Study On The Nonlinear Coupled Motion Of A Spar Under Stochastic Wave And Vortex

The Spar platform has been widely used for deep-water oil and gas exploitation in US Gulf of Mexico.This kind of platform for its flexibility,economy and excellent performance is also regarded by many oil companies as the focus and direction of deep-water oil and gas exploitation in the future.The nonlinear coupled motion response of the Spar’s heave,roll and pitch has been a focus for researchers in the recent years.In this paper,the Spar’s nonlinear coupled heave-roll-pitch hydrostatic restoring stiffness is derived according to the geometric relationship of the the Spar platform’s motion in the water,and then the nonlinear coupled motion equations are established.The platform’s first-order wave load linear transfer functions(LTFs)and second-order wave load quadratic transfer functions(QTFs)are calculated via a diffraction/radiation numerical code based on potential theory.The stochastic wave load time series are generated according to wave load transfer functions and spectrum.The Spar’s heave-roll-pitch coupling motion responses are studied considering uni-directional stochastic wave loads,multi-directional stochastic wave loads and wave loads & vortex induced loads,respectively.The main conclusions are as follows:(1)When considering uni-directional stochastic wave loads,the coupled heave-pitch coupling motion responses of a spar platform in different sea conditions are primarily dominated by two wave parameters,i.e.significant wave height Hs and peak period Tp.Of the two parameters,the latter one has a great influence on the platform’s motion responses.The second order mean wave load mainly affects the average response of heave,while it has no obvious effect on the average response of pitch.The second order low frequency wave load mainly affects the platform’s pitch amplitude,while it has little effect on the platform’s heave.The transient wave elevation has a significant influence on the platform’s heave,while its effect on pitch is small.It is essential to consider the effect of transient wave elevation when performing a heave motion analysis for a Spar platform.(2)When considering multi-directional stochastic wave loads,there is a significant response in the Spar’s roll degree,which is different from the case when considering uni-directional stochastic waves.In some sea conditions,the platform’s roll amplitude even surpassed the pitch amplitude due to the nonlinear coupling effect.The platform’s roll will decrease as the spreading parameter s increases.The wave energy’s directional distribution has little effect on the wave elevation,stochastic heave force and heave response amplitude.(3)When considering the effect of stochastic wave load and vortex-induced load at the same time,the platform’s roll motion response caused by vortex-induced loads is as important as the roll caused by stochastic wave loads.Therefore,vortex-induced roll should not be ignored when dealing with a vortex induced motion problem.