the aerodynamics of wind turbines - irphe · department of mechanical engineering technical...

Department of Mechanical EngineeringTechnical University of Denmark

The Aerodynamics of Wind Turbinesby

Jens Nrkr Srensen

Department of Mechanical Engineering (MEK)Center for Fluid Dynamics

Technical University of Denmark


Wind EnergyBrief history: The first power producing wind turbines were developed in the 1890s

The Suez crisis (1957) renewed the interest in wind energy

The energy crisis in 1973 forced a world wide interest into wind energy

National MW machines were erected in in 1980s and the first commercial MW machinewas designed in 1990

State of the art wind turbines have rotor diameters of 120 m and 5 MW installed power


Wind Energy


Wind EnergyVarious wind turbines :


Wind EnergyThe Danish Concept:

3-bladed upwind machine with gearbox and asynchroneous generator


Wind EnergyThe worlds largest wind turbineEnercon 126: P=6MW; D=126m


Wind EnergyDevelopment in wind turbine technology :


Wind EnergySome (crude) Rules of Thumb:

P: Installed Power (kW) R: Radius (m)T: Time for one turn (s)

R = 10*TP = 1.2*R**2

][]1[2]/[ mRssmtipV =

TtipVR = 2/or

]/70,/60[ smsmtipV where


Wind EnergySome characteristics numbers:

Boing 747 (Jumbo jet) wing span: 68 mDiameter of modern wind turbine : 124 m

Area of soccer field: 7.000 m**2Area of rotor plane : 12.000 m**2

Question:How much air is passing through a rotor plane at a wind speed of 10m/s? Answer:Q = rho*A*V = 1.2*12.000*10 = 144 ton per second


Wind EnergyWind turbine nacelle :

Rotorblade

Hub Tower

Shaft Gear

Disc Brake

Generator


Wind EnergyAerodynamic forces :


Rotor AerodynamicsAerodynamic forces and geometry :


Wind EnergyPressure and Forces on Airfoil :


Wind EnergyBlade-Element MomentumTheory:

Rotor divided into independent stream tubes

Forces determined from airfoil data

Induced velocities computed from general momentum theory

Finite number of blades introducedby Prandtl tip correction

Ad-hoc corrections for off-design conditions, such as dynamic effects,and yaw misalignment


Blade Element Momentum Model

Basic ingredients of the BEM model:

Based on 1-D momentum theory assuming annular independency

Loading computed using tabulated static airfoil data

Dynamic stall handled through dynamic stall models

3-dimensional stall introduced through modifications

Tip Flows based on (Prandtl) tip correction

Yaw treated through simple modifications

Heavily loaded rotors treated through Glauerts approximation

Wakes and park effects modelled using axisymmetric momentum theory


The Optimum Rotor

What is the optimum number of blades ?

What is the optimum operating condition (TSR)?

What is the maximum efficiency?


Wind Turbine Rotor AerodynamicsWhat is the optimum number of blades?

3 blades ?



3 blades ?

many blades ?



3 blades ?

many blades ?

2 blades ?



3 blades ?

many blades ?

2 blades ?

1 blade ?


Why 3 blades?

Aerodynamics: Close to optimum

Struktural-dynamics: Symmetric moment of inertia

Loadings: Forces smeared out on three blades

Estetics: Harmonic rotation

Historics: The concept is well-proven


Optimum rotor with infinite number of blades1-D Axial momentum theory:

oVva /1=

)(2 voVvoAT =

2)1(4 aaPC =593.027

16max ==PC

:31=a

Betz limit:)1(4 aaTC =

oV

)1( aoV

)21( aoV

)(22 voVvoAP = = VmT

= vTP

Axial interference factor:

Thrust Coefficient:

3 oVoAP

PC =Power coefficient:

2 oVoAT

TC =


Optimum rotor with infinite number of bladesGenerel momentum theory:

Vova /1=

rooua =

( ) = 103128 odxoxaaoPC

)14/()31( = aaa

Condition for optimum operation:

Eulers turbine equation:

0.5 0.2881.0 0.4161.5 0.4802.0 0.5122.5 0.5325.0 0.5707.5 0.58210.0 0.593

maxPCTSR


Two definitions of the ideal rotor

Joukowsky(1912)

Betz(1919)

blade span

(r)

R 0

V w const =const =V w

In both cases only conceptual ideas were outlined for rotors with finite number of blades,whereas later theoretical works mainly were devoted to rotors with infinite blades!

blade span

R0


Betz condition for maximum efficiencyof a rotor with a finite number of blades

Maximum efficiency is obtained when the pitch of the trailing vortices is constant and each trailing vortex sheet translates backward as an undeformed regular helicoidal surface


Induced velocities:Movement of vortex sheet with constant pitch and constant velocity

w2z coswu =

sincoswu =

Axial induced velocity:

Tangential induced velocity:

rwVrddz == /)(tan

== BwVBrh /)(2/tan2

Pitch:


Optimum lift distribution:

)(2//)()( wVwBhwrrG == Goldstein function:

Kutta-Joukowski theorem:o

o U2

LcCULcC ==

Combining these equations, we get

)/()/()1(2

VURrGww

LC

o

=

Solidity: oR2

Bc

= Tip Speed ratio: VR

=


The optimum rotor:


Comparison of maximum power coefficients

( )1

10

2= I G x xdx

( )1 3

3 2 20

2=+

x dxI G xx l

=wwV

Mass coefficient

Axial loss factor

1 32 1 2 2Pw wC w I I =

1 2 32 1 2 2P

a aC a J J J =

Solution of Betz rotor (Okulov&Srensen, 2008)

Solution of Joukowsky rotor (Okulov & Srensen, 2010)

Difference between power coefficients

2 2 21 2 3 1 2 1 2 3 3

1 33J J J J J J J J J

aJ J

+ +=

( )2 21 3 1 1 3 33

2

3

+ +=

I I I I I Iw

I

zuaV

=

( )13

0

2 zu x

J l xdxa

=

2

1 21 2lJR

= +2

2 2

1 112 6

JR R

= + +


Optimum 3-bladed rotor with loss:

From C. Bak: J. Physics: Conference Series, vol. 75, 2007


Wind EnergyPerformance of wind turbines :


Control and regulation of wind turbines

Stall control

Active Stall control

Pitch control

Variable speed


Rotor AerodynamicsAerodynamic forces and geometry :


Stall-regulated wind turbine:Computed power curve


Wind TurbineModern Danish Wind Turbine : Pitch-regulated P=2 MW; D=90 m Nom. Tip speed.: 70 m/s Rotor: 38t, Nacelle: 68t; Tower: 150t Control: OptiSpeed; OptiTip


Wind Turbine Rotor Aerodynamics

Basic features:

Rotor blades are always subject to separated flows

Blade aereodynamics dominated by strong rotational effects

The incoming wind is always unsteady and 3-dimensional

Wind turbines are designed to run continuously in about 20 years in all kinds of weather


Wind Turbine AerodynamicsImportant areas of research:

Aerofoil and blade design

Dynamic stall

3-dimensional stall

Tip Flows and yaw

Modelling of heavily loaded rotors

Wakes and park effects

Complex terrain and meteorology

Offshore wind energy


Research in Wind Turbine AerodynamicsNeed for models capable of coping with: Dynamic simulations of large deformed rotors

Complex geometries: Rotor tower interaction

Adjustable trailing edge flaps

Various aerodynamic accessories, such as vortex generators, blowing, Gourney flaps and roughness tape

3-dimensional stall, including laminar-turbulent transition

Unsteady, three-dimensional and turbulent inflow

Interaction between rotors and terrain

Complex terrain and wind power meteorology

Offshore wind energy: Combined wind and wave loadings


Wind Turbine Aerodynamics

Available models:

Blade-Element momentum (BEM) technique

Vortex line / Vortex lattice modelling

Actuator disc / Actuator line technique

Computational Fluid Dynamics (CFD)

Remark: All models have their individual advantages and disadvantages!


Computational Fluid DynamicsBasic Elements

Mesh generation

Turbulence modelling

Efficient computing algorithms

High-performance computers

Post-processing facilities (Validation)


The Numerical Wind Tunnel (EllipSys)

Developed in close collaboration between DTU and Ris with the aim of:

Optimizing rotors with respect to performance and noise

Analysing existing designs

Verification of simple engineering models

Gain physical understanding


Pressure Distributions at 10 m/s(Courtesy: Niels N. Srensen, Ris)


Actuating trailing edge flapAn example of a research project


Actuating trailing edge flapIn this project we investigate the possibility of using flapping trailing edge flaps to control and reduce the impact of small-scale turbulence on the loading of a wind turbine rotor


3D rotor code using Immersed Boundaries

EllipSys3D are being extended to include a trailingedge flap by using immersed boundary technique

The influence of upstream perturbations are beinginvestigated by imposing upstream vortexsources

The model has recently been extended toinclude wind tunnel walls

Upstream turbulence will be included and morevalidation will take place in the next phase


ATEF combined with curvilinear mesh


Wind tunnel measurements at DTU

A new airfoil with a trailing edge flap has beeninstalled in the 50cm x 50 cm wind tunnel atDTU Mechanical Engineering

A set-up controlling two small oscillating airfoils have been designed to create upstream disturbances

The airfoil and the wind tunnel has both beenequipped with pressure transducers (in total 64)

The set-up is operating with a controllable TEFand a LabView program to determine loadings,i.e. unsteady lift and drag coefficients

The new measurement campaign has been initiated


Status of wind tunnel measurements

The old blade mounted on a balance measuring one force component

NACA 63418 wing: 25cm chord 50cm span Mechanical hinged flap, 15% flap RC-model actuator

Department of Mechanical EngineeringTechnical University of Denmark 50

Suggestion for new flap mechanism

Flexiure

LinMot

Mechanism


New airfoil with new flap mechanism


Red wind tunnel testRed Wind Tunnel:

50cm x 50cm Max speed: 65m/s, Tu


Wind tunnel testing NACA 63418 / 64418Experimental setup :

Pressure scanner 2x32 tabs implemented, LabView measuring chain operational

Measurement of pressures on wing and tunnel walls

Sampling rate:150-200Hz (Integral loads and control)

Aerodynamic excitation - High frequency (10-20Hz) pitchable wings upstream of test wing

LinMot

Mechanism


Wind tunnel test, NACA 63418/64418

0 00 55 5

f [Hz]0 5 1/2/5/85 5 1/2/5/8

f [Hz]0 8 1/2/5/85 8 1/2/5/8

Steady flap and airfoils

Unsteady flap and steady airfoils

Steady flap and osc. airfoils

U = 30 m/s

Tu 0.1%

- main wing AOA

- flap angle

- 2 airfoils angle


Oscillating wingsTunnel:

V = 30 m/s

Oscillating wings (NACA 64015) c = 0.1m f = 5 Hz = 8o

Main wing: NACA 63418 c = 0.2ma= 0oflap = 0o fflap = 0 Hz


Flap (15%) 8HzTunnel:

V = 30 m/s

Oscillating wings (NACA 64015) c = 0.1m f = 0 Hz = 8o

Main wing: NACA 63418 c = 0.2ma= 5oflap = 5o fflap = 8 Hz


Results moving flap

Reynolds Averaged Navier-Stokes Angle of attack: = 0 Reynolds number: Re = 1.000.000

flapping angle : -9 < < +9

Frequency: f = 0.05/s


Combined pitch and flap motion


The Aerodynamics of Wind Power

Conclusion:

In spite of the many years humans have expolited the energy of the wind, there is still a big need for improving our basic knowledgeof wind turbine aerodynamics

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the aerodynamics of wind turbines - irphe · department of mechanical engineering technical...

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