# Yawed Flow Operation

While ideally the wind turbine operates with the wind direction normal to its plane of rotation, this is never achieved in practice and there is always some yaw misalignment to the wind flow. This produces a velocity component parallel to the plane of rotation of the turbine disk, which leads to unsteady aerodynamic forces and also to a skewed wake. This is analogous to the helicopter rotor in forward flight, where the wake is blown back behind the disk. This skewed wake is responsible for an inflow gradient across the wind turbine disk. While the gradients are particularly strong parallel to the direction of the wake skew, a gradient is also produced in the other direction because of the asymmetry in aerodynamic loads between the effective advancing and retreating sides of the disk.

While the origins of this induced velocity distribution are complex (see Section 13.11 for a detailed discussion), a number of mathematical models for the effects have been derived, mostly following the linear inflow models developed for the helicopter case (see Section 3.5.2). Snel (2001) gives a review. The general approach is to correct the value of the induction ratio predicted from the BEMT by using an equation of the form

aY = a{ + Ks(y)r sin jr + Kc(y)r cos jf), (13.63)

where у is the yaw misalignment angle of the turbine disk with respect to the wind and aY is the corrected value of the induction ratio. The correction technique can be applied a posteriori using the values for a in the unyawed case, although the validity of this approach is perhaps questionable. Another variant of the technique is to correct the value of a based on the yaw angle and then to perform an iterative series of momentum balances at each of the elements until the values for a converge. This is a more pleasing approach.

The coefficients Ks and Kc used in practice have been based on a number of assumptions and approaches, including results for the helicopter case (Section 3.5.2) as well as from inflow measurements made on subscale wind turbines in wind tunnels. For instance, the skewed cylindrical wake model of Coleman et al. (1945) seems to have received some

attention for use in wind turbine analyses. In this case, the Ks is related to the wake skew

angle using

Ks = tan(x/2), (13.64)

where, as shown by Burton et al. (2001), x can be related approximately to the yaw angle and induction factor using

X = (0.6a + 1) y. (13.65)

In another example, inflow measurements were made using a 1.2-m-diameter subscale wind turbine placed in the open jet wind tunnel and used to determine the inflow coefficients, including higher harmonic variations – see Schepers (1999). The mathematical form of the inflow model given in Eq. 13.63 has been compared to measurements of blade airloads. It would seem if these inflow effects are properly accounted for then considerable improvements in the prediction of the loads under yawed operations are possible, at least for small yaw misalignment angles. Nevertheless, the approach of correcting the induction ratio in this manner is not rigorously valid because it violates the principles under which the BEMT equations were derived in the first place, including the

need for axisymmetric flow. Approaches based on vortex theory are probably the next best practical level of analysis of this problem.