Asymptotic limits of some models for sound propagation in porous media and the assignment of the pore characteristic lengths

Abstract

Modeling of sound propagation in porous media requires the knowledge of several intrinsic material parameters, some of which are difficult or impossible to measure directly, particularly in the case of a porous medium which is composed of pores with a wide range of scales and random interconnections. Four particular parameters which are rarely measured non-acoustically, but used extensively in a number of acoustical models, are the viscous and thermal characteristic lengths, thermal permeability, and Pride parameter. The main purpose of this work is to show how these parameters relate to the pore size distribution which is a routine characteristic measured non-acoustically. This is achieved through the analysis of the asymptotic behavior of four analytical models which have been developed previously to predict the dynamic density and/or compressibility of the equivalent fluid in a porous medium. In this work the models proposed by Johnson, Koplik, and Dashn [J. Fluid Mech. 176, 379–402 (1987)], Champoux and Allard [J. Appl. Phys. 70(4), 1975–1979 (1991)], Pride, Morgan, and Gangi [Phys. Rev. B 47, 4964–4978 (1993)], and Horoshenkov, Attenborough, and Chandler-Wilde [J. Acoust. Soc. Am. 104, 1198–1209 (1998)] are compared. The findings are then used to compare the behavior of the complex dynamic density and compressibility of the fluid in a material pore with uniform and variable cross-sections.

A Review of Acoustical Methods for Porous Material Characterisation

“…in the above equation is the Pride parameter 9 discussed later at the end of this section making reference to the work by Horoshenkov et al 20 The above expression suggests that the flow resistivity can be determined from the asymptotic behaviour of the imaginary part of the dynamic density by estimating the low-frequency limit (ω ω v ) of Figure 3 shows the behaviour of Eq. (7) plotted as a function of frequency for reticulated foam (see Fig.…”

“…In ref. 20 it was shown that in the case of a porous medium with cylindrical pores which radius is log-normally disctributed; the Pride parameter is equivalent to β = 4/3e…”

Macro- and micro-structure designs for porous sound absorbers

“…The acoustical properties of a system of parallel identical non-uniform pores composed from n adjoining cylinders with a distribution of areas An but equal section lengths ( ) have been considered [20], but the expression given for complex density, viz.…”

“…Again, using the effective medium approximation, the overall impedance is calculated from the impedance of hard-backed porous layer section of thickness d (from equation 7in parallel with that of the unit cell shown in Fig. 6(b) (from equations (19) and (20)).…”

Outdoor Acoustics: Range Estimation Of Gunfire Over An Acoustically Soft Impedance Ground In A Homogeneous Atmosphere

“…Calculating the acoustic impedance of the ground, , can be done be various methods, however assuming the ground to be porous, the method proposed by Horoshenkov et al is used [4] in this paper. This model makes use of the median pore size which relates to the ground impedance.…”