Convocatria de lliurament del PFC

Quadrimestre de primavera 2014. Defensa Juliol 2014.

Titulaci

Enginyeria Aeronutica

Alumne

Daniel Snchez Muoz

Ttol PFC

Study of Horizontal Axis Wind Turbine Aerodynamics using Prandtl'sLifting Line Theory

Director del PFC

Vanessa del Campo Gatell

Contingut d'aquest volum -MEMRIA-

Study of Horizontal Axis Wind TurbineAerodynamics using Prandtl's Lifting Line

Theory

A Final Year Project submitted to Universitat Politcnica de Catalunya for the

title of Aeronautical Engineer at the Escola Tcnica Superior d'Enginyeries

Industrial i Aeronutica de Terrassa

Daniel Snchez Muoz

June, 2014

Director: Vanessa del Campo Gatell

Co-director: David del Campo Sud

Acknowledgments

First I would like to thank my project director, Vanessa del Campo Gatell, for

supporting and guiding me during all this project. Her knowledge and advice has

helped me to keep on track. Besides, I would like to thank my project co-director,

David del Campo Sud, for his helpful advices.

I am indebted to my university colleagues who have helped make my learning an

enjoyable and stimulating experience.

My family and friends deserve special thanks, for all their support and understanding

through all these years. Their support and care helped me overcome setbacks and

stay focused on my graduate study.

Finally, I would like to express my deepest gratitude to my beloved girlfriend Ana

Lopez for all her love, support and patience. She has been a constant source of

strength all these years.

Contents

Abstract ix

Abbreviations xi

Nomenclature xiii

Roman letters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii

Greek letters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv

1 Aim 1

2 Scope 3

2.1 In Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 Out of Project Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3 Justication 5

4 Introduction 9

4.1 Introduction to wind turbines . . . . . . . . . . . . . . . . . . . . . . 9

4.2 Project Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4.3 Project Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

5 State of the art 15

5.1 Methods for Horizontal-Axis Wind Turbines Numerical Computation 15

5.1.1 Blade Element Momentum Theory . . . . . . . . . . . . . . . 15

5.1.2 Lifting Line Theory . . . . . . . . . . . . . . . . . . . . . . . 16

5.1.3 Panel Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 17

5.1.4 CFD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

5.1.4.1 Reynolds-Averaged Navier-Stokes (RANS) . . . . . . 18

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Contents

5.1.4.2 Large Eddy Simulation (LES) . . . . . . . . . . . . 18

5.1.4.3 Direct Numerical Simulation (DNS) . . . . . . . . . 20

5.2 Current Aerodynamic Softwares for Horizontal-Axis Wind Turbines . 20

5.2.1 GH Bladed . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

5.2.2 AeroDyn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

5.2.3 FLEX5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

5.2.4 FOCUS6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

5.2.5 Qblade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

5.2.6 AWSM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

5.3 Aerodynamic Analysis of Horizontal Axis Wind Turbines based on

Lifting line method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

6 The Lifting-Line Theory 31

6.1 Prandtl's Lifting-Line Theory . . . . . . . . . . . . . . . . . . . . . . 31

6.1.1 Spanwise Circulation Distribution on an arbitrary wing . . . 36

6.1.2 Aerodynamic Loads . . . . . . . . . . . . . . . . . . . . . . . 37

6.2 Numerical Lifting-Line . . . . . . . . . . . . . . . . . . . . . . . . . . 39

6.2.1 Adaptation for Wing simulations . . . . . . . . . . . . . . . . 39

6.2.2 Adaptation for HAWTs . . . . . . . . . . . . . . . . . . . . . 51

7 Software description 61

7.1 Language . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

7.2 Structure of the developed codes . . . . . . . . . . . . . . . . . . . . 63

7.2.1 Wing code structure . . . . . . . . . . . . . . . . . . . . . . . 65

7.2.2 HAWT code structure . . . . . . . . . . . . . . . . . . . . . . 66

7.3 Input les . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

7.3.1 Wing code input les . . . . . . . . . . . . . . . . . . . . . . . 69

7.3.2 HAWT code input les . . . . . . . . . . . . . . . . . . . . . . 70

7.4 Output les . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

7.4.1 Wing code output les . . . . . . . . . . . . . . . . . . . . . . 72

7.4.2 HAWT code output les . . . . . . . . . . . . . . . . . . . . . 75

8 Results and Validation 81

8.1 Wing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

8.1.1 Verication tests . . . . . . . . . . . . . . . . . . . . . . . . . 81

Daniel Snchez Muoz ii

Contents

8.1.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

8.2 Rotor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

8.3 HAWT simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

9 Environmental Impact 97

10 Budget 99

11 Conclusions 101

12 Future Work 105

Appendix A 107

Appendix B 109

Bibliography 111

iii Daniel Snchez Muoz

Contents

Daniel Snchez Muoz iv

List of Figures

3.1 Share of new power capacity installations in EU in 2013. Total: 35181

MW. Adapted from (EWEA, [1]). . . . . . . . . . . . . . . . . . . . . 5

3.2 Annual market forecast by region 2014-2018. Adapted from (GWEC,

[2]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

4.1 Alstom ECO 80 Wind Turbines at Clachan Flats wind farm, UK.

Reproduced from (Alstom,[28]). . . . . . . . . . . . . . . . . . . . . . 10

4.2 Gantt chart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

5.1 Methods for horizontal-axis wind turbines numerical computation . . 16

5.2 Time dependence of a velocity component at a point. Reproduced

from (Ferziger and M. Peri, [12]). . . . . . . . . . . . . . . . . . . . 19

5.3 Computed non-dimensional circulation distribution along the blade.

Adapted from (Dumitrescu and Cardo, [15]). . . . . . . . . . . . . . 25

5.4 Visualization of the vortex structure downstream of the NREL rotor.

Reproduced from (Chattot, [18]). . . . . . . . . . . . . . . . . . . . . 26

5.5 Helical rotor, wake roll-up aft view. Adapted from (van Garrel, [29]). 28

6.1 Far eld horseshoe model of a nite wing. Reproduced from (Katz &

Plotkin, [38]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

6.2 Velocity induced by the segments of a typical horseshoe element. Re-

produced from (Katz & Plotkin, [38]). . . . . . . . . . . . . . . . . . 34

6.3 General wing two-dimensional section angles denition. Adapted from

(Flandro & McMahon, [42]). . . . . . . . . . . . . . . . . . . . . . . . 35

6.4 Tilting of the local lift vector by the angle induced by the trailing

vortices. Adapted from (Katz & Plotkin, [38]). . . . . . . . . . . . . . 38

6.5 Horseshoe element . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

6.6 Horseshoe element without assuming very small angle of attack . . . 40

v

List of Figures

6.7 Inuence of a straight vortex line segment at a point P. Adapted from

(Katz & Plotkin, [38]). . . . . . . . . . . . . . . . . . . . . . . . . . 41

6.8 Wing coordinate system. Adapted from (Katz & Plotkin, [38]). . . . 43

6.9 Twist and chord distribution along the simulated HAWT blade. Re-

produced from (del Campo, [31]). . . . . . . . . . . . . . . . . . . . 44

6.10 Wing discretization. . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

6.11 Horseshoe element zoom ( = 2, = 4) . . . . . . . . . . . . . . . 47

6.12 Wing Horseshoes elements. . . . . . . . . . . . . . . . . . . . . . . . 48

6.13 Wing solution algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 50

6.14 Schematic drawing of the vortex system behind a wind turbine. Adapted

from [4] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

6.15 Blade element velocities and forces. Adapted from (Burton et al., [43]) 55

6.16 Blade and helical wake discretization . . . . . . . . . . . . . . . . . 57

6.17 Blade and helical wake discretization with two blades . . . . . . . . . 58

6.18 HAWT solution algorithm. . . . . . . . . . . . . . . . . . . . . . . . 60

8.1 Elliptical wing lift distribution validation . . . . . . . . . . . . . . . 82

8.2 Elliptical wing lift distribution (element size 1 cm) . . . . . . . . . . 83

8.3 Elliptical wing bound circulation distribution. N = 1000 . . . . . . . 84

8.4 Elliptical wing induced drag distribution. N = 1000 . . . . . . . . . . 84

8.5 Elliptical wing local lift per unit length. Airfoil NACA 6409 . . . . 85

8.6 Elliptical wing local drag per unit length. Airfoil NACA 6409 . . . . 86

8.7 Rectangular wing bound circulation . . . . . . . . . . . . . . . . . . 86

8.8 Ro