Fundamental to the understanding of the various transport processes within the respiratory system, airway fluid dynamics plays an important role in biomedical research. When air flows through the respiratory tract, it is constantly changing direction through a complex system of curved and bifurcating tubes. As a result, numerical simulations of the airflow through this tracheobronchial system must be capable of resolving such fluid dynamic phenomena as flow separation, recirculation, secondary flows due to centrifugal instabilities, and shear stress variation along the airway surface. Anatomic complexities within the tracheobronchial tree, such as sharp carinal regions at asymmetric bifurcations, have motivated the application of the incompressible Computational Fluid Dynamics code PHI3D to the modeling of airflow. Developed at ORNL, PHI3D implements the new Continuity Constraint Method. Using a finite-element methodology, complex geometries can be easily simulated with PHI3D using unstructured grids. A time- accurate integration scheme allows the simulation of both transient and steady-state flows. A realistic geometry model of the central airways for the fluid flow studies was obtained from pig lungs using a new high resolution x-ray computed tomography system developed at ORNL for generating 3D images of the internal structure of laboratory animals.