1. Wind Turbine Aerodynamics Section 1 – Basic Principles E-Learning UNESCO ENEA Casaccia - February 26 2007 Fabrizio Sardella

2. 2 BASIC PRICIPLES The scope of this presentation is to clarify some basic concepts about the WTG aerodynamics starting from the rotor aerodynamics to deepen the part specifically dedicated to the wind turbines and in particular about the power control. The way the matter has been treated is not always rigorous as what it is possible to find in dedicated texts about rotor design, but it should be adequate to describe the interaction between the rotor and the rest of the turbine. The branch which will be treated is the SUBSONIC AERODYNAMICS since the air speeds interested are substantially lower than the sound speed which is about 340 m/s at sea level and in normal conditions (the tip speed in a WTG rotor in overspeed conditions is normally below 100 m/s)

3. 3 BASIC PRICIPLES For the subsonic flows the Bernoulli theorem is applicable: V∞V∞ V upper V lower Where p is the static air pressure and 1/2  V 2 is the dynamic air pressure (is the air density and V is the air speed). This assumptions corresponds also to consider an ideal not compressible fluid. p becomes lower where V is higher, being the sum p+ 1/2  V 2 constant.

4. 4 BASIC PRICIPLES The global effect is represented in the figure on the left side where the arrows going out of the profile represent a suction and the arrows going towards the profile represent an overpressure. The resultant forces are represented in the figure on the right side: L = lift D = drag M = moment and are normally used in airplane wing theory. L D M FaFa V∞V∞ α α CLCL Stall

5. 5 THE ROTOR If we divide a blade in small sections as described in the figure on the right side, we can consider each section as a small wing, calculate the forces and then sum each contribution to obtain the global forces. The blade speed due to the rotation is higher moving from the center of the rotor to the tip; if we assign the rotational speed  the relative linear blade speed due to the rotation is: V r = r the relative air speed is equal and opposite. r V r  R

6. 6 THE ROTOR To understand what happens in a single section we can consider the figure below reported: r is the speed of the air due to the rotation; if we add a wind speed we have to compose the vectors r and W to obtain V that is the speed of the air relative to the examined section. The presence of FaFa  rr F1F1 F2F2 α M V W W originates an angle of attack  which creates an aerodynamic force F a. If we decompose F a in the showed directions, we have the thrust component F 1 and the torque component F 2. 

7. 7 THE ROTOR Considering the global effect of a wind flow on a rotor, it is possible to say that the rotor decelerates the flow, extracting energy from it and converting it into a mechanical motion. The efficiency of the energy conversion is normally indicated by a coefficient, the C p coefficient. The energy extracted in the unit of time is the power: The maximum value that C p can assume is 0,593 (Betz Theorem). W wind speed [m/s] A rotor area [m 2 ]  air density [kg/m 3 ] W u u1u1

8. 8 THE ROTOR The maximum air speed is reached at the blade tip: V R = R based on this value an important parameter is defined to describe the rotor performance, the TIP SPEED RATIO: and it gives an idea of how much the angle  is opened. The greater is  the smaller is , so it is possible to have an idea also of the angle of attack. W RR  α TIP 

9. 9 THE ROTOR To represent the rotor performances a plot is normally used in which the power coefficient is represented vs. the tip speed ratio. When looking at the plot it is possible to individuate a maximum in the Cp curve; there, also the rotor efficiency is maximum.

10. 10 THE FIXED RPM MACHINES In the fixed RPM machines the generator is directly connected to the grid and it means that the rotational speed of the generator is imposed by the grid frequency. So when the wind increases the angle of attack increases, the torque on the rotor increases and the generator opposes an equi- valent torque without substantially changing its RPM. The increase in the power (P=C) is only due to the torque increase. The TSR changes due to wind speed changes being R constant.  W1W1 RR 11 α1α1 W2W2 22 α2α2 TIP

11. 11 THE FIXED RPM MACHINES As it is possible to observe in the picture the optimal angle of attack (so the maximum rotor efficiency), is obtained only at a specific wind speed. So it is possible to say that the rotor is “adapted” to that wind speed and theoretically only to specific sites.  W1W1 RR 11 α1α1 W2W2 22 α2α2 TIP This is also visible in the typical Cp plot vs. TSR where the Cpmax is reached at a specific TSR and so at a specific wind speed.

12. 12 THE VARIABLE SPEED MACHINES In the variable speed machines it is possible to maintain the angle of attack constant at its optimal value for a large range of wind speeds as shown in the figure on the left side. The effect on the energy capture is remarkable. In this case the generator is not directly con- nected to the grid; in particular the rotor currents pass through a frequency converter while the stator is directly connected to the grid. This system, named double fed generator, allows a rotational speed change of about 60% of the nominal speed and it has been patented by Vestas under the name Opti-Speed ®. W3W3 1R1R 11 α  W1W1 2R2R W2W2 3R3R TSR=constant TIP

13. 13 VARIABLE SPEED vs FIXED RPM The plot representing the rotor performance (C p ) vs. wind speed is shown in the figure below reported for both the variable sped and fixed speed machines. C p = C p max zone