Instability of a Cantilevered Flexible Plate in Viscous Channel Flow Driven by Constant Pressure Drop

A new approach for studying the stability of a cantilevered flexible plate positioned within a 2-D viscous channel flow is presented as a representation of the human upper airway. Previous work has used constant inlet velocity conditions, an unrealistic assumption when modelling inhalation. Here we model a constant pressure drop that reflects inspiratory effort. Positioning of the flexible plate within the channel can also be varied. The constant pressure drop is imposed for each time step by computing appropriate inlet velocities. The Navier-Stokes equations are solved using an explicit finite-element method written specifically for the channel geometry within which the fully coupled plate moves. The motion of the plate, driven by the pressure field, is modelled using classical thin-plate mechanics with the addition of a shear-stress induced tension term. The investigation focuses on the motion of the flexible plate (soft palate) as one of the contributors to airway blockage during sleep. It is found that the tension induced by the fluid shear-stress can be significant when the plate is sufficiently flexible. We also demonstrate that imposing constant inlet velocity generates over-predictions of energy transfer between flow and flexible plate. Finally, we show that offsetting the flexible plate within the channel leads to changes in oscillation frequency and significant change to its energy interaction with the fluid flow.