The Delany–Bazley model and the Johnson–Champoux–Allard model allow to predict the sound absorption of a material if certain material parameters of the porous medium are known.

The only unknown material parameter in the Delany–Bazley model is the static air flow resistivity . The Johnson–Champoux–Allard model additionally requires the porosity , the tortuosity , and the viscous characteristic length . GeoDict can compute these parameters based on a 3D pore-scale structure of the sound absorbing specimen.

Static air flow resistivity

The static air flow resistivity is defined as

where is the relative permeability of the porous medium (cf. Table 2). The FlowDict handbook of this User Guide describes in detail how the permeability is computed by solving the Stokes equation.

Tortuosity

The high frequency limit of the tortuosity (also called the tortuosity factor) is defined as

where is the porosity and  the relative diffusivity of the porous medium (Epstein, 1989). The DiffuDict handbook of this User Guide describes in detail how diffusivity and tortuosity are computed by solving the Laplace equation.

The low frequency limit of the tortuosity is not used in the Johnson–Champoux–Allard equations above, but may serve the user as a reference value, if needed:

where is the air velocity in the pore space and the component of  in through direction.

Viscous characteristic length

The viscous characteristic length is approximated via

with and as defined above (Johnson, 1987).

Thermal characteristic length

The thermal characteristic length is the ratio of pore volume to pore surface area:

The pore volume is computed by counting the pore voxels. The pore surface is determined by the method of Ohser and Mücklich, see the MatDict handbook of this User Guide for details. This value is not used in the Johnson–Champoux–Allard equations above, but may serve the user as a reference value, if needed.