Motions of a cantilevered flexible plate in viscous channel flow driven by a constant pressure drop

Abstract

AbstractAn improved approach for studying the stability of a cantilevered flexible plate positioned within two‐dimensional viscous channel flow is presented in the context of human upper‐airway dynamics. Previous work has used constant inlet velocity conditions. Here we model a constant pressure drop that may better reflect 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 the fluid shear‐stress‐induced tension term. The investigation focuses on low‐amplitude motions of the flexible plate (soft‐palate) that, when unstable, may be the precursors to snoring and airway blockage during sleep. We show that imposing constant inlet velocity conditions generates over‐predictions of energy transfer between flow and flexible plate during inhalation. Finally, we show that offsetting the flexible plate within the channel leads to a reduction in oscillation frequency and a significant change to its energy interaction with the fluid flow. Copyright © 2009 John Wiley & Sons, Ltd.