Large-Eddy Simulation of the Wake Flow Inside and Downwind of a Large Finite-Size Wind Farm

As the number of operating offshore large wind farms continues to increase, it is important to investigate the wake flows of these large wind farms since they could significantly affect the atmospheric boundary layer (ABL) dynamics and the performance of adjacent wind farms. Since offshore ABLs can often be considered as conventionally-neutral, large-eddy simulations (LES) of large finite-size wind farms in conventionally-neutral boundary layers are performed to investigate the wake dynamics and power extraction of such wind farms. The influences of the Coriolis force and thermal stratification are also considered. Specifically, this study focuses on a wind farm that comprises 25 rows of wind turbines, spanning a distance of 10 km. It is shown that internal boundary layers (IBL) develop both inside and downwind of the wind farms. The growth rate of the IBLs is found to agree with the 0.8 power-law proposed by Elliot (1958) when it is below the ABL height. If the wind farm is large enough, the internal boundary layer interacts with the thermally-stratified free atmosphere above, leading to a modification of the ABL height and power extraction by the wind farm. The wind profile also demonstrates a veer of around 2º as it flows through and exits the 10 km wind farm considered in the study. In addition, it is shown that large wind farms create extensive wakes, which could have an effect on potential downwind wind farms. Specifically, for the case considered here, along with the effect of velocity veer, a power deficit as large as 8% is found at a distance of 10 km downwind from the wind farm. Moreover, a simple one-dimensional (1D) model is presented for the velocity distribution in the wind farm wake based on the models proposed by Chamorro and Porté-Agel (2009) and Abkar and Porté-Agel (2012) for flow downing a rough-to-smooth surface transition. In this 1D model, the velocity profile of the wind farm wake at different downwind positions is approximated by a nonlinear weighted average function between two modified logarithmic wind profiles corresponding to the effective roughness of the wind farm and the downwind surface roughness, respectively. The performance of this 1D model is then compared with the LES simulation results.