Theory
At low velocity, the pressure gradient through a fibrous material is proportional to the velocity (Darcy). At higher velocity, inertial losses in the pores add a term proportional to : the Forchheimer correction. The program writes both coefficients into OpenFOAM's explicitPorositySource with the DarcyForchheimer model (OpenFOAM user guide, 2026), isotropically: the same in all three directions.
The factor is used by the flow solution only. The acoustic equivalent-fluid models (Acoustic (poroacoustic) model of the packing) are linear and use only the flow resistivity.
Equations
| where | meaning | unit |
|---|---|---|
| Forchheimer factor (this setting) | 1/m | |
| Flow resistivity, Flow resistivity | Pa·s/m² | |
| Dynamic viscosity of the gas | Pa·s | |
| Gas density | kg/m³ | |
| Superficial velocity through the packing | m/s | |
| Pressure gradient along the flow | Pa/m |
Default and rule
- Default
- 0 (pure Darcy)
- Rule
0: a pure Darcy loss. In a muffler, most of the flow passes the packing (behind a perforated wall) rather than through it, and the velocity in the packing is small.
- Source
The form is the OpenFOAM porosity model. The value 0 is the program's default; no published typical value of the Forchheimer factor for muffler packings is provided.
Valid range ≥ 0
Values
. 0 = Darcy only.
Measured data
Determining a Forchheimer factor requires a measurement of the pressure drop at two or more velocities; when only the flow resistivity is known, leave 0.