Simulating wind farm flows at hub height with 2D Reynolds-averaged Navier-Stokes simulations

Abstract. Wind turbines in an offshore wind farm typically have the same hub height, and in this case, the power of a wind farm could be predicted if the flow field in the horizontal 2D plane at the hub height is predicted accurately. Nevertheless, Reynolds-averaged Navier-Stokes (RANS) simulations of wind farm flows are predominantly made in full 3D domains, which are naturally more computationally expensive than 2D simulations. In this work, a systematic comparison is made between 2D and 3D RANS simulations of various wind farm configurations to assess the differences in computational cost and accuracy. For our numerical setup and the cases considered, which include layouts with up to 144 turbines, it is found that the 2D simulations are at least two orders of magnitude computationally cheaper than their corresponding 3D simulations, while the predicted farm power is within -30 % to 15 % for all cases. Only minor, but necessary, modifications have been made to the governing 2D RANS equations to avoid unphysical decay of turbulence, allowing for a simple direct comparison between the 2D to 3D simulations. Given the low computational cost and already sensible performance of the only slightly modified 2D RANS simulations demonstrated in this work, it appears attractive to further investigate this methodology and possibly introduce additional 2D modifications to improve the accuracy in future work.