Bottom-up approach for microstructure optimization of sound absorbing materials

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 phi, the thermal characteristic length Lambda('), the static viscous permeability k(0), the tortuosity alpha(infinity), the viscous characteristic length Lambda, and the sound absorption coefficient are computed. Numerical solutions of the steady Stokes and electrical equations are employed to provide k(0), alpha(infinity), and Lambda. Hybrid estimates based on direct numerical evaluation of phi, Lambda('), k(0), alpha(infinity), Lambda, 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, 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 48+/-10 microm throat size corresponding to an intermediate resistivity, a 13+/-8 microm fiber radius associated with relatively small interfiber distances, and convex triangular cross-section shape fibers allowing weight reduction.