def main():
interp = ViternaAirfoil().create_akima('mh117',
Re_scaling=False,
extend_alpha=True)
def ccblade_interp(alpha, Re, Mach):
shape = alpha.shape
x = np.concatenate(
[alpha.flatten()[:, np.newaxis],
Re.flatten()[:, np.newaxis]],
axis=-1)
y = interp(x)
y.shape = shape + (2, )
return y[..., 0], y[..., 1]
num_nodes = 1
num_blades = 3
num_radial = 15
num_cp = 6
chord = 10.
theta = np.linspace(65., 25., num_cp) * np.pi / 180.
pitch = 0.
prop_data = {
'num_radial': num_radial,
'num_cp': num_cp,
'pitch': pitch,
'chord': chord,
'theta': theta,
'spline_type': 'akima',
'B': num_blades,
'interp': interp
}
hub_diameter = 30. # cm
prop_diameter = 150. # cm
c0 = np.sqrt(1.4 * 287.058 * 300.) # meters/second
rho0 = 1.4 * 98600. / (c0 * c0) # kg/m^3
omega = 236.
prob = Problem()
comp = IndepVarComp()
comp.add_discrete_input('B', val=num_blades)
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=77.2, 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('omega', val=omega, shape=num_nodes, units='rad/s')
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')
prob.model.add_subsystem('inputs_comp', comp, promotes=['*'])
prob.model.add_subsystem('bemt_group',
BEMTGroup(num_nodes=num_nodes,
prop_data=prop_data),
promotes_inputs=[
'rho', 'mu', 'v', 'alpha', 'incidence',
'omega', 'hub_diameter', 'prop_diameter',
'pitch', 'chord_dv', 'theta_dv'
],
promotes_outputs=[
('normal_load_dist', 'openbemt_normal_load'),
('circum_load_dist', 'openbemt_circum_load')
])
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'])
comp = SimpleInflow(num_nodes=num_nodes, num_radial=num_radial)
prob.model.add_subsystem(
'inflow_comp',
comp,
promotes_inputs=['v', 'omega', 'radii', 'precone'],
promotes_outputs=['Vx', 'Vy'])
comp = CCBladeGroup(num_nodes=num_nodes,
num_radial=num_radial,
airfoil_interp=ccblade_interp,
turbine=False,
phi_residual_solve_nonlinear='bracketing')
prob.model.add_subsystem('ccblade_group',
comp,
promotes_inputs=[
'B', 'radii', 'dradii', 'chord', 'theta',
'rho', 'mu', 'asound', 'Vx', 'Vy', 'v',
'precone', 'omega', 'hub_diameter',
'prop_diameter'
],
promotes_outputs=[('Np', 'ccblade_normal_load'),
('Tp', 'ccblade_circum_load')])
prob.setup()
prob.final_setup()
prob.run_model()
make_plots(prob)
def main():
num_nodes = 1
num_blades = 3
num_radial = 15
num_cp = 6
af_filename = 'mh117.dat'
chord = np.tile(10., (num_nodes, num_cp))
theta = np.tile(np.linspace(65., 25., num_cp)*np.pi/180., (num_nodes, 1))
pitch = 0.
hub_diameter = 30. # cm
prop_diameter = 150. # cm
c0 = np.sqrt(1.4*287.058*300.) # meters/second
rho0 = 1.4*98600./(c0*c0) # kg/m^3
omega = 236.
prob = Problem()
v = np.linspace(1., 1.5, num_nodes)*77.2
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=v, 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., shape=num_nodes, units='deg')
comp.add_output('omega', val=omega, shape=num_nodes, units='rad/s')
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_nodes, num_cp), units='cm')
comp.add_output('theta_dv', val=theta, shape=(num_nodes, num_cp), units='rad')
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'])
comp = SimpleInflow(num_nodes=num_nodes, num_radial=num_radial)
prob.model.add_subsystem(
'inflow_comp', comp,
promotes_inputs=['v', 'omega', 'radii', 'precone'],
promotes_outputs=['Vx', 'Vy'])
comp = CCBladeGroup(num_nodes=num_nodes, num_radial=num_radial,
num_blades=num_blades, af_filename=af_filename,
turbine=False)
prob.model.add_subsystem(
'ccblade_group', comp,
promotes_inputs=['radii', 'dradii', 'chord', 'theta', 'rho', 'mu',
'asound', 'v', 'precone', 'omega', 'Vx', 'Vy',
'precone', 'hub_diameter', 'prop_diameter'],
promotes_outputs=['thrust', 'torque', 'efficiency'])
# prob.model.add_design_var('chord_dv', lower=1., upper=20.,
# scaler=5e-2)
# prob.model.add_design_var('theta_dv',
# lower=20.*np.pi/180., upper=90*np.pi/180.)
# prob.model.add_objective('efficiency', scaler=-1.,)
# prob.model.add_constraint('thrust', equals=700., scaler=1e-3,
# indices=np.arange(num_nodes))
# prob.driver = pyOptSparseDriver()
# prob.driver.options['optimizer'] = 'SNOPT'
prob.setup()
prob.final_setup()
st = time.time()
# prob.run_driver()
prob.run_model()
elapsed_time = time.time() - st
make_plots(prob)
return elapsed_time
def test_hover(self):
# num_nodes = 40
nstart = 0
nend = 39
num_nodes = nend - nstart + 1
chord = 0.060
theta = 0.0
Rtip = 0.656
Rhub = 0.19 * Rtip
rho = 1.225
omega = 800.0 * np.pi / 30
Vinf = 0.0
turbine = False
B = 3
r = np.linspace(Rhub + 0.01 * Rtip, Rtip - 0.01 * Rtip, 30)
num_radial = r.shape[-1]
r = np.tile(r, (num_nodes, 1))
chord = np.tile(chord, (num_nodes, num_radial))
theta = np.tile(theta, (num_nodes, num_radial))
# Airfoil interpolator.
af = af_from_files(["airfoils/naca0012v2.txt"])
pitch = np.linspace(1e-4, 20 * np.pi / 180, 40)[nstart:nend + 1]
prob = om.Problem()
comp = om.IndepVarComp()
comp.add_output('v', val=Vinf, shape=num_nodes, units='m/s')
comp.add_output('omega', val=np.tile(omega, num_nodes), units='rad/s')
comp.add_output('radii',
val=r,
shape=(num_nodes, num_radial),
units='m')
comp.add_output('chord',
val=chord,
shape=(num_nodes, num_radial),
units='m')
comp.add_output('theta',
val=theta,
shape=(num_nodes, num_radial),
units='rad')
comp.add_output('precone', val=0., shape=num_nodes, units='rad')
comp.add_output('rho', val=rho, shape=(num_nodes, 1), units='kg/m**3')
comp.add_output('mu', val=1.0, shape=(num_nodes, 1), units='N/m**2*s')
comp.add_output('asound', val=1.0, shape=(num_nodes, 1), units='m/s')
comp.add_output('hub_radius', val=Rhub, shape=num_nodes, units='m')
comp.add_output('prop_radius', val=Rtip, shape=num_nodes, units='m')
comp.add_output('pitch', val=pitch, shape=num_nodes, units='rad')
prob.model.add_subsystem('ivc', comp, promotes_outputs=['*'])
comp = SimpleInflow(num_nodes=num_nodes, num_radial=num_radial)
prob.model.add_subsystem(
"simple_inflow",
comp,
promotes_inputs=["v", "omega", "radii", "precone"],
promotes_outputs=["Vx", "Vy"])
comp = make_component(
CCBladeResidualComp(num_nodes=num_nodes,
num_radial=num_radial,
B=B,
af=af,
turbine=turbine))
comp.linear_solver = om.DirectSolver(assemble_jac=True)
prob.model.add_subsystem('ccblade',
comp,
promotes_inputs=[('r', 'radii'), 'chord',
'theta', 'Vx', 'Vy', 'rho',
'mu', 'asound',
('Rhub', 'hub_radius'),
('Rtip', 'prop_radius'),
'precone', 'pitch'],
promotes_outputs=['Np', 'Tp'])
comp = FunctionalsComp(num_nodes=num_nodes,
num_radial=num_radial,
num_blades=B)
prob.model.add_subsystem(
'ccblade_torquethrust_comp',
comp,
promotes_inputs=[
'hub_radius', 'prop_radius', 'radii', 'Np', 'Tp', 'v', 'omega'
],
promotes_outputs=['thrust', 'torque', 'efficiency'])
prob.setup()
prob.final_setup()
prob.run_model()
# these are not directly from the experimental data, but have been compared to the experimental data and compare favorably.
# this is more of a regression test on the Vx=0 case
CTcomp = np.array([
9.452864991304056e-9, 6.569947366946672e-5, 0.00022338783939012262,
0.0004420355541809959, 0.0007048495858030926,
0.0010022162314665929, 0.0013268531109981317,
0.0016736995380106938, 0.0020399354072946035,
0.0024223576277264307, 0.0028189858460418893,
0.0032281290309981213, 0.003649357660426685, 0.004081628946214875,
0.004526034348853718, 0.004982651929181267, 0.0054553705714941,
0.005942700094508395, 0.006447634897014323, 0.006963626871239654,
0.007492654931894796, 0.00803866268066438, 0.008597914974368199,
0.009163315934297088, 0.00973817187875574, 0.010309276997090536,
0.010827599471613264, 0.011322361524464346, 0.01180210507896255,
0.012276543435307877, 0.012749323136224754, 0.013223371028562213,
0.013697833731701945, 0.01417556699620018, 0.014646124777465859,
0.015112116772851365, 0.015576452747370885, 0.01602507607909594,
0.016461827164870473, 0.016880126012974343
])
CQcomp = np.array([
0.000226663607327854, 0.0002270862930229147, 0.0002292742856722754,
0.00023412703235791698, 0.00024192624628054639,
0.0002525855612031453, 0.00026638347417704255,
0.00028314784456601373, 0.00030299181501156373,
0.0003259970210015136, 0.00035194661281707764,
0.00038102864688744595, 0.0004132249034847219,
0.00044859355432807347, 0.0004873204055790553,
0.0005293656187218555, 0.0005753409000182888,
0.0006250099998058788, 0.0006788861946930185,
0.0007361096750412038, 0.0007970800153713466,
0.0008624036743669367, 0.0009315051772818803,
0.0010035766105979213, 0.0010791941808362153,
0.0011566643573792704, 0.001229236439467123, 0.0013007334425769355,
0.001372124993921022, 0.0014449961686871802, 0.0015197156782734364,
0.0015967388663224156, 0.0016761210460920718,
0.0017578748614666766, 0.0018409716992061841,
0.0019248522013432586, 0.0020103360819251357, 0.002096387027559033,
0.002182833604491109, 0.0022686470790128036
])
T = prob.get_val('thrust', units='N')
Q = prob.get_val('torque', units='N*m')
A = np.pi * Rtip**2
CT = T / (rho * A * (omega * Rtip)**2)
CQ = Q / (rho * A * (omega * Rtip)**2 * Rtip)
assert_allclose(CT, CTcomp[nstart:nend + 1], atol=1e-4, rtol=1)
assert_allclose(CQ, CQcomp[nstart:nend + 1], atol=1e-4, rtol=1)
def main():
interp = ViternaAirfoil().create_akima(
'mh117', Re_scaling=False, extend_alpha=True)
def ccblade_interp(alpha, Re, Mach):
shape = alpha.shape
x = np.concatenate(
[
alpha.flatten()[:, np.newaxis],
Re.flatten()[:, np.newaxis]
], axis=-1)
y = interp(x)
y.shape = shape + (2,)
return y[..., 0], y[..., 1]
num_nodes = 1
num_blades = 3
num_radial = 15
num_cp = 6
chord = 10.
theta = np.linspace(65., 25., num_cp)*np.pi/180.
pitch = 0.
hub_diameter = 30. # cm
prop_diameter = 150. # cm
c0 = np.sqrt(1.4*287.058*300.) # meters/second
rho0 = 1.4*98600./(c0*c0) # kg/m^3
omega = 236.
prob = Problem()
comp = IndepVarComp()
comp.add_discrete_input('B', val=num_blades)
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=77.2, 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('omega', val=omega, shape=num_nodes, units='rad/s')
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')
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'])
comp = SimpleInflow(num_nodes=num_nodes, num_radial=num_radial)
prob.model.add_subsystem(
'inflow_comp', comp,
promotes_inputs=['v', 'omega', 'radii', 'precone'],
promotes_outputs=['Vx', 'Vy'])
comp = CCBladeGroup(num_nodes=num_nodes, num_radial=num_radial,
num_blades=num_blades,
airfoil_interp=ccblade_interp, turbine=False,
phi_residual_solve_nonlinear='bracketing')
prob.model.add_subsystem(
'ccblade_group', comp,
promotes_inputs=['radii', 'dradii', 'chord', 'theta', 'rho',
'mu', 'asound', 'v', 'omega', 'Vx', 'Vy', 'precone',
'hub_diameter', 'prop_diameter'],
promotes_outputs=['thrust', 'torque', 'efficiency'])
prob.model.add_design_var('chord_dv', lower=1., upper=20.,
scaler=5e-2)
prob.model.add_design_var('theta_dv',
lower=20.*np.pi/180., upper=90*np.pi/180.)
prob.model.add_objective('efficiency', scaler=-1.,)
prob.model.add_constraint('thrust', equals=700., scaler=1e-3,
indices=np.arange(num_nodes))
prob.driver = pyOptSparseDriver()
prob.driver.options['optimizer'] = 'SNOPT'
prob.setup()
prob.final_setup()
st = time.time()
prob.run_driver()
elapsed_time = time.time() - st
make_plots(prob)
return elapsed_time
def test_camber(self):
# Copied from CCBlade.jl/test/runtests.jl
# inputs
chord = 0.10
D = 1.6
RPM = 2100
rho = 1.225
pitch = 1.0 # pitch distance in meters.
# --- rotor definition ---
turbine = False
Rhub = 0.0
Rtip = D / 2
Rhub_eff = 1e-6 # something small to eliminate hub effects
Rtip_eff = 100.0 # something large to eliminate tip effects
B = 2 # number of blades
# --- section definitions ---
num_nodes = 1
R = D / 2.0
r = np.linspace(R / 10, R, 11)
dr = r[1] - r[0]
r = np.tile(r, (num_nodes, 1))
dr = np.tile(dr, r.shape)
theta = np.arctan(pitch / (2 * np.pi * r))
jlmain.eval("""
function affunc(alpha, Re, M)
alpha0 = -3*pi/180
cl = 6.2*(alpha - alpha0)
cd = 0.008 - 0.003*cl + 0.01*cl*cl
return cl, cd
end
""")
affunc = jlmain.affunc
prob = om.Problem()
num_radial = r.shape[-1]
comp = om.IndepVarComp()
comp.add_output('v', val=[5.0], units='m/s')
comp.add_output('omega', val=np.tile(RPM, num_nodes), units='rpm')
comp.add_output('radii', val=r, units='m')
comp.add_output('dradii', val=dr, units='m')
comp.add_output('chord',
val=chord,
shape=(num_nodes, num_radial),
units='m')
comp.add_output('theta',
val=theta,
shape=(num_nodes, num_radial),
units='rad')
comp.add_output('precone', val=0., shape=num_nodes, units='rad')
comp.add_output('rho', val=rho, shape=(num_nodes, 1), units='kg/m**3')
comp.add_output('mu', val=1.0, shape=(num_nodes, 1), units='N/m**2*s')
comp.add_output('asound', val=1.0, shape=(num_nodes, 1), units='m/s')
comp.add_output('hub_radius_eff',
val=Rhub_eff,
shape=num_nodes,
units='m')
comp.add_output('prop_radius_eff',
val=Rtip_eff,
shape=num_nodes,
units='m')
comp.add_output('hub_radius', val=Rhub, shape=num_nodes, units='m')
comp.add_output('prop_radius', val=Rtip, shape=num_nodes, units='m')
comp.add_output('pitch', val=0.0, shape=num_nodes, units='rad')
prob.model.add_subsystem('ivc', comp, promotes_outputs=['*'])
comp = SimpleInflow(num_nodes=num_nodes, num_radial=num_radial)
prob.model.add_subsystem(
"simple_inflow",
comp,
promotes_inputs=["v", "omega", "radii", "precone"],
promotes_outputs=["Vx", "Vy"])
comp = make_component(
CCBladeResidualComp(num_nodes=num_nodes,
num_radial=num_radial,
B=B,
af=affunc,
turbine=turbine))
comp.linear_solver = om.DirectSolver(assemble_jac=True)
prob.model.add_subsystem('ccblade',
comp,
promotes_inputs=[('r', 'radii'), 'chord',
'theta', 'Vx', 'Vy', 'rho',
'mu', 'asound',
('Rhub', 'hub_radius_eff'),
('Rtip', 'prop_radius_eff'),
'precone', 'pitch'],
promotes_outputs=['Np', 'Tp'])
prob.setup()
prob.final_setup()
prob.run_model()
Np = prob.get_val('Np', units='N/m')
Tp = prob.get_val('Tp', units='N/m')
T = np.sum(Np * dr) * B
Q = np.sum(r * Tp * dr) * B
assert_allclose(1223.0506862888788, T, atol=1e-8)
assert_allclose(113.79919472569034, Q, atol=1e-8)
assert_allclose(prob.get_val('Np', units='N/m')[0, 3],
427.3902632382494,
atol=1e-8,
rtol=1)
assert_allclose(prob.get_val('Tp', units='N/m')[0, 3],
122.38414345762305,
atol=1e-8,
rtol=1)
assert_allclose(prob.get_val('ccblade.a')[0, 3],
2.2845512476210943,
atol=1e-8,
rtol=1)
assert_allclose(prob.get_val('ccblade.ap')[0, 3],
0.05024950801920044,
atol=1e-8,
rtol=1)
assert_allclose(prob.get_val('ccblade.u', units='m/s')[0, 3],
11.422756238105471,
atol=1e-8,
rtol=1)
assert_allclose(prob.get_val('ccblade.v', units='m/s')[0, 3],
3.2709314141649575,
atol=1e-8,
rtol=1)
assert_allclose(prob.get_val('ccblade.phi', units='rad')[0, 3],
0.2596455971546484,
atol=1e-8,
rtol=1)
# assert_allclose(prob.get_val('ccblade.alpha', units='rad')[0, 3], 0.23369406105568025, atol=1e-8, rtol=1)
assert_allclose(prob.get_val('ccblade.W', units='m/s')[0, 3],
63.96697566502531,
atol=1e-8,
rtol=1)
assert_allclose(prob.get_val('ccblade.cl')[0, 3],
1.773534419416163,
atol=1e-8,
rtol=1)
assert_allclose(prob.get_val('ccblade.cd')[0, 3],
0.03413364011028978,
atol=1e-8,
rtol=1)
assert_allclose(prob.get_val('ccblade.cn')[0, 3],
1.7053239640124302,
atol=1e-8,
rtol=1)
assert_allclose(prob.get_val('ccblade.ct')[0, 3],
0.48832327407767123,
atol=1e-8,
rtol=1)
assert_allclose(prob.get_val('ccblade.F')[0, 3],
1.0,
atol=1e-8,
rtol=1)
assert_allclose(prob.get_val('ccblade.G')[0, 3],
1.0,
atol=1e-8,
rtol=1)
theta = np.arctan(pitch / (2 * np.pi * r)) - 3 * np.pi / 180
prob.set_val('theta', theta, units='rad')
prob.run_model()
Np = prob.get_val('Np', units='N/m')
Tp = prob.get_val('Tp', units='N/m')
T = np.sum(Np * dr) * B
Q = np.sum(r * Tp * dr) * B
assert_allclose(T, 1e3 * 0.962407923825140, atol=1e-3)
assert_allclose(Q, 1e2 * 0.813015017103876, atol=1e-4)
def test_multiple_adv_ratios(self):
# num_nodes = 20
nstart = 0
nend = 19
num_nodes = nend - nstart + 1
r = 0.0254 * np.array([
0.7526, 0.7928, 0.8329, 0.8731, 0.9132, 0.9586, 1.0332, 1.1128,
1.1925, 1.2722, 1.3519, 1.4316, 1.5114, 1.5911, 1.6708, 1.7505,
1.8302, 1.9099, 1.9896, 2.0693, 2.1490, 2.2287, 2.3084, 2.3881,
2.4678, 2.5475, 2.6273, 2.7070, 2.7867, 2.8661, 2.9410
]).reshape(1, -1)
num_radial = r.shape[-1]
r = np.tile(r, (num_nodes, 1))
chord = 0.0254 * np.array([
0.6270, 0.6255, 0.6231, 0.6199, 0.6165, 0.6125, 0.6054, 0.5973,
0.5887, 0.5794, 0.5695, 0.5590, 0.5479, 0.5362, 0.5240, 0.5111,
0.4977, 0.4836, 0.4689, 0.4537, 0.4379, 0.4214, 0.4044, 0.3867,
0.3685, 0.3497, 0.3303, 0.3103, 0.2897, 0.2618, 0.1920
]).reshape((1, num_radial))
chord = np.tile(chord, (num_nodes, 1))
theta = np.pi / 180.0 * np.array([
40.2273, 38.7657, 37.3913, 36.0981, 34.8803, 33.5899, 31.6400,
29.7730, 28.0952, 26.5833, 25.2155, 23.9736, 22.8421, 21.8075,
20.8586, 19.9855, 19.1800, 18.4347, 17.7434, 17.1005, 16.5013,
15.9417, 15.4179, 14.9266, 14.4650, 14.0306, 13.6210, 13.2343,
12.8685, 12.5233, 12.2138
]).reshape((1, num_radial))
theta = np.tile(theta, (num_nodes, 1))
rho = 1.225
Rhub = 0.0254 * .5
Rtip = 0.0254 * 3.0
B = 2 # number of blades
turbine = False
J = np.linspace(0.1, 0.9, 20)[nstart:nend + 1] # advance ratio
# J = np.linspace(0.1, 0.9, 20)
omega = 8000.0 * np.pi / 30
n = omega / (2 * np.pi)
D = 2 * Rtip
Vinf = J * D * n
dr = r[0, 1] - r[0, 0]
# Airfoil interpolator.
af = af_from_files(["airfoils/NACA64_A17.dat"])
prob = om.Problem()
comp = om.IndepVarComp()
comp.add_output('v', val=Vinf, units='m/s')
comp.add_output('omega', val=np.tile(omega, num_nodes), units='rad/s')
comp.add_output('radii',
val=r,
shape=(num_nodes, num_radial),
units='m')
comp.add_output('dradii',
val=dr,
shape=(num_nodes, num_radial),
units='m')
comp.add_output('chord',
val=chord,
shape=(num_nodes, num_radial),
units='m')
comp.add_output('theta',
val=theta,
shape=(num_nodes, num_radial),
units='rad')
comp.add_output('precone', val=0., shape=num_nodes, units='rad')
comp.add_output('rho', val=rho, shape=(num_nodes, 1), units='kg/m**3')
comp.add_output('mu', val=1.0, shape=(num_nodes, 1), units='N/m**2*s')
comp.add_output('asound', val=1.0, shape=(num_nodes, 1), units='m/s')
comp.add_output('hub_radius', val=Rhub, shape=num_nodes, units='m')
comp.add_output('prop_radius', val=Rtip, shape=num_nodes, units='m')
comp.add_output('pitch', val=0.0, shape=num_nodes, units='rad')
prob.model.add_subsystem('ivc', comp, promotes_outputs=['*'])
comp = SimpleInflow(num_nodes=num_nodes, num_radial=num_radial)
prob.model.add_subsystem(
"simple_inflow",
comp,
promotes_inputs=["v", "omega", "radii", "precone"],
promotes_outputs=["Vx", "Vy"])
comp = make_component(
CCBladeResidualComp(num_nodes=num_nodes,
num_radial=num_radial,
B=B,
af=af,
turbine=turbine))
comp.linear_solver = om.DirectSolver(assemble_jac=True)
prob.model.add_subsystem('ccblade',
comp,
promotes_inputs=[('r', 'radii'), 'chord',
'theta', 'Vx', 'Vy', 'rho',
'mu', 'asound',
('Rhub', 'hub_radius'),
('Rtip', 'prop_radius'),
'precone', 'pitch'],
promotes_outputs=['Np', 'Tp'])
comp = FunctionalsComp(num_nodes=num_nodes,
num_radial=num_radial,
num_blades=B)
prob.model.add_subsystem(
'ccblade_torquethrust_comp',
comp,
promotes_inputs=[
'hub_radius', 'prop_radius', 'radii', 'Np', 'Tp', 'v', 'omega'
],
promotes_outputs=['thrust', 'torque', 'efficiency'])
prob.setup()
prob.final_setup()
prob.run_model()
CTtest = np.array([
0.12007272369269596, 0.11685168049381163, 0.113039580103141,
0.1085198115279716, 0.10319003920478352, 0.09725943970861005,
0.09086388629270399, 0.0839976424307642, 0.07671734636145504,
0.06920018426158829, 0.06146448769092457, 0.05351803580676398,
0.04536760940952122, 0.037021384017275026, 0.028444490366496933,
0.019460037067085302, 0.0101482712198453, 0.0009431056296630114,
-0.008450506440868786, -0.018336716057292365
])[nstart:nend + 1]
CPtest = np.array([
0.04881364095025621, 0.0495814889974431, 0.05010784517185014,
0.0503081363797726, 0.05016808708430908, 0.04959928236064606,
0.04857913603557237, 0.0470530147170992, 0.045034787733797786,
0.042554367414565766, 0.03958444136790737, 0.036104210007643946,
0.032085430933805684, 0.02750011065614528, 0.022307951002430132,
0.016419276860939747, 0.009846368564156775, 0.002833135813003493,
-0.004876593891333574, -0.013591625085158215
])[nstart:nend + 1]
etatest = np.array([
0.24598190455626265, 0.3349080300487075, 0.4155652767326253,
0.48818637673414306, 0.5521115225679999, 0.6089123481436948,
0.6595727776885079, 0.7046724703349897, 0.7441662053086512,
0.7788447616541276, 0.8090611349633181, 0.8347808848055981,
0.8558196582739432, 0.8715046719672315, 0.8791362131978436,
0.8670633642311274, 0.7974063895510229, 0.2715632768892098, 0.0,
0.0
])[nstart:nend + 1]
T = prob.get_val('thrust', units='N')
Q = prob.get_val('torque', units='N*m')
eff = prob.get_val('efficiency')
CT = T / (rho * n**2 * D**4)
CQ = Q / (rho * n**2 * D**5) * 2 * np.pi
assert_allclose(CT, CTtest, atol=1e-3, rtol=1)
assert_allclose(CQ, CPtest, atol=1e-3, rtol=1)
assert_allclose(eff[T > 0.0], etatest[T > 0.0], atol=1e-3, rtol=1)
def test_propeller_aero4students(self):
# Copied from CCBlade.jl/test/runtests.jl
# -------- verification: propellers. using script at http://www.aerodynamics4students.com/propulsion/blade-element-propeller-theory.php ------
# I increased their tolerance to 1e-6
# inputs
chord = 0.10
D = 1.6
RPM = 2100
rho = 1.225
pitch = 1.0 # pitch distance in meters.
# --- rotor definition ---
turbine = False
# Rhub = 0.0
# Rtip = D/2
Rhub_eff = 1e-6 # something small to eliminate hub effects
Rtip_eff = 100.0 # something large to eliminate tip effects
B = 2 # number of blades
# --- section definitions ---
num_nodes = 60
R = D / 2.0
r = np.linspace(R / 10, R, 11)
dr = r[1] - r[0]
r = np.tile(r, (num_nodes, 1))
theta = np.arctan(pitch / (2 * np.pi * r))
jlmain.eval("""
function affunc(alpha, Re, M)
cl = 6.2*alpha
cd = 0.008 - 0.003*cl + 0.01*cl*cl
return cl, cd
end
""")
affunc = jlmain.affunc
prob = om.Problem()
num_radial = r.shape[-1]
comp = om.IndepVarComp()
comp.add_output('v', val=np.arange(1, 60 + 1)[:num_nodes], units='m/s')
comp.add_output('omega', val=np.tile(RPM, num_nodes), units='rpm')
comp.add_output('radii', val=r, units='m')
comp.add_output('chord',
val=chord,
shape=(num_nodes, num_radial),
units='m')
comp.add_output('theta',
val=theta,
shape=(num_nodes, num_radial),
units='rad')
comp.add_output('precone', val=0., shape=num_nodes, units='rad')
comp.add_output('rho', val=rho, shape=(num_nodes, 1), units='kg/m**3')
comp.add_output('mu', val=1.0, shape=(num_nodes, 1), units='N/m**2*s')
comp.add_output('asound', val=1.0, shape=(num_nodes, 1), units='m/s')
comp.add_output('hub_radius', val=Rhub_eff, shape=num_nodes, units='m')
comp.add_output('prop_radius',
val=Rtip_eff,
shape=num_nodes,
units='m')
comp.add_output('pitch', val=0.0, shape=num_nodes, units='rad')
prob.model.add_subsystem('ivc', comp, promotes_outputs=['*'])
comp = SimpleInflow(num_nodes=num_nodes, num_radial=num_radial)
prob.model.add_subsystem(
"simple_inflow",
comp,
promotes_inputs=["v", "omega", "radii", "precone"],
promotes_outputs=["Vx", "Vy"])
comp = make_component(
CCBladeResidualComp(num_nodes=num_nodes,
num_radial=num_radial,
B=B,
af=affunc,
turbine=turbine))
comp.linear_solver = om.DirectSolver(assemble_jac=True)
prob.model.add_subsystem('ccblade',
comp,
promotes_inputs=[('r', 'radii'), 'chord',
'theta', 'Vx', 'Vy', 'rho',
'mu', 'asound',
('Rhub', 'hub_radius'),
('Rtip', 'prop_radius'),
'precone', 'pitch'],
promotes_outputs=['Np', 'Tp'])
prob.setup()
prob.final_setup()
prob.run_model()
Np = prob.get_val('Np', units='N/m')
Tp = prob.get_val('Tp', units='N/m')
T = np.sum(Np * dr, axis=1) * B
Q = np.sum(r * Tp * dr, axis=1) * B
tsim = 1e3 * np.array([
1.045361193032356, 1.025630300048415, 1.005234466788998,
0.984163367036026, 0.962407923825140, 0.939960208707079,
0.916813564966455, 0.892962691000145, 0.868403981825492,
0.843134981103815, 0.817154838249790, 0.790463442573673,
0.763063053839278, 0.734956576558370, 0.706148261507327,
0.676643975451150, 0.646450304160057, 0.615575090105131,
0.584027074365864, 0.551815917391907, 0.518952127358381,
0.485446691671386, 0.451311288662196, 0.416557935286392,
0.381199277009438, 0.345247916141561, 0.308716772800348,
0.271618894441869, 0.233967425339051, 0.195775319296371,
0.157055230270717, 0.117820154495231, 0.078082266879117,
0.037854059197644, -0.002852754149850, -0.044026182837742,
-0.085655305814570, -0.127728999394140, -0.170237722799272,
-0.213169213043848, -0.256515079286031, -0.300266519551194,
-0.344414094748869, -0.388949215983616, -0.433863576642539,
-0.479150401337354, -0.524801553114807, -0.570810405128802,
-0.617169893200684, -0.663873474163182, -0.710915862524620,
-0.758291877949762, -0.805995685105502, -0.854022273120508,
-0.902366919041604, -0.951025170820984, -0.999992624287163,
-1.049265666456123, -1.098840222937414, -1.148712509929845
])
qsim = 1e2 * np.array([
0.803638686218187, 0.806984572453978, 0.809709290183008,
0.811743686838315, 0.813015017103876, 0.813446921530685,
0.812959654049620, 0.811470393912576, 0.808893852696513,
0.805141916379142, 0.800124489784850, 0.793748780791057,
0.785921727832179, 0.776548246109426, 0.765532528164390,
0.752778882688809, 0.738190986274448, 0.721673076180745,
0.703129918771009, 0.682467282681955, 0.659592296506578,
0.634413303042323, 0.606840565246423, 0.576786093366321,
0.544164450503912, 0.508891967461804, 0.470887571011192,
0.430072787279711, 0.386371788290446, 0.339711042057184,
0.290019539402947, 0.237229503458026, 0.181274942660876,
0.122093307308376, 0.059623821454727, -0.006190834182631,
-0.075406684829235, -0.148076528546541, -0.224253047813501,
-0.303980950928302, -0.387309291734422, -0.474283793689904,
-0.564946107631716, -0.659336973911858, -0.757495165410553,
-0.859460291551374, -0.965266648683888, -1.074949504731187,
-1.188540970723477, -1.306072104649531, -1.427575034895290,
-1.553080300508925, -1.682614871422754, -1.816205997296014,
-1.953879956474228, -2.095662107769925, -2.241576439746701,
-2.391647474158875, -2.545897099743367, -2.704346566395035
])
assert_allclose(T, tsim[:num_nodes], atol=1e-2, rtol=1)
assert_allclose(Q, qsim[:num_nodes], atol=2e-3, rtol=1)
# Run with v = 20.0 m/s.
prob.set_val('v', 20.0, units='m/s', indices=0)
prob.run_model()
Vhub = prob.get_val('v', units='m/s', indices=0)
omega = prob.get_val('omega', units='rad/s', indices=0)
Np = prob.get_val('Np', units='N/m', indices=0)
Tp = prob.get_val('Tp', units='N/m', indices=0)
T = np.sum(Np * dr) * B
Q = np.sum(r[0, :] * Tp * dr) * B
P = Q * omega
n = omega / (2 * np.pi)
CT = T / (rho * n**2 * D**4)
CQ = Q / (rho * n**2 * D**5)
eff = T * Vhub / P
assert_allclose(CT, 0.056110238632657, atol=1e-7, rtol=1)
assert_allclose(CQ, 0.004337202960642, atol=1e-8, rtol=1)
assert_allclose(eff, 0.735350632777002, atol=1e-6, rtol=1)
def test_openbemt_optimization(self):
interp = ViternaAirfoil().create_akima('mh117',
Re_scaling=False,
extend_alpha=True)
def ccblade_interp(alpha, Re, Mach):
shape = alpha.shape
x = np.concatenate(
[alpha.flatten()[:, np.newaxis],
Re.flatten()[:, np.newaxis]],
axis=-1)
y = interp(x)
y.shape = shape + (2, )
return y[..., 0], y[..., 1]
num_nodes = 1
num_blades = 3
num_radial = 15
num_cp = 6
chord = 10.
theta = np.linspace(65., 25., num_cp) * np.pi / 180.
pitch = 0.
prop_data = {
'num_radial': num_radial,
'num_cp': num_cp,
'pitch': pitch,
'chord': chord,
'theta': theta,
'spline_type': 'akima',
'B': num_blades,
'interp': interp
}
hub_diameter = 30. # cm
prop_diameter = 150. # cm
c0 = np.sqrt(1.4 * 287.058 * 300.) # meters/second
rho0 = 1.4 * 98600. / (c0 * c0) # kg/m^3
omega = 236.
prob_ccblade = om.Problem()
prob_openbemt = om.Problem()
comp = om.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=77.2, 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('omega', val=omega, shape=num_nodes, units='rad/s')
comp.add_output('hub_diameter', val=hub_diameter, units='cm')
comp.add_output('prop_diameter', val=prop_diameter, 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')
prob_ccblade.model.add_subsystem('indep_var_comp',
comp,
promotes=['*'])
prob_openbemt.model.add_subsystem('indep_var_comp',
comp,
promotes=['*'])
comp = GeometryGroup(num_nodes=num_nodes,
num_cp=num_cp,
num_radial=num_radial)
prob_ccblade.model.add_subsystem(
'geometry_group',
comp,
promotes_inputs=[
'hub_diameter', 'prop_diameter', 'chord_dv', 'theta_dv',
'pitch'
],
promotes_outputs=['radii', 'dradii', 'chord', 'theta'])
comp = SimpleInflow(num_nodes=num_nodes, num_radial=num_radial)
prob_ccblade.model.add_subsystem(
'inflow_comp',
comp,
promotes_inputs=['v', 'omega', 'radii', 'precone'],
promotes_outputs=['Vx', 'Vy'])
comp = CCBladeGroup(num_nodes=num_nodes,
num_radial=num_radial,
num_blades=num_blades,
airfoil_interp=ccblade_interp,
turbine=False)
prob_ccblade.model.add_subsystem(
'ccblade_group',
comp,
promotes_inputs=[
'radii', 'dradii', 'chord', 'theta', 'rho', 'mu', 'asound',
'v', 'omega', 'Vx', 'Vy', 'precone', 'hub_diameter',
'prop_diameter'
],
promotes_outputs=['thrust', 'torque', 'efficiency'])
prob_ccblade.model.add_design_var('chord_dv',
lower=1.,
upper=20.,
scaler=5e-2)
prob_ccblade.model.add_design_var('theta_dv',
lower=20. * np.pi / 180.,
upper=90 * np.pi / 180.)
prob_ccblade.model.add_objective(
'efficiency',
scaler=-1.,
)
prob_ccblade.model.add_constraint('thrust',
equals=700.,
scaler=1e-3,
indices=np.arange(num_nodes))
prob_ccblade.driver = om.pyOptSparseDriver()
prob_ccblade.driver.options['optimizer'] = 'SNOPT'
prob_ccblade.setup()
prob_ccblade.final_setup()
prob_ccblade.run_driver()
ccblade_normal_load = prob_ccblade.get_val('ccblade_group.Np',
units='N/m') * num_blades
ccblade_circum_load = prob_ccblade.get_val('ccblade_group.Tp',
units='N/m') * num_blades
prob_openbemt.model.add_subsystem(
'bemt_group',
BEMTGroup(num_nodes=num_nodes, prop_data=prop_data),
promotes_inputs=[
'rho', 'mu', 'v', 'alpha', 'incidence', 'omega',
'hub_diameter', 'prop_diameter', 'pitch', 'chord_dv',
'theta_dv'
],
promotes_outputs=[('normal_load_dist', 'openbemt_normal_load'),
('circum_load_dist', 'openbemt_circum_load'),
'dradii', 'thrust', 'efficiency'])
prob_openbemt.model.add_design_var('chord_dv',
lower=1.,
upper=20.,
scaler=5e-2)
prob_openbemt.model.add_design_var('theta_dv',
lower=20. * np.pi / 180.,
upper=90 * np.pi / 180.)
prob_openbemt.model.add_objective(
'efficiency',
scaler=-1.,
)
prob_openbemt.model.add_constraint('thrust',
equals=700.,
scaler=1e-3,
indices=np.arange(num_nodes))
prob_openbemt.driver = om.pyOptSparseDriver()
prob_openbemt.driver.options['optimizer'] = 'SNOPT'
prob_openbemt.setup()
prob_openbemt.final_setup()
prob_openbemt.model.bemt_group.phi_group.nonlinear_solver.options[
'iprint'] = 0
prob_openbemt.run_driver()
openbemt_normal_load = prob_openbemt.get_val('openbemt_normal_load',
units='N')
openbemt_circum_load = prob_openbemt.get_val('openbemt_circum_load',
units='N')
dradii = prob_openbemt.get_val('dradii', units='m')
openbemt_normal_load /= dradii
openbemt_circum_load /= dradii
assert_rel_error(self, ccblade_normal_load, openbemt_normal_load, 1e-2)
assert_rel_error(self, ccblade_circum_load, openbemt_circum_load, 1e-2)
def test_multiple_adv_ratios(self):
# num_nodes = 20
nstart = 0
nend = 19
num_nodes = nend - nstart + 1
r = 0.0254 * np.array([
0.7526, 0.7928, 0.8329, 0.8731, 0.9132, 0.9586, 1.0332, 1.1128,
1.1925, 1.2722, 1.3519, 1.4316, 1.5114, 1.5911, 1.6708, 1.7505,
1.8302, 1.9099, 1.9896, 2.0693, 2.1490, 2.2287, 2.3084, 2.3881,
2.4678, 2.5475, 2.6273, 2.7070, 2.7867, 2.8661, 2.9410
]).reshape(1, -1)
num_radial = r.shape[-1]
r = np.tile(r, (num_nodes, 1))
chord = 0.0254 * np.array([
0.6270, 0.6255, 0.6231, 0.6199, 0.6165, 0.6125, 0.6054, 0.5973,
0.5887, 0.5794, 0.5695, 0.5590, 0.5479, 0.5362, 0.5240, 0.5111,
0.4977, 0.4836, 0.4689, 0.4537, 0.4379, 0.4214, 0.4044, 0.3867,
0.3685, 0.3497, 0.3303, 0.3103, 0.2897, 0.2618, 0.1920
]).reshape((1, num_radial))
chord = np.tile(chord, (num_nodes, 1))
theta = np.pi / 180.0 * np.array([
40.2273, 38.7657, 37.3913, 36.0981, 34.8803, 33.5899, 31.6400,
29.7730, 28.0952, 26.5833, 25.2155, 23.9736, 22.8421, 21.8075,
20.8586, 19.9855, 19.1800, 18.4347, 17.7434, 17.1005, 16.5013,
15.9417, 15.4179, 14.9266, 14.4650, 14.0306, 13.6210, 13.2343,
12.8685, 12.5233, 12.2138
]).reshape((1, num_radial))
theta = np.tile(theta, (num_nodes, 1))
rho = 1.225
Rhub = 0.0254 * .5
Rtip = 0.0254 * 3.0
B = 2 # number of blades
turbine = False
J = np.linspace(0.1, 0.9, 20)[nstart:nend + 1] # advance ratio
# J = np.linspace(0.1, 0.9, 20)
omega = 8000.0 * np.pi / 30
n = omega / (2 * np.pi)
D = 2 * Rtip
Vinf = J * D * n
dr = r[0, 1] - r[0, 0]
# Airfoil interpolator.
af = af_from_files(["airfoils/NACA64_A17.dat"])[0]
prob = om.Problem()
comp = om.IndepVarComp()
comp.add_output('v', val=Vinf, units='m/s')
comp.add_output('omega', val=np.tile(omega, num_nodes), units='rad/s')
comp.add_output('radii',
val=r,
shape=(num_nodes, num_radial),
units='m')
comp.add_output('dradii',
val=dr,
shape=(num_nodes, num_radial),
units='m')
comp.add_output('chord',
val=chord,
shape=(num_nodes, num_radial),
units='m')
comp.add_output('theta',
val=theta,
shape=(num_nodes, num_radial),
units='rad')
comp.add_output('precone', val=0., shape=num_nodes, units='rad')
comp.add_output('rho', val=rho, shape=(num_nodes, 1), units='kg/m**3')
comp.add_output('mu', val=1.0, shape=(num_nodes, 1), units='N/m**2*s')
comp.add_output('asound', val=1.0, shape=(num_nodes, 1), units='m/s')
comp.add_output('hub_radius', val=Rhub, shape=num_nodes, units='m')
comp.add_output('prop_radius', val=Rtip, shape=num_nodes, units='m')
comp.add_output('pitch', val=0.0, shape=num_nodes, units='rad')
prob.model.add_subsystem('ivc', comp, promotes_outputs=['*'])
comp = SimpleInflow(num_nodes=num_nodes, num_radial=num_radial)
prob.model.add_subsystem(
"simple_inflow",
comp,
promotes_inputs=["v", "omega", "radii", "precone"],
promotes_outputs=["Vx", "Vy"])
comp = ccb.LocalInflowAngleComp(num_nodes=num_nodes,
num_radial=num_radial,
num_blades=B,
airfoil_interp=af,
turbine=turbine,
debug_print=False)
comp.linear_solver = om.DirectSolver(assemble_jac=True)
prob.model.add_subsystem('ccblade',
comp,
promotes_inputs=[
'radii', 'chord', 'theta', 'Vx', 'Vy',
'rho', 'mu', 'asound', 'hub_radius',
'prop_radius', 'precone', 'pitch'
],
promotes_outputs=['Np', 'Tp'])
comp = ccb.FunctionalsComp(num_nodes=num_nodes,
num_radial=num_radial,
num_blades=B)
prob.model.add_subsystem(
'ccblade_torquethrust_comp',
comp,
promotes_inputs=[
'hub_radius', 'prop_radius', 'radii', 'Np', 'Tp', 'v', 'omega'
],
promotes_outputs=['thrust', 'torque', 'efficiency'])
prob.setup()
prob.final_setup()
prob.run_model()
etatest = np.array([
0.24598190455626265, 0.3349080300487075, 0.4155652767326253,
0.48818637673414306, 0.5521115225679999, 0.6089123481436948,
0.6595727776885079, 0.7046724703349897, 0.7441662053086512,
0.7788447616541276, 0.8090611349633181, 0.8347808848055981,
0.8558196582739432, 0.8715046719672315, 0.8791362131978436,
0.8670633642311274, 0.7974063895510229, 0.2715632768892098, 0.0,
0.0
])[nstart:nend + 1]
thrust = prob.get_val('thrust', units='N')
eff = prob.get_val('efficiency')
assert_array_almost_equal(eff[thrust > 0.0],
etatest[thrust > 0.0],
decimal=2)
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 = 0.1 * m_full * g / n_props
prob = Problem()
comp = IndepVarComp()
comp.add_discrete_output('B', val=num_blades)
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 = SimpleInflow(num_nodes=num_nodes, num_radial=num_radial)
balance_group.add_subsystem(
'inflow_comp',
comp,
promotes_inputs=['v', 'omega', 'radii', 'precone'],
promotes_outputs=['Vx', 'Vy'])
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=[
'B', 'radii', 'dradii', 'chord', 'theta', 'rho', 'mu', 'asound',
'v', 'precone', 'omega', 'Vx', 'Vy', 'precone', '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=50, iprint=2)
balance_group.nonlinear_solver.options['solve_subsystems'] = True
# prob.model.nonlinear_solver.linesearch = BoundsEnforceLS()
balance_group.nonlinear_solver.options['atol'] = 1e-9
prob.model.add_subsystem('thrust_balance_group',
balance_group,
promotes=['*'])
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('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(-3.5, -2.6, 10)
climb_velocity_nondim = np.linspace(-5.0, -2.1, 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('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 descent.
ax.plot(climb_velocity_nondim,
-induced_velocity_nondim,
label='CCBlade.jl (descent)')
# 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.))
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('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')
def test_propeller_aero4students(self):
# From test/runtests.jl
# inputs
chord = 0.10
D = 1.6
RPM = 2100
rho = 1.225
pitch = 1.0 # pitch distance in meters.
# --- rotor definition ---
turbine = False
# Rhub = 0.0
# Rtip = D/2
Rhub_eff = 1e-6 # something small to eliminate hub effects
Rtip_eff = 100.0 # something large to eliminate tip effects
B = 2 # number of blades
# --- section definitions ---
num_nodes = 60
R = D / 2.0
r = np.linspace(R / 10, R, 11)
dr = r[1] - r[0]
r = np.tile(r, (num_nodes, 1))
# print(f"r =\n{r}")
dr = np.tile(dr, r.shape)
theta = np.arctan(pitch / (2 * np.pi * r))
def affunc(alpha, Re, M):
cl = 6.2 * alpha
cd = 0.008 - 0.003 * cl + 0.01 * cl * cl
return cl, cd
prob = om.Problem()
num_radial = r.shape[-1]
comp = om.IndepVarComp()
comp.add_output('v', val=np.arange(1, num_nodes + 1), units='m/s')
comp.add_output('omega', val=np.tile(RPM, num_nodes), units='rpm')
comp.add_output('radii', val=r, units='m')
comp.add_output('dradii', val=dr, units='m')
comp.add_output('chord',
val=chord,
shape=(num_nodes, num_radial),
units='m')
comp.add_output('theta',
val=theta,
shape=(num_nodes, num_radial),
units='rad')
comp.add_output('precone', val=0., units='rad')
comp.add_output('rho', val=rho, shape=(num_nodes, 1), units='kg/m**3')
comp.add_output('mu', val=1.0, shape=(num_nodes, 1), units='N/m**2*s')
comp.add_output('asound', val=1.0, shape=(num_nodes, 1), units='m/s')
comp.add_output('hub_radius', val=Rhub_eff, units='m')
comp.add_output('prop_radius', val=Rtip_eff, units='m')
comp.add_discrete_output('B', val=B)
prob.model.add_subsystem('ivc', comp, promotes_outputs=['*'])
comp = SimpleInflow(num_nodes=num_nodes, num_radial=num_radial)
prob.model.add_subsystem(
"simple_inflow",
comp,
promotes_inputs=["v", "omega", "radii", "precone"],
promotes_outputs=["Vx", "Vy"])
comp = ccb.LocalInflowAngleComp(num_nodes=num_nodes,
num_radial=num_radial,
airfoil_interp=affunc,
turbine=turbine,
debug_print=False)
comp.linear_solver = om.DirectSolver(assemble_jac=True)
prob.model.add_subsystem('ccblade',
comp,
promotes_inputs=[
'radii', 'chord', 'theta', 'Vx', 'Vy',
'rho', 'mu', 'asound', 'hub_radius',
'prop_radius', 'precone', 'B'
],
promotes_outputs=['Np', 'Tp'])
comp = ccb.FunctionalsComp(num_nodes=num_nodes, num_radial=num_radial)
prob.model.add_subsystem(
'ccblade_torquethrust_comp',
comp,
promotes_inputs=['radii', 'dradii', 'Np', 'Tp', 'v', 'omega', 'B'],
promotes_outputs=['thrust', 'torque'])
prob.setup()
prob.final_setup()
prob.run_model()
tsim = 1e3 * np.array([
1.045361193032356, 1.025630300048415, 1.005234466788998,
0.984163367036026, 0.962407923825140, 0.939960208707079,
0.916813564966455, 0.892962691000145, 0.868403981825492,
0.843134981103815, 0.817154838249790, 0.790463442573673,
0.763063053839278, 0.734956576558370, 0.706148261507327,
0.676643975451150, 0.646450304160057, 0.615575090105131,
0.584027074365864, 0.551815917391907, 0.518952127358381,
0.485446691671386, 0.451311288662196, 0.416557935286392,
0.381199277009438, 0.345247916141561, 0.308716772800348,
0.271618894441869, 0.233967425339051, 0.195775319296371,
0.157055230270717, 0.117820154495231, 0.078082266879117,
0.037854059197644, -0.002852754149850, -0.044026182837742,
-0.085655305814570, -0.127728999394140, -0.170237722799272,
-0.213169213043848, -0.256515079286031, -0.300266519551194,
-0.344414094748869, -0.388949215983616, -0.433863576642539,
-0.479150401337354, -0.524801553114807, -0.570810405128802,
-0.617169893200684, -0.663873474163182, -0.710915862524620,
-0.758291877949762, -0.805995685105502, -0.854022273120508,
-0.902366919041604, -0.951025170820984, -0.999992624287163,
-1.049265666456123, -1.098840222937414, -1.148712509929845
])
qsim = 1e2 * np.array([
0.803638686218187, 0.806984572453978, 0.809709290183008,
0.811743686838315, 0.813015017103876, 0.813446921530685,
0.812959654049620, 0.811470393912576, 0.808893852696513,
0.805141916379142, 0.800124489784850, 0.793748780791057,
0.785921727832179, 0.776548246109426, 0.765532528164390,
0.752778882688809, 0.738190986274448, 0.721673076180745,
0.703129918771009, 0.682467282681955, 0.659592296506578,
0.634413303042323, 0.606840565246423, 0.576786093366321,
0.544164450503912, 0.508891967461804, 0.470887571011192,
0.430072787279711, 0.386371788290446, 0.339711042057184,
0.290019539402947, 0.237229503458026, 0.181274942660876,
0.122093307308376, 0.059623821454727, -0.006190834182631,
-0.075406684829235, -0.148076528546541, -0.224253047813501,
-0.303980950928302, -0.387309291734422, -0.474283793689904,
-0.564946107631716, -0.659336973911858, -0.757495165410553,
-0.859460291551374, -0.965266648683888, -1.074949504731187,
-1.188540970723477, -1.306072104649531, -1.427575034895290,
-1.553080300508925, -1.682614871422754, -1.816205997296014,
-1.953879956474228, -2.095662107769925, -2.241576439746701,
-2.391647474158875, -2.545897099743367, -2.704346566395035
])
assert_rel_error(self, tsim, prob['thrust'], 1e-5)
assert_rel_error(self, qsim, prob['torque'], 1e-5)