Fluid-structure stability analyses and nonlinear dynamics of flexible splitter plates interacting with a circular cylinder flow

Abstract

The dynamics of a hyperelastic splitter plate interacting with the laminar wake flow of a circular cylinder is investigated numerically at a Reynolds number of 80. By decreasing the plate's stiffness, four regimes of flow-induced vibrations are identified: Two regimes of periodic oscillation about a symmetric position, separated by a regime of periodic oscillation about asymmetric positions, and finally a regime of quasi-periodic oscillation occurring at very low stiffness and characterized by two fundamental (high and low) frequencies. A linear fully coupled fluid-solid analysis is then performed and reveals the destabilization of a steady symmetry-breaking mode, two high-frequency unsteady modes and one low-frequency unsteady mode, when varying the plate's stiffness. These unstable eigenmodes explain the emergence of the nonlinear self-sustained oscillating states and provide a good prediction of the oscillation frequencies. A comparison with nonlinear calculations is provided to show the limits of the linear approach. Finally, two simplified analyses, based on the quiescent-fluid or quasi-static assumption, are proposed to further identify the linear mechanisms at play in the destabilization of the fully coupled modes. The quasi-static static analysis allows an understanding of the behaviour of the symmetry-breaking and low-frequency modes. The quiescent-fluid stability analysis provides a good prediction of the high-frequency vibrations, unlike the bending modes of the splitter plate in vacuum, as a result of the fluid added-mass correction. The emergence of the high-frequency periodic oscillations can thus be predicted based on a resonance condition between the frequencies of the hydrodynamic vortex-shedding mode and of the quiescent-fluid solid modes.