Bottom-up approach for microstructure optimization of sound absorbing materials

Abstract

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.

Effect of the microstructure closed pore content on the acoustic behavior of polyurethane foams

“…This trend is coherent with the observations given by Perrot et al 13 from the numerical study of a 2D hexagonal lattice of solid fibers in air. Indeed, according to Table I of Ref. 13, for a given fiber radius, decreasing the throat size w (i.e., the distance between two consecutive fibers and thus equivalent to the pore size): (i) reduces the cell size, (ii) increases the tortuosity and airflow resistivity, and (iii) increases the ratio n ¼ K 0 =K.…”

“…Figure 5(b) confirms that the airflow resistivity r decreases with increasing the cell size. 13,14 For cell size ranging from 500 to 1500 lm, the airflow resistivity varies from 600 to 4000 N s m À4 which is considered as a relatively low airflow resistivity for typical sound absorbing materials. materials W m ¼ 0.34C s ).…”

“…8,[11][12][13][14] The idealized periodic unit cell is then reconstructed, using x-ray tomography (l-san) and advanced computational fluid dynamics analysis is performed to derive properties relevant for the acoustic behavior. These methods allow a great understanding of the impact of microstructure on acoustic behavior.…”

Microstructure, transport, and acoustic properties of open-cell foam samples: Experiments and three-dimensional numerical simulations

“…More precisely, truncated octahedra with ligaments of circular cross section shapes and a spherical node at their intersections were considered. It has been shown in a recent paper by using 2D computations 4 that the FEM results are not significantly affected by this approximation, even if the real cross-section of ligaments can be rather different.…”

“…Recently, there has been a great interest in understanding the low Reynolds viscous flow, electrical, and diffusive properties of fluids in the pore structure of real porous media on the basis of microstructural parameters 2 , as these transport phe-nomena control their long-wavelength frequency-dependent properties 3,4 . Our aim in this paper is to get insight into the microstructure of real porous media and to understand how it collectively dictates their macro-scale acoustic properties, from the implementation of first-principles calculations on a three-dimensional idealized periodic unit-cell.…”