The Aerodynamics of Wind Turbines by Jens Nørkær Sørensen (MEK) Center for Fluid Dynamics
Wind Energy Brief history: The first power producing wind turbines were developed in the 1890 s 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 1980 s and the first commercial MW machine was designed in 1990 State of the art wind turbines have rotor diameters of 120 m and 5 MW installed power
Wind Energy
Wind Energy Various wind turbines :
Wind Energy The Danish Concept: 3-bladed upwind machine with gearbox and asynchroneous generator
Wind Energy The worlds largest wind turbine Enercon 126: P=6MW; D=126m
Wind Energy Development in wind turbine technology :
Wind Energy Some (crude) Rules of Thumb: P: Installed Power (kw) R: Radius (m) T: Time for one turn (s) R = 10*T P = 1.2*R**2 V [ m/ s] = 2π Ω[ s 1] R[ m] tip or R= V /2π T tip where V tip [ 60m/ s,70m/ s]
Wind Energy Some characteristics numbers: Boing 747 (Jumbo jet) wing span: 68 m Diameter of modern wind turbine : 124 m Area of soccer field: 7.000 m**2 Area 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 Energy Wind turbine nacelle : Disc Brake Rotorblade Shaft Gear Generator Hub Tower
Wind Energy Aerodynamic forces :
Rotor Aerodynamics Aerodynamic forces and geometry :
Wind Energy Pressure and Forces on Airfoil :
Wind Energy Blade-Element MomentumTheory: Rotor divided into independent stream tubes Forces determined from airfoil data Induced velocities computed from general momentum theory Finite number of blades introduced by 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 Glauert s 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 Aerodynamics What is the optimum number of blades? 3 blades?
Wind Turbine Rotor Aerodynamics What is the optimum number of blades? 3 blades? many blades?
Wind Turbine Rotor Aerodynamics What is the optimum number of blades? 3 blades? 2 blades? many blades?
Wind Turbine Rotor Aerodynamics What is the optimum number of blades? 3 blades? 2 blades? many 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 blades 1-D Axial momentum theory: Axial interference factor: a =1 v/ V o T Thrust Coefficient: C = T ½ρA 2 o V o P Power coefficient: C = P ½ρA V 3 o o T = m V T = 2ρA o v( V o v) P 2 A 2 P = vt = ρ o v ( V o v) V o Vo ( 1 a ) Vo ( 1 2 a ) C T C P = 4a(1 a) = 4a(1 a) 2 Betz limit: a = 1 : 3 C P max = 16 27 = 0.593
Optimum rotor with infinite number of blades Generel momentum theory: a =1 v o / V u a = θo Ωo r Euler s turbine equation: C = 8λ2 1 a ( 1 a) x3 o 0 o dx P o TSR C Pmax 0.5 0.288 1.0 0.416 1.5 0.480 2.0 0.512 2.5 0.532 5.0 0.570 7.5 0.582 10.0 0.593 Condition for optimum operation: a = ( 1 3a)/(4a 1)
Two definitions of the ideal rotor Joukowsky (1912) Betz (1919) Γ=const Γ V w = const V w Γ(r) blade span blade span R 0 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! R 0
Betz condition for maximum efficiency of 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: Axial induced velocity: u = wcos 2 Φ z Movement of vortex sheet with constant pitch and constant velocity w Tangential induced velocity: u = wcosφ sinφ θ Pitch: h = 2πr tanφ/ B = 2π ( V w) / BΩ dz tanφ = = ( V w) / Ωr rdθ
Optimum lift distribution: Goldstein function: G( r) = Γ( r) / hw = BΓΩ / 2πw( V ½w) Kutta-Joukowski theorem: 2Γ Γ = ½cC U cc = L o L U o Combining these equations, we get σc L = 2w(1 ½ w) G( r / R) λ( U / V ) o Solidity: Bc σ = 2π R o Tip Speed ratio: λ = ΩR V
The optimum rotor:
Comparison of maximum power coefficients Solution of Joukowsky rotor (Okulov & Sørensen, 2010) u z a = V a a CP = 2a 1 J1 J2 J3 2 2 Solution of Betz rotor (Okulov&Sørensen, 2008) w = w V w w CP = 2w 1 I1 I3 2 2 a ( ) 2 2 2 2 2 JJ Difference between 1 2 + J3 J1J2 JJJ 1 2 3+ J 2 I1+ I3 I1 II 1 3+ I3 3 = power coefficients w = 3JJ 1 3 3I3 2 1 J1 = 1+ 2 l 2 R 2 1 1 ε 1 ε J 2 = + + 2 2 R 6 R u ( x) = 1 z J3 2l xdx a 0 Mass coefficient Axial loss factor I 1 ( ) = 2 G x xdx 0 1 3 I = 2 G x dx ( x ) x l 3 2 2 + 0
Optimum 3-bladed rotor with loss: From C. Bak: J. Physics: Conference Series, vol. 75, 2007
Wind Energy Performance of wind turbines :
Control and regulation of wind turbines Stall control Active Stall control Pitch control Variable speed
Rotor Aerodynamics Aerodynamic forces and geometry :
Stall-regulated wind turbine: Computed power curve
Wind Turbine Modern 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 Aerodynamics Important 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 Aerodynamics Need 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 Dynamics Basic 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 Risø 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. Sørensen, Risø)
Actuating trailing edge flap An example of a research project
Actuating trailing edge flap In 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 trailing edge flap by using immersed boundary technique The influence of upstream perturbations are being investigated by imposing upstream vortex sources The model has recently been extended to include wind tunnel walls Upstream turbulence will be included and more validation will take place in the next phase
ATEF combined with curvilinear mesh
ATEF combined with curvilinear mesh
Wind tunnel measurements at DTU A new airfoil with a trailing edge flap has been installed in the 50cm x 50 cm wind tunnel at DTU 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 been equipped with pressure transducers (in total 64) The set-up is operating with a controllable TEF and 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
Suggestion for new flap mechanism Flexiure LinMot Mechanism 50
New airfoil with new flap mechanism 51
Red Wind Tunnel: 50cm x 50cm Max speed: 65m/s, Tu<0.1% NACA 63418 wing: 20cm chord 50cm span Mechanical hinged flap, 15% - RC-model actuator NACA 64418 wing: 25cm chord 50cm span Flexiure flap, 15% - Linear actuator Red wind tunnel test 52
Wind tunnel testing NACA 63418 / 64418 Experimental 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 53
Wind tunnel test, NACA 63418/64418 U = 30 m/s Tu 0.1% α - main wing AOA β - flap angle γ - 2 airfoils angle Unsteady flap and steady airfoils α β f [Hz] 0 5 1/2/5/8 5 5 1/2/5/8 Steady flap and airfoils α β 0 0 0 5 5 5 Steady flap and osc. airfoils α γ f [Hz] 0 8 1/2/5/8 5 8 1/2/5/8 54
Oscillating wings Tunnel: V = 30 m/s Oscillating wings (NACA 64015) c = 0.1m f = 5 Hz γ = ±8 o Main wing: NACA 63418 c = 0.2m a= 0 o β flap = 0 o f flap = 0 Hz 55
Flap (15%) 8Hz Tunnel: V = 30 m/s Oscillating wings (NACA 64015) c = 0.1m f = 0 Hz γ = ±8 o Main wing: NACA 63418 c = 0.2m a= 5 o β flap = ±5 o f flap = 8 Hz 56
Results moving flap Reynolds Averaged Navier-Stokes Angle of attack: α = 0º Reynolds number: Re = 1.000.000 flapping angle : -9º < ß < +9º Frequency: f = 0.05/s 57
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 knowledge of wind turbine aerodynamics