Brief communication: A double Gaussian wake model

Abstract

Abstract. In this paper, an analytical wake model with a double Gaussian velocity distribution is presented, improving on a similar formulation by Keane et al. The choice of a double Gaussian shape function is motivated by the behavior of the near wake region, observed in numerical simulations and experimental measurements. The method is based on the conservation of momentum principle, while stream-tube theory is used to determine the wake expansion at the tube outlet. The model is calibrated and validated using large eddy simulations replicating scaled wind turbine experiments. Results show that the tuned double Gaussian model is superior to a single Gaussian formulation in the near wake region.

Analytical solution for the cumulative wake of wind turbines in wind farms

“…Shapiro et al. (2019 b ), Blondel & Cathelain (2020), Schreiber, Balbaa & Bottasso (2020), among others) can be consulted.…”

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

“…In this manuscript, we compare the performance of nine engineering wake models: the Gaussian 12 (G), super‐Gaussian 23 (SG), double‐Gaussian 24 (DG) and Ishihara 26 (I) single‐wake models coupled with linear superposition of velocity deficits (Lin—Equation ()) and with our new wake‐merging method (New—Equation ()). As an additional reference, we also show results from the Jensen model 11 combined with quadratic superposition (Equation ()).…”

“…In an attempt to improve the Gaussian wake model in the near‐wake region, a double‐Gaussian model was first proposed by Keane et al 25 . and further corrected and re‐calibrated by Schreiber et al 24 . In this model, the shape function is assumed to have a double‐Gaussian profile.…”

“…To improve this deficiency, the super‐Gaussian wake model uses a top‐hat shape function in the near‐wake region which evolves to a Gaussian shape in the far wake 22,23 . A different approach to improve the Gaussian wake model in the near‐wake region is offered by the double‐Gaussian wake model, 24,25 which includes the nacelle effects using two Gaussian functions which are symmetric with respect to the wake center. Results have shown that the double‐Gaussian model outperforms the Gaussian model in the near‐wake region, but it overestimates the velocity deficit far downstream of the turbine 24 .…”

“…A different approach to improve the Gaussian wake model in the near‐wake region is offered by the double‐Gaussian wake model, 24,25 which includes the nacelle effects using two Gaussian functions which are symmetric with respect to the wake center. Results have shown that the double‐Gaussian model outperforms the Gaussian model in the near‐wake region, but it overestimates the velocity deficit far downstream of the turbine 24 . Other types of models prescribe the shape function and derive the maximum velocity deficit C ( x ) by fitting of numerical results and experimental data.…”