Low-dimensional representations and anisotropy of model rotor versus porous disk wind turbine arrays

An experimental study of the wake of a model horizontal axis wind turbine with a three-bladed rotor and a turbine with a stationary disk is done within a wind turbine array in order to compare the structure of these wakes. Measurements of the flow field surrounding the center turbine in the fourth row of a 4 x 3 array are made with stereo particle image velocimetry. Rotational effects of the blade are evident in the cross-stream mean velocity component in the rotor case and are absent in the disk case. The second and third invariants of the Reynolds stress anisotropy tensor have larger ranges in the wake of the rotor case than in the disk case, with the disk case displaying higher levels of anisotropy trailing the top tip, a key location relating to kinetic energy entrainment. Application of the proper orthogonal decomposition indicates a greater emphasis on intermediate scales in the near wake of the rotor case in comparison to the disk case, with such differences being mitigated in the far wake. The eigenfunction of the lowest rank mode, which contains the highest turbulence kinetic energy, displays coherence in both the near and far wakes in the rotor case while the disk wake lacks such apparent organization. Based on the discrepancies in the structure and scales of the wake of the rotor versus that of the disk, careful judgment is advised in order to apply stationary disk parametrizations in modeling applications.