A data-based approach for fast airfoil analysis and optimization

Abstract

Airfoils are of great importance in aerodynamic design, and various tools have been developed to evaluate and optimize their performance. Existing tools are usually either accurate or efficient, but not both. This paper presents a tool that can analyze airfoils in both subsonic and transonic regimes in about one hundredth of a second, and optimize airfoil shapes in a few seconds. We use camber and thickness mode shapes derived from over one thousand existing airfoils to parameterize the airfoil shape, which reduces the number of design variables. More than one hundred thousand RANS evaluations associated with different airfoils and flow conditions are used to train a surrogate model that combines gradient-enhanced kriging, partial least squares, and mixture of experts. These surrogate models provide fast aerodynamic analysis and gradient computation, which are coupled with a gradient-based optimizer to perform rapid airfoil shape design optimization. When comparing the surrogate-based optimization with optimization based on direct RANS evaluations, the largest differences in minimum C d are 0.04 counts for subsonic cases and 2.5 counts for transonic cases. This approach opens the door for interactive airfoil analysis and design optimization using any modern computer or mobile device. ct = joint camber and thickness f = full airfoil t = airfoil thickness

Machine Learning in Aerodynamic Shape Optimization

“…This demand used to be intractable because of the challenges of training a fast, accurate, and general aerodynamic analysis model [470]. The issue has been addressed to some extent with the advanced modal shape parameterization and data-based modeling techniques, which have been applied to airfoil shape design optimization [289,290,321,337,471], wing shape design optimization [315], and conceptual design optimization of wing-fuselage transports and UAVs [336,339]. The research efforts in this area are listed in Table 5.…”

“…For detailed aerodynamic shape design optimization, a practical sampling method that ensures geometric validity (Sec. 4.1.2) is vital to the success of these works since abnormal shapes would bring too many difficulties to the training of accurate surrogate models [471]. For airfoil shape design, one may merely use real-world airfoils such as the UIUC airfoils to bypass the issue [256,388,389].…”

Comparative study of dimension reduction methods for efficient design optimization

“…An efficient reduced design variables space has been constructed using the POD by Poole et al, 2015, in which input data for POD (promising airfoil shapes) were selected from existing airfoil database. Dominant camber/thickness modes for subsonic airfoil were extracted from 1100 airfoils archiving on the UIUC airfoil coordinates database by Li et al, 2018. Reduced design variables space including all the existing airfoils was constructed to achieve fast airfoil shape optimizations. The POD has been applied to gradient information of objective function by Lukaczyk et al, 2014, which is referred to as the active subspace method.…”