def joukowsky(cls, m=-0.1+0.1j, numpoints=100):
from paraBEM.airfoil.conformal_mapping import JoukowskyAirfoil
airfoil = JoukowskyAirfoil(m)
profile = [[c.real, c.imag] for c in airfoil.coordinates(numpoints)]
# find the smallest xvalue to reset the nose
x = numpy.array([i[0] for i in profile])
profile = cls(profile, "joukowsky_" + str(m))
profile.normalize(numpy.where(x == min(x))[0][0])
profile.normalize()
profile.numpoints = numpoints
return profile
def joukowsky(cls, m=-0.1 + 0.1j, numpoints=100):
from paraBEM.airfoil.conformal_mapping import JoukowskyAirfoil
airfoil = JoukowskyAirfoil(m)
profile = [[c.real, c.imag] for c in airfoil.coordinates(numpoints)]
# find the smallest xvalue to reset the nose
x = numpy.array([i[0] for i in profile])
profile = cls(profile, "joukowsky_" + str(m))
profile.normalize(numpy.where(x == min(x))[0][0])
profile.normalize()
profile.numpoints = numpoints
return profile
from paraBEM.airfoil.conformal_mapping import JoukowskyAirfoil
from paraBEM.vtk_export import VtkWriter
from paraBEM.utils import check_path
####################################################
# analytic solution of joukowsky-airfoils #
####################################################
# -inputparameter for the joukowsky airfoil
midpoint = -0.2 + 0.0j # m is the complex mid point of a circle passing (1 + 0j)
alpha = np.deg2rad(10) # alpha is the angle of attack in rad
num_x = 300 # number of plot-points in x-direction
num_y = 300 # number of plot-points in y-direction
# -create joukowsky object
airfoil = JoukowskyAirfoil(midpoint)
# -helper functions
def complex_to_3vec(z):
return [z.real, z.imag, 0]
def zeta_velocity(z):
vel = airfoil.velocity(z, alpha)
return [vel.real, -vel.imag, 0.]
def z_velocity(z):
vel = airfoil.z_velocity(z, alpha)