Identification of non-linear effects in predicting the motion response of an offshore platform

This paper presents the results of an extensive parametric study to investigate various non-linear aspects of the prediction of the large-amplitude motion responses of a semi-submersible. The main objectives of the parametric studies were to investigate the following aspects, which can non-linearly influence the motion responses and which cannot be studied by linear frequency-domain prediction techniques. These aspects are the effects on the motion responses of flooding time and mass; non-linear wave-exciting and rigid-body induced motion (i.e. added mass and damping) forces; non-linear restoring forces; steady wind and current; variation of GM (transverse metacentric height); and the initial position of the semi-submersible. The investigations were carried out for a particular semi-submersible geometry using a numerical simulation technique in the time domain. The simulations were performed for the model during intact, progressive and post-flooding conditions under the combined loading of regular waves, steady wind and current for two different heading angles. This paper is thus intended to provide some insight into the physical effects of the non-linear terms in the equations of motion which are associated with the wave-excitation forces, rigid-body induced motion forces and restoring forces. Since the resulting motion responses could have a steady component as well as the oscillatory one, the force and motion phenomena were also highlighted through the computation of these components.     

浅水中浮体在波浪作用下运动的三维时域计算模型

港口中系泊船在波浪作用下运动问题的本质是浅水波浪与浮体的相互作用。与深水情况不同,浅水问题应当考虑水底、水域边界的影响及浅水波浪自身的特性,单一模型很难实现该模拟过程。为此,建立了Boussinesq方程计算入射波和Laplace方程计算散射波的全时域组合计算模型。有限元法求解的Boussinesq方程能使入射波充分考虑到水底、水域边界的影响和浅水波浪的特性;散射波被线性化,采用边界元法求解,并以浮体运动时的物面条件为入射波和散射波求解的匹配条件。该方法为完全的时域方法,计算网格不随时间变动,计算过程较为方便。通过与实验及其他数值方法的结果进行比较,验证了本模型对非线性波面、浮体的运动都有比较理想的计算结果,显示了本模型对非线性问题具有较好的计算能力。     

Numerical study on the interaction among a nonlinear wave,composite breakwater and sandy seabed

Most previous investigations related to composite breakwaters have focused on the wave forces acting on the structure itself from a hydrodynamic aspect. The foundational aspects of a composite breakwater under wave-induced cyclic loading are also important in studying the stability of a composite breakwater. In this study, numerical simulations were performed to investigate the wave-induced pore water pressure and flow changes inside the rubble mound of the composite breakwater and seabed foundation. The validity and applicability of the numerical model were demonstrated by comparing numerical results with existing experimental data. Moreover, the present model clearly has shown that the instantaneous directions of pore water flow motion inside the seabed induced by surface waves are in good agreement with the general wave-induced pore water flow inside the seabed. The model is further used to discuss the stability of a composite breakwater, i.e., the interaction among nonlinear waves, composite breakwater and seabed. Numerical results suggest that the stability of a composite breakwater is affected by not only downward shear flow generating on the seaward slope face of the rubble mound but, also, a high and dense pore water pressure gradient inside the rubble mound and seabed foundation.     

Parametric study of the wave-induced residual liquefaction around an embedded pipeline

Wave-induced liquefaction in a porous seabed around submarine pipeline may cause catastrophic consequences such as large horizontal displacements of pipelines on the seabed, sinking or floatation of buried pipelines. Most previous studies in relation to the wave and seabed interactions with embedded pipeline dealt with the wave-induced instaneous seabed response and possible resulting momentary liquefaction (where the soil is liquefied instantaneously during the passage of a wave trough), using theory of poro-elasticity. Studies for the interactions between a buried pipeline and a soil undergoing build-up of pore pressure and residual liquefaction have been comparatively rare. In this paper, this complicated process was investigated by using a new developed integrated numerical model with RANS (Reynolds averaged Navier–Stokes) equations used for governing the incompressible flow in the wave field and Biot consolidation equations used for linking the solid–pore fluid interactions in a porous seabed with embedded pipeline. Regarding the wave-induced residual soil response, a two-dimensional poro-elastoplastic solution with the new definition of the source term was developed, where the pre-consolidation analysis of seabed foundation under gravitational forces including the body forces of a pipeline was incorporated. The proposed numerical model was verified with laboratory experiment to demonstrate its accuracy and effectiveness. The numerical results indicate that residual liquefaction is more likely to occur in the vicinity of the pipeline compared to that in the far-field. The inclusion of body forces of a pipeline in the pre-consolidation analysis of seabed foundation significantly affects the potential for residual liquefaction in the vicinity of the pipeline, especially for a shallow-embedded case. Parametric studies reveal that the gradients of maximum liquefaction depth with various wave and soil characteristics become steeper as pipeline burial depth decreases.     

Sensitivity Analysis of Air Gap Motion with Respect to Wind Load and Mooring System for Semi-Submersible Platform Design

A design of semi-submersible platform is mainly based on the extreme response analysis due to the forces experienced by the components during lifetime. The external loads can induce the extreme air gap response and potential deck impact to the semi-submersible platform. It is important to predict air gap response of platforms accurately in order to check the strength of local structures which withstand the wave slamming due to negative air gap. The wind load cannot be simulated easily by model test in towing tank whereas it can be simulated accurately in wind tunnel test. Furthermore, full scale simulation of the mooring system in model test is still a tuff work especially the stiffness of the mooring system. Owing to the above mentioned problem, the model test results are not accurate enough for air gap evaluation. The aim of this paper is to present sensitivity analysis results of air gap motion with respect to the mooring system and wind load for the design of semi-submersible platform. Though the model test results are not suitable for the direct evaluation of air gap, they can be used as a good basis for tuning the radiation damping and viscous drag in numerical simulation. In the presented design example, a numerical model is tuned and validated by ANSYS AQWA based on the model test results with a simple 4 line symmetrical horizontal soft mooring system. According to the tuned numerical model, sensitivity analysis studies of air gap motion with respect to the mooring system and wind load are performed in time domain. Three mooring systems and five simulation cases about the presented platform are simulated based on the results of wind tunnel tests and sea-keeping tests. The sensitivity analysis results are valuable for the floating platform design.     

Mechanistic Drifting Forecast Model for A Small Semi-Submersible Drifter Under Tide-Wind-Wave Conditions

Understanding the drifting motion of a small semi-submersible drifter is of vital importance regarding monitoring surface currents and the floating pollutants in coastal regions. This work addresses this issue by establishing a mechanistic drifting forecast model based on kinetic analysis. Taking tide-wind-wave into consideration, the forecast model is validated against in situ drifting experiment in the Radial Sand Ridges. Model results show good performance with respect to the measured drifting features, characterized by migrating back and forth twice a day with daily downwind displacements. Trajectory models are used to evaluate the influence of the individual hydrodynamic forcing. The tidal current is the fundamental dynamic condition in the Radial Sand Ridges and has the greatest impact on the drifting distance. However, it loses its leading position in the field of the daily displacement of the used drifter. The simulations reveal that different hydrodynamic forces dominate the daily displacement of the used drifter at different wind scales. The wave-induced mass transport has the greatest influence on the daily displacement at Beaufort wind scale 5-6; while wind drag contributes mostly at wind scale 2-4.     

A novel decomposition of the quadratic transfer function (QTF) for the time-domain simulation of non-linear wave forces on floating bodies

In the present study, a novel method is proposed for the separation of the second-order sum- and difference-frequency wave forces—that is, quadratic transfer functions (QTFs)—on a floating body into three components due to wave–wave, wave–motion, and motion–motion action. By applying the new QTF components, the second-order wave forces on a floating body can be strictly computed in the time domain. In this work, the boundary value problems (BVPs) corresponding to the three kinds of QTF components were derived, and non-homogeneous boundary conditions on the free surface and the body surface were obtained. The second-order diffraction potentials were determined using the boundary integral equation method. In the solution procedure, the highly oscillatory and slowly converging integral on the free surface was evaluated in an accurate and effective manner. Furthermore, the application of the QTF components in the time domain was demonstrated. The second-order exciting forces in the time domain were divided into three parts. Each part of these forces was computed via a two-term Volterra series model based on the incident waves, the first-order motion response, and the QTF components. This method was applied to several numerical examples. The results demonstrated that this decomposition yields satisfactory results.     

Mechanistic Drifting Forecast Model for A Small Semi-Submersible Drifter Under Tide–Wind–Wave Conditions

Understanding the drifting motion of a small semi-submersible drifter is of vital importance regarding monitoring surface currents and the floating pollutants in coastal regions. This work addresses this issue by establishing a mechanistic drifting forecast model based on kinetic analysis. Taking tide–wind–wave into consideration, the forecast model is validated against in situ drifting experiment in the Radial Sand Ridges. Model results show good performance with respect to the measured drifting features, characterized by migrating back and forth twice a day with daily downwind displacements. Trajectory models are used to evaluate the influence of the individual hydrodynamic forcing. The tidal current is the fundamental dynamic condition in the Radial Sand Ridges and has the greatest impact on the drifting distance. However, it loses its leading position in the field of the daily displacement of the used drifter. The simulations reveal that different hydrodynamic forces dominate the daily displacement of the used drifter at different wind scales. The wave-induced mass transport has the greatest influence on the daily displacement at Beaufort wind scale 5–6; while wind drag contributes mostly at wind scale 2–4.     

Fluid Resonance Between Twin Floating Barges with Roll Motion Under Wave Action

China Ocean Engineering - The wave-induced fluid resonance between twin side-by-side rectangular barges coupled with the roll motion of the twin barges is investigated by both numerical simulation...     

The effects of variable permeability on the wave-induced seabed response

The topic of wave-seabed interaction is important for civil engineers with regard to stability analysis of foundations for offshore structures. Most previous investigations of such problems have simply assumed a seabed with uniform permeability, even if the evidence of variable permeability has been reported in the literature. This paper presents a finite-element model for investigating the wave-induced seabed response in a porous seabed, with variable permeability as a function of burial depth. The present finite formulation is established by using a combination of semi-analytical techniques and the Galerkin method. Based on the present numerical model, together with the Mohr-Coulomb failure criterion, the wave-induced seabed instability is estimated. The numerical results indicate that variable permeability affects the wave-induced seabed instability significantly, especially for gravelled seabeds.     

内孤立波中半潜平台动力响应特性

基于内孤立波mKdV理论,采用时域有限位移运动方程,结合改进的Morison公式,研究了两层流体中内孤立波与带分段式悬链系泊约束半潜平台的相互作用问题。针对东沙群岛南部海域附近某实测内孤立波特征参数,计算分析了在该内孤立波作用下SEDCO-700型半潜平台的内孤立波载荷、运动响应及其系泊张力的变化特性。研究表明,内孤立波不仅会对半潜平台产生突发性冲击载荷作用,使其产生大幅度水平漂移运动,并导致其系泊张力显著增大,因此在半潜平台等深海平台的设计与应用中,内孤立波的影响是不可忽视的。     

Establishment,validation and discussions of a three dimensional wave-induced current model

A three-dimensional numerical model was established to simulate the wave-induced currents. The depth-varying residual momentum, surface roller, wave horizontal and vertical turbulent mixing effects were incorporated as major driving forces. A surface roller evolution model considering the energy transfer, roller density and bottom slope dissipation was developed. The expression of the wave-induced horizontal turbulent mixing coefficient proposed by Larson and Kraus (1991) was extended to three-dimensional form. Plenty of experimental cases were used to validate the established model covering the wave setup, undertow, longshore currents and rip currents. Validation results showed the model could reasonably describe the main characteristics of different wave-induced current phenomena. The incorporation of surface roller for breaking waves should not be neglected in the modeling of surfzone hydrodynamics. The wave-induced turbulent mixing affects the structures of wave-induced current either in horizontal or in vertical directions. Sensitivity analysis of the major calibration parameters in the established model was made and their ranges were evaluated.     

Irregular wave-induced seepage action on cylinders resting on rubble mound foundation

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新型干树半潜式海洋平台垂荡运动性能研究

在深海油气田开发中,干式采油树比湿式采油树具有更多优势。为减小半潜平台的垂荡运动,使其能够采用干式采油树,对一种深吃水且具有大面积下浮箱的新型半潜平台的运动性能进行了探究。基于势流理论,采用频域和时域相结合的分析方法,计算了平台在多种海况下的运动响应,为新型平台的运动分析和设计提供指导。同时,开展了水池模型试验,将计算结果与试验结果相比较,验证了数值模拟结果的准确性。为进一步探究新型平台的运动性能,研究了下浮箱放置深度对平台运动性能的影响,并进行相应的模型试验。研究表明:下浮箱的存在可大幅改善新型干树半潜平台的垂荡运动性能。综合考虑平台运动性能和工程实际应用条件,确定了最合适的下浮箱放置深度值。     

PREDICTION OF MOTION OF SEMI-SUBMERSIBLE DRILLING PLATFORM IN MAVES

Starting from potential theory, this paper presents a new procedure for computing the hydrodynamic forces and six-degrees-of-freedom motion for a semi-submersible platform at an arbitrary heading in waves by using strip theory and linearized viscous damping hypothesis, taking the effects of the free surface and the interaction between main hulls into account. The differential equations of motion for the floating platform are formulated in a new way and the associated computer programs are developed. Comparisons between the theoretical computing results and the full-scale and model-scale experiments show that the present method gives more accurate results than those by previous methods.     

Wave force prediction using an autoregressive model

An autoregressive wave force model is developed which is capable of accounting for localized flow history effects. It was developed in conjunction with the analysis of a series of experiments performed to study the wave-induced forces acting on a free-to-surge vertical cylinder in random waves. The wave force model incorporates a relative motion form of the Morison equation. The formulation presented in this study is quite general, but the filter coefficients in the model must be uniquely determined for each data set. The optimal length of the filter and its sensitivity are illustrated using data from small-scale wave tank tests. A high frequency wave force component observed in the experimental data is reproduced using this model. Lastly, the autoregressive wave force model is used to predict the response of a tension-leg platform to a wave train. A comparison of the results obtained both with and without the filter model are presented.     

Experimental and Theoretical Investigation of Wave Forces on A Partially-Perforated Caisson Breakwater with A Rock-Filled Core

1.IntroductionVertical breakwaters are widely used for harbor and coastline protection in coastal engineering.Recently,perforated breakwaters have been often used in practice as they can effectively reduce thewaveforces actingon,the wave reflectionfromand…     

垂荡板对半潜式风机基础拖航过程中水动力性能及运动响应的影响分析

垂荡板对半潜式风机基础水动力性能有极大的影响,从而影响基础拖航安装过程的安全。为了研究垂荡板对半潜式基础拖航过程中运动响应的影响,建立了拖缆—WindFloat浮式风机半潜式基础拖航系统模型。首先,基于三维势流理论,采用AQWA开展了拖航系统的频域水动力分析,分析了垂荡板的尺寸及形状对基础水动力性能的影响规律;进一步采用时域方法对拖航系统的运动响应进行分析,探究了垂荡板的尺寸及形状在不同浪向下对基础运动响应的影响规律。结果表明：垂荡板能有效抑制基础的垂荡RAO,但垂荡板形状对基础的水动力性能无明显影响;具有圆形垂荡板的半潜式基础在拖航过程中的运动性能略优于六边形垂荡板,在原设计基础上继续增大垂荡板尺寸对基础运动响应的抑制效果呈现先增大后减小的趋势,说明半潜式风机基础存在一个最优的垂荡板尺寸。     

Application of smoothed particle hydrodynamics for modeling the wave-moored floating breakwater interaction

The application of a Smoothed Particle Hydrodynamics (SPH) model to simulate the nonlinear interaction between waves and a moored floating breakwater is presented. The main aim is to predict and validate the response of the moored floating structure under the action of periodic waves. The Euler equations together with an artificial viscosity are used as the governing equations to describe the flow field. The motion of the moored floating body is described using the Newton’s second law of motion. The interactions between the waves and structures are modeled by setting a series of SPH particles on the boundary of the structure. The hydrodynamic forces acting on the floating body are evaluated by summing up the interacting forces on the boundary particles from the neighboring fluid particles. The water surface elevations, the movements of the floating body and the moored forces are all calculated and compared with the available experimental data. Good agreements are obtained for the dynamic response and hydrodynamic performance of the floating body. The numerical results of different immersion depths of the floating body are compared with that of the corresponding fixed body. The effects of the relative length and the density of the structure on the performance of the floating body are analyzed.     

Mean and low frequency wave drifting forces on floating structures

A recently developed method, based on three-dimensional potential theory, to compute the mean wave drifting forces on a free floating structure in regular waves, is extended to include low frequency oscillatory components which arise when the structure is floating in regular wave groups consisting of two regular waves with small difference frequency. This completes the information necessary for the determination of the wave drifting forces under arbitrary irregular wave conditions.In regular wave groups the drifting forces not only depend on the first order velocity potential and the first body motions, but also on the wave exciting forces due to the low frequency part of the second order potential. For the general three-dimensional case the latter contribution can only be determined numerically and at the expense of long computation times. Since this contribution is generally not large compared to components which may be determined using linear potential theory it is included using a simple approximation. Results of the method of approximation are compared with some two-dimensional cases for which exact solutions are known.Results of computations of the total mean and low frequency surge forces on a rectangular barge and a column stabilized semi-submersible platform are presented. For both structures, the computed mean surge drifting forces in regular head waves are compared with results of model tests.The computed components of the total mean drifting forces are presented. It appears that for both the barge and the semi-submersible the same components are of importance.For the semi-submersible, the computed low frequency second order surge forces in head waves are compared with results obtained from a test in irregular head waves using cross-bispectral analysis methods.