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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



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



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



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



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



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.



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:



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.



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



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.



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.



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].



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.



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.



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.



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.



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.



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.



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].



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.



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.



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.



(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).



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].



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].



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.



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



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].



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.



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.



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].



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.



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.



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 .



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.



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.

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