E N G I N E E R I N G S I M U L A T I O N S Y S T E M

BLADE DESIGN OPTIMIZATION Authors : Federico Grubissa, Filippo Giacometti

Company: ENSIS di F. Giacometti & C. sas - Venice

WIND TURBINE 1st TECHNOLOGY FORUM

Venice, 12 May 2011

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INTRODUCTION The process of designing wind generators blades is now of great interest in the field of applied

engineering. The optimization of performance of a turbine generator depends on a mix of several factors, as for example:

• Airfoil profile;

• Chord and twist distribution; • Blade dimension;

• Stiffnes/Weight Ratio; • Cost.

The study of these factors requires the iterative integration of different

types of analysis that generally are developed in different software environments.

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The purpose of this work is to integrate all the design processes into a single tool developed in

MSC/PATRAN Command Language (PCL) and VBA in Excel.

The main steps of the process are:

AIM

By developing suitable scripts in these two languages, it is possible to increase the performance of the two

basic software in an automatic process that would otherwise require considerable skill and time consuming.

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cr

Lr

r

cr

WHY?

To Distributed Pressure Load

From Concentrated Aerodynamic Loads

The idea comes out from the request of easily and quickly obtaining the distribution of pressure loads

around the blade FE Model rather than the concentrated load at a predefined blade section.

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3D Geometry Optimization For insertion of the input design data (Customer

Requirement), the Excel interface was used, friendly accessible to any user: • Power

• Nominal Wind Speed • Tip Speed Ratio

• Number of Blades • Airfoil Profile from an integrated database.

Once defined the Input Data, the first step is

optimizing the blade geometry, in terms of distribution of: • chord

• twist along the wingspan, in order to obtain the best

rotor performance

The tool allows to compare performances of the

optimal designed blade with simple design blade (for example with constant chord and linear variation of the twist)

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The typical diagram can be used to study the

turbine performance

Section for rotor performance calculation

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• 3D opt Geometry optimization

• CP,max maximisation of

Power Coefficinet

• CP,max(r) thorugh power coefficient maximum at each blade sec.

• = (CD/CL)min(r) Obtained by minimization of

glide ratio

• CL,design(r) by polar diagram of the airfoil

design

Optimal inflow angle calculation

Twist calculation

Considering Tip/Hub loss correction

Chord calculation

The geometry optimization is based on the maximization of Power Coefficient

Vo

W

r

CHORD DISTRIBUTION

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.00 0.25 0.50 0.75 1.00

r/R

TWIST DISTRIBUTION

-10.00

-5.00

0.00

5.00

10.00

15.00

20.00

25.00

0.00 0.25 0.50 0.75 1.00 1.25

r/R

ottrrottrdesignL

ottrrottrottr

rBC

rFc

,,,

,,,

cossin

sincossin8

r

ottr a1

tan3

2,

,r ott design

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Finite Element Model Generation

FEM is automatically generated by means of a PCL tool that translate dimensional and geometrical information into a surface 2D mesh.

-0.080

-0.060

-0.040

-0.020

0.000

0.020

0.040

0.060

-0.100 -0.050 0.000 0.050 0.100 0.150 0.200 0.250 0.300

Serie1Serie2Serie3Serie4Serie5Serie6Serie7Serie8Serie9Serie10Serie11Serie12Serie13Serie14Serie15Serie16Serie17Serie18

Once defined blade geometry and dimension along the wingspan (i.e.): • Airfoil profile • Chord distribution • Twist distribution

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Aerodynamic Load Calculation Third step is computation of aerodynamic pressure loads around the blade in order to carry out a

detailed structural analysis. To obtain this load condition, equations of bi-dimensional potential flow around a wing sections of

arbitrary shape, according to the procedure described by Tehodorsen, were implemented in PATRAN by means of a detailed PCL:

• Jukowsky Transformation In order to solve the above computation is necessary the effective attack angle of each airfoil

section along wingspan, which is a function of tangential velocity and average wing speed profile, as calculated by:

• BEM Theory

( ) hub

hub

zV z V

z

The average wind speed profile,function of height (z) above

the ground, is:

is the power law exponent ( =0.2)

Vt= r

V(z)

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V

ui=aVo a=axial induction factor =a’2 a’=angular induction factor

po p1 r

p p

VD Vo-ui

/2=a’

In order to define the effective attack angle is necessary to

iteratively define the axial (a) and angular (a’) induction factor along wingspan, the "Blade Element Momentum (BEM) Theory“ was implemented with following corrections :

• Glauret empirical relation for axial induction factor;

• Prandtl Tip-Hub loss correction (F); • Yawed Flow Correction ( );

Definition of effective attack angle

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Theoretical computation of pressure distribution about an arbitrary

wing section has been implemented using potential flow formulation and conformal transformation of the airfoil section into a circle. Theory is exact for perfect fluid flow:

nonviscous and incompressible.

where:

Where:

• V is the velocity of undisturbed stream • the 2D angle of attack

• , , parameters functions of the airfoil

coordinates • 0 the mean value of

0 0sin sin T

vF

V

0

22 2

1

sinh sin 1

d d eF

d d

h 0.31416 0.1040

n ∫ d d d d d k'

1 0.00 0.00000 0.179 - 0.000 0.0716- 0.060 6.178

2 0.10 0.31416 0.192 0.1211 0.047 0.0526- 0.074 3.039

3 0.20 0.62832 0.208 0.038 0.0251- 0.106 1.777

4 0.30 0.94248 0.213 0.1324 -0.008 0.0123 0.124 1.326

5 0.40 1.25664 0.203 -0.055 0.0498 0.109 1.139

6 0.50 1.57080 0.180 0.1127 -0.083 0.0791 0.077 1.088

7 0.60 1.88496 0.152 -0.095 0.0983 0.048 1.147

8 0.70 2.19911 0.121 0.0755 -0.107 0.1089 0.019 1.349

9 0.80 2.51327 0.086 -0.112 0.1093 -0.018 1.856

10 0.90 2.82743 0.052 0.0334 -0.101 0.0969 -0.064 3.523

11 1.00 3.14159 0.025 -0.061 0.0704 -0.095 44.961

12 1.10 3.45575 0.014 0.0094 -0.022 0.0398 -0.095 3.586

13 1.20 3.76991 0.009 -0.003 0.0117 -0.088 1.887

14 1.30 4.08407 0.012 0.0081 0.018 0.0152- -0.081 1.371

15 1.40 4.39823 0.020 0.031 0.0391- -0.073 1.166

16 1.50 4.71239 0.031 0.0202 0.044 0.0615- -0.071 1.108

17 1.60 5.02655 0.048 0.067 0.0835- -0.067 1.163

18 1.70 5.34071 0.074 0.0472 0.095 0.1025- -0.053 1.360

19 1.80 5.65487 0.108 0.130 0.1141- -0.008 1.841

20 1.90 5.96903 0.151 0.0934 0.113 0.1046- 0.068 3.202

21 2.00 6.28319 0.179 0.000 0.0716- 0.060 6.178

Jukowsky Transformation

2

1v

CpV

Pressure distribution is given by the

pressure coefficient, evaluated by Bernoulli’s equation:

E N G I N E E R I N G S I M U L A T I O N S Y S T E M

-3.50

-3.00

-2.50

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

-20.0 0.0 20.0 40.0 60.0 80.0 100.0 120.0

alfa=8°sper

Mod Theory

cpt

Pinkerton empirical correction for

the presence of viscous effects in actual flows has been integrated in the computation when the

experimental Cl of the section is known. The parameter is modified:

EMPIRICAL MODIFICATION OF THE THEORY

Theory

Modified theory

Experiment

d d F ka (v/V) (v/V) mod cp cp mod

-0.0716 0.060 6.55 6.55 4.48- 3.19- 19.05- 9.19-

-0.0478 0.105 3.26 3.36 1.18- 0.54- 0.40- 0.71

-0.0061 0.164 1.96 2.07 0.05- 0.40 1.00 0.84

0.0535 0.205 1.49 1.60 0.44 0.84 0.81 0.30

0.1188 0.204 1.26 1.37 0.69 1.07 0.53 0.13-

0.1790 0.177 1.17 1.28 0.81 1.16 0.35 0.35-

0.2290 0.143 1.20 1.31 0.87 1.18 0.25 0.40-

0.2676 0.100 1.37 1.48 0.89 1.15 0.20 0.32-

0.2900 0.041 1.82 1.93 0.89 1.07 0.21 0.15-

0.2918 -0.033 3.30 3.41 0.86 0.97 0.26 0.06

0.2702 -0.095 0.90 0.90 0.18 0.18

0.2347 -0.126 3.25 3.14 0.91- 0.87- 0.17 0.24

0.1925 -0.146 1.72 1.61 0.97- 0.86- 0.06 0.26

0.1434 -0.162 1.26 1.15 1.04- 0.86- 0.07- 0.26

0.0916 -0.168 1.08 0.97 1.12- 0.89- 0.26- 0.20

0.0384 -0.171 1.03 0.92 1.23- 0.95- 0.51- 0.10

-0.0144 -0.162 1.08 0.97 1.38- 1.05- 0.89- 0.10-

-0.0613 -0.134 1.29 1.18 1.62- 1.24- 1.63- 0.54-

-0.0950 -0.066 1.83 1.72 2.12- 1.65- 3.51- 1.71-

-0.0997 0.037 3.42 3.32 3.32- 2.56- 9.99- 5.53-

-0.0716 0.060 6.55 6.55 4.48- 3.19- 19.05- 9.19-

mod 1 cos2

Tified

Airfoil NACA 4412 @ =8

Xfoil output:

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The PCL code computes the aerodynamic pressure loads on variable profile of the blade along the wingspan

PATRAN IMPLEMENTATION

NACA 4412 @ =8

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STRUCTURAL ANALYSIS By mean of the procedure described above, it is possible to carry out results for an optimized blade

turbine design including structural feasibility in few hours.

PATRAN Lay-up definition

Failur Index

E N G I N E E R I N G S I M U L A T I O N S Y S T E M

CONCLUSION Through the Visual Basic for Applications (VBA) and Patran Command Language (PCL), in Excel

and Patran environments respectively, an integrated process has been developed for the geometric optimization, three-dimensional modeling and structural analysis of blades of horizontal axis wind turbines in order to optimize the strategic phases of the feasibility study and design

In this work, rotor turbine performances and blades structural analysis have been computed

considering a static aerodynamic load. As continuation of this work, a dynamic analysis for determining the fatigue life of the blade will be

performed.

In this case it will be necessary to define the periodic load due to the rotation of the blade in function of the azimuth angle.

This kind of tool will be able in this way to computes a complete analysis according to the aeroelastic model defined in IEC 61400.

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Contacts: ENSIS sas Campo San Cosmo 624/625 Giudecca, 30133 VENEZIA

Tel & Fax: +39 041 2006397 info@ensis-ve.com www.ensis-ve.com