Calibration of a super-Gaussian wake model with a focus on near-wake characteristics

Abstract

Offshore wind turbine near wakes can extend downstream up to 5D due to low atmospheric turbulence intensities. They are characterised by strong velocity deficits, a transitioning Gaussian shape, and strong added turbulence intensities. Classical analytical wake models are still used due to their low computational costs, but they mainly focus on far-wake characteristics. A super-Gaussian wake model valid in near-and far-wake regions has recently been developed at IFP Energies nouvelles. This wake model requires calibration and validation. To this end, large-eddy simulations of the large DTU-10MW reference wind turbine under different neutrally stratified atmospheric flows are carried out with the LES Meso-NH model. A database is generated based on these results and used to calibrate and validate the super-Gaussian model.

LiDAR and SCADA data processing for interacting wind turbine wakes with comparison to analytical wake models

“…The tilde symbol denotes a normalisation by the wind turbine diameter,𝐷 𝑟 . The wake characteristic width is 𝜎 ̃= (0.17𝐼 𝑢 + 0.005)𝑥 ̃+ 0.2√𝛽 in the original version of the model in [15], but after the further calibration and validation performed in [37], it became 𝜎 ̃= (0.18𝐼 𝑢 + 0.0119)𝑥 ̃+ (0.0564𝐶 𝑇 + 0.13)√𝛽. Regarding 𝑛, it can be obtained using; 𝑛 ≈ 𝑎 𝑓 𝑒 𝑏 𝑓 𝑥 ̃+ 𝑐 𝑓 , with 𝑎 𝑓 = −3.11, 𝑏 𝑓 = −0.68, and 𝑐 𝑓 = 2.41 according to the original model [15], however, after calibration in [37], 𝑎 𝑓 takes the value which ensures that the maximum normalised velocity deficit at the disk, 𝑉𝐷 𝑚𝑎𝑥 (0), equals the axial induction factor (𝑎 = 0.5[1 − √1 − 𝐶 𝑇 ]), 𝑏 𝑓 = 1.59𝑒 −23.31𝐼 𝑢 − 2.15, and 𝑐 𝑓 = 2.98.…”

“…It included Aitken et al [25], Jensen [9], Frandsen et al [12], Bastankhah and Porté-Agel [13] because they were the ones that attracted the most attention according to [4]. That is in addition to the newly proposed model from Blondel and Cathelain [15,37], (see Appendix A).…”

“…As a result, it was reported that the wake velocity profiles were more consistent with observations, the velocity deficit had the expected form, and mass and momentum conservation equations were preserved [15]. However, the model required further calibration and validation, and therefore, a newer and more accurate version of the model was later proposed in Cathelain et al [37], which is used in this paper, (see Appendix A for the comparison between both versions).…”

Mechanisms of dynamic near-wake modulation of a utility-scale wind turbine

“…2016; Ishihara & Qian 2018; Cathelain et al. 2020). The centre of the wake cross-section is taken to be the centre of the Gaussian fit, which is used to determine the wake deflection angle, (figure 2 a ).…”

A new wake‐merging method for wind‐farm power prediction in the presence of heterogeneous background velocity fields

“…Blondel and Cathelain 23 proposed a first calibration of the model with parameters not dependent on the thrust coefficient and turbulence intensity values. However, in a later study, Cathelain et al 46 re‐calibrated the model by minimizing the difference between predictions and LES results using a larger weight on the error in the near‐wake than in the far‐wake region. In the current manuscript, we use the latter calibration.…”