Optimisation of Wind Turbine Blades

Journal of Materials Processing Technology 167 (2005) 463–471

Optimisation of wind turbine blades

M. Jureczko, M. Pawlak, A. Mezyk∗

Faculty of Mechanical Engineering, Silesian University of Technology, ul. Konarskiego 18a, 44-100 Gliwice, Poland

Abstract

The manufacturing cost of WT blade is about 15–20% of wind turbine production cost. The expenses of innovations in design of bladesrepresent the small amount of overall cost of wind turbine production. Profits coming from better structural model, use of suitable compositematerials and better techniques of manufacturing, both the blades and composite materials, causes necessity of application of numericalmodeling and optimization techniques.

When designing a wind turbine, the goal is to attain the highest possible power output under specified atmospheric conditions. From thetechnical point of view, this depends on the shape of the blade. The change of the shape of blade is one of the methods to modify stiffnessand stability, but it may influence aerodynamic efficiency of wind turbine. Other method to change dynamic and mechanical properties ofwind turbine is modifying the composite material, which the blade is made of. The problem of determining the optimal shape of blade anddetermining the optimal composite material is a complex one, as the mathematical description of aerodynamic load is complex and a numbero

lades. Thea a numbero©

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f constraints and objectives have to be satisfied.These considerations have prompted the authors to take up the problem of the multi-criteria optimum design of wind turbine b

im of this study was to develop a computer program package that would enable optimisation of wind turbine blades with regard tof criteria.2005 Published by Elsevier B.V.

eywords:Wind turbine blade; Composite materials; Finite element analysis; Optimisation

. Properties of the blade

The aerodynamic profiles of wind turbine blades have cru-ial influence on aerodynamic efficiency of wind turbine.owever, when blades are longer than 45 m the dynamicehaviour of the blade must be also taken into account. Then,

he position and shape of spars have to be considered andnalysed. In the article[9] is mentioned that the location of

he main spar together with the location of the stiffening ribsill have the biggest influence on the bending modes of thelade.

The model of blade (seeFig. 1) made of shell elementsas used in multi-criteria optimisation procedure. Accord-

ng to Ref.[8], the blade is to be twisted around the elasticxis. The position of elastic center can be changed by modi-

ying the position of spars and its shape. The solid model ofhe blade is created in order to obtain required properties of

∗ Corresponding author.E-mail address:[email protected] (A. Mezyk).

the blade and position of spars. We are interested aboproperties of the cross-sections. Using commercial softMSC Patran, there is possible to get information aboutmoments of inertia, shear centers and centroids. The odata, for example, cross-section of the blade is presenFig. 2.

The blade was divided to 26 cross-sections, for eacthem were received the similar data.

Now the cross-sections of the blade must be twisted athe shear axis. But the question is what with the positiospars, if they are also twisted. The conclusion is thatare not twisted in similar way as aerofoils. Leaving the sstraight, the blade would have the form shown inFig. 3.

The commercial blades does not have the spars positin this kind. The reason is the aerodynamic damping pheena. Twist of the blade decide about value of aerodynloads, but also the direction in which the blade will vibra

The blade with twisted spars is presented inFig. 4.The twist of spars decides about pitch of principal be

ing axes. Aerodynamic damping is a very important dyna

924-0136/$ – see front matter © 2005 Published by Elsevier B.V.oi:10.1016/j.jmatprotec.2005.06.055

464 M. Jureczko et al. / Journal of Materials Processing Technology 167 (2005) 463–471

Fig. 1. The structural model of the blade with spars, before twist.

Fig. 2. The calculated position of shear center and centroid.

aspect. The negative value of aerodynamic damping meansthat some additional energy is added to the blade during vibra-tion and the amplitude of vibration is increased. Aerodynamicdamping has in plane and out of plane components. Damp-ing in-plane direction will have the negative value if the bladesection produce the power. If damping in out of plane direc-

Fig. 3. The twisted blade with straight spar.

Fig. 4. The twisted blade with twisted spars.

tion is positive, by twisting the blade the value of out of planedamping will decrease (but must be still positive) and the in-plane damping will receive positives values. Due to the twistof spars, the blade will vibrate not clearly edgewise or flap-wise[5].

The second mode shape of the blade is presented inFigs. 5 and 6.

2. Aerodynamic loads

The analysis of aerodynamic loads in our case is basedon the Blade Element Momentum method (BEM[2,10]). Asthe input date, we have the free stream wind velocityV0,geometry of aerodynamic profiles used in blade with theCLandCD as the aerodynamic lift and drag coefficients uniquefor each of them. In literature, they are presented asCL(α)andCD(α), which means that they depend on the angle ofattackα (Fig. 7).

M. Jureczko et al. / Journal of Materials Processing Technology 167 (2005) 463–471 465

Fig. 5. The second mode of the blade, first edgewise mode, frequency1.5975 Hz.

Fig. 6. The second mode of the blade, flapwise.

BEM method is an iterative method, at the beginning thevalue of axial retardation coefficienta is assumed to be zero,the results of simulation (calculateda) are compared with theinitial value. If their values differ the calculation is repeatedwith the received axial retardation coefficient as initial value.If they agree the calculation is finished. Below there areshortly presented the equations used in BEM method[2].

The pitch angle is the angle between the axial wind veloc-ity and the tangential wind velocity:

tanφ = V0(1 − a)

(1 + a′) · ω · r(1)

Relative velocity of the wind is calculated from the equa-tion:

Vrel = ω · r(1 + a′)cosφ

(2)

The aerodynamic loads are expressed in the followingforms:

Lift:

L = 1

2· ρ · V 2

rel · c · CL (3)

Drag:

D = 1

2· ρ · V 2

rel · c · CD (4)

Thrust:

FN = L cosφ + D sinφ (5)

Torque:

FT = L sinφ − D cosφ (6)

-

avity,a sed inw

of wind
Fig. 7. The diagram
whereρ is the density of the air andc is the chord of aerodynamic profile.

Blades used in aeroplanes have the order of the grerodynamic and shear centers different than blades uind turbines.

velocity components.


Fig. 8. The location of the shear, gravity and aerodynamic centers.

According to Ref.[6] on the left there are elastic centers,gravity centers and aerodynamic centers. In modern windturbines the elastic center is between gravity and aerodynamiccenter. The position of the spars decide about position of shearaxis and the order of centers.

As can be seen inFig. 8 in aerodynamic center there areworking aerodynamic loads:

• tangential aerodynamic loadsFT;• normal aerodynamic loadsFN.

Also, the aerodynamic damping according to Ref.[6] isworking directly in aerodynamic center. In the gravity centerthe gravity forces are working but also inertial loads, whichare the results of rotation of the blade has to be mentioned. Theelastic axis is the axis about which the aerodynamic profilesare twisted. The elastic axis is created from elastic centers ofcross-sections.

To analyse the dynamics of the blade by the finite ele-ment method analysis, the blade model as the Timoshenkobeam elements was created. Before it, the assumption wasmade that the elastic axis is created by shear centers fromeach cross-section. The grid points are created along theaerodynamic centers. The aerodynamic forces are applieddirectly to the grid point, the forces act at the aerody-namic centers. Gravity forces are applied to the gravityc s off-s nt tot

On the model of the blade presented below there aremarked three lines, red are aerodynamic centers, green areelastic centers and black are gravity centers.

In our research, the aerodynamic analysis was done, basedon modified BEM theory described in Refs.[2,10].

We do not have pressure forces along the blade to fullyanalyse the shell model. To speed up calculation, three-dimensional model of the blade is reduced to beam elementswith data presented inFig. 9 as input. Beam elements aremodeled along the aerodynamic centers, including shearand gravity centers as vector offsets. The limitation of thismethod is the ability to use this model only in linear analysis,such as modal, static and linear transient analysis.

3. State of load on the blade

The analysis of the state of load on the wind turbine bladeis intended to verify whether the turbine will withstand theaction of load within appropriate safety range. Various casesof load on the blade, resulting from the action of variousexternal factors on the turbine, have to be considered. Thefollowing types of states of load on a wind turbine blade canbe distinguished:

• Aerodynamic loadsof a wind turbine blade are shown in

• adsrated

enters. The shear center and aerodynamic center iet from the neutral, the loads should cause the elemewist.

Fig. 10.Mass loads, as the wind turbine blade is slender, the loassociated with its inertia are limited to the loads gene


Fig. 9. The model of the wind turbine with marked aerodynamic, shear andgravity centers on the blades.

by its weight, which causes sinusoidal loads the frequencyof which corresponds to the rotorFig. 11shows the deter-mined state of load on wind turbine blade. Both mass andaerodynamic loads were investigated.

4. Material of the blade

The considered blade is made of composite materials con-taining more than one bonded material, each with differentstructural properties. One of the materials, called the rein-forcing phase is embedded in the other material of the matrix

Fig. 11. State of load on wind turbine blade.

phase. If the composite is designed and fabricated correctly,it combines the strength of the reinforcement with the tough-ness of the matrix to achieve a combination of desirableproperties not available in any single conventional material.The main advantage of composite materials is the potentialfor a high ratio of stiffness to weight. Composites used fortypical engineering applications are advanced fiber or lam-inated composites, such as fiberglass, glass epoxy, graphiteepoxy and boron epoxy. Composites are somewhat more dif-ficult to model than an isotropic material such as iron or steel.The special care must be taken in defining the properties andorientations of the various layers since each layer may havedifferent orthotropic material properties.

Majority of wind turbine blades is made of fiberglass rein-forced with polyester or epoxy resin. Construction usingwood–epoxy or other materials also can be found. Smallturbine blades are made of steel or aluminum, but they areheavier.

Lighter and more effective blades decrease materialrequirements for other wind turbines component making

cal forc
Fig. 10. The lo es on the blade.


overall costs to be lower. Longer blades require another mate-rials to be applied, usually carbon-based composites. Carbonfiber composites allow to lower blade’s mass (from 20 to 18 Tat 61.5 m long blade). Carbon-based composites allows alsoto reconstruct older blades made of fiberglass reducing massand increasing its stiffness. However, use of carbon materialsrequires increased accuracy and makes manufacturing coststo be higher.

5. FEM model of wind turbine blade

The FEM model of the wind turbine blade with a NACA63–212 airfoil was created using APDL language in ANSYS.It is a parametric model, as the thickness of the shell, com-posite material, which blade is made, number of stiffeningribs and their arrangement were the model parameters thatwere input from the authors’ program that implemented amodified genetic algorithm. A given parametric file can beused to create various blade models, modify their thicknessand basic dimensions.

The created FEM model of the blade consists of 124,042elements, 55,044 nodes and 327 areas meshed. The 8-nodalshell of the SHELL 63 type with 6 degrees of freedom waschosen as finite elements, what enabling specification of anyt ion ofe ecifi-c finingv

enc

• ebs

metryd .

Table 1Investigated composite materials

Material Elastic modulus [GPa] Density [kg/m3]

Kevlar 149 179 1470Technora 70 1390Glass E 76 2540Glass S 88 2540

Table 2Natural frequency of blade, which was made of different materials

No mode shape Frequency [Hz]

Glass E Glass E Technora Kevlar 149

1 0.72853 0.79534 0.98482 1.49962 1.6909 1.8459 2.2857 3.48053 2.0845 2.2756 2.8178 4.29074 4.1426 4.5224 5.5999 8.5275 6.0169 6.5686 8.1336 12.3856 7.1806 7.839 9.7067 14.787 10.975 11.982 14.836 22.5918 14.548 15.882 19.666 29.9469 15.035 16.414 20.324 30.948

10 16.44 17.947 22.223 33.84

6. Selection of composite materials of wind turbineblade

The aim of this study was estimation the influence ofcomposite materials, which the blade is made, on dynamicalproperties of wind turbine blades. The composite materials,which were investigated are presented inTable 1.

Modal analysis was made for blade with constant elementsthickness.Table 2shows natural frequency of blade, whichwas made of different materials.

Materials with lower density such as fiber aramid (Tech-nora) have higher natural frequencies and bigger deflection.

The comparison of fibreglass S-type and fibreglass E-typeshows increase of natural frequencies without eigenvaluechange. Another material—Kevlar, increases both naturalfrequencies and eigenvalue.

7. Formulation of the problem of multi-criteriadiscrete–continuous optimisation

It is not possible to formulate the problem of optimumdesign of wind turbine blades as a single-criterion optimi-sation task because this process requires many criteria to betaken into account. In many cases, these criteria are mutuallyincomparable, uncountable and sometimes even contradic-t

eriai

••

hickness at each node of the chosen element. Selectlements in a numerical model of a blade enables spation of various thicknesses and material data and dearious types of elements.

The following simplifying assumption was made whreating the numerical model of the blade:

the manner of connecting the shell with supporting wand stiffening ribs was neglected.

The blade was treated as a clamped beam with its geoetermined in the manner described in previous section

The FEM blade model is shown inFig. 12.

Fig. 12. FEM blade model.

ory, which precludes their simultaneous optimisation.The authors have taken into account the following crit

n the process of wind turbine blades design:

minimisation of generated blade vibrations;maximisation of output generated;


• minimisation of blade material cost;• local and global stability of blade structure;• fulfilment of appropriate strength requirements by the

blade structure.

Minimisation of vibrations is a good way to successfuldesign of blade structure and at the same time it contributesto other benefits, such as lower cost or high stability. How-ever, when minimising vibrations of the blade, the naturalfrequency of the blade must be separated from the harmonicvibration associated with rotor rotation. Such an approachprevents the occurrence of resonance, which under highamplitude of vibration could lead to destruction of the struc-ture. Frequency spacing is one of the methods of isolatingfrequencies.

The amplitude of generated vibrations of the wind turbineblade depends on its stiffness, which is a function of materialdensity, thickness of shell, number of stiffening ribs and theirarrangement along blade span. Therefore, when the vibrationminimisation criterion be taken into account, the wind turbineblade should be provided with the highest possible stiffness.

Such a formulation of the optimisation problem also sat-isfies the criterion of generated output maximisation, as theoutput of a wind turbine depends also on the optimum shapeof blades, i.e. on their optimum geometrical features.

The mass and fabrication cost of a blade depend on thes s. Ift theo ightm oft

f thes theb witha ded.

mu-l desa ul-t indi-v ture( ature( lades

ete–c

8

pti-m int seda ineb eriadm

Table 3Genetic algorithm—no copying

Variablex1 (m) 0.0201x2 (m) 0.0118x3 10x4 (m) 1.25, 33.75

Found in population 22Value of objective function (kg) 1645.1Duration of computation (s) 125352

optimisation task

minx∈ Ω f (x) (7)

whereΩ is the domain of possible solutions within the spaceof objects,x the column matrix of design variables andf(x)is the objective function, i.e. mass of blade.

The column matrix of design variables can be representedin the following form:

xT = [x1, x2, x3, x4] (8)

wherex1 is the shell thickness,x2 the web thickness,x3 thenumber of stiffening ribs andx4 is the arrangement of stiff-ening ribs.

The other criteria were expressed in the form of inequalitylimitations:

• stresses generated in the blade cannot exceed permissiblestresses—compliance with appropriate strength require-ments of the structure

σ(x) ≤ σdop (9)

• displacement of individual nodes in the numerical modelof the blade cannot exceed the set value—global stabilitymust be ensured

u(x) ≤ 0.1 m (10)

• thest be

• onic

TG

V

FVD

ame parameters as the amplitude of blade vibrationhe cost minimisation criterion were considered, thenptimisation task would have to be formulated as a weinimisation task. However, in order to ensure stability

he structure, the weight should be maximised.Furthermore, to meet the strength requirements o

tructure, optimisation of maximum displacements oflade in transverse direction would have to be carried outlimiting condition that permissible stresses be not exceeIn view of the above considerations, the authors for

ated the problem of optimum design of wind turbine blas a multi-criteria optimisation task, which enables sim

aneous investigation of several criteria. The values ofidual criteria depend on parameters of continuous nathickness of shell, thickness of webs) and of discrete nnumber of stiffening ribs, their arrangement along bpan).

The optimisation task was formulated as a discrontinuous multi-objective problem.

. Formulation of the optimisation problem

After having carried out the study of formulating an oisation criterion when minimising vibrations, consisting

he investigation of the effect of the various criteria discusbove on the amplitude of vibrations of the wind turblade, the authors formulated the problem of multi-critiscrete–continuous optimisation using the limitationsethod (described, for instance, in Ref.[4]) a single criterion

displacement of the nose of the numerical model ofblade cannot exceed the set value—local stability muensured

uTIP(x) ≤ 0.15 m (11)

separation of natural frequency of the blade from harmvibration associated with rotor rotation

freqBLADE = freqROTOR (12)

able 4enetic algorithm—copying permitted

ariablex1 (m) 0.0182x2 (m) 0.0144x3 2x4 (m) 1.75, 2.25

ound in population 43alue of objective function (kg) 1557.4uration of computation (s) 120916


Fig. 13. History of optimisation by means of a modified genetic algorithm with no copying of the best individual.

Further limitations apply to the values of design variables.These can be expressed by means of the following matrixformula:

xdown ≤ x ≤ xup (13)

wherexdown is the column matrix of lower bound variablesandxup is the column matrix of upper bound variables.

Optimisation calculations were done with the use of theauthors’ program that implemented a modified genetic algo-

rithm, for which the following assumptions were made:

• number of individuals: 20;• number of populations (STOP criterion): 50;• probability of crossing: 0.7;• probability of mutation: 0.03.

The applied probabilities of genetic operations wereadopted on the basis of studies performed, inter alia, by theauthors and presented, for instance, in Ref.[1].

odified
Fig. 14. History of optimisation by means of a m genetic algorithm with copying of the best individual.


9. Numerical calculation results

Selected results obtained for the optimisation problem aregiven inTable 3(optimisation with the use of the modifiedgenetic algorithm and with no copies of the best individual)andTable 4(optimisation with the use of the modified geneticalgorithm and with copies of the best individual).

Fig. 13 shows chosen courses of optimisation with theuse of the modified genetic algorithm including the copy-ing of the best individual, whereasFig. 14 shows chosencourses of optimisation with the use of the modified geneticalgorithm where the copying of the best individual waspermitted.

Because the genetic algorithms this the stochastic methodsof search of optimum, which belong to Pareto-optimal set,individual curves solutions (appointed with different colours)represent the course of individual optimisation process.

10. Conclusion

The developed numerical model of the wind turbine bladeand the computer program package for performing multi-criteria discrete–continuous optimisation of wind turbineblades are of general nature. Various blade models can bec ssesa . Thea lgo-r onss

e oft regs

or Vacuum-Assisted Resin Transfer Moulding (VARTM)method[8,11].

Acknowledgement

This investigation was realized within a framework ofProject No. 4T07C06828 funded by Scientific Committee(KBN).

References

[1] P. Bachorz, M. Marcinkowska, Relation between efficiency of agenetic algorithm and assumed optimization parameters, in: Pro-ceedings of the Scientific Conference Applied Mechanics, 2002, pp.11–16.

[2] O.L. Hansen Martin, Aerodynamics of Wind Turbines, James &James, London, 2002.

[4] R.T. Marler, J.S. Arora, Survey of multi-objective optimization meth-ods for engineering, Struct. Multidisciplinary Optimisation 26 (2004)369–395.

[5] J.T. Petersen, H.A. Madsen, et al., Prediction of Dynamic Loadsand Induced Vibrations in Stall, Risø-R-1045 (EN), Risø NationalLaboratory, Roskilde, Denmark, 1998.

[6] R.L. Bisplinghoff, H. Ashley, R.L. Halfman, Aeroelasticity, DoverPublications Inc., New York.

[8] Guidelines for Design of Wind Turbines, second ed., Det Norskeen-

ergy

[ epts

[ y

reated by means of an ANSYS parametric file; thicknend main dimensions of the model blade can be varieduthors’ program that implements a modified genetic aithm enables optimisation of various objective functiubjective to various constraints.

Subsequent to determination of the optimised profilhe wind turbine blade could be machined using Pre-P

Veritas and Riso National Laboratory, Jydsk Centraltrykkeri, Dmark, 2002.

[9] One-Dimensional Variations: Blades, Dutch Offshore Wind EnConverter Project, LM Glasfiber Holland BV, 2003.

10] A. Spera David, Wind Turbine Technology, Fundamental Concin Wind Turbine Engineering, ASME Press, New York, 1998.

11] J. Sleziona, Podstawy Technologii Kompozytow, Silesian Universitof Technology, Gliwice, 1998.

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Optimisation of Wind Turbine Blades