Numerical modelling of wave energy converters : state-of-the-art techniques for single devices and arrays

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 aut...

Full description

Saved in:
Bibliographic Details
Main Author Folley, Matt
Format eBook Book
LanguageEnglish
Published London Academic Press 2016
Elsevier Science & Technology
Edition1
Subjects
Electric generators
Electric power production
Electric power production > Mathematical models
Ocean wave power
Online AccessGet full text

Cover

Table of Contents:
  • Chapter 7: Identifying Models Using Recorded Data -- 7.1. Introduction and Fundamental Principles -- 7.2. Data Generation -- 7.2.1. Identification Experiments -- 7.2.1.1. Free Decay -- 7.2.1.2. Input Waves -- 7.2.1.3. Input Force -- 7.2.1.4. Prescribed Motion -- 7.3. Models for System Identification -- 7.3.1. Continuous-Time Models -- 7.3.2. Discrete-Time Models -- 7.3.2.1. Autoregressive With Exogenous Input Model (Linear) -- 7.3.2.2. Kolmogorov-Gabor Polynomial Model (Nonlinear) -- 7.3.2.3. Artificial Neural Network Model (Nonlinear) -- 7.3.2.4. Nonlinear Static Model (Nonlinear) -- 7.3.2.5. Block-Oriented Nonlinear Model (Nonlinear) -- 7.4. Identification Algorithms -- 7.4.1. System Identification -- 7.4.2. Linear Optimization -- 7.4.2.1. Time Delay and Dynamical Order Estimation (nd, na, nb) -- 7.4.2.2. Model Parameters Identification -- 7.4.3. Nonlinear Optimization -- 7.5. Case Studies -- 7.5.1. Case Study 1: Continuous-Time Models Identified From Free Responses -- 7.5.2. Case Study 2: Discrete-Time Models From Forced Oscillation -- 7.5.3. Case Study 3: Discrete-Time Models From Input Waves -- 7.6. Limitations -- 7.7. Summary -- References -- Part III: Wave Energy Converter Array Modelling Techniques -- Chapter 8: Conventional Multiple Degree-of-Freedom Array Models -- 8.1. Introduction and Fundamental Principles -- 8.2. Modelling Based on Linear Potential Flow -- 8.2.1. Frequency-Domain and Spectral-Domain Modelling -- 8.2.2. Time-Domain Modelling -- 8.3. Modelling Based on Other Techniques -- 8.4. Limitations -- 8.5. Summary -- References -- Chapter 9: Semi-analytical Array Models -- 9.1. Introduction -- 9.2. General Formulation -- 9.2.1. Mathematical Model -- 9.2.2. Partial Wave Representation of Velocity Potentials -- 9.2.2.1. Governing Equations -- 9.2.2.2. Ambient Incident Wave Potential -- 9.2.2.3. Scattered Potential
  • 9.2.2.4. Radiation Potential -- 9.2.3. Partial Wave Operators -- 9.2.3.1. Coordinate Transformation Operator -- 9.2.3.2. Diffraction Transfer Operator -- 9.3. Point Absorber Method -- 9.3.1. Background -- 9.3.2. Formulation -- 9.4. Plane Wave Method -- 9.4.1. Background -- 9.4.2. Formulation -- 9.5. Multiple Scattering Method -- 9.5.1. Background -- 9.5.2. Formulation -- 9.6. Direct Matrix Method -- 9.6.1. Background -- 9.6.2. Formulation -- 9.7. Capabilities and Limitations -- 9.7.1. Comparison Between Semi-analytical Methods -- 9.7.2. Comparison With Other Methods -- 9.7.3. Verification and Validation -- 9.8. Summary -- References -- Chapter 10: Phase-Resolving Wave Propagation Array Models -- 10.1. Introduction -- 10.2. Implementation of the WEC Simulation in the Wave Propagation Model MILDwave -- 10.2.1. General Formulation of MILDwave -- 10.2.2. Wave Generation on a Circle (for Radiated Waves) -- 10.2.3. Implementation of the Sponge Layer Technique -- 10.2.3.1. Influence of the Absorption Coefficient on the Absorption Characteristics -- 10.2.3.2. Influence of Length on the Absorption Characteristics -- 10.2.3.3. Frequency Dependent Absorption -- 10.2.4. Implementation of the Numerical Coupling Methodology -- 10.2.4.1. Introduction -- 10.2.4.2. The Generic Coupling Methodology for a Single WEC or for a WEC Farm Modelled as a Whole -- 10.2.4.3. The Generic Coupling Methodology for a WEC Farm of Individually Modelled WECs of Type (b) -- 10.3. Applications of the Numerical Techniques Using MILDwave -- 10.3.1. Wake Effects by a Single WEC of Type (a) -- 10.3.2. Wake Effects by a Farm of Type (a) WECs -- 10.3.3. Wake Effects by a Single Type (b) WEC -- 10.3.3.1. The Modelled WEC -- 10.3.3.2. Wave Conditions and Numerical Domains
  • 3.4.2. Numerical Computation of the RIRF -- 3.5. Convolution of the Radiation Forces -- 3.5.1. Direct Numerical Integration -- 3.5.2. Prony Identification Method -- 3.5.3. Time-Domain Identification -- 3.5.4. Frequency-Domain Identification -- 3.6. Hydrostatic Forces -- 3.7. Solution of the Cummins Equation -- 3.8. Case-Study: A Single-Body Heaving WEC -- 3.8.1. System Description -- 3.8.1.1. Linear PTO -- 3.8.1.2. Hydraulic PTO -- 3.8.2. Design and Verification of Time-Domain Models -- 3.9. The Influence of Simulation Duration -- 3.10. Limitations -- 3.11. Summary -- References -- Chapter 4: Spectral-Domain Models -- 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 -- References -- Part II: Other Wave Energy Converter Modelling Techniques -- Chapter 5: Nonlinear Potential Flow Models -- 5.1. Introduction and Fundamental Principles -- 5.1.1. Beyond Linear Theory -- 5.1.2. Fundamental Principles -- 5.1.3. Applications of FNPF Models in Wave Energy -- 5.2. Formulation of the Fully Nonlinear Potential Flow Model -- 5.3. Solution Methods For Fully Nonlinear Potential Flow Problems -- 5.3.1. Mixed Eulerian-Lagrangian Method -- 5.3.2. High-Order Spectral Methods -- 5.3.3. Computation of Hydrodynamic Body Forces and Motions -- 5.4. Calculating the WEC Response -- 5.4.1. WEC Response Subject to Linear PTO Forces -- 5.5. Limitations -- 5.6. Summary -- References -- Chapter 6: Computational Fluid Dynamics (CFD) Models -- 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 -- References
  • Front Cover -- Numerical Modelling of Wave Energy Converters: State-of-the-Art Techniques for Single Devices and Arrays -- Copyright -- Contents -- Contributors -- Chapter 1: Introduction -- 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 -- References -- Part I: Wave Energy Converter Modelling Techniques Based on Linear Hydrodynamic Theory -- Chapter 2: Frequency-Domain Models -- 2.1. Introduction and Fundamental Principles -- 2.2. Phenomenological Discussion -- 2.3. Potential Flow Theory -- 2.3.1. Laplace Equation -- 2.3.2. Boundary Conditions -- 2.3.3. Sinusoidal Waves -- 2.3.4. Problem Decomposition -- 2.4. Equation of Motion: Single Degree-of-Freedom WEC -- 2.4.1. Hydrodynamic Force -- 2.4.1.1. Solving the Potential Flow Boundary Value Problem -- Wave Excitation Force -- Radiation Force -- 2.4.1.2. Haskind Relation -- 2.4.1.3. Kramers-Kronig Relations -- 2.4.2. Hydrostatic Force -- 2.4.3. Reaction Forces -- 2.4.4. Complex Amplitude of the Body Motion -- 2.4.5. Power Absorption -- 2.4.5.1. Mean Power Absorption -- 2.4.5.2. Optimal PTO Control -- 2.4.5.3. Suboptimal PTO Control -- 2.4.5.4. Constrained Motion -- 2.4.5.5. Absorption Bandwidth -- 2.5. Equation of Motion: Multiple Degree-of-Freedom WEC -- 2.6. OWCs -- 2.7. Limitations -- 2.8. Summary -- References -- Chapter 3: Time-Domain Models -- 3.1. Introduction and Fundamental Principles -- 3.2. The Cummins Equation for Modelling WECs -- 3.3. Wave Excitation Forces -- 3.3.1. Wave Loads in Time-Domain Models -- 3.3.2. Excitation Forces as Superposition of Harmonic Components -- 3.3.3. Convolution of the Excitation Force -- 3.3.4. Nonlinear Wave Forces -- 3.4. The RIRF -- 3.4.1. Properties of the RIRF
  • 10.3.3.3. Modelling and Verification of the Radiated, Diffracted, and Perturbed Wave Fields Using the Coupling Methodology -- 10.4. Limitations -- 10.5. Summary -- References -- Chapter 11: Phase-Averaging Wave Propagation Array Models -- 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 -- References -- Part IV: Applications for Wave Energy Converter Models -- Chapter 12: Control Optimisation and Parametric Design -- 12.1. Introduction -- 12.2. Control of WECs -- 12.2.1. Control Effectors -- 12.2.2. Fundamental Control Results -- 12.2.3. Real-Time Model-Based WEC Control -- 12.2.3.1. A Simple but Effective WEC Controller -- 12.2.3.2. The 'Aalborg' PID Controller -- 12.2.3.3. WEC Controllers Based on Numerical Optimization -- 12.2.4. Control of WEC Arrays -- 12.2.5. Wave Forecasting -- 12.2.6. WEC Control Perspectives -- 12.3. Optimization of WECs and WEC Arrays -- 12.3.1. Geometric Optimization of WECs -- 12.3.2. WEC Array Layout Optimization -- 12.3.3. Summary -- References -- Chapter 13: Determining Mean Annual Energy Production -- 13.1. Introduction and Appropriate Modelling Techniques -- 13.2. Representation of the Wave Climate -- 13.2.1. Traditional (Scatter Table) Representation -- 13.2.2. Extensive Representation -- 13.2.3. Abridged Representation -- 13.3. Representation of Power Performance -- 13.4. Estimation of the MAEP -- 13.4.1. Power Matrix-Scatter Table -- 13.4.2. Power Matrix-Extensive/Abridged Wave Climate -- 13.4.3. Extensive/Abridged Power Performance-Extensive/Abridged Wave Climate -- 13.4.4. Abridged Power Performance-Extensive Wave Climate -- 13.5. Limitations and Constraints -- 13.6. Summary -- References -- Chapter 14: Determining Structural and Hydrodynamic Loads -- 14.1. Introduction -- 14.2. Design Principles
  • 14.2.1. General