Upload
lillian-osborne
View
228
Download
0
Tags:
Embed Size (px)
Citation preview
Wind Turbine Project RecapWind Power & 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! (with one trial fitting)
Harnessing available power in wind
Max available power
How can we predict blade performance?
Blade aerodynamicsRotor performance
Power coefficient
Cp =
Rotor powerPower 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).
Project estimates – class exercise (5 min)
Available power
Estimating maximum Pgenerated
Project estimates – class exercise (5 min)
Available power
Estimating maximum Pgenerated
P = 60 W
Atlantic City estimates – class exercise (5 min)
Now assuming the offshore wind velocity is12 m/sThe 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
Wα
R
U∞
Free stream velocity
C
Relative wind velocity
Airfoil typesNACA airfoilsNational Advisory Committee for Aeronautics
NACA 2412maximum camber of 2% located 40% from the leading edge with a maximum thickness of 12% of the chord
NACA 0012symmetrical airfoil, 00 indicating no camber.12 indicates that the airfoil has a 12% thickness to chord
Airfoil function – generation of lift
weight
thrust drag
lift
‘suction’ side
‘pressure’ side
Airfoil forces
Lift forceperpendicular to airflow
Drag forceparallel to the airflow
Calculating lift and drag
Power = Force x Velocity
geometric factor
Force generated by airfoil
Force in the wind
Coefficients of lift and drag
CD = how much of the pressure (kinetic energy) is converted to drag
Lift Lift coefficient
Drag force Drag coefficient
CL = how effectively the wing turns available dynamic pressure (kinetic energy) into lift
Coefficients of lift and drag
Coefficients of lift and drag
Geometric factorsCD and CL
Depend on:airfoil shapeangle 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
/Dra
g
Coeffi
cien
t
lift coefficient
drag coefficient
Airfoil behavior
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
LiftDrag
Thrust
Torque
Direction of translation
Rotational Speed
Relative wind velocity
Free streamWind velocity
Lift and drag on translating air foilWhat force actually provides useful work to rotate the turbine?
A) LiftB) DragC) F1
D) F2
K.L. Johnson (2006)
Lift and drag on translating air foil
F1 is force to rotate the turbine
Tower must be strong enough to withstand thrust force F2
K.L. Johnson (2006)
Connection to wind turbineslift 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 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
Things vary with r : Blade Element Theory (BET)
Blade divided into sections, on which momentum is appliedResult 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…
Circular tube of air flowing through ideal wind turbine (K.L. Johnson 2006)
Variablesr – density (constant)A – cross-section areaU – wind speedp – pressureT – 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.
BET Limitation – Axial Induction factor
Axial Induction factor
accounts for wind speed reduction as wind approaches turbineConsider the limits:
a u1 u2
u1
a 0
a 12
No reduction in wind speed
Wind stops downstream, model
invalid
)21(
)1(
14
12
auu
auu
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)
P Tu2 12A2 u1
2 u42 u2 1
2A2u13 4a 1 a 2
CP P
12 u3A
rotor _ power
power _ in _ wind4a 1 a 2
dCP
da0 a
1
3,1
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
a 2
Consider the limits:
a 0
a 12
No induced rotation
Induced rotation, w equal and opposite to rotor rotation
Angular velocity of rotor affects local wind at blade
LiftDrag
T
Q
r 1 a
U 1 a
W
drrCCcBWdT
drrCCcBWdQ
W
aU
araUW
DL
DL
**sincos***2
1
**cossin***2
1
1arcsin
11
2
2
22222
Power Generated by Turbine
Power = Torque * rotational velocity
R
r
DL drrCCcBWdQQ
QP
0
**cossin***2
1 2
Solidity ratio
Closed versus open area
B*c = net chord length of ALL blades
2pr = total circumference at radius, r
Bc
2r
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
Parameters and/or VariablesPrimary 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
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,
Coeffi
cient
of
Pow
erw, Rotational Speed
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
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 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 Recall that losses occur converting
mechanical power from the turbine to electric power by the generator
Test or find specifications for generator performance