Slow Drift Forces Research Articles

Drift simulation of a floating offshore wind turbine with broken mooring lines in a dynamic sea condition

This study investigates the aero-hydro-mooring coupled dynamics of the National Renewable Energy Laboratory (NREL) offshore 5-MW baseline wind turbine supported by the Offshore Code Comparison Collaboration Continuation (OC4) DeepCwind semisubmersible floating platform by considering the effects of suddenly broken mooring behaviour. The wind and wave loads can be selected as the Cummins time-domain equation inputs based on the Norwegian Petroleum Directorate wind and Joint North Sea Wave Project wave spectrums. The nonlinear viscous drag was estimated using the quadratic damping matrix rather than Morison's element. Additionally, the quadratic transfer function matrix was used to calculate the slow-drift force. Compared to the multi-segmented quasi-static mooring model, the lump-mass method is a dynamic mooring model that can solve real-time motion on the platform. Once a single or a pair of mooring lines is intentionally disconnected from the floating platform at a certain time, the transient responses of mooring line tensions and turbine performance will be evaluated. The novelty of this study is that the drift trajectories and power performances of OC4 DeepCwind semisubmersible floating offshore wind turbine under different conditions of environmental loads and broken mooring lines can be approximately estimated in the offshore wind farm. The analysis can be used for the environmental impact assessment in harsh sea conditions.

Response validation of a submerged floating tunnel segment

Tube segments are the main structural components of submerged floating tunnels (SFTs). Accurately estimating the hydrodynamic properties of these components is of critical importance for the optimization and safe design of SFTs. Therefore, it is essential to understand the uncertainty associated with the frequently used assumptions inherent in the state-of-the-art calculation models for SFTs. In this paper, experimental data provided by the Norwegian Public Roads Administration (NPRA) were used to validate the hydrodynamic responses of a truncated tube segment of a SFT. The excitation force and motion response of the tube segment under different loading and constraint conditions were verified. The effects of different wave headings, submerged depths, and restoring spring stiffnesses on the hydrodynamic features of the SFT's tube segment were further investigated. The numerical results generally coincide well with the experimental results. Some interesting properties of the tube segment are presented, and the uncertainty level related to the state-of-the-art models is made clear. These are for instance regarding the main tube as a Morison element and neglecting the slow-drift force effects. The aspects that need to be given more attention to achieve more trustworthy estimations of the hydrodynamic responses are summarized. The results presented should be of value in relation to verification of analysis methods for SFTs, which represents an important step towards enhancing trustworthy design models.

Hydrodynamic Simulation of the Semi-Submersible Wind Float by Investigating Mooring Systems in Irregular Waves

The present study aims to implement the software ANSYS AQWA to discuss the hydrodynamic analysis of the DeepCwind semi-submersible floating platform in waves based on the potential flow theory by considering the second-order wave exciting force. In this study, the linearized potential-flow hydrodynamic radiation and diffraction problems in the frequency domain were firstly solved by adopting the three-dimensional panel method. Subsequently, the hydrodynamic coefficients and wave loading data were transformed to time domain forms by the Cummins time domain equation as a system loading input. Furthermore, the quadratic transfer function (QTF) matrices with different frequencies and directions deduced based on the near field integration over the mean wetted hull surface were adopted for the calculation of slow-drift forces. In order to represent the damping in a real system for modeling potential flow without Morison’s elements, an additional quadratic damping matrix was added to capture the viscous drag. Eventually, both of the dynamic mooring model based on the lump-mass (LM) approach and the quasi-static mooring model based on the multi-segmented, quasi-static (MSQS) approach are introduced to discuss the mooring effect on the platform hydrodynamics. The effect of wave heading angles on the platform motion is considered as an influential parameter as well.

Multibody modeling for concept-level floating offshore wind turbine design

Existing Floating Offshore Wind Turbine (FOWT) platforms are usually designed using static or rigid-body models for the concept stage and, subsequently, sophisticated integrated aero-hydro-servo-elastic models, applicable for design certification. For the new technology of FOWTs, a comprehensive understanding of the system dynamics at the concept phase is crucial to save costs in later design phases. This requires low- and medium-fidelity models. The proposed modeling approach aims at representing no more than the relevant physical effects for the system dynamics. It consists, in its core, of a flexible multibody system. The applied Newton–Euler algorithm is independent of the multibody layout and avoids constraint equations. From the nonlinear model a linearized counterpart is derived. First, to be used for controller design and second, for an efficient calculation of the response to stochastic load spectra in the frequency-domain. From these spectra the fatigue damage is calculated with Dirlik’s method and short-term extremes by assuming a normal distribution of the response. The set of degrees of freedom is reduced, with a response calculated only in the two-dimensional plane, in which the aligned wind and wave forces act. The aerodynamic model is a quasistatic actuator disk model. The hydrodynamic model includes a simplified radiation model, based on potential flow-derived added mass coefficients and nodal viscous drag coefficients with an approximate representation of the second-order slow-drift forces. The verification through a comparison of the nonlinear and the linearized model against a higher-fidelity model and experiments shows that even with the simplifications, the system response magnitude at the system eigenfrequencies and the forced response magnitude to wind and wave forces can be well predicted. One-hour simulations complete in about 25 seconds and even less in the case of the frequency-domain model. Hence, large sensitivity studies and even multidisciplinary optimizations for systems engineering approaches are possible.

Influence of second order wave excitation loads on coupled response of an offshore floating wind turbine

This paper presents an integrated analysis about dynamic performance of a Floating Offshore Wind Turbine (FOWT) OC4 DeepCwind with semi-submersible platform under real sea environment. The emphasis of this paper is to investigate how the wave mean drift force and slow-drift wave excitation load (Quadratic transfer function, namely QTF) influence the platform motions, mooring line tension and tower base bending moments. Second order potential theory is being used for computing linear and nonlinear wave effects, including first order wave force, mean drift force and slow-drift excitation loads. Morison model is utilized to account the viscous effect from fluid. This approach considers floating wind turbine as an integrated coupled system. Two time-domain solvers, SIMA (SIMO/RIFLEX/AERODYN) and FAST are being chosen to analyze the global response of the integrated coupled system under small, moderate and severe sea condition. Results show that second order mean drift force and slow-drift force will drift the floater away along wave propagation direction. At the same time, slow-drift force has larger effect than mean drift force. Also tension of the mooring line at fairlead and tower base loads are increased accordingly in all sea conditions under investigation.

A new approach to low-frequency QTF and its application in predicting slow drift force

In this paper, the classical free surface integral formula is examined by an analysis based on the development of the free surface forcing term in a power expansion with respect to Δω. The zero order contribution to the infinite integration which produces the corresponding load of first order Δω is formulated. Then a novel approach which can be easily implemented for predicting the low-frequency QTF is proposed. By applying higher order BEM and adaptive method in element integration, a numerical program is developed. The developed program is tested on simple geometric bodies and offshore platforms. The results from the present study agree well with the results of available exact solutions. Time domain simulation and spectral analyses of the slow drift force are performed for typical kinds of platforms. Extensive discussions and comparisons of the results based on the present method, Teng's exact method and widely used Newman's approximation are presented. The effectiveness of the proposed novel method is further demonstrated by these comparisons.

Frequency Response Analysis of Truss Spar by Considering the Viscous Damping

A calculation model for Truss Spars motion response is established under the wave action by combing the potential flow theory and the modified Morison equation. The high order boundary element method is used to acquire the wave exciting force and the relevant hydrodynamic information. By numerical simulation, the surge, heave and pitch s are obtained, and the parameter analysis for influence of Morison drag coefficient on responses are conducted. The calculated results indicate that the surge and pitch motions are only sensitivity to the drag coefficient in the low frequency range, and consequently the viscous damping would play an important role when the platform undergoes 2nd order wave slow drift force. For the heave response, the heave plates installed on the Truss Spar provide large vertical viscous damping which distinctly affects the heave .

Time and frequency domain coupled analysis of deepwater floating production systems

The dynamic analysis of a deepwater floating structure is complicated by the fact that there can be significant coupling between the dynamics of the floating vessel and the attached risers and mooring lines. Furthermore, there are significant nonlinear effects, such as geometric nonlinearities, drag forces, and second order (slow drift) forces on the vessel, and for this reason the governing equations of motion are normally solved in the time domain. This approach is computationally intensive, and the aim of the present work is to develop and validate a more efficient linearized frequency domain approach. To this end, both time and frequency domain models of a coupled vessel/riser/mooring system are developed, which each incorporate both first and second order motions. It is shown that the frequency domain approach yields very good predictions of the system response when benchmarked against the time domain analysis, and the reasons for this are discussed. It is found that the linearization scheme employed for the drag forces on the risers and mooring lines yields a very good estimate of the resulting contribution to slow drift damping.

Non-linear analysis of a dynamically positioned platform in stochastic seaway

Safety is the topmost priority considered by the designers of floating systems or any other structural systems. Reliability, economy and environmental pollutions and the liability of the structure in the case of accidents are also considered by the designers. The paper concentrates on the non-linear behavior of a moored floating platform in stochastic seaway generated using the Pierson–Moskowitz spectrum. Second-order wave forces (slow drift force) acting on the structure is considered as they contribute to a major percentage of the excursion of a large platform. Wave drift damping and skin friction damping have also been considered. It has been shown that the principal frequency of the second-order motion of the platform due to drift forces closely matches the natural frequency of the system in surge motion. This has been subsequently used in tuning a PID (proportionate integral and differential)-based control system for the surge mode, where reduction in the order of 90% has been observed.

Hydrodynamic damping contributions for an advanced floating production system design

Catenary moored floating vessels used for hydrocarbon production and storage exhibit low frequency, large amplitude resonant motions predominantly in the surge direction. These motions are caused by slow drift forces resulting primarily from random wave action. Accurate predictions of the damping forces are required in order to design fit for purpose moorings. This paper considers the contribution caused by hydrodynamic damping on an innovative floating production system design that is actively being evaluated by the offshore industry. The design consists of a relatively shallow draught surface piercing monohull attached by short rectangular connectors to a fully submerged lower hull positioned below the water surface. Theoretical methods are developed to predict a lower bound on the hydrodynamic damping contributions caused by fluid interaction with the connectors. The lower bound prediction is of relevance because it provides an upper bound estimate on the large amplitude vessel surge motions and hence the maximum mooring line loads. Comparisons with experimental data are provided for model tests performed on a typical vessel and a deep draught monohull design without connectors.

On the second-order slow drift force spectrum

In this paper, it is shown that the slow drift force spectrum of a floating body, obtained from the exact quadratic transfer function, is flat in the low-frequency range of interest and can be written in the form S F = S F(0) + O( μ 2), where S F(0) can be computed from the known drift force coefficient in harmonic waves and the wave energy spectrum. It is also shown here that a special and normally used form of Newman's approximation for the exact quadratic transfer function has an error of the form [1+ O( μ 2)] at low frequencies.

不規則波中の係留構造物に働く長周期変動波漂流力 : 2次厳正理論の定式化および応用

An exact second-order theory is formulated for predicting the slow drift excitation forces on moored vessels in random seas. It is based upon direct integration of the hydrodynamic pressure on the submerged body surface in conjunction with the consistent perturbation expansion to second order in wave steepness. Green's second identity and Haskind's reciprocal relations are used to derive a formula for the second-order exciting forces due to the second-order waves. This permits the evaluation of the slow drift forces only from the solution to the first-order diffraction problem. As application of the theory, results for the slow drift forces on the semi-submersible are presented, which are evaluated by means of the source-distribution numerical technique. The results based on the present exact theory are compared with the solutions from different simplified approaches. It is concluded that Newman's method using data of mean drift forces in regular waves gives accurate results for the slow drift forces in short to moderate seas, but tends to underestimate the forces in extreme sea states with longer mean wave period.

The statistical distribution of second-order slowly-varying forces and motions

A statistical analysis of slow-drift forces and motions is presented. By extending an approach originally due to Kac and Siegert, it is shown that an explicit, closed-form solution may be given to the problem of determining the probability density function of the slow-drift process. From a practical point of view its derivation is carried out without simplifying assumptions, thus a general solution is obtained.

The Dorada Field Production Risers

Summary This paper outlines the riser analysis methodology for the Dorada field floating production system and identifies several new aspects of production riser design analysis. The analysis considers both the familiar wave-frequency fatigue damage and damage caused by wind-gust-induced low-frequency vessel motion. Pertinent analytical and experimental results are presented and the riser instrumentation system developed to produce those results are described. Introduction The Dorada field is located 12 miles (19.3 km) offshore Spain in the Mediterranean Sea in approximately 310 ft (94.5 m) of water. The field is being produced by a semisubmersible floating production system (FPS) positioned directly over three clustered subsea wells (Fig. 1). positioned directly over three clustered subsea wells (Fig. 1). ENIEPSA is the operator of the field for partners Getty Oil Co. of Spain S.A. and Union Texas Petroleum. The overall project design and operation is described in Ref. 1. This paper is concerned only with the riser design analysis that was performed. The Dorada riser design is unique because it is the first functional installation of individual string production risers. Each riser is tensioned individually to prevent buckling and to allow direct vertical access to the wellbore. Four variations of the individual riser design were investigated to arrive at a riser concept that best satisfied the site-specific design and Operating criteria:concentric-string riser system using a taper-joint end termination,concentric-string riser system using a flex-joint end termination,single-string system with a taper-joint end termination, andsingle-string system with a flex-joint end termination. For reasons of structural design and the prototype level technology then associated with taper joint risers, the latter configuration was selected. Discussions in this paper are limited to the final configuration and include (1) design criteria for the riser, (2) Copyright 1982 Society of Petroleum Engineers of AIME design analysis methodology, including some new considerations for production-riser design, (3) results of the engineering calculations, (4) riser instrumentation program, and (5) preliminary results of field performance program, and (5) preliminary results of field performance verification tests on the risers. The Dorada riser design study has shown the importance of accurate prediction and simulation of the moored-vessel motion under storm conditions. Riser design practice traditionally has considered only mean platform offset resulting from static conditions of winds, platform offset resulting from static conditions of winds, waves, and currents combined with the platform wavefrequency motion. In the present design, the low-frequency platform motions induced by wind gusts and platform motions induced by wind gusts and wave slow-drift forces are shown to have a significant effect on maximum riser stresses and fatigue life. This is because the selected design wind gust spectrum of Davenport had a peak energy at frequencies close to surge-sway platform resonance, and the lower riser stress was strongly dependent on vessel offset. This design study also has shown the importance of considering year-to-year variation in wind and wave climate at the site for proper fatigue design of production risers. This is not usually a concern for fixed platforms because of the longer design life. The riser top tension is an important design factor for the riser. An optimal tension for the riser design can be found from stress and fatigue considerations. This optimal value does not change substantially for the range of annual wind and wave climates that could be experienced. A riser instrumentation project was undertaken to provide the field operators with an on-board monitoring provide the field operators with an on-board monitoring capability and to verify the design analysis work. Preliminary results of this program generally substantiate Preliminary results of this program generally substantiate the analysis work described. Design Criteria The overall riser design strategy was to produce a riser configuration that satisfied operational requirements and minimized production interruption. JPT P. 2947