Include bias flow

Adds the resistance of a mean flow passing THROUGH the holes (bias flow) to the selected impedance model. A through-flow sheds vortices at every hole and converts acoustic energy into them, which raises the resistance roughly in proportion to the hole Mach number.

Last updated 2026-11-11

Theory

When mean flow passes through the holes, each acoustic cycle modulates the jets, and the acoustic energy goes into vorticity. The resistance added per hole is $1.15\,M_b/C_D$ , equation (1), with $M_b$ the Mach number of the flow inside the holes (Bias (through-hole) Mach number) and $C_D$ the discharge coefficient (Discharge coefficient C_D (acoustics)) (Elnady et al., 2010) eq. (6); Elnady et al. quote the term from Bauer (1977).

With this option on, the term is added to the hole impedance of the Kirby & Cummings, Lee & Ih, thin-plate and Sullivan & Crocker models.
The Elnady model already contains the term (with the same $M_b$ ) and adds nothing more.
The cross-flow model has its own through-flow resistance and hides this option.
On a micro-perforated wall (circular holes or slits) the term is added as well, but those models were derived and measured for no flow and grazing flow only Allam and Abom (2011) Kabral et al. (2014); the card and the setup check show a warning.

Equations

\zeta_h \leftarrow \zeta_h + \frac{1.15\,M_b}{C_D}, \qquad \zeta_p = \frac{\zeta_h}{\sigma}

(1)

where	meaning	unit
$M_b$	Mach number of the bias flow inside the holes	-
$C_D$	Discharge coefficient	-
$\sigma$	Open-area ratio	-

Default and rule

Default: off
Rule: Off: no bias resistance, so existing cases give an unchanged impedance.
Source: (Elnady et al., 2010) eq. (6).

Valid range on / off (the Elnady model includes it whenever a bias Mach number is non-zero; the cross-flow model has its own through-flow term)

When to use

Perpendicular baffles and cross-flow mufflers, where the flow crosses the perforated wall; not straight-through tubes, where the flow grazes the holes.

Linear

The term is linear in $M_b$ and independent of frequency; Elnady et al. do not state the validity range of Bauer's term.

Micro-perforates

Not validated for micro-perforates: the term comes from ordinary perforated plates. With flow through a micro-perforate treat the result as an estimate.

Theory

Equations

Default and rule

Valid range on / off (the Elnady model includes it whenever a bias Mach number is non-zero; the cross-flow model has its own through-flow term)

Related 4

References 3