Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Grassmannian Shape Representations for Aerodynamic Applications

Published

Author(s)

Olga Doronina, Zachary J. Grey, Andrew Glaws

Abstract

Airfoil shape design is a classical problem in engineering and manufacturing. Our motivation is to combine principled physics-based considerations for the shape design problem with modern computational techniques informed by a data-driven approach. Traditional analyses of airfoil shapes emphasize a flow-based sensitivity to deformations which can be represented generally by affine transformations (rotation, scaling, shearing, translation). We present a novel representation of shapes which decouples affine-style deformations from a rich set of data-driven deformations over a submanifold of the Grassmannian. The Grassmannian 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) improved low-dimensional parameter domain for inferential statistics informing design/manufacturing, and (iii) consistent 3D blade representation and perturbation over a sequence of nominal shapes.
Citation
ADAM AAAI 2022

Keywords

Shape representation, Grassmannian, Principal Geodesic Analysis, data-driven deformations, blade representation

Citation

Doronina, O. , Grey, Z. and Glaws, A. (2022), Grassmannian Shape Representations for Aerodynamic Applications, ADAM AAAI 2022, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=933695, https://openreview.net/forum?id=1RRU6ud9YC (Accessed March 29, 2024)
Created February 28, 2022, Updated November 29, 2022