## D corrections

In the state-of-the-art design codes 2-D aerofoil data obtained from wind tunnel experiments at the appropriate Reynolds number is used to represent the aerodynamic properties of wind turbine rotor blades. Recall that wind tunnel data is obtained from measurements on non-rotating aerofoil sections, whereas the resulting lift, drag and moment coefficients are applied to rotating wind turbine blades. This approach leads to reasonable prediction of wind turbine loads for attached or equivalently un-

separated flow, but is known to become unsatisfactory for (partially) separated flow conditions [268]. Experiments on rotating blades show a stall-delay and increased lift coefficients at angles of attack beyond the 2-D stall point. The main cause for this is the effect of rotation [14].

Although in principle relevant for all types of wind turbines, the above problem is especially important for stall regulated wind turbines. The interested reader is referred to Snel et al. [274] for the physical explanation of the differences between 2-D stall and 3-D separation on rotating blades as well as for a review of the theoretical and experimental work done on 3-D effects on rotating blades.

Consequently, the 2-D aerofoil data has to be corrected to provide accurate predictions of the aerodynamic forces in stall. For a non-rotating blade (i.e. wing) it is common to use the Prandtl correction equations [23]. In case of a rotating blade the 3-D effects become more complex because of the centrifugal forces acting on the air particles in the boundary layer of the rotor blade. At present, there is no (simple) theory to account for these effects. Hence, semi-empirical methods are to be used. The measured 2-D lift coefficients in stall are corrected by either the Snel et al. [274] or Viterna & Corrigan (semi-empirical) method [9, 279, 300].

In Fig. 2.4 the 2-D lift Cl as well as drag Cd coefficients of a NACA-63615-2D aerofoil are corrected using the aforementioned semi-empirical correction methods. A section with a chord-to-radius ratio of 0.25 is applied because 3-D effects are more pronounced near the blade root. The Snel et al. 3-D correction results in a stall-delay and increased lift coefficients at angles of attack beyond the 2-D stall point. The Viterna & Corrigan 3-D correction results in a smaller lift gradient, equal maximum value for Ci, and a smooth curve in the post-stall region. The drag coefficient is larger for attached flow, but smaller for stalled flow.

Figure 2.4: Effect of 3D-correction on 2D-lift coefficient C[2D- as function of the angle of attack a of NACA-63615-2D aerofoil for c = 0.251. Solid line: 2D-data, Dashed line: Snel et al., and Dashed-dotted line: Viterna & Corrigan.

Figure 2.4: Effect of 3D-correction on 2D-lift coefficient C[2D- as function of the angle of attack a of NACA-63615-2D aerofoil for c = 0.251. Solid line: 2D-data, Dashed line: Snel et al., and Dashed-dotted line: Viterna & Corrigan.

Obviously, the correction methods for 3-D effects in stall implemented in the state-of-the-art design codes result in quite different modified aerofoil characteristics. As 3-D correction is especially important for stall regulated wind turbines, it will become of lesser importance due to recent developments towards wind turbines operating at variable speed.

In Table 2.1, and Table 2.2 on page 40, and 41 respectively, it is summarized which correction (i.e. blade tip and root, turbulent wake state, dynamic inflow, dynamic stall and 3-D) is implemented in which state-of-the-art design code. It can be concluded that in the state-of-the-art design codes the rotor aerodynamics are - without exception - treated with Glauerts blade element momentum theory. Although the Glauert blade element momentum theory is well-established and widely used, it is necessary to have experimental verification of it for wind turbine rotor analysis. Furthermore, more research is needed to determine the most appropriate turbulent wake state model. The most challenging problem, however, for modelling rotor aerodynamics for stall regulated wind turbines is to improve the predictions of 3-D effects and that of dynamic stall. With the recent developments towards wind turbines operating at variable speed, however, these phenomena will become of lesser importance.

Relevant for all types of wind turbines, on the other hand, is accurate prediction of yawed flow. From the practical point of view, yawed flow (yaw misalignment, skewed wake effects or oblique flow) is a fact of life, and is of paramount importance since an important part of fatigue lifetime consumption of rotor blades can be attributed to these conditions. In addition, it is of importance to the load spectra of yaw bearing, tower, and rotor shaft. Hence, corrections must be made to the blade element momentum theory when the rotor operates at a yaw angle. Although considerable progress has been made, the results are not yet sufficiently accurate when compared with measurements.

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