Theory

The acoustic impedance of a perforate is computed per hole (Acoustic impedance model of a perforated wall). The hole diameter $d$ enters every model:

the viscous boundary layer in the hole scales with the radius $a = d/2$ (the Stokes number $k_s a$ , equation (1));
the inertia of the air in and around the hole grows with the end correction, a multiple of $d$ , equation (3);
the Elnady model adds a resistive end correction that is a cubic in $d$ , equation (2), and its radiation resistance depends on $kd$ .

In a CFD + acoustics case with a perforated tube (or a thick plate), the hole diameter is entered once on the flow part of the card (Hole diameter) and the acoustic field is hidden; both use the same stored value.

The diameter also selects the auto discharge coefficient (Discharge coefficient C_D (acoustics)) through the $d \times t$ table.

Equations

k_s a = \sqrt{-i\omega\rho/\mu}\;\frac{d}{2}

(1)

\delta_{re} = 0.2\,d + 200\,d^2 + 16000\,d^3 \quad (d\ \text{in m})

(2)

\text{end correction} = \epsilon\,d\ \ (\text{thin plate, } \epsilon = 0.85), \qquad 0.75\,d\ \ (\text{Sullivan \& Crocker, cross-flow}), \qquad 0.5\,d\,f_{int}\ \ (\text{Elnady, reactive})

(3)

where	meaning	unit
$d$	Hole diameter	m
$a$	Hole radius	m
$\omega$	Angular frequency	rad/s
$\rho, \mu$	Density and dynamic viscosity of the gas	kg/m³, Pa s
$\delta_{re}$	Resistive end correction of the Elnady model	m
$\epsilon$	End-correction factor	-
$f_{int}$	Hole-interaction factor	-

Default and rule

Default: 3.0 mm shown on a new wall (the case file stores none until the card is saved)
Rule: The card shows 3.0 mm for a wall that has no hole diameter yet; the value is stored when the card is saved. There is no automatic estimate: enter the real diameter of the holes. The value is stored in m and shown in mm.
Source: Resistive end correction and the other Elnady terms: (Elnady et al., 2010). Measured ranges of the models: (Lee and Ih, 2003), (Kirby and Cummings, 1998), (Sullivan and Crocker, 1978).

Valid range > 0; each impedance model has its own measured range (see Range)

Model ranges

Elnady's $C_D$ table was measured for d 0.6-2.4 mm (values up to 5 mm are extrapolated; beyond that the edge value is used); Lee & Ih 2-9 mm; Sullivan & Crocker measured one plate with d 2.49 mm.

Outside the range

The acoustic QA gate lists a diameter outside the selected model's range as a warning; the run continues.

Hole diameter (acoustics)

Theory

Equations

Default and rule

Valid range > 0; each impedance model has its own measured range (see Range)

References 4

Theory

Equations

Default and rule

Valid range > 0; each impedance model has its own measured range (see Range)

Related 7

References 4