Overview of six commercial and research wake models for large offshore wind farms

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1 Overview of six commercial and research wake models for large offshore wind farms Philippe Beaucage AWS Truepower LLC Nick Robinson AWS Truepower LLC Abstract Simulating turbine wakes offshore presents significant challenges. Experiments suggest that the standard wake models, e.g. Park (Jensen) and Eddy Viscosity (Ainslie), tend to underestimate wake losses, especially after the third or fourth row. New models are beginning to be used which are intended to improve predictions. Some are based on the surfacedrag-induced internal boundary layer approach of Frandsen (2007). Other promising alternatives include computational fluid dynamics (CFD) methods such as Reynolds-averaged Navier- Stokes (RANS) models and large eddy simulations (LES). The former are usually run in a steady state mode without buoyancy. In contrast, LES takes into account the influence of unsteadiness and thermal stratification, but with a severe cost in computing power. The performance of these various approaches to wake modeling is compared using observations for two offshore wind projects. 1 Introduction When operating, wind turbines extract kinetic energy from the airflow, leaving the air downstream (i.e., the wake) with reduced speed and static pressure as well as higher turbulence [1,2]. This phenomenon is the source of significant energy production losses in wind power plants. For over 20 years, wake-effect predictions have been based on a handful of computer models, most importantly Park [8,9] and Eddy Viscosity (EV) [11]. The Park model implements a simple formula for the size of the wake deficit and its expansion downstream with a single adjustable Michael Brower AWS Truepower LLC mbrower@awstruepower.com Chuck Alonge AWS Truepower LLC calonge@awstruepower.com parameter, the wake decay constant. The EV model solves an axisymmetric form of the Navier Stokes equations; it therefore qualifies as a simple RANS model. The wake decay is dictated by the rate of mixing of momentum from the surrounding flow into the wake zone, as determined by the ambient turbulence. With the construction of offshore wind projects of significant size, it has become apparent that the standard Park and EV models tend to underestimate wake losses in offshore arrays [13,15]. This may be in part because the models assume that wind turbines have no effect on the planetary boundary layer (PBL) other than the wakes they directly generate. As a consequence, new codes have been developed [13,15] to try to account for two-way PBL-wake interactions. Some of these, like the deep-array wake model (DAWM) within the openwind Enterprise platform, are based on the surface-drag-induced internal boundary layer approach of Frandsen [14], which modifies the wind speed profile within the PBL with increasing distance downstream of the front of a turbine array. (The EV or Park model is retained for estimating direct wake effects.) This approach is attractive for its small runtime on desktop platforms, and available data suggest it is an improvement over the standard models. However, it is limited in its ability to capture the detailed characteristics of the wakes, and its applicability to much larger projects is uncertain. Stand-alone CFD models based on the RANS equations (referred to as RANS models) are equipped to simulate turbulent flows without the simplifying assumptions of the EV model. Nevertheless they have their own weaknesses. Most RANS models are run in steady-state mode and without a complete prognostic equation for temperature (i.e., conservation of

2 energy). Therefore, they cannot typically account for the time-varying thermal structure of the boundary layer, which may substantially alter the results. Wharton and Lundquist [6] have shown that atmospheric stability can have a strong impact on the power curve of tall wind turbines, i.e. up to a 20% difference in power output between stable and convective regimes during the spring and summer seasons. In addition, the k-ε turbulence closure commonly used in RANS software has been shown experimentally to be problematic for flows containing large adverse pressure gradients [3], such as the gradient generated by the thrust force of a turbine. Several researchers are attempting to overcome the issues of the k-ε turbulence model by modifying the parameters and/or adding source and sink terms in the turbulent kinetic energy (TKE) and dissipation equations [4,30,5]. A promising alternative to RANS models is large eddy simulation (LES), which can theoretically simulate most turbine-atmosphere interactions given an adequate grid spacing and small-scale turbulence closure. LES explicitly resolve energy-containing eddies those larger than the grid spacing while simulating the effects of smaller turbulent eddies through a subgrid scale parameterization scheme. This approach has been developed several decades ago to study the PBL [23,24]. Recently, LES have been used to study single and multiple turbine-induced wakes [23-28]. For single turbine-induced wakes, LES models with a wind turbine parameterization using an actuator disk and/or actuator line model can compare favorably to wind-tunnel measurements even in the challenging nearwake region, according to Porté-Agel et al. [27]. Using the OpenFOAM software [32], Stovall et al. [28] showed that the power deficit ratios for LES and RANS simulations are within 2-4% and 15-43% of experimental data, respectively. LES offer the additional potential advantage of being able to simulate wakes and wind flow in a single, integrated, unsteady simulation. However, such benefits come with a cost: the runtime for LES simulations is approximately 60 times longer than that for RANS simulations in OpenFOAM [28]. Nevertheless, LES codes are a promising approach to simulating wakes if a high performance computing system is available. In this paper, we present comparisons of the performance of several wake models, including standard, deep-array, RANS, and LES. Power production data from two offshore wind projects in Denmark were used for the validation. 2 Measurements Wind turbine power production data from two large offshore wind farms, Horns Rev and Nysted, were kindly provided by Dr. Rebecca Barthelmie through the Prediction Of Waves, Wakes and Offshore Wind (POW'WOW) project. The data were quality controlled and processed by wind speed bins and wind direction sectors according to Barthelmie et al. [7]. The Horns Rev wind farm is located km from the western coast of Denmark while the Nysted wind farm is located 10 km from the sourthern coast of Denmark. The turbine layouts of both wind farms are shown in Figure 1, along with the seven wind direction cases centered around an exact row (ER), which corresponds to 270 at Horns Rev, 278 at Nysted. The Horns Rev wind farm consists of 80 2-MW wind turbine while Nysted has MW wind turbines. The characteristics of both wind farms can be found in Barthelmie at al. [7]. 3 Wake Models A model intercomparison is performed at the two offshore wind farms, Horns Rev and Nysted, described in the previous section. This comparison study includes six different wake models with varying degrees of complexity from standard wake models (i.e. Park, EV) to LES. 3.1 Park The Park model was developed originally by Jensen [8] and Katic et al. [9] and implemented in the WAsP software package of Risø National Laboratory. An empirical equation based on a balance of momentum is used to model single wakes. It assumes an initial velocity deficit immediately behind the turbine rotor, which is calculated from the turbine s thrust coefficient (C t ) for the inlet speed, and an empirically determined wake-decay constant (k). The wake-decay constant sets the linear rate of expansion of the wake with distance downstream. The effects of multiple wakes are taken into account by superimposing, or

3 overlapping, the wake cross-sections of the upstream turbines. A second version of the model called Modified Park differs in the way the overlapping area is defined. Park is generally used at downstream distances of three rotor diameters (3D) or more. In this study, we have used the Park model as implemented in the open source platform AWS openwind [10], with a wake-decay constant of 0.04 as recommended for offshore environments [7]. at downstream distances of at least two rotor diameters (2D) because the pressure gradient term in the radial direction is neglected. It also assumes that beyond 5D downstream, the wake profile is Gaussian and can be determined by the velocity deficit, turbine thrust coefficient (C t ) and ambient turbulence intensity. This velocity deficit is modified by mixing with the free stream wind around the wake. The rate of mixing is determined by the ambient turbulence intensity the greater the ambient turbulence intensity, the greater the rate of mixing and the faster the wind flow recovers downstream. The EV model was implemented originally by Robinson and Neilson in the WINDOPS software, which became WindFarmer [12]. A similar implementation of the Eddy Viscosity model was developed by Robinson in openwind [10]. In this study, we have used the EV model implemented in openwind. Figure 1: Wind turbine layout of the Horns Rev (top) and Nysted (bottom) wind farms. 3.2 Eddy Viscosity The Eddy Viscosity model is based on the work of Ainslie [11] to simulate single wake effects. The model solves the RANS equations in axisymmetric (cylindrical) coordinates using several simplifying assumptions including an eddy viscosity turbulence closure. The model assumes stationary conditions, and is only valid 3.3 Deep-Array Wake Model The Deep-Array Wake Model (DAWM) [13] was developed by Brower and Robinson at AWS Truepower and implemented in openwind [10]. The goal was to improve the standard wake models by accounting for the two-way interaction between the PBL and the turbines. DAWM has two major components: (a) an internal boundary layer (IBL) approach based on Frandsen [14], and (b) a standard wake model (EV by default). A conceptually similar approach was taken by GL Garrad Hassan for the Large Array Wind Farm model in WindFarmer [15], but the methods differ in the details. In DAWM, each turbine is assumed to occupy a discrete area of increased surface roughness. As the wind flow reaches a turbine, an IBL is created due to the surface roughness change and the IBL grows with distance downstream according to Garratt [16]. The wind speed profile within the IBL is defined by the turbine roughness rather than the terrain surface roughness. 3.4 Fuga Fuga is a linearized RANS model that inserts an actuator disk (an idealized model of a wind turbine rotor s effect on the airflow) to simulate the wakes. It is fully integrated within WAsP. Fuga was recently developed by Ott et al. [17] and bares some similarities to WasP, including a mixed spectral solver using pre-calculated lookup tables. The results from the Fuga model shown in this paper were kindly provided by Garza et al. [18].

4 3.5 WindModeller WindModeller is a RANS model using a k-ε turbulence closure. It is based on the commercial RANS software Ansys CFX and was further developed by Montavon et al. [19] with the addition of an actuator disk to model wakes. The results from the WindModeller model shown in this paper were kindly provided by Garza et al. [18]. 3.6 ARPS The Advanced Regional Prediction System (ARPS) is a non-hydrostatic mesoscale NWP and LES model developed at Oklahoma University [20,21]. The PBL parameterization scheme follows Sun and Chang [22], and the sub-grid scale turbulence scheme is based on Moeng [23] and Deardorff [24]. An actuator disk model was implemented in ARPS by including a sink term (drag force) in the conservation of momentum equation and a source term in the Turbulent Kinetic Energy (TKE) equation, following Adams and Keith [29] and Réthoré et al. [30]. Prior internal research at AWS Truepower [31] had established that coupled NWP-LES simulations with an actuator disk model can capture key features of wake formation and evolution, such as time- and space-varying wake meandering, under different atmospheric stability conditions. In order to capture the local wind climate and the wakes at each wind farm, we ran the ARPS NWP and LES model for a sample of 72 random days chosen over a two-year period. ARPS simulations are conducted starting with a 30-km grid spacing down to 80 m using nested grids. The initial and lateral boundary conditions to the 30-km grid are provided by the Global Forecast System (GFS) analyses. This dynamical downscaling approach allows switching ARPS from a NWP model to a LES model when going from a 400-m grid spacing to 80 m by specifying a suitable time step and SGS turbulence scheme. While 80 m is relatively coarse for LES, it was hoped for this initial round of tests that it would be sufficient to simulate the deep-array wake effects in a realistic fashion. 4 Results 4.1 Nysted wind farm In this section, the Park, EV, and DAWM models were compared to the actual power production of the Nysted wind farm under specific inflow conditions. Three cases were studied, in which the wind speeds were 6, 8 and 10 m/s (± 0.5 m/s), respectively, and the wind directions were all 278 (± 15 ). The power production was averaged within each column of turbines and normalized to the first column upwind. Figure 2 shows the averaged power production by columns of turbines over a 30 wide direction sector. The standard wake models do not capture the increasing wake losses after the third or fourth column. In other words, these two models tend to overestimate the power production deep in the array. The flattening of the EV modeled power after thethird or fourth column had been demonstrated previously [13,15]. DAWM, however, captures the continuing decrease in power, illustrating the cumulative impact of the high array roughness on the PBL downstream of the first column. DAWM was run using roughness settings optimized for Horns Rev, which has a significantly wider turbine spacing in the downwind direction than Nysted (10.3D versus 7D), while being otherwise similar [7]. This suggests the model is robust over this range of array spacings. At the same time, DAWM does not agree quite as well with observations at a fine level of detail, e.g., over 5 wide direction sectors (Fig. 3). Indeed, this is a characteristic of most models: they tend to perform better when aggregated over a range of directions than for a particular direction. Although limitations in the models may be part of the explanation, it may also reflect the messiness of the real world, in which wakes often chaotically meander, expand, and contract, rather than obey the simple picture of steady expansion along a straight line. 4.2 Horns Rev wind farm A similar analysis was carried out at the Horns Rev wind farm. The Park, EV, DAWM, and ARPS models were compared to the actual power production for defined inflow conditions. Results from the Fuga, Jensen and WindModeller models are also presented and were provided by Garza et al. [18]. Again, three cases were studied, with wind speeds of 6, 8 and 10 m/s (± 0.5 m/s), respectively, and the wind directions were all 270 (± 15 ). The power production was averaged within each column of turbines and normalized to the first upwind column.

5 Figure 3: Normalized power production averaged for each column of turbines at Nysted for a case of 8 ± 0.5 m/s when the wind directions is from 278 ± 5. Figure 4 demonstrates again that the EV model performs well within the first few columns of turbines but does not capture the increasing wake losses downstream after the fourth column. The Park model performs better at Horns Rev than it did at Nysted but, as with the EV model, the profile remains relatively flat after the fourth column. DAWM (with roughness settings optimized for Nysted) captures the progressive decrease in power deeper in the array, in much better agreement with the data. Figure 2: Normalized power production averaged for each column of turbines at Nysted for cases of 6 ± 0.5 m/s (top), 8 ± 0.5 m/s (middle) and 10 ± 0.5 m/s (bottom) when the wind directions is from 278 ± 15. The ARPS model performs relatively well for the 6 and 10 m/s cases, but not for the 8 m/s case, where the wake deficit is much too deep after the third column. Further investigation reveals that the ARPS simulations often vary a great deal over time due to transient wind gradients and veer, among other effects. (See Fig. 5 for an example of a relatively homogeneous flow condition, and Fig. 6 for an example of a transient flow condition.) It is plausible that these variations have skewed the mean results because of the limited number of samples within the narrowly defined speed and direction bins (Table 1).

6 Figure 5: Example of a relatively homogeneous wind flow over the Horns Rev wind farm, as simulated by ARPS. The background color corresponds to the wind speeds in m/s, the wind barbs are in grey and the turbines are represented by a "+" symbol. Figure 4: Normalized power production averaged for each column of turbines at Horns Rev for cases of 6 ± 0.5 m/s (top), 8 ± 0.5 m/s (middle) and 10 ± 0.5 m/s (bottom) when the wind directions is from 270 ± 15. Figure 6: Example of an extreme transient flow condition including wind speed gradient and turning or veering of the wind flow over the Horns Rev wind farm, as simulated by ARPS. The background color corresponds to the wind speeds in m/s, the wind barbs are in grey and the turbines are represented by a "+" symbol.

7 Thermal stability can influence wake losses, as unstable conditions dissipate wakes faster due to the increase in turbulent mixing, while stable conditions have the opposite effect. The thermal stability classes, i.e. unstable, near-neutral and stable, are defined by the stability parameter (z/l) where z is the measurement height and L the Monin-Obukhov length. For stable (unstable) stratification, the stability parameter is positive (negative) in a typical range of 1 to 5 ( 5 to 1) according to the American Meteorological Society (AMS) glossary. Since the measured Monin-Obukhov length in the observational data was binned by 50 m intervals, we defined L < m (L > 100 m) as unstable (stable) conditions. Table 1 indicates that near-neutral conditions are sampled 70 to 90% of the time by both the observation and modeled data for the wind speed cases of 8 and 10 ± 0.5 m/s. Therefore, thermal stability cannot account for the difference The frequency of the thermal stability classes significantly differs for the 6 ± 0.5 m/s which suggests that the sample size is too low for this particular wind speed case. The results from the Fuga and WindModeller models align very well with the observed normalized power production within the third column of turbines (Fig. 7). These results were taken from Garza et al. [18]. A comparison with DAWM and other models cannot be made at this point since Garza et al. sampled the power production only at the third row and not for all turbines. In addition, a different quality control procedure was applied to the SCADA data to select events within 10 ± 0.5 m/s and 270 ± 15. Speed (m/s) 6 ± ± ± 0.5 Samples Observed 8/70/22 3/71/26 0/81/19 stability (%) (unstable/nearneutral/stable) ARPS stability (%) (unstable/nearneutral/stable) 76/23/0 17/83/0 11/89/0 Table 1: Sample size and thermal stability frequency for wind speed cases of 6, 8, 10 ± 0.5 m/s. The frequency of time is given for unstable/near-neutral/stable conditions. The Jensen model, which is DONG Energy's version of Park (Jensen), is relatively accurate at Horns Rev (Fig. 7) which is supported by similar results of the Park model (Fig. 4). However, it was shown in Figure 2 that the Park model Figure 7: Normalized power production across columns at the third row of turbines for cases where the wind speed was 10 ± 0.5 m/s and the wind directions 270 ± 15. Results provided by Garza et al. [18]. significantly underestimates the wake losses at Nysted. As noted earlier, most models do not perform as well over a 5 wide sector sector (Fig. 8) or 10 wide sector (Fig. 9), compared to a 30 wide sector. (The exception is WindModeller.) What this indicates is that errors generated under flow conditions directly parallel to the rows (i.e. 270 ) are balanced by errors of the opposite sign for flow oblique to the rows (e.g. 255 or 285 ).

8 array much better than either the EV or Park model. The next step would be to compare the models over the full wind rose, not limited to a single directional sector. The Fuga and Windmodeller models also show promise, though a full comparison is not possible because of the different sampling strategies employed. Figure 8: Normalized power production averaged for each column of turbines at Horns Rev for a case of 10 ± 0.5 m/s when the wind directions is from 270 ± 5. ARPS performed reasonably well for these iniitial tests and merits further research. An important insight gained from the ARPS modeling is the potential importance of transient wind flow conditions, which create considerable variability in the results and require a large sample size. Acknowledgements The authors are grateful to J. Garza and colleagues at DONG Energy for their courtesy and generosity in sharing the Jensen, Fuga and WindModeller model results [18]. Many thanks to R. Barthelmie at Indiana University for the wind farm data through the Prediction Of Waves, Wakes and Offshore Wind (POW'WOW) project as well as DONG Energy, Vattenfall and E.On, owners of the Horns Rev and Nysted wind farms. The fruitful s/discussions with P.-E. Réthoré at the Risø National Laboratory are greatly acknowledged. References Figure 9: Normalized power production at the turbines within the 3rd row for cases where the wind speed was 10 ± 0.5 m/s and the wind directions 270 ± 5. These results were kindly provided by Garza et al. [18]. 5 Conclusions For flows aligned with the rows of turbine (± 15 ), we confirmed previous findings that the Park and EV models perform well in offshore projects within the first 2-3 columns of turbines from the front but can significantly overestimate production and underestimate wake losses beginning at about the fourth column. Overall, DAWM captures the wake losses in the deep [1] Crespo, A., J. Hernandez and S. Frandsen (1999). "Survey of modelling methods for wind turbine wakes and wind farms". Wind Energy, vol. 2, pp [2] Vermeer, L.J., J.N. Sørensen and A. Crespo (2003). "Wind turbine wake aerodynamics". Progress in Aerospace Sciences, vol. 39, pp [3] Bardina, J.E., Huang, P.G., Coakley, T.J. (1997), "Turbulence Modeling Validation, Testing, and Development", NASA Technical Memorandum [4] Kasmi, A. and C. Masson (2008). "An extended k-epsilon model for turbulent flow

9 through horizontal-axis wind turbines". J. Wind Eng. and Ind. Aero., vol. 96, pp [5] Cabezon D. (2009). "CFD modeling of the interaction between the surface boundary layer and rotor wake- turbulence models and mesh strategies". Presentation given at the IEA Offshore Wake Workshop, Risø National Laboratory, Roskilde, Denmark. [6] Wharton, S. and J.K. Lundquist (2010). "Atmospheric Stability Impacts on Power curves of Tall Wind Turbines - An Analysis of a West Coast North American Wind Farm". Report from the Lawrence Livermore National Laboratory, LLNL-TR , Livermore (CA), USA. [7] Barthelmie, R.J., S.C. Pryor, S.T. Frandsen, K.S. Hansen, J.G. Schepers, K. Rados, W. Schlez, A. Neubert, L.E. Neubert, L.E. Jensen, and S. Neckelmann (2010). "Quantifying the impact of wind turbine wakes on power output at offshore wind farms". J. Atmos. Ocean. Tech., vol. 27, pp [8] Katic, I., J. Hojstrup, N.O. Jensen (1986). "A simple model for cluster efficiency". Proceedings from the European Wind Energy Conference, Rome, Italy. 5 p. [9] Jensen, N.O. (1983) "A note on wind generator interaction". Technical report from the Risø National Laboratory (Risø-M-2411), Roskilde, Denmark. 16 p. [10] openwind (2010). "openwind - theoretical basis and validation". Technical report from AWS Truepower, Albany (NY), USA. 26 p. entation/openwindtheoryandvalidation.pdf [11] Ainslie, J.F. (1988). "Calculating the flowfield in the wake of wind turbines". J. Wind Eng. and Ind. Aero., vol. 27, pp [12] GH WindFarmer (2009). "GH WindFarmer - the wind farm design software: theory manual". Technical report from Garrad Hassan and Partners, Bristol, England. 50 p. [13] Brower, M. and N. Robinson (2009). "The openwind deep-array wake model: development and validation". Technical report from AWS Truepower, Albany (NY), USA. 15 p. entation/dawm_whitepaper.pdf [14] Frandsen, S.T. (2007). "Turbulence and Turbulence-Generated Structural Loading in Wind Turbine Clusters". Technical report from the Risø National Laboratory (Risø-R-1188), Roskilde, Denmark. 130p. [15] Schlez, W. and A. Neubert (2009). "New Developments in Large Wind Farm Modeling". Proceedings from the EWEA conference 2009, Marseille, France. 8 p. [16] Garratt, J.R. (1992). "The atmospheric boundary layer". Cambridge University Press. 316 p. [17] Ott, S., J. Berg and M. Nielsen (2011). "Linearised CFD Models for Wakes" Technical report from the Risø National Laboratory (Risø- R-1772), Roskilde, Denmark. 41 p. [18] Garza, J., A. Blatt, R. Gandoin and S.-Y. Hui (2011) "Evaluation of two novel wake models in offshore wind farms ". Proceedings from the EWEA Offshore conference, 29 Nov. - 1 Dec p. [19] Montavon, C., S.-Y. Hui, J. Graham, D. Malins, P. Housley, E. Dahl, P. de Villiers, B. Gribben (2011). "Offshore wind accelerator: wake modelling using CFD". Proceedings from the EWEA Offshore conference, 29 Nov. - 1 Dec [20] Xue, M., K. K. Droegemeier, and V. Wong (2000). "The Advanced Regional Prediction System (ARPS) - A multiscale nonhydrostatic atmospheric simulation and prediction tool. Part I: Model dynamics and verification". Meteor. Atmos. Physics., vol. 75, pp [21] Xue, M., K. K. Droegemeier, V. Wong, A. Shapiro, K. Brewster, F. Carr, D. Weber, Y. Liu, and D. Wang (2001). "The Advanced Regional Prediction System (ARPS) - A multiscale nonhydrostatic atmospheric simulation and prediction tool. Part II: Model physics and applications". Meteor. Atmos. Physics., vol. 76, pp [22] Sun, W-Y., and C-Z. Chang (1986). Diffusion model for a convective layer. Part I: Numerical simulation of convective boundary

10 layer. J. Clim. Appl. Meteor. vol. 25, pp [23] Moeng, C-H. (1984). "A large-eddy simulation model for the study of planetary boundary-layer turbulence". J. Atmos. Sci., vol. 29, pp American Meteorological Society, Atlanta (GA), USA. [32] OpenFOAM (2011). "OpenFOAM, the open source CFD toolbox - user guide". [24] Deardorff, J.W. (1972). "Numerical investigation of neutral and unstable planetary boundary layers". J. Atmos. Sci., vol. 29, pp [25] Jimenez, A. Crespo, A. Migoya, E. Garcia, J. (2007). "Advances in Large-eddy Simulation of a Wind Turbine Wake". Proceedings of The Science of Making Torque from Wind, J. Phys.: Conf. Ser. 75. Danish Technical University, Copenhagen Denmark, 13 p. [26] Ivanell, S. Mikkelsen, R. Sørensen, J.Henningson, D. (2009). "ACD Modelling of Wake Interaction in Horns Rev Wind Farm". Extended Abstracts for Euromech Colloquium 508 on Wind Turbine Wakes; European Mechanics Society: Madrid, Spain. [27] Porté-Agel, F., H. Lu, and Y.-T. Wu (2010). "A large-eddy simulation framework for wind energy applications". Proceedings from the 5th International Symposium on Computational Wind Engineering. Chapel Hill (NC), USA. 21 pp. [28] Stovall, T., G. Pawlas, and P. Moriarty (2010). "Wind farm wake simulations in OpenFOAM". Proceedings from the American Institue of Aeronautics and Astronautics. 13 pp. [29] Adams, M.S. and D.W. Keith (2007). "A wind farm parameterization for WRF". Proceedings from the WRF workshop, Boulder (CO), USA. 4 p. [30] Réthoré, P.-E., N.N. Sørensen, A. Bechmann, F. Zhale (2009). "Study of the atmospheric wake turbulence of a CFD actuator disc model". Proceedings from the EWEA conference 2009, Marseille, France. 9 p. [31] Beaucage, P., J. Manobianco, C. Alonge, and M. Brower (2010). "Using a large eddy simulation model to simulate wakes from large wind projects". Presentation given at the