Shape Optimisation of Wind Turbine Blades
Figure 1: Chord (A) and Twist (B) Angle Distributions of the Original and Optimised National Renewable Energy Laboratory 5MW Virtual Rotor
A 5 4 3 2 1 0 10 20 30 Optimized rotor B 15 40 Radius (m) Original rotor 50 60
Figure 2: Axial Induction Factor of the Original and Optimized National Renewable Energy Laboratory 5MW Virtual Rotor at a Wind Speed of 9m/s
0.4 0.5
0.3 0.2 0.1 0 010 20 30 Radius (m) Optimized rotor
Original rotor 40
50 60
10
To investigate why the optimised rotor with a smaller chord produces almost the same power as the original rotor, the performance of the rotor is investigated at a wind speed of 9m/s. Figure 2 shows the axial induction factor. From the figure, the axial induced velocity interference factor of the optimised rotor is found to be about one-third in the region of 30 to 50m, whereas the original rotor has a linearly changing value of 0.3 to 0.4. As it is known that the maximum power coefficient occurs at an axial induction factor of about 1/3, the optimised rotor has almost reached the maximum power coefficient and is expected to be optimal. On the other hand, since the optimised rotor has an important chord reduction in this region, the optimised rotor is economically more efficient. The almost same tangential force for the optimised rotor is achieved with a smaller twist angle at a radial position between 20 and 40m and with a smaller axial induction factor (which results a bigger angle of attack) at a radial position between 40 and 60m.
5 0 10 20 30 Optimized rotor 40 Radius (m) Original rotor
The optimisation converges after about 36 iterations. The chord and twist angle distributions of the original and optimised virtual NREL rotor are shown. A: The original rotor attains an almost linear chord distribution, whereas the optimised blade has a faster decrease after 30m. In the region between 30 and 48m, the optimised rotor has a smaller chord than the original rotor. The chord reduction reaches a maximum value of about 8.2% at a radius of 40m. Between 48 and 60m on the blade, the optimised rotor has a slightly smaller chord than the original rotor. B: The twist angle is significantly reduced in the region between 25 and 35m, whereas it is almost the same on the rest of the blade. The power of the optimised rotor is almost the same as the original National Renewable Energy Laboratory (NREL) rotor while the cost of the optimised rotor is reduced. At a rated wind speed of 11.5m/s, the output power of the optimised rotor reaches 5MW as the original NREL rotor. The virtual NREL 5MW rotor is designed as a pitch-controlled rotor. When the wind speed is greater than the rated 11.5m/s, the output power of the rotor is reduced to 5MW. The annual energy production of the optimised rotor is only reduced about 0.1%, whereas the cost of the rotor has been reduced by 2.7%. The cost of energy for the NREL virtual rotor is thus reduced by about 2.6%.
In the optimisation process, the lower limits for chord, twist angle and relative thickness were 0m, 0° and 18%, respectively, and the upper limits were 5m, 15° and 100%, respectively. The maximum values of the design variables for the optimised rotor were chosen to be the same as the original rotor. To reduce the computational time, four points along the blade were used to control the shape of the blade. The rotor diameter, rotational speed of the rotor and airfoil shapes remained unchanged in the optimisation.
To illustrate shape optimisation, the 5MW NREL virtual turbine is considered. The optimised NREL 5MW rotor attains a chord reduction of
1. 2. 3.
Fuglsang P, Bak C, Schepers JG, et al., Site-specific design optimization of wind turbines, Wind Energy, 2002;5:261–79.
Wang X, Shen WZ, Zhu WZ, et al., Shape optimization of wind turbine blades, Wind Energy, 2009;12:781–803. Shen WZ, Mikkelsen R, Sørensen JN, Bak C, Tip loss
4. 50 60
about 8.2% at a radial position of about 40m and a slightly smaller chord on the outer part of the blade. The optimisation gives a smaller twist angle (higher angle of attack) in the mid-part of the blade. With the higher angle of attack, a higher lift coefficient can be obtained and thus a smaller rotor chord is required in this region. On the outer part of the blade, the reduction in chord is achieved through an optimal axial induction factor (closer to a 1:3 ratio) where a higher lift coefficient is obtained.
Conclusion
Shape optimisation of wind turbine blades is the way to obtain an aerodynamically efficient rotor at a minimum cost. To achieve this, a high lift-drag ratio and high lift are required. The maximum energy captured by the rotor per unit area is determined by the lift-drag ratio of the airofoils employed. On the other hand, the airofoil lift at the designed angle of attack determines the chord required. A higher lift characteristic gives a smaller chord for the same power coefficient.
To illustrate shape optimisation, the 5MW NREL virtual turbine was considered. It gave an 8.2% chord reduction, higher angle of attack, higher lift coefficient and had a smaller twist angle in the middle of the blade. This optimisation led to an overall reduction in energy cost of 2.6% for the same design load cases. Although these reductions are somewhat small and only loads from normal operation are used in the optimisation, the results demonstrate that shape optimisation represents a valuable tool for designing wind turbine blades. n
corrections for wind turbine computations, Wind Energy, 2005; 8:457-475.
Fuglsang P, Madsen HA, Optimization method for wind turbine rotors, J Wind Engineering and Industrial Aerodynamics, 1999,80:191–206.
5.
Jonkman J, Butterfield S, Musial W, et al., Definition of a 5- MW Reference Wind Turbine for Offshore System Development, NRELOffshrBsline5MW, NWTC/NREL TP-500-38060, Golden, CO, National Renewable Energy Laboratory/Cole Boulevard, National Wind Technology Center, 15 February 2007.
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MODERN ENERGY REVIEW – VOLUME 2 ISSUE 2
Twist angle (º)
Chord (m)
Axial induction factor
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