Time-domain Simulation Of Second-order Hydrodynamic Force On Floating Bodies In Irregular Waves

With the continuous decline of inshore oil and gas resources in China, more and more oil and gas resources exploration activities have been moved to the deep sea. Under this circumstance, it has already become an international hot topic to develop new type of deep-water platforms in the field of the ocean engineering. It is very important to effectively simulate nonlinear wave body interaction in time domain. In order to meet the requirement of predicting the wave loads and movements on deep-water platforms precisely, the aim of this thesis is to develop a predictable method for time-domain simulation of second-order hydrodynamic force on deep-water platforms in irregular wave through investigating the characteristics of nonlinear and irregular wave body interaction.In the thesis a stable three-dimensional time-domain method, based on Rankine source, has been applied to simulate linear and nonlinear hydrodynamics in regular or irregular waves. A Multi-Transmitting Formula method (MTF) with an artificial wave speed is employed to satisfy the radiation condition to minimize the wave reflection on the Artificial Boundary (AB), and a stable Integration form of Free surface Boundary Condition (IFBC) is used to update velocity potential on the free surface. Major works done in this thesis are as follows:Firstly, the semi-sphere with heave motion and the cylinder with incident wave were simulated. The basic parameter sensitivity are studied by comparing the present results with frequency solution, including additional factor, modulation function, time step, water depth, artificial wave speed and the mesh on boundary etc. The stability and efficiency of MTF method also have been investigated by long time simulation without instability. Usually, it is not necessary to make the artificial wave speed equal to the physical wave speed so that the effective range of the artificial wave speed is obtained. Moreover, the floating bodies, for example LNG carrier and Semi-submersible platform, with arbitrary shape of AB have been simulated in time domain. It is indicated that MTF and IFBC can be used to simulate time-domain problems by long time simulation almost without reflecting waves.Secondly, the irregular wave radiation and diffraction problems have been simulated by Boundary Element Method (BEM) upon MTF and IFBC method. The semi-sphere with irregular excitation frequencies and the surface piercing cylinder with irregular incident waves have been investigated, which includes bichromatic wave diffraction and fully irregular wave diffraction based on wave spectrum. The irregular wave can be transmitted out of AB except for low sea state (h1/3=0.5m and h1/3=1.0m) in the MTF method, since the range of frequency at low sea state is greater than that at high sea state. Therefore, the MTF method only can transmit the waves which have common artificial wave speed out of AB so that the MTF can not transmit all the out-going waves out of AB effectively and it is necessary to use a new absorbing boundary condition (MTF coupled with damping zone, MTF+DZ) to simulate the full irregular wave diffraction problems. In this thesis, the efficiency of four kinds of MTF+DZ method has been investigated, and the best one of them is obtained therefrom. The smallest length of DZ is provided. At last, a truncated cylinder and semi-submersible diffraction have been simulated by MTF+DZ method and the results are transformed to frequency domain by Fast Fourier Transform (FFT), which are almost consistent with the results of Hydrostar.Thirdly, the numerical accuracy of the Source distribution method based on MTF and IFBC was investigated. The method of the thesis is applied to compute wave diffraction by surface-piercing circular cylinder. It is found that the value of the tangential velocity on the boundary is inaccurate upon comparing the results thereof with frequency solutions by Source distribution method, especially at the place where the normal vector is changed rapidly. In order to validate the above conclusion, three-dimensional uniform flow over sphere has been simulated. The conclusion is almost the same as that of wave diffraction problem. Afterwards, the Source distribution based on Galerkin technique has been employed to improve the accuracy of the tangential velocity. However, this method is not sensitive if the normal vector is changed rapidly.In fourth, the second-order wave radiation and diffraction problem have been investigated by the method of this thesis. The high-order derivatives of velocity potential are acquired by the auxiliary function, which includes second-order derivative in z direction and third-order derivative with time t and position z. The auxiliary function improves the numerical accuracy and stability without implementing finite difference method.Then, the efficiency of Artificial Boundary Conditions (ABC) and the treatment of differential terms on the free surface condition and high-order derivatives on the body surface, which has rendered that the results different from each other have been obtained by a plurality of second-order methods. Furthermore, with regard to the second-order diffraction problems, the analytical solution and its derivatives of first-order velocity potential have been used into second-order free surface condition in the thesis so that the numerical results agree well with the second-order frequency solution. It is found that the difference between the aforesaid method and analytical solution is caused by the accuracy of the Source distribution method. Accordingly, MTF and IFBC can be used to the long time simulation in time-domain second-order problems.Moreover, homogeneous and non-homogeneous second-order free surface condition and body surface condition are discussed in the thesis so as to acquire some useful conclusions. Concerning the radiation problem, the hydrodynamic force, due to second-order potential, is generated mainly by the non-homogeneous body surface condition. Although the contribution of non-homogeneous free surface condition is quite small, it has a significant influence on the overall second-order force. Concerning the diffraction problem, the result thereof is opposite to that of the radiation problem. The hydrodynamic force, due to second-order potential, is generated mainly by the non-homogeneous free surface condition. The contribution of non-homogeneous body condition gradually decreases while frequency is getting higher. However, it also greatly affects the overall amplitude of second-order force.Finally, the floating body with irregular heave motion is simulated in time domain upto second order, while the calculation of second-order irregular wave diffraction by a floating body in deep water is also included in the thesis. Long time simulations are done without instability, which indicates that the present method can be used to simulate second-order irregular wave body interaction in time domain.