def _calc_area(self):
# Calculates the panel area from the two constituent triangles
A = 0.5 * norm(
cross(self.vertices[1] - self.vertices[0],
self.vertices[2] - self.vertices[0]))
return A + 0.5 * norm(
cross(self.vertices[2] - self.vertices[0],
self.vertices[3] - self.vertices[0]))
def calc_local_coords(self, **kwargs):
"""Calculates panel local coords (dependent on flow properties).
Parameters
----------
M : float
Freestream Mach number.
"""
# Get kwargs
M = kwargs["M"]
c_0 = kwargs["c_0"]
C_0 = kwargs["C_0"]
B_0 = kwargs["B_0"]
s = kwargs["s"]
B = kwargs["B"]
# Calculate tangent vector compressible norms (if applicable)
if hasattr(self, "t"):
self.t_comp_norm = np.zeros(3)
for i, t in enumerate(self.t):
self.t_comp_norm[i] = inner(t, t)-M**2*inner(c_0, t)**2
# Calculate conormal vector
self.n_co = self.n-M**2*inner(c_0, self.n)*c_0
# Check inclination
self.n_co = np.einsum('ij,j', B_0, self.n)
self._incl = inner(self.n, self.n_co)
if abs(self._incl)<1e-10:
raise MachInclinedError
self._r = np.sign(self._incl)
# Get panel coordinate directions
v_0 = cross(self.n, c_0)
v_0 /= norm(v_0)
u_0 = cross(v_0, self.n)
u_0 /= norm(u_0)
# Calculate transformation matrix
# It should be that det(A) = B**2 (see Epton & Magnus pp. E.3-16)
self._A = np.zeros((3,3))
denom = abs(self._incl)**-0.5
self._A[0,:] = denom*np.einsum('ij,j', C_0, u_0)
self._A[1,:] = self._r*s/B*np.einsum('ij,j', C_0, v_0)
self._A[2,:] = B*denom*self.n
# Calculate area Jacobian
self._J = 1.0/B*denom
def __init__(self, **kwargs):
# Store vertices
self.vertices = np.zeros((3,3))
self.vertices[0] = kwargs["v0"]
self.vertices[1] = kwargs["v1"]
self.vertices[2] = kwargs["v2"]
self._projected = kwargs.get("projected", False)
# Calculate area and normal vector
n = cross(self.vertices[1]-self.vertices[0], self.vertices[2]-self.vertices[1])
N = norm(n)
self.A = 0.5*N
self.n = n/N
# Check for zero area in projected panel
if self.A<1e-10 and self._projected:
self.null_panel = True
else:
self.null_panel = False
# Calculate edge tangents
self.t = np.roll(self.vertices, 1, axis=0)-self.vertices
self.t /= np.linalg.norm(self.t, axis=1, keepdims=True)
self._calc_geom_props()
def __init__(self, **kwargs):
super().__init__(**kwargs)
# Store type
self._type = kwargs.get("fixed_direction_type",
"freestream_and_rotation")
# Initialize filaments
self._vertices, self.inbound_panels, self.outbound_panels = self._arrange_kutta_vertices(
)
# Store number of filaments and segments
self.N = len(self._vertices)
self.N_segments = 1
# Initialize filament directions
self.filament_dirs = np.zeros((self.N, 3))
# Get direction for custom wake
if self._type == "custom":
try:
u = np.array(kwargs.get("custom_dir"))
u /= norm(u)
self.filament_dirs[:] = u
except:
raise IOError(
"'custom_dir' is required for non-iterative wake type 'custom'."
)
def _calc_normal(self):
# Calculates the panel unit normal vector
# Assumes the panel is planar
d1 = self.vertices[1] - self.vertices[0]
d2 = self.vertices[2] - self.vertices[1]
N = cross(d1, d2)
return N / norm(N)
def __init__(self, **kwargs):
# Store vertices
self.vertices = np.zeros((4,3))
self.vertices[0] = kwargs.get("v0")
self.vertices[1] = kwargs.get("v1")
self.vertices[2] = kwargs.get("v2")
self.vertices[3] = kwargs.get("v3", self.vertices[2]) # Will get removed by _check_collapsed_vertices()
# Store edge number
self.edge = kwargs.get("edge", [0])
# Determine if this is a projected panel
self._projected = kwargs.get("projected", False)
# Check for collapsed points
self._check_collapsed_vertices(kwargs.get("tol", 1e-8))
# Calculate midpoints
self.midpoints = 0.5*(self.vertices+np.roll(self.vertices, 1, axis=0))
# Calculate normal vector; this is simpler than the method used in PAN AIR, which is able to handle
# the case where the midpoints and center point do not lie in a flat plane [Epton & Magnus section D.2]
self.n = cross(self.midpoints[1]-self.midpoints[0], self.midpoints[2]-self.midpoints[1])
self.n /= norm(self.n)
# Other calculations
self._calc_geom_props()
self._calc_skewness()
# Setup projected panel
if not self._projected:
self._initialize_projected_panel()
# Initialize subpanels
self.subpanels = []
for i in range(self.N):
# Outer subpanel
self.subpanels.append(Subpanel(v0=self.midpoints[i-1], v1=self.vertices[i], v2=self.midpoints[i], projected=self._projected))
# Inner subpanel
self.subpanels.append(Subpanel(v0=self.midpoints[i], v1=self.center, v2=self.midpoints[i-1], projected=self._projected))
# Initialize half panels (only if the panel is not already triangular)
if self.N==4:
self.half_panels = []
for i in range(self.N):
self.half_panels.append(Subpanel(v0=self.vertices[i-2], v1=self.vertices[i-1], v2=self.vertices[i]))
else:
self.half_panels = False
def _load_stl(self, stl_file):
# Loads mesh from an stl file
# Load stl file
raw_mesh = stl.mesh.Mesh.from_file(stl_file)
# Initialize storage
N = raw_mesh.v0.shape[0]
self.N = N
self.panels = []
bad_facets = []
# Loop through panels and initialize objects
for i in range(N):
# Check for finite area
if norm(raw_mesh.normals[i]) == 0.0:
self.N -= 1
warnings.warn("Panel {0} has zero area. Skipping...".format(i))
bad_facets.append(i)
continue
# Initialize
panel = Tri(v0=raw_mesh.v0[i],
v1=raw_mesh.v1[i],
v2=raw_mesh.v2[i])
self.panels.append(panel)
self.panels = np.array(self.panels)
# Store panel information
self.cp = np.zeros((self.N, 3))
self.n = np.zeros((self.N, 3))
self.dA = np.zeros(self.N)
for i in range(self.N):
self.n[i], self.dA[i], self.cp[i] = self.panels[i].get_info()
# Get vertex list
good_facets = [i for i in range(N) if i not in bad_facets]
raw_vertices = np.concatenate(
(raw_mesh.v0[good_facets], raw_mesh.v1[good_facets],
raw_mesh.v2[good_facets]))
self._vertices, inverse_indices = np.unique(raw_vertices,
return_inverse=True,
axis=0)
self._panel_vertex_indices = []
for i in range(self.N):
self._panel_vertex_indices.append([3, *inverse_indices[i::self.N]])
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 __init__(self, **kwargs):
# Store vertices
self.vertices = np.zeros((3, 3))
self.vertices[0] = kwargs.get("v0")
self.vertices[1] = kwargs.get("v1")
self.vertices[2] = kwargs.get("v2")
self.N = 3
super().__init__(**kwargs)
# Set up local coordinate transformation
n, _, _ = self.get_info()
self.A_t = np.zeros((3, 3))
self.A_t[0] = self.vertices[1] - self.vertices[0]
self.A_t[0] /= norm(self.A_t[0])
self.A_t[1] = cross(n, self.A_t[0])
self.A_t[2] = n
def set_filament_direction(self, v_inf, omega):
"""Updates the direction of the vortex filaments based on the velocity params.
Parameters
----------
v_inf : ndarray
Freestream velocity vector.
omega : ndarray
Angular rate vector.
"""
# Freestream direction
if self._type == "freestream":
u = v_inf / norm(v_inf)
self.filament_dirs[:] = u
# Freestream with rotation
elif self._type == "freestream_and_rotation":
self.filament_dirs = v_inf[np.newaxis, :] - vec_cross(
omega, self._vertices)
self.filament_dirs /= vec_norm(self.filament_dirs)[:, np.newaxis]
def __init__(self, **kwargs):
# Store vertices
self.vertices = np.zeros((4, 3))
self.vertices[0] = kwargs.get("v0")
self.vertices[1] = kwargs.get("v1")
self.vertices[2] = kwargs.get("v2")
self.vertices[3] = kwargs.get("v3")
self.midpoints = 0.5 * (self.vertices +
np.roll(self.vertices, 1, axis=0))
self.N = 4
super().__init__(**kwargs)
# Set up local coordinate transformation
n = self._calc_normal()
self.A_t = np.zeros((3, 3))
self.A_t[0] = self.midpoints[1] - self.midpoints[0]
self.A_t[0] /= norm(self.A_t[0])
self.A_t[1] = cross(n, self.A_t[0])
self.A_t[2] = n
def get_vtk_data(self, **kwargs):
"""Returns a list of vertices and line indices describing this wake.
Parameters
----------
length : float, optional
Length of the final filament segment, if set as infinite. Defaults to 20 times the filament segment length.
"""
# Get kwargs
l = kwargs.get("length", 20.0 * self.l)
# Initialize storage
vertices = []
line_vertex_indices = []
# Loop through filaments
i = 0
for j in range(self.N):
# Add vertices
for k in range(self.N_segments + 1):
vertices.append(self._vertices[j, k])
# Add indices
if k != self.N_segments:
line_vertex_indices.append([2, i + k, i + k + 1])
# Treat infinite end segment
if self._end_infinite:
u = vertices[-1] - vertices[-2]
u /= norm(u)
vertices[-1] = vertices[-2] + u * l
# Increment index
i += self.N_segments + 1
return vertices, line_vertex_indices, self.N * self.N_segments
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 finalize_kutta_edge_search(self, u_inf):
"""Determines where the Kutta condition should exist based on previously located adjacent panels and the freestream velocity.
Parameters
----------
u_inf : ndarray
Freestream velocity vector (direction of the oncoming flow).
"""
# Initialize edge storage
self._kutta_edges = []
if len(self._potential_kutta_panels) > 0:
if self._verbose:
print()
prog = OneLineProgress(len(self._potential_kutta_panels),
msg="Finalizing Kutta edge locations")
# Loop through previously determined possibilities
for i, j in self._potential_kutta_panels:
# Get panel objects
panel_i = self.panels[i]
panel_j = self.panels[j]
# Find first vertex shared by panels
found = False
for ii, vi in enumerate(panel_i.vertices):
for jj, vj in enumerate(panel_j.vertices):
# Check distance
if norm(vi - vj) < 1e-10:
# Store first shared vertex
v0 = vi
ii0 = ii
jj0 = jj
found = True
break
if found:
break
# Find second shared vertex; will be adjacent to first
poss_i_vert = [ii0 - 1, ii0 + 1]
poss_j_vert = [(jj0 + 1) % panel_j.N, jj0 - 1]
for i_same_dir, (ii, jj) in enumerate(
zip(poss_i_vert, poss_j_vert)
): # i_same_dir keeps track of if ii is still increasing
vi = panel_i.vertices[ii]
vj = panel_j.vertices[jj]
# Check distance
if norm(vi - vj) < 1e-10:
# See if we need to check the freestream condition
is_kutta_edge = False
if not self._check_freestream:
is_kutta_edge = True
# Get edge normals
else:
edge_normals_i = panel_i.get_edge_normals()
edge_normals_j = panel_j.get_edge_normals()
# Decide which edge to use
if i_same_dir:
i_edge = ii0
j_edge = jj
else:
i_edge = ii
j_edge = jj0
# Check angle edge normals make with freestream
if inner(edge_normals_i[i_edge],
u_inf) > 0.0 or inner(
edge_normals_j[j_edge], u_inf) > 0.0:
is_kutta_edge = True
# Store
if is_kutta_edge:
if ii - ii0 == 1: # Order is important for definition of circulation
self._kutta_edges.append(
KuttaEdge(v0, vi, [i, j]))
else:
self._kutta_edges.append(
KuttaEdge(vi, v0, [i, j]))
break
if self._verbose:
prog.display()
# Store number of edges
self.N_edges = len(self._kutta_edges)
else:
self.N_edges = 0
if self._verbose:
print(" Found {0} Kutta edges.".format(self.N_edges))
if self._verbose:
print()
prog = OneLineProgress(
self.N, msg="Locating panels for gradient calculation")
# Store touching and abutting panels not across Kutta edge
for i, panel in enumerate(self.panels):
# Loop through panels touching this one
for j in panel.touching_panels:
# Check for kutta edge
for kutta_edge in self._kutta_edges:
pi = kutta_edge.panel_indices
if (pi[0] == i and pi[1] == j) or (pi[0] == j
and pi[1] == i):
break
else:
panel.touching_panels_not_across_kutta_edge.append(j)
# Check if the panel is abutting
if j in panel.abutting_panels:
panel.abutting_panels_not_across_kutta_edge.append(j)
if self._verbose:
prog.display()
# Store second abutting panels not across Kutta edge
# Note we're not tracking the progress of this loop. It's super fast.
for i, panel in enumerate(self.panels):
for j in panel.abutting_panels_not_across_kutta_edge:
# This panel obviously counts
panel.second_abutting_panels_not_across_kutta_edge.append(j)
# Get second panels
for k in self.panels[j].abutting_panels_not_across_kutta_edge:
if k not in panel.second_abutting_panels_not_across_kutta_edge and k != i:
panel.second_abutting_panels_not_across_kutta_edge.append(
k)
# Set up least-squares matrices
self._set_up_lst_sq()
# Initialize wake
if self.N_edges > 0:
if self._wake_type == "fixed":
self.wake = StraightFixedWake(kutta_edges=self._kutta_edges,
**self._wake_kwargs)
elif self._wake_type == "full_streamline":
self.wake = FullStreamlineWake(kutta_edges=self._kutta_edges,
**self._wake_kwargs)
elif self._wake_type == "relaxed":
self.wake = VelocityRelaxedWake(kutta_edges=self._kutta_edges,
**self._wake_kwargs)
elif self._wake_type == "marching_streamline":
self.wake = MarchingStreamlineWake(
kutta_edges=self._kutta_edges, **self._wake_kwargs)
else:
raise IOError(
"{0} is not a valid wake type.".format(wake_type))
def _calc_area(self):
# Calculates the panel area
return 0.5 * norm(
cross(self.vertices[1] - self.vertices[0],
self.vertices[2] - self.vertices[0]))
def _calc_normal(self):
# Calculates the normal based off of the edge midpoints
n = cross(self.midpoints[1] - self.midpoints[0],
self.midpoints[2] - self.midpoints[1])
return n / norm(n)