Impact of the irregular microgeometry of polyurethane foam on the macroscopic acoustic behavior predicted by a unit-cell model

This paper deals with the prediction of the macroscopic sound absorption behavior of highly porous polyurethane foams using two unit-cell microstructure-based models recently developed by Doutres, Atalla, and Dong [J. Appl. Phys. 110, 064901 (2011); J. Appl. Phys. 113, 054901 (2013)]. In these models, the porous material is idealized as a packing of a tetrakaidecahedra unit-cell representative of the disordered network that constitutes the porous frame. The non-acoustic parameters involved in the classical Johnson-Champoux-Allard model (i.e., porosity, airflow resistivity, tortuosity, etc.) are derived from characteristic properties of the unit-cell and semi-empirical relationships. A global sensitivity analysis is performed on these two models in order to investigate how the variability associated with the measured unit-cell characteristics affects the models outputs. This allows identification of the possible limitations of a unit-cell micro-macro approach due to microstructure irregularity. The sensitivity analysis mainly shows that for moderately and highly reticulated polyurethane foams, the strut length parameter is the key parameter since it greatly impacts three important non-acoustic parameters and causes large uncertainty on the sound absorption coefficient even if its measurement variability is moderate. For foams with a slight inhomogeneity and anisotropy, a micro-macro model associated to cell size measurements should be preferred.