class Cp_Ct_Cq_Tables(ExplicitComponent):
def initialize(self):
self.options.declare('modeling_options')
# self.options.declare('n_span')
# self.options.declare('n_pitch', default=20)
# self.options.declare('n_tsr', default=20)
# self.options.declare('n_U', default=1)
# self.options.declare('n_aoa')
# self.options.declare('n_re')
def setup(self):
modeling_options = self.options['modeling_options']
rotorse_options = modeling_options['WISDEM']['RotorSE']
self.n_span = n_span = rotorse_options['n_span']
self.n_aoa = n_aoa = rotorse_options[
'n_aoa'] # Number of angle of attacks
self.n_Re = n_Re = rotorse_options[
'n_Re'] # Number of Reynolds, so far hard set at 1
self.n_tab = n_tab = rotorse_options[
'n_tab'] # Number of tabulated data. For distributed aerodynamic control this could be > 1
self.n_pitch = n_pitch = rotorse_options['n_pitch_perf_surfaces']
self.n_tsr = n_tsr = rotorse_options['n_tsr_perf_surfaces']
self.n_U = n_U = rotorse_options['n_U_perf_surfaces']
self.min_TSR = rotorse_options['min_tsr_perf_surfaces']
self.max_TSR = rotorse_options['max_tsr_perf_surfaces']
self.min_pitch = rotorse_options['min_pitch_perf_surfaces']
self.max_pitch = rotorse_options['max_pitch_perf_surfaces']
# parameters
self.add_input('v_min', val=0.0, units='m/s', desc='cut-in wind speed')
self.add_input('v_max',
val=0.0,
units='m/s',
desc='cut-out wind speed')
self.add_input(
'r',
val=np.zeros(n_span),
units='m',
desc=
'radial locations where blade is defined (should be increasing and not go all the way to hub or tip)'
)
self.add_input('chord',
val=np.zeros(n_span),
units='m',
desc='chord length at each section')
self.add_input(
'theta',
val=np.zeros(n_span),
units='deg',
desc=
'twist angle at each section (positive decreases angle of attack)')
self.add_input('Rhub', val=0.0, units='m', desc='hub radius')
self.add_input('Rtip', val=0.0, units='m', desc='tip radius')
self.add_input('hub_height', val=0.0, units='m', desc='hub height')
self.add_input('precone', val=0.0, units='deg', desc='precone angle')
self.add_input('tilt', val=0.0, units='deg', desc='shaft tilt')
self.add_input('yaw', val=0.0, units='deg', desc='yaw error')
self.add_input('precurve',
val=np.zeros(n_span),
units='m',
desc='precurve at each section')
self.add_input('precurveTip',
val=0.0,
units='m',
desc='precurve at tip')
self.add_input('presweep',
val=np.zeros(n_span),
units='m',
desc='presweep at each section')
self.add_input('presweepTip',
val=0.0,
units='m',
desc='presweep at tip')
self.add_input('rho',
val=1.225,
units='kg/m**3',
desc='density of air')
self.add_input('mu',
val=1.81e-5,
units='kg/(m*s)',
desc='dynamic viscosity of air')
self.add_input('shearExp', val=0.0, desc='shear exponent')
# self.add_discrete_input('airfoils', val=[0]*n_span, desc='CCAirfoil instances')
self.add_input('airfoils_cl',
val=np.zeros((n_span, n_aoa, n_Re, n_tab)),
desc='lift coefficients, spanwise')
self.add_input('airfoils_cd',
val=np.zeros((n_span, n_aoa, n_Re, n_tab)),
desc='drag coefficients, spanwise')
self.add_input('airfoils_cm',
val=np.zeros((n_span, n_aoa, n_Re, n_tab)),
desc='moment coefficients, spanwise')
self.add_input('airfoils_aoa',
val=np.zeros((n_aoa)),
units='deg',
desc='angle of attack grid for polars')
self.add_input('airfoils_Re',
val=np.zeros((n_Re)),
desc='Reynolds numbers of polars')
self.add_discrete_input('nBlades', val=0, desc='number of blades')
self.add_discrete_input(
'nSector',
val=4,
desc=
'number of sectors to divide rotor face into in computing thrust and power'
)
self.add_discrete_input('tiploss',
val=True,
desc='include Prandtl tip loss model')
self.add_discrete_input('hubloss',
val=True,
desc='include Prandtl hub loss model')
self.add_discrete_input(
'wakerotation',
val=True,
desc=
'include effect of wake rotation (i.e., tangential induction factor is nonzero)'
)
self.add_discrete_input(
'usecd',
val=True,
desc='use drag coefficient in computing induction factors')
self.add_input('pitch_vector_in',
val=np.zeros(n_pitch),
units='deg',
desc='pitch vector specified by the user')
self.add_input('tsr_vector_in',
val=np.zeros(n_tsr),
desc='tsr vector specified by the user')
self.add_input('U_vector_in',
val=np.zeros(n_U),
units='m/s',
desc='wind vector specified by the user')
# outputs
self.add_output('Cp',
val=np.zeros((n_tsr, n_pitch, n_U)),
desc='table of aero power coefficient')
self.add_output('Ct',
val=np.zeros((n_tsr, n_pitch, n_U)),
desc='table of aero thrust coefficient')
self.add_output('Cq',
val=np.zeros((n_tsr, n_pitch, n_U)),
desc='table of aero torque coefficient')
self.add_output('pitch_vector',
val=np.zeros(n_pitch),
units='deg',
desc='pitch vector used')
self.add_output('tsr_vector',
val=np.zeros(n_tsr),
desc='tsr vector used')
self.add_output('U_vector',
val=np.zeros(n_U),
units='m/s',
desc='wind vector used')
def compute(self, inputs, outputs, discrete_inputs, discrete_outputs):
# Create Airfoil class instances
af = [None] * self.n_span
for i in range(self.n_span):
if self.n_tab > 1:
ref_tab = int(np.floor(self.n_tab / 2))
af[i] = CCAirfoil(inputs['airfoils_aoa'],
inputs['airfoils_Re'],
inputs['airfoils_cl'][i, :, :, ref_tab],
inputs['airfoils_cd'][i, :, :, ref_tab],
inputs['airfoils_cm'][i, :, :, ref_tab])
else:
af[i] = CCAirfoil(inputs['airfoils_aoa'],
inputs['airfoils_Re'],
inputs['airfoils_cl'][i, :, :, 0],
inputs['airfoils_cd'][i, :, :, 0],
inputs['airfoils_cm'][i, :, :, 0])
n_pitch = self.n_pitch
n_tsr = self.n_tsr
n_U = self.n_U
min_TSR = self.min_TSR
max_TSR = self.max_TSR
min_pitch = self.min_pitch
max_pitch = self.max_pitch
U_vector = inputs['U_vector_in']
V_in = inputs['v_min']
V_out = inputs['v_max']
tsr_vector = inputs['tsr_vector_in']
pitch_vector = inputs['pitch_vector_in']
self.ccblade = CCBlade(
inputs['r'], inputs['chord'], inputs['theta'], af, inputs['Rhub'],
inputs['Rtip'], discrete_inputs['nBlades'], inputs['rho'],
inputs['mu'], inputs['precone'], inputs['tilt'], inputs['yaw'],
inputs['shearExp'], inputs['hub_height'],
discrete_inputs['nSector'], inputs['precurve'],
inputs['precurveTip'], inputs['presweep'], inputs['presweepTip'],
discrete_inputs['tiploss'], discrete_inputs['hubloss'],
discrete_inputs['wakerotation'], discrete_inputs['usecd'])
if max(U_vector) == 0.:
U_vector = np.linspace(V_in[0], V_out[0], n_U)
if max(tsr_vector) == 0.:
tsr_vector = np.linspace(min_TSR, max_TSR, n_tsr)
if max(pitch_vector) == 0.:
pitch_vector = np.linspace(min_pitch, max_pitch, n_pitch)
outputs['pitch_vector'] = pitch_vector
outputs['tsr_vector'] = tsr_vector
outputs['U_vector'] = U_vector
R = inputs['Rtip']
k = 0
for i in range(n_U):
for j in range(n_tsr):
k += 1
# if k/2. == int(k/2.) :
print('Cp-Ct-Cq surfaces completed at ' +
str(int(k / (n_U * n_tsr) * 100.)) + ' %')
U = U_vector[i] * np.ones(n_pitch)
Omega = tsr_vector[j] * U_vector[
i] / R * 30. / np.pi * np.ones(n_pitch)
myout, _ = self.ccblade.evaluate(U,
Omega,
pitch_vector,
coefficients=True)
outputs['Cp'][j, :, i], outputs['Ct'][j, :, i], outputs['Cq'][
j, :, i] = [myout[key] for key in ['CP', 'CT', 'CQ']]
class ComputePowerCurve(ExplicitComponent):
"""
Iteratively call CCBlade to compute the power curve.
"""
def initialize(self):
self.options.declare("modeling_options")
def setup(self):
modeling_options = self.options["modeling_options"]
self.n_span = n_span = modeling_options["WISDEM"]["RotorSE"]["n_span"]
self.n_aoa = n_aoa = modeling_options["WISDEM"]["RotorSE"][
"n_aoa"] # Number of angle of attacks
self.n_Re = n_Re = modeling_options["WISDEM"]["RotorSE"][
"n_Re"] # Number of Reynolds, so far hard set at 1
self.n_tab = n_tab = modeling_options["WISDEM"]["RotorSE"][
"n_tab"] # Number of tabulated data. For distributed aerodynamic control this could be > 1
self.regulation_reg_III = modeling_options["WISDEM"]["RotorSE"][
"regulation_reg_III"]
self.n_pc = modeling_options["WISDEM"]["RotorSE"]["n_pc"]
self.n_pc_spline = modeling_options["WISDEM"]["RotorSE"]["n_pc_spline"]
# parameters
self.add_input("v_min", val=0.0, units="m/s", desc="cut-in wind speed")
self.add_input("v_max",
val=0.0,
units="m/s",
desc="cut-out wind speed")
self.add_input("rated_power",
val=0.0,
units="W",
desc="electrical rated power")
self.add_input("omega_min",
val=0.0,
units="rpm",
desc="minimum allowed rotor rotation speed")
self.add_input("omega_max",
val=0.0,
units="rpm",
desc="maximum allowed rotor rotation speed")
self.add_input("control_maxTS",
val=0.0,
units="m/s",
desc="maximum allowed blade tip speed")
self.add_input(
"tsr_operational",
val=0.0,
desc="tip-speed ratio in Region 2 (should be optimized externally)"
)
self.add_input(
"control_pitch",
val=0.0,
units="deg",
desc=
"pitch angle in region 2 (and region 3 for fixed pitch machines)",
)
self.add_discrete_input("drivetrainType", val="GEARED")
self.add_input("gearbox_efficiency", val=1.0)
self.add_input(
"generator_efficiency",
val=np.ones(self.n_pc),
desc=
"Generator efficiency at various rpm values to support table lookup",
)
self.add_input(
"lss_rpm",
val=np.zeros(self.n_pc),
units="rpm",
desc=
"Low speed shaft RPM values at which the generator efficiency values are given",
)
self.add_input(
"r",
val=np.zeros(n_span),
units="m",
desc=
"radial locations where blade is defined (should be increasing and not go all the way to hub or tip)",
)
self.add_input("chord",
val=np.zeros(n_span),
units="m",
desc="chord length at each section")
self.add_input(
"theta",
val=np.zeros(n_span),
units="deg",
desc=
"twist angle at each section (positive decreases angle of attack)",
)
self.add_input("Rhub", val=0.0, units="m", desc="hub radius")
self.add_input("Rtip", val=0.0, units="m", desc="tip radius")
self.add_input("hub_height", val=0.0, units="m", desc="hub height")
self.add_input(
"precone",
val=0.0,
units="deg",
desc="precone angle",
)
self.add_input(
"tilt",
val=0.0,
units="deg",
desc="shaft tilt",
)
self.add_input(
"yaw",
val=0.0,
units="deg",
desc="yaw error",
)
self.add_input("precurve",
val=np.zeros(n_span),
units="m",
desc="precurve at each section")
self.add_input("precurveTip",
val=0.0,
units="m",
desc="precurve at tip")
self.add_input("presweep",
val=np.zeros(n_span),
units="m",
desc="presweep at each section")
self.add_input("presweepTip",
val=0.0,
units="m",
desc="presweep at tip")
# self.add_discrete_input('airfoils', val=[0]*n_span, desc='CCAirfoil instances')
self.add_input("airfoils_cl",
val=np.zeros((n_span, n_aoa, n_Re, n_tab)),
desc="lift coefficients, spanwise")
self.add_input("airfoils_cd",
val=np.zeros((n_span, n_aoa, n_Re, n_tab)),
desc="drag coefficients, spanwise")
self.add_input("airfoils_cm",
val=np.zeros((n_span, n_aoa, n_Re, n_tab)),
desc="moment coefficients, spanwise")
self.add_input("airfoils_aoa",
val=np.zeros((n_aoa)),
units="deg",
desc="angle of attack grid for polars")
self.add_input("airfoils_Re",
val=np.zeros((n_Re)),
desc="Reynolds numbers of polars")
self.add_discrete_input("nBlades", val=0, desc="number of blades")
self.add_input("rho",
val=1.225,
units="kg/m**3",
desc="density of air")
self.add_input("mu",
val=1.81e-5,
units="kg/(m*s)",
desc="dynamic viscosity of air")
self.add_input("shearExp", val=0.0, desc="shear exponent")
self.add_discrete_input(
"nSector",
val=4,
desc=
"number of sectors to divide rotor face into in computing thrust and power"
)
self.add_discrete_input("tiploss",
val=True,
desc="include Prandtl tip loss model")
self.add_discrete_input("hubloss",
val=True,
desc="include Prandtl hub loss model")
self.add_discrete_input(
"wakerotation",
val=True,
desc=
"include effect of wake rotation (i.e., tangential induction factor is nonzero)",
)
self.add_discrete_input(
"usecd",
val=True,
desc="use drag coefficient in computing induction factors")
# outputs
self.add_output("V",
val=np.zeros(self.n_pc),
units="m/s",
desc="wind vector")
self.add_output("Omega",
val=np.zeros(self.n_pc),
units="rpm",
desc="rotor rotational speed")
self.add_output("pitch",
val=np.zeros(self.n_pc),
units="deg",
desc="rotor pitch schedule")
self.add_output("P",
val=np.zeros(self.n_pc),
units="W",
desc="rotor electrical power")
self.add_output("P_aero",
val=np.zeros(self.n_pc),
units="W",
desc="rotor mechanical power")
self.add_output("T",
val=np.zeros(self.n_pc),
units="N",
desc="rotor aerodynamic thrust")
self.add_output("Q",
val=np.zeros(self.n_pc),
units="N*m",
desc="rotor aerodynamic torque")
self.add_output("M",
val=np.zeros(self.n_pc),
units="N*m",
desc="blade root moment")
self.add_output("Cp",
val=np.zeros(self.n_pc),
desc="rotor electrical power coefficient")
self.add_output("Cp_aero",
val=np.zeros(self.n_pc),
desc="rotor aerodynamic power coefficient")
self.add_output("Ct_aero",
val=np.zeros(self.n_pc),
desc="rotor aerodynamic thrust coefficient")
self.add_output("Cq_aero",
val=np.zeros(self.n_pc),
desc="rotor aerodynamic torque coefficient")
self.add_output("Cm_aero",
val=np.zeros(self.n_pc),
desc="rotor aerodynamic moment coefficient")
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("rated_mech",
val=0.0,
units="W",
desc="Mechanical shaft power at rated")
self.add_output(
"ax_induct_regII",
val=np.zeros(n_span),
desc="rotor axial induction at cut-in wind speed along blade span")
self.add_output(
"tang_induct_regII",
val=np.zeros(n_span),
desc=
"rotor tangential induction at cut-in wind speed along blade span",
)
self.add_output(
"aoa_regII",
val=np.zeros(n_span),
units="deg",
desc=
"angle of attack distribution along blade span at cut-in wind speed",
)
self.add_output("Cp_regII",
val=0.0,
desc="power coefficient at cut-in wind speed")
self.add_output(
"cl_regII",
val=np.zeros(n_span),
desc=
"lift coefficient distribution along blade span at cut-in wind speed"
)
self.add_output(
"cd_regII",
val=np.zeros(n_span),
desc=
"drag coefficient distribution along blade span at cut-in wind speed"
)
self.add_output("rated_efficiency",
val=1.0,
desc="Efficiency at rated conditions")
# self.declare_partials('*', '*', method='fd', form='central', step=1e-6)
def compute(self, inputs, outputs, discrete_inputs, discrete_outputs):
# Create Airfoil class instances
af = [None] * self.n_span
for i in range(self.n_span):
if self.n_tab > 1:
ref_tab = int(np.floor(self.n_tab / 2))
af[i] = CCAirfoil(
inputs["airfoils_aoa"],
inputs["airfoils_Re"],
inputs["airfoils_cl"][i, :, :, ref_tab],
inputs["airfoils_cd"][i, :, :, ref_tab],
inputs["airfoils_cm"][i, :, :, ref_tab],
)
else:
af[i] = CCAirfoil(
inputs["airfoils_aoa"],
inputs["airfoils_Re"],
inputs["airfoils_cl"][i, :, :, 0],
inputs["airfoils_cd"][i, :, :, 0],
inputs["airfoils_cm"][i, :, :, 0],
)
self.ccblade = CCBlade(
inputs["r"],
inputs["chord"],
inputs["theta"],
af,
inputs["Rhub"],
inputs["Rtip"],
discrete_inputs["nBlades"],
inputs["rho"],
inputs["mu"],
inputs["precone"],
inputs["tilt"],
inputs["yaw"],
inputs["shearExp"],
inputs["hub_height"],
discrete_inputs["nSector"],
inputs["precurve"],
inputs["precurveTip"],
inputs["presweep"],
inputs["presweepTip"],
discrete_inputs["tiploss"],
discrete_inputs["hubloss"],
discrete_inputs["wakerotation"],
discrete_inputs["usecd"],
)
# JPJ: what is this grid for? Seems to be a special distribution of velocities
# for the hub
grid0 = np.cumsum(
np.abs(
np.diff(
np.cos(
np.linspace(-np.pi / 4.0, np.pi / 2.0,
self.n_pc + 1)))))
grid1 = (grid0 - grid0[0]) / (grid0[-1] - grid0[0])
Uhub = grid1 * (inputs["v_max"] - inputs["v_min"]) + inputs["v_min"]
P_aero = np.zeros(Uhub.shape)
Cp_aero = np.zeros(Uhub.shape)
Ct_aero = np.zeros(Uhub.shape)
Cq_aero = np.zeros(Uhub.shape)
Cm_aero = np.zeros(Uhub.shape)
P = np.zeros(Uhub.shape)
Cp = np.zeros(Uhub.shape)
T = np.zeros(Uhub.shape)
Q = np.zeros(Uhub.shape)
M = np.zeros(Uhub.shape)
pitch = np.zeros(Uhub.shape) + inputs["control_pitch"]
# Unpack variables
P_rated = inputs["rated_power"]
R_tip = inputs["Rtip"]
tsr = inputs["tsr_operational"]
driveType = discrete_inputs["drivetrainType"]
# Set rotor speed based on TSR
Omega_tsr = Uhub * tsr / R_tip
# Determine maximum rotor speed (rad/s)- either by TS or by control input
Omega_max = min([
inputs["control_maxTS"] / R_tip, inputs["omega_max"] * np.pi / 30.0
])
# Apply maximum and minimum rotor speed limits
Omega = np.maximum(np.minimum(Omega_tsr, Omega_max),
inputs["omega_min"] * np.pi / 30.0)
Omega_rpm = Omega * 30.0 / np.pi
# Create table lookup of total drivetrain efficiency, where rpm is first column and second column is gearbox*generator
lss_rpm = inputs["lss_rpm"]
gen_eff = inputs["generator_efficiency"]
if not np.any(lss_rpm):
lss_rpm = np.linspace(np.maximum(0.1, Omega_rpm[0]), Omega_rpm[-1],
self.n_pc)
_, gen_eff = compute_P_and_eff(P_rated * lss_rpm / lss_rpm[-1],
P_rated, np.zeros(self.n_pc),
driveType, np.zeros((self.n_pc, 2)))
# driveEta = np.c_[lss_rpm, float(inputs['gearbox_efficiency'])*gen_eff]
driveEta = float(inputs["gearbox_efficiency"]) * gen_eff
# Set baseline power production
myout, derivs = self.ccblade.evaluate(Uhub,
Omega_rpm,
pitch,
coefficients=True)
P_aero, T, Q, M, Cp_aero, Ct_aero, Cq_aero, Cm_aero = [
myout[key] for key in ["P", "T", "Q", "M", "CP", "CT", "CQ", "CM"]
]
# P, eff = compute_P_and_eff(P_aero, P_rated, Omega_rpm, driveType, driveEta)
eff = np.interp(Omega_rpm, lss_rpm, driveEta)
P = P_aero * eff
Cp = Cp_aero * eff
# Find Region 3 index
region_bool = np.nonzero(P >= P_rated)[0]
if len(region_bool) == 0:
i_3 = self.n_pc
region3 = False
else:
i_3 = region_bool[0] + 1
region3 = True
# Guess at Region 2.5, but we will do a more rigorous search below
if Omega_max < Omega_tsr[-1]:
U_2p5 = np.interp(Omega[-1], Omega_tsr, Uhub)
outputs["V_R25"] = U_2p5
else:
U_2p5 = Uhub[-1]
i_2p5 = np.nonzero(U_2p5 <= Uhub)[0][0]
# Find rated index and guess at rated speed
if P_aero[-1] > P_rated:
U_rated = np.interp(P_rated, P_aero * eff, Uhub)
else:
U_rated = Uhub[-1]
i_rated = np.nonzero(U_rated <= Uhub)[0][0]
# Function to be used inside of power maximization until Region 3
def maximizePower(pitch, Uhub, Omega_rpm):
myout, _ = self.ccblade.evaluate([Uhub], [Omega_rpm], [pitch],
coefficients=False)
return -myout["P"]
# Maximize power until Region 3
region2p5 = False
for i in range(i_3):
# No need to optimize if already doing well
if Omega[i] == Omega_tsr[i]:
continue
# Find pitch value that gives highest power rating
pitch0 = pitch[i] if i == 0 else pitch[i - 1]
bnds = [pitch0 - 10.0, pitch0 + 10.0]
pitch[i] = minimize_scalar(
lambda x: maximizePower(x, Uhub[i], Omega_rpm[i]),
bounds=bnds,
method="bounded",
options={
"disp": False,
"xatol": TOL,
"maxiter": 40
},
)["x"]
# Find associated power
myout, _ = self.ccblade.evaluate([Uhub[i]], [Omega_rpm[i]],
[pitch[i]],
coefficients=True)
P_aero[i], T[i], Q[i], M[i], Cp_aero[i], Ct_aero[i], Cq_aero[
i], Cm_aero[i] = [
myout[key]
for key in ["P", "T", "Q", "M", "CP", "CT", "CQ", "CM"]
]
# P[i], eff[i] = compute_P_and_eff(P_aero[i], P_rated, Omega_rpm[i], driveType, driveEta)
eff[i] = np.interp(Omega_rpm[i], lss_rpm, driveEta)
P[i] = P_aero[i] * eff[i]
Cp[i] = Cp_aero[i] * eff[i]
# Note if we find Region 2.5
if (not region2p5) and (Omega[i]
== Omega_max) and (P[i] < P_rated):
region2p5 = True
i_2p5 = i
# Stop if we find Region 3 early
if P[i] > P_rated:
i_3 = i + 1
i_rated = i
break
# Solve for rated velocity
# JPJ: why rename i_rated to i here? It removes clarity in the following 50 lines that we're looking at the rated properties
i = i_rated
if i < self.n_pc - 1:
def const_Urated(x):
pitch_i = x[0]
Uhub_i = x[1]
Omega_i = min([Uhub_i * tsr / R_tip, Omega_max])
Omega_i_rpm = Omega_i * 30.0 / np.pi
myout, _ = self.ccblade.evaluate([Uhub_i], [Omega_i_rpm],
[pitch_i],
coefficients=False)
P_aero_i = float(myout["P"])
# P_i,_ = compute_P_and_eff(P_aero_i.flatten(), P_rated, Omega_i_rpm, driveType, driveEta)
eff_i = np.interp(Omega_i_rpm, lss_rpm, driveEta)
P_i = float(P_aero_i * eff_i)
return P_i - P_rated
if region2p5:
# Have to search over both pitch and speed
x0 = [0.0, Uhub[i]]
bnds = [
np.sort([pitch[i - 1], pitch[i + 1]]),
[Uhub[i - 1], Uhub[i + 1]]
]
const = {}
const["type"] = "eq"
const["fun"] = const_Urated
params_rated = minimize(lambda x: x[1],
x0,
method="slsqp",
bounds=bnds,
constraints=const,
tol=TOL)
if params_rated.success and not np.isnan(params_rated.x[1]):
U_rated = params_rated.x[1]
pitch[i] = params_rated.x[0]
else:
U_rated = U_rated # Use guessed value earlier
pitch[i] = 0.0
else:
# Just search over speed
pitch[i] = 0.0
try:
U_rated = brentq(
lambda x: const_Urated([0.0, x]),
Uhub[i - 1],
Uhub[i + 1],
xtol=1e-1 * TOL,
rtol=1e-2 * TOL,
maxiter=40,
disp=False,
)
except ValueError:
U_rated = minimize_scalar(
lambda x: np.abs(const_Urated([0.0, x])),
bounds=[Uhub[i - 1], Uhub[i + 1]],
method="bounded",
options={
"disp": False,
"xatol": TOL,
"maxiter": 40
},
)["x"]
Omega_rated = min([U_rated * tsr / R_tip, Omega_max])
Omega[i:] = np.minimum(
Omega[i:],
Omega_rated) # Stay at this speed if hit rated too early
Omega_rpm = Omega * 30.0 / np.pi
myout, _ = self.ccblade.evaluate([U_rated], [Omega_rpm[i]],
[pitch[i]],
coefficients=True)
P_aero[i], T[i], Q[i], M[i], Cp_aero[i], Ct_aero[i], Cq_aero[
i], Cm_aero[i] = [
myout[key]
for key in ["P", "T", "Q", "M", "CP", "CT", "CQ", "CM"]
]
# P[i], eff[i] = compute_P_and_eff(P_aero[i], P_rated, Omega_rpm[i], driveType, driveEta)
eff[i] = np.interp(Omega_rpm[i], lss_rpm, driveEta)
P[i] = P_aero[i] * eff[i]
Cp[i] = Cp_aero[i] * eff[i]
P[i] = P_rated
# Store rated speed in array
Uhub[i_rated] = U_rated
# Store outputs
outputs["rated_V"] = np.float64(U_rated)
outputs["rated_Omega"] = Omega_rpm[i]
outputs["rated_pitch"] = pitch[i]
outputs["rated_T"] = T[i]
outputs["rated_Q"] = Q[i]
outputs["rated_mech"] = P_aero[i]
outputs["rated_efficiency"] = eff[i]
# JPJ: this part can be converted into a BalanceComp with a solver.
# This will be less expensive and allow us to get derivatives through the process.
if region3:
# Function to be used to stay at rated power in Region 3
def rated_power_dist(pitch_i, Uhub_i, Omega_rpm_i):
myout, _ = self.ccblade.evaluate([Uhub_i], [Omega_rpm_i],
[pitch_i],
coefficients=False)
P_aero_i = myout["P"]
# P_i, _ = compute_P_and_eff(P_aero_i, P_rated, Omega_rpm_i, driveType, driveEta)
eff_i = np.interp(Omega_rpm_i, lss_rpm, driveEta)
P_i = P_aero_i * eff_i
return P_i - P_rated
# Solve for Region 3 pitch
options = {"disp": False}
if self.regulation_reg_III:
for i in range(i_3, self.n_pc):
pitch0 = pitch[i - 1]
try:
pitch[i] = brentq(
lambda x: rated_power_dist(x, Uhub[i], Omega_rpm[i]
),
pitch0,
pitch0 + 10.0,
xtol=1e-1 * TOL,
rtol=1e-2 * TOL,
maxiter=40,
disp=False,
)
except ValueError:
pitch[i] = minimize_scalar(
lambda x: np.abs(
rated_power_dist(x, Uhub[i], Omega_rpm[i])),
bounds=[pitch0 - 5.0, pitch0 + 15.0],
method="bounded",
options={
"disp": False,
"xatol": TOL,
"maxiter": 40
},
)["x"]
myout, _ = self.ccblade.evaluate([Uhub[i]], [Omega_rpm[i]],
[pitch[i]],
coefficients=True)
P_aero[i], T[i], Q[i], M[i], Cp_aero[i], Ct_aero[
i], Cq_aero[i], Cm_aero[i] = [
myout[key] for key in
["P", "T", "Q", "M", "CP", "CT", "CQ", "CM"]
]
# P[i], eff[i] = compute_P_and_eff(P_aero[i], P_rated, Omega_rpm[i], driveType, driveEta)
eff[i] = np.interp(Omega_rpm[i], lss_rpm, driveEta)
P[i] = P_aero[i] * eff[i]
Cp[i] = Cp_aero[i] * eff[i]
# P[i] = P_rated
else:
P[i_3:] = P_rated
T[i_3:] = 0
Q[i_3:] = P[i_3:] / Omega[i_3:]
M[i_3:] = 0
pitch[i_3:] = 0
Cp[i_3:] = P[i_3:] / (0.5 * inputs["rho"] * np.pi * R_tip**2 *
Uhub[i_3:]**3)
Ct_aero[i_3:] = 0
Cq_aero[i_3:] = 0
Cm_aero[i_3:] = 0
outputs["T"] = T
outputs["Q"] = Q
outputs["Omega"] = Omega_rpm
outputs["P"] = P
outputs["Cp"] = Cp
outputs["P_aero"] = P_aero
outputs["Cp_aero"] = Cp_aero
outputs["Ct_aero"] = Ct_aero
outputs["Cq_aero"] = Cq_aero
outputs["Cm_aero"] = Cm_aero
outputs["V"] = Uhub
outputs["M"] = M
outputs["pitch"] = pitch
self.ccblade.induction_inflow = True
tsr_vec = Omega_rpm / 30.0 * np.pi * R_tip / Uhub
id_regII = np.argmin(abs(tsr_vec - inputs["tsr_operational"]))
loads, derivs = self.ccblade.distributedAeroLoads(
Uhub[id_regII], Omega_rpm[id_regII], pitch[id_regII], 0.0)
# outputs
outputs["ax_induct_regII"] = loads["a"]
outputs["tang_induct_regII"] = loads["ap"]
outputs["aoa_regII"] = loads["alpha"]
outputs["cl_regII"] = loads["Cl"]
outputs["cd_regII"] = loads["Cd"]
outputs["Cp_regII"] = Cp_aero[id_regII]
class Rotor:
def __init__(self, turbine, w, old=False):
'''
>>>> add mean offset parameters add move this to runCCBlade<<<<
'''
# Should inherit these from raft_model or _env?
self.w = np.array(w)
self.Zhub = turbine['Zhub'] # [m]
self.shaft_tilt = turbine['shaft_tilt'] # [deg]
self.overhang = turbine['overhang']
self.R_rot = turbine['blade']['Rtip'] # rotor radius [m]
#yaw = 0
self.Uhub = np.array(turbine['wt_ops']['v'])
self.Omega_rpm = np.array(turbine['wt_ops']['omega_op'])
self.pitch_deg = np.array(turbine['wt_ops']['pitch_op'])
self.I_drivetrain = float(turbine['I_drivetrain'])
self.aeroServoMod = getFromDict(
turbine, 'aeroServoMod', default=1
) # flag for aeroservodynamics (0=none, 1=aero only, 2=aero and control)
# Add parked pitch, rotor speed, assuming fully shut down by 40% above cut-out
self.Uhub = np.r_[self.Uhub, self.Uhub.max() * 1.4, 100]
self.Omega_rpm = np.r_[self.Omega_rpm, 0, 0]
self.pitch_deg = np.r_[self.pitch_deg, 90, 90]
# Set default control gains
self.kp_0 = np.zeros_like(self.Uhub)
self.ki_0 = np.zeros_like(self.Uhub)
self.k_float = 0 # np.zeros_like(self.Uhub), right now this is a single value, but this may change <<< what is this?
# Set CCBlade flags
tiploss = True # Tip loss model True/False
hubloss = True # Hub loss model, True/False
wakerotation = True # Wake rotation, True/False
usecd = True # Use drag coefficient within BEMT, True/False
# Set discretization parameters
nSector = 4 # [-] - number of equally spaced azimuthal positions where CCBlade should be interrogated. The results are averaged across the n positions. 4 is a good first guess
n_span = 30 # [-] - number of blade stations along span
grid = np.linspace(
0., 1.,
n_span) # equally spaced grid along blade span, root=0 tip=1
# ----- AIRFOIL STUFF ------
n_aoa = 200 # [-] - number of angles of attack to discretize airfoil polars - MUST BE MULTIPLE OF 4
n_af = len(turbine["airfoils"])
af_used = [b for [a, b] in turbine['blade']["airfoils"]]
af_position = [a for [a, b] in turbine['blade']["airfoils"]]
#af_used = turbine['blade']["airfoils"]["labels"]
#af_position = turbine['blade']["airfoils"]["grid"]
n_af_span = len(af_used)
# One fourth of the angles of attack from -pi to -pi/6, half between -pi/6 to pi/6, and one fourth from pi/6 to pi
aoa = np.unique(
np.hstack([
np.linspace(-180, -30, int(n_aoa / 4.0 + 1)),
np.linspace(
-30,
30,
int(n_aoa / 2.0),
),
np.linspace(30, 180, int(n_aoa / 4.0 + 1))
]))
af_name = n_af * [""]
r_thick = np.zeros(n_af)
for i in range(n_af):
af_name[i] = turbine["airfoils"][i]["name"]
r_thick[i] = turbine["airfoils"][i]["relative_thickness"]
cl = np.zeros((n_af, n_aoa, 1))
cd = np.zeros((n_af, n_aoa, 1))
cm = np.zeros((n_af, n_aoa, 1))
# Interp cl-cd-cm along predefined grid of angle of attack
for i in range(n_af):
#cl[i, :, 0] = np.interp(aoa, turbine["airfoils"][i]["alpha"], turbine["airfoils"][i]["c_l"])
#cd[i, :, 0] = np.interp(aoa, turbine["airfoils"][i]["alpha"], turbine["airfoils"][i]["c_d"])
#cm[i, :, 0] = np.interp(aoa, turbine["airfoils"][i]["alpha"], turbine["airfoils"][i]["c_m"])
polar_table = np.array(turbine["airfoils"][i]['data'])
# Note: polar_table[:,0] must be in degrees
cl[i, :, 0] = np.interp(aoa, polar_table[:, 0], polar_table[:, 1])
cd[i, :, 0] = np.interp(aoa, polar_table[:, 0], polar_table[:, 2])
cm[i, :, 0] = np.interp(aoa, polar_table[:, 0], polar_table[:, 3])
#plt.figure()
#plt.plot(polar_table[:,0], polar_table[:,1])
#plt.plot(polar_table[:,0], polar_table[:,2])
#plt.title(af_name[i])
if abs(cl[i, 0, 0] - cl[i, -1, 0]) > 1.0e-5:
print(
"WARNING: Ai " + af_name[i] +
" has the lift coefficient different between + and - pi rad. This is fixed automatically, but please check the input data."
)
cl[i, 0, 0] = cl[i, -1, 0]
if abs(cd[i, 0, 0] - cd[i, -1, 0]) > 1.0e-5:
print(
"WARNING: Airfoil " + af_name[i] +
" has the drag coefficient different between + and - pi rad. This is fixed automatically, but please check the input data."
)
cd[i, 0, 0] = cd[i, -1, 0]
if abs(cm[i, 0, 0] - cm[i, -1, 0]) > 1.0e-5:
print(
"WARNING: Airfoil " + af_name[i] +
" has the moment coefficient different between + and - pi rad. This is fixed automatically, but please check the input data."
)
cm[i, 0, 0] = cm[i, -1, 0]
# Interpolate along blade span using a pchip on relative thickness
r_thick_used = np.zeros(n_af_span)
cl_used = np.zeros((n_af_span, n_aoa, 1))
cd_used = np.zeros((n_af_span, n_aoa, 1))
cm_used = np.zeros((n_af_span, n_aoa, 1))
for i in range(n_af_span):
for j in range(n_af):
if af_used[i] == af_name[j]:
r_thick_used[i] = r_thick[j]
cl_used[i, :, :] = cl[j, :, :]
cd_used[i, :, :] = cd[j, :, :]
cm_used[i, :, :] = cm[j, :, :]
break
# Pchip does have an associated derivative method built-in:
# https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.PchipInterpolator.derivative.html#scipy.interpolate.PchipInterpolator.derivative
spline = PchipInterpolator
rthick_spline = spline(af_position, r_thick_used)
# GB: HAVE TO TALK TO PIETRO ABOUT THIS
#r_thick_interp = rthick_spline(grid[1:-1])
r_thick_interp = rthick_spline(grid)
# Spanwise interpolation of the airfoil polars with a pchip
r_thick_unique, indices = np.unique(r_thick_used, return_index=True)
cl_spline = spline(r_thick_unique, cl_used[indices, :, :])
self.cl_interp = np.flip(cl_spline(np.flip(r_thick_interp)), axis=0)
cd_spline = spline(r_thick_unique, cd_used[indices, :, :])
self.cd_interp = np.flip(cd_spline(np.flip(r_thick_interp)), axis=0)
cm_spline = spline(r_thick_unique, cm_used[indices, :, :])
self.cm_interp = np.flip(cm_spline(np.flip(r_thick_interp)), axis=0)
self.aoa = aoa
# split out blade geometry info from table
geometry_table = np.array(turbine['blade']['geometry'])
blade_r = geometry_table[:, 0]
blade_chord = geometry_table[:, 1]
blade_theta = geometry_table[:, 2]
blade_precurve = geometry_table[:, 3]
blade_presweep = geometry_table[:, 4]
af = []
for i in range(self.cl_interp.shape[0]):
af.append(
CCAirfoil(self.aoa, [], self.cl_interp[i, :, :],
self.cd_interp[i, :, :], self.cm_interp[i, :, :]))
self.ccblade = CCBlade(
blade_r, # (m) locations defining the blade along z-axis of blade coordinate system
blade_chord, # (m) corresponding chord length at each section
blade_theta, # (deg) corresponding :ref:`twist angle <blade_airfoil_coord>` at each section---positive twist decreases angle of attack.
af, # CCAirfoil object
turbine['Rhub'], # (m) radius of hub
turbine['blade']['Rtip'], # (m) radius of tip
turbine['nBlades'], # number of blades
turbine['rho_air'], # (kg/m^3) freestream fluid density
turbine['mu_air'], # (kg/m/s) dynamic viscosity of fluid
turbine['precone'], # (deg) hub precone angle
self.shaft_tilt, # (deg) hub tilt angle
0.0, # (deg) nacelle yaw angle
turbine[
'shearExp'], # shear exponent for a power-law wind profile across hub
turbine[
'Zhub'], # (m) hub height used for power-law wind profile. U = Uref*(z/hubHt)**shearExp
nSector, # number of azimuthal sectors to descretize aerodynamic calculation. automatically set to 1 if tilt, yaw, and shearExp are all 0.0. Otherwise set to a minimum of 4.
blade_precurve, # (m) location of blade pitch axis in x-direction of :ref:`blade coordinate system <azimuth_blade_coord>`
turbine['blade']
['precurveTip'], # (m) location of blade pitch axis in x-direction at the tip (analogous to Rtip)
blade_presweep, # (m) location of blade pitch axis in y-direction of :ref:`blade coordinate system <azimuth_blade_coord>`
turbine['blade']
['presweepTip'], # (m) location of blade pitch axis in y-direction at the tip (analogous to Rtip)
tiploss=tiploss, # if True, include Prandtl tip loss model
hubloss=hubloss, # if True, include Prandtl hub loss model
wakerotation=
wakerotation, # if True, include effect of wake rotation (i.e., tangential induction factor is nonzero)
usecd=
usecd, # If True, use drag coefficient in computing induction factors (always used in evaluating distributed loads from the induction factors).
derivatives=
True, # if True, derivatives along with function values will be returned for the various methods
)
# pull control gains out of dictionary
self.setControlGains(turbine)
def runCCBlade(self, Uhub, ptfm_pitch=0, yaw_misalign=0):
'''This performs a single CCBlade evaluation at specified conditions.
ptfm_pitch
mean platform pitch angle to be included in rotor tilt angle [rad]
yaw_misalign
turbine yaw misalignment angle [deg]
'''
# find turbine operating point at the provided wind speed
Omega_rpm = np.interp(Uhub, self.Uhub,
self.Omega_rpm) # rotor speed [rpm]
pitch_deg = np.interp(Uhub, self.Uhub,
self.pitch_deg) # blade pitch angle [deg]
# adjust rotor angles based on provided info (I think this intervention in CCBlade should work...)
self.ccblade.tilt = np.deg2rad(self.shaft_tilt) + ptfm_pitch
self.ccblade.yaw = np.deg2rad(yaw_misalign)
# evaluate aero loads and derivatives with CCBlade
loads, derivs = self.ccblade.evaluate(Uhub,
Omega_rpm,
pitch_deg,
coefficients=True)
# organize and save the relevant outputs...
self.U_case = Uhub
self.Omega_case = Omega_rpm
self.aero_torque = loads["Q"][0]
self.aero_power = loads["P"][0]
self.pitch_case = pitch_deg
outputs = {}
outputs["P"] = loads["P"]
outputs["Mb"] = loads["Mb"]
outputs["CP"] = loads["CP"]
outputs["CMb"] = loads["CMb"]
outputs["Fhub"] = np.array(
[loads["T"][0], loads["Y"][0], loads["Z"][0]])
outputs["Mhub"] = np.array(
[loads["Q"][0], loads["My"][0], loads["Mz"][0]])
outputs["CFhub"] = np.array(
[loads["CT"][0], loads["CY"][0], loads["CZ"][0]])
outputs["CMhub"] = np.array(
[loads["CQ"][0], loads["CMy"][0], loads["CMz"][0]])
print(
f"Wind speed: {Uhub} m/s, Aerodynamic power coefficient: {loads['CP'][0]:4.3f}"
)
J = {} # Jacobian/derivatives
dP = derivs["dP"]
J["P", "r"] = dP["dr"]
# J["P", "chord"] = dP["dchord"]
# J["P", "theta"] = dP["dtheta"]
# J["P", "Rhub"] = np.squeeze(dP["dRhub"])
# J["P", "Rtip"] = np.squeeze(dP["dRtip"])
# J["P", "hub_height"] = np.squeeze(dP["dhubHt"])
# J["P", "precone"] = np.squeeze(dP["dprecone"])
# J["P", "tilt"] = np.squeeze(dP["dtilt"])
# J["P", "yaw"] = np.squeeze(dP["dyaw"])
# J["P", "shearExp"] = np.squeeze(dP["dshear"])
# J["P", "V_load"] = np.squeeze(dP["dUinf"])
# J["P", "Omega_load"] = np.squeeze(dP["dOmega"])
# J["P", "pitch_load"] = np.squeeze(dP["dpitch"])
# J["P", "precurve"] = dP["dprecurve"]
# J["P", "precurveTip"] = dP["dprecurveTip"]
# J["P", "presweep"] = dP["dpresweep"]
# J["P", "presweepTip"] = dP["dpresweepTip"]
dQ = derivs["dQ"]
J["Q", "Uhub"] = np.atleast_1d(np.diag(dQ["dUinf"]))
J["Q", "pitch_deg"] = np.atleast_1d(np.diag(dQ["dpitch"]))
J["Q", "Omega_rpm"] = np.atleast_1d(np.diag(dQ["dOmega"]))
dT = derivs["dT"]
J["T", "Uhub"] = np.atleast_1d(np.diag(dT["dUinf"]))
J["T", "pitch_deg"] = np.atleast_1d(np.diag(dT["dpitch"]))
J["T", "Omega_rpm"] = np.atleast_1d(np.diag(dT["dOmega"]))
# dT = derivs["dT"]
# .J["Fhub", "r"][0,:] = dT["dr"] # 0 is for thrust force, 1 would be y, 2 z
# .J["Fhub", "chord"][0,:] = dT["dchord"]
# .J["Fhub", "theta"][0,:] = dT["dtheta"]
# .J["Fhub", "Rhub"][0,:] = np.squeeze(dT["dRhub"])
# .J["Fhub", "Rtip"][0,:] = np.squeeze(dT["dRtip"])
# .J["Fhub", "hub_height"][0,:] = np.squeeze(dT["dhubHt"])
# .J["Fhub", "precone"][0,:] = np.squeeze(dT["dprecone"])
# .J["Fhub", "tilt"][0,:] = np.squeeze(dT["dtilt"])
# .J["Fhub", "yaw"][0,:] = np.squeeze(dT["dyaw"])
# .J["Fhub", "shearExp"][0,:] = np.squeeze(dT["dshear"])
# .J["Fhub", "V_load"][0,:] = np.squeeze(dT["dUinf"])
# .J["Fhub", "Omega_load"][0,:] = np.squeeze(dT["dOmega"])
# .J["Fhub", "pitch_load"][0,:] = np.squeeze(dT["dpitch"])
# .J["Fhub", "precurve"][0,:] = dT["dprecurve"]
# .J["Fhub", "precurveTip"][0,:] = dT["dprecurveTip"]
# .J["Fhub", "presweep"][0,:] = dT["dpresweep"]
# .J["Fhub", "presweepTip"][0,:] = dT["dpresweepTip"]
self.J = J
return loads, derivs
def setControlGains(self, turbine):
'''
Use flipped sign version of ROSCO
'''
# Convert gain-scheduling wrt pitch to wind speed, Add zero gains for parked "control"
pc_angles = np.array(turbine['pitch_control']['GS_Angles']) * rad2deg
self.kp_0 = np.interp(self.pitch_deg,
pc_angles,
turbine['pitch_control']['GS_Kp'],
left=0,
right=0)
self.ki_0 = np.interp(self.pitch_deg,
pc_angles,
turbine['pitch_control']['GS_Ki'],
left=0,
right=0)
self.k_float = -turbine['pitch_control']['Fl_Kp']
# Torque control
self.kp_tau = -turbine['torque_control']['VS_KP']
self.ki_tau = -turbine['torque_control']['VS_KI']
self.Ng = turbine['gear_ratio']
def calcAeroServoContributions(self, case, ptfm_pitch=0, display=0):
if plot_flag:
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], coefficients=True)
CP = outputs["CP"]
CT = outputs["CT"]
CQ = outputs["CQ"]
print("CP =", CP)
print("CT =", CT)
print("CQ =", CQ)
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 ---------- loads, derivs = rotor.evaluate([Uinf], [Omega], [pitch]) P = loads["P"] T = loads["T"] Q = loads["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"]
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__)), "../../../examples/_airfoil_files")
# 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
outputs, derivs = self.rotor.evaluate(Uinf, Omega, pitch)
P, T, Q = [outputs[key] for key in ("P", "T", "Q")]
# 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)