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. (2016). The choice of a double-Gaussian shape function is motivated by the behavior of the near-wake region that is 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.
Highlights
Analytical engineering wind farm models are low-fidelity approximations used to simulate the performance of wind power systems
The shape of the velocity deficit distribution in the wake is described by two Gaussian functions, which are symmetric with respect to the wake center, while the amplitude of the velocity deficit is derived using the principle of momentum conservation
A linear expansion of the width of the Gaussian profiles was assumed, and stream tube theory was used to estimate the conditions at the stream tube outlet
Summary
Analytical engineering wind farm models are low-fidelity approximations used to simulate the performance of wind power systems. Onshore wind farms tend to be closely packed, and turbine spacing often reaches values close to or even below 3 D (Schreiber et al, 2018; energiespektrum.de, 2015) This raises the necessity of developing models that accurately represent the wake far away from the rotor disk and in the near and mid-wake regions. The double-Gaussian model by Keane et al (2016), which is referred to as the Keane model in this paper, was developed in a similar fashion to the EPFL Gaussian model (Bastankhah and Porté-Agel, 2014), and it was intended to respect the principles of mass and momentum conservation In this short note, a double-Gaussian wake model, based on Keane’s model and with emphasis on near-wake flow behavior, is derived, calibrated, and validated. Appendix A derives some integrals appearing in the formulation
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