Free-Surface Wave Interaction with a Horizontal Cylinder: Effect of Nominal Submergence of Cylinder beneath Free-Surface
Submitted by lcr217 on Thu, 2013-10-10 13:39
Free-surface wave interaction with a horizontal cylinder: effect of nominal submergence of cylinder beneath free-surface. Instantaneous patterns of vorticity are compared for two values of nominal submergence of the cylinder, h/D = 0.55 and 0, at the same frame numbers N = 11 and 15 of a cinema sequence. At h/D = 0, the quiescent elevation of the free-surface is coincident with the upper surface of the cylinder.
For the deeper submergence h/D = 0.55, frame number N = 11 reveals that the layer of vorticity concentrations B and D moves to the left away from the surface of the cylinder, giving rise to a large-scale vorticity concentration B, D at N = 15. Simultaneously, a vorticity concentration A' is formed from the left surface of the cylinder. During these events, vorticity concentration A moves along its orbital trajectory about the cylinder.
When the submergence of the cylinder is sufficiently shallow, corresponding to h/D = 0, it penetrates the free-surface during a portion of the wave cycle. As a result, the processes of vortex formation from the cylinder are delayed. Vorticity concentration A forms from the bottom, rather than the top, surface of the cylinder at N = 11 and, as evident in frame N = 15, is rapidly swept to the left. In the meantime, a pronounced concentration of vorticity A' forms from the lower left surface of the cylinder. Vorticity concentration D, originally formed on the left side of the cylinder at N = 11, migrates to the left, away from the cylinder, and simultaneously induces a counter vortex E of opposite sense from the free-surface. These events lead to the remarkable formation of six counter-rotating concentrations of vorticity at N = 15.
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
