A semi-analytical model for sound propagation in sintered fiber metals

A semi-analytical model based on three-dimensional (3-D) periodical unit cells (PUCs) is developed to predict the sound absorption performance of sintered fiber metals as a function of porosity and fiber diameter. The PUC is developed from the most simplistic one (PUC1) to the comparatively complex one (PUC3) by taking into account the shifting of fiber position and the non-uniformity of fiber distribution. Upon numerically solving both the static Stokes (aiming at viscous flow) and diffusion-controlled reaction (aiming at inertial flow) equations defined inside the PUC, the transport parameters in the commonly used JCA (Johnson-Champoux-Allard) model for porous acoustic materials are obtained. Upon introducing the Kozeny number and pore shape factor, key transport parameters are determined as functions of fiber diameter and porosity using the proposed semi-analytical model. The theoretically predicted sound absorption coefficients are compared with experimental measurements of sintered fiber metal samples, with good agreement achieved. The validated model is then used to systematically analyze the influence of fiber diameter and porosity on sound absorption. The model reveals the physical mechanisms underlying viscous and thermal dissipation of sound energy due to fluid-structure interaction in sintered fiber metals.