SpectraSim Documentation
Parameter · 05 Boundary Conditions

Thin plate: use C_D

perforate.acoustic_discharge Step 05 · Boundary Conditions

An option of the thin-plate physics baseline: the hole impedance is divided by the discharge coefficient CDC_D, so that the effective open area σCD\sigma C_D is used instead of the geometric one.

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Theory

The baseline computes the exact viscous impedance of the hole as a short tube plus an end correction. A real sharp-edged hole acts as if it were narrower (vena contracta). Elnady's model (Elnady et al., 2010) accounts for this by dividing the hole impedance by CDC_D; this option applies the same step to the baseline, equation (1). With the option off, the baseline is the plain thin-plate theory, and existing cases give unchanged results.

Equations

ζh=1CD 1ρc[iωρtF(ksd)+iωρ ϵfintd]\zeta_h = \frac{1}{C_D}\,\frac{1}{\rho c}\left[\frac{i\omega\rho t}{F(k_s d)} + i\omega\rho\,\epsilon f_{int} d\right]
(1)
wheremeaningunit
CDC_DDischarge coefficient (Discharge coefficient C_D (acoustics))-
FFCrandall's viscous tube function, 1−2J1(ksa)/(ksaJ0(ksa))1 - 2J_1(k_s a)/(k_s a J_0(k_s a))-
ksk_sStokes wavenumber, ks2=−iωρ/μk_s^2 = -i\omega\rho/\mu1/m
ϵ\epsilonEnd-correction factor-
fintf_{int}Hole-interaction factor (1 without interaction)-

Default and rule

Default
off
Rule

Off.

Source

The division by CDC_D follows (Elnady et al., 2010) eq. (6).

Valid range on / off (thin-plate physics baseline only)

Applies to

The thin-plate physics baseline only; the Elnady model always uses CDC_D, the other models never do.

References 1

  1. Elnady, T., Åbom, M. and Allam, S. (2010). Modeling perforates in mufflers using two-ports. Journal of Vibration and Acoustics, 132(6), 061010. DOI 10.1115/1.4001510