Functionally Graded Material Blades with Enhanced Aeroelastic...
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MatWind2011 May 15-16, 2011, Cairo, Egypt Functionally Graded Material Blades with Enhanced Aeroelastic Performance Karam Y. Maalawi National research Centre Mechanical Engineering Department
Transcript of 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
