Optimal sound absorbing and manufacturable two-dimensional, hexagonal-like porous structure
Résumé
Results from a numerical study examining micro-macro relations linking local geometry parameters to sound absorption properties are presented. For an hexagonal structure of solid fibers, the porosity Ф, the thermal characteristic length Λ', the static viscous permeability k0, the tortuosity α∞, the viscous characteristic length Λ, and the sound absorption coefficient are computed. Numerical solutions of the steady Stokes and electrical equations are employed to provide k0, α∞, and Λ. Hybrid estimates based on direct numerical evaluation of Ф, Λ', k0, α∞, Λ and the analytical model derived by Johnson, Allard, and Champoux are used to relate varying (i) throat size, (ii) pore size, and (iii) 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, 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 48 ± 10μm throat size corresponding to an intermediate resistivity, a 13 ± 8 μm fiber radius associated with relatively small inter-fiber distances, and convex triangular cross-section shape fibers allowing weight reduction.