During acoustical characterizations involving at least three parameters, some basic checking may be made to test the consistency of the results. Although all parameters used in a particular model should be independant in general cases, some inequalities or ranges of magnitude order should be verified.
By definition, the characteristic viscous length should be lower or equal to the thermal characteristic length:
| $\Lambda \leq \Lambda'$ | (1) |
for fibrous or felts it is usually admitted that the static air-flow resistivity increases with mass density [Tar96]
For fibrous materials (which can be considered as parallel identical cylinders), numerous characterizations have shown that the values of the high frequency limit of the tortuosity (in directions perpendicular to the fiber plane) and the open porosity are approximately related by the equation:
| $\alpha_{\infty} \simeq 1+(1-\phi)$ | (2) |
[Berryman ? - Need to be confirmed] [TPLJ04]
In addition, one can check the value of
- the viscous pore shape factor $M$ for models based on Johnson-Champoux-Allard works
- the thermal pore shape factor $M'$ for models based on Johnson-Champoux-Allard-Lafarge works
The pore shape factors $M$ and $M'$ should have orders of magnitude of the order of 1 to 10 for usual acoustical porous materials.
| $M = \displaystyle{\frac{8\alpha_{\infty}\eta}{\sigma\phi\Lambda^{2}}}$ | (3) |
| $M' = \displaystyle{\frac{8k'_{0}}{\phi\Lambda'^{2}}}$ | (4) |
Check consistency of your parameter values
References
[Tar96] Tarnow V.,
Airflow resistivity of models of fibrous acoustic materials,
J. Acoust. Soc. Am. 100(6), 1996, pp. 3706-3713
[TPLJ04] Tournat V., Pagneux V., Lafarge D. and Jaouen L.
Multiple scattering of acoustic waves and porous absorbing media,
Phys. Rev. E 70, 026609, 2004
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