def panel_positions(self, DSTEP1, DSTEP2, DSTEP3, T, THETA, HEAVE):
"""Updates all the absolute-frame coordinates of the body.
Args:
DSTEP: Small incremental distance to pass into neutral_plane().
T: Time of current step.
THETA: Current pitching angle.
"""
bfx = self.BF.x
bfy = self.BF.y #No y information coming from the geometry class yet
bfz = self.BF.z
bfz_col = self.BF.z_col
V0 = self.V0 # Used only for x_le
(x_neut, y_neut, z_neut) = self.neutral_plane(bfx, bfy, T, THETA, HEAVE)
# Infinitesimal differences on the neutral axis to calculate the tangential and normal vectors
v1 = (xdp_y, ydp_y, zdp_y) = self.neutral_plane(bfx, bfy, T, THETA, HEAVE, 0, DSTEP2, DSTEP3)
v2 = (xdm_y, ydm_y, zdm_y) = self.neutral_plane(bfx, bfy, T, THETA, HEAVE, 0, -DSTEP2, -DSTEP3)
v3 = (xdp_x, ydp_x, zdp_x) = self.neutral_plane(bfx, bfy, T, THETA, HEAVE, DSTEP1, 0, 0)
v4 = (xdm_x, ydm_x, zdm_x) = self.neutral_plane(bfx, bfy, T, THETA, HEAVE, -DSTEP1, 0, 0)
# Absolute-frame panel endpoint positions for time t
afx = x_neut + point_vectors(v1,v2,v3,v4)[1]*bfz
afy = y_neut + point_vectors(v1,v2,v3,v4)[2]*bfz
afz = z_neut + point_vectors(v1,v2,v3,v4)[3]*bfz
# Absolute-frame panel midpoint positions
x_mid = (afx[1:,:-1]+afx[:-1,:-1])/2
y_mid = (afy[1:,:-1]+afy[:-1,:-1])/2
z_mid = (afz[1:,:-1]+afz[:-1,:-1])/2
# Collocation points are the points where impermeable boundary condition is forced
# They should be shifted inside or outside of the boundary depending on the dirichlet or neumann condition
# Shifting surface collocation points some percent of the height from the neutral axis
# Normal vectors point outward but positive S is inward, so the shift must be subtracted from the panel midpoints
afx_col = x_mid - self.S*panel_vectors(afx, afz)[2]*np.absolute(bfz_col)
afy_col = y_mid - self.S*panel_vectors(afx, afz)[2]*np.absolute(bfz_col)
afz_col = z_mid - self.S*panel_vectors(afx, afz)[3]*np.absolute(bfz_col)
self.AF.x = afx
self.AF.y = afy
self.AF.z = afz
self.AF.x_col = afx_col
self.AF.y_col = afy_col
self.AF.z_col = afz_col
self.AF.x_mid = x_mid
self.AF.y_mid = y_mid
self.AF.z_mid = z_mid
self.AF.x_neut = x_neut
self.AF.y_neut = y_neut
self.AF.z_neut = z_neut
# Location of leading edge (currently pitching motion only)
self.AF.x_le = V0*T
self.AF.y_le = 0
self.AF.z_le = HEAVE
def surface_kinematics(self, DSTEP, TSTEP, THETA_MINUS, THETA_PLUS, HEAVE_MINUS, HEAVE_PLUS, DEL_T, T, i):
"""Calculates the body-frame surface velocities of body panels.
Also finds the body panel source strengths based on these surface
velocities.
Args:
DSTEP, TSTEP: Incremental distance/time passed into neutral_axis().
DEL_T: Time step length.
T: Time of current step.
i: Time step number.
THETA_MINUS: Pitching angle minus a small time difference (TSTEP)
THETA_PLUS: Pitching angle plus a small time difference (TSTEP)
"""
if i == 0:
x_col = self.BF.x_col
z_col = self.BF.z_col
# Panel midpoint velocity calculations
# Calculating the surface positions at tplus(tp) and tminus(tm)
(xtpneut, ztpneut) = self.neutral_axis(x_col, T, THETA_PLUS, HEAVE_PLUS, 0)
(xtpdp, ztpdp) = self.neutral_axis(x_col, T, THETA_PLUS, HEAVE_PLUS, DSTEP)
(xtpdm, ztpdm) = self.neutral_axis(x_col, T, THETA_PLUS, HEAVE_PLUS, -DSTEP)
(xtmneut, ztmneut) = self.neutral_axis(x_col, T, THETA_MINUS, HEAVE_MINUS, 0)
(xtmdp, ztmdp) = self.neutral_axis(x_col, T, THETA_MINUS, HEAVE_MINUS, DSTEP)
(xtmdm, ztmdm) = self.neutral_axis(x_col, T, THETA_MINUS, HEAVE_MINUS, -DSTEP)
# Displaced airfoil's panel midpoints for times tplus(tp) and tminus(tm)
xctp = xtpneut + point_vectors(xtpdp, xtpdm, ztpdp, ztpdm)[2]*z_col
xctm = xtmneut + point_vectors(xtmdp, xtmdm, ztmdp, ztmdm)[2]*z_col
zctp = ztpneut + point_vectors(xtpdp, xtpdm, ztpdp, ztpdm)[3]*z_col
zctm = ztmneut + point_vectors(xtmdp, xtmdm, ztmdp, ztmdm)[3]*z_col
# Velocity calculations on the surface panel midpoints
self.vx = (xctp - xctm)/(2*TSTEP)
self.vz = (zctp - zctm)/(2*TSTEP)
elif i == 1:
# First-order backwards differencing of body collocation point positions
self.vx = (self.AF.x_mid[0,:]-self.AF.x_mid[1,:])/DEL_T - self.V0
self.vz = (self.AF.z_mid[0,:]-self.AF.z_mid[1,:])/DEL_T
else:
# Second-order backwards differencing of body collocation point positions
self.vx = (3*self.AF.x_mid[0,:]-4*self.AF.x_mid[1,:]+self.AF.x_mid[2,:])/(2*DEL_T) - self.V0
self.vz = (3*self.AF.z_mid[0,:]-4*self.AF.z_mid[1,:]+self.AF.z_mid[2,:])/(2*DEL_T)
# Body source strengths with normal vector pointing outward (overall sigma pointing outward)
(nx,nz) = panel_vectors(self.AF.x,self.AF.z)[2:4]
self.sigma = nx*(self.V0 + self.vx) + nz*self.vz
def surface_kinematics(self, DSTEP, TSTEP, DEL_T, T, i):
"""Calculates the body-frame surface velocities of body panels.
Args:
DSTEP, TSTEP: Incremental distance/time passed into neutral_axis().
DEL_T: Time step length.
T: Time of current step.
i: Time step number.
x_col, z_col: Unshifted body-frame collocation point coordinates.
"""
if i == 0:
x_col = self.BF.x_col
z_col = self.BF.z_col
# Panel midpoint velocity calculations
# Calculating the surface positions at tplus(tp) and tminus(tm)
(xtpneut, ztpneut) = self.neutral_axis(x_col, T, 0, TSTEP)
(xtpdp, ztpdp) = self.neutral_axis(x_col, T, DSTEP, TSTEP)
(xtpdm, ztpdm) = self.neutral_axis(x_col, T, -DSTEP, TSTEP)
(xtmneut, ztmneut) = self.neutral_axis(x_col, T, 0, -TSTEP)
(xtmdp, ztmdp) = self.neutral_axis(x_col, T, DSTEP, -TSTEP)
(xtmdm, ztmdm) = self.neutral_axis(x_col, T, -DSTEP, -TSTEP)
# Displaced airfoil's panel midpoints for times tplus(tp) and tminus(tm)
xctp = xtpneut + point_vectors(xtpdp, xtpdm, ztpdp, ztpdm)[2]*z_col
xctm = xtmneut + point_vectors(xtmdp, xtmdm, ztmdp, ztmdm)[2]*z_col
zctp = ztpneut + point_vectors(xtpdp, xtpdm, ztpdp, ztpdm)[3]*z_col
zctm = ztmneut + point_vectors(xtmdp, xtmdm, ztmdp, ztmdm)[3]*z_col
# Velocity calculations on the surface panel midpoints
self.vx = (xctp - xctm)/(2*TSTEP)
self.vz = (zctp - zctm)/(2*TSTEP)
elif i == 1:
# First-order backwards differencing of body collocation point positions
self.vx = (self.AF.x_mid[0,:]-self.AF.x_mid[1,:])/DEL_T - self.V0
self.vz = (self.AF.z_mid[0,:]-self.AF.z_mid[1,:])/DEL_T
else:
# Second-order backwards differencing of body collocation point positions
self.vx = (3*self.AF.x_mid[0,:]-4*self.AF.x_mid[1,:]+self.AF.x_mid[2,:])/(2*DEL_T) - self.V0
self.vz = (3*self.AF.z_mid[0,:]-4*self.AF.z_mid[1,:]+self.AF.z_mid[2,:])/(2*DEL_T)
(nx,nz) = panel_vectors(self.AF.x,self.AF.z)[2:4]
self.sigma = nx*(self.V0 + self.vx) + nz*self.vz
def panel_positions(self, DSTEP, T):
"""Updates all the absolute-frame coordinates of the body.
Args:
DSTEP: Small incremental distance to pass into neutral_axis().
T: Time of current step.
bfx, bfz: Body-frame x- and z-coordinates.
bfz_col: Body-frame collocation z-coordinates (unshifted)
V0: Free-stream velocity.
"""
bfx = self.BF.x
bfz = self.BF.z
bfz_col = self.BF.z_col
V0 = self.V0 # Used only for x_le
(x_neut, z_neut) = self.neutral_axis(bfx, T)
# Infinitesimal differences on the neutral axis to calculate the tangential and normal vectors
(xdp_s, zdp_s) = self.neutral_axis(bfx, T, DSTEP)
(xdm_s, zdm_s) = self.neutral_axis(bfx, T, -DSTEP)
# Absolute-frame panel endpoint positions for time t
afx = x_neut + point_vectors(xdp_s, xdm_s, zdp_s, zdm_s)[2]*bfz
afz = z_neut + point_vectors(xdp_s, xdm_s, zdp_s, zdm_s)[3]*bfz
# Absolute-frame panel midpoint positions
x_mid = (afx[:-1]+afx[1:])/2
z_mid = (afz[:-1]+afz[1:])/2
# Collocation points are the points where impermeable boundary condition is forced
# They should be shifted inside or outside of the boundary depending on the dirichlet or neumann condition
# Shifting surface collocation points some percent of the height from the neutral axis
# Normal vectors point outward but positive S is inward, so the shift must be subtracted from the panel midpoints
afx_col = x_mid - self.S*panel_vectors(afx, afz)[2]*np.absolute(bfz_col)
afz_col = z_mid - self.S*panel_vectors(afx, afz)[3]*np.absolute(bfz_col)
self.AF.x = afx
self.AF.z = afz
self.AF.x_col = afx_col
self.AF.z_col = afz_col
self.AF.x_mid[0,:] = x_mid
self.AF.z_mid[0,:] = z_mid
self.AF.x_neut = x_neut
self.AF.z_neut = z_neut
# Location of leading edge (assuming pitching motion only)
self.AF.x_le = V0*T
self.AF.z_le = 0.
def surface_kinematics(self, DSTEP1, DSTEP2, DSTEP3, TSTEP, THETA_MINUS, THETA_PLUS, HEAVE_MINUS, HEAVE_PLUS, DEL_T, T, i):
"""Calculates the body-frame surface velocities of body panels.
Also finds the body panel source strengths based on these surface
velocities.
Args:
DSTEP, TSTEP: Incremental distance/time passed into neutral_axis().
DEL_T: Time step length.
T: Time of current step.
i: Time step number.
THETA_MINUS: Pitching angle minus a small time difference (TSTEP)
THETA_PLUS: Pitching angle plus a small time difference (TSTEP)
"""
Nc = self.BF.x_mid.shape[0]
Ns = self.BF.x_mid.shape[1]
if i == 0:
x_col = self.BF.x_mid
y_col = self.BF.y_mid
z_col = self.BF.z_mid
# Panel midpoint velocity calculations
# Calculating the surface positions at tplus(tp) and tminus(tm)
(xtpneut, ytpneut, ztpneut) = self.neutral_plane(x_col, y_col, T, THETA_PLUS, HEAVE_PLUS, 0, 0, 0)
(xtpdp_y, ytpdp_y, ztpdp_y) = self.neutral_plane(x_col, y_col, T, THETA_PLUS, HEAVE_PLUS, 0, DSTEP2, DSTEP3)
(xtpdp_x, ytpdp_x, ztpdp_x) = self.neutral_plane(x_col, y_col, T, THETA_PLUS, HEAVE_PLUS, DSTEP1, 0, 0)
(xtpdm_y, ytpdm_y, ztpdm_y) = self.neutral_plane(x_col, y_col, T, THETA_PLUS, HEAVE_PLUS, 0, -DSTEP2, -DSTEP3)
(xtpdm_x, ytpdm_x, ztpdm_x) = self.neutral_plane(x_col, y_col, T, THETA_PLUS, HEAVE_PLUS, -DSTEP1, 0, 0)
(xtmneut, ytmneut, ztmneut) = self.neutral_plane(x_col, y_col, T, THETA_MINUS, HEAVE_MINUS, 0, 0, 0)
(xtmdp_y, ytmdp_y, ztmdp_y) = self.neutral_plane(x_col, y_col, T, THETA_MINUS, HEAVE_MINUS, 0, DSTEP2, DSTEP3)
(xtmdp_x, ytmdp_x, ztmdp_x) = self.neutral_plane(x_col, y_col, T, THETA_MINUS, HEAVE_MINUS, DSTEP1, 0, 0)
(xtmdm_y, ytmdm_y, ztmdm_y) = self.neutral_plane(x_col, y_col, T, THETA_MINUS, HEAVE_MINUS, 0, -DSTEP2, -DSTEP3)
(xtmdm_x, ytmdm_x, ztmdm_x) = self.neutral_plane(x_col, y_col, T, THETA_MINUS, HEAVE_MINUS, -DSTEP1, 0, 0)
# Displaced airfoil's panel midpoints for times tplus(tp) and tminus(tm)
xctp = xtpneut + point_vectors(Nc, Ns, (xtpdp_y, ytpdp_y, ztpdp_y), (xtpdm_y, ytpdm_y, ztpdm_y), (xtpdp_x, ytpdp_x, ztpdp_x), (xtpdm_x, ytpdm_x, ztpdm_x))[0]*z_col
xctm = xtmneut + point_vectors(Nc, Ns, (xtmdp_y, ytmdp_y, ztmdp_y), (xtmdm_y, ytmdm_y, ztmdm_y), (xtmdp_x, ytmdp_x, ztmdp_x), (xtmdm_x, ytmdm_x, ztmdm_x))[0]*z_col
yctp = ytpneut + point_vectors(Nc, Ns, (xtpdp_y, ytpdp_y, ztpdp_y), (xtpdm_y, ytpdm_y, ztpdm_y), (xtpdp_x, ytpdp_x, ztpdp_x), (xtpdm_x, ytpdm_x, ztpdm_x))[1]*z_col
yctm = ytmneut + point_vectors(Nc, Ns, (xtmdp_y, ytmdp_y, ztmdp_y), (xtmdm_y, ytmdm_y, ztmdm_y), (xtmdp_x, ytmdp_x, ztmdp_x), (xtmdm_x, ytmdm_x, ztmdm_x))[1]*z_col
zctp = ztpneut + point_vectors(Nc, Ns, (xtpdp_y, ytpdp_y, ztpdp_y), (xtpdm_y, ytpdm_y, ztpdm_y), (xtpdp_x, ytpdp_x, ztpdp_x), (xtpdm_x, ytpdm_x, ztpdm_x))[2]*z_col
zctm = ztmneut + point_vectors(Nc, Ns, (xtmdp_y, ytmdp_y, ztmdp_y), (xtmdm_y, ytmdm_y, ztmdm_y), (xtmdp_x, ytmdp_x, ztmdp_x), (xtmdm_x, ytmdm_x, ztmdm_x))[2]*z_col
# Velocity calculations on the surface panel midpoints
self.vx = (xctp - xctm)/(2*TSTEP)
self.vy = (yctp - yctm)/(2*TSTEP)
self.vz = (zctp - zctm)/(2*TSTEP)
elif i == 1:
# First-order backwards differencing of body collocation point positions
self.vx = (self.AF.x_mid[:,:,0]-self.AF.x_mid[:,:,1])/DEL_T - self.V0
self.vy = (self.AF.y_mid[:,:,0]-self.AF.y_mid[:,:,1])/DEL_T
self.vz = (self.AF.z_mid[:,:,0]-self.AF.z_mid[:,:,1])/DEL_T
else:
# Second-order backwards differencing of body collocation point positions
self.vx = (3*self.AF.x_mid[:,:,0]-4*self.AF.x_mid[:,:,1]+self.AF.x_mid[:,:,2])/(2*DEL_T) - self.V0
self.vy = (3*self.AF.y_mid[:,:,0]-4*self.AF.y_mid[:,:,1]+self.AF.y_mid[:,:,2])/(2*DEL_T)
self.vz = (3*self.AF.z_mid[:,:,0]-4*self.AF.z_mid[:,:,1]+self.AF.z_mid[:,:,2])/(2*DEL_T)
# # Body source strengths with normal vector pointing outward (overall sigma pointing outward)
(nx, ny, nz) = panel_vectors(self.AF.x, self.AF.y, self.AF.z)[0:3]
self.sigma = nx*(self.V0 + self.vx) + ny*self.vy + nz*self.vz
def surface_kinematics(self, DSTEP1, DSTEP2, DSTEP3, TSTEP, THETA_MINUS,
THETA_PLUS, HEAVE_MINUS, HEAVE_PLUS, DEL_T, T, i):
"""Calculates the body-frame surface velocities of body panels.
Also finds the body panel source strengths based on these surface
velocities.
Args:
DSTEP, TSTEP: Incremental distance/time passed into neutral_axis().
DEL_T: Time step length.
T: Time of current step.
i: Time step number.
THETA_MINUS: Pitching angle minus a small time difference (TSTEP)
THETA_PLUS: Pitching angle plus a small time difference (TSTEP)
"""
Nc = self.BF.x_mid.shape[0]
Ns = self.BF.x_mid.shape[1]
if i == 0:
x_col = self.BF.x_mid
y_col = self.BF.y_mid
z_col = self.BF.z_mid
# Panel midpoint velocity calculations
# Calculating the surface positions at tplus(tp) and tminus(tm)
(xtpneut, ytpneut,
ztpneut) = self.neutral_plane(x_col, y_col, T, THETA_PLUS,
HEAVE_PLUS, 0, 0, 0)
(xtpdp_y, ytpdp_y,
ztpdp_y) = self.neutral_plane(x_col, y_col, T, THETA_PLUS,
HEAVE_PLUS, 0, DSTEP2, DSTEP3)
(xtpdp_x, ytpdp_x,
ztpdp_x) = self.neutral_plane(x_col, y_col, T, THETA_PLUS,
HEAVE_PLUS, DSTEP1, 0, 0)
(xtpdm_y, ytpdm_y,
ztpdm_y) = self.neutral_plane(x_col, y_col, T, THETA_PLUS,
HEAVE_PLUS, 0, -DSTEP2, -DSTEP3)
(xtpdm_x, ytpdm_x,
ztpdm_x) = self.neutral_plane(x_col, y_col, T, THETA_PLUS,
HEAVE_PLUS, -DSTEP1, 0, 0)
(xtmneut, ytmneut,
ztmneut) = self.neutral_plane(x_col, y_col, T, THETA_MINUS,
HEAVE_MINUS, 0, 0, 0)
(xtmdp_y, ytmdp_y,
ztmdp_y) = self.neutral_plane(x_col, y_col, T, THETA_MINUS,
HEAVE_MINUS, 0, DSTEP2, DSTEP3)
(xtmdp_x, ytmdp_x,
ztmdp_x) = self.neutral_plane(x_col, y_col, T, THETA_MINUS,
HEAVE_MINUS, DSTEP1, 0, 0)
(xtmdm_y, ytmdm_y,
ztmdm_y) = self.neutral_plane(x_col, y_col, T, THETA_MINUS,
HEAVE_MINUS, 0, -DSTEP2, -DSTEP3)
(xtmdm_x, ytmdm_x,
ztmdm_x) = self.neutral_plane(x_col, y_col, T, THETA_MINUS,
HEAVE_MINUS, -DSTEP1, 0, 0)
# Displaced airfoil's panel midpoints for times tplus(tp) and tminus(tm)
xctp = xtpneut + point_vectors(
Nc, Ns, (xtpdp_y, ytpdp_y, ztpdp_y),
(xtpdm_y, ytpdm_y, ztpdm_y), (xtpdp_x, ytpdp_x, ztpdp_x),
(xtpdm_x, ytpdm_x, ztpdm_x))[0] * z_col
xctm = xtmneut + point_vectors(
Nc, Ns, (xtmdp_y, ytmdp_y, ztmdp_y),
(xtmdm_y, ytmdm_y, ztmdm_y), (xtmdp_x, ytmdp_x, ztmdp_x),
(xtmdm_x, ytmdm_x, ztmdm_x))[0] * z_col
yctp = ytpneut + point_vectors(
Nc, Ns, (xtpdp_y, ytpdp_y, ztpdp_y),
(xtpdm_y, ytpdm_y, ztpdm_y), (xtpdp_x, ytpdp_x, ztpdp_x),
(xtpdm_x, ytpdm_x, ztpdm_x))[1] * z_col
yctm = ytmneut + point_vectors(
Nc, Ns, (xtmdp_y, ytmdp_y, ztmdp_y),
(xtmdm_y, ytmdm_y, ztmdm_y), (xtmdp_x, ytmdp_x, ztmdp_x),
(xtmdm_x, ytmdm_x, ztmdm_x))[1] * z_col
zctp = ztpneut + point_vectors(
Nc, Ns, (xtpdp_y, ytpdp_y, ztpdp_y),
(xtpdm_y, ytpdm_y, ztpdm_y), (xtpdp_x, ytpdp_x, ztpdp_x),
(xtpdm_x, ytpdm_x, ztpdm_x))[2] * z_col
zctm = ztmneut + point_vectors(
Nc, Ns, (xtmdp_y, ytmdp_y, ztmdp_y),
(xtmdm_y, ytmdm_y, ztmdm_y), (xtmdp_x, ytmdp_x, ztmdp_x),
(xtmdm_x, ytmdm_x, ztmdm_x))[2] * z_col
# Velocity calculations on the surface panel midpoints
self.vx = (xctp - xctm) / (2 * TSTEP)
self.vy = (yctp - yctm) / (2 * TSTEP)
self.vz = (zctp - zctm) / (2 * TSTEP)
elif i == 1:
# First-order backwards differencing of body collocation point positions
self.vx = (self.AF.x_mid[:, :, 0] -
self.AF.x_mid[:, :, 1]) / DEL_T - self.V0
self.vy = (self.AF.y_mid[:, :, 0] - self.AF.y_mid[:, :, 1]) / DEL_T
self.vz = (self.AF.z_mid[:, :, 0] - self.AF.z_mid[:, :, 1]) / DEL_T
else:
# Second-order backwards differencing of body collocation point positions
self.vx = (3 * self.AF.x_mid[:, :, 0] - 4 * self.AF.x_mid[:, :, 1]
+ self.AF.x_mid[:, :, 2]) / (2 * DEL_T) - self.V0
self.vy = (3 * self.AF.y_mid[:, :, 0] - 4 * self.AF.y_mid[:, :, 1]
+ self.AF.y_mid[:, :, 2]) / (2 * DEL_T)
self.vz = (3 * self.AF.z_mid[:, :, 0] - 4 * self.AF.z_mid[:, :, 1]
+ self.AF.z_mid[:, :, 2]) / (2 * DEL_T)
# # Body source strengths with normal vector pointing outward (overall sigma pointing outward)
(nx, ny, nz) = panel_vectors(self.AF.x, self.AF.y, self.AF.z)[0:3]
self.sigma = nx * (self.V0 + self.vx) + ny * self.vy + nz * self.vz
def panel_positions(self, DSTEP1, DSTEP2, DSTEP3, T, THETA, HEAVE):
"""Updates all the absolute-frame coordinates of the body.
Args:
DSTEP: Small incremental distance to pass into neutral_plane().
T: Time of current step.
THETA: Current pitching angle.
"""
# Nc = int(0.5*(self.BF.x.shape[0]-1))
Nc = self.BF.x.shape[0]
Ns = self.BF.x.shape[1]
bfx = self.BF.x
bfy = self.BF.y #No y information coming from the geometry class yet
bfz = self.BF.z
bfz_col = self.BF.z_mid
V0 = self.V0 # Used only for x_le
(x_neut, y_neut, z_neut) = self.neutral_plane(bfx, bfy, T, THETA,
HEAVE)
# Infinitesimal differences on the neutral axis to calculate the tangential and normal vectors
v1 = (xdp_y, ydp_y,
zdp_y) = self.neutral_plane(bfx, bfy, T, THETA, HEAVE, 0, DSTEP2,
DSTEP3)
v2 = (xdm_y, ydm_y,
zdm_y) = self.neutral_plane(bfx, bfy, T, THETA, HEAVE, 0,
-DSTEP2, -DSTEP3)
v3 = (xdp_x, ydp_x,
zdp_x) = self.neutral_plane(bfx, bfy, T, THETA, HEAVE, DSTEP1, 0,
0)
v4 = (xdm_x, ydm_x,
zdm_x) = self.neutral_plane(bfx, bfy, T, THETA, HEAVE, -DSTEP1,
0, 0)
# Absolute-frame panel endpoint positions for time t
afx = x_neut + point_vectors(Nc, Ns, v1, v2, v3, v4)[0] * bfz
afy = y_neut + point_vectors(Nc, Ns, v1, v2, v3, v4)[1] * bfz
afz = z_neut + point_vectors(Nc, Ns, v1, v2, v3, v4)[2] * bfz
# Absolute-frame panel midpoint positions
x_mid = (afx[1:, :-1] + afx[:-1, :-1]) / 2
y_mid = (afy[1:, :-1] + afy[:-1, :-1]) / 2
z_mid = (afz[1:, :-1] + afz[:-1, :-1]) / 2
# Collocation points are the points where impermeable boundary condition is forced
# They should be shifted inside or outside of the boundary depending on the dirichlet or neumann condition
# Shifting surface collocation points some percent of the height from the neutral axis
# Normal vectors point outward but positive S is inward, so the shift must be subtracted from the panel midpoints
afx_col = x_mid - self.S * panel_vectors(bfx, bfy,
bfz)[0] * np.absolute(bfz_col)
afy_col = y_mid - self.S * panel_vectors(bfy, bfy,
bfz)[1] * np.absolute(bfz_col)
afz_col = z_mid - self.S * panel_vectors(bfz, bfy,
bfz)[2] * np.absolute(bfz_col)
self.AF.x = afx
self.AF.y = afy
self.AF.z = afz
self.AF.x_col = afx_col
self.AF.y_col = afy_col
self.AF.z_col = afz_col
self.AF.x_mid[:, :, 0] = x_mid
self.AF.y_mid[:, :, 0] = y_mid
self.AF.z_mid[:, :, 0] = z_mid
self.AF.x_neut = x_neut
self.AF.y_neut = y_neut
self.AF.z_neut = z_neut
# Location of leading edge (currently pitching motion only)
self.AF.x_le = V0 * T
self.AF.y_le = 0
self.AF.z_le = HEAVE
def surface_kinematics(self, DSTEP, TSTEP, THETA_MINUS, THETA_PLUS,
HEAVE_MINUS, HEAVE_PLUS, DEL_T, T, i):
"""Calculates the body-frame surface velocities of body panels.
Also finds the body panel source strengths based on these surface
velocities.
Args:
DSTEP, TSTEP: Incremental distance/time passed into neutral_axis().
DEL_T: Time step length.
T: Time of current step.
i: Time step number.
THETA_MINUS: Pitching angle minus a small time difference (TSTEP)
THETA_PLUS: Pitching angle plus a small time difference (TSTEP)
"""
if i == 0:
x_col = self.BF.x_col
z_col = self.BF.z_col
# Panel midpoint velocity calculations
# Calculating the surface positions at tplus(tp) and tminus(tm)
(xtpneut, ztpneut) = self.neutral_axis(x_col, T, THETA_PLUS,
HEAVE_PLUS, 0)
(xtpdp, ztpdp) = self.neutral_axis(x_col, T, THETA_PLUS,
HEAVE_PLUS, DSTEP)
(xtpdm, ztpdm) = self.neutral_axis(x_col, T, THETA_PLUS,
HEAVE_PLUS, -DSTEP)
(xtmneut, ztmneut) = self.neutral_axis(x_col, T, THETA_MINUS,
HEAVE_MINUS, 0)
(xtmdp, ztmdp) = self.neutral_axis(x_col, T, THETA_MINUS,
HEAVE_MINUS, DSTEP)
(xtmdm, ztmdm) = self.neutral_axis(x_col, T, THETA_MINUS,
HEAVE_MINUS, -DSTEP)
# Displaced airfoil's panel midpoints for times tplus(tp) and tminus(tm)
xctp = xtpneut + point_vectors(xtpdp, xtpdm, ztpdp,
ztpdm)[2] * z_col
xctm = xtmneut + point_vectors(xtmdp, xtmdm, ztmdp,
ztmdm)[2] * z_col
zctp = ztpneut + point_vectors(xtpdp, xtpdm, ztpdp,
ztpdm)[3] * z_col
zctm = ztmneut + point_vectors(xtmdp, xtmdm, ztmdp,
ztmdm)[3] * z_col
# Velocity calculations on the surface panel midpoints
self.vx = (xctp - xctm) / (2 * TSTEP)
self.vz = (zctp - zctm) / (2 * TSTEP)
elif i == 1:
# First-order backwards differencing of body collocation point positions
self.vx = (self.AF.x_mid[0, :] -
self.AF.x_mid[1, :]) / DEL_T - self.V0
self.vz = (self.AF.z_mid[0, :] - self.AF.z_mid[1, :]) / DEL_T
else:
# Second-order backwards differencing of body collocation point positions
self.vx = (3 * self.AF.x_mid[0, :] - 4 * self.AF.x_mid[1, :] +
self.AF.x_mid[2, :]) / (2 * DEL_T) - self.V0
self.vz = (3 * self.AF.z_mid[0, :] - 4 * self.AF.z_mid[1, :] +
self.AF.z_mid[2, :]) / (2 * DEL_T)
# Body source strengths with normal vector pointing outward (overall sigma pointing outward)
(nx, nz) = panel_vectors(self.AF.x, self.AF.z)[2:4]
self.sigma = nx * (self.V0 + self.vx) + nz * self.vz
