Wind Energy

15
Simulation of Turbulence, Gusts and Wakes
for Load Calculations
Jakob Mann
15.1 Introduction
In order to simulate dynamic loads on a wind turbine rotor it is necessary to
simulate the turbulent inflow to the rotor realistically. In this paper we review
various methods to do so. In many situations, for example for strong winds
over flat terrain, turbulence may be considered for practical load calculation
purposes not far from being Gaussian. In this situation it is enough to know the
second-order statistics, e.g. spectra and cross-spectra, to be able to simulate.
The second-order statistics are either obtained from empirical one-dimensional
spectra and coherences as in the Sandia method, or from a semi-empirical
three-dimensional spectral tensor as in the Mann model [4,5]. These methods,
which both appear in the third edition of the IEC standard 61400-1, will be
compared.
The assumptions of the models; stationarity, homogeneity, and gaussianity,
can all be questioned, especially when the terrain is not simple or when
turbines appear in wind farms. Here a variety of methods are possible and we
will present a few practical examples of these. Particular emphasis will be put
on “constrained Gaussian simulation” where extreme gusts can be embedded
in a turbulent field. This method can also be used simulate entire fields based
on measurements in a few points. Practical simulations of wake turbulence
based on meandering will also be presented together with preliminary remote
sensing measurements [2].
15.2 Simulation over Flat Terrain
The basis of most practical models to simulate the inflow turbulence for aeroelastic
codes, such as HAWC and FLEX, is the second order statistics. It
is true that real turbulence can not be gaussian. This can, for example, be
seen from the famous relation � δv�(r) 3� = − 4
5εr [3], which states that the
mean of the cube of difference in the velocity component along the separation