Theory

The hole speed is the normal flow speed through the wall divided by the open-area ratio. On auto it is taken as follows.

Cross-flow model (always uses it):

the net through-flow of the CFD's perforate samples, divided by $\sigma A$ (from the last loss-coefficient update of the flow run);
else the total inflow divided by $\sigma A$ when the flow is on (perpendicular-baffle assumption: all of the flow crosses this wall);
else 0 (acoustics only: enter the number).

Other models, with [[perforate.bias_flow]] on:

the mapped CFD field: the area mean of $|\mathbf U\cdot\mathbf n|$ over the wall, divided by $\sigma$ (acoustic medium mapped from the CFD);
else the mean hole speed $|U_n|/\sigma$ of the CFD's perforate samples;
else 0.

Without the bias-flow option (and for models other than cross-flow and Elnady's own term) the bias Mach number is 0. The cross-flow resistance is $2.57\,M_b$ (Sullivan, 1979) (eq. 16, $M_b$ = mean hole speed / c), the bias resistance $1.15\,M_b/C_D$ (Elnady et al., 2010).

Equations

M_b = \frac{1}{\sigma c}\,\frac{\sum_e |\mathbf{U}_e\cdot\mathbf{n}_e|\,A_e}{\sum_e A_e}\ \ \text{(mapped field)}, \qquad M_b = \frac{Q}{\sigma A c}\ \ \text{(whole-flow estimate)}

(1)

\theta_{cross} = 2.57\,M_b, \qquad \theta_{bias} = \frac{1.15\,M_b}{C_D}

(2)

where	meaning	unit
$M_b$	Bias Mach number in the holes	-
$\sigma$	Open-area ratio	-
$c$	Speed of sound of the local gas	m/s
$\mathbf{U}_e, \mathbf{n}_e, A_e$	Mean velocity, unit normal, area of wall triangle e	m/s, -, m²
$Q$	Total inflow (or the net through-flow of the samples)	m³/s
$A$	Area of the perforated wall	m²
$C_D$	Discharge coefficient	-

Default and rule

Default: auto: from the CFD in a flow + acoustics run (cross-flow model: net through-flow / (σA), or Q / (σA)); 0 in an acoustics-only runComputed by the program
Rule: Auto. A typed number overrides every source.
Source: Validation on the two-baffle test muffler at 0.0556 kg/s against a reference transmission loss with flow: the cross-flow model with M 0.041-0.053 gave an rms deviation of 2.5 dB (with the earlier resistance $4 \times 0.514\,M_b$ , 20 % lower than now; not repeated since); the Elnady model with grazing and bias flow (M_b 0.05-0.08) 3.0 dB. Bias resistance: (Elnady et al., 2010).

Valid range 0 ≤ M_b ≤ 0.6

Values

0 to 0.6.

Acoustics only

Without a flow solution the auto value is 0, which for the cross-flow model means the small no-flow resistance; enter the hole Mach number of the operating point.

Bias (through-hole) Mach number

Theory

Equations

Default and rule

Valid range 0 ≤ M_b ≤ 0.6

References 2

Theory

Equations

Default and rule

Valid range 0 ≤ M_b ≤ 0.6

Related 6

References 2