Theory
None of the equivalent-fluid models of Acoustic (poroacoustic) model of the packing relates the flow resistivity to the density of the material. The program offers an estimate from the only open measured data set it has: the 24 samples of Komatsu (2008), Table 3 (15 glass wools, 9 rock wools, bulk densities 20-102.4 kg/m³, resistivities measured to ISO 9053). Through each set a power law, equation (1), is fitted by least squares in log-log coordinates. The fit is recomputed from the stored table at run time and shown under the field with its scatter.
The real resistivity also depends on the fibre diameter and the binder, which the density alone does not capture; the estimate is an approximation for typical commercial products in the measured density range.
Whatever the choice, the CFD Darcy term and the acoustic model read the same effective resistivity.
Equations
| where | meaning | unit |
|---|---|---|
| Estimated flow resistivity | Pa·s/m² | |
| Bulk density of the packing, Bulk density | kg/m³ | |
| Fit constants: glass wool , ; rock wool , | - |
Default and rule
- Default
- flow resistivity
- Rule
Flow resistivity (typed). Choose the bulk-density estimate only when no measured resistivity is available.
- Source
Data: Komatsu (2008), Table 3 (the program stores the 24 points). The fit is the program's own: glass wool 9.6 % rms (18.8 % max) deviation from the measurements, rock wool 9.2 % rms (14.7 % max). The exponents are close to the value of about 1.5 usually quoted for fibrous materials.
Valid range flow resistivity | bulk density (estimate)
An estimate
About ±10 % rms on the measured products, up to 19 %. A measured flow resistivity always wins.
Density range
Outside 20-102.4 kg/m³ (glass wool) or 29.7-97 kg/m³ (rock wool) the fit is extrapolated; the field shows a warning.