Global stability of rigid-body-motion fluid-structure-interaction problems

TL;DR

This paper rigorously derives and validates linear fluid-structure interaction equations for rigid-body motion, demonstrating their accuracy and applying them to analyze symmetry breaking and eigenvalue sensitivity in FSI systems.

Contribution

The paper provides a rigorous derivation of linear FSI equations in an Eulerian framework and validates them through numerical tests, advancing understanding of stability and symmetry breaking in FSI problems.

Findings

Linear FSI equations match nonlinear results within 0.1% accuracy.

Symmetry breaking is linked to a zero-frequency unstable mode.

Eigenvalue sensitivity varies near fluid-structure resonance.

Abstract

A rigorous derivation and validation for linear fluid-structure-interaction (FSI) equations for a rigid-body-motion problem is performed in an Eulerian framework. We show that the added-stiffness terms arising in the formulation of Fanion et al. (2000) vanish at the FSI interface in a first-order approximation. Several numerical tests with rigid-body motion are performed to show the validity of the derived formulation by comparing the time evolution between the linear and non-linear equations when the base flow is perturbed by identical small-amplitude perturbations. In all cases both the growth rate and angular frequency of the instability matches within $0.1\%$ accuracy. The derived formulation is used to investigate the phenomenon of symmetry breaking for a rotating cylinder with an attached splitter-plate. The results show that the onset of symmetry breaking can be explained by the existence of a zero-frequency linearly unstable mode of the coupled fluid-structure-interaction system. Finally, the structural sensitivity of the least stable eigenvalue is studied for an oscillating cylinder, which is found to change significantly when the fluid and structural frequencies are close to resonance.