For load calculations on wind turbines it is usually assumed that the turbulence approaching the rotor does not change its statistics as it goes through the induction zone. We investigate this assumption using a nacelle-mounted forward-looking pulsed lidar that measures low-frequency wind fluctuations simultaneously at distances between 0.5 and 3 rotor diameters upstream. The measurements show that below rated wind speed the low-frequency wind variance is reduced by up to 10 % at 0.5 rotor diameters upstream and above rated enhanced by up to 20 %. A quasi-steady model that takes into account the change in thrust coefficient with wind speed explains these variations partly. Large eddy simulations of turbulence approaching an actuator disk model of a rotor support the finding that the slope of the thrust curve influences the low-frequency fluctuations.

It is routinely and often implicitly assumed in load calculations on wind turbines that the statistics of the turbulence do not change as the flow is approaching the rotor plane. As it is well known that the rotor affects the mean flow in front of the rotor it cannot be ruled out that the turbulence is also affected. In this paper we investigate this assumption experimentally with lidar measurements and large eddy simulation and compare the results with a simple model. We focus on low-frequency wind speed fluctuations.

The change in the turbulence spectrum due to the stagnation in front of the
rotor is investigated theoretically using rapid distortion theory by

In Sect.

Low-frequency fluctuations are the focus of this paper and are discussed
first. Then we summarize the results of

Low-frequency or quasi-steady fluctuations are defined as variations in the
wind speed

For a particular wind turbine, the mean wind speed on a line extending
upstream from the center of the rotor depends on the ambient wind speed

Rapid distortion theory (RDT) for smaller turbulent scales corresponding to
more rapid fluctuations is investigated by

Amplification of the low-frequency spectrum and variance of
longitudinal turbulence in the center of the rotor plane according to rapid
distortion theory in the limit at which the length scale of the turbulence is
much smaller than the rotor radius. The induction factor is

The theory assumes that the vorticity lines are advected by the mean flow and
that the approaching turbulence is isotropic as described in the Introduction
and by

Now we analyze the applicability of RDT by estimating the relevant spatial and
temporal scales. The term “rapid” in RDT means that the turbulent eddies
should not be able to interact during the time it takes for the distortion of
the flow to take place. The eddies should not “rotate” several times during
the distortion phase; in other words, their lifetime

The novelty of

The wind turbine rotor is modeled as an actuator disk (AD) using the
implementation proposed by

The thrust force per unit area applied on the disk is assumed uniform and
given by

Thrust coefficient

The loading and power of the real Siemens turbine is controlled by regulating
the rotational speed and pitch of the blades. The control essentially depends
on the local flow conditions at the rotor disk. Thus, using

The computational domain is Cartesian and has dimensions

The boundary conditions are as follows: a fixed uniform velocity
is prescribed at the inlet (

The turbulent inflow is generated using the model of

The turbulent fluctuations are introduced into the computational domain in a
cross section located 8.25

The simulations are carried out using the incompressible Navier–Stokes flow
solver EllipSys3D

The experiment took place at a 13-wind-turbine farm in northern Denmark in
generally flat terrain. A five-beam pulsed prototype lidar from Avent was
mounted on the nacelle of a Siemens 2.3MW wind turbine with a hub height of
81.8 and

The line-of-sight velocity in the range gate centered around 235 m from the
lidar and the wind speed from a WindSensor cup anemometer at the same
distance and at hub height is compared to ensure the viability of the lidar.
We find a slope deviating 1 % from 1 and a correlation coefficient of
0.98. The scatter is larger than other similar comparisons

Having ensured the quality of the measurements we calculate the 10 min
average of the

Change in low-frequency (

We now calculate the power spectrum of the velocity at each range gate in all
2 m s

The experimental results are summarized in
Fig.

Low-frequency (

We now turn to the analysis of the LES simulations. Since the turbulence is
not completely homogeneous in the stream-wise direction, we determine the
effect of the rotor on the fluctuations at a position

In Fig.

Since the theory by

Change in low-frequency (

The often used assumption that the statistics of turbulence approaching a wind turbine rotor are unaltered relative to its upstream values is investigated in this paper. Since the mean wind speed is reduced in the induction zone one cannot rule out the possibility that the turbulence is also affected.

A nacelle-mounted forward-looking pulsed lidar is used to measure low-frequency wind
fluctuations upstream of a wind turbine rotor situated in
flat, homogeneous terrain. It measures wind speeds simultaneously at
10 ranges between 0.5 and 3 rotor diameters upstream sampling at
0.2 Hz. The integral of the velocity spectrum up to a frequency of

A quasi-steady model that uses the

An implementation of an actuator disk model in a large eddy simulation is used to investigate the changes in detail. The simulation is not completely homogeneous in the along-wind direction so the changes in turbulence statistics are found by comparing otherwise identical simulation runs with and without the rotor at corresponding positions. The simulations support the finding that the slope of the thrust curve influences the low-frequency fluctuations, but the simple quasi-steady model overestimates the changes. The exact consequences for loads are not investigated in this work.

The simulation data are available on request from Niels Troldborg (niet@dtu.dk) and the lidar measurement data from Alfredo Peña (aldi@dtu.dk).

JM wrote most of the paper except
Sect.

This article is part of the special issue “Wind Energy Science Conference 2017”. It is a result of the Wind Energy Science Conference 2017, Lyngby, Copenhagen, Denmark, 26–29 June 2017.

This work is partly funded by the Unified Turbine Testing (UniTTe) project funded by the Innovation Fund Denmark (1305-00024B). Edited by: Jens Nørkær Sørensen Reviewed by: Mike Graham and one anonymous referee