Formulae for predicting non-acoustical parameters of deformed fibrous porous materials

Formulae to predict non-acoustical parameters (i.e., flow resistivity, tortuosity, and viscous and thermal characteristic lengths) of deformed fibrous porous materials are proposed provided that the original values of these parameters are known in advance. These formulae are developed using numerical fluid analyses. The flow resistivity was calculated by using the finite element method for a two-dimensional incompressible viscous fluid approximated by Oseen flow. The tortuosity and characteristic lengths were calculated by using the complex variable boundary element method for a two-dimensional potential flow. These calculations showed that the flow resistivity was inversely proportional to the porosity multiplied by the three-halves power of the compression ratio, that the tortuosity can be represented by a linear expression of the porosity, and that both characteristic lengths changed in the same manner with respect to the porosity. These tendencies agreed well with measurements of real glass wools of various bulk densities. The proposed prediction formulae for the parameters were then derived from the tendencies obtained from the numerical analyses. The predicted parameter values were compared with the calculated parameters and good agreement was obtained, confirming the validity of the proposed formulae.