def test_dpresweepTip3(self):
presweep = np.linspace(1, 10, self.n)
presweepTip = 10.1
precone = 0.0
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=True, presweep=presweep, presweepTip=presweepTip)
CP, CT, CQ, dCP_ds, dCT_ds, dCQ_ds, dCP_dv, dCT_dv, dCQ_dv = \
rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=True)
dCT_dpresweepTip = dCT_ds[0, 6]
dCQ_dpresweepTip = dCQ_ds[0, 6]
dCP_dpresweepTip = dCP_ds[0, 6]
pst = float(presweepTip)
delta = 1e-6*pst
pst += delta
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False, presweep=presweep, presweepTip=pst)
CPd, CTd, CQd = rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=True)
dCT_dpresweepTip_fd = (CTd - CT) / delta
dCQ_dpresweepTip_fd = (CQd - CQ) / delta
dCP_dpresweepTip_fd = (CPd - CP) / delta
np.testing.assert_allclose(dCT_dpresweepTip_fd, dCT_dpresweepTip, rtol=1e-4, atol=1e-8)
np.testing.assert_allclose(dCQ_dpresweepTip_fd, dCQ_dpresweepTip, rtol=1e-4, atol=1e-8)
np.testing.assert_allclose(dCP_dpresweepTip_fd, dCP_dpresweepTip, rtol=1e-4, atol=1e-8)
def test_dprecurveTip2(self):
precurve = np.linspace(1, 10, self.n)
precurveTip = 10.1
precone = 0.0
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=True, precurve=precurve, precurveTip=precurveTip)
P, T, Q, dP_ds, dT_ds, dQ_ds, dP_dv, dT_dv, dQ_dv = \
rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=False)
dT_dprecurveTip = dT_ds[0, 5]
dQ_dprecurveTip = dQ_ds[0, 5]
dP_dprecurveTip = dP_ds[0, 5]
pct = float(precurveTip)
delta = 1e-6*pct
pct += delta
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False, precurve=precurve, precurveTip=pct)
Pd, Td, Qd = rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=False)
dT_dprecurveTip_fd = (Td - T) / delta
dQ_dprecurveTip_fd = (Qd - Q) / delta
dP_dprecurveTip_fd = (Pd - P) / delta
np.testing.assert_allclose(dT_dprecurveTip_fd, dT_dprecurveTip, rtol=1e-4, atol=1e-8)
np.testing.assert_allclose(dQ_dprecurveTip_fd, dQ_dprecurveTip, rtol=1e-4, atol=1e-8)
np.testing.assert_allclose(dP_dprecurveTip_fd, dP_dprecurveTip, rtol=1e-4, atol=1e-8)
def test_dtheta3(self):
dCT_dtheta = self.dCT_dv[0, 2, :]
dCQ_dtheta = self.dCQ_dv[0, 2, :]
dCP_dtheta = self.dCP_dv[0, 2, :]
dCT_dtheta_fd = np.zeros(self.n)
dCQ_dtheta_fd = np.zeros(self.n)
dCP_dtheta_fd = np.zeros(self.n)
for i in range(self.n):
theta = np.array(self.theta)
delta = 1e-6*theta[i]
theta[i] += delta
rotor = CCBlade(self.r, self.chord, theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, self.precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False)
CPd, CTd, CQd = rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=True)
dCT_dtheta_fd[i] = (CTd - self.CT) / delta
dCQ_dtheta_fd[i] = (CQd - self.CQ) / delta
dCP_dtheta_fd[i] = (CPd - self.CP) / delta
np.testing.assert_allclose(dCT_dtheta_fd, dCT_dtheta, rtol=5e-6, atol=1e-8)
np.testing.assert_allclose(dCQ_dtheta_fd, dCQ_dtheta, rtol=7e-5, atol=1e-8)
np.testing.assert_allclose(dCP_dtheta_fd, dCP_dtheta, rtol=7e-5, atol=1e-8)
def compute(self, inputs, outputs):
# setup ccblade model
ccblade = CCBlade_PY(inputs["r"],
inputs["chord"],
inputs["theta"],
alltheafs,
inputs["blend"],
inputs["Rhub"],
inputs["Rtip"],
inputs["B"],
inputs["rho"],
inputs["mu"],
inputs["precone"],
inputs["tilt"],
inputs["yaw"],
inputs["shearExp"],
inputs["hubHt"],
inputs["nSector"],
tiploss=True,
hubloss=True,
wakerotation=True,
usecd=True,
derivatives=True)
# evaluate power, thrust
outputs["P"], outputs["T"], Q, outputs[
"Bfw"], self.dP, self.dT, self.dQ, self.dBfw = ccblade.evaluate(
inputs["Uhub"],
inputs["Omega"],
inputs["pitch"],
coefficient=False)
def test_dtheta2(self):
dT_dtheta = self.dT_dv[0, 2, :]
dQ_dtheta = self.dQ_dv[0, 2, :]
dP_dtheta = self.dP_dv[0, 2, :]
dT_dtheta_fd = np.zeros(self.n)
dQ_dtheta_fd = np.zeros(self.n)
dP_dtheta_fd = np.zeros(self.n)
for i in range(self.n):
theta = np.array(self.theta)
delta = 1e-6*theta[i]
theta[i] += delta
rotor = CCBlade(self.r, self.chord, theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, self.precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False)
Pd, Td, Qd = rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=False)
dT_dtheta_fd[i] = (Td - self.T) / delta
dQ_dtheta_fd[i] = (Qd - self.Q) / delta
dP_dtheta_fd[i] = (Pd - self.P) / delta
np.testing.assert_allclose(dT_dtheta_fd, dT_dtheta, rtol=7e-5, atol=1e-8)
np.testing.assert_allclose(dQ_dtheta_fd, dQ_dtheta, rtol=7e-5, atol=1e-8)
np.testing.assert_allclose(dP_dtheta_fd, dP_dtheta, rtol=7e-5, atol=1e-8)
def test_dpresweep2(self):
presweep = np.linspace(1, 10, self.n)
presweepTip = 10.1
precone = 0.0
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=True, presweep=presweep, presweepTip=presweepTip)
P, T, Q, dP_ds, dT_ds, dQ_ds, dP_dv, dT_dv, dQ_dv = \
rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=False)
dT_dpresweep = dT_dv[0, 4, :]
dQ_dpresweep = dQ_dv[0, 4, :]
dP_dpresweep = dP_dv[0, 4, :]
dT_dpresweep_fd = np.zeros(self.n)
dQ_dpresweep_fd = np.zeros(self.n)
dP_dpresweep_fd = np.zeros(self.n)
for i in range(self.n):
ps = np.array(presweep)
delta = 1e-6*ps[i]
ps[i] += delta
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False, presweep=ps, presweepTip=presweepTip)
Pd, Td, Qd = rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=False)
dT_dpresweep_fd[i] = (Td - T) / delta
dQ_dpresweep_fd[i] = (Qd - Q) / delta
dP_dpresweep_fd[i] = (Pd - P) / delta
np.testing.assert_allclose(dT_dpresweep_fd, dT_dpresweep, rtol=3e-4, atol=1e-8)
np.testing.assert_allclose(dQ_dpresweep_fd, dQ_dpresweep, rtol=3e-4, atol=1e-8)
np.testing.assert_allclose(dP_dpresweep_fd, dP_dpresweep, rtol=3e-4, atol=1e-8)
def test_dprecurve3(self):
precurve = np.linspace(1, 10, self.n)
precurveTip = 10.1
precone = 0.0
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=True, precurve=precurve, precurveTip=precurveTip)
CP, CT, CQ, dCP_ds, dCT_ds, dCQ_ds, dCP_dv, dCT_dv, dCQ_dv = \
rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=True)
dCT_dprecurve = dCT_dv[0, 3, :]
dCQ_dprecurve = dCQ_dv[0, 3, :]
dCP_dprecurve = dCP_dv[0, 3, :]
dCT_dprecurve_fd = np.zeros(self.n)
dCQ_dprecurve_fd = np.zeros(self.n)
dCP_dprecurve_fd = np.zeros(self.n)
for i in range(self.n):
pc = np.array(precurve)
delta = 1e-6*pc[i]
pc[i] += delta
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False, precurve=pc, precurveTip=precurveTip)
CPd, CTd, CQd = rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=True)
dCT_dprecurve_fd[i] = (CTd - CT) / delta
dCQ_dprecurve_fd[i] = (CQd - CQ) / delta
dCP_dprecurve_fd[i] = (CPd - CP) / delta
np.testing.assert_allclose(dCT_dprecurve_fd, dCT_dprecurve, rtol=3e-4, atol=1e-8)
np.testing.assert_allclose(dCQ_dprecurve_fd, dCQ_dprecurve, rtol=3e-4, atol=1e-8)
np.testing.assert_allclose(dCP_dprecurve_fd, dCP_dprecurve, rtol=3e-4, atol=1e-8)
def test_dhubht3(self):
dCT_dhubht = self.dCT_ds[0, 2]
dCQ_dhubht = self.dCQ_ds[0, 2]
dCP_dhubht = self.dCP_ds[0, 2]
hubht = float(self.hubHt)
delta = 1e-6*hubht
hubht += delta
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, self.precone, self.tilt, self.yaw, self.shearExp,
hubht, self.nSector, derivatives=False)
CPd, CTd, CQd = rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=True)
dCT_dhubht_fd = (CTd - self.CT) / delta
dCQ_dhubht_fd = (CQd - self.CQ) / delta
dCP_dhubht_fd = (CPd - self.CP) / delta
np.testing.assert_allclose(dCT_dhubht_fd, dCT_dhubht, rtol=1e-5, atol=1e-8)
np.testing.assert_allclose(dCQ_dhubht_fd, dCQ_dhubht, rtol=5e-5, atol=1e-8)
np.testing.assert_allclose(dCP_dhubht_fd, dCP_dhubht, rtol=5e-5, atol=1e-8)
def test_dhubht2(self):
dT_dhubht = self.dT_ds[0, 2]
dQ_dhubht = self.dQ_ds[0, 2]
dP_dhubht = self.dP_ds[0, 2]
hubht = float(self.hubHt)
delta = 1e-6*hubht
hubht += delta
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, self.precone, self.tilt, self.yaw, self.shearExp,
hubht, self.nSector, derivatives=False)
Pd, Td, Qd = rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=False)
dT_dhubht_fd = (Td - self.T) / delta
dQ_dhubht_fd = (Qd - self.Q) / delta
dP_dhubht_fd = (Pd - self.P) / delta
np.testing.assert_allclose(dT_dhubht_fd, dT_dhubht, rtol=1e-5, atol=1e-8)
np.testing.assert_allclose(dQ_dhubht_fd, dQ_dhubht, rtol=5e-5, atol=1e-8)
np.testing.assert_allclose(dP_dhubht_fd, dP_dhubht, rtol=5e-5, atol=1e-8)
class CCBladePower(Component):
def __init__(self, naero, npower):
super(CCBladePower, self).__init__()
"""blade element momentum code"""
# inputs
self.add_param('Uhub', val=np.zeros(npower), units='m/s', desc='hub height wind speed')
self.add_param('Omega', val=np.zeros(npower), units='rpm', desc='rotor rotation speed')
self.add_param('pitch', val=np.zeros(npower), units='deg', desc='blade pitch setting')
# outputs
self.add_output('T', val=np.zeros(npower), units='N', desc='rotor aerodynamic thrust')
self.add_output('Q', val=np.zeros(npower), units='N*m', desc='rotor aerodynamic torque')
self.add_output('P', val=np.zeros(npower), units='W', desc='rotor aerodynamic power')
# (potential) variables
self.add_param('r', val=np.zeros(naero), units='m', desc='radial locations where blade is defined (should be increasing and not go all the way to hub or tip)')
self.add_param('chord', val=np.zeros(naero), units='m', desc='chord length at each section')
self.add_param('theta', val=np.zeros(naero), units='deg', desc='twist angle at each section (positive decreases angle of attack)')
self.add_param('Rhub', val=0.0, units='m', desc='hub radius')
self.add_param('Rtip', val=0.0, units='m', desc='tip radius')
self.add_param('hubHt', val=0.0, units='m', desc='hub height')
self.add_param('precone', val=0.0, desc='precone angle', units='deg')
self.add_param('tilt', val=0.0, desc='shaft tilt', units='deg')
self.add_param('yaw', val=0.0, desc='yaw error', units='deg')
# TODO: I've not hooked up the gradients for these ones yet.
self.add_param('precurve', val=np.zeros(naero), units='m', desc='precurve at each section')
self.add_param('precurveTip', val=0.0, units='m', desc='precurve at tip')
# parameters
self.add_param('airfoils', val=[0]*naero, desc='CCAirfoil instances', pass_by_obj=True)
self.add_param('B', val=0, desc='number of blades', pass_by_obj=True)
self.add_param('rho', val=0.0, units='kg/m**3', desc='density of air')
self.add_param('mu', val=0.0, units='kg/(m*s)', desc='dynamic viscosity of air')
self.add_param('shearExp', val=0.0, desc='shear exponent')
self.add_param('nSector', val=4, desc='number of sectors to divide rotor face into in computing thrust and power', pass_by_obj=True)
self.add_param('tiploss', val=True, desc='include Prandtl tip loss model', pass_by_obj=True)
self.add_param('hubloss', val=True, desc='include Prandtl hub loss model', pass_by_obj=True)
self.add_param('wakerotation', val=True, desc='include effect of wake rotation (i.e., tangential induction factor is nonzero)', pass_by_obj=True)
self.add_param('usecd', val=True, desc='use drag coefficient in computing induction factors', pass_by_obj=True)
self.naero = naero
self.deriv_options['form'] = 'central'
self.deriv_options['step_calc'] = 'relative'
def solve_nonlinear(self, params, unknowns, resids):
self.r = params['r']
self.chord = params['chord']
self.theta = params['theta']
self.Rhub = params['Rhub']
self.Rtip = params['Rtip']
self.hubHt = params['hubHt']
self.precone = params['precone']
self.tilt = params['tilt']
self.yaw = params['yaw']
self.precurve = params['precurve']
self.precurveTip = params['precurveTip']
self.airfoils = params['airfoils']
self.B = params['B']
self.rho = params['rho']
self.mu = params['mu']
self.shearExp = params['shearExp']
self.nSector = params['nSector']
self.tiploss = params['tiploss']
self.hubloss = params['hubloss']
self.wakerotation = params['wakerotation']
self.usecd = params['usecd']
self.Uhub = params['Uhub']
self.Omega = params['Omega']
self.pitch = params['pitch']
self.ccblade = CCBlade(self.r, self.chord, self.theta, self.airfoils, self.Rhub, self.Rtip, self.B,
self.rho, self.mu, self.precone, self.tilt, self.yaw, self.shearExp, self.hubHt,
self.nSector, self.precurve, self.precurveTip, tiploss=self.tiploss, hubloss=self.hubloss,
wakerotation=self.wakerotation, usecd=self.usecd, derivatives=True)
# power, thrust, torque
self.P, self.T, self.Q, self.M, self.dP, self.dT, self.dQ \
= self.ccblade.evaluate(self.Uhub, self.Omega, self.pitch, coefficients=False)
unknowns['T'] = self.T
unknowns['Q'] = self.Q
unknowns['P'] = self.P
def list_deriv_vars(self):
inputs = ('precone', 'tilt', 'hubHt', 'Rhub', 'Rtip', 'yaw',
'Uhub', 'Omega', 'pitch', 'r', 'chord', 'theta', 'precurve', 'precurveTip')
outputs = ('P', 'T', 'Q')
return inputs, outputs
def linearize(self, params, unknowns, resids):
dP = self.dP
dT = self.dT
dQ = self.dQ
J = {}
J['P', 'precone'] = dP['dprecone']
J['P', 'tilt'] = dP['dtilt']
J['P', 'hubHt'] = dP['dhubHt']
J['P', 'Rhub'] = dP['dRhub']
J['P', 'Rtip'] = dP['dRtip']
J['P', 'yaw'] = dP['dyaw']
J['P', 'Uhub'] = dP['dUinf']
J['P', 'Omega'] = dP['dOmega']
J['P', 'pitch'] = dP['dpitch']
J['P', 'r'] = dP['dr']
J['P', 'chord'] = dP['dchord']
J['P', 'theta'] = dP['dtheta']
J['P', 'precurve'] = dP['dprecurve']
J['P', 'precurveTip'] = dP['dprecurveTip']
J['T', 'precone'] = dT['dprecone']
J['T', 'tilt'] = dT['dtilt']
J['T', 'hubHt'] = dT['dhubHt']
J['T', 'Rhub'] = dT['dRhub']
J['T', 'Rtip'] = dT['dRtip']
J['T', 'yaw'] = dT['dyaw']
J['T', 'Uhub'] = dT['dUinf']
J['T', 'Omega'] = dT['dOmega']
J['T', 'pitch'] = dT['dpitch']
J['T', 'r'] = dT['dr']
J['T', 'chord'] = dT['dchord']
J['T', 'theta'] = dT['dtheta']
J['T', 'precurve'] = dT['dprecurve']
J['T', 'precurveTip'] = dT['dprecurveTip']
J['Q', 'precone'] = dQ['dprecone']
J['Q', 'tilt'] = dQ['dtilt']
J['Q', 'hubHt'] = dQ['dhubHt']
J['Q', 'Rhub'] = dQ['dRhub']
J['Q', 'Rtip'] = dQ['dRtip']
J['Q', 'yaw'] = dQ['dyaw']
J['Q', 'Uhub'] = dQ['dUinf']
J['Q', 'Omega'] = dQ['dOmega']
J['Q', 'pitch'] = dQ['dpitch']
J['Q', 'r'] = dQ['dr']
J['Q', 'chord'] = dQ['dchord']
J['Q', 'theta'] = dQ['dtheta']
J['Q', 'precurve'] = dQ['dprecurve']
J['Q', 'precurveTip'] = dQ['dprecurveTip']
return J
plt.legend(loc='upper left')
plt.grid()
plt.show()
plt.savefig('compare_m4_m6_m66_yaw_m67_AeroForces.png')
plt.close(1)
# To get the power, thrust, and torque at the same conditions
# (in both absolute and coefficient form), use the evaluate method.
# This is generally used for generating power curves so it expects
# array_like input. For this example a list of size one is used.
# Note that the outputs are numpy arrays (of length 1 for this example).
#m1_P, m1_T, m1_Q = m1_rotor.evaluate([m1_Uinf], [m1_Omega], [pitch])
m1_CP, m1_CT, m1_CQ = m1_rotor.evaluate([m1_Uinf], [m1_Omega], [pitch], coefficient=True)
#m4_P, m4_T, m4_Q = m4_rotor.evaluate([m4_Uinf], [m4_Omega], [pitch])
m4_CP, m4_CT, m4_CQ = m4_rotor.evaluate([m4_Uinf], [m4_Omega], [pitch], coefficient=True)
#m6_P, m6_T, m6_Q = m6_rotor.evaluate([m6_Uinf], [m6_Omega], [pitch])
m6_CP, m6_CT, m6_CQ = m6_rotor.evaluate([m6_Uinf], [m6_Omega], [pitch], coefficient=True)
#m66_P, m66_T, m66_Q = m66_rotor.evaluate([m66_Uinf], [m66_Omega], [pitch])
m66_CP, m66_CT, m66_CQ = m66_rotor.evaluate([m66_Uinf], [m66_Omega], [pitch], coefficient=True)
m67_CP, m67_CT, m67_CQ = m67_rotor.evaluate([m67_Uinf], [m67_Omega], [pitch], coefficient=True)
print 'model1 CP =', m1_CP
print 'model1 CT =', m1_CT
print 'model1 CQ =', m1_CQ
class CCBladePower(Component):
def __init__(self, naero, npower):
super(CCBladePower, self).__init__()
"""blade element momentum code"""
# inputs
self.add_param('Uhub', val=np.zeros(npower), units='m/s', desc='hub height wind speed')
self.add_param('Omega', val=np.zeros(npower), units='rpm', desc='rotor rotation speed')
self.add_param('pitch', val=np.zeros(npower), units='deg', desc='blade pitch setting')
# outputs
self.add_output('T', val=np.zeros(npower), units='N', desc='rotor aerodynamic thrust')
self.add_output('Q', val=np.zeros(npower), units='N*m', desc='rotor aerodynamic torque')
self.add_output('P', val=np.zeros(npower), units='W', desc='rotor aerodynamic power')
# (potential) variables
self.add_param('r', val=np.zeros(naero), units='m', desc='radial locations where blade is defined (should be increasing and not go all the way to hub or tip)')
self.add_param('chord', val=np.zeros(naero), units='m', desc='chord length at each section')
self.add_param('theta', val=np.zeros(naero), units='deg', desc='twist angle at each section (positive decreases angle of attack)')
self.add_param('Rhub', val=0.0, units='m', desc='hub radius')
self.add_param('Rtip', val=0.0, units='m', desc='tip radius')
self.add_param('hubHt', val=0.0, units='m', desc='hub height')
self.add_param('precone', val=0.0, desc='precone angle', units='deg')
self.add_param('tilt', val=0.0, desc='shaft tilt', units='deg')
self.add_param('yaw', val=0.0, desc='yaw error', units='deg')
# TODO: I've not hooked up the gradients for these ones yet.
self.add_param('precurve', val=np.zeros(naero), units='m', desc='precurve at each section')
self.add_param('precurveTip', val=0.0, units='m', desc='precurve at tip')
# parameters
self.add_param('airfoils', val=[0]*naero, desc='CCAirfoil instances', pass_by_obj=True)
self.add_param('B', val=0, desc='number of blades', pass_by_obj=True)
self.add_param('rho', val=0.0, units='kg/m**3', desc='density of air')
self.add_param('mu', val=0.0, units='kg/(m*s)', desc='dynamic viscosity of air')
self.add_param('shearExp', val=0.0, desc='shear exponent')
self.add_param('nSector', val=4, desc='number of sectors to divide rotor face into in computing thrust and power', pass_by_obj=True)
self.add_param('tiploss', val=True, desc='include Prandtl tip loss model', pass_by_obj=True)
self.add_param('hubloss', val=True, desc='include Prandtl hub loss model', pass_by_obj=True)
self.add_param('wakerotation', val=True, desc='include effect of wake rotation (i.e., tangential induction factor is nonzero)', pass_by_obj=True)
self.add_param('usecd', val=True, desc='use drag coefficient in computing induction factors', pass_by_obj=True)
self.naero = naero
self.deriv_options['form'] = 'central'
self.deriv_options['step_calc'] = 'relative'
def solve_nonlinear(self, params, unknowns, resids):
self.r = params['r']
self.chord = params['chord']
self.theta = params['theta']
self.Rhub = params['Rhub']
self.Rtip = params['Rtip']
self.hubHt = params['hubHt']
self.precone = params['precone']
self.tilt = params['tilt']
self.yaw = params['yaw']
self.precurve = params['precurve']
self.precurveTip = params['precurveTip']
self.airfoils = params['airfoils']
self.B = params['B']
self.rho = params['rho']
self.mu = params['mu']
self.shearExp = params['shearExp']
self.nSector = params['nSector']
self.tiploss = params['tiploss']
self.hubloss = params['hubloss']
self.wakerotation = params['wakerotation']
self.usecd = params['usecd']
self.Uhub = params['Uhub']
self.Omega = params['Omega']
self.pitch = params['pitch']
self.ccblade = CCBlade(self.r, self.chord, self.theta, self.airfoils, self.Rhub, self.Rtip, self.B,
self.rho, self.mu, self.precone, self.tilt, self.yaw, self.shearExp, self.hubHt,
self.nSector, self.precurve, self.precurveTip, tiploss=self.tiploss, hubloss=self.hubloss,
wakerotation=self.wakerotation, usecd=self.usecd, derivatives=True)
# power, thrust, torque
self.P, self.T, self.Q, self.M, self.dP, self.dT, self.dQ \
= self.ccblade.evaluate(self.Uhub, self.Omega, self.pitch, coefficients=False)
unknowns['T'] = self.T
unknowns['Q'] = self.Q
unknowns['P'] = self.P
def list_deriv_vars(self):
inputs = ('precone', 'tilt', 'hubHt', 'Rhub', 'Rtip', 'yaw',
'Uhub', 'Omega', 'pitch', 'r', 'chord', 'theta', 'precurve', 'precurveTip')
outputs = ('P', 'T', 'Q')
return inputs, outputs
def linearize(self, params, unknowns, resids):
dP = self.dP
dT = self.dT
dQ = self.dQ
J = {}
J['P', 'precone'] = dP['dprecone']
J['P', 'tilt'] = dP['dtilt']
J['P', 'hubHt'] = dP['dhubHt']
J['P', 'Rhub'] = dP['dRhub']
J['P', 'Rtip'] = dP['dRtip']
J['P', 'yaw'] = dP['dyaw']
J['P', 'Uhub'] = dP['dUinf']
J['P', 'Omega'] = dP['dOmega']
J['P', 'pitch'] = dP['dpitch']
J['P', 'r'] = dP['dr']
J['P', 'chord'] = dP['dchord']
J['P', 'theta'] = dP['dtheta']
J['P', 'precurve'] = dP['dprecurve']
J['P', 'precurveTip'] = dP['dprecurveTip']
J['T', 'precone'] = dT['dprecone']
J['T', 'tilt'] = dT['dtilt']
J['T', 'hubHt'] = dT['dhubHt']
J['T', 'Rhub'] = dT['dRhub']
J['T', 'Rtip'] = dT['dRtip']
J['T', 'yaw'] = dT['dyaw']
J['T', 'Uhub'] = dT['dUinf']
J['T', 'Omega'] = dT['dOmega']
J['T', 'pitch'] = dT['dpitch']
J['T', 'r'] = dT['dr']
J['T', 'chord'] = dT['dchord']
J['T', 'theta'] = dT['dtheta']
J['T', 'precurve'] = dT['dprecurve']
J['T', 'precurveTip'] = dT['dprecurveTip']
J['Q', 'precone'] = dQ['dprecone']
J['Q', 'tilt'] = dQ['dtilt']
J['Q', 'hubHt'] = dQ['dhubHt']
J['Q', 'Rhub'] = dQ['dRhub']
J['Q', 'Rtip'] = dQ['dRtip']
J['Q', 'yaw'] = dQ['dyaw']
J['Q', 'Uhub'] = dQ['dUinf']
J['Q', 'Omega'] = dQ['dOmega']
J['Q', 'pitch'] = dQ['dpitch']
J['Q', 'r'] = dQ['dr']
J['Q', 'chord'] = dQ['dchord']
J['Q', 'theta'] = dQ['dtheta']
J['Q', 'precurve'] = dQ['dprecurve']
J['Q', 'precurveTip'] = dQ['dprecurveTip']
return J
class TestNREL5MW(unittest.TestCase):
def setUp(self):
# geometry
Rhub = 1.5
Rtip = 63.0
r = np.array([2.8667, 5.6000, 8.3333, 11.7500, 15.8500, 19.9500, 24.0500,
28.1500, 32.2500, 36.3500, 40.4500, 44.5500, 48.6500, 52.7500,
56.1667, 58.9000, 61.6333])
chord = np.array([3.542, 3.854, 4.167, 4.557, 4.652, 4.458, 4.249, 4.007, 3.748,
3.502, 3.256, 3.010, 2.764, 2.518, 2.313, 2.086, 1.419])
theta = np.array([13.308, 13.308, 13.308, 13.308, 11.480, 10.162, 9.011, 7.795,
6.544, 5.361, 4.188, 3.125, 2.319, 1.526, 0.863, 0.370, 0.106])
B = 3 # number of blades
# atmosphere
rho = 1.225
mu = 1.81206e-5
afinit = CCAirfoil.initFromAerodynFile # just for shorthand
basepath = path.join(path.dirname(path.realpath(__file__)), '5MW_AFFiles')
# load all airfoils
airfoil_types = [0]*8
airfoil_types[0] = afinit(path.join(basepath, 'Cylinder1.dat'))
airfoil_types[1] = afinit(path.join(basepath, 'Cylinder2.dat'))
airfoil_types[2] = afinit(path.join(basepath, 'DU40_A17.dat'))
airfoil_types[3] = afinit(path.join(basepath, 'DU35_A17.dat'))
airfoil_types[4] = afinit(path.join(basepath, 'DU30_A17.dat'))
airfoil_types[5] = afinit(path.join(basepath, 'DU25_A17.dat'))
airfoil_types[6] = afinit(path.join(basepath, 'DU21_A17.dat'))
airfoil_types[7] = afinit(path.join(basepath, 'NACA64_A17.dat'))
# place at appropriate radial stations
af_idx = [0, 0, 1, 2, 3, 3, 4, 5, 5, 6, 6, 7, 7, 7, 7, 7, 7]
af = [0]*len(r)
for i in range(len(r)):
af[i] = airfoil_types[af_idx[i]]
tilt = -5.0
precone = 2.5
yaw = 0.0
# create CCBlade object
self.rotor = CCBlade(r, chord, theta, af, Rhub, Rtip, B, rho, mu, precone, tilt, yaw, shearExp=0.2, hubHt=90.0)
def test_thrust_torque(self):
Uinf = np.array([3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
20, 21, 22, 23, 24, 25])
Omega = np.array([6.972, 7.183, 7.506, 7.942, 8.469, 9.156, 10.296, 11.431,
11.890, 12.100, 12.100, 12.100, 12.100, 12.100, 12.100,
12.100, 12.100, 12.100, 12.100, 12.100, 12.100, 12.100, 12.100])
pitch = np.array([0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000, 0.000,
3.823, 6.602, 8.668, 10.450, 12.055, 13.536, 14.920, 16.226,
17.473, 18.699, 19.941, 21.177, 22.347, 23.469])
Pref = np.array([42.9, 188.2, 427.9, 781.3, 1257.6, 1876.2, 2668.0, 3653.0,
4833.2, 5296.6, 5296.6, 5296.6, 5296.6, 5296.6, 5296.6,
5296.6, 5296.6, 5296.7, 5296.6, 5296.7, 5296.6, 5296.6, 5296.7])
Tref = np.array([171.7, 215.9, 268.9, 330.3, 398.6, 478.0, 579.2, 691.5, 790.6,
690.0, 608.4, 557.9, 520.5, 491.2, 467.7, 448.4, 432.3, 418.8,
406.7, 395.3, 385.1, 376.7, 369.3])
Qref = np.array([58.8, 250.2, 544.3, 939.5, 1418.1, 1956.9, 2474.5, 3051.1,
3881.3, 4180.1, 4180.1, 4180.1, 4180.1, 4180.1, 4180.1, 4180.1,
4180.1, 4180.1, 4180.1, 4180.1, 4180.1, 4180.1, 4180.1])
m_rotor = 110.0 # kg
g = 9.81
tilt = 5*math.pi/180.0
Tref -= m_rotor*g*math.sin(tilt) # remove weight of rotor that is included in reported results
P, T, Q, M = self.rotor.evaluate(Uinf, Omega, pitch)
# import matplotlib.pyplot as plt
# plt.plot(Uinf, P/1e6)
# plt.plot(Uinf, Pref/1e3)
# plt.figure()
# plt.plot(Uinf, T/1e6)
# plt.plot(Uinf, Tref/1e3)
# plt.show()
idx = (Uinf < 15)
np.testing.assert_allclose(Q[idx]/1e6, Qref[idx]/1e3, atol=0.15)
np.testing.assert_allclose(P[idx]/1e6, Pref[idx]/1e3, atol=0.2) # within 0.2 of 1MW
np.testing.assert_allclose(T[idx]/1e6, Tref[idx]/1e3, atol=0.15)
class RegulatedPowerCurve(Component): # Implicit COMPONENT
def __init__(self, naero, n_pc, n_pc_spline, regulation_reg_II5 = True, regulation_reg_III = False):
super(RegulatedPowerCurve, self).__init__()
# parameters
self.add_param('control_Vin', val=0.0, units='m/s', desc='cut-in wind speed')
self.add_param('control_Vout', val=0.0, units='m/s', desc='cut-out wind speed')
self.add_param('control_ratedPower', val=0.0, units='W', desc='electrical rated power')
self.add_param('control_minOmega', val=0.0, units='rpm', desc='minimum allowed rotor rotation speed')
self.add_param('control_maxOmega', val=0.0, units='rpm', desc='maximum allowed rotor rotation speed')
self.add_param('control_maxTS', val=0.0, units='m/s', desc='maximum allowed blade tip speed')
self.add_param('control_tsr', val=0.0, desc='tip-speed ratio in Region 2 (should be optimized externally)')
self.add_param('control_pitch', val=0.0, units='deg', desc='pitch angle in region 2 (and region 3 for fixed pitch machines)')
self.add_param('drivetrainType', val=DRIVETRAIN_TYPE['GEARED'], pass_by_obj=True)
self.add_param('drivetrainEff', val=0.0, desc='overwrite drivetrain model with a given efficiency, used for FAST analysis')
self.add_param('r', val=np.zeros(naero), units='m', desc='radial locations where blade is defined (should be increasing and not go all the way to hub or tip)')
self.add_param('chord', val=np.zeros(naero), units='m', desc='chord length at each section')
self.add_param('theta', val=np.zeros(naero), units='deg', desc='twist angle at each section (positive decreases angle of attack)')
self.add_param('Rhub', val=0.0, units='m', desc='hub radius')
self.add_param('Rtip', val=0.0, units='m', desc='tip radius')
self.add_param('hubHt', val=0.0, units='m', desc='hub height')
self.add_param('precone', val=0.0, units='deg', desc='precone angle', )
self.add_param('tilt', val=0.0, units='deg', desc='shaft tilt', )
self.add_param('yaw', val=0.0, units='deg', desc='yaw error', )
self.add_param('precurve', val=np.zeros(naero), units='m', desc='precurve at each section')
self.add_param('precurveTip', val=0.0, units='m', desc='precurve at tip')
self.add_param('airfoils', val=[0]*naero, desc='CCAirfoil instances', pass_by_obj=True)
self.add_param('B', val=0, desc='number of blades', pass_by_obj=True)
self.add_param('rho', val=0.0, units='kg/m**3', desc='density of air')
self.add_param('mu', val=0.0, units='kg/(m*s)', desc='dynamic viscosity of air')
self.add_param('shearExp', val=0.0, desc='shear exponent')
self.add_param('nSector', val=4, desc='number of sectors to divide rotor face into in computing thrust and power', pass_by_obj=True)
self.add_param('tiploss', val=True, desc='include Prandtl tip loss model', pass_by_obj=True)
self.add_param('hubloss', val=True, desc='include Prandtl hub loss model', pass_by_obj=True)
self.add_param('wakerotation', val=True, desc='include effect of wake rotation (i.e., tangential induction factor is nonzero)', pass_by_obj=True)
self.add_param('usecd', val=True, desc='use drag coefficient in computing induction factors', pass_by_obj=True)
# outputs
self.add_output('V', val=np.zeros(n_pc), units='m/s', desc='wind vector')
self.add_output('Omega', val=np.zeros(n_pc), units='rpm', desc='rotor rotational speed')
self.add_output('pitch', val=np.zeros(n_pc), units='deg', desc='rotor pitch schedule')
self.add_output('P', val=np.zeros(n_pc), units='W', desc='rotor electrical power')
self.add_output('T', val=np.zeros(n_pc), units='N', desc='rotor aerodynamic thrust')
self.add_output('Q', val=np.zeros(n_pc), units='N*m', desc='rotor aerodynamic torque')
self.add_output('M', val=np.zeros(n_pc), units='N*m', desc='blade root moment')
self.add_output('Cp', val=np.zeros(n_pc), desc='rotor electrical power coefficient')
self.add_output('V_spline', val=np.zeros(n_pc_spline), units='m/s', desc='wind vector')
self.add_output('P_spline', val=np.zeros(n_pc_spline), units='W', desc='rotor electrical power')
self.add_output('V_R25', val=0.0, units='m/s', desc='region 2.5 transition wind speed')
self.add_output('rated_V', val=0.0, units='m/s', desc='rated wind speed')
self.add_output('rated_Omega', val=0.0, units='rpm', desc='rotor rotation speed at rated')
self.add_output('rated_pitch', val=0.0, units='deg', desc='pitch setting at rated')
self.add_output('rated_T', val=0.0, units='N', desc='rotor aerodynamic thrust at rated')
self.add_output('rated_Q', val=0.0, units='N*m', desc='rotor aerodynamic torque at rated')
self.add_output('ax_induct_cutin', val=np.zeros(naero), desc='rotor axial induction at cut-in wind speed along blade span')
self.add_output('tang_induct_cutin', val=np.zeros(naero), desc='rotor tangential induction at cut-in wind speed along blade span')
self.add_output('aoa_cutin', val=np.zeros(naero), desc='angle of attack distribution along blade span at cut-in wind speed')
self.naero = naero
self.n_pc = n_pc
self.n_pc_spline = n_pc_spline
self.lock_pitchII = False
self.regulation_reg_II5 = regulation_reg_II5
self.regulation_reg_III = regulation_reg_III
self.deriv_options['form'] = 'central'
self.deriv_options['step_calc'] = 'relative'
def solve_nonlinear(self, params, unknowns, resids):
self.ccblade = CCBlade(params['r'], params['chord'], params['theta'], params['airfoils'], params['Rhub'], params['Rtip'], params['B'], params['rho'], params['mu'], params['precone'], params['tilt'], params['yaw'], params['shearExp'], params['hubHt'], params['nSector'])
Uhub = np.linspace(params['control_Vin'],params['control_Vout'], self.n_pc)
P_aero = np.zeros_like(Uhub)
Cp_aero = np.zeros_like(Uhub)
P = np.zeros_like(Uhub)
Cp = np.zeros_like(Uhub)
T = np.zeros_like(Uhub)
Q = np.zeros_like(Uhub)
M = np.zeros_like(Uhub)
Omega = np.zeros_like(Uhub)
pitch = np.zeros_like(Uhub) + params['control_pitch']
Omega_max = min([params['control_maxTS'] / params['Rtip'], params['control_maxOmega']*np.pi/30.])
# Region II
for i in range(len(Uhub)):
Omega[i] = Uhub[i] * params['control_tsr'] / params['Rtip']
P_aero, T, Q, M, Cp_aero, _, _, _ = self.ccblade.evaluate(Uhub, Omega * 30. / np.pi, pitch, coefficients=True)
P, eff = CSMDrivetrain(P_aero, params['control_ratedPower'], params['drivetrainType'])
Cp = Cp_aero*eff
# search for Region 2.5 bounds
for i in range(len(Uhub)):
if Omega[i] > Omega_max and P[i] < params['control_ratedPower']:
Omega[i] = Omega_max
Uhub[i] = Omega[i] * params['Rtip'] / params['control_tsr']
P_aero[i], T[i], Q[i], M[i], Cp_aero[i], _, _, _ = self.ccblade.evaluate([Uhub[i]], [Omega[i] * 30. / np.pi], [pitch[i]], coefficients=True)
P[i], eff = CSMDrivetrain(P_aero[i], params['control_ratedPower'], params['drivetrainType'])
Cp[i] = Cp_aero[i]*eff
regionIIhalf = True
i_IIhalf_start = i
unknowns['V_R25'] = Uhub[i]
break
if P[i] > params['control_ratedPower']:
regionIIhalf = False
break
def maxPregionIIhalf(pitch, Uhub, Omega):
Uhub_i = Uhub
Omega_i = Omega
pitch = pitch
P, _, _, _ = self.ccblade.evaluate([Uhub_i], [Omega_i * 30. / np.pi], [pitch], coefficients=False)
return -P
# Solve for regoin 2.5 pitch
options = {}
options['disp'] = False
options['xatol'] = 1.e-2
if regionIIhalf == True:
for i in range(i_IIhalf_start + 1, len(Uhub)):
Omega[i] = Omega_max
pitch0 = pitch[i-1]
bnds = [pitch0 - 10., pitch0 + 10.]
pitch_regionIIhalf = minimize_scalar(lambda x: maxPregionIIhalf(x, Uhub[i], Omega[i]), bounds=bnds, method='bounded', options=options)['x']
pitch[i] = pitch_regionIIhalf
P_aero[i], T[i], Q[i], M[i], Cp_aero[i], _, _, _ = self.ccblade.evaluate([Uhub[i]], [Omega[i] * 30. / np.pi], [pitch[i]], coefficients=True)
P[i], eff = CSMDrivetrain(P_aero[i], params['control_ratedPower'], params['drivetrainType'])
Cp[i] = Cp_aero[i]*eff
if P[i] > params['control_ratedPower']:
break
def constantPregionIII(pitch, Uhub, Omega):
Uhub_i = Uhub
Omega_i = Omega
pitch = pitch
P_aero, _, _, _ = self.ccblade.evaluate([Uhub_i], [Omega_i * 30. / np.pi], [pitch], coefficients=False)
P, eff = CSMDrivetrain(P_aero, params['control_ratedPower'], params['drivetrainType'])
return abs(P - params['control_ratedPower'])
if regionIIhalf == True:
# Rated conditions
def min_Uhub_rated_II12(min_params):
return min_params[1]
def get_Uhub_rated_II12(min_params):
Uhub_i = min_params[1]
Omega_i = Omega_max
pitch = min_params[0]
P_aero_i, _, _, _ = self.ccblade.evaluate([Uhub_i], [Omega_i * 30. / np.pi], [pitch], coefficients=False)
P_i,eff = CSMDrivetrain(P_aero_i, params['control_ratedPower'], params['drivetrainType'])
return abs(P_i - params['control_ratedPower'])
x0 = [pitch[i] + 2. , Uhub[i]]
bnds = [(pitch0, pitch0 + 10.),(Uhub[i-1],Uhub[i+1])]
const = {}
const['type'] = 'eq'
const['fun'] = get_Uhub_rated_II12
params_rated = minimize(min_Uhub_rated_II12, x0, method='SLSQP', tol = 1.e-2, bounds=bnds, constraints=const)
U_rated = params_rated.x[1]
if not np.isnan(U_rated):
Uhub[i] = U_rated
pitch[i] = params_rated.x[0]
else:
print('Regulation trajectory is struggling to find a solution for rated wind speed. Check rotor_aeropower.py')
Omega[i] = Omega_max
P_aero[i], T[i], Q[i], M[i], Cp_aero[i], _, _, _ = self.ccblade.evaluate([Uhub[i]], [Omega[i] * 30. / np.pi], [pitch0], coefficients=True)
P_i, eff = CSMDrivetrain(P_aero[i], params['control_ratedPower'], params['drivetrainType'])
Cp[i] = Cp_aero[i]*eff
P[i] = params['control_ratedPower']
else:
# Rated conditions
def get_Uhub_rated_noII12(pitch, Uhub):
Uhub_i = Uhub
Omega_i = min([Uhub_i * params['control_tsr'] / params['Rtip'], Omega_max])
pitch_i = pitch
P_aero_i, _, _, _ = self.ccblade.evaluate([Uhub_i], [Omega_i * 30. / np.pi], [pitch_i], coefficients=False)
P_i, eff = CSMDrivetrain(P_aero_i, params['control_ratedPower'], params['drivetrainType'])
return abs(P_i - params['control_ratedPower'])
bnds = [Uhub[i-1], Uhub[i+1]]
U_rated = minimize_scalar(lambda x: get_Uhub_rated_noII12(pitch[i], x), bounds=bnds, method='bounded', options=options)['x']
if not np.isnan(U_rated):
Uhub[i] = U_rated
else:
print('Regulation trajectory is struggling to find a solution for rated wind speed. Check rotor_aeropower.py')
Omega[i] = min([Uhub[i] * params['control_tsr'] / params['Rtip'], Omega_max])
pitch0 = pitch[i]
P_aero[i], T[i], Q[i], M[i], Cp_aero[i], _, _, _ = self.ccblade.evaluate([Uhub[i]], [Omega[i] * 30. / np.pi], [pitch0], coefficients=True)
P[i], eff = CSMDrivetrain(P_aero[i], params['control_ratedPower'], params['drivetrainType'])
Cp[i] = Cp_aero[i]*eff
for j in range(i + 1,len(Uhub)):
Omega[j] = Omega[i]
if self.regulation_reg_III == True:
pitch0 = pitch[j-1]
bnds = [pitch0, pitch0 + 15.]
pitch_regionIII = minimize_scalar(lambda x: constantPregionIII(x, Uhub[j], Omega[j]), bounds=bnds, method='bounded', options=options)['x']
pitch[j] = pitch_regionIII
P_aero[j], T[j], Q[j], M[j], Cp_aero[j], _, _, _ = self.ccblade.evaluate([Uhub[j]], [Omega[j] * 30. / np.pi], [pitch[j]], coefficients=True)
P[j], eff = CSMDrivetrain(P_aero[j], params['control_ratedPower'], params['drivetrainType'])
Cp[j] = Cp_aero[j]*eff
if abs(P[j] - params['control_ratedPower']) > 1e+4:
print('The pitch in region III is not being determined correctly at wind speed ' + str(Uhub[j]) + ' m/s')
P[j] = params['control_ratedPower']
T[j] = T[j-1]
Q[j] = P[j] / Omega[j]
M[j] = M[j-1]
pitch[j] = pitch[j-1]
Cp[j] = P[j] / (0.5 * params['rho'] * np.pi * params['Rtip']**2 * Uhub[i]**3)
P[j] = params['control_ratedPower']
else:
P[j] = params['control_ratedPower']
T[j] = 0
Q[j] = Q[i]
M[j] = 0
pitch[j] = 0
Cp[j] = P[j] / (0.5 * params['rho'] * np.pi * params['Rtip']**2 * Uhub[i]**3)
unknowns['T'] = T
unknowns['Q'] = Q
unknowns['Omega'] = Omega * 30. / np.pi
unknowns['P'] = P
unknowns['Cp'] = Cp
unknowns['V'] = Uhub
unknowns['M'] = M
unknowns['pitch'] = pitch
self.ccblade.induction_inflow = True
a_regII, ap_regII, alpha_regII = self.ccblade.distributedAeroLoads(Uhub[0], Omega[0] * 30. / np.pi, pitch[0], 0.0)
# Fit spline to powercurve for higher grid density
spline = PchipInterpolator(Uhub, P)
V_spline = np.linspace(params['control_Vin'],params['control_Vout'], num=self.n_pc_spline)
P_spline = spline(V_spline)
# outputs
idx_rated = list(Uhub).index(U_rated)
unknowns['rated_V'] = U_rated
unknowns['rated_Omega'] = Omega[idx_rated] * 30. / np.pi
unknowns['rated_pitch'] = pitch[idx_rated]
unknowns['rated_T'] = T[idx_rated]
unknowns['rated_Q'] = Q[idx_rated]
unknowns['V_spline'] = V_spline
unknowns['P_spline'] = P_spline
unknowns['ax_induct_cutin'] = a_regII
unknowns['tang_induct_cutin'] = ap_regII
unknowns['aoa_cutin'] = alpha_regII
class CCBlade(AeroBase):
"""blade element momentum code"""
# (potential) variables
r = Array(
iotype='in',
units='m',
desc=
'radial locations where blade is defined (should be increasing and not go all the way to hub or tip)'
)
chord = Array(iotype='in', units='m', desc='chord length at each section')
theta = Array(
iotype='in',
units='deg',
desc='twist angle at each section (positive decreases angle of attack)'
)
Rhub = Float(iotype='in', units='m', desc='hub radius')
Rtip = Float(iotype='in', units='m', desc='tip radius')
hubHt = Float(iotype='in', units='m', desc='hub height')
precone = Float(0.0, iotype='in', desc='precone angle', units='deg')
tilt = Float(0.0, iotype='in', desc='shaft tilt', units='deg')
yaw = Float(0.0, iotype='in', desc='yaw error', units='deg')
# TODO: I've not hooked up the gradients for these ones yet.
precurve = Array(iotype='in', units='m', desc='precurve at each section')
precurveTip = Float(0.0, iotype='in', units='m', desc='precurve at tip')
# parameters
airfoil_files = List(Str, iotype='in', desc='names of airfoil file')
B = Int(3, iotype='in', desc='number of blades')
rho = Float(1.225, iotype='in', units='kg/m**3', desc='density of air')
mu = Float(1.81206e-5,
iotype='in',
units='kg/(m*s)',
desc='dynamic viscosity of air')
shearExp = Float(0.2, iotype='in', desc='shear exponent')
nSector = Int(
4,
iotype='in',
desc=
'number of sectors to divide rotor face into in computing thrust and power'
)
tiploss = Bool(True, iotype='in', desc='include Prandtl tip loss model')
hubloss = Bool(True, iotype='in', desc='include Prandtl hub loss model')
wakerotation = Bool(
True,
iotype='in',
desc=
'include effect of wake rotation (i.e., tangential induction factor is nonzero)'
)
usecd = Bool(True,
iotype='in',
desc='use drag coefficient in computing induction factors')
missing_deriv_policy = 'assume_zero'
def execute(self):
if len(self.precurve) == 0:
self.precurve = np.zeros_like(self.r)
# airfoil files
n = len(self.airfoil_files)
af = [0] * n
afinit = CCAirfoil.initFromAerodynFile
for i in range(n):
af[i] = afinit(self.airfoil_files[i])
self.ccblade = CCBlade_PY(self.r,
self.chord,
self.theta,
af,
self.Rhub,
self.Rtip,
self.B,
self.rho,
self.mu,
self.precone,
self.tilt,
self.yaw,
self.shearExp,
self.hubHt,
self.nSector,
self.precurve,
self.precurveTip,
tiploss=self.tiploss,
hubloss=self.hubloss,
wakerotation=self.wakerotation,
usecd=self.usecd,
derivatives=True)
if self.run_case == 'power':
# power, thrust, torque
self.P, self.T, self.Q, self.dP, self.dT, self.dQ \
= self.ccblade.evaluate(self.Uhub, self.Omega, self.pitch, coefficient=False)
elif self.run_case == 'loads':
# distributed loads
Np, Tp, self.dNp, self.dTp \
= self.ccblade.distributedAeroLoads(self.V_load, self.Omega_load, self.pitch_load, self.azimuth_load)
# concatenate loads at root/tip
self.loads.r = np.concatenate([[self.Rhub], self.r, [self.Rtip]])
Np = np.concatenate([[0.0], Np, [0.0]])
Tp = np.concatenate([[0.0], Tp, [0.0]])
# conform to blade-aligned coordinate system
self.loads.Px = Np
self.loads.Py = -Tp
self.loads.Pz = 0 * Np
# return other outputs needed
self.loads.V = self.V_load
self.loads.Omega = self.Omega_load
self.loads.pitch = self.pitch_load
self.loads.azimuth = self.azimuth_load
def list_deriv_vars(self):
if self.run_case == 'power':
inputs = ('precone', 'tilt', 'hubHt', 'Rhub', 'Rtip', 'yaw',
'Uhub', 'Omega', 'pitch', 'r', 'chord', 'theta',
'precurve', 'precurveTip')
outputs = ('P', 'T', 'Q')
elif self.run_case == 'loads':
inputs = ('r', 'chord', 'theta', 'Rhub', 'Rtip', 'hubHt',
'precone', 'tilt', 'yaw', 'V_load', 'Omega_load',
'pitch_load', 'azimuth_load', 'precurve')
outputs = ('loads.r', 'loads.Px', 'loads.Py', 'loads.Pz',
'loads.V', 'loads.Omega', 'loads.pitch',
'loads.azimuth')
return inputs, outputs
def provideJ(self):
if self.run_case == 'power':
dP = self.dP
dT = self.dT
dQ = self.dQ
jP = hstack([
dP['dprecone'], dP['dtilt'], dP['dhubHt'], dP['dRhub'],
dP['dRtip'], dP['dyaw'], dP['dUinf'], dP['dOmega'],
dP['dpitch'], dP['dr'], dP['dchord'], dP['dtheta'],
dP['dprecurve'], dP['dprecurveTip']
])
jT = hstack([
dT['dprecone'], dT['dtilt'], dT['dhubHt'], dT['dRhub'],
dT['dRtip'], dT['dyaw'], dT['dUinf'], dT['dOmega'],
dT['dpitch'], dT['dr'], dT['dchord'], dT['dtheta'],
dT['dprecurve'], dT['dprecurveTip']
])
jQ = hstack([
dQ['dprecone'], dQ['dtilt'], dQ['dhubHt'], dQ['dRhub'],
dQ['dRtip'], dQ['dyaw'], dQ['dUinf'], dQ['dOmega'],
dQ['dpitch'], dQ['dr'], dQ['dchord'], dQ['dtheta'],
dQ['dprecurve'], dQ['dprecurveTip']
])
J = vstack([jP, jT, jQ])
elif self.run_case == 'loads':
dNp = self.dNp
dTp = self.dTp
n = len(self.r)
dr_dr = vstack([np.zeros(n), np.eye(n), np.zeros(n)])
dr_dRhub = np.zeros(n + 2)
dr_dRtip = np.zeros(n + 2)
dr_dRhub[0] = 1.0
dr_dRtip[-1] = 1.0
dr = hstack([
dr_dr,
np.zeros((n + 2, 2 * n)), dr_dRhub, dr_dRtip,
np.zeros((n + 2, 8 + n))
])
jNp = hstack([
dNp['dr'], dNp['dchord'], dNp['dtheta'], dNp['dRhub'],
dNp['dRtip'], dNp['dhubHt'], dNp['dprecone'], dNp['dtilt'],
dNp['dyaw'], dNp['dUinf'], dNp['dOmega'], dNp['dpitch'],
dNp['dazimuth'], dNp['dprecurve']
])
jTp = hstack([
dTp['dr'], dTp['dchord'], dTp['dtheta'], dTp['dRhub'],
dTp['dRtip'], dTp['dhubHt'], dTp['dprecone'], dTp['dtilt'],
dTp['dyaw'], dTp['dUinf'], dTp['dOmega'], dTp['dpitch'],
dTp['dazimuth'], dTp['dprecurve']
])
dPx = vstack([np.zeros(4 * n + 10), jNp, np.zeros(4 * n + 10)])
dPy = vstack([np.zeros(4 * n + 10), -jTp, np.zeros(4 * n + 10)])
dPz = np.zeros((n + 2, 4 * n + 10))
dV = np.zeros(4 * n + 10)
dV[3 * n + 6] = 1.0
dOmega = np.zeros(4 * n + 10)
dOmega[3 * n + 7] = 1.0
dpitch = np.zeros(4 * n + 10)
dpitch[3 * n + 8] = 1.0
dazimuth = np.zeros(4 * n + 10)
dazimuth[3 * n + 9] = 1.0
J = vstack([dr, dPx, dPy, dPz, dV, dOmega, dpitch, dazimuth])
return J
dNp_dRhub = dNp['dRhub'] dNp_dRtip = dNp['dRtip'] dNp_dprecone = dNp['dprecone'] dNp_dtilt = dNp['dtilt'] dNp_dhubHt = dNp['dhubHt'] dNp_dyaw = dNp['dyaw'] dNp_dazimuth = dNp['dazimuth'] dNp_dUinf = dNp['dUinf'] dNp_dOmega = dNp['dOmega'] dNp_dpitch = dNp['dpitch'] # 5 ---------- # 6 ---------- outputs, derivs = rotor.evaluate([Uinf], [Omega], [pitch]) P = outputs['P'] T = outputs['T'] Q = outputs['Q'] dP = derivs['dP'] dT = derivs['dT'] dQ = derivs['dQ'] npts = len(P) # npts x 1 dP_dprecone = dP['dprecone'] dP_dtilt = dP['dtilt'] dP_dhubHt = dP['dhubHt'] dP_dRhub = dP['dRhub'] dP_dRtip = dP['dRtip']
dNp_dprecone = dNp['dprecone']
dNp_dtilt = dNp['dtilt']
dNp_dhubHt = dNp['dhubHt']
dNp_dyaw = dNp['dyaw']
dNp_dazimuth = dNp['dazimuth']
dNp_dUinf = dNp['dUinf']
dNp_dOmega = dNp['dOmega']
dNp_dpitch = dNp['dpitch']
# 5 ----------
# 6 ----------
P, T, Q, dP, dT, dQ \
= rotor.evaluate([Uinf], [Omega], [pitch])
npts = len(P)
# npts x 1
dP_dprecone = dP['dprecone']
dP_dtilt = dP['dtilt']
dP_dhubHt = dP['dhubHt']
dP_dRhub = dP['dRhub']
dP_dRtip = dP['dRtip']
dP_dprecurveTip = dP['dprecurveTip']
dP_dpresweepTip = dP['dpresweepTip']
dP_dyaw = dP['dyaw']
# npts x npts
dP_dUinf = dP['dUinf']
precone = 2.5
yaw = 0.0
shearExp = 0.2
hubHt = high
nSector = 8
# create CCBlade object
aeroanalysis = CCBlade(rad, c, alpha, af, Rhub, Rtip, blade, rho, mu, precone, tilt, yaw, shearExp, hubHt, nSector)
tsr = np.linspace(0,20,100) # tip-speed ratio
Uinf = Vinf*np.ones_like(tsr) # free stream wind speed
Omega = ((Uinf*tsr)/Rtip)*(30./np.pi) # rotation rate (rad/s)
pitch = np.ones_like(tsr)*0. # pitch (deg)
# Calculating power coefficients at each tip-speed ratio
CP,_,_ = aeroanalysis.evaluate(Uinf, Omega, pitch, coefficient=True)
# Creating a power curve for the turbine (tip-speed ratio vs. power coefficient)
powercurve = Akima1DInterpolator(tsr,CP)
# Adjusting geometry for SPL calculations
r_nrel = np.array([2.8667, 5.6000, 8.3333, 11.7500, 15.8500, 19.9500, 24.0500, 28.1500, 32.2500, 36.3500, 40.4500, 44.5500, 48.6500, 52.7500, 56.1667, 58.9000, 61.6333, 63.0]) # radial positions (m)
rad = r_nrel*r_ratio
# Initialize input variables
rotorDiameter = np.ones(nturb)*rotor_diameter
generator_efficiency = np.ones(nturb)*0.944
yaw = np.ones((nwind,nturb))*0.
rpm = np.ones(nwind*nturb)*rpm_max
# Optimization
plt.plot(rstar, Tp/1e3, label='lead-lag')
plt.plot(rstar, Np/1e3, label='flapwise')
plt.xlabel('blade fraction')
plt.ylabel('distributed aerodynamic loads (kN)')
plt.legend(loc='upper left')
plt.grid()
plt.show()
# 5 ----------
# plt.savefig('/Users/sning/Dropbox/NREL/SysEng/TWISTER/ccblade-beta-setup/docs/images/distributedAeroLoads.pdf')
# plt.savefig('/Users/sning/Dropbox/NREL/SysEng/TWISTER/ccblade-beta-setup/docs/images/distributedAeroLoads.png')
# 6 ----------
P, T, Q = rotor.evaluate([Uinf], [Omega], [pitch])
CP, CT, CQ = rotor.evaluate([Uinf], [Omega], [pitch], coefficient=True)
print 'CP =', CP
print 'CT =', CT
print 'CQ =', CQ
# 6 ----------
# 7 ----------
# velocity has a small amount of Reynolds number dependence
tsr = np.linspace(2, 14, 50)
Omega = 10.0 * np.ones_like(tsr)
Uinf = Omega*pi/30.0 * Rtip/tsr
dNp_dtilt = dNp['dtilt']
dNp_dhubHt = dNp['dhubHt']
dNp_dyaw = dNp['dyaw']
dNp_dazimuth = dNp['dazimuth']
dNp_dUinf = dNp['dUinf']
dNp_dOmega = dNp['dOmega']
dNp_dpitch = dNp['dpitch']
# 5 ----------
# 6 ----------
P, T, Q, dP, dT, dQ \
= rotor.evaluate([Uinf], [Omega], [pitch])
npts = len(P)
# npts x 1
dP_dprecone = dP['dprecone']
dP_dtilt = dP['dtilt']
dP_dhubHt = dP['dhubHt']
dP_dRhub = dP['dRhub']
dP_dRtip = dP['dRtip']
dP_dprecurveTip = dP['dprecurveTip']
dP_dpresweepTip = dP['dpresweepTip']
dP_dyaw = dP['dyaw']
# npts x npts
dP_dUinf = dP['dUinf']
class RegulatedPowerCurve(Component): # Implicit COMPONENT
def __init__(self, naero, n_pc, n_pc_spline, regulation_reg_II5 = True, regulation_reg_III = False):
super(RegulatedPowerCurve, self).__init__()
# parameters
self.add_param('control_Vin', val=0.0, units='m/s', desc='cut-in wind speed')
self.add_param('control_Vout', val=0.0, units='m/s', desc='cut-out wind speed')
self.add_param('control_ratedPower', val=0.0, units='W', desc='electrical rated power')
self.add_param('control_minOmega', val=0.0, units='rpm', desc='minimum allowed rotor rotation speed')
self.add_param('control_maxOmega', val=0.0, units='rpm', desc='maximum allowed rotor rotation speed')
self.add_param('control_maxTS', val=0.0, units='m/s', desc='maximum allowed blade tip speed')
self.add_param('control_tsr', val=0.0, desc='tip-speed ratio in Region 2 (should be optimized externally)')
self.add_param('control_pitch', val=0.0, units='deg', desc='pitch angle in region 2 (and region 3 for fixed pitch machines)')
self.add_param('drivetrainType', val=DRIVETRAIN_TYPE['GEARED'], pass_by_obj=True)
self.add_param('drivetrainEff', val=0.0, desc='overwrite drivetrain model with a given efficiency, used for FAST analysis')
self.add_param('r', val=np.zeros(naero), units='m', desc='radial locations where blade is defined (should be increasing and not go all the way to hub or tip)')
self.add_param('chord', val=np.zeros(naero), units='m', desc='chord length at each section')
self.add_param('theta', val=np.zeros(naero), units='deg', desc='twist angle at each section (positive decreases angle of attack)')
self.add_param('Rhub', val=0.0, units='m', desc='hub radius')
self.add_param('Rtip', val=0.0, units='m', desc='tip radius')
self.add_param('hubHt', val=0.0, units='m', desc='hub height')
self.add_param('precone', val=0.0, units='deg', desc='precone angle', )
self.add_param('tilt', val=0.0, units='deg', desc='shaft tilt', )
self.add_param('yaw', val=0.0, units='deg', desc='yaw error', )
self.add_param('precurve', val=np.zeros(naero), units='m', desc='precurve at each section')
self.add_param('precurveTip', val=0.0, units='m', desc='precurve at tip')
self.add_param('airfoils', val=[0]*naero, desc='CCAirfoil instances', pass_by_obj=True)
self.add_param('B', val=0, desc='number of blades', pass_by_obj=True)
self.add_param('rho', val=0.0, units='kg/m**3', desc='density of air')
self.add_param('mu', val=0.0, units='kg/(m*s)', desc='dynamic viscosity of air')
self.add_param('shearExp', val=0.0, desc='shear exponent')
self.add_param('nSector', val=4, desc='number of sectors to divide rotor face into in computing thrust and power', pass_by_obj=True)
self.add_param('tiploss', val=True, desc='include Prandtl tip loss model', pass_by_obj=True)
self.add_param('hubloss', val=True, desc='include Prandtl hub loss model', pass_by_obj=True)
self.add_param('wakerotation', val=True, desc='include effect of wake rotation (i.e., tangential induction factor is nonzero)', pass_by_obj=True)
self.add_param('usecd', val=True, desc='use drag coefficient in computing induction factors', pass_by_obj=True)
# outputs
self.add_output('V', val=np.zeros(n_pc), units='m/s', desc='wind vector')
self.add_output('Omega', val=np.zeros(n_pc), units='rpm', desc='rotor rotational speed')
self.add_output('pitch', val=np.zeros(n_pc), units='deg', desc='rotor pitch schedule')
self.add_output('P', val=np.zeros(n_pc), units='W', desc='rotor electrical power')
self.add_output('T', val=np.zeros(n_pc), units='N', desc='rotor aerodynamic thrust')
self.add_output('Q', val=np.zeros(n_pc), units='N*m', desc='rotor aerodynamic torque')
self.add_output('M', val=np.zeros(n_pc), units='N*m', desc='blade root moment')
self.add_output('Cp', val=np.zeros(n_pc), desc='rotor electrical power coefficient')
self.add_output('V_spline', val=np.zeros(n_pc_spline), units='m/s', desc='wind vector')
self.add_output('P_spline', val=np.zeros(n_pc_spline), units='W', desc='rotor electrical power')
self.add_output('V_R25', val=0.0, units='m/s', desc='region 2.5 transition wind speed')
self.add_output('rated_V', val=0.0, units='m/s', desc='rated wind speed')
self.add_output('rated_Omega', val=0.0, units='rpm', desc='rotor rotation speed at rated')
self.add_output('rated_pitch', val=0.0, units='deg', desc='pitch setting at rated')
self.add_output('rated_T', val=0.0, units='N', desc='rotor aerodynamic thrust at rated')
self.add_output('rated_Q', val=0.0, units='N*m', desc='rotor aerodynamic torque at rated')
self.add_output('ax_induct_cutin', val=np.zeros(naero), desc='rotor axial induction at cut-in wind speed along blade span')
self.add_output('tang_induct_cutin', val=np.zeros(naero), desc='rotor tangential induction at cut-in wind speed along blade span')
self.add_output('aoa_cutin', val=np.zeros(naero), desc='angle of attack distribution along blade span at cut-in wind speed')
self.naero = naero
self.n_pc = n_pc
self.n_pc_spline = n_pc_spline
self.lock_pitchII = False
self.regulation_reg_II5 = regulation_reg_II5
self.regulation_reg_III = regulation_reg_III
self.deriv_options['form'] = 'central'
self.deriv_options['step_calc'] = 'relative'
def solve_nonlinear(self, params, unknowns, resids):
self.ccblade = CCBlade(params['r'], params['chord'], params['theta'], params['airfoils'], params['Rhub'], params['Rtip'], params['B'], params['rho'], params['mu'], params['precone'], params['tilt'], params['yaw'], params['shearExp'], params['hubHt'], params['nSector'])
Uhub = np.linspace(params['control_Vin'],params['control_Vout'], self.n_pc)
P_aero = np.zeros_like(Uhub)
Cp_aero = np.zeros_like(Uhub)
P = np.zeros_like(Uhub)
Cp = np.zeros_like(Uhub)
T = np.zeros_like(Uhub)
Q = np.zeros_like(Uhub)
M = np.zeros_like(Uhub)
Omega = np.zeros_like(Uhub)
pitch = np.zeros_like(Uhub) + params['control_pitch']
Omega_max = min([params['control_maxTS'] / params['Rtip'], params['control_maxOmega']*np.pi/30.])
# Region II
for i in range(len(Uhub)):
Omega[i] = Uhub[i] * params['control_tsr'] / params['Rtip']
P_aero, T, Q, M, Cp_aero, _, _, _ = self.ccblade.evaluate(Uhub, Omega * 30. / np.pi, pitch, coefficients=True)
P, eff = CSMDrivetrain(P_aero, params['control_ratedPower'], params['drivetrainType'])
Cp = Cp_aero*eff
# search for Region 2.5 bounds
for i in range(len(Uhub)):
if Omega[i] > Omega_max and P[i] < params['control_ratedPower']:
Omega[i] = Omega_max
Uhub[i] = Omega[i] * params['Rtip'] / params['control_tsr']
P_aero[i], T[i], Q[i], M[i], Cp_aero[i], _, _, _ = self.ccblade.evaluate([Uhub[i]], [Omega[i] * 30. / np.pi], [pitch[i]], coefficients=True)
P[i], eff = CSMDrivetrain(P_aero[i], params['control_ratedPower'], params['drivetrainType'])
Cp[i] = Cp_aero[i]*eff
regionIIhalf = True
i_IIhalf_start = i
unknowns['V_R25'] = Uhub[i]
break
if P[i] > params['control_ratedPower']:
regionIIhalf = False
break
def maxPregionIIhalf(pitch, Uhub, Omega):
Uhub_i = Uhub
Omega_i = Omega
pitch = pitch
P, _, _, _ = self.ccblade.evaluate([Uhub_i], [Omega_i * 30. / np.pi], [pitch], coefficients=False)
return -P
# Solve for regoin 2.5 pitch
options = {}
options['disp'] = False
options['xatol'] = 1.e-2
if regionIIhalf == True:
for i in range(i_IIhalf_start + 1, len(Uhub)):
Omega[i] = Omega_max
pitch0 = pitch[i-1]
bnds = [pitch0 - 10., pitch0 + 10.]
pitch_regionIIhalf = minimize_scalar(lambda x: maxPregionIIhalf(x, Uhub[i], Omega[i]), bounds=bnds, method='bounded', options=options)['x']
pitch[i] = pitch_regionIIhalf
P_aero[i], T[i], Q[i], M[i], Cp_aero[i], _, _, _ = self.ccblade.evaluate([Uhub[i]], [Omega[i] * 30. / np.pi], [pitch[i]], coefficients=True)
P[i], eff = CSMDrivetrain(P_aero[i], params['control_ratedPower'], params['drivetrainType'])
Cp[i] = Cp_aero[i]*eff
if P[i] > params['control_ratedPower']:
break
def constantPregionIII(pitch, Uhub, Omega):
Uhub_i = Uhub
Omega_i = Omega
pitch = pitch
P_aero, _, _, _ = self.ccblade.evaluate([Uhub_i], [Omega_i * 30. / np.pi], [pitch], coefficients=False)
P, eff = CSMDrivetrain(P_aero, params['control_ratedPower'], params['drivetrainType'])
return abs(P - params['control_ratedPower'])
if regionIIhalf == True:
# Rated conditions
def min_Uhub_rated_II12(min_params):
return min_params[1]
def get_Uhub_rated_II12(min_params):
Uhub_i = min_params[1]
Omega_i = Omega_max
pitch = min_params[0]
P_aero_i, _, _, _ = self.ccblade.evaluate([Uhub_i], [Omega_i * 30. / np.pi], [pitch], coefficients=False)
P_i,eff = CSMDrivetrain(P_aero_i, params['control_ratedPower'], params['drivetrainType'])
return abs(P_i - params['control_ratedPower'])
x0 = [pitch[i] + 2. , Uhub[i]]
bnds = [(pitch0, pitch0 + 10.),(Uhub[i-1],Uhub[i+1])]
const = {}
const['type'] = 'eq'
const['fun'] = get_Uhub_rated_II12
params_rated = minimize(min_Uhub_rated_II12, x0, method='SLSQP', tol = 1.e-2, bounds=bnds, constraints=const)
U_rated = params_rated.x[1]
if not np.isnan(U_rated):
Uhub[i] = U_rated
pitch[i] = params_rated.x[0]
else:
print('Regulation trajectory is struggling to find a solution for rated wind speed. Check rotor_aeropower.py')
Omega[i] = Omega_max
P_aero[i], T[i], Q[i], M[i], Cp_aero[i], _, _, _ = self.ccblade.evaluate([Uhub[i]], [Omega[i] * 30. / np.pi], [pitch0], coefficients=True)
P_i, eff = CSMDrivetrain(P_aero[i], params['control_ratedPower'], params['drivetrainType'])
Cp[i] = Cp_aero[i]*eff
P[i] = params['control_ratedPower']
else:
# Rated conditions
def get_Uhub_rated_noII12(pitch, Uhub):
Uhub_i = Uhub
Omega_i = min([Uhub_i * params['control_tsr'] / params['Rtip'], Omega_max])
pitch_i = pitch
P_aero_i, _, _, _ = self.ccblade.evaluate([Uhub_i], [Omega_i * 30. / np.pi], [pitch_i], coefficients=False)
P_i, eff = CSMDrivetrain(P_aero_i, params['control_ratedPower'], params['drivetrainType'])
return abs(P_i - params['control_ratedPower'])
bnds = [Uhub[i-1], Uhub[i+1]]
U_rated = minimize_scalar(lambda x: get_Uhub_rated_noII12(pitch[i], x), bounds=bnds, method='bounded', options=options)['x']
if not np.isnan(U_rated):
Uhub[i] = U_rated
else:
print('Regulation trajectory is struggling to find a solution for rated wind speed. Check rotor_aeropower.py')
Omega[i] = min([Uhub[i] * params['control_tsr'] / params['Rtip'], Omega_max])
pitch0 = pitch[i]
P_aero[i], T[i], Q[i], M[i], Cp_aero[i], _, _, _ = self.ccblade.evaluate([Uhub[i]], [Omega[i] * 30. / np.pi], [pitch0], coefficients=True)
P[i], eff = CSMDrivetrain(P_aero[i], params['control_ratedPower'], params['drivetrainType'])
Cp[i] = Cp_aero[i]*eff
for j in range(i + 1,len(Uhub)):
Omega[j] = Omega[i]
if self.regulation_reg_III == True:
pitch0 = pitch[j-1]
bnds = [pitch0, pitch0 + 15.]
pitch_regionIII = minimize_scalar(lambda x: constantPregionIII(x, Uhub[j], Omega[j]), bounds=bnds, method='bounded', options=options)['x']
pitch[j] = pitch_regionIII
P_aero[j], T[j], Q[j], M[j], Cp_aero[j], _, _, _ = self.ccblade.evaluate([Uhub[j]], [Omega[j] * 30. / np.pi], [pitch[j]], coefficients=True)
P[j], eff = CSMDrivetrain(P_aero[j], params['control_ratedPower'], params['drivetrainType'])
Cp[j] = Cp_aero[j]*eff
if abs(P[j] - params['control_ratedPower']) > 1e+4:
print('The pitch in region III is not being determined correctly at wind speed ' + str(Uhub[j]) + ' m/s')
P[j] = params['control_ratedPower']
T[j] = T[j-1]
Q[j] = P[j] / Omega[j]
M[j] = M[j-1]
pitch[j] = pitch[j-1]
Cp[j] = P[j] / (0.5 * params['rho'] * np.pi * params['Rtip']**2 * Uhub[i]**3)
P[j] = params['control_ratedPower']
else:
P[j] = params['control_ratedPower']
T[j] = 0
Q[j] = Q[i]
M[j] = 0
pitch[j] = 0
Cp[j] = P[j] / (0.5 * params['rho'] * np.pi * params['Rtip']**2 * Uhub[i]**3)
unknowns['T'] = T
unknowns['Q'] = Q
unknowns['Omega'] = Omega * 30. / np.pi
unknowns['P'] = P
unknowns['Cp'] = Cp
unknowns['V'] = Uhub
unknowns['M'] = M
unknowns['pitch'] = pitch
self.ccblade.induction_inflow = True
a_regII, ap_regII, alpha_regII,_, _ = self.ccblade.distributedAeroLoads(Uhub[0], Omega[0] * 30. / np.pi, pitch[0], 0.0)
# Fit spline to powercurve for higher grid density
spline = PchipInterpolator(Uhub, P)
V_spline = np.linspace(params['control_Vin'],params['control_Vout'], num=self.n_pc_spline)
P_spline = spline(V_spline)
# outputs
idx_rated = list(Uhub).index(U_rated)
unknowns['rated_V'] = U_rated
unknowns['rated_Omega'] = Omega[idx_rated] * 30. / np.pi
unknowns['rated_pitch'] = pitch[idx_rated]
unknowns['rated_T'] = T[idx_rated]
unknowns['rated_Q'] = Q[idx_rated]
unknowns['V_spline'] = V_spline
unknowns['P_spline'] = P_spline
unknowns['ax_induct_cutin'] = a_regII
unknowns['tang_induct_cutin'] = ap_regII
unknowns['aoa_cutin'] = alpha_regII
class TestGradients(unittest.TestCase):
def setUp(self):
# geometry
self.Rhub = 1.5
self.Rtip = 63.0
self.r = np.array([2.8667, 5.6000, 8.3333, 11.7500, 15.8500, 19.9500, 24.0500,
28.1500, 32.2500, 36.3500, 40.4500, 44.5500, 48.6500, 52.7500,
56.1667, 58.9000, 61.6333])
self.chord = np.array([3.542, 3.854, 4.167, 4.557, 4.652, 4.458, 4.249, 4.007, 3.748,
3.502, 3.256, 3.010, 2.764, 2.518, 2.313, 2.086, 1.419])
self.theta = np.array([13.308, 13.308, 13.308, 13.308, 11.480, 10.162, 9.011, 7.795,
6.544, 5.361, 4.188, 3.125, 2.319, 1.526, 0.863, 0.370, 0.106])
self.B = 3 # number of blades
# atmosphere
self.rho = 1.225
self.mu = 1.81206e-5
afinit = CCAirfoil.initFromAerodynFile # just for shorthand
basepath = path.join(path.dirname(path.realpath(__file__)), '5MW_AFFiles') + path.sep
# load all airfoils
airfoil_types = [0]*8
airfoil_types[0] = afinit(basepath + 'Cylinder1.dat')
airfoil_types[1] = afinit(basepath + 'Cylinder2.dat')
airfoil_types[2] = afinit(basepath + 'DU40_A17.dat')
airfoil_types[3] = afinit(basepath + 'DU35_A17.dat')
airfoil_types[4] = afinit(basepath + 'DU30_A17.dat')
airfoil_types[5] = afinit(basepath + 'DU25_A17.dat')
airfoil_types[6] = afinit(basepath + 'DU21_A17.dat')
airfoil_types[7] = afinit(basepath + 'NACA64_A17.dat')
# place at appropriate radial stations
af_idx = [0, 0, 1, 2, 3, 3, 4, 5, 5, 6, 6, 7, 7, 7, 7, 7, 7]
self.af = [0]*len(self.r)
for i in range(len(self.r)):
self.af[i] = airfoil_types[af_idx[i]]
self.tilt = -5.0
self.precone = 2.5
self.yaw = 0.0
self.shearExp = 0.2
self.hubHt = 80.0
self.nSector = 8
# create CCBlade object
self.rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, self.precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=True)
# set conditions
self.Uinf = 10.0
tsr = 7.55
self.pitch = 0.0
self.Omega = self.Uinf*tsr/self.Rtip * 30.0/pi # convert to RPM
self.azimuth = 90
self.Np, self.Tp, self.dNp_dX, self.dTp_dX, self.dNp_dprecurve, self.dTp_dprecurve = \
self.rotor.distributedAeroLoads(self.Uinf, self.Omega, self.pitch, self.azimuth)
self.P, self.T, self.Q, self.dP_ds, self.dT_ds, self.dQ_ds, self.dP_dv, self.dT_dv, \
self.dQ_dv = self.rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=False)
self.CP, self.CT, self.CQ, self.dCP_ds, self.dCT_ds, self.dCQ_ds, self.dCP_dv, self.dCT_dv, \
self.dCQ_dv = self.rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=True)
self.rotor.derivatives = False
self.n = len(self.r)
# X = [r, chord, theta, Rhub, Rtip, presweep, precone, tilt, hubHt]
# scalars = [precone, tilt, hubHt, Rhub, Rtip, precurvetip, presweeptip]
# vectors = [r, chord, theta, precurve, presweep]
def test_dr1(self):
dNp_dr = self.dNp_dX[0, :]
dTp_dr = self.dTp_dX[0, :]
dNp_dr_fd = np.zeros(self.n)
dTp_dr_fd = np.zeros(self.n)
for i in range(self.n):
r = np.array(self.r)
delta = 1e-6*r[i]
r[i] += delta
rotor = CCBlade(r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, self.precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False)
Npd, Tpd = rotor.distributedAeroLoads(self.Uinf, self.Omega, self.pitch, self.azimuth)
dNp_dr_fd[i] = (Npd[i] - self.Np[i]) / delta
dTp_dr_fd[i] = (Tpd[i] - self.Tp[i]) / delta
np.testing.assert_allclose(dNp_dr_fd, dNp_dr, rtol=1e-4, atol=1e-8)
np.testing.assert_allclose(dTp_dr_fd, dTp_dr, rtol=1e-4, atol=1e-8)
def test_dr2(self):
dT_dr = self.dT_dv[0, 0, :]
dQ_dr = self.dQ_dv[0, 0, :]
dP_dr = self.dP_dv[0, 0, :]
dT_dr_fd = np.zeros(self.n)
dQ_dr_fd = np.zeros(self.n)
dP_dr_fd = np.zeros(self.n)
for i in range(self.n):
r = np.array(self.r)
delta = 1e-6*r[i]
r[i] += delta
rotor = CCBlade(r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, self.precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False)
Pd, Td, Qd = rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=False)
dT_dr_fd[i] = (Td - self.T) / delta
dQ_dr_fd[i] = (Qd - self.Q) / delta
dP_dr_fd[i] = (Pd - self.P) / delta
np.testing.assert_allclose(dT_dr_fd, dT_dr, rtol=5e-5, atol=1e-8)
np.testing.assert_allclose(dQ_dr_fd, dQ_dr, rtol=3e-4, atol=1e-8)
np.testing.assert_allclose(dP_dr_fd, dP_dr, rtol=3e-4, atol=1e-8)
def test_dr3(self):
dCT_dr = self.dCT_dv[0, 0, :]
dCQ_dr = self.dCQ_dv[0, 0, :]
dCP_dr = self.dCP_dv[0, 0, :]
dCT_dr_fd = np.zeros(self.n)
dCQ_dr_fd = np.zeros(self.n)
dCP_dr_fd = np.zeros(self.n)
for i in range(self.n):
r = np.array(self.r)
delta = 1e-6*r[i]
r[i] += delta
rotor = CCBlade(r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, self.precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False)
CPd, CTd, CQd = rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=True)
dCT_dr_fd[i] = (CTd - self.CT) / delta
dCQ_dr_fd[i] = (CQd - self.CQ) / delta
dCP_dr_fd[i] = (CPd - self.CP) / delta
np.testing.assert_allclose(dCT_dr_fd, dCT_dr, rtol=5e-5, atol=1e-8)
np.testing.assert_allclose(dCQ_dr_fd, dCQ_dr, rtol=3e-4, atol=1e-8)
np.testing.assert_allclose(dCP_dr_fd, dCP_dr, rtol=3e-4, atol=1e-8)
def test_dchord1(self):
dNp_dchord = self.dNp_dX[1, :]
dTp_dchord = self.dTp_dX[1, :]
dNp_dchord_fd = np.zeros(self.n)
dTp_dchord_fd = np.zeros(self.n)
for i in range(self.n):
chord = np.array(self.chord)
delta = 1e-6*chord[i]
chord[i] += delta
rotor = CCBlade(self.r, chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, self.precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False)
Npd, Tpd = rotor.distributedAeroLoads(self.Uinf, self.Omega, self.pitch, self.azimuth)
dNp_dchord_fd[i] = (Npd[i] - self.Np[i]) / delta
dTp_dchord_fd[i] = (Tpd[i] - self.Tp[i]) / delta
np.testing.assert_allclose(dNp_dchord_fd, dNp_dchord, rtol=1e-6, atol=1e-8)
np.testing.assert_allclose(dTp_dchord_fd, dTp_dchord, rtol=5e-5, atol=1e-8)
def test_dchord2(self):
dT_dchord = self.dT_dv[0, 1, :]
dQ_dchord = self.dQ_dv[0, 1, :]
dP_dchord = self.dP_dv[0, 1, :]
dT_dchord_fd = np.zeros(self.n)
dQ_dchord_fd = np.zeros(self.n)
dP_dchord_fd = np.zeros(self.n)
for i in range(self.n):
chord = np.array(self.chord)
delta = 1e-6*chord[i]
chord[i] += delta
rotor = CCBlade(self.r, chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, self.precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False)
Pd, Td, Qd = rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=False)
dT_dchord_fd[i] = (Td - self.T) / delta
dQ_dchord_fd[i] = (Qd - self.Q) / delta
dP_dchord_fd[i] = (Pd - self.P) / delta
np.testing.assert_allclose(dT_dchord_fd, dT_dchord, rtol=5e-6, atol=1e-8)
np.testing.assert_allclose(dQ_dchord_fd, dQ_dchord, rtol=7e-5, atol=1e-8)
np.testing.assert_allclose(dP_dchord_fd, dP_dchord, rtol=7e-5, atol=1e-8)
def test_dchord3(self):
dCT_dchord = self.dCT_dv[0, 1, :]
dCQ_dchord = self.dCQ_dv[0, 1, :]
dCP_dchord = self.dCP_dv[0, 1, :]
dCT_dchord_fd = np.zeros(self.n)
dCQ_dchord_fd = np.zeros(self.n)
dCP_dchord_fd = np.zeros(self.n)
for i in range(self.n):
chord = np.array(self.chord)
delta = 1e-6*chord[i]
chord[i] += delta
rotor = CCBlade(self.r, chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, self.precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False)
CPd, CTd, CQd = rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=True)
dCT_dchord_fd[i] = (CTd - self.CT) / delta
dCQ_dchord_fd[i] = (CQd - self.CQ) / delta
dCP_dchord_fd[i] = (CPd - self.CP) / delta
np.testing.assert_allclose(dCT_dchord_fd, dCT_dchord, rtol=5e-6, atol=1e-8)
np.testing.assert_allclose(dCQ_dchord_fd, dCQ_dchord, rtol=7e-5, atol=1e-8)
np.testing.assert_allclose(dCP_dchord_fd, dCP_dchord, rtol=7e-5, atol=1e-8)
def test_dtheta1(self):
dNp_dtheta = self.dNp_dX[2, :]
dTp_dtheta = self.dTp_dX[2, :]
dNp_dtheta_fd = np.zeros(self.n)
dTp_dtheta_fd = np.zeros(self.n)
for i in range(self.n):
theta = np.array(self.theta)
delta = 1e-6*theta[i]
theta[i] += delta
rotor = CCBlade(self.r, self.chord, theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, self.precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False)
Npd, Tpd = rotor.distributedAeroLoads(self.Uinf, self.Omega, self.pitch, self.azimuth)
dNp_dtheta_fd[i] = (Npd[i] - self.Np[i]) / delta
dTp_dtheta_fd[i] = (Tpd[i] - self.Tp[i]) / delta
np.testing.assert_allclose(dNp_dtheta_fd, dNp_dtheta, rtol=1e-6, atol=1e-8)
np.testing.assert_allclose(dTp_dtheta_fd, dTp_dtheta, rtol=1e-4, atol=1e-8)
def test_dtheta2(self):
dT_dtheta = self.dT_dv[0, 2, :]
dQ_dtheta = self.dQ_dv[0, 2, :]
dP_dtheta = self.dP_dv[0, 2, :]
dT_dtheta_fd = np.zeros(self.n)
dQ_dtheta_fd = np.zeros(self.n)
dP_dtheta_fd = np.zeros(self.n)
for i in range(self.n):
theta = np.array(self.theta)
delta = 1e-6*theta[i]
theta[i] += delta
rotor = CCBlade(self.r, self.chord, theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, self.precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False)
Pd, Td, Qd = rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=False)
dT_dtheta_fd[i] = (Td - self.T) / delta
dQ_dtheta_fd[i] = (Qd - self.Q) / delta
dP_dtheta_fd[i] = (Pd - self.P) / delta
np.testing.assert_allclose(dT_dtheta_fd, dT_dtheta, rtol=7e-5, atol=1e-8)
np.testing.assert_allclose(dQ_dtheta_fd, dQ_dtheta, rtol=7e-5, atol=1e-8)
np.testing.assert_allclose(dP_dtheta_fd, dP_dtheta, rtol=7e-5, atol=1e-8)
def test_dtheta3(self):
dCT_dtheta = self.dCT_dv[0, 2, :]
dCQ_dtheta = self.dCQ_dv[0, 2, :]
dCP_dtheta = self.dCP_dv[0, 2, :]
dCT_dtheta_fd = np.zeros(self.n)
dCQ_dtheta_fd = np.zeros(self.n)
dCP_dtheta_fd = np.zeros(self.n)
for i in range(self.n):
theta = np.array(self.theta)
delta = 1e-6*theta[i]
theta[i] += delta
rotor = CCBlade(self.r, self.chord, theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, self.precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False)
CPd, CTd, CQd = rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=True)
dCT_dtheta_fd[i] = (CTd - self.CT) / delta
dCQ_dtheta_fd[i] = (CQd - self.CQ) / delta
dCP_dtheta_fd[i] = (CPd - self.CP) / delta
np.testing.assert_allclose(dCT_dtheta_fd, dCT_dtheta, rtol=5e-6, atol=1e-8)
np.testing.assert_allclose(dCQ_dtheta_fd, dCQ_dtheta, rtol=7e-5, atol=1e-8)
np.testing.assert_allclose(dCP_dtheta_fd, dCP_dtheta, rtol=7e-5, atol=1e-8)
def test_dRhub1(self):
dNp_dRhub = self.dNp_dX[3, :]
dTp_dRhub = self.dTp_dX[3, :]
Rhub = float(self.Rhub)
delta = 1e-6*Rhub
Rhub += delta
rotor = CCBlade(self.r, self.chord, self.theta, self.af, Rhub, self.Rtip,
self.B, self.rho, self.mu, self.precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False)
Npd, Tpd = rotor.distributedAeroLoads(self.Uinf, self.Omega, self.pitch, self.azimuth)
dNp_dRhub_fd = (Npd - self.Np) / delta
dTp_dRhub_fd = (Tpd - self.Tp) / delta
np.testing.assert_allclose(dNp_dRhub_fd, dNp_dRhub, rtol=1e-5, atol=1e-7)
np.testing.assert_allclose(dTp_dRhub_fd, dTp_dRhub, rtol=1e-4, atol=1e-7)
def test_dRhub2(self):
dT_dRhub = self.dT_ds[0, 3]
dQ_dRhub = self.dQ_ds[0, 3]
dP_dRhub = self.dP_ds[0, 3]
Rhub = float(self.Rhub)
delta = 1e-6*Rhub
Rhub += delta
rotor = CCBlade(self.r, self.chord, self.theta, self.af, Rhub, self.Rtip,
self.B, self.rho, self.mu, self.precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False)
Pd, Td, Qd = rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=False)
dT_dRhub_fd = (Td - self.T) / delta
dQ_dRhub_fd = (Qd - self.Q) / delta
dP_dRhub_fd = (Pd - self.P) / delta
np.testing.assert_allclose(dT_dRhub_fd, dT_dRhub, rtol=1e-5, atol=1e-8)
np.testing.assert_allclose(dQ_dRhub_fd, dQ_dRhub, rtol=5e-5, atol=1e-8)
np.testing.assert_allclose(dP_dRhub_fd, dP_dRhub, rtol=5e-5, atol=1e-8)
def test_dRhub3(self):
dCT_dRhub = self.dCT_ds[0, 3]
dCQ_dRhub = self.dCQ_ds[0, 3]
dCP_dRhub = self.dCP_ds[0, 3]
Rhub = float(self.Rhub)
delta = 1e-6*Rhub
Rhub += delta
rotor = CCBlade(self.r, self.chord, self.theta, self.af, Rhub, self.Rtip,
self.B, self.rho, self.mu, self.precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False)
CPd, CTd, CQd = rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=True)
dCT_dRhub_fd = (CTd - self.CT) / delta
dCQ_dRhub_fd = (CQd - self.CQ) / delta
dCP_dRhub_fd = (CPd - self.CP) / delta
np.testing.assert_allclose(dCT_dRhub_fd, dCT_dRhub, rtol=1e-5, atol=1e-8)
np.testing.assert_allclose(dCQ_dRhub_fd, dCQ_dRhub, rtol=5e-5, atol=1e-8)
np.testing.assert_allclose(dCP_dRhub_fd, dCP_dRhub, rtol=5e-5, atol=1e-8)
def test_dRtip1(self):
dNp_dRtip = self.dNp_dX[4, :]
dTp_dRtip = self.dTp_dX[4, :]
Rtip = float(self.Rtip)
delta = 1e-6*Rtip
Rtip += delta
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, Rtip,
self.B, self.rho, self.mu, self.precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False)
Npd, Tpd = rotor.distributedAeroLoads(self.Uinf, self.Omega, self.pitch, self.azimuth)
dNp_dRtip_fd = (Npd - self.Np) / delta
dTp_dRtip_fd = (Tpd - self.Tp) / delta
np.testing.assert_allclose(dNp_dRtip_fd, dNp_dRtip, rtol=1e-4, atol=1e-8)
np.testing.assert_allclose(dTp_dRtip_fd, dTp_dRtip, rtol=1e-4, atol=1e-8)
def test_dRtip2(self):
dT_dRtip = self.dT_ds[0, 4]
dQ_dRtip = self.dQ_ds[0, 4]
dP_dRtip = self.dP_ds[0, 4]
Rtip = float(self.Rtip)
delta = 1e-6*Rtip
Rtip += delta
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, Rtip,
self.B, self.rho, self.mu, self.precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False)
Pd, Td, Qd = rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=False)
dT_dRtip_fd = (Td - self.T) / delta
dQ_dRtip_fd = (Qd - self.Q) / delta
dP_dRtip_fd = (Pd - self.P) / delta
np.testing.assert_allclose(dT_dRtip_fd, dT_dRtip, rtol=1e-5, atol=1e-8)
np.testing.assert_allclose(dQ_dRtip_fd, dQ_dRtip, rtol=5e-5, atol=1e-8)
np.testing.assert_allclose(dP_dRtip_fd, dP_dRtip, rtol=5e-5, atol=1e-8)
def test_dRtip3(self):
dCT_dRtip = self.dCT_ds[0, 4]
dCQ_dRtip = self.dCQ_ds[0, 4]
dCP_dRtip = self.dCP_ds[0, 4]
Rtip = float(self.Rtip)
delta = 1e-6*Rtip
Rtip += delta
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, Rtip,
self.B, self.rho, self.mu, self.precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False)
CPd, CTd, CQd = rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=True)
dCT_dRtip_fd = (CTd - self.CT) / delta
dCQ_dRtip_fd = (CQd - self.CQ) / delta
dCP_dRtip_fd = (CPd - self.CP) / delta
np.testing.assert_allclose(dCT_dRtip_fd, dCT_dRtip, rtol=1e-5, atol=1e-8)
np.testing.assert_allclose(dCQ_dRtip_fd, dCQ_dRtip, rtol=5e-5, atol=1e-8)
np.testing.assert_allclose(dCP_dRtip_fd, dCP_dRtip, rtol=5e-5, atol=1e-8)
def test_dprecone1(self):
dNp_dprecone = self.dNp_dX[6, :]
dTp_dprecone = self.dTp_dX[6, :]
precone = float(self.precone)
delta = 1e-6*precone
precone += delta
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False)
Npd, Tpd = rotor.distributedAeroLoads(self.Uinf, self.Omega, self.pitch, self.azimuth)
dNp_dprecone_fd = (Npd - self.Np) / delta
dTp_dprecone_fd = (Tpd - self.Tp) / delta
np.testing.assert_allclose(dNp_dprecone_fd, dNp_dprecone, rtol=1e-6, atol=1e-8)
np.testing.assert_allclose(dTp_dprecone_fd, dTp_dprecone, rtol=1e-6, atol=1e-8)
def test_dprecone2(self):
dT_dprecone = self.dT_ds[0, 0]
dQ_dprecone = self.dQ_ds[0, 0]
dP_dprecone = self.dP_ds[0, 0]
precone = float(self.precone)
delta = 1e-6*precone
precone += delta
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False)
Pd, Td, Qd = rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=False)
dT_dprecone_fd = (Td - self.T) / delta
dQ_dprecone_fd = (Qd - self.Q) / delta
dP_dprecone_fd = (Pd - self.P) / delta
np.testing.assert_allclose(dT_dprecone_fd, dT_dprecone, rtol=1e-5, atol=1e-8)
np.testing.assert_allclose(dQ_dprecone_fd, dQ_dprecone, rtol=5e-5, atol=1e-8)
np.testing.assert_allclose(dP_dprecone_fd, dP_dprecone, rtol=5e-5, atol=1e-8)
def test_dprecone3(self):
dCT_dprecone = self.dCT_ds[0, 0]
dCQ_dprecone = self.dCQ_ds[0, 0]
dCP_dprecone = self.dCP_ds[0, 0]
precone = float(self.precone)
delta = 1e-6*precone
precone += delta
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False)
CPd, CTd, CQd = rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=True)
dCT_dprecone_fd = (CTd - self.CT) / delta
dCQ_dprecone_fd = (CQd - self.CQ) / delta
dCP_dprecone_fd = (CPd - self.CP) / delta
np.testing.assert_allclose(dCT_dprecone_fd, dCT_dprecone, rtol=1e-5, atol=1e-8)
np.testing.assert_allclose(dCQ_dprecone_fd, dCQ_dprecone, rtol=5e-5, atol=1e-8)
np.testing.assert_allclose(dCP_dprecone_fd, dCP_dprecone, rtol=5e-5, atol=1e-8)
def test_dtilt1(self):
dNp_dtilt = self.dNp_dX[7, :]
dTp_dtilt = self.dTp_dX[7, :]
tilt = float(self.tilt)
delta = 1e-6*tilt
tilt += delta
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, self.precone, tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False)
Npd, Tpd = rotor.distributedAeroLoads(self.Uinf, self.Omega, self.pitch, self.azimuth)
dNp_dtilt_fd = (Npd - self.Np) / delta
dTp_dtilt_fd = (Tpd - self.Tp) / delta
np.testing.assert_allclose(dNp_dtilt_fd, dNp_dtilt, rtol=1e-6, atol=1e-8)
np.testing.assert_allclose(dTp_dtilt_fd, dTp_dtilt, rtol=1e-5, atol=1e-8)
def test_dtilt2(self):
dT_dtilt = self.dT_ds[0, 1]
dQ_dtilt = self.dQ_ds[0, 1]
dP_dtilt = self.dP_ds[0, 1]
tilt = float(self.tilt)
delta = 1e-6*tilt
tilt += delta
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, self.precone, tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False)
Pd, Td, Qd = rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=False)
dT_dtilt_fd = (Td - self.T) / delta
dQ_dtilt_fd = (Qd - self.Q) / delta
dP_dtilt_fd = (Pd - self.P) / delta
np.testing.assert_allclose(dT_dtilt_fd, dT_dtilt, rtol=1e-5, atol=1e-8)
np.testing.assert_allclose(dQ_dtilt_fd, dQ_dtilt, rtol=5e-5, atol=1e-8)
np.testing.assert_allclose(dP_dtilt_fd, dP_dtilt, rtol=5e-5, atol=1e-8)
def test_dtilt3(self):
dCT_dtilt = self.dCT_ds[0, 1]
dCQ_dtilt = self.dCQ_ds[0, 1]
dCP_dtilt = self.dCP_ds[0, 1]
tilt = float(self.tilt)
delta = 1e-6*tilt
tilt += delta
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, self.precone, tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False)
CPd, CTd, CQd = rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=True)
dCT_dtilt_fd = (CTd - self.CT) / delta
dCQ_dtilt_fd = (CQd - self.CQ) / delta
dCP_dtilt_fd = (CPd - self.CP) / delta
np.testing.assert_allclose(dCT_dtilt_fd, dCT_dtilt, rtol=1e-5, atol=1e-8)
np.testing.assert_allclose(dCQ_dtilt_fd, dCQ_dtilt, rtol=5e-5, atol=1e-8)
np.testing.assert_allclose(dCP_dtilt_fd, dCP_dtilt, rtol=5e-5, atol=1e-8)
def test_dhubht1(self):
dNp_dhubht = self.dNp_dX[8, :]
dTp_dhubht = self.dTp_dX[8, :]
hubht = float(self.hubHt)
delta = 1e-6*hubht
hubht += delta
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, self.precone, self.tilt, self.yaw, self.shearExp,
hubht, self.nSector, derivatives=False)
Npd, Tpd = rotor.distributedAeroLoads(self.Uinf, self.Omega, self.pitch, self.azimuth)
dNp_dhubht_fd = (Npd - self.Np) / delta
dTp_dhubht_fd = (Tpd - self.Tp) / delta
np.testing.assert_allclose(dNp_dhubht_fd, dNp_dhubht, rtol=1e-5, atol=1e-8)
np.testing.assert_allclose(dTp_dhubht_fd, dTp_dhubht, rtol=1e-5, atol=1e-8)
def test_dhubht2(self):
dT_dhubht = self.dT_ds[0, 2]
dQ_dhubht = self.dQ_ds[0, 2]
dP_dhubht = self.dP_ds[0, 2]
hubht = float(self.hubHt)
delta = 1e-6*hubht
hubht += delta
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, self.precone, self.tilt, self.yaw, self.shearExp,
hubht, self.nSector, derivatives=False)
Pd, Td, Qd = rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=False)
dT_dhubht_fd = (Td - self.T) / delta
dQ_dhubht_fd = (Qd - self.Q) / delta
dP_dhubht_fd = (Pd - self.P) / delta
np.testing.assert_allclose(dT_dhubht_fd, dT_dhubht, rtol=1e-5, atol=1e-8)
np.testing.assert_allclose(dQ_dhubht_fd, dQ_dhubht, rtol=5e-5, atol=1e-8)
np.testing.assert_allclose(dP_dhubht_fd, dP_dhubht, rtol=5e-5, atol=1e-8)
def test_dhubht3(self):
dCT_dhubht = self.dCT_ds[0, 2]
dCQ_dhubht = self.dCQ_ds[0, 2]
dCP_dhubht = self.dCP_ds[0, 2]
hubht = float(self.hubHt)
delta = 1e-6*hubht
hubht += delta
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, self.precone, self.tilt, self.yaw, self.shearExp,
hubht, self.nSector, derivatives=False)
CPd, CTd, CQd = rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=True)
dCT_dhubht_fd = (CTd - self.CT) / delta
dCQ_dhubht_fd = (CQd - self.CQ) / delta
dCP_dhubht_fd = (CPd - self.CP) / delta
np.testing.assert_allclose(dCT_dhubht_fd, dCT_dhubht, rtol=1e-5, atol=1e-8)
np.testing.assert_allclose(dCQ_dhubht_fd, dCQ_dhubht, rtol=5e-5, atol=1e-8)
np.testing.assert_allclose(dCP_dhubht_fd, dCP_dhubht, rtol=5e-5, atol=1e-8)
def test_dprecurve1(self):
precurve = np.linspace(1, 10, self.n)
precurveTip = 10.1
precone = 0.0
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=True, precurve=precurve, precurveTip=precurveTip)
Np, Tp, dNp_dX, dTp_dX, dNp_dprecurve, dTp_dprecurve = \
rotor.distributedAeroLoads(self.Uinf, self.Omega, self.pitch, self.azimuth)
dNp_dprecurve_fd = np.zeros((self.n, self.n))
dTp_dprecurve_fd = np.zeros((self.n, self.n))
for i in range(self.n):
pc = np.array(precurve)
delta = 1e-6*pc[i]
pc[i] += delta
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False, precurve=pc, precurveTip=precurveTip)
Npd, Tpd = rotor.distributedAeroLoads(self.Uinf, self.Omega, self.pitch, self.azimuth)
dNp_dprecurve_fd[i, :] = (Npd - Np) / delta
dTp_dprecurve_fd[i, :] = (Tpd - Tp) / delta
np.testing.assert_allclose(dNp_dprecurve_fd, dNp_dprecurve, rtol=3e-4, atol=1e-8)
np.testing.assert_allclose(dTp_dprecurve_fd, dTp_dprecurve, rtol=3e-4, atol=1e-8)
def test_dprecurve2(self):
precurve = np.linspace(1, 10, self.n)
precurveTip = 10.1
precone = 0.0
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=True, precurve=precurve, precurveTip=precurveTip)
P, T, Q, dP_ds, dT_ds, dQ_ds, dP_dv, dT_dv, dQ_dv = \
rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=False)
dT_dprecurve = dT_dv[0, 3, :]
dQ_dprecurve = dQ_dv[0, 3, :]
dP_dprecurve = dP_dv[0, 3, :]
dT_dprecurve_fd = np.zeros(self.n)
dQ_dprecurve_fd = np.zeros(self.n)
dP_dprecurve_fd = np.zeros(self.n)
for i in range(self.n):
pc = np.array(precurve)
delta = 1e-6*pc[i]
pc[i] += delta
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False, precurve=pc, precurveTip=precurveTip)
Pd, Td, Qd = rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=False)
dT_dprecurve_fd[i] = (Td - T) / delta
dQ_dprecurve_fd[i] = (Qd - Q) / delta
dP_dprecurve_fd[i] = (Pd - P) / delta
np.testing.assert_allclose(dT_dprecurve_fd, dT_dprecurve, rtol=3e-4, atol=1e-8)
np.testing.assert_allclose(dQ_dprecurve_fd, dQ_dprecurve, rtol=3e-4, atol=1e-8)
np.testing.assert_allclose(dP_dprecurve_fd, dP_dprecurve, rtol=3e-4, atol=1e-8)
def test_dprecurve3(self):
precurve = np.linspace(1, 10, self.n)
precurveTip = 10.1
precone = 0.0
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=True, precurve=precurve, precurveTip=precurveTip)
CP, CT, CQ, dCP_ds, dCT_ds, dCQ_ds, dCP_dv, dCT_dv, dCQ_dv = \
rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=True)
dCT_dprecurve = dCT_dv[0, 3, :]
dCQ_dprecurve = dCQ_dv[0, 3, :]
dCP_dprecurve = dCP_dv[0, 3, :]
dCT_dprecurve_fd = np.zeros(self.n)
dCQ_dprecurve_fd = np.zeros(self.n)
dCP_dprecurve_fd = np.zeros(self.n)
for i in range(self.n):
pc = np.array(precurve)
delta = 1e-6*pc[i]
pc[i] += delta
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False, precurve=pc, precurveTip=precurveTip)
CPd, CTd, CQd = rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=True)
dCT_dprecurve_fd[i] = (CTd - CT) / delta
dCQ_dprecurve_fd[i] = (CQd - CQ) / delta
dCP_dprecurve_fd[i] = (CPd - CP) / delta
np.testing.assert_allclose(dCT_dprecurve_fd, dCT_dprecurve, rtol=3e-4, atol=1e-8)
np.testing.assert_allclose(dCQ_dprecurve_fd, dCQ_dprecurve, rtol=3e-4, atol=1e-8)
np.testing.assert_allclose(dCP_dprecurve_fd, dCP_dprecurve, rtol=3e-4, atol=1e-8)
def test_dpresweep1(self):
presweep = np.linspace(1, 10, self.n)
presweepTip = 10.1
precone = 0.0
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=True, presweep=presweep, presweepTip=presweepTip)
Np, Tp, dNp_dX, dTp_dX, dNp_dprecurve, dTp_dprecurve = \
rotor.distributedAeroLoads(self.Uinf, self.Omega, self.pitch, self.azimuth)
dNp_dpresweep = dNp_dX[5, :]
dTp_dpresweep = dTp_dX[5, :]
dNp_dpresweep_fd = np.zeros(self.n)
dTp_dpresweep_fd = np.zeros(self.n)
for i in range(self.n):
ps = np.array(presweep)
delta = 1e-6*ps[i]
ps[i] += delta
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False, presweep=ps, presweepTip=presweepTip)
Npd, Tpd = rotor.distributedAeroLoads(self.Uinf, self.Omega, self.pitch, self.azimuth)
dNp_dpresweep_fd[i] = (Npd[i] - Np[i]) / delta
dTp_dpresweep_fd[i] = (Tpd[i] - Tp[i]) / delta
np.testing.assert_allclose(dNp_dpresweep_fd, dNp_dpresweep, rtol=1e-5, atol=1e-8)
np.testing.assert_allclose(dTp_dpresweep_fd, dTp_dpresweep, rtol=1e-5, atol=1e-8)
def test_dpresweep2(self):
presweep = np.linspace(1, 10, self.n)
presweepTip = 10.1
precone = 0.0
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=True, presweep=presweep, presweepTip=presweepTip)
P, T, Q, dP_ds, dT_ds, dQ_ds, dP_dv, dT_dv, dQ_dv = \
rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=False)
dT_dpresweep = dT_dv[0, 4, :]
dQ_dpresweep = dQ_dv[0, 4, :]
dP_dpresweep = dP_dv[0, 4, :]
dT_dpresweep_fd = np.zeros(self.n)
dQ_dpresweep_fd = np.zeros(self.n)
dP_dpresweep_fd = np.zeros(self.n)
for i in range(self.n):
ps = np.array(presweep)
delta = 1e-6*ps[i]
ps[i] += delta
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False, presweep=ps, presweepTip=presweepTip)
Pd, Td, Qd = rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=False)
dT_dpresweep_fd[i] = (Td - T) / delta
dQ_dpresweep_fd[i] = (Qd - Q) / delta
dP_dpresweep_fd[i] = (Pd - P) / delta
np.testing.assert_allclose(dT_dpresweep_fd, dT_dpresweep, rtol=3e-4, atol=1e-8)
np.testing.assert_allclose(dQ_dpresweep_fd, dQ_dpresweep, rtol=3e-4, atol=1e-8)
np.testing.assert_allclose(dP_dpresweep_fd, dP_dpresweep, rtol=3e-4, atol=1e-8)
def test_dpresweep3(self):
presweep = np.linspace(1, 10, self.n)
presweepTip = 10.1
precone = 0.0
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=True, presweep=presweep, presweepTip=presweepTip)
CP, CT, CQ, dCP_ds, dCT_ds, dCQ_ds, dCP_dv, dCT_dv, dCQ_dv = \
rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=True)
dCT_dpresweep = dCT_dv[0, 4, :]
dCQ_dpresweep = dCQ_dv[0, 4, :]
dCP_dpresweep = dCP_dv[0, 4, :]
dCT_dpresweep_fd = np.zeros(self.n)
dCQ_dpresweep_fd = np.zeros(self.n)
dCP_dpresweep_fd = np.zeros(self.n)
for i in range(self.n):
ps = np.array(presweep)
delta = 1e-6*ps[i]
ps[i] += delta
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False, presweep=ps, presweepTip=presweepTip)
CPd, CTd, CQd = rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=True)
dCT_dpresweep_fd[i] = (CTd - CT) / delta
dCQ_dpresweep_fd[i] = (CQd - CQ) / delta
dCP_dpresweep_fd[i] = (CPd - CP) / delta
np.testing.assert_allclose(dCT_dpresweep_fd, dCT_dpresweep, rtol=3e-4, atol=1e-8)
np.testing.assert_allclose(dCQ_dpresweep_fd, dCQ_dpresweep, rtol=3e-4, atol=1e-8)
np.testing.assert_allclose(dCP_dpresweep_fd, dCP_dpresweep, rtol=3e-4, atol=1e-8)
def test_dprecurveTip1(self):
precurve = np.linspace(1, 10, self.n)
precurveTip = 10.1
precone = 0.0
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=True, precurve=precurve, precurveTip=precurveTip)
Np, Tp, dNp_dX, dTp_dX, dNp_dprecurve, dTp_dprecurve = \
rotor.distributedAeroLoads(self.Uinf, self.Omega, self.pitch, self.azimuth)
pct = float(precurveTip)
delta = 1e-6*pct
pct += delta
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False, precurve=precurve, precurveTip=pct)
Npd, Tpd = rotor.distributedAeroLoads(self.Uinf, self.Omega, self.pitch, self.azimuth)
dNp_dprecurveTip_fd = (Npd - Np) / delta
dTp_dprecurveTip_fd = (Tpd - Tp) / delta
np.testing.assert_allclose(dNp_dprecurveTip_fd, 0.0, rtol=1e-4, atol=1e-8)
np.testing.assert_allclose(dTp_dprecurveTip_fd, 0.0, rtol=1e-4, atol=1e-8)
def test_dprecurveTip2(self):
precurve = np.linspace(1, 10, self.n)
precurveTip = 10.1
precone = 0.0
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=True, precurve=precurve, precurveTip=precurveTip)
P, T, Q, dP_ds, dT_ds, dQ_ds, dP_dv, dT_dv, dQ_dv = \
rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=False)
dT_dprecurveTip = dT_ds[0, 5]
dQ_dprecurveTip = dQ_ds[0, 5]
dP_dprecurveTip = dP_ds[0, 5]
pct = float(precurveTip)
delta = 1e-6*pct
pct += delta
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False, precurve=precurve, precurveTip=pct)
Pd, Td, Qd = rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=False)
dT_dprecurveTip_fd = (Td - T) / delta
dQ_dprecurveTip_fd = (Qd - Q) / delta
dP_dprecurveTip_fd = (Pd - P) / delta
np.testing.assert_allclose(dT_dprecurveTip_fd, dT_dprecurveTip, rtol=1e-4, atol=1e-8)
np.testing.assert_allclose(dQ_dprecurveTip_fd, dQ_dprecurveTip, rtol=1e-4, atol=1e-8)
np.testing.assert_allclose(dP_dprecurveTip_fd, dP_dprecurveTip, rtol=1e-4, atol=1e-8)
def test_dprecurveTip3(self):
precurve = np.linspace(1, 10, self.n)
precurveTip = 10.1
precone = 0.0
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=True, precurve=precurve, precurveTip=precurveTip)
CP, CT, CQ, dCP_ds, dCT_ds, dCQ_ds, dCP_dv, dCT_dv, dCQ_dv = \
rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=True)
dCT_dprecurveTip = dCT_ds[0, 5]
dCQ_dprecurveTip = dCQ_ds[0, 5]
dCP_dprecurveTip = dCP_ds[0, 5]
pct = float(precurveTip)
delta = 1e-6*pct
pct += delta
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False, precurve=precurve, precurveTip=pct)
CPd, CTd, CQd = rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=True)
dCT_dprecurveTip_fd = (CTd - CT) / delta
dCQ_dprecurveTip_fd = (CQd - CQ) / delta
dCP_dprecurveTip_fd = (CPd - CP) / delta
np.testing.assert_allclose(dCT_dprecurveTip_fd, dCT_dprecurveTip, rtol=1e-4, atol=1e-8)
np.testing.assert_allclose(dCQ_dprecurveTip_fd, dCQ_dprecurveTip, rtol=1e-4, atol=1e-8)
np.testing.assert_allclose(dCP_dprecurveTip_fd, dCP_dprecurveTip, rtol=1e-4, atol=1e-8)
def test_dpresweepTip1(self):
presweep = np.linspace(1, 10, self.n)
presweepTip = 10.1
precone = 0.0
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=True, presweep=presweep, presweepTip=presweepTip)
Np, Tp, dNp_dX, dTp_dX, dNp_dpresweep, dTp_dpresweep = \
rotor.distributedAeroLoads(self.Uinf, self.Omega, self.pitch, self.azimuth)
pst = float(presweepTip)
delta = 1e-6*pst
pst += delta
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False, presweep=presweep, presweepTip=pst)
Npd, Tpd = rotor.distributedAeroLoads(self.Uinf, self.Omega, self.pitch, self.azimuth)
dNp_dpresweepTip_fd = (Npd - Np) / delta
dTp_dpresweepTip_fd = (Tpd - Tp) / delta
np.testing.assert_allclose(dNp_dpresweepTip_fd, 0.0, rtol=1e-4, atol=1e-8)
np.testing.assert_allclose(dTp_dpresweepTip_fd, 0.0, rtol=1e-4, atol=1e-8)
def test_dpresweepTip2(self):
presweep = np.linspace(1, 10, self.n)
presweepTip = 10.1
precone = 0.0
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=True, presweep=presweep, presweepTip=presweepTip)
P, T, Q, dP_ds, dT_ds, dQ_ds, dP_dv, dT_dv, dQ_dv = \
rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=False)
dT_dpresweepTip = dT_ds[0, 6]
dQ_dpresweepTip = dQ_ds[0, 6]
dP_dpresweepTip = dP_ds[0, 6]
pst = float(presweepTip)
delta = 1e-6*pst
pst += delta
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False, presweep=presweep, presweepTip=pst)
Pd, Td, Qd = rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=False)
dT_dpresweepTip_fd = (Td - T) / delta
dQ_dpresweepTip_fd = (Qd - Q) / delta
dP_dpresweepTip_fd = (Pd - P) / delta
np.testing.assert_allclose(dT_dpresweepTip_fd, dT_dpresweepTip, rtol=1e-4, atol=1e-8)
np.testing.assert_allclose(dQ_dpresweepTip_fd, dQ_dpresweepTip, rtol=1e-4, atol=1e-8)
np.testing.assert_allclose(dP_dpresweepTip_fd, dP_dpresweepTip, rtol=1e-4, atol=1e-8)
def test_dpresweepTip3(self):
presweep = np.linspace(1, 10, self.n)
presweepTip = 10.1
precone = 0.0
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=True, presweep=presweep, presweepTip=presweepTip)
CP, CT, CQ, dCP_ds, dCT_ds, dCQ_ds, dCP_dv, dCT_dv, dCQ_dv = \
rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=True)
dCT_dpresweepTip = dCT_ds[0, 6]
dCQ_dpresweepTip = dCQ_ds[0, 6]
dCP_dpresweepTip = dCP_ds[0, 6]
pst = float(presweepTip)
delta = 1e-6*pst
pst += delta
rotor = CCBlade(self.r, self.chord, self.theta, self.af, self.Rhub, self.Rtip,
self.B, self.rho, self.mu, precone, self.tilt, self.yaw, self.shearExp,
self.hubHt, self.nSector, derivatives=False, presweep=presweep, presweepTip=pst)
CPd, CTd, CQd = rotor.evaluate([self.Uinf], [self.Omega], [self.pitch], coefficient=True)
dCT_dpresweepTip_fd = (CTd - CT) / delta
dCQ_dpresweepTip_fd = (CQd - CQ) / delta
dCP_dpresweepTip_fd = (CPd - CP) / delta
np.testing.assert_allclose(dCT_dpresweepTip_fd, dCT_dpresweepTip, rtol=1e-4, atol=1e-8)
np.testing.assert_allclose(dCQ_dpresweepTip_fd, dCQ_dpresweepTip, rtol=1e-4, atol=1e-8)
np.testing.assert_allclose(dCP_dpresweepTip_fd, dCP_dpresweepTip, rtol=1e-4, atol=1e-8)
class CCBlade(AeroBase):
"""blade element momentum code"""
# (potential) variables
r = Array(iotype='in', units='m', desc='radial locations where blade is defined (should be increasing and not go all the way to hub or tip)')
chord = Array(iotype='in', units='m', desc='chord length at each section')
theta = Array(iotype='in', units='deg', desc='twist angle at each section (positive decreases angle of attack)')
Rhub = Float(iotype='in', units='m', desc='hub radius')
Rtip = Float(iotype='in', units='m', desc='tip radius')
hubHt = Float(iotype='in', units='m', desc='hub height')
precone = Float(0.0, iotype='in', desc='precone angle', units='deg')
tilt = Float(0.0, iotype='in', desc='shaft tilt', units='deg')
yaw = Float(0.0, iotype='in', desc='yaw error', units='deg')
# TODO: I've not hooked up the gradients for these ones yet.
precurve = Array(iotype='in', units='m', desc='precurve at each section')
precurveTip = Float(0.0, iotype='in', units='m', desc='precurve at tip')
# parameters
airfoil_files = List(Str, iotype='in', desc='names of airfoil file')
coordinate_files = List(Str, iotype='in', desc='names of airfoil file')
B = Int(3, iotype='in', desc='number of blades')
rho = Float(1.225, iotype='in', units='kg/m**3', desc='density of air')
mu = Float(1.81206e-5, iotype='in', units='kg/(m*s)', desc='dynamic viscosity of air')
shearExp = Float(0.2, iotype='in', desc='shear exponent')
nSector = Int(4, iotype='in', desc='number of sectors to divide rotor face into in computing thrust and power')
tiploss = Bool(True, iotype='in', desc='include Prandtl tip loss model')
hubloss = Bool(True, iotype='in', desc='include Prandtl hub loss model')
wakerotation = Bool(True, iotype='in', desc='include effect of wake rotation (i.e., tangential induction factor is nonzero)')
usecd = Bool(True, iotype='in', desc='use drag coefficient in computing induction factors')
af = Array(iotype='in', desc='CCBlade objects')
missing_deriv_policy = 'assume_zero'
def execute(self):
if len(self.precurve) == 0:
self.precurve = np.zeros_like(self.r)
af = self.af
self.ccblade = CCBlade_PY(self.r, self.chord, self.theta, af, self.Rhub, self.Rtip, self.B,
self.rho, self.mu, self.precone, self.tilt, self.yaw, self.shearExp, self.hubHt,
self.nSector, self.precurve, self.precurveTip, tiploss=self.tiploss, hubloss=self.hubloss,
wakerotation=self.wakerotation, usecd=self.usecd, derivatives=True)
if self.run_case == 'power':
# power, thrust, torque
self.P, self.T, self.Q, self.dP, self.dT, self.dQ \
= self.ccblade.evaluate(self.Uhub, self.Omega, self.pitch, coefficient=False)
elif self.run_case == 'loads':
# distributed loads
Np, Tp, self.dNp, self.dTp \
= self.ccblade.distributedAeroLoads(self.V_load, self.Omega_load, self.pitch_load, self.azimuth_load)
# concatenate loads at root/tip
self.loads.r = np.concatenate([[self.Rhub], self.r, [self.Rtip]])
Np = np.concatenate([[0.0], Np, [0.0]])
Tp = np.concatenate([[0.0], Tp, [0.0]])
# conform to blade-aligned coordinate system
self.loads.Px = Np
self.loads.Py = -Tp
self.loads.Pz = 0*Np
# return other outputs needed
self.loads.V = self.V_load
self.loads.Omega = self.Omega_load
self.loads.pitch = self.pitch_load
self.loads.azimuth = self.azimuth_load
def list_deriv_vars(self):
if self.run_case == 'power':
inputs = ('precone', 'tilt', 'hubHt', 'Rhub', 'Rtip', 'yaw',
'Uhub', 'Omega', 'pitch', 'r', 'chord', 'theta', 'precurve', 'precurveTip')
outputs = ('P', 'T', 'Q')
elif self.run_case == 'loads':
inputs = ('r', 'chord', 'theta', 'Rhub', 'Rtip', 'hubHt', 'precone',
'tilt', 'yaw', 'V_load', 'Omega_load', 'pitch_load', 'azimuth_load', 'precurve')
outputs = ('loads.r', 'loads.Px', 'loads.Py', 'loads.Pz', 'loads.V',
'loads.Omega', 'loads.pitch', 'loads.azimuth')
return inputs, outputs
def provideJ(self):
if self.run_case == 'power':
dP = self.dP
dT = self.dT
dQ = self.dQ
jP = hstack([dP['dprecone'], dP['dtilt'], dP['dhubHt'], dP['dRhub'], dP['dRtip'],
dP['dyaw'], dP['dUinf'], dP['dOmega'], dP['dpitch'], dP['dr'], dP['dchord'], dP['dtheta'],
dP['dprecurve'], dP['dprecurveTip']])
jT = hstack([dT['dprecone'], dT['dtilt'], dT['dhubHt'], dT['dRhub'], dT['dRtip'],
dT['dyaw'], dT['dUinf'], dT['dOmega'], dT['dpitch'], dT['dr'], dT['dchord'], dT['dtheta'],
dT['dprecurve'], dT['dprecurveTip']])
jQ = hstack([dQ['dprecone'], dQ['dtilt'], dQ['dhubHt'], dQ['dRhub'], dQ['dRtip'],
dQ['dyaw'], dQ['dUinf'], dQ['dOmega'], dQ['dpitch'], dQ['dr'], dQ['dchord'], dQ['dtheta'],
dQ['dprecurve'], dQ['dprecurveTip']])
J = vstack([jP, jT, jQ])
elif self.run_case == 'loads':
dNp = self.dNp
dTp = self.dTp
n = len(self.r)
dr_dr = vstack([np.zeros(n), np.eye(n), np.zeros(n)])
dr_dRhub = np.zeros(n+2)
dr_dRtip = np.zeros(n+2)
dr_dRhub[0] = 1.0
dr_dRtip[-1] = 1.0
dr = hstack([dr_dr, np.zeros((n+2, 2*n)), dr_dRhub, dr_dRtip, np.zeros((n+2, 8+n))])
jNp = hstack([dNp['dr'], dNp['dchord'], dNp['dtheta'], dNp['dRhub'], dNp['dRtip'],
dNp['dhubHt'], dNp['dprecone'], dNp['dtilt'], dNp['dyaw'], dNp['dUinf'],
dNp['dOmega'], dNp['dpitch'], dNp['dazimuth'], dNp['dprecurve']])
jTp = hstack([dTp['dr'], dTp['dchord'], dTp['dtheta'], dTp['dRhub'], dTp['dRtip'],
dTp['dhubHt'], dTp['dprecone'], dTp['dtilt'], dTp['dyaw'], dTp['dUinf'],
dTp['dOmega'], dTp['dpitch'], dTp['dazimuth'], dTp['dprecurve']])
dPx = vstack([np.zeros(4*n+10), jNp, np.zeros(4*n+10)])
dPy = vstack([np.zeros(4*n+10), -jTp, np.zeros(4*n+10)])
dPz = np.zeros((n+2, 4*n+10))
dV = np.zeros(4*n+10)
dV[3*n+6] = 1.0
dOmega = np.zeros(4*n+10)
dOmega[3*n+7] = 1.0
dpitch = np.zeros(4*n+10)
dpitch[3*n+8] = 1.0
dazimuth = np.zeros(4*n+10)
dazimuth[3*n+9] = 1.0
J = vstack([dr, dPx, dPy, dPz, dV, dOmega, dpitch, dazimuth])
return J
plt.plot(rstar, Tp / 1e3, label='lead-lag')
plt.plot(rstar, Np / 1e3, label='flapwise')
plt.xlabel('blade fraction')
plt.ylabel('distributed aerodynamic loads (kN)')
plt.legend(loc='upper left')
plt.grid()
plt.show()
# 5 ----------
# plt.savefig('/Users/sning/Dropbox/NREL/SysEng/TWISTER/ccblade-beta-setup/docs/images/distributedAeroLoads.pdf')
# plt.savefig('/Users/sning/Dropbox/NREL/SysEng/TWISTER/ccblade-beta-setup/docs/images/distributedAeroLoads.png')
# 6 ----------
outputs, derivs = rotor.evaluate([Uinf], [Omega], [pitch])
P = outputs['P']
T = outputs['T']
Q = outputs['Q']
outputs, derivs = rotor.evaluate([Uinf], [Omega], [pitch], coefficient=True)
CP = outputs['CP']
CT = outputs['CT']
CQ = outputs['CQ']
print('CP =', CP)
print('CT =', CT)
print('CQ =', CQ)
# 6 ----------
