Data-driven active control of a thin elliptical cylinder undergoing transverse flow-induced vibrations

This experimental study employs Bayesian optimisation to maximise the cross-flow (transverse) flow-induced vibration (FIV) of an elastically mounted thin elliptical cylinder by implementing axial (or angular) flapping motions. The flapping amplitude was in proportion to the vibration amplitude, with a relative phase angle imposed between the angular and transverse displacements of the cylinder. The control parameter space spanned over the ranges of proportional gain and phase difference of $0 \leq K_p^* \leq 5$ and $0 \leq \phi _d \leq 360^\circ$ , respectively, over a reduced velocity range of $3.0 \leqslant {U^*} = U/({{f_{nw}}} b) \leqslant 8.5$ . The corresponding Reynolds number range was $1250 \leqslant {{Re}} =(U b)/\nu \leqslant 3580$ . Here, $U$ is the free stream velocity, $b$ is the major cross-sectional diameter of the cylinder, ${{f_{nw}}}$ is the natural frequency of the system in quiescent fluid (water) and $\nu$ is the kinematic viscosity of the fluid. It was found that the controlled body rotation extended the wake-body synchronisation across the entire ${U^*}$ range tested, with a larger amplitude response than the non-rotating case for all flow speeds. Interestingly, two new wake-body synchronisation regimes were identified, which have not been reported in previous studies. As this geometry acts as a ‘hard-oscillator’ for ${U^*} \geqslant 6.3$ , an adaptive gain (i.e. one that varies as a function of oscillation amplitude) was also implemented, allowing the body vibration, achieved for a non-rotating cylinder using increasing ${U^*}$ increments, to be excited from rest. The findings of the present study hold potential implications for the use of FIV as a means to efficiently extract energy from free-flowing water sources, a topic of increasing interest over the last decade.