Special Issue "Nonlinear Numerical Modelling of Wave Energy Converters"

A special issue of Journal of Marine Science and Engineering (ISSN 2077-1312).

Deadline for manuscript submissions: closed (30 November 2019).

Special Issue Editor

Prof. Dr. Claes Eskilsson
E-Mail Website
Guest Editor
Department of the Built Environment, Aalborg University, Thomas Manns Vej 23, DK-9220 Aalborg Ø, Denmark
Interests: numerical modelling; wave propagation; wave–body interaction; wave energy; mooring; high-order finite element models; computational fluid dynamics
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Special Issue Information

Dear Colleagues,

The performance of wave energy converters is traditionally estimated using numerical models based on linear radiation/diffraction theory. However, over the last couple of years, we have seen an increase in the use of high-fidelity nonlinear hydrodynamic modelling for wave energy converters. The nonlinear approach is, of course, used in order to overcome the shortcomings of the small-wave-amplitude/small-motion assumptions underlying the linear approach. To include nonlinearity in the modelling is especially important for survival cases including steep and breaking waves and large amplitude motions, as well as the often highly nonlinear response in the resonance region of wave energy converter (WEC). Closely related to the resonance response is the application of phase control strategies that also increase the nonlinear response.

We would like to invite papers dealing with numerical method development especially of nonlinear models for wave energy. This includes, but is not limited to, computational fluid dynamics (CFD) as well as medium fidelity models such as fully and weakly nonlinear potential flow models and nonlinear Froude-Krylov approach. We are also interested in studies covering applications of nonlinear models in the wave energy field, and papers investigating nonlinear and viscous effects on WECs, for example parametric excitation. Additionally, experimental papers looking into nonlinear effects are highly encouraged.

Assoc. Prof. Claes Eskilsson
Guest Editor

Manuscript Submission Information

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Keywords

  • wave energy
  • numerical methods
  • nonlinear hydrodynamics
  • phase control

Published Papers (8 papers)

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Research

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Article
The Effect of Mooring Line Parameters in Inducing Parametric Resonance on the Spar-Buoy Oscillating Water Column Wave Energy Converter
J. Mar. Sci. Eng. 2020, 8(1), 29; https://doi.org/10.3390/jmse8010029 - 08 Jan 2020
Cited by 15 | Viewed by 1156
Abstract
Although it is widely accepted that accurate modeling of wave energy converters is essential for effective and reliable design, it is often challenging to define an accurate model which is also fast enough to investigate the design space or to perform extensive sensitivity [...] Read more.
Although it is widely accepted that accurate modeling of wave energy converters is essential for effective and reliable design, it is often challenging to define an accurate model which is also fast enough to investigate the design space or to perform extensive sensitivity analysis. In fact, the required accuracy is usually brought by the inclusion of nonlinearities, which are often time-consuming to compute. This paper provides a computationally efficient meshless nonlinear Froude–Krylov model, including nonlinear kinematics and an integral formulation of drag forces in six degrees of freedom, which computes almost in real-time. Moreover, a mooring system model with three lines is included, with each line comprising of an anchor, a jumper, and a clump weight. The mathematical model is used to investigate the highly-nonlinear phenomenon of parametric resonance, which has particularly detrimental effects on the energy conversion performance of the spar-buoy oscillating water column (OWC) device. Furthermore, the sensitivity on changes to jumper and clump-weight masses are discussed. It is found that mean drift and peak loads increase with decreasing line pre-tension, eventually leading to a reduction of the operational region. On the other hand, the line pre-tension does not affect power production efficiency, nor is it able to avoid or significantly limit the severity of parametric instability. Full article
(This article belongs to the Special Issue Nonlinear Numerical Modelling of Wave Energy Converters)
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Article
Development of a Blended Time-Domain Program for Predicting the Motions of a Wave Energy Structure
J. Mar. Sci. Eng. 2020, 8(1), 1; https://doi.org/10.3390/jmse8010001 - 19 Dec 2019
Cited by 10 | Viewed by 848
Abstract
Traditional linear time-domain analysis is used widely for predicting the motions of floating structures. When it comes to a wave energy structure, which usually is subjected to larger relative (to their geometric dimensions) wave and motion amplitudes, the nonlinear effects become significant. This [...] Read more.
Traditional linear time-domain analysis is used widely for predicting the motions of floating structures. When it comes to a wave energy structure, which usually is subjected to larger relative (to their geometric dimensions) wave and motion amplitudes, the nonlinear effects become significant. This paper presents the development of an in-house blended time-domain program (SIMDYN). SIMDYN’s “blend” option improves the linear option by accounting for the nonlinearity of important external forces (e.g., Froude-Krylov). In addition, nonlinearity due to large body rotations (i.e., inertia forces) is addressed in motion predictions of wave energy structures. Forced motion analysis reveals the significance of these nonlinear effects. Finally, the model test correlations examine the simulation results from SIMDYN under the blended option, which has seldom been done for a wave energy structure. It turns out that the blended time-domain method has significant potential to improve the accuracy of motion predictions for a wave energy structure. Full article
(This article belongs to the Special Issue Nonlinear Numerical Modelling of Wave Energy Converters)
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Article
Ocean Energy Systems Wave Energy Modelling Task: Modelling, Verification and Validation of Wave Energy Converters
J. Mar. Sci. Eng. 2019, 7(11), 379; https://doi.org/10.3390/jmse7110379 - 25 Oct 2019
Cited by 20 | Viewed by 1957
Abstract
The International Energy Agency Technology Collaboration Programme for Ocean Energy Systems (OES) initiated the OES Wave Energy Conversion Modelling Task, which focused on the verification and validation of numerical models for simulating wave energy converters (WECs). The long-term goal is to assess the [...] Read more.
The International Energy Agency Technology Collaboration Programme for Ocean Energy Systems (OES) initiated the OES Wave Energy Conversion Modelling Task, which focused on the verification and validation of numerical models for simulating wave energy converters (WECs). The long-term goal is to assess the accuracy of and establish confidence in the use of numerical models used in design as well as power performance assessment of WECs. To establish this confidence, the authors used different existing computational modelling tools to simulate given tasks to identify uncertainties related to simulation methodologies: (i) linear potential flow methods; (ii) weakly nonlinear Froude–Krylov methods; and (iii) fully nonlinear methods (fully nonlinear potential flow and Navier–Stokes models). This article summarizes the code-to-code task and code-to-experiment task that have been performed so far in this project, with a focus on investigating the impact of different levels of nonlinearities in the numerical models. Two different WECs were studied and simulated. The first was a heaving semi-submerged sphere, where free-decay tests and both regular and irregular wave cases were investigated in a code-to-code comparison. The second case was a heaving float corresponding to a physical model tested in a wave tank. We considered radiation, diffraction, and regular wave cases and compared quantities, such as the WEC motion, power output and hydrodynamic loading. Full article
(This article belongs to the Special Issue Nonlinear Numerical Modelling of Wave Energy Converters)
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Article
A Wave Energy Converter Design Load Case Study
J. Mar. Sci. Eng. 2019, 7(8), 250; https://doi.org/10.3390/jmse7080250 - 30 Jul 2019
Cited by 9 | Viewed by 1523
Abstract
This article presents an example by which design loads for a wave energy converter (WEC) might be estimated through the various stages of the WEC design process. Unlike previous studies, this study considers structural loads, for which, an accurate assessment is crucial to [...] Read more.
This article presents an example by which design loads for a wave energy converter (WEC) might be estimated through the various stages of the WEC design process. Unlike previous studies, this study considers structural loads, for which, an accurate assessment is crucial to the optimization and survival of a WEC. Three levels of computational fidelity are considered. The first set of design load approximations are made using a potential flow frequency-domain boundary-element method with generalized body modes. The second set of design load approximations are made using a modified version of the linear-based time-domain code WEC-Sim. The final set of design load simulations are realized using computational fluid dynamics coupled with finite element analysis to evaluate the WEC’s loads in response to both regular and focused waves. This study demonstrates an efficient framework for evaluating loads through each of the design stages. In comparison with experimental and high-fidelity simulation results, the linear-based methods can roughly approximate the design loads and the sea states at which they occur. The high-fidelity simulations for regular wave responses correspond well with experimental data and appear to provide reliable design load data. The high-fidelity simulations of focused waves, however, result in highly nonlinear interactions that are not predicted by the linear-based most-likely extreme response design load method. Full article
(This article belongs to the Special Issue Nonlinear Numerical Modelling of Wave Energy Converters)
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Article
Numerical and Experimental Modelling of a Wave Energy Converter Pitching in Close Proximity to a Fixed Structure
J. Mar. Sci. Eng. 2019, 7(7), 218; https://doi.org/10.3390/jmse7070218 - 13 Jul 2019
Cited by 2 | Viewed by 1151
Abstract
Free-floating bodies are commonly modelled using Cummins’ equation based on linear potential flow theory and including non-linear forces when necessary. In this paper, this methodology is applied to a body pitching around a fixed hinge (not free-floating) located close to a second bottom-fixed [...] Read more.
Free-floating bodies are commonly modelled using Cummins’ equation based on linear potential flow theory and including non-linear forces when necessary. In this paper, this methodology is applied to a body pitching around a fixed hinge (not free-floating) located close to a second bottom-fixed body. Due to the configuration of the setup, strong hydrodynamic interactions occur between the two bodies. An investigation is made into which non-linear forces need to be included in the model in order to accurately represent reality without losing computational efficiency. The non-linear forces investigated include hydrostatic restoring stiffness and different formulations of excitation forces and quadratic drag forces. Based on a numerical comparison, it is concluded that the different non-linear forces, except for the quadratic drag force, have a minor influence on the calculated motion of the pitching body. Two formulations of the quadratic drag force are shown to result in similar motions, hence the most efficient one is preferred. Comparisons to wave basin experiments show that this model is, to a large extent, representative of reality. At the wave periods where the hydrodynamic interactions between the bodies are largest, however, the amplitudes of motion measured in the wave basin are lower than those calculated numerically. Full article
(This article belongs to the Special Issue Nonlinear Numerical Modelling of Wave Energy Converters)
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Article
Evaluation of the Viscous Drag for a Domed Cylindrical Moored Wave Energy Converter
J. Mar. Sci. Eng. 2019, 7(4), 120; https://doi.org/10.3390/jmse7040120 - 25 Apr 2019
Cited by 4 | Viewed by 1264
Abstract
Viscous drag, nonlinear in nature, is an important aspect of the fluid–structure interaction modelling and is usually not taken into account when the fluid is assumed to be inviscid. Potential flow solvers can competently compute radiation damping, which is related to the radiated [...] Read more.
Viscous drag, nonlinear in nature, is an important aspect of the fluid–structure interaction modelling and is usually not taken into account when the fluid is assumed to be inviscid. Potential flow solvers can competently compute radiation damping, which is related to the radiated wave field. However, the drag damping primarily related to the viscous effects is usually neglected in the radiation/diffraction problems solved by the boundary element method (BEM), also known as the boundary integral element method (BIEM). This drag force can have a significant impact in the case of structures extending much deeper below the free surface, or for those that are completely submerged. In this paper, the drag coefficient C d was quantified for the heave and surge response of a structure which consists of a moored horizontally oriented domed cylinder with two surface piercing square columns located at the top surface. The domed cylinder is the primary part and is submerged. The drag coefficient is estimated using the experimental measurements related to harmonic monochromatic wave–structure interaction. Finally, this estimated drag coefficient was used in the modified time domain model, which includes the nonlinear viscous correction term, and the resulting device response in heave and surge directions is presented for an irregular incoming wave field. The comparison of the numerical model and the experiments validates the estimated C d values obtained earlier. Prior to the time domain model, frequency-dependent parameters such as added mass, radiation damping, and excitation force were computed using three mainstream potential flow packages (that is, ANSYS AQWA, WAMIT, and NEMOH), and a comparison is presented. The effect of free surface on the drag coefficient is investigated through differences in C d values between heave and surge modes. Full article
(This article belongs to the Special Issue Nonlinear Numerical Modelling of Wave Energy Converters)
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Article
Assessment of Scale Effects, Viscous Forces and Induced Drag on a Point-Absorbing Wave Energy Converter by CFD Simulations
J. Mar. Sci. Eng. 2018, 6(4), 124; https://doi.org/10.3390/jmse6040124 - 22 Oct 2018
Cited by 15 | Viewed by 1634
Abstract
This paper analyses the nonlinear forces on a moored point-absorbing wave energy converter (WEC) in resonance at prototype scale (1:1) and at model scale (1:16). Three simulation types were used: Reynolds Averaged Navier–Stokes (RANS), Euler and the linear radiation-diffraction method (linear). Results show [...] Read more.
This paper analyses the nonlinear forces on a moored point-absorbing wave energy converter (WEC) in resonance at prototype scale (1:1) and at model scale (1:16). Three simulation types were used: Reynolds Averaged Navier–Stokes (RANS), Euler and the linear radiation-diffraction method (linear). Results show that when the wave steepness is doubled, the response reduction is: (i) 3% due to the nonlinear mooring response and the Froude–Krylov force; (ii) 1–4% due to viscous forces; and (iii) 18–19% due to induced drag and non-linear added mass and radiation forces. The effect of the induced drag is shown to be largely scale-independent. It is caused by local pressure variations due to vortex generation below the body, which reduce the total pressure force on the hull. Euler simulations are shown to be scale-independent and the scale effects of the WEC are limited by the purely viscous contribution (1–4%) for the two waves studied. We recommend that experimental model scale test campaigns of WECs should be accompanied by RANS simulations, and the analysis complemented by scale-independent Euler simulations to quantify the scale-dependent part of the nonlinear effects. Full article
(This article belongs to the Special Issue Nonlinear Numerical Modelling of Wave Energy Converters)
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Review

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Review
Efficient Nonlinear Hydrodynamic Models for Wave Energy Converter Design—A Scoping Study
J. Mar. Sci. Eng. 2020, 8(1), 35; https://doi.org/10.3390/jmse8010035 - 11 Jan 2020
Cited by 27 | Viewed by 1658
Abstract
This review focuses on the most suitable form of hydrodynamic modeling for the next generation wave energy converter (WEC) design tools. To design and optimize a WEC, it is estimated that several million hours of operation must be simulated, perhaps one million hours [...] Read more.
This review focuses on the most suitable form of hydrodynamic modeling for the next generation wave energy converter (WEC) design tools. To design and optimize a WEC, it is estimated that several million hours of operation must be simulated, perhaps one million hours of WEC simulation per year of the R&D program. This level of coverage is possible with linear potential flow (LPF) models, but the fidelity of the physics included is not adequate. Conversely, while Reynolds averaged Navier–Stokes (RANS) type computational fluid dynamics (CFD) solvers provide a high fidelity representation of the physics, the increased computational burden of these models renders the required amount of simulations infeasible. To scope the fast, high fidelity options, the present literature review aims to focus on what CFD theories exist intermediate to LPF and RANS as well as other modeling options that are computationally fast while retaining higher fidelity than LPF. Full article
(This article belongs to the Special Issue Nonlinear Numerical Modelling of Wave Energy Converters)
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