The interaction between wind turbines through their wakes is an important aspect of the conception and operation of a wind farm. Wakes are characterized by an elevated turbulence level and a noticeable velocity deficit, which causes a decrease in energy output and fatigue on downstream turbines. In order to gain a better understanding of this phenomenon this work uses large-eddy simulations together with an actuator line model and different ambient turbulence imposed as boundary conditions. This is achieved by using the Simulator fOr Wind Farm Applications (SOWFA) framework from the National Renewable Energy Laboratory (NREL) (USA), which is first validated against another popular Computational Fluid Dynamics (CFD) framework for wind energy, EllipSys3D, and then verified against the experimental results from the Model Experiment in Controlled Conditions (MEXICO) and New Model Experiment in Controlled Conditions (NEW MEXICO) wind tunnel experiments. By using the predicted torque as a global indicator, the optimal width of the distribution kernel for the actuator line is determined for different grid resolutions. Then, the rotor is immersed in homogeneous isotropic turbulence and a shear layer turbulence with different turbulence intensities, allowing us to determine how far downstream the effect of the distinct blades is discernible. This can be used as an indicator of the extents of the near wake for different flow conditions.

An important aspect for the conception of wind farms is the turbine spacing, which depends on the interaction of wind turbines through their wakes. This
phenomenon can decrease the wind park energy output by up to 20 % due to
the velocity deficit propagated by the wakes

As opposed to the far-wake region

In order to evaluate the soundness of the present method, a comparative study
of the Simulator fOr Wind Farm Applications (SOWFA) framework, from the National Renewable Energy Laboratory (NREL), and EllipSys3D, from DTU, was conducted as
initially presented in

For the introduction of a turbulent inflow, different methods exist for
imposing a statistically generated velocity field, such as inserting it via a
momentum sink as done in

Then, shear layer turbulence

Finally, the numerical results are used to examine the spatial extents of the
near-wake region. While in previous work such as

The numerical simulations are based on the incompressible Navier–Stokes
equations:

The force term

Geometry and forces in an airfoil section of the blade.

The same unmodified airfoil coefficients were used as shown in

Midplane at

While the Glauert tip correction

Finally, in order to avoid spurious oscillations around the point of the
inserted force, the punctual force is distributed using a kernel function

Horizontal plane of the instantaneous axial velocity component

A synthetic velocity field representing homogeneous isotropic turbulence based on the von Kármán energy spectrum

While several implementations of this method exist, e.g.

In Fig.

Contrary to

Based on the Mann algorithm

Vertical plane of the instantaneous axial velocity component

The mean velocity profile is obtained via the power law

This work is realized within the open-source framework
OpenFOAM (version 2.2.2)

OPENFOAM (Open source Field Operation And Manipulation) is
a registered trade mark of OpenCFD Limited, producer and distributor of the
OpenFOAM software via

NWTC Design Codes (SOWFA (Simulator fOr Wind Farm
Applications) by Matt Churchfield and Sang Lee)

Axial profiles of phase-averaged (rotor position

The computational domain is cubic with an edge length of

For the boundary conditions, the velocity is imposed as a uniform inflow
velocity of

The large eddy simulations use the dynamic Lagrangian sub-grid-scale model

The pressure is resolved using a geometric agglomerated algebraic multi-grid
solver and the remaining variables are solved for with a bi-conjugate
gradient method using a diagonally based incomplete LU preconditioner. The
total simulation run-time comprises 60 rotor revolutions (

For the parameterization of the ALM, different distribution widths are chosen
in order to obtain the optimum for the examined case and 40 actuator points
are used to represent one blade in accordance with what was found in

The implementation was validated against EllipSys3D and verified against the Model Experiment in Controlled Conditions (MEXICO)
and New Model Experiment in Controlled Conditions (NEW MEXICO) experiment in

For the high-velocity case (

When refining the grid using the actuator line method, the distribution
parameter

Instead of relying on a constant

Relation between

The lower bound for the distribution parameter here is

As a general trend, it can be seen that

The optimal distribution parameter

Optimal

The curvature in Fig.

For an excerpt of the resolutions presented in Fig.

Radial profiles of time-averaged velocity components

In Fig.

In order to estimate the resolution necessary to obtain tip vortex radii as
seen in the MEXICO experiment, the vortex radii are shown in Fig.

This would necessitate a resolution of

Normalized vorticity

Normalized vortex radius

In Fig.

An important aspect when imposing a synthetic turbulence as boundary
conditions of a Computational Fluid Dynamics (CFD) simulation is respecting the Nyquist–Shannon sampling
theorem

When taking the case for TI

Despite the fact that the computational grid respects the Nyquist–Shannon criterion for signal sampling in respect to the synthetic grid, immediately at the inlet a part of the turbulence falls in the sub-grid range. Due to the numerical dissipation caused by the differencing schemes and turbulence modelling, the energy cascade hands down its energy to lesser scales than the resolved ones.

It should be kept in mind, that the turbulence intensity the rotor model is
experiencing through velocity sampling is the resolved turbulence intensity
TI

Longitudinal evolution of turbulence intensities for different
turbulent intensities at the inlet in HIT without rotor effects. For each
case the mean value

In Fig.

Normalized instantaneous axial velocity component

Normalized instantaneous vorticity

The energy spectra for the HIT based on the time series of the
axial velocity component at different points in the near wake (

In Fig.

As the velocity time series obtained from the simulations do not exhibit
periodicity, the Welch method

Vertical plane of the instantaneous axial velocity component

Instantaneous normalized vorticity

It is interesting to note that the distinct peaks in the spectra occur at the
wavenumber relating to the frequency of the blade passage and its harmonics.
The harmonics are caused by the strong excitement of the fluid by the blade
passage and its interaction with the non-linear term in the NS equations. As
the blade forces and hence the strength of the tip vortices are very
comparable, the peaks are very similar among the different cases for

When looking at the vertical planes in Fig.

While before and at the rotor position for

This means that in the near wake in a turbulent flow with an ambient turbulence
intensity of TI

The energy spectra for the shear layer flow based on the time series
of the axial velocity component at different points in the near wake
(

By using a validated actuator line implementation

It is also shown that with increasing grid resolution the spatial profiles
seem to converge. This would be one aspect of a grid-independent solution,
but it is still very far away from resolving the shed tip vortices correctly.
Although it seems to converge towards a value of

When looking at the turbulent inflow, a synthetic turbulence generated by the
Mann algorithm

As expected the wake does recover at a faster pace for a higher turbulence
intensity. It is very interesting to note that the turbulent structures of
the ambient flow eventually catch up with the amplitude of the structures
emitted by the rotor. This is already noticeable in the instantaneous
velocity fields but becomes even clearer when evaluating the spectra. When
considering the velocity fluctuations in the downstream flow caused by the
blade passages for determining the near wake, it can be observed that in this
case for TI

The SOWFA framework on which this work is based is made
available by NREL

Christian Masson is a member of the editorial board of the journal.

This work is partially supported the Canadian Research Chair on the Nordic Environment Aerodynamics of Wind Turbines and the Natural Sciences and Engineering Research Council (NSERC) of Canada. Thanks for the great work done by Matthew Churchfield and colleagues at National Wind Technology Center, Boulder, CO, by establishing the open-source framework SOWFA. The data used have been supplied by the consortium which carried out the EU FP5 project Mexico: “Model rotor EXperiments In COntrolled conditions”. Thanks a lot also to Gerard Schepers for providing results of the NEW MEXICO experiment. Edited by: Sandrine Aubrun Reviewed by: two anonymous referees