Dynamics and symmetry breaking of an elastically mounted cylinder with attached splitter plate in uniform flow

We numerically study the flow-induced rotational vibrations of an elastically mounted circular cylinder with a rigid splitter plate attached to its lee side, forming a cylinder–plate system. The cylinder–plate is mounted on a torsional spring at the cylinder's center, subjected to a uniform fluid flow. We employ a fluid–structure interaction solver that couples the incompressible Navier–Stokes equations with the harmonic rotational oscillator equation in two-dimensional coordinates. For zero damping, three distinct regimes are observed with increasing reduced velocity, namely, lock-in, desynchronization, and symmetry breaking. Lock-in and desynchronization show behavior analogous to transverse vortex-induced vibrations of an elastically mounted cylinder, as demonstrated by the amplitude response, frequency spectra, phase characteristics, and dynamic mode decomposition. The onset of symmetry breaking is explained by a quasi-static aeroelastic model. The model yields a scaling law, which shows that the square of critical reduced velocity needed for symmetry breaking scales with the structure-to-fluid density ratio. We verify this scaling with numerical simulations. Furthermore, we examine the influence of structure-to-fluid density ratio and structural damping on the coupled dynamic response. In the symmetry breaking regime, a critical damping threshold is identified beyond which symmetry is restored—an effect explained by the proposed model. The vibration amplitude and energy harvesting efficiency scale with the product of density and damping ratio in the lock-in regime, where amplitude decays exponentially and efficiency follows a Gaussian distribution.