Orbital Motion of a Cylinder in a Wave
Submitted by lcr217 on Thu, 2013-10-10 13:41
Orbital motion of a cylinder in a wave. A wave having an elliptical particle trajectory interacts with a cylinder subjected to controlled orbital motion. The flow patterns and loading are a strong function of the phase shift between the arrival of the wave crest and the crest of the orbital trajectory of the cylinder. In the left column of images, the phase shift is equal to p while in the right column, it is equal to 0. The pattern of vorticity shown in the left column exhibits pronounced concentrations, including a large-scale negative concentration shed from the upper surface of the cylinder. Correspondingly, the streamline topology exhibits a well-defined focus at the center of the vortex and a saddle point above the cylinder. In contrast, the pattern of vorticity in the right column shows only minor concentrations and the corresponding streamline pattern is dominated by that of the wave. The instantaneous drag force corresponding to images of the right column is very small relative to that for the left column. The wave amplitude H relative to the cylinder diameter D is H/D = 1.57. Ratio of major to minor axis of elliptical particle trajectory of wave is 3:1.
Abstract:
Classes of vortex formation from a horizontal cylinder adjacent to an undulating free-surface wave are characterized using high-image-density particle image velocimetry. Instantaneous representations of the velocity field, streamline topology and vorticity patterns yield insight into the origin of unsteady loading of the cylinder. For sufficiently deep submergence of the cylinder, the orbital nature of the wave motion results in multiple sites of vortex development, i.e., onset of vorticity concentrations, along the surface of the cylinder, followed by distinctive types of shedding from the cylinder. All of these concentrations of vorticity then exhibit orbital motion about the cylinder. Their contributions to the instantaneous values of the force coefficients are assessed by calculating moments of vorticity. It is shown that large contributions to the moments and their rate of change with time can occur for those vorticity concentrations having relatively small amplitude orbital trajectories. In a limiting case, collision with the surface of the cylinder can occur. Such vortex-cylinder interactions exhibit abrupt changes in the streamline topology during the wave cycle, including abrupt switching of the location of saddle points in the wave. The effect of nominal depth of submergence of the cylinder is characterized in terms of the time history of patterns of vorticity generated from the cylinder and the free-surface. Generally speaking, generic types of vorticity concentrations are formed from the cylinder during the cycle of the wave motion for all values of submergence. The proximity of the free-surface, however, can exert a remarkable influence on: the initial formation; the eventual strength; and the subsequent motion of concentrations of vorticity. For sufficiently shallow submergence, large-scale vortex formation from the upper surface of the cylinder is inhibited and, in contrast, that from the lower surface of the cylinder is intensified. Moreover, decreasing the depth of submergence retards the orbital migration of previously-shed concentrations of vorticity about the cylinder.
Album:
Vortices due to Free-Surface Distortion and Free Surface-Cylinder Interaction
