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masterproef.
The authors give permission to make this master dissertation available for consultation
and to copy parts of this master dissertation for personal use. In the case of any other
use, the limitations of the copyright have to be respected, in particular with regard to the
obligation to state expressly the source when quoting results from this master
dissertation.
Date:
Jorit Van Laeren Mathijs Peeters
Preface
In order to achieve a master degree in mechanical engineering, we present this master
dissertation in which a numerical model of the rotor blade of a 49 meter wind turbine,
fabricated by PowerComposites Limburg, is realized. We chose this subject because of
our interest in alternative energy, composite materials and numerical research. The fact
that few work exists in this field together with wind energy being a hot topic are two
other reasons that influenced our choice.
Thanks to this master dissertation, we met several interesting people who helped us to
achieve our goals, in the rest of this preface we would like to thank them.
First of all we would like to thank our promotor, prof. dr. ir. Wim Van Paepegem, to give
us the opportunity to work on this master dissertation, for his spent time during several
meetings and for his valuable insights in solving our problems.
For all our practical problems, concerning SolidWorksTM, AbaqusTM and the experimental
tests we were able to count on the expert explanation of ir. Stefan Jacques. We spent
hours in his office looking for solutions to numerous problems and we are very grateful
that he was always available to help us.
Furthermore, we would like to thank PowerComposites Limburg and especially Geert
Nouwen for their confidence in providing the blueprints of their 49 meter rotor blade and
for the effort to fabricate the many test samples.
Koen Van Der Biest did his master dissertation on the same 49 meter rotor blade, but he
investigated the wind flow around the blade. Thanks to his results, we were able to
apply a load case representing steady state power production on the rotor blade.
Lastly, we would like to thank our families and in particular our parents for their aid,
support and trust during our studies even during hard times.
Thank you all!
Jorit Van Laeren, Mathijs Peeters
Numerical simulation of a 50 metre
composite rotor blade for MegaWatt
windturbines
door
Jorit Van Laeren, Mathijs Peeters
Promotoren: prof. dr. ir. Wim Van Paepegem, prof. dr. ir. Joris Degrieck
Begeleider: ir Stefan Jacques
Masterproef ingediend tot het behalen van de academische graad van Master in de
ingenieurswetenschappen: werktuigkunde-elektrotechniek
Vakgroep Toegepaste Materiaalwetenschappen
Voorzitten: prof. dr. ir. Joris Degrieck
Faculteit Ingenieurswetenschappen en Architectuur
Academiejaar 2011-2012
Abstract
Due to the greenhouse effect and energy issues, alternative energy is rapidly gaining
importance. Wind energy is one of the more promising alternatives. To make wind
energy more cost-effective, turbines with longer blades are used. This makes the
structural design more important and difficult. A way to analyze a structural design and
its performance is by means of a finite element model. In this master dissertation, such a
model was developed for the 49 meter long blade produced by PowerComposites
Limburg. To minimize CPU-times, manual labor, human errors and to maximize the
flexibility, a Python script was developed that generates the composite layup of the blade
based on an Excel sheet with all layup data. The model consists of conventional shell
elements and is fully parametrical.
Keywords
Rotor blade, FEA, structural design, AbaqusTM, composites
Numerical simulation of a 50 metre composite
rotor blade for MegaWatt windturbines Mathijs Peeters
1, Jorit Van Laeren
2
Supervisors: Wim Van Paepegem, Joris Degrieck, Stefan Jacques
Abstract— Due to the current high prices of
conventional energy resources, alternative energy is
rapidly gaining importance, wind energy in particular has
an important potential. The advantages of wind energy are
legible: there are no emissions and the energy source is
inexhaustible. To achieve a low cost per kilowatt hour,
there is a tendency to manufacture wind turbines with
increasing rotor diameters. This induces large structural
challenges. To achieve a good structural design, a finite
element model can be an efficient and cost effective
auxiliary. In this master dissertation a numerical model is
developed corresponding to the new 49 meter long rotor
blade produced by PowerComposites Limburg.
A major challenge is linked to the large number of
composite plies in the layup of the blade: a good numerical
model allows incorporating each ply with a minimal
amount of work.
Index Terms— Rotor blade, FEA, structural design,
AbaqusTM, composites
1. INTRODUCTION
Wind turbines have inherent limitations:
theoretically, only 59% of the energy available in the
wind can be transferred to the wind turbine. Part of
this energy will be lost due to friction, this way the
effective efficiency will be between 10 and 30%. The
power of a wind turbine increases quadratic with the
rotor diameter [1]. The efficiency raises together
with the power because the relative influence of the
losses diminishes. This explains the tendency of
manufacturing even longer rotor blades. Due to the
increased loads, the amount of materials used in a
blade will have to increase more than linear with the
length of the blade. Consequently, this involves an
increase of the centrifugal forces. These, in turn,
cause additional difficulties for a good structural
design.
The structural design of a rotor blade involves two
major challenges: the ability of the blade to resist
extreme load cases while using a minimum amount
of materials.
A thorough analysis of such a complex design
requires the use of a numerical finite element model
(FEM).
2. INVESTIGATION OF THE MOST DESIGNATED ELEMENT TYPE
The software package used to conduct the finite
element analysis is AbaqusTM
. This package has
several techniques available to model the blade.
These techniques are applied onto a simplified model
of a rotor blade as shown in figure 1. Their
corresponding advantages and disadvantages are
investigated.
Figure 1: Simplified rotor blade model
The characteristics of different possible element
types are compared, especially their effect on the
CPU-time required to conduct a calculation with a
converged mesh. Furthermore, the preprocessing
time corresponding to each of the different modeling
techniques is taken into account. The final goal of
this study is to model the rotor blade in the most
optimal way: there has to exist a balance between the
accuracy of the calculations and the overall elapsed
time.
Three possible element types were studied:
conventional shell elements, continuum shell
elements and solid elements. One of the conclusions
is that both shell element types have a similar
calculation time, the solid elements on the other hand
are remarkably more time consuming. The use of
solid elements should be avoided wherever possible.
Considering the large required preprocessing time
when using continuum shell elements and the fact
that these elements are not well suited for
optimization purposes, the final model of the 49
meter rotor blade consists solely of conventional
shell elements.
3. MODELING TECHNIQUE
3.1. Assignment of the composite plies
PowerComposites Limburg provided the
blueprints of the rotor blade together with a CAD
model of the outer surface of the turbine blade.
Based on this outer surface, the model was built in
AbaqusTM
, using conventional shell elements. The
stacking sequence of the laminate was assigned to
the model using a build-in feature called “composite
layup”. This feature requires the assignment of the
specific surface of the blade covered by one ply. To
make this possible, hundreds of different partitions
have to be generated on the blade enabling the
allocation of each ply.
3.2. Python-script
To avoid intensive manual labor, a Python script
was developed enabling to automate the complete
build-up of the rotor blade. First of all, the script
generates multiple datum planes dividing the blade
into multiple partitions as indicated in figure 2.
Figure 2: Rotor blade after partitioning
Subsequently the Python script will, based on
layup data stored in an Excel-file, assign all materials
onto the blade. This method enables the generation of
a finite element model of the real rotor blade with
high precision.
3.3. Build-up of the model
The rotor blade itself consists of multiple
components, each having a different contribution to
the structural behavior of the blade. Starting from the
most important structural component (the main
girder), the model was expanded step by step. This
method allows estimation of the effect of each of the
components on the structural design of the blade.
3.4. Experimental tests
A good numerical model demands an appropriate
geometry, a mesh of sufficient quality and correct
material characteristics. Two sources of material data
are available: there are datasheets for most materials,
but to obtain more accurate data, which may differ
especially due to a different fiber volume fraction,
experimental tests were conducted. Tensile and four
point bending tests were performed onto laminate
and sandwich samples. These tests allow retrieving
stress-strain curves of the materials together with
their Poisson-coefficients.
3.5. Simulations
The final model was used to conduct a modal
analysis. The resulting eigenfrequencies are in
agreement with the design predictions.
3.6. Optimization
As the model is parametric, optimization is
possible. An optimization was attempted on the
model containing only the spar of the blade.
4. CONCLUSION
In this master dissertation, the 49 meter long wind
turbine rotor blade produced by PowerComposites
Limburg was modeled successfully. The model was
made parametric by means of a Python script. This
allows optimization of the layup. A first attempt at
this optimization was performed.
ACKNOWLEDGMENT
The authors would like to thank all supervisors
and technical personnel for their aid and suggestions
leading to the final result of this master dissertation.
REFERENCES
[1] «http://www.raeng.org.u,» [On line]. Available: http://www.raeng.org.uk/education/diploma/maths/pdf/exemplars_advanced/23_Wind_Turbine.pdf
Numerieke simulatie van een 50 meter
composiet rotorblad voor MegaWatt
windturbines Mathijs Peeters
1, Jorit Van Laeren
2
Supervisors: Wim Van Paepegem, Joris Degrieck, Stefan Jacques
Samenvatting — Door de huidige energieproblematiek
wordt alternatieve energie steeds belangrijker,
windenergie heeft hierbinnen een belangrijk potentieel. De
voordelen van het gebruik van windenergie zijn duidelijk:
geen emissies en een onuitputbare energiebron. Om een zo
laag mogelijke kost per kilowatt uur te bereiken, is er een
drijfveer naar steeds grotere rotordiameters. Dit leidt tot
grote structurele uitdagingen; om tot een goed structureel
ontwerp te komen kan een eindig elementen model een
kostenbesparend en efficiënt hulpmiddel zijn. In deze
masterproef wordt een dergelijk numeriek model opgesteld
voor het nieuwe 49 meter lange rotorblad geproduceerd
door PowerComposites Limburg. Een grote uitdaging
hierbij is afkomstig van het grote aantal lagen in de
laminaatopbouw: een goed numeriek model laat toe om elk
van deze lagen te modelleren met beperkte inspanningen.
Trefwoorden— Rotorblad, FEA, structureel ontwerp,
AbaqusTM, composieten
1. INTRODUCTIE
Windturbines hebben inherent beperkingen:
theoretisch kan slechts 59% van de energie uit de
wind onttrokken worden. Hiervan wordt nog een deel
door wrijving gedissipeerd, waardoor het effectief
rendement tussen de 10 en 30% ligt. Het vermogen
van een windturbine stijgt kwadratisch met de
rotordiameter [1]. Samen met het vermogen stijgt
ook de efficiëntie; doordat het relatieve aandeel van
de verliezen kleiner wordt. Hierdoor bestaat er een
tendens tot het gebruik van langere rotorbladen. Door
de grotere belasting dient de gebruikte
materiaalhoeveelheid voor de bladopbouw sterker
dan lineair met de bladlengte toe te nemen. Hierdoor
verhogen ook de optredende centrifugaalkrachten
wat weerom extra moeilijkheden oplevert bij het
structureel ontwerp.
Het structurele ontwerp van dergelijke rotorbladen
stelt twee grote uitdagingen: het kunnen weerstaan
van extreme belastingen waarbij tezelfdertijd het
optredende materiaalgebruik zo laag mogelijk dient
gehouden te worden.
Voor een grondige analyse van een dergelijk
ontwerp is het gebruik van een numeriek eindig
elementen model (FEA) aangewezen.
2. ONDERZOEK NAAR HET MEEST AANGEWEZEN ELEMENTTYPE
Het softwarepakket gebruikt voor het uitvoeren
van de eindige elementen analyse is AbaqusTM
. De
beschikbare modelleringwijzen die in aanmerking
komen om het rotorblad te modelleren, werden tegen
mekaar afgewogen op een vereenvoudigd bladmodel
zoals getoond in figuur 1.
Figuur 1: Vereenvoudigd bladmodel
Dit komt neer op het vergelijken van verschillende
elementtypes met hun verschillende karakteristieken.
De CPU-tijden nodig om de verschillende simulaties
te voltooien met een net geconvergeerde mesh
werden met elkaar vergeleken. Ook werd de
voorverwerkingstijd in rekening gebracht. Dit alles
om het blad optimaal te modelleren zodat er een
evenwicht ontstaat tussen enerzijds de
nauwkeurigheid van de uitgevoerde berekeningen en
anderzijds de totale verstreken tijd.
Drie mogelijke elementtypes werden bekeken:
conventionele shell elementen, continuüm shell
elementen en solid elementen. Er werd vastgesteld
dat beide shell types een gelijkwaardige rekentijd
vereisen terwijl de solid elementen veel
rekenintensiever zijn. Hun gebruik dient dan ook
zoveel mogelijk beperkt te worden.
Doordat de voorverwerkingstijd bij het gebruik
van continuüm shell elementen vele malen groter is
en deze minder geschikt zijn voor
optimalisatiedoeleinden, werd geopteerd om het
werkelijke 49 meter lange rotorblad volledig met
conventionele shell elementen te modelleren.
3. MODELLERINGSWIJZE
3.1. Toewijzing laminaat lagen
De plannen van het huidige structureel ontwerp
werden door PowerComposites Limburg aangereikt
tezamen met een CAD-model van de buitenmantel
van het turbineblad. Op basis van deze buitenmantel
werd het model in AbaqusTM
opgebouwd met
conventionele shell elementen. De stapeling van het
laminaat werd aangebracht met behulp van de
ingebouwde functie “composite layup”. Hiertoe dient
voor elke laag het bijhorende bedekte oppervlak van
het turbine blad aangeduid te worden. Dit vergt de
aanmaak van honderden partities die het blad
opdelen zodat voor elke laag het bedekte gebied kan
aangeduid worden.
3.2. Python-script
Om dit intensieve, manuele werk te omzeilen werd
een Python script ontwikkeld dat de volledige
opbouw van het blad automatiseert. Hierbij worden
in eerste instantie honderden snijvlakken aangemaakt
die het blad opdelen in talloze partities zoals
aangegeven in figuur 2.
Figuur 2: Rotorblad na de partitionering.
Vervolgens zal het Python script, op basis van een
Excel-file die de volledige layup bevat, alle
materialen toewijzen aan het rotorblad. Deze
methode laat toe om de bladopbouw zeer precies na
te bootsen.
3.3. Modelopbouw
Het rotorblad zelf bestaat uit verschillende
onderdelen, deze hebben elk een verschillende
bijdrage tot het structureel gedrag van het rotorblad.
Vertrekkende van de belangrijkste structurele
component (de main girder) werd het model stap
voor stap opgebouwd. Deze methodiek laat toe om
het effect van elk onderdeel op het gedrag van het
volledige blad kwalitatief in te schatten.
3.4. Experimentele testen
Een goed numeriek model vergt een goede
geometrie, een kwalitatieve mesh en correcte
materiaaleigenschappen. Er zijn twee bronnen van
materiaalgegevens beschikbaar: enerzijds datasheets,
maar anderzijds is het aangewezen om de werkelijke
materiaaleigenschappen te gebruiken in de
berekeningen. Hiertoe werden experimentele testen
uitgevoerd. Deze omvatten trek- en buigproeven op
laminaat en sandwich samples. Deze laten toe om de
volledige spanning-rek krommen op te stellen en
tevens de Poisson-coëfficiënten te achterhalen.
3.5. Simulaties
Op het uiteindelijke model werd een modale
analyse uitgevoerd. De hieruit volgende
eigenfrequenties zijn in overeenstemming met de
voorspellingen van het ontwerp.
3.6. Optimalisatie
Aangezien het model parametrisch is, is
optimalisatie mogelijk. Een eerste poging tot
optimalisatie werd ondernomen op het model dat
enkel de spar van het blad bevat.
4. CONCLUSIES
In deze masterproef werd het 49m windturbine
blad dat geproduceerd wordt door PowerComposites
Limburg gemodeleerd. Het model werd parametrisch
opgebouwd aan de hand van een Python script. Dit
laat optimalisatie van de laminaatopbouw toe . Een
eerste poging tot dergelijke optimalisatie werd
ondernomen.
5. DANKBETUIGING
De auteurs willen alle begeleiders en technische
medewerkers bedanken voor hun hulp en suggesties
tijdens het werken aan deze masterproef.
REFERENTIES
[1] . «http://www.raeng.org.u,» [On line]. Available: http://www.raeng.org.uk/education/diploma/maths/pdf/exe
mplars_advanced/23_Wind_Turbine.pdf
Numerical design of a 49 m rotor blade for Megawatt wind turbines Chapter 1
Mathijs Peeters – Jorit Van Laeren 1
Table of contents
1 Introduction ................................................................................................................... 6
2 Objectives .................................................................................................................... 13
2.1 Motivation ............................................................................................................ 13
2.2 Normal R&D process ............................................................................................ 13
2.3 The R&D process used in this master dissertation ............................................. 14
2.4 The model ............................................................................................................. 14
3 Design of the rotor blade ............................................................................................. 16
3.1 Mechanical design ................................................................................................ 16
3.1.1 Structure ....................................................................................................... 16
3.1.2 Certification tests .......................................................................................... 18
3.2 Aerodynamic design ............................................................................................. 19
3.2.1 Wind turbine classes ..................................................................................... 19
3.2.2 Design loads .................................................................................................. 20
3.3 Materials .............................................................................................................. 21
3.3.1 General test procedure .................................................................................. 22
3.3.2 Tensile tests .................................................................................................. 22
3.3.3 Four point bending tests ............................................................................... 23
4 Manufacturing of rotor blades .................................................................................... 24
4.1 General production methods for composite materials......................................... 24
4.1.1 Pressure bag molding .................................................................................... 24
4.1.2 Autoclave molding ......................................................................................... 25
4.1.3 Resin transfer molding ................................................................................. 25
4.1.4 Vacuum bag molding..................................................................................... 26
4.2 Production method of a rotor blade ..................................................................... 26
4.2.1 Cutting and placement of fiberglass sheets ................................................. 26
4.2.2 Infusion ......................................................................................................... 27
4.2.3 Bonding and finishing ................................................................................... 28
5 Theoretical background of finite elements ................................................................. 29
5.1 Different element types........................................................................................ 29
5.1.1 Shell elements ............................................................................................... 30
5.2 Element settings .................................................................................................. 32
Numerical design of a 49 m rotor blade for Megawatt wind turbines Chapter 1
Mathijs Peeters – Jorit Van Laeren 2
5.2.1 Choosing between first and second order elements ..................................... 32
5.2.2 Full and reduced integration ........................................................................ 32
5.3 Element related problems .................................................................................... 32
5.3.1 Hour glassing ................................................................................................ 32
5.3.2 Shear and volumetric locking ....................................................................... 32
6 Finite element simulations of rotor blades ................................................................. 33
7 Modeling of a simplified rotor blade ........................................................................... 34
7.1 The simplified model ............................................................................................ 34
7.2 Materials .............................................................................................................. 34
7.3 Loads and boundary conditions ........................................................................... 35
7.4 Mesh ..................................................................................................................... 35
7.4.1 Conventional shells and continuum shells ................................................... 36
7.4.2 Conventional shell elements ......................................................................... 41
7.4.3 Solid elements ............................................................................................... 47
7.4.4 Shell and solid elements ............................................................................... 47
7.4.5 Conclusion ..................................................................................................... 50
7.5 Adhesive bonds ..................................................................................................... 52
7.5.1 Overview of the available options ................................................................. 53
7.5.2 Adhesive layers for spars .............................................................................. 56
7.5.3 Adhesive layer for leading and trailing edge ................................................ 57
8 Modeling of a 49 m rotor blade ................................................................................... 61
8.1 Geometry of the rotor blade ................................................................................. 61
8.1.1 Original CAD-model ...................................................................................... 61
8.1.2 Two modeling strategies ............................................................................... 63
8.1.3 Automation of the partitioning ..................................................................... 67
8.2 The model layup ................................................................................................... 74
8.2.1 Modeling methods ......................................................................................... 75
8.3 General modeling technique ................................................................................ 76
8.3.1 Partitioning and layup strategy ................................................................... 77
8.3.2 Assigning regions .......................................................................................... 77
8.3.3 Partitioning ................................................................................................... 78
8.3.4 Assigning the layup....................................................................................... 80
8.3.5 Boundary conditions and loads ..................................................................... 82
8.3.6 Mesh .............................................................................................................. 82
Numerical design of a 49 m rotor blade for Megawatt wind turbines Chapter 1
Mathijs Peeters – Jorit Van Laeren 3
8.4 Python script ........................................................................................................ 82
8.4.1 Multiple scripts ............................................................................................. 84
8.5 Material properties .............................................................................................. 86
9 Calculations ................................................................................................................. 87
9.1 Main girder with spars ........................................................................................ 88
9.1.1 Mesh convergence analysis ........................................................................... 90
9.1.2 Adhesive bonds .............................................................................................. 90
9.1.3 Influence adhesive layer – remarks .............................................................. 93
9.1.4 Modal analysis .............................................................................................. 93
9.2 Pressure and suction side with spars, SW .......................................................... 94
9.3 Model without adhesive ....................................................................................... 97
9.3.1 Modal Analysis .............................................................................................. 97
9.3.2 CFD-load ..................................................................................................... 100
10 Optimization .......................................................................................................... 103
10.1 Main girder ......................................................................................................... 103
10.1.1 Results ......................................................................................................... 104
10.2 Genetic algorithm ............................................................................................... 105
10.2.1 Introduction ................................................................................................. 105
10.2.2 Optimization layup rotor blade ................................................................... 107
10.2.3 Overview genetic algorithm ........................................................................ 107
10.2.4 Interface ...................................................................................................... 108
10.2.5 Implementation of genetic algorithm ......................................................... 109
10.2.6 Create the first generation ......................................................................... 110
10.2.7 Evaluate and rank the generation: ............................................................. 111
10.2.8 Fitness function on the generation ............................................................. 111
10.2.9 Next generation ........................................................................................... 112
10.2.10 Results ..................................................................................................... 113
11 Conclusion .............................................................................................................. 116
Appendix A Principles of finite element analysis ....................................................... 117
1. Finite element principles .......................................................................................... 117
1.1. 8-node element ....................................................................................................... 117
1.2. 20-node element ..................................................................................................... 118
Appendix B Different element types ........................................................................... 120
1. Characteristics .......................................................................................................... 120
Numerical design of a 49 m rotor blade for Megawatt wind turbines Chapter 1
Mathijs Peeters – Jorit Van Laeren 4
2. Family ........................................................................................................................ 120
3. Degrees of freedom .................................................................................................... 120
4. Number of nodes and order of interpolation ............................................................. 120
5. Formulation ............................................................................................................... 121
6. Integration ................................................................................................................. 121
6.1. Choice between first and second order .................................................................. 121
6.2. Choice between full and reduced integration........................................................ 122
7. Hour glassing ............................................................................................................ 122
8. Shear and volumetric locking ................................................................................... 123
8.1. Shear locking ......................................................................................................... 123
8.2. Volumetric locking ................................................................................................. 124
12 Bibliography........................................................................................................... 125
Numerical design of a 49 m rotor blade for Megawatt wind turbines Chapter 1
Mathijs Peeters – Jorit Van Laeren 5
Abbreviations
2AX Biax (laminate)
4AX Quadrax (laminate)
CAD Computer aided design
CFD Computational fluid dynamics
FEA Finite element analysis
FEM Finite element method
GUI Graphical user interface
HAWT Horizontal axis wind turbine
LE Leading edge
PS Pressure side
SS Suction side
TE Trailing edge
UD Unidirectional (laminate)
VAWT Vertical axis wind turbine
Numerical design of a 49 m rotor blade for Megawatt wind turbines Chapter 1
Mathijs Peeters – Jorit Van Laeren 6
1 Introduction
The limited amount of fossil fuels, the climate change due to greenhouse gasses and
political instabilities have made governments aware of the hazards linked to
conventional energy resources like coal, natural gas and petrol. Nuclear energy is an
alternative, but due to the inherent hazards and the recent disaster in Fukushima,
Japan, this energy source has lost most of its attractive power. Germany has decided to
shut down most of its nuclear activities by 2022, and it will focus more on green energy,
especially wind energy.
The current goal of the European Union is to reduce the total amount of greenhouse
gasses with 1.113 million tons of CO2 in 2020 [1], this corresponds to 20% of the total
CO2 production. Only 40% of this reduction will be realized in the European Union itself,
the majority of the reduction will be achieved by buying clean air in foreign countries
outside of the EU. To meet this challenge, new and clean energy resources will be
necessary. There is no sole solution available, but several options are at hand: wind
energy, solar power, cogeneration… Since this master dissertation deals with wind
energy, only this type of energy will be discussed.
A comparison is made between the different energies available on the market today as
given in figure 1. Remarkably, wind energy is more cost-efficient than natural gas. Solar
power on the other hand should not be used for large power plants. Nuclear power looks
very promising in this graph but, like for the other energy resources, the cost of
dismantling the installation has not been taken into account. It can be expected that the
cost to dismantle a nuclear power plant will be much larger compared to other types of
energy. The decommissioning cost indicated in the graph for nuclear power plants is
linked to the after-treatment of nuclear waste material. Other advantages of wind
energy are the very low maintenance cost and the fact that production costs are
independent of political or economical instabilities. Due to new production techniques
and the development of larger wind turbines, the EU has decided to offer subsidies to
research projects aimed at the construction and development of 20 MW wind turbines.
As a consequence, the price per kWh for wind energy will further decrease.
Numerical design of a 49 m rotor blade for Megawatt wind turbines Chapter 1
Mathijs Peeters – Jorit Van Laeren 7
Figure 1: Cost price comparison per kWh for different energies.[2]
In 2010 the total amount of wind turbine power installed in the EU was 84 GW [3], the
EWEA [4] estimates that in 2020 this number will have increased to 230 GW. Wind
energy will be responsible for 77 % percent of the total exhaust gas reduction within the
EU and will cover 20 % of the total electricity demand. This share will further increase
to 33 % by 2030 [5]. If the EU extends this objective, there will be 600 GW installed
power required by 2050.
The advantages of wind energy are legible: there are no emissions and the energy source
is inexhaustible. The disadvantages are: noise, shadow, visual pollution for the
neighborhood and the discontinuity in power supply. However, the most import
disadvantage is the difficulty to recycle the composite materials used in the blades. In
fact, the rotor blades consist of an inseparable mixture of adhesives, glass or carbon
fibers which cannot be reused as composite materials. One possibility to give composite
materials a second life is to chop them into small pieces, which could be used as filler
material for other applications [6]. To this day, green energy is still considered more
expensive than conventional energies. In order to become more competitive the
production rate of wind turbines has to rise together with the use of new production
methods.
The power output of a wind turbine increases proportional to the area covered by the
rotating blades, so quadratic with the length of these blades [7]. This can easily be
understood using the following formulas.
1.
The power in the wind is given by the rate of change of energy. For a wind turbine this
energy equals, for a constant acceleration, the kinetic energy of the rotating rotor:
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Mathijs Peeters – Jorit Van Laeren 8
2.
Substituting the energy equation into the power equation gives:
3.
As the mass flow rate equals to: , where A is the surface covered by the rotating
blade so , the power equation can be rewritten as:
In 1919 German physicist Albert Betz concluded that no wind turbine can convert more
than 59.3% of the kinetic energy of the wind into mechanical energy required to turn the
rotor. This is known as the Betz Limit or Betz' Law: the theoretical maximum power
efficiency of any design of wind turbine is 0.59, this factor is called the “power
coefficient” (Cpmax).[8] Once incorporating various engineering requirements and other
aspects of a wind turbine – strength, durability, bearings, gear box – only 10-30% of the
power of the wind is transformed into electricity. Notice that a wind turbine is always
designed with a specific design point in mind, which leads to a certain peak efficiency.
Working outside this optimal design point will inevitably involve a loss in efficiency.
So the final power equation is:
Since production costs grow less quickly than the length of the blades increases, there is
an urge to manufacture larger blades. In this respect, the EU is interested in
manufacturing 20 MW wind turbines in the near future, which will require blades of
100-120 m, as shown in figure 2.
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Figure 2: Rotor diameters throughout the years [9].
Figure 3 gives an overview of the most common wind turbine types available. The
Savionius and Giromill/Darrieus turbine are vertical axis wind turbines (VAWT). They
have a main rotor shaft arranged vertically. Key advantages of this arrangement are
that the turbine does not need to be pointed into the wind to be effective. This is an
advantage on sites where the wind direction is highly variable, for example in highly
turbulent urban environments. The key disadvantages include the low rotational speeds
with the consequential higher torque and resulting higher cost of the drive train.
Furthermore the power coefficient is inherently lower. Also, a 360 degree rotation of the
aerofoil in the wind flow with each cycle results into a highly dynamic loading of the
blade. Lastly, there are some rotor designs generating a pulsating torque on the drive
train.
Darrieus turbines have good efficiency, but produce a large torque ripple and cyclic
stresses on the tower which contributes to poor reliability. Generally, they require some
sort of external power source or an additional Savonius rotor to start rotating: the
starting torque is very low.
Savonius turbines are drag-type devices with two (or more) scoops that are used in
anemometers and in some high-reliability low-efficiency power turbines. They are
always able to start themselves when there are at least three scoops present [10].
http://en.wikipedia.org/wiki/Torque
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Figure 3: Overview of possible wind turbines [11].
The following section provides a short overview of the main components, with their
functions, in a modern horizontal axis wind turbine as shown in figure 4.
1) The wind speed measurement system
Measures the wind speed and sends this data to the control system.
2) The turbine blades
Most large wind turbines have three blades. The aerodynamic shape of the blade
in addition with a minimal wind speed creates a lift force on the blades which
generates a rotation.
3) The brake
A brake which functions both mechanically and electrically can be used to halt
the rotor in case of an emergency.
4) The controller
The control system allows the rotor to rotate at wind speeds above 12 km/h and
turns it off at wind speeds above 90 km/h to avoid damage. These wind speed
values can vary according to the geographical location of the wind turbine.
5) The gear box
The gear box transforms the low speed rotation (30-60 rpm) of the wind turbine
shaft to a high speed rotation (1000-1800 rpm).
6) The generator
Most wind turbines use a standard asynchronous generator.
7) The high-speed shaft
This shaft is connected to the generator.
8) The low-speed shaft
This shaft is connected to the rotor.
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9) The nacelle
The nacelle is the housing on top of the tower. It contains the shafts, gearbox,
controller, generator and brake.
10) The pitch engines
The pitch engines rotate the rotor blade in or out of the wind, constantly
optimizing the rotation speed.
11) The rotor
The blades and the cone held together are called the rotor.
12) The tower
The tower is usually made up of steel and concrete. Because the wind speed raises
with altitude above the surface, taller wind turbines are more effective but the
tower and foundation costs will increase as well.
13) The wind direction
The wind turbine in figure 4 is a so called ‘upwind’-turbine: the rotor is turned
into the wind and is located upstream from the nacelle, while a ‘downwind’-
turbine has a rotor turned away from the wind and has its rotor downstream
from the nacelle. Downwind turbines have one serious disadvantage, namely that
the rotor blades pass through the wake created by the tower. This creates a large
cyclic load on the blade, reducing its service life. As a consequence, most wind
turbines are upwind.
14) The wind vane
This instrument measures the wind direction and communicates with the yaw
drive of the turbine to align the turbine with the wind.
15) Yaw drive
This drive is used to position the turbine correctly according to the wind direction.
A downwind turbine does not need this drive because drag on the rotor causes it
to align automatically with the wind.
16) Yaw motor
A large gear enables the yaw motor to turn the nacelle and rotor along the wind
direction.
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Figure 4: Overview of the main components onto a horizontal axis wind turbine [12].
Due to significant frictional losses in the transmission of a wind turbine, the latest
generation of turbines make use of a direct drive generator (figure 5b), making a
transmission obsolete (figure 5a). Hybrid types, with a gearbox providing limited
reduction exist as well.
One additional advantage of the direct drive configuration, other than the reduced
frictional losses, is the decreased number of components, resulting in higher reliability.
[13]
(a) (b)
Figure 5: (a): A traditional wind turbine using a gearbox. (b): a state of the art direct drive wind turbine [14].
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2 Objectives
2.1 Motivation
PowerComposites Limburg whishes to start the production of a new 49 meter long wind
turbine rotor blade. Before such a product can be put to market, it has to pass so called
type certification tests. This certification assures potential costumers that the claims of
the class of the turbine and its accompanying structural integrity are true and that the
turbine will be safe to operate. Since blade certification represents a significant financial
investment, the company has requested a finite element analysis (FEA) of their current
structural design. A research and development (R&D) process in order to obtain a
structurally improved or a potentially new design is also initiated.
When a wind turbine blade is ready to go into production, it has to be certified before it
can be sold. To obtain a certificate, the blade has to pass one or several certification
tests, depending on the certificate. The purpose of these tests is to make sure the blade
can withstand extreme loads. For the blade manufacturer, it is essential that the
produced blades pass these tests, since certification represents a significant financial
investment. This results in large safety factors. Which in turn, inevitably leads to higher
material costs as extra material is added. A good numerical model of the rotor blade
could enable lowering the safety factors without the loss of certainty of certification. In
this master dissertation a finite element model of the blade, according to its current
structural design, is developed.
2.2 Normal R&D process
Nowadays a research and development (R&D) process consists of several phases: as can
be seen in figure 6. An initial design is made using CAD software. When this is
completed, a finite element analysis is conducted to search for weaknesses in the original
design such as locally high stresses or strains. To investigate this, a certain set of loads
and boundary conditions are applied onto the numerical computer model. These results
are crucial to optimize the blade and adapt the original CAD design.
The numerical model however, has to be validated in order to make sure it aligns with
reality. This is vital, as an unrealistic model will result in a poor design. To compare the
model with reality, a prototype is manufactured. It is tested and the same boundary
conditions and loads are applied in a finite element analysis. The results of the real life
and FE tests are then correlated. The purpose of this last step is to improve the
similarity between the computer simulation and the real life behavior of the prototype.
When this is done, the design can be optimized using the FE model.
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Figure 6: Overview of a normal R&D process.
2.3 The R&D process used in this master dissertation
The R&D method in this master dissertation attempts to follow the commonly used R&D
process as much as possible. An initial structural design has been provided in the form of
blueprints. This data is used to build a FE model. This model however, cannot be
validated within the scope of this master dissertation. This is due to time and cost
limitations. Nevertheless, a first attempt at optimization is undertaken.
2.4 The model
A parametrical model is best suited for the job of optimizing the blade. This allows for
easy manipulation of its characteristics. These characteristics include the position,
thickness and material of each ply as well as the stacking sequence of the whole blade.
The advantages of this kind of model are legible. An optimization requiring many
variations of the same blade model could be conducted without the requirement of
constant manual adaptations. The final result is that a wind turbine blade can be
optimized to meet specified requirements without the need to perform expensive ‘real
life’ tests. To make the blade model parametric, a Python script was developed that
automates the partitioning and the build-up of the composite layup. This tool is modular
in the sense that it could be used on any blade on which the required basic partitions
and sets are made.
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To make the FE simulations as accurate as possible, a detailed model is needed.
However, increased detail tends to lead to the necessity of a finer mesh and thus results
in higher computation times. This is where a compromise needs to be made. An attempt
is made to obtain sufficiently accurate results while keeping computation times as low as
possible. The resulting model should allow an accurate estimation of the
eigenfrequencies, stresses and strains during various loads. These loads include the
certification tests, transport, normal operation and so on.
The model requires material properties as an input. PowerComposites Limburg provided
the data sheets of the construction materials used for the production of the current
structural design. These properties however are specified as minimal values for the
materials used by the manufacturer. To obtain the real material properties of the
construction materials used at PowerComposites Limburg, material tests are performed.
These tests are conducted, following the ASTM international standards as much as
practically possible. An overview of all tests with the retrieved properties is given in
figure 7.
Test Retrieved properties
Tensile Stress-strain curve
Poisson coefficient
Flexural Strengths and stifnesses
Load-deflection curves Figure 7: Overview of the experimental tests.
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3 Design of the rotor blade
3.1 Mechanical design
3.1.1 Structure
The rotor blade consists almost entirely out of so called sandwich material. This
sandwich material is composed of a material such as balsawood or pvc-foam in the
middle ("core") and laminate on top and bottom of these core materials ("skins"), see
figure 8. The laminate is composed of glass fibers positioned in an epoxy matrix. The
fibers can be oriented in four directions: 0°, +/- 45° and 90°. A laminate with fibers that
are all in the 0° direction will be called unidirectional (UD). When there are fibers along
the +/- 45° direction the laminate is called biax (2AX). The third possibility, with fibers
along the 0°, +/- 45° and 90° directions is called quadrax (4AX). An example of these
laminates is provided in figure 8: the four possible fiber orientations are shown in the top
left corner. Figure 9 shows a polished cross section of the laminate. Notice the fibers
embedded in the material.
Figure 8:Layup of the rotor blade with indication of the most important materials.
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Figure 9: Cross section of the laminate, the glass fibers are clearly visible.
Figure 10 shows a cross section of the rotor blade itself. Additional reinforcements are
installed near the leading and trailing edges, called leading and trailing edge girder
respectively. These girders are composed of a laminate layup and cover almost the entire
length of the blade. In the middle of both, the pressure (bottom half) and the suction side
(upper half), a third girder is positioned called the main girder. This girder consists of 52
layers of UD (unidirectional) laminate. Three vertical shear webs are attached to these
main girders. They are necessary to increase the overall stiffness of the blade. They are
fabricated in separate molds, after curing they are glued into position on to the blade as
indicated in figure 11. Together, the webs and main girders form a beam with a
rectangular cross-sectional profile. This component, often referred to as the spar, forms
the most important load bearing component.
Figure 10: Cross sectional view of the rotor blade. Additional reinforcements, so called girders, are placed near the leading and trailing edges. The spars are glued onto the main girders to add stiffness to the blade.
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Figure 11: Positions of the three spars in the model: one close to the leading edge, one close to the trailing edge and one small spar positioned at the center of the blade, close to the tip.
3.1.2 Certification tests
The blades of a wind turbine rotor are generally considered to be the most critical
components of a wind turbine system. [15] As mentioned in paragraph 2 Objectives, each
new type of rotor blade has to pass a set of certification tests performed under the
supervision of an authorized organization such as Germanischer Lloyd (GL) before it can
be commercialized. This includes both a static and dynamic tests, performed on ‘real life’
blades. These blades will suffer damage and may not be used again after the tests.
Hence, certification is a serious investment for the rotor blade manufacturers who want
to make sure their blades pass these tests successfully [15].
There are several certification guidelines. The most important standards for certification
on the international level are GL's "Regulations for the Certification of Wind Energy
Conversion Systems" and IEC WT 01 "IEC System for Conformity Testing and
Certification of Wind Turbines - Rules and Procedures" combined with IEC 61400-1.
Comparison between them shows that they are equal if a realistic material safety factor
is chosen [16].
In the case of a 49 m rotor blade a so called ‘flap max test’ (figure 12) is conducted: the
blade is placed horizontally, then the tip of the blade is moved 12 m, at this point the
blade may not have any structural damage. This is done by means of brackets positioned
at five different locations on the blade. The loads or displacements at these positions are
unknown to us.
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Figure 12: Flap max certification test, just an example to show the emplacement of the ‘flap max’ certification test (this is not the 49 m rotor blade).
3.2 Aerodynamic design
Since PowerComposites Limburg has already purchased the molds to manufacture the
49 meter long rotor blade, the aerodynamic shape of the blade is fixed and cannot be
altered. The CAD-drawings of the shape of the molds were provided and form the basis
on which the numerical structural model of the blade is built.
In parallel with this master dissertation, another master dissertation "Numerieke
simulatie van de stroming rond windturbinebladen" by Koen van der Biest, investigates
the air flow across the same 49 meter long wind turbine blade under various wind and
turbine conditions using computational fluid dynamics (CFD). The pressure distributions
across the blade's surface can be used as loads to evaluate the structural design.
3.2.1 Wind turbine classes
During the design of wind turbine blades, assumptions are made about the environment
they will have to endure. This leads to the formation of different classes. They determine
which blades are suitable for a particular site. The assumptions corresponding to each
class are described by means of average wind speed, turbulence and an extreme 50-year
gust wind. These classes are described in IEC 61400-1, "Wind turbines part1: design
requirements" and indicated in table 1 [17].
The specified blade on which this master dissertation focuses, belongs to the class IEC
IIa DIBT WZ 3 [18].
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Table 1: Overview of the different wind turbine classes with the associated design parameters [19].
3.2.2 Design loads
Wind turbines are designed with specific loads in mind, these have several different
origins: aerodynamic, actuation, gravitation and inertia. Other loads such as wakes,
earthquakes and ice are also considered. Depending on the wind turbine class, different
values for wind speed and turbulence are assumed. These values are used to calculate at
least 130 load cases. To calculate the loads under normal conditions, a wind distribution
is used, based on the normal wind profile model (NWP) and normal turbulence model
(NTM), rather than a single velocity. Similarly, for extreme conditions, the extreme wind
speed model (EWM) and extreme operating gust (EOG) are used [19]. Also, wind
direction change and wind shear are modeled. An overview of the design load cases can
be found in table 2.
As this master dissertation focuses on the structural aspect and the aerodynamic aspect
does not lie within the scope of this work, these loads could not be determined for the 49
meter blade.
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Table 2: Design load cases as described in IEC 61400-1 [19].
3.3 Materials
As mentioned paragraph 2 Objectives, the material properties form an important part of
the model. The material data that are used were obtained from data sheets and also
derived from experiments.
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The conducted experiments are tensile tests and four point bending tests. In paragraph
3.3.1 General test procedure, a brief description of these test is provided. However, the
obtained values are not listed as they are confidential.
3.3.1 General test procedure
Specifically for these tests, glass fiber/epoxy plates were manufactured by
PowerComposites Limburg. These were cut into samples of the appropriate size,
according to blueprints provided by the authors. Additional tabs were glued onto the
glass fiber/epoxy plates in order to prevent the samples from fracturing inside the claws
of the test setup.
All the tests were done using an INSTRON 5800R. To measure the applied force on the
sample a calibrated load cell of 100 kN was used.
General purpose strain gauges, were used: type CEA-06-250UN-350, produced by Vishay
Micro-measurements. These have a resistance of 350 and are temperature-
compensated for composites. They have been bonded with the M-Bond 200 adhesive kit.
All signals were acquired using a National Instruments NI DAQPAD−6052E
measurement card and LabVIEW software.
Each strain gauge was calibrated before use with a precision shunt resistance of 100 k,
simulating a strain of 0.2890 %.
The thickness and width of all specimens were measured with a micrometer (caliper)
before testing.
3.3.2 Tensile tests
The tensile tests were performed on rectangular specimens with tabs at the far sides, in
agreement with ASTM D 3039/D 3039M – 00e2 “Standard Test Method for Tensile
Properties of Polymer Matrix Composite Materials”.
Two strain gauges were attached to each sample, one in the longitudinal and one in the
transverse direction. These provided local strain data. This way stress-strain curves and
the corresponding Poisson-coefficients were obtained. Testing was done until fracture.
All tensile tests were performed at a displacement rate of 1 mm per minute, so that
visco-elastic effects are negligible. The setup of the tensile test is illustrated in figure 13.
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(a) (b)
Figure 13: (a): A laminate sample clamped in the tensile test setup. (b): Detailed view of the strain gauges that were attached to the tensile test samples.
3.3.3 Four point bending tests
The four point bending tests were performed on samples of sandwich panels as used in
the turbine blade according to ASTM C 393 -00 “Standard Test Method for Flexural
Properties of Sandwich Constructions”. Because the laminate is not smooth on one side,
it was polished, so that friction between the sample and the supports can be neglected.
These samples were equipped with a single strain gauge. The setup of the four point
bending test is illustrated in figure 14.
Figure 14: Four point bending test. The sample is equipped with a single stain gauge (at the bottom side of the sample in this picture).
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4 Manufacturing of rotor blades
4.1 General production methods for composite materials
There are several methods to fabricate composite structures, among which: vacuum bag
molding, pressure bag molding, autoclave molding and resin transfer molding. The first
of these methods is the one used to produce the rotor blades at PowerComposites
Limburg. This method will be discussed in detail in paragraph 4.2 Production method of
a rotor blade. The other methods will be described briefly.
4.1.1 Pressure bag molding
The pressure bag molding technique uses two molds. A female mold, the bottom mold in
figure 15, and a flexible male mold, the upper mold in figure 15. The reinforcement fibers
are placed inside the female mold with just enough resin to allow the fabric to stick in
place.
Resin is then applied to the mold, afterwards the flexible male membrane is filled with
heated, compressed air. In some cases the female mold can also be heated. Excess resin
is forced out along with the trapped air. Cycle times for this molding technique can vary
from 20 to 45 minutes which makes it ideally for the production of small consumer
products such as composite helmets.
Figure 15: Principal of pressure bag molding [20].
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4.1.2 Autoclave molding
Autoclave molding (figure 16) is especially suitable to fabricate small samples used in
research. This manufacturing method uses composites available as prepreg laminates.
The autoclave is simply a heated pressure vessel into which the mold, together with the
plies, is placed and subjected to the required temperature and pressure for curing. To
speed up the release process, the layup is often covered with a release fabric. A vacuum
bag with an opening is used to evacuate the present gasses [21].
Figure 16: Principle of autoclave molding [21].
4.1.3 Resin transfer molding
Resin transfer molding (RTM) is a low pressure manufacturing process where two resins
polymerize inside a mold. This technique allows the fabrication of big, complex parts
with very smooth surfaces. The process is popular in the automotive sector for serial
productions (500 – 10000 pieces per year) of specific parts.
In figure 17, the principle of RTM is explained. A mold containing a cavity with the
shape of the product to fabricate is used: (1) and (2). The mold is prepared with a release
agent and a gelcoat. After positioning the plies (5), the mold is closed and sealed using
clips (3). These clips withstand the reaction forces originating from the polymerization
reaction, pushing the mold open. The two resins A and B are forced (under pressure)
from their respective containers (7) and (8) towards the mixing head (4). After being
mixed, the resins are injected into the mold and the polymerization reaction starts (6).
Because this polymerization reaction is exothermal, heat is generated. This heat is
evacuated using a cooling system integrated in the mold [22].
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Figure 17: Principle of resin transfer molding [22].
4.1.4 Vacuum bag molding
The vacuum bag molding technique is used at PowerComposites Limburg and will be
discussed in detail in paragraph 4.2 Production method of a rotor blade.
4.2 Production method of a rotor blade
Rotor blades for wind turbines are composed of composite materials, as mentioned
earlier. These are glass-reinforced polymers (often referred to as fiberglass) and
sandwich materials. In some recent designs, carbon fibers are used because of their
higher strength and stiffness relative to their weight. Their disadvantages however are:
good electrical conductivity and a higher price. Suppose the whole blade would consist
out of carbon fiber reinforced polymer (CFRP), it would be a gigantic rotating conductor
attracting lightning leading to a very dangerous situation.
This master dissertation is commissioned by PowerComposites Limburg in Genk. This
company produces rotor blades of different lengths, but only their 49 meter blade will be
discussed in this master dissertation. The production process used at PowerComposites
Limburg is described below in several consecutive steps.
4.2.1 Cutting and placement of fiberglass sheets
The composite blade is composed of fiberglass sheets which are cut manually using
templates. This happens in advance in order to speed up the production cycle. The sheets
are positioned in the mold with the aid of a laser projection system, this system is
mandatory to position the different plies with a good accuracy.
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Some parts of the blade consist of many layers of fiberglass material such as the inserts
in the root section. These parts are fabricated in advance, in a dedicated mold and later
on placed in the main mold. This method drastically increases the production efficiency:
the curing time of the thick inserts and more importantly the time required to position
this large number of plies in the main molds, are the bottlenecks in the production
process. They take a lot of time, during which no new blade can be produced.
4.2.2 Infusion
The next step in the production process is the vacuum infusion (shown in figure 18 (a)): a
plastic bag is placed over the fiberglass sheets to form an airtight entity together with
the mold. This bag is made of a strong rubber-coated fabric. The downside is that the
pattern of this fabric indents the resin, thus after curing, the surface is far from smooth.
A vacuum pump dawns all the air out of this bag, via nipples, to achieve a vacuum. At
the same time, the resin is injected trough different connections in the bag. Thanks to
the vacuum, the resin is spread equally over the mold as illustrated in figure 18 (b).
The bag is in direct contact with the atmosphere, so a pressure of one bar is applied onto
the bag while curing. This curing is a result of the polymerization reaction taking place
between the materials inside the mold and the injected resin. The temperature can be
raised by placing a heater onto the bag, this will speed up the curing process [23] [24].
(a) (b)
Figure 18: (a): Infusion using a vacuum bag to spread the resin equally over the mold. (b): Resin spreading during infusion.
http://en.wikipedia.org/wiki/Rubberhttp://en.wikipedia.org/wiki/Fabric
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4.2.3 Bonding and finishing
Once both blade halves have been produced, they can be joined together using a
hydraulic mechanism, as shown in figure 19. The pressure and suction sides are placed
close to each other, allowing the addition of the adhesive bond line. To make sure both
halves are well connected, a large amount of adhesive is spread over the leading and
trailing edges. When both halves of the blades are pressed onto each other, the excess of
adhesive is pressed away. To remove this unnecessary adhesive and other irregularities,
the blade will be polished and a protective layer is added to prevent the origination of
small cracks due to sun exposure.
Figure 19: A hydraulic mechanism places the two halves of the blade together [25].
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5 Theoretical background of finite elements
The turbine blade can be modeled in different ways in AbaqusTM. Different types of
elements are available to achieve this, the three main categories are: solid elements,
conventional shell elements or continuum shell elements. These can be subdivided
further into linear or quadratic order elements and in elements to be used for a full or
reduced integration. The basic theoretical background of finite element analysis is
described in Appendix A: Principles of finite element analysis and Appendix B: Different
element types. To summarize these appendices; in AbaqusTM the displacements are
calculated in the nodes. The stresses on the other hand, are computed in the so called
material integration points. These points do not coincide with the nodes, but are
positioned at a certain distance towards the inside of the element. More details can be
found in the appendices mentioned earlier.
5.1 Different element types
Figure 20 gives an overview of the possible families of elements AbaqusTM offers to solve
a problem. From this figure, it is clear that only the elements mentioned earlier can be
used to model the rotor blade. A combination of different element types is also an option.
In that case, either a coupling needs to be implemented or the model has to be split into
different parts which can be meshed individually and then attached to each other using
tie constraints. Each element type has five defining characteristics:
Family
Degrees of freedom (DOF) (directly related to the element family)
Number of nodes
Formulation
Integration
Figure 20: Available families of elements in AbaqusTM
.
An overview of all possible element types to model the rotor blade along with their main
characteristics, is given in table 3. A detailed description of the different characteristics
is provided in Appendix B: Different element types.
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Solid Cont. shell
Conv. Shell
Name C3D8 C3D8R C3D20 C3D20R SC8R S4 S4R S8R
DOF 3 3 3 3 3 6 6 5 or 6
Number of nodes 8 8 20 20 8 4 4 8
Order of interpolation
1 1 2 2 1 1 1 2
Formulation L L L L L L L L
Integration F R F R R F R R
Table 3: Overview of possible element types to model the rotor blade. DOF: degrees of freedom, L: Lagrangian, F: full, R: reduced, 1: first order interpolation or linear interpolation, 2: second order interpolation or quadratic interpolation.
The solid continuum elements are the standard elements used to model an object in
AbaqusTM. They can consist out of one homogenous material or out of multiple layers of
different materials. The latter is important in case of composite materials. The main
disadvantages however, are the higher calculation time compared to the other element
types and the fact they have only three degrees of freedom (displacements). This means a
high number of elements in case of problems with large displacements as can be
expected for a rotor blade. Modeling a rotation requires many elements. The elements
used are hexahedrons.
First order triangles and tetrahedral elements need to be avoided in stress analysis:
their mesh convergence is very slow. If these elements are used, a very fine mesh will be
required resulting into a high calculation time.
5.1.1 Shell elements
Within the category of shell elements there are two important candidates to be
considered for modeling the full blade. These are the conventional shell elements and
continuum shell elements.
5.1.1.1 Conventional shell elements
Shell elements are suited for modeling bodies where the geometry in one dimension is
significantly smaller than in the other dimensions, such as thin surfaces. Conventional
shell elements are essentially two-dimensional elements, where the thickness is defined
as a section property, thereby influencing the stiffness of the element. These elements
have both displacement and rotational degrees of freedom.
Numerical design of a 49 m rotor blade for Megawatt wind turbines Chapter 5
Mathijs Peeters – Jorit Van Laeren 31
5.1.1.2 Continuum shell elements
Continuum shell elements make use of a full three-dimensional body. They are
essentially shell elements where the thickness is derived from the three-dimensional
geometry, rather than from user defined section properties. These continuum elements
only have displacement degrees of freedom. Continuum shell elements resemble three
dimensional solid elements, but their kinematic behavior corresponds to that of
conventional shell elements.
Continuum shell elements can model a linear thickness transition exactly, while
conventional shell elements cannot, therefore a piecewise approximation is needed (see
figure 55 in paragraph 8.1.2.2 Test of the second strategy: partitioning).
Figure 21: Differences between continuum shell elements and conventional shell elements [26].
Not only is the choice of the element family important, there are some other choices that
can have an important influence on the accuracy and computation time of the
simulation. These choices are listed in the next paragraphs. For more information on
every of the next topics, see Appendix B: Different element types. It is important to know
in advance which elements are most likely to perform optimal. For this reason, a
simplified model of a rotor blade is used to derive the appropriate settings, as described
in paragraph 6 Finite element simulations of rotor blades [26].
Numerical design of a 49 m rotor blade for Megawatt wind turbines Chapter 5
Mathijs Peeters – Jorit Van Laeren 32
5.2 Element settings
5.2.1 Choosing between first and second order elements
Second order elements have a higher accuracy than first order elements in problems
with simple contact surfaces or deformations. They are able to model a curved surface
with less elements and perform better in cases with major deflection. These elements
look promising for modeling the rotor blade. For the simplified blade, this is accurate:
relatively few second order elements are required to obtain a converged mesh, compared
to the amount of first order elements required to model the same problem. However for a
more detailed model (paragraph 9.1 Main girder with spars), it turned out that relatively
more second order elements are required, leading to a higher overall calculation time
compared to first order elements with the same accuracy.
5.2.2 Full and reduced integration
The choice between full and reduced integration element types is very dependent on the
nature of the problem and cannot be predicted before modeling the geometry. Sometimes
it is possible that reduced integration elements result in higher accuracy than a full
integration. This phenomenon is known as super convergence [27].
5.3 Element related problems
5.3.1 Hour glassing
Hour glassing is an issue that can occur with first order, reduced-integration elements
(CPS4R, CAX4R, C3D8R, etc.). Since these elements only have a single integration point,
it is possible that they distort in such a way that the calculated strains are all zero. The
result is an uncontrolled distortion of the mesh. The best way to avoid this problem is to
use a fine mesh. For more information about hour glassing see Appendix B: Different
element types.
5.3.2 Shear and volumetric locking
Full integration elements in AbaqusTM have no hour glassing issues. However, they can
suffer from another problem called shear locking. This can happen with first-order, full
integration elements subjected to bending. The numerical formulation of the elements
gives rise to shear strains which are not present in reality, these lead to an artificially
increased stiffness of the elements in bending mode. For more information about hour
glassing see Appendix B: Different element types.
Numerical design of a 49 m rotor blade for Megawatt wind turbines Chapter 6
Mathijs Peeters – Jorit Van Laeren 33
6 Finite element simulations of rotor blades
While nowadays full scale tests are still vital for the certification of rotor blades, it has
been suggested that within 3 to 5 years FEM can be developed which provide results
with such accuracy that full scale tests can be reduced to a minimum.[28] However,
most FE models of wind turbine blades in literature are either based on very simplified
geometry or correspond to short blades with a very simple layup. Some examples can be
found below.
In "Improved design of large wind turbine blade of fibre composites based on studies of
scale effects (Phase 1) - Summary Report”, a finite element model is used to investigate
the buckling behavior of only the spar of an existing wind turbine blade.
In the study "Structural investigation of composite wind turbine blade considering
various load cases and fatigue life", a finite element model of a real blade is developed. It
is used to test various design requirements such as minimum blade tip clearance, fatigue
etc. While the blade has a reasonable number of plies, they are assigned to only twelve
different regions. It allows the use of an extremely coarse mesh as illustrated in figure
22.
Figure 22: The FE-model used in the study "Structural investigation of composite wind turbine blade considering various load cases and fatigue life" [15].
In the study "Research on Structural Lay-up Optimum Design of Composite Wind
Turbine Blade" by Zhang Lanting, different layups are applied to FE models with the
same blade geometry. The blade is then tested under a extreme static load and the
maximum stresses and tip displacements are compared. The blade however has an
extremely simple layup, in the sense that it is uniform throughout the blade [29].
In this master dissertation, the authors propose a model of a wind turbine blade having
the same geometry and layup as the real 49 m rotor blade produced by PowerComposites
Limburg, resulting in a more realistic simulation.
Numerical design of a 49 m rotor blade for Megawatt wind turbines Chapter 7
Mathijs Peeters – Jorit Van Laeren 34
7 Modeling of a simplified rotor blade
Before modeling the real rotor blade, a decision has to be made concerning:
Type of elements to be used
Build up of the model
These points will have an impact on the quality of the numerical simulations.
In this chapter, a comparative study is performed between the different modeling
techniques discussed in paragraph 5.1 Different element types by means of a simplified
rotor blade model. These results will form the basis to make the real rotor blade model.
7.1 The simplified model
The simplified rotor blade that is used throughout this chapter is presented in figure 23.
As indicated, the model consists of an outer laminate layer, a web, adhesive layers and
two pieces of balsawood with a chamfer. The overall length is 10 000 mm. All the other
dimensions are indicated in figure 23.
(a) (b)
Figure 23: (a):Drawing with the dimensions of the simplified blade model. (b): Overview of the different parts present in this simplified model.
7.2 Materials
To speed up calculation time, all of the materials used in the simplified rotor blade are
given the same isotropic properties: a Young modulus of 210 GPa and a Poisson-
coefficient of 0.3 .
Numerical design of a 49 m rotor blade for Megawatt wind turbines Chapter 7
Mathijs Peeters – Jorit Van Laeren 35
7.3 Loads and boundary conditions
For every one of the simulations, the applied load is the same: a uniform pressure of 1
MPa on the horizontal and sloping top surfaces of the simplified blade. The model is
clamped at one side and free to move at the other end, as indicated in figure 24 .
Figure 24: A load of 1 MPa is applied onto the model having one fixed side.
7.4 Mesh
This simplified blade is meshed using the different mesh elements mentioned earlier in
paragraph 5.1 Different element types. This results in the different models discussed in
paragraphs 7.4.1 Conventional shells and continuum shells till 7.4.4 Shell and solid
elements. The difference between a first and second order interpolation as well as the
influence of using a full or reduced integration calculation is studied.
To facilitate the calculations, a Python script is used. This script enables the user to
conduct a large number of calculations in order to get a clear view of the differences
between each model without additional work. For every option, the initial element size is
1000 mm. The maximal displacements and maximum principal stresses are calculated
and recorded together with, the CPU-times and the number of mesh elements. These
results are saved in a plain text file. Furthermore, the position of the maximal
displacements and stresses is determined.
In the next step, the Python script will lower the principal dimensions of the mesh
elements and repeat the same calculation. Beyond a certain point, further mesh
refinement will not change the results significantly. At this point the mesh is converged.
The corresponding dimensions of the elements are an indication for those to be used in
the real model of the 49 m rotor blade. To determine if the mesh has converged, a
criterion from GL is adopted. This states that a mesh is converged if a doubling of the
number of elements does not result into a change in the calculated physical quantity of
more than 5% [30]. In the following sections different models are used and their
corresponding advantages and disadvantages are summarized.
Numerical design of a 49 m rotor blade for Megawatt wind turbines Chapter 7
Mathijs Peeters – Jorit Van Laeren 36
Since the outer aerodynamic shell has a negligible thickness (order of mm) compared to
its two other dimensions (order of m), this laminate will always be modeled using shell
elements (conventional or continuum) as can be seen in table 4. The three models will be
discussed in the next paragraphs: 7.4.1 Conventional shells and continuum shells till
7.4.4 Shell and solid elements.
Type of
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