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 k 0 Ј and the thermal characteristic dimension ⌳Ј. 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 kЈ(), which is completely analogous to the Johnson et al. ͓J. Fluid Mech. 176, 379 ͑1987͔͒ model of dynamic viscous permeability k(). 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 ⌳Ј.

Three-dimensional reconstruction of a random fibrous medium: Geometry, transport, and sound absorbing properties

“…This minor effect of fiber hollowness corresponds to a low interscale coupling. We notice that all of the proposed models (rigid, 11,12 limp, 21 elastic, 23 ) predict an overall sound absorption in agreement with measurements. With the elastic model, the sound absorption is almost always in accord with measurements.…”

“…The Johnson et al 11 and Lafarge et al 12 models assume a porous material having a rigid frame. In this situation, the experimentally measured effective density and effective bulk modulus could be used to quantify a 1 , K, K 0 , and k 0 0 from analytical inversion, 25,26 if one directly measures the porosity / and the permeability k 0 .…”

“…Based on the approximate formulae developed by Johnson et al 11 and Lafarge et al, 12 the effective density q eff x ð Þ and the effective bulk modulus K eff x ð Þ of the fluid phase can be evaluated as follows:…”

“…These models account for the inertial and viscous effects using an effective density q eq (x), 11 and for the thermal effects via an effective bulk modulus K eq (x). 12 Section II describes the measurement procedure for determination of geometrical properties. The geometrical properties provide input to our procedure for the generation of synthetic 3D fibrous samples.…”

Effect of the microstructure closed pore content on the acoustic behavior of polyurethane foams

“…This model assumes that the frame is motionless and is not subjected to deformation. The dynamic heat conduction phenomena in the open-cell porous media is described using the Champoux-Allard model modified by Lafarge et al 16 and the viscous dissipation from the Johnson et al model. 17 Note that these nonacoustic parameters are intercorrelated and morphology-dependent.…”