def get_vortex_influence(self, points):
"""Determines the velocity vector induced by this edge at arbitrary
points, assuming a horseshoe vortex is shed from this edge.
Parameters
----------
points : ndarray
An array of points where the first index is the point index and
the second index is the coordinate.
Returns
-------
ndarray
The velocity vector induced at each point.
"""
# Determine displacement vectors
r0 = points - self.vertices[0, :]
r1 = points - self.vertices[1, :]
# Determine displacement vector magnitudes
r0_mag = vec_norm(r0)
r1_mag = vec_norm(r1)
# Calculate influence of bound segment
with np.errstate(divide='ignore'):
d = (np.pi * r0_mag * r1_mag *
(r0_mag * r1_mag + vec_inner(r0, r1)))
n = 0.25 * ((r0_mag + r1_mag) / d)
n = np.nan_to_num(n, copy=False)
return n[:, np.newaxis] * vec_cross(r0, r1)
def get_ring_influence(self, points):
"""Determines the velocity vector induced by this panel at arbitrary
points, assuming a vortex ring (0th order) model and a unit positive
vortex strength.
Parameters
----------
points : ndarray
An array of points where the first index is the point index and
the second index is the coordinate.
Returns
-------
ndarray
The velocity vector induced at each point.
"""
# Determine displacement vectors
r = points[np.newaxis, :, :] - self.vertices[:, np.newaxis, :]
r_mag = vec_norm(r)
# Calculate influence
v = np.zeros_like(points)
with np.errstate(divide='ignore'):
for i in range(self.N):
d = (r_mag[i - 1] * r_mag[i] *
(r_mag[i - 1] * r_mag[i] + vec_inner(r[i - 1], r[i])))
n = (r_mag[i - 1] + r_mag[i]) / d
n = np.nan_to_num(n, copy=False)
v += vec_cross(r[i - 1], r[i]) * n[:, np.newaxis]
return 0.25 / np.pi * v
def _get_filament_influences(self, points):
# Determines the unit vortex influence from the wake filaments on the given points
# Determine displacement vectors: first index is point, second is filament, third is segment, fourth is vector component
if self._end_infinite:
r0 = points[:, np.newaxis, np.newaxis, :] - self._vertices[
np.newaxis, :, :
-2, :] # Don't add the last segment at this point
r1 = points[:, np.newaxis,
np.newaxis, :] - self._vertices[np.newaxis, :, 1:-1, :]
else:
r0 = points[:, np.newaxis,
np.newaxis, :] - self._vertices[np.newaxis, :, :-1, :]
r1 = points[:, np.newaxis,
np.newaxis, :] - self._vertices[np.newaxis, :, 1:, :]
# Determine displacement vector magnitudes
r0_mag = vec_norm(r0)
r1_mag = vec_norm(r1)
# Calculate influence of each segment
inf = np.sum(
((r0_mag + r1_mag) /
(r0_mag * r1_mag *
(r0_mag * r1_mag + vec_inner(r0, r1))))[:, :, :, np.newaxis] *
vec_cross(r0, r1),
axis=2)
# Add influence of last segment, if needed
if self._end_infinite:
# Determine displacement vector magnitudes
r = r1[:, :, -1, :]
r_mag = vec_norm(r)
u = self._vertices[:, -1, :] - self._vertices[:, -2, :]
u /= vec_norm(u)[:, np.newaxis]
# Calculate influence
inf += vec_cross(u[np.newaxis, :, :], r) / (
r_mag *
(r_mag - vec_inner(u[np.newaxis, :, :], r)))[:, :, np.newaxis]
return 0.25 / np.pi * np.nan_to_num(inf)
def update(self, velocity_from_body, mu, v_inf, omega, verbose):
"""Updates the shape of the wake based on solved flow results.
Parameters
----------
velocity_from_body : callable
Function which will return the velocity induced by the body at a given set of points.
mu : ndarray
Vector of doublet strengths.
v_inf : ndarray
Freestream velocity vector.
omega : ndarray
Angular rate vector.
verbose : bool
"""
if verbose:
print()
prog = OneLineProgress(4, msg=" Updating wake shape")
# Reorder vertices for computation
points = self._vertices[:, 1:, :].reshape(
(self.N * (self.N_segments), 3))
# Get velocity from body and rotation
v_ind = velocity_from_body(points) - vec_cross(omega, points)
if verbose: prog.display()
# Get velocity from wake elements
v_ind += self._get_velocity_from_filaments_and_edges(points, mu)
if verbose: prog.display()
# Calculate time-stepping parameter
U = norm(v_inf)
u = v_inf / U
dl = self._vertices[:, 1:, :] - self._vertices[:, 0, :][:,
np.newaxis, :]
d = vec_inner(dl, u[np.newaxis, :])
dt = self._K * d / U
if verbose: prog.display()
# Shift vertices
self._vertices[:, 1:, :] += dt[:, :, np.newaxis] * v_ind.reshape(
(self.N, self.N_segments, 3))
if verbose: prog.display()
def _get_filament_influences(self, points):
# Determines the unit vortex influence from the wake filaments on the given points
# Determine displacement vectors: first index is point, second is filament, third is segment, fourth is vector component
r0 = points[:, np.newaxis, np.newaxis, :] - self._vertices[
np.newaxis, :, :self.N_segments, :]
r1 = points[:, np.newaxis,
np.newaxis, :] - self._vertices[np.newaxis, :,
1:self.N_segments + 1, :]
# Determine displacement vector magnitudes
r0_mag = vec_norm(r0)
r1_mag = vec_norm(r1)
# Calculate influence of each segment
inf = np.sum(
((r0_mag + r1_mag) /
(r0_mag * r1_mag *
(r0_mag * r1_mag + vec_inner(r0, r1))))[:, :, :, np.newaxis] *
vec_cross(r0, r1),
axis=2)
return 0.25 / np.pi * np.nan_to_num(inf)
def set_condition(self, **kwargs):
"""Sets the atmospheric conditions for the computation.
V_inf : list
Freestream velocity vector.
rho : float
Freestream density.
angular_rate : list, optional
Body-fixed angular rate vector (given in rad/s). Defaults to [0.0, 0.0, 0.0].
"""
# Set solved flag
self._solved = False
# Get freestream
self._v_inf = np.array(kwargs["V_inf"])
self._V_inf = norm(self._v_inf)
self._u_inf = self._v_inf / self._V_inf
self._rho = kwargs["rho"]
self._omega = np.array(kwargs.get("angular_rate", [0.0, 0.0, 0.0]))
# Create part of b vector dependent upon v_inf and rotation
v_rot = vec_cross(self._omega, self._mesh.cp)
self._v_inf_and_rot = self._v_inf - v_rot
self._b = -vec_inner(self._v_inf - v_rot, self._mesh.n)
# Get solid body rotation
self._omega = np.array(kwargs.get("angular_rate", [0.0, 0.0, 0.0]))
# Finish Kutta edge search on mesh
self._mesh.finalize_kutta_edge_search(self._u_inf)
# Update wake
self._mesh.wake.set_filament_direction(self._v_inf, self._omega)
def export_vtk(self, filename):
"""Exports the solver results on the mesh to a VTK file. If a wake exists, the only meaningful scalar result which will be specified on the wake filaments is the filament strength. All other results are arbitrarily set to zero on the wake.
Parameters
----------
filename : str
Name of the file to write the results to. Must have '.vtk' extension.
"""
# Check extension
if '.vtk' not in filename:
raise IOError(
"Filename for VTK export must contain .vtk extension.")
# Open file
with open(filename, 'w') as export_handle:
# Write header
print("# vtk DataFile Version 3.0", file=export_handle)
print(
"PyPan results file. Generated by PyPan, USU AeroLab (c) 2020.",
file=export_handle)
print("ASCII", file=export_handle)
# Write dataset
print("DATASET POLYDATA", file=export_handle)
# Write vertices
vertices, panel_indices = self._mesh.get_vtk_data()
wake_vertices, wake_filament_indices, N_segments = self._mesh.wake.get_vtk_data(
)
print(
"POINTS {0} float".format(len(vertices) + len(wake_vertices)),
file=export_handle)
for vertex in vertices:
print("{0:<20.12}{1:<20.12}{2:<20.12}".format(*vertex),
file=export_handle)
for vertex in wake_vertices:
print("{0:<20.12}{1:<20.12}{2:<20.12}".format(*vertex),
file=export_handle)
# Determine wake filament list size
size = 0
for li in wake_filament_indices:
size += len(li)
# Write wake filaments
print("LINES {0} {1}".format(N_segments, size), file=export_handle)
for filament in wake_filament_indices:
print(" ".join([
str(index) if i == 0 else str(index + len(vertices))
for i, index in enumerate(filament)
]),
file=export_handle)
# Determine polygon list size
size = 0
for pi in panel_indices:
size += len(pi)
# Write panel polygons
print("POLYGONS {0} {1}".format(self._N_panels, size),
file=export_handle)
for panel in panel_indices:
print(" ".join([str(i) for i in panel]), file=export_handle)
# Write flow results
print("CELL_DATA {0}".format(self._N_panels + N_segments),
file=export_handle)
# Normals
print("NORMALS panel_normals float", file=export_handle)
for i in range(N_segments):
print("0.00 0.00 0.00", file=export_handle)
for n in self._mesh.n:
print("{0:<20.12} {1:<20.12} {2:<20.12}".format(
n[0], n[1], n[2]),
file=export_handle)
# Pressure coefficient
print("SCALARS pressure_coefficient float 1", file=export_handle)
print("LOOKUP_TABLE default", file=export_handle)
for i in range(N_segments):
print("0.0", file=export_handle)
for C_P in self._C_P:
print("{0:<20.12}".format(C_P), file=export_handle)
# Singularity strength
if hasattr(self, "_mu"):
print("SCALARS doublet_strength float 1", file=export_handle)
print("LOOKUP_TABLE default", file=export_handle)
for i in range(self._mesh.wake.N):
# Determine strength of filament
mu = 0
# Add for outbound panels
outbound_panels = self._mesh.wake.outbound_panels[i]
if len(outbound_panels) > 0:
mu -= self._mu[outbound_panels[0]]
mu += self._mu[outbound_panels[1]]
# Add for inbound panels
inbound_panels = self._mesh.wake.inbound_panels[i]
if len(inbound_panels) > 0:
mu += self._mu[inbound_panels[0]]
mu -= self._mu[inbound_panels[1]]
# Print out
for i in range(self._mesh.wake.N_segments):
print("{0:<20.12}".format(mu), file=export_handle)
for mu in self._mu:
print("{0:<20.12}".format(mu), file=export_handle)
# Velocity
if hasattr(self, "_v"):
print("VECTORS velocity float", file=export_handle)
for i in range(N_segments):
print("0.0 0.0 0.0", file=export_handle)
for v in self._v:
print("{0:<20.12} {1:<20.12} {2:<20.12}".format(
v[0], v[1], v[2]),
file=export_handle)
# Normal velocity
print("SCALARS normal_velocity float", file=export_handle)
print("LOOKUP_TABLE default", file=export_handle)
for i in range(N_segments):
print("0.0", file=export_handle)
for v_n in vec_inner(self._v, self._mesh.n):
print("{0:<20.12}".format(v_n), file=export_handle)
if self._verbose:
print()
print(
"Case results successfully written to '{0}'.".format(filename))
def get_influence_matrix(self, **kwargs):
"""Create wake influence matrix; first index is the influenced panels, second is the influencing panel, third is the velocity component.
Parameters
----------
points : ndarray
Array of points at which to calculate the influence.
N_panels : int
Number of panels in the mesh to which this wake belongs.
Returns
-------
ndarray
Trailing vortex influences.
"""
# Get kwargs
points = kwargs.get("points")
# Initialize storage
N = len(points)
vortex_influence_matrix = np.zeros((N, kwargs["N_panels"], 3))
# Get influence of edges
for edge in self._kutta_edges:
# Get indices of panels defining the edge
p_ind = edge.panel_indices
# Get infulence
V = edge.get_vortex_influence(points)
# Store
vortex_influence_matrix[:, p_ind[0]] = -V
vortex_influence_matrix[:, p_ind[1]] = V
# Determine displacement vector magnitudes
r = points[:, np.newaxis, :] - self._vertices[np.newaxis, :, :]
r_mag = vec_norm(r)
# Calculate influences
V = 0.25 / np.pi * vec_cross(
self.filament_dirs[np.newaxis, :, :],
r) / (r_mag *
(r_mag - vec_inner(self.filament_dirs[np.newaxis, :, :], r))
)[:, :, np.newaxis]
for i in range(self.N):
# Add for outbound panels
outbound_panels = self.outbound_panels[i]
if len(outbound_panels) > 0:
vortex_influence_matrix[:, outbound_panels[0], :] -= V[:, i, :]
vortex_influence_matrix[:, outbound_panels[1], :] += V[:, i, :]
# Add for inbound panels
inbound_panels = self.inbound_panels[i]
if len(inbound_panels) > 0:
vortex_influence_matrix[:, inbound_panels[0], :] += V[:, i, :]
vortex_influence_matrix[:, inbound_panels[1], :] -= V[:, i, :]
return vortex_influence_matrix