High fidelity simulations of the nasal flow with heat transfer and adjoint based optimization

Nasal anatomical deformities, including deviated septum, turbinate hypertrophy, and nasal valve collapse, can significantly impede airflow through the nasal passages, leading to breathing difficulties and other health issues. A deviated septum, where the nasal septum is off center, affects up to 80% of people and can cause chronic nasal congestion, frequent sinus infections, difficulty breathing, sleep problems, headaches, facial pain, and nosebleeds. Computational Fluid Dynamics (CFD) is a valuable tool for simulating and analyzing nasal airflow. By creating detailed models of the nasal cavity, CFD allows researchers and clinicians to visualize airflow patterns, identify areas of obstruction, and assess the impact of anatomical abnormalities on breathing. This technology aids in planning surgical interventions, such as septoplasty, by predicting postoperative outcomes and optimizing surgical approaches. CFD simulations have demonstrated that nasal airflow is complex and can be influenced by various factors, including the shape and size of nasal structures. For instance, studies have shown that the nasal valve area plays a crucial role in regulating airflow resistance, and its collapse can lead to significant breathing difficulties. In addition to aid surgical planning, CFD can help in understanding the physi- ological aspects of nasal breathing and the development of personalized treatment plans. By analyzing airflow dynamics, clinicians can better understand the relation- ship between nasal anatomy and respiratory function, leading to improved patient outcomes. CFD simulations have been employed to study the nasal cycle and the natural alternation of congestion and decongestion between the nasal cavities; by modeling different states of the nasal cycle, researchers can distinguish between physiological changes and structural abnormalities, leading to more accurate assessments of nasal patency and the effectiveness of surgical interventions. In clinical practice, CFD studies can be utilized to improve patient outcomes. Services are available that provide detailed CFD reports based on patient-specific CT scans, offering insights into the functional behavior of airflow in the nasal cavity. These reports can assist healthcare providers in diagnosing issues and planning effective treatments. In summary, CFD simulations serve as a powerful tool in understanding nasal airflow dynamics, evaluating the impact of anatomical variations, and planning surgical interventions to address nasal obstructions and improve patient quality of life. In this work it is also explored the application of upscaling approaches for ana- lyzing hierarchical flow problems, emphasizing their advantages in handling complex geometries with distinct scale separations. By employing multiscale homogenization techniques, effective macroscopic parameters such as Navier’s slip length and thermal- slip coefficients are derived, replacing the need for resolving intricate microstructures. These homogenized coefficients enable computationally efficient simulations whilemaintaining accuracy, making them particularly suitable for optimization frameworks. In the context of nasal airflow, a multi-objective optimization strategy is adopted, balancing aerodynamic performance and thermal conditioning efficiency. Leveraging the open-source tools dafoam and OpenMDAO, the study demonstrates that upscaled boundary conditions simplify sensitivity analysis and optimization while avoiding the challenges of resolving detailed geometry. This work highlights the potential of upscaling methodologies to achieve significant computational savings in practical thermal-fluid applications, paving the way for enhanced modeling in geometrically intricate systems. In conclusion, the integration of CFD simulations and upscaling approaches offers a comprehensive framework for analyzing nasal airflow dynamics and optimizing surgical interventions. By combining detailed anatomical modeling with efficient computational techniques, clinicians and researchers can better understand the complexities of nasal airflow, leading to improved patient outcomes and more effective treatments for nasal obstructions.