Dynamic behaviour of square and triangular offshore tension leg platforms under regular wave loads

Among compliant platforms, the tension leg platform (TLP) is a hybrid structure. With respect to the horizontal degrees of freedom, it is compliant and behaves like to a floating structure, whereas with respect to the vertical degrees of freedom, it is stiff and resembles a fixed structure and is not allowed to float freely. The greatest potential for reducing costs of a TLP in the short term is to go through previously applied design approaches, to simplify the design and reduce the conservatism that so far has been incorporated in the TLP design to accommodate for the unproven nature of this type of platform. Dynamic analysis of a triangular model TLP to regular waves is presented, considering the coupling between surge, sway, heave, roll, pitch and yaw degrees of freedom. The analysis considers various nonlinearities produced due to change in the tether tension and nonlinear hydrodynamic drag force. The wave forces on the elements of the pontoon structure are calculated using Airy's wave theory and Morison's equation, ignoring the diffraction effects. The nonlinear equation of motion is solved in the time domain using Newmark's beta integration scheme. Numerical studies are conducted to compare the coupled response of a triangular TLP with that of a square TLP and the effects of different parameters that influence the response are then investigated.     

畸形波作用下张力腿浮式风力机动力响应特性

针对张力腿系泊浮式风力机的基础运动,忽略柔性构件的影响,建立气动—水动—系泊非线性耦合运动方程。在运动控制方程中包含张力腿系泊系统的非线性回复刚度,桨距角控制以及浮式基础运动对空气动力载荷的影响。在波浪载荷的计算中考虑二阶波浪载荷的作用。采用随机频率相位角调制法生成畸形波波面时历,计算在畸形波作用下张力腿型浮式风力机的动力响应特性。数值模拟结果表明,在畸形波作用下,浮式基础的运动及空气动力性能均受到了显著的影响。其中浮式基础的纵荡和纵摇运动分别受二阶差频与和频波浪力的影响,而垂荡运动的增加则主要是受下沉运动的影响。在畸形波经过的时刻,风力机的功率系数迅速下降,水平方向的风载荷波动先减小,随后其数值急剧下降,而垂直方向的风载荷波动增大。     

Adaptive second-order Volterra filtering and its application tosecond-order drift phenomena

This paper presents an adaptive second-order Volterra filter and its application to model-test data of a prototype tension leg platform (TLP). The least-squares approach of a second-order Volterra model and its adaptive filtering algorithm based on recursive least-squares are introduced. The second-order Volterra filter is applied to identify the linear and quadratically nonlinear relationship between irregular sea wave excitation and the surge response of a tension leg platform. Next, a deconvolution technique, based on the impulse invariance standard Z-transform, is utilized to recover the linear and quadratic forces exerted on the TLP     

Influence of wave approach angle on TLP's response

The current study focuses on the response analysis of triangular tension leg platform (TLP) for different wave approach angles varying from 0° through 90° and its influence on the coupled dynamic response of triangular TLPs. Hydrodynamic loading is modeled using Stokes fifth-order nonlinear wave theory along with various other nonlinearities arising caused by change in tether tension and change in buoyancy caused by set down effect. Low frequency surge oscillations and high frequency tension oscillations of tethers are ignored in the analysis. Results show that wave approach angle influences the coupled dynamic response of triangular TLP in all degrees of freedom except heave. Response in roll and sway degrees of freedom are activated which otherwise are not present in TLP's response to unidirectional waves. Pitch and roll responses are highly stochastic in nature indicating high degree of randomness. Variation in surge, sway and heave responses are nonlinear and are not proportional to change in wave height for the same period.     

张力腿平台内孤立波作用特性数值模拟

依据三类内孤立波理论KdV、eK dV和MCC的适用性条件,采用Navier-Stokes方程为流场控制方程,以内孤立波诱导上下层深度平均水平速度作为入口边界条件,建立了两层流体中内孤立波对张力腿平台强非线性作用的数值模拟方法。结果表明,数值模拟所得内孤立波波形及其振幅与相应理论和实验结果一致,并且在内孤立波作用下张力腿平台水平力、垂向力及力矩数值模拟结果与实验结果吻合。研究同时表明,张力腿平台内孤立波载荷由波浪压差力、粘性压差力和摩擦力构成,其中摩擦力很小,可以忽略;水平力的主要成分为波浪压差力和粘性压差力,粘性压差力与波浪压差力相比较小却不可忽略,流体粘性的影响较小;垂向力中粘性压差力很小,流体粘性影响可以忽略。     

在平台振荡条件下TLP张力腿的涡激非线性响应

给出了预测张力腿涡激横向振动的时域分析,考虑了波浪、海流、张力腿平台的横漂与垂荡诸因素.张力腿平台的垂荡引起张力周期性变化,对张力腿的涡激横向振动起参数激励的作用,使其动力响应更为复杂.讨论了参数激励下涡激响应的共振条件;以尾流振子模型为基础,发展了分析张力腿在动张力作用下的涡激振动的工程方法,并分析了一座TLP实例,给出了在横漂周期内张力腿上质点的相对位移、弯矩、剪力幅值的时间历程.结果表明,平台垂荡使张力腿的涡激响应幅值升高、高频成分增加,因此它对张力腿的疲劳设计是重要的.     

A Stability Criterion for Time-Delay Tension Leg Platform Systems Subjected to External Force

Stability analysis plays a central role in nonlinear system theory and engineering application.Over the past few yeats,the stability analysis of fuzzy systems has been proposed and there are many successful applications in practical engineering.Therefore,in this paper firstly proposed is the stability analysis on oceanic structure by fuzzy models.In the present study,Takagi-Sugeno (T-S) fuzzy model is proposed for a time delay tension leg platform (TLP) system subjected to an external wave force.In terms of stability analysis,linear matrix inequality (LMI) conditions are derived via Lyapunov theory to guarantee the stability of the TLP system.     

Studies of TLP dynamic response under wind, waves and current

Investigated is the coupled response of a tension leg platform (TLP) for random waves. Inferred are the mass matrix, coupling stiffness matrix, damping matrix in the vibration differential equation and external load of TLP in moving coordinating system. Infinitesimal method is applied to divide columns and pontoons into small parts. Time domain motion equation is solved by Runge-Kutta integration scheme. Jonswap spectrum is simulated in the random wave, current is simulated by linear interpolation, and NPD spectrum is applied as wind spectrum. The Monte Carlo method is used to simulate random waves and fluctuated wind. Coupling dynamic response, change of tendon tension and riser tension in different sea conditions are analyzed by power spectral density (PSD). The influence of approach angle on dynamic response of TLP and tendon tension is compared.     

Stochastic Analysis of Short-Term Structural Responses and Fatigue Damages of A Submerged Tension Leg Platform Wind Turbine in Wind and Waves

In connection with the design of floating wind turbines, stochastic dynamic analysis is a critical task considering nonlinear wind and wave forces. To study the random structural responses of a newly designed submerged tension leg platform(STLP) wind turbine, a set of dynamic simulations and comparison analysis with the MIT/NREL TLP wind turbine are carried out. The signal filter method is used to evaluate the mean and standard deviations of the structural response. Furthermore, the extreme responses are estimated by using the mean upcrossing rate method. The fatigue damages for blade root, tower, and mooring line are also studied according to the simulated time-series. The results and comparison analysis show that the STLP gives small surge and pitch motions and mooring line tensions in operational sea states due to the small water-plane area. Additionally, in severe sea states, the STLP gives lower extreme values of platform pitch, slightly larger surge and heave motions and better towerbase and mooring line fatigue performances than those of the MIT/NREL TLP. It is found that the STLP wind turbine has good performances in structural responses and could be a potential type for exploiting the wind resources located in deep waters.     

Response behaviour of triangular tension leg platforms under impact loading

Excellent station keeping characteristics and relative insensitivity with increasing water depth make triangular tension leg platforms (TLPs) a proven concept in deep water oil exploration. TLPs are often subjected to less probable forces which arise due to collision of ships, icebergs or any other huge sea creature. Dynamic analysis of two triangular TLP models at water depths 1200 and 527.8 m is performed under regular waves along with impulse load acting at an angle of 45 degrees at the TLP column. Hydrodynamic forces on these TLPs are evaluated using modified Morison equation, based on water particle kinematics arrived at using Stokes’ fifth order wave theory. Based on numerical studies conducted, it is seen that impulse loading acting on corner column of TLP significantly affect its response while that acting on pontoons dose not affect TLPs behaviour.     

风机基础TLP平台在波浪中运动性能的CFD数值分析

随着海上风能的开发向深水发展，支撑风机的载体平台越来越受到关注。在经济性与安全性、稳定性的多重要求下，张力腿平台（TLP）在海洋风能资源的开发中体现出了重要地位。采用基于开源平台OpenFOAM开发的计算流体动力学（CFD）水动力学求解器naoe-FOAM-SJTU对一座处于中等水深下的风机基础水下TLP（STLP）的运动响应进行了数值模拟与研究。文中使用弹簧锚链模型模拟STLP的垂向系泊锁链系统，模拟该平台在不同波浪环境下的运动响应情况。首先将STLP单自由度自由衰减CFD模拟结果与已有全耦合时域分析结果进行对比，验证了naoe-FOAM-SJTU求解器及使用弹簧模型模拟STLP系泊系统的准确性与可靠性。随后在考虑非线性波浪载荷的情况下研究极端海况下与一般作业海况下STLP的运动响应情况，计算工况中的风机基础所受弯矩及锚链受力情况，并详细展示流场、速度场信息，分析高阶波浪成分、不同海况等条件对于STLP运动性能的影响。研究结果表明，TLP在中等水深中具有良好的运动性能，naoe-FOAM-SJTU求解器可以有效模拟水中生产平台在波浪环境下的水动力问题，并可以对整个流场进行可视化展示与分析。     

Nonlinear Random Motion Analysis of A Tension Leg Platform Considering the Set-down Motion of A Floating Body

The dynamic analysis of a Tension Leg Platform (TLP) in random wave is investigated by considering the set-down of a floating body. The nonlinear restoring stiffness is derived with the set-down motion of a floating body and the coupled motion of the tension leg and platform and the differential equations of the motion are established. The study focuses on the influence of the set-down motion on the nonlinear response of the platform. By considering different significant wave heights and currents, motion responses of the platform are calculated and compared. The analysis shows that the set-down motion significantly increases the heave motion with low frequency and the equilibrium position of the heave motion with the set-down motion is much lower than that without set-down motion. The results in this paper indicate that the set-down motion has a major impact on the safety of the platform inproduction operation, and it is also a threat to the strength of tension legs and risers.     

Low-frequency damping of a moored semisubmersible obtained from simulated extinction tests and mean wave drift forces

Low-frequency damping of a moored semisubmersible drilling platform was obtained from numerical extinction tests simulated in still water and in regular waves and from mean wave drift forces calculated at zero forward speed. The influence of drag forces was represented by the modified Morison equation. The platform as used for the 18th ITTC Comparative Mooring Study was analyzed in irregular beam waves. The computed time series of sway as well as the corresponding sway response spectrum compared favourably with model test measurements, demonstrating that this procedure to determine low-frequency damping can be effective.     

Dynamic behavior of offshore spar platforms under regular sea waves

Many innovative floating offshore structures have been proposed for cost effectiveness of oil and gas exploration and production in water depths exceeding one thousand meters in recent years. One such type of platform is the offshore floating Spar platform. The Spar platform is modelled as a rigid body with six degrees-of-freedom, connected to the sea floor by multi-component catenary mooring lines, which are attached to the Spar platform at the fairleads. The response dependent stiffness matrix consists of two parts (a) the hydrostatics provide restoring force in heave, roll and pitch, (b) the mooring lines provide the restoring force which are represented here by nonlinear horizontal springs. A unidirectional regular wave model is used for computing the incident wave kinematics by Airy’s wave theory and force by Morison’s equation. The response analysis is performed in time domain to solve the dynamic behavior of the moored Spar platform as an integrated system using the iterative incremental Newmark’s Beta approach. Numerical studies are conducted for sea state conditions with and without coupling of degrees-of-freedom.     

Experimental and numerical investigations on the intact and damage survivability of a floating–moored oscillating water column device

This paper investigates the intact and damage survivability of a floating–moored Oscillating Water Column (OWC) device using physical model experiments and Computational Fluid Dynamics (CFD) simulations. Different extreme wave conditions have been tested using irregular and regular wave conditions. The device was moored to the tank floor via four vertical taut lines and the effect of the mooring line pre–tension on the device response was studied. It was found that the instantaneous position of the floating device was a key factor in the survivability analysis such that a certain irregular wave train that might not include the largest wave could induce the maximum response. Reducing the pre–tension minimized the maximum surge, but significantly increased the maximum tension due to mooring slack events causing snatch loads. A design regular wave with a period equal to the peak period and a height of 1.9–2.0 times the significant wave height could reasonably predict the same maximum line tension as the irregular sea state, but a smaller wave height was required to achieve the maximum surge. A single failure in the mooring system increased the maximum tension by 1.55 times the intact tension. For a damaged mooring system, using the same design regular wave condition derived from the survivability analysis with an intact mooring system could result in overestimating the maximum tension by more than 20% in comparison to the tension from the irregular sea state, but a smaller regular wave height or a different regular wave condition representing another sea state could lead to the same maximum tension. This highlighted the importance of investigating survival conditions with a damaged mooring system instead of simply using the same conditions derived for the intact mooring system.     

Time-domain simulation of large-amplitude response of floating platforms

Two numerical simulation models to predict large-amplitude motions of floating platforms are presented. The first method is based on the application of the relative-velocity formulation of Morison's equation for force calculations. The second method developed in this work uses the three-dimensional potential theory in time domain. In this method, both the Froude-Krylov and scattering forces are calculated by considering finite wave amplitude effects in random waves. The effect of various nonlinearities on the low-frequency motions and high-frequency tether-tension response of a tension leg platform are studied using these simulation models in conjunction with power spectral methods. The presence of current and the nonlinear drag force are observed to have a significant effect on the low-frequency motions and tether tensions.     

Hill Instability Analysis of TLP Tether Subjected to Combined Platform Surge and Heave Motions

This paper presents the Hill instability analysis of Tension keg Platform （TLP） tether in deep sea. The 2-D nonlinear beanl model, which is undergoing coupled axial and transverse vibrations, is applied. The governing equations are reduced to nonlinear Hill equation by use of the Galerkin＇ s method and the modes superposition principle. The Hill instability charted up to large parameters is obtained. An important parameter M is defined and can be expressed as the functions of tether length, the platform surge and heave motion amplitudes. Some example studies are performed for various envirotnnental conditions. The results demonstrate that the nonlinear coupling between the axial and transverse vibrations has a significant effect on the response of structure. It needs to be considered for the accurate dynamic analysis of long TI2 tether subjected to the combined platfolna surge and heave motions.     

Numerical modeling of dynamic responses and mooring forces of submerged floating breakwater

Using the volume of fluid (VOF) method, a numerical model is developed to estimate the nonlinear dynamics of a pontoon type moored submerged breakwater under wave action and the forces acting on the mooring lines, for both the vertical and inclined mooring alignments. The model is developed for a two-dimensional wave field in a vertical plane. The finite displacements of the breakwater such as sway, heave and roll in a very small time step are considered and the numerical grid cells intersected by the breakwater surfaces for changing its position due to wave action are treated using the concept of porous body model. Also, two-dimensional experimental studies are carried out to investigate the performance of the proposed model. The comparison of the computed and measured results reveals that the developed numerical model can reproduce well the dynamics of the floating body and the mooring line forces.     

Nonlinear coupled dynamic response of offshore Spar platforms under regular sea waves

Many innovative floating offshore structures have been proposed for cost effectiveness of oil and gas exploration and production in water depths exceeding one thousand meters in recent years. One such type of platform is the offshore floating Spar platform. The Spar platform is modelled as a rigid body with six degrees-of-freedom, connected to the sea floor by multi-component catenary mooring lines, which are attached to the Spar platform at the fairleads. The response dependent stiffness matrix consists of two parts (a) the hydrostatics provide restoring force in heave, roll and pitch, (b) the mooring lines provide the restoring force which are represented here by nonlinear horizontal springs. A unidirectional regular wave model is used for computing the incident wave kinematics by Airy’s wave theory and force by Morison’s equation. The response analysis is performed in time domain to solve the dynamic behavior of the moored Spar platform as an integrated system using the iterative incremental Newmark’s Beta approach. Numerical studies are conducted for sea state conditions with and without coupling of degrees-of-freedom.     

Direct time domain analysis of floating structures with linear and nonlinear mooring stiffness in a 3D numerical wave tank

In this paper, motion response of a moored floating structure interacting with a large amplitude and steep incident wave field is studied using a coupled time domain solution scheme. Solution of the hydrodynamic boundary value problem is achieved using a three-dimensional numerical wave tank (3D NWT) approach based upon a form of Mixed-Eulerian–Lagrangian (MEL) scheme. In the developed method, nonlinearity arising due to incident wave as well as nonlinear hydrostatics is completely captured while the hydrodynamic interactions of radiation and diffraction are determined at every time step based on certain simplifying approximations. Mooring lines are modelled as linear as well as nonlinear springs. The horizontal tension for each individual mooring line is obtained from the nonlinear load-excursion plot of the lines computed using catenary theory, from which the linear and nonlinear line stiffness are determined. Motions of three realistic floating structures with different mooring systems are analyzed considering various combinations of linear and approximate nonlinear hydrodynamic load computations and linear/nonlinear mooring line stiffness. Results are discussed to bring out the influence and need for consideration of nonlinearities in the hydrodynamics and hydrostatics as well as the nonlinear modelling of the line stiffness.