Experimental and theoretical study of wind turbine wakes in yawed conditions

Abstract

This work is dedicated to systematically studying and predicting the wake characteristics of a yawed wind turbine immersed in a turbulent boundary layer. To achieve this goal, wind tunnel experiments were performed to characterize the wake of a horizontal-axis wind turbine model. A high-resolution stereoscopic particle image velocimetry system was used to measure the three velocity components in the turbine wake under different yaw angles and tip-speed ratios. Moreover, power and thrust measurements were carried out to analyse the performance of the wind turbine. These detailed wind tunnel measurements were then used to perform a budget study of the continuity and Reynolds-averaged Navier–Stokes equations for the wake of a yawed turbine. This theoretical analysis revealed some notable features of the wakes of yawed turbines, such as the asymmetric distribution of the wake skew angle with respect to the wake centre. Under highly yawed conditions, the formation of a counter-rotating vortex pair in the wake cross-section as well as the vertical displacement of the wake centre were shown and analysed. Finally, this study enabled us to develop general governing equations upon which a simple and computationally inexpensive analytical model was built. The proposed model aims at predicting the wake deflection and the far-wake velocity distribution for yawed turbines. Comparisons of model predictions with the wind tunnel measurements show that this simple model can acceptably predict the velocity distribution in the far wake of a yawed turbine. Apart from the ability of the model to predict wake flows in yawed conditions, it can provide valuable physical insight on the behaviour of turbine wakes in this complex situation.

A New Analytical Wake Model for Yawed Wind Turbines

“…As noted by Bastankhah and Porté-Agel [9], the above estimation of x 0 does not aim to accurately predict the near wake length, but give an initial value for the far wake model. Figure 9 shows the comparison between the wake deflections obtained from the experiment by Bastankhah and Porté-Agel [9] and those predicted by the models.…”

“…However, this model overestimates the wake deflection since the assumption of the top-hat for the velocity deficit is not accurate as pointed out by Ishihara et al [18]. Recently, Bastankhah and Porté-Agel [9] proposed an analytical model based on the assumption of the Gaussian distribution for the velocity deficit and the skew angle of the wake deflection as described in Appendix B, However, the parameters in this model were not specified.…”

“…For the value of x 0 and σ 0 , Bastankhah and Porté-Agel [9] derived the onset of the far wake region based on the idealized potential core analysis. In this study, a simple method to find the value of x 0 and σ 0 is derived from the mathematical viewpoint.…”

“…Note that these wind tunnel tests were carried out in a uniform flow. Recently, Bastankhah and Porté-Agel [9] systematically studied the wake of a yawed turbine under various thrust coefficients and yaw angles by the detailed wind tunnel measurements in a neutral stratified boundary layer. However, the effects of thrust coefficients and ambient turbulence have not been investigated systematically.…”

“…However, the model of Jiménez et al [11] overestimates the wake deflection since the assumption of top-hat for the velocity deficit is not accurate as pointed out by Ishihara et al [18]. Based on the theoretical analysis of the governing equations, Bastankhah and Porté-Agel [9] developed an analytical model to predict the wake deflection and the far wake velocity distributions for the yawed turbines. The model showed a good agreement with the experimental data.…”