Thermal and Viscous Lengths

What Are the Thermal and Viscous Lengths?

The viscous and thermal characteristic lengths are average macroscopic dimensions of the cells related to viscous and thermal losses, respectively. The former may be seen as an average radius of the smaller pores, and the later as the average radius of the larger pores.

Thermal Length

The thermal characteristic length (Λ′) is equal to twice the volume to wet surface ratio of the open porous network.

Viscous Length

The viscous characteristic length (Λ) is similar to this ratio weighted by the velocity in the volume and on the surface for an inviscid fluid.

How to Measure the Thermal and Viscous Lengths?

Equipment: FOAM-X software with an impedance and transmission tube
Standards: ASTM E1050-08, ISO 10534-2:1998, ASTM E2611-09
Method 1: Inverse acoustical method [1,2,3]
Method 2: Indirect acoustical method [3,4,5]
Parameters:

• Λ′ – Thermal characteristic length
• Λ – Viscous characteristic length

References

[1] Y. Atalla and R. Panneton, « Inverse acoustical characterization of open cell porous media using impedance tube measurements », Canadian Acoustics 33(1), 11-24 (2005).

[2] R. Panneton, Y. Atalla, and D. Blanchet, « Validation of the inverse method of acoustic material characterization, » SAE Technical Paper #2003-01-1584, 3 pages (2003).

[3] R. Panneton, « Comments on the limp frame equivalent fluid model for porous media, » J. Acoust. Soc. Am. 122(6), EL217-222 (2007).

[4] R. Panneton and X. Olny, « Acoustical determination of the parameters governing viscous dissipation in porous media, » J. Acoust. Soc. Am. 119, 2027-40 (2006).

[5] X. Olny and R. Panneton (2007), « Acoustical determination of the parameters governing thermal dissipation in porous media, » J. Acoust. Soc. Am. 123, 814-824 (2008).

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