Response of a pendulum spar to 2-dimensional random waves and a uniform current

Abstract

A linearized theory for the response of a circular pendulum spar in 2-dimensional waves and a uniform current is developed. The linear forces on the cylinder are predicted using an approximate potential flow theory for slender bodies. The dynamic equations are then amended to account for the wake effects of viscous bluff body flow by including a quadratic drag law and neglecting wave damping. A spectral model for the forces on a cylinder due to an oscillating wake, modeling the force as a frequency modulation process, is proposed. The non-linear equations of motion which result are then solved, assuming constant force coefficients, by linearization for use with a Gaussian random sea. The method of equivalent linearization is extended to include mean flow effects and a spatially distributed process. Some numerical experiments are then used to test the performance of the linearization. For a variety of environments, the linearization predicts the standard deviation of the simulation response to within 10% and the mean angle of inclination to within 30%. Results of the numerical experiments indicate that there is significant variation (order of magnitude changes) in both response and mean angle of inclination. Thus, significant changes are followed by the linearization. A laboratory experiment was carried out to test the linearized spar model in a realistic fluid environment. Only the low Keulegan Carpenter number regime was investigated. With some minimal manipulations, good agreement is obtained between the experiment and the linearized estimates. It appears that the drag coefficients for vortex induced in-line forces may be an order of magnitude larger than those reported in the literature, .5 instead of .06, and that the shedding of vortices due to steady flow may reduce the added mass coefficient significantly, as observed in oscillating flows with significant vortex shedding.