Following rhinometry measurements and patency ratings at the Monell Chemical Senses Center, participants were immediately escorted by staff to Thomas Jefferson University Hospital (Philadelphia, PA), via a 10- to 15-min subway ride, to undergo a spiral sinus CT. The CT enabled the construction of “real-time” CFD nasal airway models for each subject using methods described previously8 (link). In brief, the scans were imported into the commercial software AMIRA (Visualization Sciences Group, USA) to extract nasal cavity geometry. After necessary segmentation, smoothing, and correction for artifacts, a three-dimensional surface geometry of the nasal airway was generated. All sinuses were included in the CFD model, as long as they were shown to be open to the main nasal airway based on the CT scan. Then the commercial grid generator ICEM CFD (Ansys, Inc., USA) was applied to generate the mesh. In order to resolve the boundary layer, a thin (~0.2 mm) region consisting of four layers compact hybrid tetrahedral/pentahedral elements was generated near the surface8 (link). The thickness of each layers follow power growth law that the second layer is 1.2 times thicker than the first layer, etc. A typical initial nasal cavity mesh after boundary layers contained between 1 million and 3 million hybrid finite elements. Then the initial meshes were refined by gradient adaptation and boundary adaptation until grid independence of the solutions was achieved. The dimensionless distance for wall-bounded flow (y+) were further examined to ensure that it was within the first wall cell. The final grids contained approximately 1.8 million to 3.5 million elements.
The solutions of the three-dimensional steady Navier-Stokes and continuity equations were obtained using the commercial software package FLUENT 13.1 (Ansys, Inc.). As described in the Introduction, whether human nasal airflow during restful breathing (flow rate <200 ml/s) is turbulent is still an open question. So the low-Reynolds-number k-ω turbulence model was used to simulate the flow field with a turbulence intensity of 2.5%11 (link) of the mean velocity imposed at inlet location and compared with the laminar model to investigate possible turbulence effects. The low-Reynolds-number k-ω turbulent model has been shown to be valid, and reliable in the prediction of laminar, transitional, and turbulent flow behavior23 . Along the nasal walls, the usual no-slip velocity condition was applied, and the wall is assumed to be rigid. At the nasopharynx, the “pressure outlet” condition was adopted. At the external naris, pressure inlet with pressure drop of 15 Pa was imposed as the driving force of airflow through the nose. The resulting inhalation rate was <200 ml/s, within the restful breathing range.
The numerical solutions of the continuity, momentum, and/or turbulence transport equations were determined using the finite-volumes method. A second-order upwind scheme was used for spatial discretization. The SIMPLEC algorithm was used to link pressure and velocity. The discretized equations were then solved sequentially using a segregated solver. Convergence was obtained when the scaled residuals of continuity, momentum, and/or turbulence quantities were <10-5. Global quantities such as flow rate and pressure on the nasal walls were further monitored to check the convergence.
The solutions of the three-dimensional steady Navier-Stokes and continuity equations were obtained using the commercial software package FLUENT 13.1 (Ansys, Inc.). As described in the Introduction, whether human nasal airflow during restful breathing (flow rate <200 ml/s) is turbulent is still an open question. So the low-Reynolds-number k-ω turbulence model was used to simulate the flow field with a turbulence intensity of 2.5%11 (link) of the mean velocity imposed at inlet location and compared with the laminar model to investigate possible turbulence effects. The low-Reynolds-number k-ω turbulent model has been shown to be valid, and reliable in the prediction of laminar, transitional, and turbulent flow behavior23 . Along the nasal walls, the usual no-slip velocity condition was applied, and the wall is assumed to be rigid. At the nasopharynx, the “pressure outlet” condition was adopted. At the external naris, pressure inlet with pressure drop of 15 Pa was imposed as the driving force of airflow through the nose. The resulting inhalation rate was <200 ml/s, within the restful breathing range.
The numerical solutions of the continuity, momentum, and/or turbulence transport equations were determined using the finite-volumes method. A second-order upwind scheme was used for spatial discretization. The SIMPLEC algorithm was used to link pressure and velocity. The discretized equations were then solved sequentially using a segregated solver. Convergence was obtained when the scaled residuals of continuity, momentum, and/or turbulence quantities were <10-5. Global quantities such as flow rate and pressure on the nasal walls were further monitored to check the convergence.
