A three-dimensional technique for predicting first-and second-order hydrodynamic forces on a marine vehicle advancing in waves

This thesis presents theoretical formulations and numerical computations for predicting first- and second-order hydrodynamic forces on a marine vehicle advancing in waves. The theoretical formulation starts with the derivation of the governing equations for the boundary-value problem of potential flow and its consequence leads to linearised radiation and diffraction problems using the peturbation expansion technique. Solutions of these two problems are obtained by solving the three-dimensional Green function integral equations over the mean wetted body surface. The forward speed free surface Green function representing a translating pulsating source potential for infinite water depth and finite water depth is derived using double Fourier transformation technique. This source potential reduces to an oscillating source at zero speed or to a Kelvin source at zero frequency. In order to solve the three-dimensional Green function integral equations efficiently, symmetry properties of the Green function and the body surface are exploited in the numerical implementation. Using a fully submerged ellipsoid and a half-submerged ellipsoid as examples, the free surface and forward speed effects on hydrodynamic coefficients are investigated. Their cross coupled hydrodynamic coefficients calculated by the present theory satisfy with Timman-Newman relationships. Numerical results for the first-order hydrodynamic coefficients, the wave excitation loads and the resulting motion responses of surface ships are presented. For zero speed case excellent correlations between the calculated and experimental results are found. For the forward speed case, the three-dimensional translating pulsating source modelling and three-dimensional oscillating source modelling with simple speed corrections on the linearised body boundary condition for pitch and yaw motions are used for a realistic ship. When the calculated results are compared with available experimental data, the three-dimensional translating pulsating source, modelling gives better correlations than the three-dimensional oscillating source modelling. Based on the first-order solutions, the mean second-order forces and moments are obtained by direct integrating second-order pressures over the mean wetted body surface. Using zero speed horizontal drifting forces and mean yaw moment as examples, the predictions of the mean second-order forces and moments are compared with available experimental results and found good agreement. For forward speed case the numerical computations for the added resistances of surface ships in head waves are performed by the three-dimensional translating pulsating source modelling and three-dimensional oscillating source modelling. The performance of the former is much better than the latter in comparison with available experimental results. It is found that the successful prediction of the peak of the added resistance is critically dependent upon the motion response results, especially in pitch. Effects of ship heading, forward speed, water depth on the first-order and second-order hydrodynamic forces are investigated