1. Wind Turbine Project Recap Wind Power & Blade Aerodynamics

2. Wind Turbine Project
Turbines tested indoors under controlled conditions
A single metric for success - amount of electricity generated
Design will be executed using theoretical calculations- build and test ONCE at end! (with one trial fitting)

3. Harnessing available power in wind
Max available power
How can we predict blade performance?
Blade aerodynamics
Rotor performance

4. At best only 45% can be captured by real turbines (theoretical limit).
Power coefficient
How well is our turbine performing?
requires blade and
rotor physics
Cp =
Rotor power
Power in the wind
At best only 45% can be captured by real turbines (theoretical limit).

5. Project estimates – class exercise (5 min)
Available power
Estimating maximum Pgenerated

6. Project estimates – class exercise (5 min)
Available power
P = 60 W
Estimating maximum Pgenerated

7. Atlantic City estimates – class exercise (5 min)
Now assuming the offshore wind velocity is12 m/s
The diameter of a turbine is 73 m, there are 5 turbines
Estimate of maximum Pgenerated

8. Blade aerodynamics Turbine blades are airfoils
We need to understand blade aerodynamics to determine effectiveness and performance

9. Airfoil terminology R U∞ α W C Free stream velocity
Relative wind velocity C

10. Airfoil types NACA airfoils NACA 2412 NACA 0012
National Advisory Committee for Aeronautics
NACA 2412
maximum camber of 2% located 40% from the leading edge with a maximum thickness of 12% of the chord
NACA 0012
symmetrical airfoil, 00 indicating no camber.12 indicates that the airfoil has a 12% thickness to chord

11. Airfoil function – generation of lift
weight
thrust
drag
lift
‘suction’ side
‘pressure’ side

12. Airfoil forces Lift force perpendicular to airflow Drag force
parallel to the airflow

13. Calculating lift and drag
Power = Force x Velocity
Force in the wind
geometric factor
Force generated by airfoil

14. Coefficients of lift and drag
Lift coefficient
CL = how effectively the wing turns available dynamic pressure (kinetic energy) into lift
Drag force
Drag coefficient
CD = how much of the pressure (kinetic energy) is converted to drag

15. Coefficients of lift and drag

16. Coefficients of lift and drag5 10 15 20 25 30
0.25
0.50
0.75
1.00
1.25
1.50
1.75
Angle of Attack (degrees)
Lift/Drag Coefficient
lift
coefficient
drag
Geometric factors
CD and CL
Depend on:
airfoil shape
angle of attack
Empirically determined

17. Airfoil behavior

18. Performance parameters
Drag
Thrust
Lift
Direction of
translation
Torque
Rotational Speed
Free stream
Wind velocity
Relative
wind velocity
Wind turbine performance based on
lift and drag coefficients
Pitch angle, b - angle btwn chord line and plane of rotation
Angle of attack, a - angle btwn blade and relative wind, which changes depending on speed of blade and wind speed
K.L. Johnson (2006) a

19. Lift and drag on translating air foil
What force actually provides useful work to rotate the turbine?
Lift
Drag F1 F2
K.L. Johnson (2006)

20. Lift and drag on translating air foil
K.L. Johnson (2006)
F1 is force to rotate the turbine
Tower must be strong enough to withstand thrust force F2

21. Connection to wind turbines
lift and drag cause the rotor to spin
angle of attack changes over the span of the blade
lift and drag forces also change over the span of the blade
Next How to calculate torque generated from lift and drag on each blade?

22. Complications
Free stream characteristics change approaching and across blades
Rotation of blades causes counter rotation in wind
Things vary with r
Must use
conservation of mass
Conservation of momentum
Conservation of energy

23. Things vary with r : Blade Element Theory (BET)
Blade divided into sections, on which momentum is applied
Result is nonlinear equations that can be solved iteratively
*Does not consider shed tip vortex. Some flow assumptions made breakdown for extreme conditions when flow becomes stalled or a significant proportion of the propeller blade is in windmilling configuration while other parts are still thrust producing.

24. Free stream characteristics change…
Variables
r – density (constant)
A – cross-section area
U – wind speed
p – pressure
T – thrust of wind on turbine
If a tube of air is moving with diameter d1, speed u1, and pressure p1 as it approaches turbine, the air speed decreases, causing the tube of air to increase to d2. Air pressure rises in front of turbine and drops behind the turbine. Part of the kinetic energy (KE) of air is converted to potential energy (PE) to create the pressure increase and more KE is converted to PE after the turbine to return the pressure to atmospheric. Wind speed decreases until pressure is in equilibrium and u4 = u1.
Circular tube of air flowing through ideal wind turbine (K.L. Johnson 2006)

25. BET Limitation – Axial Induction factor
accounts for wind speed reduction as wind approaches turbine
Consider the limits:
No reduction in wind speed
Wind stops downstream, model invalid

26. Power and Power coefficient
Theoretical Power
Coefficient of Power
Theoretical max Cp, set
Sub 1/3 into Cp to get max of 16/27 = (Betz Limit) only 59% of max theoretically possible.
Value of 1 invalidates model (not btwn 0 and ½)

27. Counter rotation of wind: Blade Momentum Theory
Angular Induction factor
accounts for reduction due to rotational wake
Consider the limits:
No induced rotation
Induced rotation, w equal and opposite to rotor rotation
Rotor induces rotation in opposite direction of blade rotation
W – Rotor rotational velocity
w – Induced wind rotational velocity

28. Angular velocity of rotor affects local wind at blade
Drag T
Lift Q

29. Power Generated by Turbine
Power = Torque * rotational velocity

30. Solidity ratio Closed versus open area
B*c = net chord length of ALL blades
2pr = total circumference at radius, r

31. Blade Element Theory (cont’d)
Difference in angle between thrust and lift directions
V0 - axial flow at propeller disk, V2 - Angular flow velocity vector
V1 - section local flow velocity vector, sum of vectors V0 and V2
Blade will be set at a given geometric pitch angle (q), lift and drag components calculated so that the contribution to thrust and torque of the complete
propeller from this single element can be found

32. Constraints and Materials
Max diameter of wind turbine = 1 meter
Max number of blades is 12
Hub is given and has a radius of 0.05 meter made of plastic
Must be a horizontal axis wind turbine
With blades that are thin flat plates (remember that our model is also developed for aerodynamics of blades/airfoils that are thin flat plates), so we’ll use foam board
Attach blades to hub with wooden dowel rods

33. Parameters and/or Variables
Primary
Pitch of blades, which in turn affects angle of attack
Cord/shape of blades
Constant cord – to make simple rectangular blades
Variable cord – to make another shape (triangle, parallelogram, etc.)
Secondary
Number of blades <=12
Radius <= 0.5 meter

34. Performance metrics and evalutation
Plot theoretical results of Coefficient of Power (Cp) versus angular velocity of the hub and determine the conditions for which a max occurs (note, power is related to performance, how well does your turbine perform)
On test day, we will measure electrical output (voltage and current, recall P(elect) = V*I) and angular velocity.
You’ll see how well results match predictions. Just as in the bottle rocket project, that’s what matters to find a max for your conditions, predict it and achieve it.
Cp, Coefficient of Power
w, Rotational Speed

35. Definitions W – relative wind speed Uinf - free stream wind speed
a – angle of attack
b – blade pitch
a – axial induction factor
a’ – angular induction factor
f – relative angle of wind
B – number of blades
CL – coeficient of lift
CD – coefficient of drag
Q, dQ- total blade torque, torque on differential element
Cp - coefficient of power

36. Matlab Pseudo Code: Find these steps!
Inputs: number of blades N, chord length c, blade span R, blade angle δ
For a range of rotational speeds ψ
For a range of blade elements dr up to the blade span R
While a and a’ converge
Calculate relative wind velocity W using
Calculate a using Eq.
Calculate angle of attack χ using
Use the empirical data to evaluate CL and CD for the χ
Calculate new a and a’ using
End
Calculate the differential blade torque dQ for the blade element
Sum the elemental contributions dQ to the total torque Q
Calculate power by the product of total torque Q and rotational speed ψ
Calculate coefficient of performance Cp for the rotational speed ψ
Plot coefficient of performance as a function of rotational speeds ψ

37. Generator Performance Curves
Recall that losses occur converting mechanical power from the turbine to electric power by the generator
Test or find specifications for generator performance