Theory

A mean flow along the plate disturbs the oscillating flow in the slits and raises their acoustic resistance roughly in proportion to the grazing Mach number Kabral et al. (2014). The slit model of Guo et al. (2008), as given by Kabral et al. (2014) and Kabral (2015), adds the term $\beta M/\sigma$ to the resistance; the papers state that the reactance does not change with the flow.

The papers do not print a value of $\beta$ . The default 0.08 is derived from the authors' own model resistance at $M = 0.05$ in Fig. 6 of Kabral et al. (2014) for both panels of their Table 2: the difference between that curve and the no-flow resistance of the same equations, times $\sigma/M$ , gives 0.080 to 0.084 over the whole frequency range for both panels. The reading uncertainty of the figure is about $\pm 0.01$ . The same implementation reproduces the authors' reactance curves (their Fig. 7) to within the reading uncertainty.

Equations

r_s = \operatorname{Re}\left\{ \frac{i\omega t}{\sigma c}\left[1 - \frac{\tanh(k_s\sqrt{i})}{k_s\sqrt{i}}\right]^{-1} \right\} + \frac{4 R_s}{\sigma \rho c} + \beta\,\frac{M}{\sigma}

(1)

where	meaning	unit
$r_s$	Normalised resistance of the slit plate	-
$\omega$	Angular frequency	rad/s
$t$	Plate thickness	m
$\sigma$	Open-area ratio	-
$c$	Speed of sound	m/s
$k_s$	Shear wave number of the slit, $b\sqrt{\omega/(4\nu)}$	-
$R_s$	Surface resistance, $\tfrac{1}{2}\sqrt{2\rho\omega\eta}$	Pa s/m
$\beta$	Grazing factor	-
$M$	Grazing-flow Mach number	-

Default and rule

Default: 0.08 (derived from Kabral et al. 2014 Fig. 6, not printed in the paper)
Rule: 0.08.
Source: Derived from the model curves of Kabral et al. (2014), Fig. 6, as described above; the equation is that of Kabral et al. (2014) (eqs. 2-5), from Guo et al. (2008).

Valid range 0 - 1; 0.08 +/- 0.01

Uncertainty

The default has a reading uncertainty of about ±0.01 from the figure.

Not printed

Where the panel maker or a measurement gives β, enter that value.

Grazing factor of a slit micro-perforate

Theory

Equations

Default and rule

Valid range 0 - 1; 0.08 +/- 0.01

References 3

Theory

Equations

Default and rule

Valid range 0 - 1; 0.08 +/- 0.01

Related 4

References 3