AERODYNAMIC LIFT-TYPE WIND ENERGY TECHNOLOGY

Part B Module 1 – Wind Energy

SAILING ACROSS THE WIND

• Boat speed added to true wind

• Apparent wind exceeds true wind

• Boat speed can exceed wind speed Apparent wind

True wind

Boat speed

EARLY AERODYNAMIC LIFT-TYPE WIND MILL

• Old Portugese windmill • Cloth strung between wood

masts

Torrey, 1976

AERODYNAMICS • Sail, airplane wings,

airplane propellers, wind turbine blades, are all airfoils

• Definitions – Angle of attack – Chord length

• Air passing over airfoil generates lift and drag

Vrelative

α

Lift

Drag

Angle of attack

Chord

ANGLE OF ATTACK • Low angle of attack

– Lift exceeds drag • Moderate angle of attack

– Both increase but lift more than drag

• Steep angle of attack – Stall – More drag than lift

Lift Drag

LIFT AND DRAG COEFFICIENTS • Lift coefficient for lift force F

𝐶𝐿 =𝐿

12 𝜌𝜌𝑉𝑟𝑟𝑟2

• Drag coefficient for drag force D

𝐶𝐷 =𝐷

12 𝜌𝜌𝑉𝑟𝑟𝑟2

where A is the blade area (surface area wind flows over)

A = chord x blade length

Blade length

EFFECT OF ANGLE OF ATTACK

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 5 10 15 20

Lift

coef

ficie

nt

Angle of attack (degrees)

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0 5 10 15 20

Drag

coe

ffic

ient

Angle of attack (degrees) CL and CD values calculated for SD7062 airfoil by Huahui Tan

COMBINED EFFECT OF LIFT AND DRAG

• Ratio of CL/CD illustrates importance of angle of attack

0

20

40

60

80

100

120

140

0 5 10 15 20

C lift

/Cdr

ag

Angle of attack (degrees) CL/CD values calculated for SD7062 airfoil by Huahui Tan

BLADE SECTION GEOMETRY

r Wind

V0

v

V0

V1 Vrel

v

v = 2πrN where N =rotation

speed (rpm)

View of section from blade end Rotor axis Lift

Drag

ANGLE DEFINITIONS

V0

V1 Vrel

v

• Relative wind speed

𝑉𝑟𝑟𝑟 = 𝑉12 + 𝑣2

• Φ = relative wind angle

𝜑 = arctan𝑉1𝑣

• α = angle of attack • β = blade pitch angle

𝛽 = 𝜑 − 𝛼

Rotor axis

Lift Drag

φ β α

FORCES

V0

V1 Vrel

v

• Driving force rotates blade 𝐹𝐷𝑟𝐷𝐷𝐷𝐷𝐷 = 𝐿𝐿𝐿𝐿𝜑 − 𝐷𝐿𝐷𝐷𝜑

• Thrust force loads bearings 𝐹𝑡𝑡𝑟𝑡𝑡𝑡 = 𝐿𝐿𝐷𝐷𝜑 + 𝐷𝐿𝐿𝐿𝜑

𝐿 = 𝐶𝐿 ∙ 12𝜌𝜌𝑉𝑟𝑟𝑟2

𝐷 = 𝐶𝐷 ∙ 12𝜌𝜌𝑉𝑟𝑟𝑟2

View

Rotor axis

Lift Drag

φ β α

LIFT FORCE • Driving force on blade element:

𝐹𝐷𝑟𝐷𝐷𝐷𝐷𝐷 = 12𝜌𝜌𝑉𝑟𝑟𝑟

2 𝐶𝐿 ∙ 𝐿𝐿𝐿𝜑 − 𝐶𝐷 ∙ 𝐿𝐷𝐷𝜑

• Rotor speed v is one component of Vrel 𝑣 = 𝑟 ∙ 𝜔

where 𝜔= blade rotation frequency (radians/s)

𝐹𝐷𝑟𝐷𝐷𝐷𝐷𝐷 = 12𝜌𝜌 𝑉12 + 𝑟𝜔2 ∙ 𝐶𝐿 𝛼 ∙ 𝐿𝐿𝐿𝜑 − 𝐶𝐷 𝛼 ∙ 𝐿𝐷𝐷𝜑

where: 𝜑 = 𝑎𝑟𝐿𝑎𝑎𝐷 𝑉1𝑟𝑟

and 𝛼 = 𝜑 − 𝛽

FORCE DEPENDENCE ON ROTATING SPEED • SD7062 airfoil for illustration

– Blade tip radius R = 3.38m – V1 = 9.33m/s – β=15o – Two radii (1.8m, 3.35m) – Force/unit blade length

• 0

20

40

60

80

100

120

140

0 10 20 30

Forc

e /u

nit b

lade

leng

th

(arb

itrar

y un

its)

Rotation frequency (radians/s)

r = 1.8m

r = 3.35m

β= 15o

FORCE AT FIXED ROTATION SPEED • Often desirable to run rotor at

fixed speed to match generator synchronous speed

• Calculation shows effect of wind speed for fixed rotation speed.

• Large difference in force developed!

• Large wind turbines use blade pitch control – adjust β 0 5 10 15 20

Forc

e fr

om a

irfoi

l sec

tion

(arb

itrar

y un

its)

Wind speed (m/s)

r = 1.8m

β = 15o

Ω = 10

INTEGRATE OVER BLADE LENGTH • Define Power coefficient

𝐶𝑃 =𝑃𝑎𝑎𝑡𝑡𝑎𝑟12𝜌𝜌𝑉0

3

• Indicates the fraction of power available in the wind that is produced as electrical output:

• Depends on wind speed and on rotor speed

Blade length

POWER COEFFICIENT & TIP SPEED RATIO • Characterize rotor speed by tip

speed ratio:

𝑇𝐷𝑇 𝑆𝑇𝑆𝑆𝑆 𝑅𝑎𝑎𝐷𝐿 =2𝜋𝑅𝜋𝑉0

where: R = blade radius N = rotor speed (rpm) V0 = upstream wind speed

• TSR useful for all circumstances,

constant rotor speed or not 0 2 4 6

Pow

er co

effic

ient

Tip speed ratio

β = 15o

WHAT IS THE MAXIMUM POWER THAT CAN BE EXTRACTED FROM THE WIND?

• Betz limit is max power that can be extracted from the wind

𝑃𝑚𝑎𝑚 𝑤𝐷𝐷𝑖 𝑡𝑡𝑟𝑡𝐷𝐷𝑟 =12𝜌𝜌𝑉03

1627

• For Betz limit, CP = 0.593 • Real wind turbines have lower values of CP

SUMMARY - AERODYNAMIC LIFT-TYPE WIND ENERGY TECHNOLOGY

• Air passing over an airfoil shape (e.g. a wind turbine blade) generates lift and drag

• Blade angle of attack determines relative amounts of lift and drag

• Blade sees relative wind velocity, the vector sum of the true wind speed and the rotor speed

• Actual power output characterized by power coefficient CP, which depends on the tip speed ratio, the ratio of rotor tip speed to upstream wind speed.

PRACTICE EXERCISES

REFERENCES AND PHOTO CREDITS

References • Torrey, Volta, “Wind-Catchers; American Windmills of

Yesterday and Tomorrow,” The Stephen Greene Press, Brattleboro, Vermont, 1976.