A New Method of Determination of the Angle of Attack on Rotating Wind Turbine Blades
Abstract
:1. Introduction
2. Definitions of Effective AoA and Nominal AoA
3. Method of Computing Self-Induction
3.1. Representing Airfoil by Distributed Vortices
3.2. Representing Blade by Distributed Vortices
4. Subtraction of Blade Self-Induction
5. Determination of Effective AoA
6. Comparison and Validation
6.1. Comparison Between Nominal AoA and Effective AoA
6.2. Validation of Extracted Lift and Drag Coefficients
7. Conclusions
- The determination of AoA depends on the consideration of different inductions (disc-induction, blade self-induction, and 3D-induction) experienced by the rotor blade. The blade self-induction should always be excluded, disc–induction leads to the nominal AoA, and the sum of disc-induction and 3D-induction, i.e., the tip-root-induction, leads to the effective AoA. The discrepancies between existing methods observed by other researchers are to some extent caused by the unclassified comparisons.
- The effective AoA and the nominal AoA are close to each other at mid-board sections but have different trends when approaching the tip. From the mid-board to the tip of the studied rotor, nominal AoA decreases first and then increases, while the effective AoA presents a downward trend and drops faster in the tip region.
- The difference between the nominal AoA and the effective AoA is the downwash angle. The ratio of the downwash angle to the nominal AoA keeps an identical regularity along the blade for different wind speeds, implying the feasibility to relate the effective AoA to the nominal AoA by establishing an engineering model.
- The extracted aerodynamic polar of both the mid-board and tip sections are consistent with each other as well as with the 2-D polar, which proves that the so-called 3-D polar is an appearance rather than a substance and the fundamentally aerodynamic difference between a blade section and its 2-D airfoil is caused by the variation of effective AoA. In fact, this conclusion is a basis of the BEM, VWT, or AL/NS method that determines the section forces from the 2-D airfoil data according to the effective AoA.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
axial interference factor | |
B | number of blades |
c | chord length |
Cl, Cd | lift and drag coefficients |
Cn, Ct | normal and tangential force coefficients |
an unit vector | |
unit vector in the x direction | |
unit vector in the y direction | |
unit vector in the z direction | |
L | lift |
length of a segment | |
pressure | |
pressure on the kth segment | |
pressure of the undisturbed wind | |
r | radial location of a blade cross-section |
R | rotor radius |
local velocity | |
axial velocity after self-induction subtraction | |
tangential velocity after self-induction subtraction | |
local velocity on the kth segment | |
induced velocity | |
induced velocity of distributed vortices | |
induced velocity of airfoil entity | |
wind speed | |
α | angle of attack |
αe | effective angle of attack |
αi | downwash angle |
αn | nominal angle of attack |
circulation of kth vortex | |
Γ | circulation of concentrated vortex |
relative error | |
θ | local pitch angle |
ρ | air density |
ψ | azimuthal angle |
rotational speed |
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Zhong, W.; Shen, W.Z.; Wang, T.G.; Zhu, W.J. A New Method of Determination of the Angle of Attack on Rotating Wind Turbine Blades. Energies 2019, 12, 4012. https://doi.org/10.3390/en12204012
Zhong W, Shen WZ, Wang TG, Zhu WJ. A New Method of Determination of the Angle of Attack on Rotating Wind Turbine Blades. Energies. 2019; 12(20):4012. https://doi.org/10.3390/en12204012
Chicago/Turabian StyleZhong, Wei, Wen Zhong Shen, Tong Guang Wang, and Wei Jun Zhu. 2019. "A New Method of Determination of the Angle of Attack on Rotating Wind Turbine Blades" Energies 12, no. 20: 4012. https://doi.org/10.3390/en12204012