Nonlinear Wave Loads Research Articles

Nonlinear wave loads on an offshore oscillating-water-column wave energy converter array

This paper studies the nonlinear wave loads on a stationary platform that consists of four cylindrical Oscillating Water Column (OWC) Wave Energy Converters (WECs). The nonlinear wave action on the quad-OWC platform was simulated using a 2nd-order time-domain Higher-Order Boundary Element Method (HOBEM). A carefully instrumented experiment was carried out to validate HOBEM simulations. A circular orifice was introduced to model the nonlinear Power Take-Off (PTO) system on the ceiling of the OWC chamber. Subsequently, the sensitivities of the nonlinear wave loads to the incident wave direction and array spacing were investigated. The optimum angle of wave incidence was found to be π/4, i.e., when the quad-OWC platform is diagonally aligned with the incoming waves. A 2nd-order sloshing resonant mode was found inside each chamber of the OWC array, which leads to an increase of the wave loads. A good selection of the column and row spacing contributes to the reduced wave forces on both the front and rear OWC devices. The directions of the wave loads on the front device were analyzed. The rotational-angle peaks of the wave force and moment were always observed at high frequencies.

Framework for reconstructing wave loads on a floating cylinder using monitored data of structural motion and wave elevation

This study develops a framework for reconstructing the wave loads on a floating cylinder by utilising the monitored data of wave elevation and structural motions, which involve surge, sway, roll, and pitch motions. The proposed method can be applied to perform wave load monitoring and data collection for offshore structures in a stochastic wave field. The derivation of the wave load reconstruction based on the potential flow theory is presented in detail. The linear reconstruction method (as the basis of the proposed method) is first established to simplify the reconstruction process. A nonlinear reconstruction method considering the second-order wave effects is introduced to improve the reconstruction accuracy for nonlinear wave loads. The concept of wave load reconstruction on a complex structure is also addressed. A case analysis is performed on a floating circular cylinder under three conditions. When the structural motions are pure translational motions or pure rotational motions, the wave loads on the cylinder can be reconstructed accurately with the transfer functions ατ,n and βτ,n. When the structural motions consist of both translational and rotational motions, the transfer functions are dependent on the structural motion pattern. Singularity points with a specific motion pattern are present, whereby the reconstruction would fail. In the cases where diffraction and radiation waves occur simultaneously, the two types of waves need to be decoupled from the monitored wave elevation, and the wave loads caused by the diffraction and radiation waves are reconstructed separately.

Nonlinear wave surface elevation around a multi-column offshore structure

Surface elevation around multiple column offshore structure is an important phenomenon crucial to air gap design of offshore platforms. This paper investigates the competing hydrodynamic phenomena, i.e., wave run-up of surface elevation rising along the column and near-trapping – the increase of surface elevation due to near-resonance among the columns. Both wave run-up and near-trapping have the characteristics of generating surface elevation peak and often impact the offshore structures with nonlinear wave loads and potentially cause slamming to platforms. With the free-surface Keulegan-Carpenter number Kc<O(1) and wave steepness H/L < 0.14 considered, the free surface amplitude primarily depends on the diffraction pattern caused by the multiple columns and potential theory is applicable. The wave run-up and near-trapping due to wave interaction with a platform consisting of four-square columns with different corner ratios are obtained by numerical simulations. It is found that the increasing corner ratio results in a lower wave run-up under 0° incident wave, but a higher wave run-up under 45° incident wave. For near-trapping among four columns, the peak surface elevation decreases with increasing corner ratio. Two mechanisms namely superposition and near-resonance resulting the peak surface elevation are examined in detail for wave interaction with multiple columns.

The DeRisk database: Extreme design waves for offshore wind turbines

The estimation of extreme loads from waves is an essential part of the design of offshore wind turbines. Standard design codes suggest either to use simplified methodologies based on regular waves, or to perform fully-nonlinear computations. The former may not provide an accurate representation of the real extreme waves, while the latter is too computationally intensive for fast design iterations. Here, we address these limitations by using the fully-nonlinear solver OceanWave3D to establish the DeRisk database, a large dataset of extreme wave kinematics in a two-dimensional domain. From the database, which is open and freely available, a designer can easily extract fully-nonlinear wave kinematics for a wave condition and water depth of interest by identifying a suitable computation in the database and, if needed, by Froude-scaling the kinematics. This will ultimately enable quicker estimations of nonlinear wave loads, speeding up design evaluations. The database sea states cover a range of nondimensional depth of about h∗∈[3.0⋅10−3,6.5⋅10−2] and of nondimensional significant wave height of HS∗∈[1.0⋅10−3,8.0⋅10−3], where h∗=h/(gTP2)[−] and HS∗=HS/(gTP2)[−].The fully-nonlinear solver is validated against the DeRisk model-scale experiments, where a number of long-crested sea state realizations are generated at two different water depths, 33.0[m] and 20.0[m], and the induced force on a stiff monopile with a diameter of D=7.0[m] is measured.Comparison with the experiments shows that the database predicts maximum crest elevations at both depths very accurately. Predictions of the in-line force, obtained by application of the Rainey slender body force model with the database wave kinematics, are accurate for milder storms. However, for stronger storms, where slamming loads from breaking waves dominate, the force computations from the database kinematics provide slightly nonconservative force estimates compared with the standard methodologies such as the embedded stream function and the WiFi JIP model. This discrepancy is mainly due to the lack of a slamming load model in the applied force model. A procedure to add slamming loads to OceanWave3D and to the DeRisk database is currently being developed.

Numerical investigation of extreme wave impact on coastal bridge deck using focused waves

Horizontal and vertical impact forces on a coastal bridge deck with girders due to asymmetric and nonlinear wave loads induced by the action of focused wave groups have been investigated using open-source CFD model REEF3D. An extensive parametric study was conducted to investigate the variation of horizontal and vertical impact forces induced on bridge deck by steep focused waves. Results indicate that with increasing wave heights, while the horizontal positive force increases, the peak vertical uplift and downward forces decrease. Longer wave periods impart higher peak vertical uplift forces and horizontal positive forces. The bridge deck location at still water level, submerged and partially submerged cases are considered for the numerical study and the results are compared with the design formulae of American Association of State Highway and Transportation Officials (AASHTO). For both submerged and partially submerged scenarios, AASHTO formulae were found to highly overestimate the peak horizontal impact forces for lower wave heights and they were found to give better results for higher wave heights. In case of peak vertical impact forces, AASHTO formulae highly underestimate for lower wave heights and moderately capture the peak vertical impact force at higher wave heights and airgaps.

Practical representation of flows due to general singularity distributions for wave diffraction–radiation by offshore structures in finite water depth

The behavior of an offshore structure in regular waves – and the related (linear and nonlinear) wave loads, added-mass and wave-damping coefficients, and body-motions – are commonly analyzed via the Green-function and boundary-integral method associated with potential-flow theory. This realistic, widely-used method requires accurate and efficient numerical evaluation of flows created by distributions of singularities (source, dipole) over (flat or curved) panels of various shapes (triangle, quadrilateral) that are used to approximate the surface of an offshore structure. This basic core element of the theory of diffraction–radiation of regular waves by an offshore structure is considered for water of uniform finite depth. The special case of deep water is also considered. An analytical representation of the flow created by a general distribution of singularities over a hull-surface panel is given. This flow-representation is based on the Fourier–Kochin (FK) approach, in which space-integration over the panel is performed first and Fourier-integration is performed subsequently, unlike the common approach in which the Green function (defined via a Fourier integration) is evaluated first and subsequently integrated over the panel. The analytical and numerical complexities associated with the numerical evaluation and subsequent panel integration of the singular Green function for wave diffraction–radiation by offshore structures are then avoided in the FK approach. In this approach, panel integration merely amounts to integrating an elementary (exponential–trigonometric) function, a trivial task that can be performed accurately and efficiently. The analytical flow-representation given in the study provides a mathematically-exact smooth decomposition of free-surface effects into a non-oscillatory local flow and waves. The waves in this flow decomposition are defined by a regular single Fourier integral, and the local flow is given by a double Fourier integral with a smooth integrand that only involves ordinary functions and is dominant within a compact region near the origin of the Fourier plane. Illustrative numerical applications for typical distributions of sources and dipoles over a panel show that the flow-representation given in the study is well suited for practical numerical evaluations.

Wave-GAN: A deep learning approach for the prediction of nonlinear regular wave loads and run-up on a fixed cylinder

Machine learning techniques have inspired reduced-order solutions in the fluid mechanics field that show benefits of unprecedented capability and efficiency. Targeting ocean-wave problems, this work has developed a novel data-driven computational approach, named Wave-GAN. This new tool is based upon the conditional Generative Adversarial Network (GAN) principle, and it provides the ability to predict three-dimensional nonlinear wave loads and run-up on a fixed structure. The paper presents the principle of Wave-GAN and an application example of regular waves interacting with a vertical fixed cylinder. Computational Fluid Dynamics (CFD) is used to provide training and testing datasets for the Wave-GAN deep learning network. Upon verification, Wave-GAN proved the ability to provide accurate results for predicting wave load and run-up for wave conditions that were not informed during training. Yet the CFD-comparative results were only obtained within seconds by the deep learning tool. The promising results demonstrate Wave-GAN's outstanding potential to act as a pioneering sample of applying machine learning techniques to wave-structural interaction problems. It is envisioned that the new approach could be extended to more complex shapes and wave conditions to facilitate the various design stages of marine and offshore engineering applications such as monopiles. As a result, enhanced reliability is expected to optimise structural performance and prevent environmental disasters.

Experimental and numerical investigation of nonlinear diffraction wave loads on a semi-submersible wind turbine

In a severe sea state, nonlinear wave loads can excite resonant responses of floating wind turbines either at high (structural) or low (rigid body motions) natural frequencies. In the present work, a computational fluid dynamics (CFD) model and an engineering model based on potential-flow theory with Morison-type drag are developed to investigate nonlinear wave loads on a stationary, rigid semi-submersible wind turbine under regular and irregular waves. The numerical results are validated against experimental measurements. A trimmed floater is modelled to examine the change in nonlinear wave loads due to the mean pitch angle which occurs during operation of a floating wind turbine. Furthermore, wave loads on each column are investigated numerically. Compared to the experimental measurements, the CFD model gives better estimations than the engineering model for the first, second and third order wave diffraction loads. The engineering model based on the first- and second-order potential-flow theory has large discrepancies in the phase of high order wave diffraction loads and underpredicts the amplitude of low-frequency wave loads. In the CFD simulations for the studied wave period (12.1 s), the second and third harmonic surge forces on the starboard columns are significantly larger than those on the upstream column, while first harmonic results are consistent with potential flow. The trim angle (5°) results in an increasing surge force and pitch moment but a decreasing heave force.

Support Vector Machines Model of the Nonlinear Hydrodynamics of Fixed Cylinders

Abstract Data-driven modeling is considered as a prospective approach for many conventional physical problems including ocean applications. Among various machine learning techniques, support vector machine stands out as one of the most widely used algorithms to establish models connecting pertinent features to physical quantities of interest. This paper takes the experimental data for a fixed cylinder in shallow water as the baseline data set and explores the modeling of nonlinear wave loads by the support vector machine (SVM) regression method. Different feature and target selections are studied in this paper to establish the nonlinear mapping relations from ambient wave elevations and kinematics to nonlinear wave loads. The performance of the SVM regression model is discussed and compared with nonlinear potential flow theory focusing on the overall statistics (standard deviation and kurtosis), which is critical for fatigue and extreme statistics analysis.

Nonlinear Wave Loads on Offshore Wind Turbines: Extreme Statistics and Fatigue

Abstract The development is presented of an analytical model for the prediction of the stochastic nonlinear wave loads on the support structure of bottom-mounted and floating offshore wind turbines. Explicit expressions are derived for the time-domain and frequency-domain nonlinear exciting forces in a seastate with a significant wave height comparable to the diameter of the support structure based on the fluid impulse theory. The higher-order moments of the nonlinear load are evaluated from simulated force records, and the derivation of analytical expressions for the nonlinear load statistics for their efficient use in design is addressed.

Study on Hydrodynamic Characteristics of Wind Turbine Monopile under Nonlinear Wave

As wind power technologies become maturer, the monopile foundation of offshore wind turbine is widely used because of its simple structure, few occupied space and low cost. However, under severe sea conditions, the impact of nonlinear wave load applied against the monopile foundation on the system structure safety cannot be ignored. In this paper, the 5MW offshore wind turbine of the National Renewable Energy Laboratory (NREL) was taken as the research object, and the computational fluid analysis software ‘STARCCM +’ was used to study the hydrodynamic characteristics of the monopile foundation of the wind turbine under different wave parameters. This paper mainly analyzed the upper wave, pressure and wave forces around the monopile foundation of the wind turbine under the same period and different wave heights. And the wave force calculated by CFD was compared with the result based on potential flow theory. The research results showed that with the rise of wave height, the upper wave, pressure and wave force around the monopile foundation increase continuously, and the second-peak phenomenon appeared at some measuring points on the water surface of the monopile foundation. Because the CFD method considers the fluid viscosity and is more in line with the real sea conditions, it is more accurate to obtain wave forces based on this method.

Uncertainty Assessment of CFD Investigation of the Nonlinear Difference-Frequency Wave Loads on a Semisubmersible FOWT Platform

Current mid-fidelity modeling approaches for floating offshore wind turbines (FOWTs) have been found to underpredict the nonlinear, low-frequency wave excitation and the response of semisubmersible FOWTs. To examine the cause of this underprediction, the OC6 project is using computational fluid dynamics (CFD) tools to investigate the wave loads on the OC5-DeepCwind semisubmersible, with a focus on the nonlinear difference-frequency excitation. This paper focuses on assessing the uncertainty of the CFD predictions from simulations of the semisubmersible in a fixed condition under bichromatic wave loading and on establishing confidence in the results for use in improving mid-fidelity models. The uncertainty for the nonlinear wave excitation is found to be acceptable but larger than that for the wave-frequency excitation, with the spatial discretization error being the dominant contributor. Further, unwanted free waves at the difference frequency have been identified in the CFD solution. A wave-splitting and wave load-correction procedure are presented to remove the contamination from the free waves in the results. A preliminary comparison to second-order potential-flow theory shows that the CFD model predicted significantly higher difference-frequency wave excitations, especially in surge, suggesting that the CFD results can be used to better calibrate the mid-fidelity tools.

Ultimate load analysis of a 10 MW offshore monopile wind turbine incorporating fully nonlinear irregular wave kinematics

Loads from storm waves can in some cases be dimensioning for offshore wind turbine substructures. Accurate determination of nonlinear wave loads is therefore important for a safe, yet economic design. In this paper, the fully nonlinear waves, realized by a fully nonlinear potential wave solver OceanWave3D, are incorporated into coupled aero-servo-hydro-elastic simulations for a reduced set of wave-sensitive design load cases, in comparison with the widely used linear and constrained waves. The coupled aero-elastic simulations are performed for the DTU 10 MW reference wind turbine on a large monopile at 33 m water depth using the aero-elastic code HAWC2. Effect of the wave nonlinearity is investigated in terms of the ultimate sectional moments at tower bottom and monopile mudline. Higher ultimate moments, 5% at tower bottom and 13% at monopile mudline as maximum, are predicated when the nonlinear waves are used. It could be explained by the fact that the extreme nonlinear waves, that are close to the breaking limit, can induce resonant ringing-type responses, and hereby dominate the ultimate load responses. However, the constrained wave approach shows marginal difference compared to the standard linear wave approach. It can be concluded at least for the present configuration that the industry standard approaches (linear and constrained wave approach) underestimate the ultimate load responses on offshore wind turbines in severe sea states.

Explicit Time-Domain Approach for Random Vibration Analysis of Jacket Platforms Subjected to Wave Loads

This paper is devoted to the random vibration analysis of jacket platforms under wave loads using the explicit time-domain approach. The Morison equation is first used to obtain the nonlinear random wave loads, which are discretized into random loading vectors at a series of time instants. The Newmark-β integration scheme is then employed to construct the explicit expressions for dynamic responses of jacket platforms in terms of the random vectors at different time instants. On this basis, Monte Carlo simulation can further be conducted at high efficiency, which not only provides the statistical moments of the random responses, but also gives the mean peak values of responses. Compared with the traditional power spectrum method, nonlinear wave loads can be readily taken into consideration in the present approach rather than using the equivalent linearized Morison equation. Compared with the traditional Monte Carlo simulation, the response statistics can be obtained through the direct use of the explicit expressions of dynamic responses rather than repeatedly solving the equation of motion. An engineering example is analyzed to illustrate the accuracy and efficiency of the present approach.

Advances on simulation of wave-body interactions under consideration of the nonlinear free water surface

ABSTRACT The paper refers to a boundary element method (BEM) in the time domain for the simulation of wave-body interactions considering the free water surface. The approach solves the boundary integral equations for the velocity and the acceleration potential. The model of the free water surface in this approach is based on the mixed-Eulerian-Lagrangian (MEL) method. Validation results are presented for two well-studied test cases. The first validation case is dedicated to the free water surface. Here, the nonlinear wave loads on a truncated cylinder are analysed and compared with a higher-order panel method and experimental data. Second, results of a Wigley hull moving with forward speed in head waves are shown and compared with experimental results published by Kashiwagi. The validation results in both test cases generally show good agreement with published data and demonstrate the ability of BEM to investigate different types of hydrodynamic problems related to wave-body interactions.

On Wave-Induced Elastic Deformations of a Submerged Wave Energy Device

Structural integrity has remained a challenge for design and analysis of wave energy devices. A difficulty in assessment of the structural integrity is often laid in the accurate determination of the wave-induced loads on the wave energy devices and the repones of the structure. Decoupled hydroelastic response of a submerged, oscillating wave energy device to extreme nonlinear wave loads is studied here. The submerged wave energy device consists of an oscillating horizontal disc attached to a direct-drive power take-off system. The structural frame of the wave energy device is fixed on the seafloor in shallow water. Several extreme wave conditions are considered in this study. The nonlinear wave loads on members of the submerged structure are obtained by use of the level I Green-Naghdi equations and Morison’s equation for cylindrical members. Distribution of Von Mises stresses and the elastic response of the structure to the extreme wave loads are determined by use of a finite element method. The decoupled hydroelastic analysis of the structure is carried out for devices built by four different materials, namely stainless steel, concrete, aluminium alloy, and titanium alloy. The elastic response of these devices is studied and results are compared with each other. Points of maximum stress and deformations are determined and the structural integrity under the extreme conditions is assessed. It is shown that the proposed approaches provide invaluable information about the structural integrity of wave energy devices.

Numerical Study of the High-Frequency Wave Loads and Ringing Response of A Bottom-Hinged Vertical Cylinder in Focused Waves

This paper presents a numerical study on the high-frequency wave loads and ringing response of offshore wind turbine foundations exposed to moderately steep transient water waves. Input wave groups are generated by the technique of frequency-focusing, and the numerical simulation of focused waves is based on the NewWave model and a Fourier time-stepping procedure. The proposed model is validated by comparison with the published laboratory data. In respect of both the wave elevations and the underlying water particle kinematics, the numerical results are in excellent agreement with the experimental data. Furthermore, the local evolution of power spectra and the transfer of energy into higher frequencies can be clearly identified. Then the generalized FNV theory and Rainey’s model are applied respectively to calculate the nonlinear wave loads on a bottom-hinged vertical cylinder in focused waves. Resonant ringing response excited by the nonlinear high-frequency wave loads is found in the numerical simulation when frequency ratios (natural frequency of the structure to peak frequency of wave spectra) are equal to 3–5. Dynamic amplification factor of ringing response is also investigated for different dynamic properties (natural frequency and damping ratio) of the structure.

Effects of nonlinear wave loads on large monopile offshore wind turbines with and without ice-breaking cone configuration

In the present paper, the computational fluid dynamics (CFD) method is used to investigate the variation of linear and nonlinear wave loads on a 10-MW large-scale monopile offshore wind turbine under typical sea conditions in the eastern seas of China. The effect of adding a structural ice-breaking cone configuration close to the mean water level on the monopile’s hydrodynamic response is studied further. Results are derived with the use of the CFD model and are compared with the relevant results that are calculated using the Morison equation and the potential flow theory based on the high-order boundary element method. The fifth-order Stokes’ theorem is used to model the incoming wave kinematics, and the volume of fluid (VOF) method is used to capture the free surface of waves and to accurately calculate the wave run-up on the monopile and cone configuration. The influence of different water depths and wave heights on the wave maximum vertical extent of wave uprush on the structure, pressure and horizontal wave forces on the monopile is investigated for both with and without the use of the cone configuration. Up–downward cone configuration results in better performance compared to the inverted cone configuration in terms of reduction of hydrodynamic nonlinear excitation loads and wave maximum vertical extent of wave uprush on the structure.

Effects of random winds and waves on a long-span cross-sea bridge using Bayesian regularized back propagation neural network

Uncertainties from random multiple factors bring great challenges for assessing response of long-span bridges. This study proposes a dynamic analysis framework by integrating the wind–wave–bridge system with Bayesian regularized back propagation neural network, and then investigates stochastic response of a cross-sea cable-stayed bridge under extreme wind and wave parameters. The wind–wave–bridge system involving wind–bridge and wave–bridge interactions is constructed to calculate dynamic response of the bridge by Newmark-β method, considering stationary fluctuating wind fields and multidirectional random wave fields. To reduce the calculation cost, a Bayesian regularized back propagation neural network model is introduced, and the model evaluation is carried out to illustrate its accuracy and efficiency. After performing small-scale finite element analyses, the response statistics are obtained and later used as the known samples for training the neural network. The power spectrum analyses of the deterministic results are performed to investigate the contribution mechanism of the wind and wave. Finally, the correlation between the bridge response and the single wind–wave parameter is given by uncertainty analysis of the Bayesian regularized back propagation neural network model. The results show that the proposed framework is capable of capturing the nonlinear bridge response resulting from nonlinear wind and wave loads, which, however, is significant different from that under wind alone. The bridge response receives significant contribution from wind and waves relative to the vibration characteristic of the bridge at smaller wind and wave loads. The contribution from vibration characteristic of the bridge becomes significant at larger wind and wave loads. The uncertainty analyses illustrate the significant effects of four wind and wave parameters on girder, tower, and submerged structure.

Prediction of non-linear wave loads on large floating structures using a 3D numerical wave tank approach

In the present work, non-linear wave loads acting on large floating structures are computed using a 3D numerical wave tank (NWT) approach in an approximate manner. The hydrodynamic initial boundary value problem is solved following a Rankine panel-based boundary element method in conjunction with time integration of free-surface constraints and body-motion equations. To enable long-duration simulation for practical offshore configurations, total velocity potential is split into incident and perturbation part, and the latter effects are linearized. In our earlier works (Ganesan and Sen in J Ocean Eng Mar Energy 1:299–324, 2015; Ganesan and Sen in Appl Ocean Res 51:153–170, 2015), the 2nd order contributions from the linearized perturbation potential were neglected. In this work, we propose a modified formulation for the external load in which the full non-linear loads from the incident wave and up to 2nd order loads from the linear perturbation potential are considered. After presenting some results to validate the present method for steady drift force computations, non-linear loads from the modified formulation are compared with the unmodified form of the method and also with widely used 3D frequency-domain Green-function-based method. Comparative results between these three computations are presented for different geometries and the results are discussed to bring out the relative advantage of the modified formulation in predicting non-linear loads across the range of frequency and wave steepness.