def main():
num_nodes = 1
num_blades = 10
num_radial = 15
num_cp = 6
af_filename = 'airfoils/mh117.dat'
chord = 20.
theta = 5.0*np.pi/180.0
pitch = 0.
# Numbers taken from the Aviary group's study of the RVLT tiltwing
# turboelectric concept vehicle.
n_props = 4
hub_diameter = 30. # cm
prop_diameter = 15*30.48 # 15 ft in cm
c0 = np.sqrt(1.4*287.058*300.) # meters/second
rho0 = 1.4*98600./(c0*c0) # kg/m^3
omega = 236. # rad/s
# Find the thrust per rotor from the vehicle's mass.
m_full = 6367 # kg
g = 9.81 # m/s**2
thrust_vtol = m_full*g/n_props
prob = Problem()
comp = IndepVarComp()
comp.add_output('rho', val=rho0, shape=num_nodes, units='kg/m**3')
comp.add_output('mu', val=1., shape=num_nodes, units='N/m**2*s')
comp.add_output('asound', val=c0, shape=num_nodes, units='m/s')
comp.add_output('v', val=2., shape=num_nodes, units='m/s')
comp.add_output('alpha', val=0., shape=num_nodes, units='rad')
comp.add_output('incidence', val=0., shape=num_nodes, units='rad')
comp.add_output('precone', val=0., units='deg')
comp.add_output('hub_diameter', val=hub_diameter, shape=num_nodes, units='cm')
comp.add_output('prop_diameter', val=prop_diameter, shape=num_nodes, units='cm')
comp.add_output('pitch', val=pitch, shape=num_nodes, units='rad')
comp.add_output('chord_dv', val=chord, shape=num_cp, units='cm')
comp.add_output('theta_dv', val=theta, shape=num_cp, units='rad')
comp.add_output('thrust_vtol', val=thrust_vtol, shape=num_nodes, units='N')
prob.model.add_subsystem('indep_var_comp', comp, promotes=['*'])
comp = GeometryGroup(num_nodes=num_nodes, num_cp=num_cp,
num_radial=num_radial)
prob.model.add_subsystem(
'geometry_group', comp,
promotes_inputs=['hub_diameter', 'prop_diameter', 'chord_dv',
'theta_dv', 'pitch'],
promotes_outputs=['radii', 'dradii', 'chord', 'theta'])
balance_group = Group()
comp = CCBladeGroup(num_nodes=num_nodes, num_radial=num_radial,
num_blades=num_blades, af_filename=af_filename,
turbine=False)
balance_group.add_subsystem(
'ccblade_group', comp,
promotes_inputs=['radii', 'dradii', 'chord', 'theta', 'rho', 'mu',
'asound', 'v', 'precone', 'omega', 'hub_diameter',
'prop_diameter'],
promotes_outputs=['thrust', 'torque', 'efficiency'])
comp = BalanceComp()
comp.add_balance(
name='omega',
eq_units='N', lhs_name='thrust', rhs_name='thrust_vtol',
val=omega, units='rad/s',
lower=0.)
balance_group.add_subsystem('thrust_balance_comp', comp, promotes=['*'])
balance_group.linear_solver = DirectSolver(assemble_jac=True)
# balance_group.nonlinear_solver = NewtonSolver(maxiter=20, iprint=2)
# balance_group.nonlinear_solver.options['solve_subsystems'] = True
# balance_group.nonlinear_solver.options['atol'] = 1e-9
prob.model.add_subsystem('thrust_balance_group', balance_group,
promotes=['*'])
prob.model.nonlinear_solver = NewtonSolver(maxiter=20, iprint=2)
prob.model.nonlinear_solver.options['solve_subsystems'] = True
prob.model.nonlinear_solver.options['atol'] = 1e-9
prob.model.nonlinear_solver.linesearch = BoundsEnforceLS()
prob.model.nonlinear_solver.linesearch.options['iprint'] = 2
prob.setup()
prob.final_setup()
# Calculate the induced axial velocity at the rotor for hover, used for
# non-diminsionalation.
rho = prob.get_val('rho', units='kg/m**3')[0]
hub_diameter = prob.get_val('hub_diameter', units='m')[0]
prop_diameter = prob.get_val('prop_diameter', units='m')[0]
thrust_vtol = prob.get_val('thrust_vtol', units='N')[0]
A_rotor = 0.25*np.pi*(prop_diameter**2 - hub_diameter**2)
v_h = np.sqrt(thrust_vtol/(2*rho*A_rotor))
# Climb:
climb_velocity_nondim = np.linspace(0.1, 2., 10)
induced_velocity_nondim = np.zeros_like(climb_velocity_nondim)
for vc, vi in np.nditer(
[climb_velocity_nondim, induced_velocity_nondim],
op_flags=[['readonly'], ['writeonly']]):
# Run the model with the requested climb velocity.
prob.set_val('v', vc*v_h, units='m/s')
print(f"v = {prob.get_val('v', units='m/s')}")
prob.run_model()
# Calculate the area-weighted average induced velocity at the rotor.
# Need the area of each blade section.
radii = prob.get_val('radii',
units='m')
dradii = prob.get_val('dradii',
units='m')
dArea = 2*np.pi*radii*dradii
# Get the induced velocity at the rotor plane for each blade section.
Vx = prob.get_val('ccblade_group.Vx', units='m/s')
a = prob.get_val('ccblade_group.ccblade_comp.a')
# Get the area-weighted average of the induced velocity.
vi[...] = np.sum(a*Vx*dArea/A_rotor)/v_h
# Induced velocity from plain old momentum theory (for climb).
induced_velocity_mt = (
-0.5*climb_velocity_nondim + np.sqrt((0.5*climb_velocity_nondim)**2 + 1.))
fig, ax = plt.subplots()
ax.plot(climb_velocity_nondim, -induced_velocity_nondim,
label='CCBlade.jl (climb)')
ax.plot(climb_velocity_nondim, induced_velocity_mt,
label='Momentum Theory (climb)')
# Descent:
climb_velocity_nondim = np.linspace(-4., -2.5, 10)
induced_velocity_nondim = np.zeros_like(climb_velocity_nondim)
for vc, vi in np.nditer(
[climb_velocity_nondim, induced_velocity_nondim],
op_flags=[['readonly'], ['writeonly']]):
# Run the model with the requested climb velocity.
prob.set_val('v', vc*v_h, units='m/s')
print(f"vc = {vc}, v = {prob.get_val('v', units='m/s')}")
prob.run_model()
# Calculate the area-weighted average induced velocity at the rotor.
# Need the area of each blade section.
radii = prob.get_val('radii',
units='m')
dradii = prob.get_val('dradii',
units='m')
dArea = 2*np.pi*radii*dradii
# Get the induced velocity at the rotor plane for each blade section.
Vx = prob.get_val('ccblade_group.Vx', units='m/s')
a = prob.get_val('ccblade_group.ccblade_comp.a')
# Get the area-weighted average of the induced velocity.
vi[...] = np.sum(a*Vx*dArea/A_rotor)/v_h
# Induced velocity from plain old momentum theory (for descent).
induced_velocity_mt = (
-0.5*climb_velocity_nondim - np.sqrt((0.5*climb_velocity_nondim)**2 - 1.))
# Plot the induced velocity for descent.
ax.plot(climb_velocity_nondim, -induced_velocity_nondim,
label='CCBlade.jl (descent)')
ax.plot(climb_velocity_nondim, induced_velocity_mt,
label='Momentum Theory (descent)')
# # Empirical region:
# climb_velocity_nondim = np.linspace(-1.9, -1.5, 5)
# induced_velocity_nondim = np.zeros_like(climb_velocity_nondim)
# for vc, vi in np.nditer(
# [climb_velocity_nondim, induced_velocity_nondim],
# op_flags=[['readonly'], ['writeonly']]):
# # Run the model with the requested climb velocity.
# prob.set_val('v', vc*v_h, units='m/s')
# print(f"vc = {vc}, v = {prob.get_val('v', units='m/s')}")
# prob.run_model()
# # Calculate the area-weighted average induced velocity at the rotor.
# # Need the area of each blade section.
# radii = prob.get_val('radii',
# units='m')
# dradii = prob.get_val('dradii',
# units='m')
# dArea = 2*np.pi*radii*dradii
# # Get the induced velocity at the rotor plane for each blade section.
# Vx = prob.get_val('ccblade_group.Vx', units='m/s')
# a = prob.get_val('ccblade_group.ccblade_comp.a')
# # Get the area-weighted average of the induced velocity.
# vi[...] = np.sum(a*Vx*dArea/A_rotor)/v_h
# # Plot the induced velocity for the empirical region.
# ax.plot(climb_velocity_nondim, -induced_velocity_nondim,
# label='CCBlade.jl (empirical region)')
ax.set_xlabel('Vc/vh')
ax.set_ylabel('Vi/vh')
ax.legend()
fig.savefig('induced_velocity.png')
