Abstract
Abstract. Idealized models of the atmospheric boundary layer (ABL) can be used to leverage understanding of the interaction between the ABL and wind farms towards the improvement of wind farm flow modeling. We propose a pressure-driven one-dimensional ABL model without wind veer, which can be used as an inflow model for three-dimensional wind farm simulations to separately demonstrate the impact of wind veer and ABL depth. The model is derived from the horizontal momentum equations and follows both Rossby and Reynolds number similarity; use of such similarity reduces computation time and allows rational comparison between different conditions. The proposed ABL model compares well with solutions of the mean momentum equations that include wind veer if the forcing variable is employed as a free parameter.
Highlights
The interaction between the atmospheric boundary layer (ABL) and wind farms is important for wind energy, because it influences the energy yield and wind turbine lifetime
Many models of the ABL exist; these range from mesoscale models like the Weather Research and Forecasting (WRF) Model (Skamarock et al, 2019)1 to microscale models such as large-eddy simulation (LES) (Stoll et al, 2020) and Reynolds-averaged Navier–Stokes (RANS) (Apsley and Castro, 1997; Blackadar, 1962; van der Laan et al, 2020b)
RANS is our method of choice because it is roughly 3 orders of magnitude faster compared to LES, and it can be used to study trends of atmospheric wind farm flows
Summary
The interaction between the atmospheric boundary layer (ABL) and wind farms is important for wind energy, because it influences the energy yield and wind turbine lifetime. The simulated normalized wake losses in a wind farm using a MOST inflow follow Reynolds number similarity, as shown in van der Laan et al (2020a) This is because the viscous forces can be neglected due to the high Reynolds number of atmospheric wind farm flows, and all external forces (wind turbine forces) scale as U2/L, with U and L as characteristic velocity and length scales, respectively. The ABL profiles of the proposed model are very similar to the ABL model of Apsley and Castro (1997) including ABL depth, by applying a momentum source term that represents the balance between Coriolis force and a fixed pressure gradient but without turning of the wind with height (veer).
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