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Streszczenie:
Numerical simulation of absorption of sound in porous media is an important part of the design of the treatments for the environmental noise reduction. In the porous media, the mechanical energy carried by sound is dissipated by thermo-viscous interactions with the solid surface of the media frame, which usually has complicated geometry at the microscopic (sub-millimetre) scale. In order to be able to absorb the acoustic energy at the low frequencies of interest, a layer of porous material must be rather thick (at the order of centimetres). This is why direct numerical simulation (DNS) of the sound absorption in porous media is a rather computationally challenging task because small geometrical details must be properly resolved in a large computational domain. In order to avoid these difficulties, simplified semi-phenomenological models introducing so called effective fluid have been proposed. For example, the Johnson-Champoux-Allard-Pride-Lafarge (JCAPL) model is based on eight parameters which can be measured or calculated based on the media micro-structural geometry. Within this work, we compare the numerical results obtained by the 3D DNS with the prediction of the JCAPL model in case of several porous media represented by closely-packed spheres. The DNS calculations are performed using the linearised Navier-Stokes equations for layers of spheres of different thicknesses, the parameters for the JCAPL model are calculated subsequently using Laplace, Poisson, and Stokes flow analyses on a representative volume element of the media. Very good agreement between the results has been found.