The Contribution of Hydrodynamic Damping Induced by Mooring Chains on Low-Frequency Vessel Motions
Authors: Wichers J.E.W. , Huijsmans R.H.M. 
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 [lJ, [2J, [3J, [4J, [5J and [6], data on low frequency chain damping, however, are scarce. In this paper oscillation tests and computations on chain legs in still water and in current were carried out. The water depth amounted to 82.5 and 247.5 m. The first part of the paper concerns the determination of the chain damping due to the oscillating motions of the low frequency surge motion only. In this case the relative importance of the contribution of the chain damping to the total low frequency damping has been investigated. Therefore low frequency motion simulations have been carried out on a 200 kDWT tanker moored by means of a turret with 6 chain legs in 82.5 m water depth, while exposed to co-linearly directed irregular waves and current. In the second part the effect of the combined low frequency surge and wave frequency heave motions on the chain damping has been investigated. Due to combined motions the chain damping may increase considerably. Finally the simulation of the simultaneous occurrence of the low and high frequency motions is discussed.

INTRODUCTION
A moored tanker exposed to irregular head waves 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 correspond 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 first 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 waves 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 damping coefficient 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.