Aeroacoustic Optimization of Wind Turbine Blades

Simao Santos Rodriguessimao.rodrigues@ist.utl.pt

Instituto Superior Tecnico, Lisboa, Portugal

November 2012

Abstract

Power production from wind energy has been increasing for the past few decades, with more areasbeing used as wind farms and larger wind turbines being built. With this development, awareness of theimpact of wind energy on the environment and on human health has also increased. Much research hasbeen done to predict and reduce the noise generated by wind turbines. In this work, a blade elementmomentum theory model is used to predict the aerodynamic performance of a wind turbine, coupledto an empirical aeroacoustic noise model based on the works of Brooks et al [2] and Amiet [1], andusing the XFOIL [6] panel code for the boundary layer computations. The aeroacoustic prediction codedeveloped was validated against measurement data of the NREL Phase II and AOC 15/50 wind turbinesand used in the optimization framework pyOpt, using the genetic algorithm NSGA-II [5]. The geometryof the blade was parameterized using NURBS curves for the cross sectional airfoil shapes and Beziercurves for the twist and chord distributions. Various optimizations were performed in blades of the twoprevious turbines, both single- and multi-objective, totaling up to 62 design variables. The optimalsolutions are indicated in the obtained Pareto fronts and their geometries are discussed in detail. Thesesolutions ranged from an increase in annual energy production of 139.9% to a reduction in noise levels of10.7%. It was demonstrated that significant noise reduction could be obtained at an expense of a minoraerodynamic penalty.Keywords: Genetic algorithms, NURBS, Multi-disciplinary design optimization, Multi-objectiveoptimization

1. Introduction

For the past few decades, wind energy has seen abig development, with larger wind turbines (WT)being used and more wind farms being constructed.This increase led to an increase in awareness of theimpacts of wind energy in the environment and hu-man health, with many studies being performed onthis subject [3]. While there are no common inter-national noise standards or regulations for soundpressure levels, these are usually regulated by thelegislation of each country, which defines maximumnoise levels according to time of day and type ofarea. These limitations to generated noise make itnecessary to address the issue in the design phase ofwind turbines. The main objective of this work wasto develop a framework to perform multi-disciplinaryoptimization of wind turbine blades, with respectto their aerodynamic and aeroacoustic performance.In order to do so, a bibliographic research on thesubjects required for a complete understanding ofthe problem was performed. A wind turbine aerody-namic prediction model was implemented and latercoupled to an aeroacoustic prediction model. A pa-rameterization model of the geometry of a wind tur-

bine blade was also developed. The final predictioncode was integrated in an optimization framework,also developed in this work.

2. Theoretical Models

In this section, a theoretical background of the aero-dynamic, aeroacoustic and parameterization modelsis presented and briefly discussed.

2.1. Aerodynamic Model

The aerodynamic model, besides predicting the aero-dynamic performance of the wind turbine, providesthe detailed results necessary for the aeroacousticmodel, such as radial distribution of relative windspeed, Reynolds number and effective angle of at-tack. A Blade Element Momentum (BEM) theorymodel was implemented [9], with corrections for thehub- and tip-losses and turbulent wake state.

The airfoil data used in the BEM iterations can becorrected for 3D effects using the stall delay modelfrom Du and Selig [7], with the drag adjustmentsfrom Eggers et al [8]. The data is extrapolated usinga method developed by Viterna and Janetzke [16].

The Annual Energy Production (AEP) of thewind turbine is computed by assuming the proba-

1

bility density function of the wind to be a Weibulldistribution, modeled through of a scaling factor Aand a form factor k. The total annual energy pro-duction (AEP) can then be estimated as the productof the probability function and the power curve [9]

AEP =N−1∑i=1

12 (P (Vi+1) + P (Vi))

×f (Vi < V0 < Vi+1)×8760

, (1)

where P (Vi) is the power produced by the windturbine in a wind speed Vi, f (Vi < V0 < Vi+1) isthe probability of the wind speed lying between Viand Vi+1 and the constant term refers to the numberof hours existent in a year.

2.2. Aeroacoustic Model

The aeroacoustic prediction model developed in thiswork predicts both the turbulent inflow noise andthe five mechanisms of the airfoil-self noise. [17]

Turbulent Inflow Noise The turbulent inflownoise is predicted using the model developed byAmiet [1] and modified by Lowson [12]. For the highfrequencies, it yields

LHp,inf = 10log10

ρ2c40d

2r2e

LI2 M5k3D(1 + k2

)7/3

+ 78.4,

(2)where ρ is the density of air, c0 is the speed ofsound, d is the airfoil section span, L is the turbu-lence length scale, I is the intensity of turbulence,M is the Mach number, D denotes the effect fromsound directivity, re is the distance from the ob-server and k = k/ke is the wave number k = 2πf/Unormalized by the wave number range of energy-containing eddies ke = 3/4L. U is the local inflowvelocity. For the low frequencies, a correction factoris applied to the previous equation,

Lp,inflow = LHp,inf + 10log10

Kc

1 +Kc, (3)

where Kc is a low frequency correction factor. Thismodel, being based on experiments performed on aflat plate by Amiet, does not account for the geome-try of the airfoil, thus a correction factor developedby Moriarty et al [13, 14] is applied to Eq. 3. Thetotal turbulent inflow noise is then obtained with

Lp,airfoil = ∆Lp + Lp,flat plate + 10, (4)

where ∆Lp is the correction for the geometry of theairfoil and the term 10 is a correction to match withNRL data.

The turbulence parameters I is computed as func-tion of the surface roughness z0 and height z,

I = γln (30/z0)

ln (z/z0), (5)

where

γ = 0.24 + 0.096log10z0 + 0.016(log10z0)2. (6)

Airfoil Self-Noise Airfoil self noise is producedwhen an airfoil encounters a steady non turbulentflow field. It can be split into five mechanisms, asdescribed by Brooks, Pope and Marcolini (BP&M)[2]:

1. Turbulent boundary layer trailing edge noise,

2. Separation-stall noise,

3. Laminar boundary layer vortex shedding noise,

4. Trailing edge bluntness vortex shedding noise,

5. Tip vortex formation noise.

The 1/3 octave noise spectrum produced by thefirst three mechanisms can be predicted by semiempirical scaling laws given by BP&M, in the form

Lp,i = 10log10

(δiM

f(i)LD

r2e

)+Fi (St) +Gi (Re) ,

(7)

where δi can be either the boundary layer thicknessor displacement thickness, and f(i) a value whichdepends on the noise mechanism. The terms Fi (St)and Gi (Re) are spectral shape functions based onthe Strouhal number St and Reynolds number Re,respectively, which are different for each mechanism.Trailing edge bluntness vortex shedding and Tipvortex formation noises are also predicted in a similarway, with the first using spectral shape functionsbased on the trailing edge solid angle ΨTE andtrailing edge thickness h.

WT Rotor Noise Prediction The total noiseproduced by the WT rotor is computed by dividingthe blade in n elements. The two-dimensional noiseprediction is performed for each element and thetotal sound pressure level generated by the rotor isthe result of a summation of the noise from eachblade element Lp,i,

Lp,total = 10log10

(NB

Naz

∑i

10Lp,i

10

), (8)

where Naz is the number of azimuthal positions atwhich the blade is computed and NB is the num-ber of blades. The Overall Sound Pressure Level

2

(OASPL) can be obtained by summing the noiselevels at every frequency,

OASPL = 10log10

∑j

10Lp,j

10

, (9)

where Lp,j is the total noise level at frequency j.

Boundary Layer Parameters The boundarylayer parameters used in the noise prediction arecomputed at each element using the XFOIL [6]viscous-inviscid interactive code.

2.3. Geometry Parameterization ModelThe geometry of the blade was parameterized by aset of control points defining the twist and chorddistributions, which were either linearly interpolatedor used to construct Bezier curves, and a set of con-trol airfoil sections. After a survey on the mostcommonly used methods in airfoil shape parameter-ization, an approach using two NURBS curves, forthe upper and lower sides of the airfoil, was cho-sen. The main advantages of this parameterizationinclude the direct connection between the parame-ters and geometry, easy controllability of inflectionpoints and local approximation.

Each of the two curves is defined by seven controlpoints and a knot vector

U ={

0, 0, 0, 0, 13 ,

12 ,

23 , 1, 1, 1, 1

}. (10)

The total number of available degrees of freedom ofthe control points is 20, as schematically representedin Fig. 1.

yxy

xyx

yx

yx

yx

yxy

x

y

yy

y

Figure 1: NURBS airfoil parameterization controlpoints and respective degrees of freedom.

3. ImplementationIn this section, a description of the developed pre-diction tool is presented, followed by a descriptionof its implementation in a Multi-disciplinary DesignOptimization (MDO) framework.

3.1. WT Aeroacoustic Prediction ToolThe aerodynamic, aeroacoustic and parameteriza-tion models described in the previous section wereimplemented in an prediction tool, using C++ andPython programming languages. The prediction tool

is robust and flexible, allowing the configuration ofthe simulations in detail.

3.2. Optimization FrameworkAn MDO framework was implemented using thePython module pyOpt [15]. The chosen optimizationalgorithm was the genetic algorithm NSGA-II [5].

A convergence study was performed, in order togain insight of the minimum population size andnumber or generations required to obtained a con-verged solution. The evolution of the fitness of thepopulation of an optimization case with 8 designvariables is presented in Fig. 2, where it can be seenthat, with a population size of 8 individuals, thesolution converges with much less function calls andthe optimal solution produces an AEP value witha difference of about 1 % of the solution obtainedwith a population size of 64 individuals.

Based on this and other results, it was concludedthat a population size between n and 2n, with nbeing the number of design variables, is able toprovide an accurate solution while maintaining thecomputational costs of the optimization low.

100 101 102 103 104

Function Calls (-)

−100

−80

−60

−40

−20

0

20

40

60

AEP (

MW

h)

PopSize = 8

PopSize = 16

PopSize = 32

PopSize = 64

Figure 2: Evolution of the fitness of the populationof an optimization case with 8 design variables (twist+ chord).

3.3. Validation of the aeroacoustic predictioncode

The AOC 15/50 wind turbine is a downwind threebladed wind turbine with a rated power of 50 kW. Ituses the NREL S821, S819 and S820 profiles, definedat 40, 75 and 95 % of chord, respectively. Themeasured and predicted power curves are presentedin Fig. 3, where slight overprediction can be observedup to a wind speed of approximately 14 m s−1. Afterthat it slighly underpredicts the maximum powergenerated and fails to predict the loss in power dueto stall.

In Fig. 4, the predicted noise spectrum of thewind turbine is presented, along with measured data,in a wind speed of 8 m s−1. The simulation wasperformed assuming a trailing edge (TE) bluntnessof 1 % of the chord and a TE angle of 6 ◦. All

3

0 5 10 15 20 25

Wind Speed (m/s)

−10

0

10

20

30

40

50

60

70Po

wer

(kW

)Prediction

Exp. Data

Figure 3: AOC 15/50 predicted and measured powercurve (Measurements from Ref. [11]).

noise mechanisms were considered and the observeris located at a position of 32.5 m downwind of theturbine. Besides not being able to predict the peakbelow 1 kHz and underpredicting the noise levelsavove 2 kHz, the prediction tool can be said toprovide reasonable results.

101 102 103 104 105

Frequency (Hz)

20

30

40

50

60

70

80

SPL 1

/3 (dB)

Prediction

Exp. Data

Figure 4: AOC 15/50 overall sound pressure levelmeasurement and prediction data at wind speeds of8 m s−1 (Measurements from Ref. [10]).

4. Results

In this section, the results of the optimizations per-formed on the NREL Phase II and AOC 15/50 windturbines are presented and discussed.

All optimizations were performed assuming a winddistribution represented by a Weibull curve withthe parameters A and k of 6.48 m s−1 and 1.99,respectively, corresponding to an average wind speedof 6.11 m s−1. These parameters represent the winddistribution in the Portuguese municipality of Vilado Bispo, in the southwest of Portugal [4].

The performance of the turbine was predicted fora wind speed range from 4 to 25 m s−1, in 1 m s−1

intervals. Due to this, the noise was predicted fora wind speed of 6 m s−1, as it is the closest to theaverage wind speed of the selected site. A groundroughness value of 0.08 m was chosen. The boundary

layer parameters were computed using XFOIL.

4.1. Optimization of the NREL Phase II WTBlade

The Phase II is a three bladed wind turbine devel-oped in NREL for testing purposes. Each blade hasa radius of 5.03 m, a hub radius of 0.28 m, uses theS809 airfoil with a constant chord of 0.452 m, andhas no twist.

Case 1: Chord and twist SO optimizationThe first optimization case presented is the SingleObjective (SO) optimization of both the chord andthe twist of the blade. The chord was defined linearlyalong the blade with two control points and the twistwith a 5th order Bezier curve, leading to a total of 8design variables.

The AEP was used as the objective function tobe maximized and the following constraints wereapplied:

Chord and Twist Both chord and twist were con-strained so that there was a reduction of theirvalues towards the tip of the blade:

xcpi ≤ xcpi+1

ycpi ≥ ycpi+1

(11)

The optimization resulted in a increase of theAEP up to 46.98 MW h, as summarized in Tab. 1.

Case 2: Chord and twist MO optimizationThis optimization case consisted in the Multiple Ob-jective (MO) optimization of the problem describedin case 1. In order to do so, the OASPL was alsoused as an objective function, where its minimizationwas desired.

The initial and final populations of case 2 arepresented in Fig. 5, where it can be seen that theoptimizer was able to obtain an optimal set of solu-tions starting from a disperse set. The Pareto frontobtained is shown in detail in Fig. 6.

It is visible from that figure that a reduction ofalmost 2 dB(A) is possible, with no reduction inperformance. On the other hand, maintaining thesame noise level, an increase in AEP of 20 MW hcan be achieved. It is also visible from Fig. 6 thatthe reduction of noise levels can be achieved betweencertain ranges of OASPL while maintaining almostthe same energy production.

Case 3: Airfoil Shape SO Optimization Inthis case, the only design variables were the pointscontrolling the airfoil shape in two sections of theblade, at the root hub and tip positions. The onlyobjective function was, like in case 1, the AEP.

The search space of the design variables was de-fined around the initial airfoil shape variables with

4

50.0 50.5 51.0 51.5 52.0 52.5 53.0 53.5 54.0

OASPL (dB(A))

−60

−40

−20

0

20

40A

EP (

MW

h)

Initial Pop.

Final Pop.

Figure 5: Initial and final populations in case 2.

Min Noise

Max power

Trade-o!

Figure 6: Pareto front in optimization case 2.

a range of ±10% the initial value. The number ofdesign variables at each control section is 20, leadingto a total of 40 design variables.

The following constraints were used in this opti-mization case, in order to guarantee the representa-tion of realistic shapes by the NURBS parameteri-zation.

Control Sections

xcpi ≥ xcpi+1, upper curve

xcpi ≤ xcpi+1, lower curve(12)

The optimization resulted in an AEP value of39.22 MW h, as summarized in Tab. 1.

Case 4: Airfoil Shape MO Optimization Themulti-objective optimization of the blade, regardingthe airfoil shape resulted in the Pareto front pre-sented in Fig. 7. Like in the Pareto front obtained incase 2, this front shows a range of possible solutionswhere the noise levels can be reduced with only asmall decrease in energy production.

In Fig. 8, the three blade geometries correspondingto the solutions highlighted in Fig. 7 are presentedwith the contour plot of the radial distribution ofgenerated noise levels. There is an evident reductionin the noise levels in the outer region of the blade.

Min Noise

Max power

Trade-o!

Figure 7: Pareto front in optimization case 4.

44

42

40

38

36

34

32

30

28

26

24

22

20

18

16

14

12

10

OASPL

(dB(A))

Z

X

Y

Minimum Noise

Trade-o�

Maximum Power

Figure 8: Comparison of the radial distribution ofgenerated noise on between various optimized bladesin case 4.

Case 5: Chord, twist and airfoil shape opti-mization The last optimization case performedon the NREL Phase II wind turbine blade optimizedboth chord, twist and airfoil shape distributions withboth AEP and OASPL as objective functions. Theconstraints were the same as the previous optimiza-tion cases:

Chord and Twist Both chord and twist were con-strained so that there was a reduction of theirvalues towards the tip of the blade:

xcpi ≤ xcpi+1

ycpi ≥ ycpi+1

(13)

Control Sections

xcpi ≥ xcpi+1, upper curve

xcpi ≤ xcpi+1, lower curve(14)

The Pareto front of this case is presented in detailin Fig. 9, where it can be seen that all optimized

5

blade geometries result in a reduction of the pre-dicted noise level. It is also visible that a reductionfrom 50 to 48 dB(A) can be achieved with almostno variation in energy production.

Min Noise

Max power

Trade-o!

Figure 9: Pareto front in optimization case 5.

The chord and twist distributions of the threedifferent optimized blades are presented in Fig. 10and Fig. 11, respectively. The three solutions (seeFig. 9) were chosen similarly to the ones in theprevious cases (the one generating the minimumnoise, the one maximizing energy production and asolution in between the previous two.

Regarding the chord distribution, the three so-lutions are very similar, with a chord practicallyconstant and equal to the upper limit of 0.754 malong the blade. Although the maximum powerblade presents a slightly higher reduction of chordtowards the tip, it is only of about 4 cm.

The twist distribution is similar to the ones ob-tained in the previous cases and the three solutionsare very similar between them.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

r/R

0.71

0.72

0.73

0.74

0.75

Chord (m)

Min Noise

Trade-off

Max Power

Figure 10: Chord distributions of optimized bladesin case 5.

The initial and optimized airfoil shapes at the rootand tip positions are shown in Fig. 12 and Fig. 13,respectively. Similarly to the shapes obtained in theprevious cases, there is a slightly more accentuateds-tail in the optimized airfoils. In the root region,the three airfoils are very similar to each other, with

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

r/R

−10

0

10

20

30

40

50

Tw

ist

angle

(◦ )

Min Noise

Trade-off

Max Power

Figure 11: Twist distributions of optimized bladesin case 5.

the exception of the upper side of the minimumnoise airfoil. At the tip, the differences between theairfoils are more visible, with the trade-off airfoilhaving a lower curve similar to the maximum powerairfoil and an upper curve similar to the minimumnoise one.

0.0 0.2 0.4 0.6 0.8 1.0

x/c (-)

−0.15

−0.10

−0.05

0.00

0.05

0.10

0.15

y/c

(-)

Min Noise

Trade-off

Max Power

Figure 12: Initial and optimized airfoil shapes atthe root in optimization case 5.

0.0 0.2 0.4 0.6 0.8 1.0

x/c (-)

−0.15

−0.10

−0.05

0.00

0.05

0.10

0.15

y/c

(-)

Min Noise

Trade-off

Max Power

Figure 13: Initial and optimized airfoil shapes atthe tip, obtained in optimization case 5.

Figure 14 presents the noise field generated byeach of the three optimized blades, where it canbe seen that higher noise levels are generated when

6

the blade is descending. By comparing the threesolutions, it can be seen that the maximum powersolution presents much higher noise values than theother two and that the reduction in noise from onesolution to another happens mostly in the outer partof the blade.

Summary of NREL Phase II optimization re-sults The summary of the AEP and OASPL valuesobtained in all the previous described optimizationcases are presented in Tab. 1, where it can be seenthat with increasing number of variables used in theproblem, the optimal solutions presents lower noiselevels and higher energy production levels.

CaseAEP OASPL[MW h] [dB(A)]

Initial 23.6 52.18

1 46.98 53.28

2Min. Noise 16.7 50.22

Trade-off 38.04 51.08Max. Power 46.74 52.28

3 39.22 52.11

4Min. Noise 28.83 47.22

Trade-off 35.61 47.84Max. Power 39.01 51.38

5Min. Noise 52.01 46.61

Trade-off 55.54 48.11Max. Power 56.49 52.13

Table 1: Summary of the optimization cases per-formed on the NREL Phase II wind turbine blade.

4.2. Optimization of the AOC 15/50 windturbine blade

Due to the simplicity of the NREL Phase II blade,high aeroacoustic improvements were expected to beachieved. The results showed that reduction in noiselevels is possible without much, if any, reductionin aerodynamic performance. The previous resultsalso showed that if not properly constrained, thesolution might converge to geometries that mighthave unwanted structural characteristics. With thisin mind, an optimization was performed on the AOC15/50 turbine blade and is presented in this section.

Design Variables The AOC 15/50 airfoil shapeis defined at 4 stations, being the first at the hub con-sidered to be circular. At each control section, thecoordinates of 10 control points were used as designvariables (the same as in the previous optimizationcases minus the y-coordinates of control points 0 and12), resulting in 54 variables (18 per control section).The twist was defined using a 5th order Bezier curve,

(a) Min. Noise

(b) Trade-off

(c) Max. Power

Figure 14: Overall sound pressure level across therotor for various optimized blades from case 5.

resulting in 6 design variables. The chord definedby linear interpolation of 3 control points, resultingin 2 design variables. The search space of the con-

7

trol section variables was defined as ±10% in thex-direction and ±20% in the y-direction, relative tothe initial control points. The chord variables searchspace was defined as ±20% of the initial chord valuesand the twist as ±30% in the x-direction and and±10% in the y-direction. This resulted in a total of62 design variables.

The constraints used in this optimization casewere the following:

Chord and Twist Both chord and twist were con-strained so that there was a reduction of theirvalues towards the tip of the blade (not countingwith the chord at the root):

xcpi ≤ xcpi+1

ycpi ≥ ycpi+1

(15)

Control Sections

xcpi ≥ xcpi+1, upper curve

xcpi ≤ xcpi+1, lower curve

ycp2 ≥ ycp3

ycp10 ≥ ycp9

(16)

Run Conditions The TE thickness was assumedto be 1% of the chord, with a constant angle of 6 %.Due to the non aerodynamic shape of the sections upto 40 % of the blade, the noise was only computedin the 60% outer part.

Results The resulting Pareto front is presentedin Fig. 15 where three solutions are identified, simi-larly the previous optimization cases. A reductionin OASPL of more than 4 dB(A) is possible, rela-tive to the initial blade, without any loss in energyproduction. On the other hand, while maintain-ing the noise levels, an increase of 14 MW h canbe achieved. The Pareto front ranges between anOASPL of 56 dB(A) to about 63 dB(A) and fromabout 57.5 dB(A) to 63 dB(A) the AEP varies verylittle. The AEP and OASPL values of the initialblade and the three solutions identified in Fig. 15are presented in Tab. 2.

Figures 16 and 17 present the chord twist distribu-tions, respectively, of the three solutions indicatedin Fig. 15. The chord was maximized to the upperbounds at 0.4 and 1.0 r/R in the three solutions,with the exception of the minimum noise solution,where the chord is slightly smaller than the othersolutions at 0.4 r/R. Regarding the twist distribu-tions, the three solutions present higher twist anglesthan the initial values allover the blade, with theexception of the tip region, where the twist changerate increases and the twist angles are lower thanthe initial values.

Min Noise

Max power

Trade-o!

Figure 15: Pareto front in AOC 15/50 blade opti-mization case.

AE

P[M

Wh

]

Diff

ere

nce

[%]

OA

SP

L[d

B(A

)]

Diff

ere

nce

[%]

Initial 114.76 0 60.61 0Min. Noise 112.09 - 2.3 56 - 7.6

Trade-off 127.33 11.0 57.37 - 5.3Max. Power 129.03 12.4 62.72 3.5

Table 2: Summary of AEP and OASPL values inAOC 15/50 optimization case.

0.0 0.2 0.4 0.6 0.8 1.0

r/R

0.4

0.5

0.6

0.7

0.8

0.9

Chord

(m

)

Min Noise

Trade-off

Max Power

Initial

Figure 16: Chord distributions of optimized AOC15/50 blades.

The airfoil shapes of the three solutions are pre-sented in Figures 18 to 20. The same behavior ofprevious cases is observed in these results regard-ing the differences between the airfoil shapes of thedifferent solutions. While at 40% and 75% of theblade, the Trade-off airfoil shape is a mixture of theother two, at 95% of the blade it is much closer tothe Minimum Noise airfoil shape, particularlly theupper side. This comes as a result of the previouslymentioned fact that the noise is mainly generated

8

0.0 0.2 0.4 0.6 0.8 1.0

r/R

−2

0

2

4

6

8

10Tw

ist

angle

(◦ )

Min Noise

Trade-off

Max Power

Initial

Figure 17: Twist distributions of optimized AOC15/50 blades.

in the outer region of the blade.

0.0 0.2 0.4 0.6 0.8 1.0

x/c (-)

−0.3

−0.2

−0.1

0.0

0.1

0.2

0.3

y/c

(-)

Min Noise

Trade-off

Max Power

Figure 18: Initial and optimized airfoil shapes at 40%of the blade in the AOC 15/50 blade optimization

0.0 0.2 0.4 0.6 0.8 1.0

x/c (-)

−0.2

−0.1

0.0

0.1

0.2

y/c

(-)

Min Noise

Trade-off

Max Power

Figure 19: Initial and optimized airfoil shapes at 75%of the blade in the AOC 15/50 blade optimization

The three solutions are also compared in Fig. 21,where the radial distribution of generated noise ineach optimized blade is presented. It can be seenfrom that figure that the reduction of noise fromthe maximum power solution to the minimum noiseoccurs specially in the outer part of the blade.

0.0 0.2 0.4 0.6 0.8 1.0

x/c (-)

−0.2

−0.1

0.0

0.1

0.2

y/c

(-)

Min Noise

Trade-off

Max Power

Figure 20: Initial and optimized airfoil shapes at 95%of the blade in the AOC 15/50 blade optimization

65

62

59

55

52

49

46

42

39

36

33

29

26

23

20

16

13

10

OASPL

(dB(A))

Z

X

Y

Minimum Noise

Trade-o�

Maximum Power

Figure 21: Comparison of the radial distributionof generated noise on between different optimizedAOC 15/50 blade geometries.

5. Conclusions

In the present work, a wind turbine aerodynamicand aeroacoustic prediction model was successfullyimplemented and validated against experimentaldata.

A geometrical model of the wind turbine bladewas also developed and implemented, using NURBScurves and Bezier curves, for the definition of thecross sectional airfoil shapes and twist and chorddistributions, respectively. The NURBS parameter-ization of the airfoil shapes proved to be able toreproduce various different airfoil shapes commonlyused in wind turbines.

The code was successfully implemented into an op-timization framework, being able to produce optimalsolutions in the various performed test cases. In theoptimizations performed on the NREL Phase II windturbine, a maximum increase in AEP of 139.4 %and maximum reduction of OASPL in 10.7 % wasachieved. These large relative improvements showed

9

that this particular blade was far from being op-timal. In contrast, using another blade, from thecommercially available AOC 15/50 wind turbine, itwas possible to assess more realistically the potentialof the optimization framework. In this case, the op-timization resulted in a maximum improvement inAEP of 12.4 % and a maximum OASPL reduction of7.6 %. However, these results were not achieved inthe same blade geometry, and the trade-off betweennoise generation and energy production is visible inthe results of the optimizations.

Nowadays, tools like the framework developed areused in the design phase of any wind turbine toincrease its performance to the maximum possibleextent. As the geometries of the blades are alreadyhighly manually tuned by the designers, the use ofsuch tools might give the wind turbine a competitiveedge. The relative small computational requirementof each optimization is a key factor, as it allows fora greater diversity of geometries and configurationsto be analyzed / optimized, thus increasing theprobability of obtaining a better solution.

AcknowledgementsThe author would like to thank Dr. Andre CaladoMarta for his teachings guidance throughout thedevelopment of this thesis.

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