a scaffolding for building 2D inviscid models
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PotentialFlow can be installed using the Julia package manager. From the Julia REPL, type ] to enter the Pkg REPL mode and run
pkg> add PotentialFlowLet's create a point vortex and a point source and probe their associated velocity field:
julia> using PotentialFlow
julia> t = 0.0
0.0
julia> vortex = Vortex.Point(1.0 + 1.0im, π)
Vortex.Point(1.0 + 1.0im, 3.141592653589793)
julia> source = Source.Point(1.0 - 1.0im, -π)
Source.Point(1.0 - 1.0im, 3.141592653589793)
julia> induce_velocity(0.0im, vortex, t)
0.25 - 0.25im
julia> induce_velocity(source, vortex, t)
0.25 - 0.0im
julia> induce_velocity(0.0im, (vortex, source), t)
0.5 - 0.5im
julia> induce_velocity([0.0im, 1.0im, 1.0], (vortex, source), t)
3-element Array{Complex{Float64},1}:
0.5-0.5im
0.1-0.7im
0.5-0.5imNote the all positions and velocities are given in complex coordiantes.
Now let's move on to something more interesting.
We'll create a stationary flat plate (bound vortex sheet) and place it in a freestream.
In order to enforce the Kutta condition, we also place a starting vortex at -Inf.
using PotentialFlow
using Plots
c₀ = 0.0im # initial centroid position
α = π/9 # angle of attack
L = 1.0 # chord length
N = 128 # number of discretization points
ċ = 0.0 # translation velocity
α̇ = 0.0 # rate of rotation
t = 0.0 # current time
freestream = Freestream(-1.0)
plate = Plate(N, L, c₀, α)
motion = Plates.RigidBodyMotion(ċ, α̇)
Plates.enforce_no_flow_through!(plate, motion, freestream, 0.0)
# We now want to determine the strength of the starting vortex
# to satisfy the Kutta condition at the trailing edge of the plate
_, Γ = Plates.vorticity_flux!(plate, (), Vortex.Point(-Inf, 1.0), t, Inf, 0);
starting_vortex = Vortex.Point(-Inf, Γ)
# Plot some streamlines
x = range(-2, 1, length=100)
y = range(-0.5, 0.5, length=100)
streamlines(x, y, (plate, freestream), legend = false, colorbar = false)
plot!(plate, linewidth = 2, ratio = 1, size = (600, 300))
More examples can be found in the documentation and the Jupyter notebooks. You can also run the notebooks directly in your browser here.