Semi-Empirical Aeroacoustic 

Noise Prediction Code for 

Wind Turbines 

December 2003 • NREL/TP-500-34478 

P. Moriarty and P. Migliore 

National Renewable Energy Laboratory 

1617 Cole Boulevard 

Golden, Colorado 80401-3393 

NREL is a U.S. Department of Energy Laboratory 

Operated by Midwest Research Institute • Battelle 

Contract No. DE-AC36-99-GO10337 
National Renewable Energy Laboratory 

1617 Cole Boulevard 

Golden, Colorado 80401-3393 

NREL is a U.S. Department of Energy Laboratory 

Operated by Midwest Research Institute • Battelle 

Contract No. DE-AC36-99-GO10337 

December 2003 • NREL/TP-500-34478 

Semi-Empirical Aeroacoustic 

Noise Prediction Code for 

Wind Turbines 

P. Moriarty and P. Migliore 

Prepared under Task No. WER3.1830 
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iii

Foreword 

The U.S. Department of Energy (DOE), working through its National Renewable Energy Laboratory 

(NREL), is engaged in a comprehensive research effort to improve the understanding of wind turbine 

aeroacoustics. Motivation for this effort is the desire to exploit the large expanse of low wind speed sites 

that tend to be closer to U.S. load centers. Quiet wind turbines are an inducement to widespread 

deployment, so the goal of NREL’s aeroacoustic research is to develop tools for use by U.S. industry in 

developing and deploying highly efficient, quiet wind turbines at these low wind speed sites. NREL’s 

National Wind Technology Center (NWTC) is implementing a multifaceted approach that includes wind 

tunnel tests, field tests, and theoretical analyses in direct support of low wind speed turbine development 

by its industry partners. NWTC researchers are working hand in hand with industry engineers to ensure 

that research findings are available to support ongoing design decisions. 

This report describes the development and validation of a semi-empirical code for predicting wind turbine 

aeroacoustic emissions and the resulting sound pressure level at a receptor location. To our knowledge, it 

is the only such method currently available to U.S. wind turbine designers. The semi-empirical approach 

has its shortcomings, but improvements are already in the works. Other aspects of our research program, 

including wind tunnel tests, field tests and computational analysis, will contribute to these improvements. 

Thus, the present work needs to be considered in the context of the broader research effort on wind 

turbine aeroacoustics. 

Wind tunnel aerodynamic tests and aeroacoustic tests have been performed on six airfoils that are 

candidates for use on small wind turbines. Results are documented in the following two companion 

NREL reports: 

“Wind Tunnel Aeroacoustic Tests of Six Airfoils for Use on Small Wind Turbines,” 

Stefan Oerlemans, Principal Investigator, the Netherlands National Aerospace Laboratory 

“Wind Tunnel Aerodynamic Tests of Six Airfoils for Use on Small Wind Turbines,” 

Michael Selig, Principal Investigator, University of Illinois at Urbana-Champaign (UIUC). 

These reports provide a valuable airfoil database for designers who wish to consider the tested airfoils. 

But inevitably, they will wish to evaluate other airfoils that have not been tested. This presents a dilemma. 

Not only are wind tunnel tests expensive, it is often difficult to schedule the required facilities within the 

overall timeframe of a project development plan. This conundrum begs the question, “Is it really 

necessary to conduct wind tunnel tests, or can we rely on theoretical predictions?” Predicting the 

aeroacoustic emission spectra of a particular airfoil shape is extremely difficult, but predicting the 

aerodynamic characteristics of a particular airfoil shape is a routine, well-established practice. 

Nevertheless, there is always some uncertainty about the accuracy of the predictions compared to wind 

tunnel tests or field performance, and there are questions about the efficacy of the two principal airfoil 

analysis methods: the Eppler and XFOIL codes. To address these related issues, at least in part, a 

theoretical analysis was commissioned of the same airfoils tested in the wind tunnel. The results are 

documented in the following NREL report: 

“Theoretical Aerodynamic Analyses of Six Airfoils for Use on Small Wind Turbines Using 

Eppler and XFOIL Codes,” Dan M. Somers and Mark D. Maughmer; Principal Investigators; 

Airfoils, Incorporated 
iv

The possession of both theoretically predicted aerodynamic characteristics and wind tunnel test data for 

the same six airfoils provides the extraordinary opportunity to compare the performance, measured by 

energy capture, of wind turbine rotors designed with the different data. This will provide the desired 

insight to assist designers in deciding whether to pursue wind tunnel tests. Although some differences in 

the resulting blade planforms (chord and twist distributions) can be expected, a more important question 

relates to the difference in energy capture and its significance in driving the choices that need to be made 

during the preliminary design stage. These issues are addressed in a report that compares the differences 

in Eppler and XFOIL predictions to the UIUC wind tunnel tests and examines the planform and energy 

capture differences in resulting blade designs. This report is titled: 

“Comparison of Optimized Aerodynamic Performance of Small Wind Turbine Rotors Designed 

with Theoretically Predicted versus Experimentally Measured Airfoil Characteristics,” 

Michael Selig, Principal Investigator, University of Illinois at Urbana-Champaign (UIUC) 

Another research effort undertaken in support of the U.S. wind turbine industry involves a series of 

aeroacoustic field tests conducted at the NWTC. Using well documented, consistently applied test 

procedures, noise spectra were measured for eight small wind turbine configurations. Test results provide 

valuable information to the manufacturers, as well as the potential users of these turbines. To our 

knowledge, this is the first comprehensive database of noise data for small wind turbines. Results of this 

effort are documented in another NREL report, titled: 

“Aeroacoustic Field Tests of Eight Small Wind Turbines,” J. van Dam and A. Huskey, Principal 

Investigators, NREL’s National Wind Technology Center 

Wind tunnel tests, field tests and theoretical analyses provide useful information for the development and 

validation of NREL’s semi-empirical noise prediction code. This effort, which is described in the 

following report, will be continuously improved, but may ultimately give way to more sophisticated, 

physics-based computational aeroacoustic codes also being developed by NREL. 

“Semi-Empirical Aeroacoustic Noise Prediction Code for Wind Turbines,” Patrick Moriarty, 

Principal Investigator, NREL’s National Wind Technology Center. 

Each of the documents described above will be published as a stand-alone NREL report. Undoubtedly, 

some results will also be presented in various journal articles or conference papers. All of the NREL 

reports will be available on NREL’s NWTC Web site at http://www.nrel.gov/wind/. Collectively, these 

reports represent a significant compendium of information on the aerodynamics and aeroacoustics of 

contemporary wind turbines. Therefore, NREL will also publish a CD-ROM containing all of the reports. 

Clearly, this work represents a significant commitment of DOE resources as well as a significant human 

commitment over an extended period of time. I am sure I express the sentiments of all the research 

participants in saying we sincerely hope the results of these efforts prove beneficial to the wind energy 

community. 

Paul G. Migliore 

NREL/NWTC Project Manager 
v

Table of Contents 

Abstract...........................................................................................................................vi 

Semi-Empirical Aeroacoustic Noise Prediction Code for Wind Turbines......................... 1 

Introduction.................................................................................................................. 1

Aeroacoustic Noise Prediction Model .......................................................................... 1 

Turbulent Boundary Layer Trailing Edge (TBL-TE).................................................. 2 

Separated Flow........................................................................................................ 3 

Laminar Boundary Layer Vortex Shedding (LBL-VS)............................................... 3 

Trailing-Edge Bluntness Vortex Shedding (TEB-VS) ............................................... 3 

Tip Vortex Formation................................................................................................ 4 

Turbulent Inflow........................................................................................................ 4 

Tower Wake Interaction ........................................................................................... 5 

Atmospheric Propagation......................................................................................... 5 

Directivity ................................................................................................................. 6 

Code Validation ........................................................................................................... 7 

Two-Dimensional Airfoil Data................................................................................... 7 

Full-Scale Turbine.................................................................................................. 11 

Turbulent Length Scale ...................................................................................... 14 

Blade Pitch Angle ............................................................................................... 15 

Boundary-Layer Tripping .................................................................................... 16 

Trailing-Edge Bluntness ..................................................................................... 16 

Tip Noise ............................................................................................................ 17 

Rotor Speed ....................................................................................................... 18 

Directivity............................................................................................................ 20 

Conclusions............................................................................................................... 22 

References.................................................................................................................... 24 

Appendix: Code Operation............................................................................................ 26 

Input Files .................................................................................................................. 26

Output files ................................................................................................................ 29 
vi

Abstract 

A series of semi-empirical aeroacoustic noise prediction subroutines was written and 

incorporated into the National Renewable Energy Laboratory’s (NREL's) aeroelastic simulation 

code: FAST [1]. The subroutines predict six different forms of aerodynamically produced noise 

that were superimposed to calculate the total aeroacoustic signature of an operating wind turbine. 

The outputs of the code are sound pressure level spectra of these various sources in one-third 

octave bands. Parts of the code were validated against acoustic data from two-dimensional airfoil 

tests. Results from these validation studies were somewhat mixed. For certain wind tunnel 

conditions, the code predicted sound pressure levels within 2 decibels (dB) of the data, while for 

others the difference between prediction and data was 6 dB or more. Trends and relative 

amplitude changes in the predictions often mimicked those seen in the data. Predictions of the 

NACA 0012 airfoil were more accurate than those of the other airfoils. The code was also 

validated against measurements from a test of a full-scale wind turbine, the Atlantic Orient 

Corporation (AOC) 15/50. The noise predictions of this turbine were dominated by turbulent 

inflow noise, which was found to be sensitive to turbulence intensity and the turbulent length 

scale. It is unclear whether this dominance of turbulent inflow noise is physically realistic 

because previous studies have shown this was not the dominant source for wind turbines. Further 

study of turbulent inflow noise is recommended. Trends in the predicted sound pressure level as 

a function of wind speed and also the acoustic noise spectrum matched those of the data, 

although the absolute levels were slightly different. Several parametric studies were performed 

using the AOC model. It was verified that the total sound pressure level was most sensitive to the 

rotor’s rotational speed. Because of directivity effects, the position of the observer relative to the 

rotor plane greatly affected the perceived total sound pressure level and also the apparent source 

distribution across the rotor plane. 
1

Semi-Empirical Aeroacoustic Noise Prediction 

Code for Wind Turbines 

Introduction 

One of the most significant drivers for wind turbine design is the amount of acoustic noise that a 

turbine radiates. This issue is particularly important because turbines are placed closer to load 

centers, which typically have large population densities and restrictive noise ordinances. To date, 

the rotational speeds of most wind turbine designs have been limited by the acoustic emissions 

from the blades, for which the sound intensity is approximately proportional to the tip speed 

raised to the fifth power. Unfortunately, tip speed is also related to the cost effectiveness of the 

wind turbine design. Increasing the tip speed, even slightly, can have a dramatic effect on the 

amount of energy captured by a wind turbine and, hence, directly influences the cost of energy 

for a given design. Therefore, it is very important to be able to understand, model, and predict 

the aeroacoustic noise for a given turbine in the design process and to make design changes 

before prototypes are built and tested. The noise prediction subroutines written to interface with 

FAST [1] allow these predictions to be made. This report explains how the code was written, 

what validation against test data was performed, and how a user can implement the code to 

predict noise for any given turbine design. 

Aeroacoustic Noise Prediction Model 

The model developed for the prediction of aeroacoustic noise is based on six different noise 

sources that are assumed to independently generate their own noise signature. The assumption of 

independence is founded on the idea that the mechanisms for each noise source are 

fundamentally different from each other or occur in different locations along a turbine blade, 

such that they do not interfere with one another. These independent noise sources are 

superimposed to obtain the total noise spectra emitted from the wind turbine rotor. Five of these 

models are taken directly from the work of Brooks, Pope, and Marcolini [2], who formulated 

semi-empirical relations for the following sources of noise: turbulent boundary layer trailing 

edge, separating flow, laminar boundary layer vortex shedding, trailing edge bluntness vortex 

shedding, and tip vortex formation. These models are based on two-dimensional wind tunnel 

measurements (except for the tip vortex formation noise) of NACA 0012 airfoils. These noise 

sources, termed airfoil self-noise, are caused by the interaction between an airfoil and the 

turbulence produced in its own boundary layer and near wake when encountering a non-turbulent 

inflow. The final noise source, turbulent inflow noise, is caused by the interaction of the leading 

edge of the airfoil with a turbulent inflow. The model for this noise source was taken from the 

works of Lowson [3], who modified equations written by Amiet [4] to apply to wind turbine 

applications. 

Each semi-empirical model relates the properties of the flowfield and turbine geometry to a 

resulting sound pressure level (SPL). The SPL, given in units of dB, is proportional to the 

logarithm of the ratio of sound intensity (or mean square pressure) to a reference value: 
2















 =













 =

ref ref p

p

I

I SPL 10 [1] log 20log

where I is the sound intensity, and p is the root mean square sound pressure. The reference root 

mean square pressure is 20 μPa. 

Each of the semi-empirical models was developed for a single two-dimensional airfoil. In order 

to calculate the aerodynamic noise radiating from a wind turbine rotor, the rotor blades are first 

discretized into many individual segments. Using local flow velocities and angles of attack, the 

sound pressure level for each segment and noise source is then calculated relative to an observer 

position. Finally, the sound pressure level from each of the individual sources is summed across 

the blade to calculate the total noise signature of the rotor. For the semi-empirical models to be 

applicable, the segments are assumed to operate in predominantly two-dimensional flow. This is 

largely true for outboard blade sections, which tend to dominate the noise production. The flow 

over the segments is also assumed to be quasi-steady, such that the mechanisms that produce 

noise are stationary at each time step in the simulation. 

Turbulent Boundary Layer Trailing Edge (TBL-TE) 

The first, and perhaps most common, source of noise from an airfoil, results from the interaction 

between the turbulent boundary layer and the trailing edge of the airfoil, especially at higher 

Reynolds numbers. Based on their measurements, Brooks, Pope, and Marcolini formulated 

empirical relations to predict these noise sources based on the edge-scatter formulation of 

Ffowcs-Williams and Hall [5]. These relations account for the noise intensity being directly 

proportional to the turbulent boundary layer displacement thickness, δ*, and the fifth power of 

the mean velocity or Mach number, M5, and inversely proportional to the square of the distance 

between the observer and the airfoil trailing edge. There are also corrections for angle of attack 

and Reynolds number, as well as tripped and untripped boundary layers. Turbulent boundary 

layer noise can originate on both the suction and pressure side of the airfoil. For the pressure side 

of the airfoil, the sound pressure level is given as follows: 

1 1

1

2

* 5

10log (K 3) K

St

St

A

r

M LD

SPL p

e

p h

p + − + ∆ 















+













 = δ

 [2] 

where δ*

= δ*(α, Rec) is the boundary layer displacement thickness, in meters [m], based on α, 

the angle of attack [deg.], and Rec, the Reynolds number based on chord. The subscript p refers 

to the pressure side of the airfoil. Other parameters in Equation 2 are L, the span of the airfoil 

section [m]; Dh, the directivity function (see directivity section starting on page 6); re, the 

effective observer distance [m]; and A, an empirical spectral shape based on the Strouhal number 

St = (fδ

*

/U), where f is the frequency in hertz [Hz], and U is the local mean velocity [m/s]. Three 

other empirical relations are also used, St1 = 0.02M-0.6, K1 = K1 (Rec), and ∆K1 = ∆K1 (α, Reδ*). 

A nearly identical formulation is used to calculate the sound pressure level radiating from the 

suction side of the airfoil [2]. 
3

Separated Flow 

As the angle of attack increases from moderate to high, the size of the turbulent boundary layer 

on the suction side of the airfoil increases dramatically, and large-scale unsteady structures form. 

These structures can dominate noise production from the trailing edge. When the airfoil is fully 

separated or stalled, noise radiates from the unsteady flow over the entire chord of the airfoil. 

This is an important noise source for wind turbines because the blades operate at high angles of 

attack for significant portions of time. The empirical relation for separated flow noise, denoted 

SPLα, is very similar to Equation 2 with different scaling functions for the angle of attack 

dependence [2]. 

The total sound pressure level from the interaction of the turbulent boundary layer with the 

trailing edge can be determined through simple summation of the three different components: 

pressure side, suction side, and separated flow: 

( ) /10 /10 /10 10log 10 10 10 α SPL SPL SPL

TBL TE

p s SPL − = + + [3] 

Laminar Boundary Layer Vortex Shedding (LBL-VS) 

Another source of airfoil self noise [2] is that of laminar boundary layer vortex shedding. The 

noise from this source is created by a feedback loop between vortices being shed at the trailing 

edge and instability waves (Tollmien-Schlicting waves [6]) in the laminar boundary layer 

upstream of the trailing edge. As a laminar vortex leaves the trailing edge, its pressure waves 

propagate upstream and amplify instabilities in the boundary layer. When these instabilities 

reach the trailing edge, vortices with similar frequency content are created, forming a feedback 

loop. This source of noise is most likely to occur on the pressure side of the airfoil and is 

somewhat tonal in nature because of feedback amplification. This noise source is probably not 

significant for current utility-sized turbines because their blade airfoil sections, particularly near 

the tips, operate at fairly large Reynolds number (>1 million), but may be important for smaller 

sized turbines (i.e. <500 kW). The empirical relation for sound pressure level is as follows: 

( ) ( ) Re

Re

'

' 10log 2 1 2 3

5

α

δ

G G

St

St G

r

M LD

SPL

c o

c

e peak

p h

LBL VS +















+















+















− = [4] 

where most of the variables are identical to those in Equation 2: δp is the boundary layer 

thickness [m] on the pressure side of the airfoil; G1, G2, and G3 are empirical functions; St' is 

the Strouhal number based on δp, St'peak = St'peak(Rec) and is the peak Strouhal number; and (Rec)o

= (Rec)o(α) is a reference Reynolds number. 

Trailing-Edge Bluntness Vortex Shedding (TEB-VS) 

Another source of airfoil self noise is vortex shedding from a blunt trailing edge. The frequency 

and amplitude of this noise source are largely determined by the geometry of the trailing edge. 

The vortices shed are typically coherent in nature and can produce discrete tones similar to a Von 

Karman vortex street downstream of cylindrical objects. This noise source will dominate the 

total radiated noise if the thickness of the trailing edge is significantly larger than the thickness of 
4

the boundary layer at the trailing edge. Therefore, in addition to Mach number and boundary 

layer thickness scaling, the empirical relation to predict sound pressure level also contains 

functions dependent on the trailing edge thickness, as follows: 

















+ Ψ 















+ Ψ 















− =

e avg avg peak

p h

TEB VS St

h St G h G

r

M LD

SPL ''

'' 10log , , , 2 4 * 5 *

* 5

δ δ

δ

 [5] 

where h is the trailing edge thickness [m]; δ

*

avg is the average displacement thickness for both 

sides of the airfoil [m]; Ψ is the solid angle between both airfoil surfaces just upstream of the 

trailing edge [deg.]; St'' is the Strouhal number based on h; St''peak = St''peak(h/δ

*

avg) is the peak 

Strouhal number; and G4 and G are empirical functions of these parameters. 

Tip Vortex Formation 

The interaction of the tip vortex with the blade tip and trailing edge near the tip is also a source 

of aerodynamic noise. This noise source is different from the previous four sources in that it is 

three-dimensional in nature. The sound pressure level is a function of the vortex strength, which 

is dependent on the spanwise loading on the turbine blade. Typically, the sound pressure levels 

from tip noise are less than those of trailing edge noise, but tip noise can add significant amounts 

of noise at higher frequencies. Brooks, Pope, and Marcolini formulated the following relation for 

an untwisted, constant chord blade: 

10log 30.5(log ''' 0.3) 126 2

2

5 2

max

2

− + + 













 = St

r

M M D SPL

e

h

Tip

A [6] 

where Mmax = Mmax(αtip) is the maximum Mach number within the separated flow region near the 

tip, αtip is the equivalent angle of attack at the tip [deg.], and ) (α tip A = A is the spanwise extent of 

the separation zone [m], which is dependent on the spanwise lift distribution and the geometric 

shape of the tip (rounded or square). St''' is the Strouhal number based on A . Because this 

relation was formulated for an untwisted, constant chord blade, an equivalent αtip for twisted and 

tapered blades should be used to produce reliable results. A crude estimate for this parameter can 

be made by multiplying the geometric αtip by the ratio of the slopes of the spanwise lift 

distribution for the complex blade shape to that of Brooks, Pope, and Marcolini. If accurate 

estimates of absolute tip noise were necessary, the user would be required to tune this variable to 

match measured data, which are not easily obtained. 

Turbulent Inflow 

For wind-turbine applications, the interaction of the turbulent inflow (produced by the 

atmospheric boundary layer) with the leading edge of the turbine blades is a significant source of 

noise, particularly at low frequencies. This noise source becomes important when the length 

scale of the turbulent eddies is large in comparison to the leading edge radius of an airfoil. In the 

atmospheric boundary layer, the scales of turbulence vary by several orders of magnitude from 

approximately 1 mm to larger scales on the order of 100 m, where most of the energy resides. 
5

Depending on the size of the length scale relative to the leading edge radius of the airfoil, 

turbulent inflow can create either a dipole noise source (low-frequency) with M6

 dependence or a 

scattered quadrupole noise source (high frequency) with M5

 dependence [7]. Lowson [3] 

formulated an empirical relation for inflow turbulence noise that modeled both the low and high 

frequency behavior and is based on Amiet's [4] work on experimental airfoil measurements, as 

follows: 





 





+ = +LFC

LFC SPL SPLH

Inflow Inflow 1

10log [7] 

58.4

2 (1 )

10log 2 7 / 3

3

3 2 2

2

2 2

+















+ = L

e

H o o

Inflow D

K

K M u I

r

c lL SPL ρ [8] 

2 2 2 10 − LFC = S MK β [9] 

1 1

2 2

2 1 2.4 2 − −































 = + +

β β

πK K S [10] 

where ρo is the air density [kg/m3

]; co is the speed of sound [m/s]; l is a turbulence length scale 

(described in the next paragraph) [m]; u is the mean wind speed [m/s]; I is the turbulence 

intensity [%]; K = πfc/U is the local wave number, where f is the frequency of interest [Hz], c is 

the local airfoil chord length [m], and U is the local velocity over the airfoil section [m/s]; DL is a 

low-frequency directivity function; LFC is a low-frequency correction factor; S is the 

compressible Sears function; and β

2

 = 1-M2. 

Note that the sound intensity (the term in brackets in Eq. 8) is directly proportional to the 

turbulence length scale. Therefore, this parameter should be chosen with care because it will be 

sensitive to both the rotor size and the nature of the turbulence at the turbine site. Currently, in 

the code, the isotropic turbulence integral-scale parameter of the atmospheric boundary layer is 

used, which is a function of the hub height of the turbine, as specified in the International 

Electrotechnical Commission (IEC) standard [8]. This parameter is defined as 2.45 times the 

hub height, up to a maximum of 73.5m (30 m hub height). It should be noted for potential users 

of the code that the turbulent length scale is currently fixed at the IEC value inside the code, 

although future revisions may include this as an input value. 

Tower Wake Interaction 

Currently, the prediction code does not model the noise created by blades passing through the 

wake of the tower, either upwind or downwind. This noise source is a significant contributor for 

downwind turbines and may be modeled in the future. 

Atmospheric Propagation 

Currently, the prediction code does not model the effects of the atmosphere or terrain on the 

propagating noise. These effects include reflections off uneven terrain or buildings, atmospheric 
6

Figure 1. Angles used in directivity functions [2] 

absorption, and various modifications caused by propagation through the atmospheric boundary 

layer. These effects are important for noise propagation over long distances and may be modeled 

in the future. 

Directivity

In each of the empirical relations above, there are correction factors for the directivity of the 

noise based on the position of the observer relative to either the trailing or leading edge of the 

airfoil. These correction factors and the noise levels themselves are based on a coordinate system 

that is shifted or “retarded” relative to the original airfoil positions. This retarded coordinate 

system compensates for the fact that the noise is convected downstream as it approaches the 

observer. Source convection changes the apparent location of the noise source and also the 

relative directivity angles for the observer. In the semi-empirical code, all sources are assumed to 

convect in the direction of the mean wind speed at a velocity of 0.8 times the mean wind speed, 

which is approximately the average velocity for an atmospheric boundary layer profile with a 

power exponent of 0.2. 

Once the position of the noise source is determined in retarded coordinates, the directivity angles 

are determined (Figure 1). Note that all noise sources except for turbulent inflow noise are 

assumed to originate at the trailing edge of the airfoil, while the turbulent inflow noise originates 

at the leading edge of the airfoil. These directivity angles are then used in the following 

directivity functions, which account for some Doppler shift effects and convective amplification 

of a non-stationary noise source relative to the observer. For high-frequency noise sources 

(everything except for high-angle separation and turbulent inflow noise) the directivity function 

is as follows: 

( )2

2

2

1 2

(1 cos ) 1 ( )cos

2sin ( )sin ( , )

e c e

e e

H e e M M M

D

+ Θ + − Θ

Θ Φ Θ Φ ≈ [11] 
7

where M is the Mach number for the airfoil section, Mc is the convective Mach number, Θe and 

Φe are the directivity angles. 

For low-frequency noise sources, the directivity correction is as follows: 

4

2 2

(1 cos )

sin sin ( , )

e

e e

L e e M

D

+ Θ

Θ Φ Θ Φ ≈ [12] 

Note that for Θe = 90° and Φe = 90°, both directivity functions are equal to 1. Also, DH becomes 

increasingly inaccurate for shallow upstream angles, where Θe approaches 180°. 

Code Validation 

To assess the accuracy of the semi-empirical code for absolute and relative values of sound 

pressure level, researchers compared predicted values to measured data from two-dimensional 

airfoil tests and measurements of a full-scale wind turbine. They also performed parametric 

studies of various quantities to determine various sensitivities of the prediction code. 

Two-Dimensional Airfoil Data 

The first part of code validation involved comparing values predicted by the noise code to twodimensional airfoil data. The two-dimensional airfoil data were taken from a series of windtunnel tests performed at the National Aerospace Laboratory in the Netherlands (NLR) [9]. 

Acoustic noise spectra of several different airfoils were measured using a 48-microphone 

acoustic array. Details of the array, array processing, and measurements can be found in [9]. 

Readers of this report should consider the correction scheme used to eliminate extraneous noise 

sources from some of the data used in the present study. It should also be noted that using 

microphone array measurements to calculate absolute sound pressure levels is more 

computationally complex than measurements from a single microphone, but the technique has 

been shown to be experimentally valid [10]. Analysis of the acoustic array data provided thirdoctave sound pressure level measurements that could be directly compared to predictions given 

by the semi-empirical code. From this data set, two airfoils, a NACA 0012 and an S822 [11], 

were modeled for code validation. The chord lengths of both airfoils were 0.2286 m. 

Figure 2 shows the comparison between data and predictions for a NACA 0012 airfoil at a Mach 

number of 0.207 for a range of angles of attack. In each of the following figures, the points with 

symbols represent the measured wind-tunnel data, while the lines of similar color represent the 

predicted spectra for the same wind conditions. In Figure 2, the assumptions used for the 

prediction code are that turbulent boundary-layer trailing-edge noise (including separating flow 

noise) is the dominant source, the boundary layer is "lightly" tripped (see boundary-layer 

tripping section below), and there is no noise from laminar vortex shedding, trailing edge 

bluntness, or turbulent inflow (test section turbulence intensity ~0.5%). Because the semiempirical relations in the prediction code are based on previous measurements of a NACA 0012 

airfoil, one would expect that agreement between data and prediction to be fairly close. This is 
8

Figure 2. Comparison of two-dimensional NACA 0012 data to predictions for M = 0.207 at several 

angles of attack 

Figure 3. Comparison of two-dimensional NACA 0012 data to predictions for α = 7.18° at several 

Mach numbers 

true for frequencies near 3 kilohertz (kHz), but less so for lower frequencies where the difference 

is as large as 6 dB. At lower frequencies, the absolute sound pressure levels are overpredicted, 

but the relative trends and differences in level as a function of angle of attack are very similar to 

the data. However, the agreement between measurement and prediction worsens with increasing 

angle of attack. 

Figure 3 compares test data and predictions for a NACA 0012 airfoil at an angle of attack of 

7.18° and a range of Mach numbers. These tunnel speeds were chosen so that a direct 

comparison to the measurements of Brooks, Pope, and Marcolini [2] 
9

Figure 4. Comparison of two-dimensional NACA 0012 data to predictions for M = 0.207 at several 

angles of attack with no boundary layer tripping 

could be made. The assumptions used in the prediction code are identical to those used in Figure 

2. The agreement between data and predictions is reasonable and is within 3 dB for all Mach 

numbers, with the best agreement occurring for a Mach number of 0.163. 

Figure 4 shows data and predictions for the same airfoil over a range of angles of attack at a 

fixed Mach number under the same tunnel conditions as Figure 2, except no boundary layer 

tripping. In this figure, laminar vortex shedding noise is the dominant source, as made evident by 

the pronounced peak near 3 kHz in each of the spectra. The agreement between data and 

predictions for the 4.0° and 5.3° angle of attack cases is particularly good, with less than 1 dB 

difference in the middle frequency range. The noise peaks for the highest and lowest angles of 

attack are overpredicted, with an approximately 10 dB difference at an angle of attack of 7.3°. 

Figure 5 compares predictions and data for an S822 airfoil at a fixed Mach number, 0.038, over 

several different angles of attack. The airfoil has been "lightly" tripped (see boundary layer 

tripping section below) and turbulent boundary layer trailing edge noise is assumed dominant. 

Even though this airfoil has a significant amount of camber relative to the symmetric NACA 

0012, the predicted sound pressure levels are fairly reasonable for frequencies of 3 kHz and less. 

Above 3 kHz, the agreement between predictions and test data decreases. As seen in Figure 2, 

the trends of amplitude with frequency are predicted fairly well; however, the relative differences 

between angles of attack are not well represented by the prediction method for these particular 

test conditions. One possible reason for this discrepancy is that in the prediction code, the 

boundary layer thickness is empirically modeled from NACA 0012 data and is, therefore, 

incorrectly predicted for the S822 airfoil. A possible improvement to the prediction code, that 

will be a focus of future work, will be a more accurate prediction method for boundary layer 

thickness that can incorporate differences in airfoil shape. 
10

Figure 5. Comparison of two-dimensional S822 data to predictions for M = 0.038 at several angles 

of attack 

Figure 6. Comparison of two-dimensional S822 data to prediction for α = 4.42° at several Mach 

numbers with turbulent inflow (TI = 9%, L = 60 mm) and no boundary layer tripping 

Figure 6 compares data and the predicted sound pressure levels for an S822 airfoil in a turbulent 

inflow at various wind tunnel Mach numbers. The Reynolds numbers for these tunnel conditions, 

based on chord length, were between 200,000 and 1 million. The boundary layer of the airfoil is 

not tripped, so in addition to trailing edge and turbulent inflow noise, laminar vortex shedding 

noise from the lower surface is possible. As described above, the turbulent inflow noise is a 

function of both the turbulence intensity and the turbulent length scale in the flow. The 

turbulence in the wind tunnel was created by adding a fixed-width mesh just upstream of the test 
11

section [9]. After adding this mesh, the turbulence intensity in the center of the test section was 

measured as 9% by a hot-wire anemometer. Because the model was located only five mesh 

widths downstream of the mesh, there was insufficient distance for the turbulence to become 

fully isotropic. Therefore, the dominant turbulent length scale was assumed to be identical to the 

mesh width of 60 mm. Using these values for the parameters in the code, researchers found that 

the predicted sound pressure levels from the airfoil gave reasonable results for the lowest Mach 

numbers. Notice that there are fewer points in Figure 6 than in previous figures because it is 

believed that the frequencies above 3 kHz are contaminated by extraneous noise sources in the 

wind tunnel produced by the turbulence grid [9]. As the Mach number increases, the agreement 

between test data and predictions worsens. At the lower frequencies, the data are underpredicted, 

while the peak in the predicted spectra (primarily laminar from vortex shedding noise) 

overestimates the measured values. Note that at the highest Mach number, the differences 

between predictions and test data are as much as 10 dB. These differences may be attributed to a 

dependency of turbulence intensity and turbulent length scale on tunnel speed, which was not 

modeled. 

Full-Scale Turbine 

The next step in validation was to model a full-size wind turbine and compare the semi-empirical 

prediction to available measured data. 

Researchers chose the Atlantic Orient Corporation (AOC) 15/50 turbine, operating at the 

National Wind Technology Center (NWTC), for validation. This three-bladed turbine has a rated 

power of 50 kilowatts (kW), a rotor diameter of 15 m, a hub height of 25 m, and a fixed 

rotational speed of 64.6 RPM (independent of mean wind speed). The trailing edge thicknesses 

of the blades were assumed to be 1% of the chord length, which is typical for many wind turbine 

designs. The turbine has tip brakes on each blade and operates downwind of the tower, both of 

which produce potential noise sources that are not modeled accurately in the semi-empirical 

code. For example, the presence of the tower upwind of the rotor plane may introduce turbulent 

eddies that could contribute significantly to the noise. Also, because the AOC has no nacelle, 

gearbox noise could potentially contribute to the farfield noise. The acoustic noise measurements 

of this turbine were taken according to IEC 61400-11 [12] standards, and the sound pressure 

levels shown in this report are from a single microphone 32.5 m downwind of the tower center at 

the base [13]. 

Correctly modeling the turbulent inflow of the atmosphere was important for accurately 

estimating aeroacoustic noise. The wind inputs for the predictions were created using SNWind 

[14], NREL's three-dimensional wind simulation code. And, for turbulent inflow noise, the 

turbulent length scale for all predictions (unless otherwise noted) was 61.25 m, the IEC specified 

length for this hub height. 

Figure 7 shows the overall sound pressure level1

 (OASPL) as a function of wind speed for the 

AOC turbine. Two curves in the figure represent predictions of the turbine operating in 

turbulence level A wind conditions, as specified by the IEC standard [7], which are similar to 

conditions measured at the NWTC. The bottom curve represents the turbine operating in steady 

winds with no turbulence. The difference between the two curves with turbulence is the 

 

1

 The overall sound pressure level (OASPL) at each wind speed is the integral of the total mean square pressure 

from all contributing noise sources over the frequency range of interest at the observer location. 
12

condition of the boundary layer over the blades: tripped or not tripped. Because the turbine is 

relatively small, it is possible that laminar vortex shedding noise is radiated if the boundary layer 

is not tripped. But, because the turbine is operating in highly turbulent winds, laminar flow may 

not occur and the boundary layers over the blades are effectively tripped. Thus, both boundary 

layer conditions are modeled, because the true physical state of the boundary layer is unknown. 

As seen in the figure, the difference in predicted overall sound pressure levels between tripped 

and not tripped is no larger than 1 dB. Also, both of these predictions are fairly close to the 

measured test data, underpredicting the OASPL by only 2–3 dB at higher wind speeds. The 

predicted values using no turbulence underpredicted the measured data by 10–20 dB. 

Figure 7. OASPL vs. wind speed for AOC turbine

Figure 8 breaks down the OASPL shown in Figure 7 into various components. The total OASPL 

in this figure is identical to the line in Figure 7 for turbulence level A and no boundary layer 

tripping. From the figure, it is obvious that turbulent inflow noise dominates the total noise 

signature of the turbine with the next loudest noise sources being the blunt trailing edge noise or 

laminar vortex shedding noise, depending on mean wind speed. 

Figure 9 shows the predicted one-third octave band spectra of all noise sources for a mean wind 

speed of 8m/s along with measured test data. The turbulence intensity used to produce this figure 

was 22% (IEC level A), and the boundary layers over the blades were untripped so that laminar 

vortex shedding noise was modeled. As with the OASPL, the turbulent inflow noise dominates 

the total spectrum for most frequencies. In the narrow range between 1 and 2 kHz, tonal 

components from laminar vortex shedding and trailing edge bluntness contribute, but all other 

sources are at least 20 dB quieter and insignificant. Comparing to the measured test data, the 

predicted total noise spectrum agrees very well in the range between 1 and 5 kHz. However, the 

peak in the data near 800 Hz is not modeled, and the prediction overestimates the noise for 

frequencies below 500 Hz. 
13

Figure 8. Components of OASPL vs. wind speed for AOC turbine 

Figure 9. Components of sound pressure level vs. frequency for AOC turbine in 8m/s turbulent 

winds 

Previous studies [15], using the identical turbulent inflow model, have shown that although 

turbulent inflow noise tends to dominate at lower frequencies, it also tends to have less influence 

than airfoil self noise at higher frequencies, unlike the trend in Figure 9. These studies were of 

larger turbines than the AOC, and the dominance of turbulent inflow noise at higher frequencies 

may be a result of its relatively small size. Further studies [16] have shown that turbulent inflow 

noise is secondary to airfoil self noise. This questions the validity of the turbulent inflow noise 

model, and further research in this area is required. 
14

It should be noted that because the AOC is a downwind turbine, the tower shadow introduces 

turbulent eddies that may add significantly to the measured noise. Currently, these eddies are not 

modeled in the prediction code, but their influence on the measured data may explain the 

agreement between prediction and measurements in Figure 9, which may not occur if the AOC 

turbine operated upwind. Again, further research is required. 

Turbulent Length Scale 

Predicted turbulent inflow noise is very sensitive to the length scale of the turbulence. In 

previous studies [15], researchers assumed that length scales on the order of 100 m, the dominant 

sources of energy in the atmospheric boundary layer, were the primary contributors to turbulent 

inflow noise. In contrast, the work of Amiet [4] (where the empirical relations for inflow 

turbulence noise originated) used length scales more on the order of 1 cm. Researchers also 

know that, for downwind turbines, turbulent length scales on the order of the tower diameter 

(~1m) can be introduced. It remains unclear which length scale should be used to predict wind 

turbine noise and whether these length scales are independent of turbine size. 

Figure 10 shows the effect of turbulence length scale on the total sound pressure level2

 radiating 

from the AOC wind turbine. The plot shows predictions based on an 8 m/s mean wind speed in 

an IEC class A turbulence field (turbulence intensity = 22%). The measured data in the plot are 

for similar wind conditions. For a length scale of 61.25 m (the IEC specified length), the 

turbulence inflow noise dominates most other noise sources, as demonstrated in Figure 9. The 

predicted total sound pressure level agrees well with the measured data above 1 kHz, but not 

below this frequency. Interestingly, the data at lower frequencies seem to match most closely to 

the curve using a length scale of 6.125 m, which is on the order of the rotor radius. This suggests 

that the rotor radius may be a more appropriate length scale in this frequency range. While the 

absolute levels of sound pressure level for the largest length scales are closest to the test data, the 

spectral peak near 1000 Hz is not accurately predicted. It is possible that this peak in the data is 

caused by gearbox noise, which is not represented by the code. Further study into the correct use 

of length scale and the turbulent inflow noise model itself should be performed. 

 

Figure 10. Effect of inflow turbulence length scale on total sound pressure level for AOC wind turbine in 

turbulent 8m/s winds 

 

2

 Total sound pressure level is the sum of one-third octave band spectra from each of the six different noise sources. 
15

Blade Pitch Angle 

Figure 11 shows the effect of blade pitch angle on the total sound pressure level spectrum in a 

steady 8 m/s wind. Turbulent inflow noise is neglected because pitch angle has little effect on 

this noise source. The boundary layers over the blades are not tripped resulting in a peak from 

laminar vortex shedding noise between 400 Hz and 2 kHz. In the frequency ranges 100–300 Hz 

and 600–1000 Hz, the noise is slightly reduced by increasing the pitch angle of the blades toward 

feather. In the range between 300 and 600 Hz, the opposite is true. Because it is an integrated 

quantity, it is unclear if these changes will have any effect on the A-weighted OASPL of the 

turbine. For an untwisted blade, researchers expect that increasing blade pitch angle will 

decrease the noise produced, because the angle of attack for all airfoils is reduced. 

Figure 11. Effect of blade pitch angle on total sound pressure level for AOC wind turbine in steady 8 m/s 

winds (no turbulent inflow noise) 
16

Boundary-Layer Tripping 

In the semi-empirical code, the boundary-layer thicknesses are calculated based on two different 

settings for boundary-layer tripping: light or heavy. The heavy-trip boundary-layer thicknesses 

are based on the original measurements by Brooks, Pope, and Marcolini of a NACA 0012 [2], 

where grit was applied from the leading edge of the airfoil to 20% chord. This level of boundary 

layer tripping is unlikely to occur naturally. The light trip, considered more physically realistic, 

is calculated in the same manner as the heavy trip and then multiplied by a correction factor of 

0.6. For the natural tripping (i.e., bugs, dirt etc.) associated with wind turbines, the light-trip 

setting is most likely to model the correct physics. Turbulent inflow can also cause transition in 

the boundary layers over the blades. Therefore, newly installed “clean” turbines operating in 

highly turbulent atmospheric conditions are likely to have boundary layer properties somewhere 

between untripped and lightly tripped. 

Figure 12. Effect of boundary layer tripping on total sound pressure level for AOC wind turbine in 

steady 8 m/s winds (no turbulent inflow noise) 

Figure 12 demonstrates the effect of tripping the airfoils on the total sound pressure level 

spectrum. Turbulent inflow noise is neglected because it is unaffected by boundary layer 

properties. Adding a light trip to the turbine blades reduces the noise significantly between 400 

Hz and 2 kHz. This is a result of eliminating the laminar vortex shedding noise (Figure 9). The 

noise levels at other frequencies remain unaffected. Adding a heavy trip decreases the noise at 

frequencies above 800 Hz, but adds a large amount of noise below this frequency. Notice that the 

tonal component from trailing edge bluntness at ~1.5 kHz is also reduced. 

Trailing-Edge Bluntness 

Figure 13 shows the effect of trailing-edge bluntness on the total sound pressure level radiating 

from the AOC turbine. In this figure, turbulent inflow noise is neglected because the bluntness 

has little effect on this noise source. Again, the boundary layers over the blades are not tripped, 

resulting in a peak from laminar vortex shedding noise between 400 Hz and 2 kHz. It is obvious 
17

that blunt trailing edges add narrowband tones to the noise spectrum. The thickest trailing edge 

of 1% chord adds a large amplitude tonal peak to the spectrum around 1.5 kHz. As the thickness 

of the trailing edge decreases, the sound pressure level amplitude also decreases, while the 

frequency of the tone increases. If the trailing-edge thickness becomes infinitesimal, this noise 

source disappears altogether. 

Figure 13. Effect of trailing edge bluntness on total sound pressure level for AOC wind turbine in 

steady 8 m/s winds (no turbulent inflow noise) 

Tip Noise 

As seen in Figure 9, tip noise has the least influence on the total radiated noise level from the 

AOC turbine. However, for other configurations, this noise source may be important, particularly 

at higher frequencies. 

Tip noise (Figure 14) is highly dependent upon the strength of the vortex shed at the tip. Because 

of this, the semi-empirical code allows the user to adjust the vortex strength by modifying the 

effective angle of attack at the blade tip. As described in Brooks, Pope, and Marcolini [2], the 

multiplier for the tip angle of attack is equivalent to the ratio of the slope of the spanwise lift 

distribution (dL/dy) of the modeled blade to that of the blade (wing) used in their research, which 

consisted of an untwisted constant chord shape. Unfortunately, there is no explicit relation to 

determine this multiplier, although Brooks and Marcolini [17] provided additional guidance on 

determining this quantity for different aspect ratio blades. The more dramatic the change of lift 

near the tip, the stronger the vortex at the tip and the larger the multiplication factor (Figure 14). 

A stronger vortex directly correlates to a louder tip noise prediction. The semi-empirical code 

also has a switch (see Appendix) to allow for square (i.e., sharp angled) blade tips to be used 

instead of standard rounded tips. As seen in the figure, using square tips adds significantly to the 

low-frequency noise, but reduces high-frequency noise. 
18

Figure 14. Effect of tip vortex strength and tip shape on tip sound pressure level for AOC wind 

turbine in steady 8 m/s winds (tip noise only) 

Rotor Speed 

Figures 15 and 16 are intended to show that the effect of turbine rotor speed on total soundpressure level is highly dependent on the dominant noise sources. The boundary layers over the 

blades are not tripped in either of these figures, so laminar vortex shedding noise is modeled. 

If turbulent inflow noise is included, the sound intensity appears to scale with rotor speed to the 

fourth power (12 dB difference by doubling speed) as shown in Figure 15.3

 If turbulent inflow 

noise is neglected, as in Figure 16, the response is more complex because of the interaction of 

several different noise sources. The dominant effects are the three forms of trailing edge noise: 

laminar vortex shedding, trailing edge bluntness, and turbulent boundary layer noise, for which 

intensity will all scale with rotor speed to the fifth power (15 dB difference by doubling speed). 

However, the frequencies of the noise disturbances change nonlinearly, which prevents direct 

scaling from one spectrum to the next. 

 

3

 Notice also that the tonal component from trailing edge bluntness noise increases in amplitude and frequency with 

rotor RPM. 
19

Figure 15. Effect of rotor speed on total sound pressure level for AOC wind turbine in turbulent 

8 m/s winds (with turbulent inflow noise) 

Figure 16. Effect of rotor speed on total sound pressure level for AOC wind turbine in steady 8 m/s 

winds (no turbulent inflow noise) 
20

Directivity 

Figure 17 shows the OASPL footprint for the AOC turbine operating in steady 8 m/s winds. Note 

that because the winds are steady, there is no inflow turbulence noise present in these results. 

The boundary layers over the blades are also untripped, so laminar vortex shedding noise is 

modeled. As expected, the noise levels in the rotor plane are the lowest because of the directivity 

of the noise radiating from the blades set at 1.54° pitch angle. The cardioid shape is typical of 

dipole noise sources, such as those produced near the trailing edge. Note the noise is fairly 

symmetric upwind and downwind of the rotor plane. This symmetry is caused by the semiempirical relations, which are based on measurements [2] that were made above the upper 

surface of a symmetric airfoil. No similar measurements were made below the lower surface. 

Therefore, it was assumed that the noise radiating on both sides of the airfoil is equivalent. 

Although this assumption may be valid for trailing-edge bluntness and turbulent-inflow noise, it 

will introduce some error in separating flow and laminar boundary layer vortex shedding noise, 

which tend to radiate more from one side of the airfoil than the other. 

Figure 18 is a slice through the contour of Figure 17 for OASPL as a function of distance 

downwind of the tower centerline at a lateral position of 0 m. Near the rotor plane, the sound 

pressure is lowest, but then peaks about 15 m downstream. By doubling the distance downstream 

(e.g., from 30 to 60 m), the OASPL is reduced by approximately 4 dB. This is less than the 6 dB 

decrease expected from the behavior of a pure point-source model and is a result of various 

constant factors in Equations 2-10. 

Figure 19 provides some insight into the distribution of the noise sources in the rotor plane. This 

figure represents the average distribution of noise sources that contribute to the total sound 

pressure level, as observed 32.5 m upwind of the tower centerline at hub height. The average 

Figure 17. OASPL noise footprint for AOC turbine in steady 8 m/s winds (no turbulent inflow 

noise) 
21

Figure 18. OASPL as a function of downwind distance for AOC turbine in steady 8 m/s winds (no 

turbulent inflow noise) 

levels were obtained from a 5-minute simulation of the AOC turbine operating in steady 8 m/s 

winds. As expected, the sound pressure level of the source distribution increases along the span 

of the blades because of a linear increase in velocity. Because the observer position is at hub 

height, the apparent source distribution is fairly symmetric. The source amplitude on the top of 

the rotor is slightly higher than that on the bottom because of the mean wind speed gradient 

across the rotor plane, although the total velocity between the top and bottom is less than 1%. 

Figure 19. Total sound pressure level across rotor of AOC as measured from hub height in steady 

8 m/s winds (no turbulent inflow noise, untripped boundary layers) 
22

Figure 20. Total sound pressure level across rotor of AOC as measured from ground observer in 

steady 8 m/s winds (no turbulent inflow noise, untripped boundary layers) 

Figure 20 shows the distribution of apparent noise sources for the AOC operating in the same 

conditions, as perceived by an observer 32.5 m upwind at ground level. From this observer 

position, the source distribution is not symmetric as in Figure 19. The loudest portions of the 

rotor are in the lower right-hand portions of the rotor plane. This effect is a result of Doppler 

amplification of the perceived sound pressure level at these locations, as specified by Equations 

11 and 12. The turbine turns clockwise as seen from upwind4

 and, therefore, moves toward the 

observer on the right half of the rotor plane and away from the observer on the left. Doppler 

amplification increases the observed sound pressure level for sources moving toward the 

observer and decreases the sound pressure level for those moving away. 

Conclusions 

A series of semi-empirical acoustic noise prediction subroutines was written and incorporated 

into NREL's aeroelastic simulation code, FAST. The subroutines were used to predict relative 

amplitudes and trends of sound pressure level data from acoustic tests of two-dimensional 

airfoils and a full-size wind turbine. Prediction accuracy of the absolute sound pressure level for 

the two-dimensional airfoil data was dependent on wind tunnel test conditions and the airfoil 

model. The best predictions were made using a NACA 0012 model at moderate angle of attack 

with a laminar boundary layer. Predictions of the acoustic emission from the full-size turbine 

studied (AOC 15/50) were dominated by turbulent inflow noise. The next-loudest noise sources 

were trailing-edge bluntness and laminar vortex shedding. There is some uncertainty as to the 

absolute accuracy of the turbulent inflow model and what turbulent length scale should be used 

in the model. Comparison of the prediction to data demonstrates that the length scale should be 

smaller than that specified by the IEC standard for certain frequency ranges. Further study of this 

issue should be performed using additional data and several different-sized wind turbines. The 

total sound pressure level amplitude of a full-turbine model was found to be most sensitive to 

 

4

The sign of the y coordinate in figures 19 and 20 is opposite to the tower coordinate system used in the input file 

described in the appendix. 
23

rotor speed. Thick trailing edges on wind-turbine blades introduce large amplitude tonal noise 

sources into the noise spectrum that can add significant noise at certain frequencies. The 

directivity of the total sound pressure level was dominated by the dipole behavior of the trailingedge noise. Doppler amplification creates a skewed map of the apparent source distribution 

across the rotor plane for an observer on the ground. 

Further improvements to the semi-empirical code will include updating current modules with 

more accurate physical models and adding completely new modules that model physics. The 

next version of the code will attempt to include a routine to more accurately calculate turbulent 

inflow noise and another to more accurately predict boundary layer thickness. This will allow 

users to model different airfoil shapes for their turbines. New modules that will be added include 

tower interaction and atmospheric propagation models. As researchers continue to develop the 

code, it will be validated using data from concurrent wind tunnel testing and computational 

aeroacoustic efforts, as well as measurements of larger turbines that have been studied more 

extensively in the literature. 
24

References 

[1] Buhl, M. L.; Jonkman, J. M.; Wright, A. D.; Wilson, R. E.; Walker, S. N.; Heh, P. 2002. 

FAST User’s Guide. NREL/EL-500-29798, National Renewable Energy Laboratory: 

Golden, CO. 

[2] Brooks, T. F.; Pope, D. S.; Marcolini, M. A. 1989. "Airfoil Self-Noise and Prediction." 

NASA Reference Publication 1218, National Aeronautics and Space Administration, 

USA. 

[3] Lowson, M. V. 1992. "Assessment and Prediction of Wind Turbine Noise." Flow 

Solutions Report 92/19, ETSU W/13/00284/REP Bristol, England. 

[4] Amiet, R. K. 1975. "Acoustic Radiation from an Airfoil in a Turbulent Stream" Journal 

of Sound Vibration (41:4), pp. 407-420. 

[5] Ffowcs-Williams, J. E.; Hall, L. H. 1970. "Aerodynamic Sound Generation by Turbulent 

Flow in the Vicinity of a Scattering Half-Plane." Journal of Fluid Mechanics (40:4), pp. 

657-670. 

[6] Schlichting H. 1979. Boundary-Layer Theory, 7th Edition. McGraw-Hill, New York: NY. 

[7] Wagner, S.; Bareiss, R.; Guidati, G. 1996. Wind Turbine Noise. Springer-Verlag, New 

York: NY. 

[8] IEC/TC88. 1998. 61400-1 ed. 2. Wind turbine generator systems-part 1: Safety 

Requirements. International Electrotechnical Commission (IEC). 

[9] Oerlemans, S. Publication pending. Wind Tunnel Aeroacoustic Tests of Six Airfoils for 

Use on Small Wind Turbines. National Aerospace Laboratory, Emmeloord, The 

Netherlands. NREL SR-500-34470. National Renewable Energy Laboratory: Golden, 

CO. 

[10] Sijtsma, P. 2002. “Calculating Absolute Source Powers from Phased Arrady 

Measurements.” NLR-CR-2002-358, National Aerospace Laboratory, Emmeloord, The 

Netherlands. 

[11] Tangler, J. L.; Somers, D. M. 1995. "NREL Airfoil Families for HAWTs.” WindPower 

1995 Proceedings, American Wind Energy Association, Washington, D.C. 

[12] IEC/TC88. 1998. 61400-11 Wind turbine generator systems-part 11: Acoustic Noise 

Measurement Techniques, 88/67/FDIS. International Electrotechnical Commission (IEC). 

[13] Huskey, A.; Link, H. F.; Butterfield, C. P. 1999. Wind Turbine Generator System 

Acoustic Noise Test Report for the AOC 15/50 Wind Turbine. AOC1550-C-A-99182-

1000, National Renewable Energy Laboratory, Golden, CO. 

[14] Kelley, N. D. 1993. "Full Vector (3-D) Simulation in Natural and Wind Farm 

Environments Using an Expanded Version of the SNLWIND (Veers) Turbulence Code." 

Wind Energy 1993, S.M. Hock (ed.), SED-Vol.14, ASME. 
25

[15] Fuglsang, P.; Madsen, H. A. 1996. Implementation and Verification of an Aeroacoustic 

Noise Prediction Model for Wind Turbines. Riso-R-867(EN), Riso National Laboratory, 

Roskilde, Denmark. 

[16] Fuglsang, P.; Guidati F. 2003. Personal Communication. 

[17] Brooks, T. F.; Marcolini, M. A. 1986. "Airfoil Tip Vortex Formation Noise." AIAA 

Journal (24:2), pp. 246-252. 

[18] Laino, D. J.; Hanson, A. C. 2002. User's Guide to the Wind Turbine Aerodynamics 

Computer Software AeroDyn. Windward Engineering, Salt Lake City: UT. 
26

Appendix: Code Operation 

Before running the semi-empirical noise-prediction code, the user should become familiar with 

the FAST aeroelastic simulation code in which the aeroacoustic code is embedded [1]. This code 

has its own set of input files that describe many turbine parameters. The main FAST input file 

must be modified in order for the noise-prediction subroutines to be called, which is described 

below. It is also recommended that the user learn about the SNWind code [14], which can be 

used to create turbulent wind input files for FAST. 

Input Files 

To use the noise-prediction code, a noise-input file must be created, and the input file for FAST 

[1] must be slightly modified. 

Figure 21 shows the three additional lines that must be inserted in the FAST input file. The first 

line is added to the "features switches" section of the FAST input file and contains the variable 

CompNoise. This variable is either true or false depending on whether or not the user would like 

to compute the aerodynamic noise. Two additional lines must be inserted between the "aerodyn" 

and "output" sections. These lines are skipped if CompNoise is false. The first line is a comment 

that marks the beginning of the "noise" section of the FAST file, and the second line contains the 

variable NoiseFile, which is the location of the noise input file used by FAST. 

Figure 22 shows the input file specified by the variable NoiseFile. Note that the first 19 lines of 

this input file must have the format shown below, including blank lines, in order for the file to be 

read correctly. The first two lines of input file can be used for comments. The third line of input 

file is the speed of sound measured in meters per second. The next line is the variable ALPRAT, 

which is a multiplier for the angle of attack of the tip airfoil. This multiplier is only used in the 

calculation of tip noise and has a default value of 1.0. A value higher than 1.0 is indicative of a 

highly loaded tip that may result from spanwise twist or blade taper. The next line of the input 

file is the variable ROUND, which is true for a rounded blade tip or false for a square-edged 

blade tip. The next section of input lines are switches to determine what sources of noise are to 

be computed. The values for the switches should be set to 0 if the noise source should NOT be 

computed and 1 if the noise source should be computed (with the exception of ITRIP). 

... 

True CompAero - Compute aerodynamic forces (switch) 

True CompNoise - Calculate aerodynamic noise (switch) 

---------------------- INITIAL CONDITIONS -------------------------------------- 

... 

---------------------- AERODYN --------------------------------------------- 

"D:\acoustics\AeroDyn.ipt" ADFile - Name of file containing AeroDyn input parameters 

---------------------- NOISE ------------------------------------------------ 

"D:\acoustics\Noise.ipt" NoiseFile - Name of file containing noise input parameters 

---------------------- OUTPUT ---------------------------------------------- 

False SumPrint - Print summary data to "<RootName>.fsm" (switch) 

...

Figure 21. Sample modified FAST input file 
27

The switches in the input file should appear in the following order: IBLUNT for trailing-edge 

bluntness noise, ILAM for laminar boundary-layer noise (note, if ITRIP is any value other than 0, 

ILAM is automatically set to 0), ITIP for tip noise, ITRIP to trip the boundary layer, ITURB for 

turbulent boundary-layer trailing-edge noise, and IInflow for turbulent inflow noise (i.e., leadingedge noise). ITRIP can have a value of 0, for no boundary layer trip, or 1 for a "heavy" trip [2], 

or 2 for a "light" trip. The value of two is most likely for "naturally" tripped boundary layers on 

wind turbines (i.e., from bugs, surface defects, etc.). 

The next input line is the variable NoiseOutSwitch that determines the OASPL for each blade 

element that is output to the file with the extension ".spl" (see below). The values of 

NoiseOutSwitch for various noise sources are listed in Table 1. The next line of input contains 

the coordinates of the observer location (x, y, z) relative to the center of the tower-base in the 

tower-base coordinate system of FAST [1] (in meters). The coordinate x is the 

upwind/downwind distance, where a negative value indicates an upwind observation point. The y 

coordinate is the lateral distance from the tower centerline (positive left, looking downwind), and 

the z coordinate is the vertical distance from the tower base (positive upward). 

The final lines of the noise-input file contain two columns, the first being the thickness of the 

trailing edge (in meters) and the second being the solid angle between the upper and lower 

surface at the trailing edge (in degrees). These two parameters are used exclusively to calculate 

blunt trailing-edge noise. Note that in the figure that there are several rows of inputs, where each 

row represents a blade airfoil element identical to those specified in the Aerodyn input file [18], 

the aerodynamic module of FAST. The number of elements listed in this file must be identical to 

those of the Aerodyn file. Also, because there is only one table of input data, all blades on the 

wind turbine are assumed to have identical trailing-edge properties. 
28

Input file for aeroacoustic code 

 

344.05 C0 SPEED OF SOUND METERS/SEC 

1.0 ALPRAT TIP SPANWISE LIFT CURVE SLOPE (Default = 1.0) --- 

.TRUE. ROUND LOGICAL INDICATING ROUNDED TIP --- 

0 IBLUNT FLAG TO COMPUTE BLUNTNESS NOISE --- 

0 ILAM FLAG TO COMPUTE LBL NOISE --- 

1 ITIP FLAG TO COMPUTE TIP NOISE --- 

2 ITRIP FLAG TO TRIP BOUNDARY LAYER (=0 no trip, =1 heavy trip, =2 light trip) 

1 ITURB FLAG TO COMPUTE TBLTE NOISE --- 

1 IInflow FLAG TO COMPUTE Turbulent Inflow NOISE --- 

1 NoiseOutSwitch Switch to determine which time series of sound pressure level output 

50.00 70.00 0.000 (x,y,z) Observer location in tower-base coordinate system (m) 

Thickness (m) PSI (deg) Same elements as aerodyn inputs 

 0.00 12.5 

 0.00 12.5 

 0.00 12.5 

 0.00 12.5 

 0.00 12.5 

 0.00 12.5 

 0.00 12.5 

 0.00 12.5 

 0.00 12.5 

 0.00 12.5 

 

C Thickness SEGMENT TRAILING EDGE THICKNESS METERS 

C PSI SEGMENT BLUNTNESS ANGLE DEGREES

Figure 22. Sample noise input file 

Table 1. NoiseOutSwitch Values and Resulting Output 

NoiseOutSwitch Noise Mechanism 

1 Total OASPL 

2 Laminar boundary 

layer OASPL 

3 Total turbulent 

boundary layer OASPL 

(combination of 7,8 

and 9) 

4 Inflow turbulence 

OASPL 

5 Tip vortex OASPL (tip 

elements only) 

6 Blunt trailing-edge 

OASPL 

7 Turbulent boundary 

layer OASPL from 

pressure side of airfoil 

8 Turbulent boundary 

layer OASPL from 

suction side of airfoil 

9 Separating flow 

OASPL 
29

Output files 

Besides the regular output files of FAST, the acoustic-noise subroutines produce two additional 

files with the extensions ".spl" and ".nos." The .spl file, partially shown in Figure 23, contains 

the time-series information of the calculated sound pressure level specified by NoiseOutSwitch

for each blade element, as well as the azimuth angle (in degrees). Data in this file can be used to 

examine the time history of the noise and also to calculate azimuth averaged sound pressure 

levels, such as those seen in figures 19 and 20. This output file begins at the time specified by the 

variable TStart in the FAST input file. 

 

These predictions were generated by FAST (v4.03, 15-Jan-2003) on 04-Jun-2003 at 17:37:10. 

The aerodynamic calculations were made by AeroDyn (12.52, 28-Mar-2003). 

AOC FAST model for noise code validation 

Total Overall Sound Pressure Level (dB) 

 Time Azimuth Bl1-Elem 1 Bl1-Elem 2 Bl1-Elem 3 Bl1-Elem 4 

 10.000 275.997 34.727 40.796 45.691 49.762 

 10.005 277.935 34.708 40.784 45.674 49.736 

 10.010 279.873 34.818 40.862 45.714 49.748 

 10.015 281.811 34.923 40.937 45.753 49.761 

 10.020 283.749 34.891 40.902 45.713 49.716 

 10.025 285.687 35.120 41.079 45.827 49.787 

 10.030 287.625 35.213 41.147 45.863 49.800 

 10.035 289.563 35.305 41.213 45.898 49.813 

 10.040 291.501 35.394 41.276 45.931 49.825 

 10.045 293.439 35.480 41.338 45.963 49.837 

 10.050 295.377 35.564 41.397 45.993 49.848 

 10.055 297.315 35.645 41.454 46.021 49.857 

 10.060 299.253 35.608 41.418 45.982 49.815 

 10.065 301.191 35.682 41.480 46.020 49.835 

 10.070 303.129 35.699 41.492 46.019 49.824 

 10.075 305.066 35.716 41.504 46.018 49.813 

 10.080 307.005 35.733 41.515 46.017 49.802 

 10.085 308.943 35.748 41.526 46.015 49.792 

 10.090 310.880 35.763 41.536 46.013 49.781 

 10.095 312.819 35.776 41.545 46.011 49.771 

 10.100 314.757 35.736 41.509 45.974 49.733 

 10.105 316.694 35.799 41.560 46.005 49.749 

 10.110 318.633 35.719 41.503 45.957 49.706 

... 

Figure 23. Sample .spl output file 

The second output file with the extension .nos, seen in figures 24 and 25, contains all of the input 

information for the noise code and also the time averaged spectra for the individual acoustic 

noise sources, along with a total noise spectrum, given in units of dB. These spectra are obtained 

by time averaging the mean square pressures of the noise sources for each third octave frequency 

band and then converting them into sound pressure levels. As with .spl the file, the averaging 

process does not start until after the value of TStart is passed. This allows the user to prevent any 

startup transients in the simulation from contaminating the average spectral values. 
30

 

These predictions were generated by FAST (v4.03, 15-Jan-2003) on 04-Jun-2003 at 

The aerodynamic calculations were made by AeroDyn (12.52, 28-Mar-2003). 

 AOC FAST model for noise code validation 

10 NUMBER OF SEGMENTS --- 

344.0500 SPEED OF SOUND METERS/SEC 

1.46390E-05 KINEMATIC VISCOSITY M2/SEC 

1.000000 TIP LIFT CURVE SLOPE --- 

T LOGICAL INDICATING ROUNDED TIP --- 

 

 F FLAG TO COMPUTE BLUNTNESS NOISE --- 

 F FLAG TO COMPUTE LBL NOISE --- 

 T FLAG TO COMPUTE TIP NOISE --- 

 2 FLAG TO TRIP BOUNDARY LAYER --- 

 T FLAG TO COMPUTE TBLTE NOISE --- 

 T FLAG TO COMPUTE Turbulent Inflow NOISE --- 

 

 Mean Wind Speed = 8.092841 m/s 

 Turbulence Intensity = 21.33508 % 

 -32.50000 0.0000000E+00 0.0000000E+00 

 Observer location relative to tower base centerline 

 Segment# C L H PSI 

 1 0.494 0.470 0.005 12.500 

 2 0.579 0.748 0.006 12.500 

 3 0.680 0.752 0.007 12.500 

 4 0.744 0.748 0.007 12.500 

 5 0.738 0.752 0.007 12.500 

 6 0.677 0.740 0.007 12.500 

 7 0.616 0.760 0.006 12.500 

 8 0.558 0.740 0.006 12.500 

 9 0.497 0.760 0.005 12.500 

 10 0.436 0.740 0.004 12.500 

 

 ONE-THIRD OCTAVE 

 SOUND PRESSURE LEVELS 

 PRESSURE SUCTION SEPARATION 

 FREQUENCY(HZ) SIDE TBL SIDE TBL SIDE TBL LAMINAR 

 -------------- -------------- -------------- -------------- -------------- 

 100.000 8.596 20.990 29.807 0.000 

 125.000 11.054 22.805 30.225 0.000 

 160.000 13.550 24.701 30.622 0.000 

 200.000 15.629 26.338 31.012 0.000 

 250.000 17.562 27.915 31.547 0.000 

 315.000 19.436 29.451 32.352 0.000 

 400.000 21.260 30.804 33.430 0.000 

 500.000 22.886 31.682 34.381 0.000 

 630.000 24.508 32.058 34.726 0.000 

 800.000 26.107 31.850 33.756 0.000 

 1000.000 27.440 31.156 31.612 0.000 

... 

Figure 24. Sample .nos output file (first four columns of spectrum) 
31

 

 BLUNTNESS TIP INFLOW TOTAL 

 

 -------------- -------------- -------------- -------------- 

 0.000 -14.434 66.435 66.435 

 0.000 -8.739 66.240 66.241 

 0.000 -3.052 65.871 65.871 

 0.000 1.539 65.424 65.425 

 0.000 5.610 64.892 64.892 

 0.000 9.282 64.264 64.265 

 0.000 12.502 63.547 63.548 

 0.000 14.984 62.825 62.828 

 0.000 17.027 62.032 62.038 

 0.000 18.581 61.173 61.180 

 0.000 19.529 60.339 60.344 

... 

Figure 25. Sample .nos output file (last four columns of spectrum) 
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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE

December 2003 

3. REPORT TYPE AND DATES COVERED 

Technical Report 

4. TITLE AND SUBTITLE

Semi-Empirical Aeroacoustic Noise Prediction Code for Wind Turbines 

6. AUTHOR(S) 

P. Moriarty and P. Migliore 

5. FUNDING NUMBERS

WER3.1830 

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 

National Renewable Energy Laboratory 

1617 Cole Blvd. 

 Golden, CO 80401-3393

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NREL/TP-500-34478 

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National Technical Information Service 

U.S. Department of Commerce 

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12b. DISTRIBUTION CODE

 

13. ABSTRACT (Maximum 200 words)

A series of semi-empirical aeroacoustic noise prediction subroutines was written and incorporated into the National 

Renewable Energy Laboratory’s (NREL's) aeroelastic simulation code: FAST. The subroutines predict six different 

forms of aerodynamically produced noise that were superimposed to calculate the total aeroacoustic signature of an 

operating wind turbine. This report explains how the code was written, what validation against test data was performed, 

and how a user can implement the code to predict noise for any given turbine design. 

15. NUMBER OF PAGES

14. SUBJECT TERMS 

Wind turbine; noise; aeroacoustic simulation code; FAST; wind energy 16. PRICE CODE

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