SpectraSim Documentation
Parameter · 05 Boundary Conditions

Resistivity input

resistivity_input Step 05 · Boundary Conditions

How the flow resistivity of a packing is given: typed directly (a measured value), or estimated from the bulk density of a glass or rock wool. The value obtained is used by both the flow solution and the acoustic model.

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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

R=A ρb B,ln⁡R=ln⁡A+Bln⁡ρb  (least squares through the measured points)R = A\,\rho_b^{\,B}, \qquad \ln R = \ln A + B \ln \rho_b \ \ \text{(least squares through the measured points)}
(1)
wheremeaningunit
RREstimated flow resistivityPa·s/m²
ρb\rho_bBulk density of the packing, Bulk densitykg/m³
A,BA, BFit constants: glass wool A=93.8A = 93.8, B=1.420B = 1.420; rock wool A=53.1A = 53.1, B=1.571B = 1.571-

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.

References 1

  1. Komatsu, T. (2008). Improvement of the Delany-Bazley and Miki models for fibrous sound-absorbing materials. Acoustical Science and Technology, 29(2), 121-129. DOI 10.1250/ast.29.121