Numerical simulations of the Vestas multi-rotor demonstrator (4R-V29) are
compared with field measurements of power performance and remote sensing
measurements of the wake deficit from a short-range WindScanner lidar system.
The simulations predict a gain of 0 %–2 % in power due to the rotor
interaction at below rated wind speeds. The power curve measurements also
show that the rotor interaction increases the power performance below the
rated wind speed by 1.8 %, which can result in a 1.5 % increase in
the annual energy production. The wake measurements and numerical simulations
show four distinct wake deficits in the near wake, which merge into a
single-wake structure further downstream. Numerical simulations also show
that the wake recovery distance of a simplified 4R-V29 wind turbine is
1.03–1.44

Over the past few decades, the rated power of wind turbines has been
increased by upscaling the traditional concept of a horizontal axis wind
turbine with a single three-bladed rotor. It is expected that this trend will
continue for offshore wind turbines, although the problems that arise from
realizing large wind turbine blades (

The multi-rotor concept is an old idea that dates back to the start of 19th
century. Between 1900 and 1910, a Danish water management wind mill, was
upgraded to a twin-rotor wind mill

The tip clearances between the rotors in multi-rotor wind turbines are
typically much smaller than a single-rotor diameter, and several authors have
shown that the operating rotors strongly interact with each other.

Figure

Power curve measurements of the 4R-V29 wind turbine were carried out to
quantify the effect of the rotor interaction on the power performance. For
this purpose, a test cycle of three stages was run repetitively, as
illustrated in Fig.

Test cycle of power curve measurements of the 4R-V29 wind turbine.

The reference wind speed is measured using a commercial dual-mode
continuous-wave lidar, ZephIR 300, manufactured by ZephIR (UK)

The total number of available measurement cycles is depicted in Fig. 4b and corresponds to 549 10 min data
samples or approximately 91.5 h for each stage between wind speeds of 4 and
14 m s

The wake of the 4R-V29 turbine has been measured by three ground based
short-range WindScanners

Topography around the 4R-V29 wind turbine, and an overview of wake
measurements. Panel

Figure

Atmospheric conditions during the near- and far-wake measurements as
measured at the V52 met mast.

A near-wake case is selected from three consecutive post-processed scans
measured between 21:36 and 22:03 GMT

Profiles of wind speed and turbulence intensity measured at the met
mast and corresponding logarithmic surface layer using

The wind speed and total turbulence intensity profiles measured at the met
mast during the near- and far-wake case recordings are depicted in
Fig.

Spectra of 35 Hz wind velocity data measured by the sonic anemometer at
44 m are used to fit Mann turbulence spectra

Summary of test cases based on wake measurements and corresponding input parameters for numerical computations.

Four different simulations tools are employed to model the 4R-V29 wind turbine: Fuga, EllipSys3D RANS-AD, MIRAS-FLEX5 and EllipSys3D LES-AL-FLEX5. The simulation methodology for each model, ranked from the lowest to highest model fidelity, is described in the following sections. Note that a high model fidelity corresponds to an intended high accuracy at the price of a high computational cost, although good model performance is not guaranteed. All simulations that are used to model the 4R-V29 wind turbine only assume a neutral atmospheric surface layer inflow. In addition, only flat terrain with a homogeneous roughness length is modeled; hence, the effects of the fjord-land roughness change and sloping terrain are neglected.

Fuga is a fast linearized RANS model developed by

EllipSys3D is an incompressible finite volume flow solver, initially
developed by

For the uniform inflow case, the numerical setup is fully described in

For the atmospheric surface layer flow case, the

The inflow conditions represent a neutral atmospheric surface layer that is
in balance with the domain (without the ADs):

The in-house solver MIRAS (Method for Interactive Rotor Aerodynamic
Simulations) is a multi-fidelity computational vortex model for predicting
the aerodynamic behavior of wind turbines and the corresponding wakes. It has
been developed at the Technical University of Denmark over the last decade,
and it has been extensively validated for small to large wind turbine rotors
by

In the present study, a lifting line technique is employed as the blade aerodynamic model. The blade bound circulation is modeled by a vortex line, located at the blade quarter-chord and subdivided into vortex segments. The vorticity is released into the flow by a row of vortex filaments following the chord direction (shed vorticity, which accounts for the released vorticity due to the time variation of the bound vortex) and a row of filaments perpendicular to the chord direction (trailing vorticity, which accounts for the vorticity released due to circulation gradients along the span-wise direction of the blade).

A hybrid vortex method is used for the wake modeling, where the near wake is
modeled with vortex filaments, and further downstream the filaments'
circulation is transformed into a vorticity distribution on a uniform
Cartesian auxiliary mesh, where the interaction is efficiently calculated
using fast Fourier transform-based method developed by

The prescribed velocity–vorticity boundary layer model (P2VBL) presented in

The Mann model

The mesh used has an extent of

The structure of EllipSys3D is similar to that described in
Sect.

LES applies a spatial filter on the Navier–Stokes equations, which results in
a filtered velocity field. The large scales are solved directly by the
Navier–Stokes equations, whereas scales smaller than the filter scale are
modeled using a sub-grid-scale (SGS) model, which provides the turbulence
closure. The SGS model is a mixed-scale model based on an eddy-viscosity
approach as described by

The turbines are modeled using the actuator line (AL) technique as described
by

The atmospheric boundary layer is modeled by applying body forces throughout
the domain, see

Turbulence has also been introduced 2 D upstream the turbines using body
forces (see e.g.,

The computational mesh is

The simulations were run with time steps of 0.0063 and 0.0069 s for the near- and far-wake case, respectively.

The statistics presented are based on 10 min of data, which were sampled after the initial transients propagated through the domain, similar to the results using MIRAS-FLEX5.

Comparison of simulated mechanical power and thrust of a single V29 rotor using HAWC2, FLEX5 and EllipSys3D RANS-AD.

Comparison of simulated tangential

A comparison of the V29 rotor models from EllipSys3D RANS-AD and FLEX5 (used
by EllipSys3D LES-AL-FLEX5 and MIRAS-FLEX5) is made with a HAWC2 model of the
V29 provided by Vestas Wind System A/S. The Fuga rotor model is not
compared with the other models because the chosen thrust force distribution
is uniform and the total thrust force is a model input. Here, the deflections
are switched off in FLEX5 and HAWC2 in order to make a fair aerodynamic
comparison with EllipSys3D RANS-AD that can only model stiff blades.
The near-wake model of

The mechanical power and thrust force as function of the undisturbed wind
speed are plotted in Fig.

The normalized tangential and thrust force distributions for three different
wind speeds (7, 12 and 18 m s

Relative difference between the 4R-V29 wind turbine with all rotors in operation and the 4R-V29 wind turbine with a single rotor in operation, in terms power and thrust as function of the free-stream velocity at a height of 44.27 m.

The measured and simulated relative difference in power (

The RANS-AD simulations in Fig.

The rotor individual relative difference between the 4R-V29 wind turbine with all rotors in operation and the 4R-V29 wind turbine with a single rotor in operation, in terms of power and thrust as function of the free-stream velocity at a height of 44.27 m.

Two results of MIRAS-FLEX5 for respective wind speeds of 7 and 10.6 m s

Near-wake case: contours of stream-wise velocity at three downstream distances.

Near-wake case: profiles of stream-wise velocity at three heights and three downstream distances.

Results of the near-wake test case are discussed in
Sect.

Near-wake case: profiles of turbulence intensity at three heights and three downstream distances.

Contours of the stream-wise velocity at three downstream distances, measured
by the short-range WindScanner and simulated by four models (LES-AL-FLEX5,
MIRAS-FLEX5, RANS-AD and Fuga) are depicted in Fig.

Profiles of the stream-wise velocity normalized by the inflow at three
heights, corresponding to the bottom rotor hub height (29.04 m), the center
reference height (44.27 m) and the top rotor hub height (59.5 m) are
plotted in Fig.

The measurements and all of models, except Fuga, show the buildup of a
traditional double bell-shaped near-wake profile at the center height in
the downstream direction, as depicted in Fig.

Profiles of the turbulence intensity

Far-wake case: contours of stream-wise velocity at three downstream distances.

The results of the far-wake case are plotted in Figs.

Far-wake case: profiles of stream-wise velocity at three heights and six downstream distances.

The inflow Mann turbulence that is used in LES-AL-FLEX5 and MIRAS-FLEX5
results in a turbulent kinetic energy profile that has a higher value near
the ground and a lower value above the center height compared with the
reference turbulent kinetic energy at the center height. The turbulent
kinetic energy profile in the RANS-AD simulations is constant with height.
Hence, the comparison of the RANS-AD simulations with the LES-AL-FLEX5 and
MIRAS-FLEX5 simulations in terms of turbulence intensity
(Fig.

The presented near- and far-wake cases show that the models follow the measured trends, but there are not enough measured data to validate the simulations. More wake measurements of the 4R-V29 wind turbine are required in order to perform a model validation.

Far-wake case: profiles of turbulence intensity at three heights and six downstream distances.

Definition of the simplified 4R-V29 multi-rotor wind turbine and an equivalent V58 single-rotor wind turbine for three ambient turbulence intensities.

RANS predicted wake recovery of a simplified 4R-V29 multi-rotor wind
turbine compared with an equivalent V58 single-rotor wind turbine for three
difference turbulence intensities.

The wake recovery of a multi-rotor wind turbine is very important for placing
several multi-rotors together in wind farms. Therefore, the aim here is to
quantify the wake recovery of a multi-rotor wind turbine operating in an
atmospheric surface layer with respect to an equivalent single-rotor wind
turbine that has the same rotor area, force distributions, tip speed ratio
(TSR) and total thrust force. In order to do so, a simplification of the 4R-V29 wind
turbine is used so that a fair comparison with a equivalent single-rotor
wind turbine can be made. The simplified 4R-V29 wind turbine has a zero
toe-out angle, and the force distributions are defined by prescribed
normalized blade force distributions (calculated by

Figure

Figure 18b, d and fshow that the added wake turbulence is larger for the
multi-rotor wind turbine in the near wake for

The increased wake recovery of a multi-rotor wind turbine could be related to
the fact that the total thrust force is more distributed compared with a
single-rotor wind turbine.

Numerical simulations and field measurements of the Vestas multi-rotor wind turbine (4R-V29) have been performed. The simulations show an increased thrust force and axial induction of the 4R-V29 wind turbine compared with a single rotor. In addition, the simulations calculate a 0 %–2 % enhancement of the power performance of the 4R-V29 multi-rotor wind turbine below the rated wind speed due to the interaction of the rotors. The largest gain in power is obtained for a low turbulence intensity that is associated with a low shear. The relative power gain is largest for the bottom rotor pair. Power curve measurements of the 4R-V29 wind turbine also show that rotor interaction increases the power performance below the rated wind speed by 1.8 %, which can result in a 1.5 % increase in the annual energy production.

Two flow cases based on short-range WindScanner wake measurements of the 4R-V29 wind turbine are used to compare the multi-rotor wake deficit simulated by four numerical models. In the near wake, four distinct wake deficits are visible that merge into a single structure at a downstream distance of 2–3 D. More wake measurements are required to validate the numerical models.

The wake recovery of a simplified 4R-V29 wind turbine is quantified by
comparison with the wake recovery of an equivalent single-rotor V58 wind
turbine. RANS simulations show that the wake recovery distance in terms of
the stream-wise velocity of the simplified 4R-V29 wind turbine is
1.03–1.44

The numerical results are generated using proprietary software, although the data presented can be made available upon request from the corresponding author.

The measured effect of rotor interaction on the power production is
quantified using the test cycle in Fig.

Induction correction factor for the measured reference wind speed of the 4R-V29 wind turbine.

The influence of the ambient turbulence intensity at a height of 44.27 m on

MPVDL performed the EllipSys3D RANS-AD and Fuga simulations, produced all figures and drafted the article. SO, MPVDL and MK investigated the meteorology of the wake measurements. SJA and NRG performed the EllipSys3D LES-AD-FLEX5 and the MIRAS-FLEX5 simulations, respectively. GRP contributed to the validation of the numerical single-rotor models. NA, MS and TKM planned, executed and post-processed the WindScanner wake measurements. KHS and JXVN executed and post-processed the power curve measurements. GCL planned and managed the research related to this article. All authors jointly finalized the paper.

The authors declare that they have no conflict of interest.

This is work is sponsored by Vestas Wind System A/S.

This paper was edited by Johan Meyers and reviewed by Peter Jamieson, Dominic von Terzi and one anonymous referee.