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Characteristic 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. The thermal characteristic length is equal to twice the volume to wet surface ratio of the open porous network. The viscous characteristic length is similar to this ratio weighted by the velocity in the volume and on the surface for an inviscid fluid.

Equipment: FOAM-X software with impedance tube
Standard: 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]
Properties: Λ – viscous characteristic length; Λ′ – thermal characteristic length

viscous thermal Propertyviscous thermal formula

 

                               
[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).