Mooring Line Dynamics Research Articles

A theoretical framework for robust implementation of in situ measurements of ocean currents and waves in dynamics of mooring systems

We develop an approximated method to solve analytically the equations of motion that describe mooring line dynamics in a one-dimensional model. For the first time, we derive integral closed-form expressions to compute dynamic properties of mooring lines subject to ocean currents and waves of arbitrary time and spatial dependence, in terms of modified Bessel functions. This is done by decomposing the mooring line in three regions where different approximations and mathematical techniques of solution are carried out. Our analytical results provide a robust framework to simulate and analyze extreme realistic oceanic events when data from in situ ocean observation systems are available, regardless of the resolution or coarseness of subsurface measurements and even for long acquisition times. In order to prove the advantages of this approach, we have processed data from two stations in the National Data Buoy Center of the National Oceanic and Atmospheric Administration. From simulations with ocean currents data, we have gained insights into the coupling of the spatial modulation of ocean currents with the characteristic wavelengths of elastic lines. From simulations with ocean waves data, we have defined a scheme to analyze wave data and identify the contribution of each subset of frequency peaks to the net fluctuation of mooring line tension. This could be useful for classification of irregular waves based on their impact on mooring line tension. The development of better tools that integrate theoretical and experimental findings is necessary for the assessment of marine structures under the environmental conditions associated with climate change.

Influence of tangential hydrodynamic force and inclination angle calculation on the dynamic responses analysis of mooring line based on lumped mass method

Research on mooring line response offers a scientific foundation and technical backing for ocean engineering management. The lumped mass method is commonly used to calculate the dynamic responses of mooring line, pioneered by Walton and Polachek, although it ignores the tangential hydrodynamic force. Nakajima addressed this limitation, but the inclination angle calculation for each element is approximated by the average of the adjacent two nodes. To accurately assess the influences of these factors, this work introduces the tangential hydrodynamic force component into the equation of motion for mooring line dynamic analysis based on the lumped mass method. Meanwhile, we improve the discretization process of lumped mass nodes, analyzing half of the connected spring at both ends of each lumped mass node respectively. The detailed formulation and motion equation for static and dynamic mooring line analysis are presented. The time-domain solution procedure based on the finite difference method is adopted. Finally, different external excitations are applied to calculate the dynamic responses of mooring line. The results show that the top tension increases by about 2%–5% considering the contribution of tangential hydrodynamic force, and the inclination angle calculation significantly influences the dynamic configuration of the mooring line when it is intense change.

Coupling a nonlinear finite element mooring model with an overset CFD solver for dynamic analysis of floating structures in waves

An accurate prediction of motion responses of a moored floating structure requires high-fidelity coupled analysis between the structure and its mooring system in waves, which involves both mooring line dynamics and fluid dynamics. In this paper, we develop a nonlinear finite element dynamic mooring analysis module that allows large axial stretching of mooring lines under the open source CFD framework OpenFOAM, and couple it with an Overset CFD solver to establish a fully coupled finite element mooring-CFD analysis model for floating structures. The coupled model is advantageous over existing models in that it is able to deal with large axial mooring stretching and complex mesh motions induced by significant structure responses under severe operating conditions. The developed dynamic mooring analysis method is firstly validated against publicly available data. In order to validate the coupled model, a series of experimental tests were carried out for a semi-submersible platform moored by eight catenary lines under different operating conditions, including free decay, regular and irregular wave tests. The dynamic responses of the floating structure and mooring tension are analyzed and compared with experimental data. Results show that numerically predicted structure responses and mooring tension are generally in good agreement with experimental measurements. Meanwhile, the strongly nonlinear large-amplitude resonant motions generated by the interaction of irregular waves with the moored floating structure are also investigated. Comparisons reveal that the coupled model can accurately predict the resonant spectral peaks of the structure responses, indicating that the it is capable of simulating large-amplitude motions of moored floating structures. The coupled model developed in this paper can be further applied to study the survivability of moored floating structures under harsh sea conditions.

General formulation for floating body with elastic mooring in irregular waves: A hybrid linear and nonlinear framework and validation

In the present study, an advanced computational platform has been developed for offshore renewable energy converter systems, considering nonlinear wave input, body dynamics, mooring line dynamics, and kinematic and mechanical constraints. In particular, a hybrid linear and nonlinear hydrodynamic model is formulated through coupling with a numerical wave tank generated by OceanWave3D. A novel nodal position finite element model considering geometrical and material nonlinearities is developed to simulate the nonlinear behaviour of the mooring dynamics. Then, an implicit solver with an iteration process solves the dynamics of the rigid body, the dynamics of the mooring lines, and kinematic and mechanical constraints simultaneously. Therefore, the developed platform is capable of studying the wave body interaction with mooring lines in extreme wave conditions. Wave basin model tests of a single float on a nonlinear mooring line are carried out under a series of irregular waves for comparison. The developed model was also validated against commercial software under identical conditions for idealised cases. In steep wave conditions, the hybrid nonlinear/linear hydrodynamics give improved predictions over the linear hydrodynamic method.

Time-dependent responses and mooring tensions of a moored floating structure in tsunami waves

This study evaluates the effects of tsunami waves on the global performance of a spread-moored Floating Storage Unit (FSU) through tsunami-floater-mooring coupled dynamics simulations. The time-domain equations of motions for the FSU used the Cummins equation with a body-nonlinear method, in which the nonlinear Froude-Krylov and hydrostatic restoring forces were evaluated at the instantaneous tsunami elevation and body position at each time step. As input tsunami waves, second-order solitary waves and Tohoku-tsunami-like waves constructed by the superposition of several solitary waves were used. The lumped-mass-line model was used for the coupled mooring-line dynamics. Then, the coupled interactions between the floater and mooring system were solved by applying various tsunamis of different shapes, durations, heights, and incident angles. The body-nonlinear results were systematically compared with the linear analyses to demonstrate the pertinent nonlinear effects. Following a significant initial drift of the vessel induced by tsunamis, the moored floating structure exhibits transient motions at natural periods. Larger tsunami heights with relatively short duration result in significantly higher FSU motions and mooring tensions.

Development of an efficient calculation technique for dynamics of mooring lines by using discrete forms of rotation

Development of efficient calculation techniques is of key importance for design of deepwater moored floating structures consisting of many subsystems, such as a floating vessel, risers and mooring lines. In particular, this study focuses on a method for simulating dynamic behavior of the mooring line, since it includes a lot of degrees of freedom and geometric nonlinear effects. A modified Morison equation based on the linear potential flow theory is employed to derive the hydrodynamic forces acting on the lines. The present approach describes the mooring lines (chain) as multi-rigid bodies based on the multibody dynamics approach. In addition, a discrete form of rotation called “the rotation update equation” is introduced. This technique approximates the rotation by using incremental components of rotation in terms of the angular velocity. This approach can bypass the parameterization of rotation in the equations of motion. Clearly, it contributes to reduction of computational costs. Furthermore, a preconditioning method is applied to the equations of motions in order to prevent the ill-conditioning which affects convergence of the numerical integration procedures for the set of equations with configuration level constraints. Finally, a comparison of results by the present method and the conventional method are presented in order to show the validity of the method.

Numerical prediction of potential 3-dimensional seabed trench profiles considering complex motions of mooring line

Seabed trenches near deep-sea anchors bring risks to the mooring system's safety. The prediction of 3-dimensional (3-D) trench profiles is a key task to reduce the risk. However, the trench width related to the trench wall collapse and lateral movement of the mooring line has not been well studied. This paper first proposes a 3-D mooring line-seabed dynamics model to consider the mooring line lateral movement in the soil. Then, a seabed trenching model to simplify 3-D trench profiles is developed based on the field data. By combining the above models, a novel method to predict 3-D trench profiles around embedded mooring lines is established by considering trench wall collapse and integrating dynamics of mooring line. Based on the verified method, both static and dynamic responses of mooring lines are investigated, then a series of parametric sensitivity studies are carried out. The simulation results reveal that dynamic movement of mooring lines at fairlead may result in remarkable seabed trenches, and lateral motion of mooring lines enlarges the disturbed zone near the mooring line touchdown area. The proposed method in this paper provides a reasonable assessment of the 3-D trench profiles and reduces risks in the operation of mooring systems.

Effects of tendon breakage on the dynamic behaviour of a TLP

ABSTRACT In this paper, the dynamic behaviour of a tension leg platform (TLP) under different damaged mooring conditions is studied. ANSYS/AQWA is used to develop a nonlinear hull-tendon model, which can consider the coupling effects between the platform motion and mooring line dynamics at each time step. Noteworthily, an effective method for simulating tendon breakage is proposed. The transient effects of tendon breakage, the transient responses of the platform for simultaneous and progressive tendon breakage, and the performance changes of the platform after tendon breakage are investigated. The results show that the tendon breakage has a significant influence on the dynamic responses and performance of the platform. Therefore, the effects of tendon breakage on the platform should be examined in advance to prevent the safety of the platform from being threatened.

Coupled dynamic analysis on floating wind farms with shared mooring under complex conditions

To perform coupled dynamic analyses on floating wind farms with complex structural configurations taking into account hydrodynamic coupling and structural coupling, a universal framework for complex structural configurations is proposed and applied to shared mooring, based on which codes are developed and validated. Then extensive works on the dynamic natures of floating wind farms with shared mooring structural configuration are done and a comprehensive knowledge of the effects of unsteady wind inflow, unsteady wave incidence and mooring line dynamics is obtained, which demonstrates the effects worth attention in the design and analysis of floating wind farms with shared mooring for practical engineering. Finally, the dynamic responses after the failure of mooring lines are investigated, characterizing the risks of collision and progressive failure, which provides a methodology for the assessment of reliability of floating wind farms with shared mooring.

A DNN-based approach to predict dynamic mooring tensions for semi-submersible platform under a mooring line failure condition

The station-keeping system of offshore platforms is susceptible to complex metocean environments. The failure of the mooring line is of utmost concern due to uncertainty in the mooring line's behavior and the severe aftermath of the accidents. Once the mooring line breakage occurs, the remaining mooring lines should provide sufficient tension to warrant the continual production operations and personnel safety on the platform. This paper proposes a deep neural networks (DNN) approach to predict the dynamic mooring line tension under one mooring line failure condition. Firstly, the tension change of mooring lines induced by mooring failure is investigated in two hydrodynamic models, and then select the tensions on the mooring line with maximum sensitivity to failure as the output objective. Secondly, using the responses of floating structures and mooring tensions to construct the two datasets of different hydrodynamic models, then train two DNN models and utilize grid search to determine the optimal network structure. Finally, some case studies with different mooring arrangements and sea state conditions are employed to verify the feasibility and adaptability of two established DNN models and compare their accuracy. According to the unseen data test results, the DNN-II model shows a better prediction performance compared to the DNN-I model in all test cases. Based on the results of the two types of the correlation coefficient, the main control variables in mooring tensions prediction are believed to be significantly increased sway and surge motion induced by mooring broken. This study provides an idea for practical engineering, through combining with the mature and stable Global Positioning System (GPS) in a platform or FPSO, the remaining mooring line tensions under mooring failure conditions can be monitored and controlled in real time.

Numerical study of ice-induced loads and dynamic response analysis for floating offshore wind turbines

This paper presents a suite of ice load models using a coupled aero-hydro-servo-elastic numerical model to study dynamic response of floating offshore wind turbines in cold regions that sea ice is present. The coupled aero-hydro-servo-elastic model consists of wind inflow dynamics, rotor aerodynamics, structural multibody dynamics of the system, wave and current kinematics, hydrodynamics, mooring-line dynamics and ice loads. This open-source numerical model provides a modular framework to investigate the common wind turbine configurations, support structure systems and mooring lines for different environmental conditions. The 5MW National Renewable Energy Laboratory wind turbine is used as a target turbine. Verification studies are performed to show the accuracy of the numerical model. The analyses show that the proposed approach provides reasonable results for the calculation of ice loads on the offshore wind turbine structure as well as the system dynamic response. It is expected that the proposed model would be widely used to study, investigate and analyze the different aspects of floating offshore wind turbine design, leading to the promotion and advancement of science and technology in the offshore renewable energy industry.

Effects of one mooring line failure on the behaviour of a work ship

The dynamic performance of a work ship with a mooring line failure was studied. A fully coupled dynamic analysis program (Ansys Aqwa) was applied to simulate ship motions and mooring line dynamics. The first- and second-order wave excitation forces were calculated using the three-dimensional diffraction/radiation theory, and the behaviours of the mooring lines were analysed using a non-linear finite-element method. Under the combined environmental loads of waves and wind, one mooring line was intentionally disconnected at a certain moment. Then, the dynamic response after the mooring line breaks, the energy distribution characteristics in the motion response spectrum and the mean tension variation of the remaining mooring lines were assessed. The results showed that sudden failure of the mooring line significantly affected the performance of the ship. Therefore, to ensure the structural integrity of the ship system and the safety of personnel on deck, the influence of a mooring line failure on a ship should be investigated in advance.

A new approach to predict dynamic mooring tension using LSTM neural network based on responses of floating structure

The prediction of dynamic mooring line tension using the responses of floating structures is of great significance for the safety monitoring of the station-keeping. Due to the mooring line tension usually has the typical low-frequency and wave-frequency characteristics, this paper proposes a method of Low-frequency adds wave-frequency responses (LAWR) to predict the mooring line tension. Firstly, the optimal Long-short term memory (LSTM) neural network structure is determined through conducting the parameter sensitivity analysis on the performance of the LSTM model. Secondly, the low-frequency and wave-frequency tension are predicted using the corresponding low-frequency and wave-frequency responses as the input data, respectively. Then, the total mooring line tension is predicted by superposing the low-frequency tension and wave-frequency tension. Finally, the feasibility of the LAWR method is verified by considering the different data relevance between the training sets and validating sets, including the sea state condition contains different current direction, wave height and spectral peak frequency. The method proposed in this paper could further improve the prediction accuracy of mooring line tension more than 30%, which has great engineering significance.

Influence of turbulence models on the dynamic response of a semi-submersible floating offshore wind platform

With the aim of evaluating the effects of the selection of the wind turbulence model on the dynamic response of a semi-submersible floater supporting the DTU 10 MW RWT, we ran aero-hydro-servo-elastic simulations employing the OASIS code developed at IHCantabria. For each of the 4 sea states selected, apart from the reference case with only wave loads, we analysed 30 different realizations with coupled wind and wave loads for each of the 7 full-field turbulent winds generated by the turbulence simulator TurbSim: Kaimal and von Kármán spectral models with three different turbulence classes each and the API turbulence model.From the resulting platform motions and mooring line dynamics, it can be concluded that the selection of the wind turbulence model is not trivial. At U0=5.83 m/s, the obtained results show a high dependence on the turbulence class. However, as the wind speed increases and the wind turbine achieves the rated speed, the impact of the turbulence intensity is drastically reduced, and the design tension is dominated by the thrust force and thus by the vertical wind speed profile. The highest design tension of the windward mooring lines is obtained with the API model at U0=8.75 m/s (at least 357 Tm).

Structural responses of large-sized floating wind turbine with consideration of mooring-line dynamics based on coupled FEM simulations

ABSTRACT The dynamic response of a 5 MW floating wind turbine is examined using the coupled finite element simulations, and the dynamic effects of the catenary is considered, while the coupling between flexible components are included. The restoring performance of the mooring-line is analysed based on the vector equations and numerical simulations. The stiffness hysteresis and the influence of the catenary dynamics on the restoring performance are studied. Then the structural responses undergoing wind and wave loads, are examined. Our results show that the mooring-line tension significantly rise due to catenary dynamics, and the snap tension gets around three times larger. The mooring-line stiffness presents a hysteresis character, owing to the fluid/structural damping, which becomes more obvious with the increase of motion frequency/amplitude. Moreover, the structural response gets smaller principally because of the hysteresis effect. The spar displacement and the tower root stress become respectively 18.4% and 32.7% smaller.

Frequency domain modelling of a coupled system of floating structure and mooring Lines: An application to a wave energy converter

Floating structures for single offshore renewable energy devices, i.e. wave energy converters, tend to be significantly smaller than those of the traditional offshore industry and the interaction between floater motions and mooring line dynamics become important. Installation sites are generally subject to powerful waves and currents experiencing more dynamically excited motions. Water depths are also lower, ranging generally from 50 m to 200 m and mooring systems are to be designed to assure the station keeping of them while not interfering with the power conversion. However, floater motions may induce large dynamic tensions on mooring lines, making quasistatic analyses inaccurate in terms of design tension while non-linear time domain simulations too time consuming. This paper introduces a numerical model of lumped mass for mooring lines and rigid body motions for the floating structure coupled by means of kinematic relations, and its subsequent linearization, which is solved in the frequency domain. The linearized model is applied to a two-body floating spar type oscillating water column, subject to the 36 most occurrent sea states at the BIMEP site. Its accuracy is verified through a comparison with the equivalent time domain simulation and a review of the results and its limitations are also pointed out.

Seabed trenching near the mooring anchor: History cases and numerical studies

The floating platform with taut or semi-taut mooring systems is the main option for oil and gas exploitations in deep sea. However, it has been reported that the reciprocating motion of the mooring line tends to induce the seabed trench near the anchor, which consequently reduces the anchor capacity. In this paper, two parts of work have been carried out to enhance the understanding of the seabed trench. Firstly, the dimensions of reported trenches in the field as well as their formation conditions are summarized, and four feature points are proposed to describe the trench profile. Secondly, a numerical method considering mooring line dynamics to predict the final trench profiles is proposed, which contains two simulation modules, i.e. mooring line dynamics and seabed trenching. The method is verified using the data from the field and centrifuge tests. The influences of the mooring line tension and soil strength on trench profiles are comprehensively investigated further. The results show that obvious trenches are likely to form when the amplitude of mooring line tension variation is large and the soil shear strength is low. The main impact of the formed trenches is that the loading direction at the pad-eye tends to be horizontal.

An implementation of Three-Dimensional Multi-Component Mooring Line Dynamics Model for Multi-Leg mooring line configuration

Multi-component mooring line (MCML) system is widely used and expected to be escalated for deep water mooring operation since it has several advantages comparing with conventional mooring line. The modelling of MCML involving its dynamic effects is strongly required to predict the dynamic behaviours of the mooring line precisely. In this paper, a proposed three-dimensional dynamics model of MCML system is presented and implemented to single point multi-leg mooring line configuration operated in deep water condition. An extending three-dimensional lumped mass method is elaborated to develop the model while the combination of Manoeuvring Modelling Group (MMG) and conventional floating body motion equations is used to perform simultaneous motion between floating structure and mooring lines. The simultaneous motion is performed with respect to wind, wave, and current. The motion of the floating structure and mooring line as well as mooring line tension can be analysed properly by using the presented model. The simulation results of the model show reasonable results for both floating structure and mooring line.

Dynamic mooring lines tension of FPU operated at Madura Strait

An FPU operated at a gas field in Madura Strait is designed to be the main process component of the gas processing facilities for a service life 20 years. This vessel using a catenary mooring system which made up of 12 points mooring divided into 4 groups of 3 mooring lines. This vessel is necessary to be analyzed its mooring tension to ensure safety while operation. The mooring line tension is analyzed by using 3D-Diffraction Calculation. This study presents the result of the dynamic mooring line tension conducted for full load condition of FPU in extreme wave condition. The mooring analysis compliance is based on DNV GL’s technical standards, as well as an international accredited registrar and classification society. Verification of computed line tension against acceptance criteria has been carried out for the current condition of the mooring system. Results of the analysis indicate that mooring line tension meets the safety factor from DNVGL OS E301 with the Maximum tension of all mooring lines value is about 159.3 t, which happened in Line 4 by heading 67.5°.

Analysis on restoring stiffness and its hysteresis behavior of slender catenary mooring-line

In deeper ocean area, more and more floating oil/gas production platforms or wind turbine have been in operation instead of the fixed truss in shallow water. These floaters need to be located among a range of position by its mooring system, e.g. tension tendon and catenary mooring-line, so as to guarantee structural safety and stability under environmental loads. Catenary mooring-line is increasingly used due to its lower cost and easier installation. Its dynamics coming from structure and fluid flow becomes more obvious with the increase of structural length, which may introduce significant impact on restoring performance of mooring-line. In this study, the non-linearly restoring performance and the hysteresis behavior of mooring-line's stiffness are studied. The nonlinear dynamic model of the mooring-line is established based on the improved FEM simulations. It is found that the restoring stiffness of the catenary mooring-line presents a hysteresis characteristic, principally owing to the damping effect of the catenary dynamics, which gets more obvious with the increase of motion amplitude/frequency. And, the mooring-line dynamics has significant impacts on the tension (related to its restoring stiffness) and displacement response, e.g. the maximum tension amplitude is up to 5.2 times of the quasi-static value if slack happens.