Instabilities in collapsible channel flow with a pre-tensioned elastic beam

Hydrodynamic instability can occur when a viscous fluid is driven rapidly through a flexible-walled channel, including a multiplicity of steady states and distinct families of self-excited oscillations. In this study we use a computational method to predict the stability of flow through a planar finite-length rigid channel with a segment of one wall replaced by a thin pre-tensioned elastic beam of negligible mass. For large external pressures, this system exhibits a collapsed steady state that is unstable to low-frequency self-excited oscillations, where the criticality conditions are well approximated by a long-wavelength one-dimensional (1-D) model. This oscillation growing from a collapsed state exhibits a reduced inlet driving pressure compared with the corresponding steady flow, so the oscillating state is energetically more favourable. In some parameter regimes this collapsed steady state is also unstable to distinct high-frequency normal modes, again predicted by the 1-D model. Conversely, for lower external pressures, the system exhibits an inflated steady state that is unstable to another two modes of self-excited oscillation, neither of which are predicted by the lower-order model. One of these modes becomes unstable close to the transition between the upper and lower steady states, while the other involves small-amplitude oscillations about a highly inflated wall profile with large recirculation vortices within the cavity. These oscillatory modes growing from an inflated steady state exhibit a net increase in driving pressure compared with the steady flow, suggesting a different mechanism of instability to those growing from a collapsed state.