Surface Heat Flux Effects on Wind Turbine Wakes and Power Estimation in the Convective Boundary Layer

Full-scale wind turbines operate in the Atmospheric Boundary Layer (ABL). The Atmospheric stability is known to have an effect on recovery rates of wind turbine wakes. Different wake recovery rates lead to differences in wind turbine power production. Most of the current studies analyze the effects of stability by separating stability classes into general stable, neutral, and convective regimes. The studies show large differences between the general regimes, but this creates other questions. Are there significant changes between of different stabilities within each regime (stable, neutral, convective) and would these differences affect power prediction?

This study begins to look at different states of the convective ABL. The wind turbine recovery rates, turbulence, as well as power deficits were studied. The study used two months of meteorological tower data to determine the different states of the convective ABL. The study created a Probability Density Function (PDF) of surface heat flux to input into Large Eddy Simulations. The negative one standard deviation, mean, and positive one standard deviation surface heat flux were used as boundary conditions for three different LES cases where the geostrophic wind speed is held constant. These cases are then mapped to a single, double, and triple wind turbine simulations to study the effects of the change in surface heat flux on wind turbine characteristics. The wake recovery rates were calcualted by fitting a exponent to the equation (U_hub-U_min)/U_hub =A(x/d)^n. A larger exponent, n, means a faster recovery rate. The surface heat flux directly effected the wake recovery rate of the wind turbine. This created a large difference in the power deficit of a second wind turbine place 4 diameters downstream. The power deficit decreases with increased surface flux and is directly related to faster wake recovery. The power deficit goes from 47% in the negative one standard deviation simulation to 28% in the positive one standard deviation simulation. The large difference in the power produced by the second wind turbine shows the importance of accounting for different convective ABL states.

This study begins to quantify the effects of different convective ABL states on the characteristics of wind turbines. The results show that changes in surface heat flux relating to negative one standard deviation, mean, and positive one standard deviation have significant effects on the wake recovery of upstream wind turbines and power deficits of downstream wind turbines. The differences were not as strong on downstream wind turbine wake recovery or power deficits of wind turbines that were not aligned. The results show the importance of classifying stability when predicting power outputs of wind farms. The results also show the complex interactions between surface heat flux (stability), wind angle, and wind farm layout.