Classification of the Reynolds Stress Anisotropy Tensor in Very Large Thermally Stratified Wind Farms Using Colormap Image Segmentation

Nicholas Hamilton, Naseem Ali, Marc Calaf, Raul Cal

Research output: Contribution to journalArticlepeer-review

10 Scopus Citations


A combinatorial technique merging image segmentation via K-means clustering and colormap of the barycentric triangle is used to investigate the Reynolds stress anisotropy tensor. The clustering aids in extracting the identical features from the spatial distribution of the anisotropy colormap images by minimizing the sum of squared error between the cluster center and all data points. The dataset used to investigate the applicability of the clustering technique consists of the flow in a large wind farm for different thermal stratification representatives of a characteristic diurnal cycle. Based on the attribute values defining the colormap of the Reynolds anisotropy stress tensor, the images are converted into color space and then the K-means algorithm assesses the similarities and dissimilarities via a distance metric. In unsupervised learning problems, the K-means algorithm runs independently for different numbers of clusters. The elbow criterion is used to determine the best trade-off between the cluster number and the total variance to select the optimal number of clusters. The clustering technique improves pattern visualization and allows us to identify characteristic regions of the flow based on the structure of the Reynolds stress anisotropy. The dominant patterns reveal that there are major perturbations that control the operation of the wind farm during the diurnal cycle, including the formation and growth of the convective boundary layer and the strong stratification among the flow layers during the stably-stratified period. These parameters attempt to redistribute energy into the velocity deficit region and contribute to the energy balance in the flow domain through the distributions of the momentum flux. As a result of the weak mixing and negligible buoyancy effect, the neutral wind farm displays gradual changes from a prolate turbulence state near the rotor to an oblate turbulence state at the top of the domain.

Original languageAmerican English
Article number063305
Number of pages9
JournalJournal of Renewable and Sustainable Energy
Issue number6
StatePublished - 1 Nov 2019

Bibliographical note

Publisher Copyright:
© 2019 Author(s).

NREL Publication Number

  • NREL/JA-5000-71044


  • anisotrop
  • barycentric map
  • clustering
  • K-Means
  • unsupervised learning
  • wind energy


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