Energetics of collapsible channel flow with a nonlinear fluid-beam model

We consider flow along a finite-length collapsible channel driven by fixed upstream flux, where section of one wall planar rigid is replaced plane-strain elastic beam subject to uniform external pressure. A modified constitutive law used ensure that the energetically conservative. apply finite element method solve fully nonlinear steady and unsteady systems. In line with previous studies, we show system always has at least static solution there narrow region parameter space simultaneously exhibits two stable configurations: an (inflated) upper branch (collapsed) lower branch, connected pair limit point bifurcations unstable intermediate branch. Both configurations can each become self-excited oscillations, initiating either side multiple states. As Reynolds number increases oscillatory cycle persists into states, interaction suggests nearby homoclinic orbit. These oscillations approach zero amplitude point, resulting in tongue between oscillations. Furthermore, this new formulation allows us calculate detailed energy budget over period oscillation, both instabilities require increase work done pressure overcome increased dissipation.