How realistic are the wakes of scaled wind turbine models?

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 5 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 detailed 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.

2020): the length scale factor n l = l M /l P , where l is a characteristic length (for example the rotor radius R), and the time compression ratio n t = t M /t P , where t is time. In the present case n l = 1/162.1 and n t = 1/82.5. A more complete treatment of scaling for wind turbine rotors is given in Bottasso and Campagnolo (2020) and Canet et al. (2020).

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-Inflow. The ambient flow is obtained by simulating the passive generation of turbulence in the wind tunnel, as explained in §4.2; 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 inflow rectangular area are geometrically scaled by n l , while time is scaled by n t and speed V as V M /V P = n l /n t , resulting in a flow with exactly the same identical characteristics (e.g., shear, turbulence intensity, integral length scale, etc.) at the two scales.

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-Tip speed ratio (TSR) 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 Γ(r)/(RV ) = 1/2 (c(r)/R) C L (r)(W (r)/V ), where C L 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 (Burton et al., 2011).
Each blade sheds trailing vorticity that is proportional to the spatial (spanwise) gradient dΓ/dr. Therefore, matching the 105 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. 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 110 full-scale values, as discussed later.
-Rotor vortex shedding. The rotor Strouhal number St = f 2R/V is matched, where f is the rotor vortex-shedding characteristic frequency, which ensures the correct periodic release of vortices behind the rotor.

Approximatively matched quantities
The following quantities or effects are very nearly, but not exactly, matched:

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-Thrust coefficient C T = T /(1/2ρAV 2 ), where T is the thrust force, ρ is air density and A = πR 2 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), because the latter strongly depends on airfoil efficiency, which is affected by the Reynolds mismatch between the two models. On the other hand, drag has only a limited effect on thrust, which as a result is very 120 similar in the two models. gradient of the circulation. To match the spanwise vortex shedding of a rotor, the matching of (1/RV )dΓ/dτ should be ensured Canet et al., 2020), where τ is a non-dimensional time (for example, τ = Ω r t, Ω r being a reference rotor speed), equal for both the full and scaled models. 125 Rewriting the circulation as C Lα being the lift curve slope, the dynamic spanwise vortex shedding condition implies the matching of the nondimensional time rates of change of the sectional tangential and perpendicular flow components U P and U T , with W 2 = U 2 P + U 2 T , and of the pitch angle θ. The flow speed component tangential to the rotor disk is U T = Ωr + u T , 130 where u T contains terms due to wake swirl and yaw misalignment. The flow speed component perpendicular to the rotor disk is U P = (1 − a)V + u P , where a is the axial induction factor, and u P 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 , u P , u T 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, 135 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 by 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 modelled by a first order differential equation (Pitt and Peters, 1981), is also automatically matched thanks to the matching of the TSR Canet 140 et al., 2020). Finally, u P and u T 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 (Chen and Liou, 2011). Although this problem is not strictly related to the scaling laws discussed here, it is still an effect that 145 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 are conducted to quantify the blockage affecting the experimental setup considered here.
-Integral length scales (ILS). For 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 150 about 16% and 58% smaller that the lengths specified by Ed. 2 (IEC 61400-1, 1999) and Ed. 3 (IEC 61400-1, 2005) of the IEC 61400-1 international standards. To understand the effects of this mismatch on wake behavior, different simulations are 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:

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-The chord-based Reynolds number Re = ρW c/µ, where µ is the fluid viscosity. The Reynolds mismatch is Re M /Re P = n 2 l /n t , which is equal to 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 (Lissaman, 1983). To mitigate these effects, the G1 blade has a larger chord than the full-scale one, and uses ad hoc low-Reynolds airfoils Lyon and Selig, 1996).
Additionally, noting that the scaling relationship of the rotor speed is Ω M /Ω P = 1/n t , the time compression ratio n t 160 was chosen to further increase Reynolds on the scaled blade and reduce its mismatch .
-The power coefficient C P = P/(1/2ρAV 3 ), 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 C Q = C P /λ, then also C Q is unmatched and lower for the small-scale model than for the full-scale one, resulting in reduced wake swirling (Burton et al., 2011).

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-Tower and nacelle vortex shedding. The tower Strouhal number St = f d/V is matched when the tower diameter d is geometrically scaled. However, as noted later, the diameter of the G1 tower is 49% larger than the one of the full-scale machine, so that frequency and size of the shed vortices is accordingly affected. An even larger mismatch applies to the nacelle, which has a frontal area that is 2.6 times larger in the scaled model.
-Stall delay due to rotational augmentation (Dowler and Schmitz, 2015). Matching these effects requires the matching of 170 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 to compensate for Reynolds mismatch. The G1 simulations were conducted without correcting the inboard airfoils for rotational augmentation. To quantify the effects of rotational augmentation on wake behavior, two versions of the full-scale turbine were developed, as explained later on.

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-The chord-based Mach number Ma = W/s, where s is the speed of sound. However 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 general neutrally stable boundary layers. Although atmospheric stability has a profound effect on wakes (Abkara and Porté-Agel, 2015), this problem has already been studied elsewhere, and it is considered to be out of scope for the present 180 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 (van der Laan and . 6 https://doi.org/10.5194/wes-2020-115 Preprint. Discussion started: 10 November 2020 c Author(s) 2020. CC BY 4.0 License.

Neglected quantities
The following effects could be matched with a different experimental setup and scaling choices, but were neglected in the 185 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.

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-Unsteady airfoil aerodynamics, including linear unsteady corrections (for example, according to Theodorsen's theory (Bisplinghoff and Ashley, 2002)), and dynamic stall. It was verified that the mildly misaligned operating conditions analyzed here would not have triggered dynamic stall, except than in a few instances, similarly to what was found in Shipley (1995). Here again, these effects would hardly have any visible effects on far-wake behavior.

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Wake stability analysis shows that the vortical structures released by the blade tips and root interact in the near wake (Okulov and Sørensen, 2007).
In the outer shell of the near wake, the mutual interaction of the tip vortices -triggered by turbulent fluctuations and vortex shedding-lead to vortex pairing, leapfrogging, and eventually to the breakdown of the coherent wake structures (Sørensen, 2011). The scaled and full-scale rotors are exposed to the same inflow (including the same turbulent fluctuations), experience 200 the same vortex shedding (due to a matched Strouhal), the tip vortices have the same geometry (due to a matched TSR) and strength (due to a matched 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).

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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 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 it is well known from blade element momentum (BEM) theory, swirl is mostly concentrated in the inner core of the 210 wake, and decays rapidly with radial position (Burton et al., 2011). 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 (Wu and Porté-Agel, 2011), 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 (Martínez-Tossas et al., 2015).
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.
3 Wind turbine models 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 ms −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 225 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 (Campagnolo et al., 2016. The main features of the G1 rotor and nacelle are shown in Fig. 1a.

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A brushless motor equipped with a precision gearhead and a tachometer is installed in the rear part of the nacelle and provides for the rotor 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 in front of the aft bearing. Thrust is estimated from the tower base fore-aft bending moment, correcting for the drag of the tower and rotor-nacelle assembly.

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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 acquiring aerodynamic torque, shaft bending moments and rotor azimuth position. All other measurements 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 (Bak et al., 2013), shown in Fig. 1b, 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.  (Campagnolo et al., 2016). Right: the full-scale DTU 10 MW turbine (from Bak et al. (2013)).
The ratio of the rotor diameter D of the G1 and DTU turbines was used to define the geometric scaling factor n l . The hub 245 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 DTU turbine; similarly, the tower diameter of the G1 turbine is 49% larger than the DTU machine. This creates a mismatch in the drag of the nacelle and tower, in their local blockage and vortex shedding.

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The aerodynamic design of the rotor of the DTU turbine was modified, in order to match the characteristics of the G1 in terms of TSR and circulation distribution (and, as a consequence, also of 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 circulation is matched only between 20% and 100% of blade span. To account for the effects of 255 rotational augmentation, the inboard airfoils were corrected for delayed stall according to the model of Snel (1994).
A second rotor was designed to investigate the effects of the mismatched circulation on wake behavior. To this end, the twist angle close to the root was modified to decrease the lift inboard and match the circulation of the G1 turbine even in this part of the blade; all the other parameters of the model were kept the same of the G178 turbine. This second turbine is termed G178-MC, where MC stands for 'matched circulation'.

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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'.  Numerical results were obtained with a TUM-modified version of SOWFA (Fleming et al., 2014), more completely described in Wang et al. (2018Wang et al. ( , 2019. 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 Wang et al. (2019Wang et al. ( , 2020b).
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 (Jasak, 2009). Spatial differencing is based on the Gamma method (Jasak et al., 1999), where a higher level of upwinding is used in the near wake region to enhance stability. Time marching 280 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 turbulent kinetic energy, using the diagonal incomplete-LU factorization as preconditioner. The turbulence model is based on the Constant Smagorinsky method (Smagorinsky, 1963).
An actuator-line method (ALM) (Troldborg et al., 2007) is used to represent the effects of the blades, according to the 285 velocity sampling approach of Churchfield et al. (2017). The implementation of the actuator lines is obtained by coupling the CFD solver with the aeroservoelastic simulator FAST 8 (Jonkman and Jonkman, 2018). For improved accuracy, the airfoil polars of the G1 are tuned based on experimental operational data (Bottasso et al., 2014b;Wang et al., 2020a).
Finally, an immersed boundary (IB) formulation method (Mittal and Iaccarino, 2005;Jasak and Rigler, 2014) is employed to model the effects of the turbine nacelle and tower. The same process of passive turbulence generation was simulated by using the LES code. The mesh was generated with ANSYS-ICEM, obtaining a structured body-conforming grid around the spires (Wang et al., 2019), while the bricks placed on the floor for the higher turbulence case were modelled by the IB method. Figure 3 shows the mean streamwise velocity 310 distribution at the chamber cross-section 3.57 D in front of the rotor. The plots on the left report the results of an experimental mapping of the flow performed with triple hot wire probes, while the ones on the right report the numerical results for the medium (top row) and high (bottom row) turbulence cases; notice that measurements are available only 0.2 m 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.  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.

Code to experiment verification 330
First, experimental measurements obtained with triple hot wire probes 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 of 20 deg. Table 1 reports the experimental and simulated power and thrust coefficients in the two cases, in medium TI conditions. Figure 5 reports a comparison of horizontal scans of the wake (Wang et al., 2019) for the aligned case at various downstream distances for both the medium and high TI cases. profiles. While the match of the wake profile is excellent for all locations, the numerical results slightly overestimates turbulence intensity in the center of the near wake region. Overall, simulation and experimental results are in very good agreement.

Scaled to full-scale comparisons
Next, having established a good correspondence between the numerical results and experimental measurements, simulations 340 were conducted with the full-scale turbines to understand the effects of mismatched quantities. Table 2 shows the turbine power and thrust coefficients for the different cases, considering the G1 and 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 lower efficiency caused by the different Reynolds 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 345 a marginally lower C T . Figure 6 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. A more precise characterization of the differences between the scaled G1 model and the realistic full-scale G178 turbine is given by Fig. 7 (medium TI) and 8 (high TI), considering the misaligned case. For both figures, the first row shows the mean speed in the longitudinal direction, while the second and third rows show the Reynolds shear stress components u u /u 2 0 and u v /u 2 0 , respectively, where the prime here indicates a fluctuation with respect to the mean. Results indicate an excellent match between the scaled and full-scale wakes, for both TI levels. Some differences only appear 355 in the peaks of u u /u 2 0 immediately downstream of the rotor. However, the velocity profiles are remarkably similar already at 3 D, notwithstanding the differences around the hub and 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 inū/u 0 , 360 u u /u 2 0 or u v /u 2 0 at different downstream locations. Results are shown in Fig. 9, 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.

Effect of nacelle size and unmatched C P on swirl
For the wind-aligned operating condition, Fig. 10 shows the delta wake velocity field obtained by subtracting the G178-MC 365 from the G1 solution, looking upstream. The panel on the left represents the near wake 1 D immediately behind the rotor disk plane, while the panel on the right reports the far wake at 8 D. The color field represents the difference in the non-dimensional streamwise velocity component ∆(ū/u 0 ), whereas the arrows represent differences in the in-plane velocity vectors.
In this case, since the circulation is matched, there are only two factors that could result in non-zero difference fields: the larger frontal area of the nacelle (and, similarly, of the tower) of the G1, and its smaller power coefficient caused by the Reynolds 370 mismatch. The impacts of these two factors are clearly visible in the near wake, respectively looking at the streamwise and in-plane velocities.
In fact, the negative streamwise velocity bubble at the center of the rotor is a result of the larger blockage of the G1 nacelle.
The effect of the tower differs from that of the nacelle. 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 can increase the local turbine wake recovery by increasing turbulence intensity. As the wake rotates counter-clockwise when looking upstream as in Fig. 10, the flow influenced by tower is also convected towards the negative y direction. Figure 10. Difference in the wake velocity fields between the G1 and the G178-MC turbines, looking upstream. Color field: non-dimensional streamwise velocity difference ∆(ū/u0); arrows: difference in the in-plane velocity vectors. Left: near wake 1 D immediately behind the rotor disk plane; right: far wake at 8 D.
When looking upstream, the rotor spins counterclockwise, whereas the wake rotates clockwise by the principle of action and reaction. 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 380 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 identified 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 385 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 h wt = 3.49 D and a width w wt = 12.49 D, resulting in a cross sectional area A wt = 43.59 D. Although the resulting area ratio A wt /A = 55.5 is relatively large, the small vertical 390 ratio h wt /D 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 the left panel of Fig. 11. The actual wind tunnel height is indicated by a red square mark in the figure.
The right panel of Fig. 11 shows the non-dimensional power increase ∆P/P ∞ vs. the area ratio A wt /A, where P ∞ is the power for the largest domain -assumed to be blockage-free. Results indicate a power increase caused by blockage of about

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 400 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 P a (x/D)/P 0 =V 3 (x/D)/V 3 ∞ downstream of the turbine, where P 0 is the power output of the turbine, V ∞ is the ambient wind speed at hub height, andV (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  For the 20 deg misaligned case, the available power ratio results are shown in the left panel of Fig. 13. 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. 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 415 cross-flow force that laterally deflects the wake. As shown with the help of numerical simulations by Fleming et al. (2018), 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 Wang et al. (2018), the effects of 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 420 a turbine is operating within or close to a deflected wake, its own wake undergoes a change of trajectory -termed secondary steering-induced by the locally modified wind direction.
The change in ambient wind direction ∆Γ caused by the curled wake is reported in the right panel of Fig. 13 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 ∆Γ was computed from the wake velocity components, averaging over the rotor disk areas already used for 425 the analysis of the available power. Here again the difference in the change of 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. To understand the effects of the partially mismatched ILS on wake behavior, two turbulent inflows were generated, differing 440 only in this parameter. Unfortunately, however, the natural development 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 code TurbSim was used, selecting the Kaimal model and prescribing directly the turbulence scale parameter (see Eq. (23) in Jonkman (2009) 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 (España et al., 2011). The standard deviation of the horizontal wake 450 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 14 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 455 of the wake.

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 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 modelled or that is not accurately resolved by the 465 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 470 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 lower 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 475 of about 1.5% and negligible effects on other metrics.
-The effects of rotational augmentation, unmatched inboard 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 stresses 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 480 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 rotor vortex shedding, the geometry and strength of the helical tip vortices and the strength and shape of the speed deficit, which are all the main physical effects dictating the near-wake evolution. The mismatches that are present in the near-wake inner core 485 (due to a different swirl, inboard 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 justify the use of the TUM G1 (and similarly designed) scaled turbine for 490 the study of wake physics and applications in wind farm control and wake mixing.
The present experimental setup 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 (Chamorro and Porté-Agel, 2010), tornadoes and downbursts (WindEEE, 2020), or for the active generation of turbulent flows (Kröger et al., 2018). Regarding the models, a more realistic geometry and size of the nacelle and tower can be achieved at the price of a 495 further miniaturization. Aeroelastic effects can be included by using ad hoc scaling laws (Canet et al., 2020) to design flexible model rotor blades (Bottasso et al., 2014a;Campagnolo et al., 2014). 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.

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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