SANDWake3D: A 3D Parabolic RANS Solver for Atmospheric Surface Layers and Turbine Wakes

Despite many recent advances, modeling wind turbine wakes using semi-empirical and analytical models still faces challenges when dealing with more complicated situations involving wind shear, veer, atmospheric stratification, and wake superposition. To address these limitations, this study introduces a three-dimensional, parabolic Reynolds-averaged Navier-Stokes (RANS) k-..epsilon.. formulation which includes an atmospheric boundary layer model and an actuator disk model for turbine wakes. The full three-dimensional solution for the velocity, temperature, and turbulence variables is efficiently solved through an alternating-direction implicit scheme that requires orders of magnitude fewer computational resources than traditional high-fidelity approaches, such as fully elliptic RANS or large-eddy simulations (LESs). The results of the parabolic RANS model are compared to the equivalent LES and semi-empirical wake models at different wind speeds under stable atmospheric conditions with veer and shear at a single TI level, as well as a convectively unstable-inflow case. For the single-turbine wake the RANS model was able to capture the wake deficit behavior, including the wake stretching and skewing that was observed in the LES. The distribution of the wake turbulence in the RANS model also agreed with results from the higher-fidelity simulations. In simulations of a two-turbine, directly waked configuration, the new RANS model was able to handle the wake superposition behavior without difficulty and also correctly modeled the corresponding increase in wake turbulence when compared to LES. A demonstration of the RANS model on a nine-turbine, three-row wind farm is shown and compared to LES, and comparisons with a semi-empirical veered Gaussian model are also discussed. The work in this study can be generalized in future investigations to handle additional wind conditions and more complex wind farm configurations.