Perforation type

Chooses the steady-flow pressure-loss law of a perforated wall by its flow regime: a plate across a duct, whose jets re-expand and recover part of their momentum, or the wall of a perforated tube, whose jets discharge into a chamber, annulus or packing and lose their whole dynamic head.

Last updated 2026-11-11

Theory

A perforated wall is not meshed hole by hole. It is a zero-thickness porous jump on a cyclic pair of faces (OpenFOAM porousBafflePressure (OpenFOAM user guide, 2026)): the pressure falls across it by $\tfrac12\rho K U_n^2$ , with $U_n$ the velocity normal to the wall face (equation 1). The perforation type decides how $K$ is obtained.

Perpendicular plate. All the flow passes through the plate. Each hole forms a jet that contracts and then re-expands to fill the duct downstream; the re-expansion recovers part of the jet's momentum, so the loss is that of a sudden expansion from the contracted jet, the Borda-Carnot form, equation (2). Idelchik's thin sharp-edged plate formula has this form (Idelchik, 2008). $K$ is either typed (Resistance coefficient K) or computed from the open-area ratio with the thin- or thick-plate formula (Defined by (perforated plate), Plate formula); it stays fixed during the run.

Perforated tube. The jets leave the holes into a chamber, an annulus or a packing and do not re-expand into the same stream: no pressure is recovered (Cummings, 1984), and the whole jet head is lost, equation (3) (Rogers and Hersh, 1975) (Elnady et al., 2010). The discharge coefficient starts at its no-grazing value $C_{D0}$ (Discharge coefficient C_D0, from the hole diameter and wall thickness) and, with the grazing correction on (Grazing correction), is lowered during the run from the solved ratio of hole velocity to grazing velocity. A packing on one side does not change the law: the jet head is still lost.

Micro-perforated (laminar). Sub-millimetre holes or slits: the flow in them is viscous, so the loss is a Poiseuille (linear) term plus an inertial term, not a jet loss (Micro-perforate flow resistance). It is the flow side of a micro-perforated wall and can be used without acoustics; with acoustics the wall's acoustic model should be one of the micro-perforated models, which share its hole or slit size, thickness and open-area ratio (the setup check warns when the two do not match). The micro-perforated law is a through-flow law used for both regimes, a baffle across a duct and a tube wall, without a grazing-flow correction; it is not validated against a measured pressure drop (Micro-perforate flow resistance).

Equations

\Delta p = \tfrac12\,\rho\,K\,U_n\lvert U_n\rvert

(1)

K_{plate} = \left(\frac{1}{\sigma C_c} - 1\right)^2 \quad \text{(form of the plate laws)}

(2)

K_{tube} = \frac{1}{(\sigma\,C_d)^2}, \qquad C_d = \min\left(C_{De},\,C_{D0}\right)

(3)

where	meaning	unit
$\Delta p$	Static-pressure jump across the wall	Pa
$\rho$	Gas density	kg/m³
$K$	Loss coefficient, on the face (approach) velocity	-
$U_n$	Velocity normal to the wall face	m/s
$\sigma$	Open-area ratio (hole area / wall area)	-
$C_c$	Contraction coefficient of the jets	-
$C_d$	Discharge coefficient of the holes (with grazing flow)	-
$C_{D0}$	Discharge coefficient without grazing flow	-
$C_{De}$	Grazing-flow discharge coefficient (see Grazing correction)	-

Default and rule

Default: perforated tube (a new perforated wall); perpendicular plate (a case file that does not store the key)
Rule: A perforated wall added in the Geometry step starts as a perforated tube, the usual muffler element (with the plate's own settings preset to the open-area ratio and the thick-plate formula). A case file written before this setting existed has no such key and reads as a perpendicular plate, so its results do not change.
Source: The loss law is chosen by the flow regime, not by what lies behind the wall. The tube law follows three sources: Rogers and Hersh's steady orifice resistance $R = \rho V_i/(2 C_D^2)$ (Rogers and Hersh, 1975), Cummings's statement that pressure recovery does not occur downstream of the orifice (Cummings, 1984) and Elnady et al.'s $\Delta p = \rho\,u\lvert u\rvert/(2\sigma^2 C_D^2)$ (Elnady et al., 2010). The form $(1/C_d - 1)^2/\sigma^2$ for a tube backed by packing is not used: it misplaces $\sigma$ and gives $K \approx 0.06$ - $0.3$ for a real perforate.

Valid range perpendicular plate | perforated tube | micro-perforated (laminar)

Choice

A plate that spans the whole cross-section of a duct: perpendicular plate. The wall of a pipe inside a muffler with holes along it, the flow running along the pipe: perforated tube. Sub-millimetre holes or slits, in either position: micro-perforated (laminar). With acoustics on, the type also limits the impedance-model list to the models of its kind (Acoustic impedance model of a perforated wall).

Tube law with little through-flow

In the tube law $K$ is on the face velocity; where almost no flow crosses the wall the pressure jump is small whatever $K$ is, so the result there depends little on this setting.

Transient runs

A transient run keeps the starting $K$ of a perforated tube ( $1/(\sigma C_{D0})^2$ ): the run-time grazing update is made only by the steady solver.

Theory

Equations

Default and rule

Valid range perpendicular plate | perforated tube | micro-perforated (laminar)

Related 9

References 5