The aim of this paper is to analyze to which extent wind tunnel experiments
can represent the behavior of full-scale wind turbine wakes. The question
is relevant because on the one hand scaled models are extensively used for
wake and farm control studies, whereas on the other hand not all wake-relevant physical characteristics of a full-scale turbine can be
exactly matched by a scaled model. In particular, a detailed scaling
analysis reveals that the scaled model accurately represents the principal
physical phenomena taking place in the outer shell of the near wake,
whereas differences exist in its inner core. A large-eddy simulation
actuator-line method is first validated with respect to wind tunnel
measurements and then used to perform a thorough comparison of the wake at
the two scales. It is concluded that, notwithstanding the existence of some
mismatched effects, the scaled wake is remarkably similar to the full-scale
one, except in the immediate proximity of the rotor.
Introduction
The simulation of wind turbine wakes in wind tunnels has been gaining
increasing interest in recent years. In fact, since wakes represent a major
form of coupling within a wind plant, understanding their behavior and
accurately simulating their effects are today problems of central importance
in wind energy science, with direct practical implications on design,
operation and maintenance. Recent studies include the analysis of single and
multiple interacting wakes – see, for example, the review in
or, among others, ,
, , , , ,
, , and references therein.
Wind tunnel testing offers some unique advantages over full-scale field
testing.
The ambient conditions are repeatable and – at least to some
extent – controllable.
Detailed flow measurements are possible with a plethora of devices,
from standard pressure and hot-wire probes to particle image velocimetry (PIV)
and scanning lidars , whereas measurements
of comparable accuracy and resolution are today hardly possible at full
scale. Additionally, time flows faster in a scaled experiment than at
full scale , which
means that a large informational content can be accumulated over
relatively short periods of time.
Models can be designed ad hoc to achieve specific goals and can be
extensively instrumented , while layouts and
scenarios can be readily changed to explore different operating
conditions of interest.
Costs are limited, even for highly sophisticated models, also because
there are no energy production losses as it is often the case in the
field; additionally, the costs of sophisticated wind tunnel facilities
are typically amortized by their use for several different applications
over long periods of time.
Open datasets can be shared within the research community and
collaborations are facilitated, since there are no – or few – constraints from intellectual property than when real wind
turbine data are used.
Testing in the controlled and repeatable environment of the wind tunnel is
today contributing to the understanding of the physical processes at play,
generates valuable data for the validation and calibration of mathematical
models, and offers opportunities for the verification of control
technologies.
However, notwithstanding these and other unique advantages, a major question
still hovers over the wind tunnel simulation of wakes: how faithful are these wakes to the actual ones in the field? In fact, in private
conversations these authors have often been questioned on the actual
usefulness of wind tunnel testing, based on a perceived lack of realism of
these scaled experiments. Indeed, some skepticism is justified and completely
understandable: simulation codes are being calibrated and validated with
respect to wind tunnel measurements, and wind farm control techniques are
being compared and evaluated in wind tunnel experiments. Therefore, it is
important to quantify the level of realism of wind tunnel simulated wakes
and to identify with better clarity what aspects faithfully represent the
full-scale truth and what aspects do not.
A thorough and complete answer to this question is probably still out of
reach today. In fact, detailed inflow and wake measurements of a full-scale
turbine would be necessary, with a level of detail comparable to the ones
achievable in the tunnel. Lidar technology is making great progress
and might soon deliver suitable datasets. It should be a
goal of the scientific and industrial communities to completely open such
future datasets to research, which would surely greatly favor the scientific
advancement of the field. In the meanwhile, however, some partial answers to
the question of wake realism can still be given. This is the main goal of the
present paper.
This study considers the Technische Universität München (TUM) G1 scaled wind turbine and
a dataset obtained with this machine in the boundary layer wind tunnel of the
Politecnico di Milano in Italy. A large-eddy simulation (LES) actuator-line
method (ALM) is used to simulate the wind tunnel experiments, including the passive generation of a sheared turbulent inflow.
The code has been validated with respect to the present and other similar
measurements.
Following and , dimensional analysis
and wake physics are used here to review the main factors driving wake
behavior. The same analysis also reveals which physical aspects of full-scale
wakes cannot be matched at the reduced scale and with the considered
experimental setup. A first analysis of scaling was performed by
, considering the effects caused by the mismatch of
the rotor-based Reynolds. Experimental results based on a miniature wind
turbine showed that wake behavior is unaffected by this parameter when it is
larger than circa 105. However, in reality the behavior of the blades and, as a consequence, of the wake is much more strongly affected by the
chord-based Reynolds number, as initially discussed in
. In fact, the much lower Reynolds regime of a
small-scale model blade compared to a full-scale machine implies very
different aerodynamic characteristics of the airfoils, which in turn drive a
number of specific design choices of the scaled model
. Notwithstanding the differences caused by the
chord-based Reynolds number mismatch, it is relatively easy – as shown more
in detail later on – to match the main processes taking place in the outer
shell of the near wake, as well as the ones that govern its breakdown and the
characteristics of the far wake. On the other hand, several mismatched
effects do exist in the central core of the near wake. Dimensional analysis
also expresses the scaling relationships that allow the mapping of scaled
quantities into equivalent full-scale ones, and vice versa.
Based on the understanding provided by dimensional analysis and wake physics,
full-scale models are designed in this work to match some of the G1 scaled turbine parameters. Various versions of these models are considered, ranging from a more realistic full-scale turbine – with a larger number of mismatched effects – to less realistic ones that however match a larger set of quantities of the scaled model.
The full-scale models are then simulated with the LES-ALM code, using the
same exact numerical methods and algorithmic parameters used for the scaled
simulations. These wind turbine models are also exposed to the same identical
ambient turbulent inflow used for the scaled model. The underlying assumption
is that, since the code was found to be in very good agreement with
measurements obtained in the scaled experiments, the same code based on the
same numerical setup should deliver results of similar accuracy even at full
scale. This assumption cannot be formally proven at this stage, but it seems
to be very reasonable, and it is probably the only possible approach that can
be pursued in the absence of a detailed full-scale dataset.
Finally, the numerically simulated scaled and full-scale wakes are compared.
The analysis considers wind-aligned and misaligned conditions, typical of
wake steering control applications, and various metrics, including wake
shape, path, speed profile, Reynolds shear stresses, power available and wind
direction modification due to the curled wake in misaligned conditions. This
detailed comparison is used to quantify the degree of similarity among the
different models and across the various metrics. Since the models differ by
known mismatched effects, this also helps pinpoint and explain any source of
discrepancy.
The paper is organized according to the following plan. Section uses dimensional analysis and wake physics to identify the quantities that can be exactly matched between scaled and full-scale models, the ones that can only be partially matched, the ones that are unmatched, and those that are neglected from the present analysis. Next,
Sect. describes the scaled experimental
wind turbine and its full-scale counterparts, which include various
modifications to highlight the effects of specific mismatches.
Section describes the numerical simulation
model, including the generation of the turbulent inflow in the wind tunnel.
Results and detailed comparisons among the scaled and the full-scale models
are reported in Sect. . Finally,
Sect. summarizes the main findings of this work.
Scaling
The matched, partially matched, unmatched and neglected physical effects of the scaled and full-scale models are reviewed next. Quantities referred to
the scaled model are indicated with the subscript (⋅)M, while quantities referred to the full-scale physical system are indicated with the subscript (⋅)P. Scaling is defined by two parameters : the length scale factor nl=lM/lP, where l is a characteristic length (for example the rotor radius R); and the time compression ratio nt=tM/tP, where t is time. In the present case nl=1/162.1 and nt=1/82.5. A more complete treatment of scaling for wind turbine rotors is given in and .
Matched quantities
Inflow. The ambient flow is obtained by simulating the passive generation of turbulence in the wind tunnel, as explained
in Sect. ; the developed flow is sampled on a rectangular plane, which becomes the inflow of the scaled turbine
simulations. For the full-scale turbine simulations, the sides of the
rectangular inflow area are geometrically scaled by nl, while time is scaled by nt and speed V as VM/VP=nl/nt, resulting in a flow with exactly the same identical characteristics (e.g., shear, turbulence intensity, integral length scale) at the two scales.
Tip speed ratio (TSR). The TSR is defined as λ=ΩR/V, where Ω is the rotor speed. TSR determines not only the triangle of velocity at the blade sections, but also the pitch of the helical vortex filaments shed by the blade tips.
Non-dimensional circulation. The non-dimensional circulation is defined as Γ(r)/(RV)=1/2(c(r)/R)CL(r)(W(r)/V), where CL is the lift coefficient, c the local chord, W the local flow speed relative to the blade section and r is the spanwise blade coordinate . Each blade sheds trailing vorticity that is proportional to the spatial (spanwise) gradient dΓ/dr. Therefore, matching the
non-dimensional spanwise distribution of Γ (and, hence, also its
non-dimensional spanwise gradient) ensures that the two rotors shed the
same trailing vorticity.
The root of the G1 blade is located further away from the rotor axis than a
typical full-scale machine, due to the space required for housing the pitch
actuation system in the hub. The resulting effects caused on the wake were
investigated by developing two different full-scale models: one with the
exact same non-dimensional circulation of the G1 and one with more typical
full-scale values, as discussed later.
Rotor-based Strouhal number. The rotor-based Strouhal number
St=fD/V is matched, where f is a characteristic frequency
and D=2R is the rotor diameter. This definition of the Strouhal
number has been recently shown to characterize the enhanced wake
recovery obtained by mixing, both in the case of dynamic induction
control and by cyclic pitch excitations
.
Approximatively matched quantities
The following quantities or effects are very nearly, but not exactly,
matched.
Thrust coefficient. The thrust coefficient is defined as CT=T/(1/2ρAV2), where T is the thrust force, ρ is air density and A=πR2 is the rotor swept area. The thrust characterizes to a large extent the speed deficit in the wake. In misaligned conditions, it is also the principal cause for the lateral deflection of the wake. The thrust coefficient is very nearly matched, whereas the power coefficient is not (as discussed later). In fact, the latter strongly depends on airfoil efficiency, which is affected by the chord-based Reynolds number mismatch between the two models. On the other hand, drag has only a limited effect on thrust, which as a result is very similar in the models at the two scales.
Dynamic spanwise vortex shedding. During transients, spanwise vorticity is shed that is proportional to the temporal gradient of the circulation. To match the spanwise vortex shedding of a rotor, the matching of (1/RV)dΓ/dτ should be ensured , where τ is a
non-dimensional time (for example, τ=Ωrt, with Ωr being a reference rotor speed), equal for both the full and scaled models.
Rewriting the non-dimensional circulation asΓRV=12cRCLαWVUPUTW2-θ,with CLα being the lift curve slope, the dynamic spanwise vortex shedding condition implies the matching of the non-dimensional time rates of change of the sectional tangential and perpendicular flow components UP and UT, with W2=UP2+UT2, and of the pitch angle θ.
The flow speed component tangential to the rotor disk is UT=Ωr+uT, where uT contains terms due to wake swirl and yaw misalignment. The flow speed component perpendicular to the rotor disk is UP=(1-a)V+uP, where a is the axial induction factor, and uP is the
contribution due to yaw misalignment and vertical shear. A correct
similitude of dynamic vortex shedding is ensured if the non-dimensional
time derivatives λ′, a′, uP′, uT′ and θ′ are matched, where (⋅)′=d⋅/dτ.
Matching of λ′ is ensured here by the fact that the two rotors
operate at the same TSR in the same inflow; additionally, the simulations
were conducted by prescribing the rotor rotation (i.e., without a controller
in the loop), so that Ω′=0. The term a′ accounts for dynamic
changes in the induction, which are due to the speed of actuation (of
torque and blade pitch) and the intrinsic dynamics of the wake. The
speed of actuation is not relevant in this case, due to the absence of a
pitch–torque controller. The intrinsic dynamics of the wake, as modeled by
a first-order differential equation , is also
automatically matched thanks to the matching of the design TSR
. Finally, uP′ and uT′ are matched because the inflow is the same, with the exception of the contribution of wake swirl, which is not exactly the same because of the different torque coefficient, as noted below.
Inflow size. The cross section of the wind tunnel has a
limited size, resulting in the blockage phenomenon, i.e., in an
acceleration of the flow between the object being tested and the sides
(lateral walls and ceiling) of the tunnel . Although
this problem is not strictly related to the scaling laws discussed
here, it is still an effect that needs to be accounted for, especially
if the ratio of the frontal area of the tested objected and the cross-sectional area of the tunnel is not negligible. Simulations in domains
of increasingly larger cross sections were conducted to quantify the
blockage affecting the experimental setup considered here.
Integral length scale (ILS). Relative to the size of the TUM G1 turbines, the wind tunnel used in this research (located at
Politecnico di Milano, Italy) generates a full-scale ILS of
approximately 142 m at hub height, which is respectively about 16 % and 58 % smaller that the lengths specified by the second edition and third edition of the IEC 61400-1 international standards. To understand the effects of this mismatch on wake behavior, simulations were conducted in turbulent inflows differing only in their integral scales.
Unmatched quantities
The following quantities cannot be matched based on the current experimental
setup and scaling choices.
Chord-based Reynolds number. The chord-based definition of the Reynolds number reads Re=ρWc/μ, where μ is the fluid viscosity. The Reynolds number mismatch can be computed as ReM/ReP=nl2/nt, which is equal to 1/318.5 in the present case. This implies that the blades of the G1 model operate in a very different regime than the ones of the
full-scale blade . To mitigate these effects,
the G1 blade has a larger chord than the full-scale one and uses ad
hoc low-camber airfoils specifically conceived for low-Reynolds-number flows . Additionally, note that the scaling relationship of the rotor speed is
ΩM/ΩP=1/nt. Therefore, by increasing the rotor speed of the model ΩM (which has the effect of accelerating time by reducing the ratio nt), one can lower the Reynolds mismatch .
Power coefficient. The power coefficient is defined as CP=P/(1/2ρAV3), where P is the aerodynamic power. The power coefficient of the scaled model is lower than the one of the full-scale machine, because of the smaller efficiency of the airfoils at low-Reynolds regimes. Since the torque coefficient is CQ=CP/λ, then also CQ is unmatched and smaller for the scaled model than for the full-scale one, resulting in reduced wake swirling .
Tower and nacelle vortex shedding. Bluff bodies periodically
release vortices in their wakes , at a
characteristic frequency proportional to the Strouhal number. The
tower-based Strouhal number St=fd/V is matched when the
tower diameter d is geometrically scaled. However, as noted later,
the diameter of the G1 tower is larger than the one of the full-scale
machine, so that frequency and size of the shed vortices are
accordingly affected. An even larger mismatch applies to the nacelle,
because of power density and miniaturization constraints.
Stall delay due to rotational augmentation. Matching these effects requires the matching of the blade chord and twist distributions, of the non-dimensional circulation, and of the Rossby number Ro=Ωr/(2W). While the latter two quantities are indeed matched, the former two are not, in order to mitigate the chord-based Reynolds number mismatch. To quantify the effects of rotational augmentation on wake behavior, two versions of the full-scale turbine were developed, as explained later on.
Chord-based Mach number. The chord-based Mach number is defined as Ma=W/s, where s is the speed of sound. Although this flow parameter is not matched, compressibility effects are irrelevant for the full and scaled models considered here, as for virtually all present-day wind turbines.
Boundary layer stability and wind veer due to the Coriolis force. The wind tunnel used in the present research can only generate neutrally stable boundary layers. Although atmospheric stability has a profound effect on wakes , this problem has already been studied elsewhere, and it is considered to be out of scope for the present investigation. Similarly, Coriolis effects on the inflow and wake behavior are not represented in a wind tunnel, although they are known to have non-negligible effects on capture, loading and also on wake path .
Neglected quantities
The following effects could be matched with a different experimental setup
and scaling choices but were neglected in the present work.
All gravo-aeroelastic effects. Since the blades of the G1 turbine are not aeroelastically scaled (and are very stiff), also the full-scale model was simulated without accounting for flexibility.
Aeroelasticity could have some effects on near-wake behavior for very
flexible rotors but would probably have only a negligible role on the
characteristics of the far wake. Therefore, aeroelastic effects were
excluded from the scope of the present investigation.
Unsteady airfoil aerodynamics. Unsteady aerodynamics, including linear unsteady corrections (for example, according to Theodorsen's theory; ), and dynamic stall, was not considered in the present analysis. However, it was verified that the mildly misaligned operating conditions analyzed here would not have triggered dynamic stall, except in a few instances, similarly to what was found in . Here again, these effects would hardly have any visible effects on far-wake behavior.
Remarks
Wake stability analysis shows that the vortical structures released by the
blade tips and root interact in the near wake .
In the outer shell of the near wake, the mutual interaction of the tip vortices – triggered by turbulent fluctuations – leads to vortex pairing, leapfrogging and eventually to the breakdown of the coherent wake structures . The scaled and full-scale rotors are exposed to the same inflow (including the same ambient turbulent fluctuations), the tip vortices have the same geometry (due to a matched design TSR) and strength (due to a matched non-dimensional circulation), and the speed deficit is also essentially the same (because of the very nearly matched thrust coefficient). Hence, it is reasonable to assume a nearly identical near-wake behavior of the external wake shell, given that all main processes are matched between scaled and full-scale models (with the exception of the effects that the unmatched tower may have).
The situation is different in the near-wake inner core. Here the root vortices combine with the effects caused by the presence of the nacelle and tower. In particular, the nacelle has a much larger relative frontal area, creating a different blockage (radial redirection), nacelle wake and vortex shedding. Additionally, in the 20 % inboard portion of the blade, both the circulation and rotational augmentation effects are unmatched. Finally, the mismatch of power induces a mismatch of torque that reduces wake swirl; as shown by blade element momentum (BEM) theory, swirl is mostly concentrated in the inner core of the wake and decays rapidly with radial position . Hence, the near-wake inner core is expected to behave differently in the scaled and full-scale models. However, some of the results reported here, in addition to evidence from other sources
, indicate that the inner core near wake has only a
modest effect on far-wake behavior. For example, it is common practice to
simulate far-wake behavior with LES codes without even representing the
turbine nacelle and tower .
As a consequence, thanks to the employed scaling and matching criteria, the
far-wake behavior is expected to be extremely similar between the
wind-tunnel-generated wake and the full-scale one. The results section will
more precisely support this claim.
Wind turbine modelsThe TUM G1 scaled wind turbine
The TUM G1 is a three-bladed clockwise-rotating (looking downstream) wind
turbine, with a rotor diameter D of 1.1 m, a hub height H of 0.825 m, and rated rotor and wind speeds of 850 rpm and 5.75 m s-1, respectively. The G1 was designed based on the following requirements :
a realistic energy conversion process and wake behavior;
a sizing of the model obtained as a compromise between Reynolds
mismatch, miniaturization constraints, limited wind tunnel blockage,
and ability to simulate multiple wake interactions within the size of
the test chamber;
active individual pitch, torque, and yaw control in order to test
modern control strategies at the turbine and farm levels;
a comprehensive on-board sensorization.
The turbine has been used for several research projects and numerous wind tunnel test campaigns . The main features of the G1 rotor and nacelle are shown in Fig. a.
(a) The TUM G1 turbine . (b) The full-scale DTU 10 MW turbine (from ).
A brushless motor equipped with a precision gearhead and a tachometer is
installed in the rear part of the nacelle and generates the resisting torque,
which is in turn measured by a torque sensor located behind the two shaft
bearings. An optical encoder, located between the slip ring and the rear
shaft bearing, measures the rotor azimuth, while two custom-made load cells
measure the bending moments at the foot of the tower and on the shaft in
front of the aft bearing. Thrust is estimated from the fore–aft
bending moment measured by the load cell at the base of the tower, correcting for the drag of the tower and rotor–nacelle assembly.
Each wind turbine model is controlled by its own dedicated real-time modular
Bachmann M1 system, implementing supervisory control functions,
pitch–torque–yaw control algorithms, and all necessary safety, calibration
and data logging functions. Measurements from the sensors and commands to the
actuators are transmitted via analogue and digital communication. The
Bachmann M1 system is capable of acquiring data with a sample rate of
2.5 kHz, which is used for aerodynamic torque, shaft bending moments and
rotor azimuth position. All other measurements on the turbine are acquired
with a sample rate of 250 Hz.
Full-scale wind turbine
A full-scale wind turbine was designed through a backward-engineering
approach to match the characteristics of the G1 scaled machine. The DTU 10 MW wind turbine , shown in Fig. b, was used as a starting design for this purpose. This turbine has a rotor diameter of 178 m and a hub height of 119 m, and the modified version used here is termed G178.
The ratio of the rotor diameter D of the G1 and DTU turbines was used to
define the geometric scaling factor nl. The hub height H of the full-scale machine was slightly adjusted to match the ratio D/H of the G1 turbine.
The shape of nacelle and tower were kept the same as the DTU reference,
creating a mismatch with the G1 turbine. In fact, the scaled model – due to miniaturization constraints – has a frontal area of the nacelle that is 2.6 times larger than the one of the scaled DTU turbine; similarly, the tower diameter of the G1 turbine is 49 % larger than the scaled one of the DTU machine. This creates a mismatch in the drag of the nacelle and tower, in their local blockage and vortex shedding.
The aerodynamic design of the rotor of the DTU turbine was modified, in order
to match the characteristics of the G1 in terms of design TSR and
non-dimensional circulation distribution (and, as a consequence, to match
also the thrust). Three versions of the rotor were realized. The standard
G178 uses the same airfoils of the DTU turbine over the entire blade span,
while chord and twist distributions were modified to satisfy the matching
criteria. As the root of the G1 blade is located further away from the rotor
axis than in the case of the G178, the non-dimensional circulation is matched
only between 20 % and 100 % of blade span. To account for the effects of
rotational augmentation, the inboard airfoils were corrected for delayed
stall according to the model of .
A second rotor was designed to investigate the effects of the mismatched
non-dimensional circulation on wake behavior. To this end, the twist angle
close to the root was modified to decrease the lift inboard and match the
non-dimensional circulation of the G1 turbine even in this part of the blade;
all the other parameters of the model were kept the same as in the G178
turbine. This second turbine is termed G178-MC, where MC stands for “matched
circulation”.
A third version of the rotor was obtained by eliminating from the G178 the
rotational augmentation model, to investigate its effects. The resulting
rotor is termed in the following G178-nRA, where nRA stands for “no
rotational augmentation”.
The blades of the reference turbine are equipped with the four airfoils
FFA-W3-241, FFA-W3-301, FFA-W3-360 and FFA-W3-480 , respectively from tip to root. For the operating
conditions analyzed in this paper, the chord-based Reynolds of the G1 varies
along the blade span within the range 60 000–85 000. Airfoils operating at a Reynolds number below 100 000 experience significant parasitic drag due to
the formation of a laminar separation bubble , which
affects their maximum lift coefficient and lift-to-drag ratio. To limit these
effects, the low-Reynolds airfoil RG14 is used
throughout the whole span of the G1. Trips can be employed for triggering the
boundary layer transition and eliminating or reducing the laminar bubble
. However, tripping is not used on the G1 blades,
because it is not effective on these low-camber airfoils
.
The efficiency E=CL/CD vs. non-dimensional span r/R of the reference and scaled blade is shown in Fig. at rated conditions. The airfoil efficiency for the scaled rotor is almost half the one of the full-scale machine in the outer span of the blade; since most of the power is indeed extracted in this region, the reduced efficiency results in a lower power coefficient for the scaled model. The FFA-series airfoil characteristics were computed with Ansys Fluent , while the RG14 ones were obtained by correcting the baseline values of with rotor power and thrust measurements through the tuning approach of .
Efficiency E along the blade span r/R for the G178 and
G1 turbines at rated TSR.
Distributions of the twist, chord, lift coefficient and non-dimensional
circulation of the G1 and of the full-scale rotors are shown in
Fig. . Chord distributions are normalized by their respective arithmetic mean c0 over the span. Lift coefficient and circulation are evaluated at rated conditions using the BEM method implemented in the code FAST 8 . The lift coefficient of the G1 is significantly smaller than the one of the full-scale turbines, which is a result of its larger rotor solidity. The lower lift is however compensated for by a larger chord and different twist distributions, resulting in a matched non-dimensional circulation from 20 % span to the blade tip for the G178 turbine. For the G178-MC model, the non-dimensional circulation is matched over the whole blade span. The difference in lift and circulation between G178 and G178-nRA is due to rotational augmentation.
Distributions of twist θ(a),
non-dimensional chord c/c0(b), lift coefficient CL(c) and non-dimensional circulation Γ/RV(d), for the G1 and for the G178, G178-MC and G178-nRA full-scale turbines.
Simulation modelLES-ALM CFD code
Numerical results were obtained with a TUM-modified version of SOWFA
, more completely described in
. The code has been used extensively to
numerically replicate wind tunnel tests conducted with G1 turbines, achieving
an excellent correlation with the experimental measurements in a wide range
of conditions, including full and partial wake overlaps, wake deflection,
static and dynamic induction control, and individual pitch control (for
example, see ).
The finite-volume LES solver is based on the standard Boussinesq PISO
(Pressure Implicit with Splitting of Operator) incompressible formulation
and is implemented in OpenFOAM . Spatial differencing
is based on the Gamma method , where a higher level of
upwinding is used in the near-wake region to enhance stability. Time marching
is based on the backward Euler scheme. The pressure equation is solved by the
conjugate gradient method, preconditioned by a geometric-algebraic
multi-grid, while a bi-conjugate gradient is used for the resolved velocity
field, dissipation rate and turbulence kinetic energy, using the diagonal
incomplete-LU factorization as preconditioner. The turbulence model is based
on , where the Smagorinsky constant is equal to 0.16.
An actuator-line method (ALM) is used to represent
the effects of the blades, according to the velocity sampling approach of
. The implementation of the actuator lines is
obtained by coupling the computational fluid dynamics (CFD) solver with the aeroservoelastic simulator
FAST 8 . For improved accuracy, the airfoil polars of the G1 are
tuned based on experimental operational data
. The rotor speed is set to a
constant value to precisely match the desired TSR .
Finally, the immersed boundary (IB) formulation method
is employed to model the effects of the
turbine nacelle and tower.
Details on the mesh and other algorithmic settings are described in the
following sections.
Turbulent inflow
Experiments with the G1 turbine took place in the large boundary layer test
section of the wind tunnel at the Politecnico di Milano, where a turbulent
flow is generated passively by the use of spires. Without the spires, the
flow at the inlet has a turbulence intensity (TI) of about 1 %–2 % and a small horizontal variability caused by the presence of 14 fans and internal
transects upstream of the chamber. The non-uniform blockage caused by the
spires decelerates the flow close to the wind tunnel floor, generating an
initial vertical shear; furthermore, large vortical structures develop around
the edges of the spires, which then break down as the flow evolves moving
downstream.
Two setups are considered, with two different TI levels. To mimic a typical
medium-turbulence offshore condition, 14 type-B spires were placed side by
side 1 m from each other, 1 m downstream of the test chamber inlet. A type-B spire consists of an equilateral trapezoid and a supporting board. The height of the trapezoid is 2.0 m, while the widths of the bottom and top edges are 0.26 and 0.1 m, respectively. The developed turbulent flow where the turbine is located (19.1 m downstream of the inlet) has a vertical shear with a power coefficient equal to 0.12, a small horizontal shear, and hub-height speed and TI of 5.75 m s-1 and 5 %, respectively. A second higher-turbulence inflow was generated using nine triangular spires with a height of 2.5 m and a base of 0.8 m, placed at a distance of 1.55 m from each other. In addition, 24 rows of 0.23×0.23×0.1 m bricks were placed on the ground, with 12 bricks in odd rows and 13 bricks in even ones, resulting in a staggered brick distribution. This second configuration resulted in a vertical shear with a power coefficient equal to 0.19, a small horizontal shear, and hub-height speed and TI of 5.75 m s-1 and 14 %, respectively.
The simulations were conducted in two phases: first, developed turbulent flows were obtained by simulating the interaction of the chamber inlet wind
with the spires and bricks; next, the results of these precursor simulations
were sampled on a plane 3.59 D upstream of the rotor disk and used as inlet for the simulations of the turbine and its wake. For the
turbulence-generating precursor simulations, the mesh was obtained with
Ansys ICEM, which resulted in a structured body-conforming grid around the
spires , entirely consisting of hexahedral elements. The
bricks placed on the floor for the higher turbulence case were modeled by
the IB method. All simulations included the floor, side walls and the ceiling
of the tunnel. Boundary layers on these surfaces were modeled by wall
functions with an average y+ value of 50, achieved with local mesh
refinement. The chamber cross section has a width of 13.84 m and a height of
3.84 m, resulting in some vertical blockage, whose effects were quantified by running various simulations for increasing values of the chamber height, as reported later.
Frontal (a) and lateral (b) views of the
computational domain and refinement zones used for the wind turbine
simulations. Precursor simulations were used to generate turbulent inlet
conditions at a plane 3.59 D upstream of the rotor disk. The cell size in
the three zones is 0.055, 0.027 and 0.014 D, respectively.
Streamwise velocity distribution on a cross section of the
test chamber 3.59 D in front of the rotor. (a, c) Experimental
measurements; (b, d) numerical simulations; (a, b) medium-TI case; (c, d) high-TI case.
The grid for the wind turbine simulations uses three zones of increasing
density, as shown in Fig. , with the smallest cells having a
size of 0.015 m (i.e., 1.4×10-2D). The ALM discretization used 108 points over the blade span, i.e., a spacing equal to 4.7×10-3D. The simulations were run for 360 rotor revolutions, which were enough for reaching a turbulent steady-state regime.
For the full-scale machine, each inflow was scaled in space and time, as
previously explained, resulting in flows with the same identical
characteristics at the two scales. Similarly, the same LES and ALM grids were
geometrically upscaled and used for the full-scale simulations; this means
that also the full-scale simulations have the same slight anisotropic
blockage effects of the wind tunnel case.
Figure shows the streamwise velocity u‾/u0, where
(⋅)‾ indicates a time-averaged quantity and u0 the
time-constant hub-height wind speed, at the chamber cross section 3.59 D in front of the rotor. Figure a and c report the results of an experimental mapping of the flow performed with triple hot-wire probes, while Fig. b and d report the numerical results; Fig. a and b correspond to the medium turbulence case, while Fig. c and d correspond to high turbulence. Notice that measurements are available only 0.18 D above the floor. A good match between experimental measurements and simulation results can be observed over the whole cross section of the test chamber, including not only the vertical shear but also the slight horizontal non-uniformities. These are made even more clear by Fig. , which reports the
Reynolds shear stress component u′v′‾/u02, where the prime here indicates a fluctuation with respect to the mean.
Shear stress distribution on a cross section of the test
chamber 3.59 D in front of the rotor. (a, c) Experimental
measurements; (b, d) numerical simulations; (a, b) medium-TI case; (c, d) high-TI case.
For the same plane, Fig. a shows the mean (i.e.,
time-averaged) speed profile along a vertical line directly in front of the
rotor center, while Fig. b reports the TI profile on
the same line. Here again, a good match between experimental measurements and
simulations can be observed, except in the immediate proximity of the floor.
Mean velocity (a) and turbulence intensity (b)
distributions along a vertical line 3.59 D in front of the rotor.
ResultsCode to experiment verification
First, experimental measurements obtained with the G1 are compared with the
corresponding numerical simulations. Two operating conditions in the partial
load regime (region II) are considered: one aligned with the flow and one
with a misalignment angle γ equal to 20∘. Table reports the experimental and simulated power and thrust coefficients in the two cases, in medium-TI conditions. Notice that the power coefficient of the G1 is lower than the one of the G178. Using BEM, this difference can be fully explained by the lower efficiency of the airfoils of the scaled blade (see Fig. ), since TSR and circulation are matched.
Experimental and simulated power and thrust coefficients for the G1 turbine, in the medium-TI case.
Figure shows hub-height time-average
horizontal profiles of the streamwise velocity and of turbulence intensity
. In the experiments, wake data were measured with triple
hot-wire probes at a sampling frequency of 2000 Hz for a duration of
40 s, which corresponds to almost 1 h at full scale. Results are
reported for the aligned case at various downstream distances, for both the
medium (Fig. a) and high (Fig. b) TI cases. The downstream distances are different for the two TI cases, because the datasets were obtained in previously performed unrelated experiments. While the match of the wake profile is excellent for all locations, the numerical results slightly overestimate turbulence intensity in the center of the near-wake region. Overall, simulation and experimental results are in very good agreement.
Horizontal hub-height profiles of normalized time-average
streamwise velocity and turbulence intensity, for the medium (a) and high (b) inflow TI cases. Black o symbols: experimental results; blue dashed line: G1 simulations.
Scaled to full-scale comparisons
Next, having established a good correspondence between the numerical results
and experimental measurements, simulations were conducted with the full-scale
turbines to understand the effects of mismatched quantities.
Power and thrust coefficients for the different turbine models in the two considered operating conditions.
Table shows the turbine power and
thrust coefficients for the different cases, considering the G1 and the three
G178 turbine models. As expected, the power coefficient of the G1 turbine is
lower than the one of all full-scale G178s, because of the reduced efficiency
caused by the lower Reynolds number regime. On the other hand, there is a
good match of the thrust coefficient, especially for G178; the nRA and MC versions produce a slightly lower lift in the inboard section of the blade and hence have a marginally lower CT.
Figure gives a qualitative overview of the wakes
of the G1 and G178 turbines for the aligned and misaligned cases. The wake
deficits are similar, except for the central region of the near wake, as
expected. Even this qualitative view shows a significant effect of the much
larger nacelle of the G1. This difference however disappears moving
downstream, and the far wakes of two turbines appear to be almost identical.
Wakes of the scaled G1 (a, b) and full-scale G178 (c, d) turbines. (a, c) Aligned case; (b, d) yaw misaligned case.
A more quantitative characterization of the differences between the scaled G1 model and the realistic full-scale G178 turbine is given by
Fig. (medium TI) and Fig. (high TI), considering the misaligned case. For both figures, panel a shows the mean speed in the longitudinal direction, while panels b and c show the Reynolds stress components
u′u′‾/u02 and u′v′‾/u02, respectively.
Hub-height profiles of normalized time-average streamwise
velocity (a), normal stress (b) and shear stress (c), in the misaligned and medium-TI condition.
Hub-height profiles of normalized time-average streamwise
velocity (a) and shear stresses (b, c), in the misaligned
and high-TI condition.
Results indicate an excellent match between the scaled and full-scale wakes,
for both TI levels. Some differences only appear in the peaks of
u′u′‾/u02 immediately downstream of the rotor. However, the
velocity profiles are remarkably similar already at 3 D, notwithstanding the differences around the hub and the blade inboard sections between the two
machines. Similar conclusions are obtained for the aligned case.
Effects of unmatched inboard circulation and rotational augmentation
The effects of unmatched inboard circulation and rotational augmentation are
quantified by computing the differences in u‾/u0,
u′u′‾/u02 or u′v′‾/u02 at various downstream locations. Results are shown in Fig. , where differences are computed subtracting the G178 solution from the G178-MC or G178-nRA ones. As indicated by the figure, these effects are extremely small and possibly discernible from numerical noise only in the immediate proximity of the rotor.
Difference in the profiles of the normalized time-average
streamwise velocity (a), normal stress (b) and shear
stress (c) along hub-height horizontal lines, in yaw misaligned and
medium-TI conditions. Dash-dotted blue line: effect of rotational
augmentation, i.e., G178 results subtracted from G178-nRA results. Red solid
line and ∘ symbols: effect of mismatched circulation close to the root, i.e., G178 results subtracted from G178-MC results.
Effect of nacelle size and unmatched <inline-formula><mml:math id="M133" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">P</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> on swirl
For the wind-aligned operating condition, Fig. shows the delta wake velocity deficit obtained by subtracting the G178-MC from the G1 solution, looking upstream. Figure a represents the near wake 1 D immediately behind the rotor disk plane, while Fig. b reports the far wake at 8 D. The color field represents the difference in the non-dimensional streamwise velocity deficit component Δ(u‾-u0)/u0, whereas the arrows represent differences in the in-plane velocity vectors.
Difference in the wake velocity fields, obtained subtracting
the G178-MC solution from the G1 one, looking upstream. Color field:
streamwise velocity deficit difference Δ(u‾-u0)/u0;
arrows: difference in the in-plane velocity vectors. (a) Near wake 1 D immediately behind the rotor disk plane. (b) Far wake at 8 D.
In this case, since the non-dimensional circulation is matched, there are
only two factors that could result in non-zero difference fields: the larger
relative frontal area of the nacelle (and, similarly, of the tower) of the G1 and its smaller power coefficient caused by the chord-based Reynolds number mismatch. The impacts of these two factors are clearly visible in the near wake, respectively looking at the streamwise and in-plane velocities.
Considering first the streamwise component, the larger blockage of the G1 nacelle creates the negative velocity bubble that is clearly visible at the center of the rotor, which indicates a larger deficit behind the G1 than
behind the G178-MC in this part of the wake.
The effect of the tower is different from the one of the nacelle and leads
to a positive streamwise speed difference instead of a negative one. In fact,
while the nacelle is almost a pure blockage in the center of the rotor where
wake recovery is the weakest, the presence of the tower wake increases the
local turbulence intensity, with the effect of increasing the recovery of the
turbine wake. This results in the vertical region of higher streamwise speed
that can be seen in the figure in the lower part of the rotor disk. When
looking upstream, the rotor spins counterclockwise, whereas the wake rotates
clockwise by the principle of action and reaction, and this explains why the
region affected by the tower wake is convected towards the negative y direction.
Wind tunnel blockage effect. (a) Cross-sectional areas.
(b) Percent power increase with respect to the unrestricted flow
vs. area ratio A/Awt.
Consider next the in-plane velocities. Compared to the wake of the G178-MC
turbine, the wake of the G1 rotates at a slower pace, as indicated by the
counterclockwise rotation of the difference field shown in the picture. The
slower rotation of the G1 wake is a direct consequence of its smaller power
coefficient that, for the same TSR, implies also a reduced torque
coefficient. As expected, the mismatch in the swirl rotation is only
concentrated close to the hub and decays quickly with radial position.
As the flow propagates downstream and the wake progressively recovers,
differences between the velocity fields decay, and the effects of the
mismatches can hardly be seen at 8 D. The only difference that can still be appreciated is the effect of the larger tower. This results in some blockage close to the ground that has not yet fully recovered at this distance, resulting in about a 6 % difference in the longitudinal velocity component immediately above the floor and, hence, in a slightly enhanced shear below hub height. Elsewhere, differences between the two fields never exceed 3 %.
Effect of wind tunnel blockage
Considering the G1 turbine, the wind tunnel test chamber has a height
hwt=3.49D and a width wwt=12.5D, resulting in a cross-sectional area Awt=43.6D2. Although the resulting area ratio A/Awt=0.018 is relatively small, the non-negligible vertical ratio D/hwt=0.286 can cause some anisotropic blockage. To quantify this effect, numerical simulations were conducted in domains of increasing height from 1.75 D to 10.47 D, as shown in Fig. a. The actual wind tunnel height is indicated by a red square mark in the figure.
Figure b shows the non-dimensional power
increase ΔP/P∞ vs. the area ratio A/Awt, where
P∞ is the power for the largest domain – assumed to be blockage-free. Results indicate a power increase caused by blockage of about
1.5 %.
Wind farm control metrics
The previous analysis has shown that the wake of the G1 turbine has a very
close resemblance to the one of the full-scale G178, although some
differences are present in the near-wake region. However, it is difficult to
appreciate the actual relevance of these differences, and a more practical
quantification of the accuracy of the match would be desirable. The G1 turbine is mostly used for studying wake interactions within clusters of
turbines and for testing mitigating control strategies. This suggests the
use of wind-farm-control-inspired metrics for judging the differences between
the scaled and full-scale machines.
The first metric considered here is the available power ratio downstream of
the turbine, noted Pa(x/D)/P0=u^3(x/D)/u03, where P0 is the power output of the turbine, and u^(x/D) is the rotor-effective wind speed at the downstream location x/D. The available power ratio depends on the shape of the wake, its recovery and trajectory. This quantity was computed from the longitudinal flow velocity component in the wake on the area of the rotor disk at various downstream positions directly behind the wind turbine, as shown in Fig. .
Wake of the G1 turbine for the yaw misaligned case. The black dashed lines indicate the locations of virtual downstream turbines.
For the 20∘ misaligned case, the available power ratio results are
reported in Fig. a. As shown in the
figure, the available power changes moving downstream because the wake
expands, recovers and – since the turbine is misaligned with respect to the
wind vector – shifts progressively more to the side of the impinged
(virtual) rotors. The difference of the available power behind the G1 and
G178 turbines is small and decreases quickly moving downstream. The figure
also shows the effects of blockage, by reporting the results for the actual
wind tunnel size using a solid line and the ones for the unrestricted case
using a dashed line; here, again, this effect is very modest.
(a) Available power ratio in the wake Pa/P0 as a function of downstream position x/D. (b) Change in wind direction ΔΓ caused by the curled wake as a function of downstream position x/D. Both results are for the 20∘ misaligned and medium-TI case. Black ∘ symbols: G1; red □ symbols: G178. Solid lines: actual wind tunnel size; dashed lines: unrestricted case (no blockage).
The second metric considered here is the ambient flow rotation in the
immediate proximity of a deflected wake. By misaligning a wind turbine rotor
with respect to the incoming flow direction, the rotor thrust force is
tilted, thereby generating a cross-flow force that laterally deflects the
wake. As shown with the help of numerical simulations by
, this cross-flow force induces two counter-rotating
vortices that, combining with the wake swirl induced by the rotor torque,
lead to a curled wake shape. As observed experimentally by
, these vortices result in additional lateral flow
speed components, which are not limited to the wake itself but extend also
outside of it. By this phenomenon, the flow direction within and around a
deflected wake is tilted with respect to the upstream undisturbed direction.
Therefore, when a turbine is operating within or close to a deflected wake,
its own wake undergoes a change in trajectory – termed secondary steering – induced by the locally modified wind direction.
The change in ambient wind direction ΔΓ caused by the curled wake
is reported in Fig. b as a function of the
downstream distance x/D; even in this case, the effects of blockage can be
appreciated by comparing the solid and dashed lines. The angle ΔΓ
was computed from the wake velocity components, averaging over the rotor disk
areas already used for the analysis of the available power. Here again the
difference in the change in ambient wind direction behind the G1 and G178
turbines is quite small. A non-perfect match is probably due to the slightly
different strength of the central vortex generated in response to the rotor
torque. On the other hand, the two counter-rotating vortices caused by the
tilted thrust are well matched – given the good correspondence of this force component between the two models.
Effect of integral length scale
The ILS of the wind tunnel flow was obtained by first computing the
time autocorrelation of the wind speed at one position in front of the
turbine and then multiplying the result by the mean wind speed. The length
scales obtained from measurements in the wind tunnel and the simulated flow
resulted in nearly identical values, as already shown by . A
second estimate of the ILS was based on the space autocorrelation between
simultaneous values of the simulated wind speed at two points in front of the
turbine. For the size of the G1 turbine, this second estimate of the ILS
resulted in a full-scale value of approximatively 142 m. On the other hand,
the IEC 61400-1 international standards prescribe space-autocorrelation-based
lengths of 170 m in the second edition and of 340 m in the third edition
. Although the ILS presents a significant natural
variability at each location and across different sites ,
the value achieved in the wind tunnel with the G1 is undoubtedly in the low
range of naturally occurring scales.
To understand the effects of the partially mismatched ILS on wake behavior,
two turbulent inflows were generated, differing only in this parameter.
However, the passive development through spires and bricks of two inflows
with different ILS values, but exactly the same TI and vertical shear, is
clearly an extremely difficult task. To avoid this complication, the
turbulent flow field generator TurbSim was used, selecting
the Kaimal model and prescribing directly the turbulence scale parameter (see
Eq. (23) in ). The resulting turbulent wind time histories were specified as Dirichlet inflow conditions for the subsequent LES-ALM simulations.
Spectra of turbulent kinetic energy components.
The two resulting developed CFD flows are characterized by an ILS of 176 and 335 m and have a vertical shear exponent equal to 0.18, a hub-height
speed of 11.3 m s-1 and a TI of 6.0 %. These two different flows were used for conducting dynamic simulations with the G178 turbine in a 20∘ yaw misaligned condition. Figure shows the spectra of the turbulence kinetic energy components, where the Kaimal second-edition result is reported in Fig. a, while the one of the upscaled wind tunnel flow is reported in Fig. b. Whereas the streamwise components are very similar, it appears that the upscaled wind tunnel flow is slightly more isotropic than the Kaimal second-edition one.
The ILS indicates the dimension of the largest coherent eddies in the flow.
Hence, the main effect of a larger ILS is that of inducing a more pronounced
meandering of the wake. To quantify this effect, the instantaneous wake
center was computed according to the deficit-weighted center of mass method
. The standard deviation of the horizontal wake
position 5 D downstream of the rotor was found to be equal to 0.089 D for the low-ILS (176 m) case and equal to 0.12 D for the high-ILS (335 m) one, according to expectations.
The effects of a different ILS are much smaller, although still appreciable,
when considering mean quantities. Figure reports the profiles of speed and shear stresses at different downstream distances. The mean velocity profile is only very slightly affected, with a maximum change of about only 2 %. A clearer effect is noticeable in the shear stresses at the periphery of the wake.
Hub-height profiles of normalized time-average streamwise
velocity (a) and shear stresses (b, c), for the low- and high-ILS cases in yaw misaligned conditions.
Discussion and conclusions
This paper has analyzed the realism of wind-tunnel-generated wakes with
respect to the full-scale case. In the absence of comparable scaled and
full-scale experimental measurements, a hybrid experimental-simulation
approach was used here for this purpose. A LES-ALM code was first verified
with respect to detailed measurements performed in a large boundary layer
wind tunnel with the TUM G1 scaled wind turbine. Next, the same code
– with the same exact algorithmic settings – was used to simulate different
full-scale versions of the scaled turbine. These different full-scale models
were designed to highlight the effects of mismatched quantities between the
two scales.
Clearly, this approach has some limits and therefore falls short of providing
a comprehensive answer to the realism question. In fact, the comparison is
clearly blind to any physical process that is not modeled or that is not
accurately resolved by the numerical simulations. Additionally, it is assumed
that a numerical model that provides good quality results with respect to
reality at the small scale is also capable of delivering accurate answers at
the full scale.
Keeping in mind these limits, the following conclusions can be drawn from the
present study.
Overall, the far (above approximatively 4 D) wake of the G1 scaled
wind turbine is extremely similar to the wake of a corresponding
full-scale machine considering all classical mean metrics, i.e., wake
deficit, turbulence intensity, shear stresses, wake shape and path,
both in aligned and misaligned conditions.
Small differences of fractions of a degree are present in the local
wind direction changes caused by the curled wake, because of a
different swirl generated by the smaller aerodynamic torque of the
scaled model. The trends in terms of downstream distance and yaw
misalignments (not shown here) are however extremely similar.
The effects of blockage are very limited in the large wind tunnel of
the Politecnico di Milano, with differences in power of about 1.5 % and negligible effects on other metrics.
The effects of rotational augmentation, unmatched inboard
non-dimensional circulation and nacelle size are clearly visible in the
inner near-wake region. However, they decay quickly with downstream
distance and are typically small enough not to alter the qualitative
shape of the speed deficit, turbulence intensity and shear stress
distributions in this region of the wake.
The lower ILS of the flow generated in the wind tunnel at the scale
of the G1 has very modest effects on mean wake metrics, although it
causes a reduced meandering.
In summary, it appears that the G1 scaled turbine faithfully represents not
only the far-wake behavior, but also produces a very realistic near wake.
This is obtained by a design of the experimental setup that matches the
turbulent inflow, the geometry and strength of the helical tip vortices, and
the strength and shape of the speed deficit. These are all the main physical
effects dictating the evolution of the near wake. The mismatches that are
present in the near-wake inner core (due to a different swirl, inboard
non-dimensional circulation, rotational augmentation and a different
geometry of the nacelle) do leave a visible mark but overall do not seem to
significantly alter the behavior of the wake, as expected. The larger size of
the tower leaves a more visible trace further downstream, because it affects
the wake recovery by generating a local extra turbulence intensity, in turn
altering shear below hub height.
Overall, the realism of both the near and far wake justifies the use of the TUM G1 (and similarly designed) scaled turbines for the study of wake physics and applications in wind farm control and wake mixing.
How would these result change in case of smaller or larger scaled models? For
larger models, one would still be able to match all quantities that are
matched for the G1, while improving some of the unmatched quantities
described in Sect. . The out-of-scale
nacelle and tower of the G1 are due to miniaturization constraints of the
sensors and actuators , a problem that would be
alleviated with larger models, resulting in a reduced mismatch of the vortex
shedding frequency. Similarly, larger blades would reduce the mismatch of the
rotation-induced stall delay and of the chord-based Reynolds number. This
would lead to a better match of the power coefficient and to improvements of
some of the approximately matched quantities, such as the dynamic spanwise
vortex shedding and the thrust coefficient. On the other hand, for a same
wind tunnel, testing a larger model might increase blockage and the ILS
mismatch. Essentially the opposite would happen for smaller models. A large
chord-based Reynolds mismatch could be mitigated by increasing the rotor
angular velocity, which however leads to higher power and a larger nacelle,
and is eventually constrained by compressibility and by the wind tunnel speed
through the TSR constraint. Additionally, one may increase solidity, although
this moves the optimal TSR away from the reference
. Even with very small rotors
, it is conceptually possible to match
the non-dimensional circulation and thrust coefficient, while only the latter can
be matched using porous disks .
The experimental setup used in this study can be further improved, for an
even increased realism and expanded capabilities. Regarding the inflow,
several facilities have been recently designed or upgraded to generate
unstable boundary layers , tornadoes and
downbursts , or for the active generation of turbulent
flows . Regarding the models, a more realistic
geometry and size of the nacelle and tower can be achieved at the price of a
further miniaturization. Aeroelastic effects can be included by using ad hoc
scaling laws to design flexible model rotor blades
. Advances in 3D printing and
component miniaturization will certainly lead to advancements in the design
of ever more sophisticated and instrumented models. Regarding measurement
technology, a more detailed characterization of salient features of the flow
can be obtained by PIV or lidars, for example in support of the study of
dynamic stall, vortex and stall-induced vibrations.
Although advancements in the testing of scaled wind turbines come with
significant design, manufacturing, measurement and operational challenges,
wind tunnel testing remains an extremely useful source of information for
scientific discovery, the validation of numerical models and the testing of
new ideas. A quantification of the realism of such scaled models is therefore
a necessary step in the acceptance of the results that they generate.
Code and data availability
The LES-ALM program is based on the open-source codes
foam-extend-4.0 and FAST 8. The data used for the present analysis can be
obtained by contacting the authors.
Author contributions
CW performed the simulations and analyzed the results.
CLB devised the original idea of this research, performed the scaling
analysis, interpreted the results and supervised the work. FC was
responsible for the wind tunnel experiments and the analysis of the
measurements and co-supervised the work. HC designed the full-scale turbine
models. DB validated the full-scale turbine models with BEM and CFD codes.
CW and CLB wrote the manuscript. All authors provided important input to this
research work through discussions, through feedback and by improving the manuscript.
Competing interests
The authors declare that they have no conflict of
interest.
Acknowledgements
The authors express their appreciation to the Leibniz Supercomputing Centre (LRZ) for providing access and computing time on the SuperMUC-NG system.
Financial support
This work has been supported by the CL-Windcon project,
which received funding from the European Union Horizon 2020 research and
innovation program under grant agreement no. 727477, and by the CompactWind II project (FKZ: 0325492G), which receives funding from the German Federal Ministry for Economic Affairs and Energy (BMWi).
Review statement
This paper was edited by Sandrine Aubrun and reviewed by two anonymous referees.
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