Flow resistivity

The static airflow resistivity of an absorptive packing: the pressure gradient per unit superficial velocity through the material. It is the single material property used both by the flow solution (a Darcy momentum sink) and by the acoustic equivalent-fluid models.

> warn: Enter the room-temperature value; the program scales it with temperature | Flow resistivity is measured with room-temperature air (a laboratory at 20-25 °C). Enter that measured value. During the solution the program does NOT keep it constant: in every cell it is scaled with the viscosity of the local gas, $R(T) = R_0\,\mu(T)/\mu(20\,°\text{C})$ (equation 3), in the flow solution and in the acoustics alike. Hot gas is more viscous, so the packing resists more: 1.20x at 100 °C, 1.52x at 250 °C, 1.88x at 450 °C, 2.25x at 700 °C. Many other simulation tools keep the entered resistivity constant regardless of temperature. When a hot-gas result is compared with such a tool, the pressure drop of the packing and its acoustic damping differ for this reason alone; to compare like with like, enter $R_0\,\mu(20\,°\text{C})/\mu(T)$ here, or enter in the other tool the resistivity scaled to the gas temperature.

Last updated 2026-11-04

Theory

In the flow solution, the packing is a region of the fluid mesh with a Darcy-Forchheimer momentum sink: OpenFOAM's explicitPorositySource with the DarcyForchheimer coefficients (OpenFOAM user guide, 2026), equation (1). The Darcy coefficient $d$ is the flow resistivity divided by the viscosity of air at 20 °C (Sutherland's law with the material's coefficients), isotropic in all three directions, equation (2). OpenFOAM multiplies $d$ by the viscosity of the gas in each cell, so the resistivity the flow meets is $R_0\,\mu(T)/\mu(20\,°\text{C})$ , equation (3): the same value the acoustics uses. For an incompressible case, $\mu(T)$ is the constant viscosity of the material, i.e. the value at the material temperature. The packing cells are those whose CENTRE lies inside the packing surface (topoSet with searchableSurfaceToCell).

In the acoustics, the resistivity enters the equivalent-fluid model selected in Acoustic (poroacoustic) model of the packing. Because a resistivity is quoted for room-temperature air, both solvers scale it with the viscosity of the local gas, equation (3), with the viscosity from Sutherland's law Sutherland (1893). Hot exhaust gas is more viscous and the packing resists more (1.52x at 250 °C, 1.88x at 450 °C, 2.25x at 700 °C for air). The pressure drop through the packing and its acoustic resistance are therefore based on the same material property.

When Resistivity input is "bulk density", this field is not used: $R$ is estimated from Bulk density and Fibre type.

The reference temperature is fixed at 20 °C. A value measured at 25 °C is therefore treated as 1.3 % too low (the viscosity ratio between 25 °C and 20 °C). This is well within the scatter of a resistivity measurement, so no correction is needed.

Equations

\mathbf{S} = -\left(\mu\,d + \tfrac{1}{2}\,\rho\,\lvert\mathbf{U}\rvert\,f\right)\mathbf{U}

(1)

d = \frac{R_0}{\mu(293.15\ \text{K})}, \qquad \mu(T) = \frac{A_s\,T^{3/2}}{T + T_s}

(2)

where	meaning	unit
$\mathbf{S}$	Momentum source per unit volume in the packing cells	N/m³
$R$	Flow resistivity (this setting, or the estimate from the bulk density)	Pa·s/m²
$d$	Darcy coefficient	1/m²
$f$	Forchheimer (inertial) factor, Inertial (Forchheimer) factor	1/m
$\mu$	Dynamic viscosity of the gas	Pa·s
$\rho$	Gas density	kg/m³
$\mathbf{U}$	Superficial velocity	m/s
$A_s, T_s$	Sutherland coefficients of the material	kg/(m·s·K^½), K

R(T) = R_0\,\frac{\mu(T)}{\mu(293.15\ \text{K})}

(3)

where	meaning	unit
$R_0$	Flow resistivity as entered (room temperature)	Pa·s/m²
$R(T)$	Resistivity the gas meets at the local temperature $T$ (CFD sink and acoustic model alike)	Pa·s/m²

Default and rule

Default: 20 000 Pa·s/m²
Rule: 20 000 Pa·s/m², a mid-range glass wool. Enter the measured value of the actual material when it is known.
Source: The Darcy-Forchheimer form is the OpenFOAM porosity model. Validation on a straight two-body pipe: $\Delta p = R\,U\,L$ within 1.1 % for $R = 500$ Pa·s/m², 10 m/s and 0.3 m of packing. The viscosity scaling of the resistivity, applied in both solvers, is the program's own choice, physically motivated by the viscous origin of the flow resistance; it is not taken from a published source. Typical values for fibrous materials are the measured glass and rock wools of Komatsu (2008) (6 000-73 000 Pa·s/m² at 20-102 kg/m³).

Valid range ≥ 0; glass and rock wools roughly 5 000-70 000 Pa·s/m²

Values

$R \ge 0$ ; 0 removes the Darcy term. Fibrous packings: about 5 000 to 70 000 Pa·s/m².

Measured value first

A measured resistivity (ISO 9053 type test) is always preferable to the estimate from the bulk density, which scatters by about ±10 % rms.

Hot gas

Enter the room-temperature value. Both solvers scale it with $\mu(T)/\mu(20\,°\text{C})$ . Some commercial acoustic tools do not scale it; a comparison with such a model at high temperature differs for that reason.

Theory

Equations

Default and rule

Valid range ≥ 0; glass and rock wools roughly 5 000-70 000 Pa·s/m²

Related 6

References 3