Visco-inertial effects
In 1987, Johnson Koplik and Dashen [JKD87] proposed a semi-phenomenological model to describe the complex density of an acoustical porous material with a motionless skeleton having arbitrary pore shapes. This expression is:
APMR
Acoustical Porous Material Recipes
In 1987, Johnson Koplik and Dashen [JKD87] proposed a semi-phenomenological model to describe the complex density of an acoustical porous material with a motionless skeleton having arbitrary pore shapes. This expression is:
4 parameters are invloved in the calculation of this dynamic density: the static air flow resistivity $\sigma$, the open porosity $\phi$, the high frequency limit of the tortuosity $\alpha_{\infty}$ and the viscous characteristic length $\Lambda$.
The low frequency limit of the real part of the dynamic density expression is not exact.
In 1991, Champoux and Allard [CA91] introduced an expression for the dynamic bulk modulus for the same kind of porous material based on the previous work by Johnson et al.
2 parameters are invloved in the calculation of this dynamic bulk modulus: the open porosity $\phi$ and the thermal characteristic length $\Lambda'$.
The expression given by Johnson, Koplik & Dashen does not describe the exact behavior of the dynamic mass density as $\omega$ tends to zero: the imaginary part of $\widetilde{\rho}$ is underestimated at low frequencies.
Pride, Morgan & Gangi [PMG93] have proposed a modified expression of the dynamic density. However, the expression given by Pride, Morgan & Gangi and further modified by D. Lafarge [Laf93] is rarely used as new required parameters cannot be characterized yet.
Changes to the JCA model by Pride et al. and D. Lafarge are detailed in the Johnson-Champoux-Allard-Pride-Lafarge model.
Having a closer look at the dynamic bulk modulus expression given by Champoux and Allard, one can notice that visco-inertial and thermal parameters are linked together:
This observation leads Lafarge et al. [LLAT97] to introduce a new parameter, the static thermal permeability $k'_{0}$, in order to break the dependence between visco-inertial and thermal parameters while keeping a "symmetry" between the two dissipative phenomena.
Changes to the JCA model by Lafarge et al. are detailed in the Johnson-Champoux-Allard-Lafarge model.