NeuralFoil: An Airfoil Aerodynamics Analysis Tool Using Physics-Informed Machine Learning

TL;DR

NeuralFoil optimization is able to produce airfoils nearly identical in performance and shape to expert-designed airfoils within seconds; these computationally-optimized airfoils provide a useful starting point for further expert refinement.

Abstract

NeuralFoil is an open-source Python-based tool for rapid aerodynamics analysis of airfoils, similar in purpose to XFoil. Speedups ranging from 8x to 1,000x over XFoil are demonstrated, after controlling for equivalent accuracy. NeuralFoil computes both global and local quantities (lift, drag, velocity distribution, etc.) over a broad input space, including: an 18-dimensional space of airfoil shapes, possibly including control deflections; a 360 degree range of angles of attack; Reynolds numbers from $10^2$ to $10^{10}$; subsonic flows up to the transonic drag rise; and with varying turbulence parameters. Results match those of XFoil closely: the mean relative error of drag is 0.37% on simple cases, and remains as low as 2.0% on a test dataset with numerous post-stall and transitional cases. NeuralFoil facilitates gradient-based design optimization, due to its $C^\infty$-continuous solutions, automatic-differentiation-compatibility, and bounded computational cost without non-convergence issues. NeuralFoil is a hybrid of physics-informed machine learning techniques and analytical models. Here, physics information includes symmetries that are structurally embedded into the model architecture, feature engineering using domain knowledge, and guaranteed extrapolation to known limit cases. This work also introduces a new approach for surrogate model uncertainty quantification that enables robust design optimization. This work discusses the methodology and performance of NeuralFoil with several case studies, including a practical airfoil design optimization study including both aerodynamic and non-aerodynamic constraints. Here, NeuralFoil optimization is able to produce airfoils nearly identical in performance and shape to expert-designed airfoils within seconds; these computationally-optimized airfoils provide a useful starting point for further expert refinement.

Figures (14)

• Figure 1: User-facing inputs and outputs of the NeuralFoil model.
• Figure 2: Geometry input parameterization used by NeuralFoil. Parameterization is an 18-parameter CST (Kulfan) parameterization kulfanUniversalParametricGeometry2008kulfanModificationCSTAirfoil2020mastersGeometricComparisonAerofoil2017. Each colored line in the figure represents a mode shape associated with one of these parameters; modes are linearly combined to form the airfoil shape.
• Figure 3: Illustration of the automatic procedure for handling control surface deflections in NeuralFoil.
• Figure 4: Accuracy of NeuralFoil on an airfoil with large control surface deflections. Here, we show aerodynamics results from both NeuralFoil and XFoil. All runs are on a NACA0012 airfoil at $\rm Re_c = 10^6$ and $\alpha = 0\degree$, with varying control surface deflections on a trailing-edge flap hinged at $x/c=0.70$.
• Figure 5: Illustration of the "image" approach used to structurally embed symmetry with respect to angle of attack in NeuralFoil.