Hydrodynamic damping of a circular cylinder at low KC: Experiments and an associated model

This paper investigates the hydrodynamic damping of a smooth circular cylinder undergoing forced oscillations at Keulegan-Carpenter (KC) numbers smaller than 5 and Reynolds (Re) numbers from 10³–10⁵ with and without background steady currents. A series of experiments are conducted with a circular cylinder oscillating in still water, in-line currents and cross currents. The measured drag coefficients of the smooth cylinder in the still water condition match with the well-published results and the theoretical solution of Stokes and Wang at very small KC numbers. The hydrodynamic damping increases with the in-line steady current whereas it remains almost constant at small transverse velocities and increases notably when the latter becomes large. To predict the hydrodynamic damping in in-line steady currents, the performance of the Morison equation based on relative velocity and independent velocity is explored, respectively. The latter model, by separating the drag into two independent parts, leads to a better fit of the drag force than the former, which is not surprising. However, the former is still a preferable option for engineering design due to its simplicity. The experimental data suggest that the existing design guidelines such as ISO-19902 or DNVGL-RP-C205 should be used with caution for KC < 5.