Queen Mary, University of London

CFD Study of a Wind Turbine Rotor

Federico Malatesta

Supervisor : Professor John Williams

April, 2012

School of Engineering and Materials Science

Third Year Project

DEN 318

This report entitled:

CFD Study of a Wind Turbine Rotor

was composed by me and is based on my own work. Where the work of the others has

been used, it is fully acknowledged in the text and in captions to table illustrations. This

report has not been submitted for any other qualification.

Name: Federico Malatesta

Signed:

Date: April 4, 2012

Abstract

There is nowadays strong debates in regard to the effects on the environment of fossil-

based energy sources and countries have applied new energy policies with the aim to be

less dependent on such energy sources while increasing the development of energies based

on renewable sources such as wind, sun and water. Wind based energy is having an

important role, but to properly develop, more advanced design tools are needed.

Computational Fluid Dynamics is here being applied to the study of a full scale small-

sized two-bladed wind turbine to gain a general understanding of the aerodynamics and

performance features. The wind turbine is based on the one used in the well-known NREL

Unsteady Aerodynamics Experiment Phase VI.

By using the commercial CFD package ANSYS FLUENT, this study tried to simulate

the experiment for wind speed velocities of 7, 10 and 15 m/s. Results of pressure and

torque have been directly compared and suggested that results appear to provide accurate

results for pre-stall velocities, whereas for higher velocities where stall effects occur, the

study fails to provide acceptable data.

Contents

List of Symbols iv

List of Figures vii

List of Tables x

1 Introduction 1

1.1 World Energy Today . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Overview of Wind Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 NREL Unsteady Aerodynamics Experiment Phase VI . . . . . . . . . . . . 4

1.4 Motivation and Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.5 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Aerodynamics and Performance of Wind Turbines 9

2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2 Working principles of HAWTs . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3 Aerodynamics of aerofoils . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.4 Wind turbine aerodynamics theory . . . . . . . . . . . . . . . . . . . . . . 12

2.4.1 Actuator disk method . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.4.2 Blade element method . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.4.3 Navier-Stokes equation solvers . . . . . . . . . . . . . . . . . . . . . 18

3 Numerical Modelling of Wind Turbines 20

3.1 Navier-Stokes equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.2 Turbulence Modelling and Simulation . . . . . . . . . . . . . . . . . . . . . 21

3.2.1 SST κ− ω model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.3 Computational mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.4 FLUENT NS Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

i

3.4.1 Single moving reference frame . . . . . . . . . . . . . . . . . . . . . 26

4 Method 29

4.1 Geometry model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.2 Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.2.1 Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.2.2 Prismatic layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.3 FLUENT setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.3.1 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.3.2 Solution method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.3.3 Post-processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5 Results 40

5.1 Flow visualisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.1.1 U∞ = 7m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.1.2 U∞ = 10m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.1.3 U∞ = 15m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

5.2 Pressure distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

5.2.1 Pressure coefficients at U∞ = 7m/s . . . . . . . . . . . . . . . . . . 46

5.2.2 Pressure coefficients at U∞ = 10m/s . . . . . . . . . . . . . . . . . 47

5.2.3 Pressure coefficients at U∞ = 15m/s . . . . . . . . . . . . . . . . . 48

5.2.4 Surface blade pressure and limiting streamlines . . . . . . . . . . . 49

5.3 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

6 Discussion 52

6.1 Comparison with the NREL Phase VI experiment . . . . . . . . . . . . . . 52

6.2 Comparison with previous work . . . . . . . . . . . . . . . . . . . . . . . . 54

7 Conclusions and future work 58

7.1 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

Acknowledgements 60

References 61

A NREL Phase VI blade data 65

ii

B Wake flow visualization 67

B.1 U∞ = 10m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

B.2 U∞ = 15m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

iii

List of Symbols

Acronyms

BC Boundary Condition

CFD Computational Fluid Dynamics

DNS Direct Numerical Simulation

FVM Finite Volume Method

HAWT Horizontal Axis Wind Turbine

LES Large Eddy Simulation

MRF Multiple Moving Reference Frame

NREL National Renewable Energy Laboratory

NS Navier-Stokes

SRF Single Moving Reference Frame

SST Shear Stress Transport

TSR Tip Speed Ratio

UAE Unsteady Aerodynamic Experiment

UNFCC United Nations Framework Convention on Climate Change

VAWT Vertical Axis Wind Turbine

Greek letters

λr Local speed ratio

α Angle of attack

iv

ηmech Mechanical or electrical efficiency

ηoverall Overall efficiency

ω,Ω Angular velocity [rad/s]

ρ Density [kg m−3]

λR Blade tip speed ratio

Roman letters

−→r 0 Distance vector of the origin of the moving coordinate system from the origin

of the stationery system

−→v t Translating velocity vector of the moving coordinate system

A Cross-section area [m2]

a Axial induction factor

a′ Angular induction factor

c Aerofoil chord length [m]

CD Coefficient of drag

CL Coefficient of lift

CP Coefficient of power

Cp Coefficient of pressure

CT Coefficient of thrust

D Drag force [N]

L Lift force [N]

p Pressure [N m−2]

Q Torque [Nm]

Re Reynolds number

T Thrust [N]

t time [s]

v

U∞ Freestream wind velocity [m/s]

Ud Flow velocity going through the rotor [m/s]

Uw Flow velocity in the rotor wake region [m/s]

y+ Non-dimensional height of the first cell from the solid wall

τ Shear and normal surface force [N m−2]

vi

List of Figures

1.1 Dutch windmills, World Heritage Site, Kinderdijk, The Netherlands . . . . 2

1.2 Top 10 Countries by Wind Energy Capacity . . . . . . . . . . . . . . . . . 3

1.3 NASA Ames National Research Centre Complex (a) and the wake flow

visualization of the NREL rotor (b). . . . . . . . . . . . . . . . . . . . . . 4

1.4 NREL S809 blade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1 Schematic view of a wind turbine components . . . . . . . . . . . . . . . . 10

2.2 Aerofoil profile as seen by virtually cutting a wind turbine . . . . . . . . . 11

2.3 Parts of an aerofoil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.4 Summary of forces acting on an aerofoil . . . . . . . . . . . . . . . . . . . . 12

2.5 Stream-tube concept used for Actuator Disk method . . . . . . . . . . . . 13

2.6 Variation of Ct and Cp as function of induction factor a . . . . . . . . . . . 15

2.7 Power coefficient variation with TSR . . . . . . . . . . . . . . . . . . . . . 18

3.1 Main steps of a pressure-based solution . . . . . . . . . . . . . . . . . . . . 26

3.2 Single moving reference frame . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.1 Three dimensional model of the NREL Phase VI blade . . . . . . . . . . . 29

4.2 Aerofoil profiles of the blade . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.3 Blade tip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.4 Semi-cylindrical domain and dimensions . . . . . . . . . . . . . . . . . . . 32

4.6 Surface mesh of the blade . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.7 Details of the mesh of the blade tip . . . . . . . . . . . . . . . . . . . . . . 32

4.5 Section view of the volume mesh showing higher density of elements in

proximity of the downstream wake. . . . . . . . . . . . . . . . . . . . . . . 33

4.8 Section view of the volume mesh at 30 % of the blade . . . . . . . . . . . . 34

4.9 Details of the prismatic layers in proximity of the leading edge (a) and

trailing edge (b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

vii

4.10 Names given to mesh parts . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.11 Convergence plot of Cm and CL at U∞ = 7m/s . . . . . . . . . . . . . . . . 38

5.1 Streamlines (left) and contours (right) of relative velocity magnitude in

m/s. U∞ = 7m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.2 Contours of velocity magnitude for all radial stations in m/s. U∞ = 7m/s . 43

5.3 Streamlines (left) and contours (right) of relative velocity magnitude in

m/s. U∞ = 10m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.4 Contours of velocity magnitude for all radial stations in m/s. U∞ = 10m/s 44

5.5 Streamlines (left) and contours (right) of relative velocity magnitude in

m/s. U∞ = 15m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

5.6 Contours of velocity magnitude for all radial stations in m/s. U∞ = 15m/s 45

5.7 Cp at U∞ = 7m/s r/R = 0.3 . . . . . . . . . . . . . . . . . . . . . . . . 46

5.8 Cp at U∞ = 7m/s r/R = 0.63 . . . . . . . . . . . . . . . . . . . . . . . . 46

5.9 Cp at U∞ = 7m/s r/R = 0.95 . . . . . . . . . . . . . . . . . . . . . . . . 46

5.10 Cp at U∞ = 10m/s r/R = 0.3 . . . . . . . . . . . . . . . . . . . . . . . . 47

5.11 Cp at U∞ = 10m/s r/R = 0.63 . . . . . . . . . . . . . . . . . . . . . . . 47

5.12 Cp at U∞ = 10m/s r/R = 0.95 . . . . . . . . . . . . . . . . . . . . . . . 47

5.13 Cp at U∞ = 15m/s r/R = 0.3 . . . . . . . . . . . . . . . . . . . . . . . . 48

5.14 Cp at U∞ = 15m/s r/R = 0.63 . . . . . . . . . . . . . . . . . . . . . . . 48

5.15 Cp at U∞ = 15m/s r/R = 0.95 . . . . . . . . . . . . . . . . . . . . . . . 48

5.16 Limiting streamlines with contours of static surface pressure on the blade

in Pa. U∞ = 7m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.17 Limiting streamlines with contours of static surface pressure on the blade

in Pa. U∞ = 10m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.18 Limiting streamlines with contours of static surface pressure on the blade

in Pa. U∞ = 15m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

5.19 Experimental and computational torque variation with U∞ . . . . . . . . . 50

5.20 Variation of the NREL experimental and computational power output as

function of wind speed velocity . . . . . . . . . . . . . . . . . . . . . . . . 51

5.21 Change of experimental and computational CP as function of TSR . . . . 51

5.22 Variation of computational and experimental CP with wind speed . . . . . 51

6.1 Comparison of computational results of torque obtained from previous work 54

6.2 Computed limiting streamlines comparison from 7 to 15 m/s (top to bottom) 56

viii

A.1 NREL Phase VI wind turbine blade data . . . . . . . . . . . . . . . . . . . 65

A.2 S809 Aerofoil coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

B.1 Front view of the rotor. U∞ = 10m/s . . . . . . . . . . . . . . . . . . . . . 67

B.2 SIde view of the wake. U∞ = 10m/s . . . . . . . . . . . . . . . . . . . . . 68

B.3 Top view of the wake. U∞ = 10m/s . . . . . . . . . . . . . . . . . . . . . 68

B.4 Front view of the rotor U∞ = 15m/s . . . . . . . . . . . . . . . . . . . . . 69

B.5 Side view of the wake U∞ = 15m/s . . . . . . . . . . . . . . . . . . . . . . 70

B.6 Top view of the wake U∞ = 15m/s . . . . . . . . . . . . . . . . . . . . . . 70

ix

List of Tables

1.1 World total primary energy supply . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Phases of the NREL Phase VI experiment . . . . . . . . . . . . . . . . . . 4

4.1 Number of elements and nodes by parts and total . . . . . . . . . . . . . . 35

4.2 Assigned boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.3 Spatial Discretization scheme . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.4 Machine specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

x

Chapter 1

Introduction

1.1 World Energy Today

World’s largest economies are to face important challenges in the next near future; energy

demand is not likely to decrease and simultaneously the need for shifting from fossil fuel

to renewable sources has become a priority.

Even though world’s economies are still in an uncertain financial situation, in 2010 the

world energy consumption grew 5.6 % in 2010 which is the largest increase since 1973 [1]

with fossil fuels still being the major source of energy as can be seen in Table 1.1 [2].

Table 1.1: World total primary energy supply [2]

Fuel %

Oil 32.8

Coal 27.3

Natural gas 20.9

Biofuels and waste 10.2

Nuclear 5.8

Hydro 2.3

Other* 0.8

*Other includes solar, wind, heat, geothermal etc.

Fossil fuels are the main cause of the environmental changes that our planet is expe-

riencing such as Greenhouse effect and air pollution with direct consequences on human

health, further some of the major countries exporting oil petroleum are in rather unstable

political and economical situations including wars.

These listed features, are among the many that caused many countries to adopt new

energy policies aimed at addressing climate changes and gathered together in numerous

occasions such as the Kyoto Protocol in 1997 where more than 160 countries under the

1

United Nations Framework Convention on Climate Change (UNFCC) reached an agree-

ment imposing to the 37 most industrialised economies to decrease greenhouse gas (GHG)

emissions to a level of 5 % compared to 1990 levels over a period of 5 years from 2008 to

2012 [3]. A similar UN conference took place in December 2009 in Copenhagen [4] which

reinforced the goal to set the maximum temperature rise from the pre-industrial era to

2 C. Subsequently, G9 member countries reached an agreement in July of the same year

in which a reduction of global emissions of 50 % by 2050 was set.

Even though no specific strategy was given to reach those targets [4], renewable energy

sources such as wind and sunlight have experienced a large development in the last years

and if properly developed could increase its share in the global energy supply. For example,

according to Jacob and Masters [5], if 214,000-236,000 wind turbines of 1.5 MW rating

were installed in the U.S., roughly 60 % of coil generated energy could be replaced by

wind energy, thus complying with the Kyoto Protocol.

1.2 Overview of Wind Energy

The use of wind as a form of energy dates from 5000 B.C. in Egypt where people navigated

the Nile River on sail boats powered by wind. Windmills were first utilised in China then

in the Middle East for food processing by the 11th century. Then, Europeans imported

this technology to do mechanical work as especially seen in the Netherlands for draining

lakes and rivers (Figure 1.1 ).

Figure 1.1: Dutch windmills, World Heritage Site, Kinderdijk, The Netherlands[6]

With the advent of the Industrial Era, windmills continued to be used and towards

2

the end of the nineteenth century first experiments took place first in the USA and later

in Denmark to generate electricity from wind. Afterwards, years of low interest in wind

energy began and lasted till the oil crisis in the 1970’s, which caused many countries to

seek new forms of energy sources [6].

Nowadays wind power is a fully active contributor to electricity production and as

reported in [7] in the last two decades there have been tremendous advances in the energy

efficiency of wind turbines, in fact a 2006 wind turbine would produce 180 times more

electricity than one at the same location installed 20 years before and at half the cost per

kilowatt-hour (kWh).

Looking at Table 1.1, wind energy as part of renewable energy only represents a small

fraction of the total global energy supply, however the same is not true for many Western

countries; for instance in the European Union, in 2005, energy produced by wind resources

was 2.8 % and is set to reach 22.6 % by 2030 [7]. Similar is the scenario for the United

States where in 2008 wind energy amounted to 2.7 % and is foreseen that it will reach

20% by 2030 [8].

European countries, along with the USA and China, generate most of the world wind

power (see Figure 1.2) and also host leading wind turbine manufacturing companies, in

fact in 2004 it was estimated that 82 % of all turbine in the world were built by European

companies [7].

Figure 1.2: Top 10 Countries by Wind Energy Capacity [9]

3

1.3 NREL Unsteady Aerodynamics Experiment Phase VI

Although the overall flow physics of wind turbines was understood, experimental data

were needed to promote advance in technology and to confirm theoretical and numerical

models. This task was addressed by more than one research centre such as the National

Renewable Energy Laboratory in the USA and later by a consortium composed mainly by

european institutions named MEXICO (Model rotor EXperiments In COntrolled COndi-

tions) concluded in 2006.

(a) (b)

Figure 1.3: NASA Ames National Research Centre Complex (a) and the wake flow visualization of theNREL rotor (b).

In this report, given the large amount of literature, the experiment carried out by the

NREL will be the one used for CFD simulation, namely NREL Unsteady Aerodynamics

Experiment (UAE) Phase VI [10] [11]. This experiment took place in 2000 at the NASA

Ames Research Centre 80 ft × 120 ft wind tunnel (the largest wind tunnel in the world).

The wind tunnel has capability of reaching speed in the test section up to 50 m/s but

in the experiment, speed ranged from 5 to 25 m/s which corresponds to real cut-in and

cut-off wind speeds and its typical turbulence intensity is generally less than 0.5 %. In

figure Table 1.2 a summary of the different experimental phases is shown.

Table 1.2: Phases of the NREL Phase VI experiment [10]

Case Air Density ( kgm3 ) Wind speed (m

s ) Rotational speed (RPM)

1 1.244 5.0 71.7

2 1.246 7.0 71.9

3 1.246 10.0 72.1

4 1.227 13.1 72.1

5 1.224 15.1 72.1

6 1.221 20.1 72.0

7 1.220 25.1 72.1

The rotor featured a rated power of 19.8 kW with two twisted blades based on the

4

S809 aerofoil with a diameter of 10.1 m (see Figure 1.4). The rotational speed was kept

constant for each phase of the experiment at a value of roughly 72 RPM. The rotor was

supported by a 0.4 m diameter tower with height of 12.2 m (see Figure 1.3). Yawed and

non-yawed flow configurations were tested as well as upwind and downwind ones.

One blade of the rotor was equipped with pressure taps at 30, 47, 63, 80 and 95 % of

the blade span allowing to have pressure reading and subsequently, values of Cn, Ct and

Cm were obtained.

Figure 1.4: NREL S809 blade [10]

5

1.4 Motivation and Objectives

Wind power has great potential to increase its efficiency and therefore its development.

Aerodynamics is one of the major factor that affects the functioning of wind turbines

and the NREL experiment was indeed aimed at obtaining a clear overview of the flow

behaviour along with structural dynamics. But also aeroacoustics, aeroelasticity, wind

farm design and boundary layers dynamics are important related scientific fields that

need to be better explored [11].

Prior to recent experiments, theoretical models such as the Actuator Disk Method

were developed and were able to give quite accurate results for performance prediction,

then improvements were achieved with the Blade Element Method which allowed to look

closer at the dynamics of rotating blades but was mainly valid in two dimensions and

approximate corrections had to be made to obtain realistic three-dimensional results.

These methods are therefore not enough to progress in wind power.

A quite recent alternative came from Computational Fluid Dynamics which thanks to

experiments such as the NREL Phase VI, could rely on a validation tool.

The goal of this research project is indeed to reproduce the NREL Phase VI experiment

by using the commercial CFD package called ANSYS FLUENT. To achieve this, a number

of steps, which also represent objectives of this work, were laid out at the beginning of

the project which can be summarised as follows:

1. Research and acquire basic knowledge of wind turbine aerodynamics and related

numerical modelling;

2. Carry out extensive reading of related scientific publications or any relevant docu-

mentation;

3. Generate an adequate mesh for the problem;

4. Identify and apply a correct simulation setup;

5. Extract results and compare with experimental data and results from previous nu-

merical studies;

6. Identify source of errors.

6

1.5 Literature review

One very important stage in the progress of the project is to acquire as much information

regarding past and current state of the wind turbine aerodynamics paying particular

attention to what has been achieved in CFD regarding the NREL UAE experiment.

In 2000, in conjunction with the NREL report release a total number of 18 institutions

from Europe and the United States participated in modelling the experiment using dif-

ferent models such as Panel and Vortex methods, BEM and NS solvers. The results and

comparison were published in [12].

The NREL UAE experiment provided to be an important validation tool for a wide

range of computational methods and after the release of this material, a large numbers of

scientific papers have been published by institutions from many countries. Since reporting

a full list of papers would a very laborious process, only the most important and the ones

that have been of great help for this project will be reported.

The PhD theses by Carcangiu [13] and Ivanell [14], provided to be important documents

for the scope of this project, giving important specific details regarding the simulation of

wind turbines, in particular, the thesis by Carcangiu provided useful guidelines for wind

turbines modelling using the code FLUENT.

Equally, Master’s theses also were found to give useful information on this topic such as

the one from Chen [15] and Mozafari [16], with the former regarding the simulation of the

NREL experiment and the latter concerning the numerical modelling of a tidal turbine,

both using FLUENT. Instead, Gupta [17] modified the code PUMA2 to conduct Large

Eddy Simulation (LES) including the NREL experiment; Gupta also collaborated with

Sezer-Uzol and Long to carry out a comparison of inviscid and LES results [18] . Again

the same experiment was studied by Disgrakar [19] making use of the code OpenFoam.

In regard to published articles, the NREL Phase VI experiment has been simulated

using a wide range of numerical methods and turbulence models. Different mesh config-

urations were tested with the NS solver NSU3D by Potsdam and Mavriplis at the Wind

Energy Research Center of the University of Wyoming [20]. A Detached-Eddy simulation

was performed by Johansen et al. [21] using the code EllipSys3D.

Studies were also carried out to improve and optimise aerodynamic characteristics of

the rotor, such as the one performed by Chao and van Dam [22] who modified the original

S809 aerofoil with a thickened inboard part and the sharp trailing edge was replaced with

7

a flatback one.

Regarding CFD studies of the NREL with the use of the FLUENT code, the following

material was also found: [23] [24] [25] [26] [27].

8

Chapter 2

Aerodynamics and Performance of

Wind Turbines

2.1 Overview

There are two main categories of Wind turbines, namely Horizontal Axis Wind Turbines

(HAWT) and Vertical Axis Wind Turbines (VAWT). HAWTs compared to VAWTs have

higher power outputs making them more cost-effective, therefore are today the most

common used concept. However HAWTs operate at their maximum only if the quality

of the wind is high, that is for low turbulence intensity whereas VAWTs can still operate

efficiently [28].

2.2 Working principles of HAWTs

Wind turbines generate power by extracting kinetic energy from the wind and transform-

ing it in mechanical energy and ultimately transformed in electrical energy via a generator.

As the air passes through the rotor, there will be a force distribution acting on the blade,

which subsequently generates a torque acting about the rotor shaft [14]. The process

between the shaft and generator can be of different types and below is a list of the most

currently used ones [14] (Figure 2.1 shows the main components of HAWTs):

1. Wind turbine with gearbox, also called Danish concept : The rotor shaft is connected

to the generator through a gearbox that increases the angular velocity;

2. Wind turbine with gearbox: This is a newer concept and does not require a gearbox

which is substituted by a direct drive;

9

3. Hybrid: This type is a combination of the previous two, and presents a gearbox with

fewer steps. But due to this, the size of the generator has to be larger.

Figure 2.1: Schematic view of a wind turbine components [6]

The environmental air flow is not continuous and is subjected to oscillations in its

magnitude and direction. To overcome this, modern turbines are able to change pitch

and to yaw. Further, angular velocity can also be adjusted following the change in the

wind speed.

The wind speed at which a turbine starts operating is called cut-in and is about 3.5

m/s, then the velocity at which it stops is called cut-off, this value is determined by the

wind turbine manufacture, although generally is around 25 m/s, the RPM is also limited

for safety reasons [13]. Following these reasoning, other three categories can be listed as

follows [14]:

1. Pitch control: As wind speed increases, the pitch angle can be modified in order

to properly adjust to the wind direction. This helps the turbine to reach the rated

power;

2. Stall control: As for the NREL Phase VI turbine, blades are designed to work well

within a specific range of wind speeds. Above this, the blades will encounter stall

and thus a lift drop will be experienced. The maximum power output occurs at the

stall speed;

3. Active stall: Once the rated power is achieved, stall is voluntarily initialised by

pitching the blades.

10

2.3 Aerodynamics of aerofoils

Analysing a section view of a wind turbine, it could be clearly seen that the cross section

of the blade has the shape of an aerofoil profile (Figure 2.2), in fact a blade is built using

aerofoil profiles at different angles and chords belonging to one or more aerofoil families.

It can be then understood first of all, that a two-dimensional aerodynamics of an aerofoil

must be analysed.

Figure 2.2: Aerofoil profile as seen by virtually cut-ting a wind turbine blade [6] Figure 2.3: Parts of an aerofoil

The literature regarding aerofoils is wide (for example [29] [30]) therefore only a brief

review will be reported.

As shown in Figure 2.3, a typical aerofoil has an upper and lower surface. The sharp

rear and the soft front ends of the aerofoil are called trailing edge and leading edge respec-

tively and the line that connects them is named chord line and its total length is c. The

maximum distance between the chord line and mean camber line is called camber. The

angle between the chord line and the direction of the incoming air flow is named angle of

attack, α. As the wind flows over the aerofoil, velocity will increase on the upper surface

and decrease on the lower one, additionally, according to the Bernoulli’s principle:

1

2ρU2 + p = 0 (2.1)

higher pressure will occur on the bottom and lower pressure on the upper part.

11

As can be see in Figure 2.4 the air flowing over the aerofoil generates two forces, one

pointing upward and perpendicular to the wind speed direction called lift L, and one

pointing parallel and in opposite direction of the wind namely drag D caused by pressure

distribution and friction force. The resultant force of lift and drag is called normal force

N. Further, this force distribution acting on the aerofoil will create a moment force which

usually acts at a quarter of the chord length.

Figure 2.4: Summary of forces acting on an aerofoil

As the angle of attack increases so will lift and drag steadily up to a point where the

flow will separate from the aerofoil, at this point, the aerofoil is said to have reached stall.

2.4 Wind turbine aerodynamics theory

Over the years, size of wind turbines increased exponentially and so did the level of

complexity, therefore the then used methods had to be improved from Momentum Theory

till the nowadays softwares capable of solving Navier-Stokes equations.

In this paragraph a brief review of the most important models used for wind turbines

performance and aerodynamics will be illustrated.

As summarised in [13] and [14], the most common models used for the study of wind

turbines or other rotating machineries are as follows:

1. Actuator Disk Method

2. Blade Element Method

3. Navier-Stokes equations solvers

12

2.4.1 Actuator disk method

This method, here being applied in 1-D, is very useful for analysing the energy extracted

by the rotor even though no information is given for the rotor itself. As can be seen in

picture below (Figure 2.5) the rotor is represented by a disk, the incoming free stream

flow is enclosed in a so-called stream-tube with a smaller radius than the disk, then

downstream the rotor the same stream-tube concept is applied to the flow but with a

larger radius.

Figure 2.5: Stream-tube concept used for Actuator Disk method

Thrust T is defined as being the force acting on the stream wise direction and is

obtained by the pressure difference between the two faces of the rotor:

T = ∆pA (2.2)

where A = πr2 is the area covered by the rotor and r is the radius of the rotor.

As can be seen in Figure 2.5, U∞ represents the freestream air velocity, Ud is the flow

speed going through the rotor and Uw is the the one in the wake region.

In using this model the flow is assumed stationery, frictionless and incompressible [31]

therefore the Bernoulli’s principle can be applied through the stream tube and an equation

for the pressure difference occurring through the rotor can be found:

∆p =1

2ρ(U2

∞ − U2w) (2.3)

By applying momentum integral equation to a control volume surrounding all stream

tubes, the following relation can be derived:

T = ρUdA(U∞ − Uw) = m(U∞ − Uw) (2.4)

13

where m is called the mass flow rate.

Then combining equations (2.2), (2.3) and (2.4) the following relation can be derived:

Ud =1

2(U∞ + Uw) (2.5)

Which means that the flow through the rotor travels at a velocity which is the mean

value of the freestream and downstream ones.

By then applying Energy Equation to this control volume, an expression for the Power

can be also found as follows:

P =1

2ρuA(U2

∞ − U2w) (2.6)

Then the following axial induction factor, a can be introduced:

Ud = (1− a)U∞ (2.7)

then combining equation (2.7) and (2.5) the following can be obtained:

Uw = (1− 2a)U∞ (2.8)

if then (2.8) is substituted in (2.7) and (2.4):

P = 2ρU3∞a(1− a)2A (2.9)

and

T = 2ρU2∞a(1− a)A (2.10)

Then available power can be defined as:

Pavl =1

2ρAU3

∞ (2.11)

for which a dimensional parameter, namely CP can be defined as:

CP =P

12ρU3∞A

(2.12)

Likewise, thrust coefficient, Ct is given by:

14

Ct =T

12ρU2∞A

(2.13)

If CP and Ct are plotted against variation of the axial induction factor a (Figure 2.6)

some important features can be observed.

Figure 2.6: Variation of Ct and Cp as function of induction factor a [31]

The maximum CP = 1627

, which occurs for a = 13, is known as the Betz limit, and a = 1

for a = 0.5.

It must be remembered that this theory considers an ideal wind turbine and is known

that for factors greater than 0.5 this theory is no more valid due to increase in the

complexity in the flow behaviour; further a real flow leads to a decrease in the value of

CP,max due to the followings [32]:

• Rotation of the wake downstream the rotor;

• Finite number of blades and related losses;

• Aerodynamic drag.

The power output of the rotor can also be expressed in terms of efficiency:

ηoverall =Pout

12ρAU3

= ηmechCP (2.14)

where ηmech is the mechanical, or electrical, efficiency of the components of the wind

turbine.

Next the effect of rotation will be included in the above explained linear momentum

theory. If ω is used to denote the angular velocity applied to the flow and Ω to denote

15

the actual angular velocity of the turbine rotor and a control volume is created rotating

at the same Ω, the energy equation can be applied in order to obtain an expression for

the pressure difference between just upstream and downstream of the rotor [32]:

p2 − p3 = ρ(Ω +1

2ω)ωr2 (2.15)

it is already been observed in equation (2.2) that the torque is equal to pressure differ-

ence multiplied by area, therefore if (2.15) is multiplied by an element of length dA the

thrust for said element, dT , is:

dT = (p2 − p3)dA = [ρ(Ω +1

2ω)ωr2]2πrdr (2.16)

Then an angular induction factor a′ can be expressed as:

a′ = ω

2Ω(2.17)

Therefore (2.16) becomes:

dT = 4a′(1 + a′)1

2ρΩ2r22πrdr (2.18)

Moreover, a thrust expression can also be written in terms of the axial induction factor

a:

dT = 4a(1− a)1

2ρU2∞2πrdr (2.19)

If then (2.19) and (2.18) are set equal to each other, the following is obtained:

a(1− a)

a′(1 + a′) =Ω2r2

U2∞

= λ2r (2.20)

where λr is the local speed ratio and if the the radius of the rotor, R, is substituted in

the above expression, the parameter tip speed ratio TSR is found:

λr =ΩR

U∞(2.21)

Next, the momentum equation will be applied to the same control volume and for this

case the equilibrium dictates that the torque Q being applied on the rotor must be equal

to the change in the angular momentum of the wake; therefore, if an annular element is

16

considered, the momentum equation reduces to:

dQ = 4a′(1− a)1

2ρU∞Ωr22πrdr (2.22)

Therefore, at this element, power, dP is:

dP = ΩdQ (2.23)

Then, substituting for dQ from and applying the definition of λr, (2.23) becomes:

dP =1

2ρAU3

∞[8

λ2a′(1− a)λ3rdλr] (2.24)

Then, dP can be expressed in a non-dimensional form:

dCp =dP

12ρAU3

∞(2.25)

which represents the contribution to the total Cp from a singular annular element.

Then, after a series of mathematical steps including integration, change of variables and

substitution (as described extensively in [32] the following is obtained:

Cp,max =8

729λ2

64

5x5 + 72x4 + 124x3 + 382 − 63x− 12 lnx− 4x−1

0.25

1−3a(2.26)

Cp,max can the be plotted as a function of different values of ration in Figure 2.7 which

also reports the Betz limit from the previous simple linear momentum theory and from

the graph it can be observed that as the ratio increases, Cp approaches its theoretical

maximum value.

2.4.2 Blade element method

The Blade Element Method (BEM) which was invented by Glauert in 1935 [31] consists

in applying the conservation of momentum to annular control volumes and is widely used

for calculations of aerodynamic loads and performances [33] As presented in the previous

chapter, one dimensional momentum theory coupled with rotational effects gives expres-

sion for power and torque, however no specific information is given regarding phenomena

occurring on the blade, thus no specific details regarding rotor geometry such as twist,

size and number of blades can be obtained. With BEM, by coupling momentum theory

17

Figure 2.7: Power coefficient variation with TSR [32]

with local aerodynamic phenomena, these features can indeed be studied.

Nowadays, BEM is widely applied as a design tool in industry and is not as expensive

as CFD in terms of computing resources.

In applying these method, two important assumption have to be taken into account

[31]:

• Each annular element is independent from each other;

• Forces applied on the flow by the action of the blades are constants which conse-

quently implies the assumption of infinite blades.

In order to correct the last assumption, a parameter named Prandtl’s Tip Loss Factor

is used, also, since the method is created for working in two dimensions, further corrections

have to be introduced.

Since derivation of the BEM governing equations is not in the interest of this report,

if the reader is interested in further readings, a more detailed explanation can be found

in books such as [31] or [32]

2.4.3 Navier-Stokes equation solvers

With the development of Computational Fluid Dynamics, many flow problems that before

were unsolvable by analytical methods or by experiments, could finally be studied. With

CFD, the Navier-Stokes (NS) equations are discretised with various methods such as

Finite Difference or Finite Volume Methods (FVM) [34] that transform the differential

NS equations into an algebraic form which can be then put into computer programming

18

languages such as FORTRAN or C (as used in FLUENT) which resolves the problem and

output results in form of data and graphics.

Then with the advance of computing capabilities, more user-friendly softwares (or

codes) such as FLUENT (which uses FVM) were created giving a wider access to CFD

capabilities.

19

Chapter 3

Numerical Modelling of Wind

Turbines

The choice of modelling strategy for wind turbines is vital to the successful outcome of

the simulation and there are, nowadays, different methods that can be applied [7]. In this

chapter the main features of CFD and how is applied to the study of wind turbines will

be discussed.

3.1 Navier-Stokes equations

Navier-Stokes equations named after their creators’ names represent in mathematical form

all fluid mechanics phenomena and here are presented in their non-conservation form (for

the derivation from first principles of said equations, the reader is suggested to refer to

[34]):

Conservation of Mass :

Dρ

Dt+ ρ5 ·−→V = 0 (3.1)

20

Conservation of Momentum:

ρDu

Dt= −∂p

∂x+∂τxx∂x

+∂τyx∂x

+∂τzx∂z

+ ρfx (3.2)

ρDv

Dt= −∂p

∂y+∂τxy∂x

+∂τyy∂y

+∂τzy∂z

+ ρfy (3.3)

ρDw

Dt= −∂p

∂z+∂τxz∂x

+∂τyz∂y

+∂τzz∂z

+ ρfz (3.4)

Where−→V represents the velocity vector, u, v and w are the components of the velocity

in the x, y and z direction respectively, p is pressure, τ ’s represent normal and shear

stresses acting on the surfaces of the 3D fluid particle, then fx, fy and fz represent the

body forces per unit in the x, y and z direction respectively.

The mathematical notation D indicates a so-called substantial derivative of a scalar

quantity, e.g :

Dρ

Dt=∂ρ

∂t+−→V · 5ρ (3.5)

It should be noted that the energy equation has not been mentioned, indeed in this

CFD study, this equation is not solved because thermal phenomena are small enough to

be considered as negligible.

The above set of partial differential equations represent a suitable form of the continuity

and momentum equation for numerical calculations.

3.2 Turbulence Modelling and Simulation

Many fluid mechanics problems are commonly solved by applying assumptions such as

incompressible, inviscid, laminar and steady flow. These assumptions are needed because

fluid flow, such as in rotating machineries, presents a rather unpredictable behaviour

which would cause a full solution to be highly complex. Among these complicated fea-

tures, turbulence is one that ’shines’ among the others.

In this section, given the size and complexity of the subject, only a brief introduction will

be given with slightly more emphasis on turbulence modelling for wind turbines.

But before an important non-dimensional number named Reynolds number Re which

21

expresses the ratio of inertial forces to viscous forces has to be introduced and is defined

as:

Re =ρU∞L

µ(3.6)

where µ is the dynamic viscosity, U∞ is the freestream flow velocity and L is the

reference length which in the case of an aerofoil is the chord length c.

Turbulent flow is widely present in nature, examples are cloud formations or smoke

forming from a fire and in simple words this type of flow could be described as having

significant irregularities, unsteady motion and recirculation in position and time [35]. As

Re increases the inertia forces increase their action up to a point where this increasing

action is so significant that causes the formation of turbulent scales in the flow [36],

subsequently, as a general rule of thumb, the following Re are defined as starting points

of turbulence:

• Re > 500, 000 along a surface or > 20, 000 along an obstacle for external flows

• Re > 2, 300 for internal flows

Given its complexity turbulence is a major ’target’ of numerical modelling and below

is a list of the most important numerical methods (all information were taken from [35]):

• Direct Numerical Simulation (DNS): DNS features the complete solution of the

Navier-Stokes equations coupled with some initial boundary conditions. Virtually,

DNS has the capability to produce high quality results, but its applicability is lim-

ited by the required computational power. Given the advance in computing efficiency

that occurred in the last few decades, DNS is now taking an important role in the

subject.

• Turbulence-Viscosity models : With this method, the Reynolds equations are solved

by averaging the velocity field to a mean value. There are different types of this

particular model and some are listed below:

1. κ−ε: This models presents two equations being solved in terms of two turbulence

parameters, namely κ and ε. It is widely used in CFD commercial packages.

2. κ− ω: This model is similar to the previous one except for the way the second

parameter is mathematically treated. It is too widely used in CFD.

22

3. Spalart - Allmaras. Here, only one equation is being solved. The model has its

best application in aerodynamics and has proven to be rather accurate. Further,

it has the important advantage of being computationally faster than others.

• Reynolds stress : In previous models, turbulent viscosity is ruled by a hypothesis,

which therefore limits the accuracy of those models. For Reynolds-stress models,

instead, stress parameters are solved which in turn gives further information in regard

turbulence length or time scale.

• Large-Eddy simulation (LES): LES focuses on directly solving the large structures

(or eddies) of the flow whereas the smaller ones are modelled, thus it has high appli-

cability for flow presenting vortices or separation.

3.2.1 SST κ− ω model

The κ − ω proves to provide good performance in free shear flows , adverse pressure

gradients and separated flows (with the last two being fully experienced in wind turbines),

however its accuracy is limited by the dependency of the model from the freestream

boundary conditions. [13]. An implementation to this model comes from the Shear-Stress

Transport (SST) κ−ω model created by Menter in 1993 [37]. And as reported in [38] the

two methods mainly differ for the following characteristics:

• Starting from the inner part of the boundary layer and going towards the more

outside region, the SST κ−ω change from a κ−ω to κ− ε giving a better treatment

of the boundary layer.

• In SST κ − ω the treatment for the turbulent viscosity is changed to accommodate

for the transport effects of the principal turbulent shear stress.

For reference the SST κ− ω equations are listed below:

∂

∂t(ρκ) +

∂

∂xi(ρκVi) =

∂

∂xj(Γk

∂k

∂xj) + Gk − Yk + Sk (3.7)

∂

∂t(ρω) +

∂

∂xi(ρωVi) =

∂

∂xj(Γω

∂ω

∂xj) +Gω − Yω +Dω + Sω (3.8)

where Gk is the turbulence kinetic energy generated by mean velocity gradients, Gω

represents the generation of ω, Yκ and Yω are the dissipation due to turbulence of κ and

23

ω, Γκ and Γ represent the diffusivity of κ and ω, Dω is the cross-diffusion term, Sκ and

Sω are the source source terms arbitrarily defined by the user [38].

In regard to the near-wall turbulence modelling, an important parameter is the so-

called non-dimensional wall distance (generally called y+) which is defined as:

y+ =u∗y

ν(3.9)

where u∗ is the friction velocity (which is defined as u∗ =√

τwρ

where τw is the wall

shear stress at the wall), ν is the kinematic viscosity and y is the normal distance from

the wall of the first cell.

With the application of the SST κ− ω, as explained in [38], in order to fully solve the

boundary layer, a y+ of 1 should be achieved, although it has been observed that even

values up to 6-7 are acceptable [23].

3.3 Computational mesh

As previously introduced, a computational grid or mesh is needed to be generated to

proceed with the CFD calculation, indeed, this could potentially be the most important,

and as was experienced in this project, the most difficult one. A general definition can

be found in [39] which states that ”.. a mesh is discretization of a geometric domain into

small shapes..”; in two dimensions these shapes would be triangles or quadrilaterals, and

tetrahedral and hexahedra in three. Alternatively, a mesh can also be defined as being the

locus where partial differential equations are solved according to the solver discretization

method.

Meshes can be divided in three main groups based on the shapes of the elements,

namely structured, unstructured and hybrid. In the first one, the structure presents itself as

quite homogeneous and vertices of the elements are all of similar dimensions. Unstructured

mesh instead presents elements of different vertices and shapes and are often used for

complex shapes. Finally a hybrid mesh can be either a combination of the previous

ones or different blocks of structured elements built together to form an unstructured

configuration.

All of the above types of meshes have been successfully used for wind turbines, however

a structured hexahedral mesh tends to be quite the preferable choice due to its ability to

generate less elements than an unstructured mesh of same size and quality.

24

3.4 FLUENT NS Solver

The software ANSYS FLUENT solves the governing flow conservation equations by ap-

plying the Finite Volume Method with which in the case of a wind turbine problem will

restrict to the solution continuity and momentum equation only. The method can be

summarised in the following steps [40] [13]:

• The flow domain is discretized into a finite set of control volumes;

• Solution by integration of the governing equations in each control volume in order to

obtain algebraic equation equations in which the unknowns are velocities, pressure

and other scalar quantities

• Numerical solution of the equation to solve the entire solution field. Based on the

problem specifications, two different numerical strategies can be chosen, namely

Pressure-based and Density-based solver. The former which is the one chosen for

this study, is aimed at the solution of low-speed incompressible flows whereas the

latter is for high-speed flows where the compressibility effects are significant.

The main steps involved in a pressure-based solution can be defined as follows [40] [13]:

1. Velocities are solved through the momentum equation;

2. Continuity is satisfied by solving a pressure correction equation, which basically

consists in obtaining a velocity field being corrected by pressure until continuity is

satisfied, which can be achieved by two algorithms:

3. Solution is achieved by means of iterations according to the chosen algorithm. Fluent

allows to choose between:

• segregated : equations are solved one after the other. The required memory is

relatively low, however this causes the simulation to take longer time to conclude;

• coupled : it requires 1.5 to 2 times more memory than the previous and solves

momentum and pressure-based continuity equation simultaneously as form of

a system while the remaining scalar equations are solved as in the segregated

algorithm.

Figure 3.1 represents the above steps expressed as form of a flow graph.

25

Figure 3.1: Main steps of a pressure-based solution

3.4.1 Single moving reference frame

This study concerns a rotating object therefore the mesh must be properly modelled to

achieve this and in FLUENT there are different strategies that can be used. The one used

here is called single moving reference frame (SRF).

A moving reference frame permits an unsteady problem respect to the absolute refer-

ence frame to become steady in respect to the moving reference frame. In simple words,

the whole computational domain is assumed to be rotating at the angular velocity of

the turbine rotor. This particular method is well suited for this problem since there is

only one rotating wall, in fact, if there were more than one rotating in opposite direc-

tion and/or different rotational speed, such as a rotor-stator problem, then the domain

should be divided in more volumes with each one being assigned a different reference

frame namely Multiple Moving Reference Frame (MRF). In both cases, the mesh itself

remains unmodified unlike dynamic mesh which allows to change the mesh shape [38].

In applying SRF, the governing equations have to be properly modified by including

two more acceleration terms, namely the Coriolis and Centripetal acceleration.

From a theoretical point of view, this methodology can be explained as follows [38]:

considering a moving coordinate system (blue) translating −→v t and rotating at an angular

velocitiy −→ω respect to a stationery coordinate system (green) as shown in Figure 3.2. The

26

distance between the origin of the moving and stationary coordinate systems is represented

by vector −→r 0 and the axis of rotation is defined as −→ω = ωa.

Figure 3.2: Single moving reference frame [38]

Now, introducing a CFD system in Figure 3.2 and denoting its distance at any point

from the origin of the moving reference frame with the −→r , a velocity relation can be

expressed:

−→v r = −→v −−→u r (3.10)

where −→u r = −→v t +−→ω× and −→v r is the relative velocity as seen from the moving frame,

−→v is the absolute velocity as viewed from the stationery frame, −→u r is the velocity of

the moving frame relative to the stationery frame, −→v t is the translational velocity of the

moving frame and −→ω is the angular velocity.

Then, using an absolute velocity formulation, that is, where the absolute velocity

terms in the momentum equation are expressed as dependent variables, the continuity

and momentum equation can be reformulated as follows:

∂ρ

∂t+5 · (ρ−→v r) = 0 (3.11)

and

∂

∂t(ρ−→v ) +5 · (ρ−→v r

−→v ) + ρ[−→ω × (−→v −−→v t)] = −5 p+5× ¯τ +−→F (3.12)

The term −→ω × (−→v − −→v t) represents a combined expression for both the Centripetal

27

and Coriolis acceleration [38]

28

Chapter 4

Method

After having introduced some general information regarding wind turbines and main

features of numerical modelling, the following chapter will be focused on explaining the

methodology applied for this wind turbine study.

4.1 Geometry model

A three-dimensional geometry model of the NREL blade was generated in SOLIDWORKS

(see Figure 4.1 and 4.2) based on the S809 aerofoil and NREL blade data given in [10]

(see Appendix A for blade and aerofoil geometry data).

The trailing edge was modified in order to have a few millimetres thick edge, this better

represents the real blade and also helps to avoid low quality mesh elements, as a very thin

edge would be hard to be handled by the meshing software.

(a) (b)

Figure 4.1: Three dimensional model of the NREL Phase VI blade

29

(a) (b)

Figure 4.2: Aerofoil profiles of the blade

In regard to the tip of the blade, since no specific data is given in the geometry

documentation, it was approximated to a soft dome as shown in Figure 4.3. It must be

noted that the blade tip plays an important role in the generation of torque, therefore it

is recommended that the 3D model represent real geometry.

Figure 4.3: Blade tip

4.2 Mesh

The chosen software used for the generation of the mesh is ANSYS ICEM CFD and is ca-

pable of generating structured, unstructured and hybrid meshes and different algorithms

are available to the user based on the desired type of the final grid.

30

4.2.1 Dimensions

At the initial stages of the project, efforts were focused on trying to create a structured

mesh, however, due to its complexity and required level of experience, it was decided to

create an unstructured mesh, although this brings the disadvantage of generation of a

higher number of elements, therefore increasing the computational times.

It also has to be noted that although the rotor is featured with two blades, only one

blade is actually being treated thus allowing to halve the computational mesh (see Figure

4.4). This is due to the application of periodic boundary conditions which are explained

in Section 4.3.

The unstructured mesh is made of triangular elements for the surface parts (see Figure

4.6), tetrahedral elements for the flow volume domain (Figure 4.5) and prismatic elements

were used for creating layers around the blade surface in order to have a finer mesh in

proximity of the boundary layer (Figure 4.9 and 4.8).

Half of a cylindrical domain was built around the blade and as shown in Figure 4.4,

given the radius of the blade R = 5.029m, the inlet was placed at 3×R upstream of the

blade, the outlet at 6×R downstream, the length of the radius of the domain was set to

3×R. Further, since the hub of the blade was not included in the geometry, half cylinder

with a radius of 0.508m was set as a boundary of the volume as shown in Figure 4.4. It is

believed that the negligence of the hub may introduce inaccuracies, however as was learnt

in previous literature such as [18], [15] and [24], this approximation should not introduce

relevant errors.

From readings, it was found that various combinations of the domain dimensions were

used and mostly gave acceptable results; for example Cargangiu [13] placed the outlet

at 10 × R from the blade, whereas Mahu and Popescu [26] used a 20 × R, instead Van

Rooij and Arens [24] used a downstream length of 6× R. Other used dimensions can be

found in the list of references given in the Literature review (1.5). To conclude, it seemed

reasonable that the domain dimensions used for this simulation would have the potential

to provide acceptable results.

31

Figure 4.4: Semi-cylindrical domain and dimensions

Mesh elements size can be well controlled in the software and therefore allowed to

input larger elements at the outer boundaries of the mesh and a very fine mesh on the

blade surface (Figure 4.6 and 4.7) and as can be seen in Figure 4.5, the finer density

mesh occurs at the location of the blade and in proximity of the downstream wake and

upstream incoming flow field. The reason for having finer elements in the wake lays on

the fact that the wake flow field directly affects the flow through the wind turbine and

therefore pressure and torque distribution.

Figure 4.6: Surface mesh of the blade Figure 4.7: Details of the mesh of the blade tip

32

Figure 4.5: Section view of the volume mesh showing higher density of elements in proximity of thedownstream wake.

4.2.2 Prismatic layers

For treating the boundary layer zone, for unstructured meshes, prismatic layers are gen-

erated. The methodology used consisted in first generating a surface mesh, then create

prismatic layers and finally fill the volume with tetrahedral elements. This avoided pyra-

midic elements (which are not handled well by FLUENT) between the prismatic layers

and the rest of the volume (Figure 4.8 and 4.9).

The number of layers was chosen to be 20 at a growth ratio from the first cell at 30 %

and in regard to the estimation of the height of the first layer, it was found that based

on a Re of 1 × 106, to achieve a y+ of 4 ∼ 5, the first cell height should be 2 × 10−5m

then refinements will be performed directly in FLUENT in order to achieve an average of

y+ = 1.

33

Figure 4.8: Section view of the volume mesh at 30 % of the blade

(a) Leading edge (b) Trailing edge

Figure 4.9: Details of the prismatic layers in proximity of the leading edge (a) and trailing edge (b)

34

The total size of the mesh turned out to be rather large with a total number of roughly

8.28×106 elements and 2.93×106 nodes (Table 4.2). It has to be noted that mesh element

counting increased with simulations due y+ refinements causing the prismatic layers to

be subdivided in further layers.

Table 4.1: Number of elements and nodes by parts and total

Part Elements Nodes

Blade surface 303,350 -

Other surfaces 17,198 -

Volume 3,375,276 -

Prismatic layers 4,580,220 -

Total 8,277,746 2,931, 056

In comparison for example, Carcangiu [13] with a structured mesh had 3.5 millions,

Uzol and Long [18] with an unstructured tetrahedral mesh had 3.6 and 9.6 millions whereas

Huang et al. [43] had 3.06 millions elements with a structured one. Overall, it appears

that element number could be drastically lowered by adopting a structured methodology.

4.3 FLUENT setup

When the mesh was completed, it then could be imported into FLUENT and after check-

ing for possible errors and overall quality of the mesh, the simulation setup could be

started.

As was explained in Section 3.4.1, the application of a single moving reference frame

gives the advantage of rendering the transient nature of a rotating problem a steady

problem, however it was observed that at high wind speed velocities, when residuals

reached a constant value, a small quasi-sinusoidal trend would develop; this suggests,

that the problem still presents unsteady features, therefore, an appropriate transient

input should be given in the software as done by Carcangiu [13].

Each part of the mesh was named as shown in the Figure 4.10.

4.3.1 Boundary conditions

The setting of the Boundary Conditions (BCs) is a very important step, therefore BCs

have to be properly applied. Below is a list of the used boundary conditions:

35

Figure 4.10: Names given to mesh parts

• Velocity-Inlet

When dealing with incompressible flows, the velocity must be specified at the inlet

of the mesh. It can be specified as both constant and variable, either normal to the

surface or acting with a specified angle (as would be in a yaw-study case). In this

case it was specified as constant and perpendicular to the boundary. Turbulence

conditions also have to be defined here and the default turbulence parameters of the

NASA Ames Wind Tunnel were used, that is, inlet turbulence intensity of 0.5 % and

viscosity ratio set to 10 [12].

• Pressure-Outlet

This boundary condition was applied at the outlet of the domain and sets the pressure

at the boundary at a specific static pressure value. In this study, the obvious choice

was to put the value equal to zero so that the pressure at the outlet would be equal

to the atmospheric operating pressure (standard pressure at sea level was used, i.e.

101,325 Pa)

• No-Slip Wall

This condition is applied to the solid surface of the blade, and implies the velocity

of the fluid particle to be zero at the wall.

• Periodic

Since the wind turbine rotor rotates at a constant angular velocity thus presenting

a periodically repeating nature; the software allows to apply periodic boundary con-

36

ditions to specific surfaces as shown in Figure 4.10 giving the great advantage of

reducing the size of the domain. In this study, since, a two-blade wind turbine is

considered, the domain can be halved (180 ); instead if the wind turbine was three-

bladed, the computational domain would reduce to a third (120 ) of the original

size.

• Symmetry

This boundary conditions allows a surface to be treated as a zero-shear wall.

A summary of the assigned boundary conditions is given below.

Table 4.2: Assigned boundary conditions

Part BC type

Blade No-slip wall

Farfield Symmetry

Inlet Velocity-Inlet

Periodic faces Periodic

Outlet Pressure-Outlet

Half cylinder Symmetry

4.3.2 Solution method

As was introduced in Section 3.4, the pressure-based discretization scheme is being applied

and since computing hardware permitted, the coupled algorithm, which solves in one step

the system of momentum and pressure-based continuity equation, could also be used, thus

reducing computational times.

With FVM, scalar quantities are defined at the centre of cells whereas convection terms

are stored at the face of the cells. These last terms can only be found by means of inter-

polation from the centre of the control volume, namely upwind scheme. In the software,

there are different methods that can be used such as first- or second-oder upwind scheme.

According to the FLUENT Theory Guide [38], the latter is in most cases preferable as

error margins are decreased. However, as recommended by FLUENT, the solution should

initialised with first-order upwind scheme and when some convergence is achieved, it can

be switched to second order. This is done in order to limit divergence problems.

A summary of the inputs for the discretization method is given in Table 4.3.

37

Table 4.3: Spatial Discretization scheme

Gradient Least Squares Cell Based

Pressure Standard

Momentum Second Order Upwind

Turbulent Kinetic Energy Second Order Upwind

Specific Dissipation Rate Second Order Upwind

Initially simulations were run on computers available to students at Queen Mary, Uni-

versity of London, then with an increased computing power demand, final simulations

were run with parallel computing offered by FLUENT on a machine with the following

characteristics (Table 4.4).

Table 4.4: Machine specifications

Processor name Intel i7-2600K

Number of cores 4

Number of threads 8

Memory size 32 GB

Three simulations were run at a freestream velocity of 7, 10 and 15 m/s with a constant

angular velocity of 72 RPM (7.54 rad/s). For each simulation, computational time was

between 4-5 hours, and coefficient of moment along with coefficient of lift and continuity

were used as convergence parameters. In Figure 4.11 the convergence plots for Cm and CL

for the 7 m/s simulation is shown. It can also be observed that at the 100th iteration, the

discretization schemes for momentum, turbulent kinetic energy and specific dissipation

ratio are switched from first to second order upwind which causes a visible increase in

coefficient of moment.

0 50 100 150 200 250 300 350−1.5

−1

−0.5

0

0.5

1

1.5

2

I terati on

Resid

uals

CL

Cm

Figure 4.11: Convergence plot of Cm and CL at U∞ = 7m/s

38

4.3.3 Post-processing

When solution is completed a wide range of data can be extracted from the code and can

be read on either the solver itself or on third-part softwares specialised in post-processing.

Care must be taken when extracting results, especially for integral aerodynamics which

require the specification of reference values of length and velocities.

39

Chapter 5

Results

In this chapter the results of the three simulations will be presented. The quantity and

type of results that can be extracted from this type of numerical study is large, starting

from integral aerodynamics, to pressure distribution and up to including wake study.

Provided the aim of this report, results will restrict to pressure and pressure coefficients

distribution on the blade, generated torque and a general overview of the flow field around

the rotor.

From literature review it was found that the pressure coefficient distribution at differ-

ent radial stations of the blade is one of the main parameter to be analysed and compared

with experimental data. This is mainly because a direct and simple comparison can be

performed, further, pressure controls most of aerodynamic phenomena, therefore errors

in pressure values will probably affect other parameters too.

First, as presented in next section, the flow field at radial stations r/R = 0.3, 0.63

and 0.95 will be shown with both streamlines and contours of relative velocity. From

these figures, flow separation and circulation can be easily spotted. Then in 5.2, using

the same radial positions −Cp (as usual in aerodynamics) will be plotted against the non-

dimensional chord distance x/c where is the chord length of the aerofoil at each section.

Values of coefficients of pressures were computed with the following formula:

Cp =P − P∞

0.5ρ(U2∞ + (rΩ)2)

(5.1)

Where the P − P∞ represents static pressure, r is the blade radius at each specific

radial position and Ω, which is the rotor angular velocity, is equal to 7.54 rad/s.

40

Further information regarding the separation of the flow is given in 5.2.4 where both

faces of the blade are presented with surface pressure and limiting streamlines.

Lastly, turbine performance results are given in terms of torque, power and coefficient

of power as a function of free stream velocity and tip speed ratio.

From the torque values extracted from FLUENT, power was found by multiplying

the torque by the angular velocity, the coefficients of power were obtained with equation

(2.12). Values of the TSR were found with (2.21). More figures of the flow field can ca

be found in Appendix B.

41

5.1 Flow visualisation

5.1.1 U∞ = 7m/s

(a) r/R = 0.3 (b) r/R = 0.3

(c) r/R = 0.63 (d) r/R = 0.63

(e) r/R = 0.95 (f) r/R = 0.95

Figure 5.1: Streamlines (left) and contours (right) of relative velocity magnitude in m/s. U∞ = 7m/s

42

Figure 5.2: Contours of velocity magnitude for all radial stations in m/s. U∞ = 7m/s

5.1.2 U∞ = 10m/s

(a) r/R = 0.3 (b) r/R = 0.3

(c) r/R = 0.63 (d) r/R = 0.63

(e) r/R = 0.95 (f) r/R = 0.95

Figure 5.3: Streamlines (left) and contours (right) of relative velocity magnitude in m/s. U∞ = 10m/s

43

Figure 5.4: Contours of velocity magnitude for all radial stations in m/s. U∞ = 10m/s

5.1.3 U∞ = 15m/s

(a) r/R = 0.3 (b) r/R = 0.3

(c) r/R = 0.63 (d) r/R = 0.63

(e) r/R = 0.95 (f) r/R = 0.95

Figure 5.5: Streamlines (left) and contours (right) of relative velocity magnitude in m/s. U∞ = 15m/s

44

Figure 5.6: Contours of velocity magnitude for all radial stations in m/s. U∞ = 15m/s

45

5.2 Pressure distribution

5.2.1 Pressure coefficients at U∞ = 7m/s

0 0.2 0.4 0.6 0.8 1

−1

0

1

2

3

4

5

r/R = 0.30

x/c

−C

p

ExperimentCFD

Figure 5.7: Cp at U∞ = 7m/s r/R = 0.3

0 0.2 0.4 0.6 0.8 1

−1

0

1

2

3

4

5

r/R = 0.63

x/c

−C

p

ExperimentCFD

Figure 5.8: Cp at U∞ = 7m/s r/R = 0.63

0 0.2 0.4 0.6 0.8 1−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

3

r/R = 0.95

x/c

−C

p

ExperimentCFD

Figure 5.9: Cp at U∞ = 7m/s r/R = 0.95

46

5.2.2 Pressure coefficients at U∞ = 10m/s

0 0.2 0.4 0.6 0.8 1

−1

0

1

2

3

4

5

r/R = 0.30

x/c

−C

p

ExperimentCFD

Figure 5.10: Cp at U∞ = 10m/s r/R = 0.3

0 0.2 0.4 0.6 0.8 1

−1

0

1

2

3

4

r/R = 0.63

x/c−

Cp

ExperimentCFD

Figure 5.11: Cp at U∞ = 10m/s r/R = 0.63

0 0.2 0.4 0.6 0.8 1

−1

0

1

2

3

4

r/R = 0.95

x/c

−C

p

ExperimentCFD

Figure 5.12: Cp at U∞ = 10m/s r/R = 0.95

47

5.2.3 Pressure coefficients at U∞ = 15m/s

0 0.2 0.4 0.6 0.8 1

−1

0

1

2

3

4

5

r/R = 0.30

x/c

−C

p

ExperimentCFD

Figure 5.13: Cp at U∞ = 15m/s r/R = 0.3

0 0.2 0.4 0.6 0.8 1−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

r/R = 0.63

x/c

−C

p

ExperimentCFD

Figure 5.14: Cp at U∞ = 15m/s r/R = 0.63

0 0.2 0.4 0.6 0.8 1

−1

0

1

2

3

4

r/R = 0.95

x/c

−C

p

ExperimentCFD

Figure 5.15: Cp at U∞ = 15m/s r/R = 0.95

48

5.2.4 Surface blade pressure and limiting streamlines

(a) Pressure side

(b) Suction side

Figure 5.16: Limiting streamlines with contours of static surface pressure on the blade in Pa. U∞ =7m/s

(a) Pressure side

(b) Suction side

Figure 5.17: Limiting streamlines with contours of static surface pressure on the blade in Pa. U∞ =10m/s

49

(a) Pressure side

(b) Suction side

Figure 5.18: Limiting streamlines with contours of static surface pressure on the blade in Pa. U∞ =15m/s

5.3 Performance

6 8 10 12 14 16 18 20400

500

600

700

800

900

1000

1100

1200

1300

1400

V eloc i ty, U!(m/s)

Torque(N

m)

CFD

Experiment

Figure 5.19: Experimental and computational torque variation with U∞

50

7 8 9 10 11 12 13 14 15 16

3

4

5

6

7

8

9

10

11

V eloc i ty, U∞(m/s)

Pow

er

(kW

)

CFDExperiment

Figure 5.20: Variation of the NREL experimentaland computational power output as function of windspeed velocity

2.5 3 3.5 4 4.5 5 5.5 60

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

t i p speed ratio !

CP

CFD

Experiment

Figure 5.21: Change of experimental and compu-tational CP as function of TSR

6 8 10 12 14 160

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

V eloc i ty, U∞(m/s)

Pow

ercoef

fic

ien

t,C

P

CFDExperiment

Figure 5.22: Variation of computational and ex-perimental CP with wind speed

51

Chapter 6

Discussion

This chapter will focus on the analysis of the results given in the previous chapter. Par-

ticular attention is given to understand the physics of the flow field and how affects the

performance of the wind turbine.

With the help of results obtained in the material listed in the Literature Review, a

comparison of computational results will also be presented. This, in parallel with the

comparison with experimental results, can give important details regarding inaccuracy

occurred in the study and how results may be improved in the possibility of future works

or for the benefit of the reader.

The reader must note that the same mesh has been used for all three computations,

therefore changes were not made except for y+ refinements which were performed directly

in the software. The mesh was created based on many trials of the 7m/s case and therefore

properly optimised for this particular flow field. However, at 15m/s, flow phenomena

experienced by the rotor are much different from the ones at 7m/s which may suggest

that a new mesh should be generated with particular attention to the mesh in the region

of the boundary layer.

6.1 Comparison with the NREL Phase VI experiment

From page 30 to 32, streamlines and contours of relative velocity magnitude are displayed;

the reader must note the relative velocity is the one seen by the leading edge of the blade

and not the one seen standing far from the rotating rotor. This type of velocity is preferred

since it gives more information for aerofoil aerodynamics.

In Figure 5.1 can be observed that at U∞ = 7m/s the flow is attached on most of the

blade surface except for small regions shown in (c) and (e), in fact at 30 % of the blade,

52

the separation seems to be minimum. Figure 5.16 (b) gives more precise information;

indeed it can be observed that on the suction side, starting from roughly x/c = 50−60%,

streamlines deviates from the parallel inboard streamlines, deviating their path towards

a spanwise direction which is due to centrifugal acceleration caused by rotation [23].

At U∞ = 10m/s separation seems to be widely experienced at 63 % of the blade, further

Figure 5.17 shows that the spanwise movements now occupy most of the suction side blade

except for a small area starting from roughly 60 % to the tip. Then separation effects are

magnified at all section for a wind speed of 15 m/s here according to experiment analysis

the blade has encountered stall, for which this large flow separation would be explained.

Now key information will be given from the pressure coefficient distribution and as

shown in pages 44 to 46, at U∞ = 7m/s the Cp plots at three radial stations agree rather

well with experimental ones, although, lower pressure is experienced at the inbound region

(Figure 5.8 and 5.9). Disagreement seems to increase with wind speed and especially for

the suction side of the blade. Indeed, at U∞ = 10m/s, a significant region of higher

pressure is experienced at r/R = 0.63 from the leading edge up roughly 45 % of the chord

for the low pressure side. However at other sections, C ′ps show rather good agreements

with experimental data although fluctuations are noticeable on the suction sides.

Lastly, plots at 15 m/s wind speed clearly show significant errors on all suction sides

with usually higher values than experimental ones. Still, it is interesting to note, that on

all pressure sides, agreement is mostly present.

The above paragraphs suggest that the numerical method is not properly capturing

highly circulating turbulent flows occurring at post-stall speeds. This can be indeed

confirmed by performance results, in fact, as displayed in Figures 5.19 and 5.20, the com-

putational error increases with higher wind speeds; in fact at 7 m/s, the predicted torque

and power are 7.5 % higher than the calculated ones which, for the purpose of this report,

is an acceptable results. It is not the case for higher speeds such as at 10 m/s where the

error is up to 27.5 % and for the post-stall wind speed of 15 m/s where the torque is 65.25

% lower than expected.

It is easy to conclude that the simulation for U∞ = 7m/s, for which the mesh was

specifically optimised, is the one that gave the best results.

53

6.2 Comparison with previous work

However, this is not the whole picture, in fact, a comparison with previous work will pro-

vide an insight to how well other numerical simulations have performed in this particular

NREL study.

In the graph below, a comparison of shaft torque values obtained from previous studies

with results from FLUENT and with the NREL experiment is presented. The results are

taken from the following articles with the used CFD code written in brakets: Sørensen et

al.(EllipSys3D)[41], Mo and Lee (FLUENT) [23], Le Pape and Lecanu (elsA) [42], Huang

et al. (P-WENO) [43] and Potsdam and Mavriplis (OVERFLOW) [20]. It has to be noted

that results at 13 m/s have been included in the comparison although the case was not

performed in this study.

6 8 10 12 14 16 18 20200

400

600

800

1000

1200

1400

1600

1800

2000

V eloc i ty, U (m/s)

Torque(N

m)

CFD − FLUENT

Experiment

Sorensen et al.

Mo and Lee

Le Pape and Lecanu

Huang et al.

Potsdam and Mavriplis

Figure 6.1: Comparison of computational results of torque obtained from previous work

As can be observed, CFD results have large disagreements among each other and

present a wide range errors and discrepancies from the experimental results. The studies

that compare better are the ones from Sørenses et al., Huang et al. and Mo and Lee,

with the latter presenting a better simulation of performance in the range from 13 m/s to

15 m/s, which is the one where most studies encounter higher inaccuracies This gives an

54

overview of the difficulty that CFD solvers encounter in processing torque results especially

for post-stall velocities, in fact at 7 m/s most results appear to agree accurately. Results

obtained in this study are generally of lower quality in comparison to others, nevertheless,

if compared with results from Le Pape and Lecanu (2004) , results appear in the same

range and coincide at 15 m/s (although the 13 m/s case was not treated). As reported in

the same publication, the SST κ − ω turbulence model is used and reasons for incorrect

drop in the generated torque appears to be due to unexpected early loss of torque and

normal force coefficient and at 15 m/s the main contribution to torque appears to be

supplied by the blade root, whereas the laboratory results show the opposite. It may

be summarised that according to Le Pope and Lecanu (2004), the NS solver encounters

difficulties at capturing important effects of flow separation at stall speed, in fact, after

this initial loss, torque is recovered comparing well with NREL experiment [42].

In regard to the simulation carried out by Mo and Lee [23] with FLUENT, torque is

predicted very well as well as pressure distribution. The SST κ− ω model is again used

(confirming being a favourite choice) and the mesh is structured with 3× 106 hexahedral

elements. As commented by the authors in the article, predicted results were surprisingly

accurate and the stall was properly being simulated [23].

Next, a comparison will also be made in terms of surface limiting using results from

the last two mentioned references (Figure 6.2). The blades shown in (a) represent the

surface streamlines obtained from this study, then in (b) and (c), results from Le Pape

and Lecanu, and Mo and Lee are presented respectively.

If (c) is taken as reference, it can be seen that at 7 m/s in (c) flow is mostly two

dimensional meaning that radial movements are very limited to a small area close to

the root (this is due to an high angle of attack ), instead in (b) and even more (c) this

area expands towards the which clearly should not occur. At a higher wind speed of 10

m/s, (c) shows that from x/c ≈ 0.5 down to the trailing edge, spanwise components of

the streamlines have increased their effects; instead in (c), separated flow occupies larger

surface which is again magnified in (a). Then at post-stall speed, radial translations cover

the whole suction surface for which a direct comparison cannot really made, however the

reader might have observed a pattern, in the sense that results obtained in this study

clearly show that the stall phenomenon occurs at an earlier stage.

55

(a) FLUENT

(b) Le Pape and Lecanu [42]

(c) Mo and Lee [23]

Figure 6.2: Computed limiting streamlines comparison from 7 to 15 m/s (top to bottom)

The reader must note that further data is much needed in order to have a clear and

thorough overview of the whole flow field, such as integral aerodynamics (lift, drag, normal

and tangential force) and its dependancy with variation angle of attack, which goes beyond

the scope of this report. Further a wake study as performed by Ivanell [14] and tip

56

aerodynamic analysis such as the one done by Ferrer and Munduate [44] can provide

further and important details.

57

Chapter 7

Conclusions and future work

General aspects of capabilities of Computational Fluid Dynamics applied to wind turbines

have been analysed and discussed. A total of three simulations have been computed

and results of pressure, torque and power and flow field velocity magnitudes have been

compared with experimental results. It has been observed that good agreement with

the NREL experiment occur for low speed wind velocity where the flow on the blade is

attached and stall effects are minimum or absent.

The following conclusions can be drawn:

• CFD codes such as ANSYS FLUENT are powerful tools and are experiencing im-

portant developments. However, as observed in recent research publications, the

accuracy of said packages is debatable. Therefore as of now, they are not reliable in

form of designing tools.

• The application of CFD to wind turbines is relatively recent. Increase in number of

publications has been seen after the release of the NREL UAE Phase VI experimental

data providing an important validation tool for CFD methods.

• Although with few exceptions, as seen in Chapter 5 and 6, stall phenomenon is

predicted with difficulties by CFD packages and turbulence models. Among these,

the SST κ− ω is a common choice for wind turbine studies.

• Results obtained from simulations agree well with experiments at 7 m/s and with

increasing velocities inaccuracy increases. However the shapes of the trends for pres-

sure and performance results have been predicted.

58

7.1 Future work

Given the nature of a dissertation of undergraduate level, important aspects of such

computational study have been excluded. For example 2D dimensional CFD studies are

very important in the process of optimisation and for identifying the correct method, and

a mesh independence study have been carried out bur without a methodic approach. This

was mainly due to time constraints, in fact such studies can be taken to Master and PhD

levels.

In the possibility of future studies in the field CFD applied to wind turbine or rotating

machineries, it is recommended that ’step-by-step’ method be adopted, starting from

the basics of CFD and wind turbine theory and gradually up to solution of a full scale

three-dimensional problem. In particular, meshing strategy and turbulence modelling are

among the important factors to be considered in such study.

59

Acknowledgements

I would like to thank my family, friends and my supervisor for all their support. I also

would like to thank Aleksandar Pasic from the Faculty of Mechanical Engineering and

Naval Architecture (FAMENA), University of Zagreb for providing important inputs and

computing resources.

60

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Appendix A

NREL Phase VI blade data

Figure A.1: NREL Phase VI wind turbine blade data [10]

65

Figure A.2: S809 Aerofoil coordinates

66

Appendix B

Wake flow visualization

B.1 U∞ = 10m/s

Figure B.1: Front view of the rotor. U∞ = 10m/s

67

Figure B.2: SIde view of the wake. U∞ = 10m/s

Figure B.3: Top view of the wake. U∞ = 10m/s

68

B.2 U∞ = 15m/s

Figure B.4: Front view of the rotor U∞ = 15m/s

69

Figure B.5: Side view of the wake U∞ = 15m/s

Figure B.6: Top view of the wake U∞ = 15m/s

70