APOYO Y TRABAJO MANCOMUNADO CON LAS DIFERENTES SECRETARIAS:

Accurate predictions of wind turbine wakes are important for the performance analysis of the turbines and their optimal positioning within tightly-spaced wind farms. In the past, CFD was considered a tool confined to the near-wake analysis due to the inherent numerical dissipation of CFD solvers. With progress, however, in numerical methods and mesh density, CFD is emerging as a good tool for the analysis of the wakes since it can accurately capture the development of core instabilities that will lead to the wake breakdown.

Ivanell et al.[64] studied the stability of tip vortices in an azimuthally periodic domain using the actuator-line method (one blade was simulated with spatial periodicity assumed). Perturbations were added to the solution and it was found that when the oscillations of vortices from one spiral to the next were out of phase the instabilities were larger than for in-phase modes. Likewise, the non-linear development of the wake instability resulted in vortex pairing. They also correlated the length of the stable wake with turbulence intensity at the free-stream.

Troldborget al.[153]studied the wake behind the Tjaereborg wind turbine with LES and for different tip speed ratios. At high tip speed ratio (λ=11.78), the wake broke shortly downstream of the rotor, while atλ=7.07 the instabilities were present at 10R. In Troldborget al.[154], they compared the wake behind the NREL 5MW wind turbine (126m diameter) with RANS and DES computations, employing the full rotor geometry as well as actuator line and actuator disc methods. The RANS results with the three representations of the rotor were very similar. However, DES computations showed that the use of an actuator line or disc methods are not optimal for a good wake capture when the inflow is laminar. Due to the coarseness of the employed grid (minimum cell size of 500mm), the results presented an early wake breakdown at approximately one diameter downstream, see Figure 1.8. There was a jump from finer to coarser grid and, therefore, the wake breakdown might be attributed to numerical dissipation.

LES computations, using the commercial CFD solverFLUENT, were performed by Mo et al.[103]

for the NREL Phase VI wind turbine (10m diameter) inside a wind tunnel at 7m/s wind speed (λ =5.42), with grid cell sizes of 250mm on the wake. An increase in the turbulent intensity was observed from the

2_{Full citation of: M. Carri´onet al., Understanding Wind Turbine Wake Breakdown using CFD,AIAA Journal, Accepted May}

rotor plane to three diameters downstream and a gradual decrease in the region where the wake started to be unstable (at approximately 4D downstream). It finally broke down at 5D downstream and, as a result, the turbulence levels increased again. They also demonstrated that a deficit of velocity was noticeable at downstream distances of 20D. The same authors studied the effect of the wind speed on the wake instability [102]_{, keeping a constant rotational speed of 72rpm. They found that the instability started to develop later} in time and further downstream when the wind speed, and therefore the tip speed ratio, increased: while at 7m/s the instability region was located at 4D, at 10m/s it was located at 6D and at 15m/s it was at 11D downstream. Gundling et al.[53] used a free-vortex wake model coupled with a growth/diffusion vortex model for the prediction of wind turbine far wakes. The NREL Phase VI and WPS–30 wind turbines were used and the results were compared with actuator line LES (FLOWYO solver) and full-rotor DES (HELIOSsolver) simulations, using adaptive mesh refinement. For laminar inflow and wind speed of 10m/s (λ=3.77), the free-vortex wake model only captured the vortices up to 4R and were dissipated downstream, since high levels of dissipation were added for stability reasons, see Figure 1.20 (a). Employing the full- rotor representation, however, wake instabilities were predicted between 8R and 10R downstream (Figure 1.20 (c)). Additionally, the actuator line captured the wake very poorly, see Figure 1.20 (b).

(a)Free-vortex model. (b)Actuator Line.

(c)Full Rotor representation.

Figure 1.20: Prediction of wake instabilities using a(a)Free-vortex model, and DES with(b)actuator line and(c)full rotor representation, with adaptative grid refinement method, by Gundling[53]. The wind speed was 10m/s (λ =3.77) and the inflow was uniform.

Table 1.4 lists the conditions and grids employed in the works in the literature, as well as the location of the predicted instabilities.

Table 1.4: Wind turbine wake breakdown computations in the literature.

Reported Wind Turb. Rotor Tu int. Mesh Wake res. λ Ins.

by Turbine Model Model (%) size (mm) (R)

F.R. (P) 860M 6.67 4.5

Current work MEXICO RANS F.R. (P) 2.58 860M 6 10 1.25

F.R. 2B 10 1.25

Ivanell[64] Tjaereborg LES AL (P) 1.0 10M 435 7.07 4

3.21 -

Troldborg[153] _{Tjaereborg LES AL 0.0 8.4M 1000 5.05 -}

7.07 5

11.78 2

AL 7

Troldborg[154] _{NREL 5MW RANS AD 0.0 23M 500 7.6 -}

F.R. -

AL 7

Troldborg[154] NREL 5MW DES AD 0.0 23M 500 7.6 -

F.R. 2

AL 2

Troldborg[154] _{NREL 5MW DES AD 6.0 23M 500 7.6 -}

F.R. 2

FV BEM - N.A. - / -

Gundling[53] NREL Phase VI LES AL 0.0 5.9M N.A. 3.77 / 7.53 - / -

DES F.R. 33M N.A. 8 / 2

FV BEM - N.A. -

Gundling[53] WPS-30 LES AL 13.0 5.9M N.A. -

DES F.R. 33M N.A. -

2.51 22 Mo[102] NREL Phase VI LES F.R. 0.2 3.6M 250 2.89 18 3.79 12

5.41 8

F.R.: Full Rotor representation; F.R. (P): Full Rotor representation with azimuthally periodic domain; AD: Actuator Disk; AL: Actuator Line; Tu int.: Turbulence intensity at the inflow; Wake res.: resolution of the cells at the wake in mm; Ins.: Relative location from the rotor plane where the instability is predicted; FV: Free-Vortex Wake method; BEM: Blade Element Model; N.A.: Information not available.