Wind Turbine Project Recap
Wind Power & Blade Aerodynamics
Wind Turbine Project
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Turbines tested indoors under controlled conditions
A single metric for success - amount of electricity
generated
Design will be executed using theoretical calculationsbuild and test ONCE at end! (with one trial fitting)
Harnessing available power in wind
Max available power
How can we predict blade performance?
Blade aerodynamics
Rotor performance
Power coefficient
How well is our turbine performing?
Rotor power
Cp =
Power in the wind
At best only 45% can be
captured by real turbines
(theoretical limit).
requires blade
and
rotor physics
Project estimates – class exercise (5 min)
Available power
Estimating maximum Pgenerated
Project estimates – class exercise (5 min)
Available power
P = 60 W
Estimating maximum Pgenerated
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
Blade aerodynamics
Turbine blades are airfoils
We need to understand blade
aerodynamics to determine
effectiveness and performance
Airfoil terminology
R
Free stream
velocity
U∞
W
α
Relative
wind velocity
C
Airfoil types
NACA airfoils
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
Airfoil function – generation of lift
lift
thrust
drag
weight
‘suction’ side
‘pressure’ side
Airfoil forces
Lift force
perpendicular to airflow
Drag force
parallel to the airflow
Calculating lift and drag
Power = Force x Velocity
Force in the wind
geometric factor
Force generated by airfoil
Coefficients of lift and drag
Lift
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
Coefficients of lift and drag
Coefficients of lift and drag
1.75
Depend on:
airfoil shape
angle of attack
Empirically determined
1.50
Lift/Drag Coefficient
Geometric factors
CD and CL
lift
coefficient
1.25
1.00
0.75
0.50
drag
coefficient
0.25
0
5
10
15
20
25
Angle of Attack (degrees)
30
Airfoil behavior
Performance parameters
Drag
Thrust Lift
Torque Rotational Speed
Direction of
translation
b
a

 Relative

wind velocity

Free stream
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
Lift and drag on translating air foil
What force actually provides useful work to rotate the turbine?
A)
B)
C)
D)
Lift
Drag
F1
F2
K.L. Johnson (2006)
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
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?
Complications
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Free stream
characteristics change
approaching and across
blades
Rotation of blades causes
counter rotation in wind
Things vary with r
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Must use
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conservation of mass
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Conservation of
momentum
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Conservation of energy
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.
http://www-mdp.eng.cam.ac.uk/web/library/enginfo/aerothermal_dvd_only/aero/propeller/prop1.html
Free stream characteristics change…
Variables
r – density (constant)
A – cross-section area
U – wind speed
p – pressure
T – thrust of wind on turbine
Circular tube of air flowing
through ideal wind turbine
(K.L. Johnson 2006)
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.
BET Limitation – Axial Induction factor
Axial Induction factor
a
u1  u2
u1
u2  u1 (1  a)
u4  u1 (1  2a)
accounts for wind speed reduction as wind approaches turbine

Consider the limits:
a0
a1

No reduction in wind speed
2
Wind stops downstream, model invalid
Power and Power coefficient
2
Theoretical P  Tu2  1 rA2 u12  u4 2 u2  1 rA2u13 4a1 a
2
2
Power
P
rotor_ power
2

 4a1  a
Coefficient of Power CP  1
3
r
u A power_ in _ wind
2

dCP
1
 0 a  ,1
da
3
Theoretical max Cp, set

Sub 1/3 into Cp to get max of 16/27 = 0.5927 (Betz Limit) only
59% of max theoretically
possible.

Value of 1 invalidates model (not btwn 0 and ½)
Counter rotation of wind:
Blade Momentum Theory
Angular Induction factor a 
w
2W
accounts for reduction due to
rotational wake 
Consider the limits:
Rotor induces rotation in
opposite direction of blade
rotation
W – Rotor rotational velocity

w – Induced wind rotational
velocity
a  0
a  1
No induced rotation
2
Induced rotation, w equal
and opposite to rotor
rotation
Angular velocity of rotor affects local wind at
blade
Drag
Lift
T
Q
wr1 a
b
W  U  1  a   w r 1  a
2
2
2 2
a
2

W

 U  1  a  

  b  a  arcsin

 W


1
dQ  rW 2 * B * c * C L sin    C Dcos * r * dr
2
1
dT  rW 2 * B * c * C L cos   C D sin  * r * dr
2

U 1 a
Power Generated by Turbine
Power = Torque * rotational velocity
P  Qw
R
1
Q   dQ   rW 2 * B * c * C L sin    C D cos * r * dr
2
r0
Solidity ratio
Bc
Closed versus open area  
2pr
B*c = net chord length of ALL blades
2pr = total circumference
at radius, r

Constraints and Materials
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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
Parameters and/or Variables
Primary
 Pitch of blades, which in turn affects angle of attack
 Cord/shape of blades
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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
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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)
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On test day, we will measure
electrical output (voltage and
current, recall P(elect) = V*I) and
angular velocity.
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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
Performance metrics and evalutation
w, Rotational Speed
Definitions
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W – relative wind speed
Uinf - free stream wind speed
a – angle of attack
b – blade pitch
a – axial induction factor
a’ – angular induction factor
 – 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
Matlab Pseudo Code: Find these steps!
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Inputs: number of blades N, chord length c, blade span R, blade
angle δ
For a range of rotational speeds ψ
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For a range of blade elements dr up to the blade span R
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While a and a’ converge
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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
End
Calculate power by the product of total torque Q and rotational speed ψ
Calculate coefficient of performance Cp for the rotational speed ψ
End
Plot coefficient of performance as a function of rotational speeds ψ
Generator Performance Curves
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Recall that losses occur converting mechanical power
from the turbine to electric power by the generator
Test or find specifications for generator performance