Separable shape tensors for aerodynamic design

Author:

Grey Zachary J1ORCID,Doronina Olga A2,Glaws Andrew2

Affiliation:

1. National Institute of Standards and Technology, Applied and Computational Mathematics Division , Boulder, CO 80305, USA

2. National Renewable Energy Laboratory, Computational Science Center , Golden, CO 80401, USA

Abstract

AbstractAirfoil 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.

Funder

ARPA-E

Publisher

Oxford University Press (OUP)

Subject

Computational Mathematics,Computer Graphics and Computer-Aided Design,Human-Computer Interaction,Engineering (miscellaneous),Modeling and Simulation,Computational Mechanics

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