On The Coupling Terms In The Low-Frequency Viscous Reaction Forces Of Moored Tankers In Deep Water

Abstract

Abstract Due to the restricted water depth of experimental facilities one has to rely more on computational tools for the design of turret and spread moored tanker based FPSOs in deep water. These tools have to be as accurate as possible. The mechanics to compute dynamically mooring lines and risers are understood. By means of potential theory the first order tanker motions and wave drift forces with and without current can be adequately computed nowadays, see for instance Ref. 1. Besides the low-frequency (lf) wave drift forces also the lf viscous reaction forces (damping) exist in still water and current. The lf reaction forces/moment induced by the lf motions in the horizontal plane are mostly dominated by viscosity and hardly to compute. By means of model tests the viscous forces in the separate surge, sway and yaw modes of motion were measured in still water and in a current field, see for instance Ref. 2. The importance of the coupling terms due to the combined modes of motions, however, is not known. By means of a lf large stroke mechanical oscillator prescribing combined motions on the tanker hull the coupling terms were investigated in still water and in current. The results will be presented in the paper. Introduction In order to compute the lf motions of a moored tanker the equations of the lf motion have to be established. Most of the maneuvering models are based on the model as for instance presented by Abkowitz, Ref. 3. In this model the maneuverability is described by means of linear and nonlinear derivatives of the hydrodynamic forces and moments by perturbation models. Contrary to normal maneuvering applications (high speed, high rate of turn and relative small drift angles) specific requirements have to be fulfilled for a moored tanker e.g.:large drift angles (0-360 degrees)small values of drift velocities (combined low frequency tanker motions in still water or in a current field)small values of oscillating rate of turnrelatively large transverse motionsin steady state in a current field the hydrodynamic forces have to correspond with the steady current loads. These requirements do not satisfy the model of Abkowitz. The full equations of the lf motion as applied for a moored tanker in still water and in a current field should be established. A present formulation is presented. Starting in an ideal and irrotational fluid the equations of motion as given by Norrbin (Ref. 4), taking into account the Munk-moment (Ref. 5) can be established. In real fluid, however, viscosity is involved. The viscosity modifies the Munk-moment and introduces additional resistance forces (d'Alembert paradox). By means of model tests using a lf large stroke oscillator the viscous forces in the separate surge, sway and yaw modes of motion can be determined. A comprehensive description is given in Ref. 2. Moored tankers in general, however, perform fish tailing motions. A fish tailing motion consists of a combined motion in the horizontal plane.