Separable Shape Tensors for Aerodynamic Design

TL;DR

This paper introduces a novel shape representation for aerodynamic design that separates affine deformations, enabling richer shape variations, improved low-dimensional modeling, and consistent 3D blade perturbations based on physics-informed data.

Contribution

It presents a new separable shape tensor model that decouples affine deformations, enhancing aerodynamic shape analysis and design capabilities.

Findings

Enables novel 2D airfoil deformations not in existing data

Provides a low-dimensional parameter domain for design optimization

Supports consistent 3D blade representation and perturbation

Abstract

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 2D and 3D aerodynamic shapes reveal a flow-based sensitivity to specific deformations that can be represented generally by affine transformations (rotation, scaling, shearing, 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.