On the application of the Jensen wake model using a turbulence‐dependent wake decay coefficient: the Sexbierum case

Abstract

We present a methodology to process wind turbine wake simulations, which are closely related to the nature of wake observations and the processing of these to generate the so-called wake cases. The method involves averaging a large number of wake simulations over a range of wind directions and partly accounts for the uncertainty in the wind direction assuming that the same follows a Gaussian distribution. Simulations of the single and double wake measurements at the Sexbierum onshore wind farm are performed using a fast engineering wind farm wake model based on the Jensen wake model, a linearized computational fluid dynamics wake model by Fuga and a nonlinear computational fluid dynamics wake model that solves the Reynolds-averaged Navier-Stokes equations with a modified k-" turbulence model. The best agreement between models and measurements is found using the Jensen-based wake model with the suggested post-processing. We show that the wake decay coefficient of the Jensen wake model must be decreased from the commonly used onshore value of 0.075 to 0.038, when applied to the Sexbierum cases, as wake decay is related to the height, roughness and atmospheric stability and, thus, to turbulence intensity. Based on surface layer relations and assumptions between turbulence intensity and atmospheric stability, we find that at Sexbierum, the atmosphere was probably close to stable, although the stability was not observed. We support these assumptions using detailed meteorological observations from the Høvsøre site in Denmark, which is topographically similar to the Sexbierum region.

A New Analytical Wake Model for Yawed Wind Turbines

“…where k w is the wake decay factor and the recommended values is k w = 0.4I a for the flat terrain under the neutral conditions [39]. As shown in Figure 12, the proposed model gives more accurate predictions for the mean velocity distributions under the different yawed conditions than those by the top-hat shape used in the Jimenez's model, which underestimates the velocity deficit in the center of the wake and overestimates them in the outside regions.…”

“…where is the wake decay factor and the recommended values is = 0.4 for the flat terrain under the neutral conditions [39]. Figure 12 and a scale of turbulence intensity with the value of 0.3 in Figure 13, respectively.…”

“…k w is the wake expansion factor and the recommend values is k w = 0.4I a for the flat terrain under neutral conditions [39]. As shown by Gebraad et al [5] and Howland et al [40], the wake deflection was determined by integrating the skew angle θ in x and using y d(x=0) = 0:…”

Ten Years of Boundary-Layer and Wind-Power Meteorology at Høvsøre, Denmark

“…The behaviour of T I with wind speed is mainly due to stability effects, which are more pronounced at the low wind-speed range. When selecting near-neutral conditions T I is nearly constant with wind speed for easterlies at Høvsøre (Peña et al 2015a). The figure also shows in the solid grey line an estimation of T I assuming σ U = 2.5u * , which, combined with Eq.…”

“…On the basis of these findings the 'Høvsøre tall wind profile' cases were prepared and cover a range of stability, forcing and baroclinic conditions, which can be used to evaluate PBL models (Peña et al 2014a). Peña et al (2014b) used several of these cases to study the turning of the wind with height, and found that within the PBL and under barotropic conditions, the more stable the conditions the greater the wind at Høvsøre veered; under baroclinic conditions the wind could even turn anticlockwise.…”