Stability of a Flexible Wall Separating Two Inviscid Channel Flows

Abstract

The stability of a finite flexible wall occupying part of a rigid wall that separates two inviscid channel flows is investigated. The two-dimensional system is solved using a boundary-element method coupled with a finite-difference method. The motion of the wall is driven by the transmural pressure while the no-flux condition at the wall provides the kinematic boundary condition for each of the flows. Flows and structure are fully coupled to yield a system equation that is then transformed into state-space form so that its eigenvalues can be analysed. The flow velocities at which divergence and modal-coalescence flutter of the flexible wall occur are then determined as are mode shapes. We show that decreasing the channel heights and increasing the fluid density causes instabilities to occur at lower flow velocities. When the channels flow in opposite directions it is possible to suppress modal-coalescence of the first two modes.