Dynamics of the upper airway
Fluid—structure interaction problems occur in everyday life, from medicine to aerospace engineering. One of the general questions from the field of bio-engineering is related to the interaction of a flexible cantilevered plate embedded in a channel flow. Further examining this problem, the motivation for the current study is the desire to elucidate the instability mechanisms of the upper airway with a view to understanding the medical conditions of snoring and obstructive sleep apnoea/hypopnea (OSAH). Snoring is caused by fluttering motions of the soft palate. OSAH involves complete or partial blockage of the airway due to a flow-induced collapse of the pharynx and/or large deflections of the soft palate thereby restricting the air flow to the lungs. The present work addresses the interaction of a flexible plate with viscous channel flow at Reynolds numbers up to 1500, which is about half of the typical Reynolds numbers for the maximal inspiratory flow rate of 0.001m3/s. To perform this investigation, a stable numerical simulation methodology for fluid—structure interaction was developed. To this end a computational model is constructed in which the fluid and flexible plate equations are solved concurrently. The Navier-Stokes equations are solved using an explicit finite-element method while the equations of motion of the plate are solved using an implicit finite-difference method; the latter permits plate deformations to evolve without prescription. A rapid mesh generator able to cope with an arbitrarily deforming geometry of the coupled problem has been implemented. Each of the fluid and solid computational elements of the method has been tested against a variety of unit and benchmark cases. The coupled model has then been used to perform a series of numerical simulations. For flow through both (oral and nasal) airways, the palate experiences a flutter-type of instability caused by a phase shift between the pressure difference across the plate and its motion. This yields an irreversible flow of energy into the plate. In contrast, when one airway is blocked, the plate loses its stability essentially due to divergence. In this case, a deformation is amplified because the pressure forces on the plate exceed the restorative structural forces in the plate; the amplification then serves to increase the force imbalance and further deflection growth ensues. Throughout the time series the full coupling method allows for unrestricted interaction between the viscous fluid flow and the flexible cantilevered plate. The computational model developed here holds much promise for the study of real, spatially varying, geometries and temporal variation of the mean flow. Moreover, the methodology can readily be extended to a similar configuration but with flexible channel walls more realistically representing the pharynx.