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

J.-L Pfister,O Marquet

doi:10.1017/jfm.2020.284

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.

Highlights

The interaction of fluids with structures has long attracted the attention of scientists due to its importance in the design of products in many traditional engineering fields 896 A24-2J.-L
We review previous studies, first on the flow past a circular cylinder with rigid and flexible splitter plates, and on the linear fluid–solid stability analyses of rigid and flexible structures interacting with wake flows
We expect to decrease the restoring elastic force compared to the hydrodynamic pressure force and to obtain vibrations modes initially of higher frequency interacting with the flow

Summary

Introduction

The interaction of fluids with structures has long attracted the attention of scientists due to its importance in the design of products in many traditional engineering fields 896 A24-2J.-L. The interaction of fluids with structures has long attracted the attention of scientists due to its importance in the design of products in many traditional engineering fields 896 A24-2. Marquet such as aeronautics, wind engineering and off-shore oil extraction. The divergence and flutter analysis of wings is for instance an important step in the design of an aircraft, since these phenomena may induce premature fatigue and even lead to fracture of the structure. The vortex-induced vibration of elongated marine risers is another example of an industrial system where structural oscillations are detrimental. Because of the high flow speeds and the large scales of the structures encountered in most of these applications, inviscid models have often been used to describe the high Reynolds number flows (Dowell 2004)

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