Sammendrag
This Master's thesis extends previous work conducted in the collaboration project called Modelling of obstructive sleep apnea by fluid-structure interaction in the upper airways. The main objective of the current work was to investigate the importance of including turbulence in CFD models of the human upper airways, and how model parameters (e.g. boundary conditions and grid size) affected simulation results. Computational Fluid Dynamics (CFD) was employed to do investigations of an obstructive sleep-apnea syndrome (OSAS) patient who underwent nasal surgery. The realizable k-ε turbulence model was utilized in the investigations. A set of boundary conditions is chosen as the base case for pre- and post-operative CFD simulations: at the inlet, i.e. both nostrils, a gauge pressure of 0 Pa, a turbulent intensity of 5% and a turbulent viscosity ratio of 10 is set, while a uniform velocity corresponding to a volumetric flow rate of 250 ml/s is prescribed at the outlet.
Simulations were performed on both the pre- and post-operative models of the airway geometries. The post-operative results showed an accelerated flow in the front part of the nasal cavity compared to the pre-operative results. As expected, the higher velocity led to a higher pressure drop, inherently meaning a higher resistance in the flow. These results are contradictory to the rhinomanometry data used for validation, since the rhinomanometry data show a lower pressure drop after surgery. To understand what is causing this discrepancy, a sensitivity study of the pre-operative geometry was performed.
A narrower, pre-operative airway geometry model, i.e. reduced cross-sectional areas, was made to assess the effect of uncertainty in the interpretation of the CT images used to make the 3D-geometries. The smaller cross-sections resulted in higher values for the pressure drop, turbulence kinetic energy and velocity modulus. Although the pressure drop in the narrower geometry was about twice the value found in the base-case geometry, it was still lower than what was expected from the rhinomanometry data.
The effect of outlet boundary condition type was investigated by changing it from a uniform velocity to a gauge pressure of -36 Pa, a value which was determined by the pre-operative base-case calculations. The results were unaffected by the change, indicating that it is insignificant whether the outlet condition is a uniform pressure or a uniform velocity condition. The effect of type of inlet boundary condition was assessed by changing it to a velocity inlet instead of a gauge pressure. Again, the results were identical, leading to the conclusion that it is insignificant whether the inlet condition is a pressure or a velocity boundary condition.
The wall boundary condition was examined by adding a roughness height of 0.2 mm along the wall. The pressure drop in the flow was only minorly impacted, as was expected due to the low Reynolds numbers in the flow. The preliminary conclusion was that wall roughness cannot explain the observed discrepancy between CFD models and measurements.
The grid sensitivity was studied by comparing pre-operative results from three different meshes; the base-case mesh with 1.4 million cells and two finer meshes with 6.8 million cells and 10.1 million cells. The results were virtually the same for the coarsest and the finest mesh, while the results from the 6.8M grid deviated a little from the other two, which is believed to stem from poor grid quality in the 6.8M mesh. From this it is concluded that the coarsest mesh consisting of 1.4M cells is sufficiently fine.
Simulations were performed on both the pre- and post-operative models of the airway geometries. The post-operative results showed an accelerated flow in the front part of the nasal cavity compared to the pre-operative results. As expected, the higher velocity led to a higher pressure drop, inherently meaning a higher resistance in the flow. These results are contradictory to the rhinomanometry data used for validation, since the rhinomanometry data show a lower pressure drop after surgery. To understand what is causing this discrepancy, a sensitivity study of the pre-operative geometry was performed.
A narrower, pre-operative airway geometry model, i.e. reduced cross-sectional areas, was made to assess the effect of uncertainty in the interpretation of the CT images used to make the 3D-geometries. The smaller cross-sections resulted in higher values for the pressure drop, turbulence kinetic energy and velocity modulus. Although the pressure drop in the narrower geometry was about twice the value found in the base-case geometry, it was still lower than what was expected from the rhinomanometry data.
The effect of outlet boundary condition type was investigated by changing it from a uniform velocity to a gauge pressure of -36 Pa, a value which was determined by the pre-operative base-case calculations. The results were unaffected by the change, indicating that it is insignificant whether the outlet condition is a uniform pressure or a uniform velocity condition. The effect of type of inlet boundary condition was assessed by changing it to a velocity inlet instead of a gauge pressure. Again, the results were identical, leading to the conclusion that it is insignificant whether the inlet condition is a pressure or a velocity boundary condition.
The wall boundary condition was examined by adding a roughness height of 0.2 mm along the wall. The pressure drop in the flow was only minorly impacted, as was expected due to the low Reynolds numbers in the flow. The preliminary conclusion was that wall roughness cannot explain the observed discrepancy between CFD models and measurements.
The grid sensitivity was studied by comparing pre-operative results from three different meshes; the base-case mesh with 1.4 million cells and two finer meshes with 6.8 million cells and 10.1 million cells. The results were virtually the same for the coarsest and the finest mesh, while the results from the 6.8M grid deviated a little from the other two, which is believed to stem from poor grid quality in the 6.8M mesh. From this it is concluded that the coarsest mesh consisting of 1.4M cells is sufficiently fine.