Aeroacoustics of wind turbines

Chapter 8

Aeroacoustics of wind turbines Chapter outline 8.1 8.2 8.3 8.4 8.5

Introduction Noise levels HAWT noise sources Governing equations Propagation models 8.5.1 Lighthill’s acoustic analogy 8.5.2 Ffowcs-Williams & Hawkings analogy 8.5.3 Parabolic equation models 8.6 Empirical prediction methods

8.1

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8.7 Computational flow fields 8.7.1 Eddy simulation 8.7.2 RANS models 8.7.3 Acoustic splitting technique 8.7.4 Domain splitting method 8.8 Wind farm acoustics 8.9 Summary Acknowledgements References Further reading

476 476 479 480 482 486 487 488 488 491

Introduction

The number of installed wind turbines around the world has increased significantly in the last 20 years and continues to grow, with most turbines installed in wind farm groups [63]. Noise exposure is one of the main public concerns when siting new wind farms, particularly those near urban and suburban areas [83]. As a consequence, it is important to estimate and mitigate noise levels before installation [80]. There are three main considerations in an aeroacoustic analysis of turbines; the mechanisms that produce the sources of sound, the propagation of sound and the perception of noise. This chapter is a brief review of the methods used to make predictions for aerodynamically generated wind turbine noise using analytical and computational models for horizontal axis wind turbines.

8.2

Noise levels

Sound is generated by pressure fluctuations that propagate in a compressible medium, and the mechanism associated with the time varying pressure is the ‘source’ of the sound. The speed of the travelling wave pressure fluctuation is called the speed of sound, c, and it has a value due to compressibility of the medium, such as air. It can be estimated from the derivative of pressure with Wind Turbines and Aerodynamics Energy Harvesters. https://doi.org/10.1016/B978-0-12-817135-6.00008-9 © 2019 Elsevier Inc. All rights reserved.

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density at constant entropy, s. At most frequencies the sound from a wind turbine is predominantly transmitted via the atmosphere, which can generally be modelled as an ideal gas to give, s ffiffiffiffiffiffiffiffiffiffiffiffiffi ffi pffiffiffiffiffiffiffiffi ∂p ¼ γRT , (8.1) c¼ ∂ρ s where γ is the adiabatic index for air, R is the specific gas constant, and T is the air the temperature in Kelvin. This relationship gives a value for the speed of sound of 340 m/s at sea level conditions. It is approximately constant for most audible frequencies. There is no universal standard to regulate the sound generated by wind turbines and wind farms. However, many countries such as the US, UK and Canada use customized versions of the International Electrotechnical Commission standards (IEC-61400-11) [39]. In New Zealand the wind turbine noise related issues are governed by New Zealand Standard 6808, which was also developed based on IEC-61400 [16]. These standards cover the noise generated from all types of wind turbines. The standards are also valid for offshore wind farms if they have an effect on people living in onshore locations within hearing. According to NZS 6808, noise is defined as: “Sound that serves little or no purpose for the exposed person and is commonly described as unwanted sound. If a person’s attention is unwillingly attracted to the noise it can be distracting and annoying, and if this persists, it will provoke a negative reaction. However, low or controlled levels of noise are not necessarily unreasonable.” Acoustic standards regulate measuring equipment and devices, indicating the quality, type and calibration of the instruments used for acoustic measurements. These standards also describe the placement of microphones, the minimum time-period and other conditions for collection of data. Additionally, post-processing and reporting requirements are outlined. The sound pressure level (SPL) is the primary indicator used to quantify and compare noise sources in the standards. It uses a logarithmic scale with units of decibels (dB),   prms , (8.2) Lp ¼ 20 log 10 p0 where prms is the acoustic pressure characterized by the root-mean-square (RMS) value and p0 is a reference pressure, which has a value in air of 20 μPa. This reference is often regarded as the lower limit of human hearing. The range of frequencies perceived by most humans is approximately from 20 Hz to 20 kHz. Bolin and Bluhm [10] suggested that newer wind turbines produce more low frequency noise compared to the older wind turbines. This may be due to increases in turbine diameter to maximize aerodynamic performance, as it is expected that low frequency sources increase with increasing size [4].

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Low frequency sound is defined as occurring at frequencies below 200 Hz, therefore it can be in the audible (20 Hz to 200 Hz) and relatively inaudible (but maybe perceivable) infrasound range below 20 Hz. The importance of further studies and collection of low frequency noise data from wind turbines, including infrasound has also been emphasized in recent reviews [20, 67, 57]. Human hearing is more sensitive to mid-range frequencies (200 Hz to 10 kHz) and the highest sensitivity is shown at frequencies 1–5 kHz [3]. Therefore, noise in this frequency range is often reported as more disturbing compared to other frequencies. High frequency sound (>10 kHz) is attenuated more effectively by the atmosphere and therefore has less effect at a far field receiver [44]. Time-averaged measurements of sound often use the A-weighted equivalent continuous sound pressure level LAeq,   ð t2 2 1 pA ðtÞ dt , (8.3) LAeqðt2 t1 Þ ¼ 10 log 10 ðt2  t1 Þ t1 p20 where, t1 and t2 are the start and end time of the measurement, and pA is the A-weighted pressure. This is a smooth function of frequency that has a peak at frequencies near the peak of human perception (3–4 kHz) and decays above and below this range. Filtering a one-third octave spectrum using the standard A-weighting curve is often used to better match perception of noise levels with respect to human hearing [38]. Additionally, the character (the time-changing spectra) of the sound may also influence the disturbance. For example, it has been shown that impulsive sounds may increase annoyance [7]. Tonal noise (sound generated at a single frequency) is also known to be distinctive and disturbing. A particular challenge for noise prediction is the occurrence of ‘swishing’ and ‘thumping’ phenomena associated with low frequencies and often reported by the public near wind farms. The source of these sounds are still not well understood [70], though analytical progress has been made using time varying spectral models with some qualitative agreement to experiments [15]. Experimental results have linked swishing to the downward movement of the blades [58] as they rotate towards the ground. Wind turbine noise limits are most often used to protect nearby communities against sleep disturbance [8]. These limits are usually based on an internationally accepted indoor noise level of 30 dB LA90(10min) and 40 dB LA90(10min) (35 dB LA90(10min) at night). This means that at any wind speed the A-weighted sound pressure levels from a wind farm must not be above 40 dB for 90% (subscript 90 above) of the 10-min measurement time and should not exceed the background noise level by >5 dB [29]. There has also been a move to place wind farms offshore, where lower populations may be subject to noise, but installation and maintenance costs may be higher. There are no specific methods defined in the standards for noise level prediction. However during any prediction exercise, the following factors should

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be take into account; the sound pressure level and the positions of wind turbines, the noise source directivity patterns and attenuation due to atmospheric absorption, and the meteorological conditions [16]. It is suggested that noise predictions from the specific wind turbine should be for the case where the power generation is 95% of the rated power, and that results are presented in octave bands ranging from at least 63 Hz to 4 kHz. To be useful in wind farm planning, predictions should aim to determine the 35 dB LA90(10min) contours from the source [18]. Simulating aerodynamically generated noise requires creating well-resolved and detailed information of the transient flow field around the wind turbine from which the acoustic pressure sources can be extracted (source modelling), followed by the accurate calculation of the propagation of the acoustic wave through time and space (transport modelling) [78].

8.3 HAWT noise sources There are two main types of noise source generated by an operating wind turbine; mechanical and aerodynamic [49]. Mechanical noise is generated by friction and vibration of mechanical parts. In a modern HAWT, the mechanical noise is predominantly generated by the gearbox within the nacelle, and in particular the meshing gears can result in tonal noise components that are a function of the rotational speed of the turbine. This sound may be radiated directly from the structure. There may also be other contributions from the generator, fans and yaw motors. Most of the radiating mechanical noise sources can be ameliorated by the addition of sound insulation within the nacelle. Some noise is also transmitted through the structure of the turbine to the ground, and this can be at least partially addressed by flexible mountings for mechanical components to absorb vibrations. There is some indication that infrasound may be efficiently transmitted by this route [66]. The aerodynamic sources are more difficult to predict and locate, though a variety of attempts have been made to identify all possible generation mechanisms. A categorization for noise generated directly by the wind turbine blades of a HAWT could include: trailing edge noise, flow separation noise, tip vortex noise, vortex shedding noise and trailing edge bluntness noise [49]. These mechanisms are illustrated in Fig. 8.1. Other sources include a tonal noise associated with the blades passing the tower [85], and noise generated by the interaction of turbulence upstream encountering the turbine [12]. Trailing edge noise is generated by flow fluctuations in the boundary layer on either side of the turbine blades that interact at the trailing edge of the aerofoil shape. It has been measured extensively in the laboratory and is the dominant source for an isolated, static aerofoil at low angles of attack [35]. A boundary layer is the fluid layer near a surface where shear stresses are significant. The thickness of the boundary layer is defined as the distance normal to the wall where fluid velocity reaches 99% of the free stream velocity [68].

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Leading edge separation possible

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Tip vortex

Trailing edge flow Wake

Turbulence in oncoming flow Transition laminar/ turbulent Surface boundary FIG. 8.1 Schematic of the noise sources generated by fluid flow near the surface of an aerofoil. (Adapted from W. Liu, A review on wind turbine noise mechanism and de-noising techniques, Renew. Energy 108 (2017) 311–320.)

The turbulent boundary layer thickness at the trailing edge of the aerofoil can be estimated using the Blasius Equation for a flat plate [82], 1=5

δ  0:382C= ReC ,

(8.4)

where C is the Chord of the aerofoil. ReC is the Reynolds number based on chord length defined using the onset flow velocity U∞, the air density ρ and dynamic viscosity μ, ReC ¼

ρU∞ C : μ

(8.5)

Velocity and pressure fluctuations increase when the boundary layer transitions to turbulence at high Reynolds numbers. The critical ReC which defines the onset of turbulent flow over an aerofoil section is approximately 5  105 [37]. Oerlemans et al. showed that surface roughness on the blade reduces the critical Reynolds number and that smooth blades produce less noise than rough ones [61]. Blades can be cleaned to remove the accretion of insects and airborne contaminants, but this cleaning is expensive for large HAWT devices. Flow separation noise is associated with high angles of attack and stall phenomena, where larger vortices are generated on the suction surface and trailing edge of the blade. It can be the dominant source when stall occurs, usually at locally high angles of attack or for stall-regulated turbines operating above rated (design) speed. There are no widely accepted models for separation/stall noise [12].

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The flow noise from the end of the blade is generated by a vortex that occurs due to flow around the tip caused by the pressure difference on either face of the blade. This is only a minor contribution to the overall sound field at rated speeds. Vortex shedding noise is associated with perturbations in the boundary layers on the blade and may produce regular pressure fluctuations in the wake, resulting in tonal noise sources. The Strouhal number is a non-dimensionalized frequency used in models of vortex shedding [82], St ¼

fL , U∞

(8.6)

where f is the vortex shedding frequency and L is a characteristic length associated with the generation mechanism, such as the chord of the blade C. The trailing edge of a wind turbine blade is not perfectly sharp due to manufacturing considerations, and the thickness at the trailing edge can also lead to a regular vortex shedding process, giving rise to tonal noise. Atmospheric turbulence encountering the turbine can generate noise by creating unsteady forces along the blades, and this source may become more significant at higher wind speeds [14]. The turbulent eddies present in the inflow are often described using two parameters; turbulence intensity I and turbulence length scale Λ [72], urms , (8.7) I¼ u where urms is the root mean square of the fluctuating velocity component and u is the temporal mean velocity at a point in the flow. Generally, higher turbulence in the inflow results in more noise generated by a rotating HAWT. The length scale can be evaluated from the spatial distribution of velocity fluctuations,   ∂urms 2 , (8.8) Λ2 ¼ ðurms Þ2 = ∂x where ∂u∂xrms is the fluctuating rate of strain. An estimate of the turbulence length scale is sometimes used to generate a simulated fluctuating flow field as the input to a numerical aerodynamic computation [51, 74]. An additional noise mechanism is due to the interaction between the rotating blade wake and the turbine tower. This mechanism has a tonal character where the tones are integer multiples of the blade passing frequency of the rotor [52]. Blade tower noise is particularly significant for HAWT designs where the blades rotate in the wake of the tower, this is why most turbine designs have the rotor upwind [28]. Each of the noise generation mechanisms is related through the flow velocity and pressure fields, and there may be resulting feedback and resonance interactions between them. This situation is further complicated as most wind

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turbines use more than one aerofoil shape at different radial sections along the blade, each with its own characteristics, such that instantaneously regions of vortex shedding, bluntness noise and turbulence can occur at multiple points along a rotating blade. This means that most analytical models are combinations of terms representing multiple factors that may be applied piecewise along the blade. The different sources can also each produce sound with different amplitude and frequency content [4], so that the noise perceived by an observer has an acoustic spectrum with energy at many frequencies that can vary significantly with wind speed, direction, weather and time of day. It is desirable to predict the frequency spectrum of the acoustic pressure accurately and this means using models that capture as many of the noise sources as possible.

8.4

Governing equations

The principles of conservation of mass and momentum govern the motion of a fluid or acoustic medium such as air [82]. The compressible continuity equation can be written in tensor notation as, ∂ρ ∂ ðρui Þ ¼ 0: + ∂t ∂xi

(8.9)

The Navier–Stokes equations for conservation of momentum in an unsteady compressible flow can be written as,  ∂ ∂  ðρui Þ + ρui uj + pδij  σ ij ¼ 0, ∂t ∂xj

(8.10)

where i ¼ 1, 2, 3…, δij is the Kronecker delta and the viscous stress σ ij is given by,    ∂ui ∂uj 2 ∂uk  (8.11) + δij : σ ij ¼ μ ∂xj ∂xi 3 ∂xk It has been observed that while fluid compressibility effects are important for the propagation of sound, most of the dominant sources are pressure fluctuations generated near the wind turbine blade, for which the pressure field can be adequately described by incompressible flow solutions. The Mach number is used to determine the relative importance of compressibility in a fluid flow. It is given by, M¼

juj , c

(8.12)

where ju j is the magnitude of the flow velocity and c is the local speed of sound measured at the same point in the flow.

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The Mach number is much less than unity for most HAWT blades. This has led to the development of de-coupled models, where noise sources and propagation can be solved separately. Typically, local pressure fluctuations are solved in a small region near the blade using a flow solver, and this data is used as an input to a simpler wave propagation method in a larger spatial domain that is less expensive to solve [75].

8.5 Propagation models Acoustic propagation can be modelled analytically, empirically or computationally [79]. Propagation calculations always require a some model of the acoustic source [86]. This can either be a single point representing the turbine, a moving source distributed along the blades, or a time and space varying source field usually obtained from a transient model. For example the aerodynamic parameters from blade element momentum theory can be used in semiempirical acoustic prediction codes [56]. A three-dimensional aerodynamic low-order panel method has also been used [26]. More accurate acoustic predictions require a detailed aerodynamic solution to determine the fluctuating pressure, on the surface of the blades and in the surrounding volume.

8.5.1 Lighthill’s acoustic analogy The earliest analytical approach to model aeroacoustic noise propagation was that of Lighthill [45, 46], where the compressible Navier-Stokes equations were rearranged into an inhomogeneous wave equation in terms of density given by, ∂2 ρ 2 2 ∂2  c r ρ ¼ Tij : 0 ∂t2 ∂xi ∂xj

(8.13)

The right-hand side of this expression is often described as a source term, where Tij is called the Lighthill stress tensor. The left hand side of this equation may be thought of as modelling the propagation of the acoustic wave in both the spatial and temporal domains for a medium at rest. Tij represents the fluctuating internal stresses and is defined as, Tij ¼ ρui uj + Pij  c20 ρδij :

(8.14)

The first term in this quantity is the product of fluctuating velocity components and is known as the Reynolds stress. The second term is the stress tensor that includes viscous stresses, Pij ¼ p0 δij  σ ij ,

(8.15)

where p0 ¼ p  p0 is the acoustic pressure. Lighthill’s formulation is known as an acoustic analogy and solutions are exact solutions to the Navier–Stokes equations. However, interpreting the stress

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terms as described assumes that acoustic fluctuations do not influence the fluid flow significantly (which is generally true for low Mach number flows), that the sound source is stationary and that sound waves are radiating into free space. Assuming a constant ambient atmospheric density, Lighthill’s equation can be transformed into an expression for pressure fluctuations. Direct numerical methods resolve the wave propagation throughout the domain, where the acoustic wave equation above or the linearized Euler equation is solved using a numerical approach such as a finite difference solver. This is computationally expensive and produces large sets of data [54]. As a result, direct methods are rarely used for acoustic problems.

8.5.2

Ffowcs-Williams & Hawkings analogy

The inability to describe moving surfaces and moving volumes limits the application of Lighthill’s analogy for rotating wind turbine blades. Ffowcs-Williams and Haw-kings (FW-H) [25] extended Lighthill’s equation allowing noise generated by moving surfaces,

1 ∂2 p 0 ∂2 2 0  r p ¼ Tij Hð f Þ ∂xi ∂xj c20 ∂t2

∂ ∂  Pij nj + ρui ðun  vn Þ δð f Þ + f½ρ0 vn + ρðun  vn Þδð f Þg,  ∂xi ∂t (8.16)

where f defines the mathematical surface of a moving body such that f < 0 inside the body and f > 0 outside. δ(f) is the Dirac delta function and H(f) is the Heaviside function. ni is the unit vector in the i direction, un is the fluid velocity normal to the integration surface (f ¼ 0) and vn is the surface velocity normal to the 0 surface of integration (f ¼ 0). p is the acoustic pressure in the far field. Solving the FW-H equation at every grid point in a fluid domain requires a fine computational grid and is therefore computationally expensive [78]. The right-hand side of the FW-H equation can be interpreted as the addition of three acoustic sources. The first term is a quadrupole generated by fluctuating Reynolds stresses in a volume around the blade in the Lighthill tensor [45]. Quadrupoles have four lobes of directivity and are weak radiators of sound. This term is related to the product of fluctuating velocity in the flow outside the surface, and can generally be expected to be generated by turbulent scales, which are small compared to the chord, and therefore it is likely to produce relatively high frequency broadband noise. It can be shown using Lighthill’s formulation that the acoustic intensity from turbulence in free space at some distance r is given by,  2 l I2 (8.17) Ia ∝ρc3 M8 r

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where l is a characteristic length scale of the turbulent region such as Λ. This relationship shows that the intensity is proportional to the eighth power of Mach number. The contribution is small when the Mach number is low (≪ 1), which is true for most sections of HAWT blades. Often, the quadrupole sources are neglected from the calculation, as they are assumed to have no significant acoustic contribution to a far-field receiver at low Mach numbers [42]. The second term in the FW-H equation is related to an acoustic dipole source generated by fluctuating forces acting on the blade surface (when δ(f) ¼ 1) [79]. Dipoles have two lobes in their directivity pattern and are likely to be the dominant source of noise generated by the blades in many cases. This type of sound is also known as ‘loading noise’. The turbulent inflow noise is a dipole that can be estimated by assuming that each section of the blade is a flat plate, and that only fluctuations normal to the blade (plate) surface are important to the radiated sound. This leads to,  2 3 6 As I 2 cos 2 ðΦÞ， (8.18) Ia ∝ρc M Ar where As and Ar are the blade section area and rotor area respectively. The directivity factor that generates the dipole distribution of sound is a function of Φ, which is measured normal to the blade span direction. This inflow noise is a function of Mach number to the sixth power. The trailing and leading edge noise can also be estimated using a scattering formulation to be,   sl (8.19) Ia ∝ρc3 M5 2 I 2 cos 3 ðΨ Þ sin 2 ðΘ=2Þ， r where s is the blade section span and Θ is measured normal to the chord. This shows a relationship for acoustic intensity that depends on Mach number to the fifth power, and therefore at a given receiver location the sound intensity has decayed less than other sources for low Mach numbers. The same result is used in a simpler (though much less used) model by Grosveld [36] that assumes the sound is generated by a point source at the turbine hub. The final FW-H term may be interpreted as monopole source also occurring on the moving surface. A monopole has dilation as a physical mechanism, originating from a change in volume [65]. Monopoles are omnidirectional and efficient radiators. This term is often called ‘thickness noise’ as it is associated with displacement of the air by the thickness of the blade. In acoustic analysis of a wind turbine, often the requirement is to predict the noise at a single receiver point located in the far field. Farassat analytically calculated the noise using generalized function theory and the free space Green’s function [23]. The WOPWOP and PSU WOPWOP [11] codes have demonstrated the applicability of this method for noise prediction from helicopter rotors (neglecting the quadrupole terms). In this case the total acoustic pressure

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at a far field receiver location is given by combination of a thickness contribution and a loading contribution on the aerofoil surface [33], p0 ¼ p0T + p0L ,

(8.20)

0

where the blade thickness contribution (pT) is,

# # ð " _ ð " ρ0 U n + Un ρ0 Un r M_ r + c0 ðMr  M2 Þ 0 4πpT ðx, tÞ ¼ ds + ds: 2 r 2 ð1  M r Þ3 f ¼0 r ð1  Mr Þ f ¼0 ret ret (8.21) Mr is the Mach number of a point on the moving surface and r is the distance to the observer. The subscript ret. denotes that the integrals are computed at the corresponding retarded times, tret ¼ t  r/c0, where t is the observer time. The dot above a variable represents the source-time derivative of that variable. The loading contribution (pL0 ) is, # # ð " ð " 1 Lr  LM L_ r 0 4πpL ðx, tÞ ¼ ds + ds 2 c0 f ¼0 r ð1  Mr Þ2 f ¼0 r 2 ð1  Mr Þ ret ret 1 + c0

"

# Lr r M_ r + c0 ðMr  M2 Þ

ð

r 2 ð1  Mr Þ3

f ¼0

ds

(8.22)

ret

where Ui and Li are given as, U i ¼ vi +

ρ ðui  vi Þ, ρ0

Li ¼ Pij δij nj + ρui ðun  vn Þ:

(8.23) (8.24)

A detailed derivation of these expressions can be found in other work by Farassat [24]. This method is computationally efficient compared to a direct calculation. A highly accurate flow field solution near the surface is required for source evaluations using Farassat’s formulation. This is often achieved by solving the incompressible Navier–Stokes equations, which is valid for acoustic predictions of a compact object [41]. A compact acoustic object is a region that has a much smaller characteristic length compared to the acoustic wavelengths of interest. However, such an incompressible solution does not resolve the acoustic wave propagating along the surface and therefore neglects selfscattering effects, and may produce erroneous surface source data. Goldstein suggested that a Green’s function tailored to the geometry is more appropriate for solving such a problem [34].

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8.5.3 Parabolic equation models An alternative propagation method is to use a parabolic equation solver, which is typically used for far-field noise propagation, which assumes the receiver is far from the noise sources [17]. In this formulation a harmonic solution of the wave equation is obtained using a finite angle for propagation given by,   2i ∂ui ∂2 2ik + u∙r P0 ðr Þ ¼ 0 (8.25) r 2 + k 2 ð 1 + εÞ  ω ∂xj ∂xi ∂xj c0 0

where k ¼ ω/c and ε ¼ c20/c2–1. P (r) is the monochromatic (single frequency sine wave) pressure field. This expression can be simplified further by assuming that the medium is motionless, u ¼ 0, which yields the Helmholtz Eq. [6]. Further manipulation is required to make this a one way parabolic Eq. [62]. The solution for each frequency is steady-state; multiple successive solutions are required to calculate time-varying frequency data.

8.6 Empirical prediction methods Semi-empirical aeroacoustic noise prediction approaches do not use direct source models, but use indirect parameters coupled with an empirical relationship to predict noise. These parameters could be as simple as the diameter of wind turbine, or the tip speed ratio, which can be used to estimate an approximate value for far-field noise from a wind turbine. More complex parameters, such as local wind speed, angle-of-attack, aerofoil shape, boundary layer thickness and turbulent kinetic energy near the trailing edge, are also used for wind turbine noise prediction [77]. These parameters are often obtained using computationally cheaper calculation methods such as RANS (solutions to the Reynolds-averaged Navier-Stokes equations) [78], or potential flow simulations (e.g. Xfoil [21]). They are popular amongst the aeroacoustic community due to their relatively low computational cost. Amiet derived a widely used numerical model to predict the aeroacoustic noise spectrum due to inflow turbulence [1],   ωρ0 C 2 ^ Þj2 Φvv ðkx , 0Þ, πU∞ sjGðω (8.26) Spp ð0, y, 0, ωÞ ¼ c0 y ^ Þ is the aerofoil lift response for a sinusoidal gust. Φvv(kx, 0) is the where Gðω energy spectrum of oncoming turbulence, and can be estimated using the turbulence kinetic energy measured 2C upwind from the leading edge of the aerofoil or from published data. ^ < π=4, For Mω ( ) h 

i 1 ^ =β2∗ J0 M2 ω ^ =β2∗  iJ1 M2 ω ^ =β2∗ ^Þ ¼ Se ω (8.27) ei^ω , G ðω β∗ ^ > π=4, and for Mω

Aeroacoustics of wind turbines Chapter

1i ^ Þ ¼ pffiffiffiffiffi E∗ Gðω ^ M πω

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi! 4^ ωM : π ð1 + MÞ

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475

(8.28)

In this expression Se is Sears function that describes the compressibility of the flow as a function of frequency, J0 and J1 are Bessel functions of the first ^ is the dimensionless circular frequency; ω ^ ¼ ωC=U∞ : kind, ω Amiet [2] also derived a model to predict trailing edge noise from a flat plate with a semi-infinite chord. This method has been used to estimate the noise from rotating turbine blades. The surface pressure spectrum near the trailing edge Sqq(ω,0) is used,   ωCy 2 ly ðωÞsjLi j2 Sqq ðω, 0Þ, (8.29) Spp ðx, y, 0, ωÞ ¼ 2πc0 σ 2 where, ω is the circular frequency. The coordinates of the far field receiver are rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ffi 2 2 2 2 (x,y,z) where z ¼ 0 is the mid-span plane. σ ¼ x + β∗ ðy + z Þ . The length scale normal to the trailing edge is approximated as ly(ω)  2.1Uc/ω. Li is the integral of the aerofoil pressure distribution,

  (sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi )   1 1 + M + kx =μ ∗  i2Θ i2Θ E ½2μð1 + x=σ Þe , Li ¼ ð1 + iÞ  E∗ ½2ðð1 + MÞμ + kx Þ + 1  e  Θ 1 + x=σ (8.30)

pffiffiffiffiffiffiffiffiffiffiffiffiffiffi where Θ ¼ kx + μ(M  x/σ), kx ¼ ω/Uc, μ ¼ MωC/U∞ β∗, β∗ ¼ 1  M2 , M is the Mach number. E∗[] represents Fresnel integration. The pressure spectrum can be measured at data points on both sides of the aerofoil surface, slightly upwind to the trailing edge; at 0.99C [2], assuming that turbulence is unaffected by the trailing edge. The far field trailing edge noise spectrum is the sum of Spp for both sides of the aerofoil. The convective velocity Uc is usually approximated to be 0.8 U∞. This model can be used for blade leading edge noise predictions [80]. The semi-empirical model of Schlinker and Amiet [69] identified blade trailing edge noise as the main noise source from a rotational propeller. Noise prediction from this model was inconsistent due to a lack of low frequency pressure data. Later Brooks and Schlinker [13] formulated two main aeroacoustics broadband noise generation mechanisms for rotating aerofoil sections in order to simplify understanding of these complex sources, and to implement models in a semi-empirical noise prediction code. Moriarty [55] developed a semiempirical wind turbine noise prediction method based on previous work by Brooks [12]. However, the predicted noise levels differed significantly from experimental data at both low and high frequencies. More recently, Oerlemans and Schepers [59] used a semi-empirical noise prediction method to predict noise from two GE 2.3 MW and GAMESA G58

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850 kW wind turbines, assuming trailing edge is the only noise source. The semi-empirical code showed inconsistent acoustic results compared to experimental data. This method calculated noise based on the trailing edge boundary layer thickness using a modification of X-foil, which is a two-dimensional potential flow solution code [21]. However, three-dimensional effects due to rotation could affect the boundary layer of a wind turbine [22], therefore X-foil may give misleading results.

8.7 Computational flow fields The Navier–Stokes equations can be solved for complete flow field information by direct numerical simulation (DNS) where fluctuations are resolved down to the smallest time and length scales of the flow [43]. However, the computational effort required to directly solve a transient phenomena, such as the production of acoustic perturbations is proportional to the maximum frequency resolved and the duration simulated. Acoustic pressure fluctuations are several orders of magnitude smaller than aerodynamic pressure fluctuations in the far field, and acoustic wavelengths are several orders larger compared to the scale of the turbulent eddies that generate the acoustic disturbances [78]. Therefore, to capture the noise sources requires fine discretization of the domain and therefore DNS is extremely computationally expensive and rarely used to simulate complex three-dimensional fluid flows like full-scale turbines [40].

8.7.1 Eddy simulation Large Eddy Simulation (LES) is a method less computationally expensive than direct flow simulation that can give a high-resolution transient solution for an aerodynamic problem. In LES, the large scale eddies are simulated using a filtered version of the Navier–Stokes equations, but small fluctuations below a specific length scale (the sub-grid scale SGS) are modelled using a simple turbulence closure. Hence, an LES mesh can be much coarser than the smallest perturbations, and a flow field solution requires less computational effort, though a fine mesh may still be required around the blade surface [73]. The filtered mass continuity equation is, ∂ρ ∂ + ðρui Þ ¼ 0 ∂t ∂xi

(8.31)

The filtered incompressible unsteady three-dimensional Navier–Stokes equations are,  ∂   ∂p ∂τij ∂ ∂  ðρui Þ + ρui uj ¼ σ ij   , ∂t ∂xj ∂xj ∂xi ∂xj

(8.32)

where ui is the filtered velocity component, τij is the sub-grid scale stress tensor, σ ij is the stress tensor due to molecular viscosity given by,

Aeroacoustics of wind turbines Chapter

 σ ij  μ

  ∂ui ∂uj 2 ∂uk  + δij : ∂xj ∂xi 3 ∂xk

The sub-grid scale stress tensor can be modelled by [71],    τij ¼ 2Cs △2 S Sij ,

8

477

(8.33)

(8.34)

where, Cs is the Smagorinsky constant, △ is the sub-grid filter width and   qffiffiffiffiffiffiffiffiffiffiffiffi S ¼ 2Sij Sij , where Sij is the rate of strain tensor. However, the optimum Cs value varies for each part of the flow and has to be reduced near solid walls in order to reduce the numerical dissipation introduced by the sub-grid scale model, this is particularly the case for wind turbine blades where the surface fluctuations are assumed to be the main acoustic sources. Therefore, the dynamic Smagorinsky method can be used [31]. In this model an extra filter level known as the test filter is used in combination with sub-grid scale filter level, in order to estimate a value of Cnew s , which is a function of time and space. Germano’s Identity explains the relationship between the two filter levels, 



L^ij ¼ui uj  ui uj ¼ Fij  fij :

(8.35)

The stress tensor at the sub-grid level fij, and at the test filter level Fij are modelled in the same way as in the Smagorinsky model where,    Tij ¼ 2Cs △ 2 S Sij :

(8.36)



The test filter has a filter width of △ , which is 1twice that of the grid filter width △. For a finite-volume based method △ ¼ V 3 , where V is the local cell volume. L^ij can be calculated using the values from the resolved large eddy field using, L^ij  2Cnew s △Mij ,

(8.37)

 2   Mij ¼ △ =△ S Sij :

(8.38)

where,

The model coefficient Cnew s is assumed to be independent of the filter A stable expression for Cnew has been introduced which increased s the stability during the dynamic procedure [47],

¼ C2s ). (Cnew s

2 Cnew s △ ¼

Lij Mij : Mij Mij

(8.39)

LES has been developed as a tool for aeroacoustics of wind turbines in the last decade as available computing power has increased. The earliest example of direct noise source calculation using LES simulated the noise from the WINDMELIII wind turbine using a finite difference method based LES [3]. However,

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the results differed from far-field experimental noise measurements due to insufficient spanwise grid resolution. A more recent study by Mo et al. [53] used LES to predict the aeroacoustic noise from the NREL Phase VI wind turbine. However, the maximum frequency resolved was 500 Hz, which is outside the range of 1–5 kHz where the human ear is most sensitive [30]. The effects of the tonal noise due to the blade passing frequency were not quantified, even though the entire wind turbine including the tower was modelled. The acoustic data was also not validated against experimental data. To further reduce the computational requirements it is necessary to resolve a smaller range of scales in the flow. For example, Ghasemian and Nejat [33] used detached eddy simulation (DES) to investigate the effect of observer distance from the turbine on the sound pressure level from an NREL Phase VI HAWT blade, shown in Fig. 8.2. This study used a combination of DES for broadband

FIG. 8.2 The effect of distance of predicted sound pressure level from a rotating blade, generated used detached eddy simulation combined with Farassat’s method, demonstrating that the peak low frequency noise decays more quickly with distance than higher frequency contributions. (Adapted from M. Ghasemian, A. Nejat, Aerodynamic noise prediction of a horizontal axis wind turbine using improved delayed detached eddy simulation and acoustic analogy, Energy Convers. Manag. 99 (2015) 210–220.)

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noise and Farassat’s model for thickness and loading noise, and demonstrated differences in the propagation of low frequency tonal noise compared to higher frequency sources. DES resolves less of the fine structure of the turbulence than LES and uses a coarser mesh. The range of vertical structures in the wake of the rotating blade is shown in Fig. 8.3 for two different upstream velocities. At low speeds the tip noise is more strongly apparent, whereas vortex shedding is visible as the ReC is increased at higher speeds.

8.7.2

RANS models

The most comprehensive study using a commercial RANS solver was by Tadamasa and Zangeneh [75]. This study used a finite volume solution for the NREL Phase VI model turbine blade to generate acoustic sources used in a modified ‘permeable’ frequency domain FW-H solver. The computational domain is shown in Fig. 8.4. The RANS noise sources method was validated with experimental data propellers, and used to investigate the noise as a function of rotational speed, as shown in Fig. 8.5. The observer was placed at the location specified in the standards, on the ground on a line normal to the axis of rotation at a distance of the rotor radius plus the tower height. Unsteady RANS (URANS) has also been used with an acoustic analogy to study the blade-tower interaction noise for a small model turbine, by studying the effect of distance between a rotor and the tower [85]. Fig. 8.6 shows the effect of this distance on the power spectral density (PSD) of the rotor when powered to rotate for two separations. This work concluded that the tower is the dominant noise component and that it is primarily tonal.

FIG. 8.3 Vortices coloured by velocity, showing the wider range of scales that are produced as the inflow wind speed increases for a rotating NREL Phase VI blade at two different inflow velocities U ∞ ¼ 7 m/s (left) and 15 m/s (right). (Adapted from M. Ghasemian, A. Nejat, Aerodynamic noise prediction of a horizontal axis wind turbine using improved delayed detached eddy simulation and acoustic analogy, Energy Convers. Manag. 99 (2015) 210–220.)

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FIG. 8.4 Two views of the unstructured mesh used for computation of the blade noise by Tadamasa and Zangeneh. The mesh shows two regions; a fine inner rotating mesh around the blade used to estimate noise sources, and a coarser stationary mesh used for the FW-H calculations. (Adapted from A. Tadamasa, M. Zangeneh, Numerical prediction of wind turbine noise, Renew. Energy 36(7) (2011) 1902–1912.)

8.7.3 Acoustic splitting technique A splitting method has been widely used at the DTU in Denmark [86] in the research CFD code EllipSys. In this technique, the compressible Navier–Stokes equations are ‘split’ into an incompressible part and expressions representing acoustic pressure fluctuations. These are coupled by auxiliary equations that include pressure correlations and velocity fluctuations as follows, ∂ρ∗ ∂fi + ¼0 ∂t ∂xi

(8.40)

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NREL blade: Total noise

Sound Pressure Level (dB)

100 90

30rpm

80

45rpm 50rpm 55rpm 60rpm 72rpm 95rpm

70 60 50 40

130rpm 175rpm 210rpm

115rpm

30 20 10 0 0

500

1000

1500

2000

2500

3000

Frequency (Hz)

FIG. 8.5 Sound pressure level as a function of rotations per minute for an NREL Phase VI blade using a RANS solution for acoustic source input. (Adapted from A. Tadamasa, M. Zangeneh, Numerical prediction of wind turbine noise, Renew. Energy 36(7) (2011) 1902–1912.)

FIG. 8.6 Power spectral density of the pressure as a function of distance d between a fan rotor and tower, normalized by tower diameter D. The background noise spectrum is also shown in Ref. [85]. (Adapted from B. Zajamsek, Y. Yauwenas, C.J. Doolan, K.L. Hansen, V. Timchenko, J. Reizes, C.H. Hansen, Experimental and numerical investigation of blade–tower interaction noise, J. Sound Vib. 443 (2019) 362–375.)

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∂p∗ ∂ρ∗ ∂P  c2 ¼ (8.41) ∂t ∂t ∂t         ∂fi ∂ 2 ∂ ∗ ∂U i ∂U j + fi U j + u∗j + ρ0 U i u∗j + p∗ + ρ∗ k δij ¼ ρ vt + ∂t ∂xj ∂xj ∂xi 3 ∂xj (8.42) where νt is a turbulent eddy viscosity and unknowns with the superscript (∗) are acoustic variables. Capital letters are used for the incompressible flow variables determined from an LES or unsteady RANS solver. The velocity correlation is given by, fi ¼ ρu∗i + ρ∗ Ui :

(8.43)

The speed of sound is determined using the relationship for an idea gas, c2 ¼

P + p∗ : ρ0 + ρ ∗

(8.44)

The flow equations and acoustic equations can be solved separately in a coupled manner using different time steps and different order numerical differencing schemes; this can lead to accelerated computations. Fig. 8.7 shows and example of a flow and acoustic solution for a NACA aerofoil shape using EllipSys.

8.7.4 Domain splitting method The acoustic camera measurements of Oerlemans et al. [60] suggest that the majority of the noise sources are located at the 75–95% span section of the wind

FIG. 8.7 Example pressure contours (left) and sound pressure distribution (right) for flow past a NACA 0012 aerofoil at ReC ¼ 100, 000, M ¼ 0.2 and angle of attack 5° obtained using the acoustic splitting method [86]. (Adapted from W.J. Zhu, W.Z. Shen, E. Barlas, F. Bertagnolio, J.N. Sørensen, Wind turbine noise generation and propagation modeling at dtu wind energy: a review, Renew. Sust. Energ. Rev. 88 (2018) 133–150.)

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turbine blade, where the local flow velocities are relatively high. Further analysis of Oerle-mans’s data shows that at span-wise locations below approximately 75% the dominant noise sources are frequencies below 1 kHz, and beyond this location, most of the acoustic power is radiated at higher frequencies. Zahle et al. [84] suggested that at high tip speed ratios (TSR), when the turbines are noisiest, the outboard region of the blade has a flow field of a tangential nature. Therefore, it was proposed by Wasala et al. [80] that the noise generated at the inboard region of the blade can be neglected, when considering noise disturbance and does not need to be modelled. Simulating only the outboard region of the blade, assuming there is no radial flow, reduces the computational cost compared to a full wind turbine simulation, and may produce sufficient acoustic source data for accurate far field noise prediction. In Wasala et al. [81], a large eddy simulation of the CART-2 wind turbine blade section in an annular domain was conducted using the dynamic Smagorinsky model to estimate the far field noise due to unsteady aerodynamic loading. A hybrid computational mesh of the rotational annular section of the 75%–95% span of the CART-2 wind turbine blade is simulated as shown in Fig. 8.8. The Ffowcs-Williams and Hawkings (FW-H) acoustic analogy is used to calculate the acoustic pressure at a far field receiver location and the results obtained are compared with experimental data.

FIG. 8.8 A section of the CART-2 blade in an annular domain. Boundary conditions for the LES computation are also labelled [81]. (Adapted from S.H. Wasala, R.C. Storey, S.E. Norris, J.E. Cater, Aeroacoustic noise prediction for wind turbines using large eddy simulation, J. Wind Eng. Ind. Aerodyn. 145 (2015) 17–29.)

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Only a single rotational blade section was numerically simulated using LES. However, the CART-2 turbine has two blades, therefore the final noise calculation has to take into account sources from both blades. The noise from the second blade is simulated by placing an extra identical source at the relative location of the second blade. Summing the sound pressure levels will give a time averaged approximation of the noise due to both of the blades, assuming that the acoustic sources are incoherent, and thus that there is no noise cancellation due to the phase difference. A full rotation of 360°is simulated by placing 36 receivers in a plane parallel to the turbine plane with a radius of H, 58 m downwind. The acoustic results for the CART-2 wind turbine model are presented in Fig. 8.9, compared with the experimental and model data. The acoustic power spectrum of the numerical simulation is in good agreement with the experimental data. However, the peak at approximately 100 Hz in the experiment is not evident in the numerical results. It was suggested that this peak could be due to mechanical noise from the gearbox, which may account for the observed discrepancy [55]. These results show that acoustic noise estimates can be made with less computational expense than by performing full wind turbine simulations, and with higher accuracy than using semi-empirical noise prediction codes. Additionally, this work validates the assumption of zero radial flow for calculating the far field noise at high tip speed ratios.

FIG. 8.9 Comparison of simulated CAA results for the CART-2 wind turbine (), with the acoustic field measurements by Moriarty [55] (◇), and the semi-empirical model from the same work (solid line) [81]. ((Adapted from S.H. Wasala, R.C. Storey, S.E. Norris, J.E. Cater, Aeroacoustic noise prediction for wind turbines using large eddy simulation, J. Wind Eng. Ind. Aerodyn. 145 (2015) 17–29.))

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FIG. 8.10 Acoustic footprint of CART-2 wind turbine noise for 250 Hz, 500 Hz, 1 kHz, 2 kHz, and 4 kHz (…), shown on the left. A contour of the overall SPL integrated from 100 Hz to 4 kHz is shown on the right [81]. ((Adapted from S.H. Wasala, R.C. Storey, S.E. Norris, J.E. Cater, Aeroacoustic noise prediction for wind turbines using large eddy simulation, J. Wind Eng. Ind. Aerodyn. 145 (2015) 17–29.))

Fig. 8.10 shows the acoustic footprint data at a 58 m radius at ground level around the CART-2 HAWT turbine, first as selected frequency bands, and secondly as overall sound pressure level (OASPL). This is an indication of the directivity of acoustic wave propagation. The rotational plane of the turbine shows the minimum noise levels and this agrees with the predicted acoustic noise footprint from the semi-empirical code [55]. However, the noise levels in the upwind direction are slightly higher than for downwind, particularly at high frequencies. This differs from the results of the semi-empirical code and is due to the Doppler effect caused by the onset wind. The FW-H calculations include convective effects so that the propagation velocity of the acoustic wave upstream is slower than downstream. Therefore, the acoustic spectrum upstream is shifted to higher frequencies and the SPL of related individual bands increases. Conversely, in the downstream direction, there is a shift to slightly lower frequencies. At high frequencies, the directivity pattern exhibits the expected dipole pattern. At lower frequencies, the directivity gradually changes to a more omni-directional shape. Observers in the rotational plane are shown to experience the lowest overall noise levels.

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LES was also used to study the time-varying SPL from a turbine in work by Barlas et al. [6]. This work also observed higher SPL levels upstream from a HAWT in the near field under some conditions. The main conclusion was that atmospheric conditions played a critical part in determining the observed SPL. High ambient turbulence was seen to increase SPL levels substantially, particularly at low frequencies. High wind shear increased downwind propagation. These results have not been taken into account by any commercial noise prediction software to date. A number of different methods for reducing the noise of the rotating blades have been suggested including either using different blade aerofoil shapes [50], actively changing the blade shapes using flaps [27], or passive flow control mechanisms like leading edge hooks [32] and vortex generators [27]. Most of these techniques aim to change the flow field over the blade in such a way as to reduce surface dipoles, sometimes at the expense of increasing quadrupole noise, and only modest (< 1 dB) decreases in noise have been observed. No blade tip devices have been demonstrated to significantly reduce SPL. However, blade tip noise is usually only important at low wind speeds. Oerlemans et al. [58] showed experimentally that using a serrated blade reduced trailing edge noise at low frequencies at the expense of increasing tip noise.

8.8 Wind farm acoustics In principle, the noise generated by a wind farm should be able to be determined by combining predictions from individual turbines, and logarithmic addition is sometimes used assuming spherical propagation. However, at a particular location there can be constructive or destructive interference between pressure waves. There are a number of additional factors that also need to be considered when modelling the propagation of wind turbine noise through the atmosphere at wind farm scale including; absorption of the pressure wave by the air, reflections from the ground and other topological features (such as trees or buildings), and the speed and direction of the prevailing wind that can change the directivity of the sound. The effect of wind conditions is also difficult to predict [70]; although correlations exist between wind speed and turbulence length scales, these are sensitive to landscape topology. The landscape can also attenuate noise by absorption. Porous surfaces, such as those covered by vegetation can reduce sound levels, though higher frequency sounds are generally reduced more than low frequencies. Screens and barriers can be porous or reflective and are often used for noise control purposes, but are most effective when placed between the receiver and the noise source. Other sources of noise, such as traffic or wind noise in trees can have a masking effect. A simple method for considering these environmental effects is the VDI 2714 method used in German acoustic standards [76]. In this technique, the SPL at a receiver location is given by, Lp ¼ Lw + D + K  Ld  La  Lg  Lv  Lb  Ls ,

(8.45)

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where D is a factor that accounts for the directivity of the source and K is a correction used for reflections from walls in the domain (3 dB is added for each vertical surface). Ld is used to account for the distance from the source to the receiver, usually Ld ¼ 10log10 (4πr2). The absorption effect is modelled by a linear function La ¼ αr, where α is a function of frequency (f in kHz) that may be modelled using, α ¼ (0.02 + 0.36f + 0.036f 2), with units of 102 dB/m. Lg is used to model the effect of the ground, Lg ¼ [4.8  (2 h/r)(17 + (300/r))], where h is the average elevation of the source and receiver. The terms Lv, Lb, and Ls are used to account for vegetation, building and screens respectively. More complex models are required for other factors such as refraction of sound waves in the atmosphere due to temperature/density gradients, that can alter the propagation direction of the pressure waves. This can either enhance or reduce the perceived noise at a distant observer. Complex terrain may be dealt with either by explicit simulations or piecewise approximations. An alternative computational propagation method is to use ray tracing [9]. In this method the noise from each turbine in a farm is modelled as a point source (typically at hub height), and the noise is propagated along lines or arcs from the turbine to a receiver location. This can be done for the entire noise spectrum. The results from all the turbines can be added together at a receiver location, assuming that the noise from each turbine is uncorrelated. Additional complexity such as scattering by objects and atmospheric turbulence can be added to the ray tracing formulation, as well as wind shear and refraction [64]. Good agreement has been observed with measured results for model terrain. A more sophisticated method has recently been developed to couple Amiet’s models with a parabolic equation solver for propagation in an inhomogeneous atmosphere [17]. Trailing edge noise and turbulent inflow noise were both considered along with the effects of wind shear and atmospheric turbulence. The coupling approach was validated by comparison with an analytical solution for the propagation over a finite impedance ground in a homogeneous atmosphere. The validity of the point source approximation used in other models was also examined. However, this method exaggerates interference in the spectra, and was not able to correctly predict the amplitude modulation without future modifications.

8.9

Summary

Horizontal-axis wind turbines are the most common type installed in wind farms and the aeroacoustic noise generated by their rotating blades is known to be the most significant noise source. In particular, the surface dipoles generated near the edges of the turbine blades have the largest contribution to the frequency spectrum at the frequencies at which humans are most sensitive, though they may be modulated by blade pass frequency and Doppler effects. Most acoustic standards use one-dimensional additive models to predict the noise generated by turbines in a wind farm. Commercial noise prediction

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software is either based on these standards, or uses ray tracing techniques that use point noise sources to model the turbines. The most advanced use techniques based on Amiet’s methods [1, 2], or parabolic equation solvers. The current state of the art in detailed aeroacoustic source modelling is large eddy simulation [19], which has been restricted to a single turbine, combined with an acoustic analogy, such as FW-H. LES can be used to investigate improved blade shapes for noise reduction and performance in extreme wind conditions [73].

Acknowledgements The author would like to acknowledge the assistance and contributions for Dr. Sahan Wasala, Chalmers University of Technology in Sweden.

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Further reading [87] E. Barlas, K.L. Wu, W.J. Zhu, F. Porte-Agel, W.Z. Shen, Variability of wind turbine noise over a diurnal cycle, Renew. Energy 126 (2018) 791–800. [88] W. Liu, A review on wind turbine noise mechanism and de-noising techniques, Renew. Energy 108 (2017) 311–320.