A Novel Complete Second-order Method For The Motion Response Of Floating Bodies In The Time-domain And An Investigation On The Nonlinear Near-trapping Phenomenon

With the advent of ocean exploration toward deep sea, the nonlinear characteristics of deep-sea platforms have been the research focus, and the studies on the nonlinear motion response and the nonlinear near-trapping phenomenon have been important topics in the field of ocean engineering. Under such research background, the nonlinear motion response of deep sea platforms is investigated by the indirect time-domain method. As the conventional Cummins method makes rough calculation of the second-order exciting forces applied on moving bodies, the present study focuses on the problem and a complete second-order method for the response of floating bodies in the time-domain is developed. This method can make accurate calculation of the second-order exciting forces by using the QTF components. Investigation on the near-trapping phenomenon is also carried out in the present study. Through the investigation of the nonlinear wave elevation around multi-column platforms, the nonlinear near-trapping phenomenon for these platforms is revealed.In deep sea, the environmental condition is severe. Due to the nonlinear effects from waves and the mooring system the structure no longer follows a harmonic oscillation pattern and a time-domain method should be used to predict the body response. When the Cummins method is used, only the motion equation needs to be solved in the time-domain, and the exciting forces in the time-domain can be calculated according to the Volterra series model. Compared with the other time-domain methods, the Cummins method is more applicable to the engineering practice. When the nonlinear interaction between waves and floating structures is investigated by the Cummins method, the second-order sum-or difference-frequency exciting forces are conventionally calculated based on QTF. QTF is defined as the second-order exciting forces applied on the structure under bi-chromatic incident waves of unit amplitudes. For a moving body, QTF is calculated based on the accurate simulation of the first-order body response. However, QTF is calculated in the preparation stage for the time-domain simulation and the actual first-order body response is unknown during the calculation of QTF. It suggests that QTF cannot be directly used in the time-domain simulation. In view of this, a perturbation expansion of QTF is carried out in this study based on the amplitude of the first-order harmonic body motion and the amplitude of the incident wave. As a result a decomposition of QTF is derived. From the decomposition, three kinds of QTF components can be obtained. The QTF components of the first kind represent the exciting forces applied on a fixed structure in bi-chromatic waves of unit amplitudes, the QTF components of the second kind correspond to a monochromatic incident wave and a body motion in a single model, and the QTF components of the third kind correspond to body motions in two independent modes. The BVPs correspond to the QTF components are studied. After the non-homogeneous boundary conditions on the free surface and body surface are derived, the second-order diffraction potential is determined by using a boundary-integral equation method. For the free surface integral that decays slowly to infinity in a highly oscillatory manner, an efficient and high accuracy computation can be obtained by dividing the free surface into different regions in which the integrals are treated differently. For the body surface integral, it has been found advantageous to use the Stokes theorem to deal with the second derivative terms involved in the body surface integral. Then the calculation is carried out for a structure moored by linear springs. Through comparing present results with frequency-domain results, the validation of the present method is examined. Moreover, the calculation is carried out for the JIP Spar moored by a non-linear mooring system. Through comparing present results with experimental results, the validation of the present method is further examined. As examples of the application of the present method to practical problems, the nonlinear motions of offshore platforms are also simulated.Deep sea platforms such as tension leg platforms (TLPs) are supported by vertical columns. As the columns are closely spaced, the interference effect between the columns is significant. At certain frequencies an important phenomenon known as near-trapping could occur inside the array. When this phenomenon occurs, only a small amount of scattered wave energy radiates outwards and a near standing wave with a rather large amplification of free surface oscillations can be observed within the local vicinity of the cylinders. Although this phenomenon has been studied by the numerical method and the theoretical method, it has rarely been investigated in the experiment. In the present study a series of experiments is carried out in Dalian University of Technology's three-dimensional wave basin to study the wave diffraction by a four-cylinder structure. The experiment is designed to measure the free surface elevation at multiple locations close to the cylinder surface. By an analysis of the measured data the amplitudes of the first-order and second-order harmonic wave elevation are obtained. To examine the validation of the diffraction theory in predicting the free surface elevation, comparison is carried out between the experimental results and the numerical results. Even for higher steepness, the second-order diffraction theory is shown to be effective to predict the free surface elevation around large scale structures. Moreover, the important phenomenon of the near-trapping is investigated in the experiment. For a specific incident wave frequency a near standing wave motion can be observed inside the array. Besides the experimental investigation, numerical investigation is also conducted for the first-order and second-order wave elevation in the vicinity of a TLP. The existing researches for predicting the air gap of the TLPs focus on the supporting columns while pays little attention to the horizontal pontoons. In the present study the effect of pontoons on the diffracted wave field in the vicinity of a TLP is investigated. The diffraction of regular waves by a square array of truncated cylinders and a whole TLP structure is studied in detail. To study the effect of the pontoons on the free surface elevation comparisons are carried out between the results of the two structures. Numerical results show that the interaction between waves and a TLP can induce the near-trapping phenomenon and leads to a significantly increased wave height around the TLP. The pontoons are shown to make no influence on the near-trapping frequency. When the near-trapping phenomenon occurs at second-order, the pontoons increase the largest response notably and an enhancement factor should be considered if we only examine the wave interaction with columns alone.