Modelling Of Noise From Wind Turbines Wei Jun Zhu, s010845 Mechenical Department,DTU DK-2800,Lyngby 2004.02.02

Preface The present work was carried out to fulfil my study of M.Sc. Programme in Wind Energy. The thesis work was started at 15th of July in 2003 and finished after 7 months. During this period, professor Jens Nørkær Sørensen and associate professor Wen Zhong Shen were attached as my supervisors. I’m most thankful for their marvellous ideas and kindness guidance. Also I would like to give my appreciation to those who were mentioned in the reference. Both acoustics and aerodynamics knowledge were covered in this project. And due to the limitation of my knowledge, there could be some mistakes in the report. Any critics and advices will be most welcome.

W ei Jun Zhu 05/02, 2004

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Abstract The aim of this report is to give a new prediction model for the aerodynamical generated noise from wind turbines. A 2D wind turbine noise propagation model is also developed using acoustic sound ray theory. Aerodynamic noise is generated when the rotor encounters smooth flow. It contains airfoil self-noise and turbulence inflow noise. The present semiempirical model is coupled with CFD and aerodynamic calculation so as to improve the accuracy of the prediction model. By doing CFD computations, boundary layer parameters for some relevant airfoil profiles are stored as a database which is used directly for the noise prediction model. The total noise spectrum for a given wind turbine is compared with experiment and encouraging result is obtained. The sound pressure level at receiver point is further corrected by coupling with the sound propagation model. A wind turbine is regarded as a dipole sound source placed at the hub height. To determine the changes of sound pressure level, several factors are considered: Geometric spreading, Directivity, Air absorption, Wind effect, Temperature gradient effects and Ground effects.

Contents 1 Introduction

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2 Introduction of sound and noise 2.1 Noise and sound fundamentals . . . . . . . . . . . . . . . . 2.1.1 The physical phenomena of sound wave . . . . . . . 2.1.2 The mathematical description of sound wave . . . . 2.1.3 Frequency f . . . . . . . . . . . . . . . . . . . . . . . 2.1.4 Sound Pressure Level Lp , Sound Power Level Lw . 2.2 Sound radiation . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Basic theory of aerodynamic sound radiation . . . . 2.2.2 Aeroacoustic theory applied for case of wind turbine 2.3 Wind turbine noise standards and regulations . . . . . . . . 2.3.1 Sound power level measurement standards . . . . . . 2.3.2 Regulations for acceptable noise level . . . . . . . .

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8 8 8 9 11 13 16 16 17 18 18 19

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20 20 22 22 24 26 27 28 28 30

4 Noise prediction model for wind turbines 4.1 Classification of the present model . . . . . . . . . . . . . . . 4.2 Prediction model for inflow turbulence noise . . . . . . . . . . 4.2.1 Turbulence characteristic . . . . . . . . . . . . . . . . 4.2.2 Inflow noise prediction . . . . . . . . . . . . . . . . . . 4.3 Prediction model for TBL-TE noise and separation-stall noise 4.4 Prediction model for LBL-VS noise . . . . . . . . . . . . . . .

31 31 33 33 35 37 41

3 Noise mechanisms of wind turbines 3.1 Mechanical noise . . . . . . . . . . . . . . . . . . . . . 3.2 Aerodynamic noise . . . . . . . . . . . . . . . . . . . . 3.2.1 Low-frequency noise . . . . . . . . . . . . . . . 3.2.2 Turbulent inflow noise . . . . . . . . . . . . . . 3.2.3 Turbulent boundary layer trailing edge noise . 3.2.4 Laminar boundary layer vortex shedding noise 3.2.5 Tip vortex formation noise . . . . . . . . . . . 3.2.6 Trailing edge bluntness vortex shedding noise . 3.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . .

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4.5 4.6 4.7 4.8 4.9 4.10

Prediction model for Tip vortex formation Prediction model for TEB-VS noise . . . . Boundary layer thickness calculations . . Aerodynamic calculation . . . . . . . . . . Sound directivity . . . . . . . . . . . . . . Wind turbine coordinate systems . . . . .

5 Analysis of the noise prediction model 5.1 The effect by different airfoil contours 5.2 Effect of the tip pitch angle . . . . . . 5.3 Effect of sound directivity . . . . . . . 5.4 Trailing edge bluntness . . . . . . . . . 5.5 Tip shape . . . . . . . . . . . . . . . . 5.6 Sawtooth trailing edge . . . . . . . . . 5.7 Conclusion . . . . . . . . . . . . . . .

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6 Noise propagation model for wind turbine 6.1 Introduction . . . . . . . . . . . . . . . . . . . . 6.2 General propagation model . . . . . . . . . . . 6.3 Air absorption . . . . . . . . . . . . . . . . . . 6.4 Effect of terrain . . . . . . . . . . . . . . . . . . 6.4.1 Flat terrain . . . . . . . . . . . . . . . . 6.4.2 Valley-shaped terrain . . . . . . . . . . 6.5 Wind and temperature effect . . . . . . . . . . 6.6 Results and analysis . . . . . . . . . . . . . . . 6.6.1 Effect of air absorption . . . . . . . . . 6.6.2 Example based on flat ground surface . 6.6.3 Example based on valley shaped surface 6.7 Conclusion . . . . . . . . . . . . . . . . . . . .

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7 Bibliography

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A List of symbols

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B List of figures

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C List of tables

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D Spherical Reflection Coefficient Q

88

E Calculation of the size of the Fresnel-zone

91

F Coordinate transformation matrix

93

G Deterministic model for wind

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3

H Calculation of reference source height and receiver height

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I

99

The effect of wedge

J Program guide

102

4

Chapter 1

Introduction In June 2003, the total capacity in European countries amounted to 24,904 MW reported by EWEA1 [1]. Europe is becoming a major side for exploitation of wind engery in the near future. By 2010, wind power would be generating an annual 167 Tera watt hours of electricity which is enough to satisfy half of the increase in renewable energy output expected under the European Union’s own projection for 2010. The future of using wind energy is so exciting that it has many advantages such as: no air pollution, no need of any fossil or nuclear resources during operation. But with the fast increase of wind energy development, it also gives rise to the problems concerning public acceptance of wind energy. The noise and visual impact are the main drawbacks. The visual impact is the effect of a wind turbine on the terrain which is experienced by the observer. The way to minimize this visual pollution is not discussed in this report. The noise from wind turbines may annoy people who live around. This problem becomes especially serious due to the fact that wind turbines are densely covered in Europe in contrast to many other countries outside of Europe. Therefore it’s necessary to estimate the noise level in the field where the wind turbines are installed. This is discussed in details in this report. Generally, the noise from wind turbine is composed with mechanical noise and aerodynamic noise. The mechanical noise is caused by the different operating machine elements which can be reduced efficiently by many engineering methods and will certainly not reduce the power output. However, the way to reduce aerodynamic noise from wind turbines is a bit complex which should be studied together with power efficiency. A fully established method to predict the wind turbine noise is still limited. 1

The European Wind Energy Association

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In June 2001, a numerical algorithm for acoustic noise generation from a 2D airfoil is extended[2]. This is a purely theoretical method and involves two steps comprising a viscous incompressible flow part and an inviscid acoustic part. However, the calculation will be very large to predict the noise from a whole wind turbine. For engineering purpose of use, several semiexperimental noise prediction models are available. Some of the models are originally developed for application on helicopter and aircraft wings. One of the first model was carried out by Grosveld [4] in 1985. In 1986, a similar model by De Wolf [5] is followed. In 1981, Viterna [6] applied a method to the low-frequency noise estimation from a wind turbine. Another method from Lohmann [7] is based on the principle of aerodynamic loads with a lifting surface method. A rather complex self-noise prediction model for NACA series airfoil is published by NASA[3] in 1989. Brooks, Pope and Marcolini[3] performed a set of experiments for NACA0012 airfoil sections (with seven different chord length). All acoustic and aerodynamic measurements are performed at Reynolds numbers between 4 × 10 5 and 1.5 × 106 . The measurements were performed with low turbulent freestream wind speed up to 71.3 m/s and angle of attack in the range 0 to 25 degrees. The boundary layer parameters at trailing edge were measured by hot-wire probe on both sides of the airfoil. The sound pressure levels were calculated based on both the tripped (forced transition) and untipped (natural transition) boundary layer parameters. They investigated five selfnoise mechanisms by doing different set of measurements. For all these five self-noise mechanisms, an extensive empirical scaling law was found to fit the aerodynamic and acoustic wind tunnel tests of single airfoil sections, see chapter 4. However, the aerodynamic and acoustic measurements were only based on NACA0012 airfoil which may not suitable for other airfoil profiles. The airfoil sections of most wind turbine blades change with the blade radius and also the flow conditions are various at different blade positions. Therefore, the boundary layer parameters at trailing edge should be calculated instead of using experimental data from NACA0012 airfoil. In order to do so, it is assumed that the acoustic measurements performed for the NACA0012 airfoil simply scale with boundary layer parameters of the applied airfoil. Thus a database is created to store boundary layer parameters at trailing edge for various airfoil profiles. To model the velocity field around the tower, the 2D potential flow is assumed. Also the induced velocities at each blade element are found from the aerodynamic calculation. Thus the relative wind velocity at each blade element is computed more accurately. All these will improved the accuracy of the angle of attacks which are the most important parameter to determine the boundary layer thickness.

6

For turbulent inflow noise, the turbulent intensity and length scale are determined at each blade sections instead of using single data at the hub height position since different turbulence intensity and length scales are found at various blade sections.

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Chapter 2

Introduction of sound and noise Sound is the effect of the wave motion in gases, liquids and solids. It can be caused by numerous mechanisms. And it’s always associated with rapid small-scale pressure fluctuations which produces sensations to the human ear. Noise is defined as any unwanted sound. This is due to the complicated human ear organ [8].

2.1 2.1.1

Noise and sound fundamentals The physical phenomena of sound wave

Since fluids are not able to transmit shear forces, so that they are lack of holding their shapes. Therefore, the volume change leads to the change of pressure at the mean time. This pressure change generates sound waves in the fluid which is compressional oscillating. The small molecules of the fluid oscillate back and forth in the direction of sound propagation. And the oscillatory pressure in the fluid is normally very small compare to the static pressure. When the fluctuating pressure is at the level about 10 −4 times the standard atmospherical pressure, the correspond sound pressure level is up to 120 dB in the normal air condition. This sound pressure level is extremely high which is close to the threshold of pain. To simplify the irregular sound crests, sound rays are often used to predict the wave. A sound ray is an arrow which shows where each part of a wave front is headed. Wave propagate in different directions will interf ere. When sound waves reach a rigid barrier it will be ref lected. Their angles of incidence and reflection will be equal. If the barrier is more or less soft, the wave will be absorbed and some of the wave energy will be reflected back in opposite shape. The sound ray will change it’s direction if it prop-

8

agates in an inhomogeneous medium. This is called ref raction. It occurs when the medium has temperature gradient or density gradient. The sound waves will be scattered by small obstacles. Waves can be dif f racted for instance bend around edges. When the wave propagate into an aperture, that section passing through its center is unaffected. Where the wavefront ends touch the aperture edges, diffraction reshapes them into arcs. The amount of diffraction is affected by aperture size and wavelength. Some properties of sound ray are shown in figure 2.1-2.4.

Figure 2.1: Reflected by plane ob- Figure 2.2: Reflected by concave stacle obstacle

Figure 2.3: Refraction

2.1.2

Figure 2.4: Diffraction

The mathematical description of sound wave

The governing equations for the aerodynamic sound generation and propagation are the well-known control equations of fluid dynamics: i) The mass equation; ii)The momentum equation; iii) The energy equation. To express the equation with the dynamic sound pressure, the result is the linear wave equation: ∂ 2 p0 ∂ 2 p0 ∂ 2 p0 1 ∂ 2 p0 + + = ∂x2 ∂y 2 ∂z 2 c2 ∂t2 9

(2.1)

where p’ is the acoustic pressure which is defined as the pressure difference between dynamic pressure and the static pressure(the pressure when the fluid is at rest). c is the sound speed at a certain fluid. In perfect gases, c is the function of the adiabatic bulk modulus and the equilibrium density of the medium: p (2.2) c = Ks /ρ For gases, Ks = γp0 , where γ is the specific heat at constant pressure to that at constant volume and p0 is the static atmospheric pressure. Sound waves have two different types: i)Plane sound waves and ii)Spherical sound waves. They are distinguished by the type of their wavefronts. The plane wave is the basic concept throughout the acoustic technology. For plane waves, the wavefronts which is far from the sound source are regarded as plane instead of a curvature of spherical. At a certain time and on any plane perpendicular to the direction of propagation, the local variables on this plane are the same. Therefore, the plane wave can be written as a one-dimensional linear wave equation: 1 ∂ 2 p0 ∂ 2 p0 = ∂x2 c2 ∂t2

(2.3)

As an example, a harmonic plane wave propagation in x-direction can be written as:
ω (2.4) p0 = p1 sin (ct − x) + ϕ = p1 sin(ωt − kx + ϕ) c

where p1 is the amplitude of the wave, ω is defined as 2π times the frequency f , and ϕ is the phase angle. k is the wave number which is defined as k = ω/c.

A sinusoidal source will generate a sound field which varies harmonically at all positions with a same frequency from the harmonica sound source. Therefore, at any given position the sound pressure is often expressed with a complex form: pˆ0 = Aej(ωt+ϕ) (2.5) For a plane wave that propagates in the x-direction, the complex form is written as: pˆ0 = pi ej(ωt−kx) (2.6) The sound field varies with ejωt , in eq.(2.1), if we replace ∂/∂t with jω 1 and replace ∂ 2 /∂t2 by −ω 2 , the Euler’s equation of motion can be rewritten into: jωρˆ u + ∇ˆ p0 = 0 1

The first derivative of ejωt with respect of time is jωejωt

10

(2.7)

where u is the particle velocity in the plane propagating wave. And the wave equation can be simplified into Helmholtz equation form: ∂ 2 pˆ0 ∂ 2 pˆ0 ∂ 2 pˆ0 + + + k 2 pˆ0 = 0 ∂x2 ∂y 2 ∂z 2

(2.8)

The other sort of sound waves is spherical sound waves. If the sound source is spherically symmetric, the sound wave equation in a free field can be expressed in spherical coordinate system. It can be simply written as: ∂ 2 p0 2 ∂p0 1 ∂ 2 p0 + = ∂r 2 r ∂r c2 ∂p0 2

(2.9)

This is also identical in form with the one-dimensional wave equation. A harmonic spherical sound wave is a solution of the Helmholtz equation: ∂ 2 (r pˆ0 ) + k 2 r pˆ0 = 0 ∂r 2

(2.10)

The diverging wave in the complex notation can be written as: pˆ0 = A

2.1.3

ej(ωt−kr) r

(2.11)

Frequency f

A sound single can be broadband or narrowband. It is characterized by whether the sound spectrum covers a wide range of frequencies or not. To analysis a sound source, the frequency spectrum of the sound source has to be determined. If the sound source is unsteady, the sound pressure will be a function of time. It is much more convenient to study the frequency domain of the sound source than to look at the dynamic pressure. In the later chapters, the noise level emitted from the wind turbines will be investigated in frequencies range of 20Hz to 20kHz2 . And it shows that the frequency domains are different due to different noise mechanisms. With different center frequencies, the frequency range of the spectrum can be divided into several bands. A sound single can be decomposed into some spectral components by using digital analyzers. The analyzer can filter a series of frequencies with relative bandwidth which is a certain percentage of the center frequency. The most common filters in acoustics are narrow band,1/3-octave band and octave band. Narrow band is used when the sound single has strong periodic or tonal 2

The frequency range which human ear may respond.

11

signal. Such a spectrum gives the most detailed diagram of the sound single. The terms of one octave and one-third octave denote the frequency ratio of lower limiting frequency and the upper limiting frequency which is the the boundary of the band. An octave is frequency ratio of 2:1. The frequency ratio of lower boundary frequency and the upper boundary frequency is 1/2. Which means: fl = fc /21/2 , fu = 21/2 fc (2.12) and the center frequency is the geometric mean value: p fc = f l fu

(2.13)

In a similar way, the one-third octave band is defined: fl = fc /21/6 ,

fu = 21/6 fc ,

fc =

p f l fu

(2.14)

It follows that each one-octave band is formed by three adjacent one-third octave bands. Ten one-third octaves are nearly equal to a decade, and a one-third octave is nearly equal to one tenth of a decade. The standard octave and one-third octave band center frequencies are given in table 2.1 which follows ISO standard[9]. To obtain the sound pressure for a frequency band for any stationary sound single, the mean square value identical with the sum of mean square values of their frequency components. This can be obtained by a parallel bank of contiguous filters: X p2rms = p2rms,i (2.15) i

Human ear is not equally sensitive for all the frequencies. The auditory system changes significantly with the frequencies. The maximum response for human hearing occurs for frequencies between 1000Hz and 5000Hz. It is of very weak sensitive for low frequencies. This should be taken into account to modify the measured sound pressure level. There are several weighting curves to modify this change although such simple curves can not imply the complicated human auditory system. These curves are shown in figure 2.5. And the correspond weighting value are listed in table 2.1. A-weighting is most commonly used. This A-curve correlates in general better with the main effects of noise than measurements of the sound pressure level with a flat frequency response. However, if strong low frequency sound pressure level presents in the spectrum diagram, B or C-weighting is much more reasonable to choose3 . 3

Fortunately, the low-frequent noise generates from wind turbine is not at very high pressure level(see the results in later chapters). Thus A-weighting filter is used to predict the wind turbine noise.

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1/3-oct. frequency (Hz) 10 12.5 16 20 25 31.5 40 50 63 80 100 125 160 200 250 315 400 500 630 800 1000 1250 1600 2000 2500 3150 4000 5000 6300 8000 10000 12500 16000 20000

A-weighted (dB) -70.4 -63.4 -56.7 -50.5 -44.7 -39.4 -34.6 -30.2 -26.2 -22.5 -19.1 -16.1 -13.4 -10.9 -8.6 -6.6 -4.8 -3.2 -1.9 -0.8 0.0 -0.6 1.0 1.2 1.3 1.2 1.0 0.5 -0.1 -1.1 -2.5 -4.3 -6.6 -9.3

B-weighted (dB) -38.2 -33.2 -28.5 -24.2 -20.4 -17.1 -14.2 -11.6 -9.3 -7.4 -5.6 -4.2 -3.0 -2.0 -1.3 -0.8 -0.5 -0.3 -0.1 0.0 0.0 0.0 0.0 -0.1 -0.2 -0.4 -0.7 -1.2 -1.9 -2.9 -4.3 -6.1 -8.4 -11.1

C-weighted (dB) -14.3 -11.2 -8.5 -6.2 -4.4 -3.0 -2.0 -1.3 -0.8 -0.5 -0.3 -0.2 -0.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -0.1 -0.2 -0.3 -0.5 -0.8 -1.3 -2.0 -3.0 -4.4 -6.2 -8.5 -11.2

Table 2.1: The response of standard A-,B-,C-weighting filters in frequency bands

2.1.4

Sound Pressure Level Lp , Sound Power Level Lw

As we know it is the sound pressure which makes sense to our ear. And the most important measurement of sound is the root mean square sound 13

Figure 2.5: Standard frequency weighting curves

pressure: prms =

q

p2 =

1 T →∞ T lim

Z

0

T

p2 (t)dt


1/2

(2.16)

However, since the human ear does not response linearly to the amplitude of the sound pressure, such a rms pressure can not give sufficient information about the sound. So that the sound pressure level is always given in logarithmic scale and presented with decibels(dB). This is close to the real response of the human hearing. Lp = 10log10

prms
p2 rms
= 20log10 2 p ref pref

(2.17)

where pref is the standard reference sound pressure. This reference sound pressure level is 2.0 × 10−5 Pa(or 20µP a) for sound waves in the normal air. This reference pressure corresponds to the lowest audible sound at 1000Hz which is the weakest audible sound or threshold of human hearing[8]. The unit for Lp is dB. As we knew from previews section, weighting filters are often used to correct the human hearing, thus an A-weighted sound pressure is often labelled LpA with a unit dB(A). In order to get some feeling of sound pressure level in terms of dB, some examples are shown in figure 2.6. 14

Figure 2.6: Sound pressure level examples(Source: Br¨ uel & Kjær)

Apparently, doubling the sound source will increase the sound pressure level with approximately 3dB(because 10log 10 2 ≈ 3dB). It’s not twice as loud. A very important characteristic of sound pressure level is that the mean square sound pressure levels from difference sources are additive which is the basis of the present wind turbine noise prediction model. Lp,total = 10log10

X

100.1Lp,i

i




(2.18)

Sound power level Lw is another acoustic quantity. LW = 10log10

15

Pa Pref

(2.19)

where Pref = 1pW , is the reference sound power. And P a is the sound power from the source. It is calculated by integrating the mean square pressure on a spherical surface which encloses the sound source. Z
Pa = p2rms /(ρc) dS (2.20) S

The relation between sound pressure level and sound power level is often written as: 4πR2
(2.21) LW = Lp,total − K + 10log10 S0

and K is the correction for reflection from the hard board, R is the distance from the observer to the sound source center. And S 0 = 1m2 is the reference integrating area.

2.2

Sound radiation

Noise can be generated by various mechanisms. One of the most simplest noise source is vibrating surface. It is commonly seen from machinery. The noise from wind turbine gear box is of this type. However, what is interested in our work is the aerodynamical generated noise. This section is emphasized on aerodynamical origin of sound radiation.

2.2.1

Basic theory of aerodynamic sound radiation

For the past 50 years,Lighthill’s[10] acoustic analogy has been the dominant theory of aeroacoustics which is evaluated directly by the solution of wave equations. It is especially widely used in jet noise prediction. This theory is based on the sound generated from the unsteady flow with low Mach number in a infinite fluid region. Outside of this region the flow is regarded to has static properties. From the continuity and momentum equations, the Lighthill’s equation is derived as following: 2
∂ 2 Tij ∂2 2 ∂ − c (ρ − ρ ) = 0 ∂t2 ∂xi 2 ∂xi ∂xj

(2.22)

It shows that the governing equation has rearranged with an acoustic source term at the right-handed side and the left-handed side consists a wave equation. Where Tij is Lighthill stress tensor: Tij ≈ ρui uj , and ui uj denotes the convection of the momentum component. This convection term is dominated by the turbulent motion of the fluid.

16

Lighthill’s equation gives exactly the theoretical solution for the noise emitted by turbulent flows. However, the main limitation of this theory is that it is strictly valid only for an unbounded fluid such as jet flow. So that it only suitable for the problems where the solid surface do not play the role. In case of wind turbine noise, the boundaries are of great importance. Therefore, some extension of Lighthill’s theory are carried out. Among these theories, Ffowcs Williams-Hawking[11] equation and Helmholtz[12] Integral equation are commonly used.

2.2.2

Aeroacoustic theory applied for case of wind turbine

This section gives a brief view of some important cases for wind turbine noise radiation originating. And the dependency of some main parameters are shown with formulas. i) Noise from free turbulence: The noise from free turbulence was investigated by Lighthill since 1952 [13]. The origination of this kind of noise is by the small dynamic fluctuation of the Reynolds stress. The acoustic intensity depends on the following parameters: l Iac ∝ ρc3 Ma 8 ( )2 I 2 r

(2.23)

where Ma = U/c is the Mach number. l is the length scale of turbulent region and I is the turbulent intensity. Here I is a normalized quantity which σ . V10,min is the ten minutes mean wind velocity. is defined as: I = V10,min R ∞ 2 σ = 0 P SD(f )df is the definition of varians which is the integration of the PSD function(Power Spectrum Density). The equation shows that the acoustic intensity is proportional to the eighth power of Mach number. ii) Turbulent inflow noise: Suppose that a wind turbine blade has been divided into several sections, thus each section can be considered as a flat plate which is a compact sound source(i.e. as acoustic point dipole). Further we assume that the velocity fluctuates on the airfoil section surface in the vertical direction(The fluctuation in horizontal direction can be neglected compare with the normal direction). Thus the unsteady wind velocity causes a periodic change of the aerodynamic forces on the airfoil section. The relation of acoustic intensity and other parameters are shown with a equation: Iac ∝ ρc3 Ma 6 (

Ab 2 2 2 ) I cos (Φ) Ar

(2.24)

Ar and Ab are the blade section area and the rotor area respectively. Φ is the directivity factor which shows the dipole distribution of the sound noise, this will be explained in details later. It is seen that the acoustic intensity varies with sixth power of the Mach number which is different from the case 17

of free turbulence flow. iii) Trailing edge and leading edge noise: The tailing edge noise is the most important airfoil self-noise origination. It is caused by the boundary layer around the airfoil. Scattering occurs when the turbulent inflow interacts with the leading edge or/and the trailing edge of and airfoil. The scattering at the edge can be computed by the using the Helmholtz equation and Greens function for half plane. The resulting acoustic intensity can be arranged in the following way: Iac ∝ ρc3 Ma 5 (

sl 2 3 ¯ 2 ¯ ¯ )I cos (Θ)sin(ϕ)sin (Θ/2) r2

(2.25)

Here the angles Θ and ϕ describe the observer angles. s is the airfoil span. The trailing edge noise and high frequency noise depends on the fifth power of Mach number. More details are outlined in later chapters which give out the specific prediction models based on BPM[3].

2.3

Wind turbine noise standards and regulations

The noise standards and regulations for wind turbine are of two types: Wind turbine sound power level measurement standards and National regulations for acceptable wind turbine noise sound power level.

2.3.1

Sound power level measurement standards

There are some standards exist and among those the following two standards are introduced here [14]: • American Wind Energy Association Standard: Procedure for Measurement of Acoustic Emissions From Wind Turbine Generator Systems, Tier I - 2.1 (AWEA, 1989) • International Electrotechnical Commission IEC 61400-11 Standard: Wind turbine generator systems C Part 11: Acoustic noise measurement techniques (IEC, 2001) The standard in Europe is IEC 61400-11 standard which is also often used in the US. It defines: • The quality, type and calibration of instrumentation to be used for sound and wind speed measurements. • Locations and types of measurements to be made. 18

• Data reduction and reporting requirements. The broad band noise measurement is required in this standard. Measurement of frequency below 20Hz is performed since it is close to the eigenfrequency of buildings and may cause resonances. Measurement of threshold of pain is optional.

2.3.2

Regulations for acceptable noise level

The noise regulations are defined in almost all the countries. The noise regulations vary by different locations and time. The table below shows several cases in some EU countries. Seen from the table that the noise regulations Country Denmark Germany day night Netherlands day night

Commercial

Mixed

Residential 40

Rural 45

65 50

60 45

55 40

50 35

50 40

45 35

40 30

Table 2.2: Noise regulations for equivalent sound pressure levels L Aeq [dB(A)] in some European countries[15] are more strict in the rural district than in the commercial area due to the low background noise. Therefore, wind turbines installed in the suburb are required to have low noise emission level.

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Chapter 3

Noise mechanisms of wind turbines Nowadays, the size of wind turbine and the capacity of wind farms are becoming larger. The noise generated from wind turbines is considerably higher than before. A large amount of effort has to be gone into reducing noise emission from wind turbines to make wind energy the really green energy. The noise is generated from the wind turbine blades, gearbox and generator. There are two potential types of noise from wind turbines. M echanical noise comes from the metal components moving or knocking against each other. Aerodynamic noise is caused by the blade passing through air. Types of wind turbine noise: • Mechanical noise • Aerodynamic noise - Low-frequency noise - Turbulent inflow noise - Turbulent boundary layer trailing edge noise - Laminar boundary layer vortex shedding noise - Tip vortex formation noise - Trailing edge bluntness vortex shedding noise

3.1

Mechanical noise

Mechanical noise is generated mainly from the rotating components in the gear box and the generator. Also some other auxiliary equipments generate 20

noise, such as cooling fans, yaw system, pumps and compressors. Mechanical noise from modern wind turbines has been reduced to half of its level compare to the turbines of 1980s. The main reason is that the gearbox has been carefully designed and machined that the steel wheels of the gearbox have a semi-soft, flexible core, but a hard surface to ensure strength and long time wear. Furthermore, other techniques to reduce the mechanical noise include applying anti-vibration mountings and couplings to reduced the structureborne noise1 , acoustic damping of the nacelle and oil-cooler(instead of using the fan-cooler) for the generator. Table 3.1 shows the values of sound power level and the transmission paths Element Gearbox Gearbox Generator Hub(from gearbox) Blades(from gearbox) Tower(from gearbox) Auxiliaries

Sound power level (dB(A)) 97.2 84.2 87.2 89.2 91.2 71.2 76.2

Air-borne or structure-borne Structure-borne Air-borne Air-borne Structure-borne Structure-borne Structure-borne Air-borne

Table 3.1: Sound power levels of mechanical noise of a 2MW Experimental wind turbine (after Wangner, Bareis and Guidati, 1996)[16] from individual structure components. This is quoted by Wagner,Bareis and Guidati[21] in 1996 for a 2MW experimental wind turbine. The sound power level from the structure components are determined by measuring the sound pressure level at downwind direction with 115 meters away from the experimental wind turbine. The effect of air absorption was neglected. It may be seen that the dominant noise is from gearbox. A gearbox for a wind turbine normally has a transmission ratio of 50:1. The pinion at the generator side has a rotating speed 50 times than the rotor blades. The emission of noise from gearbox is due to the transmission errors of gear pair meshes and the dynamic loading on the gears. A well manufactured gear pair may reduce much noise, e.g. doubling the transmission errors may increase the noise by about 6dB. Also the technic of mounting the gears are very important. As we know the shaft will have certain deformation when the wind turbine is loaded, therefore the gears should be soft-mounted on the shaft or have a little skew angle to pre-deform itself. Furthermore, helical 1

The noise transmission path can be air-borne and structure-borne. Air-borne is that the noise propagates directly from the surface of the component into the air. Structureborne means that the noise is first transmitted along other structural components before it is radiated from the other surface.

21

Figure 3.1: Mechanical components of a wind turbine[17]

gears are quieter than spur gears. The noise caused by wind turbine mechanical components are of tonal 2 property,e.g. noise from the meshing gears. Due to the better engineering practices, mechanical noise of modern wind turbine has been dropped to a very low level and is not the main problem any longer.

3.2

Aerodynamic noise

The causes of aerodynamic noise are mainly divided into three types: - Low-frequency noise - Turbulent inflow noise - Air foil self-noise

3.2.1

Low-frequency noise

Low frequency noise from wind turbine is originated by the changes of the wind speed experienced by the blades due to the presence of the tower and the wind shear. The wind turbine tower normally has a cylindrical cross section. Most wind turbines in EU are of upwind type which have less effect from the tower and atmospheric wind shear compare with a downwind turbine. For upwind turbine, the flow around the tower is assumed to be a two dimensional potential flow which is discussed in Appendix(G). However, for 2

Tonal noise is noise at discrete frequencies.

22

the downstream case the flow don’t follow(if the turbine is under operation) the curvature of the cylinder surface but separate. As is shown in figure 3.2. As mentioned before, the human ear is not linearly response for the sound

Figure 3.2: Flow around a downwind wind turbine and the tower[18] level with the frequencies. If we apply the A-weighting curve, the low frequency noise is really not an important part in the spectrum. However, low-frequency noise may excite vibrations for buildings around the wind turbines. For upwind turbines, the tower effect can be reduced by increasing the clearance between the rotor plan and the tower. The noise spectrum is determined by the blade-passing frequencies. The frequencies range between 1Hz to 20Hz depending on the blade numbers and the rotation speed etc. Wind turbines are always working under condition of low Mach number(M 20000

Table D.1: Flow resistivity for various surface types (After Ref.[27])

The surface impedance Z is calculated as following: Z = 1 + 9.08(1000f /σ)−0.75 + j11.9(1000f /σ)−0.73

(D.1)

Here Z is the normalized acoustic impedance, f is the one-third octave band centre frequency in Hz and σ is the flow resistivity (see table D1). If σ is close to ∞, the reflection coefficient Q trends to be 1.

88

Q = Rp (θ) + (1 − Rp (θ))E(ρ)

(D.2)

The plane wave reflection coefficient R p : Rp (θ) =

cos(θ) − 1/Z cos(θ) + 1/Z

(D.3)

θ is the reflection angle and (π/2 − θ) is the grazing angle Ψ G (see figure 6.1). E(ρ) is calculated by eq.D4 where erf c(Z) is the complementary error function : √ −2 E(ρ) = 1 + j πρeρ erf c(−jρ)

(D.4)

√ ρ = (1 + j)/2 kR(cos(θ) + 1/Z)

(D.5)

2

The complex function w(ρ) = e−ρ erf c(−jρ) is calculated with following method where x and y are the terms of ρ = x + jy. For x > 6 or y > 6: w(ρ) = jρ

ρ2

0.5124 0.0518
+ 2 − 0.2753 ρ − 2.7247

(D.6)

else For x > 3.9 or y > 3: w(ρ) = jρ

ρ2

0.4613 0.09999 0.00288
+ 2 + 2 − 0.1902 ρ − 1.7845 ρ − 5.5253

(D.7)

Else: h = 0.8

(D.8)

A1 = cos(2xy)

(D.9)

B1 = sin(2xy)

(D.10)

C1 = e−2yπ/h − cos(2xπ/h)

(D.11)

D1 = sin(2xπ/h)

(D.12)

P2 = 2e−(x

2 +2yπ/h−y 2 )

89

A1 C1 − B 1 D1 C1 2 + D 1 2

(D.13)

Q2 = 2e−(x

2 +2yπ/h−y 2 )

5

H=

A1 D1 + B 1 C1 C1 2 + D 1 2

(D.14)

2 2

hy 2yh X e−n h (x2 + y 2 + n2 h2 ) + π(x2 + y 2 ) π n=1 (y 2 − x2 + n2 h2 )2 + 4x2 y 2 5

(D.15)

2 2

2xh X e−n h (x2 + y 2 − n2 h2 ) hx + K= π(x2 + y 2 ) π n=1 (y 2 − x2 + n2 h2 )2 + 4x2 y 2

(D.16)

For y > π/h : w(ρ) = H + jK

(D.17)

For y = π/h : P2 Q2 + j(K − ) 2 2

(D.18)

w(ρ) = H + P2 + j(K − Q2 )

(D.19)

w(ρ) = H + For y < π/h :

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Appendix E

Calculation of the size of the Fresnel-zone As shown in figure E.1, the size of Fresnel-zone is simplified with the length of P1 P2 . P1 P2 = a 1 + a 2

(E.1)

Figure E.1: Fresnel-zone in a two-dimensional sound propagation model where a1 and a2 are calculated from: a1 = |P1 O| = f (rS , rR , π − ΨG )

(E.2)

a2 = |P2 O| = f (rS , rR , ΨG )

(E.3)

where function f (rS , rR , ΨG ) is defined as following: r = r S + rR

(E.4)

l = r + Fλ λ

(E.5)

A = 4(l2 − r 2 cos2 (ΨG ))

(E.6)

2 − rS2 ) + 4(rS − rR )l2 cos(ΨG ) B = 4rcos(ΨG )(rR

91

(E.7)

2 2 2 2 C = −l4 + 2(rS2 + rR )l − (rS2 − rR ) √ −B + B 2 − 4AC f (rS , rR , ΨG ) = 2A

where Fλ is the fraction of the wavelength λ.

92

(E.8) (E.9)

Appendix F

Coordinate transformation matrix System System System System System

1: 2: 3: 4: 5:

The base of the tower In the nacelle The rotating shaft Aligned with the whole blade Each small blade element

Step 1: Find the transformation matrix a 12 of system 1 and 2. System 2 rotates about x-axis with a yaw angle, this gives:   1 0 0 a1 =  0 cosθyaw sinθyaw  0 −sinθyaw cosθyaw System 2 rotates about y-axis with a  cosθtilt a2 =  0 sinθtilt

tilt angle, this gives:  0 −sinθtilt  1 0 0 cosθtilt

System 2 does not rotate about z-axis,  1 a3 =  0 0

this gives:  0 0 1 0  0 1

The transformation matrix for system 1 and system 2 is: a 12 = a3 · a2 · a1 . 93

a12



 cosθtilt 0 −sinθtilt =  sinθyaw sinθtilt cosθyaw sinθyaw cosθtilt  cosθyaw sinθtilt −sinθyaw cosθyaw cosθtilt

So it is found in coordinate system 2: X 2 = a12 ·X1 , Where X1 = (x1 , y1 , z1 ), X2 = (x2 , y2 , z2 ). Step 2: Find the transformation matrix a 23 of system 2 and 3. Consider the rotation about z-axis with a wing angle:   cosθwing sinθwing 0 a23 =  −sinθwing cosθwing 0  0 0 1 Similarly, X3 = a23 · X2 . Step 3 : Find the transformation matrix a 34 of system 3 and 4. Consider the rotation about y-axis with a cone angle:   cosθcone 0 −sinθcone  a34 =  0 1 0 sinθcone 0 cosθcone Therefore, X4 = a34 · X3 Step 4 : Find the transformation matrix a 45 of system 4 and 5. Consider the rotation about x-axis with a twist angle:   1 0 0 a45 =  0 cosθtwist sinθtwist  0 −sinθtwist cosθtwist Finally, at any observer location the vector is found from : r = r 1 + r2 + r3 + r4

Then the sound directivity angle Θ and Φ can be easily found by projecting the vector r in two directions as shown in figure.

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Appendix G

Deterministic model for wind The model includes the atmospheric boundary layer effect and the influent of the tower. The model of the tower effect is assumed as potential flow, as shown in figure G1.

Figure G.1: Flow field around the tower section

Suppose that the tower cross section radius a(x) are various with the tower height x. The velocity components V x and Vy are found by solving the potential flow passing the cylinder. This yields: Vy = Vr cosθ − Vθ sinθ

(G.1)

Vz = −Vr sinθ − Vθ cosθ

(G.2)

cosθ = z/r, sinθ = −y/r

(G.3)

Vr = V0 (1 − (a(x)/r)2 )cosθ

(G.4)

where, and, Vθ = −V0 (1 + (a(x)/r)2 )sinθ 95

(G.5)

r is the distance to the tower center, r =

p y2 + z 2 .

To avoid the velocity jump when the blades enter into the tower shadow zone(when blades pass through the horizontal position), an additional model at the top of the tower is constructed as shown in figure G2.

Figure G.2: A conic model at the tower top

The example shows the radius of the conic a(x) changes smoothly from 0 to a(H). The assumption of potential flow is also applied at the conic section.

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Appendix H

Calculation of reference source height and receiver height The reference source height hS,F z and receiver height hR,F z are obtained by solving the equation: |SPS | + |PS R0 | − |SR0 | = Fλ λ

(H.1)

Fλ is the fraction of the wavelength λ.

Figure H.1: Reference source height and receiver height

x1 = (

q h2R + d22 − Fλ λ)2

x2 = h2R + (d1 + d2 )2 − d21 − x1 97

(H.2) (H.3)

hS,F z

A = 4h2R − 4x1

(H.4)

B = 4hR x2

(H.5)

C = x22 − 4d21 x1 √ −B − B 2 − 4AC = 2A

The same procedure is repeated to find h R,F z by replacing S with R.

98

(H.6) (H.7)

Appendix I

The effect of wedge The calculation method is based on Hadden and Pierce[28]. The idea is to apply a four rays model. A spherical reflection coefficient to the image rays is calculated and therefore we get a solution for a wedge or screen with any impedance on its surface. The equation of I.1 is the sum of four terms. pdif f r = −

4 1X ejkl Qn A(θn )Ev (A(θn )) π n=1 l

(I.1)

The four different angles θn corresponds to the four rays in the wedge case: θ1 = θ S − θ R

(I.2)

θ2 = θ S + θ R

(I.3)

θ3 = 2β − (θS + θR )

(I.4)

θ4 = 2β − (θS − θR )

(I.5)

Figure I.1: Wedge effect

99

The reflection coefficient Qn : Q1 = 1

(I.6)

Q2 = Q R

(I.7)

Q3 = Q S

(I.8)

Q4 = Q S QR

(I.9)

The function Ev is defined in I.10. where v = π/β is the wedge index : ejπ/4 π sin|A(θn )| q AD (B) (I.10) Ev (A(θ)) = √ 2 2 A(θn ) n )| 1 + (2RS RR /l2 + 0.5) cos |A(θ v2 Function A(θn ) and AD (B) are given in eq. I.11-I.13 : v (−β − π + θn ) + πH(π − θn ) (I.11) 2 H(x) is Heavisides’ steps function, H = 1 for x ≥ 0 and H = 0 for x < 0. A(θn ) =

AD (B) = sign(B)(f (|B|) − jg(|B|)) r 4kRS RR cos|A(θn )| B= 2R R πl v 2 + ( Sl2 R + 0.5)cos2 |A(θn )|

(I.12) (I.13)

There are three functions in eq. I.12. where sign(B) is the signum function, sign = 1 for x > 0,sign = 0 for x = 0 and sign = −1 for x < 0. The auxiliary Fresnel functions f (x) and g(x) are calculated using polynomial fit. If x ≥ 5f (x) and x ≥ 5g(x) : 1 πx 1 g(x) = 2 2 π x f (x) =

(I.14) (I.15)

else, f (x) =

12 X

an xn

(I.16)

bn xn

(I.17)

n=0

g(x) =

12 X

n=0

100

an and bn are listed in the table : a12 a11 a10 a9 a8 a7 a6 a5 a4 a3 a2 a1 a0

0.00000019048125 -0.00000418231569 -0.00002262763737 0.00023357512010 -0.00447236493671 0.03357197760359 -0.15130803310630 0.44933436012454 -0.89550049255859 1.15348730691625 -0.80731059547652 0.00185249867385 0.49997531354311

b12 b11 b10 b9 b8 b7 b6 b5 b4 b3 b2 b1 b0

-0.00000151974284 0.00005018358067 -0.00073624261723 -0.00631958394266 -0.03513592318103 0.13198388204736 -0.33675804584105 0.55984929401694 -0.50298686904881 -0.06004025873978 0.80070190014386 -1.00151717179967 0.50002414586702

Table I.1: Constants in the polynomial fit.

101

Appendix J

Program guide To predict the noise from wind turbine, one has to know some geometry data of the wind turbine. The special data required here are the trailing edge angle and trailing bluntness which are normally not used for other calculations. In Figure J.1, all the input data should be filled. You can only choose three airfoil profiles for each blade, an interpolation will be performed for the other blade segments. There are lots of help commands for each input data.

Figure J.1: User interface of noise prediction model

102

To use the noise propagation model, one has to run the noise prediction model beforehand. Then the input data for the noise source are found in the output file from the noise prediction model. The gound surfaces are distiguished with flat and nonflat shape. The ground surface properties are required as an important input. It will bring you convenience by using Ctrl+c and Ctrl+v command.

Figure J.2: User interface of noise propagation model

103