2.1 YALES2: an aerodynamic solver

2.1.3 Wind turbine modeling

In YALES2, the ALM is used to model operating wind turbines. As stated in the Introduction, the approach allows us to model the forces applied by wind turbine blades on an incident flow. It is particularly suitable for investigating the physics of wind turbine wakes at a reasonable cost. Each blade geometry is replaced by a simple line, discretized into 1D elements of equal width w. The center point of an element is called the particle. The particle location is also chosen to match the quarter-chord point of the corresponding airfoil. In order to ease its handling, the rotor is simplified geometry relies on a set of 3D bases.

• The rotor basis (RB). Linked to the rotor center, this basis allows us to represent the tilt and yaw angles. However, its orientation remains independent of the azimuthal rotation.

• The blade bases (BB). Their origins coincide with the blade roots. They accurately translate the orientation of each blade, by taking into account their azimuthal position and the pitch angle. The turbine coning can also be represented by their means.

• The particle bases (PB). They are attached to each blade element. They allow us to represent the local twist angle, as well as the prebend and sweep of the blades.

All these additional bases, illustrated in Fig. 1, are given in the global (GB) reference frame of YALES2 (Y2). For instance, the rotor basis can thus be written as the transition matrix ${\mathbf{T}}_{\mathrm{GB}\mathrm{Y}\mathrm{2}}^{\mathrm{RB}\mathrm{Y}\mathrm{2}}$. This natural framework proves very advantageous for navigating from one basis to another. Initially, the particle bases are linearly interpolated in a lookup table, which defines the blade undeformed geometry and contains similar bases associated with specific spanwise positions along the blade.

Figure 1Additional set of bases used in the ALM framework of YALES2.

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The lift L and drag D forces, assumed constant on each blade element, are computed at the particle location as follows:

$$\begin{array}{}\text{(3)}& {\displaystyle }L={\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}\mathit{\rho }{u}_{\mathrm{rel}}^{\mathrm{2}}c\left(s\right)w{C}_{\mathrm{L}}(\mathit{\alpha },s),\text{(4)}& {\displaystyle }D={\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}\mathit{\rho }{u}_{\mathrm{rel}}^{\mathrm{2}}c\left(s\right)w{C}_{\mathrm{D}}(\mathit{\alpha },s),\end{array}$$

where u_rel is the magnitude of the fluid velocity seen by the moving airfoil and ρ is the fluid density. The lift and drag coefficients, denoted C_L and C_D, respectively, here, are interpolated linearly in the aforementioned lookup table, which provides them as a function of both the angle of attack α and the spanwise position s along the blade. The airfoil chord c is also retrieved from the same lookup table. The velocity u_rel is further defined as a combination of both the local fluid velocity u_f and the particle velocity ${\dot{\mathit{x}}}_P$:

$$\begin{array}{}\text{(5)}& {\mathit{u}}_{\mathrm{rel}}={\mathit{u}}_{\mathrm{f}}-{\dot{\mathit{x}}}_{\mathrm{P}}.\end{array}$$

Once given in the particle frame, this velocity enables us to compute the angle of attack α.

Yet, the forces obtained this way are singular and must be smoothed before being added as a body force in the Navier–Stokes equations. In the ALM framework, this operation is known as the mollification process. It acts as a spatial filtering operation, typically based on a Gaussian-like kernel η (Sørensen and Shen, 2002):

$$\begin{array}{}\text{(6)}& \mathit{\eta }\left(d\right)={\displaystyle \frac{\mathrm{1}}{{\mathit{ϵ}}^{\mathrm{3}}{\mathit{\pi }}^{\mathrm{3}/\mathrm{2}}}}\text{exp}\left[-{\left({\displaystyle \frac{d}{\mathit{ϵ}}}\right)}^{\mathrm{2}}\right],\end{array}$$

where d is the distance to the kernel center and ϵ is the kernel radius. The latter is usually chosen as twice the maximum cell size encountered in the rotor region.

For an exhaustive description of the ALM implementation in YALES2, the reader is referred to the PhD thesis of Houtin-Mongrolle (2022). Issues regarding the optimization of the ALM computational cost are also covered.

2.2 BHawC: an aero-servo-elastic solver

BHawC (Rubak and Petersen, 2005) is a nonlinear aero-servo-elastic solver intended to support the design and certification of wind turbines. Validated continuously against field data, the code allows a fast assessment of a wind turbine structural response to external loads so as to investigate numerous design load cases (DLCs) in a reasonable time. Indeed, for an appropriate discretization of the structure, the code can provide a 1:1 time to solution.¹

A BHawC run can only handle one turbine at a time as it allows the definition of only one inflow. The assessment of the performance of a wind farm for given free-stream wind conditions, as well as the prediction of the loads applied to each individual turbine, remains feasible, provided that each BHawC instance relies on an appropriate inflow model (such as a DWM model). Nevertheless, all considered inflows are fully decoupled and thus possibly inconsistent.²

The modeling of a wind turbine consists of several sub-structures used to represent the foundation, tower, nacelle, hub, drivetrain, shafts, and rotor blades. Most of the sub-structures are modeled with equilibrium-based non-homogeneous anisotropic beam elements counting 12 degrees of freedom: three rotations and three translations per node (Krenk and Couturier, 2017). The drivetrain and the different bearings are modeled as purely torsional elements. Similarly to YALES2, BHawC also makes use of additional frames to manage the mentioned sub-structures and the elements used to discretize them. In particular, all the bases discussed in Sect. 2.1.3 have their twin in the BHawC (BH), even though their orientations can differ. This is the case for the blade bases, depicted in Fig. 2.

Figure 2Blade bases in BHawC.

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All the structural degrees of freedom, as well as their velocity and acceleration, are solved in BHawC (BH) global frame, which is attached to the bottom of the turbine foundation. The vector containing all the degrees of freedom is denoted by x(t) and its first and second derivative by $\dot{\mathit{x}}$ and $\ddot{\mathit{x}}$, respectively. BHawC targets the following equilibrium at each time step (Skjoldan, 2011):

where f_iner, f_damp, f_int, and f_ext are the inertial, viscous damping, internal, and external loads, respectively. Especially the latter encompasses the aerodynamic loads. To solve the previous equation, the Newton–Raphson method is used to derive its residual form and iterate over it:

where M, C, and K are the mass, damping, and stiffness matrices, respectively. Additionally, the Newmark method is used to advance the system in time and relate $\ddot{\mathit{x}}$ and $\dot{\mathit{x}}$ to x. This solution procedure leads to a linear system at each Newton iteration, where the correction vector δx is the only unknown. An LU factorization method is typically used to invert the system. Once δx is factored into x, the code updates the aforementioned matrices and all the components of the residual r except for the aerodynamic loads.

Those are computed only once per time step, prior to the first Newton iteration. To do so, BHawC relies on a blade element momentum (BEM) method (Sørensen, 2016), enhanced by many corrections. For instance, BHawC benefits from a modeling of the dynamic stall phenomenon (Leishman and Beddoes, 1989) and from the Prandtl correction for the tip/root losses, to cite only a few examples.

Finally, a complete framework is available in BHawC to include an emulation of a real controller in the wind turbine modeling. As a result, the rotor rotation speed is intrinsically unsteady. This approach also allows us to update other operating parameters in time, especially the pitch angles.

4.1 Numerical setups

The geometry of the computational domain used with YALES2 and the cell size mapping enforced within are provided in Fig. 8. The mesh counts 10 899 287 nodes and thus as many control volumes because YALES2 is node centered. The smallest cells are located in close vicinity to the turbine, and their size is set to ${\mathrm{\Delta }}_{\mathrm{grid}}=D/\mathrm{64}$ to comply with the ALM common guidelines (Jha et al., 2014). The mesh size in the wake is however set to twice this value so that the whole mesh remains of reasonable size despite the domain extents. Close to the lower boundary, the mesh size is also set to $D/\mathrm{32}$ to properly capture the stronger velocity gradient occurring in this region because of the wind shear.

Figure 8Mesh and geometry of the computational domain used to investigate turbine F07 with YALES2–BHawC.

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Regarding the boundary conditions, the lateral and upper surfaces are modeled as slipping walls. On the bottom surface, a classical logarithmic wall law including a roughness parameter is used to work around the full resolution of the atmospheric boundary layer. Due to the lack of reliable wind-assessment tools on the field, the inlet conditions result from a wind estimator. First, the recorded mean nacelle yaw angle is assumed to provide the wind direction. In the considered field data samples, the recorded mean yaw angles indicated a wind coming almost exactly from the north, with all deviations being below 1^∘. Still, it should be noted that the standard deviations of the yaw angles were not zero, reaching 3.14^∘ at most. This was deemed small enough to overlook the neighboring turbines' influence on the results. Second, the wind speed U_h and turbulence intensity at hub height are computed based on the power output and pitch angles of the turbine. In this study we consider three operating points, as given in Table 1. The inlet boundary condition is finally modeled as follows:

where $(u^{\prime },v^{\prime },w^{\prime })$ denotes a synthetic turbulent velocity field based on the Mann model (Mann, 1994, 1998) and W(y) is the power law given by

The exponent α is set to 0.13, as this is a typical value for offshore applications (Burton et al., 2011). The velocity fluctuations are computed prior to the actual simulations, using the turbulence simulator from the International Electrotechnical Commission (IEC) (DTU Wind Energy, 2018), and then saved into periodic 3D boxes. Although anisotropic, this synthetic turbulence remains homogeneous, meaning for instance that the turbulence damping induced by the sea in the vertical direction is not factored in. The velocity field considered by BHawC in the BEM method is modeled identically.

Table 1Mean wind speeds and target turbulence intensities (TIs) at hub height on the inlet boundary.

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As additional noteworthy parameters, the air density and kinematic viscosity are set to ρ=1.235 kg m⁻³ and $\mathit{\nu }=\mathrm{1.448}\times {\mathrm{10}}^{-\mathrm{5}}$ m² s⁻¹, respectively. For simplicity's sake, we also enforce $\mathrm{\Delta }{t}_{\mathrm{Y}\mathrm{2}}=\mathrm{\Delta }{t}_{\mathrm{BH}}=\mathrm{0.02}$ s in all simulations, thus putting aside the sub-stepping capability described in Sect. 3. For all considered wind speeds, this time-step size complies with the CFL conditions based on the flow velocity and the particle velocity.³

Concerning the turbine modeling, 75 evenly distributed aerodynamic nodes were used in BHawC to discretize each blade. Similarly, 75 particles were evenly distributed along each actuator line in YALES2–BHawC. This number was chosen to prevent interpolation errors when getting the aerodynamic coefficients from the blade lookup table. Indeed, 75 blade sections were referenced in the latter, which are at the exact same spanwise positions, respectively, as the defined aerodynamic nodes. The isotropic mollification kernels in YALES2 are defined with a radius $\mathit{\epsilon }=D/\mathrm{32}=\mathrm{2}{\mathrm{\Delta }}_{\mathrm{grid}}$. This choice was motivated by two main reasons. First this value, used along with a constant cell size in the rotor area, is widely used in the literature (Troldborg, 2009; Jha et al., 2014). Second, this work addresses the question of using LESs in an industrial context to further support improvements of lower-fidelity approaches, such as BEM-like methods or analytical wake models. The LES approach, from an industrial perspective at least, is still considered very costly due to the required CPU resources. Therefore, some trade-offs must be found between achievable accuracy and simulation cost. It is indeed shown in the literature that one should ideally opt for a varying value of ε along the blade span, to comply with the local length c of the blade section chord. The value of ε=0.25 c was for instance reported as a suitable choice (Shives and Crawford, 2013). Yet, as one must still comply with ε≥2Δ_grid, the consistent mesh size in the rotor region would become prohibitive.

From a structural point of view, the blades are discretized with 19 beam elements of various lengths in order to achieve a suitable representation of the elastic-axis geometry at a reasonable cost. The nacelle and tower are not represented on the YALES2 side. Accordingly, the loads acting on them are forced to zero on the BHawC side, at all times. Regarding the wind turbine actual controller, it is emulated thanks to external libraries compiled beforehand.

4.2 Results

For confidentiality reasons, all the quantitative results shown in the current section are made nondimensional. Also, we first define the following operators:

where • is a quantity of interest, θ_N is defined as in Sect. A1, and T=600 s is a physical duration. These operators refer to azimuth-averaged and time-averaged results, respectively. We also introduce an additional discrete operator, referring to a mean value obtained at a given azimuth Θ:

For each wind speed considered, Fig. 9 starts by comparing the field data with the numerical results obtained with YALES2–BHawC and BHawC standalone, in terms of time-averaged rotation speed, pitch angle (first blade), and electrical power output. Overall, average values and standard deviations are well predicted with YALES2–BHawC for all the wind speeds of interest. The time-averaged values provided by BHawC appear to be almost the same as those given by the coupled code. However, one can observe meaningful differences in the standard deviations. Those obtained with BHawC standalone are up to 3 times lower than those given by the coupled code. This is especially visible for the rotation speed at low wind speed.

Figure 9Comparison of the time-averaged rotation speed, total pitch angle (first blade), and power, for the three wind speeds of interest. The corresponding standard deviations are depicted as error bars.

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The edgewise and flapwise bending moments at a spanwise position close to the blade root are compared for the first blade in Fig. 10. Field data were also available for such quantities thanks to strain gauges. Again, the results numerically obtained with both codes are fairly accurate. Discrepancies, reaching up to 20 % of the field data, are visible, but the trends are very well captured.

Figure 10Comparison of the time-averaged edgewise and flapwise bending moments, on the first blade and at the strain gauge location. The standard deviations are depicted as error bars.

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In what follows, the numerical results are now compared in greater detail. Despite the lack of field data for the quantities considered, the results from BHawC stand as a reference. Indeed this tool is a keystone in the design cycles of actual turbines and thus has been extensively validated against field data in those specific conditions (no yaw error and no upstream wake).

The first-blade tip deflection δ_f in the flapwise direction Y_BB BH is compared for all wind speeds in Fig. 11. Results of both codes are depicted for N=10 rotor full revolutions. The periodicity due to the rotor revolution is clearly visible in the two signals, while the turbulent inflow causes additional fluctuations. One can note significant differences between the curves. This is expected as the rotor azimuth at a given time has no reason to be the same in the two simulations. Indeed, inductions at the aerodynamic nodes' location are not computed in the same way, which leads to different aerodynamic loads and in the end to a different feedback from the controller. Besides, the turbulence seen by the rotor is not exactly the same in both codes, even initially. The reason is further developed later in this section. Yet, the amplitude of the deflections compares very well for all wind speeds.

Figure 11Comparison of the first-blade tip deflection δ_f, in the flapwise direction, over the 10 last revolutions of the rotor, as obtained by BHawC and YALES2–BHawC.

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In Fig. 12, the comparison is continued in polar coordinates to visualize the distribution of discrepancies according to the azimuthal position. To this end, we compare the mean deflection obtained at 36 azimuthal positions, based on the data from the last N=50 revolutions of the rotor. Overall, the results from both codes agree fairly well at all wind speeds, with discrepancies mostly lying in the range $[-\mathrm{5}\mathit{\%},\mathrm{5}\mathit{\%}]$. No clear trend appears, meaning the coupled code does not tend to either over-predict or under-predict the results from BHawC. The local gap between the results peaks in the azimuthal range $[\mathrm{180}{}^{\circ },\mathrm{270}{}^{\circ }]$, for the high-wind-speed case, where the deflection predicted by YALES2–BHawC is on average 10 % higher than the one computed by BHawC. For the medium wind speed, we can notice that the discrepancies also reach their maximum (in algebraic values) in the same azimuthal range. However, the same cannot be said for the low-wind-speed case, where the relative difference in the results remains constant over all the azimuth positions. This behavior is not fully understood yet. It may be related to the turbulence injected in YALES2 not being in equilibrium with the mean flow, especially close to the ground. An artificial boundary layer developing on the bottom wall from the inlet was indeed observed. Its thickness increased while moving downstream, all the more at low wind speed to encompass the whole rotor. In the high-wind-speed case, on the other hand, this artificial boundary layer only partially overlaps the rotor area.

Figure 12Comparison of the first-blade tip deflection δ_f in the flapwise direction, averaged per azimuthal position. The data from the last 50 revolutions of the rotor are considered.

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To deepen the analysis, Fig. 13 compares the frequency decomposition of the flapwise deflection just discussed for all the investigated wind speeds. To get representative results, the data from the last N=50 revolutions of the rotor were considered input. For each wind speed, the main peak matches the frequency f_rot, derived from the time-averaged rotation speed of the rotor. This peak, as well as its two first harmonics, is well captured by both codes. In the three wind speed scenarios, a good overlap between the results from BHawC and YALES2–BHawC is obtained overall. Nonetheless, the peaks are slightly more diffused in the results of the coupled code. This is consistent with the standard deviations of the rotation speed being higher in YALES2–BHawC than in BHawC (see Fig. 9).

Figure 13Fast Fourier transform of the first-blade tip deflection δ_f in the flapwise direction, considering the results from the last 50 revolutions of the rotor for both YALES2–BHawC and BHawC.

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Figure 14Comparison of the internal loads (forces and moments) at several spanwise positions across the first blade. The quantity σ_T(•) refers to the standard deviation of the argument over the time range T.

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Figure 15Comparison of the damage equivalents loads, computed from the internal loads (forces and moments) at several spanwise positions across the first blade.

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The time-averaged internal force F and moment M obtained in the flapwise direction Y_BB BH and edgewise direction X_BB BH, respectively, are now compared at several spanwise positions across the first blade. The results are provided in Fig. 14 for all the wind speeds of interest. The discrepancies between the results from YALES2–BHawC and BHawC are given relatively to 3 times the standard deviation in time σ_T of BHawC results. Most of the discrepancies appear to lie within the range [−10 %, 10 %]. Still, one can observe higher gaps in the low-wind-speed case, especially close to the blade tip, where the loads computed by YALES2–BHawC are shown to be significantly lower than those coming from BHawC standalone. Nevertheless, it seems important to stress that the standard deviations in time of the depicted loads, as their time-averaged values, become smaller and smaller when heading towards the blade tip, to be almost zero at the tip.

The variability in the internal loads in time is also of great interest for engineers as it conditions the structural fatigue. Thus, the damage equivalent loads (DELs) were computed from the internal loads F and M just discussed. The Palmgren–Miner rule (Miner, 1945) allows the assessment of the damage d of a blade element, resulting from an unsteady internal force F (or moment M) acting during the period T:

The whole variation range of F is split into N_b bins, which define as many discrete amplitudes F_j for the included loading cycles. A rainflow algorithm (Matsuishi and Endo, 1968) is used to count the number of cycles n_j associated with each amplitude F_j. The quantity ${\widehat{n}}_j$ denotes the maximum number of loading cycles of amplitude F_j that the blade element can withstand before breaking by fatigue. Simply put, the previous law states that a pure sinusoidal load F^′, of amplitude F_eq and frequency $f_{\mathrm{eq}}={\widehat{n}}_{\mathrm{eq}}/T$, will lead to the same damage as the real load F would. The number of cycles ${\widehat{n}}_j$ is usually provided through a Wöhler curve (also known as S–N curve), which can be fitted by the following law:

where k and m are material-dependent properties. For a wind turbine blade, even though it may vary with the deformation direction, the value m=10 is traditionally used (Sutherland, 1999; Lee et al., 2012), as it refers to the glass fiber which comes in the composition of the blade reinforced parts (Mishnaevsky et al., 2017). The combination of Eqs. (20) and (21) leads to the following expression for F_eq:

Only the choice of the frequency f_eq remains. In order to compare the results from all cases, we set f_eq=1 Hz, which is decorrelated from the wind conditions.

The relative differences in the results obtained are reported in Fig. 15. They are shown to be significantly higher than those observed in the results commented on previously. This is particularly true for the low-wind-speed and medium-wind-speed cases, for which the equivalent loads predicted by YALES2 exceed those of BHawC by about 30 % on average, considering the entire blade span. Two trends are also noticeable depending on the wind speed. In the medium-wind-speed and high-wind-speed cases, the discrepancies increase from the root to the mid-span region and then tend to decrease slightly before significantly increasing back when heading towards the blade tip. On the contrary, the discrepancies obtained in the low-wind-speed case evolve differently, especially for the flapwise equivalent moment, for which they are maximum in the blade root region.

4.3 Discussion on the reported discrepancies

Given their amplitude, the gaps observed in the numerical results reported in the previous sub-section likely relate to three main factors. First, as mentioned at the end of Sect. 3, BHawC includes the model of Beddoes–Leishman (Leishman and Beddoes, 1989) to take into account the dynamic stall effect and correct the aerodynamic coefficients accordingly. As suggested by Øye (1991), the dynamic stall effect can be roughly translated into a time relaxation of the aerodynamic loads. Disabling this model in BHawC was impossible in practice, as this led to the failure of the structural solver.

Second, BHawC computes annular inductions, which could also weaken the shear-induced variability in the aerodynamic loads inferred afterwards.

Third, the turbine in BHawC does not exactly face the same turbulent structures as in the coupled code, primarily because the relative position between the turbine and the turbulence box differs. Besides, the turbulence is static in BHawC, meaning the velocity fluctuations factored into the induction computation are the ones present in the Mann boxes. Similarly, the shear profile remains equal to the one provided at all times. On the other hand in YALES2–BHawC, the Mann turbulence will evolve while being convected to the rotor position, especially close to the ground. A slight distortion of the shear profile is also expected. Such shortcomings directly result from the unbalanced combination of the injected synthetic turbulence, the power law, and the boundary conditions (especially the one used at the bottom boundary). To better illustrate this, the streamwise time-averaged velocity and the streamwise turbulence intensity considered in both YALES2–BHawC and BHawC are depicted in Figs. 16 and 17. It can be seen that the turbulence injected at the inlet in YALES2 first tends to decay at hub height, while it significantly increases close to the bottom boundary and then induces the most significant distortions of the shear profile. As complementary results, the mean turbulence intensity in the projected rotor area was assessed in all coupled simulations at several streamwise positions: one and two diameter(s) upstream of the turbine as well as in the rotor plane. The obtained values are gathered in Table 2. Considering the low-wind-speed and medium-wind-speed cases in the rotor plane, it appears that the turbulence intensity is above the target values from Table 1. While this overall issue cannot be fully worked around, one way to address it would be to replace the Mann boxes in BHawC with velocity fluctuations extracted from the YALES2–BHawC simulation, say one diameter upstream of the turbine (Houtin-Mongrolle, 2022).

Figure 16Comparison of the shear profile imposed in BHawC (left column) with the one actually obtained in YALES2–BHawC two diameters and one diameter upstream of the rotor. The rotor position is depicted in each plot as a black circle.

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Figure 17Comparison of the turbulence intensity imposed in BHawC (left column) with the one actually obtained in YALES2–BHawC two diameters upstream of the rotor and in the rotor plane. The rotor position is depicted in each plot as a black circle.

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Table 2Mean effective streamwise turbulence intensities obtained in YALES2–BHawC one and two diameters upstream of the rotor, as well as in the rotor plane, in the projected rotor area.

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Considering all the aforementioned sources of discrepancies, the results given by the code YALES2–BHawC for the structural part are therefore deemed encouraging and promising. As for the prediction of the main operating parameters and performance of the turbine, the coupled code already provides accurate results. Even though additional investigations are definitely needed, the results so far presented constitute an encouraging first step towards a full validation of YALES2–BHawC.

4.4 Surrounding flow

Unlike BHawC standalone, YALES2–BHawC provides insights into the flow surrounding the turbine. For all the wind speeds considered, Fig. 18 presents the streamwise instantaneous velocity field and the corresponding time-averaged field in vertical slices. All the fields shown are divided by the related target velocity at hub height U_h to allow easy comparisons. One can observe the wake regions to be very different. The velocity deficit behind the turbine is indeed stronger in the low-wind-speed scenario, which is indicative of a significantly higher induction. This is consistent with the low wind speed being slightly below the rated one. Conversely, the velocity deficit obtained at high wind speed is about 20 %. This is caused by the rotation speed being only 8 % higher than in the low-wind-speed case (see Fig. 9) while the wind speed is close to being 100 % higher. Therefore the resulting blockage effect is lower. Additionally, the cell size mapping used in the mesh allows the representation of a wide range of velocity fluctuations, both upstream of the turbine and in the wake.

Figure 18Vertical slices, including the rotor center, of the instantaneous (a, c, e) and time-averaged (b, d, f) streamwise velocity fields $w^{*}=w/U_{\mathrm{h}}$ for the low (a, b), medium (c, d), and high (e, f) wind speeds. Extents of the region focused on are given in a number of rotor diameters D.

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Figure 19Horizontal slices, taken at hub height, of the instantaneous (a, c, e) and time-averaged (b, d, f) streamwise velocity fields $w^{*}=w/U_{\mathrm{h}}$ for the low (a, b), medium (c, d), and high (e, f) wind speeds. Extents of the region focused on are given in a number of rotor diameters D.

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Figure 19 shows the same fields but in a horizontal plane taken at hub height. The comments made previously stand, but one can further notice some meandering in the wake, especially at low wind speed.

4.5 Computing performance

Finally, we briefly report the computing performance obtained with BHawC standalone and YALES2–BHawC. All the numerical simulations previously commented on were run on the AMD Rome partition of the Joliot-Curie supercomputer from TGCC. The simulations carried out with BHawC standalone (BH) were handled with only one CPU core, as the code is fully serial, while all the coupled simulations (YALES2–BHawC: Y2-BH) used 255 CPU cores: one for BHawC and the remaining ones for YALES2. The return time of each simulation, given per second of computed physical time, is reported in Table 3. In all cases, the exclusivity flag of the job scheduler was deliberately activated to achieve a better computing performance. Still, one should note that all the simulations were run only once to save CPU hours. Thus, the values given in Table 3 could be slightly biased. Yet, as expected, the return times of the coupled simulations are shown to be significantly higher.

Table 3Return times of the numerical simulations, given per second of computed physical time.

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