Ashby / wind turbine PC 3

PHY563 – 13/01/2021

JF Guillemoles

N. Schneider

Materials for Energy[PHY563]

Ashby / wind turbine

PC 3

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References

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• Assemble data database

• Formulate list of constraints

• Decide on the criterion to rank the candidates objectives

• Research the top-ranked candidates seek documentation

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Material selection strategies

Ashby, Materials and the Environment: Eco-informed Material Choice, 2012, 2nd edition

Simple example: choosing a car

If 2 or more objectives, a compromise is neededtrade-off methods

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Simple example: selecting a material for a portable bike shed

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• Translation

= Convert design requirement into contraints and objectives that can be applied to

material databases

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• Screening = constraints on material property charts

Material property charts : bar and bubble charts

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• Ranking = indices on material property charts

(indices are necessary as often more than one property is required)

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• Ranking = indices on material property charts

(indices are necessary as often more than one property is required)

Possibility to use these indices for scaling and evaluating material substitution

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Ashby, Materials and the Environment: Eco-informed Material Choice, 2012, 2nd

edition

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Wind turbine – Materials for blades

What is the best material for the blade of a wind turbine?

What are the two main loadson the blades?

How does it translate intomaterials requirements?

Which physical propertiesshould we look at?

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Several materials issuesBlades, magnets, Towers,

Several sizesDifferent mechanical needs

(working conditions)Different costs


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Mechanical properties

• Stiff : keep good aerodynamic performanceYoung’s module

•Strength : long-fatigue life to reduce degradation (cracking, buckling…) Lifetime >20 years

Elasticity / SN curve

•Light : no gravity effects, easy installation, dynamic equilibrium (reactivity with wind fluctuations)

volume density


http://www-materials.eng.cam.ac.uk/mpsite/

http://www-materials.eng.cam.ac.uk/mpsite/

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Stiffness:- Performance- Specifications

Stiffness / Density- Deformation versus weight


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Appendixes

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Mechanical problems – Bending of the tower

3 Blades : 50x3m²Tower h=100m r=4m t=0.5mWind velocity : 50m/s

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What is the deflection at the top of the tower?Evidence the importance of the E/ρ ratio for a mass optimisation ?

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Beam deflections :

Rod of length L, radius r :

= 4 L3 F / 3p E r4

M = p L r2

Solve and substitute:

M = (4pL5F / 3)1/2 ( / E 1/2)

M1 = ( / E 1/2)

F

L

Example: rotor for wind turbine

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Strength


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Buckling

Wind turbines:

• Buckling effect assuming a weight

of 100 tonnes (rotor+nacelle) ?

• Smallest mass within specs?

PHY563 – JF Guillemoles

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Tube buckling :

? ?

Post of length L :1. Mass:

m = 2p r tL

2. Moment of inertia

I= p r3t

3. Critical force for buckling

Fcrit = p 2 EI = p 3Er3t

L2 L2

Solve and substitute:

m = (2L3 Fcrit / p 2 r²).(/ E)

M2 = ( / E)~ 1/vsoundExample: Tower for solar thermal or wind turbine


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2 MW wind turbine is:

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Material selection charts

Light and rigid design: log-log scales makes optimal indices readily

apparent

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Same line => same mass =>

cost evaluation

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Materials Selection Charts

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Disc deflection

= 0.67 Mga2

p E t3

Mass = pa2 t

solve for t and substitute:

M = (0.67g / )1/2 pa4 (/ E1/3)3/2

M3 = (/ E1/3)

2a

t

W=mg

Example: parabolic mirror for solar thermal

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x10 the wind speed

Power coefficient variations – Pmeca/Pwind max at 59.25% by Betz

Angle of attackBlade design

Most common


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Example : Betz boundary (1)36

Hypothèses : fluide incompressible

Densité volumique de masse : ρ

Th. de Bernouilli : r v2

2+ P+ rgz= Cste

Surface de section balayée par les pales : A

Variation de la vitesse : V1>V>V2

Conservation de la masse :

rA1V1 = rAV = rA2V2

Puissance extraite (énergie cinétique) :

Wout =1

2rAV( ) V1

2 -V2

2( )

Puissance extraite (impulsion) :

F = rAV( ). V1 -V2( )

Wout = F.V = rAV2. V1 -V2( )

V =V1 +V2

2

Puissance maximale :

dWout

dV2

= 0®V2 =V1

3

Ligne de débit constant.

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Example : Betz boundary(2)37

Puissance extraite :

Wout =1

2rAV( )

8

9V1

2

Efficacité d’extraction de l’énergie :

h =Wout

Win

Attention aux définitions ! Quelle est la puissance incidente ?

Puissance incidente (Betz) :

Win =1

2rAV1

3 ®h =16

27» 59%

Puissance incidente (J-M Rax) :

Win =1

2rAV( )V1

2 ®h =8

9» 89%

• La limite ne vient pas de phénomènes de dissipation et de production d’entropie, mais de l’incompressibilité du fluide.

• Compromis entre l’efficacité d’extraction et le débit.

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Pressure vessel

38Références

Stress on wall

Mass

Ashby / wind turbine PC 3

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