Theory

In the JCA and JCAL models (Johnson et al., 1987), (Champoux and Allard, 1991) the packing is an equivalent fluid whose density and bulk modulus are those of the gas in the pores divided by $\phi$ (the macroscopic form, equations (1)-(2)). The porosity scales both: a lower porosity raises the effective density and stiffness and so the characteristic impedance of the packing. It also enters the estimate of the viscous characteristic length when Viscous characteristic length (JCA / JCAL) is left blank, equation (3), and the JCA value of the thermal permeability.

Fibrous packings (glass, rock, steel wool) have porosities of about 0.9-0.99; the empirical models of Acoustic (poroacoustic) model of the packing assume a value near 1 implicitly.

Equations

\rho_{eq} = \frac{\alpha_\infty\rho_0}{\phi}\left[1 + \frac{R\,\phi}{i\omega\rho_0\alpha_\infty}\sqrt{1 + i\,\frac{4\alpha_\infty^2\eta\rho_0\omega}{R^2\Lambda^2\phi^2}}\right]

(1)

K_{eq} = \frac{\gamma P_0/\phi}{\gamma - (\gamma - 1)\left[1 - i\,\dfrac{\phi\,\eta/\mathrm{Pr}}{k'_0\rho_0\omega}\sqrt{1 + i\,\dfrac{4 k_0'^2\rho_0\omega}{(\eta/\mathrm{Pr})\Lambda'^2\phi^2}}\right]^{-1}}

(2)

\Lambda = \sqrt{\frac{8\,\eta\,\alpha_\infty}{R\,\phi}}\ \ \text{(when blank)}, \qquad k'_0 = \frac{\phi\Lambda'^2}{8}\ \ \text{(JCA)}

(3)

where	meaning	unit
$\phi$	Open porosity (this setting)	-
$\alpha_\infty$	Tortuosity	-
$R$	Flow resistivity at the local temperature	Pa·s/m²
$\Lambda, \Lambda'$	Viscous and thermal characteristic lengths	m
$k'_0$	Static thermal permeability	m²
$\rho_0, \eta, \gamma, P_0, \mathrm{Pr}$	Density, viscosity, ratio of specific heats, absolute pressure and Prandtl number of the gas	SI
$\omega$	Angular frequency	rad/s

Default and rule

Default: 0.95
Rule: 0.95, typical of a fibrous packing.
Source: The equations are the macroscopic JCA / JCAL form, consistent term by term with Atalla and Panneton (2000). The default is the program's choice of a typical value for a fibrous packing; it is not derived from measured porosities of muffler packings.

Valid range 0 < φ ≤ 1; warning below 0.7

Values

$0 < \phi \le 1$ (refused otherwise).

Low porosity

Below 0.7 the acoustic QA gate warns: low for a fibrous or foam packing.

Verified

Checked in a full acoustic run of a packed resonator (2026-11-11): every quality check passes; with estimated parameters the TL agrees with Miki within about 1 dB below 1 kHz and falls 7-9 dB below it at 2 kHz.

Porosity (JCA / JCAL)

Theory

Equations

Default and rule

Valid range 0 < φ ≤ 1; warning below 0.7

References 3

Theory

Equations

Default and rule

Valid range 0 < φ ≤ 1; warning below 0.7

Related 6

References 3