The hydrodynamic response of a floating offshore wind turbine (FOWT) in extreme environments presents a challenge for Computational Fluid Dynamics (CFD) codes. However, the use of high-fidelity codes is expanding to achieve greater accuracy in numerical simulations. This study compares experimental data from the 2018 SAIPEM campaign at the Hydrodynamic and Ocean Engineering tank of Centrale Nantes (France) using the Hexafloat concept with numerical simulations with different approaches: mid-fidelity code with DeeplinesWind and a high-fidelity code. The CFD numerical model couples a nonlinear potential flow solver for the incident wave (HOS), a lumped-mass mooring dynamics model (Moordyn), and a CFD code named foamStar, based on OpenFOAM and developed by Centrale Nantes and Bureau Veritas. First, the experimental setup will be presented. Then, the different numerical models used for comparison will be detailed. This includes the CFD solver for the Navier-Stokes equations, the dedicated nonlinear wave solver, the mooring model, and the mid-fidelity approaches with Deeplines software. Finally, a test case with an irregular wave is presented (significant wave height Hs=14m, peak period Tp=16s). A detailed analysis of the results will be presented for the motion and acceleration of the platform (surge, heave, and pitch) and the fairleads tension. These quantities are used to evaluate the accuracy of the numerical model against the physical test.

This paper summarises the work conducted within the 1st FOWT (Floating Offshore Wind Turbine) Comparative Study organised by the EPSRC (UK) ‘Extreme loading on FOWTs under complex environmental conditions’ and ‘Collaborative computational project on wave structure interaction (CCP-WSI)’ projects. The hydrodynamic response of a FOWT support structure is simulated with a range of numerical models based on potential theory, Morison equation, Navier-Stokes solvers and hybrid methods coupling different flow solvers. A series of load cases including the static equilibrium tests, free decay tests, operational and extreme focused wave cases are considered for the UMaine VolturnUS-S semi-submersible platform, and the results from 17 contributions are analysed and compared with each other and against the experimental data from a 1:70 scale model test performed in the COAST Laboratory Ocean Basin at the University of Plymouth. It is shown that most numerical models can predict similar results for the heave response, but significant discrepancies exist in the prediction of the surge and pitch responses as well as the mooring line loads. For the extreme focused wave case, while both Navier–Stokes and potential flow base models tend to produce larger errors in terms of the root mean squared error than the operational focused wave case, the Navier-Stokes based models generally perform better. Given the fact that variations in the solutions (sometimes large) also present in the results based the same or similar numerical models, e.g., OpenFOAM, the study highlights uncertainties in setting up a numerical model for complex wave structure interaction simulations such as those involving a FOWT and therefore the importance of proper code validation and verification studies.

A time-domain potential-flow solver is developed to study the linearized ship-wave interaction problem with forward speed. A Rankine panel method is implemented to model both a hull advancing in calm water and in waves. The former case is important in evaluating the wave-making resistance of hulls while the latter gives the hydrodynamic loads and motion responses for ships interacting with ocean waves. A constant panel method with an indirect approach is adopted to obtain a robust and efficient simulation tool. The problem is formulated such that no connectivity information on the mesh is necessary, allowing the use of multi-resolution meshes that reduce the computational costs in a simple and efficient way. The calm water problem is validated on a Wigley hull. A convergence analysis is conducted, investigating both the wave resistance and the wave profile. For the unsteady seakeeping problem, tests with an impulse wave are implemented to reduce simulation times. The radiation and diffraction loads, and the motion responses for the RIOS bulk carrier in head waves are presented. In addition, the S175 containership is studied in head and in following seas, showing the method is capable of predicting the hull response in both sea conditions with forward speed. A final test in irregular waves demonstrates the ability of the solver in simulating realistic sea conditions.

Potential flow theory-based solvers are commonly used in ocean engineering to investigate the interactions between ocean waves and floating bodies. Depending on assumptions, several methods have been proposed. Among them, the Weak-Scatterer method is an interesting trade-off in the sense that this approach is not limited in theory by the small wave amplitudes and small body motions assumptions of linear methods. Moreover, this approach is in practice more stable than the fully non-linear methods. An implementation of the Weak-Scatterer method is the WS-CN code (Letournel, 2015; Chauvigné, 2016; Wuillaume, 2019).The computational time of the WS-CN code which is considered in the present study is relatively long for engineering purposes. In order to reduce it, the present paper presents an implementation of the Parareal method in the WS-CN code. The Parareal method is an algorithm for parallelizing a simulation in time that can accelerate the complete simulation (Lions, 2001) . This is a key difference in comparison to other acceleration techniques which have been studied in the literature (e.g. the Fast Multipole Method (FMM), the precorrected Fast Fourier Transform (pFFT) method, … ). To the authors’ knowledge, the present study is the first to couple the Parareal method to a potential flow theory-based wave-structure interaction solver. It is shown that the method can significantly reduce the computational time for small wave steepness, but that the performance decreases rapidly with increasing steepness.

An efficient methodology for simulating nonlinear irregular waves in a Computational Fluid Dynamics (CFD) solver is proposed. The High Order Spectral (HOS) method is used to generate nonlinear irregular waves in an open ocean and a numerical wave tank. The inverse Fast Fourier Transforms (FFTs) and multi-dimensional interpolation from the HOS simulation results are used for the efficient reconstruction of nonlinear waves in the CFD solver. The proposed procedure is published as an open-source project called Grid2Grid, which is developed to interface with a generic CFD solver. It provides the function Application Programming Interface (API), which can communicate with different programming languages. Extreme wave events were used to validate the proposed procedure. The predicted wave breaking events are reported both in OpenFOAM CFD and HOS simulations, and the wave elevations of CFD during simulations show good agreement with experiments and with HOS simulation.

This article presents a wave energy converter exploiting the pitch of a floating body moored to the seabed. When the floating body tilts under the action of an incoming wave, a movable mass, placed inside the hull, moves relative to the floating body and actuates an electrical generator. Most devices of this type have the drawback that the moving mass sequentially accelerates, slows down, stops and then repeats this sequence in the opposite direction. This generates an irregular instantaneous power output. The proposed concept consists of (at least) two eccentric bodies having the same mass and revolving atopposite speeds around a vertical axis. In this « counterrotating » solution, the oscillations of the float result in the continuous circular motion of the direct-drive PTO, though the global centre of gravity of the eccentric bodies moves back-and-forth along the symmetry axis of the device. If the eccentric bodies move at constant speed, their global centre of gravity moves in a sinusoidal manner along its pathway. The present study aims to investigate, through modelling and numerical simulations, the influence of the main parameters, such as the phase and the PTO mass moment, on the performance of a counter-rotating device exposed to waves of various heights and various wavelengths. Optimal phase and mass moment are determined numerically. The resulting output power is close to the theoretical maximum power that can be harvested by the floating body.

An alternative expression of the time domain free surface Green's function is proposed. Its source and image source contribution satisfies the homogeneous Neumann condition on the mean free surface, therefore it can be useful for the boundary element method based on the double-body flow linearization. Furthermore, it is proved that it is also the solution of Clement's 4th order Ordinary Differential Equation (Clement, 1998). The Frobenius method with time step movement proposed by Chuang et al. (2007) is adopted for accurate and efficient evaluation.

Optimizing the production of wave energy converters using Model Predictive Control (MPC) requires a real-time, deterministic prediction of the waves arriving at the device. This study presents a new method for deterministic sea wave prediction, using the horizontal velocity profile over the water column as a boundary condition for a dedicated nonlinear wave model. However, direct measurement of the horizontal velocity component over the whole vertical column is hardly achievable at sea. A method to reconstruct this profile from measurement devices currently at use, such as ADCPs, is thus presented and evaluated. The performance of the prediction method itself is then tested using synthetic numerical data. First, the reconstruction of the horizontal velocity profile as a boundary condition is evaluated. Then, the whole prediction procedure is assessed. In both these stages, the simulations are based on synthetic numerical data and the outcomes are compared with numerical reference solutions. The results show that the method is promising enough to justify further investigation through wave tank experiments.

This study aims at the experimental investigation of wave-induced motions and loads of a containership model without forward speed in -120 degree oblique regular waves to study the influence of the wave steepness and provide reference data for future benchmark studies. A mooring system with 4 horizontally arranged spring lines was used to maintain the heading angle of a 1/65 scaled 9-segmented model designed to be as rigid as possible. Focuses were on studying the nonlinear effects due to the wave steepness on the vertical bending moment (VBM) and horizontal bending moment (HBM) near amidships, and 6-DOF motions at the center of gravity (COG) of the model. Several wave series that are distinguished by wave steepness were considered in the experiment accordingly. Each series consists of waves with various periods that were intended to cover the peak of the wave bending moment transfer functions. Through this, the nonlinear wave effects on the responses of the rigid body at various periods were determined. It was confirmed that the steeper wave contributes to the increase in the higher-order harmonic components including slamming events in the bending moments measured. The change in the characteristics of the wave bending moments according to the change in wave steepness was found to be very different from the linear response. A detailed discussion was made on the influence of the mooring system on the asymmetric horizontal bending moment (HBM) and the change in the average yaw motion. Experiments with and without a mooring system under the same wave condition were conducted, and the effect of the mooring system was identified. It was qualitatively confirmed that the mooring system's restoring moment correlates with the asymmetric HBM and average yaw movement change.

Extreme waves can be modelled in a numerical wave tank (NWT) as a focusing wave in order to generate events that are crucial for designing any offshore structures. The focused wave generation implemented in the completely nonlinear potential solver Higher Order Spectral method (HOS-NWT) with the time-reversal technique was used in the present work. The OpenFOAM based solvers foamStar and foamStarSWENSE which use the domain decomposition and the functional decomposition approach, respectively, were used to couple with a HOS-NWT to perform the focusing wave interaction with the structure (in this case, a cylinder). The incident waves from HOS-NWT are blended into a foamStar and foamStarSWENSE subdomain, where the waves will propagate and interact with the structure within their domain. In the SWENSE methodology, the total field in the computational domain is divided into the incident field and a complementary field. foamStar solves for the total flow fields, and foamStarSWENSE solves for the complementary (total minus incident) flow fields. The Volume of Fluid (VoF) method was selected to capture the interface. 2D parametric studies for focused wave generation were carried out with both solvers, and 3D wave interactions for different mesh types (coarse, medium, and fine) were investigated to understand the convergence for such transient type problems. For verification, the case’s uncertainty was quantified using the Richardson extrapolation approach, and validation was then done by comparing the results to the experiment. The computational efficiency of the two coupling techniques was also compared, and recommendations for solver improvements are made. In general, when solving the problem of wave generation and propagation in 2D and 3D conditions, foamStarSWENSE surpassed foamStar in accuracy. On the other hand, when the simulation included a structure in the domain, the accuracy of the solution in foamStar and foamStarSWENSE was nearly the same, but the foamStar performed better in terms of computational cost. Overall, both coupling approaches generate a realistic depiction of focused wave interaction and force over the cylinder at a minimum computational cost.

Extreme waves endanger offshore structures under severe environmental conditions. These large and steep waves are highly nonlinear, which can cause high-intensity and short-duration impact forces. It is vital to understand the impact created by such extreme events over any structure. The objective is to investigate wave impact forces on a vertical surface piercing cylinder subjected to breaking waves. The numerical simulation is carried out with a hybrid coupled solver named foamStar. It couples a High-Order Spectral (HOS) based nonlinear potential model and an OpenFOAM based CFD model.The HOS model describes accurately in a fully nonlinear potential flow framework the focused breaking wave without the structure. The CFD model is based on the incompressible Reynolds-averaged Navier–Stokes equations and the volume of fluid for the free surface. The coupled model is a CFD based numerical wave tank. First, the focused wave onset of breaking is validated in HOS-NWT and foamStar, and then its interaction with the cylinder is addressed. The experimental results used in this paper correspond to the experiments performed in Ludwig-Franzius-Institute, Germany[1]. The experimentally measured main wave crest of the breaking focused wave group with its total forces and pressure over a cylinder is fairly well captured in the numerical simulation. Further, the evolution of focused breaking waves along the tank and their characteristics were examined. An overall good degree of agreement is reported, which denotes that the model can be a helpful tool to evaluate breaking wave forces on structures.

This paper presents a comparative study of long-time irregular waves and equivalent design waves (EDW) in terms of geometric similarity and probability of exceedance (POE) distribution of the wave crest. For a proper comparison between the two wave types, the same nonlinear model was applied in the wave generation by application of the Higher-Order Spectral-Numerical Wave Tank (HOS-NWT), a fully nonlinear propagation solver.Numerical and experimental Monte-Carlo results were obtained through a number of realizations of a given sea state, and results were used as a reference for the EDW results.The experimental measurements and numerical simulations for a given sea state were analyzed and compared in terms of the wave spectrum estimation and the POE distribution of wave crests. The agreement between experimental and numerical results in wave quality seemed sufficient for it to be used as a reference for EDW cases. The First-Order Reliability Method (FORM) approach was applied in the calculation of EDW. The geometrical similarity between the measured EDW wave signal and the corresponding irregular wave signals measured in a given sea state was reviewed. It confirmed that the FORM-based EDW generates a comparable wave profile. In the statistical analysis, however, the results showed that for some EDW cases in relatively severe sea states, the POE estimates by the FORM method appeared to have conservative values compared to the Monte-Carlo reference POE distribution, whereas for the EDW cases in moderate sea states, the estimated POEs were in very good agreement with the empirical wave crest POE distribution of a given sea state.

The coupled (Potential theory and Navier-Stokes) solver is applied to simulate the interaction of sea waves with substructure of floating offshore wind turbines (FOWT) platform, notably similar to the OC3 Hywind SPAR structure. The intention is to develop a numerical tool that allows the study of the survivability of floating structures in extreme sea states. In this study, the moorings are modeled in two ways. One is by considering the mooring lines as a linear spring with defined spring stiffness, and another is by coupling the solver (foamStar) with a lumped-mass mooring dynamics model (MoorDyn). MoorDyn represents mooring line behavior subject to axial elasticity, hydrodynamic forces, and vertical contact forces with the seabed. The coupled model has been validated against the experiments carried out as part of the SOFTWIND project. The numerical model results of free surface elevation, floating body motions and mooring tensions are compared with the experiments. For wave cases with mild and moderate amplitudes, mooring in the form of a stiffness matrix is sufficient. However, dynamic mooring simulation (MoorDyn) is required for the extreme sea state conditions.

This paper proposes an efficient potential and viscous flow decomposition method for wave-structure interaction simulation with single-phase wave models and two-phase Computational Fluid Dynamics (CFD) solvers. The potential part - represents the incident waves - is solved with spectral wave models; the viscous part - represents the complementary perturbation on the incident waves - is solved with the CFD solver. The decomposition strategy is called Spectral Wave Explicit Navier-Stokes Equations (SWENSE), originally proposed for single-phase CFD solvers ( Ferrant et al., 2003). Firstly, this paper presents a new two-phase SWENS Equations with interface capturing technique. To achieve this single-phase and two-phase decomposition, the incident fields are extended in the air with a density-weighted pressure. Secondly, an accurate and efficient interpolation method is proposed to transfer High Order Spectral (HOS) wave model's result on CFD mesh, which reduces drastically the divergence error of the interpolated velocity. Implemented within OpenFOAM, these methods are tested by three verification, validation, and application cases, considering incident wave propagation, high-order loads on a vertical cylinder in regular waves, and a Catenary Anchor Leg Mooring buoy in both regular and irregular waves. Speed-ups between 1.7 and 4.2 are achieved. The wave models and the interpolation method are released open-source to the public.

This paper presents the comparative study carried out for focused waves interaction with the fixed cylinder in ISOPE 2020. The paper discusses qualitative and quantitative comparison between 20 different numerical solvers from various universities across the world for a fixed cylinder. The moving cylinder cases are reported in the companion paper as Part B. The numerical solvers presented in this paper are recent state of the art in the field, mostly developed in-house by various academic institutes. Majority of the participants used hybrid modeling, i.e. a combination of potential flow and Navier-Stokes solvers. The qualitative comparison based on the wave probe and pressure probe time histories and spectral components between laminar, turbulent and potential flow solvers are presented in this paper. Furthermore, the quantitative error analysis based on the overall relative error in peak and phase shift in the wave probe and pressure probe of all the 20 different solvers are reported. The quantitative error with respect to different spectral component energy level (i.e., in primary, sub and super harmonic region) capturing capability are reported. Thus, the paper discusses about maximum, minimum and median relative error present in the recent solvers for application to industrial problems rather than attempting to find the best solver. Further, recommendations are drawn based on the analysis.

A consistent frame for the numerical simulation of lowering operations is investigated in this paper from a new wave-structure coupling. The mechanical modeling is based on the Composite-Rigid-Body Algorithm, which is able to simulate the nonlinear dynamics of multibody systems. The hydrodynamic model is based on the weak-scatterer approach, which allows the computation of unsteady hydrodynamic loads without being limited by the classical hypotheses of the linear potential flow theory. The coupling of these two models leads to the numerical simulation of articulated multibody systems with large relative motions in waves. The coupling equation is derived in this paper. This new numerical modeling is compared to the classical linear potential flow theory in the case of a lowering operation with a payload in the water. The impact of the lowering velocity is studied. Results show that this new model matches the classical approach for small lowering velocities but as soon as nonlinearities arise, differences between the two models appear.

This paper examines the hydroelastic response of a monopile structure, supporting an offshore wind turbine. A new numerical simulation tool is presented, coupling a nonlinear potential flow solver to a structural model based on modal superposition. The hydrodynamic solver is based on the Weak-Scatterer (WS) approach and assumes small perturbations of the incident flow. A finite element method (FEM) solver is used to compute the modal parameters, which are then superposed to compute the dynamics of the system in time domain. Small deformations are assumed in the coupling. The two theories are tightly coupled in time domain. The theory of the coupling is fully described in the paper. The new coupled solver WS_CN-FEM is then applied to the case of a large diameter monopile. Results are compared to simulations using the Morison equation to compute the hydrodynamic loads and a beam element FEM model to compute the response of the structure and to experimental measurements made on a monopile-based offshore wind turbine model. The physical model has Froude-scaled geometry and natural frequencies, which allows an accurate validation of the hydroelastic numerical models including realistic flexible modes of the structure and wave–structure interaction. The results of WS_CN-FEM show a good agreement with the experimental measurements, and in particular on the first and second mudline bending moments' harmonics in a series of regular waves of various wave steepness.