AirfoilInverseDesign.jl

AirfoilInverseDesign.jl is a Julia package that implements the Modified Garabedian-McFadden Method (MGM) for airfoil inverse design. The tool accepts a target pressure distribution as input and generates the corresponding airfoil geometry. It also includes a parametrization of the pressure distribution, allowing the airfoil geometry to be optimized for a particular application.

Features

• Modified Garabedian-McFadden Method (MGM) for airfoil inverse design
• Capability to generate the airfoil geometry that generates a given target pressure distribution
• Parametrization of the pressure distribution for optimal airfoil design ("flow feature parametrization")
• Embedded Multi Fidelity Inverse Design (EMFID) method for low-cost global and local airfoil optimization
• Low-dimensional searching space
• Robust nonlocal and smooth geometry variations to avoid over-optimized geometries
• Easy performance constraints (e.g. on the operating CL value)

Installation

To install AirfoilInverseDesign.jl, follow these steps:

1. Open Julia REPL by running julia in your terminal or command prompt.
2. Press the ] key to enter in Package manager mode.
3. Run add https://github.com/pavanandrea/AirfoilInverseDesign.jl to add the package to your Julia environment.
4. Load the package by running using AirfoilInverseDesign.

Getting started

Here is a simple example to use AirfoilInverseDesign.jl:

using AirfoilInverseDesign;
using Plots;

#define the starting airfoil (a NACA-0009 with 100 nodes)
(airfoil0,airfoil0header) = generatenaca4airfoil("0009", 100);

#define the target pressure distribution from a set of 10 parameters
#and evaluate it at the airfoil0 nodes
params = [0.263625, -0.658409, 0.379949, 0.946806, -0.099668, 0.039979, -0.268271, 0.997283, 0.999967, 0.173235];
cptarget = cpgen10h(params, airfoil0[:,1]);

#airfoil inverse design
(airfoil,status) = mgm(cptarget, airfoil0);

#analyze the generated airfoil with an inviscid panel method at α=0°
(cp,CL,CM,CD,_) = panel1(airfoil, 0);

#compare pressure distributions
plt1 = plot(cptarget[:,1], cptarget[:,2], label="Target",
    title = "Pressure distribution comparison",
    xlabel = "x/c",
    ylabel = "cp",
    yflip = true
);
plot!(plt1, cp[:,1], cp[:,2], label="Generated");
display(plt1);

#plot the new airfoil geometry
plt2 = plot(airfoil0[:,1], airfoil0[:,2], label="Starting",
    title = "Airfoil comparison",
    xlabel = "x/c",
    ylabel = "y/c",
    aspect_ratio = :equal
);
plot!(plt2, airfoil[:,1], airfoil[:,2], label="Generated");
display(plt2);

This will produce a plot showing the target pressure distribution and the resulting airfoil geometry:

Airfoil optimization

AirfoilInverseDesign.jl can easily optimize the shape of an airfoil given the operating conditions. The following pictures show how a NACA-4412 can be locally optimized to work better at low CL values, while maintaining the same CLmax and thickness:

Note that this example only takes a few minutes on an average desktop computer to increase aerodynamic efficiency by 14% at CL=0.4!

Airfoil	CD @CL=0.4	CL/CD @CL=0.4	CD @CL=0.8	CL/CD @CL=0.8
NACA-4412	0.008053	49.7	0.008582	93.2
Optimized	0.007027	56.9 (+14.5%)	0.008169	97.9 (+5.1%)

The resulting polar curve does not exhibit the classic "spike" that plagues airfoils optimized by traditional methods. Instead, thanks to the flow-feature parametrization, it presents a wide plateau that facilitates the practical use of the airfoil and makes the design less sensitive to perturbations. Obviously the NACA-4412 performs better at high CL values, since the optimizer sacrificed efficiency outside the desired range.

See example/airfoil_global_optimization.jl and example/airfoil_local_optimization.jl and the documentation for more details.

License

AirfoilInverseDesign.jl is licensed under the MIT License. See the file named LICENSE for more information.

Contributions

This package is a scratch reimplementation in Julia of my Bachelor's final project, which was originally written in MATLAB within the LiftUp student team. The goal of the project was to design an optimized airfoil for a fixed-wing drone to compete in the Air Cargo Challenge.

For this reason, I'm not accepting contributions to the codebase. However I welcome any question, feedback or request you may have.

Issues

If you encounter any issues while using AirfoilInverseDesign.jl, please open an issue ticket and provide detailed information about the problem you are experiencing.