Airfoil Generation

Parameter Types

Most of the parameterizations below have associated composite types whose fields are the parameters used in defining the airfoil geometries. Each of these composite types is defined using the @kwdef macro such that the user does not need to remember the order of the fields, but can simply define the fields as though they were keyword arguments. In general, few of the fields are given defaults with the exception of things like trailing edge gap or y-positions, which are always defaulted to zero. In addition, some parameterization methods have specific values inherent to their methods. These are exposed to the user for convenience, but are also defaulted to the values inherent in the parameterization method.

Coordinates

All coordinates are given clockwise from the trailing edge, even if the coordinates are split between upper and lower sides. In other words, the coordinates are given from the lower trailing edge to the leading edge, then the leading edge back to the upper side trailing edge. In general, if the coordinates are given in an upper and lower split, the leading edge point is repeated. Note that all coordinates are given with x being in the chord-wise direction and y being orthogonal to x (just like a standard Cartesian x,y plot). Airfoil geometries are all given normalized to the chord length, so the x values will generally have the leading edge at x=0 and the trailing edge at x=1, though there may be some slight variation depending on camber and trailing edge gap.

NACA Parameterizations

NACA 4-series

We begin with the standard NACA 4-series airfoil defined by maximum camber, position of maximum camber, and maximum thickness.

using FLOWFoil.AirfoilTools
using Plots
using LaTeXStrings

parameters = NACA4(;
    maximum_camber=2.0,
    maximum_camber_position=4.0,
    maximum_thickness=12.0,
    blunt_trailing_edge=false,
)

FLOWFoil.AirfoilTools.NACA4{Float64, Float64, Float64, Bool}(2.0, 4.0, 12.0, false)

Defaults

The NACA4 parameter type is the only one with fully defined defaults, which happen to default to the NACA 2412 airfoil with a sharp trailing edge due to its ubiquity.

We can then determine the x,y coordinates from the parameters.

x, y = naca4(parameters)

plot(x, y; aspectratio=1, xlabel=L"x", ylabel=L"y", label="")

If you are already familiar with a specific parameterization method, you can also forego defining the parameter object and call the method directly.

x, y = naca4(2.0, 4.0, 12.0)

plot(
    x,
    y;
    aspectratio=1,
    xlabel=L"x",
    ylabel=L"y",
    label="Direct",
    linewidth=4,
    linestyle=:dash,
)

If you have a set of coordinates, and would like to fit NACA 4-series parameters to them, you can use the determine_naca4 function.

fit_parameters = determine_naca4(x,y)

x, y = naca4(fit_parameters)

plot!(x, y; label="Fit")

FLOWFoil.AirfoilTools.NACA4 — Type

NACA4

Fields

maximum_camber::Float=2.0 : maximum camber in % chord
maximum_camber_position::Float=4.0 : x-position of maximum camber point in 1/10 chord
maximum_thickness::Float=12.0 : maximum thickness in % chord
blunt_trailing_edge::Bool=false : flag for whether to use the blunt trailing edge NACA 4-series definition or not.

Parameter	Definition
$r_{LE}$	Leading Edge Radius
$x_u$	Chordwise position of maximum thickness of upper surface
$x_l$	Chordwise position of maximum thickness of lower surface
$y_u$	y-coordinate at maximum thickness of upper surface
$y_l$	y-coordinate at maximum thickness of lower surface
$y_{xx_u}$	Second derivative of upper surface curve at point of maximum thickness
$y_{xx_l}$	Second derivative of lower surface curve at point of maximum thickness
$\alpha_{TE}$	Trailing edge angle
$\beta_{TE}$	Boat-tail angle
$y_{TE}$	y-position of center of trailing edge
$\Delta y_{TE}$	y-distance between upper and lower surface trailing edge points

Original Parameter	Modified Parameter	New Definition
$\alpha_{TE}$	$\theta_{TE_u}$	Upper surface trailing edge tangent angle
$\beta_{TE}$	$\theta_{TE_l}$	Upper surface trailing edge tangent angle
$y_{TE}$	$y_{TE_u}$	y-coordinate of upper surface trailing edge
$\Delta y_{TE}$	$y_{TE_l}$	y-coordinate of lower surface trailing edge