Numerical Modelling of Wave Energy Converters

Numerical Modelling of Wave Energy Converters

State-of-the-Art Techniques for Single Devices and Arrays

1st Edition - June 13, 2016

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  • Editor: Matt Folley
  • Paperback ISBN: 9780128032107
  • eBook ISBN: 9780128032114

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Numerical Modelling of Wave Energy Converters: State-of-the Art Techniques for Single WEC and Converter Arrays presents all the information and techniques required for the numerical modelling of a wave energy converter together with a comparative review of the different available techniques. The authors provide clear details on the subject and guidance on its use for WEC design, covering topics such as boundary element methods, frequency domain models, spectral domain models, time domain models, non linear potential flow models, CFD models, semi analytical models, phase resolving wave propagation models, phase averaging wave propagation models, parametric design and control optimization, mean annual energy yield, hydrodynamic loads assessment, and environmental impact assessment. Each chapter starts by defining the fundamental principles underlying the numerical modelling technique and finishes with a discussion of the technique’s limitations and a summary of the main points in the chapter. The contents of the chapters are not limited to a description of the mathematics, but also include details and discussion of the current available tools, examples available in the literature, and verification, validation, and computational requirements. In this way, the key points of each modelling technique can be identified without having to get deeply involved in the mathematical representation that is at the core of each chapter. The book is separated into four parts. The first two parts deal with modelling single wave energy converters; the third part considers the modelling of arrays; and the final part looks at the application of the different modelling techniques to the four most common uses of numerical models. It is ideal for graduate engineers and scientists interested in numerical modelling of wave energy converters, and decision-makers who must review different modelling techniques and assess their suitability and output.

Key Features

  • Consolidates in one volume information and techniques for the numerical modelling of wave energy converters and converter arrays, which has, up until now, been spread around multiple academic journals and conference proceedings making it difficult to access
  • Presents a comparative review of the different numerical modelling techniques applied to wave energy converters, discussing their limitations, current available tools, examples, and verification, validation, and computational requirements
  • Includes practical examples and simulations available for download at the book’s companion website
  • Identifies key points of each modelling technique without getting deeply involved in the mathematical representation


graduate students and researchers in the area of wave energy conversion, engineering professionals involved in the development of wave energy converters.

Table of Contents

  • Chapter 1: Introduction

    • Abstract
    • 1.1 The Challenge of Wave Energy
    • 1.2 A Short History of the Numerical Modelling of WECs
    • 1.3 Current Challenges and Future Developments
    • 1.4 Why This Book
    • 1.5 How to Use This Book
    • 1.6 Acknowledgements

    I: Wave Energy Converter Modelling Techniques Based on Linear Hydrodynamic Theory

    Chapter 2: Frequency-Domain Models

    • Abstract
    • 2.1 Introduction and Fundamental Principles
    • 2.2 Phenomenological Discussion
    • 2.3 Potential Flow Theory
    • 2.4 Equation of Motion: Single Degree-of-Freedom WEC
    • 2.5 Equation of Motion: Multiple Degree-of-Freedom WEC
    • 2.6 OWCs
    • 2.7 Limitations
    • 2.8 Summary

    Chapter 3: Time-Domain Models

    • Abstract
    • 3.1 Introduction and Fundamental Principles
    • 3.2 The Cummins Equation for Modelling WECs
    • 3.3 Wave Excitation Forces
    • 3.4 The RIRF
    • 3.5 Convolution of the Radiation Forces
    • 3.6 Hydrostatic Forces
    • 3.7 Solution of the Cummins Equation
    • 3.8 Case-Study: A Single-Body Heaving WEC
    • 3.9 The Influence of Simulation Duration
    • 3.10 Limitations
    • 3.11 Summary

    Chapter 4: Spectral-Domain Models

    • Abstract
    • 4.1 Introduction and Fundamental Principles
    • 4.2 Formulation of the Spectral-Domain Model
    • 4.3 Solving a Spectral-Domain Model
    • 4.4 Examples of Spectral-Domain Modelling
    • 4.5 Further Developments
    • 4.6 Limitations
    • 4.7 Summary

    II: Other Wave Energy Converter Modelling Techniques

    Chapter 5: Nonlinear Potential Flow Models

    • Abstract
    • 5.1 Introduction and Fundamental Principles
    • 5.2 Formulation of the Fully Nonlinear Potential Flow Model
    • 5.3 Solution Methods For Fully Nonlinear Potential Flow Problems
    • 5.4 Calculating the WEC Response
    • 5.5 Limitations
    • 5.6 Summary

    Chapter 6: Computational Fluid Dynamics (CFD) Models

    • Abstract
    • 6.1 Introduction and Fundamental Principles
    • 6.2 Incompressible CFD Models
    • 6.3 Compressible Two-Phase CFD Models
    • 6.4 Smoothed-Particle Hydrodynamic Models
    • 6.5 Limitations
    • 6.6 Future Developments
    • 6.7 Summary

    Chapter 7: Identifying Models Using Recorded Data

    • Abstract
    • 7.1 Introduction and Fundamental Principles
    • 7.2 Data Generation
    • 7.3 Models for System Identification
    • 7.4 Identification Algorithms
    • 7.5 Case Studies
    • 7.6 Limitations
    • 7.7 Summary

    III: Wave Energy Converter Array Modelling Techniques

    Chapter 8: Conventional Multiple Degree-of-Freedom Array Models

    • Abstract
    • 8.1 Introduction and Fundamental Principles
    • 8.2 Modelling Based on Linear Potential Flow
    • 8.3 Modelling Based on Other Techniques
    • 8.4 Limitations
    • 8.5 Summary

    Chapter 9: Semi-analytical Array Models

    • Abstract
    • 9.1 Introduction
    • 9.2 General Formulation
    • 9.3 Point Absorber Method
    • 9.4 Plane Wave Method
    • 9.5 Multiple Scattering Method
    • 9.6 Direct Matrix Method
    • 9.7 Capabilities and Limitations
    • 9.8 Summary

    Chapter 10: Phase-Resolving Wave Propagation Array Models

    • Abstract
    • 10.1 Introduction
    • 10.2 Implementation of the WEC Simulation in the Wave Propagation Model MILDwave
    • 10.3 Applications of the Numerical Techniques Using MILDwave
    • 10.4 Limitations
    • 10.5 Summary

    Chapter 11: Phase-Averaging Wave Propagation Array Models

    • Abstract
    • 11.1 Introduction and Fundamental Principles
    • 11.2 Supragrid Models of WEC Arrays
    • 11.3 Subgrid Models of WEC Arrays
    • 11.4 Limitations
    • 11.5 Summary

    IV: Applications for Wave Energy Converter Models

    Chapter 12: Control Optimisation and Parametric Design

    • Abstract
    • 12.1 Introduction
    • 12.2 Control of WECs
    • 12.3 Optimization of WECs and WEC Arrays

    Chapter 13: Determining Mean Annual Energy Production

    • Abstract
    • 13.1 Introduction and Appropriate Modelling Techniques
    • 13.2 Representation of the Wave Climate
    • 13.3 Representation of Power Performance
    • 13.4 Estimation of the MAEP
    • 13.5 Limitations and Constraints
    • 13.6 Summary

    Chapter 14: Determining Structural and Hydrodynamic Loads

    • Abstract
    • 14.1 Introduction
    • 14.2 Design Principles
    • 14.3 Site Characterization
    • 14.4 Device Considerations
    • 14.5 Design Criteria
    • 14.6 Structural Assessment
    • 14.7 Summary

    Chapter 15: Environmental Impact Assessment

    • Abstract
    • 15.1 Introduction
    • 15.2 Ecological Processes
    • 15.3 Modelling Approach
    • 15.4 Limitations
    • 15.5 Summary

Product details

  • No. of pages: 306
  • Language: English
  • Copyright: © Academic Press 2016
  • Published: June 13, 2016
  • Imprint: Academic Press
  • Paperback ISBN: 9780128032107
  • eBook ISBN: 9780128032114

About the Editor

Matt Folley

Matt Folley
Matt Folley is currently a Senior Research Fellow in the Marine Renewables Research Group at Queen’s University Belfast and member of the SuperGen UK Centre for Marine Energy Research, dedicated to the establishment of marine technology as a means of sustainable power generation. He has been modelling wave energy converters for over 25 years and has first-hand experience of developing and using a wide range of numerical models of wave energy converters and wave energy converter arrays. He was a co-founder and inaugural convenor of the wave energy converter array network (WECAN), which is an international expert group focused on the modelling of wave energy converter arrays. He is also chair of the IEC international committee for the development of standards for the assessment and characterisation of the wave energy resource and UK principle expert on the IEC international committee for the development of standards for the assessment of the performance of wave energy converters. He has worked with a number of companies on modelling their wave energy converters, including WaveGen and Aquamarine Power.

Affiliations and Expertise

Senior Research Fellow, Marine Renewables Research Group, Queen’s University Belfast and member of the SuperGen UK Centre for Marine Energy Research

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