Progress in Large Eddy Simulation studies of wind turbine wakes and wind farms

Abstract: The talk centers on modeling wind farms using Large Eddy Simulations (LES). In the first part of the talk we review the basic properties of the Wind Turbine Array Boundary Layer (WTABL), a new type of boundary layer in which the bottom surface includes arrays of large turbomachines extracting momentum and energy from the flow. We summarize the basic properties of this flow and highlight the role that LES has played in generating the new insights. We distinguish between actuator disk and actuator line modeling approaches. Using actuator-disk based LES, the structure of the mean flow as well as the spatio-temporal statistics of the fluctuations will be discussed. Then, we describe recent efforts to improve the actuator line model (ALM), a commonly used tool to represent wind turbine blades in LES. We utilize a family of analytical solutions to the Euler equation describing inviscid flow past Gaussian body force fields. Using this analytical formulation, we find that using a Gaussian body force with a kernel size of about 1/4 of the chord length yields most accurate predictions of the velocity field and loads along the blades. This result is consistent with empirical findings by several groups, when ALM is implemented and tested using various filter sizes. In simulations it is shown that it is the accurate representation of the thickness of the tip vortices and the associated downwash close to the tip which results in accurate predictions of the tip losses. For coarser-scale LES that cannot afford resolving the optimal kernel size, an additional correction must be introduced, which can also be expressed using the analytical solutions to flow over Gaussian body forces. We show that this result is equivalent to a Gaussian filtered version of a generalized Prandtl's lifting line theory. Motivated by practical implementation needs, we introduce several approximations based on a numerical solution of the resulting Fredholm integral equation. Results confirm that by using the proposed correction, kernel-size independent predictions of lift coefficient and total lift forces that agree very well with those obtained with the optimal kernel size. This work is a collaboration with Tony Martinez-Tossas, Matt Churchfield, Richard J.A.M. Stevens, Juliaan Bossuyt, Johan Meyers and Dennice Gayme. We are grateful for fruitful conversations with Jens Sorensen on ALM. CM is funded by the National Science Foundation (the WINDINSPIRE project).