def compute_thrust_cfd(u, params):
dim_u = np.shape(u)[0]
front_rotors = u[:dim_u // 2, :]
rear_rotors = u[dim_u // 2:, :]
azimuthal_grid = params['AzimuthalGrid'].reshape(-1, 1)
azimuthal_grid = (np.pi/180)*azimuthal_grid
d_theta = np.diff(azimuthal_grid, axis=0)
d_theta = np.vstack((d_theta, d_theta[1]))
front_rotors = weighting(front_rotors, d_theta, mode='repelem')/(2 * np.pi)
force_front = params['n_b']*np.sum(front_rotors, axis=0)
force_front = np.around(force_front, decimals=2)
rear_rotors = weighting(rear_rotors, d_theta, mode='repelem')/(2 * np.pi)
force_rear = params['n_b']*np.sum(rear_rotors, axis=0)
force_rear = np.around(force_rear, decimals=2)
force_front = force_front.reshape(1, -1)
force_rear = force_rear.reshape(1, -1)
return force_front, force_rear
def compute_torque_rmac(u, params):
dim_u = np.shape(u)[0]
front_rotors = u[:dim_u // 2, :]
rear_rotors = u[dim_u // 2:, :]
R = params['R']
radial_grid = R * params['RadialGrid'].reshape(-1, 1)
azimuthal_grid = params['AzimuthalGrid'].reshape(-1, 1)
azimuthal_grid = (np.pi / 180) * azimuthal_grid
dr = np.diff(radial_grid, axis=0)
dr = np.vstack((dr[1], dr))
d_theta = np.diff(azimuthal_grid, axis=0)
d_theta = np.vstack((d_theta[1], d_theta))
front_rotors = weighting(front_rotors, radial_grid, mode='repmat')
front_rotors = weighting(front_rotors, dr, mode='repmat')
front_rotors = weighting(front_rotors, d_theta, mode='repelem') / (2 * np.pi)
rear_rotors = weighting(rear_rotors, radial_grid, mode='repmat')
rear_rotors = weighting(rear_rotors, dr, mode='repmat')
rear_rotors = weighting(rear_rotors, d_theta, mode='repelem') / (2 * np.pi)
force_front = params['n_b'] * np.sum(front_rotors, axis=0)
force_rear = params['n_b'] * np.sum(rear_rotors, axis=0)
force_front = np.around(force_front, decimals=2)
force_rear = np.around(force_rear, decimals=2)
force_front = force_front.reshape(1, -1)
force_rear = force_rear.reshape(1, -1)
return force_front, force_rear
def disk_plot_comparison_old(u1,
u2,
params,
force_dir,
location,
save=False,
cfd=False):
force = "Lift" if force_dir == "L" else "Drag"
type_snap = 'cfd' if cfd else 'rmac'
err_front, err_rear = l2error(u1, params, type_snap, u2, params, type_snap)
if cfd:
radial_grid = params['RadialGrid'].reshape(-1, 1)
dr = np.diff(radial_grid, axis=0)
dr = np.vstack((radial_grid[1], dr))
u1 = weighting(u1, 1 / dr, mode='repmat')
u2 = weighting(u2, 1 / dr, mode='repmat')
if np.shape(u1)[0] == np.shape(u2)[0]:
n_row = np.shape(u1)[0]
else:
print('Dimensions of Snapshot to compare must be the same')
return
dx, dy = get_dx_dy(location, params)
n_r = params['n_r']
n_theta = params['n_theta']
azimuths = np.radians(params['AzimuthalGrid'])
zeniths = params['RadialGrid']
theta, r = np.meshgrid(azimuths, zeniths)
front_rotor = u1[0:n_row // 2]
rear_rotor = u1[n_row // 2:]
front_rotor1 = np.reshape(front_rotor, (n_r, n_theta), 'F')
rear_rotor1 = np.reshape(rear_rotor, (n_r, n_theta), 'F')
front_rotor = u2[0:n_row // 2]
rear_rotor = u2[n_row // 2:]
front_rotor2 = np.reshape(front_rotor, (n_r, n_theta), 'F')
rear_rotor2 = np.reshape(rear_rotor, (n_r, n_theta), 'F')
plt.rc('grid', linestyle="-", color='black', lw=0.8)
fig, axes = plt.subplots(3,
2,
figsize=(10, 12),
subplot_kw=dict(projection='polar'))
fig.subplots_adjust(wspace=0.3, hspace=0.35)
# config = "$(d_x, d_y)$ = (" + str(dx) + ", " + str(dy) + ")"
# title = fig.suptitle(("Disk Plots of {} [N/m] at " + config).format(force), fontsize=14)
# title.set_position([0.5, 0.95])
axes[0, 0].set_title('Front Rotor Snapshot', fontsize=12, pad=15)
axes[0, 1].set_title('Rear Rotor Snapshot', fontsize=12, pad=15)
axes[1, 0].set_title('Front Rotor Reconstruction', fontsize=12, pad=15)
axes[1, 1].set_title('Rear Rotor Reconstruction', fontsize=12, pad=15)
axes[2, 0].set_title('Difference, L2 error =' + str(err_front) + '%',
fontsize=12,
pad=15)
axes[2, 1].set_title('Difference, L2 error =' + str(err_rear) + '%',
fontsize=12,
pad=15)
im1 = axes[0, 0].contourf(theta,
r,
front_rotor1,
vmax=2700,
levels=150,
cmap='rainbow')
axes[0, 0].set_theta_direction(-1)
fig.colorbar(im1, ax=axes[0, 0], fraction=0.046, pad=0.04)
plt.grid()
im2 = axes[0, 1].contourf(theta,
r,
rear_rotor1,
vmax=2700,
levels=150,
cmap='rainbow')
fig.colorbar(im2, ax=axes[0, 1], fraction=0.046, pad=0.04)
plt.grid()
im3 = axes[1, 0].contourf(theta,
r,
front_rotor2,
vmax=2700,
levels=150,
cmap='rainbow')
axes[1, 0].set_theta_direction(-1)
fig.colorbar(im3, ax=axes[1, 0], fraction=0.046, pad=0.04)
plt.grid()
im4 = axes[1, 1].contourf(theta,
r,
rear_rotor2,
vmax=2700,
levels=150,
cmap='rainbow')
fig.colorbar(im4, ax=axes[1, 1], fraction=0.046, pad=0.04)
plt.grid()
im5 = axes[2, 0].contourf(theta,
r,
front_rotor1 - front_rotor2,
vmax=500,
vmin=-500,
levels=100,
cmap='rainbow')
axes[2, 0].set_theta_direction(-1)
fig.colorbar(im5, ax=axes[2, 0], fraction=0.046, pad=0.04)
plt.grid()
im6 = axes[2, 1].contourf(theta,
r,
rear_rotor1 - rear_rotor2,
vmax=500,
vmin=-500,
levels=100,
cmap='rainbow')
fig.colorbar(im6, ax=axes[2, 1], fraction=0.046, pad=0.04)
plt.grid()
if save:
fig_name = ("Disk_Plot_{}_Comparison_dx=" + str(dx) + "dy =" +
str(dy) + ".png").format(force)
plt.savefig(fig_name, bbox_inches='tight')
plt.show()
def disk_plot(u, location, params, force_dir, save=False, cfd=False):
""" Returns the disk plots of u seen as front and rear rotor r-theta matrix """
if cfd:
radial_grid = params['RadialGrid'].reshape(-1, 1)
dr = np.diff(radial_grid, axis=0)
dr = np.vstack((radial_grid[1], dr))
u = weighting(u, 1 / dr, mode='repmat')
n_row = np.shape(u)[0]
dx, dy = get_dx_dy(location, params)
n_r = params['n_r']
n_theta = params['n_theta']
azimuths = np.radians(np.linspace(0, 360, n_theta))
zeniths = params['RadialGrid']
theta, r = np.meshgrid(azimuths, zeniths)
front_rotor = u[0:n_row // 2]
rear_rotor = u[n_row // 2:]
front_rotor = np.reshape(front_rotor, (n_r, n_theta), 'F')
rear_rotor = np.reshape(rear_rotor, (n_r, n_theta), 'F')
plt.rc('grid', linestyle="-", color='black', lw=0.8)
fig, (ax1, ax2) = plt.subplots(1,
2,
figsize=(12, 8),
subplot_kw=dict(projection='polar'))
force = "Lift" if force_dir == "L" else "Drag"
# config = "$(d_x, d_y)$ = (" + str(dx) + ", " + str(dy) + ")"
# title = fig.suptitle(("Disk plots of {} [N/m] at" + config).format(force), fontsize=16)
# title.set_position([.5, 0.9])
# type_snap = 'cfd' if cfd else 'rmac'
# err_front, err_rear = l2error(u1, params, type_snap, u2, params, type_snap)
# ax1.set_title('Front L2 Error = ' + str(err_front) + '%', fontsize=20, pad=20)
# ax2.set_title('Rear L2 Error = ' + str(err_rear) + '%', fontsize=20, pad=20)
ax1.set_title('Front Rotor', fontsize=20, pad=20)
ax2.set_title('Rear Rotor', fontsize=20, pad=20)
im1 = ax1.contourf(theta,
r,
front_rotor,
vmin=0,
levels=100,
cmap='rainbow')
ax1.set_theta_direction(-1)
fig.colorbar(im1, ax=ax1, fraction=0.046, pad=0.04)
plt.grid()
im2 = ax2.contourf(theta,
r,
rear_rotor,
vmin=0,
levels=100,
cmap='rainbow')
fig.colorbar(im2, ax=ax2, fraction=0.046, pad=0.04)
plt.grid()
plt.show()
if save:
fig_name = ("Disk_plot_{}_dx=" + str(dx) + "dy=" + str(dy) +
".png").format(force)
plt.savefig(fig_name, bbox_inches='tight')
def disk_plot_comparison(u1,
params1,
type1,
u2,
params2,
type2,
force_dir,
location,
save=False):
force = "Lift" if force_dir == "L" else "Drag"
err_front, err_rear = l2error(u1, params1, type1, u2, params2, type2)
dx, dy = get_dx_dy(location, params1)
if type1 == 'cfd':
radial_grid = params1['RadialGrid'].reshape(-1, 1)
dr = np.diff(radial_grid, axis=0)
dr = np.vstack((radial_grid[1], dr))
u1 = weighting(u1, 1 / dr, mode='repmat')
if type2 == 'cfd':
radial_grid = params2['RadialGrid'].reshape(-1, 1)
dr = np.diff(radial_grid, axis=0)
dr = np.vstack((radial_grid[1], dr))
u2 = weighting(u2, 1 / dr, mode='repmat')
azimuths1 = np.radians(params1['AzimuthalGrid'])
zeniths1 = params1['RadialGrid']
theta1, r1 = np.meshgrid(azimuths1, zeniths1)
n_row = np.shape(u1)[0]
n_r, n_theta = params1['n_r'], params1['n_theta']
front_rotor = u1[0:n_row // 2]
rear_rotor = u1[n_row // 2:]
front_rotor1 = np.reshape(front_rotor, (n_r, n_theta), 'F')
rear_rotor1 = np.reshape(rear_rotor, (n_r, n_theta), 'F')
azimuths2 = np.radians(params2['AzimuthalGrid'])
zeniths2 = params2['RadialGrid']
theta2, r2 = np.meshgrid(azimuths2, zeniths2)
n_row = np.shape(u2)[0]
n_r, n_theta = params2['n_r'], params2['n_theta']
front_rotor = u2[0:n_row // 2]
rear_rotor = u2[n_row // 2:]
front_rotor2 = np.reshape(front_rotor, (n_r, n_theta), 'F')
rear_rotor2 = np.reshape(rear_rotor, (n_r, n_theta), 'F')
plt.rc('grid', linestyle="-", color='black', lw=0.8)
fig, axes = plt.subplots(3,
2,
figsize=(10, 12),
subplot_kw=dict(projection='polar'))
fig.subplots_adjust(wspace=0.3, hspace=0.35)
config = "$(d_x, d_y)$ = (" + str(dx) + ", " + str(dy) + ")"
title = fig.suptitle(("Disk Plots of {} [N/m] at " + config).format(force),
fontsize=16)
title.set_position([0.55, 1])
axes[0, 0].set_title('Front Rotor \nCFD', fontsize=14, pad=15)
axes[0, 1].set_title('Rear Rotor \nCFD', fontsize=14, pad=15)
axes[1, 0].set_title('RMAC', fontsize=12, pad=15)
axes[1, 1].set_title('RMAC', fontsize=12, pad=15)
axes[2, 0].set_title('Difference $L_2$ Error =' + str(err_front) + '%',
fontsize=12,
pad=15)
axes[2, 1].set_title('Difference $L_2$ Error =' + str(err_rear) + '%',
fontsize=12,
pad=15)
im1 = axes[0, 0].contourf(theta1,
r1,
front_rotor1,
vmin=0,
vmax=450,
levels=150,
cmap='rainbow')
axes[0, 0].set_theta_direction(-1)
fig.colorbar(im1, ax=axes[0, 0], fraction=0.046, pad=0.04)
plt.grid()
im2 = axes[0, 1].contourf(theta1,
r1,
rear_rotor1,
vmin=0,
vmax=450,
levels=150,
cmap='rainbow')
fig.colorbar(im2, ax=axes[0, 1], fraction=0.046, pad=0.04)
plt.grid()
im3 = axes[1, 0].contourf(theta2,
r2,
front_rotor2,
vmin=0,
vmax=450,
levels=150,
cmap='rainbow')
axes[1, 0].set_theta_direction(-1)
fig.colorbar(im3, ax=axes[1, 0], fraction=0.046, pad=0.04)
plt.grid()
im4 = axes[1, 1].contourf(theta2,
r2,
rear_rotor2,
vmin=0,
vmax=450,
levels=150,
cmap='rainbow')
fig.colorbar(im4, ax=axes[1, 1], fraction=0.046, pad=0.04)
plt.grid()
[u1, u2, ax1, ax2] = matrix_interpol(front_rotor1, zeniths1, azimuths1,
front_rotor2, zeniths2, azimuths2)
im5 = axes[2, 0].contourf(ax2,
ax1,
u1 - u2,
vmin=-150,
vmax=150,
levels=100,
cmap='rainbow')
axes[2, 0].set_theta_direction(-1)
fig.colorbar(im5, ax=axes[2, 0], fraction=0.046, pad=0.04)
plt.grid()
[u1, u2, ax1, ax2] = matrix_interpol(rear_rotor1, zeniths1, azimuths1,
rear_rotor2, zeniths2, azimuths2)
im6 = axes[2, 1].contourf(ax2,
ax1,
u1 - u2,
vmin=-150,
vmax=150,
levels=100,
cmap='rainbow')
fig.colorbar(im6, ax=axes[2, 1], fraction=0.046, pad=0.04)
plt.grid()
if save:
model = 'RMAC' if type2 == 'rmac' else 'CFD'
fig_name = ("{}_{}_dx=" + str(dx) + "dy =" + str(dy) + ".png").format(
model, force)
plt.savefig(fig_name, bbox_inches='tight')
plt.show()
def l2error(u1, params1, type1, u2, params2, type2):
if type1 == 'cfd':
radial_grid = params1['RadialGrid'].reshape(-1, 1)
dr = np.diff(radial_grid, axis=0)
dr = np.vstack((radial_grid[1], dr))
u1 = weighting(u1, 1 / dr, mode='repmat')
if type2 == 'cfd':
radial_grid = params2['RadialGrid'].reshape(-1, 1)
dr = np.diff(radial_grid, axis=0)
dr = np.vstack((radial_grid[1], dr))
u2 = weighting(u2, 1 / dr, mode='repmat')
u1_front = u1[:u1.size // 2, :]
u1_rear = u1[u1.size // 2:, :]
u2_front = u2[:u2.size // 2, :]
u2_rear = u2[u2.size // 2:, :]
# If the disk plots are differently sized, interpolation is used
if type1 != type2:
# The rmac snapshot radial grid must be scaled w.r.t. the radius R
if type1 == 'cfd':
ax1_1 = params1['RadialGrid']
ax2_1 = params1['AzimuthalGrid']
ax1_2 = params2['RadialGrid'] * params2['R']
ax2_2 = params2['AzimuthalGrid']
else:
ax1_1 = params1['RadialGrid'] * params1['R']
ax2_1 = params1['AzimuthalGrid']
ax1_2 = params2['RadialGrid']
ax2_2 = params2['AzimuthalGrid']
# Interpolation to get same dimension disk plots
u1_front, u2_front, _, _ = vector_interpol(u1_front, ax1_1, ax2_1,
u2_front, ax1_2, ax2_2)
u1_rear, u2_rear, _, _ = vector_interpol(u1_rear, ax1_1, ax2_1,
u2_rear, ax1_2, ax2_2)
# L2 Relative Errors
err_rel_front = np.linalg.norm(u2_front -
u1_front) / np.linalg.norm(u2_front)
err_rel_rear = np.linalg.norm(u2_rear - u1_rear) / np.linalg.norm(u2_rear)
err_rel_front = Decimal(err_rel_front)
err_rel_rear = Decimal(err_rel_rear)
err_rel_front = round(100 * err_rel_front, 2)
err_rel_rear = round(100 * err_rel_rear, 2)
print('')
print('L2 Relative Error for Front Rotor in %:')
print(err_rel_front)
print('L2 Relative Error for Rear Rotor in %:')
print(err_rel_rear)
print('')
return err_rel_front, err_rel_rear