Separable Shape Tensors for Aerodynamic Design

Research output: Contribution to journalArticlepeer-review

2 Scopus Citations


Airfoil shape design is a classical problem in engineering and manufacturing. In this work, we combine principled physics-based considerations for the shape design problem with modern computational techniques using a data-driven approach. Modern and traditional analyses of two-dimensional (2D) and three-dimensional (3D) aerodynamic shapes reveal a flow-based sensitivity to specific deformations that can be represented generally by affine transformations (rotation, scaling, shearing, and translation). We present a novel representation of shapes that decouples affine-style deformations over a submanifold and a product submanifold principally of the Grassmannian. As an analytic generative model, the separable representation, informed by a database of physically relevant airfoils, offers: (i) a rich set of novel 2D airfoil deformations not previously captured in the data, (ii) an improved low-dimensional parameter domain for inferential statistics informing design/manufacturing, and (iii) consistent 3D blade representation and perturbation over a sequence of nominal 2D shapes.

Original languageAmerican English
Pages (from-to)468-487
Number of pages20
JournalJournal of Computational Design and Engineering
Issue number1
StatePublished - 2023

Bibliographical note

Publisher Copyright:
© 2023 Published by Oxford University Press on behalf of the Society for Computational Design and Engineering.

NREL Publication Number

  • NREL/JA-2C00-82759


  • airfoils
  • data-driven
  • generative model
  • Grassmannian
  • manifolds
  • shape tensors


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