhou and Sheng (1989); Gasser et al (2003); and Chevillotte et al (2010). Coupling the technique to a finite element-based solution approach increases its flexibility and allows analysis of pore spaces with varied geometries (Auriault et al, 1985;Zhou and Sheng, 1989;Gasser, 2003;Lee et al, 2009).…”

Prediction of the acoustic behavior of a parallel assembly of hollow cylinders

“…It consisted in solving the creeping flow equation for different radii of straw and circular boundary. Then the airflow resistivity is determined by averaging the incompressible velocity field [11]. To finish, a linear regression between the inverse of the permeability r=g and the squared inverse of the thermal length Finally, Fig.…”