# Effect of Subglottic Stenosis on Expiratory Sound Using Direct Noise Calculation
## 2 Methods  
### Simulation Setup  
The simulations were conducted using an ANSYS Fluent (R19.2.0, Ansys, Inc., Canonsburg, PA, USA), in which both flow and acoustics were solved simultaneously using the compressible Navier-Stokes equations, which are a so-called direct noise calculation method [40]. While the airflow in the upper airway is of low Mach numbers and can be considered as incompressible, a compressible solver, while computationally expensive, was necessary to capture the coupling between the flow and the sound [41]. The laminar viscous model was used with viscous heating enabled, which meant that the flow was solved using direct numerical simulation (DNS) without any turbulence modeling. This choice was based on the axisymmetric configuration that will be introduced next. The pressure-basedsolver was used with the Coupled algorithm for pressure-velocity coupling. Air was modeled as an ideal gas with default constant properties (a viscosity of \(1.7894\times 10^{-5}\) kg/(m s), a thermal conductivity of 0.0242 W/(m K), specific heat of 1006.43 J/(kg K), and a molecular weight of 28.966 kg/kmol). For spatial derivatives, pressure was discretized using the second-order scheme and other variables using the QUICK scheme. The second-order implicit time marching scheme was used with a constant time increment size of \(5\times 10^{-6}\) s. A steady flow field was obtained before marching the solution in time. To reduce computational cost and to make the parametric simulations feasible, the simulation domain (and the flow) was assumed to be axisymmetric. In this way, only a two-dimensional (2D) profile section (Figure 1a) needed to be resolved with mesh. The axisymmetric setup enforced the spatial coherence of the vortical structures. It also precluded vortex stretching and, consequently, the production of turbulence. While the glottal jet is more of a 2D structure, axisymmetric configurations have been used in some previous studies on glottal flow and aeroacoustics in phonation [42; 43]. It was observed in these studies that, due to lack of vortex stretching and small-scale turbulence, all vortices generated at the glottis survived and convected downstream instead of being dissipated. Axisymmetric configurations have also been used to represent obstructed upper airways [12; 44]. Compared to a 2D configuration, the axisymmetric configuration ensured the actual area ratio between stenosis and the vocal tract, which was important in this current study. The effects of the axisymmetric assumption in relation to the present results are discussed in Section 4.3. The simulation domain (Figure 1) comprises the trachea, true vocal folds, vocal tract, and a half-circular environmental domain. The trachea and vocal tract were simplified as straight tubes with a diameter of 2 cm, which is approximately the average measurement of adult tracheas [45; 46]. The length of the trachea and the vocal tract were 10 cm and 15 cm, respectively, based on average adult measurements [46; 47]. The radius of the environmental domain was 2 m. A pressure probe was placed 0.1 m from the mouth at a 45-degree angle  
Figure 1: (**a**) Computational domain (to the right) and a zoomed-in view of the tract system showing the setup of boundary conditions. (**b**) SGS–glottis subsystem. In the figure, \(o=0.6\) cm, \(g=1.1\) cm, and \(d=2.0\) cm. (**c**) Sources of acoustic resonance in the system, including the vocal tract (VT, from glottal exit to mouth), the extended tract (XT, from SGS opening to mouth), and the SGS–VFs cavity. to the jet (Figure 1a). This was to mimic the typical way that sound is recorded on a human subject using a microphone. Analysis in this paper was based on signals collected using this probe. The solver and domain setup parameters are summarized in Table 1.  
The vocal fold profile was defined using the M5 model [48]. The base thickness of the vocal fold (thickness of the lateral surface) was fixed at 0.9 cm.