Analysis of low-frequency noise from wind turbines
using a temporal noise code
Franck BERTAGNOLIO(1) , Helge Aa. MADSEN(2) , Andreas FISCHER(3)(1)(2)

DTU Wind Energy, Denmark, frba@dtu.dk

DTU Wind Energy, Denmark, hama@dtu.dk(3)

DTU Wind Energy, Denmark, asﬁ@dtu.dk

Abstract
This study is concerned with the modelling of low-frequency noise from wind turbines and the comparisonof model predictions with experimental data. The model consists of a wind turbine aeroelastic code that canaccount for the effects of atmospheric turbulence combined with a noise generation model. The latter is basedon the well-known Farassat 1A formulation that can compute the noise generated by aerodynamic loadings on
the blades in the far-ﬁeld. The results of the overall model are compared with noise measurements conducted
on two wind turbines. The input parameters of the turbulence model are tuned to reﬂect the actual atmosphericconditions during the measurement periods. The comparisons show a relative good agreement between thepredicted and measured low-frequency noise levels.
Keywords: Low-frequency noise, Wind turbine, Noise modelling, Field measurements

1

INTRODUCTION

With the deployment of increasingly larger wind turbines in rural area, but still relatively close to dwellings,
wind turbine noise is one of the major environmental concerns associated to wind energy. In this respect,
low-frequency noise (LFN) is pointed out as a possible threat to human health [15].
In the present study, a model is derived in order to evaluate the LFN emitted by a wind turbine. This model isbased on an existing aeroelastic code that can simulate the dynamic response of a wind turbine to the incoming
turbulent atmospheric wind. Here, mechanical noise is not taken into account. However, it is considered that
improvements of the sound insulation of the hub contribute to make this mechanism less pronounced for modern
wind turbines [14]. Two noise generation mechanisms are considered in the present model. The ﬁrst one is theinteraction of the blades with the atmospheric turbulence (from about 10 Hz to a few hundred Hz). The second
is the blade-tower interaction with a blade passage frequency of the order of 1 Hz to a few Hz depending on
the wind turbine operational mode. Both mechanisms can be explained by the unsteady aerodynamic loadingon the blades which generates sound waves.
In the above-mentioned aeroelastic code, both the impact of the tower and of the atmospheric turbulence can bemodelled and the subsequent loading of the blades can be calculated. Using the noise model, it is then possible
to calculate the LFN generation.
The paper is organized as follows. The following section presents the several components of the proposed modelthat is used to simulate LFN from wind turbines. The third section is concerned with the model veriﬁcation
using existing LFN measurement data. Finally, conclusions are drawn.

2

A LOW-FREQUENCY NOISE MODEL FOR WIND TURBINES

The present LFN model consists of two components. The ﬁrst one is the aeroelastic code HAWC2 whichcalculates the aeroelastic dynamic response of a wind turbine to the incoming atmospheric wind. The second
is a noise generation model which converts the previously calculated aerodynamic loading on the blades into
noise predictions in the far-ﬁeld. Both models are detailed below. Thereafter, the inputs for the aeroelastic code4414

in the form of the parameters deﬁning the incoming turbulent ﬂow ﬁeld are analyzed.
2.1 The HAWC2 Aeroelastic CodeThe HAWC2 code [9, 1] is a multibody aeroelastic code designed to simulate the dynamic response of a windturbine to aerodynamic loading. It is used to predict structural vibrations and loads. Thus, it can be used as adesign tool for wind turbines. Each individual blade is discretized along its span into a number of elementary
beams. On each of these elements, the Blade Element Momentum theory by Glauert [7] is applied in order tocalculate the aerodynamic loading resulting from the incoming wind and the rotation of the blades. A variety of
unsteady atmospheric loadings (e.g. turbulence, gust) and other ﬂow characteristics (e.g. wake from an upwind
turbine, tower ﬂow disturbances and wake) can be accounted for in this model.
In particular, the model used to simulate atmospheric turbulence is the Mann model [12, 13]. It is based on aspectral description of the turbulent ﬂow ﬁeld which is converted into a random turbulent velocity ﬂow ﬁeld.
The latter is convected together with the main wind speed assuming frozen turbulence (see Section 2.3 for moredetails).
The ﬂow disturbances created by the tower are altering the aerodynamic loading on the blades. The modiﬁed
ﬂow upwind of the tower can be calculated and is used to simulate the case of an upwind rotor. The downwind
tower wake ﬂow deﬁcit can also be simulated, together with its impact on the blades of a downwind rotor (seedetails in Section 2.3).
The HAWC2 code calculates in the time domain the aerodynamic loading on each of the discrete blade elements
in term of aerodynamic lift and drag. The resulting time-series for these quantities can be used to compute thenoise emissions as described in the next section.
2.2 Formulation 1A Model by Farassat
The method developed by Farassat [5] is shortly speaking a more advanced expression of Ffowcs WilliamsHawking solution [6] of the original Lighthill’s acoustic analogy [10]. Its main asset lies in the fact that ityields relatively accurate numerical evaluation of the acoustic pressure generated by a surface or object moving
in a ﬂuid and interacting with it through some ﬂuctuating aerodynamic loading, as well as the acoustic pressure
resulting from the displacement of the ﬂuid created by the thickness of the object itself. Nevertheless, thelatter mechanism is negligible in the context of wind turbine operation. This noise generation model has been
implemented into the HAWC2 code as described in a previous publication [4].
Note that this model predicts time-series of acoustic pressure at prescribed locations away from the noise sources(in our case, the discrete beam elements along the blade, see above) in the far-ﬁeld. This time-series can be
Fourier transformed to obtain noise spectra, much in the same way that acoustic pressure recordings from a
microphone in the ﬁeld are converted to sound pressure level spectra.
It should be noted here that noise propagation is not included in the present model. Only the geometricalspreading of the noise as it radiates away from the turbines is accounted for. Nevertheless, the noise data thatare analyzed later in this paper are measured relatively close to the test turbines that are investigated. Therefore,
it is believed that other noise propagation mechanisms (e.g. air absorption) are relatively negligible.
2.3 Wind Velocity and Atmospheric Turbulence
As described earlier, the LFN generation is driven by two main mechanisms which are discussed in this section.
Firstly, the blade-tower interaction can occur in two distinct conﬁgurations. In the case of an upwind rotor, theﬂow disturbances by the tower are simulated using a model based on the potential ﬂow solution of the ﬂow
around a circular cylinder as described in [9]. In the case of a downwind rotor, the tower shadow model (theso-called JET wake model) is based on the boundary layer solution for a jet ﬂowing into a ﬂuid at rest and is
described in detail in the paper by Madsen et al [11].
Secondly, the Mann model [12, 13] is used to simulate the atmospheric turbulence. This model requires three4415

input parameters:• the turbulent energy content in the form of αε 2/3 where ε is the turbulent kinetic energy dissipation rateand α a scaling constant,• the turbulence integral length scale L, and• the anisotropy factor Γ.
The deﬁnition of the numerical values assigned to each of these parameters for the simulations is discussed
below.
It is found that the anisotropy factor Γ has little inﬂuence on the results. The value Γ=3.9 from the IEC 61400-1
standard for wind turbine design requirements is used [2].
A recent publication by Kelly [8] shows that the integral length scale L can be evaluated with reasonableaccuracy from standard 10 mins average anemometer measurements using the following approximation:L ≈ σu /(dU/dz)(1)where σu is the shear stress of the main wind velocity component and the denominator is the wind shear. For
the experimental data considered in this article, both values will be extracted from mast sonic anemometers. An
anemometer located at hub height is used for the shear stress. The wind shear is also evaluated at hub heightusing the 6 other anemometers along the mast height (see below).
In the same above paper [8], the ratio between the measured σu2 and the theoretical variance of the velocity
2
for isotropic turbulence is found to be approximately equal to 5/3. This approximation should
components σisoremain valid as long as the surrounding terrain is not too complex (as it is the case for the terrain around the
Risø test station where the two turbines considered in the next section are located). Integrating the velocity
spectrum derived from the well-known von Kármán energy spectrum yields the following value for the varianceof an isotropic turbulent ﬂow:
2
= 0.688 αε 2/3 L2/3
σisoCombining the previous equation with the above mentioned ratio and length scale approximation gives thefollowing approximation for the remaining Mann model’s input parameter:
αε 2/3 = 0.872 σu2 L−2/3 ≈ 0.872 σu (dU/dz)2/3
4/3

(2)

Concerning, the inﬂow wind velocity impinging the turbine rotor, a logarithmic proﬁle is enforced in the calculations presented later in this article. Denoting UH the velocity at hub height z = H, where z is the elevationfrom the ground, then the wind velocity reads:
U(z) = UH ln(z/z0 )/ ln(H/z0 )(3)where z0 is the roughness length which is tuned to ﬁt the 10 mins averaged wind velocity proﬁles measured by
the met mast anemometers. From these values, the wind shear at hub height can be evaluated as:
dU/dz(z = H) = UH / H ln(H/z0 )(4)which in turn is used to compute the turbulence length scale L according to Eq. (1) and αε 2/3 according to
Eq. (2) as inputs of Mann model.
The procedure to quantitatively deﬁne the above parameters to be used for modelling speciﬁc noise measurement
data in the next section is described below. Wind velocity proﬁles are evaluated from anemometers along themet mast height using 10 mins average time-series. The roughness length is tuned so that the average measured
wind speed values match the computed value using Eq. (3). Thereafter, the wind shear can be computed using
Eq. (4). Its value is evaluated at hub height. It is important to note here that the inﬂuence of the wind shear

4416

on L and αε 2/3 as deﬁned by Eqs. (1) and (2) is considered as a characteristics of the particular atmosphericconditions for the day (or rather the few hours) of the considered measurement campaign. It is thereby assumed
that the atmospheric boundary layer conditions remain qualitatively constant during that period of time. The
wind velocity at hub height is averaged over the whole measurement campaign and the resulting hub heightwind shear computed with Eq. (4) is considered as representative of the speciﬁc atmospheric conditions for thatday, and this latter quantity is used in Eqs. (1) and (2). In parallel, the met mast anemometer at hub height isused to compute σu (H,UH ) and a linear regression is performed based on 10 mins averaged of the wind speed
at hub height. The value of σu used in Eqs. (1) and (2) to evaluate L and αε 2/3 makes use of this linear
regression using the wind speed of interest for each speciﬁc noise measurement data set (which are binned
according to the mean wind speed at hub height, see next section).

3

MODEL VERIFICATIONThe results of the proposed model are confronted to experimental data that were acquired when measuring noisefrom two wind turbines.
3.1 Risø Test Station for Wind Turbines
Noise measurements were conducted at the DTU-Risø campus on two wind turbines. The ﬁrst one is the
NordTank NTK 500 with a 41 m rotor diameter and a hub height of 36 m. It is stall-regulated and operates witha constant rotational speed. The second is a Vestas V52 pitch-regulated turbine with a rotor diameter of 52 m
and a hub height of 44 m.
Both turbines are equipped with various sensors that record the operational conditions such as rotational speed,
blade pitch, etc. In addition, met masts are located near the turbines. Wind speeds and directions, temperatureand other atmospheric quantities are measured at various heights up to the tip of the wind turbines. The
sampling frequencies for the acquisition systems are 35 Hz for the NTK 500 and 50 Hz for the V52 turbine.
Concerning the noise measurements, 8 ground microphones are placed on plywood boards around the turbines.
The microphones and the acquisition system are described in details in a previous article [3] where some of theresults of the experimental campaigns for the NTK 500 turbine were investigated. The set-up is identical for theV52 measurement campaign.
3.2 Wind Velocity Proﬁles and Turbulence Parameters
As explained earlier, the results of the LFN model primarily depend on the inputs to the Mann model which
reduce to two main parameters: wind shear and turbulence intensity at hub height. Wind shear is computedfrom the mean wind speed proﬁle during the considered campaign, assuming that it does not signiﬁcantly
change during that period. Figs. 1(a-c) displays the average wind velocity proﬁles, as measured by the met
masts anemometers, using a binning from the nacelle anemometers for the NTK turbine on Oct. 15-16 and 23
for the two ﬁrst ﬁgures, respectively, and for the V52 turbine for the third one. From this measured data,
logarithmic velocity proﬁle can be ﬁtted by tuning the roughness length z0 in Eq. (3) for each individual case.
The second parameter of interest, the standard deviation σu , is evaluated from 10 mins time-series from met mastanemometers at hub height and a linear regression is used in order to evaluate its actual value as a function ofwind speed. Both the 10 mins variances and the linear regression are plotted in Fig. 2(a-b) for the four cases
considered above.
Using the above measurement data, the parameters used as input for the Mann’s turbulence model are computed
according to the procedure described in Section 2.3 and quantitative values are summarized in Table 1 for thedifferent measurement campaigns.

4417

60

70

50

50

60

40

40

30
20
Oct.15 - Vnacelle= 6m/s
Oct.15 - Vnacelle= 8m/s
Oct.15 - Vnacelle=10m/s
Oct.15 - Vnacelle=12m/s
Oct.16 - Vnacelle= 6m/s

10
0
2

3

4

5

8

9

10

30
20

log-law z0=1.0m
log-law z0=1.0m
log-law z0=1.0m
log-law z0=1.0m
log-law z0=1.5m

6
7
Umast [m/s]50
Height [m]Height [m]Height [m]600(a) NTK turbine on Oct. 15 & 16 - z0 =1.0 & 1.5 m

30
20

10

11

40

Vnacelle= 6m/s
Vnacelle= 8m/s
Vnacelle=10m/s
56

7

log-law z0=0.1m
log-law z0=0.1m
log-law z0=0.1m
8
9
Umast [m/s]

Vnacelle=10m/s
Vnacelle=12m/s
Vnacelle=14m/s

10
10

11

12

0

8

9

10

log-law z0=1.e-5m
log-law z0=1.e-5m
log-law z0=1.e-5m
11
12
Umast [m/s]

13

14

15

(c) V52 turbine - z0 = 10−5 m(b) NTK turbine on Oct. 23 - z0 = 0.1 m

Figure 1. Wind velocity proﬁles (Lines: logarithmic proﬁles according to Eq. (3), Points: averaged velocities
measured by met mast anemometers and binned using nacelle anemometer).
2.5

σu [m/s]2
1.5

NTK 15 Oct. - 10 mins. average
NTK 16 Oct. - 10 mins. average
NTK 23 Oct. - 10 mins. average
V52 - 10 mins. average
σu = 0.176·UH + 0.406
σu = 0.174·UH + 0.137
σu = 0.104·UH - 0.0911
σu = - 0.0713·UH + 2.060

1
0.5
0

2

4

6
8
Wind Speed UH [m/s]

10

12

14

Figure 2. σu as a function wind speed as measured by met mast anemometer at hub height for NTK 500 andV52 measurement campaigns.
3.3 Low-Frequency Noise Spectra
Noise measurements, as well as background noise, for the NTK and the V52 turbines are reported in Figs. 3(a-c)
and 3(d), respectively. It can be observed that background noise contaminates the NTK turbine noise measurements in the 40-100 Hz frequency band, mostly at low wind speeds, as far as the broadband noise spectra areconcerned. This part of the background noise probably originates from nearby road trafﬁc, and possibly vegetation noise. In addition, numerous spurious peaks are also observed and these may be attributed to machinery
noise from the nacelle. Noise measurements for the V52 turbine also exhibit such peaks in this frequency range.
The peaks present in the background noise probably also originate from the wind turbine nacelle where internal
machinery still operates during standstill (e.g. cooling fans).
Background noise also contaminates the measurements below 20 Hz except for the NTK case on Oct. 16. It is
attributed to vegetation or ambient noise which is less predominant on Oct. 16 because of the relative lower
wind speeds that day (see Fig. 2). Note however that the microphones’ manufacturer provides a calibration
sheet down to 20 Hz with a very ﬂat response function down to that frequency. Nevertheless, the measurement
data appear consistent with the model below this frequency, unless there is a surmised high background noise

4418

Table 1. Turbulence parameters for experimental campaigns at considered wind speeds.
Campaign/Wind speed
NTK Oct. 15 - UH = 6 m/s
NTK Oct. 15 - UH = 10 m/s
NTK Oct. 16 - UH = 4 m/s
NTK Oct. 23 - UH = 6 m/s
NTK Oct. 23 - UH = 10 m/s
V52 - UH = 10 m/s
V52 - UH = 14 m/s

z0 [m]

dU/dz(H) [s−1 ]1.00.05951.5

0.03550.1

0.038810−50.0174σu [m/s]
1.511
2.109
1.115
0.565
0.889
1.347
1.061

L [m]
25.41
35.46
31.41
14.57
22.93
77.47
61.06

αε 2/3 [m4/3 /s2 ]0.23050.35950.10900.04660.08540.08700.0633

which is also consistent with the measured wind turbine noise spectra (see above).
The model results, using the input parameters for each test case as deﬁned earlier, are also displayed in theﬁgures. It can be seen that there exists a general good qualitative agreement between measurements and model
results (leaving out background noise contaminations). The model reproduces correctly the quantitative increaseof LFN as a function of wind speed, although in some cases and some frequency ranges discrepancies between
the actual noise levels are observed.

4

CONCLUSIONS

A model for calculating the LFN emitted by wind turbines is proposed. One of the components of this modelis the Mann turbulence model used to simulate atmospheric turbulence. This latter model input parameters are
tuned using experimental data extracted from met mast measurements near the turbines that are investigated.
The Mann model is the primary component of the proposed model, in the sense that it is used to deﬁne
the turbulent ﬂow ﬁeld that impact the turbines and generate noise by interacting with the blades. The othercomponents of the model, which consist of the wind turbine aeroelastic model together with the generation of
LFN from aerodynamic ﬂuctuations on the blades, are also described in this paper.
The results of the combined model are compared to existing noise measurements on two wind turbines. There isa fair agreement between the model predictions and the experimental data. However, this is a preliminary study
and additional turbines must be investigated to validate the model. Indeed, the two turbines considered in thepresent study are relatively old and small compared to modern MW-size turbines. Furthermore, the contributionof the blade-tower interaction to the LFN emissions, even if these are included in the present calculations,remains to be investigated in more detail. More speciﬁcally, the LFN emission from downwind rotors is ofparticular interest.

ACKNOWLEDGEMENTS
This study was conducted as part of the program "Cross-Cutting Activities" internally funded by DTU Wind
Energy.
The authors would like to thank Kasper Clemmensen, Karen Enevoldsen, Per Hansen, Uwe S. Paulsen, Claus
B. M. Pedersen and Michael Rasmussen from DTU Wind Energy for participating in the design of the experiment, preparing the hardware and acquisition software, and conducting the ﬁeld measurements.

REFERENCES[1] HAWC2 Aeroelastic Simulation of Wind Turbines. http://www.hawc2.dk. Accessed: 2017-04-28.
[2] International Standard, Wind Turbines - Part 1: Design Requirements. IEC 61400-1, International Elec-

4419

Model - UH = 6m/s
UH =10m/s
Wind turbine noise - VN = 6m/s
VN =10m/s
Background noise - VN = 6m/s
VN =10m/s

SPL [dB /Hz]

70
60
50
40

80

30
20

Model - UH = 6m/s
Wind turbine noise - VN = 6m/s
Background noise - VN = 6m/s

70
SPL [dB /Hz]

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10

Frequency [Hz]

20

100

10

(a) NTK turbine 15 Oct. - z0 = 1.0 m

Model - UH = 6m/s
UH =10m/s
Wind turbine noise - VN = 6m/s
VN =10m/s
Background noise - VN = 6m/s
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SPL [dB /Hz]

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100

(b) NTK turbine 16 Oct. - z0 = 1.5 m
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UH =14m/s
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VN =12m/s

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SPL [dB /Hz]80

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Frequency [Hz]100(c) NTK turbine 23 Oct. - z0 = 0.1 m

20

10Frequency [Hz]100(d) V52 turbine - z0 = 10−5 m

Figure 3. Sound pressure level spectra for the NTK and V52 turbines (Thick lines: model, Thin lines: measurements, Dashed lines: frequencies below 20 Hz for measured spectra).
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