This paper applies a large-eddy actuator line approach to the simulation of wind turbine wakes. In addition to normal operating conditions, a specific focus of the paper is on wake manipulation, which is performed here by derating, yaw misalignment and cyclic pitching of the blades. With the purpose of clarifying the ability of LES methods to represent conditions that are relevant for wind farm control, numerical simulations are compared to experimental observations obtained in a boundary layer wind tunnel with scaled wind turbine models. Results indicate a good overall matching of simulations with experiments. Low-turbulence test cases appear to be more challenging than moderate- and high-turbulence ones due to the need for denser grids to limit numerical diffusion and accurately resolve tip-shed vortices in the near-wake region.
Wind plants are collections of wind turbines often operating in close
proximity of one another. Several complex phenomena take place within a wind
farm. First, there is an interaction between the atmospheric boundary layer
and the whole wind farm caused by the smaller-scale interaction between the
atmospheric flow and each individual wind turbine. Second, within the power
plant itself, there is an interaction among upstream and downstream wind
turbines through their wakes. In turn, the wakes themselves interact with the
atmospheric flow and other wakes, playing a central role in determining
the overall behavior of the plant. Wakes produced by upstream wind turbines
may have a profound influence on the performance of downstream operating
machines. In fact, waked turbines experience lower power output and increased
loading compared to clean isolated conditions. A thorough understanding of
these complex phenomena is clearly indispensable for optimizing the layout
and operation of wind plants. However, even an optimal layout will still
incur negative effects due to wake
interactions, at least in some wind and environmental conditions. To mitigate
these effects, a number of control strategies are currently being
investigated to optimize the operation of wind power plants, including power
derating, wake deflection and enhanced wake recovery
The current research in this field is very active, covering a broad spectrum
that ranges from high-fidelity numerical simulations to reduced order models,
from scaled experiments in the wind tunnel to direct measurements in the
field, all the way to control methods and various supporting technologies.
Among the many studies reported in the literature, meteorological and
performance data collected at the Horns Rev and Middelgrunden offshore wind
farms have been systematically investigated
With the significant increase in computational performance in recent
years (thanks to advancements in hardware, software and algorithms), LES has
gained an increasing adoption by the wind farm research community
Although LES is an approach based on first principles, it is still not
completely tuning-free. For example, when used in conjunction with an
actuator line method (ALM) to represent wind turbine blades, there is a need
to properly tune the procedure used for mapping lifting line aerodynamic
forces onto the volumetric grid
In general, most of the published research focuses on the use of CFD to study wake behavior and control strategies, but pay relatively less attention to the problem of ensuring the fidelity of such simulations to reality. In fact, a comprehensive validation of LES methods for wind turbine wakes is still missing. This is clearly not due to a lack of attention to this problem, but rather to a lack of comprehensive high-quality data sets. Unfortunately, experiments in the field are not without hurdles: in fact, wind conditions cannot be controlled, and measurements at full scale are not always possible or complete. In this sense, testing at scale in a wind tunnel is gaining attention as a means to perform experiments with much more precise knowledge and control of the testing conditions.
As a contribution towards a better understanding of the capabilities and
limits of LES for modeling wind turbine wakes, this paper applies a recently
developed computational framework to the simulation of scaled wind turbines.
These models were operated in a large boundary layer wind tunnel in a variety
of conditions. A complete LES-based digital model of the experiments is
developed in this work, including a model of the wind tunnel and of the
passive generation of sheared and turbulent flows. The paper specifically
focuses on operating conditions that are relevant to wind farm control. In
fact, the existing literature either uses LES to study wind farm control
conditions without comparing simulations against experiments
The present LES framework is characterized by some distinguishing features.
First, the tuning-free immersed boundary (IB) method of
The problem of computational cost is addressed in a companion paper
The paper is organized according to the following plan. The numerical method
is described in Sect.
The present LES framework is developed within
The rotor is modeled in terms of actuator lines by direct coupling with the
aeroservoelastic simulator
Both the constant Smagorinsky (CS)
The IB formulation of
ALM-modeled blades and an IB-modeled nacelle and tower
introduce local numerical dispersion and diffusion, which affect simulation
stability and accuracy
Table
Linear algebraic solvers used for the precursor and the wind turbine–wake simulations (CG: conjugate gradient; GAMG: geometric–algebraic multigrid; DIC: diagonal incomplete Cholesky; GS: Gauss–Seidel; DILU: diagonal incomplete LU factorization; NOC: non-orthogonal corrector).
Clearly, the accuracy of the sectional aerodynamic coefficients is a crucial
ingredient of the ALM formulation. A method to tune the aerodynamic polars of
lifting lines was described in
Nominal values of both the lift and drag coefficients
The unknown correction terms are computed by maximizing the likelihood
function of a sample of
More than 100 operating points were measured experimentally. The operating conditions were determined in order to cover a desired range of angles of attack and Reynolds numbers, and they were obtained by operating the scaled wind turbine model at different tip speed ratios (TSRs) and blade pitch angles. Experiments were then grouped in terms of average blade Reynolds number, and for each group a separate identification was performed, yielding a calibrated version of the polars at that specific Reynolds.
The LES-ALM numerical model was used to create a complete digital copy of the
experiments, which were conducted in the 36 m
A first simulation is used to generate the turbulent inflow (precursor) used
as an inlet for successive wind turbine–wake (successor) simulations. The layout
of the partially overlapped precursor and successor domains is represented in
Fig.
Layout of the partially overlapped precursor and successor computational domains.
Dirichlet-type nonslip conditions are used for the resolved velocity vector
The inflow speed at the inlet equals 4.7 m s
Figure
Normalized time-averaged streamwise velocity
Figure
Turbulent kinetic energy spectrum
The computational setup for the wind turbine–wake simulation follows
Two different flow conditions are considered in the present study. In the
first case, the flow velocity is obtained from a lidar-scanned low-turbulence
(
The treatment of the domain walls is as follows. Dirichlet-type nonslip wall
conditions for
Dirichlet-type nonslip wall conditions are used for the IB-modeled nacelle
and tower in the low-turbulence case, for which a laminar boundary layer (or, at least, a not fully developed
turbulent boundary layer) is expected to extend over the entire IB surface
due to the steadiness of the incoming flow. Despite the maximum
Slip wall IB surface conditions are used for the moderate-turbulence case in order to mitigate numerical stability issues. Although this neglects the boundary-layer-induced blockage and turbulence, results indicate a negligible impact on the downstream wake profile. This is probably explained by the background turbulence that, by enhancing mixing, diffuses the signature of the tower and nacelle on the downstream flow.
Tests were performed with the G1 scaled wind turbine model, whose rotor
diameter and optimal TSR are equal to 1.1 m and 8.25, respectively. The
model, already used within other research projects
The flow within the wind tunnel was measured with hot-wire probes or stereo
PIV. The latter technique was used to measure the flow characteristics in the
near-wake (0.56 D) and far-wake (6 D) regions. The measurement planes cover a
significant fraction of the wind turbine wake. In order to achieve a higher
spatial resolution of the velocity field, the measurement area was divided
into several windows with small overlaps between them. A rapid scanning of
the entire measurement area was achieved by the use of an automated
traversing system moving both the laser and the cameras. The measuring
windows were divided into
The baseline simulation represents an isolated flow-aligned wind turbine. The
machine is operated in a low-turbulence flow with a rotor-averaged inflow
velocity equal to 5.9 m s
This first case is used to determine the optimal values of the Smagorinsky
constant
Using a simple trial-and-error approach, the three parameters
The rotor integral quantities of power and thrust are compared first by time averaging over 10 s. The wind turbine power was found to be equal to 45.79 W in the experiment and equal to 45.45 W for LES, showing a good agreement between these two values. A slightly larger discrepancy was obtained for the thrust, which was found to be 15.18 and 16.05 N for the experiment and simulation, respectively. This may be explained by the fact that thrust is directly measured at the shaft in the numerical simulation, while it is reconstructed from the fore–aft bending moment at the tower base in the experiment. This requires estimating the contribution of the nacelle and tower, which is done by a dedicated experiment performed on the wind turbine without the blades. As a result, this indirect calculation of the experimental thrust is affected by approximations, and it cannot be regarded to be as accurate as the measurement of rotor torque (and hence of power).
Next, the characteristics of the wake are compared between PIV measurements
and the CS LES simulation. Figure
Streamwise velocity contours for the CS LES model and PIV experimental measurements, on a plane 0.56 D downstream of the rotor. Black arrows indicate the crosswind velocity component at a number of sampling points.
The figure also shows that the simulation overestimates the local wake
deficit behind the nacelle and tower as a result of the enhanced blockage
effect mentioned in Sect.
Next, hot-wire probe measurements are used to compare wake profiles at 3, 4,
7 and 8 D downstream positions. Figure
Both CS and LDS show a good agreement with the experimental curves. Indeed,
the temporally and spatially averaged streamwise velocity difference
The rotor-averaged streamwise velocity difference between the simulation
(with nacelle and tower) and experiment
Profiles of normalized time-averaged streamwise velocity
LES underestimates the rotor-averaged turbulence intensity
Comparing the turbulence intensity results with and without the nacelle and tower shows that there is an increased turbulence in the wake of the former case, which causes an earlier vortex breakdown and produces a higher turbulence intensity at the far wake. In turn, this generates a faster wake recovery, as shown in the speed deficit plots. Here again, this confirms the need for including the nacelle and tower in the simulation.
In this section, the characteristics of the LES framework are assessed with reference to three wake control strategies, namely power derating (or axial induction control), wake steering by yaw misalignment and wake-enhanced recovery by cyclic pitch control (CyPC). The flow conditions and setup of the simulations are the same as described earlier in the baseline case.
Power derating was accomplished in the experiment by providing the turbine
power controller with modified values of the rotor speed and torque.
Specifically, for a power partialization factor
The resulting pitch and rotor speed changes modify the angle of attack and Reynolds number at the blade sections. Therefore, tests that include power derating are useful for evaluating the quality of the identified multi-airfoil tables. Indeed, to accurately estimate rotor power and thrust, the lifting line airfoil polars need to match the aerodynamic characteristics of the corresponding blade sections in order to generate and project the proper body forces onto the fluid domain.
Simulations are conducted by prescribing the rotor speed and blade pitch
measured in the experiment. Four power settings are considered, namely
100 %, 97.5 %, 95 % and 92.5 % of rated power.
Figure
Normalized time-averaged streamwise velocity
However, the situation is less satisfactory for rotor power and thrust, as
shown in Table
Power and thrust at 100 %, 97.5 %, 95 % and 92.5 % power settings.
Next, the LES model is verified in yaw misalignment conditions, which are
relevant to wake deflection control. Hub-height wake profiles measured in low-turbulence
conditions are used for the comparison for yaw misalignment
angles of
Simulated and measured longitudinal speed profiles are presented at a
downstream distance of 4 D in Fig.
Normalized time-averaged streamwise velocity profiles at hub height
for different yaw misalignments 4 D downstream of the rotor. Red
A third wake control strategy in the same low-turbulence conditions is
considered, in which the rotor blades are cyclicly pitched. The effect of cyclic
pitching is changing the angle of attack of the blade sections
cyclically over one rotor revolution. In turn, this results in an azimuthal
change in the out-of-plane forces generated by the section, which then has
the effect of correspondingly modifying the local induced velocity. A simple
analytical model of the effects of cyclic pitching was developed in
Each blade is pitched according to
Given the effects of CyPC on the induced velocity and on the near-wake
behavior, a more complete analysis can be performed by using the PIV
measurements than considering the simple hub-height line scans obtained by
hot-wire probes. Figure
Streamwise velocity contour plots for the PIV
measurements
The discrepancy between the simulation and experiment is 2 times larger than in
the baseline case. One possible reason for this is that unsteady aerodynamic
effects of the airfoils are neglected. This could be improved by using
unsteady aerodynamic models in the lifting line, including, for example, a
Theodorsen correction and a dynamic stall model. Although the
Beddoes–Leishman approach
The comparison of LES and the experiment in the far wake (6 D) is slightly
better, as can be observed in the right part of Fig. 8. The wake
recovery is reasonably good in terms of flow speed, although the slight
tilting towards the right shown by the PIV measurements is not apparent in
the LES results. Lastly, it should be remarked that CyPC leads to a faster
recovery of the wake than in the baseline case, as already noted by
Next, a turbulent case is considered in which a flow characterized by a 6 %
hub-height turbulence intensity is generated by the precursor simulation
described in Sect.
The aerodynamic power output, averaged over a 60 s time window, is equal to 31.0 W for the experiment and to 30.5 and 31.2 W for the prescribed speed and closed-loop torque simulations, respectively. In this latter case, the average rotor speed was only 2.2 % higher than the one measured on the wind turbine, which clearly indicates a good overall match of the numerical model with the experiment. On the other hand, the power standard deviation was 0.2, 0.6 and 0.3 W, respectively, for the experiment, prescribed speed and closed-loop simulations. Clearly, prescribing a constant speed to the rotor in the numerical simulation induces significant torque oscillations because the rotor cannot adjust to the turbulent flow fluctuations. When loads are of interest, it is therefore essential to also use a closed-loop controller in the simulation. However, in this case the simulation might drift away from the operating condition realized in the experiment if the numerical model has a significant mismatch with respect to reality. Apparently, this is not the case here, and the numerical model seems to be well in line with the experimental one.
Figure
Normalized time-averaged streamwise velocity
Contrary to the baseline low-turbulence simulation, the two turbulence
intensity peaks induced by the blade tip vortices are well predicted in this
case. To explain this phenomenon, we report in
Fig.
Vorticity shed by the tips in the near wake is quite similar for the low- and
moderate-turbulence cases. Turbulence intensity is, on the other hand, very
different in the blade tip region for these two different ambient turbulence
cases. In fact, the higher background turbulence of the turbulent inflow case
triggers the instability of the tip vortical structures
Instantaneous streamwise speed component
This paper has employed an LES approach for the simulation of wind turbine
wakes, obtaining a complete digital copy of scaled experiments performed in a
boundary layer wind tunnel. The main goal of the paper was to try to quantify
the ability of LES to represent operating conditions relevant to wind farm
control. To this end, numerical results were compared to wind tunnel
measurements of one single wind turbine, while multiple machines and wake
interactions are studied in
A low-turbulence normal-operation problem is considered first, showing that simulations are in good agreement with experiments both in terms of rotor quantities (thrust and power) and wake behavior. Next, the three wake control strategies of power derating, wake steering by yaw misalignment and wake-enhanced recovery by cyclic pitch control are studied. Results show a good agreement of simulations with experiments for yaw misalignment, but are less satisfactory for derating, probably on account of inaccuracies in the airfoil drag. The wake turbulence intensity shows some discrepancies, which were here attributed to a lack of refinement of the grid that in turn affects the breakdown of the near-wake vortical structures. Slightly less accurate results are obtained for cyclic pitching, possibly due to un-modeled unsteady airfoil aerodynamics.
The paper continues by considering a moderately turbulent wind. The characteristics of the simulated turbulent flow are in good agreement with measurements. The average streamwise velocity is within 1 % of the experiments, and the average turbulence intensity within 5 %–7 %, while the turbulent kinetic energy spectrum and integral timescale also exhibit a good matching. The wake characteristics are in very good agreement with the experiments, since tip vortices break down earlier than in the low-turbulence condition, relaxing the need for very dense grids in the near-wake region. The use of a controller in the loop leads to a more realistic response of the model turbine to the turbulent flow, which is important if the load response of the machine is of interest. Remarkably, the model in the loop also operates at essentially the same rotor speed as the experiment, which demonstrates the overall fidelity of the digital model to the experimental one.
Results shown in this work indicate that the present LES-ALM approach is a viable way of simulating scaled wind tunnel experiments. Results are, however, not perfect, and areas of improvement include a more sophisticated and accurate calibration of the airfoil polars, the inclusion of airfoil unsteady aerodynamic effects (which also call for the calibration of these models with dedicated data sets), and a more efficient refinement of the grid where necessary by the use of unstructured meshing and adaption techniques.
These encouraging results motivate and justify the application of the present simulation framework to the analysis of clusters of wake-interacting wind turbines, for which we have gathered an ample collection of data sets in multiple operating conditions. Hopefully, this will lead to a better understanding of wake behavior, which is of crucial importance for the design and operation of wind turbines and wind power plants. The final validation of the present and similar simulation approaches can undoubtedly benefit from the use of scaled wind tunnel experiments, as attempted in this work, as an intermediate step towards their application to the full-scale case.
Data can be provided upon request. Please contact the corresponding author Carlo L. Bottasso (carlo.bottasso@tum.de).
The authors declare that they have no conflict of interest.
This work has been supported in part by the CL-WINDCON project, which receives funding from the European Union Horizon 2020 research and innovation program under grant agreement no. 727477. The first author was supported by the Chinese Scholarship Council. All tests were performed at the wind tunnel of the Politecnico di Milano, with the support of Alessandro Croce, Alex Zanotti, Gabriele Campanardi and Donato Grassi. The authors wish to thank Emmanouil M. Nanos of the Technische Universität München and Vlaho Petrović, now at the University of Oldenburg, for their contribution to the experimental work. The authors also express their appreciation to the Leibniz Supercomputing Centre (LRZ) for providing access and computing time on the SuperMUC Petascale System. This work was supported by the German Research Foundation (DFG) and the Technical University of Munich (TUM) in the framework of the Open-Access Publishing Program. Edited by: Luciano Castillo Reviewed by: two anonymous referees