This article explores the applicability of numerical homogenization techniques for analyzing transport properties in real foam samples mostly open-cell, to understand long-wavelength acoustics of rigid-frame air-saturated porous media, on the basis of microstructural parameters. Experimental characterization of porosity and permeability of real foam samples are used to provide the scaling of a polyhedral unit-cell. The Stokes, Laplace, and diffusioncontrolled reaction equations are numerically solved in such media by a finite element method in three-dimensions; an estimation of the materials' transport parameters is derived from these solution fields. The frequency-dependent visco-inertial and thermal response functions governing the long-wavelength acoustic wave propagation in rigid-frame porous materials are then determined from generic approximate but robust models and compared to standing wave tube measurements. With no adjustable constant, the predicted quantities were found to be in acceptable agreement with multi-scale experimental data, and further analyzed in light of scanning electron micrograph observations and critical path considerations.

Results from a numerical study examining micro-/macrorelations linking local geometry parameters to sound absorption properties are presented. For a hexagonal structure of solid fibers, the porosity , the thermal characteristic length ⌳Ј, the static viscous permeability k 0 , the tortuosity ␣ ϱ , the viscous characteristic length ⌳, and the sound absorption coefficient are computed. Numerical solutions of the steady Stokes and electrical equations are employed to provide k 0 , ␣ ϱ , and ⌳. Hybrid estimates based on direct numerical evaluation of , ⌳Ј, k 0 , ␣ ϱ , ⌳, and the analytical model derived by Johnson, Allard, and Champoux are used to relate varying ͑i͒ throat size, ͑ii͒ pore size, and ͑iii͒ fibers' cross-section shapes to the sound absorption spectrum. The result of this paper tends to demonstrate the important effect of throat size in the sound absorption level, cell size in the sound absorption frequency selectivity, and fibers' cross-section shape in the porous material weight reduction. In a hexagonal porous structure with solid fibers, the sound absorption level will tend to be maximized with a 48Ϯ 10 m throat size corresponding to an intermediate resistivity, a 13Ϯ 8 m fiber radius associated with relatively small interfiber distances, and convex triangular cross-section shape fibers allowing weight reduction.

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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.

Is it possible to find a two-dimensional ͑2D͒ periodic unit cell representative of the dynamic viscous dissipation properties of a real porous media? This is a challenging question addressed in this paper through a review of tools and methods of experimental and computational micro͑poro͒mechanics. The combination of advanced experimental imaging and numerical homogenization techniques provides a unique opportunity to understand and assess the limits of two-dimensional models of microstructures, as a potential basis for the engineering prediction of macroscopic properties of acoustical materials. This is illustrated for a real sample of open-cell aluminum foam. The conclusion, based on this analysis, is that the 2D periodic foam model geometry provides a reliable estimate of the dynamic permeability, except in the low frequency range. This is not surprising because in the 2D periodic foam model geometry, ligaments are always perpendicular to the flow direction, thus decreasing artificially the static permeability of the viscous flow.