A Numerical Scheme for Investigating the Influence of the Three Dimensional Geometrical Features of Porous Polymeric Foam on Its Sound Absorbing Behavior

The acoustic performance of sound absorbing foams is determined by a large number of processes and parameters. Chemical formulation, blowing agent and production processes influence the formation of the microstructure of foam. The interaction between the microstructure of a foam and an applied static or oscillatory air flow is a critical factor in understanding the acoustic performance of a porous sound absorber. This paper presents the results of a study of the effect of the 3D geometry of the microstructure of polymeric foams on sound absorption. The relation between oscillatory fluid flow and real physical features of the morphology of foam-like structures such as closed cell content, the influence of cell size and, to lesser degree, polydispersity and pore size connections is investigated. A methodology to generate three dimensional discrete geometries by using numerical tools and x-ray computerized micro-tomography is presented. These structures can be seen as a representative volume element of a real sound absorbing polymeric foams and can be used in a numerical treatment for investigating their respective thermal, acoustical and mechanical properties. It is shown that is possible to predict in a reliable manner the sound absorption for the audible frequency range and other single valued key parameters that are commonly used to differentiate the acoustic performance of porous sound absorbers. This is done by numerically generating three dimensional microstructures ideal foams similar to a Weaire-Phelan foam and by numerically reconstructing a fully reticulated polyurethane foam from image data of μCT-scan. The sound absorption of these structures is then examined by using advanced computational fluid dynamics. The obtained numerical results are compared to results obtained by the commonly used 'rigid-frame' or 'equivalent fluid' model introduced by Johnson et al., Champoux et al. and Lafarge et al.