Download Design of a 50kW Wind Turbine

Design of a 50kW Wind Turbine
Mathematics in Industry Study Group
African Institute for Mathematical Sciences
Neville, Faikah, Guy Olivier, Tshifhango, Belinda, Rayhab,
Sergio
January 15, 2010
Contents
Introduction
Wind Turbine Design
Blade Design
Tower
Power
Results and Conclusion
Introduction
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Description of the problem
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Motivation
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Design of a wind turbine for an eco-village in the north
coast of Durban utilising the increasing sea wind
Load shedding
Back energy supply and hybrid systems
Objective
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Vane size and Blade shape
Number of blades
Height of the tower
Contents
Introduction
Wind Turbine Design
Blade Design
Tower
Power
Results and Conclusion
Wind Turbines
Orientation - HAWT vs VAWT
Figure: Horizontal Axis Wind Turbine; Vertical Axis Wind Turbine
Orientation - HAWT vs VAWT
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Vertical Axis Wind Turbines (VAWT)
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Advantages
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Disadvantages
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Omnidirectional
Components can be mounted at ground level
Can theoretically use less materials to capture the same
amount of wind
Omnidirectional
Poor self-starting capabilities
Overall poor performance and reliability
Horizontal Axis Wind Turbines (HAWT)
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Advantages
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Rotors are usually up-wind of tower
Commercially successful
Disadvantages
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More expensive
Orientation - Upwind vs Downwind
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Upwind Turbines
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Downwind Turbines
Orientation - Yaw
Yaw
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Active Yaw : all medium and large turbines
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Anemometer on nacelle tells controller which way to point
rotor - into the wind
Yaw drive turns gears to point rotor into wind
Passive Yaw : Most small turbines
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Wind forces alone direct rotor
Tail vanes
Downwind turbines
Contents
Introduction
Wind Turbine Design
Blade Design
Tower
Power
Results and Conclusion
Blades
Airfoil: Characteristics
Wind turbines use the same aerodynamic principals as aircraft
Airfoil: Angles
The relative wind speed is the wind speed seen by the airfoil,
i.e. vector sum of U (free stream wind) and ΩR (tip speed).
There is an optimum angle of attack, αA , which creates the
highest lift to drag ratio.
Airfoil: Lift and Drag
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The Lift Force is perpendicular to the direction of motion.
We want to make this force BIG.
The Drag Force is parallel to the direction of motion. We
want to make this force small.
Airfoil: Stall
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Stall arises due to separation of flow from airfoil
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Stall results in decreasing lift coefficient with increasing
angle of attack
Tip Speed Ratio
Tip speed ratio, λ, is the ratio of the speed of
the rotating blade tip, ΩR, to the wind speed, U.
Because the angle of attack, αA , is dependant on wind speed,
there is an optimum tip-speed ratio:
λ=
ΩR
U
Twist and Taper
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Tapering minimises the vortex shredding
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To optimize angle of attack, αA , all along the blade, it must
twist from root to tip
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Number of Blades
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One
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Three
Two
Solidity
Solidity is the ratio of the total blade area to the swept area.
Material
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Wood -
Strong, lightweight, cheap
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Metal (steel, aluminium) subject to metal fatigue
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Fiberglass Lightweight, strong, inexpensive,
good fatigue characteristics
Expensive,
Contents
Introduction
Wind Turbine Design
Blade Design
Tower
Power
Results and Conclusion
Tower
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Monopole
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Lattice Steel Structure
Contents
Introduction
Wind Turbine Design
Blade Design
Tower
Power
Results and Conclusion
Scaling, Scaling, Scaling: The Rotor Power Coeff
The maximum available power from the wind per unit area is
Pw =
1 3
ρU :
2 w
U the vel of the wind, ρ density of the air.
Can’t do better!
Now on dimensional and physical grounds we have:
The Rotor Power Coeff: (Efficiency)
PT /A
= fn(λ, α, dimensionless geom blade factors, Re, · · · )
Pw
PT is the power output from the turbine, A the rotor area.
Scaling Again
ET =
PT /A
= fn(λ, α, dimensionless geom blade factors, Re, · · · )
Pw
In order of importance:
ΩD/2
Uw
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λ is the tip speed ratio
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α is pitch angle (sort of angle of blades to the wind)
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S the ‘solidity’= Projected area of blades/A
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B blade number
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Blade taper=t/b, Tip shape,
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Blade sectional shape
(D rotor diam),
Pitch Angle, Retardation
If additionally we choose α = αopt (λ) we get
PT /A
= fn(λ, S, B, t/b, Re, · · · )
Pw
Ideally we would use theory to find fn, but we can use
experiments, computing, theory.
ET =
Figure: Retardation: Actuator Disk Theory
Retardation: Betz Limit
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The major performance limitation is caused by ‘retardation’.
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The rotor diverts air away from the rotor (Rankine-Froude
Theory).
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The fractional loss (area entering rotor/A) is 16/27,
i.e. (0.59), The Betz Limit. So if we write,
∗∗E =
16
· fn1 (λ, S, B, t/b, Re, · · · ) ∗ ∗
27
16
Can’t do better than E = 27
!
**With correct design we can almost achieve this limit!**
Tip Speed: Air Rotation Losses
The rotor introduces rotation in it’s wake; an energy loss.
Evidently tip speed is the primary parameter here: Also one
needs to extract energy from the rotor (how much?).
(Blade Element Theory, Vortex Theory.)
Figure: Tip Speed Effects: Blade Element Theory
Note by correctly choosing λ we get within 10% of Betz Limit!
So all other design features are marginal!
Solidity and Blade Number Effects
Solidity= fractional area of A covered by the blades
Its values affects the fractional time the foils obstruct the air
flow, the aerodynamics etc. Blade element theory gives:
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S = .029, .034 achieves optimum power output.
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B = 2, 3
Figure: solidity: blades with equal and unequal solidity
Other design Features
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Taper
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Tip shape
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Sectional shape
Note that these are all marginal issues!
Design Principles
1. Use Betz Limit + cost function C = C(H, D) to determine
H, D
16 1 3
∗ ∗ PT =
ρU (π(D/2)2 ) ∗ ∗
27 2
2. Adjust machinery to give λ = 5
3. Choose solidity S = .029, B = 2 or 3
Note ∝ to D 2 U 3 .
4. Choose standard sectional area, blade designs
Look at local wind variations: use Weibull model to see
variability of power output over a year.
Contents
Introduction
Wind Turbine Design
Blade Design
Tower
Power
Results and Conclusion
Wind Speed
Using the formula
ρ π
P = cP η vw3 D 2
2 4
We note that the power is dependant on U 3 and we solve for
the rotor diameter, D, with varying wind speeds:
U = 15; 12.5; 10 and 5 m/s
Height of the Tower
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Wind Boundary
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Height
Height of the Tower
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For equivalent power output, either large rotor diameters
with a shorter height or a smaller rotor diameter with a
much higher tower
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Once again the cost in manufacture and maintenance
becomes vital
Number of blades
We note that the power is dependant on D 2 . For the number of
blades we looked at the solidity of the turbine
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For equivalent values of the solidity
3
=2
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Same power output
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Advantages and disadvantages become a factor,
especially the cost involved in the manufacture and
maintenance of the blades
Blade Design
Considering all the factors involved
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Taper
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Tip shape
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Sectional (airfoil) shape
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Twist
together with the calculations, we note that these are all
marginal issues!
Thank You