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 windMax 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 aerodynamicsTurbine blades are airfoils

We need to understand blade aerodynamics to determine effectiveness and performance

Airfoil terminology

Wα

RU∞

Free stream velocity

CRelative wind velocity

Airfoil typesNACA airfoilsNational Advisory Committee for AeronauticsNACA 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 forcesLift forceperpendicular to airflow

Drag forceparallel to the airflow

Calculating lift and dragPower = 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 determined0 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/D

rag

Coeffi

cient

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

a

b

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) F1D) 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 bladeNext 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 factorAxial 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 speedWind stops downstream, model invalid

)21()1(

14

12

auuauu

Power and Power coefficientTheoretical 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 12rA2 u1

2 u42 u2 1

2rA2u13 4a 1 a 2

CP P

12 ru3A

rotor _ power

power _ in _ wind4a 1 a 2

dCP

da0 a

13

,1

Counter rotation of wind:Blade Momentum Theory

Rotor induces rotation in opposite direction of blade rotationW – Rotor rotational velocityw – Induced wind rotational velocity

Angular Induction factor

accounts for reduction due to rotational wake

a w2W

Consider the limits:

a 0

a 12

No induced rotationInduced rotation, w equal and opposite to rotor rotation

Angular velocity of rotor affects local wind at blade

LiftDrag

T

Q

wr 1 a

U 1 a

W

drrCCcBWdT

drrCCcBWdQ

WaU

araUW

DL

DL

**sincos***21

**cossin***21

1arcsin

11

2

2

22222

r

r

ab

w

a

b

Power Generated by TurbinePower = Torque * rotational velocity

R

rDL drrCCcBWdQQ

QP

0

**cossin***21 2 r

w

Solidity ratioClosed versus open area

B*c = net chord length of ALL blades

2pr = total circumference at radius, r

Bc2pr

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, C

oeffi

cient

of P

owerw, 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 – 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