Aerodynamic Shape Optimization with Grassmannian Shape Parameterization Method

Abstract

The conventional method of optimizing the aerodynamic performance of an airfoil heavily depends on the confines of the design space. The design variables create a non-normalized space that is fragmented into several different clusters of airfoils. An approach that is data-driven and deforms airfoils over a Grassmannian submanifold is utilized in the work that is being presented here. The affine deformation, which includes camber and thickness, can be uncoupled from the method that is currently in use, and the operations that are performed on the airfoil shape can be made smooth enough to prevent unreasonable shapes from being produced. The CST method is also a part of the current study so that a comparison can be made between the two. A new method to describe the airfoil geometries over the Grassmannian space was generated using a dataset that contained 7007 different shapes of airfoils. These two methods are used to parameterize the subsonic (NACA0012) and transonic (RAE2822) airfoils, and the new method cuts the number of design variables from twelve to six, resulting in a reduction in overall complexity. The findings demonstrate that the new method maintains a high degree of consistency regardless of the flow conditions.

G2Aero: A Python package for separable shape tensors

“…In Doronina et al (2022), we concisely summarized the framework and demonstrated the advantages of an improved parameter domain for ML/AI algorithms. Zhang et al (2022) tested Grassmannian shape representation and demonstrated robustness for shape optimization applications. Jasa et al (2022) used airfoils generated by G2Aero coupled with NREL's Wind-Plant Integrated System Design Engineering Model (WISDEM) (Dykes et al, 2021) to design blade shapes with reduced costs of energy compared to traditional design methods.…”

A geometry-based deep learning feature extraction method for airfoils

“…Recently, deep learning has demonstrated its effectiveness in feature extractions. However, the curve of an airfoil has been shown to exist in Riemannian space 6 . Dissimilar to Euclidean space, there does not exist a single Cartesian coordinate system to which the Riemannian space consisting of curves of airfoils is homeomorphic 7 .…”