Aerodynamic models of 3D wings using the Vortex Step Method

The Vortex Step Method (VSM) is an enhanced lifting line method that improves upon the classic approach by solving the circulation system at the three-quarter chord position, among the most important details. This adjustment allows for more accurate calculations of lift and drag forces, particularly addressing the shortcomings in induced drag prediction. VSM is further refined by coupling it with 2D viscous airfoil polars, making it well-suited for complex geometries, including low aspect ratio wings, as well as configurations with sweep, dihedral, and anhedral angles.

The software presented here includes a couple of examples: a rectangular wing, a leading-edge inflatable kite and a ram-air kite.

This package was translated from the Python code version 1.0.0 available at https://github.com/ocayon/Vortex-Step-Method with some extensions as documented in News.md.

Installation

Install Julia 1.10 or later, if you haven't already. On Linux, make sure that Python3 and Matplotlib are installed: sudo apt install python3-matplotlib Furthermore, the packages TestEnv and ControlPlots must be installed globally: julia -e 'using Pkg; Pkg.add("TestEnv"); Pkg.add("ControlPlots")'

Before installing this software it is suggested to create a new project, for example like this: bash mkdir vsm cd vsm julia --project=. Then add VortexStepMethod from Julia's package manager, by typing: julia using Pkg pkg"add VortexStepMethod" at the Julia prompt. You can run the unit tests with the command: julia pkg"test VortexStepMethod" To run the examples, type: julia using VortexStepMethod VortexStepMethod.install_examples() include("examples/menu.jl")

Running the examples as developer

If you have git installed, check out this repo because it makes it easier to understand the code: bash mkdir repos cd repos git clone https://github.com/OpenSourceAWE/VortexStepMethod.jl cd VortexStepMethod.jl You can launch Julia with: bash julia --project or with: bash ./bin/run_julia In Julia, first update the packages: julia using Pkg Pkg.update() and then you can display a menu with the available examples: julia include("examples/menu.jl") To browse the code, it is suggested to use VSCode with the Julia plugin.

Input

Three kinds of input data is needed:

• The wing geometry, defined by section:

  • for the rectangular wing two sections, two points in CAD reference frame + polars
    (three different options to provide them) per section
  • kite wing: model of polars included, n sections to define

• The airflow and turn rate:

  • v_app vector and omega (turn rate) vector in Kite Body (KB) reference frame

• The configuration:

  • how many panels
    --> two sections make a panel.

Apart from the wing geometry there is no input file yet, the input has to be defined in the code.

Example for defining the required input:

```julia

Step 1: Define wing parameters

npanels = 20 # Number of panels span = 20.0 # Wing span [m] chord = 1.0 # Chord length [m] va = 20.0 # Magnitude of inflow velocity [m/s] density = 1.225 # Air density [kg/m³] alphadeg = 30.0 # Angle of attack [degrees] alpha = deg2rad(alphadeg)

Step 2: Create wing geometry with linear panel distribution

wing = Wing(npanels, spanwisedistribution=LINEAR)

Add wing sections - defining only tip sections with inviscid airfoil model

addsection!(wing, [0.0, span/2, 0.0], # Left tip LE [chord, span/2, 0.0], # Left tip TE INVISCID) addsection!(wing, [0.0, -span/2, 0.0], # Right tip LE [chord, -span/2, 0.0], # Right tip TE INVISCID)

Step 3: Initialize aerodynamics

body_aero = BodyAerodynamics([wing])

Set inflow conditions

velapp = [cos(alpha), 0.0, sin(alpha)] .* va setva!(wa, velapp) `` It is possible to import the wing geometry using an.objfile as shown in the exampleramairkite.jl`. During the import the polars are calculated automatically using XFoil. This approach is valid for rigid wings and ram-air kites, but not for leading edge inflatable kites.

Surfplan files can be converted to an input for VortexStepMethod.jl using the SurfplanAdapter.

Output

• the aerodynamic forces Fx, Fy, Fz
• the aerodynamic moments Mx, My, Mz
• the force coefficients CL, CD, CS (side force coefficient)
• the status of the solver (is the result valid)

In addition, the spanwise distribution of these and additional values are available.

See also the documentation.

Citation

If you use this project in your research, please consider citing it. Citation details can be found in the CITATION.cff file included in this repository.

License

This project is licensed under the MIT License - see the LICENSE file for details.

WAIVER

Technische Universiteit Delft hereby disclaims all copyright interest in the package “VortexStepMethod.jl” written by the Author(s).

Prof.dr. H.G.C. (Henri) Werij, Dean of Aerospace Engineering

Copyright

Copyright (c) 2022 Oriol Cayon

Copyright (c) 2024 Oriol Cayon, Jelle Poland, TU Delft

Copyright (c) 2025 Oriol Cayon, Jelle Poland, Bart van de Lint, Uwe Fechner