Second-order Wave Loads Research Articles

An efficient frequency-domain based methodology for the preliminary design of FOWT substructures

An efficient frequency domain numerical tool for the preliminary design of the Floating Offshore Wind (FOW) substructures is developed, and validated against one of the leading state-of-the-art time domain based numerical tools: OpenFAST. It has been proven that the present tool enables to reach to similar conclusions as the state-of-the-art tools with a substantial reduction of the computational effort. This is achieved through two novel methods that obtain the hydrodynamic loads acting on the floating substructures. One estimates the linear hydrodynamic coefficients, and the other predicts the second-order wave loads. When combined with a simplified frequency domain response model, a quick assessment of the dynamics of numerous platform designs can be performed, accelerating the floater preliminary design process. The proposed method has been validated by carrying out a comparative analysis on a semi-submersible platform design space, characterised by the column diameter, the separation between the columns and the platform draft. The response motions have been compared against OpenFAST. Furthermore, the high efficiency of the proposed frequency domain tool makes it suitable to perform several sensitivity analyses that will allow for a better understanding of the dynamics and fine tune the foundations design accordingly from the early stages of design.

Second-order wave loads on a floating bridge of T-type cross section

An analytical model for the complete second-order wave loads on a floating bridge of T-type cross section is established within the framework of potential flow theory. The first-order problem is solved using the matched eigenfunction expansion method (MEEM). Meanwhile, the second-order wave loads are divided into two distinct parts which are computed separately. The first part is dependent on the quadratic products of the first-order velocity potential and its derivative. It has been evaluated through two different ways. One is based on a direct pressure integration, i.e., a near-field method. To ensure a high accuracy of the computation, a local expansion is applied to determine the spatial derivative of the first-order velocity potential at a sharp corner. The other is based on the momentum conservation over a control volume. The effect of the control surface location on the computation has been discussed. In addition, the two proposed methods have been applied to both the time-independent wave-load component as well as the second-harmonic component, respectively. The second part of the complete second-order wave loads is due to the second-order velocity potential. It is evaluated based on an indirect method by introducing an auxiliary potential. Detailed numerical investigation is then conducted. The influence law of the sectional geometric parameters on the second-order wave loads is investigated. The numerical results reveal that the cantilever plate imposes an apparent protection effect on the inner web beam. Such effect gets obviously enhanced as the section net width or section height decreases or as the plate width or draft increases.

Second-order wave loads on floating wind parks with shared mooring

Wave loads on lattices of marine structures, such as wind parks with shared mooring systems, are considered. Modal excitation induced by second-order low-frequency wave loads is derived, leading to modal quadratic transfer functions. The consequence for the modal loads, of applying Newman’s approximation is investigated.

Multivariable design optimization for adaptive resonance of a surface riding wave energy converter

Since the ocean waves feature irregular waves varying over time, a wave energy converter with adaptive resonance, which feasibly changes the natural frequency for different sea states, is considered. To find its optimum design, multi-dimensional parametric optimization is formed in sequence of setting ranges of submerged geometry for hydrodynamic performance, finding design specifications including the generator for maximum resonance peaks, and locating the natural frequency for individual sea states to achieve the adaptive resonance that converts the maximum annual mechanical power for the given geometry. The multivariable design optimization is performed for a kilowatt-scale Surface-Riding Wave Energy Converter, which controls the pitch natural frequency through relocating a mass vertically. The optimized design presents that the adaptive resonance improves the mechanical power conversion up to 11 times compared to the conventional fixed resonance design. Furthermore, the adaptive resonance for diverse wave spectra indicates that the optimum natural frequencies for individual sea states, maximizing the annual mechanical power conversion, do not coincide with the waves’ peak or energy period. The second-order wave loads entails further change of the optimum natural frequency resulting in subsequent 10 times performance improvement for severe sea states with high peak periods.

NEMOH: Open-source boundary element solver for computation of first- and second-order hydrodynamic loads in the frequency domain

NEMOH is developed to solve potential flow problems using the boundary element method for computing wave loads on offshore structures. The solver solves the first-order problem in the frequency domain. An extended module enables computation of the second-order loads on a structure in bi-chromatic bi-directional waves. NEMOH is released as open-source, developed, and distributed under the terms of GNU General Public License (GPLv3). Along with the source code, a user manual is available which facilitates the compilation and execution of the source files. In this new release, NEMOH v3.0 has new features; irregular frequencies removal method, new linear system solvers for enhancing computational efficiency, and a new module for computing the full quadratic transfer function (QTF) of drift forces. Verification cases are shown for a truncated cylinder, a truncated cylinder with a thin heave plate, a spar buoy platform (SOFTWIND), and a semi-submersible platform (OC4). The results are compared with reference data from commercial software, WAMIT, DIODORE, and HYDROSTAR, and the comparison showed that NEMOH v3.0 is accurate and efficient. Program summaryProgram Title: NEMOHCPC Library link to program files:https://doi.org/10.17632/k9v4hjb5xj.1Developer's repository link:https://gitlab.com/lheea/NemohCode Ocean capsule:https://codeocean.com/capsule/9256007Licensing provisions: GPLv3Programming language: FortranExternal libraries and programs: BLAS [1], LAPACK [2]Nature of problem: NEMOH solves the potential flow problems of diffraction and radiation in wave-structure interactions. Typical use is the estimation of the dynamic response of floating structures, e.g. floating offshore wind turbine platforms, or wave-energy converters.Solution method: The linear potential flow problems, diffraction and radiation, are expressed in the boundary integral of the source distribution formulation. The equations are solved in the frequency domain and implemented using the boundary element method with quadrilateral panels. The source distribution on the body panels is obtained by solving the linear system. The hydrodynamic coefficients are computed with the known source distribution. The second-order potential flow problem is not solved directly; the Green formulation is used with an assisting function which is the instantaneous radiation potential, that allows the computation of second-order force for given first-order hydrodynamic quantities.Additional comments including restrictions and unusual features:•The previous version, NEMOH v2.0 [3], was available only for computing first-order hydrodynamic coefficients without the irregular frequency removal method. NEMOH v3.0 has new features, the extended boundary integral method is implemented for removing the irregular frequencies, new linear system solvers are added for enhancing computational efficiency, and a new module is added for computing second-order wave loads. NEMOH v3.0 has better accuracy than v2.0 due to finer interpolation points of the free-surface Green function and a better integration method for constructing the influence coefficients.•For the free-surface piercing bodies problem, it is known that non-unique solutions exist in the boundary integral equation at certain frequencies. In NEMOH, the extended boundary integral equation is applied to remove the irregular frequencies by providing the lid panels on the body waterplane. The second-order loads require the computation of the free-surface forcing terms in the integral forms. These free-surface integrals are essential for the sum-frequency wave loads but may be negligible in the difference-frequency loads. For now, it is suggested not to apply the lid panels when the free-surface integrals are computed.

A second-order slender-body approach for computing wave induced forces with application to a simplified semi-submersible FOWT model

This paper presents a slender-body approximation to evaluate the first- and second-order wave loads acting on a floating structure comprised of slender cylinders. It combines Rainey’s equation, which can be seen as an extension of the inertial part of Morison’s equation to include nonlinear terms, with Pinkster’s formulation for the low-frequency second-order loads on floating bodies. The objective is to obtain expressions that allow the evaluation of second-order wave loads considering the mean body position, so that an Inverse Fast Fourier Transform algorithm can be used to efficiently compute the second-order wave loads in a real sea condition directly in time domain. Similarly to Morison’s equation, this approach is incapable of modeling wave scattering and radiation effects, but this is acceptable as long as the diameters of the cylinders that compose the structure are small in face of the length of the incoming waves. To verify the method, it is applied to the computation of the slow motions of a simplified semi-submersible FOWT model, first under the action of bichromatic waves and then of an irregular sea, and the results are compared with the ones obtained with WAMIT, OpenFAST and experiments.

Methodology for global structural load effect analysis of the semi-submersible hull of floating wind turbines under still water, wind, and wave loads

In designing the support structures of floating wind turbines (FWTs), a key challenge is to determine the load effects (at the cross-sectional load and stress level). This is because FWTs are subjected to complex global, local, static, and dynamic loads in stochastic environmental conditions. Up to now, most of the studies of FWTs have focused on the dynamic motion characteristics of FWTs, while minimal research has touched upon the internal load effects of the support structure. However, a good understanding of the structural load effects is essential since it is the basis for achieving a good design. Motivated by the situation, this study deals with the global load effect analysis for FWT support structures. A semi-submersible hull of a 10-MW FWT is used in the case study. A novel analysis method is employed to obtain the time-domain internal load effects of the floater, which account for the static and dynamic global loads under the still water, wind, and wave loads and associated motions. The investigation of the internal stresses resulting from various global loads under operational and parked conditions and the dynamic behavior of the structural load effects in various environmental conditions are made. The dominating load components for structural responses of the semi-submersible floater and the significant dynamic characteristics under different wind and wave conditions are identified. The dynamic load effects of the floating support structure are investigated by considering the influence of the second-order wave loads, viscous drag loads induced global motions, and wind and wave misalignments. The main results are discussed, and the main findings are summarized. The insights gained provide a basis for improving the design and analysis of FWT support structures.

Hydrodynamic and environmental modelling influence on numerical analysis of an innovative installation method for floating wind

This paper presents a numerical modelling methodology for an innovative installation method of floating wind turbines. The study analyses the influence of hydrodynamic and environmental modelling factors on the dynamics of a multibody system consisting of a catamaran with three wind turbines and a spar foundation with a mooring system. The research focuses on features such as viscous drag on the spar, hydrodynamic interaction between floating bodies, long- and short-crested waves, first- and second-order wave loads, wave directions, and wave peak periods. The study found that hydrodynamic modelling factors had a significant effect on the horizontal motion of the installation system but a negligible effect on vertical motion and mooring system tension. Therefore, it is recommended to consider viscous drag forces, hydrodynamic interaction, and first- and second-order wave forces when developing mechanical damping and control systems to reduce horizontal motion. The study also suggests using both long- and short-crested waves for numerical analysis when estimating the weather window for installation operability analysis. Overall, this study contributes to the development of an efficient and practical installation method for floating wind turbines by analysing the impact of hydrodynamic and environmental factors on the dynamics of the multibody system.

Accelerated second-order hydrodynamic load calculation on semi-submersible floaters

A rapid method for calculation of second-order hydrodynamic wave loads on semi-submersible platforms is developed and validated against radiation–diffraction theory. The method is based on slender-body theory and builds on modal truncation of the quadratic transfer function (QTF). The semi-submersible floater is split into individual members and the existing theory for vertical cylindrical columns is extended to include the heave force. Further expressions for the surge, heave and pitch load on the horizontal pontoons are derived and implemented. The accuracy of the method is assessed by comparison to radiation–diffraction results using the Pinkster approximation. We find that the slender-body approximation for the column surge force is most accurate for small values of the diameter-to-draft ratio. For the three sea states considered, this error is below 10% for diameter-to-draft ratios less than 0.2.Error analysis is provided for the column heave and pitch and the pontoon loads. For all members, application of 128 modes in the QTF approximation is found sufficient to accurately represent the full slender-body QTF solution.Next, the first- and second-order loads on the full floater under different sea state conditions are compared to radiation–diffraction theory. With 128 modes, the second-order loads are obtained 2500 times faster than with conventional approaches with error levels of 22% for surge, 10% for pitch and zero error for heave. The surge error is discussed and linked to the small draft of the columns. The numerical efficiency of the method allows the consideration of second-order loads in the first stages of the design and optimisation of semi-submersible floaters.

Time-domain simulation of sum-frequency hydrodynamic performance of a TLP-type floating wind turbine in multidirectional seas

Previous studies (Ren et al., 2022) by the authors have confirmed that the second-order diffracted wave loads are very sensitive to the wave directional spreading of the so-called storm-swell mixed seas where the storm-driven local seas combined with long-period swells propagating from different angles. In this paper, particular attention is paid to estimate the sum-frequency hydrodynamic forces and motion responses of a TLP-type floating wind turbine (FWT) in such complex sea states. A time-domain potential flow model is developed for the second-order interaction between the multidirectional irregular waves and moored structures. The boundary value problems for the scattered potential are solved by a higher-order boundary element method (HOBEM). The fourth-order Adams–Bashforth–Moulton method is used to update the wave surface and the Newmark method combined with the Newton–Raphson iteration scheme is adopted to solve the body motion equations.For validation, a freely floating hemisphere in unidirectional bichromatic waves is investigated and good agreement is found by comparing with Kim and Yue's frequency-domain results. Numerical tests are conducted on the TLP-type FWT with different combinations of incident angles and spreading factors of the storm-swell mixed seas. The effects of the wave headings and directional spreading on the sum-frequency hydrodynamic response are discussed. It is noted that when the swells approach the storm seas from large relative angles, the sum-frequency vertical response of the FWT can be up to seven times greater than that in the collinear mixed seas. In addition, the present model can extend the rotor-floater-tether coupled dynamic simulator of FWT to more realistic seas such as storm-swell mixed seas.

Nonlinear Low-Frequency Response of a Floating Offshore Wind Turbine Integrated With a Steel Fish Farming Cage

In this article, the effects of Morison drag force and the second-order hydrodynamics on a state-of-the-art floating system integrating a floating offshore wind turbine with a steel fish farming cage (FOWT-SFFC) are studied. To numerically solve the second-order hydrodynamic problem with ease, a simplified structure is adopted. Convergence study is carried out on the full difference-frequency quadratic transfer function (QTF). The middle-field method is recommended to be used in the calculation of QTF. For the aero-hydro-servo-elastic simulations of FOWT-SFFC, the time-domain solver OrcaFlex is used. The effects of the Morison drag force and second-order hydrodynamics on the dynamic responses under a variety of conditions are discussed. The comparison between the results with and without Morison drag force shows that Morison drag force has twofold effects on the low-frequency responses, making the excitation and damping level both larger. The results obtained by including first-order wave loads only and involving both first-order and second-order wave loads are also compared. The comparison reveals that the low-frequency contents of the dynamic responses, particularly heave and pitch, can be boosted when the second-order hydrodynamic forces are included. In contrast to the full QTF method, the known Newman's approximation leads to underprediction of the low-frequency responses of FOWT-SFFC.

The Effect of the Second-order Difference-frequency Wave Force on the Motions of an Underwater Vehicle Near the Surface

_ When an underwater vehicle performs tasks, such as power recharge, air exchange, deployment, and retrieval near the surface, the low-frequency suction force and pitch moment will interfere with its motion. This paper presents a study on the effect of second-order difference-frequency wave force on the motions of the DARPA SUBOFF model at various submergence depths and environmental conditions. Ignoring the second-order wave force component induced by the second-order difference-frequency force may underestimate the second-order effect in irregular waves in the time domain. Comparisons were made between Newman’s approximation, which sets the off-diagonal difference-frequency quadratic transfer function (QTF) value to the average over the corresponding diagonal values, and the full QTFs based on the Pinkster approximation in the frequency and time domains. The QTFs-based prediction is significantly larger values than Newman’s approximation. Time-domain simulations were conducted, to investigate the effect of the second-order difference-frequency wave loads on motion responses at different nondimensional submergence depths and various sea conditions. The results of the computation indicate that ignoring the second-order difference-frequency wave force may underestimate the motion and dynamic responses of underwater vehicles; in addition, the pitch and heave motion responses are dominated by the low-frequency response. Introduction When an underwater vehicle travels close to the water surface, it experiences an upward force and pitch moment, known as surface suction. This can significantly affect the underwater vehicle’s behavior when power recharge, air exchange, deployment, and retrieval are incorporated into the underwater vehicle simulations. Veillon et al. (1996) noted that for a 10,000-ton submarine at a depth of 50 m, the surface suction due to waves will require around 20–30 tons of compensation to stop the submarine from surfacing. In addition, Hirom (1974) indicated that in waves, the fluctuating forces on a submarine can be on the order of 1000 kN, with a steady component of approximately 10 kN. In calm water, suction occurs owing to a higher flow velocity and a lower pressure above an underwater vehicle when sailing near the surface, and the wave pattern generated by the underwater vehicle complicates the surface effect. The longitudinal position of the center of pressure is after the amidships, which induces the pitch moment. In the presence of waves, the first-order wave force, which is the oscillatory force at the wave frequency, acts on the underwater vehicle. In addition, waves and model motions induce low-frequency suction force and pitch moment. Using any internal compensation and control surfaces to offset the induced suction force and pitch moment requires a good and early understanding of the magnitude of these forces, for designing sufficient-capacity compensation tanks (Crossland 2013). Therefore, the surface suction and pitch moment effects are essential components of the hydrodynamic characteristics of underwater vehicles sailing near the water surface.

Coupled dynamic response analysis of multi-column floating offshore wind turbine with low center of gravity

To realize the application of the floating offshore wind turbine (FOWT) from deep to relatively shallow waters, a new concept of multi-column floating wind turbine platform with low center of gravity (CG) is designed and validated. The multi-column low CG platform is designed to support a 6MW wind turbine class and operated at a water depth of 50m in the South China Sea. The frequency domain software WADAM and time domain software NREL-FAST are used to simulate coupled dynamic responses of the floating wind turbine system with second-order wave loads considering. The dynamic behaviors of multi-column low CG FOWT system under normal operation and parked conditions are presented. The influence of second-order wave force on the motion responses of the multi-column platform, fore-aft force and moment of the tower base and mooring force are researched respectively. The results demonstrate that the coupled dynamic responses at rated operating condition and extreme condition meet the normal operating requirements and extreme survival requirements of FOWT system in the shallow water (50m) of South China Sea. In addition, it is found that, the wave frequency response gradually replaces the second-order low frequency response as the main influencing factor of the coupled dynamic response of the FOWT system with the increasing severity of the sea states. However, in general, the magnitude of second-order low frequency response increases with the increasing severity of the design load case. Thus, in the subsequent design of the shallow water FOWT system, the second-order effects should be paid enough attention.

On the complementarity of the slender-body and Newman’s approximations for difference-frequency second-order wave loads on slender cylinders

As reported in the literature, Newman’s and the slender-body approximations for second-order wave loads (the latter often referred to as Rainey’s equation) present an interesting complementarity for the case of a bottom mounted vertical cylinder, indicating that each one captures different physical aspects of the problem. In light of that result, the present work aims at analyzing this complementarity by inspecting the different components that constitute the second-order wave loads, including the ones due to body motions, and by relating them to the incident and diffracted waves. This is done by analyzing the case of a single surface piercing cylinder under the action of long-crested bichromatic waves, first considered to be bottom mounted and then in floating condition. It is also shown that the second-order terms from Rainey’s formulation are indeed relevant, reminding one that the common practice of analyzing second-order loads by simply applying Morison’s equation with second-order wave kinematics is not strictly correct.In order to include the effects of body motions, Rainey’s equation, which can be seen as an extension of the inertial part of Morison’s equation to include nonlinear terms, is combined with Pinkster’s approach for the low-frequency second-order loads on floating bodies. This combination is made in order to allow the evaluation of the forces considering the mean body position, in opposition to the original approach that considers the instantaneous body position, allowing an IFFT algorithm to efficiently compute second-order wave loads in a real sea condition directly in time domain. As a drawback of the slender-body approximation, end effects due to the extremities of the cylinder and effects due to wave scattering and radiation are lost, as is the case when using Morison’s equation to evaluate first-order loads, and the question is to what extent they can be neglected when dealing with second-order wave loads.

Hydrodynamic Responses of a Barge-Type Floating Offshore Wind Turbine Integrated with an Aquaculture Cage

The dynamic responses of a new structure combining a barge-type floating offshore wind turbine and an aquaculture cage is investigated numerically. First, a 5 MW barge-type floating offshore wind turbine with an aquaculture cage (FOWT-AC) is designed and the numerical model is established in ANSYS-AQWA. The numerical model of the barge-type FOWT-AC is then checked, and the natural periods of the six degrees of freedom motion satisfy the recommendations of the DNV specification. Based on the reasonable model, the comparison study of dynamic responses between the barge-type FOWT-AC and FOWT under the environmental conditions of the South China Sea is carried out, and it is observed that the FOWT-AC produces a basically lower standard deviation of the motion responses. To investigate the new structure of the barge-type FOWT-AC deeply, the analyses of second-order hydrodynamic response, typical environmental conditions and the mooring line breaking scenario are carried out. The simulation results show that the second-order wave loads increase the dynamic response of the barge-type FOWT-AC slightly unless it causes resonance for the structure. In addition, the motion responses of the floating structures increase significantly when the currents are applied, especially when the aquaculture cage is integrated into the barge-type FOWT. When one of the mooring lines connected to the offshore or onshore side of the platform breaks, the presence of the aquaculture cage results in a smaller standard deviation in the motion responses of the coupled structure, which means that the barge-type FOWT-AC structure is more stable.

Frequency domain modeling of long-span sea-crossing bridge under stochastic wind and waves

In this study, a frequency domain modeling framework that assembles aero- and hydro-dynamic approaches to characterize the structural motions of a long-span sea-crossing bridge under stochastic wind and waves is proposed as an efficient alternative for the conventional time-consuming time domain analysis. The improved quasi-steady buffeting model is employed to investigate the fluctuating wind actions on structural components and the aero-elastic effect of bridge decks. Potential flow theory associated with constant boundary element method is applied to calculate the linear as well as quadratic hydrodynamic transfer functions and both first- and second-order wave loads are considered and coupled in the modeling framework. The proposed methodology is well validated using a benchwork experiment of a flexible cylinder subjected to wind and waves. The dynamic performance of a long-span sea-crossing bridge under extreme wind and wave conditions is modeled using the proposed framework. The effects of wind and waves, different mode combinations, directionality and nonlinear wave loads on global responses are discussed. In the proposed approach, a combination of only a few main modes is necessary to yield plausible displacement responses of bridge deck, while more modes are required to obtain converged internal force responses.

Second-order difference-frequency wave loads on a floating body in uniform current in the frequency domain

ABSTRACT In this study, a formulation for the second-order difference-frequency wave load in the presence of steady uniform current (or forward speed) is presented, and a practical approximate approach is proposed. A potential flow-based solution is formulated to include terms up to the second-order in wave slope and first-order in current speed. In the uniform-flow approximation, the body disturbed and ship-generated steady flows are neglected, assuming slender bodies and low uniform flow speed. The free-surface integral is not included in evaluating the difference-frequency force quadratic transfer function (QTF) considering its relatively unimportant contribution compared to other terms, which significantly reduces the cost of the computational implementation. The present numerical results compare well against published experimental and numerical result. The importance of directly calculating off-diagonal terms of the QTF in the presence of uniform flow is investigated by comparing the present model with other existing approximation methods and with cases without uniform flow.

Second-order monopile wave loads at linear cost

A method to compute the second-order free surface elevation, depth integrated force and mud line moment for a slender circular vertical cylinder is presented. The method is valid for unidirectional irregular waves and includes inertia loads and viscous loads.We first derive the linear transfer functions for free surface elevation, depth-integrated force and moment from the complex Fourier amplitudes of the velocity potential. Next, the second-order contributions are expressed through closed form quadratic transfer functions, which are further diagonalized through eigen decomposition. Hereby the second-order contributions can be computed as products of pseudo time series calculated by FFT, with the eigenvectors acting as transfer functions on the linear Fourier amplitudes.For a sample 3-hour sea state, we find that eight eigen vectors are sufficient to achieve an accuracy of 1% for the maximum peak value of force and moment and 1.3% for free surface elevation, relative to the standard deviation of each signal. These results are obtained 2500 faster than with the conventional approach and we demonstrate that the computational effort of the new method scales like O(NlogN), similar to linear wave loads, where N is the number of frequencies. For the eight mode approximation, the error bound of 1% for loads and 4% for free surface elevation are found to hold across various values of the normalized peak wave number from shallow to deep water. The accuracy is adjustable through the number of modes and is found to be independent of the time series length. The methods potential in practical design is discussed.

Experimental and numerical studies on the low-frequency responses of a spar-type floating offshore wind turbine

Accurate modeling of low-frequency (LF) wave loads and responses is important but challenging in the design of spar-type floating offshore wind turbines (FOWTs), especially for shallow and intermediate water depths. A 6 MW spar-type FOWT system designed for a water depth of 100 m is investigated both experimentally and numerically to study the nonlinear hydrodynamics responses in waves. The second-order LF wave loads are modeled in the time-domain tool FAST using two different methods based on full Quadratic Transfer Functions (QTF) and Newman's approximation, respectively. To account for viscous effects in calculating the LF responses, linear and quadratic damping models calibrated from model tests are comparatively studied and the latter is found to be more suitable and easier to implement in the time-domain simulations. It is demonstrated that it is crucial to include the 2nd order difference-frequency wave excitation in the analysis of motions in both horizontal and vertical planes. With the considered water depth, a full QTF method is seen to greatly improve the prediction of LF responses compared with Newman's approximation. In general, it is observed that the wave-frequency (WF) responses are higher in amplitude than the LF responses for surge and heave, while the LF pitch motions are higher than the corresponding WF contribution.

Effects of second-order hydrodynamics on an ultra-large semi-submersible floating offshore wind turbine

Second-order wave loads on floating offshore wind turbine (FOWT) may excite severe resonance at the eigenfrequencies of the floating system and cause fatigue damage. The hydrodynamic coefficients including first- and second-order wave force transfer functions are calculated, and fully coupled time-domain simulation by FAST is conducted for selected environmental conditions. Each load case is simulated without second-order loads, and with difference-frequency full quadratic transfer functions (QTFs), sum-frequency full QTFs, and complete second-order solution. The effect of second-order difference- and sum-frequency wave loads on the dynamic behaviors of the 10 MW semi-submersible FOWT is discussed. Subsequently, the effect of second-order wave loads on the structural fatigue behavior of the 10 MW and 5 MW semi-submersible FOWTs is investigated and compared by computing ultimate and damage-equivalent loads (DELs). The results show that ignoring second-order difference-frequency wave loads may underestimate the low-frequency responses, and second-order sum-frequency wave loads significantly affect the structural dynamics of the 10 MW FOWT. In addition, the effect of second-order wave loads on the fatigue damage of the 5 MW and 10 MW semi-submersible FOWTs are significantly different.