A comparison of methods for computation of wave forcing

Table of Contents

1 INTRODUCTION

1.1 Background

1.2 Outline

2 STATE OF THE ART

2.1 Regular Waves

2.1.1 Description

2.1.2 Linear Wave Theory

2.1.2.1 Basic equations

2.1.2.2 Boundary conditions

2.1.2.3 Wave kinematics and pressure

2.1.3 Stretched Airy Theory

2.2 Irregular Waves

2.2.1 Description in the Frequency Domain

2.3 Hydrostatics of Floating Structures

2.3.1 Static Stability

2.4 Hydrodynamics of Rigid Bodies

2.4.1 Coordinate Systems

2.4.2 Diffraction Theory

2.5 Hydrostatic- and Dynamic Loads on Floating Structures

2.5.1 Fundamentals

2.5.2 Forces and Moments

2.5.3 Radiation and Diffraction Loads

2.5.4 Wave Excitation Loads

2.5.5 Hydrostatic Loads

2.6 Floating Structures in Waves

2.6.1 Coupled Equations of Motion

2.6.2 Motions in Regular Waves

2.6.2.1 Response amplitude operator

2.6.3 Motions in Irregular Waves

3 FLOATING WIND TURBINE MODEL

3.1 OC3 Hywind

3.1.1 Tower and Platform Structural Properties

3.1.2 Floating Platform Hydrodynamic Properties

3.1.3 Mooring System Properties

4 MATLAB

4.1 Morison Forces

4.1.1 Morison Forces due to Regular Waves

4.1.2 Morison forces due to Irregular Waves

5 SESAM

5.1 GeniE

5.1.1 The Modelling Process

5.2 HydroD

5.2.1 Coordinate System

5.2.2 Panel Model

5.2.3 Mass Model

5.2.4 Analysis Preparation

5.2.5 Wadam

5.2.5.1 Global Response Analysis in Wadam

5.2.6 Postresp

6 FAST

6.1 Basic Assumptions

6.2 Hydrodynamic Module (HydroDyn)

6.2.1 Diffraction Problem

6.2.2 Radiation Problem

6.3 Hydrodynamic Results

6.3.1 Regular Waves

6.3.2 Irregular Waves

7 COMPARISONS OF THE METHODS

7.1 Comparison of Excitation Loads

7.2 Comparison of Response Motions

8 SUMMARY AND CONCLUSION

Objectives & Scope

This thesis aims to investigate the wave-induced loads acting on an OC3 Hywind spar-buoy and to analyze the resulting motions of its support platform. By comparing different numerical methods—specifically Morison's equation in MATLAB, diffraction theory via SESAM, and the fully coupled aero-hydro-servo-elastic simulations in FAST—the research evaluates how these approaches model hydrodynamic interactions, platform responses, and the overall dynamic behavior of floating offshore wind turbines.

• Comparison of Morison's equation, potential theory, and numerical time-domain simulations.
• Analysis of hydrodynamic load computation and resulting floating structure motions.
• Evaluation of steady-state and transient responses in both regular and irregular wave conditions.
• Investigation of the OC3 Hywind platform's hydrodynamic properties and mooring system influence.
• Benchmarking FAST, SESAM, and MATLAB for offshore wind turbine engineering applications.

Extract from the Book

Summary of Chapters

1 INTRODUCTION: Outlines the motivation for renewable energy, the development of offshore wind turbines, and the scope of this research regarding numerical simulations of FOWT dynamics.

2 STATE OF THE ART: Provides the theoretical foundations of wave theory, hydrostatics, and hydrodynamics of rigid bodies, including definitions of boundary conditions and motion equations.

3 FLOATING WIND TURBINE MODEL: Details the structural, hydrodynamic, and mooring properties of the OC3 Hywind spar-buoy system used as the baseline for this study.

4 MATLAB: Covers the application of Morison’s equation to calculate wave forces on the platform in both the time and frequency domains.

5 SESAM: Describes the design and hydrodynamic analysis workflow within the DNV SESAM software suite, focusing on panel model generation and frequency-domain response analysis.

6 FAST: Introduces the open-source code FAST and the HydroDyn module for time-domain simulation of fully coupled aero-hydro-servo-elastic models.

7 COMPARISONS OF THE METHODS: Analyzes and compares the results from the different computational methods, focusing on excitation loads and response motion spectra.

8 SUMMARY AND CONCLUSION: Summarizes key findings, discusses differences between the used methodologies, and provides recommendations for future research.

Keywords

Floating offshore wind turbine, OC3 Hywind, Wave forces, Platform motions, Morison’s equation, Linear wave theory, Wheeler stretching, Hydrodynamics, Potential theory, SESAM, FAST, MATLAB, Response amplitude operator, JONSWAP spectrum, Mooring system

Frequently Asked Questions

What is the fundamental focus of this thesis?

This work focuses on comparing different numerical methods to compute wave forces and the subsequent platform motions of a floating offshore wind turbine (FOWT), specifically the OC3 Hywind model.

Which specific themes are central to the study?

The central themes include the application of Morison's equation, linear diffraction theory, and fully coupled time-domain simulations to estimate the hydrodynamic response of floating structures.

What is the primary goal of this research?

The primary goal is to evaluate the accuracy and consistency of different computational approaches (MATLAB, SESAM, and FAST) in predicting the loads and movement of an OC3 Hywind spar-buoy in varied sea states.

Which scientific methods are utilized?

The study employs linear wave theory, Morison’s equation, the panel method for diffraction analysis, and numerical simulation of coupled equations of motion in both time and frequency domains.

What content is covered in the main section?

The main sections cover the theoretical background of wave physics, the specification of the turbine model, the simulation processes in each program (MATLAB, SESAM, FAST), and a comparative analysis of the resulting hydrodynamic loads and response spectra.

Which keywords best characterize this work?

The most important keywords include Floating offshore wind turbine, OC3 Hywind, Wave forces, Platform motions, Morison’s equation, and Hydrodynamics.

Why are results from FAST and SESAM compared?

Comparing them helps identify how different assumptions—such as steady-state vs. transient responses or frequency-domain vs. time-domain calculations—affect the predicted stability and motion of the structure.

Does the work address resonance?

Yes, the thesis performs an eigenanalysis of the OC3 Hywind platform to ensure that the excitation frequencies of the waves do not lead to significant resonant responses in the platform motion.

How is the Wheeler stretching method applied?

It is used in the MATLAB calculations to modify the kinematics of the linear wave theory up to the instantaneous free water surface, rather than stopping at the mean sea level.