Energy map analysis of the flow-induced transverse and orbital vibration of rectangular cylinders

This study investigates the orbital (simultaneous streamwise and transverse) flow-induced vibration (FIV) of rectangular cylinders with a chord-to-thickness ratio of c/d=2, contrasting the characteristics of orbital vibration to the more commonly studied pure transverse vibration mode. Only circular orbits are examined, and the effect of cylinder geometry is explored by testing both sharp and round-edged cylinders. While the main motivation for this work is the vibration of precision air-drop suspension lines (PADS), the study is relevant to energy harvesting and other FIV applications. Because PADS typically encounter Reynolds numbers Red ≤ 10000, the focus of this study is at Re_d= 2500 and 7500. Forced transverse and orbital vibrations in a water tunnel are employed over a wide range of frequencies and amplitudes to encompass vortex-induced vibration (VIV) and galloping regimes. The prescribed motion and measured forces at each frequency and amplitude for a given case are used to calculate the net energy transfer between the cylinder and the fluid. From this, we construct energy maps for each cylinder geometry and Re_d that allows us to predict how the vibration would be affected by the mass, stiffness and damping in a freely oscillating system. The results show that orbital motion could reduce the steady state amplitude of oscillation. When present, this effect is more pronounced at the lower Reynolds number, and it depends on the geometry as well as, in some cases, the direction of rotation.