COMPARISON OF STRUCTURED AND UNSTRUCTURED MESHES …
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DEPARTMENT OF FLUID AND HEAT ENGINEERING Faculty of Mechanical Engineering and Informatics University of Miskolc Hungary LABORATORY OF FLUID DYNAMICS & TECHNICAL FLOWS Institute of Fluid Dynamics & Thermodynamics Otto von Guericke University Magdeburg Germany COMPARISON OF STRUCTURED AND UNSTRUCTURED MESHES FOR THE COMPUTATIONS OF AN H-TYPE DARRIEUS WIND TURBINE FINAL THESIS Energetics engineering MSc, Specialization in Energy Performance of Buildings BENCE MOLNÁR Neptun code: XCTPT2 Magdeburg 2014
Transcript of COMPARISON OF STRUCTURED AND UNSTRUCTURED MESHES …
DEPARTMENT OF FLUID AND HEAT
ENGINEERING
Faculty of Mechanical Engineering and Informatics
University of Miskolc
Hungary
LABORATORY OF FLUID DYNAMICS
& TECHNICAL FLOWS
Institute of Fluid Dynamics & Thermodynamics
Otto von Guericke University Magdeburg
Germany
COMPARISON OF STRUCTURED AND UNSTRUCTURED
MESHES FOR THE COMPUTATIONS OF AN H-TYPE
DARRIEUS WIND TURBINE
FINAL THESIS
Energetics engineering MSc,
Specialization in
Energy Performance of Buildings
BENCE MOLNÁR Neptun code: XCTPT2
Magdeburg
2014
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Lehrstuhl für Strömungsmechanik und Strömungstechnik (LSS)
MSc Thesis Start: 22.09.2014
"Comparison of Structured and Unstructured Meshes for the Computations of
an H-Type Darrieus Wind Turbine "
Task
Literature overview of the wind power and wind turbine technology with focusing
on vertical axis wind turbines (H-type Darrieus)
Review the scientific literature of CFD computations of H-type Darrieus wind
turbines with focus on the applied mesh
Development of an automatic block structured mesh generation process for
realistic airfoil geometries (for 3 bladed H- Darrieus wind turbines)
Evaluation of the performance, torque, lift and drag coefficients for a given
geometry (used in the experiments) with Computational Fluid Dynamics for two
different structured mesh resolutions
Comparison of the different time dependent coefficients for the two structured
and one unstructured mesh, analysis of the differences
Comparison of the convergence speed of the different meshing approaches
Draw the conclusions from the comparison and summarizing the advantages and
disadvantages provided by structured and unstructured approaches, applicability
in real world problems
Required qualifications
- Experience with mesh generation, commercial mesh generation software (ICEM
CFD) and Computational Fluid Dynamics (ANSYS, Fluent or CD-Adapco STAR-
CCM+)
- Excellent academic grades in Computational Fluid Dynamics or in equivalent course
- Good English knowledge
Supervisors
László Daróczy, MSc:
Gábor Janiga, Priv. Doz.:
[email protected], (0391) 67 18194
[email protected], (0391) 67 18196
Art of work: Experimental ☐ Numeric Theoretical/Literature
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OTTO VON GUERICKE UNIVERSITY
MAGDEBURG Institute of Fluid Dynamics &
Thermodynamics Laboratory of Fluid Dynamics
& Technical Flows Germany
Energetic engineering MSc,
Specialization in Energy Performance
of Buildings Reference number:
EV/400-16/2014
UNIVERSITY OF MISKOLC
Faculty of Mechanical Engineering and Informatics Department of Fluid and Heat
Engineering 3515 Miskolc – Egyetemváros
Hungary
MASTER THESIS
Bence Molnár
XCTPT2
For a second year Master of Science student in Energetic Engineering
Field: Energetics, Computational Fluid Dynamics
Title of the thesis: Comparison of Structured and Unstructured Meshes for the
Computations of an H-Type Darrieus Wind Turbine
TASKS:
1. Literature overview of the wind power and wind turbine technology with focusing
on vertical axis wind turbines (H-type Darrieus)
2. Review the scientific literature of CFD computations of H-type Darrieus wind
turbines with focus on the applied mesh
3. Development of an automatic block structured mesh generation process for
realistic airfoil geometries (for 3 bladed H-Darrieus wind turbines)
4. Evaluation of the performance, torque, lift and drag coefficients for a given
geometry (used in the experiments) with Computational Fluid Dynamics for two
different structured mesh resolutions
5. Comparison of the different time dependent coefficients for the two structured
and one unstructured mesh, analysis of the differences
6. Comparison of the convergence speed of the different meshing approaches
7. Draw the conclusions from the comparison and summarizing the advantages
and disadvantages provided by structured and unstructured approaches,
applicability in real world problems
Supervisor at the University of Miskolc: Péter Bencs
Supervisors at the OvGU Magdeburg: Dr. Gábor Janiga, László Daróczy
Start: 22 September 2014
Deadline: 19 December 2014
................................................
Place of the seal Prof. Dr. Szilárd Szabó
Head of the Department
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1. Location of final internship: ...................................................................................
2. External advisor’s name: .......................................................................................
3. The thesis tasks require / do not require modification1:
date supervisor
If modification is needed, please list on a separate sheet
4. Dates of supervision:
date supervisor
5. The thesis is / is not ready for submission.
date
supervisor
advisor
6. The thesis contains pages,
and the following documents:
drawings
supplementary documents
other supplements (CD, etc.)
7. The thesis is / is not ready to be sent to the external reviewer.1
The external reviewer’s name:
date
Head of Department
8. Final evaluation of thesis:
External reviewer’s opinion: ................................
Departmental opinion: ................................
Decision of the State Examining Board: ................................
Miskolc, ………………………..… …………………..……..
President of the State Examining Board
1 Please underline appropriate text.
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Declaration of authenticity/ Eredetiségi nyilatkozat
Alulírott Molnár Bence (Neptun kód: XCTPT2), a Miskolci Egyetem Gépészmérnöki
és Informatikai Karának végzős Energetikai mérnök szakos hallgatója ezennel
büntetőjogi és fegyelmi felelősségem tudatában nyilatkozom és aláírásommal
igazolom, hogy a Comparison of Structured and Unstructured Meshes for the
Computations of an H-Type Darrieus Wind Turbine című komplex feladatom/
szakdolgozatom/ diplomamunkám2 saját, önálló munkám; az abban hivatkozott
szakirodalom felhasználása a forráskezelés szabályi szerint történt.
Tudomásul veszem, hogy plágiumnak számit:
szószerinti idézet közlése idézőjel és hivatkozás megjelölése nélkül;
tartalmi idézet hivatkozás megjelölése nélkül;
más publikált gondolatainak saját gondolatként való feltüntetése.
Alulírott kijelentem, hogy a plágium fogalmát megismertem, és tudomásul veszem,
hogy plágium esetén a szakdolgozat visszavonásra kerül.
Miskolc, 20 év hó nap
2 Megfelelő rész aláhúzandó
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I. SUMMARY
Nowadays, when renewable energy sources come to the forefront, wind energy
represents important role because the installation of wind turbine technology
reduces dependence on fossil fuels and provides a cost effective and reliable
approach. Moreover, wind turbines are able to produce large amounts of electricity
without emitting harmful gases, thus they are environment friendly. In the last few
years, wind energy generation has increased significantly due to tightening
environmental regulations. Although initially the concept of the VAWT (Vertical Axis
Wind Turbine) (also known as Darrieus turbine) was promising, the large HAWTs
(Horizontal Axis Wind Turbines) quickly displaced them. However, VAWTs perform
better in urban regions compared to HAWTs because they do not have to be pointed
to the oncoming wind (they are omnidirectional). Hence, there is an increased
interest in VAWTs, especially the H-type Darrieus concept, because of their simple
design and their suitability for lower wind speeds. In urban areas the wind
continuously changes direction, thus VAWT is a good option to harness the kinetic
energy from the wind. For H-type Darrieus turbines usage to spread, it is essential
to ensure the appropriate efficiency, which is achievable with CFD-based
(Computational Fluid Dynamic) optimizations, which require reliable and accurate
computations. However, in contrast to horizontal axis wind turbines, in the case of
the H-Darrieus turbines the flow is not only turbulent but also strongly unsteady, with
significantly varying Angles of Attack (AoA) (and thus aerodynamic characteristics)
even during a single rotation. Furthermore, the dominant physical phenomena are
dynamic stall and the blade-wake interaction, which make the flow even more
complicated. The simulation of the dynamic stall and the extremely complex flow
structure is possible only by using a high resolution and fine quality numerical mesh.
The Institute of Fluid Dynamics & Thermodynamics at the Otto-von-Guericke
University Magdeburg has a research project which is dealing with the optimization
of H-type Darrieus wind turbine airfoil profile in order to achieve higher performance
and efficiency. The simulations are prepared using the in-house parameterization,
design-of-experiment and optimization software of the institute, OPAL++. In the
earlier studies, an unstructured (partially structured) mesh was used, which is easy
to obtain for this construction. However, there was an assumption that using
structured mesh for the computations may provide significant advantages over the
unstructured mesh.
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Therefore the goal of the current thesis was to create a fine quality block-structured
computational mesh for a 2D H-type Darrieus wind turbine for CFD simulations and
then the compare the structured and unstructured meshes in terms of the
computational results. The structured mesh was expected to improve accuracy of
the computation and yield fewer residual errors and lower computational time.
A high quality 2D structured mesh was generated using the ANSYS ® ICEM CFD
software, where a sliding mesh model was used to simulate the rotation. Moreover,
the development of an automatic block structured mesh generation process for
realistic airfoil geometries for three-bladed H-Darrieus wind turbines for the
optimization software was part of the task as well.
The numerical simulations were performed on a three-bladed H type Darrieus rotor
using the same solvers and options as in the former studies. The simulations were
carried out for three different TSR (tip-speed ratio) values with two different mesh
resolution in the commercial CFD software CD Adapco ® Star CCM+.
The performance, torque, lift and drag coefficients were evaluated for two different
structured mesh resolutions. Then the different time dependent coefficients for the
two structured meshes were compared against the unstructured mesh, and the
differences were analysed. Then, the convergence speed and the residual errors
were compared for the different mesh approaches.
The thesis starts with a literature overview of the wind energy and wind turbine
technology, detailing VAWTs with the focus on the H-type Darrieus wind turbine.
Thereafter the state of the art is described and the scientific literature of CFD
computations of H-type Darrieus wind turbines with a focus on the applied mesh is
presented. Finally, after presenting the mesh generation process and the
computational results, conclusions are drawn.
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II. ÖSSZEFOGLALÁS
Napjainkban, amikor a megújuló energiaforrások egyre inkább előtérbe
kerülnek, a szélenergia fontos szerepet tölt be, ugyanis a szélturbinák telepítése
mindamellett, hogy csökkenti a fosszilis üzemanyagoktól való függőséget,
költséghatékony, és megbízható megoldást biztosít. Továbbá egy környezetbarát
technológia, hiszen a szélturbinák képesek nagy mennyiségű elektromos energia
megtermelésére szennyező anyagok kibocsátása nélkül. A szigorodó
környezetvédelmi előírások következtében, az elmúlt néhány évben a szélenergia
termelés jelentősen megnövekedett. Habár kezdetben a függőleges tengelyű
szélturbinák (mint például Darrieus turbina) biztatóak voltak, a nagyméretű
vízszintes tengelyű szélturbinák gyorsan kiszorították őket. Azonban városi
környezetben, a függőleges tengelyű szélturbinák jobban teljesítenek a vízszintes
tengelyű szélturbináknál. Ezáltal megnövekedett az érdeklődés a függőleges
tengelyű szélturbinák, elsősorban a H-típusú Darrieus koncepció iránt, az egyszerű
felépítésének köszönhetően, valamint, mert jól alkalmazható alacsony szélsebség
esetén is. Városi környezetben a szél folyamatosan változatja az irányát, így a
függőleges tengelyű szélturbina egy jó alternatíva a szélben rejlő kinetikus energia
kinyerésére. A H-típusú Darrieus szélturbina elterjesztésének érdekében,
szükségszerű a megfelelő hatásfok biztosítása, mely elérhető CFD alapú
optimalizálás segítségével, amely megbízható és pontost számítást igényel.
Azonban, a vízszintes tengelyű szélturbinákkal ellentétben a H-típusú Darrieus
szélturbinák esetében, az áramlás nem csupán turbulens, de erősen instacioner is,
jelentősen változó megfúvási szögekkel (és ezáltal áramlási karakterisztikával) már
egyetlen körülfordulás alatt is. Továbbá, a domináns fizikai jelenségek, a dinamikai
átesés és a lapát-örvény kölcsönhatás, melyek az áramlást még bonyolultabbá
teszik. A dinamikus átesés és a bonyolult áramlási struktúrák numerikus
szimulációja, csak nagy felbontású és nagyon jó minőségű numerikus hálók
segítésével lehetséges.
A magdeburgi Otto von Guericke Egyetem, Áramlástani és Hőtani Intézete egy
kutatási projekt keretében, magasabb teljesítmény és hatásfok elérésének céljából,
egy H-típusú Darrieus szélturbina lapátprofiljának optimalizálásával foglalkozik. A
szimulációk az intézet saját parametrizáló, kísérlettervezési és optimalizáló
szoftverével, az OPAL++-al készülnek. Az eddigi tanulmányok során strukturálatlan
(részben strukturált) hálót alkalmaztak, melyet egyszerű kivitelezni erre a
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konstrukcióra. Ellenben felvetődött, hogy strukturált háló használata a
számításokhoz, jelentős előnyöket biztosíthat a strukturálatlan hálóhoz képest. A
strukturált háló használatától a számítások pontosságának növekedése, a
numerikus hibák csökkenése, alacsonyabb reziduális hibák és rövidebb számítási
idő volt az elvárás.
Ezért jelen diplomamunka célja egy jó minőségű blokk strukturált számítási háló
kivitelezése volt egy kétdimenziós H-típusú Darrieus szélturbinára CFD
szimulációkhoz. A számítási háló elkészítéséhez az ANSYS ® ICEM CFD szoftver
került alkalmazásra, mellyel jó minőségű 2D blokk strukturált háló lett előállítva.
Továbbá, a feladat részét képezte, egy olyan automatikus blokk strukturált
hálógeneráló folyamat kidolgozása az optimalizáló szoftverhez, mely képes a
valóságban megvalósítható lapátprofil geometriák esetén, egy 2D három-lapátos H-
típusú Darrieus szélturbinára, jó minőségű strukturális hálót automatikusan
generálni. Szintén a feladat részét képezte, a numerikus szimulációk eredményeit
felhasználva, a strukturált és strukturálatlan hálók összehasonlítása.
A numerikus szimulációk egy három-lapátos H-típusú Darrieus szélturbinán, a
korábbi tanulmányokban használt megoldók és beállítások használatával lettek
kivitelezve. A szimulációk a CD Adapco ® Star CCM+ kereskedelmi CFD
szoftverben, 3 különböző gyorsfutási számon lettek elvégezve, két különböző
hálófelbontáson.
A teljesítmény, nyomaték, felhajtóerő és ellenállás tényezők kiértékelésre kerültek
a két különböző strukturált hálófelbontáson. Ezt követően a két strukturált háló
esetén kapott eredmények összehasonlításra kerültek a strukturálatlan háló
eredményeivel, majd a különbségeket elemzésre kerültek. Végül a számítási idő és
a reziduális hibák kerültek összehasonlításra a különböző hálók esetén.
A dolgozat irodalomkutatással kezdődik a szélenergiáról és szélturbinákról
általánosságban, különös tekintettel a függőleges tengelyű szélturbinákra, ezen
belül is a H-típusú Darrieus szélturbinára fókuszálva. Ezt követően diplomamunka
célja kerül részletezésre, majd a tudományos irodalomból néhány példát kiemelve
a H-típusú Darrieus szélturbinák CFD szimulációja során alkalmazott számítási
hálók kerülnek bemutatásra. Végül, a hálógenerálási folyamat és a számítási
eredmények bematatását követően, a dolgozat a konklúziók levonásával zárul.
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TABLE OF CONTENTS
1. NOMENCLATURE ..................................................................................................... 2
2. INTRODUCTION ........................................................................................................ 3
2.1. Wind power ........................................................................................................ 3
2.2. Wind turbine technology .................................................................................. 4
2.3. Vertical axis wind turbines ............................................................................. 10
2.3.1. Principle of operation .............................................................................. 11
2.3.2. Savonius wind turbines ........................................................................... 12
2.3.3. Darrieus wind turbines ............................................................................ 13
2.4. Problem statement .......................................................................................... 16
2.5. State of the art ................................................................................................. 17
2.6. Literature overview ......................................................................................... 19
2.7. Structure of the thesis .................................................................................... 20
3. COMPUTATIONAL METHODS ............................................................................... 21
3.1. Governing equations ...................................................................................... 23
3.2. Sliding mesh .................................................................................................... 26
3.3. Reference values, initial conditions and boundary conditions.................... 26
4. GENERATION OF THE COMPUTATIONAL MESH ................................................ 28
4.1. Block structure ................................................................................................ 30
4.2. Mesh generation .............................................................................................. 32
4.3. Final steps ....................................................................................................... 36
4.4. Application of the script to different airfoils ................................................. 37
5. COMPUTATIONAL RESULTS ................................................................................ 38
5.1. Comparison of aerodynamic coefficients ..................................................... 39
5.1.1. Torque coefficient for one blade ............................................................. 39
5.1.2. Comparison of drag coefficients and lift coefficients ........................... 48
5.1.3. Comparison of power coefficients .......................................................... 58
5.2. Comparison of residual errors and computational times ............................. 58
6. CONCLUSIONS ....................................................................................................... 61
7. ACKNOWLEDGEMENTS ........................................................................................ 63
8. REFERENCES ......................................................................................................... 64
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1. NOMENCLATURE
List of symbols:
A [m2] Projected area of rotor
c [mm] Chord length
CL [-] Lift coefficient
CD [-] Drag coefficient
CT=T/[ρR2HU∞2] [-] Torque coefficient
CP=P/[1/2ρAU∞3] [-] Power coefficient
D [m] Turbine diameter (2R)
FL [N] Lift force
FD [N] Drag force
M [-] Mach number
n [rpm] Rotational speed of rotor
N [-] Number of blades
P=2πNT/60 [W] Output power
R [m] Turbine radius
T [Nm] Output torque
t [s] Time
U∞ [m/s] Main wind velocity
W [m/s] Relative wind speed
α [°] Angle of attack
λ=ωR/U∞ [-] Tip speed ratio
ρ [kg/m3] Density
µ [kg/ms] Dynamic viscosity
σ=Nc/R [-] Turbine solidity
ω [1/s] Angular speed
Abbreviations:
AoA Angle of Attack
BEM Blade Element Momentum
CFD Computational Fluid Dynamics
HAWT Horizontal Axis Wind Turbine
DNS Direct Numerical Simulation
LES Large Eddy Simulation
RANS Reynolds- Averaged Navier- Stokes
SDR Specific Dissipation Rate
SST Shear Stress Transport
TSR Tip Speed Ratio
URANS Unsteady Reynolds- Averaged Navier- Stokes
VAWT Vertical Axis Wind Turbine
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2. INTRODUCTION
In this chapter and its sub-chapters, I present the basic information about the
importance of wind power and I describe some fundamental details about wind
turbine technology. Then, I write about the vertical axis wind turbines (VAWTs), as
this particular project is related to this type of wind machines. Thereafter, the aim of
the work is presented in more detail. In the following, the introduction will be
presented based on the literature review [1-27].
2.1. Wind power
Nowadays, fossil fuels are the most used widely energy sources. However,
according to the opinions of many, they are the major causes of the environmental
deterioration and global climate change. It is a fact that the power generation from
fossil fuels has many negative environmental effects and because of the tightening
environmental regulations the demand for clean energy production is growing
continuously.
Because of the rising world population, the demand for and the consumption of
energy increased significantly in the twentieth century. Rapid industrial and technical
development also contributes to the growth of the demand. With this ever increasing
energy claim in the world, it will be more and more important to investigate
alternative methods of generating electricity.
The price of the energy from the conventional energy sources is increasing with the
demand. Hence, to achieve lower cost in the electricity generation, numerous
countries are searching for low-cost technologies. The expensive and depleting oil
and gas compel us to use other available energy sources, such as nuclear energy,
solar energy, hydro power, geothermal energy, biofuel sources, and wind energy.
The traditional, non-renewable energy sources are limited and they are depleting
fast, so the interest in renewable energy sources increases every year. The fact,
that the renewables are of abundant supply, is a huge benefit compared to the
conventional energy sources. Renewable energy sources help to eliminate the
dependence on the oil and gas, which are the most important in these days.
In spite of the fact that nuclear power plants are good alternatives to fossil fuels,
they have several drawbacks. They require high initial investments and have
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dangerous radiation effects. Furthermore, the radiation can be even more
dangerous than during proper operation of a nuclear power plants; some serious
nuclear power plant accidents have occurred already. After the Japanese disaster
in Fukushima (2011), the German government decided to close all the nuclear
power plants gradually in the country, thus the generation of sufficient electrical
power has to be solved in another way.
Therefore, cheap renewable energy is the future and the solution to every problem,
but to provide economical and effective energy production, continuous improvement
is essential. The engineering society has the great mission to invent new
technologies and improve the existing ones. This tendency can be observed all over
the world, not only in Germany and in the European Union.
It is clear from above that renewable energy has an important function nowadays
and its importance is increasing continuously. The renewables which are currently
in use include hydro power, solar energy, biomass, geothermal energy and the wind
energy.
Beside the other renewable energy sources, in the recent years wind power has
become more and more important, because it provides an effective and efficient
solution to reduce the emissions of pollutants and fossil fuel consumption as well.
Among the renewables the interest of many is focused on wind power generation,
since it is available almost everywhere and requires only a small area for the
installation (as compared to e.g., solar energy), thus it represents a very important
function for many countries nowadays. The dependence on the fossil fuels and the
awareness of the limited resources and the increasing pollution are giving a push
forward to wind turbine technology.
The wind is always all around us, it is plentiful and free so we have to try to find the
way to use it the most effectively.
2.2. Wind turbine technology
This thesis does not give an overall review of wind turbines, just a glimpse into
this huge topic in order to present the basic information needed for this particular
work.
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Wind turbines basically use the kinetic energy of the wind to generate electricity:
They harness the kinetic energy contained in the wind and convert it into mechanical
power, driving an electrical generator which produces electricity. With the
appropriate shape of the turbine blades the kinetic energy can be converted to
electrical energy with good efficiency. To achieve the optimal performance, the best
is to install the rotor at an appropriate height (i.e., at the top of a tower), where the
wind is blowing continuously [1].
Sail boats and windmills are good examples, that the wind has been used as an
energy source since the earliest civilization. Windmills were used for many
applications such as grind graining or pumping water in antiquity and the Middle
Ages [1]. One of the first attempts to generate electricity by using the wind was made
in the United States by Charles Brush in 1888 [2]. The first attempts were
encouraging. However, after the initial enthusiasm, the interest and the development
decreased due to several reasons, such as low efficiency and performance, large
investment costs, limited technical possibilities, the easily usable and cheap fossil
fuels and the two World Wars.
The interest in wind turbine technology renewed and increased significantly after the
oil embargo in 1973 because of the increased cost of electrical energy production
from fossil fuels. Several countries invested large amounts of money to improve the
technique at this time, while today this tendency has renewed because of the
depleting and costly fossil fuels. Hence, many nations plan to make large
investments, and the presence of support policies is feeding interest in developing
wind turbines. Nowadays, the technology is getting more attention since it is
possible to generate large amount of clean electrical energy with a relatively small
initial investment. Thus, the number of the installed wind turbines and hereby, the
wind power capacity increases every year. The wind turbine technology is capable
of satisfying residential, commercial and industrial requirements. Furthermore, it is
an attractive electricity source, especially in the parts of the world where the
electrical grid is not available. Since it is modular, it can be built quickly, and it is
easy to fit to the electricity demand and supply. Moreover, as mentioned earlier, the
wind turbine technology inflicts no harmful environmental effects, since during the
operation there are essentially no emissions [3].
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Wind turbines have many advantages, so in the following, I summarise the major
benefits briefly. Perhaps, the most important fact is the pollution free operation, thus
it is environmentally friendly after the equipment has been produced. The
technology is affordable in the most cases. The operational costs are low and the
price of the generated electricity has decreased significantly in the last decades,
thus nowadays it is much cheaper than the electrical energy from fossil fuels and
competitive with the other renewable energy sources [4]. The wind turbine does not
need 24 hour personnel employment during operation, which reduces the costs, but
careful maintenance is required to avoid breakdowns in case of storms. In the areas
where an electrical grid is not available, it is almost the only possibility to supply
electricity. Nowadays, the technology is effective and delivers electricity with high
reliability.
In spite of its many advantages, it has some drawbacks as well and it would be
unfair not to mention a few of them. First of all, the most annoying problem with the
wind turbines is that they can be loud, especially in case of high constructions and
big rotor sizes. So in this case, it is important to choose the installation site carefully,
far from residential areas, commercial buildings and schools. Moreover, the turbine
blades might be dangerous to birds and bats. Furthermore, in case of the large
blades and towers, the visual impression of the wind turbines can be a negative
factor as well. Besides, the initial cost of investment can be quite high depending on
many factors, for example output power rating, tower height and site selection. In
case of any damage to the structure, the repairs might be very expensive.
To achieve the optimal efficiency of wind turbines, they require unique installation
specifications. The location of the site, the spacing between two units, the height of
the towers, and the optimum parameters for rotor blades all have to be chosen
carefully. These installation requirements provide safe, reliable and efficient
operation with low maintenance and operation costs.
In the case of wind turbines the power coefficient describes how efficiently wind
power is utilized and converted into useful turbine power. It can be defined as:
𝐶𝑃 =𝑃
12 ∙ 𝜌 ∙ 𝐴 ∙ 𝑈∞
3 (3.1)
7
where CP is the power coefficient, P is the power output, ρ is the density of air, A is
the projected area of rotor and U∞ is the main wind velocity. The maximum
achievable power coefficient is 59.26 percentage according to the Betz limit named
for the Albert Betz who published his theory first in 1919 [4].
The power coefficient is affected by the tip speed ratio (TSR) of the turbine. The tip
speed ratio is a ratio between the tip blade speed (𝜔 ∙ 𝑅) and the wind speed. It is
defined as:
𝜆 =𝜔 ∙ 𝑅
𝑈∞ (3.2)
where ω is the angular speed, R is the rotor radius and U∞ is the main wind speed.
Figure 1 shows the power coefficients of the different wind turbine types in the
function of their tip speed ratio.
Figure 1 Power coefficients of wind rotors of different designs [5]
In order to make it the discussion about the different type of wind turbines in the
following sections easier, a few quantities should be defined first.
The torque coefficient is given by the following formula:
𝐶𝑇 =𝑇
12 ∙ 𝜌 ∙ 𝑅 ∙ 𝐴 ∙ 𝑈∞
2 (3.3)
8
where T is the output torque, ρ is the density of the air, A is the projected area of
rotor and U∞ is the main wind velocity.
Solidity is a measure of airflow blockage with the turbine. It can be defined in several
ways, in this thesis the following formula is used:
𝜎 =𝑁 ∙ 𝑐
𝑅 (3.4)
where N is the number of the blades and c is the chord length.
Modern wind turbines are classified into two different types depending on the
orientation of their axis of rotation. They can be divided into two main groups, the
horizontal axis wind turbines (HAWTs) and the vertical axis wind turbines (VAWTs).
The most common type is the HAWT, but there are several other types of vertical
axis turbines, such as Darrieus and Savonius wind turbines [6].
HAWTs generally have two or three blades. The tapering and the shape of the
blades are chosen to maximize the efficiency. The rotor is mounted to the top of a
tall tower, thus it is able to take advantage of the larger wind speeds in the
atmosphere, so it has higher capacity and efficiency. Nowadays, most of the HAWTs
have a similar design. Figure 2 shows the structure of a typical three- bladed
horizontal- axis wind turbine.
Figure 2 The construction of a typical HWAT [2]
9
This type of wind turbine is usually more efficient at converting wind energy into
electricity than VAWTs. Therefore, they are more popular in the commercial utility
scale wind power market, hence almost all of the commercial wind turbines are
HAWTs.
Nevertheless, they have many drawbacks that include the low starting torque, the
need of high starting wind velocity and the need of a yaw mechanism to turn the
rotor toward the wind, which leads to power loss, when the rotor follows the wind
direction. Moreover, in case of a storm it has to be rotated out from the wind
direction. These properties are disadvantages, which are not easy to solve.
Vertical axis wind turbines, however are capable to capture the wind from any
direction so they do not need to be adjusted into the direction of the wind in order to
function. The VAWT has a lower rotational speed, thus higher torque. Moreover, the
maintenance is easier than in case of HAWTs because the gearbox and the
generator can be placed near to the ground. Conversely, the output capacity of the
VAWT is much lower than of HAWTs, so they are used for low-power applications
[7].
Vertical axis wind turbines are more suitable for urban areas than HAWTs but they
are appropriate for suburban areas as well. The most important advantage is that
because of their cylindrical shape, they can be easily installed between buildings,
while it is impossible for HAWTs with large propellers. Moreover, they have a lower
noise level because of their construction so they are better in the populated city
area. Furthermore, in the built areas the wind speed is lower and lower wind speeds
can be used by vertical axis wind turbines more efficiently than by their counterparts.
Even though the efficiency of the VAWTs is smaller than that of the HAWTs, they
provide a good solution for individual energy production in the cities. In addition, in
isolated areas without an electric grid, the small investment cost and easy
maintenance has made this rotor an increasingly popular option [8].
Considering these facts, it is clear why the interest in the accomplishment of wind
energy conversation systems in a domestic environment has renewed in the last
years. Vertical axis wind turbines are becoming more and more popular nowadays,
since they have several features that make them more usable in many cases than
HAWTs. The research into this technology is intensive today, in order to achieve
higher efficiency and performance and to improve on its negative features, such as
10
the poor self-starting ability, which is still an open issue. Therefore it is not surprising,
that this type of wind machine is in the main focus of this thesis. Hence, in the next
sub-chapter I present the vertical axis wind turbines in more detail.
2.3. Vertical axis wind turbines
The first wind machines- the windmills- were vertical axis turbines. They were
especially used to grind wheat or pump water. Approximately two centuries ago, the
interest in electrical energy production increased and thus the investigation of wind
power generation renewed. Vertical axis machines were developed parallel with
horizontal ones, but the financial support was smaller for VAWTs than for HAWTs.
However, these studies revealed the capability of the VAWTs to produce electricity.
They were considered promising in the beginning because of their low wind speed
utilization, but then they were superseded by the horizontal axis wind turbines
because of their comparatively low efficiency and performance. Nowadays, there is
a resurgence of interest in VAWTs because of the different application areas and
the numerous advantages over HAWTs [9].
Although the performance is lower, VAWTs are more suitable in the built
environment because of the lower sound emission and because they are capable
of utilizing lower wind speed. Another important reason is that the VAWT overcomes
the problem that the rotor has to be pointed into direction of the wind. The greatest
benefit is the easier and cheaper maintenance because the gear box and the
generator can be placed at the base of the tower. Since they are usually smaller
than the HAWTs, they result in a more acceptable visual impact. Moreover, the
construction is much cheaper than for HAWTs for many reasons-, including the lack
of need of yaw control. Therefore, in some cases, where low cost is important, the
VAWTs are the better choice [7] [8].
In spite of their many benefits they have some drawbacks as well. The major
disadvantage is that VAWTs are not always self-starting. Since they are constructed
closer to the ground level, they are subject to lower wind speed and more
turbulence, thus generally they have lower power output than the HAWTs. In
particular cases they require guy wires to hold the structure in place because the
VAWTs work under centrifugal loads. Due to the working principle, the power output
and the torque fluctuate during the operation of VAWTs because of the periodic
11
manner during every rotation when the blades move in and out of the wind, while
the HAWTs have fairly constant torque and power output. This phenomenon can
cause serious vibrations and fatigue so it has to be considered during the
development [7], [10]. However, sometimes these drawbacks can be avoided with
careful planning and with development. The weaknesses can be improved with
continuous research. My current work hopefully contributes to it.
In the following, I present the working principle of VAWTs. Then I show the two most
important types of VAWTs. Finally, I detail the aim of my work and show some
related previous studies from the literature.
2.3.1. Principle of operation
As its name shows, the rotor shaft orientation of the VAWT is vertical and the blades
are mounted vertically as well to the rotating shaft. Thus it is essential that during
the rotation of the turbine the wind speed and the flow direction vary.
The VAWTs are divided into two subgroups, the drag type and the lift type machines
as shown in Figure 3. This classification is based on the transmission mechanism
of the kinetic energy of the wind.
a) Drag driven VAWT
b) Lift driven VAWT
Figure 3 The two subgroups of VAWTs [6]
These two types have totally different characteristics and this is true for their turbine
efficiency and the self-starting capability as well. The drag driven VAWTs use the
drag forces to generate energy and have low efficiency but good self-starting
capability. However, the lift driven types use the hydrodynamic lift on the blade, have
higher efficiency but very poor self-starting capability [6].
Nowadays, the two most popular and widely used VAWTs belong to two different
types. The Darrieus wind turbine is a lift based wind turbine, while the Savionius
type is drag based. Beyond these types the VAWTs have a wide range of designs
as a result of many investigations.
12
In the following, I present only the two major types, mainly focusing on Darrieus
turbines, since it is related to my work but I write a brief section about the Savonius
turbines, just to give a total picture about the different types.
2.3.2. Savonius wind turbines
The simplest wind turbines are drag type devices which produce mechanical
power and later electrical energy from the drag force. The Savonius turbine is a drag
type VAWT which was invented by a Finnish engineer S. J. Savonius, in 1924 [2].
The turbine has semi-cylindrical blades which rotate around the central axis, as
shown in Figure 4.
Figure 4 Savonius wind turbine with two half-cylinder blades3
At the basic level, the S-rotor consists of two half-cylinders to catch the wind and
convert it into torque. The concave blade produces positive torque while the convex
blade of the Savonius turbine always produces negative torque. In spite of the very
low wind speed, with their large surface area, the Savonius turbines are able to
produce a large amount of torque. However it is not constant because of the
fluctuating load. Thus the voltage and the output frequency vary as well, which
means that Savonius turbines cannot be connected directly to the grid.
This type of VAWT is not very suitable for electricity generation because it cannot
rotate faster than the wind speed since it is drag type. Furthermore, compared to
other designs, it has lower efficiency and very limited power output. For high
capacities, this type requires a large amount of materials what is very expensive,
hence not cost effective. Moreover, it is obvious that the construction is not
appropriate for higher wind speeds.
On the other hand it can be economical for small power requirements since it is
reliable and easy to maintain and has low noise production. So it can be used where
efficiency is less important than reliability, and economy is most important. The best
3 „Source: http://techniphilia.blogspot.de/2011/11/comparison-of-savonius-variations.html”
[Accessed: 25 October 2014]
13
feature of the Savonius wind turbine is its simplicity, although for similar power
output as other wind turbines, the structure would be large and heavy.
The typical fields of application are for instance: water pumps, heat pumps, fans or
anemometers. It is usually chosen where high torque is needed at low speeds.
Usually VAWTs are not self-starting, however the Savonius turbines is an exception.
In order to provide the self-starting ability, two or more rotors are required as shown
in Figure 5. This is a great advantage because in even case of weak winds it allows
the auto start-up operation
Figure 5 Self-starting Savonius wind turbine4
The Savonius wind turbine is not the main focus of this thesis.
2.3.3. Darrieus wind turbines
One of the most common and popular VAWT is the Darrieus wind turbine, which
was invented by and named after the famous French inventor, Georges Darrieus. It
was developed in the 1920s and as the prototype proved to be reliable and quite
efficient it was patented in 1931 [11].
Lift driven VAWTs consist of blades which are able to capture the wind energy in
the form of lift force and thus produce torque on a shaft which drives a generator
and produces electricity. The Darrieus type belongs to the lift driven wind machines
thus it operates on the mentioned principle. It employs aerodynamic lifting surface
to generate useful torque. The starting torque is much poorer than with the Savonius
drag type wind machines, but the Darrieus types are more efficient. High efficiency
4 „Source: http://cdn.instructables.com/F1S/M75G/GCI8OQTT/F1SM75GGCI8OQTT.LARGE.jpg”
[Accessed: 25 October 2014]
14
is the major benefit of Darrieus turbines, which makes it appropriate for electricity
production.
There are several different shapes of blades. The original design is the so called
eggbeater from its typical shape. It may have two or three blades and it usually
needs guy wires to support the shaft. Figure 6 shows the common Troposkien
Darrieus wind turbine with two blades.
Figure 6 Curved blade Darrieus wind turbine 5
However, the guy wire is unnecessary for straight bladed wind turbines, where the
bended blades are replaced with straight ones. These wind turbines are usually
named H-type Darrieus wind turbines or giromills. The blades are airfoils and
mounted to the central shaft in parallel, through support arms. These blades are
easier to manufacture (e.g., with simple extrusion) than the blades of Troposkien
Darrieus or of the HAWTs. The H-Darrieus turbines may have two, three or more
blades (see Figures 3 and 7). The two- bladed turbines are lightweight, while the
three- bladed construction has lower noise. The major benefit of these turbines is
the simple construction so it is relatively easy and cheap to build and maintain it.
Figure 7 H-Darrieus wind turbine 6
5 „Source: http://upload.wikimedia.org/wikipedia/commons/9/92/Darrieus_rotor002.jpg”
[Accessed: 03 November 2014] 6 „Source: http://upload.wikimedia.org/wikipedia/commons/4/42/Windgenerator_antarktis_hg.jpg”
[Accessed: 03 November 2014]
15
The H-type Darrieus wind turbine works on the same principle as the common type:
the forces generated by the wind are split into lift and drag force and they make the
turbine rotate. It is capable of accepting the wind from any direction, like the other
VAWTs, but it is more suitable in turbulent wind conditions. Hence, it is a good
choice where the HAWTs are not suitable. They work well in extreme wind
conditions, for example in gusts.
The H-Darrieus turbine is usually mounted on rooftops or towers in order to capture
higher wind speed, thus its efficiency could be similar to a horizontal axis wind
turbine. Therefore, considering the advantages already mentioned, the Darrieus
turbines are the most suitable for urban applications.
However, it does not matter if the blades are curved or straight, in case of low speed
wind, they produce little or no torque, thus rotor does not start by itself. In order to
overcome this problem, several solutions have born.
For instance in a cycloturbine, which is a variant of the H-type Darrieus wind turbine,
the blades are able to rotate around their axis and they can be pitched mechanically,
thus they always have an angle of attack relative to the wind. As a result, this kind
of wind turbine is able to generate nearly constant torque with 3 blades, which is
near to its maximum, so it can generate more power. Moreover, the biggest
advantage is the self-starting ability at low wind speed. If the blades are adjusted to
face to the wind direction, they generate drag forces, which creates a starting torque.
Later, when the rotation speed increases, the rotor can be accelerated by pitching
the blades, thus the wind flow near on the airfoil generates lift forces. The pitching
mechanism is heavy and quite complicated and the system requires wind direction
sensors in order to pitch the blades accurately [12].
There is another solution to overcome the low initial torque and the self-starting
problem. The Savonius turbine can be used as a starter of the rotor for a Darrieus
turbine. The combined rotor is widely used nowadays.
In spite of the many innovative solutions, the simplest and cheapest construction is
the H-type Darrieus wind turbine. For that reason, it is still in the focus of many
investigations with modern tools, in order to optimise the operation and achieve
higher performance and efficiency or self-starting ability. My work is also related to
16
the development of the H-Darrieus wind turbines. In the next section, I show the
problems with this type of machine, which motivate the continuous investigations.
2.4. Problem statement
In the case of VAWTs, during rotation the angle of attack varies continuously,
thus these machines have non-stationary aerodynamic behaviour. This
phenomenon has a large effect on the generated power and thus on performance,
and on the dynamic loads of the rotor as well. Moreover, the wind in urban areas is
relatively low speed and very turbulent, and this makes the flow structure very
complicated.
It is very difficult to analyse the VAWTs because of the variation of the flow
conditions as the blades are rotating around the shaft. The quantitative prediction of
the performance of a Darrieus wind turbine is not simple because as mentioned, the
aerodynamics of the rotor is complicated. The blades work within a wide range of
angles of attack and the change is fast so the airfoils produce dynamic stall, which
is not completely understood yet. Furthermore, beyond the angle of attack, the local
dynamic pressure and the torque change as well during the revolution. Thus the
power output is fluctuating. Moreover, the biggest problem with the VAWTs is the
self-starting problem; hence, it is the subject of most of studies.
The new developments suggest many conceptual changes which would result in
better features for the VAWTs. This study focuses on the H-type Darrieus turbine,
where the performance and efficiency increase is the main concern of the
development.
H-Darrieus wind turbines were mainly made only with symmetrical airfoil profiles.
However, just a few profiles are appropriate to achieve optimal power output and
performance. By using an optimised airfoil profile, the performance and efficiency
can be increased [13]. In spite of the many investigations, the optimisation of the
blade profile has not been fully achieved yet.
In the last years the application of the computational fluid dynamics (CFD) for the
examination of VAWTs has increased significantly because of the availability of
more and more computational power. These models provide enhanced fidelity in
17
simulating unsteady effects and dynamic stall compared to the earlier Blade
Element Momentum (BEM) models [14] [15].
2.5. State of the art
The Institute of Fluid Dynamics & Thermodynamics at the Otto-von-Guericke
University has a research project related to vertical axis wind turbines. The research
focus is on the optimization of the H-type Darrieus wind turbines. The aim of the
investigations is to improve the performance and efficiency of the turbines by
studying the characteristics of different airfoil profiles. However, this is not easy,
because due to the change of the angle of attack during the rotation the H-type
Darrieus wind turbine has unsteady aerodynamic behaviour. Furthermore, at low tip
speed ratios, the dynamic stall has a significant impact on the power output, and
since this phenomenon is not completely understood yet, it is hard to examine [8].
So to analyse this very complex unsteady aerodynamic behaviour of the VAWTs
with CFD is a very difficult task.
The institute has an in-house parameterisation, design-of-experiment and
optimisation software, OPAL++ (developed by L. Daróczy) [16]. This software is able
to generate different airfoil profile coordinates with a genetic algorithm. The software
can generate both symmetric and asymmetric airfoils based on an extended NACA4
parameterization, and the optimisation is performed using a genetic evolutionary
algorithm. To analyse different airfoil profiles numerical simulations have been used:
in order to reduce the runtime only 2D sections of the rotor were simulated.
In order to achieve accurate results with numerical simulations, a fine quality mesh
is indispensable. Thus, to create the appropriate numerical mesh for the geometry
of an H-type Darrius wind turbine is an essential task. Throughout the optimisation
the creation of the geometry and mesh has to be performed in a completely
automatic way, which - in light of the large parameter space - is very difficult to
achieve.
While unstructured and partially structured meshes are easier to be generated, a
structured mesh usually provides improved speed and accuracy due to increased
orthogonality. The exact difference in the accuracy and speed is however dependent
on the exact problem, thus it remains a question whether the easier and faster
unstructured approach is enough, or if the structured mesh provides significant
18
advantages. Structured meshes are much more difficult to generate and it requires
more time to create a fine quality structured mesh around a three- bladed wind
turbine than to form an unstructured. Usually, in the research dealing with that kind
of wind machines, unstructured or just partially structured meshes are in use. In the
previous studies performed by the Institute of Fluid Dynamics & Thermodynamics
in Magdeburg, a partially structured mesh has been used, as shown in Figure 8 [17],
[18].
Figure 8 Partially structured mesh on one blade of the H-type Darrieus wind turbine 7
Nevertheless, by using a structured mesh, the computational time should be
reduced and the residual error should be smaller than in the case of an unstructured
mesh. These are very important aspects: therefore, the goals of my work were (1)
to create a high resolution and fine quality block structured mesh, using the
ANSYS® ICEM CFD commercial mesh generation software; (2) to run simulations
with the structured mesh for the same airfoil profile and with the same parameters
and settings as formerly performed with unstructured mesh; (3) and to compare the
results and find out the differences. I expected to find a reduction in computational
time and decrease of numerical errors, because the main aim is to keep the run time
of the simulation appropriate for optimization.
Moreover, in order to automate the optimisation to different blade profiles, OPAL++
requires a script for the mesh generation, which can be used by the blade
optimization module. Using the feature of the ICEM CFD, that it is able to record a
script from the mesh generation process, my task was to develop a method which
is capable of generating an appropriate quality mesh for most of the blade profiles.
Thus, if the structured mesh proves to be better than the unstructured, the
7 „Source: [Daróczy et.al former investigation]”
19
optimization software can switch to the script I have created as the main task of my
Master’s thesis.
2.6. Literature overview
Many attempts have been made to improve on the disadvantages of Darrieus
wind turbine by using numerical simulations. The demand on new design
approaches for the urban areas and the complexity of the problem contribute to the
use of CFD modelling. Various authors have investigated the performance and self-
starting ability of VAWTs, e.g. [6], [19].
Since my particular task was to create a structured mesh for an H-type Darrieus
wind turbine and compare the results with the simulations with unstructured mesh,
here only investigations are presented where the authors investigated an H-Darrieus
wind turbine with two- dimensional numerical simulation.
The literature survey revealed that most of the authors use an unstructured mesh
for the investigation of this type of wind turbine. In most of the cases, a structured
mesh is used in the vicinity of the blades but then in the further fields an unstructured
mesh is applied, as can be seen in Figure 8. In the following, I mention some
examples from the literature.
Mohamed used unstructured mesh in his performance investigations of the H-type
Darrieus wind turbines [6], [13]. Gossellin et al. performed a parametric study of
Darrieus wind turbines using an unstructured mesh for the whole examined area
except near the blade in the boundary layer, where a structured mesh was applied.
[20].
An unstructured mesh has generally been applied in the case of water turbines as
well. For instance, Torresia et al. used a partially structured mesh for numerical
investigation of a Darrieus turbine for hydropower generation [21]. Moreover, Maître
et al. accomplished a wall refinement analysis by modelling the flow in a Darrieus
water turbine using a partially structured mesh as well [22].
Several other studies have been performed in recent years using unstructured or
partially structured mesh for the numerical simulation of an H-type Darrieus wind
turbine: [23], [24], [25], [26].
20
The application of fully structured mesh for a straight- bladed Darrieus wind turbine
is really rare. However, some exceptions can be found in the literature, for instance
Vaishnav used structured mesh for the investigation of the aerodynamic
performance of a VAWT in his thesis [27]. Furthermore, Malael et al. applied a
structured mesh during his study where he examined the different methods, RANS
and URANS in case of VAWTs [28].
As is clear from the above, the unstructured mesh is more common in the
examination of VAWTs. The question is: is it worth it to use a structured mesh?
2.7. Structure of the thesis
This thesis is organized into 8 chapters. The literature review, the statement of
the problem and the state of the art have been presented in this chapter.
The next chapter presents the computational methods that have been used in this
particular study. Then it is followed by Chapter 4, where the generation of the
computational mesh is described in detail. The results are discussed in Chapter 5.
Finally, Chapter 6 presents the conclusions of the study.
21
3. COMPUTATIONAL METHODS
As has been mentioned earlier, the flow around an H-Darrieus wind turbine is
unsteady due to the variation of the angle of attack during the rotation. In each
revolution, vortices separate from the blade surfaces. This separation plays an
important role for the efficiency of the turbine. The vortices separate both from the
leading edge and the trailing edge when the angle of attack increases. First, they
separate from the leading edge then from the trailing edge. These vortices which
shed from the blade’s edges and their interactions with other blades result in a
complex flow structure. The presence of the dynamic stall phenomena makes the
flow even more complicated. This is particularly significant in the operation of low tip
speed ratios. As Almohammadi state: “as the angle of attack increases, an
increased adverse pressure is developed over the airfoil surface, thus causing the
flow separation and reattachment, and this initiates the dynamic stall which results
in an overshoot in the lift coefficient followed by a sudden loss in the lift due to vortex
shedding. The failure to capture the dynamic stall accurately would result in a wrong
prediction of the turbine overall performance” [23, p. 483].
Although dynamic stall can have a positive effect on the power generation of wind
turbine, the presence of these vortices causes problems, such as noise, vibrations
and the unsteady forces can cause fatigue on the blade material. Due to the
mentioned complexity, in the recent years much research has been performed on
the simulation of the H-Darrieus wind turbines, but it is still a challenging task.
In the present work, computational fluid dynamics has been used for the
investigation of an H-type Darrieus wind turbine. Numerical simulations provide
knowledge of the flow characteristics in detail, such as velocity field, vorticity field,
pressure field, etc. Due to the unsteady nature of the flow around the rotor, the CFD
simulation of a Darrieus wind turbine is a very difficult task. Therefore it is necessary
to prepare the numerical model with great care. Despite the time and care needed
to prepare the numerical model, CFD methods still provide low cost, accurate and
reliable results.
The simulations were performed using the commercial CFD code STAR-CCM+ from
CD-Adapco®. Previous studies performed at the Institute of Fluid Dynamics &
Thermodynamics at the Otto-von-Guericke University have shown that the use of
22
this software for analysing the flow around an H-type Darrieus wind turbine is very
effective. In order to be able to compare the results of the previously used
unstructured mesh to the structured mesh, the same solvers and settings were used
for the simulation of the Darrieus wind turbine that proved to be appropriate in former
studies [17], [18].
Considering the unsteady characteristic of the flow and the presence of dynamic
stall it was necessary to use STAR-CCM+ in transient mode. Although the Darrieus
turbine is three-dimensional, in order to reduce the computational time and cost,
only a 2D section was investigated. Computations were performed in parallel. Use
of moving sub-grids was necessary in order to reproduce the operation of the wind
turbine. Thus, the computational domain contains two sub-domains: a rectangular
outer zone with a circular opening, which is the stationary domain, and a circular
sub-grid which includes the Darrieus rotor, which is the rotating domain. Across the
two regions a non-conformal interface allows computation of the fluxes. The
numerical simulations were carried out by solving the governing differential
equations and by using a structured grid methodology with sliding mesh technique.
STAR-CCM+ contains a wide range of physics models. In the case of an H-type
Darrieus wind turbine one needs to carefully consider the selection of the most
appropriate model due to the presence of flow separation, reattachment and the
transition of the flow from laminar to turbulent near the blade. In this particular case,
the Coupled solver was applied to solve the equations. The usable turbulence
models are mostly based on Reynolds Averaged Navier-Stokes equations. In order
to capture the unsteadiness like the continuous change in the angle of attack of the
blade with the revolution, the incompressible Unsteady Reynolds-Averaged Navier-
Stokes (URANS) was used. Turbulence closure was provided by the k-ω Shear
Stress Transport (SST) turbulence model.
The workflow of the numerical analysis starts with the pre-processing, comprised of
the generation of the 2D computational domain and the high quality meshing which
will be presented in the next chapter. Moreover, the pre-processing consists of the
settings of the simulation solver and the initial conditions, the reference values and
boundary conditions which are decisive factors for the problem. They play a vital
role in defining the accuracy of the simulation process. Therefore, it is really
important to choose the appropriate boundary conditions in order to achieve good
23
results. These values will be described in Chapter 4.3. The workflow continues with
the calculation, and finally with the post-processing of the results, which will be
presented in the Chapter 7.
In the following, I present the governing equations used for this particular simulation
by STAR-CCM+.
3.1. Governing equations
The governing equations in CFD fundamentally consist of conservation of
energy, continuity equation, and the conservation of momentum, which is known as
Navier-Stokes equation. These equations are also known as transport equations or
conservation equations. The Navier-Stokes equations govern the motion of viscous
fluids. In order to analyse a fluid dynamic problem the Navier-Stokes equations have
to be solved on an appropriate spatial discretization.
In this study, unsteady and incompressible flow is considered. The Navier-Stokes
equation for an incompressible flow is given as follows:
𝜌 (𝜕𝒗
𝜕𝑡+ 𝒗 ∙ ∇𝒗) = −∇𝑝 + 𝜇∇2𝒗 + 𝒇 (4.1)
where v is the flow velocity, ρ is the fluid density, p is the pressure, µ is the dynamic
viscosity, and f represents body forces acting on fluid.
The continuous governing equations are converted into a form that can be solved
numerically with finite volume method in the STAR-CCM+. There are two different
approaches to solve the governing equations, the segregated approach (where the
flow equations are solved one after the other and linked using a correction equation)
and the coupled approach (where the coupled system of equations is solved
simultaneously) [29]. In this study coupled approach was applied.
Using pseudo-time marching approach, the conservation equations for momentum,
mass and energy are solved simultaneously by the Coupled Flow model. For solving
flows with dominant source term, such as rotation, this model provides the benefit
of robustness. In case of a coupled solver, the convergence rate does not worsen
as the mesh is refined, in other words, the CPU time scales linearly with cell count,
which is another benefit of this solver [29]. Previous studies have shown, that while
24
for PISO more than 100 iterations are required, the coupled solver is able to solve
a time-step with no more than 25 inner iterations [18].
Governing equations (the basic flow and energy) in their coupled continuous integral
form are presented in the below.
For an arbitrary control volume V with differential surface area da, the Navier-Stokes
equations in Cartesian integral form may be written:
𝜕
𝜕𝑡∫ 𝑾𝜒
𝑉
𝑑𝑉 + ∮[𝑭 − 𝑮] ∙ 𝑑𝒂 = ∫ 𝑯𝑑𝑉
𝑉
(4.2)
where:
𝑾 = [
𝜌𝜌𝒗𝜌𝐸
] , 𝑭 = [
𝜌(𝒗 − 𝒗𝒈)
𝜌(𝒗 − 𝒗𝒈) ⊗ 𝒗 + 𝑝𝑰
𝜌(𝒗 − 𝒗𝒈)𝐻 + 𝑝𝒗𝑔
]
𝑮 = [0𝑻
𝑻 ⋅ 𝒗 + �̇�′′] , 𝑯 = [
𝑆𝑢
𝒇𝒓 + 𝒇𝒈 + 𝒇𝒑 + 𝒇𝒖 + 𝒇𝝎 + 𝒇𝐿
𝑆𝑢
]
(4.3)
and 𝒗𝒈 is the grid velocity vector, T is the viscous stress tensor, E is the total energy
per unit mass and �̇�′′ is the heat flux vector.
Total energy is related to the total enthalpy H by:
𝐸 = 𝐻 − 𝑝/𝜌 (4.4)
where:
𝐻 = ℎ + |𝒗|2/2 (4.5)
and ℎ = 𝐶𝑝𝑇. H is the vector of body forces [29].
The k-ω SST model of URANS viscous equations is used for the turbulence closure.
The k-ω turbulence model offers accurate analysis along the boundary layer regions
and in fully developed flow.
The k-ω SST turbulence model is a hybrid model. It combines two models in order
to calculate the flow more precisely in the near wall region. The k-ε model has
unsatisfactory near-wall performance for boundary layers with adverse pressure
25
gradients. The boundary layer flow plays important role on the results, thus proper
modelling of near-wall flow is important for the accuracy of the calculations.
Therefore the k-ω SST model is applied for simulation in this study. This uses a
modified k-ε model near the wall using the dissipation rate (ω) as a second variable
instead of turbulent kinetic energy dissipation term (ε), while using standard k-ε
model to obtain the flow properties in the free-stream flow region far from the wall
[30].
Compared to the other turbulent models, the k-ω is more precise for low Reynolds
number flows having strong adverse pressure gradients like in the flow past an H-
type Darrieus turbine. The accuracy within the computational domain depends on
the order of the discretization, not only on the flow coupling and turbulence closure.
A second-order discretization scheme for the continuity, momentum and turbulence
equations is applied in order to ensure higher accuracy.
For the SST k- ω model, the transport equations are:
𝑑
𝑑𝑡∫ 𝜌𝑘𝑑𝑉 + ∫ = 𝜌𝑘(𝒗 − 𝒗𝑔) ∙ 𝑑𝒂
𝐴𝑉
∫(𝜇 + 𝜎𝑘𝜇𝑡)∇𝑘 ∙ 𝑑𝒂 + ∫(𝛾𝑒𝑓𝑓𝐺𝑘 − 𝛾′𝜌𝛽∗𝑓𝛽∗(𝜔𝑘 − 𝜔0𝑘0) + 𝑆𝑘)𝑑𝑉
𝑽𝐴
(4.6)
𝑑
𝑑𝑡∫ 𝜌𝜔𝑑𝑉 + ∫ 𝜌𝜔(𝒗 − 𝒗𝑔) ∙ 𝑑𝒂 =
𝐴𝑉
∫ (𝜇 + 𝜎𝜔𝜇𝑡)∇𝜔 ∙ 𝑑𝒂 + ∫(𝐺𝑘 − 𝜌𝛽𝑓𝜷(𝜔2 − 𝜔02) + 𝐷𝜔)𝑑𝑉
𝑽𝐴
(4.7)
where 𝑆𝑘 and 𝑆𝜔 are the user-specified source terms, 𝑘0 and 𝜔0 are the ambient
turbulence values in source terms that counteract turbulence decay, 𝛾𝑒𝑓𝑓 is the
effective intermittency provided by the Gamma ReTheta Transition model (it is unity
if this model is not activated) and:
𝛾′ = min[max(𝛾𝑒𝑓𝑓 , 0.1) , 1] (4.8) [29]
26
Details of the further governing equations can be found in the STAR CCM+ User
Guide [29].
3.2. Sliding mesh
The appropriate governing equations were solved in the computational domain,
which is divided into two sub-domains. The computational domain comprises a large
rectangular static domain and a rotating circular sub-domain. The location of the
circular rotor domain coincides exactly with the circular opening in the rectangular
stationary domain is and centred on the turbine rotational axis.
Both domains are bounded with interface, which provides a connection between the
two domains during the simulation analysis process. Both areas are connected by
a sliding mesh interface. The sliding mesh method was used due to the movement
of the rotor.
The use of moving sub-grids was necessary, since the goal of the work was to
reproduce the operation of the Darrieus wind turbine. The rotor domain simulates
the revolution of the wind turbine, thus it is characterised by a moving mesh. The
rotor domain is rotating at the same angular velocity as the turbine so the interface
slides at the specified speed. Momentum and mass are transported through the
interface from the rotor domain to the stationary domain.
Using an unsteady sliding mesh is reasonable when time-accurate behaviour is
required, and STAR-CCM+ provides the option to move the mesh vertices of a
region during a transient analysis. This mesh motion is specified as rotation and
translation motion. Applying of this motion results in mesh vertices being displaced
in each time step [29].
In Chapter 5 the specific features and dimensions of the two sub-domains are
presented in detail.
3.3. Reference values, initial conditions and boundary conditions
The various settings and parameters used to set up the simulation of the H-
Darrieus wind turbine in the STAR CCM+ are presented in detail in this section.
27
Numerical simulations were performed for tip speed ratio λ=2, 3.3, and 4.5, and
were carried out imposing a constant wind speed 8 m/s (in direction x) in all of the
simulations.
The unsteady flow characteristics was calculated by using k-ω SST with second
order convection. “All y+ Wall Treatment” was used for wall modelling. The air was
considered incompressible (as the tip speed is well below 0.3M) and the density
was specified as 𝜌 = 1.225 𝑘𝑔/𝑚3 (based on the DIN EN 61400 standard) with the
corresponding dynamic viscosity of 𝜇 = 1.7894 ∙ 10−5𝑃𝑎 ∙ 𝑠. The gradients were
computed with hybrid Gauss LSQ (Least Squares) method. Venkatakrishnan limiter
method was applied for the second order implicit time discretization with a coupled
solver. The boundary conditions were compound to the initial conditions. Turbulent
viscosity ratio was low (10). The flow was slightly turbulent, with 0.1% turbulent
intensity. This assumption was valid because on the frequency corresponding to the
rotor rotation speed, the spectrum of turbulence of the wind shows low intensity.
(Under the interval of 2 s, it is less than 2%, while the time periods of the rotor were
0.589 s, 0.31 s and 0.2618 s, corresponding to TSR=2, 3.3 and 4.5, respectively.)
The time step was chosen in such a way that for each time step the turbine rotates
0.5 degrees (with 24 inner iterations per time step). Using a constant value of time
step, at least 5 seconds of physical time were computed for every case.
Simulations were performed in parallel on 3 computers - with Intel Xeon E5-2620
Processors (2.1 GHz) and 32 GB of RAM memory installed.
28
4. GENERATION OF THE COMPUTATIONAL MESH
Generating the appropriate computational domain for a CFD problem is an
important part of the modelling process. There are different requirements which
have to be taken into account. First of all, the computational domain should not be
so large as to unnecessarily increase the number of cells of the grid and thus the
computational time. Moreover, it should not be too small, because the aim is to
reproduce the flow (and expansion of streamlines) around the rotor accurately. In
addition, the domain has to be able to reproduce the rotation of the turbine suitably.
The geometry and the computing grid were generated with ICEM CFD program from
ANSYS®. In order to facilitate comparison of the simulation results with previous
studies, the geometry from the earlier investigations using an unstructured mesh
was retained [17], [18].
The computational domain comprises two sub-domains with an interface at the
boundary between them. Hence the two domains interact with each other across
the sliding interface. The rectangular far-field is stationary, while the circular rotor
domain is rotary.
The rotor domain contains the turbine geometry. The stationary domain provides
space for eddy dissipation and ensures an appropriate distance between the blades
and the outer boundary. As the aim of the present work is the simulation of an H-
Darrieus turbine in open field conditions, it is necessary to define a large domain.
Thus, the inlet and outlet boundary conditions were placed respectively 8 diameters
upwind and 14.66 diameters downwind with respect to the rotor vertical axis in order
to allow the full development of the wake. Hence, in order to allow the vortex shed
of the wind turbine surfaces to dissipate before encountering the outer boundary,
the stator domain is sufficiently larger than the rotating domain. The large far field
helps to avoid the boundary effect which might influence the accuracy of the
simulation. Several studies were performed in the earlier investigations to determine
the appropriate size of the domain. The exact dimensions of the domain can be seen
in Figure 9.
The investigated H-Darrieus rotor is equipped with three blades. Each blade chord
length is 0.16 m located at 120° from one another. The diameter of the rotor is 3 m,
29
while the rotor sub-domain has a radius of R=2.2 m. The shaft has a diameter of
0.1 m.
In the present study, a symmetrical airfoil profile was used which had been studied
previously at the Institute of Fluid Dynamics & Thermodynamics in Magdeburg using
an unstructured mesh and whose profile was investigated with measurements
earlier (results are confidential).
The computational domain with the two sub-domains is presented in Figure 9, which
shows the main dimensions of the geometry. The names of the boundaries are
highlighted in Figure 9 as well.
Figure 9 Schematic view of the computational domain with dimensions, part names and boundary conditions
The geometry of the computational model was created step by step together with
the mesh generation steps. The two sub-domains were created and meshed
separately and then merged together. First of all the rotor domain was meshed and
thereafter the stationary domain.
𝝎
x
y
ve
locity inle
t
pre
ssure
outlet
symmetry
24 m 44 m
58 m
shaft (wall)
rotor
domain
symmetry
blade (wall)
sliding interface
u
stator
domain
R 1.5 m
R 2.2 m
30
4.1. Block structure
The ICEM CFD offers several techniques for generating meshes. Among them,
the blocking technique was applied in order to create an appropriate layout to be
able to generate structured mesh on the 2D H-type Darrieus turbine. In the following,
I present the process of the block and mesh generation step by step in detail, since
it was the main part of my work.
The first step was to import the coordinates generated by the OPAL++ optimisation
software. The first airfoil profile generated by the blade optimisation software was
used in this particular study, which is the same airfoil as was investigated
experimentally. From the leading edge to the trailing edge the curves contain 351
node points for the upper and for the lower side. From the two curves one part was
created and named “blade”, as it highlighted in Figure 9. The blade coordinates are
already positioned into the correct position place with respect to the axis of the shaft,
with a radius of 1.5 m. In the next step, a 120° section of the rotor geometry was
created, as shown in Figure 10.
Many attempts were made to achieve the optimal blocking since it is a very important
part of the structured mesh creation process. The script must be applicable for other
airfoil profiles (asymmetrical as well), which made the planning even more
complicated. Namely, as I have mentioned earlier, using the feature of the ICEM
CFD that is able to record the mesh generation process in a script, the aim was to
develop a script which is able to generate structured mesh for any airfoil profiles,
and can thus be implemented into the blade optimisation software of the
Department. Hence, the script record function was turned on from the very
beginning of the process, thus the script is able to read the formatted point data
automatically.
Among several attempts to create the appropriate blocking, the following
compromise proved to be the best. 2-D planar blocking was generated around the
section, then the block was split into several parts to capture the airfoil geometry.
The block’s side edges were associated to the boundary curves of the 120° rotor
section. Around the blade an O-grid was applied, which allows a uniform mesh
around the geometry. The area near the blade was created with O-grid to provide
sufficiently dense mesh around the airfoil. Figure 10 shows the blocking on the 120°
rotor section.
31
Figure 10 Block structure on the 120° section of the rotor
The proper edge-curve association is important to achieve a fine mesh, thus all of
the edges were associated to the appropriate curves. It is especially important for
the blade. In order to enable for the script to generate the mesh to different airfoil
profiles, points were placed on the blade’s curves at particular places. These points
are highlighted in Figures 10 and 11. Points were placed at the leading edge and
trailing edge as well, and other two points were placed half-way between them on
the upper curve and on the lower curve. Moreover, the program makes it possible
to place points on the curves by specifying the exact place of the points with the
blade’s length parameter in percentage. Thus, two other points were placed at 5%
of the curves length from the leading edge and other two were placed at 0.8% of the
curve’s length form the trailing edge. The block’s vertices were associated to these
points.
Figure 11 Points on the blade's curve
32
These points were also used as reference points for the area near the blade. Points
were created in every direction at 353 mm distance from the points which are placed
at the blade’s edges.
Points 5 and 9 in Figure 10 were placed on the same horizontal line as their
corresponding points: the leading edge and the trailing edge, respectively. Point 7
and 11 were placed on the same vertical lines as their corresponding points on the
blade, half-way between the leading edge and trailing edge. Points 4, 6, 8 and 10
were positioned 45° relative to their corresponding points. The near blade block’s
vertices were associated to the mentioned points, and this resulted in an octahedral
near blade block, where the O-grid was used. Point 2 was projected to the rotor’s
arc from Point 11. Two vertices on the left and the right hand (number 1 and number
3) on the arc were defined in a distance of 550 mm from Point 2. Hence, using the
replay function of the ICEM CFD, the blocking created by the script is suitable for
almost all airfoil profiles.
Later, in order to get the 3-bladed vertical axis wind turbine rotor, the geometry of
the 120° rotor section has to be copied and rotated together with the mesh. To
provide a matched mesh on boundaries of the sections, the periodicity in the global
mesh setup had to be defined by setting up base, axis and angle. Furthermore, in
the edit tool block the periodic vertices setting was applied, and the pairs of the
opposite vertices were set as seen in Figure 10.
4.2. Mesh generation
After the block structure was ready, the next step was to generate a high quality
mesh. In order to reduce engineering time to prepare CFD simulations usually
unstructured meshes are used, considering the fact that unstructured meshes are
easy to obtain for complex geometries too. Although, generating a high quality
structured computational domain is a more complicated task, in particular cases it
can provide may advantages over the unstructured mesh. According to the opinions
of many, the generating of really fine quality grids is an art.
Edge meshing parameters were used to get a fine quality mesh. The mesh size was
carefully controlled near the walls in order to capture the aerodynamic behaviour
near the boundary layer, which is important to understand Darrieus turbine
33
aerodynamics. The y+ resolution has to be around 1 in order to reproduce the flow
near the blades correctly.
The boundary layer is measured using the dimensionless wall distance parameter
y+:
𝑦+ =𝜌𝑢𝜏𝑦
𝜇 (5.2.1)
where y is the normal distance form wall at the cell centre, 𝑢𝜏 = √𝜏𝑤/𝜌 is the friction
velocity and 𝜏𝑤 = 𝜇𝜕𝑢/𝜕𝑛 is the wall shear stress, defined by the normal velocity
gradient at wall [22].
The y+ is a non-dimensional distance which shows how fine or coarse a mesh is for
a particular flow pattern. The y+ should be in most modern commercial software
either below 1 (full resolution of boundary flow) or above 30 (wall functions). The
turbulence model used in this study requires fine mesh near the walls.
To capture the boundary layer flow with enough precision, the vicinity of the blades
was covered with a very fine mesh. Different levels of grid resolutions were tested
in STAR-CCM+ to reach y+<1. Thus, the distance of the first row of nodes in
direction normal to the blade’s wall was 0.0033 mm. The growth factor of 1.175 was
set on the O-grid area edges. In the near blade area the mesh size is never larger
than 4.75 mm. Figure 12 shows the O-gird around a blade.
Figure 12 O-type grid around the airfoil
34
Figure 13 a) shows the grid on the leading edge, while 13 b) shows the grid on the
trailing edge.
a.) Grid on the leading edge
b.) Grid on the trailing edge
Figure 13 Closer view of the O-grid
The boundary layer effect was considered on the shaft as well, thus the distance of
the first row was carefully chosen and the same growth factor was used on the block
edges. In the areas of the rotor farther from the blade and shaft, the edge meshing
parameters were used to obtain a high quality mesh. The mesh size is nowhere
larger than 13.75 mm in the rotor far-field area with a growth rate of 1.175. The
maximum mesh sizes and the growth rate were taken from previous studies [17],
[18]. After all the settings were applied, smoothing was applied for the orthogonality
of the mesh in order to obtain an even finer mesh. Thus high quality structured mesh
was generated for the rotor. Figure 14 shows the mesh of the 120° section of a rotor.
Figure 14 Mesh on the 120° section of the rotor
35
To get a complete H-Darrieus rotor, the 120° section was copied and rotated.
However, since STAR-CCM+ does not accept a structured mesh pattern, the
structured mesh was converted into unstructured mesh before the mentioned step.
Then, the mesh was checked for possible errors like periodicity, uncovered faces,
unconnected vertices and single elements. Figure 15 shows the mesh on the rotor
domain.
Figure 15 Computational mesh on the rotor domain
The far-field domain was prepared separately in another ICEM mesh generating
process. The far-field mesh is less dense compared to the mesh in the rotor domain.
The mesh density has to be much higher for the rotating domain than for the stator
domain in order to capture the fine details of vortices.
The mesh of the far-field zone is block structured as well. Near the rotor zone an O-
grid was applied. The mesh sizes were controlled carefully. The maximum mesh
sizes and growth rate were taken from the former studies, as in the case of the rotor.
A growth rate of 1.175 was used here as well. At the far-field’s interface the cells
have the same dimensions as the largest cells on the rotor domain interface in order
to reduce the interpolation errors of non-conformal mesh. A stator-domain mesh
was saved into a separate file, then this mesh was opened in the other process and
fit together with the rotor domain mesh. The whole computational mesh is shown in
Figure 16 for both the stator zone and the rotor zone.
36
Figure 16 Computational mesh on the whole domain
Two meshes were created with two different resolution of the grid on the blade. In
the first case, the resolution was 0.75 while in the second case it was 0.5, hence a
coarse mesh and a fine mesh were obtained. The meshes prepared for the whole
computational domain have about 700,000 cells for the coarse grid and 1,280,000
cells for the fine drid. Both the meshes have excellent quality: the quality criterion
and the orthogonal quality show very good values in both of the meshes. All the
values are well above the requirements. The y+ has a good value, well below the
limit of 1.
4.3. Final steps
After the quality of mesh was checked, the solver was selected. Then the
boundary conditions were set, because it is very important to define the correct
boundary conditions to reproduce the physical problem.
The velocity inlet and pressure outlet were considered on the left and right
boundaries of the domain, respectively. The two horizontal sides of the rectangular
domain were set as symmetry boundary conditions. In order to ensure the continuity
in the flow field between the rotor domains a stator domain, the circumference
37
around the circular opening centred on the turbine rotational axis, was set as an
interface like the circumference around the rotor domain. The rotor domain
simulates the revolution of the turbine, therefore sliding mesh was needed. Wall-
type boundary conditions were used for blades and the shaft.
Finally, the mesh was exported into readable format by STAR-CCM+. In the solver,
the mesh was checked again, which did not indicate any problem.
4.4. Application of the script to different airfoils
The grid generation process was recorded by the ICEM CFD into a script. This
script was tested on several airfoil profiles and proved that it is able to generate fine
quality mesh for different profiles. Figure 17 shows script generated meshes around
different asymmetrical blades.
Figure 17 Computational mesh generated by the script automatically for asymmetrical airfoil profiles
The quality criterion and the orthogonal quality values were well above the
requirements, thus the script was built into the OPAL++ optimisation software as an
option to choose structured mesh as mesh generation method.
38
5. COMPUTATIONAL RESULTS
The computations were performed at tip speed ratio TSR=2, 3.3 and 4.5 on
coarse mesh, while on the fine mesh only at TSR=2 and 3.3, because at higher
TSRs, the differences would not be significant between the two structured meshes
due to the decreased complexity of the flow. Thus, in order to reduce the
computational time TSR=4.5 was not simulated on the fine mesh.
The aerodynamic simulation of Darrieus wind turbines is very complicated because
the flow around the blades is extremely transient with strongly varying angle of
attack. With decreasing tip speed ratio the angle of attack increases and the blade
goes into deep stall. The theoretical analytical angle of attack (ignoring the
expansion of streamlines) is shown in Figure 18 at TSR=2, 3.3 and 4.5. In the figure
it is clearly visible that below TSR=4.5, the angle of attack is over the boundary of
static stall in at least two domains.
Figure 18 Angle of attack in the function of blade azimuth angle at different TSRs
At TSR=4.5 it can be seen that the maximum angle of attack is around 12-13°, which
is the same as the limit of static stall for most classic airfoils [22]. In contrast, at
TSR=3.3 the angle of attack reaches 17°. However, at TSR=2 the angle of attack is
over 30°, which together with the fast change of the angle of attack results in deep
dynamic stall. At high TSR values the simulation does not cause problems for the
turbulence models, however with the increase of the angle of attack the flow physics
becomes very complex.
39
In the following, the computational results are presented in two sub-chapters, where
the results of the former study using partially structured mesh are compared to the
results of the new computations using structured meshes. In the first sub-chapter,
the comparison of aerodynamic coefficients are presented, then the residual errors
and the computational times are compared.
5.1. Comparison of aerodynamic coefficients
The flow properties, such as the torque coefficient (CT), drag coefficient (CD), lift
coefficient (CL) and the power coefficient (CP) were obtained from the last revolution.
Consequently, in this section the figures show the coefficients in the last revolution
with respect to the first blade.
The partially mesh used in the former investigations was denoted as unstructured
mesh using the abbreviation of US. The coarse structured mesh with 750,000 cells
and the fine structured mesh with 1,128,000 cells were denoted as S-750k and S-
1280k, respectively.
5.1.1. Torque coefficient for one blade
In the following, the torque coefficient is presented in the function of blade azimuth
angle (Θ) where the blade azimuth angles correspond to the angles shown in the
Figure 19.
Figure 19 Blade azimuth angles
40
Figure 20 shows the comparison of coarse structured and fine structured meshes
for torque coefficient at TSR=2.
Figure 20 Comparison of CT for coarse and fine structured meshes at TSR=2
From 0° the blade enters the upstream region, then with a low angle of attack, both
meshes show very good performance and provide similar results. Between 90°and
160° the blade reaches the maximum angle of attack and this results in dynamic
stall, which can be observed from the prominent CT values (due to the negative
rotation direction, positive CT values indicate loss of performance). The blade loses
further performance between 210° and 330°, due to the interaction with the wake
which was caused by the blade in the earlier positions and due to the Kármán vortex
street caused by the shaft. Although differences can be observed between the
curves, their behavior is qualitatively similar and the time average is similar too,
while the quantitative difference arises from the complicated blade vortex
interaction, which is the consequence of insufficient mesh resolution. This
phenomenon is well known, since the computation of the vortex structure behind a
shaft alone requires extremely large resources [31]. The simulation of these
phenomena are not feasible with URANS turbulence models, but would require LES
or DNS based computations. However, it is observable in the figure, that in the
region where the blade interacts with the vortices the performance fluctuates around
zero, while in the upstream region, which supplies the performance, the results of
both meshes are the same.
41
Figure 21 Difference between coarse and fine structured meshes at TSR=2
Figure 21 shows the difference between the two meshes. It can be observed in the
figure that there are two regions where the difference is more significant: the
dynamic stall region and the wake interaction. In the other regions, the difference is
fluctuating around zero. The dynamic stall starts around 100°, in the upper part of
the upstream region, while the wake interaction is around 270°. The large amount
of electricity is generated in the lower part of the upstream region, where the angle
of attack is small.
Figure 22 shows the comparison of unstructured and coarse structured meshes for
CT at TSR=2.
Figure 22 Comparison of CT for unstructured and coarse structured meshes at TSR=2
42
Except for the large difference that can be seen around 270°, which is the wake
interaction with the blade, the results of unstructured mesh and coarse structured
are closer to each other than the two results of the structured meshes.
Comparison of unstructured and fine structured meshes for CT at TSR=2 can be
seen in Figure 23.
Figure 23 Comparison of CT for unstructured and fine structured meshes at TSR=2
The characteristics and the behavior of the changes mostly correspond to the earlier
described process. Figures 22 and 23 show that dynamic stall takes place between
90° and 150° and the recovery finishes around 150°. In this area, nearly the same
difference can be observed in the coarse and the fine structured meshes, while in
the wake interaction the fine structured mesh is closer to the results with the
unstructured mesh (this may be due to fact that the unstructured mesh used 0.325
mm resolution on the blades). The largest difference can be observed in the wake
interaction region in the case of the fine structured mesh. The dynamic stall region
values are fairly close to each other in all the cases. There are larger differences
around 210° in both cases in the region where the blade interact with the vortices
shed earlier from the dynamic stall. In the remaining regions the values are nearly
the same.
Regarding to the fact that it is not easy to decide which structured mesh is closer to
the unstructured solution, because the differences between the unstructured and
structured meshes are quite small, Figure 24 helps to decide this. Figure 24 shows
the differences between the unstructured and structured meshes.
43
Figure 24 Difference between unstructured and structured meshes at TSR=2
In the dynamic stall region the coarse mesh is closer to the unstructured mesh, while
in the wake interaction region the higher resolution structured mesh is closer at 270°
but not anywhere else. The rest of the regions are almost the same.
Figure 25 shows the vorticity magnitude for the coarse mesh at TSR=2, 3.3 and 4.5,
where the very complicated vortex structure at the low tip speed ratio is clearly
visible, while at higher TSRs the vortex structure is much simpler, thus it is easier to
compute.
At TSR=2 the vortices shed from the blade with dynamic stall and the Kármán vortex
street caused by the shaft can be seen in Figure 25. Due to the complex nature of
the vortex structure at low TSRs, it is very hard to calculate these cases, and this is
the reason why the differences show up between the structured and unstructured
meshes. At higher TSRs, the vortex structure is simpler, as the figures show, thus
the differences experienced at TSR=2 are smaller.
44
a) TSR=2
b) TSR=3.3
c) TSR=4.5
Figure 25 Vorticity magnitude at different TSR values for the coarse structured mesh
45
Figure 26 shows the comparison of CT for coarse and fine structured meshes at
TSR=3.3.
Figure 26 Comparison of CT for coarse and fine structured meshes at TSR=3.3
The two structured meshes give nearly the same result. The only difference can be
experienced in the wake interaction region.
Figures 27 and 28 show the comparison of unstructured and structured meshes for
CT on coarse and fine meshes, respectively.
Figure 27 Comparison of CT for unstructured and coarse structured meshes at TSR=3.3
46
Figure 28 Comparison of CT for coarse and fine structured meshes at TSR=3.3
Considering the differences for the unstructured and structured meshes, the same
tendency can be observed on both of the meshes, which is most likely thanks to the
different resolution. Thus, in order to decide which solution is mesh independent
and where the mesh independency limit is for the exact computation of the wake
interaction, further investigations would be necessary.
At TSR=4.5 the difference is even smaller between results of the meshes due to the
small angles of attack. Figure 29 shows the comparison of unstructured and coarse
structured meshes for CT.
Figure 29 Comparison of CT for unstructured and coarse structured meshes at TSR=4.5
47
A small difference can be observed in the azimuth angle in the wake interaction but
the rest of the values are the same.
The CT average values can be seen in Table 1, while Figure 30 shows the values in
absolute value on a bar chart.
Table 1 Comparison of CT average values for the different meshes
TSR CT average
Unstructured Structured~ 750k Structured~ 1,280k
𝜆 = 2 -0.038 -0.030 -0.034
𝜆 = 3.3 -0.140 -0.142 -0.144
𝜆 = 4.5 -0.072 -0.072 -
Figure 30 Comparison of CT average values for the different meshes on bar chart
In Table 2 the CT maximum values are presented for the different meshes, while
Figure 31 shows the same on a bar chart.
Table 2 Comparison of CT maximum values for the different meshes
TSR CT maximum
Unstructured Structured~ 750k Structured~ 1,280k
𝜆 = 2 0.164 0.141 0.141
𝜆 = 3.3 0.226 0.228 0.229
𝜆 = 4.5 0.144 0.144 -
Figure 31 Comparison of CT average values for the different meshes on bar chart
0
0,05
0,1
0,15
0,2
TSR=2 TSR=3.3 TSR=4.5
CT average
Unstructured Structured- 750k Structured- 1,280k
0
0,05
0,1
0,15
0,2
0,25
TSR=2 TSR=3.3 TSR=4.5
CT maximum
Unstructured Structured- 750k Structured- 1280k
48
It can be seen from the tables and figures that the differences between the meshes
are quite small, and in the case of higher TSRs they are negligible.
As a conclusion, it can be said that the blade performance can be calculated
comparatively well with all three meshes, except for the wake interaction region,
which would require higher order methods.
5.1.2. Comparison of drag coefficients and lift coefficients
In the following, the drag coefficients (CD) and lift coefficients (CL) are presented as
a function of the angle of attack. All the values are transformed from the global
coordinate system to the local rotating coordinate system. The coefficients are
calculated from these forces using the following equations:
𝐶𝐿 =𝐹𝐿
12 𝜌𝑐𝑊2
(5.1)
𝐶𝐷 =𝐹𝐷
12 𝜌𝑐𝑊2
(5.2)
where FL and FD are the lift and drag forces on the blade, respectively, ρ is the
density, c is the camber of the blade and W is the relative wind speed.
Figure 32 shows the comparison of drag coefficient for the two structured meshes
at TSR=2.
Figure 32 Comparison of CD for coarse and fine structured meshes at TSR=2
49
Between angle of attack -15° and 25°, where the blade enters the upstream region
and produces performance, the results are the same; the differences between the
curves are really small or negligible. However, in the dynamic stall region and in the
wake interaction region, where the angle of attack is the highest, the differences
between the two meshes are larger. The same characteristic can be observed in
Figure 33, where CL is compared for the two structured meshes at TSR=2.
Figure 33 Comparison of CL for coarse and fine structured meshes at TSR=2
In the dynamic stall region around AoA 25°, the differences are not significant, while
in the recovery region and in the wake interaction region the differences are larger.
The large displacement between the curves is most probably due to the nature of
the transformation: as the real local angle of attack and local velocities cannot be
computed, the theoretical values have to be used, which do not take into account
the vortex structures, interactions or expansion of streamlines.
Figure 34 shows the comparison of CD for unstructured and coarse structured
meshes at TSR=2.
50
Figure 34 Comparison of CD for unstructured and coarse structured meshes at TSR=2
The differences appear between the meshes in the dynamic stall region, in the
recovery region and the wake interaction region again, but the displacement is
small.
In Figure 35 CD is compared for the unstructured mesh and fine structured mesh at
TSR=2.
Figure 35 Comparison of CD for unstructured and fine structured meshes at TSR=2
The results of the fine structured mesh seem to be closer to those of the
unstructured mesh, which is again probably the result of the similar mesh resolution
51
on the surface of the blade. The displacement between the two curves is even
smaller. The differences between the two results can be observed in the same
regions as on the coarse mesh.
Figures 36 and 37 show the comparison of CL for unstructured and coarse structured
and fine structured meshes at TSR=2, respectively.
Figure 36 Comparison of CL for unstructured and coarse structured meshes at TSR=2
Figure 37 Comparison of CL for unstructured and fine structured meshes at TSR=2
In these figures the same characteristic can be observed as for CD. Both the coarse
mesh and the fine mesh give the same results between AoA -5° and 20°, while in
52
the dynamic stall region, the recovery region and the wake interaction they show
small differences.
The results of drag coefficients and lift coefficients show that the meshes and the
simulations are very sensitive to the vortex shedding.
Figure 38 shows the comparison of CD for coarse structured and fine structured
meshes at TSR=3.3, while Figure 39 shows the same for CL.
Figure 38 Comparison of CD for coarse and fine structured meshes at TSR=3.3
Figure 39 Comparison of CL for coarse and fine structured meshes at TSR=3.3
53
The two curves are practically the same, except at the highest angle of attack in the
wake interaction, which results a slightly different hysteresis curve. The same
phenomenon can be observed in the comparison of unstructured and structured
meshes shown in Figures 39- 42.
Figure 40 Comparison of CD for unstructured and coarse structured meshes at TSR=3.3
Figure 41 Comparison of CL for unstructured and coarse structured meshes at TSR=3.3
54
Figure 42 Comparison of CD for unstructured and fine structured meshes at TSR=3.3
Figure 43 Comparison of CL for unstructured and fine structured meshes at TSR=3.3
In the most of the regions, it is very difficult to define which structured mesh is closer
to the unstructured mesh, but at high angles of attack, the difference is smaller
between the fine structured mesh and the unstructured mesh than the difference
between the unstructured and coarse structured meshes.
Figures 44 and 45 show the comparison of CD and CL for unstructured and coarse
structured meshes at TSR=4.5.
55
Figure 44 Comparison of CD for unstructured and coarse structured meshes at TSR=4.5
Figure 45 Comparison of CL for unstructured and coarse structured meshes at TSR=4.5
The differences between the two curves are negligible; the only displacement
appears in the wake interaction region at the highest angle of attack.
Table 3 and Figure 46 show the comparison of average drag coefficient values for
the unstructured and structured meshes.
Table 3 Comparison of CD average values for different meshes
TSR CD AVERAGE
Unstructured Structured~ 750k Structured~ 1,280k
𝜆 = 2 0.570 0.530 0.565
𝜆 = 3.3 0.919 0.920 0.926
𝜆 = 4.5 1.040 1.037 -
56
Figure 46 Comparison of CD average values for the different meshes on bar chart
The values are quite close to each other, the differences at higher TSRs are
negligible.
In Table 4 and Figure 47 the maximum CD values are presented.
Table 4 Comparison of CD maximum values for different meshes
TSR CD maximum
Unstructured Structured~ 750k Structured~ 1,280k
𝜆 = 2 0.747 0.853 0.885
𝜆 = 3.3 1.175 1.176 1.178
𝜆 = 4.5 1.434 1.429 -
Figure 47 Comparison of CD maximum values for the different meshes on bar chart
The characteristic is similar to the average CD, at higher TSRs the values are almost
the same, while at TSR=2 the differences are bigger but not significantly.
Table 5 shows the comparison of average lift coefficient values for the different
meshes, while Figure 48 shows the CL averages in absolute value on a bar chart.
Table 5 Comparison of CL average values for different meshes
TSR CL average
Unstructured Structured~ 750k Structured~ 1,280k
𝜆 = 2 0.018 0.022 0.019
𝜆 = 3.3 -0.109 -0.109 -0.107
𝜆 = 4.5 -0.155 -0.150 -
0
0,5
1
1,5
TSR=2 TSR=3.3 TSR=4.5
CD average
Unstructured Structured- 750k Structured- 1280k
0
0,5
1
1,5
2
TSR=2 TSR=3.3 TSR=4.5
CD maximum
Unstructured Structured- 750k Structured- 1280k
57
Figure 48 Comparison of CL average values for the different meshes on bar chart
The tendency is almost the same as in the case of the CD average. The CL average
values at TSR=2 are closer to each other on the unstructured and fine structured
mesh, while at TSR=3.3 the unstructured and the coarse structured meshes show
the closer values.
In Table 6 and Figure 49 the maximum lift coefficient values are compared for the
unstructured and structured meshes.
Table 6 Comparison of CL maximum values for different meshes
TSR CL maximum
Unstructured Structured~ 750k Structured~ 1,280k
𝜆 = 2 0.359 0.323 0.324
𝜆 = 3.3 0.407 0.407 0.400
𝜆 = 4.5 0.626 0.624 -
Figure 49 Comparison of CL maximum values for the different meshes on bar chart
At TSR=2 the two different structured meshes show the same deviation, while at
TSR=3.3 the results of the coarse structured mesh are closer to the unstructured
results. At TSR=4.5 the difference between the CL maximum values is negligible.
In summary, the CD and CL values show very good agreement for the unstructured
and the structured meshes. At higher TSRs the differences are mostly quite small
or negligible, while at TSR=2 the deviation is not significant.
0
0,05
0,1
0,15
0,2
TSR=2 TSR=3.3 TSR=4.5
CL avergage
Unstructured Structured- 750k Structured- 1280k
0
0,2
0,4
0,6
0,8
TSR=2 TSR=3.3 TSR=4.5
CL maximum
Unstructured Structured- 750k Structured- 1280k
58
5.1.3. Comparison of power coefficients
The power coefficient is the most important value for VAWTs. The investigations
and the computations are mostly performed in order to define and improve the
power coefficient of the wind turbine. Thus this value plays an important role in this
current simulation, to find whether the values show a significant difference or not.
Table 7 and Figure 50 show the comparison of objective power coefficient values
for unstructured and structured meshes.
Table 7 Comparison of CP objective values for different meshes
TSR CP- objective
Unstructured Structured~ 750k Structured~ 1,280k
𝜆 = 2 0.0764 0.061 0.069
𝜆 = 3.3 0.464 0.470 0.476
𝜆 = 4.5 0.326 0.326 -
Figure 50 Comparison of CP objective values for the different meshes on bar chart
The differences at TSR=3.3 and 4.5 are quite small, while at TSR=2 they are not
significant. Therefore it can be said that the structured meshes do not provide much
better accuracy, since the divergences between the coefficients presented in this
chapter are not significant.
5.2. Comparison of residual errors and computational times
The coarse structured mesh (with around 750,000 cells) and the unstructured
mesh were initialized to the flow field with 15 revolutions using coarse time
resolution. Then one revolution was performed using fine time resolution at TSR=2.
The computations for both meshes were performed on the same computer. The
computational time needed for the computation of the last revolution was normalized
by the number of cells and recorded. The unnormalized residual errors were
recorded and then compared with the following results.
0
0,2
0,4
0,6
TSR=2 TSR=3.3 TSR=4.5
CP objective
Unstructured Structured- 750k Structured- 1280k
59
The normalized computational time for the last revolution using coarse structured
and unstructured meshes 0.5603 min/kcell are and 0.5753 min/kcell, respectively.
These values are very similar, which indicates an efficient parallelization of STAR-
CCM+.
Figure 51 shows the residual errors of the continuity equation.
Figure 51 Residual errors of continuity equation
As it can be seen, the structured mesh provides near constant lower residual errors
compared to the unstructured mesh. The decrease in the residual errors is the result
of the increased orthogonality of the mesh. The same tendency is the same for the
residual errors of momentum equations, see Figure 52.
Figure 52 Residual errors of x-momentum
60
For the turbulent kinetic energy the residuals are the same order of magnitude, see
Figure 52.
Figure 53 Residual errors of total kinetic energy
61
6. CONCLUSIONS
As the previous chapter showed, the coefficients of the wind turbine obtained
with the numerical simulations using structured and unstructured meshes are close
to each other; the differences are very small or negligible. At higher TSRs (3.3 and
4.5), the differences are not significant; the results are almost the same. At the
smallest TSR (2), the differences - due to the very complex vortex structure - are
slightly bigger but still not significant. The presence of dynamic stall and the wake
interaction have an effect on the computations, thus at TSR=2 the curves of the
coefficients are different in these regions. However, as the results show, the
computations obtained with the structured meshes are able to simulate properly the
dynamic stall phenomena, while the accurate computation of the wake interaction
would require a higher order computational method. The more accurate computation
of the wake interaction with structured mesh would require further mesh
independency investigations. For the accurate computation of the wake interaction
I suggest using Large Eddy Simulations using a 3D model.
Nevertheless, the model is appropriate for the investigation of the performance of
an H-type Darrieus turbine, since the wake interaction has no significant influence
on the power generation of the turbine. The power coefficients given by the
computations are realistic and can be used for the performance optimization of an
H-Darrieus wind turbine.
In some cases, the results of the coarse mesh are closer to the results of the
unstructured mesh, while there are some cases where the fine mesh shows better
agreement. However, in general, taking into account all the available results
obtained with the simulations, it can be said that the fine structured mesh is slightly
closer to the unstructured mesh.
The advantage of the structured mesh is the residual errors. This decrease
originates from the orthogonality, which simplifies the computation of the first and
second derivatives based on the Least-Square Method and increases the quality of
the derivatives. However, it is very difficult to create a structured mesh and it
requires a longer time compared to an unstructured. The unstructured mesh is much
easier to obtain. Moreover, for the same mesh size on the blade the structured mesh
requires far more element and thus far longer computational times than an
unstructured mesh, because at the structured mesh the mesh resolution on the
62
blade determines the global resolution as well due to the prescribed conformity on
the interiors.
In summary, the differences between the results on structured and unstructured
meshes are not significant, thus the necessity to use structured mesh for all
computations does not seem to be valid for the present case. By probably increasing
the mesh resolution near to the blade, the structured mesh would give a slightly
more accurate solution but the number of cells would increase significantly and this
would result in an increase in computational time.
63
7. ACKNOWLEDGEMENTS
Firstly, I would like to express my sincere gratitude to Prof. Szilárd Szabó and
Dr. Gábor Janiga for the opportunity and financial support to complete my Master’s
thesis at the Otto von Guericke University in Magdeburg.
I am greatly indebted to my supervisor, László Daróczy, for his invaluable guidance
and for his continuing help. Without his advice and help this thesis would not have
been possible. I am also very grateful to Dr. Gábor Janiga for his great and valuable
suggestions, help and friendly assistance during the process of this work and my
stay in Magdeburg.
Furthermore, I gratefully acknowledge my supervisor at the University of Miskolc,
Péter Bencs, for all his support and advice - not only during writing my thesis, but
for all the help during the Master course.
In addition, I am extremely grateful to Robin Nagano for checking the English of my
thesis and I would like to gratefully acknowledge her very useful and valuable
advice.
I am also thankful to all of my friends and those people who are associated with me
and whose contribution helped this thesis attain a successful completion. I am
privileged to have such friends helping me at the required moments.
Finally, most of all, sincere acknowledgement to my family for their love and support
throughout my educational journey. I am forever indebted to my parents and brother
for their patience and endless encouragement, when it was most required. At last, I
owe a debt of gratitude to my fiancée, Diána, for her constant support.
64
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