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

Abstract

SUMMARYAn improved approach for studying the stability of a cantilevered flexible plate positioned within twodimensional 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.

Interaction between a simplified soft palate and compressible viscous flow

“…Based on their numerical results, when both upper and lower inlets are open, a flutter-type instability is initiated at a critical Reynolds number, while if one of the inlets is closed, a divergence-type instability occurs at a critical velocity. Although Tetlow and Lucey (2009) imposed a constant pressure drop along the channel rather than 70 assuming velocity-driven flow, flutter instabilities similar to those found by Balint and Lucey (2005) were observed.…”

“…In contrast to the studies mentioned above, Balint and Lucey (2005) and Tetlow and Lucey (2009) included viscous effects directly in their instability analysis by solving the Navier-Stokes 60 equation in a 2D channel surrounding a cantilever plate. Whereas Balint and Lucey (2005) modeled the motion of a thin plate using linear plate theory under differential pressure, Tetlow and Lucey (2009), added a tension term defined as the skin friction force acting on both the upper and lower sides of the plate.…”

“…Whereas Balint and Lucey (2005) modeled the motion of a thin plate using linear plate theory under differential pressure, Tetlow and Lucey (2009), added a tension term defined as the skin friction force acting on both the upper and lower sides of the plate. In both studies, the finite element method was employed in order to solve the unsteady, laminar Navier-Stokes equations in a channel geometry with inlet boundaries above and below the flexible plate and to estimate fluid loads interfacing with the plate.…”

A predictive capability for the aerodynamic deformation of convertible car roofs

“…The omission of a tension cross-term is justified by the near independence between deformations of the perpendicular fibres that constitute the material. Also neglected are the effects of geometric non-linearity because the amplitude-towavelength ratio of the deformations is small, and the effects of fluid friction and in-plane deformation because these are typically an order of magnitude smaller than the out-of-plane effects modelled herein (see, for example, reference [14]). …”

The effect of inertial inhomogeneity on the flutter of a cantilevered flexible plate

“…The flow-plate configuration has been extended to that of a flexible plate mounted in plane-channel flow; see Auré gan and Depollier (1995) and Guo and Païdoussis (2000). All of these studies predict that the plate loses its stability through flutter that sets in beyond a critical uniform flow speed or Reynolds number in the case of viscous channel flow; for the latter refinements, see Balint and Lucey (2005) and Tetlow and Lucey (2009). For short plates the flutter mode is predicted to comprise mainly a combination of the first and second in vacuo modes while for long plates, or plates with heavy fluid loading, the critical mode is dominated by higher-order mode content.…”