ezaero - Aerodynamics in Python

Under construction

ezaero (easy-aero) is an open source Python package oriented to implement numerical methods for Aerodynamics, such as the Vortex lattice Method for lifting surfaces.

Steady VLM module

The ezaero.vlm.steady module includes a Vortex Lattice Method implementation for lifting surfaces.

References

1

Katz, J. et al., Low-Speed Aerodynamics, 2nd ed, Cambridge University Press, 2001: Chapter 12

class ezaero.vlm.steady.FlightConditions(ui: float = 100, aoa: float = 3.141592653589793, rho: float = 1)

Container for the flight conditions.

ui

Free-stream flow velocity.

Type

float

angle_of_attack

Angle of attack of the wing, expressed in radians.

Type

float

rho

Free-stream flow density.

Type

float

class ezaero.vlm.steady.MeshParameters(m: int = 4, n: int = 16)

Container for the wing mesh parameters.

m

Number of chordwise panels.

Type

int

n

Number of spanwise panels.

Type

int

class ezaero.vlm.steady.Simulation(wing: ezaero.vlm.steady.WingParameters, mesh: ezaero.vlm.steady.MeshParameters, flight_conditions: ezaero.vlm.steady.FlightConditions)

Simulation runner.

wing

Wing geometry definition.

Type

WingParameters

mesh

Mesh specification for the wing.

Type

MeshParameters

flight_conditions

Flight conditions for the simulation.

Type

FlightConditions

plot_cl()

Plot lift coefficient distribution on the wing.

plot_wing(**kwargs)

Generate 3D plot of wing panels, vortex panels, and panel control points.

run()

Run end-to-end steady VLM simulation.

Returns

Object containing the results of the steady VLM simulation.

Return type

SimulationResults

class ezaero.vlm.steady.SimulationResults(dp: numpy.ndarray, dL: numpy.ndarray, cl: numpy.ndarray, cl_wing: float, cl_span: numpy.ndarray)

Container for the resulting distributions from the steady VLM simulation.

dp

Distribution of pressure difference between lower and upper surfaces.

Type

np.ndarray, shape (m, n)

dL

Lift distribution.

Type

np.ndarray, shape (m, n)

cl

Lift coefficient distribution.

Type

np.ndarray, shape (m, n)

cl_wing

Wing lift coefficient.

Type

float

cl_span

Spanwise lift coefficient distribution.

Type

np.ndarray, shape (n, )

class ezaero.vlm.steady.WingParameters(root_chord: float = 1, tip_chord: float = 1, planform_wingspan: float = 4, sweep_angle: float = 0, dihedral_angle: float = 0)

Container for the geometric parameters of the wing.

root_chord

Chord at root of the wing.

Type

float

tip_chord

Chord at tip of the wing.

Type

float

planform_wingspan

Wingspan of the planform.

Type

float

sweep_angle

Sweep angle of the 1/4 chord line, expressed in radians.

Type

float

dihedral_angle

Dihedral angle, expressed in radians.

Type

float

Examples

Simple steady VLM demo

Simple steady VLM demo

Minimal example of simulation execution.

• 
• 

Out:

Wing lift coefficient: 0.20335518605804598
Elapsed time: 0.010579347610473633 s

import time

import matplotlib.pyplot as plt
import numpy as np

import ezaero.vlm.steady as vlm

# definition of wing, mesh and flight condition parameters
wing = vlm.WingParameters(
    root_chord=1,
    tip_chord=0.6,
    planform_wingspan=4,
    sweep_angle=30 * np.pi / 180,
    dihedral_angle=15 * np.pi / 180,
)
mesh = vlm.MeshParameters(m=4, n=16)
flcond = vlm.FlightConditions(ui=100, aoa=3 * np.pi / 180, rho=1.0)

sim = vlm.Simulation(wing=wing, mesh=mesh, flight_conditions=flcond)

start = time.time()
res = sim.run()
print(f"Wing lift coefficient: {res.cl_wing}")
print(f"Elapsed time: {time.time() - start} s")

# plot wing panels, vortex panels, and collocation points
sim.plot_wing()
plt.show()

# plot cl distribution on wing
sim.plot_cl()
plt.show()

Dihedral angle effect

Dihedral angle effect

Effect of dihedral on the lift coefficient slope of rectangular wings.

References

1

Katz, J. et al., Low-Speed Aerodynamics, 2nd ed, Cambridge University Press, 2001: figure 12.21

Out:

Elapsed time: 1.1781010627746582 s

import time

import matplotlib.pyplot as plt
import numpy as np

import ezaero.vlm.steady as vlm

start = time.time()

# dihedral angles grid
deltas = np.array([-45, -30, -15, 0, 15, 30]) * np.pi / 180

# define mesh parameters and flight conditions
mesh = vlm.MeshParameters(m=8, n=30)
# slope for each dihedral calculated using two flight conditions
flcond_0 = vlm.FlightConditions(ui=100.0, aoa=0.0, rho=1.0)
flcond_1 = vlm.FlightConditions(ui=100.0, aoa=np.pi / 180, rho=1.0)
cla_list = []  # container for the lift coefficient slope
for delta in deltas:
    # The figure in the book uses an aspect ratio of 4. It does not
    # correspond to the planform, but the "real" wingspan, hence we project
    # the wingspan with the dihedral angle
    bp = 4 * np.cos(delta)
    # define rectangular wing (same cr and ct), with no sweep (theta).
    wing = vlm.WingParameters(
        root_chord=1.0,
        tip_chord=1.0,
        planform_wingspan=bp,
        sweep_angle=0,
        dihedral_angle=delta,
    )
    res_0 = vlm.Simulation(wing=wing, mesh=mesh, flight_conditions=flcond_0).run()
    res_1 = vlm.Simulation(wing=wing, mesh=mesh, flight_conditions=flcond_1).run()
    d_cl = res_1.cl_wing - res_0.cl_wing
    d_alpha = flcond_1.aoa - flcond_0.aoa
    slope = d_cl / d_alpha * np.cos(delta)  # project load
    cla_list.append(slope)

end = time.time()
elapsed = end - start

print("Elapsed time: {} s".format(elapsed))

fig = plt.figure()
plt.plot(deltas * 180 / np.pi, cla_list, "o-")
plt.xlabel(r"$\delta$[deg]")
plt.ylabel(r"CL$_\alpha$")
plt.ylim(0, 4)
plt.grid()
plt.xlim(deltas.min() * 180 / np.pi, deltas.max() * 180 / np.pi)
plt.show()