Wind Energy

S(ƒ)(m/s) 2 /Hz
15 Simulation of Turbulence, Gusts and Wakes for Load Calculations 89
1
0.1
0.01
Meas. on blade
Veers 1D
Veers 1D (dir.)
1 2 3
Frequency ƒ (Hz)
S(ƒ)(m/s) 2 /Hz
0.01
Fig. 15.1. Rotationally sampled turbulence spectra
15.3 Constrained Gaussian Simulation
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0.1
Meas. on blade
3D Simul.
1 2 3
Frequency ƒ (Hz)
Special phenomena such as micro-bursts or weird gusts in complex terrain are
not taken into account in the simulation described above. Here constrained
simulation may be of value. Constrained for wind turbines has been created
recently [1] and developed further and formulated differently by Risø.
An example is shown in Fig. 15.2, where a wind increase of 10 m s −1 over
20 m (corresponding to a time 20 m/U) in the center of the rotor plane is simulated.
The field is random but is required to display the sudden velocity jump.
It should be emphasized that the constrained simulation is still Gaussian and
that incompressibility is still obeyed [6]. The three-dimensional second-order
tensor behind the simulation is described in detail elsewhere [4].
The flexibility of the method is tremendous, but it is not clear how to
determine the shape and amplitude of the most critical gusts at a given site.
15.4 Wakes
Another important aspect of dynamic loads is wakes. Turbines in parks often
experience large fluctuations in wind speed because an upwind turbine creates
a meandering wake. Blades going in and out of this wake can, if the turbines
are very close to each other, cause very large loads.
15.4.1 Simulation
We would like to construct simple models of the inflow to turbines in wakes
able to produce wind fields suitable for dynamic load calculations.
One such model is shown in Fig. 15.3 where the velocity deficit from eight
turbines is advected passively by a large scale turbulent field. This field is
simulated according to Mann (1998), but on a quite crude resolution. The
wakes expand according to CFD calculation in essentially laminar flow.