Data-driven stability analysis and near-wake jet control for the vortex-induced vibration of a sphere

We present a stability analysis for the vortex-induced vibration (VIV) of a sphere and a suppression control technique using a base bleed actuation. The reduced-order model (ROM) for the system is developed via the eigensystem realization algorithm (ERA), which provides a low-order representation of the unsteady flow dynamics in the neighborhood of the equilibrium steady state. A systematic ROM-based stability analysis is performed to understand the frequency lock-in mechanism and self-sustained VIV phenomenon by examining the eigenvalue trajectories for a range of reduced oscillation frequencies (F_s) at fixed Reynolds number (Re) and mass ratio (⁠$m*$⁠). Consistent with the full-order simulations, the ERA-based ROM predicts the frequency lock-in branches arising due to resonance and combined mode instabilities. The dependence of these lock-in branches is explored as a function of mass ratio. The base bleeding mechanism in the near-wake region of a sphere and its influence over the flow dynamics, the wake characteristics, and the VIV response are investigated for the freely vibrating sphere system at Re = 300. A base bleed coefficient (C_q) is defined as a ratio of near-wake jet flow rate to the freestream inflow rate to perform a parametric analysis on the hydrodynamic coefficients and the flow features. It is found that a near-wake jet with $Cq=1%$ inhibits the synchronization of the shedding process and completely suppresses the large-amplitude oscillations for all VIV branches studied. In addition, we demonstrate the reduction of the mean drag coefficient by more than 14% in comparison to the sphere alone system. The stability analysis of the near-wake jet is performed for the sphere VIV. The resulting ROM provides an effective approach for the parameter space exploration and is able to characterize the effectiveness of the designed controller on the VIV suppression. Results from the ROM analysis are consistent with those obtained from our full-order nonlinear fluid–structure interaction simulations. The present study illustrates that VIV can be suppressed by altering the structure mode via shifting the unstable wake modes to the stable region. This finding is realized through the simulations of an active control device, wherein the presence of near-wake jet flow breaks the self-sustenance of the wake–body interaction cycle. Overall, the proposed base-bleed control is found to be effective in suppressing the vortex shedding and the VIV for a range of reduced velocities and mass ratios.