Resonant Heave Dumping of Tension Leg Platforms

Abstract

SUMMARY The present paper describes an experimental investigation of the resonant heave ("springing") damping of a tension leg platform column with sharp lower edge. The results show that even the damping due to vortex shedding at the sharp edge (pressure drag) Is linear In velocity. Even at the smallest amplitudes the total hydrodynamic damping is several times larger than can be explained by skin friction. The paper introduces a theory for calculating the hydrodynamic part of the resonant heave damping. The theory is based on simple wake and momentum considerations. Comparison with the experiments shows that the theory predicts correctly the fact that the pressure drag damping is linear. It also predicts fairly accurately the quantitative value of the damping. 1. INTRODUCTION Tension leg platforms are normally designed to have their heave roll and pitch resonant frequencies well above the frequencies of the wave spectrum. This is in order to prevent first order wave forces from Inducing excessive resonant motions in these directions, which could lead to serious fatigue stresses in the tethers. However. due to non-linear wave forces there will be some excitation forces occurring at the sum-frequencies of the components in the wave spectrum. Thus there is still a possibility of significant fatigue stresses in the tethers due to resonant heave, pitch and roll. The phenomenon is often referred to as "springing" of the platform. Present-day theories for second order excitation forces have limitations regarding accuracy. Even more serious is the lack of theory for prediction of the hydrodynamic damping of the very small. high-frequency motions in question. This lack of theory also makes the scaling of model tests uncertain. The objective of the present paper Is to provide experimental data on the resonant heave damping of TLP columns. Furthermore, it suggests and Investigates the applicability of a calculation procedure for theoretical prediction of the damping. The procedure. would hopefully also assist in providing a rational basis for the scaling of results from model tests with tension leg platforms. The main problem is to evaluate the drag damping due to the shedding of vortices along the lower edge. The basic idea of the present paper IS to apply wake and momentum considerations in such a way that the drag coefficient in stationary flow can be used. 2. THEORY General Let us consider a single cylindrical column with vertical axis, having diameter D and draught H. The bottom of the cylinder is assumed to be horizontal, the lower edge being a sharp 90 degrees corner. Fig. 1 shows the geometry. The cylinder is assumed to oscillate harmonically in vertical direction. The diameter. draught and motion amplitudes are assumed to be such that there is negligible damping due to wave generation. Thus there are only two contributions to the hydrodynamic damping left:Skin friction dampingPressure drag on the bottom of the cylinder due to the flow (vortex shedding) at the sharp edge