Computation Model on a Chain-Turret-Moored Tanker in Irregular Seas
Authors: Huijsmans R.H.M. , Wichers J.E.W. 
Published: October 2008

Abstract
To compute the low frequency mooring forces of, for instance, a turret moored storage/production tanker exposed to survival conditions the hydrodynamic excitation and reaction forces have to be known. The low frequency excitation is assumed to be caused by the velocity dependent wave drift forces. The hydrodynamic reaction forces consist of the added mass forces, the low frequency viscous forces and the wave drift damping on the tanker and the damping forces acting on the chain legs. Although in the past several investigations on chain damping have been carried out, see references [1],[2],[3],[4], [5],[6],[7], data on low frequency chain damping, however, is scarce. In order to make a proper account of the effect of the mooring reaction force on the low frequency motions of the vessel, interaction effects have been established between the mooring system and the vessel hydrodynamics. To evaluate these interaction effects model tests have been performed on a 200 kDWT tanker moored by means of a 6 chain leg turret. A mathematical model describing the interaction effects between the mooring system and the vessel hydrodynamics is presented. Based on an analytical description of the chain dynamics the complete low frequency vessel motions with correct high frequency mooring loading have been established.

Introduction
A moored tanker exposed to irregular head seas performs small amplitude wave frequency pitch, heave and surge motions and relatively large amplitude low frequency surge motions. The frequency of the slowly oscillating motions corresponds to the natural surge frequency of the system. While the wave frequency motions are caused by the first order wave forces, the slowly oscillating motions are caused by the second order wave drift forces. Since the total damping of the low frequency motions is relatively small, resonance motions take place. Because in an irregular sea low frequency excitation will occur, the magnitude of the transfer function will be determined by the value of the damping. In case no interference between the fist and second order motions of the tanker exists, the first order and the slow oscillating motions can be treated separately. In this case the equation of motion of the low frequency surge motion of a chain pattern-turret moored tanker exposed to irregular seas and current may be determined by the following quantities:current velocity dependent, wave drift excitation on the tanker,the mean current force on the tanker,the virtual mass of the tanker,the current velocity dependent wave drift damping of the tanker,the low frequency viscous chain damping and the friction between mooring chains and the seabed. Except for the low frequency chain damping the mentioned quantities are comprehensively discussed by Withers in [8] and [9]. Withers et al. [7] discussed the effect of current on the mooring damping and its effects on the low frequency motions of the vessel. In order to link the high frequency hydrodynamics with the low frequency motions one usually decouples the equations of motion into equations for high frequency motions and low frequency motions.