functionally graded material blades with enhanced aeroelastic...

MatWind2011

May 15-16, 2011, Cairo, Egypt

Functionally Graded Material Blades with

Enhanced Aeroelastic Performance

Karam Y. Maalawi

National research Centre

Mechanical Engineering Department

Main Aim of This PresentationImprovement of aeroelastic stability ofcomposite blades using FGM s concept.

Simplified model of a composite tapered bladeis analyzed, where the composition of thematerial of construction is optimized usingeither continuous or discrete variations ofvolume fractions along the blade length.

The major aim is to tailor the materialdistribution in the spanwise direction so as tomaximize the critical wind speed at which bladefailure might occur without the penalty ofincreasing structural mass.

What is FGM ?

FGMs may be defined as advancedcomposite materials that fabricated to havegraded variation of the relative volumefractions of the constituent materials.

Example: A composite material made from a

mixture of ceramic and metal. Ceramicprovides high temperature resistancebecause of its low thermal conductivitywhile metal secures the necessary strengthand stiffness.

Material Grading

Production of laminated Composites

The knowledge on processing methods forpolymer FGMs is limited.

Long-fiber reinforced polymers with gradedcomposition can be produced by laminationtechniques.

The resins are redistributed between theprepreg layers during molding.

Design variables

- Properties of fibers and resins

-No. of layers.

-Thickness of each layer.

-Fiber orientation in each layer.

-Fiber volume fraction in each layer.

o90

o60

o90

o0

o0

o0

o0

o60

o60

o60

12/07/1432 Lamination Theory 10

y

z

x

Exploded view of a [+60/0/-60] quasi-isotropic laminate

)x-1( p

Power-law model:

Vf(x)=Vfr

Material grading.The physical and mechanical properties areallowed to vary lengthwise, yielding to gradingof the material in the direction of the bladeaxis. Assuming no voids are present, we have:

Volume fractions : VA(x) + VB(x) =1

Mass density : (x) = VA(x) A + VB(x)

B

Young’s Modulus : E(x) = VA(x) EA+ VB(x) EB

Shear Modulus

+)G/G(

1-)G/G(= ,

V-1

V+1G=G

mf

mf

f

fm12

G=f1 G12

Advantages of Fabricating Blades from Composites

Higher stiffness-to-weight ratio.

Superior fatigue characteristics.

Corrosion resistant.

Material anisotropy provides direct bending-axial-torsion elastic coupling.

Use of aeroelastic tailoring to improve rotor blade design.

Optimization

is the art of obtaining best policies to satisfy

certain objectives, at the same time satisfying

fixed requirements.

Design Optimization is the process for the

selection of the best choice from among all

possible designs that are available.

General Statement of theOptimum Design Problem.

Find the set of design variables Xnx1 that will

Minimize Fi (X) , I=1,2,…k Subject to

Gj(X) 0 , j=1,2,………I

Gj(X) = 0 , j=I+1,I+2,….m

Integrated formulation (FEM)

[K]{U}={P} [K]{U}-{P}={0}

Design Optimization Packages

FE Software are developed including optimization capabilities.

CONMIN _ NASTRAN _ ANSYS

ASTROS _ GENESIS _ ABACUS

MATLAB Optimization Tool Box

Optimization routines are made available as MATLAB M-files.

The user supplies the Objective function and constraints information to the tool box as M-files.

www.mathworks.com/access/helpdesk/help/toolbox/optim

Multi-Objective Optimization

Design Objectives of an Advanced Blade

High Power

Coeff.

High

Stiffness/Weight

Low vibration

Long fatigue life

The Optimal Design Problem

Stiffness.wWeight.w)XF( .Min 2f1f

? w

? w

f2

1f

Weight minimization and Stiffness maximization

The Optimal Frequency Problem

ii

fiw)XF( .Max

XXX

MM

UL

0

Natural frequencies are the most representative of the overall Stiffness/Weight level of the blade structure

Subject to

Resonance avoidance

XXX

M Mto Subject

)(w)XF( .Min

UL

o

2*i

iifi

Aeroelastic Optimization

Aeroelasticity is the study of the effect ofaerodynamic loads on elastic bodies.

Aeroelasticity is one of the most importantconsiderations in aerospace industry.

When the energy of the flow is rapidlyabsorbed by the structure, violent vibrationswith rapidly increasing amplitude occur,which might cause structural dynamicinstability termed as Flutter.

An illustration: Blade divergence

The rotation of the airfoil, and theconsequent twisting of the blade, is afunction of the airspeed.

Structural failure Xe

UD

U

Elastic twist vs wind speed

Aeroelastic Phenomena

When the wind speed exceeds a certain value calleddivergence speed, Vdiv, the aerodynamic twist momentapplied to the blade exceeds the restoring elastic momentof its structure.

This causes static torsional instability of the blade, whichmay twist to failure.

Therefore, high divergence speed can be regarded as amajor aspect in designing an efficient blade with enhancedtorsional stability.

Max. Divergence Speed

•Maximization of the divergence speed can have other

desirable effects on the overall structural design.

•It helps in avoiding the occurrence of large displacements,

distortions and excessive vibrations, and may also reduce

fretting among structural parts, which is a major cause of

fatigue failure .

•A solution that can be promising to enhance aeroelastic

stability of composite blades is the use of the concept of

functionally graded materials , FGMs.

The associated Eigenvalue Problem

0=

Boundary Conditions

at x=b 0=x∂

∂GJ

at x=0

0=)x(eaCV2

1+)

xd

dGJ(

xd

d1

22

11

Considering tapered blade with thin-walled airfoil section

)x̂-1(C=C o

)x̂-1(h=h o

L

xx̂

)Δ-1(=

)x̂-1(hC∝J4

o3o

I-Continuous linear model

Power Series Solution

)x(λ∑C=)x(α m

2

1=mm

∑ )x(a=)x(λ∞

m=n

1-nn,mm

m=1, 2 (n m)

y

)ya2(YA-

y

)ya2(JA=)y(

k22

k21

II-Piecewise model

Bessel’s function method

Case Study

Linear distribution of V(x)

Piecewise model: 2-panel blade

Combined Material and Thickness Grading

CONCLUSIONS

Efficient model for enhancing aeroelastic stability ofa wind turbine blade using FGM has been formulated.

Exact solutions have been given analytically usingBessel’s function method.

The model formulation is independent on the size ofthe rotor, blade geometry and type of material.

Extension of this work shall consider simultaneousgrading in both thickness and span directions.

http://www.intechopen.com/books/ show/title/wind-turbines

Hurghada Wind Farm. Thank You