A short note on turbulence characteristics in wind-turbine wakes

Analytical wake models need formulations to mimic the impact of wind turbines on turbulence level in the wake region. Several correlations can be found in the literature for this purpose, one of which is the formula proposed in A. Crespo, J. Hernandez, Turbulence characteristics in wind-turbine wakes, Journal of Wind Engineering and Industrial Aerodynamics 61 (1) (1996) 71-85, which relates the added turbulence to the induction factor of the turbine, ambient turbulence intensity, and normalized distance from the rotor through an equation with one coefficient and three exponents for the effective parameters. Misuse of this formula with an incorrect exponent for the ambient turbulence intensity is propagating in the literature. In this note, we implement the original and the incorrect formulation of turbine-induced added turbulence in a Gaussian wake model to quantify its impact by studying the Horns Rev 1 wind farm. The results reveal that the turbulence intensity and the normalized power of the waked turbines predicted by the wake model with the correct and the incorrect implementation of turbine-induced added turbulence correlation have a difference equal to 1.94% and 3.53%, respectively, for an ambient turbulence intensity of 7.7%. For an ambient turbulence intensity of 4%, these discrepancies grow to 2.7% and 4.95%.

Automated summary

Analytical wake models require formulas to replicate the effect of wind turbines on turbulence levels in the wake region. One such formula proposed by A. Crespo, J. Hernandez in 1996 relates added turbulence to turbine induction factor, ambient turbulence intensity, and normalized distance from the rotor using one coefficient and three exponents. However, an incorrect exponent for ambient turbulence intensity has been mistakenly used in the literature. This study implemented both the correct and incorrect formulations of turbine-induced added turbulence in a Gaussian wake model to assess their impact on the Horns Rev 1 wind farm. Results indicate differences of 1.94% and 3.53% in predicted turbulence intensity and normalized power of waked turbines between the correct and incorrect formulations, respectively, at an ambient turbulence intensity of 7.7%. These discrepancies increase to 2.7% and 4.95% at an ambient turbulence intensity of 4%.