Wind Energy

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45 Modeling of the Far Wake behind a Wind Turbine 247
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Fig. 45.2. Average axial (a) and azimuthal (b) velocity profiles calculated by extended
model (boldline) and by the Joukowski model (dashedboldline). The symbols
are experimental data measured by Medici & Alfredsson [5] in different cross-sections
downstream from the rotor plane: z/a =2.8(square); 3.8 (diamond)and4.8(bullet)
time they need to fit to experimental observations. The proposed model obeys
both properties. To validate the extended model (45.3) we compare it to the
experimental results of Medici and Alfredsson [5]; see Fig. 45.2. A very good
agreement between modeled and measured velocity distributions are seen for
both the axial and azimuthal velocity components. In contrast to this, the
Joukowski model (45.1) results in an unrealistic 1/r behavior for the azimuthal
velocity and a constant for the axial velocity.
45.2 Unsteady Behavior
An interesting finding in the measurements of [5] was the appearance of a low
frequency in the wake. The frequency was an order of magnitude smaller than
that of the rotational frequency of the tip vortices. Medici and Alfredsson attributed
the phenomenon to be similar to the vortex shedding occurring in the
wake behind a solid disc determined from the Strouhal number. We will utilise
their experimental results to validate the developed model. In Fig. 45.3a we
depict a meandering wake subject to low-frequency oscillations. The measured
time signal of the axial velocity (Fig. 45.3c) near the boundary of the wake
is dominated by two frequencies with very high peaks superposed the highest
frequency. Such amplifications may be of crucial importance for the lifetime
of wind turbines located fully or partly in a wake. By adjusting the amplitude
of the low frequency to the measurements we compute a time signal of the
velocity (Fig. 45.3d) by de-centering the extended model (45.3) as shown in
Fig. 45.3b. The resemblance of the two time histories is striking.
Hence, with the new model, it is possible to model and predict unsteady
behavior of far wakes behind wind turbines.
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