THE EFFECT OF MASS AND WEB
SPACING ON THE LOADS AND
STRUCTURAL RESPONSE OF
INCREASING WIND TURBINE
BLADE SIZE
JEFFREY BENNETT
Master of Science Thesis Stockholm, Sweden 2012
T
urbomac
H
inery Ae
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omechanical
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ity
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raining
THRUST
THE EFFECT OF MASS AND WEB SPACING ON THE
LOADS AND STRUCTURAL RESPONSE OF INCREASING
WIND TURBINE BLADE SIZE
Jeffrey Bennett
MSc Thesis 2012
Department of Energy Technology Division of Heat and Power Technology
Royal Institute of Technology 100 44 Stockholm, Sweden
The Effect of Mass and Web Spacing on the Loads and Structural Response of Increasing Wind Turbine Blade Size
Jeffrey Bennett
Approved Examiner Supervisor
September 14, 2012 Damian Vogt Kim Branner Commisioner Contact Person
Abstract
The research presented considers the effect of varying shear web spacing and mass for two blades; a 61.5m 5MW blade (based on the NREL5MW reference turbine) and a 100m 13.2MW blade (based on the SNL100 blade).
The variations are analyzed using HAWC2 aeroelastic simulations and Abaqus/CAE finite element simu-lations; and the effect of the variations is measured by comparing natural frequencies, loads, tip deflection, equivalent fatigue loads, material strength and buckling. Additionally, a tool was developed to facilitate the modeling of blade variations.
Varying the web spacing showed that the web placement is able to reduce loads, tip deflection, and equiv-alent fatigue loads. Mass variations demonstrated that reducing the mass will decrease edge-wise loading and equivalent fatigue loads. The increase in blade size has shown that edge-wise fatigue loads become larger than the flap-wise fatigue loads for the larger blade.
Acknowledgments
I would like to thank Lisa and my Family for their love and support.
Thanks to my supervisors Damian Vogt of KTH and Kim Branner of DTU Wind Energy for their guid-ance and the opportunities they have opened to me.
Next I would like to thank Robert Bitsche for his help with Abaqus/CAE, and Taeseong Kim for his help with HAWC2.
Lastly, I would like to thank my fellow THRUST students and the students at DTU Wind Energy for their friendship throughout this journey.
Abstract 4 Acknowledgements 5 Table of Contents 8 List of Figures 9 List of Tables 10 Nomenclature 11 1 Background 13 1.1 Introduction . . . 13
1.2 Wind Energy for a Sustainable Future . . . 13
1.3 Modern Wind Energy . . . 14
1.3.1 Wind Turbine . . . 14
1.3.2 Blade . . . 14
1.3.3 Blade Cross-section . . . 14
1.4 Prior Research . . . 15
1.4.1 Similar Study . . . 15
1.4.2 Structural Variation - Mass . . . 16
1.4.3 Structural Variation - Web Spacing . . . 17
1.5 Blades Considered . . . 17 1.6 Metrics . . . 17 1.6.1 Natural Frequencies . . . 18 1.6.2 Loads . . . 20 1.6.3 Tip Deflection . . . 21 1.6.4 Fatigue . . . 21 1.6.5 Material Strength . . . 23 1.6.6 Buckling . . . 25 2 Objectives 27 3 Methodology 28 3.1 Creating Blade Models . . . 28
3.1.1 BLADEMODELER . . . 28
3.1.2 BLADEMODELER to BECAS . . . 31
3.2 Aeroelastic Simulations . . . 31
3.2.1 Aeroelastic Code . . . 31
3.2.2 Choice of Wind Simulations . . . 33
3.2.3 Metric 1: Natural Frequencies . . . 34
3.2.4 Metric 2: Tip Deflection . . . 35
3.2.5 Metric 3: Loads . . . 35
3.3 Finite Element Analysis . . . 36
3.3.1 Overview . . . 36
3.3.2 Metric 5: Material Strength . . . 37
3.3.3 Metric 6: Buckling . . . 38 4 Model Set-up 39 4.1 Blade Models . . . 39 4.1.1 Baseline 13.2MW . . . 39 4.1.2 Baseline 5MW . . . 40 4.1.3 Blade Variations . . . 42 4.1.4 Numerical Settings . . . 44 4.2 Turbine Models . . . 44 4.2.1 Baseline 5MW . . . 44 4.2.2 Baseline 13.2MW . . . 45 4.2.3 Blade Variations . . . 45 4.2.4 Numerical Settings . . . 46 5 Results 47 5.1 Natural Frequencies . . . 47 5.1.1 Web Variations . . . 47 5.1.2 Mass Variations . . . 48 5.2 Loads . . . 49
5.2.1 Baseline Ultimate Loads . . . 49
5.2.2 Ultimate Loads of Web Variations . . . 50
5.2.3 Ultimate Loads of Mass Variations . . . 51
5.3 Tip Deflection . . . 52
5.3.1 Baseline Tip Deflections . . . 52
5.3.2 Tip Deflections of Web Variations . . . 52
5.3.3 Tip Deflections of Mass Variations . . . 53
5.4 Fatigue Loads . . . 54
5.4.1 Baseline Fatigue Loads . . . 54
5.4.2 Fatigue Loads of Web Variations . . . 55
5.4.3 Fatigue Loads of Mass Variations . . . 55
5.5 Material Strength . . . 57
5.5.1 Baseline Material Strength . . . 57
5.5.2 Results of 5MW variations . . . 59
5.5.3 Results of 13.2MW variations . . . 60
5.6 Buckling . . . 61
5.6.1 Buckling of the Baselines . . . 61
5.6.2 Buckling modes of the Web Variations . . . 61
5.6.3 Buckling modes of the Mass Variations . . . 62
6 Discussion 66 6.1 Verification of FE Methods . . . 66
6.1.1 Finite Element Mesh Convergence . . . 66
6.1.2 Buckling Methodology . . . 66
6.2 Interesting Results . . . 67
6.2.1 Comparison of 13.2MW Results . . . 67
6.2.2 Tip Deflections of the 5MW Web Variations . . . 68
6.3 Contribution to Research . . . 69
6.3.1 Web variations . . . 69
6.3.2 Mass Variations . . . 70
6.3.4 BLADEMODELER . . . 71 6.3.5 Layup of a 5MW Blade . . . 72 6.4 Lessons learned . . . 72 7 Conclusions 73 7.1 Future Work . . . 74 Bibliography 75
1.1 Typical modern wind turbine configuration. . . 15
1.2 Spring-Mass 1 Degree of Freedom system. . . 19
1.3 Typical wind turbine blade eigenmodes. . . 19
1.4 Aerodynamic forces. . . 21
1.5 Gravity Loading. . . 22
1.6 Tower Strike. . . 23
1.7 Fatigue Illustrations . . . 24
1.8 Composite Material Ply. . . 25
1.9 Buckling. . . 26
3.1 User defined airfoil sections. . . 29
3.2 Lofting sections. . . 30
3.3 Finite element material orientation. . . 30
3.4 Process of analyzing blade cross-sections. . . 32
3.5 Rayleigh wind speed distribution. . . 34
3.6 Point forces calculated to reconstruct the bending moment curve. . . 36
3.7 Shell finite element. . . 37
4.1 Baseline 13.2MW blade in Abaqus/CAE. . . 40
4.2 SNL100 Blade comparison. . . 42
4.3 NREL5MW blade match. . . 43
5.1 Comparison of baseline flap-wise ultimate loads. . . 49
5.2 Comparison of baseline edge-wise ultimate loads. . . 50
5.3 Tip deflection comparison of ultimate load cases. . . 52
5.4 Equivalent flap-wise fatigue load comparison of ultimate load cases. . . 54
5.5 Equivalent fatigue edge-wise load comparison of ultimate load cases. . . 55
5.6 Flap-wise displacement comparison of the baseline blades. . . 57
5.7 Flap-wise strain distribution comparisons of the baseline blades. . . 58
5.8 Edge-wise strain distribution comparisons of the baseline blades. . . 59
5.9 Comparison of buckling location and mode shapes for the baseline blades. . . 61
5.10 Comparison of buckling mode shapes and locations of the 5MW variations. . . 64
5.11 Comparison of buckling mode shapes and locations of the 13.2MW variations. . . 65
2.1 Summary of thesis objectives. . . 27
3.1 Load cases. . . 34
4.1 SNL100 Blade Comparison. . . 40
4.2 5MW layup developed for this thesis. . . 41
4.3 Blade variations. . . 43
4.5 Key properties of the 5MW and 13.2MW turbines. . . 44
4.4 Finite element analysis settings. . . 44
4.6 Matched NREL5MW natural frequencies. . . 45
4.7 Natural frequencies of the baseline 13.2MW blade. . . 46
4.8 Aeroelastic simulation settings. . . 46
5.1 Blade natural frequencies of the web variations. . . 47
5.2 Blade natural frequencies of the mass variations. . . 48
5.3 Maximum loads of the blade web variations. . . 50
5.4 Maximum loads of the blade mass variations. . . 51
5.5 Maximum tip deflections of blade web variations. . . 52
5.6 Maximum tip deflections of blade mass variations. . . 53
5.7 Lifetime equivalent fatigue loads for the blade web variations. . . 55
5.8 Lifetime equivalent fatigue loads for the blade mass variations. . . 56
5.9 Material strength results (in micro-strain) of the 5MW blade variations. . . 59
5.10 Material strength results (in micro-strain) of the 13.2MW blade variations. . . 60
5.11 Buckling Modes. . . 61
5.12 Buckling modes of the web variations. . . 62
5.13 Buckling modes of the blade mass variations. . . 63
6.1 Mesh Convergence Study. . . 66
6.2 Effect of pre-load on buckling analyses (13.2MW Baseline). . . 67
6.3 Comparison of loads and tip deflection of the SNL100 to the 13.2MW blade. . . 68
Nomenclature
Latin Symbols C Damping matrix D Damage E Modulus of Elasticity F , f Force g Gravity I Identity matrix I Moment of Inertiak, K Stiffness, Stiffness matrix
L Length
m, M , M Mass, Mass matrix, Bending Moment
N Cycles P Load r Radius S Shear strength S Stress t Time V Shear Force v Velocity x Displacement ˙ x Velocity ¨ x Acceleration X Axial strength Y Transverse strength Greek Symbols λ Eigenvalues π Constant σ1 Axial stress σ2 Transverse stress τ12 Shear stress ωn Natural Frequency Subscripts g Gravity i Cycle number
Abbreviations
BECAS BEam Cross section Analysis Software BEM Blade Element Momentum Theory CAE Computer Aided Engineering CFD Computational Fluid Dynamics CFRP Carbon Fiber Reinforced Plastic DNV Det Norske Veritas
DOF Degrees of Freedom
DOWEC Dutch Offshore Wind Energy Converter DTU Danish Technical University
FE, FEA Finite Element, Finite Element Analysis ECD Extreme Coherent gust with Direction change ETM Extreme Turbulence Model
GFRP Glass Fiber Reinforced Plastic
IEC International Electrotechnical Commission LE Leading Edge
m meter
MW megawatt
NWP Normal Wind Profile NTM Normal Turbulence Model
NREL National Renewable Energy Laboratory SNL Sandia National Laboratory
SS Suction Side PS Pressure Side TE Trailing Edge
1.1 Introduction
This thesis investigates the effect of structural blade variations for increasing blade size on natural fre-quencies, loads, material strength, buckling, fatigue and tip deflection. The purpose of this chapter is to introduce readers to the field of work by providing a background of important principles and terminology necessary to understand subsequent chapters.
The background will begin by explaining the motivation towards researching wind energy, and then present the configuration and terminology of a state of the art utility scale wind turbine. Next the thesis statement will be explained by dissecting it into three parts. First prior research will be presented as a means of explaining the applications and originality of the structural blade variations being investigated. Second increasing blade size will be elaborated by describing the wind turbine blades being considered. Third the principles of the metrics being used, natural frequencies, loads, material strength, buckling, fatigue and tip deflection, will be explained.
1.2 Wind Energy for a Sustainable Future
For a sustainable future, world leaders are recognizing the need for wind and other emission-free renewable energy to replace greenhouse gas emitting fossil fuel energy. President Obama proposed that 80% of the United States’ electricity come from clean energy sources by 2035 [1]. Similarly, by 2050 the European Union has proposed to decrease greenhouse gas emissions below 1990 levels by 80-95% [2].
To achieve these ambitious goals many renewable energy installations are necessary. Installations to re-place current energy sources, and additional installations to account for the growing energy need.
Renewable energy also offers independence. Hansen has explained that renewable energy sources would allow countries that depend on imported fossil fuel to become self-reliant [3].
To make a business case for renewable energy, the price must become competitive against traditional fossil fuel energy. If an electricity provider needs to add or replace energy sources, it will do so while minimizing cost in order to maximize profits. If the cost of wind energy is reduced, than it will more likely be chosen for new installations. To reduce the cost of wind energy, innovations through research and development are necessary.
A growing field of wind energy with opportunities for innovation is offshore wind energy. Offshore wind energy offers great wind resources.
Van Kuick et al. have documented that the cost of offshore wind energy does not depend on the size of the wind turbine, rather the cost is dominated by planning and installation costs [4]. Therefore, increasing the turbine size is one way of reducing the cost of energy. Larger turbines would make it possible to produce the same amount of energy from fewer turbines, reducing the total number of installations, and thus the cost.
The UpWind project [5] has investigated the feasibility of building wind turbines capable of producing 20 megawatts (MW), that is 10 times more power than the production from a modern onshore 2MW wind turbine. UpWind has shown that structural design and material research is necessary to build blades large and strong enough to produce 20MW. The goal of this thesis is to contribute to this research need.
1.3 Modern Wind Energy
To better understand the terminology used in this thesis, a state of the art wind turbine is presented and the key components related to blade design are explained. First the overall turbine structure will be described, second a blade and third the cross-section of a blade.
1.3.1 Wind Turbine
A state of the art wind turbine is illustrated in Figure 1.1a. A modern wind turbine has three blades that connect at the hub to the main shaft, and rotate clockwise as viewed from the direction of the wind. The three blades connected to the hub is called the rotor. The rotor is upwind of the tower, meaning that the wind passes through the blades before passing the tower. The height of a turbine is referred to by the height of the hub. The main shaft is tilted upwards several degrees in order to reduce the likelihood of the blades bending and striking the tower, as explained further in the Metrics Section on Tip Deflection.
The wind causes the blades to spin, turning the main shaft. The shaft is connected to a gearbox-generator assembly housed inside the nacelle. The constant variation of wind means constantly changing power production. Power electronics are used to modify the electricity into a form usable by the electrical grid. These may be housed in the nacelle or at the base of the tower, and connect the turbine to the grid. Electricity is transmitted down the tower through large cables.
The turbine best operates when directly facing the wind. So as the wind changes direction, in order to reposition the assembly in the direction of the wind, yaw motors, located in the nacelle, rotate or yaw the nacelle-rotor-assembly to face the wind.
1.3.2 Blade
The blades operate on the same working principle as aircraft wings. As the air passes over the wind turbine blades, the unique aerodynamic shape - the airfoil, directs the air to cause a higher pressure on one side and a lower pressure, a suction, on the other. The pressure difference pushes the blades and causes them to rotate. A blade is illustrated in Figure 1.1b. The end of the blade that connects to the hub is the root, and the free end the tip. The length of the blade is called the span. The root generally has a cylindrical shape to better withstand the high loads and bending moments upon it. Further out in the blade the outer geometry is specified by airfoils to give a favorable aerodynamic shape. Motors located in the hub allow the blade to rotate or pitch to gain a more favorable angle of attack.
1.3.3 Blade Cross-section
A blade cross-section is illustrated in Figure1.1c. The exterior of the blade is designed for aerodynamic performance, and the interior for structural strength. The primary structural members are the spar caps and shear webs. The spar caps resist bending in the flap-wise direction (from spar cap to spar cap) and the shear webs resist shear and buckling. When the blade bends in the edgewise direction (from nose to tail) the reinforcement in the nose and tail resist. The reinforcement of the aerodynamic shell resists torsion. These deformations are further explained in the Metrics section on Natural Frequencies.
Pressure Side Suction Side Spar Caps Shear Webs Tail/ Trailing Edge (TE) Root Tip Span Tower Blades Nacelle Hub
a) Turbine Assembly
b) Wind Turbine Blade
c) Wind Turbine Blade Cross-Section
Wind Wind Pressure Side (PS) Suction Side (SS) Nose/ Leading Edge (LE) Wind ChordFigure 1.1: Typical modern wind turbine configuration: a)Turbine Assembly, b) Wind Turbine Blade, c)Wind Turbine Blade Cross-Section.
1.4 Prior Research
The applications and originality of the structural variations investigated are demonstrated by presenting prior research. Additionally a similar study is explained to verify the thesis approach.
1.4.1 Similar Study
Part of the Dutch Offshore Wind Energy Converter (DOWEC) project was a study by Kooij [6] that varied the structural pitch of a turbine blade and investigated its effect on the fatigue, tip deflection and natural frequencies. The structural pitch refers to the manufactured twist of the spar and webs along the length of the blade. This study showed that the spar and web placement largely impact the bending modes. The study was unable to identify a trend for structural pitch, but one of the variations was able to reduce the tip deflection and bending moment by 10% and 12%, respectively. The variations presented in this study did not predict any significant change in fatigue.
The study is similar to this thesis in the respect that a structural parameter was varied and its effect on the structural response was investigated. Therefore the approach of this thesis is concluded acceptable as it
has been taken in a prior research project. The primary differences between the study and this thesis are the parameters being varied, and the look into comparing the results for turbines of two different MW ratings.
1.4.2 Structural Variation - Mass
The first structural variation considered is varying the blade mass. This will be achieved by varying the density of the materials used. Two applications of this variation are representing a change in material and representing an accumulation of ice.
Material Change
Gardiner has documented that the material used today for building wind turbine blades by most manu-facturers is glass fiber reinforced plastic (GFRP) and some manumanu-facturers have opted to use carbon fiber reinforced plastic (CFRP) for larger blades [7]. Compared to GFRP, CFRP has a lower density and a higher stiffness, however it comes with a higher cost. A lighter blade would offer weight reductions for the rest of the turbine and as such offer lower costs for other turbine components. Additionally, a stiffer blade would have a lower tip deflection thus reducing the risk of tower strike.
In one research project, the feasibility of using CFRP for wind turbine blades was evaluated by Griffin and Ashwill [8]. The study included the design of hybrid GFRP/CFRP blades for 3 and 5MW turbines.
As explained CFRP is being used by some manufacturers, and has been evaluated in a previous research project. As part of this thesis, reducing the blade mass will be considered as a simplified approach to representing a change to CFRP or another lightweight material. This thesis will contribute to literature by exploring the effect of CFRP for larger blades and exploring its effect on natural frequencies, loads, material strength, buckling, fatigue and tip deflection. Reducing the blade mass is a simplification to represent a change to CFRP as the stiffness is unaffected. However reducing the blade mass could also represent using a higher quality GFRP with reduced mass for the same stiffness. As not all manufacturers are using CFRP, the mass variation presented in this thesis could provide justification for manufacturers to reconsider using CFRP or other lightweight materials.
Ice Accumulation
In cold climates ice is prone to form on wind turbine blades causing an increase in blade mass. If turbines can be designed to handle ice and other cold weather effects then it could become a more common energy source for cold climates.
Frohboese and Anders investigated the effect of predicted ice accumulation on the loading and fatigue [9]. For a 2MW turbine, it was found that the mass of the ice did not greatly increase the loads, but the concern of a mass imbalance due to two blades iced and one without ice was highlighted. Also discussed was a change in performance due to the aerodynamic profile being altered by the uneven formation of ice.
Another study by Virk et al. simulated the accretion of ice using computational fluid dynamics (CFD), and demonstrated that the distribution of ice is larger towards the outer portions of the blade [10].
This thesis will contribute to icing research by simulating the effect of increasing the blade mass. In particular this thesis investigates larger turbines, and the results may be used to determine if icing is more or less critical as the size of the turbine increases.
1.4.3 Structural Variation - Web Spacing
The second structural variation investigated is varying the web spacing. This refers to changing the chord-wise distance between the shear webs. An application of varying the web spacing is optimizing the blade cross-section.
There are many methods and parameters that could be varied to optimize the design of a wind turbine blade. An example of a blade optimization study is presented by Jureczko et al. [11].
One study [12] by Bonnet and Dutton created a blade modeling tool and investigated the impact of web spacing on tip deflection. However neither blade size nor loading are presented with the results so there is not much that can be gathered with respect to the impact of web spacing. The study focused more on the creation and capabilities of the blade modeling tool.
This thesis is going to contribute to optimization studies by simulating several web spacings and draw trends from the results. If an optimal web spacing is found or if it makes no difference across increasing turbine size, then this could be one less parameter to vary in future designs. If it greatly affects the results then it will be noted that it should be included in future blade optimization studies.
Web spacing is expected to impact the metric of buckling. The theory behind buckling will be further explained in the Metrics Section. Moving the web is expected to support parts of the blade better than others reducing the risk of buckling in some areas, and increasing the risk in others. This leaves room for finding an appropriate balance.
1.5 Blades Considered
This thesis investigates changes for increasing blade size. This is done by simulating blades of two different sizes and drawing trends between the results. The research presented in this thesis uses publicly available reference wind turbine blades as the basis for the analysis. An advantage of using publicly available blades is that they have been used in other research projects, making the the work presented here more easily comparable and repeatable.
The blades considered are the 61.5 meter (m) National Renewable Energy Laboratory (NREL) 5MW reference turbine developed by Jonkman et al. [13], and the Sandia National Laboratory (SNL) 100m 13.2MW blade developed by Griffith and Ashwill [14]. Both of these blades use the same airfoil schedule originally designed by Kooijman et al. for the Dutch Offshore Wing Energy Converter (DOWEC) 6MW project [15]. The NREL 5MW turbine was created to represent a typical 5MW turbine. The SNL 13.2MW turbine was created to be a baseline for future large turbine designs, and is based upon upscaling existing 5MW designs, including the NREL 5MW turbine.
The reports outlining these blades contain many but not all of the details necessary for modeling. As part of the research presented, missing details were filled in as later explained in the Model Set-up Chapter. Hereafter, the blades from literature will be referred to as the NREL5MW blade and the SNL100 blade; and the blades developed in this report will be referred to as the 5MW blade and 13.2MW blade.
1.6 Metrics
The metrics used to quantify the effect of the structural variations are natural frequencies, loads, tip deflection, fatigue, material strength and buckling. This section will present a brief theoretical overview of each metric. Additionally, the international wind turbine design standards developed by the International Electrotechnical Commission (IEC) [16] and Det Norske Veritas (DNV) [17] are related to each metric where applicable.
1.6.1 Natural Frequencies
The first metric to be analyzed is the natural frequencies. As explained by Meirovitch [18] all mechanical systems have natural modes of vibration.
A mechanical system can be represented by a collection of springs (representing stiffness), masses and dampers, such as illustrated in Figure 1.2. Every system has a discrete number of degrees of freedom (DOF). DOF refers to all of the rotations and translations that are possible in the system. In the Figure each mass is constrained such that it can only move up and down, thus 1 DOF per mass.
A mode refers to the shape of the system when vibrating. For example, all of the masses could be moving in unison, or two could be moving upwards while the other is moving downwards. Each possibility is a mode shape. As the system gets more complex, so do the possible mode shapes.
Each natural mode is caused by an excitation at a corresponding natural frequency. Other names for natural frequency are characteristic frequency or eigenfrequency. “Eigen” is German for own, and thus signifies that the frequency is a natural characteristic of the system. If the system had no damping, then the vibration of the system when excited at a natural frequency would be very large and uncontrollable, a phenomenon called resonance. Resonance can be quite destructive and permanently damage a system. Most engineering structures have low damping and therefore when operating a mechanical system it is important to know the natural frequencies of the system, and to avoid exciting them.
Wind turbine blades, like other complex systems, have a large number of DOF, and as many natural frequencies as DOF. When analyzing natural frequencies, only the frequencies that could be excited are considered.
The typical vibration modes of a wind turbine blade are shown in Figure 1.3. They are flap-wise, edge-wise and torsion. As the natural frequency increases, the mode shape becomes more complex.
The DNV Standard explains that it is important to experimentally test wind turbine blades to verify that the natural frequencies match the natural frequencies predicted in simulations [17]. Simple methods such as a hammer test exist for such an experiment and thus provide an easy way of verifying that simulations have accurately represented the structure. Wind turbine components are designed such to prevent exciting the natural frequencies. If they have not been predicted properly, than an accidental excitation may occur.
Aeroelastic simulations and finite element analysis will be used to calculate the natural frequencies of the blades. These methods express the system as a series of masses, springs and dampers such as previously seen. From Newton’s second law, the equation of motion of the system can be derived,
M· ¨x + C · ˙x + K · x = f(t) (1.1)
where x represents displacement, ˙x represents velocity, ¨x represents acceleration, f (t) represents external
forces applied to the system, and M , C and K represent system matrices for the mass, damping and stiffness respectively. If the system had only 1 DOF, then the natural frequency ωnwould be,
ωn=
√
k
m (1.2)
where m is the mass, and k is the stiffness. A wind turbine has more than 1 DOF so a more advanced approach is necessary. One such approach is to transform the system into state-space and express it in terms of the classical eigenvalue problem,
(A− λ · I) z = 0 (1.3) where A is the rearranged matrices M , C and K in state-space, λ is a vector of eigenvalues, I the identity matrix, and z the degrees of freedom in state-space. The classical eigenvalue problem can then be solved using numerical techniques for the eigenvalues which then lead to the natural frequencies of the system. This approach can be applied to complex systems such as a wind turbine blade.
m k c f(t) x(t) m1 k1 c1 x1(t) m2 k2 c2 x2(t) m3 k3 c3 f(t) x3(t)
A) Single degree of freedom system
B) Multiple degree of freedom system
Figure 1.2: Spring-Mass 1 Degree of Freedom system.
Flapwise
Edgewise
Torsion
1.6.2 Loads
The second metric is the loads or forces acting on the wind turbine. The primary loads on wind turbines are caused by aerodynamic, gravitational and inertial forces, as explained by Hansen [3]. The thesis will compare how the extreme loads change due to structural variations.
Aerodynamic Forces
To better understand the aerodynamic forces on a wind turbine blade, it is important to understand the wind. The wind is constantly changing in both direction and speed. The wind speed also varies with height, this is called wind shear, and so as the blades rotate they experience a varying force, with the tips going from high to low wind speeds. Additionally the wind is chaotic. Although there is a dominant wind direction, locally the wind is constantly changing direction. The chaos is called turbulence and it is measured in turbulence intensity.
The IEC has designated several classes of wind [16]. The wind classes in decreasing order are I, II and III. Additionally there are designations for turbulence intensity, the highest turbulence intensity is designated A followed by B and C. Each wind turbine is designed for a particular wind class.
In addition to wind classes, the IEC has also outlined particular wind scenarios, called load cases [16]. The scenarios are used to ensure that wind turbines are designed to withstand normal operation as well as worst case scenarios such as a gust with a change in direction. The load cases used in this thesis will be presented in the Methodology Chapter.
The aerodynamic forces depend on the wind speed and direction as well as the unique shape of the blade. The blade cross-sectional profiles, called airfoils, cause two forces lift and drag. Lift is due to the unique airfoil shape that causes pressure to be higher on one side than the other, thus pushing the airfoil perpendicular to the flow. Drag is caused by the force of air hitting the airfoil and pushing it in the direction of the flow. These forces are illustrated in Figure 1.4. For wind turbines, lift and drag are broken into 2 components, one pointing in the direction of rotation, causing the blade to continue spinning, and another in the direction of the shaft. The component in the direction of the shaft bends the blade in the direction of the nacelle and transmits forces to the nacelle and tower. The bending of the blade towards the tower may cause tower strike which will be further discussed in the subsection on Tip Deflection.
The magnitude of the lift and drag depend on the relative wind speed and angle of the airfoil with respect to the wind direction, called angle of attack.
The aerodynamic profile of the blades will not be varied in this thesis, however changing the structural behavior will change how the blade behaves in the wind. For example a lighter blade may be more likely to bend, and as it bends the angle of attack would change and thus the aerodynamic forces.
Gravitational Forces
The second type of force to consider is gravity. Gravity is constantly pulling the blades towards the Earth. The force of gravity Fgis equal to,
Fg=−m · g (1.4)
where m is the mass and g is the gravitational constant. As the blade is swinging downwards gravity is pulling on the leading edge side of the blade, and when spinning upwards on the trailing edge side. This is illustrated in Figure 1.5. The alternating nature of these loads makes it a concern for fatigue as discussed in the Subsection on Fatigue. As the gravitational forces vary directly with mass, it is expected that the gravitational forces will change when the mass of the blade is varied.
Lift Drag Wind High Pressure Pressure Side (PS) Suction Side (SS) Low Pressure
Figure 1.4: Aerodynamic forces.
Inertial Forces
The third primary source of forces are due to inertia. Hansen explains that the inertial loads are caused by the accelerations and decelerations of the rotor [3]. Such as when the wind speed increases and the blade starts to spin faster or a mechanical brake is applied to stop the rotation. Another source of inertial forces is due to the rotation of the blade. The mass of the blade wants to pull away from the hub, but the centripetal force acting on the blade pulls it back inwards. The centripetal force Fcacting on a rotating
mass is equal to,
Fc=
m· v2
r (1.5)
where m is the mass, v is the velocity, and r the radius. The inertial forces depend on mass, so it is expected that they will change along with gravitational forces when the mass of the blade is varied.
1.6.3 Tip Deflection
The third metric to be considered is tip deflection. As mentioned in the section on loads, the blade under aerodynamic loading is prone to bend towards the tower. An important consideration in wind turbine blade design is the maximum tip deflection. If the tip of the blade deflects far enough it will strike the tower as shown in Figure 1.6. The IEC [16] and DNV [17] standards state that interference between the blade and tower deflection must be prevented . This may break the blade and cause a large rotor imbalance, or break the tower causing the entire turbine to collapse. Therefore it is very important to consider tip deflection during the design process.
1.6.4 Fatigue
Gravity load Towards LE Direction of rotation Gravity load towards TE Trailing Edge (TE) Leading Edge (LE)
Figure 1.5: Gravity Loading.
As explained by Hansen [3], to analyze fatigue a varying load is broken into two components the mean stress σmand alternating stress σashown in Figure 1.7a. Failure may occur even if σmand σaare lower
than the limits of material strength, thus fatigue is important to consider for any structure experiencing large varying loads. On a microscopic level, fatigue can be seen as the initiation and growth of cracks until rupture.
To understand fatigue, many experimental tests have been conducted. Each experiment consists of sub-jecting a test specimen to a given mean and alternating stress until fracture. The number of cycles are counted, and the experiment is repeated for different combinations of mean and alternating stresses. The results are fit with a curve known as an S-N or Wöhler curve as shown in Figure 1.7b. As presented in the DNV standard [17], these curves provide the relationship between the number of cycles N sustain-able under an alternating stress S for a given mean stress. Using an S-N curve to predict fatigue failure is straightforward if the mean and alternating stresses do not change. However the wind is constantly changing, and thus are the stress levels.
To determine the amplitude of the alternating stress as well as the number of cycles, the rainflow counting technique is used. The method can be illustrated as in Figure 1.7c by plotting the stress versus time curve on its side, and tracing the path raindrops travel. A summary of the technique based upon an explanation by Rychlik [19] follows. A new raindrop begins at each peak, and follows several rules. If it begins at a maximum it continues until it reaches a larger maximum, and for a minimum it travels until it reaches a more extreme minimum. Lastly the raindrop stops if it collides with a drop from above. Additional rules are then applied to count half cycles based upon how the raindrops have fallen. This process continues for the stress time history counting the number of raindrops as the number of cycles, and the magnitude of the cycles based upon how far the raindrop travels.
Now that the number of cycles and load levels have been counted, the lifetime needs to be predicted. The Palmgren-Miner rule, as explained in the IEC standard [16], is used to account for varying stress levels by treating fatigue as an accumulation of damage. Failure occurs when the damage exceeds 1. The total
A) Turbine at standstill B) Tower strike
Wind
Figure 1.6: Tower Strike.
damage is equal to a sum of the damage caused by each load cycle. The damage due to each load cycle is considered the fraction of cycles the material can withstand at the given load. For example, if a material can withstand four cycles at σaequal to 200MPa, then the damage due to one cycle at 200MPa is 14. The
total damage D is calculated as,
D =∑
i
1
N (Si)
(1.6)
where the fraction N (S1
i) is summed at each cycle i, and N is the number of cycles from the S-N curve
for a given alternating stress Si.
Wind turbines are designed for a lifetime of 20 years. With the alternating direction of gravitational forces, and varying wind speeds, it is thus important to combine experimental S-N curves, with the rainflow counting technique and Palmgren-Miner rule to ensure that the wind turbine will safely operate for its designed lifetime.
1.6.5 Material Strength
The fifth metric to be considered is material strength. Wind turbine blades must be built with materials strong enough to withstand the loads. As previously explained, modern wind turbines are built using glass fiber reinforced plastic (GFRP) and carbon fiber reinforced plastic (CFRP) [7].
Understanding the mechanics of the material is important to accurately predict its strength. GFRP and CFRP are both composite materials. Although the term composite material refers to a material produced by joining two or more materials together, hereafter it will only refer to fibers laid in a matrix. The fibers are very long compared to their diameter, and the matrix is an adhesive holding the fibers in place, such as epoxy. Composites are made in sheets called plies and then stacked to form laminates. A ply is visualized in Figure 1.8. Laminates can be made to consist of plies with varying ply orientations. These types of laminates are named based on the number of different directions the fibers run in. If all of the fibers are oriented in the same direction it is called uni-directional (UD), two-directions bi-axial (BIAX), and three directions tri-axial (TRIAX).
Mean Stress Alternating Stress Stress
σ
Time t Number of cycles N
Alternating Stress S Time t Stress σ a) b) c) Total Stress
Figure 1.7: a) Fatigue cycle highlighting mean and alternating stress levels, b) S-N curve also known as Wöhler curve, c) Rainflow counting.
Composite materials are used in wind turbine blades because they are lightweight. Another advantage is that the material properties of a laminate can be tailored to the application by modifying the ply orienta-tions.
Along with the complex composition of composite materials comes more complex failure mechanism as compared to metals. An example of failure at the ply level is the breaking of the matrix or fibers and at the laminate level the plies may separate. The DNV standard [17] further explains these advanced failure mechanisms. Instead of investigating each one of these failure mechanisms individually, a strength criterion could be used.
There are a number of approaches to evaluating the strength of composite materials, and none are always accurate. One approach of evaluating material strength is to compare maximum strain levels. If a structure exceeds material strain limits taken from experiments then the design must be changed. This thesis will use this approach to evaluate the material strength.
Traditional strength criterions such as Von Mises are unable to capture these advanced failures, so more complex criterions have been developed such as the Tsai-Wu and Tsai-Hill criterions. These criterions can be found in simplified form, such as explained by Jones [20] as,
σ12 X2 + σ1σ2 X2 + σ22 Y2 + τ122 S2 = 1 (1.7)
where X is the axial strength, Y is the transverse strength, S is the shear strength, σ1 is the stress in
the direction of the fibers, σ2 is the stress perpendicular to the fibers and still within the ply, and τ12
is the shear stress within the ply. The material is considered to fail as soon as the criterion exceeds 1. The implementations of Tsai-Hill and Tsai-Wu differ in terms of how the strengths are calculated. These strength criterions require that the model be detailed to the ply level. Therefore the simpler approach of comparing maximum strains was adopted for this thesis.
Fibers Matrix
Figure 1.8: Composite Material Ply.
1.6.6 Buckling
The sixth metric to be considered is buckling. Buckling is an instability phenomenon associated with structural members under compression.
The concept of buckling is illustrated in Figure 1.9 using a column under compression. As explained by Beer et al. [21], if the compressive load becomes slightly off-center and the column is stable it will recover, however if it is unstable, the column will buckle. Buckling depends primarily on the length L of the member, as shown in Euler’s formula,
Pcr =
π2· EI
L2 (1.8)
where Pcris the critical load, E the modulus of elasticity, and I the moment of inertia.
In composite materials, fibers behave like long thin columns, and as such buckling must be considered whenever composites are put under compression. As wind turbine blades bend in the wind, one side of the blade experiences tension and the other compression. Therefore as expressed in the IEC standard [16], wind turbines must avoid buckling.
To analyze the blades in this thesis for buckling, a finite element software will be used. The DNV standard [17] recommends carefully determining boundary conditions and ensuring the mesh has been sufficiently refined. The approach used in this thesis will be further explained in the Methodology Chapter.
A) Unbuckled beam B) Buckled beam
This chapter summarizes the objectives of this thesis, building on the principles presented in the previous chapter.
The purpose of this thesis is to investigate the effect of structural blade variations for increasing blade size on the loads and structural response. The structural variations were modifying the mass, and web spacing. The same variations were applied to two blades; the NREL 61.5m 5MW and the SNL 100m 13.2MW. The effect of the variations was measured by analyzing the changes in natural frequency, loads, tip deflection, fatigue, material strength and buckling.
As explained in the Background Chapter, increasing wind turbine blade size is a way of reducing the cost of energy for offshore wind energy. The goal of this thesis is to contribute to efforts at making larger blades, by providing a better understanding of blade design trends for larger blades. Varying the mass will provide a deeper insight into changing blade materials and icing. Web spacing variations will aide blade optimization and help better understand fundamental blade design choices. These objectives have been summarized in Table 2.1.
Aeroelastic simulations were used to simulate the blades under critical wind scenarios. From the aeroelastic simulations, the natural frequencies, loads, tip deflection and fatigue were be measured. Next the loads were applied to a finite element model to perform material strength and buckling analyses. This process are detailed in the next chapter on the research methodology.
Goal Evaluate structural variations for increasing blade size
Structural Variations
• Mass - represents material change, icing • Web spacing - represents blade optimization
For increasing blade size
• NREL 5MW - 61.5m blade • SNL 13.2MW - 100m blade Evaluations based on • Natural frequencies • Loads • Tip deflection • Fatigue • Material strength • Buckling
This chapter explains the approach taken to evaluate the effect of wind turbine blade structural variations on the loads and structural response. Six metrics were used to quantify the change caused by the structural variations: natural frequencies, loads, tip deflection, fatigue, material strength and buckling. To evaluate these metrics two types of simulation tools were used, an aeroelastic simulation code and a finite element software. The aeroelastic simulation code was used to evaluate natural frequencies, loads, tip deflection, and fatigue; and the finite element software then used the loads resulting from the aeroelastic simulations to evaluate the material strength and buckling.
The methodology will now be explained in three parts. First, the process of creating the blade models used to represent each blade variation in the simulations. Second, the set-up and analysis of the aeroelastic simulations, and third the set-up and evaluation using finite element software.
3.1 Creating Blade Models
The aeroelastic code and the finite element software each require a different type of blade model. The aeroelastic code requires a blade model in terms of macroscopic structural parameters, such as mass and stiffness distributions, while the finite element software requires a detailed geometric definition including the location, orientation and thickness of materials at every point of the blade .
The process of creating the two types of blade models was simplified by using the BEam Cross section Analysis Software [22] version 2.0 (BECAS) developed at DTU Wind Energy. BECAS analyzes a finite element model for macroscopic structural properties and writes the results in a format useable by the aeroelastic code HAWC2. This allowed the author to create a finite element model, apply BECAS, and then have both blade models necessary for the simulations.
Creating finite element models of a wind turbine blade is a time consuming process. As many blades variations were envisioned to be created, a need was identified to create a tool. The tool served two pur-poses: first it sped up the creation of the blade modeling process, and second it ensured the repeatable creation of high quality finite element models with varying geometry. The tool entitled BLADEMOD-ELER was created by expanding and generalizing work done by Robert Bitsche at DTU Wind Energy with his permission.
This section will explain the development of BLADEMODELER and how it has been linked to BECAS.
3.1.1 BLADEMODELER
BLADEMODELER is based upon work done by Robert Bitsche. The program is a collection of MAT-LAB and Python scripts and is designed to be installed as a library. It is set-up such that the user first creates one input file, and then a finite element model is created by running one MATLAB and one Python script.
The first part of BLADEMODELER, the approach to create the outer shell of the blade, is taken from Robert Bitsche’s work. The remaining steps of BLADEMODELER use Robert Bitsche’s work as a guide,
X Y
Z
Figure 3.1: User defined airfoil sections.
with a new approach and implementation. The outer shell is created by taking airfoils, along with twist, and chord distributions defined from the input file and interpolating, resizing and twisting the airfoils to match the user input.
The next step is to define the layup, that is the location, thickness and orientations of material layers. The layup is defined by splitting the airfoil into user defined sections, each shown as a different color in Figure 3.1. At user defined span-wise locations, the position and layup of each section is defined which is then interpolated to give the layup throughout the entire blade.
Shear webs are defined by connecting the boundaries of two sections of the suction side (SS) with two sections of the pressure side (PS). This ensures that the edges of the webs align with edges of the airfoil shell. The layup for the shear webs is defined in the same manner as the airfoil sections.
The finite element model is created using the finite element software Abaqus/CAE version 6.11[23] (Com-puter Aided Engineering). Abaqus/CAE commands are executed through a Python script. Automation of creating the model and applying the layup was made possible by using coordinates to keep track of all of the edges, faces and elements.
Two approaches were taken in Abaqus/CAE. The first was to create the airfoil sections as separate parts and then merge them together to create the blade. This resulted in a poor quality model with gaps in the blade, so a new approach was developed. The second approach was to draw every airfoil with each section as a separate spline. The outer airfoil shell was then created by connecting the airfoils shown in Figure 3.2 in a process called lofting. Due to the separate splines, the lofted blade consisted of a separate face for each airfoil section. Throughout the process the script stored the coordinates of each spline, and later used these coordinates to re-identify each airfoil section and apply the intended material layup.
The webs were created by lofting the edge located between two airfoil sections on the PS with the edge located between two airfoil sections on the SS. This technique resulted in a high quality model because it ensured a connection between the PS and SS with neither gaps nor the creation of new edges. This came with the limitation that each airfoil section and each web must run the entire length of the blade.
Another limitation of BLADEMODELER is the inability to create blade tips with a chord that is an order of magnitude smaller than the average chord. Thus very sharp tips must be truncated in order for Abaqus/CAE to successfully loft the blade. From a structural point of view this is expected to have a small impact on results as there is so little material at the tip it hardly impacts the mass and stiffness and thus the behavior of the blade, especially for a very sharp tip.
The finite element model was created using a structured mesh of 8 node shell elements. The section later on in this chapter on Finite Element Analysis will give an explanation of how these elements behave.
−2 −1 0 1 −1 0 1 0 10 20 30 40 50 60 Blade Span [m] Chord [m] Thickness [m]
Figure 3.2: Lofting sections.
1 2 3 (a) Z Y X RP X Y Z (b)
Figure 3.3: The material stack in (a) begins at the purple surface in (b) and continues in the direction of the orange surface.
Materials were positioned such that the airfoil shell is the exterior, and materials were stacked inwards. This can be seen in Figure 3.3.
The last step of the BLADEMODELER program is to select elements at 21 evenly spaced spanwise locations. These will be used by BECAS to create the macroscopic blade model for the aeroelastic code.
The development of BLADEMODELER has enabled the author to efficiently and repeatedly create high quality finite element blade models, a task performed for each blade variation presented in this thesis.
3.1.2 BLADEMODELER to BECAS
The BECAS package, as previously mentioned, can be used to take a finite element model and prepare the macroscopic blade structural model used by the aeroelastic code HAWC2. The link between BLADE-MODELER and BECAS was made with shellexpander, a tool developed by Robert Bitsche and currently distributed with BECAS.
A brief overview of the process is presented here. A slice of shell finite elements defined by BLADE-MODELER shown in Figure 3.4a, is taken by shellexpander and “expanded” so that each shell element is replaced by multiple elements where each represents a different material, and has the thickness associated with that layer. This is shown in Figure 3.4b. The final step of shellexpander is to transform the model into a two dimensional model in a format readable by BECAS. BECAS then analyzes each cross-section as shown in Figure 3.4c for macroscopic properties that represent the entire cross-section.
The method used in this thesis is to analyze 21 cross-sections using BECAS to create the aeroelastic blade model. Each of these cross-sections correlate to the 21 nodes used in the aeroelastic model where the forces will be measured and analyzed.
3.2 Aeroelastic Simulations
After the wind turbine blade models have been created, the next step is to run the aeroelastic simulations. The aeroelastic code used was HAWC2 [24] developed by DTU Wind Energy. The aeroelastic code simulates the operation of the turbine under prescribed wind conditions.
This section will give an overview of how the aeroelastic code works and then explain the post-processing of HAWC2 simulations to determine the first four metrics: natural frequencies, tip deflection, loads anal-ysis and fatigue analanal-ysis.
3.2.1 Aeroelastic Code
This subsection will give a brief overview of the structural and aerodynamic theory implemented in HAWC2 and the role of the turbine controller.
Structure
HAWC2 uses a multibody formulation to define the turbine structure. This allows the user to define any number of bodies, position them and define the number and location of nodes within each body. The structural behavior of the structure follows the finite element method, further explained in the next section. The structure uses 2 node elements, each with 6 degrees of freedom (DOF). The structural properties of each body are defined in macroscopic terms as explained in the previous section.
(a) BLADEMODELER. (b) Shellexpander.
(c) BECAS.
Aerodynamics
The aerodynamics are simulated using Blade Element Momentum (BEM) theory. Although advanced computational methods exist such as computational fluid dynamics (CFD), they require large computa-tional resources that are impractical considering the large number of wind scenarios necessary for the design of a wind turbine blade as well as the large size of the wind turbine.
BEM theory assumes that the change in momentum of the wind when passing through a wind turbine is wholly due to the change in momentum of the blade. The drop in wind speed across the rotor is accom-panied by a change in pressure. Using BEM theory the flow field around the turbine can be predicted by calculating the response of the flow field to a drop in pressure across the rotor.
HAWC2 treats each cross-section of the blade separately assuming that there are no 3D effects between the separate cross-sections. From the flow field calculated with BEM theory, the wind speed and angle of attack at each cross-section is determined. Then using tabulated experimental data the coefficient of lift and drag are found for the angle of attack. Lastly the lift and drag of each cross-section is then calculated using the wind speed.
Controller
The third important aspect of a turbine configuration is the controller. This is the brain of the wind turbine that decides when and how much to pitch the blades and yaw the rotor. Decisions are based upon wind speed and wind direction sensors that are typically placed on top of the nacelle. Two identical turbines with different controllers may behave very differently in the same wind conditions.
3.2.2 Choice of Wind Simulations
As explained in the Background Chapter, the wind is constantly varying. The IEC Standards have outlined what are considered standard load cases. Due to the time and computational restraints of this Master’s Thesis, it was unrealistic to run every load case for each blade variation. Instead simulations were chosen to find the loads of most interest to this thesis, ultimate and fatigue loads.
The ultimate load cases were chosen by taking the IEC load cases found to create the most extreme loads for the SNL100, and removing the cases with electrical faults which are considered abnormal cases. The remaining cases were normal wind profile (NWP), extreme coherent gust with direction change (ECD), and extreme turbulence model (ETM). Each of these scenarios was simulated at three different wind speeds, 9.4 m/s, 11.4 m/s and 13.4 m/s. 11.4 m/s is the wind speed at which the turbines produce rated power, this means the controller is about to begin pitch regulation of the blades. 9.4 m/s and 13.4 m/s are chosen to be +/-2m/s of the rated wind speed with the lower being before pitch regulation and the higher being within pitch regulation. The ECD case was run twice at each wind speed to represent a wind change in two different directions. Another wind case listed in the SNL100 report was the extreme wind shear scenario, but initial simulations gave unrealistic results, so it was eliminated. So it was removed from the list. Using the load cases used in the design of the SNL100 there is greater confidence that the ultimate loads will be discovered, and it allowed the possibility to directly compare the results from the SNL100 with the 13.2MW blade. This was used to validate the experimental set-up.
The loads used for fatigue analysis were simulated by running 11 simulations in the range of cut-in and cut-out wind speeds with the normal turbulence model (NTM). NTM was chosen because it is designed to represent normal wind conditions. The number of hours each simulation is designed to represent was calculated using a Rayleigh distribution that is shown in Figure 3.5. Through these simulations, 90% of
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Figure 3.5: Rayleigh wind speed distribution.
Acronym Explanation NWP Normal Wind Profile
ECD Extreme coherent gust with direction change ETM Extreme Turbulence Model
NTM Normal Turbulence Model
Table 3.1: Load cases.
the 20 year lifetime is represented, and the majority of the remaining 10 % falls below the cut-in wind speed. The analysis of these loads will be presented later.
The turbulence of the wind leads to variations between aeroelastic simulations with the same mean wind speed. Typically aeroelastic simulations with turbulence are repeated 6 times to ensure reasonable results. Due to the time and computational limitations it was not possible to take this into account for each simulation. It was later found that the ETM case caused the maximum edge-wise loads of the scenarios analyzed, so this case was simulated with 5 additional turbulence scenarios for each blade to confirm these results, bringing the total ultimate load cases up to 17.
In total 28 simulations were run for each blade variation, 17 for ultimate loads, and 11 for fatigue loads.. Table 3.1 shows the acronyms used throughout the report to refer to the different wind scenarios. The computational time to run 28 aeroelastic simulations for one blade variation is approximately 15 hours.
3.2.3 Metric 1: Natural Frequencies
HAWC2 calculated the natural frequencies of the blades and turbines. The turbine natural frequencies were used to validate the baselines, and the blade natural frequencies to compare blade variations. The
natural frequencies of the blades were calculated with the blade simulated as one body versus the ten bodies typically used during normal operation.
3.2.4 Metric 2: Tip Deflection
Position sensors were included in the tip of each blade to measure tip deflection. HAWC2 output the tip deflection at every time step and using a statistical package distributed with HAWC2 the maximum tip deflection was found for each blade for each simulation. Further post-processing determined the maxi-mum for each simulation and then compared simulations to find the maximaxi-mum for each blade variation. The maximum tip deflections across all wind simulations were then compared.
3.2.5 Metric 3: Loads
To measure the loads on each blade, force and moment sensors were included at each node on each blade. As with the tip deflection results, the statistical package distributed with HAWC2 allowed the determination of maximum and minimum forces and moments at each node. Further post-processing calculated the forces and moments for each simulation and then determined the maximum and minimum for each blade variation.
The IEC standards outline four load cases as the most critical. These are flap-wise bending in the PS and SS directions, and edge-wise bending in the LE and TE directions. Therefore these were the four cases chosen for analysis. These are also the four cases later investigated for material strength and buckling using finite element analysis.
HAWC2 output the integrated bending moments at each node. To recreate the bending moments on the finite element model, point forces were needed to be calculated. The theoretical relationship between shear forces and bending moments is defined in mechanics of materials theory [21] as,
V = dM
dx (3.1)
where V is the shear force, M the bending moment, and x the blade radial position. The first step was to fit a curve to the integrated bending moment curve output by HAWC2. Then using the relationship of Equation 3.1 the integrated shear curve was found by taking the derivative of the bending moment curve. The last step was to determine the point forces to be applied to each node. This was done by moving from the blade tip to the root and adding forces to each node such that the total force at any point was equal to the derived shear force curve. An example of this process is shown in Figure 3.6. It is clear that the bending moment curve from HAWC2 is recreated through the use of point forces. There is variation between the applied shear force curve and the shear forces from HAWC2, but this is acceptable as the primary objective is to recreate the bending moment curve.
3.2.6 Metric 4: Fatigue Analysis
Fatigue analysis was performed using the fatigue function distributed with HAWC2. The 11 normal turbulence model (NTM) simulations representing wind speeds between cut-in at 3m/s to cut-out at 25m/s were input into the function, along with the number of hours the turbine is expected to operate at each of these wind speeds, as shown in Figure 3.5.
Using the rainflow counting method explained in the Background Chapter, the function keeps track of the number of cycles and cycle amplitude for each simulation. The number of cycles at each load is then
0 20 40 60 80 100 0 5 10 15x 10 4 Blade Radius [m] Bending Moment [kN−m] Flap−wise SS M: HAWC2 M: Applied 0 20 40 60 80 100 0 500 1000 1500 2000 2500 Blade Radius [m] Shear Force [kN] Flap−wise SS V: HAWC2 V: Applied Point Forces
Figure 3.6: Point forces calculated to reconstruct the bending moment curve.
scaled by the number of hours expected at that wind speed. The simulations are then combined by adding the number of cycles at each amplitude.
It is difficult to compare this spectrum for different blade variations. Instead an equivalent load is used to compare. The equivalent load is determined by applying the Palmgren-Miner rule and calculating the damage that would be done to a material with a Wöhler (S-N) curve with an expected slope of 10 as used in the SNL100 design. The equivalent load is the load necessary to cause an equivalent amount of damage as the determined load history if applied once per second for 20 years. A decrease in equivalent load represents an increase in expected lifetime. The calculation of the lifetime is not considered in this thesis, this is an area for future work.
3.3 Finite Element Analysis
The final step of the blade variation study is running finite element analysis. It is performed by applying the loads envelope determined through the aeroelastic simulations onto the finite element model created at the beginning of the process.
This section gives a brief overview of the finite element method, and then explains the process of per-forming material strength and buckling analyses.
3.3.1 Overview
The finite element method allows the simulation of forces onto complex geometries by constructing a model made of many small, finite, pieces each with a well-defined behavior. These pieces or elements represent well studied objects such as a beam with a response that is well understood and defined by analytical relations.
As the behavior of each element can be predicted, so can the behavior of the entire model. Prior to the development of this method, new designs were either simplified to an understood geometry or experi-mentally tested. The finite element method allows greater accuracy and reduces the need for experiments.
Different types of elements exist for different applications. The type of element used in this research for the finite element analysis is an eight node shell element as shown in Figure 3.7. Each node has six DOF,
Z Y
X
Figure 3.7: Shell finite element.
three translation and three rotation. The shell element is much longer and wider than it is thick. This makes it a suitable element for wind turbine blades at they are thin hollow structures. Another aspect of shell elements making them suitable for wind turbine blades, is their ability to represent several materials stacked upon one another. Abaqus/CAE calculates the macroscopic properties of the element after being provided the detailed structural layup.
An important aspect of finite element analysis is the application of boundary conditions. This is to ensure the blade responds appropriately. For the analyses later described, the root of the blade is clamped such that the edge can neither translate nor rotate in any direction. This is to simulate the blade being attached to the hub of the turbine.
Another important aspect of finite element analysis is the application of loads. According to classical aerodynamic theory, the aerodynamic forces for a thin symmetric airfoil act on the 1/4 chord point of the airfoil [25]. To simulate this, constraints were placed on the blade corresponding to each HAWC2 node to distribute the force at the 1/4 chord to the surrounding airfoil. The total force applied is unchanged by this process, this method simply allows a more accurate distribution of the forces.
Next the application of the finite element method to determining material strength will be described.
3.3.2 Metric 5: Material Strength
To determine the material strength of each blade variation, the four critical load cases from the aeroelastic simulations were applied to the finite element model. These load cases were flap-wise moments in the PS and SS directions, and edge-wise moments in the TE and LE directions. Each load case was conducted as a separate analysis. For each analysis the loads were applied at 20 evenly spaced locations to distribute the load.
A linear static analysis was then performed. This type of simulation represents the forces being applied to the blade, then the blade deforming until it is in equilibrium with the applied force. From the deformed blade, strains and stresses are determined. Part of this analysis is to determine which blade experiences the largest strains. Another interesting part is to look at the composite failure criterions.
3.3.3 Metric 6: Buckling
Finite element analysis is also used to determine if buckling is a concern for some blade variations more than others. Buckling as described in the Background Chapter, can be a concern when objects are under compression.
Buckling was investigated for the case of extreme flap-wise loading in the SS direction, as this was the sit-uation with the highest loads. The analysis was performed by first applying 1/10th of the maximum load to pre-load the structure. Next a buckling analysis was performed. Abaqus/CAE incrementally increased the loading until buckling occurred taking into account the nonlinear deformation of the preloaded struc-ture. The first five buckling modes were extracted. Each mode shows which part of the blade will buckle and provides a multiplication factor representing the force at which buckling occurs. If buckling occurs at a force much greater than the maximum then it is not a concern. However if that is not the case then it must be further investigated.
This chapter will explain the implementation of setting up the blade and aeroelastic simulations for the 5MW and 13.2MW blades.
4.1 Blade Models
This section will explain the process of creating the baseline 13.2MW and 5MW blades and how they were modified to create the blade variations being investigated in this thesis. It will end by giving an overview of the numerical settings used for the creation of the finite element models.
4.1.1 Baseline 13.2MW
The baseline 13.2MW blade model was based upon the published SNL100 design from Sandia National Laboratories (SNL) which included the blade structural layup and majority of the material properties. Material properties not found in the SNL100 report [14] were found in the SNL100 simulation files available from Sandia National Laboratories [26] or through the SNL/MSU/DOE Composite Material Fatigue Database [27] referenced in the SNL100 report. Two modifications were made to the blade design to allow the recreation of the blade with the BLADEMODELER tool.
Firstly, BLADEMODELER can only create shear webs that run the entire length of the blade. The SNL100 blade has three shear webs, one only running for part of the blade, from 14.6% to 60% span. This shear web was removed to enable the creation of the blade by BLADEMODELER. According to the SNL100 report, the third shear web was included to improve buckling resistance as earlier design iterations experienced buckling issues. With it removed buckling was expected to become a problem.
The second simplification was with the blade tip. The tip of the SNL100 blade was designed with a chord of 0.1m which is much smaller than the maximum chord of 7.6m at 19.5% span, and thus BLADEMOD-ELER was unable to model it. Therefore the finite element model was truncated at 98.6m so that the tip chord was 1.2m, but in the aeroelastic simulations it was still simulated as a 100m blade. This is not expected to affect results greatly as the tip of the blade provides little structural strength due to its small size. The 13.2MW baseline blade used in this thesis is shown in Figure 4.1.
The SNL100 was created with the two design modifications by BLADEMODELER and then compared against the original SNL100. Structural property comparisons are shown from BECAS in Figure 4.2 and from Abaqus/CAE in Table 4.1. It is clear from the comparisons that although the design modifications were kept at a minimum and only to allow the creation of the blade model with BLADEMODELER that the blades are different. The results also suggest that BLADEMODELER needs further refinement. Therefore the blade created for this thesis will be referred to as the 13.2MW blade, and the blade created by SNL as the SNL100. The center of gravity and total blade mass as calculated in the finite element software show match within 2%. The stiffnesses as computed for the aeroelastic simulations however show more variance. With the exception of a spike at 25% span, the flap-wise and edge-wise stiffnesses of the SNL100 are on average 11% higher than the 13.2MW blade. The torsional stiffness of the SNL100 is larger at the root and significantly lower for the rest of the blade.
