Wind Power amp Blade Aerodynamics 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 ID: 757270
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Slide1
Wind Turbine Project RecapWind Power & Blade AerodynamicsSlide2
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)Slide3
Harnessing available power in wind
Max available power
How can we predict blade performance?
Blade aerodynamics
Rotor performanceSlide4
Power coefficient
C
p
=
Rotor power
Power in the wind
requires blade
and
rotor physics
How well is our turbine performing?
At best only 45% can be captured by real
turbines (theoretical limit
)
.Slide5
Project estimates – class exercise (5 min)
Available power
Estimating maximum
P
generatedSlide6
Project estimates – class exercise (5 min)
Available power
Estimating maximum
P
generated
P
= 60
WSlide7
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
P
generatedSlide8
Blade aerodynamics
Turbine blades are
airfoils
We need to understand blade aerodynamics to determine effectiveness and performanceSlide9
Airfoil terminology
W
α
R
U
∞
Free stream velocity
C
Relative wind velocitySlide10
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 chordSlide11
Airfoil function – generation of lift
weight
thrust
drag
lift
‘suction’ side
‘pressure’ sideSlide12
Airfoil forces
Lift force
perpendicular to airflow
Drag force
parallel to the airflowSlide13
Calculating lift and drag
Power = Force
x
Velocity
geometric factor
Force generated by airfoil
Force in
the windSlide14
Coefficients of lift and drag
C
D
= how much of the
pressure (kinetic energy)
is converted
to drag
Lift
Lift coefficient
Drag force
Drag coefficient
C
L
= how effectively
the
wing
turns
available dynamic
pressure (kinetic energy)
into liftSlide15
Coefficients of lift and dragSlide16
Coefficients of lift and drag
Geometric factors
C
D
and C
L
Depend on:
airfoil shape
angle of attack
Empirically
determined
0
5
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
coefficientSlide17
Airfoil behaviorSlide18
Performance parameters
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
Lift
Drag
Thrust
Torque
Direction of
translation
Rotational Speed
Relative
wind
velocity
Free stream
Wind velocitySlide19
Lift and drag on translating air foil
What force
actually provides useful work to rotate the turbine?
Lift
Drag
F
1
F
2
K.L. Johnson (2006)Slide20
Lift and drag on translating air foil
F
1
is force to rotate the turbine
Tower
must be strong
enough to withstand thrust force F
2
K.L. Johnson (2006)Slide21
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?Slide22
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 energySlide23
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.htmlSlide24
Free stream characteristics change…
Circular tube of air flowing through ideal wind turbine
(K.L. Johnson 2006)
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 d
1
, speed u1
, and pressure p1 as it approaches turbine, the air speed decreases, causing the tube of air to increase to d
2. 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 u
4 = u1.Slide25
BET Limitation – Axial Induction factor
Axial Induction factor
accounts for wind speed reduction as wind approaches turbine
Consider the limits:
No reduction in wind speed
Wind stops downstream, model invalidSlide26
Power and Power coefficient
Theoretical
Power
Coefficient of Power
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) Slide27
Counter rotation of wind:Blade Momentum Theory
Rotor induces rotation in opposite direction of blade rotation
W
– Rotor rotational velocity
w
– Induced wind rotational velocity
Angular Induction factor
accounts for reduction due to rotational wake
Consider the limits:
No induced rotation
Induced rotation,
w
equal and opposite to rotor rotationSlide28
Angular velocity of rotor affects local wind at blade
Lift
Drag
T
QSlide29
Power Generated by Turbine
Power = Torque * rotational velocitySlide30
Solidity ratio
Closed versus open area
B*
c = net chord length of ALL blades
2
p
r = total circumference at radius,
rSlide31
Blade Element Theory (cont’d)
V
0
- axial flow at propeller disk, V
2
- Angular flow velocity vector
V
1 - section local flow velocity vector, sum of vectors V
0
and V
2
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 foundhttp://www-mdp.eng.cam.ac.uk/web/library/enginfo/aerothermal_dvd_only/aero/propeller/prop1.html
Difference in angle between thrust and lift directionsSlide32
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 plasticMust be a horizontal axis wind turbineWith 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 rodsSlide33
Parameters and/or Variables
Primary
Pitch of blades, which in turn affects angle of attack
Cord/shape of bladesConstant cord – to make simple rectangular bladesVariable cord – to make another shape (triangle, parallelogram, etc.)
Secondary
Number of blades <=12
Radius <= 0.5 meter Slide34
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 SpeedSlide35
Definitions
W – relative wind speed
U
inf - free stream wind speed
a
– angle of attack
b
– blade pitcha – axial induction factora’ – angular induction factor
f
– relative angle of wind
B – number of blades
C
L – coeficient of liftC
D – coefficient of dragQ, dQ- total blade torque, torque on differential elementCp
- coefficient of powerSlide36
Matlab Pseudo Code: Find these steps!
Inputs: number of blades
N, chord length c, blade span R, blade angle
δFor a range of rotational speeds ψ
For a range of blade elements
dr
up to the blade span R
While a and a’ convergeCalculate 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 EndCalculate the differential blade torque dQ
for the blade elementSum the elemental contributions dQ
to the total torque QEndCalculate power by the product of total torque Q and rotational speed ψCalculate coefficient of performance Cp for the rotational speed ψ
EndPlot coefficient of performance as a function of rotational speeds ψSlide37
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