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Wind power Part 3: Technology

Wind power Part 3: Technology. San Jose State University FX Rongère February 2009. Wind Turbine Aerodynamics. Energy balance over the stream tube. Inlet: index 1 Outlet: index 2 Turbine: index T. Betz’s Simplified Approach.

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Wind power Part 3: Technology

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  1. Wind powerPart 3: Technology San Jose State University FX Rongère February 2009

  2. Wind Turbine Aerodynamics • Energy balance over the stream tube Inlet: index 1 Outlet: index 2 Turbine: index T

  3. Betz’s Simplified Approach • The turbine is perfect: there is no internal entropy generation Then, when air considered as an incompressible fluid:

  4. Betz’s Simplified Approach • Energy balance equation is reduced to: • In addition, we assume that the wind speed stay axial through the turbine: • Balance of Forces: The power of the torque absorb by the turbine is equal to the power taken from the air flow

  5. Betz’s Simplified Approach • Momentum equation on the system: Then: And:

  6. Betz’s Simplified Approach • Introducing a the interference factor: Then:

  7. Betz’s Simplified Approach • The power absorbed by the turbine is maximum if: Betz’s law Then

  8. Other factors • Other factors limit the performance of wind turbines • Wake rotation • Aerodynamic drag • Finite number of blades and interaction between them • Blade tip losses

  9. Wake rotation • In fact, the air is rotating downstream the rotor by reaction to the torque applied to the rotor

  10. Maximum conversion rate with wake rotation: Glauert’s law • To characterize this effect we introduce: • Angular velocity of the rotor : ΩT • Angular velocity imparted to the flow: ω • Angular induction factor: a’ = ω/2ΩT • Axial interference factor: • Blade tip speed : λ = ΩTR/v1 • We can then show that the transfer power is maximum if:

  11. Maximum conversion rate with wake rotation: Glauert’s law • Then the maximum conversion rate is given by the following equation: With a(λ) defined by: Betz’s law corresponds to: and:

  12. Maximum conversion rate with wake rotation: Glauert’s law • By drawing CpMax we can show that: • Larger is the blade tip ratio higher is the conversion rate • For blade tip ratio greater than 4 conversion rate is close to Betz’s law • The optimal axial interference factor is close to 1/3 for large enough blade tip ratio Angular induction factor λ λ

  13. Aerodynamic drag • The aerodynamics of a blade is defined by: L: Lift force v: Wind speed on the blade c: Chord of the blade D: Drag force l: Span of the blade α: Angle of attack

  14. Lift and Drag • Lift and Drag are related: • Lift transfers power • Drag generates losses • Bearings • Viscous Friction • Noise • About 10 -15% of aerodynamic inefficiencies

  15. Design optimization • Blade shape may be optimized using laboratory test and numerical modeling • See: Wind Energy, Explained by J.F. Manwell, J.G. McGowan and A.L.Rogers, John Wiley, 2002, for detailed explanations • See also: Riso DTU – National Laboratory for Renewable Energy http://www.risoe.dtu.dk/

  16. Two Blade Wind Turbine Three Blade Wind Turbine Vertical axis Wind Turbine (Darrieus) Multiblade Wind pump Interaction between blades • Blade tip speed is limited by the interaction between the blades. Typically, if the rotation is too fast (λ>λMax) then the flow for each is perturbed by the previous one λ

  17. Blade tip losses • Local rotating airflow at the tip of the blades due to the difference of pressure between the faces of the blades • Similar to aircraft wings • Thesis at DTU has shown a gain of 1.65% but with an increase in thrust of 0.65% Performance glider with winglets Wingtip loss of Boeing 737 Source: Mads Døssing Vortex Lattice Modelling of Winglets on Wind Turbine Blades Risø-R-1621(EN) Aug. 2007

  18. Actual Wind Turbine Conversion Rate • Example: Liberty of Clipper Windpower Power curve

  19. Actual Turbine Conversion rate • Power curve and Conversion rate

  20. Optimization Parameters Max Power Cut out Cut in Efficiency

  21. Generated Energy • Generated Energy = Wind Speed Distribution x Turbine Power Curve

  22. Capacity Factor • Lower Capacity factor allows higher energy capture • Generally preferred CF is between 30% and 40% Characteristics of the tested turbine

  23. Wind Turbine Optimization

  24. Wind and Power Distribution CF=24% Captured Energy =33%

  25. Wind and Power Distribution vm = 9m/s CF=44% Captured Energy =22%

  26. Companies to follow • GE: www.ge.com • Clipper Windpower: www.clipperwind.com • Vestas: www.vestas.com • Repower: www.repower.com • Gamesa: www.gamesa.com • Suzlon: www.suzlon.com • Mitsubishi: www.mitsubishi.com

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