Excitation and Damping Fluid Forces on a Cylinder Undergoing Vortex-Induced Vibration

Abstract

In the context of flow-induced vibration, the component of the hydrodynamic coefficient in-phase with the velocity of an oscillating body, $C_v$, can be termed `positive excitation' or `negative damping' if $C_v>0$. While this empirical approach is of long standing in the literature it does not account for distinct physical mechanisms that can be associated with fluid excitation and fluid damping. In this work, we decompose the total hydrodynamic force into a drag component aligned with the time-dependent vector of the relative velocity of a cylinder oscillating transversely with respect to a free stream and a lift component normal to the drag component. The drag and lift components are calculated from laboratory measurements of the components of the hydrodynamic force in the streamwise and cross-stream directions combined with simultaneous measurements of the displacement of an elastically mounted rigid circular cylinder undergoing vortex-induced vibration. It is shown that the drag component only does negative work on the oscillating cylinder, i.e. it is a purely damping force as expected from theoretical considerations. In contrast to this the lift component mostly does positive work on an oscillating cylinder, i.e. it is the sole component providing fluid excitation. In addition, the new excitation (lift) coefficient, $C_L$ displays the same scaling as the linear theory predicts for the traditional excitation coefficient, $C_v$, even though $C_L$ is two orders of magnitude higher than $C_v$. More importantly, while $C_v$ depends on the mechanical properties of the hydro-elastic system, according to linear theory, we provide here evidence that $C_L$ depends solely on fluid-dynamical parameters. Finally, an effective drag is calculated that represents the dissipation of energy within the fluid, and it is found that the effective drag is not equal to the mean value of the drag component. The effective drag provides complementary information that characterizes the state of the wake flow. Its variation suggests that the wake can dissipate the kinetic energy most vigorously at the end of the initial branch.