A Twice Expansion Analysis Method For Large Drift Motion Of Platforms In Deep Sea

Floating platforms(Spar,TLP,FPSO)are always subjected to the combined effects of random waves,wind and current loads when they work in the sea.The interaction between wave conponents of each two frequencies produces sum-frequency and difference-frequency i.e.,the higher order wave components,especially in irregular wave.The difference-frequency components are always close to the nature frequency and cause platforms large low frequency motion,which will reduce and even terminate the drilling.The vertical vibration may be caused by the sum-frequency conponents and high frequency motion leads to the fatigue problems of the mooring and riser structures.For this reason,we want to simulate the motion response of the floating platform as accurately as possible.Based on the above background,a twice expansion wave-body interaction numerical model in fully time domain is established based on the potential flow theory in this paper.By taking the 2D/3D Laplace equation as the basic governing equation,a 2D/3D twice expansion mathematical model about second-order time-domain wave-body interaction is proposed for computing wave interaction with a body experiencing large amplitude drift motion The body displacement is divided into two components,a low frequency and a high frequency oscillations.The low frequency oscillation is computed with time matching in the computation,and is called as the low frequency mean position.Then body boundary and free surface conditions are expanded at the low frequency mean and still free surface by Taylor expansion.and body and free surface meshes move with low frequency position constantly.At this time,the first and the second order boundary conditions are also established here by a perturbation expansion method which would guarantee that the expansion factors are always small.The velocity potential is separated into the incident,the scattering and the steady disturbance potentials.The scattering and the steady disturbance potentials are confuted by solving integral equations respectively.Subsequently,the formulations of wave forces are developed in detail and the motion response equations are established.The low frequency mean position,which becomes the mean position of Taylor expansion and perturbation expansion,is obtained by the expansion of motion response using wavelet transform technique.Then the perturbation expansion and Taylor series expansion are carried out again.This cycle repeats itself until the calculation time meets the requirements,which reinforce the solution of floaters large amplitude drift motion in time domain.In order to validate the twice expansion wave-body interaction numerical model,the simulation method of mean position is varified firstly.Con^ared with other simulation methods,it is commended to use the filter method based on wavelet transform to solve the mean position.It is can be seen that as long as the appropriate wavelet scale is chosen,even with different wavelet basis functions,the mean position of the time series can be found.Subsequently,the motion response of the 2D floater large slow drift motion,wave force of forward moving uniform cylinder and motion response of 3D floating box are carried out respectively.Their objects are the validations of twice expansion method.By means of the comparisons of the analytical results,fully nonlinear results and experimental data,it is demonstrated that this model is more correct in the calculation of large drift motion than the perturbation expansion method.The wave forces and motion responses of floating structures with large amplitude motion are calculated by applying twice expansion method,the results of twice expansion are compared with those from the original direct expansion method about the overall mean position,which proves the correctness of the twice expansion method.The first evaluation is about the large amplitude forced oscillation of a truncated cylinder in monochromatic waves.The comparisons show that the twice expansion method can consider the changes in the phase,amplitude and the encounter frequency of wave loads due to body drift motion at low frequency.Then the calculation is about the couple analysis of bichromatic waves and truncated cylinder.The first order and total motion responses are compared between twice expansion method and direct expansion method.We study the effects of wave amplitude difference and frequency on the motion response and find the results are quite different,then the corresponding explanations are described.All the results prove the correctness of the twice expansion method.The last part of this paper.introduce the application of the twice expansion method in the actual ocean platform.The couple analysis of bichromatic waves and Spar platform,a semisubmersible platform in wind and irregular waves are studied.The computational results include the wave force,the platform motion,the mooring tension and wave surface 3D contour map.The natural frequency of the platform will move to lower frequency due to the influence of wave drift damping by means of studying the couple analysis of bichromatic waves and Spar platform,which can not reflect in direct expansion method.Subsequently,it is in accurate to use the direct expansion method to calculate the large amplitude slow drift motion.In the end,this paper studies the differences between twice expansion method and direct expansion method in small amplitude motion and large amplitude motion by means of the research of wind and irregular waves action on HYSY-981 semisubmersible.It is proved that the results obtained by twice expansion method is more reliable in the situation of large amplitude motion,and the arrangement of semisubmersible in actual wave is also proposed.