NUMERICAL SIMULATION OF VORTEX-INDUCED OSCILLATION OF AN ELASTICALLY MOUNTED CIRCULAR CYLINDER USING BODY-FITTED COORDINATES
ALLEN, DONALD WAYNE
Doctor of Philosophy
Vortex-induced oscillation during lock-in of an elastically mounted circular cylinder is numerically modeled herein for two-dimensional flow. The model solves the incompressible Navier-Stokes equations for flow-fields containing one or more moving boundaries. A body-fitted coordinate technique is used to generate a grid that contains coordinate lines coincident with the physical boundaries. The technique maps each curvilinear line segment in the physical plane to a straight line in a computational plane by a chain-rule transformation. The model allows for time-dependent transformations so that flow-fields containing one or more arbitrarily moving boundaries may be easily transformed to the fixed computational plane. This investigation focuses on vortex-induced vibration of a circular cylinder when the flow is laminar near a Reynolds number of 100. Both steady and unsteady flow solutions are also presented for flow over a stationary circular cylinder. The solutions for vortex-induced oscillations are performed during lock-in (synchronization of the vortex-shedding frequency and the natural frequency of the elastically mounted cylinder) for different amounts of structural damping and different ratios between the structural natural frequency and the stationary cylinder vortex shedding frequency. Special attention is given to the controversy presented by several experimental researchers regarding a discontinuity in the Strouhal-Reynolds number relationship for flow over a stationary cylinder at a Reynolds number near 100. Results of a test attempting to find two Strouhal shedding frequencies in this Reynolds number range are presented. These results indicate that the discontinuity observed in some experiments is not caused by purely fluid mechanical effects.