Streamwise oscillations of a cylinder in steady current. Part 2. Free-surface effects on vortex formation and loading

Abstract

A cylinder in a steady current beneath a free surface is subjected to oscillations in the streamwise direction. Techniques of high-image-density particle image velocimetry and instantaneous force measurement provide the relationship between the instantaneous, global flow patterns and the unsteady loading on the cylinder.

The existence of locked-on states for the fully submerged cylinder is addressed in the companion study of Cetiner & Rockwell (2001). The present investigation shows that it is possible to generate distinctly different locked-on states of vortex formation, provided the cylinder is located immediately beneath the free surface. As a consequence, the time-dependent transverse force is phase-locked to the cylinder motion. In the event that a finite gap exists between the cylinder and the free surface, however, instantaneous, jet-like flow through the gap acts to destabilize such locked-on states. Lissajous representations of the forces demonstrate the degree of phase-locking or, in some cases, a loss of lock-on and associated phase drift. Moreover, the degree of submergence of the cylinder beneath the free surface has remarkable consequences for the magnitudes of positive and negative spikes of the time-dependent force signatures, as well as the averaged spectra of the transverse force. In turn, these alterations of the unsteady transverse force are accompanied by substantial changes of the averaged in-line and transverse forces.

Vortex systems can exist at locations both upstream and downstream of the cylinder. They are due to vorticity from the cylinder surface and/or the free surface. The space–time development of the entire system of vorticity concentrations is interpreted in terms of the time histories of the relative velocity of the cylinder and the instantaneous forces on the cylinder. In turn, these features of the vorticity field are related to critical points near the free surface, deduced from topologies of the corresponding velocity and streamline patterns. Despite the fact that changes in the patterns of vorticity and the corresponding topologies occur in conjunction with large fluctuations of the transverse force coefficient, the dimensionless strength of the vortices is below the threshold for which distinguishable, localized deformations of the free surface occur.