Aerodynamics API

boundary_vector(panels, u)

Create the vector for the boundary condition of the problem given an array of Panel2Ds and velocity $u$.

doublet_matrix(panels_1, panels_2)

Create the matrix of doublet potential influence coefficients between pairs of panels₁ and panels₂.

influence_matrix(panels, wake_panel :: AbstractPanel2D)

Assemble the Aerodynamic Influence Coefficient matrix consisting of the doublet matrix, wake vector, Kutta condition given Panel2Ds and the wake panel.

kutta_condition(panels)

Create the vector describing Morino's Kutta condition given Panel2Ds.

solve_linear(panels, u, wakes)

Solve the linear aerodynamic system given the array of Panel2Ds, a velocity $\vec U$, a vector of wake Panel2Ds, and an optional named bound for the length of the wake.

The system of equations $A[φ] = [\vec{U} ⋅ n̂] - B[σ]$ is solved, where $A$ is the doublet influence coefficient matrix, $φ$ is the vector of doublet strengths, $B$ is the source influence coefficient matrix, and $σ$ is the vector of source strengths.

solve_linear(panels, u, sources, bound)

Solve the system of equations $[AIC][φ] = [\vec{U} ⋅ n̂] - B[σ]$ condition given the array of Panel2Ds, a velocity $\vec U$, a condition whether to disable source terms ($σ = 0$), and an optional named bound for the length of the wake.

doublet_matrix(panels_1, panels_2)

Create the matrix of source potential influence coefficients between two arrays of Panel2Ds.

source_strengths(panels, freestream)

Create the vector of source strengths for the Dirichlet boundary condition $σ = \vec U_{\infty} ⋅ n̂$ given Panel2Ds and a Uniform2D.

wake_vector(woke_panel :: AbstractPanel2D, panels)

Create the vector of doublet potential influence coefficients from the wake on the panels given the wake panel and the array of Panel2Ds.

surface_velocities(panels, φs, u, sources :: Bool)

Compute the surface speeds and panel distances given the array of Panel2Ds, their associated doublet strengths $φ$s, the velocity $u$, and a condition whether to disable source terms ($σ = 0$).

Horseshoe(r1, r2, rc, normal, chord)

Define a horseshoe vortex with a start and endpoints $r₁, r₂$ for the bound leg, a collocation point $r$, a normal vector $n̂$, and a finite core size.

The finite core setup is not implemented for now.

References(V, ρ, μ, S, b, c, r)
References(; 
    speed, density, viscosity,
    sound_speed, area, span, 
    chord, location
)

Define reference values with speed $V$, density $ρ$, dynamic viscosity $μ$, area $S$, span $b$, chord $c$, location $r$ for a vortex lattice analysis. A constructor with named arguments is provided for convenience:

Arguments

• speed :: Real = 1.: Speed (m/s)
• density :: Real = 1.225: Density (m)
• viscosity :: Real = 1.5e-5: Dynamic viscosity (kg/(m ⋅ s))
• sound_speed :: Real = 330.: Speed of sound (m/s)
• area :: Real = 1.: Area (m²)
• span :: Real = 1.: Span length (m)
• chord :: Real = 1.: Chord length (m)
• location :: Vector{Real} = [0,0,0]: Position (m)

VortexLatticeSystem

A system consisting of the relevant variables for a vortex lattice analysis for post-processing.

Arguments

The accessible fields are:

• vortices: The array of vortices, presently of AbstractVortex types.
• circulations: The circulation strengths of the vortices obtained by solving the linear system.
• influence_matrix: The influence matrix of the linear system.
• boundary_vector: The boundary condition corresponding to the right-hand-side of the linear system.
• freestream :: Freestream: The freestream conditions.
• reference :: References: The reference values.

VortexLatticeSystem(
    aircraft, 
    fs :: Freestream, 
    refs :: References, 
    compressible = false, 
)

Construct a VortexLatticeSystem for analyzing inviscid aerodynamics of an aircraft (must be a ComponentArray of Horseshoes or VortexRings) with Freestream conditions and References for non-dimensionalization. Options are provided for compressibility corrections via the Prandtl-Glauert transformation (false by default) and axis system for computing velocities and forces (Geometry by default).

VortexRing(r1, r2, r3, r4, r_c, n̂, ε)

A vortex ring consisting of four points $r_i, i = 1,…,4$, a collocation point $r_c$, a normal vector $n̂$, and a core size $ε$. The following convention is adopted:

    r1 —front leg→ r4
    |               |
left leg       right leg
    ↓               ↓
    r2 —back leg-→ r3

bound_leg_center(hs :: Horseshoe)

Compute the midpoint of the bound leg of a Horseshoe.

bound_leg_vector(hs :: Horseshoe)

Compute the direction vector of the bound leg of a Horseshoe.

bound_velocity(r, hs :: Horseshoe, Γ, u_hat)

Compute the induced velocity at a point $r$ from the bound leg with constant strength $Γ$ of a given Horseshoe.

boundary_condition(vortices, U, Ω)

Assemble the boundary condition vector given an array of AbstractVortex, the freestream velocity $U$, and a quasi-steady rotation vector $Ω$.

center_of_pressure(system :: VortexLatticeSystem)

Determine the center of pressure $x_{cp}$ of the VortexLatticeSystem.

This is computed based on the nearfield lift $C_L$ and moment $Cₘ$ coefficients, and the reference location $xᵣ$ and chord length $cᵣ$ from References: $x_{cp} = xᵣ -cᵣ(Cₘ / C_L)$

farfield(system :: VortexLatticeSystem)

Compute the total farfield force coefficients of the VortexLatticeSystem. These are in wind axes by definition.

farfield_coefficients(system :: VortexLatticeSystem)

Compute the total farfield force coefficients for all components of the VortexLatticeSystem. These are in wind axes by definition.

farfield_forces(system :: VortexLatticeSystem)

Compute the farfield forces in wind axes for all components of the VortexLatticeSystem.

freestream_derivatives(
    system :: VortexLatticeSystem;
    axes :: AbstractAxisSystem = Stability(),
    name = :aircraft,
    print = false,
    print_components = false,
    farfield = false
)

Compute the force and moment coefficients of the components of a VortexLatticeSystem and their derivatives with respect to freestream values: Mach $M$ (if compressible), angles of attack $α$ and sideslip $β$, and non-dimensionalized rotation rates $p̄, q̄, r̄$ (in stability axes).

The axes of the force and moment coefficients can be changed by passing any AbstractAxisSystem (such as Body(), Geometry(), Wind(), Stability()) to the named axes argument. The nearfield force and moment coefficients are reported in stability axes by default. Note that the derivatives with respect to the rotation rates will still refer to the rotation vector in stability axes $(p̄, q̄, r̄)$.

Optional printing arguments are provided for the components and the entire system, along with the corresponding farfield coefficients if needed.

influence_matrix(vortices)
influence_matrix(vortices, u_hat)

Assemble the Aerodynamic Influence Coefficient (AIC) matrix given an array of AbstractVortex and the freestream direction $û$.

nearfield(system :: VortexLatticeSystem)

Compute the total nearfield force and moment coefficients for all components of the VortexLatticeSystem. These are in wind axes by default.

nearfield_coefficients(system :: VortexLatticeSystem)

Compute the nearfield force and moment coefficients for all components of the VortexLatticeSystem. These are in wind axes by default.

print_coefficients(
    nf_coeffs, ff_coeffs, 
    name = ""
)

Print a pretty table of the nearfield and farfield coefficients with an optional name.

print_coefficients(
    system :: VortexLatticeSystem, 
    name = :aircraft;
    components = false
)

Print a pretty table of the total nearfield and farfield coefficients of a VortexLatticeSystem with an optional name.

A named Boolean argument components is provided to also enable the printing of any possible components.

print_derivatives(
    nf_coeffs, ff_coeffs, name = "";
    farfield = false,
)

Print a pretty table of the aerodynamic coefficients and derivatives with an optional name, and a named argument for enabling printing of farfield coefficients.

surface_dynamics(
    system :: VortexLatticeSystem; 
    axes :: AbstractAxisSystem = Geometry()
)

Compute the forces and moments for all components of the VortexLatticeSystem in a specified reference axis system as a named argument.

The reference axis system is set to the geometry axes defined in the construction of the VortexLatticeSystem by default.

surface_forces(
    system :: VortexLatticeSystem; 
    axes :: AbstractAxisSystem = Geometry()
)

Compute the forces for all components of the VortexLatticeSystem in a specified reference axis system as a named argument.

The reference axis system is set to the geometry axes defined in the construction of the VortexLatticeSystem by default.

surface_moments(
    system :: VortexLatticeSystem; 
    axes :: AbstractAxisSystem = Geometry()
)

Compute the moments for all components of the VortexLatticeSystem in a specified reference axis system as a named argument.

The reference axis system is set to the geometry axes defined in the construction of the VortexLatticeSystem by default.

trailing_velocity(r, hs :: Horseshoes, Γ, u_hat)

Compute the induced velocity at a point $r$ from the semi-infinite trailing legs with constant strength $Γ$ of a given Horseshoe hs.

transform(hs :: Horseshoe, T :: LinearMap)

Generate a new Horseshoe with the points and normal vectors transformed by the LinearMap $T$.

transform(ring :: VortexRing, T :: LinearMap)

Generate a new VortexRing with the points and normal vectors transformed by the LinearMap $T$.

solve_linear(horseshoes, normals, U, Ω)

Evaluate and return the vortex strengths $Γ$s given an array of Horseshoes, their associated normal vectors, the velocity vector $U$, and the quasi-steady rotation vector $Ω$.

surface_coefficients(
    system :: VortexLatticeSystem; 
    axes :: AbstractAxisSystem = Geometry()
)

Compute the force and moment coefficients of the surfaces over all components in a given VortexLatticeSystem, in a specified reference axis system as a named argument.

The reference axis system is set to the geometry axes defined in the construction of the VortexLatticeSystem by default.

surface_velocities(
    system :: VortexLatticeSystem; 
    axes :: AbstractAxisSystem = Geometry()
)

Compute the induced velocities for all components of the VortexLatticeSystem in a specified reference axis system as a named argument.

The reference axis system is set to the geometry axes defined in the construction of the VortexLatticeSystem by default.

velocity(r, ring :: VortexRing, Γ)

Computes the velocity at a point $r$ induced by a VortexRing with constant strength $Γ$.

velocity(r, hs :: Horseshoe, Γ, u_hat = [1.,0.,0.])

Compute the induced velocity at a point $r$ of a given Horseshoe with a bound leg of constant strength $Γ$ and semi-infinite trailing legs pointing in a given direction $û$, by default û = x̂.

velocity(freestream :: Freestream, ::Geometry)

Compute the velocity of Freestream in the geometry axis system.