Realistic Sea States Research Articles

GWECS: An indicator to describe the energy absorption characteristics of wave energy converter arrays in real sea states

Grouping wave energy converters (WECs) into an array has become a trend to improve power production and achieve economies of scale. Therefore, the performance of a WEC array in real sea states is of vital importance. To intuitively reflect an array's frequency-based energy absorption characteristics instead of only the total extractable power in given irregular wave conditions, a new indicator of group wave energy capture spectrum (GWECS) is proposed by extending the concept of wave energy capture spectrum (WECS) to an array. A practical method to measure the indicator by estimating the absorbed wave surface from the array's power signal is also given. Simulations in two-dimensional conditions with a 2-cuboid WEC array and in three-dimensional conditions with a 2-cylinder WEC array are conducted to study the concept. The results examine the consistency in capture efficiency between the newly proposed indicator and conventional ones, and present the effect of various parameters, including linear power take-off (PTO) damping, buoy permutation, separation distance, and incident wave angle on the GWECS.

Effects of coupled platform motions on the aerodynamic performance and wake characteristics of a floating horizontal-axis wind turbine

ABSTRACT The aerodynamics of floating horizontal-axis wind turbines (FHAWTs) are complex due to platform motions in real sea states. The impacts of coupled platform motions on the aerodynamic loads, wake structure, and wake recovery of FHAWTs were investigated through computational fluid dynamics simulations. Results show that the increases in the maximum rotor power of FHAWTs (compared with the fixed-base ones) under sinusoidal pitch-surge motions (3892 kW) were close to the sum of those under pitch (2121 kW) and surge (1622 kW) motions. The wake tilt angles under pitch-surge motions agreed with those under pitch motions, causing similar wake recovery. The increase in wave periods (Tw ) amplified the resonance between waves and platforms under the wind-wave coupling, increasing the maximum rotor power and thrust. Compared with Tw = 16 s, the relative decreases in the averaged wake velocity, which was 7D (where D is the rotor diameter) downwind of the FHAWTs, were 5.93% and 2.64% at Tw = 8 s and 12 s, respectively. Long Tw increased pitch periods, yielding fast wake recovery by enhancing the interaction between blade-tip vortices and hub ones. The output power of a floating wind farm was higher than the fixed-base counterpart due to fast wake recovery.

Geometric Evaluation of the Hydro-Pneumatic Chamber of an Oscillating Water Column Wave Energy Converter Employing an Axisymmetric Computational Model Submitted to a Realistic Sea State Data

Geometric Evaluation of the Hydro-Pneumatic Chamber of an Oscillating Water Column Wave Energy Converter Employing an Axisymmetric Computational Model Submitted to a Realistic Sea State Data

Investigating the influence of geometry on the performance of a wave-powered marine observation buoy: The wave-to-wire approach

As an important marine monitoring platform, marine observation buoys have been widely used in marine environmental monitoring, marine resource surveys, etc., attracting great attention worldwide. However, the lack of a reliable power supply is a crucial problem that seriously restricts buoys’ operation lifetime and carrying capacity. The floating buoy with an inbuilt wave energy harvester is a promising solution to the long-term and sustainable energy supply problem. This study develops a fully coupled wave-to-wire (W2W) mathematical model where the relevant friction parameters and power-take-off system parameters are identified from flume experimental results. Besides, the influence of geometry on the buoy’s electric power performance is investigated under regular and irregular waves, respectively. Numerical results imply that the cylinder-cone-shape buoy produces the most electric power when the three shapes have the same geometric sizes, while the cylinder-sphere-shape buoy performs the best W2W efficiency among the three shapes with the same mass. Moreover, a high W2W efficiency of up to 23.13% is gained under a regular wave. Finally, according to the similarity theory, the averaged electric power of a full-size buoy is estimated at 4.84kW in realistic sea states.

Wavy approach for fluid–structure interaction with high Froude number and undamped structure

This paper addresses the fluid–structure interaction problem, with an interest on the interaction of a gravity wave with a flexible floating structure, anchored to a seabed of constant depth. To achieve this goal, we make use of the model equations, namely, the Navier–Stokes equations and the Navier–Lamé equation, as well as the associated the boundary conditions. Applying the multi-scale expansion method, these set of equations are reduced to a pair of nonlinearly coupled complex cubic Ginzburg–Landau equations (CCGLE). By applying the proposed modified expansion method, the group velocity dispersion and second-order dispersion relation are deduced. In the same vein, modulation instability (MI) is investigated as a mechanism of formation of pulse trains in fluid–structure system using a CCGLE. For the analytical analysis, we made use of the inverse scattering method to find analytical solutions to the coupled nonlinear equations. Through that method, the obtained solutions depict rogue-shaped waves. Our results suggest that uncontrolled MI within the interaction between a flexible body and gravity waves in viscous flow may be considered as the principal source of many structural ruptures, which are the first cause of critical damage due to the great energy and unpredictability of rogue waves. The present work aims to provide tools to model a wide range of physical problems regarding the interaction of surface gravity waves and an offshore-anchored structure, and it aims to be essential to our understanding of the nonlinear characteristics of offshore structures in real-sea states.

Overtopping Flow Velocity Characterisation Of Focused Waves On Promenades Using The Bubble Image Velocimetry Technique

This study characterises the flow velocity of individual extreme waves that overtop promenades using the bubble image velocimetry (BIV) technique (Ryu et al., 2005). Experimental tests were carried out in the small-scale wave flume CIEMito, at the Marine Engineering Laboratory (LIM) of the Universitat Politècnica de Catalunya – BarcelonaTech (UPC), and the obtained images were post-processed to calculate the flow velocities. The ultimate objective of the experimental campaign is to develop more precise models for forecasting wave overtopping of structures with an emergent toe, commonly found on sandy beaches and frequently utilized as promenades or waterfronts in most urbanized coastal environments. The NewWave theory (Tromans et al., 1991) was used to simulate the extreme individual wave overtopping in a real random sea state. The NewWave theory establishes a correlation between the expected form of a large wave in a linear sea state and the bulk characteristics of the sea state. Using focused wave groups instead of long-duration irregular wave time series offers several benefits. It improves the ability to repeat experiments and enhances measurement capabilities by providing greater temporal resolution in models used to investigate significant wave interactions (Hofland et al., 2014). Additionally, due to the compactness of focused wave groups, wave absorption becomes unnecessary. The research identifies two distinct case studies with varying wave forcing, tidal regimes and coastal layouts. This work presents a case study of a typical Mediterranean Sea configuration, which is a micro-tidal environment with steep and relatively short foreshores and pocket beaches. The study aims to characterize the overtopping flow velocity on the selected structure, and the feasibility of non-intrusive measurements such as a BIV technique has been investigated. The work includes preliminary results.

Analytical study on dynamic performance of a hybrid system in real sea states

A mathematical model is developed to investigate the performance of a hybrid system comprising semi-submersible floating offshore wind turbines (FOWT) coupled to an array of point-absorbing wave energy converters (WECs) under irregular waves and dynamic winds. In this study, the hydrodynamic interaction of the hybrid system is conducted by applying the matching-method of eigenfunctions to solve the diffraction and radiation velocity potentials. Non-linearities of the hybrid system are taken into account in the Cummins framework, covering aerodynamic, catenary mooring, PTO system, fluid viscosity modeling, and frequency–time domain transformation of hydrodynamic coefficients. After running the convergence analysis and model validation, the present model is employed to perform a multiparameter effect analysis. Case studies are presented to clarify the effects of WEC parameters (including radius, draft, PTO damping, and layout) on the performance of a hybrid system. Nevertheless, a significant aspect of this work revolves around the development of a precise and efficient mathematical model, capable of accurately computing hydrodynamic coefficients for specific marine structures and evaluating the motion response of the interconnected floaters. Additionally, the study offers valuable insights into the preliminary design of hybrid systems and lays a mathematical foundation along with corresponding code for hybrid system projects.

An attention mechanism model based on positional encoding for the prediction of ship maneuvering motion in real sea state

An attention mechanism model based on positional encoding for the prediction of ship maneuvering motion in real sea state

Constructal Design Applied to an Oscillating Water Column Wave Energy Converter Device under Realistic Sea State Conditions

In this work, we conducted a numerical analysis of an oscillating water column (OWC) wave energy converter (WEC) device. The main objective of this research was to conduct a geometric evaluation of the device by defining an optimal configuration that maximized its available hydrodynamic power while employing realistic sea data. To achieve this objective, the WaveMIMO methodology was used. This is characterized by the conversion of realistic sea data into time series of the free surface elevation. These time series were processed and transformed into water velocity components, enabling transient velocity data to be used as boundary conditions for the generation of numerical irregular waves in the Fluent 2019 R2 software. Regular waves representative of the sea data were also generated in order to evaluate the hydrodynamic performance of the device in comparison to the realistic irregular waves. For the geometric analysis, the constructal design method was utilized. The hydropneumatic chamber volume and the total volume of the device were adopted as geometric constraints and remained constant. Three degrees of freedom (DOF) were used for this study: H1/L is the ratio between the height and length of the hydropneumatic chamber, whose values were varied, and H2/l (ratio between height and length of the turbine duct) and H3 (submergence depth of hydropneumatic chamber) were kept constant. The best performance was observed for the device geometry with H1/L= 0.1985, which presented an available hydropneumatic power Phyd of 29.63 W. This value was 4.34 times higher than the power generated by the worst geometry performance, which was 6.83 W, obtained with an H1/L value of 2.2789, and 2.49 times higher than the power obtained by the device with the same dimensions as those from the one on Pico island, which was 11.89 W. When the optimal geometry was subjected to regular waves, a Phyd of 30.50 W was encountered.

Numerical study on self-power supply of large marine monitoring buoys: Wave-excited vibration energy harvesting and harvester optimization

With the diversification of marine monitoring buoy functions, limited onboard batteries have been unable to meet the energy demand of multifarious carrying sensors. Finding a self-sustained power supply for marine monitoring buoys is an urgent problem, while wave energy is an ideal and promising option to address that problem. In this study, two wave-excited vibration energy harvesters (WVEHs) are proposed, which can be installed inside large buoys to provide a sustainable power supply. A full-coupled wave-to-wire model is developed to investigate the influence of blocks’ mass, geometric size of buoys, mooring system and WVEH’s quantity on the electric power performance of harvesters in realistic sea states. Parametric studies based on the Taguchi method imply that the sea state and the WVEH’s quantity have a significant effect on the device’s electric power performance. Numerical results indicate that the optimized two harvesters can produce a mean electric power of 777.50 W and 747.43 W, respectively, under a sea state with a peak wave period of 7 s and a significant wave height of 1.6 m. A high wave-to-wire efficiency of 2.60% is obtained for a specific system parameter combination. Furthermore, more electric power generation can be achieved by installing multiple harvesting units.

The nonlinearity of scattering waves due to interaction between focusing waves and floating production storage and offloading

The study of the full-scale wave–structure interaction is essential to our understanding of the nonlinear characteristics of offshore structures in real-sea states. This paper deals with full-scale numerical studies of the interactions between focusing waves and a fixed floating production storage and offloading (FPSO) in an efficient potential-viscous coupled method. The potential-viscous method combines in-house computational fluid dynamics code developed at Shanghai Jiao Tong University (SJTU) for naval architecture and ocean engineering (naoe) based on an open field operation and manipulation (FOAM), i.e., naoe-FOAM-SJTU solver, with high-order spectral method. The approach is verified on a model-scaled case and shows reasonably good agreement with experimental data. A phase-separation method and a dynamic mode decomposition method are utilized to extract linear and higher-order harmonic components from the scattering waves. The scattering waves around the FPSO are found to affect the higher-order harmonic components. Two kinds of scale ratios are considered to magnify the focusing wave and FPSO by 10 and 100 times to discuss the scale effect, both non-breaking and green water conditions are included to investigate the flow phenomenon. The harmonic components of scattering waves are not proportional to the scale ratio, and the scale effects influence more on higher-order harmonic components. The third- and fourth-order harmonic components of scattering waves around the FPSO in large-scale cases are obvious.

Nonlinear WEC modeling using Sparse Identification of Nonlinear Dynamics (SINDy)

Modeling oscillating surge wave energy converter (OSWEC) systems to accurately predict their behavior has been a notoriously difficult challenge for the wave energy field. This is particularly challenging in realistic sea states where nonlinear WEC dynamics are common due to complex fluid-structure interaction, breaking waves, and other phenomena. Common modeling techniques for OSWECs include using potential flow theory to linearize the governing equations and ease computations, or using CFD to solve the full Navier-Stokes equations coupled with rigid body motion. However, both of these options have significant limitations. Potential flow theory breaks down in realistic sea conditions where nonlinear WEC dynamics are present, and CFD is often too computationally expensive for many applications such as real-time state prediction and optimal control, two areas of active research in the wave energy field. In particular, OSWEC dynamics are dominated by diffractive and viscous forces, often making common assumptions and linearization approximations (including small-body approximations) unreasonable, and CFD computationally intractable.
 To bridge this gap in modeling methods, we propose using Sparse Identification of Nonlinear Dynamics (SINDy) to build nonlinear reduced-order models (ROMs) that describe OSWEC behavior in response to large-amplitude regular waves. SINDy is an equation-free, data-driven algorithm that identifies dominant nonlinear functions present in system state dynamics using a library of nonlinear functions created from time series measurement data. The result is an ordinary differential equation (ODE) in time that can be solved from an initial condition to model and predict time behavior of the states. SINDy is parsimonious, meaning it uses a sparsity-promoting hyperparameter with the goal of only including the minimum number of terms to capture dominant dynamics, resulting in interpretable and generalizable results that are not overfit to the data. Using the discovered ROMs and integrating in time, not only can SINDy provide time series models and future state predictions of OSWEC dynamics, it can also give insights into which variables are critical in describing the underlying dynamics of the state. 
 In this study, we use SINDy to describe the nonlinear dynamics of a lab-scale OSWEC in a wave tank subjected to large-amplitude regular waves. We use nonlinear simulation data to generate kinematic, force, and torque data and use it as input to SINDy to identify ODEs that describe the measurement variables in time. We then integrate the ODEs to recreate the time series as well as predict future system behavior. We directly compare the resulting time series to the original data input to assess the accuracy of the SINDy model. We also interpret the dominant terms in the ODEs to gain insight on underlying mechanisms of the observed nonlinearity.
 Early results show SINDy is a promising tool for modeling nonlinear OSWEC dynamics. We are able to build ROMs for variables such as angular kinematics and the moment about the hinge that generate an accurate recreation of data measurements. We found strong dominance in cubic and quintic terms of the ROMs, suggesting higher-order nonlinearities in the system dynamics. These findings inspire future work in identifying underlying mechanisms driving nonlinearity.

Nonlinear statistical characteristics of the multi-directional waves with equivalent energy

Directional distribution is believed to have a significant impact on the statistical characteristics in multi-directional sea states. In real sea states, short-crested waves are discrete not only in frequency but also in direction. For the former one, they are well explained in unidirectional mode, but for the latter one, they are not. In this paper, the kurtosis of short-crested waves with equivalent energy is first discussed. Unimodal-spectrum-multi-direction sea states and bimodal-spectrum-multi-direction sea states are simulated for a long time in a numerical wave basin based on the high-order spectral method. In the equivalent sea-swell sea state, the spatial evolution of kurtosis becomes more inhomogeneous, along with the maximum value of kurtosis being larger and the area where the maximum value occurs wider in the configuration with a crossing angle β = 40° than that with β = 0°, while little variations in swell-dominated and wind-sea-dominated states. A positive linear correlation between wavelet group steepness and kurtosis is obtained in a unimodal sea state, but not applied to a crossing sea state characterized by a bimodal spectrum. The exceedance probability of wave height and wave crest distribution at maximum kurtosis is also given. These findings can help predict the probability of extreme waves occurring, guiding the selection of ocean engineering sites to avoid extreme configurations.

Investigation of Numerical Irregular Wave Generation Using Transient Discrete Data as Boundary Conditions of Prescribed Velocity

This work presents a two-dimensional numerical analysis of a wave channel. The goal is to investigate a methodology that uses transient velocity data as means to impose velocity boundary condition for generating numerical waves. To do so, a numerical wave channel was simulated using irregular waves. These waves were obtained using the WaveMIMO methodology, which converts sea data from a spectral model into time series of free surface elevation, and then converts this elevation into transient discrete wave velocity data. For the numerical analysis, computational fluid dynamics ANSYS Fluent software was employed, which is based on the finite volume method. The computational domain and mesh were generated using GMSH software, and the nonlinear multiphase model volume of fluid (VOF) was applied to tackle water-air interaction. In general, the results obtained through the use of discrete data as velocity boundary condition presented a good agreement with free surface elevation converted from the spectral model, and the tests performed provided further insight into the parameters which affect this methodology. Since many studies use regular waves, the proposed investigation stands out for its capacity to improve the use of realistic sea state data in numerical simulations of wave energy converters.

Towards autonomous contact-free operations in aquaculture

As offshore fish farms are established farther away from the shore, increased exposure to the elements prevents regular operations from being performed safely with vessels moored alongside the flexible fish cage and personnel performing tasks standing on the collar. Due to the higher environmental impact at more exposed locations, new concepts and solutions for automating daily aquaculture operations need to be developed. One solution that has been proposed is to carry out operations using a robotic arm mounted on the main deck of a service vessel while it does stationkeeping next to the cage. The purpose of this article is to summarise our research on the viability of this concept. Vessel motions are simulated for a representative vessel model and realistic sea states, and a robotic arm does motion-compensated trajectory tracking while mounted on a hexapod platform moving according to the simulated vessel motions. Relevant challenges in marine aquaculture operations are summarised, the method used to obtain realistic simulated vessel motions is documented, the results of the experiments are presented, and the remaining open questions to evaluate the potential of the proposed system are discussed.

Study on the energy capture spectrum (ECS) of a multi-DoF buoy under random waves

Energy Capture Spectrum (ECS) and Wave Height Take-Off (WHTO) are two methods for evaluating the energy extraction of a wave energy converter (WEC) by treating energy capture as equivalent wave or wave height loss. This paper demonstrates the relationship between the two in the real sea state and proposed the concept of WHTO under random waves, which is helpful in improving the energy capture evaluation system of WECs. To design and optimize WECs in the preliminary stage, a new ECS calculation method based on potential flow theory is also presented. A case study of a multi-DOF (degree of freedom) buoy was carried out on this method to analyze its ECS characteristics in three main energy-capture DOFs (heave, surge, and pitch). Physical model tests were conducted to measure the initial load and validate the accuracy of the mathematic model. Based on the case study, the characteristics of ECS of the buoy in different DoFs with PTO change were presented and discussed. This paper aims to provide new methods and ideas for the design and optimization of WECs in the real sea state.

INVESTIGATION ON THE DISCRETIZATION OF THE REALISTIC IRREGULAR WAVE GENERATION REGION THROUGH THE WAVEMIMO METHODOLOGY

Aiming to contribute to the research related to the sea wave energy conversion, the present paper approaches an investigation of the discretization used in the region of imposition of the prescribed velocity boundary condition, which is necessary for the WaveMIMO methodology. This methodology is employed for the numeric generation of irregular waves based on realistic sea state data. These data (obtained from TOMAWAC software in the present study) are treated to obtain orbital profiles of wave propagation velocity, which are imposed as boundary conditions on the wave channel. In this study, the realistic data considered refers to a point close to the Molhes da Barra, located on the coast of the municipality of Rio Grande, Rio Grande do Sul, Brazil. The numerical simulations were performed in Fluent, a computational fluid dynamics (CFD) software based on the finite volume method (FVM). The volume of fluid (VOF) multiphase model was used on the treatment of the water-air interface. Free surface elevation data obtained when the region of imposition of the prescribed velocity boundary condition was subdivided into 8, 11 and 14 segments were compared. The results found show that the 14 segments discretization represents more precisely the free surface elevation of irregular waves.

Experimental study of extreme waves based on nonlinear Schrödinger equation under background of a random sea

The Peregrine breather (PB) solution of the nonlinear Schrödinger equation is used to model ocean extreme waves in a water wave flume. Triangular spectral features of wave elevations are observed over the nonlinear evolution of the extreme waves, which can be applied for early detection of the formation of extreme waves. To model a more realistic sea state, a background random wave is superposed to the PB in this study. We examine the spectral features of the nonlinear wave evolution with random background waves by the spectral analysis. It is found that the wave elevations show similar triangular spectral features for extreme waves with a relatively mild background wave. Moreover, we find that the second harmonic elevations of the extreme waves also show triangular spectral features, suggesting the potential use of the second harmonic elevations (in addition to the first) for detection of the formation of extreme waves.

Offloading operation bivariate extreme response statistics for FPSO vessel

The Floating Production Storage and Offloading unit (FPSO) is an offshore unit producing and storing crude oil prior to tanker transport. An important design concern is an accurate prediction of risky dynamic hawser tensions during FPSO offloading operations. Bivariate extreme hawser tension contours are important for selecting proper design values. This paper employed the AQWA hydrodynamic software to analyze vessel hydrodynamic wave loads dynamic response, acting on FPSO vessels under realistic sea state conditions. This paper presents an efficient method for estimating FPSO bivariate response statistics based on numerical simulations validated by various experiments. The bivariate Average Conditional Exceedance Rate (ACER2D) method offers an accurate bivariate extreme value probability distribution and return period contours estimation, utilizing available data efficiently. The two-dimensional probability contours, corresponding to low probability return periods, are easily obtained by the ACER2D method. The performance of the presented method has shown that the ACER2D method provides an efficient and accurate prediction of extreme return period contours. The suggested approach may be used for FPSO vessel design, minimizing potential FPSO hawser damage. Bivariate contours yield bivariate design points, as opposed to a pair of uncoupled univariate design points with the same return period as currently adopted in the industry.

Simplified analytical solutions to the yaw dynamics of modular floating structures

Climate change has necessitated the development of modular floating structures (MFS) as a sustainable solution to enhance the resiliency of coastal cities against flooding and sea level rise. Hence, it is imperative that simplified methods of analysis are introduced to the design community. This technical note presents closed-form expressions parameterizing the response amplitude operators (RAO) of rectangular pontoons subject to yaw (rotation about the vertical z axis) to complement solutions derived by Wang (2022) for the five remaining degrees of freedom. Following validation, a parametric investigation was implemented to assess the influence of pontoon geometry on the yaw response of an idealized MFS exposed to realistic sea states. It was identified that pontoons exhibiting a characteristic width smaller than the wavelength are generally more resistant to yaw excitation as they become squarer in shape. Conversely, while larger pontoons are less sensitive to geometric effects, they exhibit heightened sensitivity to changes in wave conditions. The simplified analytical approach thus provides an accessible pathway towards the structural or architectural design of floating structures as a precursor to detailed computational modeling.