Response of a pendulum spar to 2dimensional random waves and a uniform current
Citable URI
http://hdl.handle.net/1912/1549DOI
10.1575/1912/1549Keyword
Ocean waves; Ocean currents; Wakes; Equations of motion; Fluid dynamicsAbstract
A linearized theory for the response of a circular pendulum
spar in 2dimensional 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 nonlinear
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 inline 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.
Description
Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution August, 1978
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