# Effects of Vertical Glottal Duct Length on Intraglottal Pressures in the Convergent Glottis
## 2 Materials and Methods
### Computational Method  
In order to obtain intraglottal aerodynamic parameters, especially for the pressure distributions on the vocal fold surface, our previous studies have used both a laryngeal Plexiglas model (static physical model M5, 7.5 times larger than real life [1; 38; 39]) and a numerical computational method (computational fluid dynamics code ANSYS Fluent [2; 3; 5; 7; 40]). Comparing results between these two methods suggests that ANSYS Fluent can provide relatively highly accurate matches to the values obtained in the physical model M5. Therefore, ANSYS Fluent 6.3 and Gambit (ANSYS, Inc., Canonsburg, PA, USA; [[http://www.ansys.com/Products/Fluids/ANSYS-Fluent](http://www.ansys.com/Products/Fluids/ANSYS-Fluent)]([http://www.ansys.com/Products/Fluids/ANSYS-Fluent](http://www.ansys.com/Products/Fluids/ANSYS-Fluent)), accessed on: 21 March 2012) commercial computational fluid dynamics codes were used in this study to obtain the intraglottal aerodynamic parameters for the different glottal geometries and transglottal pressures. Fluent was used to solve the Navier-Stokes equations for laminar and incompressible airflow based on the control-volume technique. Gambit was used to generate grids with both structured and unstructured meshes for each case. Because the shape of the glottal minimal diameter region had significant variation, the unstructured meshes were employed in this region, and the structured meshes were used in other relatively regular regions. The grid types were Quad-Pave and Quad-Map. The mesh size varied from 412,000 to 1,022,500 nodes and was made very fine in regions where high gradients in pressure or velocity were expected. The boundary conditions in Fluent were the following: fluid type, pressure-inlet (corresponding to 500, 1000, and 1500 Pa transglottal pressure for each case), pressure-outlet (constant at 0 gauge pressure), and stationary wall with the no-slip condition. The SIMPLE algorithm was selected for pressure-velocity coupling in Fluent. All of the computational cases were performed unsteady, and the second order upwind scheme was employed for momentum discretization, with the convergence criterion for both velocity and continuity being \(10^{-4}\). Static geometries, constant transglottal pressures, and constant volume flows were used in the computational models in this study for quasi-steady assumption reasons [41; 42]. Only half of the flow field was modeled in Fluent, as the flow field was assumed symmetric across the midline of the glottis [3; 5; 7; 40].  
The number of grids or grid size is a significant factor relative to the accuracy of the computation results. A grid independence test was carried out to check the influence of the number of grids on the predicted values of intraglottal pressures and volume flows. Table 1 shows the grid independence test for increasing the number of grid elements. The table indicates that the intraglottal pressure average, minimal pressure, and volume flow are close for the first three cases, when the number of elements was larger than 410,000. Therefore, 748,593 elements (case 2) were selected for the simulations. Each simulation was run for more than 24 h, and the number of iterations was always beyond 100,000.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Case** & **Number of Elements** & **Average Intraglottal Pressure (Pa)** & **Minimal Pressure (Pa)** & **Volume Flow (cm3/s)** \\ \hline
1 & 912,521 & 207.8692 & \(-\)91.2530 & 23.2837 \\
2 & 748,593 & 207.8632 & \(-\)91.4702 & 23.2921 \\
3 & 410,020 & 207.8867 & \(-\)91.2804 & 23.2889 \\
4 & 323,785 & 244.1898 & \(-\)88.5606 & 23.3201 \\
5 & 286,694 & 264.3649 & \(-\)87.1646 & 23.3947 \\ \hline \end{tabular}
\end{table}
Table 1: Results of the grid independence test.