Anisotropic double‐Gaussian analytical wake model for an isolated horizontal‐axis wind turbine

Abstract

An anisotropic double Gaussian (DG) model for analytical wake modeling to predict the streamwise wake velocity behind an isolated non-yawed horizontal-axis wind turbine is proposed. The proposed model is based upon the conservation of mass and momentum inside a streamtube control volume. The wake growth rate parameters to distinguish the wake expansion rate between lateral and vertical directions were tuned based on numerical and measurement data of utility-scale turbines. It was found that the proposed model can give feasible predictions within the full-wake region under different inflow conditions. In addition, the other analytical models based on top-hat shape and single Gaussian approaches were evaluated for comparison. The root-mean-square error statistical analysis was used to evaluate the performance of each examined model under different flow conditions. In general, the proposed model outperformed the other examined models in all wake region categories, particularly within the near-wake region and the onset of the far-wake region, which are beyond the scope of the conventional approach for analytical wake modeling. This advantage gives the potential for the proposed model to provide a better prediction for the wake flow estimation within tightly packed wind farms.

A linear wake expansion function for the double‐Gaussian analytical wake model

“…This advantage was confirmed using computational fluid dynamics (CFD) data, where the root mean square error results showed the superiority of the DG model against the SG model for lateral velocity deficit predictions within a full‐wake region 30 . Most recently, the anisotropic DG model was compared with the anisotropic SG model referring to large eddy simulation (LES) and lidar data 37 . The results showed that the anisotropic DG model could perform better than the anisotropic SG model within the full‐wake region, thus reconfirming the effectiveness of the DG‐based wake model.…”

“…Based on turbine micro‐siting practices, the HAWTs within a wind farm are rarely installed over 11 D for the interrow spacing 37 . Within this spacing distance, it was observed both experimentally 26 and numerically 14,27 that the single HAWT wakes expanded linearly under different turbine operating and inflow conditions.…”

“…Thus, it should be solved numerically, one of which is by employing the Matlab function vpasolve . After numerically solving σ w 1 , the wake radius at the far‐wake onset r w1 [ D ] located at x/D = x 1 can be calculated as follows: $$${r}_{{\rm{w}}1}={r}_{\min }+2.58{\sigma }_{{\rm{w}}1},$$$where r min [ D ] denotes the radial position of Gaussian minima and its value has been determined empirically equal to r min = 0.26 37 . Meanwhile, the streamwise position of the far‐wake onset, x 1 [ D ], is approximated using the following formula 33,37 : $$${x}_{1}=\frac{1+\sqrt{1-{C}_{{\rm{T}}}}}{\sqrt{2}c(4aT{I}_{x,\mathrm{hub}}+2b(1-\sqrt{1-{C}_{{\rm{T}}}})},$$$where the coefficients a = 0.58 and b = 0.077, 33 c = 1.2, 37 and TI x ,hub is the streamwise turbulence intensity of the incoming streamwise velocity at the hub height.…”

“…Hence, TI x ,hub becomes another input parameter for the expansion function in addition to C T . The proposed function was applied to the existing DG wake model, 37 as summarized in Table 1.…”

“…36 The DG distribution is formed immediately after a significant velocity deficit around the centerline due to the nacelle blockage effect recovered by mixing with the faster air surrounding the nacelle. Since this significant centerline deficit recovered rapidly over a relatively short distance, 37 thus the DGbased approach is still reasonable to represent the wake characteristic within the near-wake region.…”