# Effect of Subglottic Stenosis on Expiratory Sound Using Direct Noise Calculation
## 2 Methods
### Validation  
Since acoustic feedback and resonance were involved in the production of the whistling sound, it was critical that the simulation setup was able to resolve acoustic feedback and accurately predict resonance frequencies. To validate this, an experimental whistle configuration was chosen from reference [33], which examined the whistling frequency in a range of flow speeds and geometric parameters. The experiment was designed to investigate the human oral whistle, and it had comparable geometric dimensions and Reynolds numbers to the current issue of interest. The configuration was axisymmetric with  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Flowrate** & **Metrics** & **73 K Cells** & **105 K Cells** & **Error** \\ \hline \multirow{2}{*}{300 mL/s} & Overall SPL(dB) & 86.1 & 89.6 & 3.5 (dB) \\ \cline{2-5}  & Primary frequency (Hz) & 1785 & 1806 & 1.16\% \\ \hline \multirow{2}{*}{1000 mL/s} & Overall SPL (dB) & 111.0 & 113.1 & 2.1 (dB) \\ \cline{2-5}  & Primary frequency (Hz) & 2897 & 2941 & 1.50\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: Solution comparison between the two densest meshes.  
Figure 2: Solution independence. (**a**) Overall sound pressure level versus the number of grid cells. (**b**) Power spectrum of the probed acoustic pressure showing grid independence. (**c**) An example of statistically steady solution.  
a cylindrical cavity enclosed by two identical concentric orifice plates with rounded edges (Figure 3a). The upstream orifice was connected to a large reservoir, and the downstream orifice opened up to free space. Whistling occurred within a limited range of jet speeds when air was blown through the device, and the frequency of the whistling depended on the geometric parameters. A 1:1 geometry model was generated for numerical validation. The simulation setup (including the domain, grid resolution, and solver settings) was similar to that of the SGS simulations, except for the use of a large open tube (20D) upstream of the first orifice to mimic the experiment's reservoir. A pressure probe located at the center of the cylindrical cavity near the wall was used to determine the resonance frequency, and the jet speed was varied to cover the range reported in [33], with the corresponding Reynolds numbers ranging from 2000 to 4200.  
Figure 3b shows the comparison of the resonance frequencies between the simulations and experiments in a range of jet speeds for the selected whistling configuration. The results show a good overall match with errors below 4% for the resonance frequency. The simulation also predicts the trend of the resonance frequency increasing with jet speed. The range of jet speeds where whistling occurred in the original experiment was reported to be 225 to 380 in/s (5.72 to 9.65 m/s). In the simulations, when the jet speed was outside the resonance range (the grey triangles in Figure 3b), the pressure signal (the grey lines in the subfigures) became much weaker, indicating the offset of resonance. The estimated range of the resonance was 5.59 to 9.91 m/s. This validation case demonstrates that the current setup accurately predicts the resonance frequency and the jet speed range for whistling, indicating that the setup was capable of capturing both the acoustic feedback and flow-sustained tones.