Dynamic compressibility of air in porous structures at audible frequencies

Abstract

Measurements of dynamic compressibility of air-filled porous sound-absorbing materials are compared with predictions involving two parameters, the static thermal permeability k0′ and the thermal characteristic dimension Λ′. Emphasis on the notion of dynamic and static thermal permeability—the latter being a geometrical parameter equal to the inverse trapping constant of the solid frame—is apparently new. The static thermal permeability plays, in the description of the thermal exchanges between frame and saturating fluid, a role similar to the viscous permeability in the description of the viscous forces. Using both parameters, a simple model is constructed for the dynamic thermal permeability k′(ω), which is completely analogous to the Johnson et al. [J. Fluid Mech. 176, 379 (1987)] model of dynamic viscous permeability k(ω). The resultant modeling of dynamic compressibility provides predictions which are closer to the experimental results than the previously used simpler model where the compressibility is the same as in identical circular cross-sectional shaped pores, or distributions of slits, related to a given Λ′.