Darcy coefficient D

The viscous (linear-in-velocity) part of the pressure jump across a perpendicular perforated plate, in addition to the $\tfrac12\rho K U^2$ part. It is 0 for an ordinary sheet-metal perforate, whose loss is inertial.

Last updated 2026-11-03

Theory

OpenFOAM's porousBafflePressure jump has a Darcy term proportional to the velocity and an inertial (Forchheimer) term proportional to its square, both multiplied by the jump's length $t$ (the plate thickness) (OpenFOAM user guide, 2026). At muffler velocities a perforated sheet is dominated by the inertial term. A Darcy term is meant for a fine screen, a sintered plate or a woven mesh whose loss rises linearly at low velocity. $D$ is the inverse permeability: $\mu D t$ is the linear resistance per unit area in Pa·s/m.

The field is hidden for a perforated tube; its stored value (0 unless typed earlier for a plate) is still written to the boundary condition.

Equations

\Delta p = \mu\,D\,t\,U_n + \tfrac12\rho\,K\,\lvert U_n\rvert U_n

(1)

where	meaning	unit
$\Delta p$	Pressure jump	Pa
$\mu$	Dynamic viscosity of the gas	Pa·s
$D$	Darcy coefficient	1/m²
$t$	Plate thickness (length of the jump)	m
$U_n$	Velocity normal to the plate face	m/s
$K$	Loss coefficient	-

Default and rule

Default: 0
Rule: 0 (no viscous term).
Source: The jump law: (OpenFOAM user guide, 2026). There is no measured default: the value has to come from a test of the screen (pressure drop against velocity, the slope at low velocity).

Valid range D ≥ 0

Values

$D \ge 0$ . A linear resistance $R$ (Pa·s/m) of the plate corresponds to $D = R/(\mu t)$ .

Not for the acoustics

The acoustic perforate models do not read $D$ ; they have their own resistance terms.

References 1

OpenCFD Ltd. (2026). OpenFOAM user guide. openfoam.com. Web page

Theory

Equations

Default and rule

Valid range D ≥ 0

Related 3

References 1