Design, performance and wake characterization of a scaled wind turbine with closed-loop controls

. This paper describes the design and characterization of a scaled wind turbine model, conceived to support wake and wind farm control experiments in a boundary layer wind tunnel. The turbine has a rotor diameter of 0.6 meters, and was designed to match the circulation distribution of a target conceptual full-scale turbine at its design tip speed ratio. In order to enable the testing of plant-level control strategies, the model is equipped with closed-loop pitch, torque and yaw control, and is sensorized with integrated load cells, as well as with rotor azimuth and blade pitch encoders. 5 After describing the design of the turbine, its performance and wake characteristics are assessed by conducting experiments in two different wind tunnels, in laminar and turbulent conditions, collecting wake data with different measurement techniques. A large-eddy simulator coupled to an actuator-line model is used to develop a digital replica of the turbine and of the wind tunnel. For increased accuracy, the polars of the low-Reynolds airfoil used in the numerical model are tuned directly from measurements obtained from the rotor in operation in the wind tunnel. Results indicate that the scaled turbine performs as ex- 10 pected, measurements are repeatable and consistent, and the wake appears to have a realistic behavior in line with expectations and with a similar slightly larger scaled model turbine. Furthermore, the predictions of the numerical model are well in line with experimental observations. 3 ◦ s − 1 . This value is smaller than the typical maximum operational pitch rate of full-scale turbines, which is approximately in the range [6 − 9] ◦ s − 1 . Aeroelastic simulations of the DTU 10 MW turbine were conducted in the full-load regime (region III) with a turbulence intensity of 10% . The analysis of these simulations indicates that the pitch actuation exceeds 2 . 3 ◦ s − 1 for only 5% of the time. Based on these results, the speed of the pitch actuator was deemed acceptable.

small clusters of wake-interacting turbines.
One of the principal design choices for a scaled wind turbine is its size. The literature shows that this choice implies crucial tradeoffs. In fact, smaller models alleviate the problem of blockage (Barlow et al., 1999), i.e. the effects on the flow -and hence also on the tested object-caused by the finite size of the test section. Smaller models can be tested in relatively smallsize wind tunnels or, in larger facilities, allow for more numerous clusters of models to be simulated, for example in support 70 of the study of multiple-wake interactions (Campagnolo et al., 2016b or deep-array effects. A small size, however, limits the complexity of the model because of miniaturization and power density constraints ; additionally, a small size leads also to very low chord-based Reynolds numbers, which may limit the aerodynamic characteristics of the model. On the other hand, larger sizes enable advanced features -as for example closed-loop controls, aeroelastic scaling, and a more comprehensive sensorization-, and therefore more sophisticated applications. While a larger 75 size relaxes somewhat the constraints due to Reynolds and miniaturization, on the other hand it also fundamentally limits the use of the models because of blockage.
Against this background, the aim of the present study is the design of a scaled turbine with similar characteristics to the G1, but with a smaller size. The main design requirements for this new turbine are the following: -The turbine should be smaller than the G1 to expand the range of usable wind tunnels, to allow deeper array configura-80 tions than the three G1s in a row that can be tested in Milano, and it should be usable for complex terrain studies as the one described in Nanos et al. (2020).
-Despite its smaller size, the rotor should generate realistic wakes, even in the near-wake region (Wang et al., 2020a) to support the study of closely-spaced configurations.
-The model should feature closed-loop controls, to enable wind farm control studies, and should install sensors to measure 85 loads.
It is another goal of this work to contribute to the literature, by providing a detailed description of the design, manufacturing and characterization of this new scaled wind turbine.
The material is organized as follows. Section 2 describes the design methodology and gives an overview of the model characteristics. Then, Sect. 3 presents the main performance characteristics of the turbine and its wake. Finally, Sect. 4 summarizes 90 the main findings and gives an outlook towards future work.
2 Model description and design methodology 2.1 General description Figure 1 shows the model with its principal components, while the main turbine characteristics are reported in Table 1. The model features a 0.6 m three-bladed clockwise rotating rotor, and a hub height of 0.64 m. It is equipped with load sensors on 95 the shaft and at tower base. Collective pitch control is realized by an actuator and bevel gear system integrated in the hub, while active yaw control is achieved with a standalone turning base. In the nacelle, two ball bearings support the shaft, which carries a slip ring to serve the pitch actuator and shaft load sensors; an optical encoder placed immediately behind the slip ring provides the rotor azimuthal position. A torque-meter is placed behind the aft shaft bearing, while the torque actuator is placed at the very end of the drive train. More details on the various model sub-systems are given in the following sections.
100 Figure 1. The G06 turbine with its main components.

Sizing of the model
As previously argued, one of the principal design choices requires the determination of the general model size, and in particular of the rotor diameter upon which many other dimensions eventually depend. Since a compact size is a basic requirement for this new model, the aim is to reduce the rotor diameter as much as possible. However, other design requirements impose constraints on how small the rotor can be: 105 -The model should be usable for simulating wake effects, including wake-induced loads, and for supporting wind farm control applications. These usage scenarios imply that: 1. Load-induced strains should be high enough to guarantee a sufficient precision of the measurements obtained from the installed transducers, notwithstanding the small aerodynamic loads. In the present case, this requirement was one of the main drivers of the geometric scaling factor. 110 2. The actuators and control hardware and software should be fast enough, accounting for the fact that down-scaling implies an acceleration of time with respect to the full-scale case (Bottasso et al., 2014b). This has also a strong effect on power density, which grows rapidly with time scaling .
-Very small sizes increase the influence of manufacturing imperfections on blade aerodynamics, leading to performance deterioration and/or discrepancies among different blades (which cause rotor imbalances and differences of behav-115 ior among different models). More importantly, very small blades operate in low chord-based Reynolds conditions, which negatively influence aerodynamic performance. Wiring and miniaturization become also increasingly difficult with smaller sizes.
Other Reynolds-related conditions have an effect only for extremely small models, which however are not suitable for the present controls-oriented applications. In fact, wake behaviour is independent from the rotor-based Reynolds number when this 120 parameter is larger than circa 10 5 (Chamorro et al., 2012). Similarly, Reynolds-independent flows over complex terrains are obtained for terrain-height-based Reynolds numbers above 10 4 (McAuliffe and Larose, 2012). Unless extremely small scale factors are considered, these conditions are readily met when testing in air in tunnels that produce wind speeds of the same order of magnitude of full-scale flows.
Considering these various requirements and constraints, the rotor diameter was finally chosen as D= 0.6 m.

General considerations
The DTU 10 MW wind turbine (Bak et al., 2013) is chosen as a baseline full-scale reference for the scaling of the G06. This machine has a rotor diameter of 178.3 m, an optimum TSR λ opt = 8 and a rated wind speed of 11.4 ms −1 .
The detailed aerodynamic design of the rotor aims at defining the geometry of the blade (airfoil profile(s), twist and chord 130 distributions) that fulfills the requirements. Ideally, one would like to achieve an exact kinematic and dynamic flow similarity between scaled and reference wind turbine rotors. Kinematic similarity translates into flow streamlines that are geometrically similar, and it is directly connected to the matching of TSR. Dynamic similarity implies that the ratio of the forces acting on the model and full-scale airfoils is matched; this is a more difficult condition to achieve, as it would require matching the chord-based Mach and Reynolds numbers (for a more in-depth discussion on the topic of scaling, see Anderson (2001) and 135 Bottasso and Campagnolo (2020)).
For the Mach number it is sufficient to guarantee that an upper bound is not exceeded, in order to ensure the absence of compressibility effects . The situation is, however, quite different for the Reynolds number.
In fact, when testing in air, Reynolds scales as Re M /Re F = n 2 /n t = nn v (Canet et al., 2021;Bottasso and Campagnolo, 2020), where Re M is the Reynolds number of the scaled model and Re F the one at full scale, n is the geometric scaling factor, 140 n t is the time scaling, and n v = n/n t is the scaling of speed. Bottasso and Campagnolo (2020) present a detailed analysis of the effects of scaling on chord-based Reynolds, including those caused by changes of chord solidity (see Fig. 1.1 of that paper). However, even a rough order-of-magnitude calculation shows the nature of the problem. In fact, scaling down the 10 MW DTU rotor to the 0.6 m diameter of the G06, implies that n ≈ 3.3 · 10 −3 . Additionally, typical testing speeds in the boundary layer wind tunnel in Milano are around 5 ms −1 ; such a value, assuming experiments conducted around the full-scale 145 rated wind speed, leads to n v ≈ 1/2. In these conditions the Reynolds mismatch is O(10 −3 ), which is a substantial difference.
Incidentally, notice that this implies n t = O(10 −2 ), which means that time flows about two orders of magnitude faster in the experiment than in reality. While this is a benefit in terms of data collection time (one day at full scale reduces to about 15 minutes in the tunnel), it is also a drawback in terms of real-time control, actuation rate, and sampling requirements.
Aerodynamic efficiency is defined as E = C L /C D , where C L and C D are the lift and drag coefficients, respectively. In 150 general, typical airfoils suffer from a drastic drop in aerodynamic efficiency below a Reynolds number of about 70,000 (Selig et al., 1995) because of the formation of a laminar separation bubble. In addition, as shown in Fig. 2, at these low Reynolds a standard wind turbine airfoil as S-806 (Tangler, 1987) suffers from multiple stall-reattachment cycles even at small angles of attack. An improved behavior is obtained by ad hoc low-Reynolds airfoils, such as the RG-14 profile (Selig et al., 1995).
Notice however that the efficiency of these special airfoils is lower than the one of typical wind energy airfoils when operating 155 at full-scale; for example, the RG-14 has an efficiency of 33.3 for a Reynolds of 5 · 10 4 , while the efficiency of S-806 is about 120 for a Reynolds of 10 6 . In the end, this limits the achievable maximum power coefficient of scaled rotors. Based on these considerations, the G06 blade uses the RG-14 over its entire span, with the exception of the root region in close proximity of the pitch bearing. Tripping, which can be employed for triggering the boundary layer transition and eliminate or reduce the laminar bubble (Selig and McGranahan, 2004), is not used on the G06 blades because it is not effective on low-camber airfoils. Wake similarity is obtained by matching the geometry and strength of the vortex filaments released by the blades (Canet et al., 2021;Bottasso and Campagnolo, 2020).
The correct vortex geometry is obtained by ensuring kinematic similarity, i.e. matching the TSR λ = ΩR/U , where Ω is the rotor speed, R = D/2 the rotor radius, and U the ambient wind speed.
On the other hand, the correct strength of the vortex filaments is obtained by matching the spanwise circulation distribution.

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According to Prandtl lifting line theory (Anderson, 2001), a blade can be represented as a superposition of vortices of strength Γ (circulation). Due to Helmholtz's theorem, each vortex extends as two free vortices trailing downstream all the way to infinity.
Biot-Savart law states that each filament induces a velocity w = Γ/4πh at an arbitrary point located at a filament-orthogonal distance h away. Eventually, the velocity at any point in the flowfield is the combination of the free-stream velocity and the velocities induced by all vortex filaments at that point. The lift per unit span dL at a blade segment of span dr is related to the 170 circulation Γ of this segment by the Kutta-Joukowski theorem: where ρ is air density, W is the relative flow velocity, lift is dL = 1/2ρW 2 cC L dr, where c is the chord length. Inserting the expression for lift into Eq. (1) and nondimensionalizing by the free stream velocity and the rotor radius yields: 175 Wake similarity is obtained by matching the circulation distribution, as expressed by Eq.
(2), along the span of the scaled and reference turbines.

Rotor design methodology
The rotor design problem is formulated as the following constrained optimization: s.t.: Re av. ≥ 70, 000, where the power coefficient is C P = P/(0.5ρU 3 πR 2 ), P indicates power, and subscript i stands for a generic spanwise control section along the blade.
The optimization problem seeks the blade twist θ and chord c distributions that maximize the rotor power coefficient C P .

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The power coefficient is estimated by using BEM (Burton et al., 2001), and chord and twist distributions are discretized using splines. The optimal design problem is solved using the Interior Point Method, as implemented in Matlab (Mathworks, 2019).
The optimization is constrained by the matching of the nondimensional circulation at a number N of spanwise control stations. A second constraint condition sets a lower limit for the average Reynolds number along the blade, which can be met by the optimizer by locally increasing the chord with respect to the one of the reference turbine. Since there is no explicit 190 constraint on solidity, it should be noted that the maximum power coefficient of the scaled rotor is not necessarily coincident with the optimum TSR λ opt of the reference rotor , which is however not a concern in this case.
The rated rotor speed of the scaled model, Ω scaled,rated = 2, 250 rpm, was primarily determined by the requirement to avoid compressible effects over the blade, as expressed by the condition Ω scaled,rated R/c s ≤ 0.3, c s being the speed of sound. The blade comprises of three parts: the carbon fiber skin, which determines the external shape of the blade and carries the loads, a foam filler in Rohacell, and an aluminum root used to connect with the pinion gear.
The manufacturing process uses a high-precision aluminum female mold in two halves. Each mold half is laminated with carbon fiber sheets of 0.25 mm of thickness, using two plies close to the root and one from mid-span onwards towards the tip.

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The metal root is then inserted into position. The Rohacell foam filler is placed on the molds, which are then joined together and placed in the oven for the curing process. The Rohacell foam expands during curing, pushing the carbon fiber sheets onto the molds, thereby ensuring a smooth external surface. Given the relatively small size of the G06, an individual pitch control system would increase cost and complexity. Considering also its typical use cases, a collective pitch control system was chosen for this model.
The pitch mechanism is realized through a bevel gear system, featuring a crown and three pinions (see Fig. 4). The crown is connected through a flexible coupling with a Maxon gearhead, and each pinion is connected with its own respective blade.
The gearhead has a 84:1 ratio, and it is driven by a Maxon 30 W DC motor. According to the manufacturer, a 1.3 • backlash is 215 to be expected for the gearhead. Given that the bevel gear ratio is 27:15, this gearhead backlash translates into a 2 • play at the blade pitch angle, which is unacceptable. To eliminate this backlash, each blade is attached to a torsional spring. The spring constant and its position ensure that the spring is always under tension within the pitch angle operational range, and that the applied torque is always higher than the aerodynamic pitching moment on the blade. Consequently, the loading direction on the gearhead is always the same, resulting in a solution that presents no backlash of the blade pitch motion.

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The pitch motor is controlled through a two-channel encoder, thus only relative angular displacements are possible. The absolute pitch rotation of the blade is obtained by Hall sensors, as described later in Sect. 2.5.2.
To verify the suitability of the actuator, the pitch actuation system dynamics were modeled in Simulink. The maximum continuous pitch rate is 550 • s −1 . Considering that the time scale factor between the G06 and the full-scale reference is n t ≈ 1/240, this corresponds to a full-scale pitch rate of approximately 2.3 • s −1 . This value is smaller than the typical maximum 225 operational pitch rate of full-scale turbines, which is approximately in the range [6 − 9] • s −1 . Aeroelastic simulations of the DTU 10 MW turbine were conducted in the full-load regime (region III) with a turbulence intensity of 10%. The analysis of these simulations indicates that the pitch actuation exceeds 2.3 • s −1 for only 5% of the time. Based on these results, the speed of the pitch actuator was deemed acceptable. With this pitch rate, the G06 actuation system is suitable also for other non-standard applications, such as dynamic induction 230 wind farm control (Frederik et al., 2020;Munters and Meyers, 2018). For example, a high (above the optimal) Strouhal frequency St = f D/U = 0.6 and a pitch amplitude of 6 • are well within the limits of the present system.

Torque actuator
The torque actuator provides either a torque or a speed operation mode, depending on the application. In torque mode, the actuator plays the same role of the generator in a real wind turbine, whereas in speed mode it provides the torque that is 235 necessary to spin the rotor at a desired angular velocity. The actuator is a Maxon DC 120 W motor, equipped with a gearhead with a 4.4:1 gear ratio, produced by the same manufacturer. The motor is controlled through an analog Maxon ESCON Module 50/5 controller, which allows for the user to select between the two modes (torque or speed) of operation.
When the motor works as a generator, current flows from the motor to the controller and from there to the power supply. To dissipate this flow of current, the motor controller is connected in parallel with an 8 Ohm resistor capable of dissipating up to 240 100 W of power.

Yaw actuation system
Due to the small size of the G06 model, integrating the yaw mechanism into the tower -as done for the G1 and G2 turbineswould increase the tower diameter. An excessively out-of-scale tower creates a wider wake and has a mismatched vortex realized through a separate turning base on which the G06 is mounted.
This solution not only enables the design of a thinner tower, but also decouples the yaw mechanism from the turbine itself, making the assembly process easier and faster. Despite the physical decoupling, the yaw actuation mechanism is controlled through the same control hardware and software as the other models of the TUM family of scaled wind turbines.
2.5 Sensorization of the model 250

Force and torque sensors
The G06 is equipped with strain sensors to measure bending and torsional moments on its shaft. To this end, three fullstrain gauge bridges are located immediately in front of the first bearing ( Fig. 5a); two bridges are sensitive to shaft bending, whereas the third is sensitive to torsion. Bending information is used for assessing the loading on the turbine, optionally after transforming the rotating signals into a fixed frame of reference. Torsional loads are used for the evaluation of the rotor 255 performance by measuring the aerodynamic torque. Each bridge is connected to a conditioning board mounted on the hub.
Signals and power to/from the conditioning boards are transferred to the control unit through a 12-channel slip ring. In addition to the strain gauges, a high-precision commercial torque-meter (Lorenz Messtechnik GmbH) is placed between the aft bearing and the generator. The torque-meter has a higher precision and sampling frequency than the strain gauges, but its readings are affected by the friction in the bearings and the slip ring. This friction, which depends on various factors and may change over 260 time because of temperature and wear, can be estimated by the difference between the readings of the strain gauges and the torque-meter. Two additional full bridges are placed at the base of the tower to measure fore-aft and side-side bending (Fig. 5b). The thrust generated by the rotor can be estimated from the former bending moment. In fact, as shown in Fig. 5c, the total fore-aft moment M o measured by the strain gauges is the sum of the moments due to the rotor thrust M T , the tower and nacelle drag M D , and 265 the nacelle weight M G , i.e.
where M T = T l 1 , l 1 being the moment arm of thrust T , which is assumed to be applied at the The shaft and tower bridges are calibrated prior to each experiment by the use of known loads, measuring the voltage and correlating loads and output via a linear regression.

Position sensors
Two kinds of position sensors are used in the model: Hall sensors and rotary optical encoders. Both the torque and pitch motors 275 have their own internal optical encoders, which are used by the respective internal controllers.
The pitch motor is used to rotate the blades to a specific angular position, but can only be commanded through a relative angular displacement. The absolute orientation of the blades is obtained by a Hall sensor. As shown in Fig. 4a, the Hall sensor is stationary and placed on the casing of the blade bearings, while magnets are placed on the bevel gear and rotate together with the blades. The relationship between Hall sensor output and blade pitch angle is determined by a calibration procedure.

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Using an adapter, an inclinometer is mounted on the blade. The blade is then rotated at several different pitch angles, and the readings of the Hall sensor output and the inclinometer are recorded. Before the model can be used, a "homing procedure" is performed where the blades are moved to a predefined known position, thereby providing the desired reference.
A third optical encoder is placed on the main shaft for measuring the rotating speed of the rotor and its azimuthal position, which is necessary for interpreting shaft loads and for performing phase-locked flow measurements. Instead of using a Hall 285 sensor, in this case the calibration is performed manually by placing the rotor at a known azimuthal position.

Measurement uncertainty
For every experimental activity it is necessary to estimate the error of the results that it generates. For the tower and shaft loads, given the sensitivity of the strain gauges and the expected strain within the operational regime, the uncertainty is estimated to be 1%. Similarly, the uncertainty of the torque measurement obtained from strain gauges is estimated to range between 2% 290 and 3%, depending on the operating point. The manufacturer gives a value of 0.05% for the torque-meter, and below 1% for the Hall sensor. Given the very small dimensions of the collective pitch mechanism assembly and all the uncertainties that this implies, a tolerance of ±0.3 • can be estimated for the blade pitch angle. Uncertainties in the dimensions of the model (blade length, tower height etc.) and in the measurement of the rotor angular velocity are considered to be negligible.

Control software 295
The G06 is operated by a Bachmann M1 (Bachmann, 2020) programmable logic controller (PLC), which runs in real time the supervisory logic and the pitch-torque-yaw controllers.
Two analog acquisition modules and one counter module are used for acquiring the sensor readings (strain gauges, encoder), as well as the wind speed. All signals are gathered at a frequency of 250 Hz, except for the torque-meter and shaft bending moments that are sampled at 2.5 kHz. All sensors readings are provided as inputs to the supervisory controller, which is real-300 time executed by the M1-CPU unit with a clock time of 4 ms; the control pitch, torque and yaw demands are sent to the actuator control boards via a M1-CAN module or by analog output. The real-time controller is organized into several applications written in the C programming language, each handling specialized tasks such as communicating with the actuators, recording data, or calculating actuator demands according to a control algorithm and the state of the machine (idle, power generation etc.).

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The control hardware and software is the same for all models of the TUM scaled wind turbine family. Each individual model is uniquely identified by its own ID, which allows the software to select the appropriate model-specific parameters, such as friction tables, controller gains etc. This unified framework simplifies software maintenance and development, and shortens the preparation time for the experimental setup.

Model characterization 310
This section presents the basic characteristics of the G06 in terms of its rotor aerodynamic performance, comparing design predictions with measurements obtained in two different wind tunnels. Additionally, the wake is characterized in terms of velocity deficit and wake center deflection in misaligned conditions, and compared to the G1 scaled model and to an engineering wake model. Further results are presented for turbulence intensity (TI), turbulent momentum fluxes and turbulence dissipation rate. lenses. A Quantel Evergreen HP laser was used with 380 mJ/pulse, and the cameras were calibrated with a 300 mm by 300 mm dual-plane target. The wake was measured in planes perpendicular to the flow at several downstream distances. All planes In both wind tunnels, two different inflow conditions were generated: the first is characterized by a low turbulence and uniform velocity profile, as obtained by the natural development of the flow in the clean wind tunnel; the second was obtained by the use of spires located at the test section inlet and by roughness elements placed on the floor, leading to a higher turbulence and a sheared velocity profile. The resulting conditions are labelled UTD-or TUM-(depending on the tunnel) LT (for low 335 turbulence) and HT (for high turbulence), and are reported in Table 2, together with the testing conditions in terms of TSR λ and thrust coefficient C T = T /0.5ρU 3 πR 2 . Figure 7 shows the vertical profile of the normalized streamwise inflow speed u/U hub for TUM-HT and UTD-HT. The aerodynamic performance characterization was performed in the BLAST wind tunnel in UTD-LT conditions (see Table 2).
Since blockage is below 5%, no correction was deemed necessary.
Figures 8a-c report the power, thrust and torque coefficients as functions of TSR for several pitch angles. The maximum measured power coefficient is C Pmax ≈ 0.41, which is a good result for such a small rotor, yet 20% lower than the one of the full-scale reference. The maximum power coefficient is achieved at λ = 7.5, which is close to the value of 8 of the reference model. However, the difference in performance between λ = 7.5 and 8 is insignificant due to the flat shape of the curve. At the optimum pitch and TSR, the thrust coefficient is C T ≈ 0.75, which is in line with expectations for a full-scale turbine.
Figures 8d-f show the variation of the power C P , thrust C T and torque C Q = C P /λ coefficients with respect to TSR for different inflow speeds at a fixed (optimum) pitch angle. The observed dependency of performance on wind speed is relevant because the G06 turbine is intended for use in waked conditions, where the impinging flow is slower than the free stream. Even 350 though utility scale wind turbines performance coefficients are essentially insensitive to wind speed (except for deformationinduced effects, which however are not present here since the model is rigid), this is not the case for scaled models. Indeed, as seen in the figure, there is an evident performance deterioration as the inflow speed is reduced. This can be explained by the rapid increase in the airfoil drag with decreasing Reynolds number, as shown in Fig. 9. The resulting drop in efficiency affects primarily the C P coefficient, as expected, whereas it generates only modest changes in C T , which is mostly driven by 355 lift and not drag. It should be noted that, notwithstanding the reduced and condition-dependent C P , a rotor designed with the criteria adopted here still results in a very realistic wake behavior, as shown later on and more in detailed discussed in Wang et al. (2020a). Additionally, for a wake management application, these characteristics of the power coefficient are not really an issue if the control solution demonstrates improvement over a baseline case. This is in fact one of the roles of scaled models: although not all physics can always be matched at scale, and therefore absolute values cannot be accurately captured, these 360 models can still typically show trends and changes with respect to a reference (Canet et al., 2021). Figure 10a shows the variation of power with respect to the yaw misalignment angle γ, at the optimum pitch angle and tip speed ratio. Fitting the cosine power loss model to the experimental data yields: The power loss exponent for the G1 scaled wind turbine is 2.17 , while Pedersen (2004)

Numerical simulations: polar identification
One of the intended uses of the G06 turbine is the validation of simulation tools. Most numerical models of rotor aerodynamics depend on the airfoil lift and drag coefficients (polars). Especially for scaled models, the determination of the airfoil polars involves considerable uncertainties. In fact, manufacturing imprecisions, in combination with the small dimensions of the blade, can have significant effects on the airfoil shape and, consequently, on its polars. As a result, the nominal polars used for 375 designing the rotor might not be completely accurate.  This method was used here to tune the polars, using 160 different operating conditions measured in the UTD wind tunnel in UTD-LT inflow. Figure 11a shows the airfoil efficiency as a function of angle of attack for the nominal and tuned polars.
Results show that, although not identical, the difference between the two sets of polars is small, which seems to indicate a good overall manufacturing precision of the blades. This small difference has also a relatively small effect on the circulation 385 distribution, as shown in Fig. 11b. This same figure also reports the normalized circulation distribution of the reference model obtained with FAST (Jonkman and Jonkman, 2018). Results show that, outboard of r/R = 0.3, the circulation of the G06 blade is almost identical to the reference one when using the nominal polars; this is expected, as this condition is explicitly enforced in the rotor design problem (see Eq. (3)). When considering the identified polars, the circulation matching error is less than 2%, which is a more than satisfactory result given the small size of the rotor. The difference between the G06 and reference 390 circulations in the innermost 30% of blade span is due to the rather long extent of the cylindrical root of the scaled blade, due to manufacturing reasons.

Velocity deficit, recovery and wake deflection
This section aims at characterizing the wake of the G06 turbine in terms of velocity deficit, recovery rate, and path deflection 395 as a function of misalignment angle. Considering the number of parameters that can affect the results, the repeatability of wake measurements was verified in different wind tunnels and with different measurement techniques. To this end, the turbine wake was measured at different downstream distances in the UTD wind tunnel in UTD-LT conditions using S-PIV, and in the TUM wind tunnel in the comparable TUM-LT inflow using hot-wire probes. Figure 12 shows an excerpt from this data set, reporting both the lateral (panel a) 400 and vertical (panel b) wake profiles obtained at x/D = 3.5. Results show a very good agreement between the two measurements, with an average error of 1.5% and a standard deviation of 1%. Similar results, not shown here for brevity, were obtained at other downstream distances. The good match between these two sets of measurements serves as an additional validation of the calibration, measurement and postprocessing procedures.  has not yet initiated and the deficit is mainly driven by the extraction of kinetic energy from the flow performed by the wind turbine. On the other hand, the evolution further downstream is markedly different, on account of the different TI.  shows that lower thrust coefficients are associated with slower recovery rates, which partially explain why static derating wind farm control strategies lead to only limited power gains (Annoni et al., 2016;Campagnolo et al., 2016a). The wake of the G06 was also compared to the one of the G1 model, a scaled turbine designed using similar criteria and already extensively used for wake and wind farm control studies (Campagnolo et al., 2016b;Schreiber et al., 2017b;Wang et al., 2019Wang et al., , 2020aBottasso and Campagnolo, 2020;Campagnolo et al., 2020). Figure  with the same code, using exactly the same numerical methods and algorithmic parameters. Specifically, the fluid grid and the ALM discretization were scaled up according to the geometric scaling factor, whereas all other numerical and algorithmic 435 parameters of the solver were kept exactly the same for the scaled and full-scale simulations. The two wind turbine models were also exposed to the same identical ambient turbulent inflows at their respective scales. To achieve this result, first the G06 inflow was obtained by simulating the UTD wind tunnel test section to match the UTD-HT conditions (see Fig. 7); next, the DTU 10 MW inflow was generated by scaling up the G06 one based on the time and length scaling factors, following the approach described in Wang et al. (2020a).
440 Figure 16 shows contours (looking upstream) of the normalized streamwise velocity difference in the wakes of the G06 and of the DTU 10 MW reference, computed as where the subscripts (·) G06 and (·) DTU stand for the respective turbines; in the same figure, the arrows indicate the difference in the normalized in-plane velocity components. The comparison is made at two downstream distances, namely immediately 445 behind the rotor disk at x/D = 1 (panel a) and at x/D = 5 (panel b).
To isolate the effects due to the rotor, the turbine tower and nacelle were not included in the simulations. The models were operating at their respective optimum pitch angle and at TSR λ = 8. In these conditions the G06 has a C P = 0.41 and a C T = 0.75, whereas the full-scale turbine has a C P = 0.47 and a C T = 0.81.
The figure indicates that at x/D = 1 the G06 wake speed is faster on a ring that covers approximately 50% of the blade span, 450 on account of the lower C T . There is also a difference at the center of the wake because of the larger hub diameter of the G06 (see Fig. 11b). The counterclockwise rotation of the in-plane velocity difference indicates a stronger swirl of the DTU 10 MW wake, because of its higher C Q . Notwithstanding these differences immediately behind the rotor, at x/D = 5 the wakes appear to be very similar, with errors in the longitudinal speed component around 1−2% for most of the domain, reaching a maximum of 3% in the center of the wake. At this distance the wake rotation has dissipated almost completely, and the in-plane velocity 455 vectors have been removed from the figure. That study shows that a scaled rotor -designed according to the principles followed also here for the G06-generates wakes that are in very good agreement with full-scale ones with respect to a number of different metrics.

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Within the wake of a wind turbine, the TI level is typically different than the ambient one. In fact, additional turbulence is produced by the boundary layers forming on the rotor blades, by the flow that separates from the tower and the nacelle, and by the velocity shear within the wake (Quarton and Ainslie, 1990). The so-called "added" TI (Ainslie, 1986) is used to quantify the change in turbulence with respect to the ambient conditions, and it is defined as where I is the TI at a generic point, while I hub is the TI at hub height. Figure 17 shows contour lines of I add in UTD-HT inflow at several downstream distances in aligned conditions for C T = 0.72, as obtained from the post-processing of S-PIV measurements in the UTD tunnel. The figures show that the influence of the rotor on the flow is highly nonuniform. In fact, the added TI has a horseshoe shape with a maximum at the top of the 470 rotor; this region of higher TI is sharp and highly localized immediately behind the rotor and diffuses moving downstream.
The lower-center part of the wake is characterized by an added TI that is either negligible or slightly negative, i.e. lower than the ambient one. This effect could have the following exegesis: due to the presence of the boundary layer, the velocity deficit induced by the rotor results in an increased vertical shear in the top part of the wake, whereas a decreased vertical shear is generated at the bottom of it (see also the vertical speed profiles in Fig. 13). Therefore, the reduced -with respect to the 475 ambient condition-vertical shear in the lower part of the wake results in a reduction of turbulence intensity. Similar results have been reported by Bastankhah and Porté-Agel (2017c).  Several studies have considered the modelling of added TI, because of its importance in wake recovery and in the loading experienced by downstream machines. Figure 19 shows a comparison between experimental data for the G06 in UTD-HT 485 inflow and the empirical model for the maximum added TI proposed by Crespo and Hernández (1996). This empirical model is applicable beyond 5D downstream of the rotor, and it writes: where a is the axial induction factor. The figure shows that there is a very good agreement between the estimated and the measured maximum added TI. This provides an additional confirmation of the realistic behavior of the wake even from this point 490 of view, since this model has been verified against numerical simulations and field data at full scale (Crespo and Hernández, 1996;Niayifar and Porté-Agel, 2015).

I add [-]
Crespo model Experimental data Figure 19. Maximum added TI vs. downstream distance, for the G06 in UTD-HT inflow and the the empirical model of Crespo and Hernández (1996).

Turbulent momentum fluxes
After Reynolds decomposition and time averaging (Durst, 2008), the momentum equation reads:  core. This is in agreement with previous studies (Bastankhah and Porté-Agel, 2017a) and in line with the observation that the breakdown of the tip vortices, which occurs at approximately x/D = 4, removes a separation layer between the wake and the ambient flow, thereby facilitating the exchange of momentum (Medici, 2006).   turbulent fluxes is probably related to the rotating motion of the wake (Chamorro and Porté-Agel, 2009). Furthermore, it appears that the lateral momentum flux maximum value is higher than the vertical one at any position, similarly to the results obtained in wind tunnel tests by Bastankhah and Porté-Agel (2017c)

Dissipation rate
The analysis of the turbulent energy budget provides further insight into wake behavior. The kinetic energy equation for the turbulent flow is derived from the momentum equation after averaging over time and subtracting the energy equation of the mean flow, which results into the expression where k is the turbulent kinetic energy and D k , P κ and κ are the turbulent kinetic energy diffusion, production, and dissipation, respectively. This last term represents the rate at which turbulent kinetic energy is transformed into heat, and it is an important parameter for the evolution of the wake.
Despite its relevance, only a few studies report an analysis of the dissipation rate of wind turbine wakes: Smalikho et al.

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(2013) and Lundquist and Bariteau (2015) analyzed data from field experiments, while Hamilton et al. (2012) calculated the dissipation rate in a scaled wind farm employing hot wire anemometry with a high sampling frequency of 40 kHz. In fact, the dissipation rate of turbulent kinetic energy can be directly calculated from experimental data, provided that the sampling frequency is sufficiently high to capture the smallest eddies in the flow. If this requirement is not fulfilled, the inertial dissipation approach can be employed (Champagne, 1978). This method is based on the inertial subrange theory, which suggests that the energy cascade. Therefore, a sensor that is capable of capturing the inertial subrange of the energy cascade is also adequate for calculating the dissipation rate according to the following formula: where S u (f ) is the power spectrum of the velocity u in the inertial subrange, while f is frequency and k = 0.52 is the 535 Kolmogorov constant (Fairall and Larsen, 1986;Lundquist and Bariteau, 2015). The inertial subrange can be estimated from the fast Fourier transform of the u velocity. Next, the average value of f 5/3 S u (f ) can be computed over this frequency band.
This same approach was used here. Figures 23a and 23b show, respectively, the horizontal and vertical profiles of the dissipation rate at different downstream distances, for TUM-HT inflow conditions. A qualitative analysis of the results shows that the dissipation rate inside the wake 540 is almost two orders of magnitude higher than in the ambient flow, which agrees with the observations of Lundquist and Bariteau (2015). Moreover, the dissipation rate profiles have a similar shape to the added TI ones (see Fig. 18). Even though the sampling frequency requirements suggested in the literature are met here, the accurate quantification of the dissipation rate was a rather tedious procedure with a considerable degree of uncertainty, similarly to what reported in Bluteau et al. (2011). The main sources of uncertainty are the estimation of the inertial subrange frequency band and the assumption of the Kolmogorov constant, in addition to important factors in the calculation of the dissipation rate -such as flow characteristics (anisotropy, shear etc.) and instrumentation limitations (signal to noise ratio, sampling frequency). More specifically, for isotropic flows, the constant was found to have a mean value of 0.53 with a standard deviation of 10%.
Given that the Kolmogorov constant appears in Eq. (11) to the power of 3/2, a 10% deviation in the constant leads to a 15% deviation in the dissipation rate.

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This paper has presented the design and characterization of the new scaled multipurpose wind turbine model G06. The need to design the G06 arose from an increased interest in the understanding of plant and complex-terrain flows, including improved operation by wind farm control. In fact, given the challenges posed by full-scale field measurements, experiments conducted in boundary layer wind tunnels with sophisticated small-scale wind turbines are attracting an increased attention from the research community and are providing additional opportunities for the collection of high-quality data sets. The characterization 560 of the model served the purposes of verifying that the turbine operates as intended, and represented an opportunity to generate reference measurements to support future studies.
The foreseen use cases demand close-loop controls and sensorization in a compact size, yet with realistic aerodynamic characteristics, including at the rotor and in the near-and far-wake regions. The blade was designed to match the circulation were mitigated by the use of an ad hoc airfoil. To evaluate the as-manufactured performance of the blades, the airfoil polars were identified directly from rotor power and thrust measurements using a dedicated estimation procedure. The identified polars are only marginally different from the nominal ones, resulting in a very good quality match of the circulation distribution over the outboard 75% of the blade span. High fidelity LES-ALM simulations of the G06 and its full-scale reference showed a very good agreement between the two wakes, resulting in errors of a few percent points in the streamwise velocity component of 570 the developed far wake; additionally, the two turbines have an almost identical thrust coefficients at the design TSR. Lastly, the comparison between two different G06 rotors achieved extremely similar characteristics, demonstrating the repeatability and consistency of the manufacturing, calibration and measuring procedures.
The G06 wake was extensively tested in two different boundary layer wind tunnels and two different inflows, a laminar one and a sheared turbulent one. The measurements in both wind tunnels revealed the expected strong influence of inflow conditions 575 on the wake profiles and recovery rate. Comparisons with the G1 turbine and with an engineering wake model showed very good agreement, both in terms of velocity deficit within the wake and wake deflection in yaw misaligned conditions.
The wind tunnel data was also used to analyze high-order flow statistics, including added TI, turbulent momentum fluxes and turbulence dissipation rate. Contour plots of the added TI revealed a horseshoe shape, with a maximum in the upper wake region and small or negative values in the center-lower region. Comparison of the measured maximum added TI with the 580 Crespo and Hernandez empirical model showed a very good agreement.
Profiles of the turbulent momentum fluxes showed that higher thrust coefficients lead to a higher transfer of momentum flux from the ambient flow inside the wake, leading to a faster wake recovery. The turbulent momentum fluxes reach a maximum at x/D = 3.5, where also the fastest speed recovery is found, probably on account of the vortex breakdown taking place in this region of the wake.

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The turbulence dissipation rate was also characterized in this work, for the first time directly from wind tunnel measurements.
It was found that the inertial dissipation method poses challenges in the accurate estimation of the inertial subrange frequency band and the Kolmogorov constant. Nevertheless, the resulting shape of the profiles were found to be rather insensitive to the uncertainties, and were also in line with similar field measurements at full scale.
The characterization conducted so far seems to indicate that the new scaled G06 turbine satisfies the initial requirements, 590 works reliably without any evident weakness, and is ready for supporting future wind tunnel test campaigns. Undoubtedly, the turbine can be further improved and several of the topics addressed in this paper can be analyzed in greater depth. On the hardware side, a second generation of the turbine could include individual pitch control, for example by using a swashplate, and simplifications in the wiring, for example eliminating the slip ring in favour of wireless technology. Faster, simpler and even more precise manufacturing of the blades could be obtained by 3D printing. Regarding capabilities, the wind observation 595 technology of Schreiber et al. (2018Schreiber et al. ( , 2020b has still to be demonstrated and validated on the G06, in support of advanced wind farm control strategies. Finally, the fidelity of the wake of the G06 with respect to the full-scale reference should be more extensively verified, following the approach of Wang et al. (2020a) and even using higher fidelity CFD simulations. In fact, a