A novel method of vertical axis wind turbine

noise prediction

Jason Daniel Michael Botha, Henry RiceDepartment of Mechanical and Manufacturing Engineering, Trinity College Dublin, Ireland.

SummaryVertical Axis Wind Turbines are becoming more commonplace in urban environments but to datethere has not been much computational work done to quantify their noise outputs. The EU FP7project: SWIP (New innovative solutions, components and tools for the integration of wind energyin urban and peri-urban areas) aims to deal with, and overcome, the main barriers that slow downthe largescale deployment of small and medium size wind turbines. One of the outputs of the projectis a novel, six bladed, vertical axis wind turbine rated at 2kW.This work aims to predict aeroacoustic noise generated by the SWIP vertical axis wind turbine bymeans of a novel noise prediction method. Due to the high computational cost of LES an approachis proposed in which ANSYS Fluent is used to determine the transient flow solution, using un-steady RANS calculation, on a 2D section of the wind turbine undergoing rotation. Acoustic signalsare calculated by employing a MATLAB code which uses the CFD solution as input data into asemi-empirical solver based a number of airfoil noise prediction algorithms. The 2D CFD data is in-terpolated onto a 3D model of the turbine using a quasi-steady time stepping approach. An estimateof the aeroacoustic noise of the turbine is established and the sensitivity of the code to changes intime step and discretisation is considered.

PACS no. 43.28.Ra

1. Introduction

1.1. Vertical Axis Wind Turbines

Vertical Axis Wind Turbines (VAWT’s) are a typeof wind turbine used to convert kinetic energy frommoving air into electrical power by means of lift pro-ducing blades. They differ to the conventional Hori-zontal Axis Wind Turbines (HAWT’s) by having themain shaft transversely aligned with the wind direc-tion. Vertical Axis Wind Turbines are seen as a viablesolution to urban and peri-urban power generation re-quirements leading into 2020.

1.2. VAWT Aerodynamics

Wind turbines use standard airfoil sections to gen-erate lift from an oncoming flow. As wind turbineairfoils rotate through clean air they produce noisefrom the interactions between the fluid (air) and thesolid (turbine blade). The noise generated by theturbine blades is thus proportional to a number ofaerodynamic parameters of the blades themselvesand therefore it is advantageous to understand how

(c) European Acoustics Association

the aerodynamic forces on the blades are producedand how to predict them.

Wind turbine aerodynamic performance can bepredicted in a number of ways, each method outlinedindicates an increase in computational effort inproportion to the fidelity of the model. As with anymathematical model there is a diminishing return ofsolution accuracy against computational effort.

- Double Multiple Streamtube Model: This model usesa number of streamtubes to predict rotor perfor-mance based on input data from a 2D airfoil polar.The method is used in the code QBlade [1]. Thecode, however, cannot solve for boundary layer ve-locity profiles or turbulent inflow parameters.

- Unsteady 2D CFD: By solving the Navier-Stokesequations for a rotating blade an estimate of itsaerodynamic performance can be predicted. How-ever, any 3D flow effects such as tip losses or crossflow would be negated in a 2D calculation.

- Unsteady 3D CFD: An extension of the previousmethod would yield better aerodynamic results,these results could be used to predict rotor poweroutput.

- DES: Using a Deattached-Eddy Simulation (DES)should yield even more accurate results at a very

Copyright© (2015) by EAA-NAG-ABAV, ISSN 2226-5147All rights reserved

303

high accuracy. Results of these simulations wouldallow one to solve directly the Ffowcs-WilliamsHawkings equations to propagate sound signals toa far field listener location. Similar work is done byMohamed, 2014 [2].As a single VAWT blade rotates around its own

axis it experiences a number of different inflow condi-tions based on its azimuth angle. Figure 4 shows anexample of a model of a single VAWT blade rotatingabout its axis. A full VAWT maxhine would consistof multiple equi-spaced blades. The blade encountersa series of dynamic stall events during rotation. Fromgeometric considerations the resultant velocity thatthe blade experiences at any given azimuth angle (✓)is defined as W [m/s] (equation (1)), where U [m/s] isthe freestream velocity and � is the Tip Speed Ratio(TSR) (equation (2)). For equation (2) ! is the angu-lar velocity [rad/s] and R is the radius of the turbine[m]. The effective angle of attack (angle between theblade chord and oncoming flow) of the turbine bladeat any given azimuth angle is defined by ↵ in (3).

W = U

p1 + 2�cos✓ + �

2 (1)

� =!R

U

(2)

↵ = tan

�1(sin✓

cos✓ + �

) (3)

Figure 1 show the relationship between the effectiveinflow velocity and angle of attack for changes in theazimuth angle. It should be noted that even thoughthe blade undergoes a geometric rotation of 360� itnever experiences more than a certain effective angle

of attack due to the velocity vectors acting on theblade. In the case of figure 1 the oncoming flow is aconstant 8.41 m/s and the blade is rotating at 17.226rad/s in a counter-clockwise direction.

1.3. Wind Turbine Aerodynamic Noise

Noise generated by Vertical Axis Wind Turbines isbroadband in nature and is produced by two primarynoise generation mechanisms: Inflow noise [3] andTurbulent Boundary Layer Trailing Edge (TBL-TE)noise [4].

Until present there has not been much need topredict the aerodynamic noise generated by VAWTmachines as they have generally been considered tobe quiet enough. It is, however, still imperative toquantify the noise that is to be generated by suchdevices in order to aid in the swift acceptance ofbuilding plans when designing a new turbine for anurban or peri-urban location.

Most manufacturers do not perform detailed noisestudies of their designs and merely provide a single

Azimuth Angle θ0 50 100 150 200 250 300 350

Eff

ecti

ve

Angle

of

Att

ack α

-30

-20

-10

0

10

20

30

Eff

ecti

ve

Inlo

w V

eloci

ty (

m/s

)

5

10

15

20

25

30

35

Angle of AttackEffective Inflow Velocity

Figure 1. Relationship between angle of attack and effec-tive inflow velocity with change in azimuth angle.

figure on their specification sheets saying that the de-vices adhere to requirements for noise levels in urbanenvironments. Table I highlights the noise specifica-tions given by some manufacturers of Vertical AxisWind Turbines. The turbines selected are in the range1.5 to 3 kW rated power save for the QR5 which wasselected for the table due to the detailed noise mea-surements provided on their datasheet.

2. Prediction Model and Approach

The modelling approach used to predict noise fromairfoils requires aerodynamic data from the windturbine blades. Traditionally, low order predictionmodels will use rough estimates of aerodynamicforces on blades to provide input data to the relevantnoise calculation modules of these particular typesof codes [11]. The success of these codes lies inthe assumption that the upstream blades have noeffect on their downstream counterparts (a suitableHAWT assumption); however, during the rotationof a VAWT there is considerable interaction fromupstream blade wake on downstream elements [12]that can be accounted for by performing a CFDcalculation.

A novel noise modelling approach is proposed herewhich utilises aerodynamic data from CFD modelsas input data to a noise prediction algorithm basedon two separate sets of semi-empirical airfoil noisecodes. The CFD simulation provides a calculationfor the boundary layer velocity profile and inflowturbulence parameters of a turbine blade undergoingrotation. This CFD data is written to ASCII files andis read by the noise prediction algorithm (developedin MATLAB).

This approach has been developed to predict thenoise generated by the V2 VAWT which has been de-

EuroNoise 201531 May - 3 June, Maastricht

J. Botha: A Novel Method...

304

Table I. Noise measurements of Vertical Axis Wind Turbines as provided by manufacturers

Turbine Power Rating (kW) Noise Level Wind Speed (m/s) Distance from Turbine (m)

Aerocopter [5] 2.0 <37 dB - -Aeolos-V [6] 2.0 <45 dB - -DS-3000 [7] 3.0 <40 dB (A-weighted) - -P3000-AB [8] 3.0 - - -QR5 [9] 6.5 57.9 dB (max) 10.0 22.5VisionAir5 [10] 3.0 <38 dB 5.0 -

Table II. V2 Turbine ParametersParameter Value

Chord 0.3 mPitch -2.0�

Rotor radius 1.0 mBlade span 4.5 mBlade offset angle 90�

Number of blades 6Airfoil Data withheldRated power (operating point) 2.0 kW

signed by the blades design group project partners onthe SWIP project. The specifications of the V2 designare summarised in table II.

2.1. Aerodynamic Modelling

The approach used to resolve the aerodynamic forcesfor the suggested model of the given VAWT hasbeen to implement a Computational Fluid Dynamics(CFD) model. As well as being used as input datato the aerodynamic solver this CFD data will alsobe used to fine-tune the model in the future. Thereis additional scope for finding an alternative aero-dynamic model, but first an understanding of theexisting conditions affecting the confluence betweenthe blades needs to be achieved.

It is of fundamental importance to accuratelypredict the boundary layer velocity profiles at thetrailing edge of the blades as well as predicting theturbulent inflow conditions at some location justahead of the oncoming blade. A data probe writes outthe required data for each time step, within a singlerotation, along lines normal to both the pressure andsuction sides of the trailing edge as well as a lineprotruding from the leading edge.

ANSYS Fluent is used as the CFD code to solve theNavier-Stokes Equations within the computationaldomain. A number of simplifying assumptions areimposed in order to speed up computational timewithout losing model fidelity. To model turbulence ak-! SST turbulence model is selected. The selectionthereof is due to Shear Stress Transport (SST)models showing success in predicting separated flows[13].

Table III. Simulation ParametersParameter Value

Wind speed (operating point) 8.41 m/sRotational velocity (!)(operating point) 17.226 rad/sTurbulence Model k-! SSTTurbulent Length Scale 11 mTurbulent Intensity 20 %Time Step 0.338 msNumber of Rotations 6Time Steps per Rotation 1 080

The computational domain is discretised into agrid consisting of about 220 000 nodes. The sizeof the domain is shown in figure 2 where C is anondimentional measure of the airfoil chord length.The spacing of the nodes is more refined at the wallsof the airfoils and less refined near the boundaries.The airfoil walls require more refinement in order topredict the large velocity gradient boundary layerflows in these regions. The time-step of the transientmodel is selected to provide sufficient numericalaccuracy of results pertaining to the rotation of theturbine. It is decided to use a timestep of 0.338ms/timestep which corresponds to 1080 timestepsper rotation or 3 timesteps per azimuth rotationdegree. Further refinement of the input data will beperformed at a later stage to determine the sensitivityof the noise computations to the quality of the inputdata. Table III summarises the boundary conditionsof the CFD simulation.

Figure 3 shows the thrust and normal force gener-ated by a single blade of the turbine during rotation.This can be compared with other simulation data asit becomes available. As expected the turbine showsa large production of thrust for the first 120� of rota-tion to coincide with the increasing effective angle ofattack of the blade (see figure 1). As the blade stalls itgradually generates less thrust until, at roughly 220�azimuth angle the blade actually produces a smallamount of drag.

2.2. Acoustic Modelling

A quasi-steady approach is used to model the noisegenerated by the wind turbine. The length of a singleblade is discretised into a number of strip sections,each representing a finite point source. The point

EuroNoise 201531 May - 3 June, Maastricht

J. Botha: A Novel Method...

305

50 C 150 C15

0C

x

y

8.41 m/s

! = 17.226rad/s

Figure 2. Computational domain and boundary condi-tions. Rotor size exaggerated for clarity.

Azimuth Angle θ0 40 80 120 160 200 240 280 320 360

Norm

alis

ed F

orc

e C

oef

fici

ent

-1

-0.6

-0.2

0.2

0.6

1

1.4

1.8

CT

CN

Figure 3. Relationship between angle of attack and effec-tive inflow velocity with change in azimuth angle.

sources are all located at the trailing edge of theblade. The number of point sources and geometry ofthe blade (blade span, pitch, chord length, angular

offset, quarter chord location, hub radius) can all bedefined by the user but should correspond to themodel used for the CFD input data. Figure 4 showsan example of the discretisation scheme employedfor an arbitrary VAWT blade. In this figure thecoordinate system corresponds with that of the CFDmodel and the angle ✓ is the azimuth angle of thesource blade. The contribution of all the point sourcesalong a single blade are averaged during each timestep and then the contribution of the noise of all theblades is summed to obtain the total noise producedby a single rotation of the rotor.

At present the total aerodynamic noise generatedby the turbine is modelled as the contribution fromtwo major airfoil noise generating mechanisms;namely, Turbulent Boundary Layer - Trailing Edgeand Inflow Noise. According to Moriarty et al. [14]most noise generated by wind turbines, especiallyat low frequencies, is dominated by inflow noise.Due to the location of the turbine being in a highlyturbulent environment for the SWIP project this willbe an important contributing factor to be modelled.

Leading EdgeTrailing EdgeChord

x

y

z

✓

Figure 4. Model of single VAWT blade indicating coordi-nate system and point sources.

Secondly the most common noise generation mech-anism will be from the TBL-TE noise will also bemodelled. Additional contributions from other noisegeneration mechanisms will be outside the scope ofthe model for the moment.

Turbulent Boundary Layer - Trailing Edge (TBL-TE) noise is calculated using the empirical modelsfrom Brooks et al. [4] as seen in equations 4 - 6. Theequations are summed to predict the TBL-TE noisefor contributions from (as in the subscripts); s, thesuction side of the airfoil; p, the pressure side of theairfoil and ↵ the angle dependent airfoil noise contri-bution related to stall. Furthermore the equations area function of; �⇤, the trailing edge boundary layer dis-placement thickness [m]; M , the airfoil mach number;L, the airfoil length [m]; D̄, the directivity functions 1

(which are modified for high and low frequency correc-tions); re, the distance to the receiver; A, the spectralshape function for TBL-TE noise; St, the Strouhalnumbers and; factors K, various constants.

SPLp = 10log

✓�

⇤pM

5LD̄h

r

2e

◆+A

✓Stp

St1

◆

+ (K1 � 3) +�K1 (4)

SPLs = 10log

✓�

⇤sM

5LD̄h

r

2e

◆+A

✓Sts

St1

◆

+ (K1 � 3) (5)

SPL↵ = 10log

✓�

⇤sM

5LD̄h

r

2e

◆+B

✓Sts

St2

◆+K2 (6)

1For the low frequency directivity function there is a pure

dipole behaviour arising from the length scale of the turbu-

lence and the chord of the airfoil being of comparable sizes.

For the high frequency directivity a baffled dipole behaviour is

seen.

EuroNoise 201531 May - 3 June, Maastricht

J. Botha: A Novel Method...

306

In the VAWT prediction code, inflow noise is han-dled by semi empirical equations from Amiet [15] andreformulated by Lowson [3] as in equations 7 to 10.Where LFC is the low frequency correction, ⇢0 is airdensity [kg/m3], c0 is the speed of sound [m/s], l is theturbulent length scale [m], L is chord length [m], M isblade Mach number, u is turbulent velocity in the at-mospheric boundary layer [m/s], I is turbulent inten-sity [%] and K is the wave number (K = (⇡fL)/W )[kg/m3], D̄h is low frequency directivity as before, S2

is the Sears function and � is a Mach number correc-tion (�2 = 1�M

2).

SPLInflow = SPL

HInflow+

10log

✓LFC

1 + LFC

◆(7)

SPL

HInflow = 10log

✓⇢

20c

20lL

2r2eM

3u

2I

2

K

3

(1 +K

2)7/3D̄L

◆+ 58.4 (8)

LFC = 10S2MK

2�

�2 (9)

S

2 =

2⇡K

�

2+

✓1 + 2.4

K

�

2

◆�1!�1

(10)

A directivity correction is included to account forthe propagation of each of the noise sources to thereceiver. Both a high and low frequency correctionbased on the direction vector between the receiverand the point source in question are implemented.

The total noise generated by the device is calculatedas the summed contribution of noise generated by asingle blade throughout 360� rotation multiplied bythe number of blades the turbine has.

2.3. Results and Comparisons

The code is run using an approximate model for theSWIP V2 wind turbine. A constant one dimensionalflow field is used and the centre rotor is disregarded.The receiver is located at a distance 10m belowand 10m upstream of the base of the turbine as perthe coordinate system in figure 4. Results of thenoise prediction are A-weighted and presented as theOverall Sound Pressure Level (dB) of the turbine.

It was observed that the noise prediction code wassensitive to the selected discretisation scheme fortime stepping as well as the number of point sourcesalong a blade length. This sensitivity can be seenin figure 5 which shows the average SPL produced

1010

10

2020

20

3030

30

4040

40

5050

50

6060

607070

70

Step Size100200300400500

Aver

age

SP

L (

dB

)

36

38

40

42

44

46

48

Num

ber

of

Sourc

es a

long B

lade

10

20

30

40

50

60

70

Figure 5. Convergence of the solution based on discretisa-tion of time step and number of sources along the blade

Frequency (Hz)10

110

210

310

4

SP

L (

dB

)

-50

-40

-30

-20

-10

0

10

20

30

40

Total

Inflow

TBL-TE

Figure 6. A-weighted overall sound pressure level duringa single turbine rotation

by the turbine for changes in step size and numberof point sources. It was observed that there wasa negligible change in results with changes in stepsize beyond 200 steps. The number of point sourcesalong the blade, however, did contribute greatly toresults showing an increasing trend up until about 70sources are selected.

Figure 6 shows the results of the noise prediction fora single rotation of the given VAWT machine. The av-eraged overall sound pressure level is a combinationof the Inflow Noise (27.19 dB) and the TBL-TE noise(46.96 dB) providing a total average overall soundpressure level of 47.0 dB. It is seen from the spec-tral analysis that the noise is broadband in nature (asassumed by the models used) and tends to be domi-nated by (TBL-TE) noise effects. This is attributed tothe fact that, unlike in a horizontal axis machine, therotation of the blades around their own axis causes adecrease of the length scale of the inflow turbulence.

EuroNoise 201531 May - 3 June, Maastricht

J. Botha: A Novel Method...

307

0 40 80 120 160 200 240 280 320 360

Tu

rbu

len

t L

eng

th S

cale

[m

]

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Turb

ule

nce

Vel

oci

ty (

u')

[m

/s]

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Turbulent Length ScaleTurbulence Velocity

Figure 7. Turbulence during rotation

It is understood that, from the CFD simulation, theairfoils begin to generate their own turbulence duringrotation. For the current simulation the inflow lengthscale is defined at the inlet as 11m but during turbineoperation the length scale decreases considerably tothe levels seen in figure 7.

3. CONCLUSIONS

A prediction code is developed to estimate the noisegenerated by a Vertical Axis Wind Turbine. Thecode requires a series of design parameters for avertical axis wind turbine, a listener location as wellas information with regards to the boundary layerprofiles and airfoil inflow turbulence conditions (inthis case from a CFD model). Two primary noisegeneration mechanisms are modelled for the sourcemodelling. Subsequently the code returns the SPLproduced by the turbine in the frequency domain.

The code is seen to be sensitive to the selectionof the number of point sources along the blade butnot overly sensitive to the selection of the step size.For the given configuration it was seen that noisegeneration was dominated by TBL-TE noise andthat results from the code are of the same order ofmagnitude as those reported by manufacturers ofturbines with similar power ratings.

It was of interest to see that Inflow noise had aconsiderably lower contribution to total noise thanTBL-TE noise and this will be further investigatedthrough experiments. Future work on the code willinvolve observing sensitivity to different types of in-put data from more refined CFD models.

Acknowledgement

This project has received funding from the EuropeanUnion’s Seventh Programme for research, techno-logical development and demonstration under grantagreement No. 608554.

References

[1] D. Marten, J. Wendler, G. Pechlivanoglou, C. Nay-eri, and C. Paschereit, “Qblade: an open source toolfor design and simulation of horizontal and verticalaxis wind turbines,” International Journal of Emerg-

ing Technologies and Advanced Engineering, vol. 3,no. 3, pp. 264–269, 2013.

[2] M. Mohamed, “Aero-acoustics noise evaluation of h-rotor darrieus wind turbines,” Energy, vol. 65, no. 0,pp. 596 – 604, 2014.

[3] M. V. Lowson, “Assessment and prediction of windturbine noise,” tech. rep., Flow Solutions Ltd., Bristol(United Kingdom), 1993.

[4] T. F. Brooks, D. S. Pope, and M. A. Marcolini, Airfoil

self-noise and prediction, vol. 1218. National Aero-nautics and Space Administration, Office of Manage-ment, Scientific and Technical Information Division,1989.

[5] Artbau Wind, “Aerocopter 450 Technical Specifica-tions,” tech. rep., Mayo, Ireland, 2012.

[6] Aeolos Wind Energy Co Ltd, “Aeolos-V VerticalWind Turbine Brochure,” tech. rep., London, UnitedKingdom, 2014.

[7] H. T. Corp., “DS-3000 Technical Specifications,” tech.rep., Taipei, Taiwan, 2014.

[8] State of the Art Wind Technologies, “P3000-AB Technical Specifications,” tech. rep., Shanghai,China, 2013.

[9] quietrevolution, “quietrevolution noise statement, qr5wind turbine,” tech. rep., London, United Kingdom,2008.

[10] U. G. Energy, “VisionAir5 Technical Specifications,”tech. rep., New York, USA, 2014.

[11] S. Lee and S. Lee, “Numerical and experimental studyof aerodynamic noise by a small wind turbine ,” Re-

newable Energy, vol. 65, no. 0, pp. 108–112, 2014.SI:AFORE 2012.

[12] C. S. a. Ferreira, The near wake of the VAWT 2D and

3D views of the VAWT aerodynamics. PhD thesis,Technische Universiteit Delft, 2009.

[13] F. R. Menter, “Zonal two equation k-turbulence mod-els for aerodynamic flows,” AIAA paper, vol. 2906,p. 1993, 1993.

[14] P. Moriarty, “Nafnoise users guide,” National Wind

Technology Center, National Renewable Energy Lab-

oratory, 2005.[15] R. Amiet, “Acoustic radiation from an airfoil in a

turbulent stream,” Journal of Sound and vibration,vol. 41, no. 4, pp. 407–420, 1975.

EuroNoise 201531 May - 3 June, Maastricht

J. Botha: A Novel Method...

308