development of an aeroacoustic prediction tool for wind ......formulation 1a of farassat. the...

Development of an Aeroacoustic Prediction Tool for WindTurbine Noise

João Henrique dos Santos Rodrigues Nogueira Souto

Thesis to obtain the Master of Science Degree in

Aerospace Engineering

Supervisor: Prof. Fernando José Parracho Lau

Examination Committee

Chairperson: Prof. Filipe Szolnoky Ramos Pinto CunhaSupervisor: Prof. Fernando José Parracho Lau

Member of the Committee: Prof. Edgar Caetano Fernandes

July 2017

This dissertation is dedicated to my Father, Henrique Souto

iii

Acknowledgments

I would like to thank my friends and family for the support during my studies, and specially my mother,

without whose insistence I could not have persisted.

I would also like to thank my supervisor, Professor Fernando Lau, for his rigor, guidance and patience,

without whose this dissertation would not be possible.

A special thank you to Gaël de Oliveira Andrade, for the numerous hours of his time spent teaching

me about wind turbine’s aerodynamics and general operating behaviour, providing in-depth insight over

the current research being developed on this field, as well as for serving as a liaison agent between IST

and TU Delft.

v

Resumo

De entre as várias fontes de energias renováveis, a energia eólica é uma das que tem apresentado um

mais rápido desenvolvimento. No entanto, com este rápido desenvolvimento e expansão de turbinas

eólicas, aumentam também os impactos destas mesmas turbinas no meio ambiente e na saúde hu-

mana. Uma parte considerável da investigação tem-se focado no impacto sonoro que as turbinas

eólicas têm e em formas de o mitigar, melhorando a performance das turbinas no processo. O objetivo

deste trabalho foi a criação de um software modular, capaz de prever o ruı́do produzido por diferentes

geometrias de pás, permitindo ao utilizador definir novas pás, com diferentes números de secções e

painéis, perfis e outras caracterı́sticas geométricas, tais como o ângulo de torção. Neste trabalho, a

teoria dos elementos de pás-momento linear foi implementada para obter a performance aerodinâmica

das turbinas, acoplada a um código de painéis (XFOIL). A implementação da teoria dos elementos de

pás-momento linear e do modelo aeroacústico semi-empı́rico foram validadas com dados experimentais

das turbinas NREL Phase II e AOC 15/50, enquanto a Formulação 1A de Farassat foi verificada com

dados obtidos através de uma ferramenta validada, e utilizada pela universidade TU Delft. As capaci-

dades aeroacústicas do software são apresentadas no final do documento, servindo de exemplo para o

género de resultados que podem ser alcançados com os corretos ficheiros de entrada.

Palavras-chave: Aerodinâmica de turbinas eólicas, Aeroacústica de turbinas eólicas, Formulação1A, Modelo aeroacústico semi-empı́rico

vii

Abstract

From all the renewable sources of energy, wind energy is among the ones with a more rapid develop-

ment. With this rapid deployment of wind turbines, so does the impact of wind turbines grow, leading

to an increase in the awareness about these impacts on the environment and human health. A con-

siderable part of the research has focused on the noise impact of wind turbines, improving the perfor-

mance of the turbines in the process. The objective of this work was to create a modular software, that

could be used to predict the noise produced by different blade geometries, allowing the user to define

new blades, with different number of sections and panels, airfoil profiles and geometric characteristics,

namely twist angle. In this work, a blade element momentum theory model is implemented to predict

the aerodynamic performance of wind turbines, coupled with the panel code XFOIL for automation of

the procedure and blade geometry discretization. Two aeroacoustic prediction models were then em-

ployed, a semi-empirical model, based on the works of Brooks et al and Amiet, and a theoretical model,

Formulation 1A of Farassat. The semi-empirical model was validated against measurement data of the

NREL Phase II and AOC 15/50 wind turbines, while Formulation 1A of Farassat was verified against a

validated tool used by TU Delft. The software aeroacoustic capabilities are presented at the end of the

work, with an example of the type of results that can be achieved with the proper input data.

Keywords: Wind turbine aerodynamics, Wind turbine aeroacoustics, Formulation 1A, Aeroa-coustic semi-empirical model

ix

Contents

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

Resumo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii

Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix

Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxv

1 Introduction 1

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Wind Energy Today . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2.1 Wind Energy Worldwide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2.2 The Case of Europe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.3 The Case of Portugal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3 Wind Turbines Side Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3.1 Impact on the Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3.2 Impact on People’s Lives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.4 Wind Energy for the Future . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.4.1 Noise Legislation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.5 State-of-the-Art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.6 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.7 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2 Wind Turbine Noise 17

2.1 Acoustics Theoretical Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.2 Sources of Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3 The Ffwocs Williams-Hawkings Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.4 Formulation 1A of Farassat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.4.1 Numerical Algorithms for Noise Prediction . . . . . . . . . . . . . . . . . . . . . . . 30

2.5 Semi-Empirical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

xi

3 Wind Turbine Aerodynamics 33

3.1 Actuator Disc Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.2 Blade Element Momentum Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.2.1 Blade Element Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.2.2 Momentum Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.2.3 BEM Theory Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.2.4 BEM Theory Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.2.5 3D Stall-Delay Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.2.6 Extending the Angle of Attack Range . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.2.7 BEM Theory Iterative Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.2.8 BEM Theory Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4 Software Description 47

4.1 Module I: Aerodynamic Loading & Blade Surface Meshing . . . . . . . . . . . . . . . . . . 49

4.1.1 Aerodynamic Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.1.2 Blade Surface Discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.2 Module II: Noise Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.2.1 Input Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.2.2 Thickness Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.2.3 Loading Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.2.4 Signal and Noise Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5 Validation and Verification 61

5.1 Aerodynamic Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.1.1 Validation with Experimental Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.1.2 Verification with Aerodyn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

5.1.3 Discussion of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

5.2 Aeroacoustics Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

5.2.1 Formulation 1A of Farassat - Test Case . . . . . . . . . . . . . . . . . . . . . . . . 68

5.2.2 Semi-Empirical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

5.2.3 Comparison between aeroacoustic models . . . . . . . . . . . . . . . . . . . . . . 72

5.2.4 Discussion of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

5.3 Prove of Software Aeroacoustic Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . 75

6 Conclusions 79

6.1 Achievements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

6.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

Bibliography 83

A Formulation 1A Derivation (final steps) 97

xii

B Input Files Specifications 99

B.1 Main Input File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

B.2 Aerodynamic Loading Input File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

B.3 Mesh file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

B.4 Input Airfoils Input File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

C Scale of 1/3 Octave Bands 105

xiii

List of Tables

1.1 Installed Capacity in the EU-28 in 2014, 2015 and 2016, by country (Source: [7, 8]) . . . . 4

1.2 Portuguese legal limits for noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.3 German legal limits for noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.4 Danish legal limits for noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.1 Surface roughness lengths for representative locations (Source: [124]) . . . . . . . . . . . 41

3.2 Different parameters evaluated by the BEM Theory model . . . . . . . . . . . . . . . . . . 45

4.1 Geometric parameters of interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

5.1 BEM validation reference wind turbine characteristics . . . . . . . . . . . . . . . . . . . . 62

5.2 BEM verification reference wind turbine characteristics . . . . . . . . . . . . . . . . . . . . 64

5.3 NREL’s 5 MW Distributed Blade Aerodynamic Properties . . . . . . . . . . . . . . . . . . . 64

5.4 BEM verification test run definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65



5.7 Noise Semi-Empirical Models reference wind turbine characteristics . . . . . . . . . . . . 71

5.8 Hypothetical scenario characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

5.9 Hypothetical scenarios OASPL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

C.1 Scale of 1/3 Octave Bands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

xv

List of Figures

1.1 Annual installed capacity by region 2008-2016 (Source: [26]) . . . . . . . . . . . . . . . . 3

1.2 Global cumulative installed wind capacity (Source: [26]) . . . . . . . . . . . . . . . . . . . 3

1.3 Share of new renewable power capacity installations in 2015 and 2016 (MW). (Source:

Adapted from [7, 8]) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Annual onshore and offshore wind installations in the EU. (Source: [8]) . . . . . . . . . . . 5

1.5 Total capacity installed in Portugal throughout the years (Data source: [32]) . . . . . . . . 5

1.6 Diferent sources of Energy Production in Continental Portugal in January and August,

2016 (Source: Adapted from [35, 36]) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.7 Representation of the several impacts that wind turbines have on the environment (Source:

[3]) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.8 The range of human hearing (Source:[70]) . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.9 Size growth of commercial wind turbines (Source: [2]) . . . . . . . . . . . . . . . . . . . . 11

2.1 Example of a Wind Turbine noise spectra with different weighting scales (Adapted from

[106]) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2 Aerodynamic noise sources associated with wind turbine blades (Source: [109]) . . . . . 19

2.3 Graphical representation of the moving surface (Source: [115]) . . . . . . . . . . . . . . . 22

3.1 Actuator Disc Concept (Source: [124]) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.2 Blade element representation (Source: [124]) . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.3 Blade element velocity and force vectors (Source: [124]) . . . . . . . . . . . . . . . . . . . 36

3.4 Blade annulus representation (Source: [124]) . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.5 CT curve including Glauert’s empirical relationship for F = 0.9 (Data source: [131]) . . . . 39

4.1 Computational Modules developed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.2 Logical flowchart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.3 Example of aerodynamic loading obtained . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.4 NREL’s phase VI mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.5 Generic mesh panel (Source: Adapted from [115]) . . . . . . . . . . . . . . . . . . . . . . 52

4.6 Interpolation procedure illustrative representation . . . . . . . . . . . . . . . . . . . . . . . 56

4.7 Verification of the FFT implementation with MATLAB . . . . . . . . . . . . . . . . . . . . . 58

xvii

5.1 NREL’s phase VI blade planform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.2 NREL’s phase VI chord and twist distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.3 Force coefficients comparison between BEM model and experimental results . . . . . . . 63

5.4 Comparison between BEM model and experimental results . . . . . . . . . . . . . . . . . 63

5.5 Comparison between BEM model and Aerodyn results: Test case 1 . . . . . . . . . . . . 65



5.8 Verification of Farassat 1A implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

5.9 Frequency analysis in 1/3 octave bands . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

5.10 AOC 15/50 chord and twist distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

5.11 Noise generated by the AOC 15/50 wind turbine in 8 m/s winds . . . . . . . . . . . . . . . 72

5.12 Comparison of aeroacoustic methods for the NACA 0018 wing with flow velocity of 20 m/s 72

5.13 Different terms of the semi-empirical method, compared with Formulation 1A . . . . . . . 73

5.14 Comparison of Farassat 1A and Semi-empirical methods, without Laminar Boundary

Layer - Vortex Shedding Noise component . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

5.15 Different mesh geometry representations of the adapted blade (Down-sampled to fit view-

ing resolution) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

5.16 Hypothetical noise generated by the adapted NREL’s wind turbine . . . . . . . . . . . . . 77

5.17 Hypothetical noise generated by the adapted NREL’s wind turbine with different rotational

speeds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

xviii

Nomenclature

Greek symbols

α Angle of attack.

αj Quadrature weight coefficient.

αstall Stall angle of attack.

β Pitch angle.

χ Wake skew angle.

∆ Representation of a step/jump.

δ(f) Dirac delta function.

δij Kronecker delta.

η Lagrangian coordinates.

γ Yaw misalignment.

κ Total misalignment angle.

Λ Tip speed ratio.

λr Local speed ratio.

µ Molecular viscosity coefficient.

∇ Vector field divergence.

Ω Rotor rotational velocity.

φ Inflow angle.

ψ Azimuthal angle.

ρ Fluid density.

ρ0 Reference fluid density.

�2 D’Alembertian operator in 3D space.

xix

τ Blade axial torque.

τ Emission time.

θ local angle between the normal to the surface and radiation direction ~r.

ξ Tilt angle.

ζ Hellman’s exponent.

Roman symbols

A Aspect ratio.

a Axial induction/inflow factor.

a′ Tangential induction/inflow factor.

A∞ Cross-section area far upstream.

Ad Disc cross-section area.

Aw Wake cross-section area.

c̄ Airfoil chord.

c Speed of sound.

CD 3D drag coefficient.

Cd 2D drag coefficient.

CL 3D lift coefficient.

Cl 2D lift coefficient.

CM 3D moment coefficient.

CP Power coefficient.

CT Thrust coefficient.

Ca Axial force coefficient.

Cr Radial force coefficient.

f Function that describes the sound source surface.

fCd 3D drag coefficient correction factor.

fCl 3D lift coefficient correction factor.

Fhub Hub correction factor.

Ftip Tip loss correction factor.

xx

G Free-space Green’s function.

g Equal to τ − t+ r/c.

H Heaviside function.

h Height.

h0 Reference height.

I Acoustic Intensity.

Int Interpolation operator.

J Jacobian.

Ki Approximation of an integral over a mesh element.

L̇ Rate of change of angular momentum.

Lden Equivalent sound pressure level.

Ld Average sound pressure level during the day.

Le Average sound pressure level during the evening.

Ln Average sound pressure level during the night.

Ṁr Derivative of Mr in respect to the source time, Ṁir̂i.

Ṁ Rate of change of momentum.

ṁ Mass flow rate.

M Mach number.

Mr Mach number in the radiation direction, Mir̂i.

ni Unit outward normal.

Nb Number of blades.

ṗ Time derivative of p.

p Aerodynamic pressure.

p Pressure.

p′ Acoustic pressure.

p+ Pressure upstream of rotor disc.

p− Pressure downstream of rotor disc.

Pij Compressive stress tensor.

xxi

Q Generic function of space, ~x, and time, t.

r̂i Unit vector in the radiation direction, r̂i = (xi − yi)/ri.

R Blade length.

r Blade local radius.

r Distance between sound source and observer.

Rhub Hub radius.

S Sound source area.

T Thrust acting on a blade.

t Observer time.

Tij Lighthill’s stress tensor.

Ū Mean flow velocity.

pref Reference pressure.

prms Root mean square pressure.

u Velocity vector.

u, v, w Velocity Cartesian components.

U∞ Inflow velocity.

Ud Flow velocity at the rotor disc.

Uw Flow velocity at the rotor wake.

v̇n Derivative of Mr in respect to the source time, v̇ini.

vh Velocity at reference height h.

vn Local normal velocity of the surface, vini.

vr Velocity in the radiation direction.

vhref Flow velocity at reference height.

W Relative flow velocity.

z0 Roughness length.

Subscripts

i, j, k Computational indexes.

x, y, z Cartesian components.

xxii

e Emission time.

∞ Free-stream condition.

hub Relative to the rotor hub.

L Loading noise.

lower Lower limit of a value.

n Normal component.

previous Value of the previous iteration.

ref Reference condition.

ret Retarded time.

rms Root mean square.

T Thickness noise.

tip Relative to the blade tip.

upper Upper limit of a value.

Superscripts

iter Iteration.

xxiii

Glossary

BEM Blade element momentum theory is a theory

that combines blade element theory with mo-

mentum theory.

BPF Blade passing frequency is defined as the prod-

uct between the rotational frequency of a blade

and the number of blades of the rotor.

BVI Blade Vortex interaction is a phenomenon

that describes the interaction between vortexes

shed by a blade’s wake and the next blade.

CAA Computacional Aeroacoustics is a branch of

fluid dynamics that uses numerical methods to

study sound phenomena.

CFD Computational Fluid Dynamics is a branch of

fluid dynamics that uses numerical methods

and algorithms to solve problems that involve

fluid flows.

DFT Discrete Fourier Transform refers to the origi-

nal algorithm used in the Fourier analysis of a

discrete signal.

DNS Direct Numerical Simulation is a CFD simu-

lation in which the Navier-Stokes equations

are numerically solved without any turbulence

method. Is it the most computationally expen-

sive method used to solve the Navier-Stokes

equations.

EU The European Union is a political and eco-

nomic union of 28 member states located in Eu-

rope.

xxv

FFT Fast Fourier Transform refers to an algorithm

used to calculate the Discrete Fourier Trans-

form of a signal.

FW-H Ffowcs Williams - Hawking refers to an inte-

gration method, condensed in an equation by

Ffowcs Williams and Hawking and represents

an extension of Lighthill’s acoustic analogy.

GHG Greenhouse Gases are gases that exist in the

atmosphere and that absorb and emit infrared

radiation, being responsible for the so called

greenhouse effect.

HAWT Horizontal Axis Wind Turbine is a wind turbine

which rotor rotates around a vertical axis.

IEC International Electrotechnical Commission is a

international standards organization, that pub-

lishes International Standards for electrotechni-

cal technologies.

LES Large-Eddy Simulation is a CFD simulation in

which the smallest scales of turbulence are ig-

nored in order to save computational cost.

NASA The National Aeronautics and Space Adminis-

tration is an independent agency of the United

States federal government responsible for the

civilian space program, as well as aeronautics

and aerospace research.

NIMBY Not In My Back Yard is a term used to char-

acterize an attitude of opposition that certain

individuals take regarding new developments

because they are close to them (In their back-

yard).

NREL National Renewable Energy Laboratory is an

American laboratory dedicated to the research,

development, commercialization and deploy-

ment of renewable energy and energy effi-

ciency technology.

OASPL Overall Sound Pressure Level is the total en-

ergy contained in a frequency spectrum.

xxvi

PIV Particle image velocimetry is an optical method

of flow visualization. It is used to obtain velocity

fields together with related properties in fluids.

RANS Reynolds-Averaged Navier Stokes equations

are a set of equations that form the base of a

turbulent CFD method. They were derived by

Osborne Reynolds.

SPL Sound Pressure Level is a measure of the

sound produced by a variation in pressure. It

uses a logarithmic scale to deal with the large

scale of acoustic power involved.

VAWT Vertical Axis Wind Turbine is a wind turbine

which rotor rotates around a vertical axis.

WHO World Health Organization is a specialized

agency of the United Nations that is concerned

with international public health.

WT A wind turbine is a device that converts the

wind’s kinetic energy into electrical energy.

XFOIL XFOIL is an interactive program for the design

and analysis of subsonic isolated airfoils.

xxvii

xxviii

Chapter 1

Introduction

The use of the energy of the wind in human activities has a long history, from the propulsive power used

to impel boats and ships to the creation of wind mills used to make flour and to the first attempts to fly

heavier than air objects [1, 2]. With the industrial revolution and the discovery of how to harness the

energy contained within fossil fuels, society turned to the cheapest ways to obtain power in order to fuel

economical growth [2]. More recently, renewable sources of energy have been increasing in significance

as environmental concern grows [3, 4]. At the end of 2015, in Paris, “The 2015 International Climate

Change Agreement” was penned and the international community reached the first legally binding global

climate agreement where countries pledge on taking concerted action in order to “put the world on an

emissions pathway that will keep the global temperature rise below 2o Celsius” [5], in comparison to

pre-industrial levels.

From all the renewable sources of energy, wind energy is among the ones with a more rapid devel-

opment [6–8]. As the technology is developed and reaches a more mature state, wind power becomes

more and more accessible, to the state that it becomes competitive with more traditional sources of

energy, such as fossil fuels [1, 2, 9, 10]. Besides being a way to combat global warming and having a

smaller footprint on the planet (than other more pollutant sources of energy), wind energy can also be a

way to achieve energy independence from traditional sources of energy and from foreign countries that

supply them. It is also a way to supply electric power to remote areas of the planet and populations that

do not have access to electricity [10, 11].

1.1 Motivation

Despite wind energy’s growing importance, there are several negative consequences of the implantation

of wind turbines (WTs) [2–4]. These vary from impact on the environment, namely on birds and bats

[12, 13], to direct impact on people’s lives, particularly to those that live nearby wind turbines and are

annoyed by their noise and visual impact on the landscape (see section 1.3.1) [1, 4, 14, 15]. Phenom-

ena such as the Not In My Back Yard (NIMBY), together with other groups of people who are against

1

wind turbine development, present opposition to the growth of wind turbine technology and to an even

faster deployment [16–18]. Noise is one of the biggest causes for concern when people consider the

implementation of onshore WTs [2, 14, 15]. This has to do with the fact that the majority of WTs installed

onshore are located near residential areas, where the noise produced by WTs can be a source of an-

noyance (see section 1.3.2) [15, 19–22].

Noise is therefore a very important aspect of the WT operation that cannot be neglected, if wind

energy is to play an increasing role as a dependable energy source. Although future scenarios point out

to an increasing development of offshore technology, onshore technology has still a room for expansion,

mainly on countries with low employment of renewable sources of energy and with vast areas where

turbines can be implemented [23, 24].

1.2 Wind Energy Today

Wind energy’s industry is now well established and it’s importance as an alternative to fossil fuels is

recognized worldwide, with WT presenting a “payback” period of between 3 and 9 months, in terms of

Greenhouse Gases (GHG) emissions. With this in mind and as of 2014, for every new megawatt of

capacity installed in a country in a given year, 14 jobs are created in the WT complete supply chain [23].

Although the installed capacity changes significantly according to geographical region and from country

to country, there is a clear tendency to invest in renewable sources of energy and specifically, in wind

energy [7, 10, 23, 25].

In this section, three topics will be examined, the state of wind energy worldwide, with focus on the

macro factors that enable or disable the development of WT, the state of wind energy in Europe, with

special care for the European Union (EU) and its regulatory framework, and the state of wind energy in

Portugal, where details will be given regarding the particular aspects that allowed for the implementation

of the technology.

1.2.1 Wind Energy Worldwide

As previously mentioned, the investment in wind energy is very dependent on regional factors, such as

wind potential, political support and availability of other sources of energy, among others. This can easily

be observed in Figure 1.1.

2

Figure 1.1: Annual installed capacity by region 2008-2016 (Source: [26])

Overall, there is a growth trend (see Figure 1.2), with countries like China leading the charge [23].

Figure 1.2: Global cumulative installed wind capacity (Source: [26])

1.2.2 The Case of Europe

Europe is a case of interest, as the presence of the EU and its regulatory framework enables the imple-

mentation of policies that have an impact on all member-states. In 2000, only 2.4% of the total installed

power capacity in the EU came from wind energy; in 2016, it accounted for 17%. With this increase in

installed capacity, in 2015 wind energy supplanted hydro as the third largest power generation in the EU

and as the first renewable energy technology in installed capacity [7, 27].

In 2015, wind energy accounted for 44.2% of all the renewable sources of power installed, that

together made up 77% of all new installed capacity in the EU. In 2016, these values increased to 51%

and 86% respectively and wind energy came to overtake coal as the second largest form of power

generation capacity in Europe [8, 27].

3

Figure 1.3: Share of new renewable power capacity installations in 2015 and 2016 (MW). (Source:Adapted from [7, 8])

Despite the regulatory framework and the stimulation of “green” sources of energy, there are signifi-

cant differences between countries in terms of installed capacity (See Table 1.1).

Table 1.1: Installed Capacity in the EU-28 in 2014, 2015 and 2016, by country (Source: [7, 8])Installed Capacity (MW) Installed 2014 Installed 2015 Installed 2016 End 2016

Austria 405 323 228 2.632Belgium 293.5 274.2 177 2,386Bulgaria 10.1 - - 691.2Croatia 85.7 45 34 422.7Cyprus - 10.8 - 158

Czech Republic 14 - - 282Denmark 104.9 216.8 220 5,228Estonia 22.8 0.7 7 310Finland 184.3 379.4 570 1571France 1,042.1 1,073.1 1,581 11,939

Germany 5,242.5 6,013.4 5,443 50,019Greece 113.9 172.2 239 2391Hungary - - - 329Ireland 213.0 224 384 2,870

Italy 107.5 295 282 9230Latvia 0.4 - 2 63

Lithuania 0.5 144.7 178 602Luxembourg - - - 58

Malta - - - -Netherlands 175 586 887 4,328

Poland 444.3 1,266.2 682 5,782Portugal 222 132 268 5,316Romania 354 23 52 3,028Slovakia - - - 3.1Slovenia 0.9 2.5 - 3.4

Spain 27.5 - 49 23,074Sweden 1,050.2 614.5 493 6,519

UK 1,923.4 975.1 736 14,339Total EU-28 12,037.4 12,800.2 13,926 161,330

In the preceding table there is no distinction between onshore and offshore, but while the onshore

market presents a consistent behaviour in the last five years, offshore installations more than doubled

in 2015 compared to 2014. In 2016 there was a 48.4% decrease in offshore installations compared with

4

2015, which was an exceptional year due to grid-connection delays in Germany being resolved [8]. (see

Figure 1.4).

Figure 1.4: Annual onshore and offshore wind installations in the EU. (Source: [8])

The recent investments made in offshore technology suggest that a trend towards offshore WTs is in

place [28–30].

1.2.3 The Case of Portugal

In Portugal, before the WT boom, the electrical grid was privately owned and the companies that owned

the grid were not interested in the restructuring costs needed to make the grid viable for the variable

energy that comes from WTs. Only after governmental intervention was the grid infrastructure made

public and prepared for the inclusion of energy from WTs. Then, together with the help of feed-in tariffs

(where there is a state subsidy for each kW produced with wind energy) the conditions were set to allow

a significant growth of the installed capacity in the following years (see Figure 1.5) [31].

Portugal appears in eighth position in terms of installed capacity in the EU at the end of 2016, with

a capacity of 5,316 MW. 2016 represented a recovery in terms of installed capacity (268 MW), after the

decrease in 2015 (from 222 MW in 2014 to 132 MW)(See Table 1.1).

0

1000

2000

3000

4000

5000

6000

1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016

Cu

mu

lati

ve

Inst

alle

d C

apac

ity (

MW

)

Year

Figure 1.5: Total capacity installed in Portugal throughout the years (Data source: [32])

5

In more recent years the growth rate has decreased, in part as a consequence of the economic

crisis but also as the availability of suitable areas to place turbines onshore decreases and is reaching

its saturation point [33]. Renewable sources of energy play already a very important part in the por-

tuguese market, with more than 50% of the total energy produced in Portugal during 2016 originating

from “variable” renewable sources of energy, with wind energy contributing to 22% of the total [34].

Figure 1.6: Diferent sources of Energy Production in Continental Portugal in January and August, 2016(Source: Adapted from [35, 36])

In what was a record and reached international news [37, 38], in 2016, Portugal ran on renewable

energy alone, for four days straight (more precisely 107 hours), from May 7th to May 11th. This further

consolidates the rational behind the bet on renewable sources of energy regarding environmental ob-

jectives set for the near future. Nevertheless, there is still a long way to go in terms of the contribution

of renewable sources of energy to achieve the objectives of using 40% of all the energy consumed from

renewable sources by 2030 [35]. Together with a bet in different sources of energy, such as solar and

biomass, wind energy will play an important rule in the coming years while increasing efforts are being

made in the development of offshore technologies, as in the rest of Europe [7, 28].

1.3 Wind Turbines Side Effects

Although once thought to be a free of impact source of energy, wind energy (in the way it is harvested

today) is not completely harmless and its impact should be known and well studied in order to be mini-

mized [3, 4, 12, 22]. In this section, the impacts of WTs will be presented and analysed, in two different

parts, one where the environmental impacts will be presented and a second part where the impact on

modern society and people’s lives will be reviewed, given their importance.

1.3.1 Impact on the Environment

Although the energy obtained from the wind using turbines is clean energy, meaning that the planet is

not being polluted in the process, there are some environmental impacts that should be assessed. From

all the different effects that WTs cause on the environment, the ones presented in the following figure

(see Figure 1.7) are usually referred [2, 3].

6

Impacts of Wind Turbines

Visual Impact

Noise

Shadow Flicker

Impact on the Wildlife

Land Requirements

Climate Change

Figure 1.7: Representation of the several impacts that wind turbines have on the environment (Source:[3])

The first three items are usually considered to have a meaningful impact on people’s lives, and will

be reviewed separately on the following section (See 1.3.2). The other items will be analyzed together.

One of the most visible consequences of the installation of inland WTs is the direct impact on wildlife.

Avian and bat mortality increases and there are also impacts regarding the destruction of habitat in the

installation sites of big wind farms [2–4]. While birds die when they hit the turbine blades or tower, bats

can also suffer from barotraumas due to pressure differences that exist in the rotor plane [4, 13].

Several studies have been performed in order to understand how and why these collisions occur and

in ways to mitigate them [12, 13, 39–42]. The most significant impact of turbines on birds occurs on

species of long longevity and low reproductive rates, such as raptors, which are more vulnerable to loss

of individuals [12].

It has been found that different species can be more or less likely to hit WTs, due to their behaviour

and/or general characteristics [12, 39, 40]. For instance, it has been found that wing loading and aspect

ratio are relevant parameters, as they define the flight characteristics of the species and therefore the

risk of collision [40]. Some species also present habits that make them particularly suitable to collision.

These habits are usually related with hunting and foraging [4, 12, 40]. Migrating species can also be

severely affected, particularly when their migrating route passes by a wind farm [4, 40, 42].

Offshore WTs also present some impacts on marine birds that need to be taken into account when

evaluating the impact of offshore turbines installation [4, 43]. These range from increasing mortality of

marine birds to the loss of habitat for several marine species due to operational noise emissions and

vibrations. Although the creation of artificial reefs by the installed turbines can be seen as something

positive, it leads to changes in the local ecosystem. The installation, as well as other maintenance

operations of the turbines are also periods of great disturbance for wildlife, with several species being

affected [44].

7

Overall, the location of the WTs is considered one of the most important aspect when trying to

minimize the impact in wildlife. The turbine arrangement in a wind farm is also important [4, 40, 42].

Measures to reduce these impacts include a priori studies of the installation site to evaluate possible

bird and bat communities that live there, together with long-term analysis of the location, to verify if the

turbines will not be installed in the migrating path of any species of bird or bat [4, 42, 45].

An alternative, and one of the most effective ways to decrease bird mortality is restricting turbine

operation when birds are found near the turbines or whenever bad weather decreases visibility of the

turbines. This approach has the downside of needing human or other type of surveillance running [46].

Several deterrents have also been employed, with distinct effectiveness. Auditory deterrents are among

the most effective although long-term use loses effectiveness. Other deterrents include bioacoustic tech-

niques and the use of lasers. Increasing turbine visibility has also been a research topic [40].

In terms of the space required to install an inland WT, a 3 MW turbine requires about 1600 m2 of

land (or about 40 m × 40 m) [2]. Although the installation of WTs does not prevent the surrounding

grounds from being used agriculturally or in other way, when large deployments of turbines are planned

it may be difficult not to find conflicts between the land requirements for the wind farms and the existing

land-use. Besides these effects, the installation of the turbines industrially may lead to the contamination

of the construction site with waste-water and oil which may cause serious damage to the ecosystem and

keeping the terrain around the turbines completely clear of vegetation during turbine operation can lead

to soil erosion and also loss of biodiversity [4].

Although renewable sources of energy, and particularly WTs, are generally regarded as a solution

for global warming, there is now evidence that WTs can also cause weather and climate changes [47].

This is still not a widely spread discussion topic and only a few significant studies have been performed

to date [47, 48]. Research suggests that the causes associated with these local climate changes can

be associated with the turbulent wake of the turbines, that promotes the mixing of different layers of air,

that would otherwise remain unmixed. In one study, it was found that the wind farm analysed had an

warming effect during the night and a cooling effect during the day [48]. The question now is whether

these consequences are mild enough so that the use of WTs is still preferable to conventional sources

of energy, as deployment of WTs keeps on growing.

1.3.2 Impact on People’s Lives

One generally considers health to be a state in which a person is without diseases or infirmities. How-

ever, the World Health Organization (WHO) defined health in a much more complete way, stating that

“Health is a state of complete physical, mental and social well-being and not merely the absence of dis-

ease or infirmity” [49]. This definition dates back to 1946 and since 1948 it has not suffered any amend

[50]. It is a relevant definition to keep in mind as it shows that not only direct impact events like diseases

should be taken into account, and that even small perturbation on people’s lives caused by WTs can

impact the nearby population’s health.

8

When analysing the effect that WTs have on people’s lives, several aspects come into play. The ones

people find the most relevant for their lives are the noise emitted by the turbines and the visual impact

of turbines on the landscape. Interestingly, most studies reviewed found that there is a relation between

the two, and that people are the most annoyed by the turbine’s noise when they found them visually

unpleasant or oppose the use of WTs [4, 22, 51–53].

One study shows that the colours of the WT tower play an important rule on how the turbine noise is

perceived by people and how well it is accepted in the landscape, with colours like red and brown found

to be more clashing with the surroundings [51]. The attitude towards the WTs was found to be one of the

most important factors when considering the annoyance perceived by people who live in the vicinities of

WTs, [19, 52, 53]. This may explain why people who benefit economically from the turbines do not find

the same noise as annoying as people who do not [19, 21, 54].

WTs visual impact is highly subjective and personal views on the advantages and disadvantages

of wind energy influence how people regard the impact that WTs have on the landscape. This impact

changes according to the landscapes’ perceived aesthetic value, with landscapes seen as pleasant to

the eye being more negatively impacted, while less attractive landscapes might even benefit from the

introduction of WTs turning unpleasant sights into greener environments [55]. It is clear that annoyance

is dependent on personal attitudes towards WTs, together with several other interconnected factors,

namely local natural and/or cultural heritage, distance from inhabited areas and number and disposition

of WTs [52, 55]. WTs’ visual impact can also be felt negatively on property value and tourism [56, 57].

Shadow Flicker is a phenomenon that may occur in certain conditions, where shadows are casted in

a oscillatory fashion due to the blade rotation of WTs. It happens more frequently early in the morning

and late in the afternoon, when the sun is lower in the sky. Although photo-induced epilepsy is generally

a concern [58, 59], WTs currently employed in large wind farms have a rotational speed lower than 60

rpm (which would match the risk frequency of 3 Hz ,according to Harding [59]) and therefore WT photo-

induced epilepsy is unlikely [22]. Careful sitting can lead to a minimization of the occurrences and to a

decrease in nuisance as most authors note that shadow and light flicker can be evaluated as a visual

cue that can contribute to visual annoyance [22, 58, 60].

Although most studies find that the noise produced by the WTs is a cause of annoyance, the majority

of the studies reviewed states that a direct link between this noise and negative health consequences

was not yet found [4, 22, 60]. Despite this, some studies reported that people who are annoyed by the

noise are more likely to suffer from sleep disturbances and other symptoms related with a decrease in

quality of life [22, 61, 62]. Most studies agree that the best way to manage and reduce the downsides

of the implementation of the WTs is to openly discuss the project with the affected populations, in order

to minimize the concerns of the population and eventual consequences related with turbine noise and

visual impact on the landscape [16, 63, 64].

9

The direct use of the energy produced with the turbines is also of importance for the affected popu-

lations, with studies finding that people see with good eyes when the local community benefit from the

energy produced locally [17, 65], while on the other hand, the “export” of this energy is not well seen by

the local community [64].

WTs produce the highest levels of sound in a lower frequencies range (up to 2000 Hz) [66]. Infra-

sound is considered to be sound of frequencies below about 20 Hz (exact value depends from country

to country [67]), and low-frequency sound is considered to be sound between 20 - 200 Hz [14, 68]. The

human hear can perceive sound in the frequency range of 20 - 20,000 Hz, being more sensitive to the

sounds in the range from 1 to 5 kHz (see Figure 1.8) [69].

Figure 1.8: The range of human hearing (Source:[70])

Most studies find correlation between the sound level emmited by WTs and the risk of annoyance

registered by the populations [20, 21], with one of these studies showing that the percentage of people

who notice the sound coming from the WTs increased almost linearly with increasing Sound Pressure

Level (SPL) [20].

One interesting finding in the literature review is that WT noise can be annoying, even without being

in the audible range and perceived as sound by the human brain [22]. Salt and Hullar [71] investigated

the sensitivity of the human ear to infrasounds and found that there is the possibility that a specific type

of cells present in the ear can sense infrasounds, even though they are not perceived as sound and our

brains do not interpret them that way. These discoveries, not yet fully understood, suggest that more

research is required and lead the way for new investigations and new concerns about the impacts of

WTs in peoples’ lives.

Sound pressure level and sound intensity are concepts that translate the physical variable respon-

10

sible for sound, pressure, into more usable scales, namely a logarithmic scale in the case of sound

pressure level and a power scale for sound intensity. The mathematical definition of this concepts is

given in detail in section 2.1, together with a more in-depth analysis of the noise produced by WTs.

1.4 Wind Energy for the Future

Sustainable growth is in the order of the day and increasing resources are being allocated to find solu-

tions for the climate change and to keep the global temperature increase below 2o Celsius, the maximum

rise scientists predict to be the limit, above which climate change cannot be reversed [5].

Taking a closer look in the near future and as 2020 approaches, wind energy is one of the bets of

the EU regarding sustainable growth and meeting the 3 big objectives: reducing by 20% the emission of

GHG (when compared to 1990 emissions); reaching 20% of consumed energy from renewable sources;

and increasing energy efficiency by 20% [72]. Wind energy capacity has been growing steadily (See

Figure 1.2 ) which has lead to a flourishing industry in Europe, with 27.5 billion Euro invested to finance

wind energy development in 2016, in a 5% increase over the previous year. To this contributed several

reasons being the political support one of the most relevant [7, 9, 27, 73, 74]. One important aspect to

note is that investment in offshore wind energy increased 39% year on year, while investment in onshore

wind energy dropped to 9.3 billion Euro, which represented the first decrease in 5 years.

Throughout the last couple of decades and as WTs claimed evermore power from the wind, so did

technological improvements grow [2, 10]. This, together with an increasing demand for energy globally

[75] lead to considerable turbine size growth (See Figure 1.9) [30, 58, 76–78].

Figure 1.9: Size growth of commercial wind turbines (Source: [2])

This increase in size allows for the capture of more energy, while at the same time allowing for a

reduction of the carbon footprint per unit energy generated [2]. Currently, the largest WTs prototypes

being made have blades that span in excess of 80 m, the same as Airbus’ A380 wing span [79, 80].

As global energetic demands continue to increase, so must new solutions be encountered to face this

issue. So, at least for a near future, predictions point to ever growing turbines with the ability to harness

11

more power [10].

The most recent developments are being made in offshore technology, regarding locations where the

winds are faster and steadier when compared to inland locations [29, 30]. Although most WTs installed

offshore to date are usually close to shore and in shallow waters, there has been increasing efforts to

take the technology further away from the coast, to deep waters [28, 30]. There are still some problems

to overcome, namely the support structure needed to allow deployment in deep waters. The availability

of offshore WTs, together with the maintenance required is also a problem, one dependent on sea/ocean

conditions [30]. All these obstacles increase the cost of offshore WTs when compared to their inland

counterpart [9, 58]. Despite this, these problems are being addressed and better cost effective solutions

are expected to appear in the coming years [29].

1.4.1 Noise Legislation

Noise Legislation is a sensitive topic, and one that needs attention when designing wind turbines, since

different countries have different rules. In fact, in the EU, there is no common legislation regarding

environmental noise, and much less, wind turbines’ specific noise. There is in place an Environmental

Noise Directive (Directive 2002/49/EC), which serves as a guideline by which all member-states should

develop noise management plans. It is by no means a tool to set noise limits and set target values [81].

That being said, it is important to study the legislation that is binding in different countries, to understand

the different perspectives that are in place regarding noise control.

Three countries have been selected and their specific laws respecting noise will be presented. These

countries are Portugal, Germany and Denmark.

Portugal

In Portugal, no specific noise legislation regarding WTs is in effect, being applied the general noise

regulation [82]. It specifies three different zones, a sensitive one, reserved for residential use and related

utilizations, a mixed zone, defined as an area with different uses from those defined in the sensitive zone

and an ’urban consolidated zone’, defined as a sensitive or mixed zone with stable occupation in terms

of edification. The following table presents the limits that are set for each zone.

Table 1.2: Portuguese legal limits for noiseZone Max Lden dB(A) Max Ln dB(A)

Sensitive 55 45Mixed 65 55Urban Consolidated 63 53

12

Where Lden is given by

Lden = 10 log1

24

13× 10Ld10 + 3× 10Le + 510 + 8× 10Ln + 510 , (1.1)

where Ld is the average SPL during the day, Le the average SPL during the evening and Ln during the

night.

Germany

Germany is the European country with the largest amount of wind energy power capacity installed,

with more than double the second largest, Spain. In Germany, as in Portugal, there is no specific noise

legislation regarding WTs in effect, being applied the general noise regulation [83]. It specifies different

zones, and different limits for both day and night. The Day period is defined between 6 a.m. and 10 p.m.

and the Night period as the remainder.

Table 1.3: German legal limits for noiseZone Day dB(A) Night dB(A)

Industrial 70 70Commercial 65 50Core areas, village areas and mixed-use 60 45General residential areas and small residential estate areas 55 40Purely residential areas 50 35Sensitive areas, with hospitals and nursing homes 45 35

Denmark

Denmark is the European country with the largest wind penetration rate, and one of the few that has

specific noise legislation regarding WTs in effect [84]. This country also includes specific legislation in

respect to low frequency noise. A novelty that has since then been adopted by researchers in different

countries [85]. Besides this, it is also specified a different noise limit according to the wind speed,

since it is considered that at higher wind speeds, noise increases naturally, and therefore there is a

masking effect of the noise produced by wind turbines. Two wind speed are considered, measured at

IEC (International Electrotechnical Commission) reference height of 10 m. The following table presents

the noise limits currently being applied.

Table 1.4: Danish legal limits for noiseZone v(h=10) = 6m/s v(h=10) = 8m/s

Open countryside 42 dB(A) 44 dB(A)Noise sensitive land 37 dB(A) 39 dB(A)

In both cases, the limit for low frequency noise is 20 dB. This limit is applied to the calculated indoor

noise level at both 6 and 8 m/s wind speed. Low-frequency noise is considered to be noise emitted with

frequencies between 10 and 160 Hz. [86].

13

A quick analysis of the legislation of these three countries reveals how substantially different the laws

are geographically. While both Portugal and Germany have no specific legislation for the noise produced

by wind turbines, Denmark has a different approach, with noise limitations to be applied specifically to

Wind Turbine noise. Denmark even goes one step further, by defining a noise limit for low-frequency

noise. All countries have differences in the way they stablish different zones with different noise limits.

When comparing Portugal and Germany, it is interesting to note that Germany presents twice the number

of zones Portugal does. At the same time, Germany’s upper noise limit is 73 dB(A) (Lden), for an

industrial setting, which is higher that the higher noise limit in Portugal.

1.5 State-of-the-Art

Wind Turbine noise prediction models can be divided in two types, semi-empirical correlations and the-

oretical models, derived from fundamental aerodynamic and aeroacoustic formulations. Semi-empirical

correlations are mostly used to compute 1/3 octave bands noise, using formulas derived from aerody-

namics, experiments and fittings. Some of these codes are the work by Brooks et al. [87] to obtain airfoil

self-noise, Lowson [88] for blade inflow noise and Amiet and Paterson [89] for turbulent inflow noise.

On the other hand, Farassat’s 1A formulation belongs to the theoretical model category. This for-

mulation is derived from Ffowcs Williams-Hawkings’ Equation [90], which in turn, is based on Lighthill’s

acoustic analogy [91]. Although the evolution of computational power has led to a great development of

previously untapped techniques, computational aeroacoustics (CAA) is an area of interest that has been

slow becoming broadly used. This is mainly because of its intrinsic complexity, given the involvement

of several disciplines which are still in frank expansion. Such areas, exemplified by computational fluid

dynamics (CFD), form the bases of CAA.

These techniques, which are used to obtain detailed aerodynamic data, are still computationally

expensive and their use is limited by their complexity. Several techniques have been used to obtain

the data required by the acoustic numeric models, and the results vary with the model used [92, 93].

Some of the models used are Reynolds-Averaged Navier Stokes (RANS) but results are somewhat

lacklustre, giving the difficulty presented in obtaining turbulent models compatible with the unsteady,

viscous dominated features of the flow around wind turbine blades [94, 95]. On the other hand, fully-

resolved simulations, using either Direct Numerical Simulation (DNS) or Large-Eddy Simulation (LES),

still require more computational power than what is presently available. This has led to the development

of Hybrid approaches [94].

This means that robust and fast techniques, such as the previously mentioned semi-empirical mod-

els, continue to be widely used in the initial design steps and optimization procedures. Complete nu-

merical simulations are then used to investigate details of noise production mechanisms and to validate

experimental results and final blade designs [96, 97]. One very important aspect to consider is that

aeroacoustic models are as good as the input data they receive (given that they are properly imple-

mented) [96, 98].

In recent years, research has been focused in quantifying the trailing edge noise, one of the dominant

14

sound sources in most operating conditions wind turbines face, while at the same time being of great

aerodynamic interest, with the development of new types of trailing edges, for example with serrated

edges and control surfaces [99–101].

This does not mean that all development of theoretical models able to predict wind turbine noise

have seen their development halted, but that fast, accurate and precise models are being used more

and more, given the greater demand for tools which can be used in optimization processes. This lead

to several improvements being made to semi-empirical correlations, in order to increase their accuracy

and reliability, which means that interest in theses models is not lost, but simply that focus is shifted,

given the current demands [98, 102, 103].

Alongside the involvement of different disciplines, such as Aerodynamics, Aeroacoustics, Computa-

tional Mathematics and Modelling, the current interest in the development of more silent, more efficient

WTs together with design and production constraints, make this subject of great relevance in Engineer-

ing, particularly in the Aerospace branch.

1.6 Objectives

As inland wind turbines grow in number and the best locations for their placement are already taken by

wind farms, wind turbines are increasingly being placed near populated areas. Together with the visual

impacts on populations, the noise emitted by wind turbines is one of the principal concerns when placing

a wind turbine. This makes the correct estimation of the noise produced by a particular wind turbine

design an important design tool. As it has been seen, there are different approaches to the determination

of the noise produced by a wind turbine, which can be divided in two main groups, the experimental

correlations based algorithms and the theoretically developed ones. The principal objective of this work

is to implement the Formulation 1A of Farassat in order to correctly estimated the noise emitted by

wind turbines. However, in order to be able to implement Formulation 1A of Farassat, aerodynamic

loading data and wind turbine blade surface meshing are necessary. Since this information is not readily

available, there is the need to also obtain it. This way, the primary goals of this thesis are to develop a

versatile tool, which may use precision aerodynamic data as input for noise calculations, but also with

the possibility of obtaining initial aerodynamic loading prediction with an in-house simulation.

• Develop a computational tool that can be used for the noise prediction of WTs;

• Develop a computational tool that can be used for the noise prediction of linear moving bodies,

coupled with a panel surface discretization and aerodynamic pressure information as inputs;

• Predict the thickness and loading noise generated by the rotor at any observer position;

• Predict the aerodynamic loadings acting on a wind turbine rotor;

• Discretize the blade geometry.

15

1.7 Thesis Outline

This thesis is divided in 7 chapters, including the present, introductory one.

Chapter 2 sets the grounds for the wind turbine’s aeroacoustic prediction methodologies. Several

important acoustic concepts are introduced and the aeroacoustic models to be used are explained.

Chapter 3 introduces the basic concepts on wind turbine aerodynamics, and how the fundamen-

tal variables of interest regarding wind turbine aerodynamics are obtained through the use of a blade

element momentum theory (BEM) model.

Chapter 4, entitled ‘Software Description’, presents the basic algorithms and reasoning behind the

workings of the computational tool developed, focusing in detail to Formulation 1A, the primary objective

of this work.

Chapter 5 presents the results obtained with the different computational modules developed, focusing

on the validation and verification of the models implemented, namely the aerodynamic BEM model and

the aeroacoustic semi-empirical and theoretical models. Still included in this chapter is a small section

which pretends to demonstrate aeroacoustic software capabilities, showing the type of acoustic results

expected when using Formulation 1A of Farassat coupled to the correct type of input data, with unsteady

aerodynamic loading file.

Finally, chapter 7 presents this dissertation’s conclusions and how the work developed could be im-

proved or build upon, with added functionalities and new/better capacities, with the objective of obtaining

a more accurate wind turbine aeroacoustic tool.

Furthermore, this dissertation includes several appendixes, referred to throughout the document,

which complement some aspects of this work, namely by exemplifying the input files required by the

different computational modules.

16

Chapter 2

Wind Turbine Noise

In this chapter wind turbine noise will be analysed. First, an overview of the fundamental concepts of

acoustics to retain will be made (section 2.1), followed by a description of the sources of sound in a

wind turbine (section 2.2). Acoustic models are then regarded. The derivation of the Ffowcs-Williams-

Hawking equation is the starting point (section 2.3). Finally, the mathematical derivation of Formulation

1A of Farassat is presented (section 2.4).

2.1 Acoustics Theoretical Overview

Sound is defined as a pressure oscillation propagating through a medium. This pressure oscillation can

have different magnitudes, leading to different sound intensities. Sound propagates at around 340 m/s

in air and 1500 m/s in water. Due to the considerable range of acoustic power from different sound

sources (from a human shout with 10−5 watt to a rocket launch with a acoustic power of 107 watt [69]), a

logarithmic scale is used, the bel. The sound pressure level (SPL) has decibel units (dB) and is defined

as:

SPL = 10 log10

(p2rmsp2ref

)= 20 log10

(prmspref

), (2.1)

where pref is the reference pressure, representing the minimum value of pressure oscillation to which the

human auditory system is capable of perceiving and prms is the root mean square value of the pressure

oscillation (pref is usually assumed to be 2× 10−5Pa in the air for a sound with 1000 Hz [104]):

p2rms = limT→∞

(1

T

∫ T0

p(t)2

). (2.2)

Sound Intensity, depicted in Figure 1.8 and previously mentioned in section 1.3, also known as acous-

tic intensity, represents the energy carried by a sound wave per unit area (W/m2 in SI). Mathematically

it is given by ~I = p · ~u.

17

Noise, as defined by the Merriam-Webster dictionary, is sound “that lacks agreeable musical quality

or is noticeably unpleasant” or “any sound that is undesired or interferes with one’s hearing of something”

[105]. It is noise then, that engineers try to understand and correctly estimate in order to discover means

to eliminate/mitigate.

It is usual to employ a weighted decibel scale when performing acoustic measurements. The db(A)

is used to try and correct for the different sensibility that the human ear has at different frequencies [66].

In this scale, frequencies below the 200 Hz have a much lower “weight”. Different scales are used to

measure the impact of different sources of sound; for instance the sound produced by wind turbines,

primarily in the lower frequency range, can be measured with a C or G weighting scale, leading to dB

readings significantly different from those obtained with the A weighting scale (see Figure 2.1).

100 101 102 103

f(Hz)

10

20

30

40

50

60

70

80

90

100

SP

L (

dB

)

Unweighted Spectrum

A weighted spectrum

C weighted spectrum

G weighted spectrum

Figure 2.1: Example of a Wind Turbine noise spectra with different weighting scales (Adapted from [106])

As seen before, in section 1.5, governmental institutions use the A-weighting scale when imposing

noise limits. IEC 61400 is the International Standard that regulates WT design requirements, acoustic

noise measurement techniques, power performance measurements among several other aspects. Part

11 of this Standard contains all the information regarding acoustic noise measurement techniques [107].

This document defines the guidelines for the uses of these three weighting scales. In most cases, A-

weighting is the scale that should be used. The other two scales should be used in specific situations,

when disturbance is expected to occur due to low-frequency and/or infrasound.

Low frequency noise is considered by the standard to be noise emitted between 20 and 100 Hz. In

these cases, the A-weighting scale may not appropriately describe the annoyance caused by this sound,

underestimating its nuisance; The C-weighting scale should be used.

Infrasound noise is considered by the standard to be noise emitted below 20 Hz. In such cases,

sound is barely perceptible to the human ear, as seen before, but can lead to vibrations in the sur-

rounding environment and in extremis, to annoyance; The G-weighting scale should then be applied,

according to ISO 7196 [107]. Even though it can usually be dismissed as unimportant in terms of an-

noyance, infrasound noise, generated by the passing of the blades in front/back of the tower, gives

WT sound its characteristic “thumping” noise, with frequencies which are multiples of the blade passing

18

frequency (BPF) [108].

2.2 Sources of Noise

Wind Turbine noise can be of two distinct origins: Mechanical and Aerodynamic. Mechanical sources of

sound are generally negligible in most modern WTs [66, 109, 110] and will only be summarized here.

These noise sources include: Gearboxes; Generator; Yaw Drives; Cooling Fans.

Sound of aerodynamic origin dominates the noise spectrum of a modern WT. Aerodynamic noise can

generally be divided into narrowband (discrete-harmonics) and broadband components. The discrete-

frequency noise contains the deterministic components of the thickness and loading noise, as well as

the BPF and multiple integers. Broadband noise arises from the interaction of the rotating blades and

tower with the inflow, usually turbulent in nature. The following figure (Figure 2.2) shows the different

phenomena behind the emission of noise by a moving blade.

Figure 2.2: Aerodynamic noise sources associated with wind turbine blades (Source: [109])

Wind turbines’ aerodynamic noise can generally be divided in different categories [66, 109]:

• Turbulent Inflow Noise;

• Turbulent Boundary Layer Trailing Edge Noise;

• Separated Stall Noise;

• Trailing Edge Bluntness Vortex Shedding Noise;

• Laminar Boundary Layer Vortex Shedding Noise;

• Tip Vortex Noise.

These different noise sources will be shortly explained.

19

Turbulent Inflow Noise

Turbulent Inflow Noise has its origin in the interaction between the atmospheric turbulence and the

rotating blades of the WT. Atmospheric turbulence is caused by two effects, aerodynamic and thermal.

Aerodynamic turbulence results from the interaction between the wind and the environment, ground

surface and topology. Thermal turbulence results from the thermodynamic processes that occur at the

Earth’s surface which lead to convection currents.

Turbulence is characterized by its intensity and length scale. Turbulence intensity is a measure of the

turbulent fluctuations that occur in the flow, and is given by the ratio between the standard deviation and

the averaged mean wind velocity. Turbulence length scale is indicative of the size of the eddies present

in the flow. The size of this eddies change the nature of the noise generated. Eddies larger than the

airfoil affect the aerodynamic loading acting on the blade as a whole, while small eddies lead to local

fluctuations of the loads acting on the WT’s blade, inducing higher frequency noise.

Turbulent Boundary Layer Trailing Edge Noise

Turbulent Boundary Layer Trailing Edge Noise is the result of the interaction between the turbulent

boundary layer that develops over the blade surface and its trailing edge. A boundary layer develops on

the surface of any airfoil within a flow, beginning at the stagnation point close to the leading edge. When

certain conditions are met (specific angle of attack and Reynolds number), this boundary layer changes

its nature from laminar to turbulent, at a certain point along the chordwise direction. This turbulent

boundary layer induces pressure fluctuations that are in the origin of noise. Turbulent boundary layer

trailing edge noise is usually broadband in nature.

Separated Stall Noise

With increasing angles of attack (AOA), flow can separate from the airfoil surface on the suction

side and the airfoil stalls, creating an area of highly unsteady flow. This phenomenon, associated with

vortices shedding into the wake of the airfoil, originates Separated Stall Noise.

Trailing Edge Bluntness Vortex Shedding Noise

Trailing Edge Bluntness Vortex Shedding Noise results from vortex shedding due to blunt trailing

edges. This vortex shedding originates a fluctuating pressure at the trailing edge, originating a tonal

radiation of sound from the trailing edge. This noise source is extremely dependent on the geometry of

the trailing edge, with thicker trailing edges leading to increased noise amplitude.

Laminar Boundary Layer Vortex Shedding Noise

Laminar Boundary Layer Vortex Shedding Noise results from interactions between laminar boundary

layer instabilities and the vortexes shed at the trailing edge. Most modern WTs operate in conditions

where the Reynolds number is high and the flow is turbulent around the blades, meaning that this noise

mechanism does not yield a big contribution.

Tip Vortex Noise

Tip Vortex Noise results from the interaction between the vortices released at the blade tip and its

surface. These vortices are released due to the pressure differential between the suction and pressure

surface and this noise mechanism is dependent on tip geometry.

20

Formulation 1A of Farassat leads to a different division of noise terms, which result from the solution

of two wave equations (Equations 2.11, 2.12). These equations yield the Loading and Thickness noise.

This will be examined in detail further ahead (refer to section 2.3). Thickness and Loading Noise are

known together as rotational noise and represent the results from linear aeroacoustic theory. Thickness

noise represents the noise generated by the fluid that is displaced by the blades (displacement that is

proportional to the thickness of the blade) while Loading Noise represents the noise generated due to

the aerodynamic load acting on the blade.

In other machines with rotating components, such as helicopters, another phenomena may occur,

called blade vortex interaction (BVI), where the rotating blades interact with the wake released from a

blade that was previously in that position in space. This usually occurs in low-speed descents and/or

hover conditions. Due to the lower rotational speed of WTs, this is not a common problem.

On the other hand, the tower of an horizontal axis wind turbine (HAWT) disturbs the inflow passing

through the blades at the BPF. Whenever a blade passes through the tower there is a load fluctuation

that leads directly to an acoustic pulse [66, 111], phenomenon that goes by the name of Impulsive Noise.

2.3 The Ffwocs Williams-Hawkings Equation

Several acoustic models and formulations are based on Ffowcs Williams-Hawkings equation

(FW-H equation), including Farassat’s formulations. This equation appeared for the first time in 1980

[90] and it is a extension of the ideas presented by Lighthill’s in his acoustic analogy [91]. It expands

the acoustic analogy to include general surfaces in arbitrary motion. The main ideas behind the deriva-

tion of the FW-H equation will be presented in this section. The development of the rational behind the

derivation of the FW-H equations follows [90, 112].

Aeroacoustic theory is based on the equations of mass and momentum conservation of a compress-

ible fluid, together with an equation of state. These equations, valid in the region exterior to any closed

internal surface, lead to an inhomogeneous wave equation when combined. This equation character-

izes the generation and propagation of sound waves in the exterior region to the closed internal surface.

However, it is merely valid in the volume outside the surface, an inhomogeneous situation in space.

This problem is overcome by conceptualizing an unbounded fluid, divided into regions which are

described as mathematical surfaces that have a correspondence with the real surfaces. The motion of

the fluid on and outside those surfaces is equivalent to the real one, while the motion of the fluid inside

the surfaces can differ (it is usually assumed simpler and therefore different from the exterior flow). In

order to preserve the physical discontinuities, mass and momentum sources have to be introduced,

which act as sound generators.

21

The concept of generalized function is used quite extensively, for providing a simpler handling of

the discontinuities present in the flow, namely by allowing the validity of the mass and momentum con-

servation equations in the flow. In a very simple way, generalized functions allow for the treatment of

discontinuous or non-smooth functions as working with smooth functions in classical analysis.1 As it

is needed to understand some important steps of the derivation of the FW-H equation, the concept of

generalized derivative will be introduced.

Lets consider a function q(~x), function of ~x = (x1, x2, x3) with a discontinuity across the surface

f(~x) = 0. If a jump ∆q of q is defined across the surface f = 0 as ∆q = q(f = 0+) − q(f = 0−), the

generalized partial derivative is:

∂̄q

∂xi=

∂q

∂xi+ ∆q

∂f

∂xiδ(f), (2.3)

where δ(f) is the Dirac delta function.

In our case of interest, the moving surface in the flow is defined mathematically by f(~x, t) = 0, in a

way that Of = ~n, where ~n is the unit outward normal vector. This implies that f > 0 outside the surface

and f < 0 inside it. (see Figure 2.3)

Figure 2.3: Graphical representation of the moving surface (Source: [115])

The mass and momentum conservation equations outside the surface (f > 0) are given by equations

2.4 and 2.5, respectively:

∂ρ

∂t+

∂

∂xi(ρui) = 0, (2.4)

∂ρui∂t

+∂

∂xj(ρuiuj + Pij) = 0, (2.5)

where ρ is the fluid density, ρui is the component of fluid momentum and Pij is the compressive tensor.

1For further details on generalized functions and applications to Aerodynamics and Aeroacoustics see [113, 114].

22

By interpreting all the variables as generalized functions (holding all the conservation laws valid),

and by using the generalized partial derivative rule (eq. 2.3) on the mass and momentum conservation

equations (2.4 and 2.5), one can write:

∂̄ρ

∂t+

∂̄

∂xi(ρui) =

∂ρ

∂t+ ∆ρ

∂f

∂tδ(f) +

∂

∂xi(ρui) + ∆(ρui)

∂f

∂xiδ(f), (2.6)

∂̄

∂t(ρui) +

∂̄

∂xj(ρuiuj + Pij) =

∂

∂t(ρui) + ∆(ρui)

∂f

∂tδ(f) +

∂

∂xj(ρuiuj + Pij) + ∆(ρuiuj + Pij)

∂f

∂xjδ(f)

. (2.7)

If we are dealing with a solid, impermeable surface, the normal velocity of the fluid at the surface is

the same as the normal velocity of the surface (un = vn), where un = uini is the local fluid velocity in

the direction normal to the data surface. The derivative ∂f/∂xi gives the component of the unit outward

normal to the surface f = 0, ni and vn = −∂f/∂t is the local normal velocity of the surface f = 0. With

this in mind, equations (2.6 and 2.7) can be simplified:

∂̄ρ

∂t+

∂̄

∂xi(ρui) =

∂ρ

∂t+

∂

∂xi(ρui) + ∆ρ(−vn)δ(f) + ∆(ρui)

∂f

∂xiδ(f)

= (ρ− ρ0)(−vn)δ(f) + (ρun)∂f

∂xiδ(f)

= ρ0vnδ(f) + ρ(un − vn)δ(f)

= ρ0vnδ(f)

, (2.8)

∂̄

∂t(ρui) +

∂̄

∂xj(ρuiuj + Pij) =

∂

∂t(ρui) +

∂

∂xj(ρuiuj + Pij) + ∆(ρui)

∂f

∂tδ(f)

+∆(ρuiuj + Pij)∂f

∂xjδ(f)

= (ρui)(−vn)δ(f) + (ρuiuj + Pij)njδ(f)

= ρui(un − vn)δ(f) + Pijnjδ(f)

= Pijnjδ(f)

. (2.9)

In these equations, the jumps correspond to ∆ρ = (ρ − ρ0), ∆(ρui) = (ρui) and ∆(ρuiuj + Pij) =

(ρuiuj + Pij). The jump in the stress tensor Pij can be interpreted as a difference between the stress

tensor and its mean value, effectively acting mathematically as if the value of the jump is given by Pij .

23

The final steps to obtain the FW-H equation follow the derivation of the jet noise by Lighthill. The only

difference is that the derivatives are regarded as generalized. It is then taken the derivative∂̄

∂tof both

sides of equation (2.8) and the derivative∂̄

∂xiof both sides of equation (2.9) and the result from the latter

is subtracted from the former. Then, from the resulting equation, the term ∇2[c2(ρ− ρ0)

]is subtracted

from both sides and the equation is rearranged to maintain the wave operator acting on c2(ρ − ρ0) on

the left-hand side. Replacing c2(ρ − ρ0) = p′ the result is the Ffowcs William-Hawking equation for an

impermeable surface:

�̄2p′(~x, t) =∂

∂t[ρovnδ(f)]−

∂

∂xi[Pijnjδ(f)] +

∂2

∂xi∂xj[H(f)Tij ] . (2.10)

The symbol �2 =1

c2∂2

∂t2− ∇2 is the wave or D’Alembertian operator in 3D space and Tij =

ρuiuj +Pij− c2(ρ−ρ0)δij represents the Lighthill stress tensor. H(f) represents the Heaviside function,

δij is the Kronecker delta.

In the previous equation, one can see the appearance of the thickness and loading noise source

terms 2 , respectively:

�2p′T =∂

∂t[ρovnδ(f)] , (2.11)

�2p′L = −∂

∂xi[Pijnjδ(f)] , (2.12)

where p′T , p′L represent the pressure perturbation due to the thickness and loading noise sources, re-

spectively.

The last term on the right-hand side of the FW-H equation (eq. 2.10) models all the non-linearities of

the noise generation problem due to the local sound speed variation and the finite fluid velocity near the

surface of the blade and represents a quadrupole noise source. This term gains importance with high

rotational velocities, and is required if high speed impulsive noise is a concern. However, the inclusion

of this term is rather computationally expensive. This is the reason why, up until recently, it was usually

neglected in acoustic calculations [112]. These are also the reasons why it was decided that this noise

source would not be implemented in the developed software.

2Thickness and loading noise sources are often labelled monopole and dipole sources, respectively. Care should be takenwhen one is dealing with moving surfaces, since then, the nature of these sources is distinct from stationary monopole and dipolesources.

24

2.4 Formulation 1A of Farassat

In this section, the Formulation 1A of Farassat will be derived. It is this formulation that serves the base

for the numerical prediction of wind turbine noise in this work. Formulation 1A follows Formulation 1 of

Farassat, that contrary to Formulation 1A, has an observer time derivative that is taken numerically and

that increases computational effort and reduces accuracy. Formulation 1A of Farassat appeared for the

first time in [116], however the derivation here presented follows [117], for Farassat’s simpler approach.

Formulation 1 of Farassat will be derived as an intermediate step in the derivation of Formulation 1A.

Like previously stated, the quadrupole term is computationally demanding, requiring volume integra-

tion and accurate flow field conditions in order to attain accurate results. Besides this requirements,

this noise source is more significant for high-speed applications, near the transonic regime. For these

reasons, the quadrupole source will be ignored from here on out. The goal of this procedure is then to

obtain the solutions of the two wave equations (2.11) and (2.12). These equations are in the form:

�2p′ = Q(~x, t)δ(f). (2.13)

The solution of the equation can be derived using the free-space Green’s function:

G(~x, t; ~y, τ) =

0, τ > tδ(τ − t+ r/c)/4πr, τ 6 t, (2.14)where r =| ~x − ~y |, with (~x, t), (~y, t) being the observer and source space-time variables. The term

between brackets τ − t+ r/c is usually replaced by g. The solution to equation (2.13) is then given as:

4πp′(~x, t) =

∫Q(~y, τ)δ(f)

δ(g)

rd~y dτ. (2.15)

It is important to emphasize that the ~x, ~y frames are fixed to the undisturbed medium. It is usual to

introduce Lagrangian coordinates with a ~η-frame of reference that moves with the moving surface, which

allows for an easier manipulation of the variables involved. The introduction of this moving frame of

reference leads to the conclusion that once the motion of the blade is specified, the trajectory of a point

on the moving surface described by a fixed ~η is specified in the ~y-frame. This means that y is a functi

development of an aeroacoustic prediction tool for wind ......formulation 1a of farassat. the...

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