Mean kinetic energy distribution in finite-size wind farms: A function of turbines arrangement

In this work the redistribution and recovery of mean kinetic energy in a realistic, finite size wind farm is studied for neutral atmospheric boundary layer conditions. Five different wind farm configurations, with different wind turbine arrangements, are considered, with four different inter-turbine spacings. By means of a localized control volume analysis, this work quantifies the mean kinetic energy recovery mechanisms as a function of downstream distance from the wind farm leading edge. Results illustrate the dependence of the mean kinetic energy distribution on the turbines’ arrangement and the spatial evolution of the dominant transport mechanisms (advection and vertical flux). In the first rows of turbines, advection dominates the wake recovery, while for the last rows of turbines vertical flux of mean kinetic energy is the dominant transport mechanism. In between, a smooth transition exists between both mechanisms. From the results a low-order power output predictor model for a finite size wind farm is developed. This model allows estimating the harvested power at each wind turbine row with only the geometrical wind farm layout as an input. The low-order model is compared with other published models and validated using published experimental measurements. The new model performs very well, with errors smaller than 5%.Postprint (author's final draft