A comparison of methods for computation of wave forcing

Abstract

Unlike fossil fuels (e.g. oil, coal and natural gas), wind energy is a renewable energy resource. Since winds at sea are stronger and more consistent than onshore winds, the demand for offshore wind turbines has increased over the last years. As energy can be produced more efficient in deeper water, several floating offshore wind turbine constructions, such as the OC3 Hywind spar-buoy, have been proposed. The design of floating wind turbines depends on the simulation of the system behavior caused by exciting forces. This thesis deals with the comparison between different methods for calculating wave forces and resulting platform motions of a floating offshore wind turbine. On the one hand, wave exciting loads computed with Morison’s equation are compared to the hydrodynamic forces simulated by the open source code FAST on the basis of the diffraction theory. On the other hand, response motions of the floating structure are simulated by the commercial offshore software SESAM in the frequency domain and compared with the motions calculated by FAST in the time domain.

Keywords: Floating offshore wind turbine, OC3 Hywind, Wave forces, Platform motions

Zusammenfassung

Im Gegensatz zu fossilen Brennstoffen wie Öl, Kohle und Erdgas, gilt Windenergie als eine erneuerbare Energiequelle. Im Laufe der letzten Jahre ist insbesondere die Nachfrage nach Offshore-Windenergieanlagen gestiegen, da durch diese zum einen das Leben auf dem Binnenland nicht wesentlich beeinflusst und zum anderen ein höherer Energieertrag als durch Onshore-Windkraftanlagen erreicht wird. Insbesondere im Tiefwasserbereich kann Windenergie aufgrund kontinuierlicher Windbedingungen und hoher durchschnittlicher Windgeschwindigkeiten effizient gewonnen werden. Vor diesem Hintergrund wurden bisher unterschiedliche Modelle für schwimmende Windkraftanlagen, wie z.B. die OC3 Hywind Struktur, entwickelt. Im Wesentlichen basiert die Planung von Offshore-Windenergieanlagen auf Simulationen von Strukturbewegungen verursacht durch einwirkende äußere Kräfte. In der vorliegenden Arbeit werden verschiedene Methoden zur Berechnung von Wellenkräften und der resultierenden Plattformbewegungen vorgestellt und miteinander verglichen. Dabei werden zunächst Wellenkräfte basierend auf der Morison Gleichung berechnet und mit Simulationen von hydrodynamischen Kräften des Programms FAST verglichen. Außerdem wird ein Vergleich zwischen den mithilfe der kommerziellen Software SESAM ermittelten Bewegungen im Frequenzbereich und Simulationen der Plattformbewegungen im Zeitbereich aus FAST gezogen.

Schlagwörter: Schwimmende Windkraftanlagen, OC3 Hywind, Wellenkräfte, Plattformbewegung

INHALTSVERZEICHNIS

LIST OF FIGURES.. IV

LIST OF TABLES.. VIII

SYMBOLS AND ABBREVIATIONS.. IX

1 INTRODUCTION.. 1

1.1 Background.. 1

1.2 Outline.. 1

2 STATE OF THE ART.. 3

2.1 Regular Waves.. 5

2.1.1 Description.. 5

2.1.2 Linear Wave Theory.. 7

2.1.2.1 Basic equations.. 8

2.1.2.2 Boundary conditions.. 8

2.1.2.3 Wave kinematics and pressure.. 11

2.1.3 Stretched Airy Theory.. 14

2.2 Irregular Waves.. 15

2.2.1 Description in the Frequency Domain.. 17

2.3 Hydrostatics of Floating Structures.. 21

2.3.1 Static Stability.. 21

2.4 Hydrodynamics of Rigid Bodies.. 25

2.4.1 Coordinate Systems.. 25

2.4.2 Diffraction Theory.. 26

2.5 Hydrostatic- and Dynamic Loads on Floating Structures.. 29

2.5.1 Fundamentals.. 29

2.5.2 Forces and Moments.. 30

2.5.3 Radiation and Diffraction Loads.. 31

2.5.4 Wave Excitation Loads.. 34

2.5.5 Hydrostatic Loads.. 36

2.6 Floating Structures in Waves.. 37

2.6.1 Coupled Equations of Motion.. 37

2.6.2 Motions in Regular Waves.. 38

2.6.2.1 Response amplitude operator.. 39

2.6.3 Motions in Irregular Waves.. 39

3 FLOATING WIND TURBINE MODEL.. 43

3.1 OC3 Hywind.. 43

3.1.1 Tower and Platform Structural Properties.. 44

3.1.2 Floating Platform Hydrodynamic Properties.. 46

3.1.3 Mooring System Properties.. 47

4 MATLAB.. 49

4.1 Morison Forces.. 50

4.1.1 Morison Forces due to Regular Waves.. 51

4.1.2 Morison forces due to Irregular Waves.. 54

5 SESAM.. 60

5.1 GeniE.. 61

5.1.1 The Modelling Process.. 62

5.2 HydroD.. 65

5.2.1 Coordinate System.. 66

5.2.2 Panel Model.. 67

5.2.3 Mass Model.. 69

5.2.4 Analysis Preparation.. 69

5.2.5 Wadam.. 71

5.2.5.1 Global Response Analysis in Wadam.. 71

5.2.6 Postresp.. 73

6 FAST.. 79

6.1 Basic Assumptions.. 80

6.2 Hydrodynamic Module (HydroDyn).. 81

6.2.1 Diffraction Problem.. 83

6.2.2 Radiation Problem.. 86

6.3 Hydrodynamic Results.. 87

6.3.1 Regular Waves.. 88

6.3.2 Irregular Waves.. 91

7 COMPARISONS OF THE METHODS.. 95

7.1 Comparison of Excitation Loads.. 95

7.2 Comparison of Response Motions.. 97

8 SUMMARY AND CONCLUSION.. 101

9 REFERENCES.. 103

1 Introduction

1.1 Background

Currently, most of the energy worldwide is obtained by nonrenewable resources such as coal, oil, natural gas and nuclear power. Fossil fuels are, however, limited in supply and the increasing consumption is harmful to the environment. For example, dangerous nuclear waste is constantly produced by obtaining energy from nuclear power. The safe storage and disposal of this radioactive waste as well as the increased risk from terrorism, radioactive accident and nuclear proliferation pose serious problems (Jonkman, 2007). Against this background, the demand for renewable energy has increased significantly in the past years. Onshore wind power has been the fastest growing energy source worldwide for more than a decade. Due to the limited availability of land and vast shallow-water wind resources at the North and Baltic seas, Europe is the global leader in the development of offshore wind turbines (Lefebvre, et al., 2012). A substantial advantage of offshore wind turbines is a higher wind energy production in comparison to land-based wind turbines. This occurred as the wind is more consistent and stronger over the sea because of less turbulence at sea than onshore. As offshore structures are usually produced near the coastline, the size of these constructions is not limited by road or rail logistical constraints, which results in lower transport costs and increasing flexibility in construction.

With regard to offshore wind turbine systems, a distinction is made between bottom-fixed and floating platforms. Bottom-fixed offshore wind turbines are installed in water depths up to 60 meters. Since the installation and maintenance of such structures is associated with substantial costs and effort, floating offshore wind turbines (FOWT) are used in deeper water. Through the positioning of the FOWT in the open ocean, visual and noise annoyances can be avoided. Besides, in contrast to the bottom-fixed wind turbines, the floating platforms do not have to be inserted into the seabed. The installation of the wind turbine system in the ground causes significant habitat disturbance for marine mammals and fish (Henderson, et al., 2003).

In nature, floating wind turbines are subject to not only aerodynamic loads, but also to hydrodynamics. Unlike bottom-fixed platforms, the dynamic behavior of FOWT is mainly influenced by structural properties of the floating system, hydrodynamic processes and further external loads (Butterfield, et al., 2005). To avoid instabilities of the FOWTs, research on support platform motions is indispensable. Several studies have been carried out on preliminary design of FOWTs, such as by Bulder (2005), Lee (2005) and Wayman et al., (2006). However, floating support platforms for wind turbines are still in its research and development phase. The first full-scale prototype, the so-called OC3 Hywind spar-buoy, has been developed by the Norwegian oil corporation Statoil and was deployed in 2009 (Lefebvre, et al., 2012).

1.2 Outline

The aim of this thesis is to investigate wave loads acting on an OC3 Hywind spar-buoy and to analyze the resulting motions of the support platform. A general overview of regular and irregular waves as well as hydrostatic and hydrodynamic loads acting on floating structures is given in chapter 2. Furthermore, essential formulations for calculating motions of FOWTs are given at the end of this chapter. Since all simulations carried out in this thesis are based on the OC3 Hywind concept, detailed information about this floating wind turbine model are given in chapter 3. Three different methods are used for the estimation of wave induced loads and motions. Section 4 describes a modified Morison formulation in the time domain which is applied by the commercially available software MATLAB. On the basis of the diffraction theory, the commercial offshore software package SESAM simulates wave excitation forces and responding motions which are presented and discussed in chapter 5. The third method is the open source code FAST that computes wave induced loads and motions based on the first-order potential theory and Kane’s equation of motion. Basic formulations used in FAST and essential hydrodynamic results are shown in chapter 6. The comparisons between the simulations of the three programs are represented and the individual results are analyzed in chapter 7. Finally, a brief summary and conclusion are given in section 8.

2 State of the Art

As offshore wind energy is a clean, domestic and renewable resource, academic interest in offshore wind turbines has attracted considerable attention from industry over the last few years and consequently, a significant amount of funding has been invested to the development of offshore wind turbines (Roddier, et al., 2009). Substructures of offshore wind turbines can be categorized depending on the water depth, as illustrated in Figure 2.1. Wind turbines in shallow water (less than 30 meters) are built on monopoles and gravity bases which extend to the sea bottom. In a water depth between 30 and 60 meters, also known as transitional depth, multi-pile structures and frames (e.g. jackets), which reach to the seabed, are used. At a water depth of more than 60 meters, however, bottom-mounted platforms are not feasible anymore because the installation and maintenance is associated with higher costs and effort as well as with significant habitat disturbance for marine mammals and fish (e.g. dolphins and harbor porpoises). For that reason, prototypes of floating substructures are developed (see Figure 2.1), which proved to be the most economical option for generating electricity in the open sea (Song, et al., 2012).

Figure 2.1: Illustration of onshore wind turbines in comparison with offshore wind turbines in shallow water, transitional water and deep water (Song, et al., 2012)

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Until a few years ago, most of the offshore wind turbines in the world were located in shallow water. However, much of the offshore wind resource potential in China, Japan, Norway, the United States and other countries is available in deeper water (Jonkman, 2010). Based on significant research and development efforts, the world’s first full-scale floating platform for offshore wind turbines in deep water has been installed in the North Sea off the coast of Norway in 2009. The support platform is developed by the Norwegian oil corporation Statoil as part of the so-called Hywind-project and can be installed in water depths from 120 meters to 700 meters (AFK, 2009). A more detailed explanation of this project, which is an essential part of this thesis, is given in chapter 3.

In general, several floating support platform constructions were developed for offshore wind turbines with modifications to the mooring systems, tanks and ballast options in accordance with the offshore oil and gas (O&G) configurations. Three different concepts of offshore floating wind turbines are depicted in Figure 2.2. The spar-buoy construction is moored by taut lines and contains additional ballast to reach static stability by lowering the center of mass below the center of buoyancy. The tension leg platform (TLP) is stabilized by the mooring line tension (see Figure 2.2b) and the barge achieves stability through distributed buoyancy and the use of weighted water plane area for righting moment (Jonkman, 2007).

Figure 2.2: Depiction of three different concepts of offshore floating wind turbines: a) Spar-buoy, b) Tension leg platform and c) Barge (Jonkman, 2007)

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One of the fundamental challenges concerning floating structures is the ability to estimate loads and resulting responses of the system. In the offshore environment, floating wind turbines are exposed to several loads due to wind, waves, currents, sea ice and so on. Figure 2.3 shows the essential impacts on a floating wind turbine. In contrast to a bottom fixed structure, the dynamic behavior of a floating wind turbine is changed by hydrodynamics, the external loads and the structure itself. So far, the hydrodynamic loads acting on offshore structures are not well understood (Butterfield, et al., 2005).

This thesis deals with motions of floating bodies caused by wave induced forces. In order to provide an overview of basic characteristics of incident waves, formulations for regular and irregular waves are defined in chapter 2.1 and 2.2. These wave induced loads acting on a floating offshore structure may cause an instabil condition. For this reason, the essential processes and coefficients in the hydrostatic equilibrium condition are outlined in chapter 2.3. To gain an overview of basic motions of floating structures, the hydrodynamics of a simple rigid body in an ideal fluid are clarified in chapter 2.4. The determination of hydrostatic and hydrodynamic loads acting on a FOWT are described in chapter 2.5 and the calculation of motions of floating systems are presented in chapter 2.6.

Figure 2.3: Definition of the impacts acting on a FOWT in accordance with Elliott et al. (2012)

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2.1 Regular Waves

The essential parameters of regular waves are discussed and illustrated in chapter 2.1.1. Then, basic equations, boundary conditions and wave kinematics according to the linear wave theory are presented in chapter 2.1.2. Since the linear wave theory neglects the kinematics above mean sea level, the so-called Wheeler Stretching method is introduced, which enables the calculation of the kinematics up to the free water surface (see section 2.1.3).

2.1.1 Description

In general, the spatial and temporal development of the sea state can be examined by the linear or non-linear wave theory. The first-order theory is based on the assumption of small wave steepness, which is defined as the ratio between wave height H and wavelength L, and considers the movement of the water particles on orbits. Figure 2.4 depicts the change of orbits depending on the water depth h. For wave steepness H/L greater than 1/50, waves with a finite amplitude behave nonlinearly. In this case, non-linear wave theories should be applied (EAK, 2002). This thesis basically deals with the first-order theory.

Figure 2.4: Illustration of the change of orbits depending on the water depth h according to EAK (2002)

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The basis for this is the mathematical and physical description of gravity waves. Surface waves arise through vertical movements of the sea surface which can be caused by the tides, volcano eruptions, tsunamis, gravity or capillary waves. The two latter are short surface waves. The surface tension of the capillary waves which are considered to be the shortest waves at the water surface has the effect of a restoring force. In contrast, gravity waves have the restoring influence of gravity or buoyancy in terms of swell and wind waves. For the derivation of the mathematical and physical description of gravity waves the assumption of a monochromatic wave, which spreads with an amplitude ζ_a in the direction θ, is made. The amplitude ζ_a describes the crest height above mean sea level and is defined as half of the wave height H (see Figure 2.5). Thus, the wave height is the difference between wave crest and wave trough. The surface elevation ζ is directed upward from the undisturbed water surface which is illustrated in Figure 2.5.

Figure 2.5: Depiction of basic parameters of a two-dimensional regular wave (according to Zanke (2002))

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Some properties of a two-dimensional regular wave are pictured in Figure 2.5. The illustration shows, among others, the directions of the wave velocities w and u for a two-dimensional surface wave and the water depth h. The wavelength L characterizes the range between two adjacent wave crests or troughs and describes the wavenumber k as follows:

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The wave period T indicates the time taken for one complete cycle of the wave to pass a reference point = (x, y). Equivalently, it describes the time between successive wave crests and wave troughs. The frequency is the inverse of the wave period

[Formulas are omitted from this preview.]

and is related to the angular frequency by

[Formulas are omitted from this preview.]

With regard to the undisturbed water surface the equation

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describes a spatial and temporal variation of the surface elevation ζ in meters. In equation (2.4) t denotes the time and φ the phase angle. The latter represents the displacement of the wave referring to a time t = 0 or to the coordinate origin x = 0 and y = 0 (Mai, et al., 2004).

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