The aim of the present study is the validation of the implementation of an
actuator disc (ACD) model in the computational fluid dynamics (CFD) code
PHOENICS. The flow behaviour for three wind turbine cases is investigated
numerically and compared to wind tunnel measurements: (A) the flow around a
single model wind turbine, (B) the wake interaction between two in-line model
wind turbines for a uniform inflow of low turbulence intensity and (C) the
wake interaction between two in-line model wind turbines at different
separation distances in a uniform or sheared inflow of high turbulence
intensity. This is carried out using Reynolds-averaged Navier–Stokes (RANS)
simulations and an ACD technique in the CFD code PHOENICS. The computations
are conducted for the design condition of the rotors using four different
turbulence closure models and five different thrust distributions. The
computed axial velocity field as well as the turbulence kinetic energy are
compared with hot-wire anemometry (HWA) measurements. For the cases with two
in-line wind turbines, the thrust coefficient is also computed and compared
with measurements. The results show that for different inflow conditions and
wind turbine spacings the proposed method is able to predict the overall
behaviour of the flow with low computational effort. When using the

The study of wake properties is important for assessing the optimal layout of
modern wind farms. Wind turbine wake development may be studied using field
experiments, small-scale wind tunnel measurements or numerical simulations
with computational fluid dynamics (CFD). There are several advantages of CFD
over field experiments and small-scale wind tunnel measurements, e.g. no
violation of similarity requirements, control over inflow conditions and
information about the relevant parameters, e.g. wind velocity, over the entire flow.
However, as CFD results are sensitive to the experience and knowledge of the
user of the CFD code and to the numerous computational parameters and
assumptions involved, it is imperative to perform validation studies.
Previous work on validating CFD wake models using a wind turbine tested in
wind tunnels has been presented by

Advanced methods of wake modelling with CFD may be implemented by using
large-eddy simulation (LES) techniques in which the wind turbine forces may
either be prescribed with an actuator line (ACL) method or an actuator disc
(ACD) method. Work along these lines has been performed by numerous
researchers such as

The aim of the present study is the validation of the implementation of an
ACD model in the CFD code PHOENICS

As this method is intended to be used for industrial purposes, it therefore
needs to provide accurate and reliable results with low computational effort.
The simulations are performed according to the “Blind test 1”, “Blind
test 2” and “Blind test 4” invitation workshops organized by NOWITECH and
NORCOWE (

Illustration of wind tunnel layout for

The paper unfolds as follows: Sect. 2 presents the experimental set-up of the workshops, in which the three test cases are outlined. This is followed by a description of the numerical method and of the computational settings used to perform the simulations. The results from the numerical simulations are introduced and discussed in Sect. 3. Lastly, in Sect. 4 the main conclusions of this study are presented.

The experiments are performed in the large closed-return wind tunnel
facility at the Norwegian University of Science and Technology (NTNU). The
test section for all three cases has the width (

In case A, the three-bladed wind turbine is positioned at a distance of
3.660 m from the inlet. The model wind turbine has a tower that consists of
four cylinders of different radii. The hub height is

Overview of cases.

For case B the stream-wise inlet velocity and turbulence intensity are
similar to case A. Here, two in-line wind turbines horizontally centred in
the wind tunnel are investigated, where the downwind wind turbine is the same
one as used in case A. The upstream wind turbine hereafter is always referred
to as

Case C is divided into two sub-cases, C1 and C2. For both sub-cases the same
wind turbines as in case B are used with a hub height of 0.827 m instead of
0.817 m. The distinction between sub-cases is made because the wind turbines
are exposed to different inflow conditions in terms of the wind velocity
profile and turbulence intensity as seen in Table

The simulations are performed with the commercial CFD code PHOENICS in which
the RANS equations are solved using four different turbulence models. The
turbulence models are (1) the standard

Thrust distributions over the disc, where

For the simulations no tower or hub effects are considered. The presence of
the rotor is modelled using an ACD method based on the 1-D momentum
theory. The thrust force

Normalized plot of all four distributions along a diameter of the disc.

For the first part of the simulations (case A) the numerical domain was
defined according to the wind tunnel geometry as reported in

For case B the domain geometry and the positioning of the wind turbines are
in accordance with the invitation sent out by

Lastly, for case C the domain geometry and the positioning of the wind
turbines are in accordance with the invitation sent out by

A grid independence study is carried out according to the recommended
procedure of

According to

Grid levels and size.

Overview of the cases for which results will be presented.

Normalized axial velocity and spatial discretization error computed
behind a single model wind turbine (case A) for three grids at

Normalized axial velocity for different wall functions plotted against the experimental data for four downstream distances from the inlet.

A summary of the cases for which results will be presented is shown in Table

Normalized axial velocity contours for the

Figure

Figure

Figure

For case A, the computed results are validated against HWA measurements for
the normalized axial velocity and normalized turbulence kinetic energy; see
Fig.

In Fig.

When keeping the turbulence model constant and changing the thrust
distribution, it is observed in Fig.

For case B when using the undistributed thrust, the normalized axial velocity
and stream-wise variance of the velocity at three positions downstream of
the second turbine are shown in Fig.

Empty-domain stream-wise velocity and turbulence intensity results
for case C1

For case B in which the wakes of both wind turbines interact, similar to the
results of case A, the

Thrust coefficients for case B and sub-cases C1 and C2 when using
the

Concerning sub-cases C1 and C2, empty-domain vertical profile results for
the stream-wise velocity and the turbulence intensity at four axial
positions downstream of the inlet are shown in Fig.

The empty-domain simulations presented in Fig.

Lastly, in terms of computational time or CPU hours, herein defined as the
number of CPUs

Averaged computational effort in CPU hours to perform the simulations of case A.

The main conclusions of this study are summarized as follows: (i) the present
results, considering the simplicity and low computational needs of the
method, generally show satisfactory agreement between the simulations and the
measurements used for both the set-up with one wind turbine (case A) and the set-up with two
in-line wind turbines (cases B and C). (ii) The effect of using
different thrust distributions on the profiles is generally present in the
near wake and fairly absent in the far wake. Moreover, the impact on the near
wake is more pronounced for the set-up with a single wind turbine than in the set-up with two
wind turbines. (iii) The uniform and undistributed thrust
distributions generally outperformed the other distributions in terms of the
estimated wake. Please note however that the uniformly distributed thrust
might not be the best suited when considering near-wake effects if a full-size wind turbine that typically has a non-uniform thrust
distribution is modelled. (iv) Changing the turbulence model has a noticeable impact on
the wake development in the cases with low background turbulence intensity. When
using the

This method has shown to give reliable results for a number of different wind flow conditions and separation distances with respect to the case with a single in-line wind turbine and the case with two in-line wind turbines. However, it has not been validated yet for wind turbines operating in a situation in which only a part of the rotor is in the wake of the upstream wind turbine (partial wake situation). Moreover, it has also not been validated against operational data measured within existing wind farms operating in full-scale atmospheric conditions. Therefore, future research will focus on validating the method against data retrieved from operating wind farms. Cases in which wind turbines operate partially in the wake of the upstream turbine will be of special interest as well.

The data presented in this article can be obtained by contacting the corresponding author.

The authors declare that they have no conflict of interest.

This work is financially supported by the Research Council of Norway (project no. 231831). The authors would also like to thank the Norwegian Technical National University and especially Jan Bartl for providing the experimental data. Andrew Barney is also gratefully acknowledged for assisting in the proof-reading of the paper. Edited by: Horia Hangan Reviewed by: Paul van der Laan and one anonymous referee