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

Abstract

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.

The cascade structure of linear instability in collapsible channel flows

“…And then at a slightly higher flow velocity, the system loses stability to second-mode flutter; this is followed by third-mode flutter at a still higher velocity. A similar finding is discovered in a one-dimensional softpalate model of snoring (Lucey & Pitman 2006;Tetlow, Lucey & Balint 2006), and for a tensioned-riser in the sea (Bearman & Huarte 2006), although in the latter, mode switching in vortex-induced vibration is related to a Strouhal frequency in the excitation, and the mechanism may be very different from what is discussed here.…”

Heat transfer performance of flag vortex generators in rectangular channels

“…Others have explored flag flutter for its potential application to instrumentation [34]. In an attempt to understand snoring, flag flutter models were also implemented to study the human palate [35,36]. Similar investigations [37,38] were also conducted to understand the dynamics of paper flutter in printing presses and paper machines.…”