How to plot Joukowski airfoil?
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We have an asymmetric potential flow past the cylinder (i.e. 2D circle) of radius R of well-known complex velocity W:
˜W=v∞e−iα+iΓ2π(ζ−μ)−v∞R2eiα(ζ−μ)2
where μ=μx+iμy is the complex coordinate of cylinder axis (circle center) and the rest is just as usual (e.g. the wikipedia article). Circulation Γsatisfies the Kutta condition.
How do I calculate parameters of the airfoil and streamlines?
The transformed velocity should be:
W=˜Wdzdζ=˜W1−ℓζ2.
And the airfoil? How do I properly transform the circle defined in a plane corresponding to ˜W
˜W=v∞e−iα+iΓ2π(ζ−μ)−v∞R2eiα(ζ−μ)2
where μ=μx+iμy is the complex coordinate of cylinder axis (circle center) and the rest is just as usual (e.g. the wikipedia article). Circulation Γsatisfies the Kutta condition.
How do I calculate parameters of the airfoil and streamlines?
The transformed velocity should be:
W=˜Wdzdζ=˜W1−ℓζ2.
And the airfoil? How do I properly transform the circle defined in a plane corresponding to ˜W
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Here is a Python code for generating the streamlines of the flow past a Joukowski airfoil (static plot and animated streamlines, asociated to a rotating airfoil)
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