structural optimization design of large wind turbine blade...

Research ArticleStructural Optimization Design of Large Wind Turbine Bladeconsidering Aeroelastic Effect

Yuqiao Zheng,1,2 Yongyong Cao,1,2 Chengcheng Zhang,1,2 and Zhe He1,2

1Key Laboratory of Digital Manufacturing Technology and Application,TheMinistry of Education, Lanzhou University of Technology,Lanzhou 730050, China2College of Mechano-Electronic Engineering, Lanzhou University of Technology, Lanzhou 730050, China

Correspondence should be addressed to Yuqiao Zheng; [email protected]

Received 27 July 2017; Revised 2 September 2017; Accepted 6 September 2017; Published 10 October 2017

Academic Editor: Chanho Jung

Copyright © 2017 Yuqiao Zheng et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This paper presents a structural optimization design of the realistic large scale wind turbine blade. The mathematical simulationshave been compared with experimental data found in the literature. All complicated loads were applied on the blade when itwas working, which impacts directly on mixed vibration of the wind rotor, tower, and other components, and this vibration candramatically affect the service life and performance of wind turbine.The optimizedmathematicalmodel of the bladewas establishedin the interaction between aerodynamic and structural conditions. The modal results show that the first six modes are flapwisedominant. Meanwhile, the mechanism relationship was investigated between the blade tip deformation and the load distribution.Finally, resonance cannot occur in the optimized blade, as compared to the natural frequency of the blade. It verified that theoptimized model is more appropriate to describe the structure. Additionally, it provided a reference for the structural design of alarge wind turbine blade.

1. Background and Motivation

As a key wind turbine component, the blade is a determiningfactor for energy harvesting efficiency and a main source ofcomplicated and extreme loads. Aeroelasticity is a key issue inthe continuing development of wind turbines towards large,flexible, highly optimized machines. In the design optimiza-tion process, multiple objectives (maximum annual energyproduction, minimum cost of energy, minimummass, mini-mumextreme load, andminimumnoise) are usually includedand may be contradictory with each other. With the windturbine design development in the super large scale, extra-long blades catching the wind are an urgent need. However,flutter occurs in coupled rigid and flexiblemultibody systems.On account of the coupling effect conditions of aerodynamicforces, elastic forces, and inertial forces, coupled with thewind turbine often running in the stall condition, the bladewill easily undergo deformation and flutter for the largewind turbine. Consequently, studying the deformation andvibration of the blade under fluid structure interaction is of

great significance to the safe operation of large wind tur-bines.

Recently, many scholars have studied the structuraldynamics of wind turbine blades in the aerodynamic andstructural coupling conditions. For instance, Zheng et al. [1]studied the optimization design of blade by using geneticalgorithm under the aerodynamic and structural couplingcondition. Liu and Ren [2] investigated vibration and aeroe-lastic stability of slender composite beams with thin-walledclosed cross sections based on the extendedGalerkinmethod.Twisty and flapwise vibration of rotating beams featuringcomposite material thin-walled was studied with a numberof factors. The modal under fluid structure interaction wascalculated and analyzed through the establishment of afull size fluid structure coupling model by Hu et al. [3].Theoretical analysis and numerical calculation modes of theblade in the different rotation speeds and material pavingmethods were carried out by Yin et al. [4]. Cardenas et al.[5] presented a numerical validation of a thin-walled beamfinite element model of a realistic wind turbine blade.

HindawiMathematical Problems in EngineeringVolume 2017, Article ID 3412723, 7 pageshttps://doi.org/10.1155/2017/3412723

https://doi.org/10.1155/2017/3412723

2 Mathematical Problems in Engineering

T

G

0 x

y

hxe

Figure 1: Simplified dynamic model of the blade.

Harte et al. [6] established the coupling model of the windturbine; then the modal was analyzed under different loads.The modal of composite blades was analyzed in the case ofthe fluid structure interaction by Kang et al. [7]. Cortınezand Piovan [8] developed a theoreticalmodel for the dynamicanalysis of composite thin-walled beams with open or closedcross sections. Shokrieh and Rafiee [9] researched on thestatic analysis with a full 3Dfinite elementmethod (FEM) andthe critical zone where fatigue failure begins was observed.Malcolm and Laird [10] utilized shell element to extractthe equivalent beam properties and generate the completeaeroelastic model of the blade.

In this work, the theoretical basis of aerodynamics wasadopted. Meanwhile, taking the aerodynamic and structuralcoupling effect conditions into consideration, the mathe-matical model was established by taking the minimal massof the blade as the optimization objective, the interactionmechanism between the blade tip deformation and loaddistribution was studied by usingmodal analysis. At the sametime, it was illustrated that the establishment mathematicalmodel is reasonable, and it also can improve the bladedynamic performance.

2. Problem Statement

Themathematical model is implemented in this work for thefluid dynamics optimization design of a wind turbine basedon the differential equation motion. In the aerodynamicand structure coupling effect, airflow change was used asthe excitation, and the blade deformation was used as theresponse. Studying on the dynamic design of thewind turbineblade can be described by Spring-Damping-Mass system.Thesimplified dynamic model of the cross section of a blade forunit length is shown in Figure 1.𝐺 is the center of the blade mass, 𝑇 is torsional center,𝑥𝑒 is a distance from the center of mass to the torsionalcenter, ℎ is the mean displacement of the centroid of theblade, and 𝜃 is the angular displacement around the center ofmass.

The kinetic energy of unit blade vibration is given as

𝑇 = 12𝑚ℎ2 + 12𝐽 𝜃2. (1)

Potential energy of the system can be obtained by thefollowing equation:

𝑈 = 12𝑘ℎ (ℎ − 𝜃𝑥𝑒)2 + 12𝑘𝜃𝜃2, (2)

where 𝑘ℎ is bending stiffness coefficient and 𝑘𝜃 is torsionalstiffness coefficient.

Based on (1)∼(2) and using Lagrange formulation,

𝑑𝑑 (𝜕 (𝑇 − 𝑈)𝜕 𝑞𝑖 ) − 𝜕 (𝑇 − 𝑈)𝜕𝑞𝑖 = 𝑄𝑖. (3)

The discrete differential motion can be expressed as fol-lows:

𝑚ℎ + 𝑘ℎℎ − 𝑘ℎ𝑥𝑒𝜃 − 𝐹 = 0,𝐽 𝜃 − 𝑘ℎ𝑥𝑒ℎ + 𝑘ℎ𝑥2𝑒𝜃 + 𝑘𝜃𝜃 −𝑀𝑦 = 0. (4)

Equation (4) can be also written as matrix form:

[𝑚 00 𝐽][

ℎ𝜃] + [

𝑘ℎ −𝑘ℎ𝑥𝑒−𝑘ℎ𝑥𝑒 𝑘ℎ𝑥2𝑒 + 𝑘𝜃][

ℎ𝜃] = [

𝐹𝑀𝑦] . (5)

3. Optimizing the MathematicalModel of the Blade

In order to improve the efficiency, reliability, and stability,the optimization and design method were critically neededaccording to aerodynamic and structural conditions. In thiscase, establishing mathematical model is a profound signifi-cant to design blade. In this study, the blade twist angle, chordlength, and relative layer thickness are, respectively, defined asoptimization design variables, and these variables determinethe blade aerodynamic performance.The tip deformation andoutput power are used as a constraint. Finally, the minimummass of flexible blade is considered as the optimized objective.As a result, the mathematic model of the optimal designprocess is defined by

𝑋= [𝑥𝛽1, 𝑥𝛽2, . . . , 𝑥𝛽𝑛, 𝑥𝑐1, 𝑥𝑐2, . . . , 𝑥𝑐𝑛, 𝑥𝑡1, 𝑥𝑡2, . . . , 𝑥𝑡𝑛]𝑃 ≥ 𝐶1𝐿 ≤ 𝐶2𝐹 (𝑥)min = 𝑚 = ∑

𝑖

𝜌𝑖𝑉𝑖

(6)

in which 𝑥𝛽𝑖 (𝑖 = 1, 2, 3, . . . , 𝑛) is the twist angle of 𝑖thcross section (∘); 𝑥𝑐𝑖 (𝑖 = 1, 2, 3, . . . , 𝑛) is the chord lengthof 𝑖th cross section (m); 𝑥𝑡𝑖 (𝑖 = 1, 2, 3, . . . , 𝑛) is the layerthickness of 𝑖th cross section (mm); 𝑃 is power (Kw); 𝐶1 and

Mathematical Problems in Engineering 3

Table 1: The corresponding parameters of the wind turbine.

Rated power/kw 1500Rotor diameter/m 83Rated speed/rpm 17.2Cut-in wind speed/(m⋅s−1) 3Cut-out wind speed/(m⋅s−1) 25Tip speed ratio 8.5

Initial valueWithout considering coupling optimization

10 15 20 25 30 35 405Blade length position R (m)

Coupling optimization

0

0.5

1

1.5

2

2.5

3

3.5

4

Chor

d (m

)

Figure 2: Comparison of chord optimization curve.

𝐶2 are given constant; 𝐿 is the tip deformation (m);𝑚 is blademass (kg); 𝜌𝑖 is the 𝑖th material density; 𝑉𝑖 is the 𝑖th materialvolume.

4. Results and Discussion

4.1. Airfoil Data. The four airfoils of S809-32, S808-25,S825-24, and S825-21 were selected, where the results wereobtained using the aerodynamics characteristics. The fourairfoils are more popular symmetrical airfoils; meantime, theexperimental data of these airfoils are public; as a result,there are more experimental data available in the literature.The corresponding parameters of wind turbine are listed inTable 1.

4.2. Optimizing Calculation. The blade chord length, twistangle, and ply thickness are regarded as the optimizationdesign variables; the blademass is used as optimization objec-tive [11]. Figure 2 shows the curve of the blade chord lengthbefore and after coupling optimization under aerodynamicand structural conditions.

The overall chord lengths tend to decrease after opti-mization, but the reduction is smaller near the tip relativeto the blade root. However, it can be also observed that theincrease chord in the middle distribution along the spanwisedirection. Considering tip and root factor in the calculating,the optimization process mainly consists of increasing chordof the tip and root of blade to compensate for their energy

0

Initial valueWithout considering coupling optimizationCoupling optimization


−4

−2

0

2

4

6

8

10

12

Twist

angl

e (m

)

Figure 3: Comparison of twist optimization curves.

Initial valueWithout considering coupling optimizationCoupling optimization


0

0.01

0.02

0.03

0.04

0.05

Ply

thic

knes

s of t

he m

ain

gird

er ca

p (m

)

Figure 4: Comparison of thicknesses of beam optimization curves.

losses. In rigid case, such phenomenon is more prominent,which is consistent with the actual conditions. Figure 3 showsthe curve of the blade twist angle before and after cou-pling optimization under aerodynamic and structural condi-tions.

It can be seen that the overall twist angle significantlyincreased after optimization with the rigid conditions fromthe curve of the blade twist angle after coupling optimizationunder aerodynamic and structural. Considering the influenceof aerodynamic and structural interaction, the chord lengthvalue after optimization becomes smaller, while twist angleincrease can contribute to the regional power. It indicated thatthe decrease chord can compensate for the energy losses.Thetwist angle decrease of the root of blade was also the mainreason for the chord increase of the root.

As shown in Figure 4, the curve of the ply thickness ofmain girder has been changed before and after coupling opti-mization of aerodynamic and structural conditions. The ply


Z1Z2

Z3 Z4

Z5 Z6

Z7 Z8

Z9 Z10

Z11 Z12

Z13

x

Figure 5: Blade partition along the span.

thickness of the main girder cap after optimization increasedin the blade root and decreased in the blade tip under therigid conditions, which repositioned the center of mass of theblade girder close to the blade root. However, considering thecoupling influence conditions and the interaction betweenaerodynamic and structural conditions, the ply thicknessdistribution of the main girder cap is just the opposite, whichrepositions the mass center of the blade girder close to theblade tip.

5. FE Model of Wind Turbine Blade

5.1. FE Model. The FE model of the wind turbine bladewith S809 airfoil was created in ANSYS software. The 8-nodal shell of the SHELL 99 type with 6 degrees of freedomwas chosen as finite elements. It is a parametric model, asthe thickness of the shell, composite material, which bladeis made, number of stiffening ribs, and their arrangementwere the model parameters that were input from the authors’program that implemented a modified genetic algorithm.The FE model of the sample blade was built. The blade’slayup methods are different in the aspects of the chord andspanwise direction. It was difficult in dividing the meshbasis for the actual structure areas. Implying assumptionwas made when creating the numerical model of the blade;blade can be simplified by being divided into 13 sections byeach cross section of the airfoil along the direction of thedevelopment to the aerodynamic layout. The FE blade modelis shown in Figure 5, which is division partition along thespan.

Due to the structure design results, the top and bottomskins can be divided into 6 separate zones by using plychange position; specifically P6 is the web plate partition (seeFigure 6).

5.2. Constraints. The blade was fixed to a hub by bolts asrigid connection, so the blade can be simplified as a cantileverbeam structure. The whole constraint is adopted in the bladeroot. Both of mass and aerodynamic loads were investigated.The boundary constraint is illustrated in Figure 7.

The aim of this study was estimation of the influenceof composite materials, with which the blade is made, on

P2

P4

P1

P2

P3

P4

P5

P6P6

P3

Figure 6: The division of blade along chord direction.

1ElementsUROT

Figure 7: Boundary constraints.

Table 2: Layup thickness of partitions unit: mm.

Spanwise location PartitionP1 P2 P3 P4 P5 P6

Z1 0.57 0.97 1.39 0.57 0.97 2.28Z2 0.57 0.97 1.39 0.57 0.97 4.55Z3 0.57 0.97 1.39 0.57 0.97 4.55Z4 0.57 0.97 1.39 0.57 0.97 3.42Z5 0.57 0.97 1.39 0.57 0.97 3.42Z6 0.57 0.97 1.39 0.57 0.97 3.42Z7 0.57 0.97 1.39 0.57 0.97 2.28Z8 0.57 0.97 1.39 0.57 0.97 2.28Z9 0.57 0.97 1.39 0.57 0.97 2.28Z10 0.57 0.97 1.39 0.57 0.97 2.28Z11 0.57 0.97 1.39 0.57 0.97 2.28Z12 0.57 0.97 1.39 0.57 0.97 2.28Z13 0.57 0.97 1.39 0.57 0.97 2.28

dynamical properties of wind turbine blades.Themechanismrelationshipwas investigated between the composite blade tipdeformation and the load distribution. For the skin bearingstructure with a one-way layer, the 45∘ unidirectional layermaterial is 5 : 1 resin matrix composites, which has a densityof 1550 kg/m3 and Poisson’s ratio of 0.26. The layup thicknessof all partitions along the span-wise are listed in Table 2.


1Elements

Figure 8: The finite element model.

Table 3: The first six natural frequencies unit: Hz.

Order Optimized blade Conventional blade1st 1.3254 1.612nd 2.7531 3.583rd 3.6507 —4th 7.0956 —5th 7.6972 —6th 12.739 —

The created FE model of the blade consists of 62042elements, 26363 nodes, and 327 areas meshed. The firstprocess was based on theANSYS software SHELL99 elementsconformed by 9038DOF. Because of its large sizes, this modelwas able to reproduce the blade’s geometry and layup veryaccurately. The element shape was adopted as a triangularmesh. The Block Lanczos method not only has higher speedand precision but also further handle the rigid vibrationtypes, which is used to extract modal number of the blades.The FE model is presented in Figure 8.

5.3. PrestressedModal Analysis. During analysis, the PSTRESswitch of software was used, because the composite bladehas a low rotational speed. Only extracting the first sixfrequencies of vibration was needed. The natural frequenciesbehavior of the blade is analyzed comprehensively and calcu-lated when the rotational speed is 0m/s, taking full constraintload mode on the blade root. In other words, all nodes ofthe blade root are fully fixed, so the blade is regarded as acantilever beam model. The first two natural frequencies ofthe optimized blade and a conventional blade are listed inTable 3.

Table 3 shows the variation of the first and second naturalfrequencies of optimized blade, which is lower than thatof the commercial blade, because the commercial bladeis subjected to the influence of specific external airflow.Furthermore, with the aerodynamic and structure couplingconditions, the airflow density going through the blade andthe mass of blade is increased, causing the natural frequencyof blade to significantly decrease. It is fully illustrated that

the interaction with aerodynamic and structural conditionscannot be neglected. The first six modes shapes of the bladeare presented in Figure 9.

Figure 9 shows that the modes of the blade are mostlyflapwise vibration.The first four modes of the blade are all forflapwisemode of vibration.Due to the twist of spars, the bladewill not clearly vibrate with edgewise or flapwise. However,the blades begin to appear edgewise and flapwise, and thefirst order has mixed modes with flapwise and torsional. Therated rotational speed is V = 10m/s; the tip speed of bladeis V = 85m/s. The excitation frequency of the rotating blade,namely, the first-order flapwise frequency, is 1.3254Hz (whenrotational speed is 79.524 rpm). Obviously, the rotationalspeed (79.524 rpm) is far more than the operation speed(12.18∼17.2 rpm). Therefore, the blades appear at the startduring normal working.

6. Conclusions

(1) The proposed mathematical model represents a simplealternative tool for the optimal design of the wind blade,especially for turbines with multi bladed rotors, where theproposed optimization can improve the efficiency. Com-pared to the natural frequency of the commercial blade, amathematical optimization model is proposed to describethe cross section of the blade in the interaction betweenaerodynamic and structural conditions. In particular, theminimummass of blade is used as the optimization objectiveand the tip deformation and output power are used asconstraint condition. It is shown that the overall performanceof the blade is gradually enhanced by optimization calcula-tion.

(2) The modes of the blade consist of flapwise, edgewise,and torsional; the frequencies of flapwise and edgewise werelower than that of torsional.

(3) Compared to the natural frequency of a commercialblade, in the aerodynamic and structural coupling effectconditions, the interaction mechanism relationship betweenblade deformation and the load distribution was analyzed.The optimized blade does not exhibit resonant behav-ior.


1Nodal solution

STEP = 1SUB = 1FREQ = 1.325USUM (AVG)RSYS = 0DMX = .67677SMX = .67677

0

.007

52

.015

039

.022

559

.030

079

.037

598

.045

118

.052

638

.060

157

.067

677

MX

(a) The 1st mode of the blade

1Nodal solution


0

.006

419

.012

838

.019

257

.025

675

.032

094

.038

513

.044

932

.051

351

.057

77

MX

(b) The 2nd mode of the blade1Nodal solution


0

.009

043

.018

085

.027

128

.036

17

.045

213

.054

256

.063

298

.072

341

.081

383

MX

(c) The 3th mode of the blade

1Nodal solution


0

.009

702

.019

404

.029

107

.038

809

.048

511

.058

213

.067

916

.077

618

.087

32

MX

(d) The 4th mode of the blade1Nodal solution


0

.008

518

.017

035

.025

553

.034

071

.042

588

.051

106

.059

624

.068

141

.076

659

MX

(e) The 5th mode of the blade

1Nodal solution


0

.010

478

.020

956

.031

434

.041

912

.052

391

.062

869

.073

347

.083

825

.094

303

MX

(f) The 6th mode of the bladeFigure 9: The first six modes of the blade.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

The authors would like to acknowledge the support providedby the National Natural Science Foundation of China (Grantno. 51565028).

References

[1] Y. Zheng, R. Zhao, and H. Liu, “Research of aerodynamic andstructural coupling optimization design for blade of large-scalewind turbine,”TaiyangnengXuebao/Acta Energiae Solaris Sinica,vol. 36, no. 8, pp. 1812–1817, 2015.

[2] T. R. Liu and Y. S. Ren, “Vibration and flutter of wind tur-bine blade modeled as anisotropic thin-walled closed-sectionbeam,” Science China Technological Sciences, vol. 54, no. 3, pp.715–722, 2011.


[3] D. Hu, Z. Zhichao, and Z. Jianping, “Modal analysis of windturbine blade based on fluid-structure interaction,” RenewableEnergy Resources, vol. 32, pp. 1168–1174, 2014.

[4] J. Yin, W. Liu, and P. Chen, “Modal re-analysis of rotary windturbine blades in refinement design,” Wind Energy, vol. 15, no.6, pp. 864–881, 2012.

[5] D. Cardenas, A. A. Escarpita, H. Elizalde et al., “Numericalvalidation of a finite element thin-walled beam model of acomposite wind turbine blade,” Wind Energy, vol. 15, no. 2, pp.203–223, 2012.

[6] M. Harte, B. Basu, and S. R. K. Nielsen, “Dynamic analysis ofwind turbines including soil-structure interaction,” EngineeringStructures, vol. 45, pp. 509–518, 2012.

[7] B.-Y. Kang, J.-Y. Han, C.-H. Hong, and B.-Y. Moon, “Dynamicanalysis of hybrid wind power composite blades according tostacking properties method,” International Journal of PrecisionEngineering andManufacturing, vol. 13, no. 7, pp. 1161–1166, 2012.

[8] V. H. Cortınez and M. T. Piovan, “Vibration and buckling ofcomposite thin-walled beams with shear deformability,” Journalof Sound and Vibration, vol. 258, no. 4, pp. 701–723, 2002.

[9] M. M. Shokrieh and R. Rafiee, “Simulation of fatigue failure ina full composite wind turbine blade,” Composite Structures, vol.74, no. 3, pp. 332–342, 2006.

[10] D. J. Malcolm and D. L. Laird, “Extraction of equivalent beamproperties from blade models,” Wind Energy, vol. 10, no. 2, pp.135–157, 2007.

[11] Y. Zheng, R. Zhao, andH. Liu, “Optimizationmethod for girderof wind turbine blade,” Mathematical Problems in Engineering,vol. 2014, Article ID 898736, pp. 7–9, 2014.

Submit your manuscripts athttps://www.hindawi.com

Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttp://www.hindawi.com

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation http://www.hindawi.com Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Journal of

Hindawi Publishing Corporationhttp://www.hindawi.com

Volume 2014 Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014

Stochastic AnalysisInternational Journal of

structural optimization design of large wind turbine blade...

Documents