Scale-adaptive simulation of wind turbines , and its verification with respect to wind tunnel measurements

This paper considers the application of a scale-adaptive simulation (SAS) CFD formulation for the modeling of single and waked wind turbines in flows of different turbulence intensities. The SAS approach is compared to a large-eddy simulation (LES) formulation, as well as to experimental measurements performed in a boundary layer wind tunnel with scaled wind turbine models. The motivation for the use of SAS is its significantly reduced computational cost with respect to 5 LES, made possible by the use of less dense grids. Results indicate that the two turbulence models yield in general results that are very similar, in terms of rotor-integral quantities and wake behavior. The matching is less satisfactory in very low turbulence inflows. Given that the computational cost is about one order of magnitude smaller, SAS is found to be an interesting alternative to LES for repetitive runs where one can sacrifice a bit of accuracy for a reduced computational burden. 10


Introduction
Wake simulations provide for valuable and quantitative insight into the complex physics governing interactions among wind turbines and of wind turbines with the atmospheric boundary layer.A range of different models and numerical methods have been developed for wake interaction research, spanning different fidelity levels.velocity ũ, dissipation rate ω and turbulent kinetic energy k, using the diagonal incomplete-LU factorization as preconditioner.
The framework uses the actuator-line method (ALM) to represent the effects of the blades, implemented according to the velocity sampling method of Churchfield et al. (2017).The implementation of the actuator lines is obtained by coupling the CFD solver with the aeroservoelastic simulator 90 FAST (Jonkman and Buhl Jr, 2005).
An immersed boundary (IB) formulation (Wang et al., 2017b) is employed to model the wind turbine nacelle and tower.Compared to an actuator line model of these two components, IB significantly improves the near wake performance and the accuracy of higher order quantities (vorticity and turbulence intensity) (Wang et al., 2017b).

SAS model
The derivation of the SAS model follows the work of Menter andEgorov (2005, 2006); Egorov and Menter (2008) and Lindblad et al. (2014), and it is formulated in incompressible form with minor modifications.
Similar to the k-ω SST model, the kinematic eddy viscosity is modeled as ν t = k/ω.In the SAS 100 model, however, an additional source term Q SAS is introduced to improve ν t .The k and ω transport equations of the SAS model read 105 where c µ and σ k are the closure coefficients in the k equation, while α, β, σ ω and σ ω2 are the closure coefficients in the ω equation.F 1 is a blending function that transitions between the k-ω and k-modes.The dissipation terms c µ kω and βω 2 are discretized in implicit form to improve convergence and stability (Lindblad et al., 2014).The present implementation does not consider any prediction-correction iteration between the momentum and the two transport equations: in the 110 k and ω equations, ũ is considered as a known velocity field resolved by the PISO scheme, solving the transport equations in segregated form (Lindblad et al., 2014).Therefore, the implementation of SAS does not require a change in the PISO algorithm.
Through the boundary layer length scale, the blending term is in charge of shifting between boundary layer and free-stream type conditions, which is the main idea behind the SST approach.Such 115 formulation, however, cannot detect local flow inhomogeneities and requires the modeling of an additional source term.The Q SAS term originates from Rotta's k-kL model of the correlation-based length scale (Egorov and Menter, 2008) , and it is formulated as where parameters ζ 2 , σ Φ and C were obtained from experiments.F SAS behaves as a scaling pa-120 rameter that dictates the amount of numerical damping injected in the flowfield.The value of F SAS requires specific calibration.L is the length scale of the modeled turbulence, and L vK the von Kármán length scale.In order to preserve the SST characteristics of the formulation, the Q SAS term is defined as a strictly positive term.Regarding the scaling ratio (L/L vK ) n , numerical experiments have shown that the linear length scale ratio (also used in Egorov and Menter (2008)) leads to bet-125 ter stability and robustness of the formulation when compared to the quadratic form of Menter and Egorov (2010); Egorov et al. (2010).The choice n = 1 is therefore adopted in this work.
The von Kármán length scale L vK is formulated based on Rotta's equation, and it writes ensuring the scale-adaptive characteristics of the method (Menter and Egorov, 2005).In fact, L vK 130 reflects the size of resolved eddies in the flow, while the SST model only considers length-scales associated with the boundary layer thickness.
The second derivative of the velocity field ∇ 2 ũ detects inhomogeneities in the resolved turbulence scales, and brings this information into the eddy viscosity term.As mentioned earlier, the SST model is only associated with the boundary layer length scale (i.e., the F 1 term), but it is not adjusted to 135 the local flow characteristics (Menter and Egorov, 2005;Younsi et al., 2008).Therefore, when the SST model is used in free-stream high-Reynolds wake flows, it cannot adapt ω in the wake regime, often resulting in a highly diffusive behavior.By introducing ∇ 2 ũ, the improved formulation is capable of adjusting the eddy viscosity to better control the amount of numerical diffusion to the local characteristics of the flow.In addition, to avoid an insufficient damping at high wave numbers, 140 a lower limit to L vK is imposed, which is proportional to the model parameter C k and the cell size CV , Ω CV being the cell volume.In summary, the formulation of L vK achieves a balance between the production and destruction of turbulence kinetic energy, providing for a suitable numerical diffusion at the sub-grid scales.
By introducing the Q SAS term into the ω equation, the SAS model improves the SST formulation 145 on three aspects: an improved modeling of the eddy viscosity, a more accurate prediction of the breakdown of turbulent structures, and a better high wave number damping for the resolved eddies down to the grid limit (Egorov and Menter, 2008).Such improvements eventually lead to a LES-like behavior of the SAS formulation.

Computational setup 150
The simulation model represents a complete digital copy of experiments conducted in a boundary layer wind tunnel, including the passive generation of a sheared and turbulent flow and its interaction with scaled wind turbines.Since a same turbulent flow can be used for different turbine simulations, the computational domain is subdivided into two partitions: a precursor simulation, charged with the modeling of the flow evolution along the tunnel, and a successor simulation -whose inflow is 155 obtained from the precursor-modeling the wind turbines.

Precursor simulation
The precursor simulation is used to generate the turbulent inflow for a successive wind turbine run.
The precursor domain uses a structured body-conforming volume mesh (entirely composed of hexahedral elements) to discretize the volume around turbulence-generating spires at the wind tunnel inlet, as well as the rest of the wind tunnel test section.Only the LES model is employed for precursor simulations, as generating a turbulent inflow is not a repetitive task.Therefore the reduction of its computational costs is not a priority, while the resulting flow should be of the highest possible quality.
The mesh density is designed not to fully resolve the boundary layer, and the average y + is equal 165 to 50.In fact, a wall-modeled simulation significantly reduces the computational costs compared with a fully resolved one.The precursor mesh contains 59 million cells with the current setup, and it would require one or two orders of magnitude more cells for y + close to 1.As shown later on, this approach is still capable of a good matching with experimental measurements.
There are two types of turbulence-generating spires: one is used to generate a moderate turbulence 170 (≈ 6%), while the second type is for high turbulence (≈ 20%) conditions.The time-averaged wind speed at hub-height is equal to 5 m/s for both cases.The maximum Courant number is limited to one.After reaching steady state conditions, which takes about 15 s of physical time, the flow field is recorded at a plane 19 m downstream of the tunnel inlet, to serve as input for subsequent wind turbine simulations.A detailed description of the precursor simulation setup is given in Wang et al.

(2018c).
In this paper, also a low turbulence inflow condition is considered.In that case, the inflow to the wind turbine simulation is not obtained by a precursor, but simply by prescribing a time-constant velocity measured by scanning LiDARs 29 m downstream of the tunnel inlet (Van Dooren et al., 2016).The computational setup for the wind turbine simulation follows Wang et al. (2018b).The domain layout is shown in Fig. 1, which is used for both the low (standalone) and moderate/high (coupled with the precursor inflow) turbulent conditions.The domain width is reduced to 3.6D, which is 4.2 185 times shorter than the test section width to reduce the computational cost while avoiding blockage effects.A coordinate reference frame is centered at the hub of the front turbine, as shown in the same figure.The mesh uses three different densities: zone 1 is the base mesh, with cubic cells of 0.08 m in size, while the cells in zone 2 have a size of 0.04 m.Zone 3 is the finest grid, used in close proximity of the wind turbines and their wakes.The cell size in this region of the domain differs depending 190 on the turbulence model: for LES the cells have a size of 0.01 m, while for SST and SAS the size is 0.02 m.As a result, the SST and SAS models are run on a grid that has about 7.8 times fewer cells than in the LES case (which has a total cell number of about 39 millions).In all cases, cells are cubic except for polihedral elements used for connecting together the zone boundaries, which however account for less than 1% of the total cell count.As shown later on, results indicate that the velocity and turbulence intensity fields are very similar between LES and SAS in moderate and high turbulence conditions.In this sense, SAS is capable of achieving a performance similar to LES, but with much coarser grids.As a verification of mesh convergence, the SAS model was also run on the finer LES grid, obtaining essentially identical results to the ones found on its coarser grid.

200
On the other hand, finer grids would be necessary for LES for a more accurate solution of the low turbulence case.As discussed later in this work, low turbulent conditions have much more stringent requirements in the resolution of the near wake vortical structures and their breakdown.Such a high accuracy is not needed at higher turbulence, as this becomes the dominating factor that dictates vortex breakdown.Finer grids were however not used here, because of the dramatic increase in 205 computational cost caused by the current structured grid approach.
For both SAS and LES, the grid implicitly operates a spatial filtering on the solution.Similarly, although a temporal filtering is implicitly performed by the time marching algorithm, no explicit temporal filtering is applied a priori on the solution, in contrast to the URANS model.In this regard, SAS can be considered as a LES dynamic sub-grid scale model, which exhibits a LES-like behavior 210 at the resolved scales (Menter and Egorov, 2005).

Boundary conditions
The same boundary conditions for the flow velocity ũ, pressure p and temperature T are used for the

Numerical implementation
The SAS and SST models implement the same linear solvers used in the LES case for the resolved scales, as described in §2.1.Regarding sub-grid scale quantities, central differencing could in principle be used for the convective terms of the k and ω equations for both the SAS and LES models.

235
However, due to the von Kármán length scale in the ω equation of the SAS model, oscillations may be generated that, by affecting the eddy viscosity, can eventually cause the simulation to diverge.
Accordingly, a strictly bounded Van Leer differencing scheme is used for the k and ω transport equations to minimize numerical stability issues.Although such a discretization may cause significant numerical diffusion, boundedness should be favored over accuracy for a scalar field scheme 240 (Greenshields, 2015).The k and ω equations for both the SST and SAS model are solved by the conjugate gradient algorithm with diagonal incomplete-LU preconditioning.

Parameter tuning
The time step length for all three turbulence models is limited by imposing that the lifting line representing the blade does not cross more than one cell in one step (Martinez et al., 2012), which is 245 equivalent to 0.3 of the maximum Courant number.Since the size of the smallest cells for the LES grid is half that of the SAS and SST ones, the time step is accordingly smaller.The difference in grid size (and hence the number of cells) and in time step length are the main factors driving the different computational costs of these methods.In fact, although SAS and SST require the solution of two additional transport equations, the resulting additional cost is negligible when compared to 250 the effects of grid size and time step.On average, SST and SAS are roughly 13 times faster than LES for the simulation cases considered here.
The Gaussian width of the ALM is set to 2.5 times the cell size at the rotor disk, which once again results in different values on account of the different grid densities of the turbulence models.
The constant Smagorinsky model is employed for the LES case, using C s equal to 0.13.The scal- Table 1 illustrates the main characteristics of the machine.The hub-height wind speed for the three operating conditions (low, moderate and high turbulence inflow) is lower than the rated speed of the wind turbine, so that blades were set to their fine pitch setting.The turbulence intensity is 2% for the 265 low turbulence condition, while it is 6% and 20% at hub height for the moderate and high turbulence ones, respectively.
A look-up table torque controller in the loop was used in the experiments, while a fixed rotating speed equal to the average experimentally measured one was used in the simulations.In reality, the angular speed of the rotor will vary because of turbulent fluctuations in the flow field.It was verified 270 that, as expected according to intuition, imposing a constant rotor speed in a CFD-ALM simulation does significantly affect the estimation of loads (Wang et al., 2018a).However, it was also verified that such simplification does not significantly influence the downstream wake, which is the focus of this paper.
Triple hot-wire anemometers were used to measure the flow velocity components at several dis-275 tances behind the rotor.Sensors integrated onboard the scaled wind turbine were used to measure the instantaneous rotor torque, tower base bending and rotating speed.along a hub-height horizontal line in the flowfield, which are then spatially averaged along the rotor diameter.The percentage average velocity error is defined as ∆(u) = ( u sim − u exp )/ u exp .The root mean square (RMS) error is used to quantify the spatial fit between simulations and experiments (Chai and Draxler, 2014), and it is defined as 285 where u j is a time-averaged velocity component at a given spatial point j.The calculation of turbulence intensity σ/ u needs to account for the turbulence both at the resolved and modeled scales.To this end, modeled fluctuations are summed to the resolved ones, yielding where u i,j represents a velocity component at a given spatial point j and at time step i.The term 290 2/3 k j is the velocity fluctuation corresponding to the modeled turbulence kinetic energy k j .
In addition to the point-wise turbulence intensity σ j / u j , rotor-average turbulence intensity σ/ u and turbulence intensity RMS(σ/ u ) are defined similarly to the velocity case.

Single-turbine baseline case
A first baseline case is used to tune the parameters for the three turbulence models, parameters 295 that are then used unchanged in the other cases considered herein.The baseline case represents an isolated flow-aligned wind turbine operating in a low turbulence environment in the partial load region.The CPU time ratio of LES and SAS for this case is CPU LES /CPU SAS =16.9.
The wind turbine power measured in the experiment is 45.8 W, while for SST, SAS and LES it is 44.8 W, 45.1 W and 45.5 W, respectively.Hence, the power output predicted by SAS appears to be 300 in good agreement with both LES and measurements.As previously stated, the same ALM Gaussian width in terms of cell size is used for all methods.
Figure 2 shows vorticity contours for the LES, SAS and SST simulations, respectively from left to right.It appears that LES is capable of a significantly higher resolution of the tip and root vortices than SAS, thanks to its denser grid.Additionally, a much higher vorticity is produced by SAS 305 compared to SST, due to its enhanced ability of resolving small scale features.
For a more precise understanding of these different representations of vorticity and of the overall modeling of wake structures, experimental measurements at hub height and at different distances downstream of the rotor are considered.Figure 3 shows the normalized time-averaged longitudinal The average percent error ∆(u x ) between simulation and experiment for LES is equal to -2.7%, -1.6% and -1.1% at 3D, 4D and 8D, respectively.For SAS, the error is -4.1%, -5.315 The SAS velocity profiles show a reasonable agreement with both LES and the experimental curves.
On the other hand, the error at the same distances for SST is 11%, 13% and 13%, which is significantly larger than for SAS.The SST RMS(u x ) is also on average twice as large than for SAS.
These results suggest that, by including local flow inhomogeneities through ∇ 2 ũ , the modeling of the wake is significantly improved, by a locally adjusted eddy viscosity and limited numerical 320 diffusion.
It is interesting to observe that, close to the rotor (0.56D), SST and SAS predict nearly the same speed profile.In fact, in the near wake region the flow is not yet strongly affected by mixing and numerical diffusion, so that differences in the modeling of unresolved scales play a lesser role.In this region of the wake, the behavior is mostly governed by the rotor thrust, which indeed is quite 325 similar for all three models.The 10 s time-averaged thrust is in fact 16.1 N, 15.9 N and 15.7 N for LES, SAS and SST, respectively.On the other hand, moving downstream away from the rotor, the overestimated eddy viscosity of the SST model begins to show its effects on the wake deficit, as apparent in the plots starting at the 3D location all the way to the end of the domain.
It should be noticed that at 3D and 4D the velocity profiles of LES match very well those of 330 the experiments, while SAS predicts a slightly larger wake width.This phenomenon is due to a lack of resolution of the blade tip vortices.Further downstream, the tip vortices collapse and break down, and therefore this effect is reduced.In particular, SAS curves show a very good match with LES at 10D and 11D.This indicates that numerical diffusion is well controlled by the SAS model throughout the propagation of the wake, and flow mixture is properly resolved.

335
It should also be remarked that the resolution of tip vortices plays a lesser role than in the present case for moderate/high turbulence inflows.In fact, in those conditions vortex breakdown will take place earlier due to the higher background ambient turbulence.Therefore, the accuracy of SAS is expected to improve for more turbulent cases, as in fact confirmed by results shown later on in this work.From this point of view, this initial baseline scenario represents a particularly difficult 340 problem.
LES underestimates turbulence intensity by 23% and 12% at 3D and 4D, respectively, while for SAS the error is 11% and 10%.The consistent underprediction of turbulence intensity for low turbulence inflow conditions in the near wake region has already been observed by Troldborg et al. (2015).However, results are quite similar for the two models considered here, which indicates the 345 ability of SAS in resolving second order quantities in the near wake region.
There is a significant lack of symmetry in the profiles left (looking downstream, i.e. for positive y values) and right of the rotor axis for both methods, as in fact the left peak is significantly underpredicted.This lack of symmetry however does not appear in the experimental results.This is probably due to a combination of lack of resolution of the tip vortices and their interaction with the wake shed by nacelle and tower.This problem is analyzed in detail further on, in reference to a yaw misaligned case.The effects of this lack of symmetry on turbulence intensity is consistent with a small lack of symmetry in wake recovery.In fact, especially at 7D and 8D, the numerical velocity profiles exhibit a reduced wake recovery on the left of the wake compared with the experimental measurements.
This fact is attributable to the lower upstream turbulence intensity on this same side of the wake,

355
shown in the bottom row of plots of Fig. 3.
Regarding the far wake at 10D and 11D, SAS overestimates turbulence intensity by more than 50%, which may lead to a faster wake recovery further downstream.However, such a problem is only limited to low turbulence conditions, and the situation improves for higher turbulence.
Since SST is clearly unable to provide for sufficiently accurate estimates of the wake behavior, it 360 is not considered further in the present work.

Single-turbine yaw-misaligned case
A correct estimation of wake behavior in yaw misaligned conditions is crucial, especially when significant intentional misalignments are generated for wake deflection wind plant control.The CPU time consumption ratio for this case is CPU LES /CPU SAS =14.4.
Figure 4 shows a comparison of the velocity (top) and turbulence intensity (bottom) profiles for the 370 considered yaw misalignment angles.The velocity profile of the SAS model shows a relatively good agreement with both the experiment and LES.The maximum average-velocity error for SAS is 5.2% at -10 deg, while it is 4.1% for LES at 20 deg.The overall error over the six yaw configurations is 4% and 1% for SAS and LES, respectively.Likewise, the maximum RMS(u x ) for SAS is 0.54 m/s and it is 0.35 m/s for LES.The overall RMS(u x ) over the 6 yaw configurations is 0.45 m/s and 375 0.29 m/s for SAS and LES, respectively.As noted in the baseline case, SAS overpredicts the wake width, due to a lack of resolution of the tip vortices.However, other than this, it is in a reasonably good agreement with LES.
The overall average turbulence intensity error over the 6 yaw configurations is 11% and 20% for SAS and LES, respectively.In both cases, turbulence intensity is not everywhere matching well 380 with the experiments.Here again, one of the two external peaks of the profiles is typically severely underpredicted by both methods, similarly to what was observed for the baseline case.
In fact, the turbulence intensity peaks correspond to the blade tip region, where the mesh is not fine enough for an accurate modeling of the tip vortices.For LES, the blade tip chord length is 1.8 times the cell size, which is clearly not enough to precisely resolve the tip vortices.The situation of an increased computational effort.The left peak in Fig. 4 is particularly much lower than in the experimental case.Since the SAS cell size at the blade tip is twice as large as in the LES case, this peak for SAS is even lower than the one for LES.The same phenomenon can also be observed in Fig. 5, where the blade tip vorticity and turbulence intensity contours all indicate that the SAS model 390 is less capable of resolving tip vortices than LES.
On the other hand, the turbulence intensity peak on the right is well predicted by both SAS and LES.This phenomenon can be explained by the interaction of the wake shed by the tower with the tip vortices.Since the rotor spins in a clockwise direction (looking downstream), the wake has a counterclockwise swirling motion, as shown by the two bottom plots of Fig. 5.In turn, this causes 395 the tower wake to move slightly to the right and upwards, increasing the turbulence intensity at hub height in this region of the wake.This effect is well illustrated by the LES turbulence intensity color plot of Fig. 5.The higher turbulence intensity on the right of the wake promotes a faster decay of the tip vortices than on the left, as shown by the vorticity color plot of the same figure.Because of this enhanced mixing, it is not necessary to have an extremely fine resolution of the grid, and even the 400 relatively coarse mesh used here is enough to capture reasonably well the turbulence intensity peak on the right of the wake.The situation is different on the left: here, there is a very low background turbulence, as the incoming flow is almost uniform and there is little or no effect from the tower  wake.Hence, to estimate the correct turbulence intensity one would have to resolve very accurately the tip vortices, something that is however not possible with the current grid density.

405
This interpretation of the results was confirmed by a simulation conducted without nacelle and tower.In that case, which is not reported here for brevity, very similar turbulence intensity peaks were observed to both the right and left of the wake.
The good matching of the right peak deserves a further comment.In fact, here the turbulence intensity matches well the experiment, while the results on the left peak demonstrate a general lack 410 of resolution of the tip vortices.Hence, to compensate for this, the turbulence generated by the immersed boundaries of tower (and nacelle) must probably be overestimated.Indeed, this is very probable, based on the large difference between SAS and LES (which has a twice as dense mesh) in turbulence intensity in the hub-height core of the wake shown in Fig. 5.
The analysis can be applied to the baseline case described in §5.1, which shows a very similar 415 behavior of the turbulence intensity peaks.

Single-turbine moderate-turbulence case
Next, an isolated wind turbine is considered in a moderate turbulence environment.The turbulent inflow is generated by the precursor simulation, as described in §3.1.The machine is aligned with 420 the flow and operates at the fixed rotating speed of 720 RPM with a collective pitch of 1.4 deg.
The numerical models use the same exact parameters employed for the low turbulence cases.The CPU time ratio between the two turbulence models is CPU LES /CPU SAS =9.37 in this case.The 60 s average rotor power is equal to 31.0 W for the experiment, 30.5 W for LES and 30.1 W for SAS.
Figure 6 shows the normalized velocity and turbulence intensity profiles for the experiment, LES 425 and SAS at -1.5D, 1.4D, 1.7D, 2D, 3D, 4D, 6D and 9D.The first measurement station at -1.5D is upstream of the wind turbine, where the flow can be regarded as the undisturbed free stream.The velocity profiles are all, in general, in a good agreement with one another.The overall simulation error ∆(u x ) , averaged over all distances, is equal to 0.9% for LES and it is 1.1% for SAS.At 4D downstream, where a second wind turbine is located in other experiments, ∆(u x ) is 2.1% for 430 LES and for Throughout the wake propagation from near (1.4D) to far (9D), the RMS(u x ) for gradually reduces from 0.18 m/s to 0.13 m/s, while for SAS it decreases from 0.21 m/s to 0.08 m/s.Comparing to the low turbulence case of §5.1, the RMS values are drastically reduced, which indicates a significant increase of the simulation accuracy for the present moderate turbulence condition.

435
From 1.4D to 9D, the average turbulence intensity error for SAS is 2.6%, 5.1%, 6.3% 10.7%, 12.1%, 8.2% and 7.6%, respectively.Contrary to the low turbulence (baseline) case, turbulence in- environment.For instance, the turbulence intensity RMS at 8D was 0.03 in the low turbulence case, while it is 0.01 in the present case at 9D (measurements at the same location are not available in the 440 two experimental data sets).A good estimation of turbulence intensity is necessary for the correct estimation of wake deficit.The good match observed here at 9D is therefore encouraging for the use of the present simulation models both for closely spaced wind farms, where the wake might be interacting with multiple machines, and for larger spacings, where one needs to account for impingement of wakes shed by machines far upstream.

445
In the near wake, a proper estimation of the effects of tip vortices can be observed, differently from the low turbulence case discussed in §5.1.The two turbulence intensity peaks can be clearly observed from 1.4D to 4D, covering the whole near wake range.It is possible that even a coarser grid could be used in this case, although a precise characterization of the degradation of the results with decreasing mesh density was not performed.Results indicate a good agreement between SAS and LES, both in terms of velocity and of turbulence intensity, as shown in Fig. 7.Here again, one can notice that the difference between the two models tends to decrease in higher turbulence conditions.This is particularly true in the near hub region, which is probably due to the higher mixture created by the background turbulence.

Three aligned turbines 460
Results shown up to here indicate that SAS achieves in general a good agreement with LES both in terms of wake deficit and turbulence intensity.The match is of a better quality for increasing turbulence, while it is less satisfactory for low turbulence conditions.However, the moderate and high turbulence flows considered here represent more realistic atmospheric boundary layers, while very low turbulence conditions are less likely to be encountered in actual conditions in the field.

Figure 1 .
Figure 1.Experimental layout and computational domain.
SST, SAS and LES methods.The domain inlet uses the velocity inflow map obtained from either the LiDAR scanned inflow map(Van Dooren et al., 2016) (low turbulence case) or the turbulent 215 precursor simulation (moderate and high turbulence cases).Boundary conditions on the left/right side walls are as follows.Since the domain width is reduced with respect to the actual one, Neumann type surface conditions are set for p and T , while mixed type wall conditions are used for ũ, setting the wall-normal velocity component to zero to ensure mass conservation and numerical stability.The ceiling and floor use Dirichlet-type non-slip wall conditions.The IBs of nacelle and tower use 220 7 Wind Energ.Sci.Discuss., https://doi.org/10.5194/wes-2018-47Manuscript under review for journal Wind Energ.Sci. Discussion started: 3 July 2018 c Author(s) 2018.CC BY 4.0 License.Dirichlet-type non-slip wall conditions for the low turbulence condition, while slip wall conditions are used in the turbulent cases on account of numerical stability issues.Apart from the resolved flow quantities, boundary conditions are also set for sub-grid scale quantities.The constant Smagorinsky LES model uses Neumann and Dirichlet-type surface conditions for eddy viscosity µ t at left/right and ceiling/floor faces, respectively.In the Dirichlet case, a value 225 equal to 1 × 10 −5 m 2 /s is used at the centroids of boundary cells to account for the negligible turbulence near the surface.The eddy viscosity µ t , on the other hand, is the ratio of the two additional variables k and ω for the SST and SAS models.Dirichlet-type wall conditions are imposed on both the ceiling and floor surfaces for k and ω, using the values 1×10 −4 and 2×10 −2 , respectively, based on Menter and Esch (2001) and simulation stability tests.Results are also largely insensitive to the 230 boundary values for k and ω, which therefore do not require a precise calibration.
Sci. Discuss., https://doi.org/10.5194/wes-2018-47Manuscript under review for journal Wind Energ.Sci. Discussion started: 3 July 2018 c Author(s) 2018.CC BY 4.0 License.ing parameter F SAS is set to 2 for the SAS model.Tests have shown that the performance of the SAS model is dependent on this parameter, so that its careful calibration becomes essential for the accuracy of the results.4 Experimental setup Experiments were conducted in a 36 m by 16.7 m by 3.84 m boundary layer wind tunnel at Politec-260 nico di Milano(Bottasso et al., 2014).The scaled wind turbine are of the G1 model type, with a rotor diameter of 1.1 m and more completely described inCampagnolo et al. (2016cCampagnolo et al. ( , a, b, 2018))].
LES and SAS are compared to experiments, by considering hub-height velocity profiles 4D downstream of 365 the rotor for six different yaw misalignment angles, namely ±5 deg, ±10 deg and ±20 deg.The flow conditions are the same low turbulence ones of the baseline case.Therefore, as previously observed, SAS results are somewhat affected by a lack of resolution of the tip vortices in the near wake region.

Figure 5 .
Figure 5. From top to bottom, vorticity magnitude |∇ × u| and turbulence intensity σ/ ux on a hub-height horizontal plane, and turbulence intensity on a vertical plane (looking downstream) 4D behind of the rotor.Black arrows indicate the cross-flow velocity vector at a number of sampling points.

Figure 6 .
Figure 6.Normalized time-averaged stream-wise velocity (top) and turbulence intensity (bottom) profiles at hub height and at several positions.Experiment: black • symbols; LES: red + symbols; SAS: blue × symbols.
fully-waked wind turbines are considered, The machines are aligned with the flow, with their rotors pointing into the incoming wind and spaced among themselves of 4.1D.Experimental measurements are not available in this case.The same moderate turbulence flow of §5.3.1 is used even in this case.The first upstream machine 470 operates in the same exact conditions of the isolated wind turbine case, while the two downstream Wind Energ.Sci.Discuss., https://doi.org/10.5194/wes-2018-47Manuscript under review for journal Wind Energ.Sci. Discussion started: 3 July 2018 c Author(s) 2018.CC BY 4.0 License.machines are operated in closed by a pitch-torque controller, in order to adjust their operating point to the local incoming wind.

Figure 8 Figure 8 .
Figure 8 shows velocity and turbulence intensity profiles at various distances from the rotor.Notice that the wind turbines are located at 0D, 4.1D and 8.2D.The two simulation models show nearly 475

Table 1 .
Main characteristics of G1-type wind turbine model.quantities are used to evaluate the simulation accuracy with respect to experimental measurements.The average velocity u is computed based on time-averaged velocity components sampled 9 Wind Energ.Sci.Discuss., https://doi.org/10.5194/wes-2018-47Manuscript under review for journal Wind Energ.Sci. Discussion started: 3 July 2018 c Author(s) 2018.CC BY 4.0 License.Three