A Simulation Model for a Single Point Moored Tanker
It is the intention of this thesis to formulate a simulation model, which can be used to compute the behaviour of a tanker moored to a single point. Exposed to current, wind and long crested irregular waves the motions of the tanker and the forces in the mooring sytem consist of both high (= wave) frequency and low frequency components. When computing the low frequency motions, difficulties arise in the description of the mean and second order wave drift forces and the low frequency hydrodynamic reactive forces. For survival and operational weather conditions the wave drift excitation and the hydrodynamic reactive forces are discussed in this thesis. For the survival condition the computer model is restricted to colinearly directed current, wind and long crested irregular waves. The water is assumed relatively deep. For most of the mooring systems this condition will determine the design. Experiments on model scale showed that the magnitude of the amplitudes of the low frequency surge motions will be influenced by the low frequency velocity dependkncy of the wave drift force excitation. The velocity dependency is caused by the Doppler effect on the vessel in a wave field. To account for this effect use is made of the velocity potential for small values of forward speed of the tanker. For small values of forward speed the first order motions were solved. By means of the direct integration method the low velocity dependent second order wave drift forces in regular waves were computed. For the simulation the velocity dependent wave drift force is split up into a current velocity dependent wave drift force and a wave drift damping coefficient. The complete matrix of the wave drift force is approximated employing the main diagonal only. In the low frequency range the wave drift damping and the wave radiated damping can be derived from potential theory. The wave radiated damping is negligibly small. Except for the damping forces of potential origin also damping forces of viscous nature are present. The viscous damping terms cannot be computed and have to be derived from physical experiments. By means of computations and verified by model tests the importance of the velocity dependency of the wave drift excitation has been confirmed. In operational conditions the combination of current, wind and irregular long crested waves can be arbitrary in terms of occurrence and directions. In order to formulate the simulation model for the low frequency motions of the tanker in the horizontal plane two problems must be solved. First, a set of equations of motion must be drawn up, which describe the large amplitude low frequency motions. Secondly, the components in the equations of motion, which adequately describe the low frequency hydrodynamic resistance forces, must be derived while the low frequency viscous resistance coefficients must be known. The flow pattern around the tanker, which performs low frequency oscillations, will be different in still water or in a current field. For both conditions semi-theoretical mathematical models were derived. The viscous resistance coefficients were experimentally determined for a 200 kTDW tanker in a water depth of 82.5 m. The derived results were compared with existing formulations of the viscous resistance. The equations of motion are evaluated by means of results of physical model tests for a 200 kTDW tanker moored by means of a bow hawser to a fixed mooring point. To determine the stability of this kind of mooring system the stability .criterium of Routh has been applied to the tanker exposed to wind and current. In order to demonstrate the validity of the derived formulations with respect to arbitrary weather direcions in operational conditions computer simulations were carried out. It is shown that the model tests confirm the results of the computations.