Response Of Wave Energy Converter Research Articles

Performance characterization and modeling of an oscillating surge wave energy converter

Testing wave energy converters in the ocean could be expensive and complex, which necessitates the use of numerical modeling. However, accurately modeling the response of wave energy converters with high-fidelity simulations can be computationally intensive in the design stage where different configurations must be considered. Reduced-order models based on simplified equations of motion can be very useful in the design, optimization, or control of wave energy converters. Given the complex dynamics of wave energy converters, accurate representation, and evaluation of relative contributions by different forces are required. This effort is concerned with a performance characterization of the hydrodynamic response of an oscillating surge wave energy converter that is based on a reduced-order model. A state-space model is used to represent the radiation damping term. Morison’s representation of unsteady forces is used to account for the nonlinear damping. Wave tank tests are performed to validate simulations. A free response simulation is used to determine the coefficients of the state-space model. Torque-forced simulations are used to identify the coefficients of the nonlinear damping term for different amplitudes and wave frequencies. The impact of varying these coefficients on the response is investigated. An assessment of the capability of the model in predicting the hydrodynamic response under irregular forcing is performed. The results show that the maximum error is 3% when compared with high-fidelity simulations. It is determined that the nonlinear damping is proportional to the torque amplitude and its effects are more pronounced as the amplitude of the flap oscillations increases.

Incorporating Mooring Dynamics into the Control Design of a Two-Body Wave Energy Converter

Mooring systems are a critical component of all floating wave energy converter (WEC) systems, yet the impact of amooring system on the WEC dynamics is often neglected during the initial assessment of candidate designs. The purpose of this study was to investigate how the inclusion of mooring dynamics in the early stages of the WEC design process influences decisions regarding hydrodynamic features and control strategies. The study was executed within a mechanical circuit framework to represent the WEC response in the frequency domain. Thevenin’s theorem was applied within this framework to transform a multi-body WEC into a single-body canonical form. This work specifically focused on self-reacting point absorbers and examined how four realistic mooring designs impact WEC intrinsic mechanical impedance across a range of common wave frequencies. We show how the mooring can easily be included in this framework, and a simple approach to identifying the mooring model parameters is described. It was observed that if mooring dynamics are considered within the WEC control design process, a 40% reduction in the required range of the controller physical variable can be achieved while yielding up to 16% more useful power. These results suggest that considering the mooring system early can enhance WEC design.

A CFD-FEM analysis for Anaconda WEC with mooring lines

Anaconda wave energy converter (WEC) [1] is a typical flexible tube WEC design. In the past decade, the hydro-elastic performance of Anaconda model has been studied through experiments [2-3] and reduced-order numerical simulations [4-5]. However, to date, most of the undertaken research assumes that both ends of the tube are fixed, neglecting mooring lines that exist at designed conditions. The tube is allowed to move freely head to waves when mooring lines are considered. This is evident by an experiment conducted by Checkmate Flexible Engineering Ltd., where they observed a significant heave motion of Anaconda WEC, which may impact the dynamic response of WEC and further the energy conversion [6]. In our previous work [7], supported by the EPSRC project BASM-WEC (No. EP/V040553/1), a coupled numerical analysis tool using computational fluid dynamics (CFD) and finite element method (FEM) has been proposed to perform a numerical study for an Anaconda WEC model without considering mooring lines.In this paper, the coupled fluid-structure interaction (FSI) analysis tool [7] based on CFD-FEM method will be used to investigate Anaconda WEC with mooring lines. To account for the effects of free motion of WEC, we develop a sub-module to be embedded into the existing tool. The fluid and structure are solved by a two-phase CFD solver developed based on OpenFOAM and a three-dimensional FEM code CalculiX, respectively. The strong coupling between OpenFOAM and CalculiX is achieved by a multi-physics coupling tool preCICE.For the flexible tube, a commercial Natural Rubber material is studied. The hyper-elastic model YEOH is utilized to describe the nonlinear behaviour of material, and the model constants are calculated from the bi-axial tests. With the tool developed, numerical simulations are performed for different given regular waves. The flow details, velocity and pressure variation, structure deformation and stress distribution will be fully examined to better understand energy conversion performance of Anaconda WEC with mooring lines.
 References[1] Farley F J M D, Rainey R C T. Distensible tube wave energy converter: U.S. Patent 7,980,071[P]. 2011-7-19.[2] Chaplin J R, Heller V, Farley F J M, et al. Laboratory testing the Anaconda[J]. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2012, 370(1959): 403-424.[3] Heller V, Chaplin J R, Farley F J M, et al. Physical model tests of the anaconda wave energy converter[C]//Proc. 1st IAHR European Congress. 2000.[4] Farley F J M, Rainey R C T, Chaplin J R. Rubber tubes in the sea[J]. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2012, 370(1959): 381-402.[5] Babarit A, Singh J, Mélis C, et al. A linear numerical model for analysing the hydroelastic response of a flexible electroactive wave energy converter[J]. Journal of Fluids and Structures, 2017, 74: 356-384.[6] Checkmate Flexible Engineering, https://www.checkmateukseaenergy.com/, accessed 15th December 2022.[7] Huang Y, Xiao Q, Idarraga G, et al. Numerical analysis of flexible tube wave energy converter using CFD-FEA method[C]//International Conference on Offshore Mechanics and Arctic Engineering. American Society of Mechanical Engineers, 2023 (submitted).

Maximizing the surge amplitude of a floater through an adaptable mooring tightening technique

Abstract
 A technique to optimize the response of Wave Energy Converters (WECs) by maximizing the amplitude of motion along the surge direction is presented. This is achieved by utilizing an adaptable mooring tightening technique for a floater moored with tension legs (tendons). To gain a deeper understanding of the effect of sea states and mooring cable lengths on the surge response of the system, a series of numerical simulations were conducted for various wave conditions while varying the length of the mooring cables. WEC-Sim [1] was used to solve the multi-body dynamics of a rectangular cuboid floater by solving the equations of motion using a time-domain formulation. The dynamics of the mooring cables were simulated using the MoorDyn model with a lumped-mass formulation [2]. To validate the accuracy of the numerical methods, a series of experimental tests were performed in a small-scale wave tank. It was observed that tightening the mooring cables by decreasing their length amplifies the surge motion of the floater while the mooring forces in the heave direction rise due to the increased tension in the cables. Stretching the cables further was found to (i) decrease the surge amplitude and (ii) drastically increase the mooring forces, threatening the integrity of the cables. Therefore, there is an optimum value of the length of the cables that maximizes the surge amplitude of the floater while ensuring that the cables will not break. The impact of other mooring cable parameters such as diameter and material properties were also evaluated. More specifically, increasing the stiffness by increasing the diameter or the tensile modulus of elasticity was found to reduce the floater’s surge amplitude. For the geometry used in this study, the optimum length, diameter and properties of the cables are provided for several sea states. The current results lay the foundations for the design of new types of WECs that harness the surge motion of a floater rather than the heave which is the most common approach for floating WECs.
 References
 [1]: Kelley Ruehl, David Ogden, Yi-Hsiang Yu, Adam Keester, Nathan Tom, Dominic Forbush, Jorge Leon, Jeff Grasberger, and Salman Husain. (2022, September), WEC-Sim (Version v5.0.1), DOI: 10.5281/zenodo.7121186.
 [2]: Hall, M., & Goupee, A. (2015). Validation of a lumped-mass mooring line model with DeepCwind semisubmersible model test data. Ocean Engineering, 104, 590–603. https://doi.org/10.1016/j.oceaneng.2015.05.035

Reducing the uncertainty of ULS load estimates in offshore structural design

The design process of any offshore structure, including Wave Energy Converters (WECs), aims to assess a series of critical conditions, often encapsulated in the concept of ‘limit states’, that define the ‘design boarders’ across which a structure is unlikely to respond satisfactorily, potentially leading to functional failure(s). The Load and Resistance Factor Design (LRFD) method aims to quantify such ‘design boarders’ with adequate safety margins on both the loading and the resistance sides of the design inequality. An inherent risk of such approach is that the definition of ‘adequate’ may be clouded by multiple sources of uncertainty, making it challenging to assess if a system is likely to be under- or over-designed from inception.
 Although overall guidance for the design process of a WEC can be sought from related industries – see e.g. [1], and while noting that generic guidance for WEC design is available in e.g. [2], there is at present limited (practical) guidance on how to derive estimates of long-term return period loads. In recent work, comparative assessments of different load estimation methods have been made, illustrating the dependence of the outputs on the underlying method – see e.g. [3]. Additionally, and in connection with the assessment of extreme loads acting on WECs, the load post-processing methodology was identified in [4] as the major contributor to the uncertainty in Ultimate Limit State (ULS) load estimates.
 This paper presents a novel post-processing methodology to assess the uncertainty when estimating ULS loads acting on an offshore structure. To assess which statistical distributions are best suited to estimate long-term extreme loads, goodness-of-fit tests were performed using a series of input load time-series. The methodology was applied to evaluate the 50-year return load acting on the foundation of a generic Submerged Pressure Differential (SPD) WEC, based on the generic configuration originally defined in [5]. Results suggest that current conventional practices based on visual inspection(s) may lead to the selection of non-representative fitting functions which, in turn, likely lead to inaccurate extreme load estimations.
 Ultimately, the methodology described in this paper aims to contribute to a probabilistic approach to the definition of suitable safety factors, which in turn is expected to reduce the uncertainty in key design metrics and the risk of either under- or over-design.
 This study was conducted as part of the H2020 VALID and H2020 IMPACT projects.
 References
 [1] DNVGL-ST-0437. (2016). Loads and site conditions for wind turbines.
 [2] IEC/TS 62600-2. (2019). Marine energy — Wave, tidal and other water current converters Part 2: Design requirements for marine energy systems.
 [3] Michelen, C., Coe, R. Comparison of Methods for Estimating Short-Term Extreme Response of Wave Energy Converters, Sandia National Laboratories, SAND2015-6890C.
 [4] Atcheson, M., Cruz, J., Martins, T., Johannesson, P., Svensson, T. (2019). Quantification of load uncertainties in the design process of a WEC, Proc. 13th European Wave and Tidal Energy Conference (EWTEC 2019), Naples, Italy.
 [5] Babarit, A., Hals, J., Muliawan, M.J. et al. (2012). Numerical benchmarking study of a selection of wave energy converters. Renewable Energy 41, 44-63.

Experimental study of multiple hemisphere wave energy converters arrayed in a water channel resonator

In this study, the performance of multiple hemisphere Wave Energy Converters (WECs) arrayed in a Water Channel Resonator (WCR) has been investigated in irregular waves. First, we determine the characteristics of wave responses from model tests, using 16 wave probes in a WCR. Second, the pitch motion responses of three WECs in a WCR are determined. Experimental results are compared with the numerical solutions using the time-domain SeaFEM and OrcaFlex commercial code and agree well with the numerical results. Both experimental and numerical results indicate that when the incident peak period is close to one of the natural periods in a closed WCR, resonance occurs in the WCR. This resonance induces a large wave response and causes a high pitch motion response of WECs. The present study highlights the advantages of using a WCR for energy amplification and lays the necessary foundation for the commercialization of the present WEC system.

Performance analysis of a tuned point absorber using SPH calm water and wave tank simulations

In this paper, two smoothed particle hydrodynamics (SPH) models, namely SPH-W and SPH-C were used to evaluate the motion response of a point absorber wave energy converter (WEC). In the SPH-W model, a long wave flume was constructed and a long simulation was performed to obtain the motion response of the WEC. In the SPH-C model, the SPH method is only used to find the hydrodynamic coefficients of the device by analysing a few seconds of free-decaying motion of WEC in calm water in a much smaller numerical flume. Then, these coefficients were inserted in the equation of motion of a heaving WEC that was solved using a 4th order Runge-Kutta (ODE45) solver in MATLAB. First, the energy conservation property of the WCSPH model was examined through a standing wave benchmark test. Then, the wave-point absorber interaction was simulated. While the simulation time for SPH-C model is much smaller than that of SPH-W, it gave almost similar results for the motion response of WEC. These two models were used to evaluate the effects of the control force and the draft of a cone-cylinder point absorber on its hydrodynamic responses. The results showed that compared to the effect of the supplementary inertia, changes in the draft of the WEC have a small influence on its hydrodynamic responses. The buoy draft has an inverse relationship with both added mass and damping coefficients. However, increasing the supplementary mass increases the added mass and decreases the hydrodynamic damping coefficients.

Effects of mooring systems on dynamic response of wave energy converter

Effects of mooring systems on dynamic response of wave energy converter

Tank testing experiment of the Mocean M100 wave energy converter: linear non-causal optimal control and wave prediction

This paper presents tank testing experimental results of applying a non-causal optimal control strategy to a hinged-raft wave energy converter (WEC). The linear non-causal optimal control (LNOC) algorithm is designed and implemented in real-time to calculate the PTO torque signal based on the WEC response feedback information and the incoming wave feed-forward information. A controllable DC motor is used to provide the required torque to the WEC hinge. Tank testing results show that, compared with a well-tuned passive damper, the LNOC can improve the absorbed mechanical power in most of the tested sea conditions by up to 126%.

A new method for predicting the extreme dynamic responses of wave energy converters

The copula-based environmental contour approach in the existing literature is only ‘partially’ non-parametric. Theoretically, the derived environmental contours from this ‘non-parametric’ copula-based approach will still be somewhat rigid. Optimally, the environmental contours for a specific ocean site should be developed based on a joint model of the environmental variables and the joint model should be directly estimated by a two-dimensional non-parametric approach. In this study, the use of a bivariate kernel density estimation approach for generating environmental contours is proposed. The advantages of the proposed new method were validated using two calculation examples based on measured wave data at two offshore locations. It was found, in a wave energy converter (WEC) application example, that the design value will increase by 23.4% if the proposed method is used in comparison to using the technique based on the non-parametric Gumbel copula environmental contour method. It was also concluded that the design value will increase by 15.98% if the proposed method is used in comparison to using the technique based on the non-parametric Clayton copula environmental contour method. The calculation results in this paper clearly demonstrate that the proposed new method can be used to effectively forecast the extreme dynamic responses of WECs.

Development of a numerical model of the CECO wave energy converter using computational fluid dynamics

As the world strives to remove its reliance on fossil fuels, wave energy presents a reliable source of renewable energy with a very high potential. Numerical simulations offer an inexpensive alternative, in comparison to physical modelling, for the development of wave energy converters. In this paper, a computational fluid dynamics model of the CECO wave energy converter (WEC) has been developed using the commercial software ANSYS CFX. In order to reduce on the computational resources required, a 2-dimensional model of this sloped (combination of heave and surge) motion WEC has been developed and then successfully validated with experimental results from physical model tests, demonstrating the capability of such models to accurately describe the response of WECs. The validated numerical model was then used to investigate the non-linear effects on the motions of CECO and to obtain more insights in relation to wave loading during a wave cycle and the viscous effects associated to the dissipation of energy in the flow around its floaters. The water particle velocity and vorticity around CECO and the heave and surge loadings on CECO, while it is in operation, are analysed and discussed. The numerical model, not only aid in the development of a new and enhanced geometry for CECO but, also, it can be used to model and analyse similar WECs.

Power Performance of the Combined Monopile Wind Turbine and Floating Buoy with Heave-type Wave Energy Converter

Abstract This study deals with a new concept of near-shore combined renewable energy system which integrates a monopile wind turbine and a floating buoy with heave-type wave energy converter( WEC). Wave energy is absorbed by power-take-off (PTO) systems. Four different shapes of buoy model are selected for this study. Power performance in regular waves is calculated by using boundary element method in ANSYS-AQWA software in both time and frequency domains. This software is based on three-dimensional radiation/diffraction theory and Morison’s equation using mixture of panels and Morison elements for determining hydrodynamic loads. For validation of the approach the numerical results of the main dynamic responses of WEC in regular wave are compared with the available experimental data. The effects of the heaving buoy geometry on the main dynamic responses such as added mass, damping coefficient, heave motion, PTO damping force and mean power of various model shapes of WEC in regular waves with different periods, are compared and discussed. Comparison of the results showed that using WECs with a curvature inward in the bottom would absorb more energy from sea waves.

Classification systems for wave energy resources and WEC technologies

Classification systems for wave energy resources and wave energy converter (WEC) technologies could provide similar benefits to those for the wind energy industry: resource classification facilitating reconnaissance studies and project planning at both regional and national scales; and WEC classification streamlining and reducing costs of WEC device design and manufacturing. In the present study, a classification system for U.S. wave resources is used to investigate the feasibility of WEC classification. Wave spectra inputs from three wave energy resource classes delineated in this system are used to derive distributions of optimized WEC design scaling factors, as well as WEC design responses. Preliminary results indicate that a single standard WEC design class could serve within a given resource class, and corresponding regional wave climate, due to distinct wave energy distributions and concentrations of energy within partitioned period bands for each resource class. The WEC response to extreme loads was found to vary considerably within the most energetic of the resource classes examined, suggesting the need for these standard design classes to meet structural design requirements based on the upper limits of load response within a given resource class. However, the observed load metric variation is lower than the inter-region resource variations.

On a submerged wave energy converter with snap-through power take-off

This paper investigates the performance of a bistable snap-through power take-off (PTO) operating inside a submerged wave energy converter (WEC). The equation of motion of the surging WEC is derived in the time domain using the Euler–Lagrange equations. The dynamic response of the WEC in regular waves is studied first. It is found that the wave amplitude has a significant impact on the energy conversion efficiency with the proposed energy extraction mechanism. With larger waves impacting on the WEC, the conversion efficiency of the present nonlinear PTO increases significantly. Three response regimes, i.e. local oscillation, aperiodic snap-through, and periodic snap-through, of the nonlinear PTO system are observed with various wave amplitudes. This nonlinear feature is quite different from the linear PTO mechanism that is independent of the wave amplitude. Further, the dynamic response of the nonlinear WEC subjected to irregular wave sea conditions is investigated. Parametric studies have been carried out to determine the optimum operating conditions of the bistable device in order to maximize the wave energy extraction. The utilization of the snap-through PTO can enhance the efficiency of the WEC over its linear counterpart in irregular waves.

Wave Climate Resource Analysis Based on a Revised Gamma Spectrum for Wave Energy Conversion Technology

In order to correctly predict and evaluate the response of wave energy converters (WECs), an accurate representation of wave climate resource is crucial. This paper gives an overview of wave resource modeling techniques and applies a methodology to estimate the naturally available and technically recoverable resource in a given deployment site. The methodology was initially developed by the Electric Power Research Institute (EPRI), which uses a modified gamma spectrum to interpret sea state hindcast parameter data produced by National Oceanic and Atmospheric Administration’s (NOAA’s) WaveWatch III. This gamma spectrum is dependent on the calibration of two variables relating to the spectral width parameter and spectral peakedness parameter. In this study, this methodology was revised by the authors to increase its accuracy in formulating wavelength. The revised methodology shows how to assess a given geographic area’s wave resource based on its wave power density and total annual wave energy flux.

Analysis and optimization of a tethered wave energy converter in irregular waves

An understanding of the fundamental system dynamics of wave energy converters (WECs) is required to safely and reliably benefit from the available wave energy resource to produce electricity. The effects of the geometry, mooring system, and mass distribution on the idealized power takeoff of a tethered wave energy absorber in irregular waves are examined. The effects on coupled pitch and sway motions are also considered using a linear frequency-domain method, based on potential flow theory, to obtain the hydrodynamic coefficients. Superposition is used to calculate the response in irregular waves. The objectives of this paper are to examine the characteristic system response of WECs, and to demonstrate the use of an efficient potential-based method for the optimization of a WEC to maximize the annual power takeoff while ensuring system safety at a given site. The analyses suggest that the idealized power takeoff damping increases with the size of the WEC, with the intensity of motion limited. A relatively light mooring system has little effect on the power takeoff, but it introduces a low-frequency coupled pitch-surge resonance that can cause system failure if subject to long-period swells. To mitigate the risk of coupled surge-pitch related failures, a low center of gravity and a low radius of gyration of the floater about the center of floatation are recommended. The results also demonstrate the importance of tuning the system for the site-specific probabilistic wave climate in order to maximize total energy capture and avoid potential failures. ► Fundamental dynamic response of moored wave energy converters in 3 degrees of freedom. ► Semi-analytical method to maximize energy extraction and ensure structural safety. ► Important to tune resonance frequencies to site-specific probabilistic wave climate. ► Mooring lines introduce additional low-frequency resonance. ► Low center of gravity and low radius of gyration minimize coupled pitch-surge motion.